TSTP Solution File: SWW381+1 by CSE---1.7
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%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : SWW381+1 : TPTP v8.2.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Jun 24 18:08:55 EDT 2024
% Result : Theorem 187.18s 188.04s
% Output : CNFRefutation 187.39s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SWW381+1 : TPTP v8.2.0. Released v5.2.0.
% 0.08/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35 % Computer : n025.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Jun 19 08:10:54 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.22/0.50 start to proof:theBenchmark
% 186.89/187.88 %-------------------------------------------
% 186.89/187.88 % File :CSE---1.7
% 186.89/187.88 % Problem :theBenchmark
% 186.89/187.88 % Transform :cnf
% 186.89/187.88 % Format :tptp:raw
% 186.89/187.88 % Command :java -jar mcs_scs.jar %d %s
% 186.89/187.88
% 186.89/187.88 % Result :Theorem 173.110000s
% 186.89/187.88 % Output :CNFRefutation 173.110000s
% 186.89/187.88 %-------------------------------------------
% 186.89/187.89 %------------------------------------------------------------------------------
% 186.89/187.89 % File : SWW381+1 : TPTP v8.2.0. Released v5.2.0.
% 186.89/187.89 % Domain : Software Verification
% 186.89/187.89 % Problem : Hoare's Logic with Procedures 435609, 5000 axioms selected
% 186.89/187.89 % Version : Especial.
% 186.89/187.89 % English :
% 186.89/187.89
% 186.89/187.89 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% 186.89/187.89 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% 186.89/187.89 % Source : [Bla11]
% 186.89/187.89 % Names : hoare_435609.5000.p [Bla11]
% 186.89/187.89
% 186.89/187.89 % Status : ContradictoryAxioms
% 186.89/187.89 % Rating : 0.86 v8.2.0, 0.81 v8.1.0, 0.83 v7.5.0, 0.84 v7.4.0, 0.93 v7.3.0, 0.86 v7.1.0, 0.83 v7.0.0, 0.90 v6.4.0, 0.85 v6.3.0, 0.83 v6.2.0, 0.92 v6.1.0, 0.93 v6.0.0, 0.91 v5.5.0, 0.93 v5.4.0, 0.96 v5.3.0, 1.00 v5.2.0
% 186.89/187.89 % Syntax : Number of formulae : 5241 (1727 unt; 0 def)
% 186.89/187.89 % Number of atoms : 12613 (4521 equ)
% 186.89/187.89 % Maximal formula atoms : 13 ( 2 avg)
% 186.89/187.89 % Number of connectives : 8381 (1009 ~; 155 |; 720 &)
% 186.89/187.89 % ( 896 <=>;5601 =>; 0 <=; 0 <~>)
% 186.89/187.89 % Maximal formula depth : 22 ( 6 avg)
% 186.89/187.89 % Maximal term depth : 19 ( 2 avg)
% 186.89/187.89 % Number of predicates : 144 ( 143 usr; 2 prp; 0-6 aty)
% 186.89/187.89 % Number of functors : 382 ( 382 usr; 54 con; 0-7 aty)
% 186.89/187.89 % Number of variables : 16651 (16506 !; 145 ?)
% 186.89/187.89 % SPC : FOF_CAX_RFO_SEQ
% 186.89/187.89
% 186.89/187.89 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 186.89/187.89 % 2011-03-01 12:56:04
% 186.89/187.89 %------------------------------------------------------------------------------
% 186.89/187.89 %----Relevant facts (4986)
% 186.89/187.89 fof(fact_ext,axiom,
% 186.89/187.89 ! [V_g_2,V_f_2] :
% 186.89/187.89 ( ! [B_x] : hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x)
% 186.89/187.89 => V_f_2 = V_g_2 ) ).
% 186.89/187.89
% 186.89/187.89 fof(fact_asm,axiom,
% 186.89/187.89 ! [V_G_2,V_ts_2,T_a] :
% 186.89/187.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)),V_ts_2),V_G_2))
% 186.89/187.89 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,V_ts_2) ) ).
% 186.89/187.89
% 186.89/187.89 fof(fact_weaken,axiom,
% 186.89/187.89 ! [V_ts_2,V_ts_H_2,V_G_2,T_a] :
% 186.89/187.89 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,V_ts_H_2)
% 186.89/187.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)),V_ts_2),V_ts_H_2))
% 186.89/187.89 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,V_ts_2) ) ) ).
% 186.89/187.89
% 186.89/187.89 fof(fact_thin,axiom,
% 186.89/187.89 ! [V_G_2,V_ts_2,V_G_H_2,T_a] :
% 186.89/187.89 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_H_2,V_ts_2)
% 186.89/187.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)),V_G_H_2),V_G_2))
% 186.89/187.89 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,V_ts_2) ) ) ).
% 186.89/187.89
% 186.89/187.89 fof(fact_cut,axiom,
% 186.89/187.89 ! [V_G_2,V_ts_2,V_G_H_2,T_a] :
% 186.89/187.89 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_H_2,V_ts_2)
% 186.89/187.89 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,V_G_H_2)
% 186.89/187.89 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,V_ts_2) ) ) ).
% 186.89/187.89
% 186.89/187.89 fof(fact_finite__imageI,axiom,
% 186.89/187.89 ! [V_h_2,T_b,V_Fa_2,T_a] :
% 186.89/187.89 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_Fa_2))
% 186.89/187.89 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_a,T_b,V_h_2),V_Fa_2))) ) ).
% 186.89/187.89
% 186.89/187.89 fof(fact_finite__surj,axiom,
% 186.89/187.89 ! [V_f_2,V_B_2,T_b,V_A_2,T_a] :
% 186.89/187.89 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.89/187.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)))
% 186.89/187.89 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ) ).
% 186.89/187.89
% 186.89/187.89 fof(fact_equalityI,axiom,
% 186.89/187.89 ! [V_B_2,V_A_2,T_a] :
% 186.89/187.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 186.89/187.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 186.89/187.89 => V_A_2 = V_B_2 ) ) ).
% 186.89/187.89
% 186.89/187.89 fof(fact_order__refl,axiom,
% 186.89/187.89 ! [V_x,T_a] :
% 186.89/187.89 ( class_Orderings_Opreorder(T_a)
% 186.89/187.89 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_x)) ) ).
% 186.89/187.89
% 186.89/187.89 fof(fact_subset__image__iff,axiom,
% 186.89/187.89 ! [V_A_2,V_f_2,T_b,V_B_2,T_a] :
% 186.89/187.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2)))
% 186.89/187.89 <=> ? [B_AA] :
% 186.89/187.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),B_AA),V_A_2))
% 186.89/187.89 & V_B_2 = hAPP(c_Set_Oimage(T_b,T_a,V_f_2),B_AA) ) ) ).
% 186.89/187.89
% 186.89/187.89 fof(fact_image__mono,axiom,
% 186.89/187.89 ! [V_f_2,T_b,V_B_2,V_A_2,T_a] :
% 186.89/187.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 186.89/187.89 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2))) ) ).
% 186.89/187.89
% 186.89/187.89 fof(fact_rev__finite__subset,axiom,
% 186.89/187.89 ! [V_A_2,V_B_2,T_a] :
% 186.89/187.89 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 186.89/187.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 186.89/187.89 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ).
% 186.89/187.89
% 186.89/187.89 fof(fact_finite__subset,axiom,
% 186.89/187.89 ! [V_B_2,V_A_2,T_a] :
% 186.89/187.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 186.89/187.89 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 186.89/187.89 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ).
% 186.89/187.89
% 186.89/187.89 fof(fact_le__fun__def,axiom,
% 186.89/187.89 ! [V_g_2,V_f_2,T_a,T_b] :
% 186.89/187.89 ( class_Orderings_Oord(T_b)
% 186.89/187.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2))
% 186.89/187.89 <=> ! [B_x] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) ) ).
% 186.89/187.89
% 186.89/187.89 fof(fact_le__funD,axiom,
% 186.89/187.89 ! [V_x_2,V_g_2,V_f_2,T_a,T_b] :
% 186.89/187.89 ( class_Orderings_Oord(T_b)
% 186.89/187.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2))
% 186.89/187.89 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2))) ) ) ).
% 186.89/187.89
% 186.89/187.89 fof(fact_le__funE,axiom,
% 186.89/187.89 ! [V_x_2,V_g_2,V_f_2,T_a,T_b] :
% 186.89/187.89 ( class_Orderings_Oord(T_b)
% 186.89/187.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2))
% 186.89/187.89 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2))) ) ) ).
% 186.89/187.89
% 186.89/187.89 fof(fact_image__image,axiom,
% 186.89/187.89 ! [V_A_2,V_g_2,T_c,V_f_2,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(c_Set_Oimage(T_c,T_b,V_g_2),V_A_2)) = hAPP(c_Set_Oimage(T_c,T_a,hAPP(hAPP(c_COMBB(T_b,T_a,T_c),V_f_2),V_g_2)),V_A_2) ).
% 186.89/187.89
% 186.89/187.89 fof(fact_linorder__le__cases,axiom,
% 186.89/187.89 ! [V_y,V_x,T_a] :
% 186.89/187.89 ( class_Orderings_Olinorder(T_a)
% 186.89/187.89 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 186.89/187.89 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ).
% 186.89/187.89
% 186.89/187.89 fof(fact_xt1_I6_J,axiom,
% 186.89/187.89 ! [V_z,V_x,V_y,T_a] :
% 186.89/187.89 ( class_Orderings_Oorder(T_a)
% 186.89/187.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 186.89/187.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y))
% 186.89/187.89 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) ) ) ) ).
% 186.89/187.89
% 186.89/187.90 fof(fact_xt1_I5_J,axiom,
% 186.89/187.90 ! [V_x,V_y,T_a] :
% 186.89/187.90 ( class_Orderings_Oorder(T_a)
% 186.89/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 186.89/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 186.89/187.90 => V_x = V_y ) ) ) ).
% 186.89/187.90
% 186.89/187.90 fof(fact_order__trans,axiom,
% 186.89/187.90 ! [V_z,V_y,V_x,T_a] :
% 186.89/187.90 ( class_Orderings_Opreorder(T_a)
% 186.89/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 186.89/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z))
% 186.89/187.90 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) ) ) ) ).
% 186.89/187.90
% 186.89/187.90 fof(fact_order__antisym,axiom,
% 186.89/187.90 ! [V_y,V_x,T_a] :
% 186.89/187.90 ( class_Orderings_Oorder(T_a)
% 186.89/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 186.89/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 186.89/187.90 => V_x = V_y ) ) ) ).
% 186.89/187.90
% 186.89/187.90 fof(fact_xt1_I4_J,axiom,
% 186.89/187.90 ! [V_c,V_a,V_b,T_a] :
% 186.89/187.90 ( class_Orderings_Oorder(T_a)
% 186.89/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 186.89/187.90 => ( V_b = V_c
% 186.89/187.90 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ).
% 186.89/187.90
% 186.89/187.90 fof(fact_ord__le__eq__trans,axiom,
% 186.89/187.90 ! [V_c,V_b,V_a,T_a] :
% 186.89/187.90 ( class_Orderings_Oord(T_a)
% 186.89/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 186.89/187.90 => ( V_b = V_c
% 186.89/187.90 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ).
% 186.89/187.90
% 186.89/187.90 fof(fact_xt1_I3_J,axiom,
% 186.89/187.90 ! [V_c,V_b,V_a,T_a] :
% 186.89/187.90 ( class_Orderings_Oorder(T_a)
% 186.89/187.90 => ( V_a = V_b
% 186.89/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_b))
% 186.89/187.90 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ).
% 186.89/187.90
% 186.89/187.90 fof(fact_ord__eq__le__trans,axiom,
% 186.89/187.90 ! [V_c,V_b,V_a,T_a] :
% 186.89/187.90 ( class_Orderings_Oord(T_a)
% 186.89/187.90 => ( V_a = V_b
% 186.89/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
% 186.89/187.90 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ).
% 186.89/187.90
% 186.89/187.90 fof(fact_order__antisym__conv,axiom,
% 186.89/187.90 ! [V_x_2,V_y_2,T_a] :
% 186.89/187.90 ( class_Orderings_Oorder(T_a)
% 186.89/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2))
% 186.89/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 186.89/187.90 <=> V_x_2 = V_y_2 ) ) ) ).
% 186.89/187.90
% 186.89/187.90 fof(fact_order__eq__refl,axiom,
% 186.89/187.90 ! [V_y,V_x,T_a] :
% 186.89/187.90 ( class_Orderings_Opreorder(T_a)
% 186.89/187.90 => ( V_x = V_y
% 186.89/187.90 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 186.89/187.90
% 186.89/187.90 fof(fact_order__eq__iff,axiom,
% 186.89/187.90 ! [V_y_2,V_x_2,T_a] :
% 186.89/187.90 ( class_Orderings_Oorder(T_a)
% 186.89/187.90 => ( V_x_2 = V_y_2
% 186.89/187.90 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 186.89/187.90 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ) ).
% 186.89/187.90
% 186.89/187.90 fof(fact_linorder__linear,axiom,
% 186.89/187.90 ! [V_y,V_x,T_a] :
% 186.89/187.90 ( class_Orderings_Olinorder(T_a)
% 186.89/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 186.89/187.90 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ).
% 186.89/187.90
% 186.89/187.90 fof(fact_finite__code,axiom,
% 186.89/187.90 ! [V_A_2,T_a] :
% 186.89/187.90 ( class_Finite__Set_Ofinite(T_a)
% 186.89/187.90 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ).
% 186.89/187.90
% 186.89/187.90 fof(fact_finite,axiom,
% 186.89/187.90 ! [V_A_2,T_a] :
% 186.89/187.90 ( class_Finite__Set_Ofinite(T_a)
% 186.89/187.90 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ).
% 186.89/187.90
% 186.89/187.90 fof(fact_equalityE,axiom,
% 186.89/187.90 ! [T_a,V_B_2,V_A_2] :
% 186.89/187.90 ( V_A_2 = V_B_2
% 186.89/187.90 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 186.89/187.90 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ).
% 186.89/187.90
% 186.89/187.90 fof(fact_subset__trans,axiom,
% 186.89/187.90 ! [V_C_2,V_B_2,V_A_2,T_a] :
% 186.89/187.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 186.89/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))
% 186.89/187.90 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 186.89/187.90
% 186.89/187.90 fof(fact_equalityD2,axiom,
% 186.89/187.90 ! [T_a,V_B_2,V_A_2] :
% 186.89/187.90 ( V_A_2 = V_B_2
% 186.89/187.90 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) ) ).
% 186.89/187.90
% 186.89/187.90 fof(fact_equalityD1,axiom,
% 186.89/187.90 ! [T_a,V_B_2,V_A_2] :
% 186.89/187.90 ( V_A_2 = V_B_2
% 186.89/187.90 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 186.89/187.90
% 186.89/187.90 fof(fact_set__eq__subset,axiom,
% 186.89/187.90 ! [T_a,V_B_2,V_A_2] :
% 186.89/187.90 ( V_A_2 = V_B_2
% 186.89/187.90 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 186.89/187.90 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ).
% 186.89/187.90
% 186.89/187.90 fof(fact_subset__refl,axiom,
% 186.89/187.90 ! [V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_A_2)) ).
% 186.89/187.90
% 186.89/187.90 fof(fact_finite__dom__body,axiom,
% 186.89/187.90 hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody))) ).
% 186.89/187.90
% 186.89/187.90 fof(fact_MGT__Body,axiom,
% 186.89/187.90 ! [V_Procs_2,V_G_2] :
% 186.89/187.90 ( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),V_G_2),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Hoare__Mirabelle_OMGT),c_Com_Ocom_OBODY)),V_Procs_2)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Hoare__Mirabelle_OMGT),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),V_Procs_2))
% 186.89/187.90 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname),V_Procs_2))
% 186.89/187.90 => c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,V_G_2,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Hoare__Mirabelle_OMGT),c_Com_Ocom_OBODY)),V_Procs_2)) ) ) ).
% 186.89/187.90
% 186.89/187.90 fof(fact_folding__image__simple__idem_Osubset__idem,axiom,
% 186.89/187.90 ! [V_B_2,V_A_2,V_Fa_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 186.89/187.90 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_Fa_2)
% 186.89/187.90 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 186.89/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 186.89/187.90 => hAPP(hAPP(V_f_2,hAPP(V_Fa_2,V_B_2)),hAPP(V_Fa_2,V_A_2)) = hAPP(V_Fa_2,V_A_2) ) ) ) ).
% 186.89/187.90
% 186.89/187.90 fof(fact_image__ident,axiom,
% 186.89/187.90 ! [V_Y_2,T_a] : hAPP(c_Set_Oimage(T_a,T_a,c_COMBI(T_a)),V_Y_2) = V_Y_2 ).
% 186.89/187.90
% 186.89/187.90 fof(fact_finite__subset__image,axiom,
% 186.89/187.90 ! [V_A_2,V_f_2,T_b,V_B_2,T_a] :
% 186.89/187.90 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 186.89/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2)))
% 186.89/187.90 => ? [B_C] :
% 186.89/187.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),B_C),V_A_2))
% 186.89/187.90 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_C))
% 186.89/187.90 & V_B_2 = hAPP(c_Set_Oimage(T_b,T_a,V_f_2),B_C) ) ) ) ).
% 186.89/187.90
% 186.89/187.90 fof(fact_com_Osimps_I6_J,axiom,
% 186.89/187.90 ! [V_pname_H_2,V_pname_2] :
% 186.89/187.90 ( hAPP(c_Com_Ocom_OBODY,V_pname_2) = hAPP(c_Com_Ocom_OBODY,V_pname_H_2)
% 186.89/187.90 <=> V_pname_2 = V_pname_H_2 ) ).
% 186.89/187.90
% 186.89/187.90 fof(fact_predicate1D,axiom,
% 186.89/187.90 ! [V_x_2,V_Q_2,V_P_2,T_a] :
% 186.89/187.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_P_2),V_Q_2))
% 186.89/187.90 => ( hBOOL(hAPP(V_P_2,V_x_2))
% 186.89/187.90 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ).
% 186.89/187.90
% 186.89/187.90 fof(fact_rev__predicate1D,axiom,
% 186.89/187.90 ! [V_Q_2,T_a,V_x_2,V_P_2] :
% 186.89/187.90 ( hBOOL(hAPP(V_P_2,V_x_2))
% 186.89/187.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_P_2),V_Q_2))
% 186.89/187.90 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ).
% 186.89/187.90
% 186.89/187.90 fof(fact_MGT__BodyN,axiom,
% 186.89/187.90 ! [V_G_2,V_pn_2] :
% 186.89/187.90 ( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,V_pn_2))),V_G_2),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn_2)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
% 186.89/187.90 => c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,V_pn_2))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ) ).
% 186.89/187.90
% 186.89/187.90 fof(fact_hoare__derivs_OBody,axiom,
% 186.89/187.90 ! [V_Procs_2,V_Q_2,V_P_2,V_G_2,T_a] :
% 186.89/187.90 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)),V_G_2),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_a),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_a)),V_P_2)),c_Com_Ocom_OBODY)),V_Q_2)),V_Procs_2)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_a),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_a)),V_P_2)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),V_Q_2)),V_Procs_2))
% 186.89/187.90 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_a),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_a)),V_P_2)),c_Com_Ocom_OBODY)),V_Q_2)),V_Procs_2)) ) ).
% 186.89/187.90
% 186.89/187.90 fof(fact_evalc_OBody,axiom,
% 186.89/187.90 ! [V_s1,V_s0,V_pn] :
% 186.89/187.90 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn))),V_s0),V_s1))
% 186.89/187.90 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_pn)),V_s0),V_s1)) ) ).
% 186.89/187.90
% 186.89/187.90 fof(fact_evalc__elim__cases_I6_J,axiom,
% 186.89/187.90 ! [V_s1,V_s,V_P] :
% 186.89/187.90 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_P)),V_s),V_s1))
% 186.89/187.90 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_P))),V_s),V_s1)) ) ).
% 186.89/187.90
% 186.89/187.90 fof(fact_sup1CI,axiom,
% 186.89/187.90 ! [T_a,V_A_2,V_x_2,V_B_2] :
% 186.89/187.90 ( ( ~ hBOOL(hAPP(V_B_2,V_x_2))
% 186.89/187.90 => hBOOL(hAPP(V_A_2,V_x_2)) )
% 186.89/187.90 => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ) ).
% 186.89/187.90
% 186.89/187.90 fof(fact_sup1E,axiom,
% 186.89/187.90 ! [V_x_2,V_B_2,V_A_2,T_a] :
% 186.89/187.90 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2))
% 186.89/187.90 => ( ~ hBOOL(hAPP(V_A_2,V_x_2))
% 186.89/187.90 => hBOOL(hAPP(V_B_2,V_x_2)) ) ) ).
% 186.89/187.90
% 186.89/187.90 fof(fact_finite_OemptyI,axiom,
% 186.89/187.90 ! [T_a] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ).
% 186.89/187.90
% 186.89/187.90 fof(fact_finite_OinsertI,axiom,
% 186.89/187.90 ! [V_a_2,V_A_2,T_a] :
% 186.89/187.90 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.89/187.90 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2))) ) ).
% 186.89/187.90
% 186.89/187.90 fof(fact_empty__subsetI,axiom,
% 186.89/187.90 ! [V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_A_2)) ).
% 186.89/187.90
% 186.89/187.90 fof(fact_empty__not__insert,axiom,
% 186.89/187.90 ! [V_A_2,V_a_2,T_a] : c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) != hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2) ).
% 186.89/187.90
% 186.89/187.90 fof(fact_insert__not__empty,axiom,
% 186.89/187.90 ! [V_A_2,V_a_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ).
% 186.89/187.90
% 186.89/187.90 fof(fact_bot__fun__def,axiom,
% 186.89/187.90 ! [V_x_2,T_b,T_a] :
% 186.89/187.90 ( class_Orderings_Obot(T_a)
% 186.89/187.90 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,T_a)),V_x_2) = c_Orderings_Obot__class_Obot(T_a) ) ).
% 186.89/187.90
% 186.89/187.90 fof(fact_bot__apply,axiom,
% 186.89/187.90 ! [V_x_2,T_b,T_a] :
% 186.89/187.90 ( class_Orderings_Obot(T_a)
% 186.89/187.90 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,T_a)),V_x_2) = c_Orderings_Obot__class_Obot(T_a) ) ).
% 186.89/187.90
% 186.89/187.90 fof(fact_Un__empty__left,axiom,
% 186.89/187.90 ! [V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_B_2) = V_B_2 ).
% 186.89/187.90
% 186.89/187.90 fof(fact_Un__empty__right,axiom,
% 186.89/187.90 ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = V_A_2 ).
% 186.89/187.90
% 186.89/187.90 fof(fact_Un__absorb,axiom,
% 186.89/187.90 ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_A_2) = V_A_2 ).
% 186.89/187.90
% 186.89/187.90 fof(fact_Un__commute,axiom,
% 186.89/187.90 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2) ).
% 186.89/187.90
% 186.89/187.90 fof(fact_insert__is__Un,axiom,
% 186.89/187.90 ! [V_A_2,V_a_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_A_2) ).
% 186.89/187.90
% 186.89/187.90 fof(fact_insert__absorb2,axiom,
% 186.89/187.90 ! [V_A_2,V_x_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2) ).
% 186.89/187.90
% 186.89/187.90 fof(fact_Un__left__absorb,axiom,
% 186.89/187.90 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ).
% 186.89/187.90
% 186.89/187.90 fof(fact_insert__commute,axiom,
% 186.89/187.90 ! [V_A_2,V_y_2,V_x_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_y_2),V_A_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_y_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) ).
% 186.89/187.90
% 186.89/187.90 fof(fact_Un__insert__right,axiom,
% 186.89/187.90 ! [V_B_2,V_a_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ).
% 186.89/187.90
% 186.89/187.90 fof(fact_Un__left__commute,axiom,
% 186.89/187.90 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ).
% 186.89/187.90
% 186.89/187.90 fof(fact_Un__empty,axiom,
% 186.89/187.90 ! [V_B_2,V_A_2,T_a] :
% 186.89/187.90 ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 186.89/187.90 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 186.89/187.90 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ).
% 186.89/187.90
% 186.89/187.90 fof(fact_Un__insert__left,axiom,
% 186.89/187.90 ! [V_C_2,V_B_2,V_a_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) ).
% 186.89/187.90
% 186.89/187.90 fof(fact_Un__assoc,axiom,
% 186.89/187.90 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) ).
% 186.89/187.90
% 186.89/187.90 fof(fact_bex__Un,axiom,
% 186.89/187.90 ! [V_P_2,V_B_2,V_A_2,T_a] :
% 186.89/187.90 ( ? [B_x] :
% 186.89/187.90 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
% 186.89/187.90 & hBOOL(hAPP(V_P_2,B_x)) )
% 186.89/187.90 <=> ( ? [B_x] :
% 186.89/187.90 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 186.89/187.90 & hBOOL(hAPP(V_P_2,B_x)) )
% 186.89/187.90 | ? [B_x] :
% 186.89/187.90 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_B_2))
% 186.89/187.90 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ).
% 186.89/187.90
% 186.89/187.90 fof(fact_ball__Un,axiom,
% 186.89/187.90 ! [V_P_2,V_B_2,V_A_2,T_a] :
% 186.89/187.90 ( ! [B_x] :
% 186.89/187.90 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
% 186.89/187.90 => hBOOL(hAPP(V_P_2,B_x)) )
% 186.89/187.90 <=> ( ! [B_x] :
% 186.89/187.90 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 186.89/187.90 => hBOOL(hAPP(V_P_2,B_x)) )
% 186.89/187.90 & ! [B_x] :
% 186.89/187.90 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_B_2))
% 186.89/187.90 => hBOOL(hAPP(V_P_2,B_x)) ) ) ) ).
% 186.89/187.90
% 186.89/187.91 fof(fact_doubleton__eq__iff,axiom,
% 186.89/187.91 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
% 186.89/187.91 ( hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(T_a),V_c_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_d_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))
% 186.89/187.91 <=> ( ( V_a_2 = V_c_2
% 186.89/187.91 & V_b_2 = V_d_2 )
% 186.89/187.91 | ( V_a_2 = V_d_2
% 186.89/187.91 & V_b_2 = V_c_2 ) ) ) ).
% 186.89/187.91
% 186.89/187.91 fof(fact_insert__code,axiom,
% 186.89/187.91 ! [V_x_2,V_A_2,V_y_2,T_a] :
% 186.89/187.91 ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(T_a),V_y_2),V_A_2),V_x_2))
% 186.89/187.91 <=> ( V_y_2 = V_x_2
% 186.89/187.91 | hBOOL(hAPP(V_A_2,V_x_2)) ) ) ).
% 186.89/187.91
% 186.89/187.91 fof(fact_singleton__inject,axiom,
% 186.89/187.91 ! [V_b_2,V_a_2,T_a] :
% 186.89/187.91 ( hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))
% 186.89/187.91 => V_a_2 = V_b_2 ) ).
% 186.89/187.91
% 186.89/187.91 fof(fact_com__det,axiom,
% 186.89/187.91 ! [V_u,V_t,V_s,V_c] :
% 186.89/187.91 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_t))
% 186.89/187.91 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_u))
% 186.89/187.91 => V_u = V_t ) ) ).
% 186.89/187.91
% 186.89/187.91 fof(fact_sup1I2,axiom,
% 186.89/187.91 ! [V_A_2,T_a,V_x_2,V_B_2] :
% 186.89/187.91 ( hBOOL(hAPP(V_B_2,V_x_2))
% 186.89/187.91 => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ) ).
% 186.89/187.91
% 186.89/187.91 fof(fact_sup1I1,axiom,
% 186.89/187.91 ! [V_B_2,T_a,V_x_2,V_A_2] :
% 186.89/187.91 ( hBOOL(hAPP(V_A_2,V_x_2))
% 186.89/187.91 => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ) ).
% 186.89/187.91
% 186.89/187.91 fof(fact_triple_Oinject,axiom,
% 186.89/187.91 ! [V_fun2_H_2,V_com_H_2,V_fun1_H_2,V_fun2_2,V_com_2,V_fun1_2,T_a] :
% 186.89/187.91 ( hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_fun1_2),V_com_2),V_fun2_2) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_fun1_H_2),V_com_H_2),V_fun2_H_2)
% 186.89/187.91 <=> ( V_fun1_2 = V_fun1_H_2
% 186.89/187.91 & V_com_2 = V_com_H_2
% 186.89/187.91 & V_fun2_2 = V_fun2_H_2 ) ) ).
% 186.89/187.91
% 186.89/187.91 fof(fact_subset__singletonD,axiom,
% 186.89/187.91 ! [V_x_2,V_A_2,T_a] :
% 186.89/187.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))
% 186.89/187.91 => ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 186.89/187.91 | V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ) ) ).
% 186.89/187.91
% 186.89/187.91 fof(fact_hoare__derivs_Oinsert,axiom,
% 186.89/187.91 ! [V_ts_2,V_t_2,V_G_2,T_a] :
% 186.89/187.91 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),V_t_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))))
% 186.89/187.91 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,V_ts_2)
% 186.89/187.91 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),V_t_2),V_ts_2)) ) ) ).
% 186.89/187.91
% 186.89/187.91 fof(fact_derivs__insertD,axiom,
% 186.89/187.91 ! [V_ts_2,V_t_2,V_G_2,T_a] :
% 186.89/187.91 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),V_t_2),V_ts_2))
% 186.89/187.91 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),V_t_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))))
% 186.89/187.91 & c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,V_ts_2) ) ) ).
% 186.89/187.91
% 186.89/187.91 fof(fact_folding__image__simple__idem_Oidem,axiom,
% 186.89/187.91 ! [V_x_2,V_Fa_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 186.89/187.91 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_Fa_2)
% 186.89/187.91 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ).
% 186.89/187.91
% 186.89/187.91 fof(fact_image__constant__conv,axiom,
% 186.89/187.91 ! [V_c_2,T_b,T_a,V_A_2] :
% 186.89/187.91 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 186.89/187.91 => hAPP(c_Set_Oimage(T_a,T_b,hAPP(c_COMBK(T_b,T_a),V_c_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
% 186.89/187.91 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 186.89/187.91 => hAPP(c_Set_Oimage(T_a,T_b,hAPP(c_COMBK(T_b,T_a),V_c_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ) ).
% 186.89/187.91
% 186.89/187.91 fof(fact_folding__image__simple__idem_Ounion__idem,axiom,
% 186.89/187.91 ! [V_B_2,V_A_2,V_Fa_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 186.89/187.91 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_Fa_2)
% 186.89/187.91 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 186.89/187.91 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 186.89/187.91 => hAPP(V_Fa_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_Fa_2,V_A_2)),hAPP(V_Fa_2,V_B_2)) ) ) ) ).
% 186.89/187.91
% 186.89/187.91 fof(fact_folding__image__simple__idem_Oinsert__idem,axiom,
% 186.89/187.91 ! [V_x_2,V_A_2,V_Fa_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 186.89/187.91 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_Fa_2)
% 186.89/187.91 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 186.89/187.91 => hAPP(V_Fa_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_Fa_2,V_A_2)) ) ) ).
% 186.89/187.91
% 186.89/187.91 fof(fact_MGT__def,axiom,
% 186.89/187.91 ! [V_c_2] : hAPP(c_Hoare__Mirabelle_OMGT,V_c_2) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),c_fequal),V_c_2),c_Natural_Oevalc(V_c_2)) ).
% 186.89/187.91
% 186.89/187.91 fof(fact_finite__Un,axiom,
% 186.89/187.91 ! [V_G_2,V_Fa_2,T_a] :
% 186.89/187.91 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_Fa_2),V_G_2)))
% 186.89/187.91 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_Fa_2))
% 186.89/187.91 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_G_2)) ) ) ).
% 186.89/187.91
% 186.89/187.91 fof(fact_finite__UnI,axiom,
% 186.89/187.91 ! [V_G_2,V_Fa_2,T_a] :
% 186.89/187.91 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_Fa_2))
% 186.89/187.91 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_G_2))
% 186.89/187.91 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_Fa_2),V_G_2))) ) ) ).
% 186.89/187.91
% 186.89/187.91 fof(fact_finite__insert,axiom,
% 186.89/187.91 ! [V_A_2,V_a_2,T_a] :
% 186.89/187.91 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)))
% 186.89/187.91 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ).
% 186.89/187.91
% 186.89/187.91 fof(fact_Un__upper1,axiom,
% 186.89/187.91 ! [V_B_2,V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ).
% 186.89/187.91
% 186.89/187.91 fof(fact_Un__upper2,axiom,
% 186.89/187.91 ! [V_A_2,V_B_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ).
% 186.89/187.91
% 186.89/187.91 fof(fact_subset__Un__eq,axiom,
% 186.89/187.91 ! [V_B_2,V_A_2,T_a] :
% 186.89/187.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 186.89/187.91 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ).
% 186.89/187.91
% 186.89/187.91 fof(fact_Un__absorb1,axiom,
% 186.89/187.91 ! [V_B_2,V_A_2,T_a] :
% 186.89/187.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 186.89/187.91 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ).
% 186.89/187.91
% 186.89/187.91 fof(fact_Un__absorb2,axiom,
% 186.89/187.91 ! [V_A_2,V_B_2,T_a] :
% 186.89/187.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 186.89/187.91 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ).
% 186.89/187.91
% 186.89/187.91 fof(fact_Un__least,axiom,
% 186.89/187.91 ! [V_B_2,V_C_2,V_A_2,T_a] :
% 186.89/187.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2))
% 186.89/187.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))
% 186.89/187.91 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2)) ) ) ).
% 186.89/187.91
% 186.89/187.91 fof(fact_Un__mono,axiom,
% 186.89/187.91 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_a] :
% 186.89/187.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2))
% 186.89/187.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_D_2))
% 186.89/187.91 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_D_2))) ) ) ).
% 186.89/187.91
% 186.89/187.91 fof(fact_subset__insertI,axiom,
% 186.89/187.91 ! [V_a_2,V_B_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2))) ).
% 186.89/187.91
% 186.89/187.91 fof(fact_subset__insertI2,axiom,
% 186.89/187.91 ! [V_b_2,V_B_2,V_A_2,T_a] :
% 186.89/187.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 186.89/187.91 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_B_2))) ) ).
% 186.89/187.91
% 186.89/187.91 fof(fact_insert__mono,axiom,
% 186.89/187.91 ! [V_a_2,V_D_2,V_C_2,T_a] :
% 186.89/187.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_D_2))
% 186.89/187.91 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_C_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_D_2))) ) ).
% 186.89/187.91
% 186.89/187.91 fof(fact_image__Un,axiom,
% 186.89/187.91 ! [V_B_2,V_A_2,V_f_2,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_B_2)) ).
% 186.89/187.91
% 186.89/187.91 fof(fact_image__insert,axiom,
% 186.89/187.91 ! [V_B_2,V_a_2,V_f_2,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_B_2)) ).
% 186.89/187.91
% 186.89/187.91 fof(fact_finite_Oequations_I1_J,axiom,
% 186.89/187.91 ! [T_a] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ).
% 186.89/187.91
% 186.89/187.91 fof(fact_subset__empty,axiom,
% 186.89/187.91 ! [V_A_2,T_a] :
% 186.89/187.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))
% 186.89/187.91 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 186.89/187.91
% 186.89/187.91 fof(fact_empty__is__image,axiom,
% 186.89/187.91 ! [V_A_2,V_f_2,T_b,T_a] :
% 186.89/187.91 ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2)
% 186.89/187.91 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 186.89/187.91
% 186.89/187.91 fof(fact_image__empty,axiom,
% 186.89/187.91 ! [V_f_2,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ).
% 186.89/187.91
% 186.89/187.91 fof(fact_image__is__empty,axiom,
% 186.89/187.91 ! [V_A_2,V_f_2,T_a,T_b] :
% 186.89/187.91 ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 186.89/187.91 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 186.89/187.91
% 186.89/187.91 fof(fact_empty,axiom,
% 186.89/187.91 ! [V_G_2,T_a] : c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))) ).
% 186.89/187.91
% 186.89/187.91 fof(fact_hoare__derivs_Oequations_I1_J,axiom,
% 186.89/187.91 ! [V_a_2,T_a] : c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))) ).
% 186.89/187.91
% 186.89/187.91 fof(fact_weak__Body,axiom,
% 186.89/187.91 ! [V_Q_2,V_pn_2,V_P_2,V_G_2,T_a] :
% 186.89/187.91 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn_2))),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))))
% 186.97/187.91 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ).
% 186.97/187.91
% 186.97/187.91 fof(fact_BodyN,axiom,
% 186.97/187.91 ! [V_G_2,V_Q_2,V_pn_2,V_P_2,T_a] :
% 186.97/187.91 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Q_2)),V_G_2),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn_2))),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))))
% 186.97/187.91 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ).
% 186.97/187.91
% 186.97/187.91 fof(fact_bot__least,axiom,
% 186.97/187.91 ! [V_x,T_a] :
% 186.97/187.91 ( class_Orderings_Obot(T_a)
% 186.97/187.91 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x)) ) ).
% 186.97/187.91
% 186.97/187.91 fof(fact_evalc_Oequations_I9_J,axiom,
% 186.97/187.91 ! [V_a3_2,V_a2_2,V_a1_2] :
% 186.97/187.91 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_a1_2)),V_a2_2),V_a3_2))
% 186.97/187.91 <=> hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_a1_2))),V_a2_2),V_a3_2)) ) ).
% 186.97/187.91
% 186.97/187.91 fof(fact_Body__sound__lemma,axiom,
% 186.97/187.91 ! [V_Procs_2,V_Q_2,V_P_2,V_G_2,T_a] :
% 186.97/187.91 ( c_Hoare__Mirabelle_Ohoare__valids(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)),V_G_2),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_a),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_a)),V_P_2)),c_Com_Ocom_OBODY)),V_Q_2)),V_Procs_2)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_a),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_a)),V_P_2)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),V_Q_2)),V_Procs_2))
% 186.97/187.91 => c_Hoare__Mirabelle_Ohoare__valids(T_a,V_G_2,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_a),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_a)),V_P_2)),c_Com_Ocom_OBODY)),V_Q_2)),V_Procs_2)) ) ).
% 186.97/187.91
% 186.97/187.91 fof(fact_Body1,axiom,
% 186.97/187.91 ! [V_pn_2,V_Procs_2,V_Q_2,V_P_2,V_G_2,T_a] :
% 186.97/187.91 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)),V_G_2),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_a),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_a)),V_P_2)),c_Com_Ocom_OBODY)),V_Q_2)),V_Procs_2)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_a),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_a)),V_P_2)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),V_Q_2)),V_Procs_2))
% 186.97/187.91 => ( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),V_pn_2),V_Procs_2))
% 186.97/187.91 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),hAPP(V_P_2,V_pn_2)),hAPP(c_Com_Ocom_OBODY,V_pn_2)),hAPP(V_Q_2,V_pn_2))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ) ).
% 186.97/187.91
% 186.97/187.91 fof(fact_MGF__complete,axiom,
% 186.97/187.91 ! [V_Q_2,V_P_2,V_c_2] :
% 186.97/187.91 ( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,V_c_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
% 186.97/187.91 => ( c_Hoare__Mirabelle_Ohoare__valids(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),V_P_2),V_c_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
% 186.97/187.91 => c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),V_P_2),V_c_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ) ) ).
% 186.97/187.91
% 186.97/187.91 fof(fact_MGF,axiom,
% 186.97/187.91 ! [V_c_2] :
% 186.97/187.91 ( c_Hoare__Mirabelle_Ostate__not__singleton
% 186.97/187.91 => ( c_Com_OWT__bodies
% 186.97/187.91 => ( hBOOL(hAPP(c_Com_OWT,V_c_2))
% 186.97/187.91 => c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,V_c_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ) ) ) ).
% 186.97/187.91
% 186.97/187.91 fof(fact_finite__pointwise,axiom,
% 186.97/187.91 ! [V_Q_2,V_P_2,V_Q_H_2,V_c0_2,V_P_H_2,V_G_2,T_b,V_U_2,T_a] :
% 186.97/187.91 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_U_2))
% 186.97/187.91 => ( ! [B_p] :
% 186.97/187.91 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),hAPP(V_P_H_2,B_p)),hAPP(V_c0_2,B_p)),hAPP(V_Q_H_2,B_p))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 186.97/187.91 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),hAPP(V_P_2,B_p)),hAPP(V_c0_2,B_p)),hAPP(V_Q_2,B_p))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) )
% 186.97/187.91 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,hAPP(c_Set_Oimage(T_a,tc_Hoare__Mirabelle_Otriple(T_b),hAPP(hAPP(c_COMBS(T_a,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(c_COMBS(T_a,tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),T_a),c_Hoare__Mirabelle_Otriple_Otriple(T_b)),V_P_H_2)),V_c0_2)),V_Q_H_2)),V_U_2))
% 186.97/187.91 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,hAPP(c_Set_Oimage(T_a,tc_Hoare__Mirabelle_Otriple(T_b),hAPP(hAPP(c_COMBS(T_a,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(c_COMBS(T_a,tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),T_a),c_Hoare__Mirabelle_Otriple_Otriple(T_b)),V_P_2)),V_c0_2)),V_Q_2)),V_U_2)) ) ) ) ).
% 186.97/187.91
% 186.97/187.91 fof(fact_the__elem__eq,axiom,
% 186.97/187.91 ! [V_x_2,T_a] : c_Set_Othe__elem(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_x_2 ).
% 186.97/187.91
% 186.97/187.91 fof(fact_MGT__alternD,axiom,
% 186.97/187.91 ! [V_c_2,V_G_2] :
% 186.97/187.91 ( c_Hoare__Mirabelle_Ostate__not__singleton
% 186.97/187.91 => ( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_Com_Ostate),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_HOL_Obool,tc_Com_Ostate),c_HOL_OAll(tc_Com_Ostate))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Com_Ostate),hAPP(c_COMBC(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Com_Ostate),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Com_Ostate),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fimplies)),c_Natural_Oevalc(V_c_2))))),c_fequal))),V_c_2),c_fequal)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
% 186.97/187.91 => c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,V_c_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ) ) ).
% 186.97/187.91
% 186.97/187.91 fof(fact_sup__fun__def,axiom,
% 186.97/187.91 ! [V_x_2,V_g_2,V_f_2,T_b,T_a] :
% 186.97/187.91 ( class_Lattices_Olattice(T_a)
% 186.97/187.91 => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,T_a)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ) ).
% 186.97/187.91
% 186.97/187.91 fof(fact_triple_Osimps_I2_J,axiom,
% 186.97/187.91 ! [V_fun2_2,V_com_2,V_fun1_2,V_f1_2,T_a,T_b] : c_Hoare__Mirabelle_Otriple_Otriple__case(T_b,T_a,V_f1_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_fun1_2),V_com_2),V_fun2_2)) = hAPP(hAPP(hAPP(V_f1_2,V_fun1_2),V_com_2),V_fun2_2) ).
% 186.97/187.91
% 186.97/187.91 fof(fact_triple_Orecs,axiom,
% 186.97/187.91 ! [V_fun2_2,V_com_2,V_fun1_2,V_f1_2,T_a,T_b] : c_Hoare__Mirabelle_Otriple_Otriple__rec(T_b,T_a,V_f1_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_fun1_2),V_com_2),V_fun2_2)) = hAPP(hAPP(hAPP(V_f1_2,V_fun1_2),V_com_2),V_fun2_2) ).
% 186.97/187.91
% 186.97/187.91 fof(fact_sup__apply,axiom,
% 186.97/187.91 ! [V_x_2,V_g_2,V_f_2,T_b,T_a] :
% 186.97/187.91 ( class_Lattices_Olattice(T_a)
% 186.97/187.91 => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,T_a)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ) ).
% 186.97/187.91
% 186.97/187.91 fof(fact_MGT__alternI,axiom,
% 186.97/187.91 ! [V_c_2,V_G_2] :
% 186.97/187.91 ( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,V_c_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
% 186.97/187.91 => c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_Com_Ostate),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_HOL_Obool,tc_Com_Ostate),c_HOL_OAll(tc_Com_Ostate))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Com_Ostate),hAPP(c_COMBC(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Com_Ostate),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Com_Ostate),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fimplies)),c_Natural_Oevalc(V_c_2))))),c_fequal))),V_c_2),c_fequal)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ) ).
% 186.97/187.91
% 186.97/187.91 fof(fact_equalityCE,axiom,
% 186.97/187.91 ! [V_c_2,T_a,V_B_2,V_A_2] :
% 186.97/187.91 ( V_A_2 = V_B_2
% 186.97/187.91 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2))
% 186.97/187.91 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) )
% 186.97/187.91 => ~ ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2))
% 186.97/187.91 => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) ) ) ) ).
% 186.97/187.91
% 186.97/187.91 fof(fact_emptyE,axiom,
% 186.97/187.91 ! [V_a_2,T_a] : ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ).
% 186.97/187.91
% 186.97/187.91 fof(fact_insertCI,axiom,
% 186.97/187.91 ! [V_b_2,V_B_2,V_a_2,T_a] :
% 186.97/187.91 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_B_2))
% 186.97/187.91 => V_a_2 = V_b_2 )
% 186.97/187.91 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_B_2))) ) ).
% 186.97/187.91
% 186.97/187.91 fof(fact_insertE,axiom,
% 186.97/187.91 ! [V_A_2,V_b_2,V_a_2,T_a] :
% 186.97/187.91 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_A_2)))
% 186.97/187.91 => ( V_a_2 != V_b_2
% 186.97/187.91 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ).
% 186.97/187.91
% 186.97/187.91 fof(fact_subsetD,axiom,
% 186.97/187.91 ! [V_c_2,V_B_2,V_A_2,T_a] :
% 186.97/187.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 186.97/187.91 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2))
% 186.97/187.91 => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) ) ) ).
% 186.97/187.91
% 186.97/187.91 fof(fact_image__eqI,axiom,
% 186.97/187.91 ! [T_a,V_A_2,T_b,V_x_2,V_f_2,V_b_2] :
% 186.97/187.91 ( V_b_2 = hAPP(V_f_2,V_x_2)
% 186.97/187.91 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 186.97/187.91 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2))) ) ) ).
% 186.97/187.91
% 186.97/187.91 fof(fact_UnCI,axiom,
% 186.97/187.91 ! [V_A_2,V_B_2,V_c_2,T_a] :
% 186.97/187.91 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2))
% 186.97/187.91 => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) )
% 186.97/187.91 => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ).
% 186.97/187.91
% 186.97/187.91 fof(fact_UnE,axiom,
% 186.97/187.91 ! [V_B_2,V_A_2,V_c_2,T_a] :
% 186.97/187.91 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
% 186.97/187.91 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2))
% 186.97/187.91 => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) ) ) ).
% 186.97/187.91
% 186.97/187.91 fof(fact_eq__mem,axiom,
% 186.97/187.91 ! [V_y_2,V_x_2,T_a] :
% 186.97/187.91 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_fequal,V_y_2)))
% 186.97/187.91 <=> V_x_2 = V_y_2 ) ).
% 186.97/187.91
% 186.97/187.91 fof(fact_eq__mem__trans,axiom,
% 186.97/187.91 ! [V_A_2,T_a,V_b_2,V_a_2] :
% 186.97/187.91 ( V_a_2 = V_b_2
% 186.97/187.91 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2))
% 186.97/187.91 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ).
% 186.97/187.91
% 186.97/187.91 fof(fact_eqelem__imp__iff,axiom,
% 186.97/187.91 ! [V_A_2,T_a,V_y_2,V_x_2] :
% 186.97/187.91 ( V_x_2 = V_y_2
% 186.97/187.91 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 186.97/187.91 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) ) ) ).
% 186.97/187.91
% 186.97/187.91 fof(fact_eqset__imp__iff,axiom,
% 186.97/187.91 ! [V_x_2,T_a,V_B_2,V_A_2] :
% 186.97/187.91 ( V_A_2 = V_B_2
% 186.97/187.91 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 186.97/187.91 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ).
% 186.97/187.91
% 186.97/187.91 fof(fact_mem__def,axiom,
% 186.97/187.91 ! [V_A_2,V_x_2,T_a] :
% 186.97/187.91 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 186.97/187.91 <=> hBOOL(hAPP(V_A_2,V_x_2)) ) ).
% 186.97/187.91
% 186.97/187.91 fof(fact_pred__equals__eq,axiom,
% 186.97/187.91 ! [V_S_2,V_R_2,T_a] :
% 186.97/187.91 ( hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_R_2) = hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_S_2)
% 186.97/187.91 <=> V_R_2 = V_S_2 ) ).
% 186.97/187.91
% 186.97/187.91 fof(fact_equals0D,axiom,
% 186.97/187.91 ! [V_a_2,T_a,V_A_2] :
% 186.97/187.91 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 186.97/187.91 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ).
% 186.97/187.91
% 186.97/187.91 fof(fact_empty__iff,axiom,
% 186.97/187.91 ! [V_c_2,T_a] : ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ).
% 186.97/187.91
% 186.97/187.91 fof(fact_ex__in__conv,axiom,
% 186.97/187.91 ! [V_A_2,T_a] :
% 186.97/187.91 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 186.97/187.91 <=> V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 186.97/187.91
% 186.97/187.91 fof(fact_all__not__in__conv,axiom,
% 186.97/187.91 ! [V_A_2,T_a] :
% 186.97/187.91 ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 186.97/187.91 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 186.97/187.91
% 186.97/187.91 fof(fact_insert__absorb,axiom,
% 186.97/187.91 ! [V_A_2,V_a_2,T_a] :
% 186.97/187.91 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 186.97/187.91 => hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2) = V_A_2 ) ).
% 186.97/187.91
% 186.97/187.91 fof(fact_insertI2,axiom,
% 186.97/187.91 ! [V_b_2,V_B_2,V_a_2,T_a] :
% 186.97/187.91 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_B_2))
% 186.97/187.91 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_B_2))) ) ).
% 186.97/187.91
% 186.97/187.91 fof(fact_insert__ident,axiom,
% 186.97/187.91 ! [V_B_2,V_A_2,V_x_2,T_a] :
% 186.97/187.91 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 186.97/187.91 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2))
% 186.97/187.91 => ( hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_B_2)
% 186.97/187.91 <=> V_A_2 = V_B_2 ) ) ) ).
% 186.97/187.91
% 186.97/187.91 fof(fact_insert__iff,axiom,
% 186.97/187.91 ! [V_A_2,V_b_2,V_a_2,T_a] :
% 186.97/187.91 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_A_2)))
% 186.97/187.91 <=> ( V_a_2 = V_b_2
% 186.97/187.91 | hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ).
% 186.97/187.91
% 186.97/187.91 fof(fact_insertI1,axiom,
% 186.97/187.91 ! [V_B_2,V_a_2,T_a] : hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2))) ).
% 186.97/187.91
% 186.97/187.91 fof(fact_set__mp,axiom,
% 186.97/187.91 ! [V_x_2,V_B_2,V_A_2,T_a] :
% 186.97/187.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 186.97/187.91 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 186.97/187.91 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ).
% 186.97/187.91
% 186.97/187.91 fof(fact_set__rev__mp,axiom,
% 186.97/187.91 ! [V_B_2,V_A_2,V_x_2,T_a] :
% 186.97/187.91 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 186.97/187.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 186.97/187.91 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ).
% 186.97/187.91
% 186.97/187.91 fof(fact_in__mono,axiom,
% 186.97/187.91 ! [V_x_2,V_B_2,V_A_2,T_a] :
% 186.97/187.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 186.97/187.91 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 186.97/187.91 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ).
% 186.97/187.91
% 186.97/187.91 fof(fact_rev__image__eqI,axiom,
% 186.97/187.91 ! [T_b,V_f_2,V_b_2,V_A_2,V_x_2,T_a] :
% 186.97/187.91 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 186.97/187.91 => ( V_b_2 = hAPP(V_f_2,V_x_2)
% 186.97/187.91 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) ) ) ).
% 186.97/187.91
% 186.97/187.91 fof(fact_imageI,axiom,
% 186.97/187.91 ! [V_f_2,T_b,V_A_2,V_x_2,T_a] :
% 186.97/187.91 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 186.97/187.91 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) ) ).
% 186.97/187.91
% 186.97/187.91 fof(fact_image__iff,axiom,
% 186.97/187.91 ! [V_A_2,V_f_2,T_b,V_z_2,T_a] :
% 186.97/187.91 ( hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2)))
% 186.97/187.91 <=> ? [B_x] :
% 186.97/187.91 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 186.97/187.91 & V_z_2 = hAPP(V_f_2,B_x) ) ) ).
% 186.97/187.91
% 186.97/187.91 fof(fact_UnI2,axiom,
% 186.97/187.91 ! [V_A_2,V_B_2,V_c_2,T_a] :
% 186.97/187.91 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2))
% 186.97/187.91 => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ).
% 186.97/187.91
% 186.97/187.91 fof(fact_UnI1,axiom,
% 186.97/187.91 ! [V_B_2,V_A_2,V_c_2,T_a] :
% 186.97/187.91 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2))
% 186.97/187.91 => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ).
% 186.97/187.91
% 186.97/187.91 fof(fact_Un__iff,axiom,
% 186.97/187.91 ! [V_B_2,V_A_2,V_c_2,T_a] :
% 186.97/187.91 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
% 186.97/187.91 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2))
% 186.97/187.91 | hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) ) ) ).
% 186.97/187.91
% 186.97/187.91 fof(fact_bot__empty__eq,axiom,
% 186.97/187.91 ! [V_x_2,T_a] :
% 186.97/187.91 ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_x_2))
% 186.97/187.91 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ) ).
% 186.97/187.91
% 186.97/187.91 fof(fact_pred__subset__eq,axiom,
% 186.97/187.91 ! [V_S_2,V_R_2,T_a] :
% 186.97/187.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_R_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_S_2)))
% 186.97/187.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_R_2),V_S_2)) ) ).
% 186.97/187.91
% 186.97/187.91 fof(fact_sup__Un__eq,axiom,
% 186.97/187.91 ! [V_x_2,V_S_2,V_R_2,T_a] :
% 186.97/187.91 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_R_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_S_2)),V_x_2))
% 186.97/187.91 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_R_2),V_S_2))) ) ).
% 186.97/187.91
% 186.97/187.91 fof(fact_singletonE,axiom,
% 186.97/187.91 ! [V_a_2,V_b_2,T_a] :
% 186.97/187.91 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))
% 186.97/187.91 => V_b_2 = V_a_2 ) ).
% 186.97/187.91
% 186.97/187.91 fof(fact_singleton__iff,axiom,
% 186.97/187.91 ! [V_a_2,V_b_2,T_a] :
% 186.97/187.91 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))
% 186.97/187.91 <=> V_b_2 = V_a_2 ) ).
% 186.97/187.91
% 186.97/187.91 fof(fact_insert__subset,axiom,
% 186.97/187.91 ! [V_B_2,V_A_2,V_x_2,T_a] :
% 186.97/187.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)),V_B_2))
% 186.97/187.91 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2))
% 186.97/187.91 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 186.97/187.91
% 186.97/187.91 fof(fact_subset__insert,axiom,
% 186.97/187.91 ! [V_B_2,V_A_2,V_x_2,T_a] :
% 186.97/187.91 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 186.97/187.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_B_2)))
% 186.97/187.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 186.97/187.91
% 186.97/187.91 fof(fact_insert__image,axiom,
% 186.97/187.91 ! [V_f_2,T_b,V_A_2,V_x_2,T_a] :
% 186.97/187.91 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 186.97/187.91 => hAPP(hAPP(c_Set_Oinsert(T_b),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)) = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2) ) ).
% 186.97/187.91
% 186.97/187.91 fof(fact_folding__image__simple__idem_Oin__idem,axiom,
% 186.97/187.91 ! [V_x_2,V_A_2,V_Fa_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 186.97/187.91 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_Fa_2)
% 186.97/187.91 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 186.97/187.91 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 186.97/187.91 => hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_Fa_2,V_A_2)) = hAPP(V_Fa_2,V_A_2) ) ) ) ).
% 186.97/187.91
% 186.97/187.91 fof(fact_hoare__sound,axiom,
% 186.97/187.91 ! [V_ts_2,V_G_2,T_a] :
% 186.97/187.91 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,V_ts_2)
% 186.97/187.91 => c_Hoare__Mirabelle_Ohoare__valids(T_a,V_G_2,V_ts_2) ) ).
% 186.97/187.91
% 186.97/187.91 fof(fact_sup_Oidem,axiom,
% 186.97/187.91 ! [V_a,T_a] :
% 186.97/187.91 ( class_Lattices_Osemilattice__sup(T_a)
% 186.97/187.91 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_a) = V_a ) ).
% 186.97/187.91
% 186.97/187.91 fof(fact_sup__idem,axiom,
% 186.97/187.91 ! [V_x,T_a] :
% 186.97/187.91 ( class_Lattices_Osemilattice__sup(T_a)
% 186.97/187.91 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ).
% 186.97/187.91
% 186.97/187.91 fof(fact_sup_Ocommute,axiom,
% 186.97/187.91 ! [V_b,V_a,T_a] :
% 186.97/187.91 ( class_Lattices_Osemilattice__sup(T_a)
% 186.97/187.91 => 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) ) ).
% 186.97/187.91
% 186.97/187.91 fof(fact_inf__sup__aci_I5_J,axiom,
% 186.97/187.91 ! [V_y,V_x,T_a] :
% 186.97/187.91 ( class_Lattices_Olattice(T_a)
% 186.97/187.91 => 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) ) ).
% 186.97/187.91
% 186.97/187.91 fof(fact_sup__commute,axiom,
% 186.97/187.91 ! [V_y,V_x,T_a] :
% 186.97/187.91 ( class_Lattices_Osemilattice__sup(T_a)
% 186.97/187.91 => 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) ) ).
% 186.97/187.91
% 186.97/187.91 fof(fact_sup_Oleft__idem,axiom,
% 186.97/187.91 ! [V_b,V_a,T_a] :
% 186.97/187.91 ( class_Lattices_Osemilattice__sup(T_a)
% 186.97/187.91 => 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) ) ).
% 186.97/187.91
% 186.97/187.91 fof(fact_inf__sup__aci_I8_J,axiom,
% 186.97/187.91 ! [V_y,V_x,T_a] :
% 186.97/187.91 ( class_Lattices_Olattice(T_a)
% 186.97/187.91 => 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) ) ).
% 186.97/187.91
% 186.97/187.91 fof(fact_sup__left__idem,axiom,
% 186.97/187.91 ! [V_y,V_x,T_a] :
% 186.97/187.91 ( class_Lattices_Osemilattice__sup(T_a)
% 186.97/187.91 => 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) ) ).
% 186.97/187.91
% 186.97/187.91 fof(fact_sup_Oleft__commute,axiom,
% 186.97/187.91 ! [V_c,V_a,V_b,T_a] :
% 186.97/187.91 ( class_Lattices_Osemilattice__sup(T_a)
% 186.97/187.91 => 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)) ) ).
% 186.97/187.91
% 186.97/187.91 fof(fact_inf__sup__aci_I7_J,axiom,
% 186.97/187.91 ! [V_z,V_y,V_x,T_a] :
% 186.97/187.91 ( class_Lattices_Olattice(T_a)
% 186.97/187.91 => 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)) ) ).
% 186.97/187.91
% 186.97/187.91 fof(fact_sup__left__commute,axiom,
% 186.97/187.91 ! [V_z,V_y,V_x,T_a] :
% 186.97/187.91 ( class_Lattices_Osemilattice__sup(T_a)
% 186.97/187.91 => 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)) ) ).
% 186.97/187.91
% 186.97/187.91 fof(fact_sup_Oassoc,axiom,
% 186.97/187.91 ! [V_c,V_b,V_a,T_a] :
% 186.97/187.91 ( class_Lattices_Osemilattice__sup(T_a)
% 186.97/187.91 => 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)) ) ).
% 186.97/187.91
% 186.97/187.91 fof(fact_inf__sup__aci_I6_J,axiom,
% 186.97/187.92 ! [V_z,V_y,V_x,T_a] :
% 186.97/187.92 ( class_Lattices_Olattice(T_a)
% 186.97/187.92 => 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)) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_sup__assoc,axiom,
% 186.97/187.92 ! [V_z,V_y,V_x,T_a] :
% 186.97/187.92 ( class_Lattices_Osemilattice__sup(T_a)
% 186.97/187.92 => 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)) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_image__constant,axiom,
% 186.97/187.92 ! [V_c_2,T_b,V_A_2,V_x_2,T_a] :
% 186.97/187.92 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 186.97/187.92 => hAPP(c_Set_Oimage(T_a,T_b,hAPP(c_COMBK(T_b,T_a),V_c_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_le__supE,axiom,
% 186.97/187.92 ! [V_x,V_b,V_a,T_a] :
% 186.97/187.92 ( class_Lattices_Osemilattice__sup(T_a)
% 186.97/187.92 => ( 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))
% 186.97/187.92 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 186.97/187.92 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_sup__mono,axiom,
% 186.97/187.92 ! [V_d,V_b,V_c,V_a,T_a] :
% 186.97/187.92 ( class_Lattices_Osemilattice__sup(T_a)
% 186.97/187.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 186.97/187.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 186.97/187.92 => 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))) ) ) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_sup__least,axiom,
% 186.97/187.92 ! [V_z,V_x,V_y,T_a] :
% 186.97/187.92 ( class_Lattices_Osemilattice__sup(T_a)
% 186.97/187.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 186.97/187.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x))
% 186.97/187.92 => 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)) ) ) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_le__supI,axiom,
% 186.97/187.92 ! [V_b,V_x,V_a,T_a] :
% 186.97/187.92 ( class_Lattices_Osemilattice__sup(T_a)
% 186.97/187.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 186.97/187.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 186.97/187.92 => 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)) ) ) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_sup__absorb1,axiom,
% 186.97/187.92 ! [V_x,V_y,T_a] :
% 186.97/187.92 ( class_Lattices_Osemilattice__sup(T_a)
% 186.97/187.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 186.97/187.92 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_x ) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_sup__absorb2,axiom,
% 186.97/187.92 ! [V_y,V_x,T_a] :
% 186.97/187.92 ( class_Lattices_Osemilattice__sup(T_a)
% 186.97/187.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 186.97/187.92 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_y ) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_le__supI2,axiom,
% 186.97/187.92 ! [V_a,V_b,V_x,T_a] :
% 186.97/187.92 ( class_Lattices_Osemilattice__sup(T_a)
% 186.97/187.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 186.97/187.92 => 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))) ) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_le__supI1,axiom,
% 186.97/187.92 ! [V_b,V_a,V_x,T_a] :
% 186.97/187.92 ( class_Lattices_Osemilattice__sup(T_a)
% 186.97/187.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 186.97/187.92 => 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))) ) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_le__sup__iff,axiom,
% 186.97/187.92 ! [V_z_2,V_y_2,V_x_2,T_a] :
% 186.97/187.92 ( class_Lattices_Osemilattice__sup(T_a)
% 186.97/187.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),V_y_2)),V_z_2))
% 186.97/187.92 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2))
% 186.97/187.92 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_z_2)) ) ) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_le__iff__sup,axiom,
% 186.97/187.92 ! [V_y_2,V_x_2,T_a] :
% 186.97/187.92 ( class_Lattices_Osemilattice__sup(T_a)
% 186.97/187.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 186.97/187.92 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),V_y_2) = V_y_2 ) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_sup__ge2,axiom,
% 186.97/187.92 ! [V_x,V_y,T_a] :
% 186.97/187.92 ( class_Lattices_Osemilattice__sup(T_a)
% 186.97/187.92 => 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))) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_inf__sup__ord_I4_J,axiom,
% 186.97/187.92 ! [V_x,V_y,T_a] :
% 186.97/187.92 ( class_Lattices_Olattice(T_a)
% 186.97/187.92 => 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))) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_sup__ge1,axiom,
% 186.97/187.92 ! [V_y,V_x,T_a] :
% 186.97/187.92 ( class_Lattices_Osemilattice__sup(T_a)
% 186.97/187.92 => 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))) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_inf__sup__ord_I3_J,axiom,
% 186.97/187.92 ! [V_y,V_x,T_a] :
% 186.97/187.92 ( class_Lattices_Olattice(T_a)
% 186.97/187.92 => 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))) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_sup__bot__left,axiom,
% 186.97/187.92 ! [V_x,T_a] :
% 186.97/187.92 ( class_Lattices_Obounded__lattice__bot(T_a)
% 186.97/187.92 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x) = V_x ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_sup__bot__right,axiom,
% 186.97/187.92 ! [V_x,T_a] :
% 186.97/187.92 ( class_Lattices_Obounded__lattice__bot(T_a)
% 186.97/187.92 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),c_Orderings_Obot__class_Obot(T_a)) = V_x ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_sup__eq__bot__iff,axiom,
% 186.97/187.92 ! [V_y_2,V_x_2,T_a] :
% 186.97/187.92 ( class_Lattices_Obounded__lattice__bot(T_a)
% 186.97/187.92 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),V_y_2) = c_Orderings_Obot__class_Obot(T_a)
% 186.97/187.92 <=> ( V_x_2 = c_Orderings_Obot__class_Obot(T_a)
% 186.97/187.92 & V_y_2 = c_Orderings_Obot__class_Obot(T_a) ) ) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_MGF__lemma1,axiom,
% 186.97/187.92 ! [V_c_2,V_G_2] :
% 186.97/187.92 ( c_Hoare__Mirabelle_Ostate__not__singleton
% 186.97/187.92 => ( ! [B_x] :
% 186.97/187.92 ( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),B_x),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody)))
% 186.97/187.92 => c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,B_x))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) )
% 186.97/187.92 => ( hBOOL(hAPP(c_Com_OWT,V_c_2))
% 186.97/187.92 => c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,V_c_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ) ) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_folding__one_Oinsert,axiom,
% 186.97/187.92 ! [V_x_2,V_A_2,V_Fa_2,V_f_2,T_a] :
% 186.97/187.92 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_Fa_2)
% 186.97/187.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.92 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 186.97/187.92 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 186.97/187.92 => hAPP(V_Fa_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_Fa_2,V_A_2)) ) ) ) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_folding__one__idem_Ounion__idem,axiom,
% 186.97/187.92 ! [V_B_2,V_A_2,V_Fa_2,V_f_2,T_a] :
% 186.97/187.92 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_Fa_2)
% 186.97/187.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.92 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 186.97/187.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 186.97/187.92 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 186.97/187.92 => hAPP(V_Fa_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_Fa_2,V_A_2)),hAPP(V_Fa_2,V_B_2)) ) ) ) ) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_folding__one__idem_Osubset__idem,axiom,
% 186.97/187.92 ! [V_B_2,V_A_2,V_Fa_2,V_f_2,T_a] :
% 186.97/187.92 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_Fa_2)
% 186.97/187.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.92 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 186.97/187.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 186.97/187.92 => hAPP(hAPP(V_f_2,hAPP(V_Fa_2,V_B_2)),hAPP(V_Fa_2,V_A_2)) = hAPP(V_Fa_2,V_A_2) ) ) ) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_finite__subset__induct,axiom,
% 186.97/187.92 ! [V_P_2,V_A_2,V_Fa_2,T_a] :
% 186.97/187.92 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_Fa_2))
% 186.97/187.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_Fa_2),V_A_2))
% 186.97/187.92 => ( hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))
% 186.97/187.92 => ( ! [B_a,B_F] :
% 186.97/187.92 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_F))
% 186.97/187.92 => ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2))
% 186.97/187.92 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),B_a),B_F))
% 186.97/187.92 => ( hBOOL(hAPP(V_P_2,B_F))
% 186.97/187.92 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Set_Oinsert(T_a),B_a),B_F))) ) ) ) )
% 186.97/187.92 => hBOOL(hAPP(V_P_2,V_Fa_2)) ) ) ) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_folding__one__idem_Oinsert__idem,axiom,
% 186.97/187.92 ! [V_x_2,V_A_2,V_Fa_2,V_f_2,T_a] :
% 186.97/187.92 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_Fa_2)
% 186.97/187.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.92 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 186.97/187.92 => hAPP(V_Fa_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_Fa_2,V_A_2)) ) ) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_escape,axiom,
% 186.97/187.92 ! [V_Q_2,V_c_2,V_G_2,T_a,V_P_2] :
% 186.97/187.92 ( ! [B_Z,B_s] :
% 186.97/187.92 ( hBOOL(hAPP(hAPP(V_P_2,B_Z),B_s))
% 186.97/187.92 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_a),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),B_s))),V_c_2),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_a),hAPP(V_Q_2,B_Z)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) )
% 186.97/187.92 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),V_c_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_hoare__derivs_Oequations_I7_J,axiom,
% 186.97/187.92 ! [V_a2_2,V_a1_2,T_a] : c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_a1_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_a2_2),c_Com_Ocom_OSKIP),V_a2_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_hoare__derivs_OSkip,axiom,
% 186.97/187.92 ! [V_P_2,V_G_2,T_a] : c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),c_Com_Ocom_OSKIP),V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_the__elem__def,axiom,
% 186.97/187.92 ! [V_X_2,T_a] : c_Set_Othe__elem(T_a,V_X_2) = c_HOL_OThe(T_a,hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),hAPP(c_fequal,V_X_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_conseq1,axiom,
% 186.97/187.92 ! [V_P_2,V_Q_2,V_c_2,V_P_H_2,V_G_2,T_a] :
% 186.97/187.92 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_H_2),V_c_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))))
% 186.97/187.92 => ( ! [B_Z,B_s] :
% 186.97/187.92 ( hBOOL(hAPP(hAPP(V_P_2,B_Z),B_s))
% 186.97/187.92 => hBOOL(hAPP(hAPP(V_P_H_2,B_Z),B_s)) )
% 186.97/187.92 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),V_c_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_evalc__elim__cases_I1_J,axiom,
% 186.97/187.92 ! [V_t,V_s] :
% 186.97/187.92 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_s),V_t))
% 186.97/187.92 => V_t = V_s ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_evalc_OSkip,axiom,
% 186.97/187.92 ! [V_s] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_s),V_s)) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_folding__one__idem_Oidem,axiom,
% 186.97/187.92 ! [V_x_2,V_Fa_2,V_f_2,T_a] :
% 186.97/187.92 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_Fa_2)
% 186.97/187.92 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_evalc_Oequations_I1_J,axiom,
% 186.97/187.92 ! [V_a] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_a),V_a)) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_com_Osimps_I18_J,axiom,
% 186.97/187.92 ! [V_pname_H] : c_Com_Ocom_OSKIP != hAPP(c_Com_Ocom_OBODY,V_pname_H) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_com_Osimps_I19_J,axiom,
% 186.97/187.92 ! [V_pname_H] : hAPP(c_Com_Ocom_OBODY,V_pname_H) != c_Com_Ocom_OSKIP ).
% 186.97/187.92
% 186.97/187.92 fof(fact_WT_OSkip,axiom,
% 186.97/187.92 hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_WT_Oequations_I1_J,axiom,
% 186.97/187.92 hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_folding__one_Osingleton,axiom,
% 186.97/187.92 ! [V_x_2,V_Fa_2,V_f_2,T_a] :
% 186.97/187.92 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_Fa_2)
% 186.97/187.92 => hAPP(V_Fa_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_x_2 ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_folding__one__idem_Oin__idem,axiom,
% 186.97/187.92 ! [V_x_2,V_A_2,V_Fa_2,V_f_2,T_a] :
% 186.97/187.92 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_Fa_2)
% 186.97/187.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.92 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 186.97/187.92 => hAPP(hAPP(V_f_2,V_x_2),hAPP(V_Fa_2,V_A_2)) = hAPP(V_Fa_2,V_A_2) ) ) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_folding__one_Oclosed,axiom,
% 186.97/187.92 ! [V_A_2,V_Fa_2,V_f_2,T_a] :
% 186.97/187.92 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_Fa_2)
% 186.97/187.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.92 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 186.97/187.92 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(V_f_2,B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),hAPP(hAPP(c_Set_Oinsert(T_a),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))
% 186.97/187.92 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(V_Fa_2,V_A_2)),V_A_2)) ) ) ) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_conseq2,axiom,
% 186.97/187.92 ! [V_Q_2,V_Q_H_2,V_c_2,V_P_2,V_G_2,T_a] :
% 186.97/187.92 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),V_c_2),V_Q_H_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))))
% 186.97/187.92 => ( ! [B_Z,B_s] :
% 186.97/187.92 ( hBOOL(hAPP(hAPP(V_Q_H_2,B_Z),B_s))
% 186.97/187.92 => hBOOL(hAPP(hAPP(V_Q_2,B_Z),B_s)) )
% 186.97/187.92 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),V_c_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_folding__one__idem_Ohom__commute,axiom,
% 186.97/187.92 ! [V_N_2,V_h_2,V_Fa_2,V_f_2,T_a] :
% 186.97/187.92 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_Fa_2)
% 186.97/187.92 => ( ! [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))
% 186.97/187.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
% 186.97/187.92 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 186.97/187.92 => hAPP(V_h_2,hAPP(V_Fa_2,V_N_2)) = hAPP(V_Fa_2,hAPP(c_Set_Oimage(T_a,T_a,V_h_2),V_N_2)) ) ) ) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_Comp,axiom,
% 186.97/187.92 ! [V_R_2,V_d_2,V_Q_2,V_c_2,V_P_2,V_G_2,T_a] :
% 186.97/187.92 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),V_c_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))))
% 186.97/187.92 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_Q_2),V_d_2),V_R_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))))
% 186.97/187.92 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),c_Com_Ocom_OSemi(V_c_2,V_d_2)),V_R_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_folding__image__simple_Oinsert,axiom,
% 186.97/187.92 ! [V_x_2,V_A_2,V_Fa_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 186.97/187.92 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_Fa_2)
% 186.97/187.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 186.97/187.92 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 186.97/187.92 => hAPP(V_Fa_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_Fa_2,V_A_2)) ) ) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_the__eq__trivial,axiom,
% 186.97/187.92 ! [V_a_2,T_a] : c_HOL_OThe(T_a,hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2)) = V_a_2 ).
% 186.97/187.92
% 186.97/187.92 fof(fact_the__sym__eq__trivial,axiom,
% 186.97/187.92 ! [V_x_2,T_a] : c_HOL_OThe(T_a,hAPP(c_fequal,V_x_2)) = V_x_2 ).
% 186.97/187.92
% 186.97/187.92 fof(fact_LoopF,axiom,
% 186.97/187.92 ! [V_c_2,V_b_2,V_P_2,V_G_2,T_a] : c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_a),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj)),V_P_2))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate),c_fNot),V_b_2))),c_Com_Ocom_OWhile(V_b_2,V_c_2)),V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_folding__one_Oremove,axiom,
% 186.97/187.92 ! [V_x_2,V_A_2,V_Fa_2,V_f_2,T_a] :
% 186.97/187.92 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_Fa_2)
% 186.97/187.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.92 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 186.97/187.92 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 186.97/187.92 => hAPP(V_Fa_2,V_A_2) = V_x_2 )
% 186.97/187.92 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 186.97/187.92 => hAPP(V_Fa_2,V_A_2) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_Fa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_finite__induct,axiom,
% 186.97/187.92 ! [V_P_2,V_Fa_2,T_a] :
% 186.97/187.92 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_Fa_2))
% 186.97/187.92 => ( hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))
% 186.97/187.92 => ( ! [B_x,B_F] :
% 186.97/187.92 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_F))
% 186.97/187.92 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),B_F))
% 186.97/187.92 => ( hBOOL(hAPP(V_P_2,B_F))
% 186.97/187.92 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Set_Oinsert(T_a),B_x),B_F))) ) ) )
% 186.97/187.92 => hBOOL(hAPP(V_P_2,V_Fa_2)) ) ) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_folding__one_Ounion__inter,axiom,
% 186.97/187.92 ! [V_B_2,V_A_2,V_Fa_2,V_f_2,T_a] :
% 186.97/187.92 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_Fa_2)
% 186.97/187.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 186.97/187.92 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 186.97/187.92 => hAPP(hAPP(V_f_2,hAPP(V_Fa_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(V_Fa_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(V_f_2,hAPP(V_Fa_2,V_A_2)),hAPP(V_Fa_2,V_B_2)) ) ) ) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_inf1E,axiom,
% 186.97/187.92 ! [V_x_2,V_B_2,V_A_2,T_a] :
% 186.97/187.92 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2))
% 186.97/187.92 => ~ ( hBOOL(hAPP(V_A_2,V_x_2))
% 186.97/187.92 => ~ hBOOL(hAPP(V_B_2,V_x_2)) ) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_inf1I,axiom,
% 186.97/187.92 ! [T_a,V_B_2,V_x_2,V_A_2] :
% 186.97/187.92 ( hBOOL(hAPP(V_A_2,V_x_2))
% 186.97/187.92 => ( hBOOL(hAPP(V_B_2,V_x_2))
% 186.97/187.92 => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_IntE,axiom,
% 186.97/187.92 ! [V_B_2,V_A_2,V_c_2,T_a] :
% 186.97/187.92 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
% 186.97/187.92 => ~ ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2))
% 186.97/187.92 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) ) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_IntI,axiom,
% 186.97/187.92 ! [V_B_2,V_A_2,V_c_2,T_a] :
% 186.97/187.92 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2))
% 186.97/187.92 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2))
% 186.97/187.92 => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_DiffE,axiom,
% 186.97/187.92 ! [V_B_2,V_A_2,V_c_2,T_a] :
% 186.97/187.92 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
% 186.97/187.92 => ~ ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2))
% 186.97/187.92 => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) ) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_DiffI,axiom,
% 186.97/187.92 ! [V_B_2,V_A_2,V_c_2,T_a] :
% 186.97/187.92 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2))
% 186.97/187.92 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2))
% 186.97/187.92 => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_finite__Int,axiom,
% 186.97/187.92 ! [V_G_2,V_Fa_2,T_a] :
% 186.97/187.92 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_Fa_2))
% 186.97/187.92 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_G_2)) )
% 186.97/187.92 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_Fa_2),V_G_2))) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_finite__Diff,axiom,
% 186.97/187.92 ! [V_B_2,V_A_2,T_a] :
% 186.97/187.92 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.92 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_evalc_OWhileFalse,axiom,
% 186.97/187.92 ! [V_c_2,V_s_2,V_b_2] :
% 186.97/187.92 ( ~ hBOOL(hAPP(V_b_2,V_s_2))
% 186.97/187.92 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b_2,V_c_2)),V_s_2),V_s_2)) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_evalc_OWhileTrue,axiom,
% 186.97/187.92 ! [V_s2_2,V_s1_2,V_c_2,V_s0_2,V_b_2] :
% 186.97/187.92 ( hBOOL(hAPP(V_b_2,V_s0_2))
% 186.97/187.92 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c_2),V_s0_2),V_s1_2))
% 186.97/187.92 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b_2,V_c_2)),V_s1_2),V_s2_2))
% 186.97/187.92 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b_2,V_c_2)),V_s0_2),V_s2_2)) ) ) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_WTs__elim__cases_I6_J,axiom,
% 186.97/187.92 ! [V_c_2,V_b_2] :
% 186.97/187.92 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(V_b_2,V_c_2)))
% 186.97/187.92 => hBOOL(hAPP(c_Com_OWT,V_c_2)) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_evalc_OSemi,axiom,
% 186.97/187.92 ! [V_s2,V_c1,V_s1,V_s0,V_c0] :
% 186.97/187.92 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c0),V_s0),V_s1))
% 186.97/187.92 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1),V_s1),V_s2))
% 186.97/187.92 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c0,V_c1)),V_s0),V_s2)) ) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_WTs__elim__cases_I4_J,axiom,
% 186.97/187.92 ! [V_c2,V_c1] :
% 186.97/187.92 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(V_c1,V_c2)))
% 186.97/187.92 => ~ ( hBOOL(hAPP(c_Com_OWT,V_c1))
% 186.97/187.92 => ~ hBOOL(hAPP(c_Com_OWT,V_c2)) ) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_inf1D2,axiom,
% 186.97/187.92 ! [V_x_2,V_B_2,V_A_2,T_a] :
% 186.97/187.92 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2))
% 186.97/187.92 => hBOOL(hAPP(V_B_2,V_x_2)) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_inf1D1,axiom,
% 186.97/187.92 ! [V_x_2,V_B_2,V_A_2,T_a] :
% 186.97/187.92 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2))
% 186.97/187.92 => hBOOL(hAPP(V_A_2,V_x_2)) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_com_Osimps_I5_J,axiom,
% 186.97/187.92 ! [V_com_H_2,V_fun_H_2,V_com_2,V_fun_2] :
% 186.97/187.92 ( c_Com_Ocom_OWhile(V_fun_2,V_com_2) = c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2)
% 186.97/187.92 <=> ( V_fun_2 = V_fun_H_2
% 186.97/187.92 & V_com_2 = V_com_H_2 ) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_com_Osimps_I3_J,axiom,
% 186.97/187.92 ! [V_com2_H_2,V_com1_H_2,V_com2_2,V_com1_2] :
% 186.97/187.92 ( c_Com_Ocom_OSemi(V_com1_2,V_com2_2) = c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2)
% 186.97/187.92 <=> ( V_com1_2 = V_com1_H_2
% 186.97/187.92 & V_com2_2 = V_com2_H_2 ) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_com_Osimps_I47_J,axiom,
% 186.97/187.92 ! [V_com2_2,V_com1_2,V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OSemi(V_com1_2,V_com2_2) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_com_Osimps_I46_J,axiom,
% 186.97/187.92 ! [V_com_H_2,V_fun_H_2,V_com2_2,V_com1_2] : c_Com_Ocom_OSemi(V_com1_2,V_com2_2) != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_Diff__Int2,axiom,
% 186.97/187.92 ! [V_B_2,V_C_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)),V_B_2) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_Diff__Int__distrib2,axiom,
% 186.97/187.92 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_Int__assoc,axiom,
% 186.97/187.92 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_Int__Diff,axiom,
% 186.97/187.92 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_Diff__idemp,axiom,
% 186.97/187.92 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_Diff__Int__distrib,axiom,
% 186.97/187.92 ! [V_B_2,V_A_2,V_C_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_Int__left__commute,axiom,
% 186.97/187.92 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_Int__left__absorb,axiom,
% 186.97/187.92 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_Int__commute,axiom,
% 186.97/187.92 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_Int__absorb,axiom,
% 186.97/187.92 ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_A_2) = V_A_2 ).
% 186.97/187.92
% 186.97/187.92 fof(fact_inf__apply,axiom,
% 186.97/187.92 ! [V_x_2,V_g_2,V_f_2,T_b,T_a] :
% 186.97/187.92 ( class_Lattices_Olattice(T_a)
% 186.97/187.92 => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,T_a)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_minus__apply,axiom,
% 186.97/187.92 ! [V_x_2,V_B_2,V_A_2,T_b,T_a] :
% 186.97/187.92 ( class_Groups_Ominus(T_a)
% 186.97/187.92 => hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,T_a)),V_A_2),V_B_2),V_x_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(V_A_2,V_x_2)),hAPP(V_B_2,V_x_2)) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_inf__assoc,axiom,
% 186.97/187.92 ! [V_z,V_y,V_x,T_a] :
% 186.97/187.92 ( class_Lattices_Osemilattice__inf(T_a)
% 186.97/187.92 => 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)) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_inf__sup__aci_I2_J,axiom,
% 186.97/187.92 ! [V_z,V_y,V_x,T_a] :
% 186.97/187.92 ( class_Lattices_Olattice(T_a)
% 186.97/187.92 => 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)) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_inf_Oassoc,axiom,
% 186.97/187.92 ! [V_c,V_b,V_a,T_a] :
% 186.97/187.92 ( class_Lattices_Osemilattice__inf(T_a)
% 186.97/187.92 => 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)) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_inf__left__commute,axiom,
% 186.97/187.92 ! [V_z,V_y,V_x,T_a] :
% 186.97/187.92 ( class_Lattices_Osemilattice__inf(T_a)
% 186.97/187.92 => 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)) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_inf__sup__aci_I3_J,axiom,
% 186.97/187.92 ! [V_z,V_y,V_x,T_a] :
% 186.97/187.92 ( class_Lattices_Olattice(T_a)
% 186.97/187.92 => 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)) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_inf_Oleft__commute,axiom,
% 186.97/187.92 ! [V_c,V_a,V_b,T_a] :
% 186.97/187.92 ( class_Lattices_Osemilattice__inf(T_a)
% 186.97/187.92 => 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)) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_inf__left__idem,axiom,
% 186.97/187.92 ! [V_y,V_x,T_a] :
% 186.97/187.92 ( class_Lattices_Osemilattice__inf(T_a)
% 186.97/187.92 => 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) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_inf__sup__aci_I4_J,axiom,
% 186.97/187.92 ! [V_y,V_x,T_a] :
% 186.97/187.92 ( class_Lattices_Olattice(T_a)
% 186.97/187.92 => 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) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_inf_Oleft__idem,axiom,
% 186.97/187.92 ! [V_b,V_a,T_a] :
% 186.97/187.92 ( class_Lattices_Osemilattice__inf(T_a)
% 186.97/187.92 => 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) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_inf__commute,axiom,
% 186.97/187.92 ! [V_y,V_x,T_a] :
% 186.97/187.92 ( class_Lattices_Osemilattice__inf(T_a)
% 186.97/187.92 => 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) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_inf__sup__aci_I1_J,axiom,
% 186.97/187.92 ! [V_y,V_x,T_a] :
% 186.97/187.92 ( class_Lattices_Olattice(T_a)
% 186.97/187.92 => 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) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_inf_Ocommute,axiom,
% 186.97/187.92 ! [V_b,V_a,T_a] :
% 186.97/187.92 ( class_Lattices_Osemilattice__inf(T_a)
% 186.97/187.92 => 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) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_inf__fun__def,axiom,
% 186.97/187.92 ! [V_x_2,V_g_2,V_f_2,T_b,T_a] :
% 186.97/187.92 ( class_Lattices_Olattice(T_a)
% 186.97/187.92 => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,T_a)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_fun__diff__def,axiom,
% 186.97/187.92 ! [V_x_2,V_B_2,V_A_2,T_b,T_a] :
% 186.97/187.92 ( class_Groups_Ominus(T_a)
% 186.97/187.92 => hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,T_a)),V_A_2),V_B_2),V_x_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(V_A_2,V_x_2)),hAPP(V_B_2,V_x_2)) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_inf__idem,axiom,
% 186.97/187.92 ! [V_x,T_a] :
% 186.97/187.92 ( class_Lattices_Osemilattice__inf(T_a)
% 186.97/187.92 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_inf_Oidem,axiom,
% 186.97/187.92 ! [V_a,T_a] :
% 186.97/187.92 ( class_Lattices_Osemilattice__inf(T_a)
% 186.97/187.92 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_a) = V_a ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_Diff__triv,axiom,
% 186.97/187.92 ! [V_B_2,V_A_2,T_a] :
% 186.97/187.92 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 186.97/187.92 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_Diff__disjoint,axiom,
% 186.97/187.92 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_Un__Diff__Int,axiom,
% 186.97/187.92 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = V_A_2 ).
% 186.97/187.92
% 186.97/187.92 fof(fact_Diff__Un,axiom,
% 186.97/187.92 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_Diff__Int,axiom,
% 186.97/187.92 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_le__infE,axiom,
% 186.97/187.92 ! [V_b,V_a,V_x,T_a] :
% 186.97/187.92 ( class_Lattices_Osemilattice__inf(T_a)
% 186.97/187.92 => ( 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)))
% 186.97/187.92 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 186.97/187.92 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_inf__mono,axiom,
% 186.97/187.92 ! [V_d,V_b,V_c,V_a,T_a] :
% 186.97/187.92 ( class_Lattices_Osemilattice__inf(T_a)
% 186.97/187.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 186.97/187.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 186.97/187.92 => 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))) ) ) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_inf__greatest,axiom,
% 186.97/187.92 ! [V_z,V_y,V_x,T_a] :
% 186.97/187.92 ( class_Lattices_Osemilattice__inf(T_a)
% 186.97/187.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 186.97/187.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z))
% 186.97/187.92 => 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))) ) ) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_le__infI,axiom,
% 186.97/187.92 ! [V_b,V_a,V_x,T_a] :
% 186.97/187.92 ( class_Lattices_Osemilattice__inf(T_a)
% 186.97/187.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 186.97/187.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 186.97/187.92 => 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))) ) ) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_inf__absorb2,axiom,
% 186.97/187.92 ! [V_x,V_y,T_a] :
% 186.97/187.92 ( class_Lattices_Osemilattice__inf(T_a)
% 186.97/187.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 186.97/187.92 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_y ) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_inf__absorb1,axiom,
% 186.97/187.92 ! [V_y,V_x,T_a] :
% 186.97/187.92 ( class_Lattices_Osemilattice__inf(T_a)
% 186.97/187.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 186.97/187.92 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_x ) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_le__infI2,axiom,
% 186.97/187.92 ! [V_a,V_x,V_b,T_a] :
% 186.97/187.92 ( class_Lattices_Osemilattice__inf(T_a)
% 186.97/187.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 186.97/187.92 => 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)) ) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_le__infI1,axiom,
% 186.97/187.92 ! [V_b,V_x,V_a,T_a] :
% 186.97/187.92 ( class_Lattices_Osemilattice__inf(T_a)
% 186.97/187.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 186.97/187.92 => 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)) ) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_le__inf__iff,axiom,
% 186.97/187.92 ! [V_z_2,V_y_2,V_x_2,T_a] :
% 186.97/187.92 ( class_Lattices_Osemilattice__inf(T_a)
% 186.97/187.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y_2),V_z_2)))
% 186.97/187.92 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 186.97/187.92 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2)) ) ) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_le__iff__inf,axiom,
% 186.97/187.92 ! [V_y_2,V_x_2,T_a] :
% 186.97/187.92 ( class_Lattices_Osemilattice__inf(T_a)
% 186.97/187.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 186.97/187.92 <=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),V_y_2) = V_x_2 ) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_inf__le2,axiom,
% 186.97/187.92 ! [V_y,V_x,T_a] :
% 186.97/187.92 ( class_Lattices_Osemilattice__inf(T_a)
% 186.97/187.92 => 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)) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_inf__sup__ord_I2_J,axiom,
% 186.97/187.92 ! [V_y,V_x,T_a] :
% 186.97/187.92 ( class_Lattices_Olattice(T_a)
% 186.97/187.92 => 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)) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_inf__le1,axiom,
% 186.97/187.92 ! [V_y,V_x,T_a] :
% 186.97/187.92 ( class_Lattices_Osemilattice__inf(T_a)
% 186.97/187.92 => 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)) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_inf__sup__ord_I1_J,axiom,
% 186.97/187.92 ! [V_y,V_x,T_a] :
% 186.97/187.92 ( class_Lattices_Olattice(T_a)
% 186.97/187.92 => 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)) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_inf__bot__left,axiom,
% 186.97/187.92 ! [V_x,T_a] :
% 186.97/187.92 ( class_Lattices_Obounded__lattice__bot(T_a)
% 186.97/187.92 => 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) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_inf__bot__right,axiom,
% 186.97/187.92 ! [V_x,T_a] :
% 186.97/187.92 ( class_Lattices_Obounded__lattice__bot(T_a)
% 186.97/187.92 => 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) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_inf__sup__absorb,axiom,
% 186.97/187.92 ! [V_y,V_x,T_a] :
% 186.97/187.92 ( class_Lattices_Olattice(T_a)
% 186.97/187.92 => 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 ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_sup__inf__absorb,axiom,
% 186.97/187.92 ! [V_y,V_x,T_a] :
% 186.97/187.92 ( class_Lattices_Olattice(T_a)
% 186.97/187.92 => 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 ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_inf__sup__distrib1,axiom,
% 186.97/187.92 ! [V_z,V_y,V_x,T_a] :
% 186.97/187.92 ( class_Lattices_Odistrib__lattice(T_a)
% 186.97/187.92 => 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)) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_sup__inf__distrib1,axiom,
% 186.97/187.92 ! [V_z,V_y,V_x,T_a] :
% 186.97/187.92 ( class_Lattices_Odistrib__lattice(T_a)
% 186.97/187.92 => 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)) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_inf__sup__distrib2,axiom,
% 186.97/187.92 ! [V_x,V_z,V_y,T_a] :
% 186.97/187.92 ( class_Lattices_Odistrib__lattice(T_a)
% 186.97/187.92 => 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)) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_sup__inf__distrib2,axiom,
% 186.97/187.92 ! [V_x,V_z,V_y,T_a] :
% 186.97/187.92 ( class_Lattices_Odistrib__lattice(T_a)
% 186.97/187.92 => 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)) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_DiffD2,axiom,
% 186.97/187.92 ! [V_B_2,V_A_2,V_c_2,T_a] :
% 186.97/187.92 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
% 186.97/187.92 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_DiffD1,axiom,
% 186.97/187.92 ! [V_B_2,V_A_2,V_c_2,T_a] :
% 186.97/187.92 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
% 186.97/187.92 => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_Diff__iff,axiom,
% 186.97/187.92 ! [V_B_2,V_A_2,V_c_2,T_a] :
% 186.97/187.92 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
% 186.97/187.92 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2))
% 186.97/187.92 & ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) ) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_IntD2,axiom,
% 186.97/187.92 ! [V_B_2,V_A_2,V_c_2,T_a] :
% 186.97/187.92 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
% 186.97/187.92 => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_IntD1,axiom,
% 186.97/187.92 ! [V_B_2,V_A_2,V_c_2,T_a] :
% 186.97/187.92 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
% 186.97/187.92 => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_Int__iff,axiom,
% 186.97/187.92 ! [V_B_2,V_A_2,V_c_2,T_a] :
% 186.97/187.92 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
% 186.97/187.92 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2))
% 186.97/187.92 & hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) ) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_Diff__cancel,axiom,
% 186.97/187.92 ! [V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_Diff__empty,axiom,
% 186.97/187.92 ! [V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = V_A_2 ).
% 186.97/187.92
% 186.97/187.92 fof(fact_empty__Diff,axiom,
% 186.97/187.92 ! [V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_finite__Diff2,axiom,
% 186.97/187.92 ! [V_A_2,V_B_2,T_a] :
% 186.97/187.92 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 186.97/187.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
% 186.97/187.92 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_disjoint__iff__not__equal,axiom,
% 186.97/187.92 ! [V_B_2,V_A_2,T_a] :
% 186.97/187.92 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 186.97/187.92 <=> ! [B_x] :
% 186.97/187.92 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 186.97/187.92 => ! [B_xa] :
% 186.97/187.92 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_B_2))
% 186.97/187.92 => B_x != B_xa ) ) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_Int__empty__right,axiom,
% 186.97/187.92 ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_Int__empty__left,axiom,
% 186.97/187.92 ! [V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_double__diff,axiom,
% 186.97/187.92 ! [V_C_2,V_B_2,V_A_2,T_a] :
% 186.97/187.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 186.97/187.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))
% 186.97/187.92 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)) = V_A_2 ) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_Diff__mono,axiom,
% 186.97/187.92 ! [V_B_2,V_D_2,V_C_2,V_A_2,T_a] :
% 186.97/187.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2))
% 186.97/187.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_D_2),V_B_2))
% 186.97/187.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_D_2))) ) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_Diff__subset,axiom,
% 186.97/187.92 ! [V_B_2,V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_A_2)) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_insert__inter__insert,axiom,
% 186.97/187.92 ! [V_B_2,V_A_2,V_a_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_Un__Diff,axiom,
% 186.97/187.92 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_Un__Diff__cancel2,axiom,
% 186.97/187.92 ! [V_A_2,V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_Un__Diff__cancel,axiom,
% 186.97/187.92 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_Int__mono,axiom,
% 186.97/187.92 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_a] :
% 186.97/187.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2))
% 186.97/187.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_D_2))
% 186.97/187.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_D_2))) ) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_Int__greatest,axiom,
% 186.97/187.92 ! [V_B_2,V_A_2,V_C_2,T_a] :
% 186.97/187.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2))
% 186.97/187.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2))
% 186.97/187.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_Int__absorb1,axiom,
% 186.97/187.92 ! [V_A_2,V_B_2,T_a] :
% 186.97/187.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 186.97/187.92 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_Int__absorb2,axiom,
% 186.97/187.92 ! [V_B_2,V_A_2,T_a] :
% 186.97/187.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 186.97/187.92 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_Int__lower2,axiom,
% 186.97/187.92 ! [V_B_2,V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_B_2)) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_Int__lower1,axiom,
% 186.97/187.92 ! [V_B_2,V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_A_2)) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_Un__Int__crazy,axiom,
% 186.97/187.92 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_Un__Int__distrib2,axiom,
% 186.97/187.92 ! [V_A_2,V_C_2,V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)) ).
% 186.97/187.92
% 186.97/187.92 fof(fact_Int__Un__distrib2,axiom,
% 186.97/187.93 ! [V_A_2,V_C_2,V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_Un__Int__distrib,axiom,
% 186.97/187.93 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_Int__Un__distrib,axiom,
% 186.97/187.93 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_folding__image__simple_Ounion__inter,axiom,
% 186.97/187.93 ! [V_B_2,V_A_2,V_Fa_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 186.97/187.93 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_Fa_2)
% 186.97/187.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 186.97/187.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 186.97/187.93 => hAPP(hAPP(V_f_2,hAPP(V_Fa_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(V_Fa_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_Fa_2,V_A_2)),hAPP(V_Fa_2,V_B_2)) ) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_evalc_Oequations_I7_J,axiom,
% 186.97/187.93 ! [V_a2_2,V_a3_2,V_a1_2] :
% 186.97/187.93 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),V_a2_2),V_a2_2))
% 186.97/187.93 <=> ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 186.97/187.93 => ? [B_s1] :
% 186.97/187.93 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),B_s1))
% 186.97/187.93 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),B_s1),V_a2_2)) ) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_evalc_Oequations_I8_J,axiom,
% 186.97/187.93 ! [V_a5_2,V_a2_2,V_a3_2,V_a1_2] :
% 186.97/187.93 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),V_a2_2),V_a5_2))
% 186.97/187.93 <=> ( ( V_a5_2 = V_a2_2
% 186.97/187.93 & ~ hBOOL(hAPP(V_a1_2,V_a2_2)) )
% 186.97/187.93 | ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 186.97/187.93 & ? [B_s1] :
% 186.97/187.93 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),B_s1))
% 186.97/187.93 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),B_s1),V_a5_2)) ) ) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_com_Osimps_I58_J,axiom,
% 186.97/187.93 ! [V_pname_H_2,V_com_2,V_fun_2] : c_Com_Ocom_OWhile(V_fun_2,V_com_2) != hAPP(c_Com_Ocom_OBODY,V_pname_H_2) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_com_Osimps_I59_J,axiom,
% 186.97/187.93 ! [V_com_2,V_fun_2,V_pname_H_2] : hAPP(c_Com_Ocom_OBODY,V_pname_H_2) != c_Com_Ocom_OWhile(V_fun_2,V_com_2) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_While,axiom,
% 186.97/187.93 ! [V_b_2,V_c_2] :
% 186.97/187.93 ( hBOOL(hAPP(c_Com_OWT,V_c_2))
% 186.97/187.93 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(V_b_2,V_c_2))) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_WT_Oequations_I6_J,axiom,
% 186.97/187.93 ! [V_a1_2,V_a2_2] :
% 186.97/187.93 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(V_a2_2,V_a1_2)))
% 186.97/187.93 <=> hBOOL(hAPP(c_Com_OWT,V_a1_2)) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_inf__Int__eq,axiom,
% 186.97/187.93 ! [V_x_2,V_S_2,V_R_2,T_a] :
% 186.97/187.93 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_R_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_S_2)),V_x_2))
% 186.97/187.93 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_R_2),V_S_2))) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_com_Osimps_I17_J,axiom,
% 186.97/187.93 ! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OSKIP ).
% 186.97/187.93
% 186.97/187.93 fof(fact_com_Osimps_I16_J,axiom,
% 186.97/187.93 ! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_evalc_Oequations_I4_J,axiom,
% 186.97/187.93 ! [V_a5_2,V_a2_2,V_a4_2,V_a1_2] :
% 186.97/187.93 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(V_a1_2,V_a4_2)),V_a2_2),V_a5_2))
% 186.97/187.93 <=> ? [B_s1] :
% 186.97/187.93 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a1_2),V_a2_2),B_s1))
% 186.97/187.93 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a4_2),B_s1),V_a5_2)) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_com_Osimps_I48_J,axiom,
% 186.97/187.93 ! [V_pname_H,V_com2,V_com1] : c_Com_Ocom_OSemi(V_com1,V_com2) != hAPP(c_Com_Ocom_OBODY,V_pname_H) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_com_Osimps_I49_J,axiom,
% 186.97/187.93 ! [V_com2,V_com1,V_pname_H] : hAPP(c_Com_Ocom_OBODY,V_pname_H) != c_Com_Ocom_OSemi(V_com1,V_com2) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_WT_OSemi,axiom,
% 186.97/187.93 ! [V_c1,V_c0] :
% 186.97/187.93 ( hBOOL(hAPP(c_Com_OWT,V_c0))
% 186.97/187.93 => ( hBOOL(hAPP(c_Com_OWT,V_c1))
% 186.97/187.93 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(V_c0,V_c1))) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_WT_Oequations_I4_J,axiom,
% 186.97/187.93 ! [V_a2_2,V_a1_2] :
% 186.97/187.93 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(V_a1_2,V_a2_2)))
% 186.97/187.93 <=> ( hBOOL(hAPP(c_Com_OWT,V_a1_2))
% 186.97/187.93 & hBOOL(hAPP(c_Com_OWT,V_a2_2)) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_com_Osimps_I13_J,axiom,
% 186.97/187.93 ! [V_com2_H,V_com1_H] : c_Com_Ocom_OSemi(V_com1_H,V_com2_H) != c_Com_Ocom_OSKIP ).
% 186.97/187.93
% 186.97/187.93 fof(fact_com_Osimps_I12_J,axiom,
% 186.97/187.93 ! [V_com2_H,V_com1_H] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(V_com1_H,V_com2_H) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_folding__image__simple_Oinsert__remove,axiom,
% 186.97/187.93 ! [V_x_2,V_A_2,V_Fa_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 186.97/187.93 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_Fa_2)
% 186.97/187.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 186.97/187.93 => hAPP(V_Fa_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_Fa_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)))))) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_folding__image__simple_Ounion__disjoint,axiom,
% 186.97/187.93 ! [V_B_2,V_A_2,V_Fa_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 186.97/187.93 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_Fa_2)
% 186.97/187.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 186.97/187.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 186.97/187.93 => ( 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))
% 186.97/187.93 => hAPP(V_Fa_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_Fa_2,V_A_2)),hAPP(V_Fa_2,V_B_2)) ) ) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_distrib__inf__le,axiom,
% 186.97/187.93 ! [V_z,V_y,V_x,T_a] :
% 186.97/187.93 ( class_Lattices_Olattice(T_a)
% 186.97/187.93 => 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)))) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_distrib__sup__le,axiom,
% 186.97/187.93 ! [V_z,V_y,V_x,T_a] :
% 186.97/187.93 ( class_Lattices_Olattice(T_a)
% 186.97/187.93 => 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)))) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_insert__Diff1,axiom,
% 186.97/187.93 ! [V_A_2,V_B_2,V_x_2,T_a] :
% 186.97/187.93 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2))
% 186.97/187.93 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_insert__Diff__if,axiom,
% 186.97/187.93 ! [V_A_2,V_B_2,V_x_2,T_a] :
% 186.97/187.93 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2))
% 186.97/187.93 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) )
% 186.97/187.93 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2))
% 186.97/187.93 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_insert__Diff__single,axiom,
% 186.97/187.93 ! [V_A_2,V_a_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_Diff__insert2,axiom,
% 186.97/187.93 ! [V_B_2,V_a_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_B_2) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_Diff__insert,axiom,
% 186.97/187.93 ! [V_B_2,V_a_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_finite__Diff__insert,axiom,
% 186.97/187.93 ! [V_B_2,V_a_2,V_A_2,T_a] :
% 186.97/187.93 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2))))
% 186.97/187.93 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_Int__insert__left__if1,axiom,
% 186.97/187.93 ! [V_B_2,V_C_2,V_a_2,T_a] :
% 186.97/187.93 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_C_2))
% 186.97/187.93 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_Int__insert__right__if1,axiom,
% 186.97/187.93 ! [V_B_2,V_A_2,V_a_2,T_a] :
% 186.97/187.93 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 186.97/187.93 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_Int__insert__left__if0,axiom,
% 186.97/187.93 ! [V_B_2,V_C_2,V_a_2,T_a] :
% 186.97/187.93 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_C_2))
% 186.97/187.93 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_Int__insert__right__if0,axiom,
% 186.97/187.93 ! [V_B_2,V_A_2,V_a_2,T_a] :
% 186.97/187.93 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 186.97/187.93 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_Int__insert__left,axiom,
% 186.97/187.93 ! [V_B_2,V_C_2,V_a_2,T_a] :
% 186.97/187.93 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_C_2))
% 186.97/187.93 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) )
% 186.97/187.93 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_C_2))
% 186.97/187.93 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_Int__insert__right,axiom,
% 186.97/187.93 ! [V_B_2,V_A_2,V_a_2,T_a] :
% 186.97/187.93 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 186.97/187.93 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) )
% 186.97/187.93 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 186.97/187.93 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_image__diff__subset,axiom,
% 186.97/187.93 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_B_2))),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_Diff__subset__conv,axiom,
% 186.97/187.93 ! [V_C_2,V_B_2,V_A_2,T_a] :
% 186.97/187.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2))
% 186.97/187.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_Diff__partition,axiom,
% 186.97/187.93 ! [V_B_2,V_A_2,T_a] :
% 186.97/187.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 186.97/187.93 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) = V_B_2 ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_image__Int__subset,axiom,
% 186.97/187.93 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,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_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_B_2)))) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_Un__Int__assoc__eq,axiom,
% 186.97/187.93 ! [V_C_2,V_B_2,V_A_2,T_a] :
% 186.97/187.93 ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))
% 186.97/187.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_folding__image__simple_Oempty,axiom,
% 186.97/187.93 ! [V_Fa_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 186.97/187.93 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_Fa_2)
% 186.97/187.93 => hAPP(V_Fa_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = V_z_2 ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_folding__image__simple_Oremove,axiom,
% 186.97/187.93 ! [V_x_2,V_A_2,V_Fa_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 186.97/187.93 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_Fa_2)
% 186.97/187.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 186.97/187.93 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 186.97/187.93 => hAPP(V_Fa_2,V_A_2) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_Fa_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)))))) ) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_insert__Diff,axiom,
% 186.97/187.93 ! [V_A_2,V_a_2,T_a] :
% 186.97/187.93 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 186.97/187.93 => hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = V_A_2 ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_Diff__insert__absorb,axiom,
% 186.97/187.93 ! [V_A_2,V_x_2,T_a] :
% 186.97/187.93 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 186.97/187.93 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_A_2 ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_diff__single__insert,axiom,
% 186.97/187.93 ! [V_B_2,V_x_2,V_A_2,T_a] :
% 186.97/187.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_B_2))
% 186.97/187.93 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 186.97/187.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_B_2))) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_subset__insert__iff,axiom,
% 186.97/187.93 ! [V_B_2,V_x_2,V_A_2,T_a] :
% 186.97/187.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_B_2)))
% 186.97/187.93 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 186.97/187.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_B_2)) )
% 186.97/187.93 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 186.97/187.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_folding__one_Oinsert__remove,axiom,
% 186.97/187.93 ! [V_x_2,V_A_2,V_Fa_2,V_f_2,T_a] :
% 186.97/187.93 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_Fa_2)
% 186.97/187.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.93 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 186.97/187.93 => hAPP(V_Fa_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 )
% 186.97/187.93 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 186.97/187.93 => hAPP(V_Fa_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_Fa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_folding__one_Ounion__disjoint,axiom,
% 186.97/187.93 ! [V_B_2,V_A_2,V_Fa_2,V_f_2,T_a] :
% 186.97/187.93 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_Fa_2)
% 186.97/187.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.93 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 186.97/187.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 186.97/187.93 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 186.97/187.93 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 186.97/187.93 => hAPP(V_Fa_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_Fa_2,V_A_2)),hAPP(V_Fa_2,V_B_2)) ) ) ) ) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_flat__lub__def,axiom,
% 186.97/187.93 ! [V_b_2,V_A_2,T_a] :
% 186.97/187.93 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))
% 186.97/187.93 => c_Partial__Function_Oflat__lub(T_a,V_b_2,V_A_2) = V_b_2 )
% 186.97/187.93 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))
% 186.97/187.93 => c_Partial__Function_Oflat__lub(T_a,V_b_2,V_A_2) = c_HOL_OThe(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_diff__eq__diff__less__eq,axiom,
% 186.97/187.93 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
% 186.97/187.93 ( class_Groups_Oordered__ab__group__add(T_a)
% 186.97/187.93 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_c_2),V_d_2)
% 186.97/187.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2))
% 186.97/187.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c_2),V_d_2)) ) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_fun__upd__image,axiom,
% 186.97/187.93 ! [V_y_2,V_f_2,T_b,V_A_2,V_x_2,T_a] :
% 186.97/187.93 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 186.97/187.93 => hAPP(c_Set_Oimage(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_y_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) )
% 186.97/187.93 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 186.97/187.93 => hAPP(c_Set_Oimage(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_y_2)),V_A_2) = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_finite__empty__induct,axiom,
% 186.97/187.93 ! [V_P_2,V_A_2,T_a] :
% 186.97/187.93 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.93 => ( hBOOL(hAPP(V_P_2,V_A_2))
% 186.97/187.93 => ( ! [B_a,B_A] :
% 186.97/187.93 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_A))
% 186.97/187.93 => ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),B_A))
% 186.97/187.93 => ( hBOOL(hAPP(V_P_2,B_A))
% 186.97/187.93 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),B_A),hAPP(hAPP(c_Set_Oinsert(T_a),B_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) )
% 186.97/187.93 => hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_folding__image__simple_Ounion__inter__neutral,axiom,
% 186.97/187.93 ! [V_B_2,V_A_2,V_Fa_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 186.97/187.93 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_Fa_2)
% 186.97/187.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 186.97/187.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 186.97/187.93 => ( ! [B_x] :
% 186.97/187.93 ( 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)))
% 186.97/187.93 => hAPP(V_g_2,B_x) = V_z_2 )
% 186.97/187.93 => hAPP(V_Fa_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_Fa_2,V_A_2)),hAPP(V_Fa_2,V_B_2)) ) ) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_fun__left__comm__idem__remove,axiom,
% 186.97/187.93 ! [T_a] : c_Finite__Set_Ofun__left__comm__idem(T_a,tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_psubset__insert__iff,axiom,
% 186.97/187.93 ! [V_B_2,V_x_2,V_A_2,T_a] :
% 186.97/187.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_B_2)))
% 186.97/187.93 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2))
% 186.97/187.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) )
% 186.97/187.93 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2))
% 186.97/187.93 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 186.97/187.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_B_2)) )
% 186.97/187.93 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 186.97/187.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_fold__graph_H_Ointros_I2_J,axiom,
% 186.97/187.93 ! [V_y_2,V_z_2,V_f_2,T_b,V_A_2,V_x_2,T_a] :
% 186.97/187.93 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 186.97/187.93 => ( c_Nitpick_Ofold__graph_H(T_a,T_b,V_f_2,V_z_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_y_2)
% 186.97/187.93 => c_Nitpick_Ofold__graph_H(T_a,T_b,V_f_2,V_z_2,V_A_2,hAPP(hAPP(V_f_2,V_x_2),V_y_2)) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_Inf__fin_Oremove,axiom,
% 186.97/187.93 ! [V_x_2,V_A_2,T_a] :
% 186.97/187.93 ( class_Lattices_Olattice(T_a)
% 186.97/187.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.93 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 186.97/187.93 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 186.97/187.93 => c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2) = V_x_2 )
% 186.97/187.93 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 186.97/187.93 => c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_Sup__fin_Oremove,axiom,
% 186.97/187.93 ! [V_x_2,V_A_2,T_a] :
% 186.97/187.93 ( class_Lattices_Olattice(T_a)
% 186.97/187.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.93 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 186.97/187.93 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 186.97/187.93 => c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2) = V_x_2 )
% 186.97/187.93 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 186.97/187.93 => c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_Diff1__fold__graph,axiom,
% 186.97/187.93 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_b,T_a] :
% 186.97/187.93 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_y_2))
% 186.97/187.93 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 186.97/187.93 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),hAPP(hAPP(V_f_2,V_x_2),V_y_2))) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_fun__upd__triv,axiom,
% 186.97/187.93 ! [V_x_2,V_f_2,T_b,T_a] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),hAPP(V_f_2,V_x_2)) = V_f_2 ).
% 186.97/187.93
% 186.97/187.93 fof(fact_order__less__irrefl,axiom,
% 186.97/187.93 ! [V_x,T_a] :
% 186.97/187.93 ( class_Orderings_Opreorder(T_a)
% 186.97/187.93 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_x)) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_linorder__neq__iff,axiom,
% 186.97/187.93 ! [V_y_2,V_x_2,T_a] :
% 186.97/187.93 ( class_Orderings_Olinorder(T_a)
% 186.97/187.93 => ( V_x_2 != V_y_2
% 186.97/187.93 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
% 186.97/187.93 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) ) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_not__less__iff__gr__or__eq,axiom,
% 186.97/187.93 ! [V_y_2,V_x_2,T_a] :
% 186.97/187.93 ( class_Orderings_Olinorder(T_a)
% 186.97/187.93 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
% 186.97/187.93 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2))
% 186.97/187.93 | V_x_2 = V_y_2 ) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_linorder__less__linear,axiom,
% 186.97/187.93 ! [V_y,V_x,T_a] :
% 186.97/187.93 ( class_Orderings_Olinorder(T_a)
% 186.97/187.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 186.97/187.93 | V_x = V_y
% 186.97/187.93 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_linorder__antisym__conv3,axiom,
% 186.97/187.93 ! [V_x_2,V_y_2,T_a] :
% 186.97/187.93 ( class_Orderings_Olinorder(T_a)
% 186.97/187.93 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2))
% 186.97/187.93 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
% 186.97/187.93 <=> V_x_2 = V_y_2 ) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_linorder__neqE,axiom,
% 186.97/187.93 ! [V_y,V_x,T_a] :
% 186.97/187.93 ( class_Orderings_Olinorder(T_a)
% 186.97/187.93 => ( V_x != V_y
% 186.97/187.93 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 186.97/187.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_less__imp__neq,axiom,
% 186.97/187.93 ! [V_y,V_x,T_a] :
% 186.97/187.93 ( class_Orderings_Oorder(T_a)
% 186.97/187.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 186.97/187.93 => V_x != V_y ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_order__less__not__sym,axiom,
% 186.97/187.93 ! [V_y,V_x,T_a] :
% 186.97/187.93 ( class_Orderings_Opreorder(T_a)
% 186.97/187.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 186.97/187.93 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_order__less__imp__not__less,axiom,
% 186.97/187.93 ! [V_y,V_x,T_a] :
% 186.97/187.93 ( class_Orderings_Opreorder(T_a)
% 186.97/187.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 186.97/187.93 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_order__less__imp__not__eq,axiom,
% 186.97/187.93 ! [V_y,V_x,T_a] :
% 186.97/187.93 ( class_Orderings_Oorder(T_a)
% 186.97/187.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 186.97/187.93 => V_x != V_y ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_order__less__imp__not__eq2,axiom,
% 186.97/187.93 ! [V_y,V_x,T_a] :
% 186.97/187.93 ( class_Orderings_Oorder(T_a)
% 186.97/187.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 186.97/187.93 => V_y != V_x ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_order__less__asym_H,axiom,
% 186.97/187.93 ! [V_b,V_a,T_a] :
% 186.97/187.93 ( class_Orderings_Opreorder(T_a)
% 186.97/187.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 186.97/187.93 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_xt1_I9_J,axiom,
% 186.97/187.93 ! [V_a,V_b,T_a] :
% 186.97/187.93 ( class_Orderings_Oorder(T_a)
% 186.97/187.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 186.97/187.93 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_ord__eq__less__trans,axiom,
% 186.97/187.93 ! [V_c,V_b,V_a,T_a] :
% 186.97/187.93 ( class_Orderings_Oord(T_a)
% 186.97/187.93 => ( V_a = V_b
% 186.97/187.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
% 186.97/187.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_xt1_I1_J,axiom,
% 186.97/187.93 ! [V_c,V_b,V_a,T_a] :
% 186.97/187.93 ( class_Orderings_Oorder(T_a)
% 186.97/187.93 => ( V_a = V_b
% 186.97/187.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_b))
% 186.97/187.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_psubset__trans,axiom,
% 186.97/187.93 ! [V_C_2,V_B_2,V_A_2,T_a] :
% 186.97/187.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 186.97/187.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))
% 186.97/187.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_ord__less__eq__trans,axiom,
% 186.97/187.93 ! [V_c,V_b,V_a,T_a] :
% 186.97/187.93 ( class_Orderings_Oord(T_a)
% 186.97/187.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 186.97/187.93 => ( V_b = V_c
% 186.97/187.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_xt1_I2_J,axiom,
% 186.97/187.93 ! [V_c,V_a,V_b,T_a] :
% 186.97/187.93 ( class_Orderings_Oorder(T_a)
% 186.97/187.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 186.97/187.93 => ( V_b = V_c
% 186.97/187.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_order__less__trans,axiom,
% 186.97/187.93 ! [V_z,V_y,V_x,T_a] :
% 186.97/187.93 ( class_Orderings_Opreorder(T_a)
% 186.97/187.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 186.97/187.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z))
% 186.97/187.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_xt1_I10_J,axiom,
% 186.97/187.93 ! [V_z,V_x,V_y,T_a] :
% 186.97/187.93 ( class_Orderings_Oorder(T_a)
% 186.97/187.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
% 186.97/187.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y))
% 186.97/187.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_order__less__asym,axiom,
% 186.97/187.93 ! [V_y,V_x,T_a] :
% 186.97/187.93 ( class_Orderings_Opreorder(T_a)
% 186.97/187.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 186.97/187.93 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_linorder__cases,axiom,
% 186.97/187.93 ! [V_y,V_x,T_a] :
% 186.97/187.93 ( class_Orderings_Olinorder(T_a)
% 186.97/187.93 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 186.97/187.93 => ( V_x != V_y
% 186.97/187.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_fun__upd__idem__iff,axiom,
% 186.97/187.93 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] :
% 186.97/187.93 ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_y_2) = V_f_2
% 186.97/187.93 <=> hAPP(V_f_2,V_x_2) = V_y_2 ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_fun__upd__upd,axiom,
% 186.97/187.93 ! [V_z_2,V_y_2,V_x_2,V_f_2,T_b,T_a] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_y_2)),V_x_2),V_z_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_z_2) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_fun__upd__same,axiom,
% 186.97/187.93 ! [V_y_2,V_x_2,V_f_2,T_a,T_b] : hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_a),V_f_2),V_x_2),V_y_2),V_x_2) = V_y_2 ).
% 186.97/187.93
% 186.97/187.93 fof(fact_fun__upd__apply,axiom,
% 186.97/187.93 ! [V_y_2,V_f_2,T_b,T_a,V_x_2,V_z_2] :
% 186.97/187.93 ( ( V_z_2 = V_x_2
% 186.97/187.93 => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_y_2),V_z_2) = V_y_2 )
% 186.97/187.93 & ( V_z_2 != V_x_2
% 186.97/187.93 => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_y_2),V_z_2) = hAPP(V_f_2,V_z_2) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_fun__upd__twist,axiom,
% 186.97/187.93 ! [V_d_2,V_b_2,V_m_2,T_b,T_a,V_c_2,V_a_2] :
% 186.97/187.93 ( V_a_2 != V_c_2
% 186.97/187.93 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_m_2),V_a_2),V_b_2)),V_c_2),V_d_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_m_2),V_c_2),V_d_2)),V_a_2),V_b_2) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_fun__upd__other,axiom,
% 186.97/187.93 ! [V_y_2,V_f_2,T_b,T_a,V_x_2,V_z_2] :
% 186.97/187.93 ( V_z_2 != V_x_2
% 186.97/187.93 => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_y_2),V_z_2) = hAPP(V_f_2,V_z_2) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_fun__upd__idem,axiom,
% 186.97/187.93 ! [T_a,T_b,V_y_2,V_x_2,V_f_2] :
% 186.97/187.93 ( hAPP(V_f_2,V_x_2) = V_y_2
% 186.97/187.93 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_a),V_f_2),V_x_2),V_y_2) = V_f_2 ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_fun__left__comm__idem_Ofun__left__idem,axiom,
% 186.97/187.93 ! [V_z_2,V_x_2,V_f_2,T_b,T_a] :
% 186.97/187.93 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2)
% 186.97/187.93 => 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) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_diff__eq__diff__less,axiom,
% 186.97/187.93 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
% 186.97/187.93 ( class_Groups_Oordered__ab__group__add(T_a)
% 186.97/187.93 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_c_2),V_d_2)
% 186.97/187.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2))
% 186.97/187.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),V_d_2)) ) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_fun__upd__def,axiom,
% 186.97/187.93 ! [V_b_2,V_f_2,T_b,T_a,V_a_2,V_x_2] :
% 186.97/187.93 ( ( V_x_2 = V_a_2
% 186.97/187.93 => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_a_2),V_b_2),V_x_2) = V_b_2 )
% 186.97/187.93 & ( V_x_2 != V_a_2
% 186.97/187.93 => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_a_2),V_b_2),V_x_2) = hAPP(V_f_2,V_x_2) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_fun__left__comm__idem_Ofun__left__comm__idem__apply,axiom,
% 186.97/187.93 ! [V_g_2,T_c,V_f_2,T_b,T_a] :
% 186.97/187.93 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2)
% 186.97/187.93 => c_Finite__Set_Ofun__left__comm__idem(T_c,T_b,hAPP(hAPP(c_COMBB(T_a,tc_fun(T_b,T_b),T_c),V_f_2),V_g_2)) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_fold__graph_H_Ointros_I1_J,axiom,
% 186.97/187.93 ! [V_z_2,V_f_2,T_b,T_a] : c_Nitpick_Ofold__graph_H(T_a,T_b,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_z_2) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_fold__graph_H_Oequations_I1_J,axiom,
% 186.97/187.93 ! [V_a2_2,V_a1_2,T_b,T_a] : c_Nitpick_Ofold__graph_H(T_a,T_b,V_a1_2,V_a2_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_a2_2) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_less__fun__def,axiom,
% 186.97/187.93 ! [V_g_2,V_f_2,T_a,T_b] :
% 186.97/187.93 ( class_Orderings_Oord(T_b)
% 186.97/187.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b)),V_f_2),V_g_2))
% 186.97/187.93 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2))
% 186.97/187.93 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_g_2),V_f_2)) ) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_linorder__not__less,axiom,
% 186.97/187.93 ! [V_y_2,V_x_2,T_a] :
% 186.97/187.93 ( class_Orderings_Olinorder(T_a)
% 186.97/187.93 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
% 186.97/187.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_linorder__not__le,axiom,
% 186.97/187.93 ! [V_y_2,V_x_2,T_a] :
% 186.97/187.93 ( class_Orderings_Olinorder(T_a)
% 186.97/187.93 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 186.97/187.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_linorder__le__less__linear,axiom,
% 186.97/187.93 ! [V_y,V_x,T_a] :
% 186.97/187.93 ( class_Orderings_Olinorder(T_a)
% 186.97/187.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 186.97/187.93 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_order__less__le,axiom,
% 186.97/187.93 ! [V_y_2,V_x_2,T_a] :
% 186.97/187.93 ( class_Orderings_Oorder(T_a)
% 186.97/187.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
% 186.97/187.93 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 186.97/187.93 & V_x_2 != V_y_2 ) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_less__le__not__le,axiom,
% 186.97/187.93 ! [V_y_2,V_x_2,T_a] :
% 186.97/187.93 ( class_Orderings_Opreorder(T_a)
% 186.97/187.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
% 186.97/187.93 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 186.97/187.93 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_order__le__less,axiom,
% 186.97/187.93 ! [V_y_2,V_x_2,T_a] :
% 186.97/187.93 ( class_Orderings_Oorder(T_a)
% 186.97/187.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 186.97/187.93 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
% 186.97/187.93 | V_x_2 = V_y_2 ) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_leI,axiom,
% 186.97/187.93 ! [V_y,V_x,T_a] :
% 186.97/187.93 ( class_Orderings_Olinorder(T_a)
% 186.97/187.93 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 186.97/187.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_not__leE,axiom,
% 186.97/187.93 ! [V_x,V_y,T_a] :
% 186.97/187.93 ( class_Orderings_Olinorder(T_a)
% 186.97/187.93 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 186.97/187.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_linorder__antisym__conv1,axiom,
% 186.97/187.93 ! [V_y_2,V_x_2,T_a] :
% 186.97/187.93 ( class_Orderings_Olinorder(T_a)
% 186.97/187.93 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
% 186.97/187.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 186.97/187.93 <=> V_x_2 = V_y_2 ) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_order__neq__le__trans,axiom,
% 186.97/187.93 ! [V_b,V_a,T_a] :
% 186.97/187.93 ( class_Orderings_Oorder(T_a)
% 186.97/187.93 => ( V_a != V_b
% 186.97/187.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 186.97/187.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_xt1_I12_J,axiom,
% 186.97/187.93 ! [V_b,V_a,T_a] :
% 186.97/187.93 ( class_Orderings_Oorder(T_a)
% 186.97/187.93 => ( V_a != V_b
% 186.97/187.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 186.97/187.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_leD,axiom,
% 186.97/187.93 ! [V_x,V_y,T_a] :
% 186.97/187.93 ( class_Orderings_Olinorder(T_a)
% 186.97/187.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 186.97/187.93 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_order__less__imp__le,axiom,
% 186.97/187.93 ! [V_y,V_x,T_a] :
% 186.97/187.93 ( class_Orderings_Opreorder(T_a)
% 186.97/187.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 186.97/187.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_linorder__antisym__conv2,axiom,
% 186.97/187.93 ! [V_y_2,V_x_2,T_a] :
% 186.97/187.93 ( class_Orderings_Olinorder(T_a)
% 186.97/187.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 186.97/187.93 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
% 186.97/187.93 <=> V_x_2 = V_y_2 ) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_order__le__imp__less__or__eq,axiom,
% 186.97/187.93 ! [V_y,V_x,T_a] :
% 186.97/187.93 ( class_Orderings_Oorder(T_a)
% 186.97/187.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 186.97/187.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 186.97/187.93 | V_x = V_y ) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_order__le__neq__trans,axiom,
% 186.97/187.93 ! [V_b,V_a,T_a] :
% 186.97/187.93 ( class_Orderings_Oorder(T_a)
% 186.97/187.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 186.97/187.93 => ( V_a != V_b
% 186.97/187.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_xt1_I11_J,axiom,
% 186.97/187.93 ! [V_a,V_b,T_a] :
% 186.97/187.93 ( class_Orderings_Oorder(T_a)
% 186.97/187.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 186.97/187.93 => ( V_a != V_b
% 186.97/187.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_order__less__le__trans,axiom,
% 186.97/187.93 ! [V_z,V_y,V_x,T_a] :
% 186.97/187.93 ( class_Orderings_Opreorder(T_a)
% 186.97/187.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 186.97/187.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z))
% 186.97/187.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_xt1_I7_J,axiom,
% 186.97/187.93 ! [V_z,V_x,V_y,T_a] :
% 186.97/187.93 ( class_Orderings_Oorder(T_a)
% 186.97/187.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
% 186.97/187.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y))
% 186.97/187.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_order__le__less__trans,axiom,
% 186.97/187.93 ! [V_z,V_y,V_x,T_a] :
% 186.97/187.93 ( class_Orderings_Opreorder(T_a)
% 186.97/187.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 186.97/187.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z))
% 186.97/187.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_xt1_I8_J,axiom,
% 186.97/187.93 ! [V_z,V_x,V_y,T_a] :
% 186.97/187.93 ( class_Orderings_Oorder(T_a)
% 186.97/187.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 186.97/187.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y))
% 186.97/187.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_psubsetD,axiom,
% 186.97/187.93 ! [V_c_2,V_B_2,V_A_2,T_a] :
% 186.97/187.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 186.97/187.93 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2))
% 186.97/187.93 => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_not__psubset__empty,axiom,
% 186.97/187.93 ! [V_A_2,T_a] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_less__supI2,axiom,
% 186.97/187.93 ! [V_a,V_b,V_x,T_a] :
% 186.97/187.93 ( class_Lattices_Osemilattice__sup(T_a)
% 186.97/187.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b))
% 186.97/187.93 => 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))) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_less__supI1,axiom,
% 186.97/187.93 ! [V_b,V_a,V_x,T_a] :
% 186.97/187.93 ( class_Lattices_Osemilattice__sup(T_a)
% 186.97/187.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
% 186.97/187.93 => 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))) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_less__infI1,axiom,
% 186.97/187.93 ! [V_b,V_x,V_a,T_a] :
% 186.97/187.93 ( class_Lattices_Osemilattice__inf(T_a)
% 186.97/187.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x))
% 186.97/187.93 => 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)) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_less__infI2,axiom,
% 186.97/187.93 ! [V_a,V_x,V_b,T_a] :
% 186.97/187.93 ( class_Lattices_Osemilattice__inf(T_a)
% 186.97/187.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x))
% 186.97/187.93 => 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)) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_psubset__eq,axiom,
% 186.97/187.93 ! [V_B_2,V_A_2,T_a] :
% 186.97/187.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 186.97/187.93 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 186.97/187.93 & V_A_2 != V_B_2 ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_subset__iff__psubset__eq,axiom,
% 186.97/187.93 ! [V_B_2,V_A_2,T_a] :
% 186.97/187.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 186.97/187.93 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 186.97/187.93 | V_A_2 = V_B_2 ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_psubset__imp__subset,axiom,
% 186.97/187.93 ! [V_B_2,V_A_2,T_a] :
% 186.97/187.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 186.97/187.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_psubset__subset__trans,axiom,
% 186.97/187.93 ! [V_C_2,V_B_2,V_A_2,T_a] :
% 186.97/187.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 186.97/187.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))
% 186.97/187.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_subset__psubset__trans,axiom,
% 186.97/187.93 ! [V_C_2,V_B_2,V_A_2,T_a] :
% 186.97/187.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 186.97/187.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))
% 186.97/187.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_Inf__le__Sup,axiom,
% 186.97/187.93 ! [V_A_2,T_a] :
% 186.97/187.93 ( class_Lattices_Olattice(T_a)
% 186.97/187.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.93 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 186.97/187.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2))) ) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_fold__graph_Oequations_I1_J,axiom,
% 186.97/187.93 ! [V_z_2,V_f_2,T_b,T_a] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_z_2)) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_fold__graph_OemptyI,axiom,
% 186.97/187.93 ! [V_z_2,V_f_2,T_b,T_a] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_z_2)) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_empty__fold__graphE,axiom,
% 186.97/187.93 ! [V_x_2,V_z_2,V_f_2,T_b,T_a] :
% 186.97/187.93 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_x_2))
% 186.97/187.93 => V_x_2 = V_z_2 ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_fold__graph__imp__finite,axiom,
% 186.97/187.93 ! [V_x_2,V_A_2,V_z_2,V_f_2,T_b,T_a] :
% 186.97/187.93 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_x_2))
% 186.97/187.93 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_Sup__fin_Osingleton,axiom,
% 186.97/187.93 ! [V_x_2,T_a] :
% 186.97/187.93 ( class_Lattices_Olattice(T_a)
% 186.97/187.93 => c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_x_2 ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_Inf__fin_Osingleton,axiom,
% 186.97/187.93 ! [V_x_2,T_a] :
% 186.97/187.93 ( class_Lattices_Olattice(T_a)
% 186.97/187.93 => c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_x_2 ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_fun__left__comm__idem__insert,axiom,
% 186.97/187.93 ! [T_a] : c_Finite__Set_Ofun__left__comm__idem(T_a,tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a)) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_fun__left__comm__idem__sup,axiom,
% 186.97/187.93 ! [T_a] :
% 186.97/187.93 ( class_Lattices_Osemilattice__sup(T_a)
% 186.97/187.93 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_fun__left__comm__idem__inf,axiom,
% 186.97/187.93 ! [T_a] :
% 186.97/187.93 ( class_Lattices_Osemilattice__inf(T_a)
% 186.97/187.93 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_sup__Inf__absorb,axiom,
% 186.97/187.93 ! [V_a_2,V_A_2,T_a] :
% 186.97/187.93 ( class_Lattices_Olattice(T_a)
% 186.97/187.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.93 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 186.97/187.93 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a_2),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)) = V_a_2 ) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_Sup__fin_Oin__idem,axiom,
% 186.97/187.93 ! [V_x_2,V_A_2,T_a] :
% 186.97/187.93 ( class_Lattices_Olattice(T_a)
% 186.97/187.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.93 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 186.97/187.93 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2) ) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_Inf__fin_Oin__idem,axiom,
% 186.97/187.93 ! [V_x_2,V_A_2,T_a] :
% 186.97/187.93 ( class_Lattices_Olattice(T_a)
% 186.97/187.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.93 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 186.97/187.93 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2) ) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_inf__Sup__absorb,axiom,
% 186.97/187.93 ! [V_a_2,V_A_2,T_a] :
% 186.97/187.93 ( class_Lattices_Olattice(T_a)
% 186.97/187.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.93 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 186.97/187.93 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a_2),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)) = V_a_2 ) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_fold__graph_OinsertI,axiom,
% 186.97/187.93 ! [V_y_2,V_z_2,V_f_2,T_b,V_A_2,V_x_2,T_a] :
% 186.97/187.93 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 186.97/187.93 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_y_2))
% 186.97/187.93 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)),hAPP(hAPP(V_f_2,V_x_2),V_y_2))) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_Sup__fin_Oinsert__idem,axiom,
% 186.97/187.93 ! [V_x_2,V_A_2,T_a] :
% 186.97/187.93 ( class_Lattices_Olattice(T_a)
% 186.97/187.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.93 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 186.97/187.93 => c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)) ) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_Inf__fin_Oinsert__idem,axiom,
% 186.97/187.93 ! [V_x_2,V_A_2,T_a] :
% 186.97/187.93 ( class_Lattices_Olattice(T_a)
% 186.97/187.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.93 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 186.97/187.93 => c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)) ) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_Sup__fin_Osubset__idem,axiom,
% 186.97/187.93 ! [V_B_2,V_A_2,T_a] :
% 186.97/187.93 ( class_Lattices_Olattice(T_a)
% 186.97/187.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.93 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 186.97/187.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 186.97/187.93 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_B_2)),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2) ) ) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_Inf__fin_Osubset__idem,axiom,
% 186.97/187.93 ! [V_B_2,V_A_2,T_a] :
% 186.97/187.93 ( class_Lattices_Olattice(T_a)
% 186.97/187.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.93 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 186.97/187.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 186.97/187.93 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_B_2)),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2) ) ) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_Sup__fin_Ounion__idem,axiom,
% 186.97/187.93 ! [V_B_2,V_A_2,T_a] :
% 186.97/187.93 ( class_Lattices_Olattice(T_a)
% 186.97/187.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.93 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 186.97/187.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 186.97/187.93 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 186.97/187.93 => c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_B_2)) ) ) ) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_Inf__fin_Ounion__idem,axiom,
% 186.97/187.93 ! [V_B_2,V_A_2,T_a] :
% 186.97/187.93 ( class_Lattices_Olattice(T_a)
% 186.97/187.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.93 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 186.97/187.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 186.97/187.93 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 186.97/187.93 => c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_B_2)) ) ) ) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_diff__eq__diff__eq,axiom,
% 186.97/187.93 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
% 186.97/187.93 ( class_Groups_Oab__group__add(T_a)
% 186.97/187.93 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_c_2),V_d_2)
% 186.97/187.93 => ( V_a_2 = V_b_2
% 186.97/187.93 <=> V_c_2 = V_d_2 ) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_Sup__fin_Oidem,axiom,
% 186.97/187.93 ! [V_x,T_a] :
% 186.97/187.93 ( class_Lattices_Olattice(T_a)
% 186.97/187.93 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_Inf__fin_Oidem,axiom,
% 186.97/187.93 ! [V_x,T_a] :
% 186.97/187.93 ( class_Lattices_Olattice(T_a)
% 186.97/187.93 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_Sup__fin_Oinsert,axiom,
% 186.97/187.93 ! [V_x_2,V_A_2,T_a] :
% 186.97/187.93 ( class_Lattices_Olattice(T_a)
% 186.97/187.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.93 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 186.97/187.93 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 186.97/187.93 => c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)) ) ) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_Inf__fin_Oinsert,axiom,
% 186.97/187.93 ! [V_x_2,V_A_2,T_a] :
% 186.97/187.93 ( class_Lattices_Olattice(T_a)
% 186.97/187.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.93 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 186.97/187.93 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 186.97/187.93 => c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)) ) ) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_Sup__fin_Oinsert__remove,axiom,
% 186.97/187.93 ! [V_x_2,V_A_2,T_a] :
% 186.97/187.93 ( class_Lattices_Olattice(T_a)
% 186.97/187.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.93 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 186.97/187.93 => c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 )
% 186.97/187.93 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 186.97/187.93 => c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_Inf__fin_Oinsert__remove,axiom,
% 186.97/187.93 ! [V_x_2,V_A_2,T_a] :
% 186.97/187.93 ( class_Lattices_Olattice(T_a)
% 186.97/187.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.93 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 186.97/187.93 => c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 )
% 186.97/187.93 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 186.97/187.93 => c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_Sup__fin_Ounion__inter,axiom,
% 186.97/187.93 ! [V_B_2,V_A_2,T_a] :
% 186.97/187.93 ( class_Lattices_Olattice(T_a)
% 186.97/187.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 186.97/187.93 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 186.97/187.93 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_B_2)) ) ) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_Sup__fin_Ounion__disjoint,axiom,
% 186.97/187.93 ! [V_B_2,V_A_2,T_a] :
% 186.97/187.93 ( class_Lattices_Olattice(T_a)
% 186.97/187.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.93 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 186.97/187.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 186.97/187.93 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 186.97/187.93 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 186.97/187.93 => c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_B_2)) ) ) ) ) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_Inf__fin_Ounion__inter,axiom,
% 186.97/187.93 ! [V_B_2,V_A_2,T_a] :
% 186.97/187.93 ( class_Lattices_Olattice(T_a)
% 186.97/187.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 186.97/187.93 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 186.97/187.93 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_B_2)) ) ) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_Inf__fin_Ounion__disjoint,axiom,
% 186.97/187.93 ! [V_B_2,V_A_2,T_a] :
% 186.97/187.93 ( class_Lattices_Olattice(T_a)
% 186.97/187.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.93 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 186.97/187.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 186.97/187.93 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 186.97/187.93 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 186.97/187.93 => c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_B_2)) ) ) ) ) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_fold1Set_Ointros,axiom,
% 186.97/187.93 ! [V_x_2,V_A_2,V_a_2,V_f_2,T_a] :
% 186.97/187.93 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,V_f_2,V_a_2,V_A_2),V_x_2))
% 186.97/187.93 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 186.97/187.93 => hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_a,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)),V_x_2)) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_Inf__fin_Oclosed,axiom,
% 186.97/187.93 ! [V_A_2,T_a] :
% 186.97/187.93 ( class_Lattices_Olattice(T_a)
% 186.97/187.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.93 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 186.97/187.93 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),hAPP(hAPP(c_Set_Oinsert(T_a),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))
% 186.97/187.93 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)),V_A_2)) ) ) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_Sup__fin_Oclosed,axiom,
% 186.97/187.93 ! [V_A_2,T_a] :
% 186.97/187.93 ( class_Lattices_Olattice(T_a)
% 186.97/187.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.93 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 186.97/187.93 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),hAPP(hAPP(c_Set_Oinsert(T_a),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))
% 186.97/187.93 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)),V_A_2)) ) ) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_fold__graph_H_Oequations_I2_J,axiom,
% 186.97/187.93 ! [V_a5_2,V_a1_2,V_a2_2,V_a4_2,V_a3_2,T_b,T_a] :
% 186.97/187.93 ( c_Nitpick_Ofold__graph_H(T_a,T_b,V_a3_2,V_a4_2,V_a2_2,hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2))
% 186.97/187.93 <=> ( ( V_a2_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 186.97/187.93 & hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = V_a4_2 )
% 186.97/187.93 | ? [B_x,B_y] :
% 186.97/187.93 ( hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = hAPP(hAPP(V_a3_2,B_x),B_y)
% 186.97/187.93 & hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_a2_2))
% 186.97/187.93 & c_Nitpick_Ofold__graph_H(T_a,T_b,V_a3_2,V_a4_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_a2_2),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),B_y) ) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_Inf__fin_Ohom__commute,axiom,
% 186.97/187.93 ! [V_N_2,V_h_2,T_a] :
% 186.97/187.93 ( class_Lattices_Olattice(T_a)
% 186.97/187.93 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),B_x),B_y)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
% 186.97/187.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
% 186.97/187.93 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 186.97/187.93 => hAPP(V_h_2,c_Big__Operators_Olattice__class_OInf__fin(T_a,V_N_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(c_Set_Oimage(T_a,T_a,V_h_2),V_N_2)) ) ) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_Sup__fin_Ohom__commute,axiom,
% 186.97/187.93 ! [V_N_2,V_h_2,T_a] :
% 186.97/187.93 ( class_Lattices_Olattice(T_a)
% 186.97/187.93 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),B_x),B_y)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
% 186.97/187.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
% 186.97/187.93 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 186.97/187.93 => hAPP(V_h_2,c_Big__Operators_Olattice__class_OSup__fin(T_a,V_N_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(c_Set_Oimage(T_a,T_a,V_h_2),V_N_2)) ) ) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_image__eq__fold__image,axiom,
% 186.97/187.93 ! [V_f_2,T_b,V_A_2,T_a] :
% 186.97/187.93 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.93 => hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(T_b,tc_HOL_Obool),T_a,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_a,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_a),c_Set_Oinsert(T_b)),V_f_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))),V_A_2) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_setsum__diff1,axiom,
% 186.97/187.93 ! [V_f_2,V_a_2,V_A_2,T_a,T_b] :
% 186.97/187.93 ( class_Groups_Oab__group__add(T_b)
% 186.97/187.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.93 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 186.97/187.93 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)) )
% 186.97/187.93 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 186.97/187.93 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2) ) ) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_setsum__diff1__ring,axiom,
% 186.97/187.93 ! [V_f_2,V_a_2,V_A_2,T_a,T_b] :
% 186.97/187.93 ( class_Rings_Oring(T_b)
% 186.97/187.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.93 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 186.97/187.93 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)) ) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_fold__graph__permute__diff,axiom,
% 186.97/187.93 ! [V_a_2,V_x_2,V_A_2,V_b_2,T_a] :
% 186.97/187.93 ( class_Groups_Oab__semigroup__mult(T_a)
% 186.97/187.93 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a),V_b_2,V_A_2),V_x_2))
% 186.97/187.93 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 186.97/187.93 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2))
% 186.97/187.93 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a),V_a_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),V_x_2)) ) ) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_setsum__product,axiom,
% 186.97/187.93 ! [V_B_2,V_g_2,T_c,V_A_2,V_f_2,T_b,T_a] :
% 186.97/187.93 ( class_Rings_Osemiring__0(T_a)
% 186.97/187.93 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_a),V_g_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),T_a),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_a),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_a),T_b),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_a)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,T_a),tc_fun(T_c,T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,T_a),tc_fun(tc_fun(T_c,T_a),tc_fun(T_c,T_a)),T_b),c_COMBB(T_a,T_a,T_c)),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Groups_Otimes__class_Otimes(T_a)),V_f_2))),V_g_2))),V_B_2)),V_A_2) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_setsum__left__distrib,axiom,
% 186.97/187.93 ! [V_r_2,V_A_2,V_f_2,T_b,T_a] :
% 186.97/187.93 ( class_Rings_Osemiring__0(T_a)
% 186.97/187.93 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_f_2),V_A_2)),V_r_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Groups_Otimes__class_Otimes(T_a)),V_f_2)),V_r_2)),V_A_2) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 186.97/187.93 ! [V_c,V_b,V_a,T_a] :
% 186.97/187.93 ( class_Groups_Oab__semigroup__mult(T_a)
% 186.97/187.93 => 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)) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_setsum__commute,axiom,
% 186.97/187.93 ! [V_A_2,V_B_2,V_f_2,T_c,T_b,T_a] :
% 186.97/187.93 ( class_Groups_Ocomm__monoid__add(T_a)
% 186.97/187.93 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),T_a),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_a),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_a),T_b),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_a)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_a),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_a),tc_fun(tc_fun(T_b,tc_HOL_Obool),T_a),T_c),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a)),hAPP(c_COMBC(T_b,T_c,T_a),V_f_2))),V_A_2)),V_B_2) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_setsum__right__distrib,axiom,
% 186.97/187.93 ! [V_A_2,V_f_2,T_b,V_r_2,T_a] :
% 186.97/187.93 ( class_Rings_Osemiring__0(T_a)
% 186.97/187.93 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r_2),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,T_b),hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r_2)),V_f_2)),V_A_2) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_mult__left__idem,axiom,
% 186.97/187.93 ! [V_b,V_a,T_a] :
% 186.97/187.93 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 186.97/187.93 => 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) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_mult__idem,axiom,
% 186.97/187.93 ! [V_x,T_a] :
% 186.97/187.93 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 186.97/187.93 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = V_x ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_times_Oidem,axiom,
% 186.97/187.93 ! [V_a,T_a] :
% 186.97/187.93 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 186.97/187.93 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) = V_a ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_fold__image__empty,axiom,
% 186.97/187.93 ! [V_z_2,V_g_2,V_f_2,T_b,T_a] : hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_a,T_b,V_f_2),V_g_2),V_z_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = V_z_2 ).
% 186.97/187.93
% 186.97/187.93 fof(fact_setsum__subtractf,axiom,
% 186.97/187.93 ! [V_A_2,V_g_2,V_f_2,T_b,T_a] :
% 186.97/187.93 ( class_Groups_Oab__group__add(T_a)
% 186.97/187.93 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBS(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Groups_Ominus__class_Ominus(T_a)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_g_2),V_A_2)) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_fun__left__comm__idem,axiom,
% 186.97/187.93 ! [T_a] :
% 186.97/187.93 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 186.97/187.93 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a)) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_fold__image__insert,axiom,
% 186.97/187.93 ! [V_z_2,V_g_2,V_a_2,V_A_2,T_a,T_b] :
% 186.97/187.93 ( class_Groups_Oab__semigroup__mult(T_b)
% 186.97/187.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.93 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 186.97/187.93 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(V_g_2,V_a_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),V_z_2),V_A_2)) ) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_fold1Set__nonempty,axiom,
% 186.97/187.93 ! [V_x_2,V_A_2,V_f_2,T_a] :
% 186.97/187.93 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_a,V_f_2,V_A_2),V_x_2))
% 186.97/187.93 => V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_empty__fold1SetE,axiom,
% 186.97/187.93 ! [V_x_2,V_f_2,T_a] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_a,V_f_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_x_2)) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_folding__image__simple_Oeq__fold__g,axiom,
% 186.97/187.93 ! [V_A_2,V_Fa_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 186.97/187.93 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_Fa_2)
% 186.97/187.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 186.97/187.93 => hAPP(V_Fa_2,V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_a,T_b,V_f_2),V_g_2),V_z_2),V_A_2) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_setsum__diff__nat,axiom,
% 186.97/187.93 ! [V_f_2,V_A_2,V_B_2,T_a] :
% 186.97/187.93 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 186.97/187.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 186.97/187.93 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,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_a,tc_Nat_Onat),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_B_2)) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_fold__graph__insert__swap,axiom,
% 186.97/187.93 ! [V_z_2,V_y_2,V_A_2,V_b_2,T_a] :
% 186.97/187.93 ( class_Groups_Oab__semigroup__mult(T_a)
% 186.97/187.93 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a),V_b_2,V_A_2),V_y_2))
% 186.97/187.93 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2))
% 186.97/187.93 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a),V_z_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_A_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z_2),V_y_2))) ) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_setsum__diff1__nat,axiom,
% 186.97/187.93 ! [V_f_2,V_A_2,V_a_2,T_a] :
% 186.97/187.93 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 186.97/187.93 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)) )
% 186.97/187.93 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 186.97/187.93 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_A_2) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_setsum__diff,axiom,
% 186.97/187.93 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] :
% 186.97/187.93 ( class_Groups_Oab__group__add(T_b)
% 186.97/187.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 186.97/187.93 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_B_2)) ) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_fold1Set__sing,axiom,
% 186.97/187.93 ! [V_b_2,V_a_2,V_f_2,T_a] :
% 186.97/187.93 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_a,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_b_2))
% 186.97/187.93 <=> V_a_2 = V_b_2 ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_comm__monoid__big_OF__eq,axiom,
% 186.97/187.93 ! [V_g_2,V_A_2,V_Fa_2,V_z_2,V_f_2,T_b,T_a] :
% 186.97/187.93 ( c_Big__Operators_Ocomm__monoid__big(T_a,T_b,V_f_2,V_z_2,V_Fa_2)
% 186.97/187.93 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 186.97/187.93 => hAPP(hAPP(V_Fa_2,V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_a,T_b,V_f_2),V_g_2),V_z_2),V_A_2) )
% 186.97/187.93 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 186.97/187.93 => hAPP(hAPP(V_Fa_2,V_g_2),V_A_2) = V_z_2 ) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_fold__Un__disjoint,axiom,
% 186.97/187.93 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] :
% 186.97/187.93 ( class_Groups_Ocomm__monoid__mult(T_b)
% 186.97/187.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 186.97/187.93 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 186.97/187.93 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),c_Groups_Oone__class_Oone(T_b)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),c_Groups_Oone__class_Oone(T_b)),V_A_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),c_Groups_Oone__class_Oone(T_b)),V_B_2)) ) ) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_setsum__strict__mono,axiom,
% 186.97/187.93 ! [V_g_2,V_f_2,V_A_2,T_a,T_b] :
% 186.97/187.93 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 186.97/187.93 & class_Groups_Oordered__cancel__ab__semigroup__add(T_b) )
% 186.97/187.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.93 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 186.97/187.93 => ( ! [B_x] :
% 186.97/187.93 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 186.97/187.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 186.97/187.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2))) ) ) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_setsum_Oremove,axiom,
% 186.97/187.93 ! [V_g_2,V_x_2,V_A_2,T_a,T_b] :
% 186.97/187.93 ( class_Groups_Ocomm__monoid__add(T_b)
% 186.97/187.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.93 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 186.97/187.93 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_setsum__diff1_H,axiom,
% 186.97/187.93 ! [V_f_2,V_a_2,V_A_2,T_a,T_b] :
% 186.97/187.93 ( class_Groups_Ocomm__monoid__add(T_b)
% 186.97/187.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.93 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 186.97/187.93 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ).
% 186.97/187.93
% 186.97/187.93 fof(fact_fold1Set_Oequations,axiom,
% 186.97/187.93 ! [V_a3_2,V_a2_2,V_a1_2,V_f_2,T_a] :
% 186.97/187.93 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_a,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a1_2),V_a2_2)),V_a3_2))
% 186.97/187.93 <=> ? [B_a,B_A] :
% 186.97/187.93 ( hAPP(hAPP(c_Set_Oinsert(T_a),V_a1_2),V_a2_2) = hAPP(hAPP(c_Set_Oinsert(T_a),B_a),B_A)
% 186.97/187.94 & hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,V_f_2,B_a,B_A),V_a3_2))
% 186.97/187.94 & ~ hBOOL(hAPP(hAPP(c_member(T_a),B_a),B_A)) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_insert__fold1SetE,axiom,
% 186.97/187.94 ! [V_x_2,V_X_2,V_a_2,V_f_2,T_a] :
% 186.97/187.94 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_a,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_X_2)),V_x_2))
% 186.97/187.94 => ~ ! [B_a,B_A] :
% 186.97/187.94 ( hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_X_2) = hAPP(hAPP(c_Set_Oinsert(T_a),B_a),B_A)
% 186.97/187.94 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,V_f_2,B_a,B_A),V_x_2))
% 186.97/187.94 => hBOOL(hAPP(hAPP(c_member(T_a),B_a),B_A)) ) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_fold1__Un,axiom,
% 186.97/187.94 ! [V_B_2,V_A_2,T_a] :
% 186.97/187.94 ( class_Groups_Oab__semigroup__mult(T_a)
% 186.97/187.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.94 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 186.97/187.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 186.97/187.94 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 186.97/187.94 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 186.97/187.94 => hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),V_A_2)),hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),V_B_2)) ) ) ) ) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_fold1__insert,axiom,
% 186.97/187.94 ! [V_x_2,V_A_2,T_a] :
% 186.97/187.94 ( class_Groups_Oab__semigroup__mult(T_a)
% 186.97/187.94 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 186.97/187.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.94 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 186.97/187.94 => hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),V_A_2)) ) ) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_one__reorient,axiom,
% 186.97/187.94 ! [V_x_2,T_a] :
% 186.97/187.94 ( class_Groups_Oone(T_a)
% 186.97/187.94 => ( c_Groups_Oone__class_Oone(T_a) = V_x_2
% 186.97/187.94 <=> V_x_2 = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 186.97/187.94 ! [V_c,V_b,V_a,T_a] :
% 186.97/187.94 ( class_Groups_Oab__semigroup__add(T_a)
% 186.97/187.94 => 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)) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_add__left__cancel,axiom,
% 186.97/187.94 ! [V_c_2,V_b_2,V_a_2,T_a] :
% 186.97/187.94 ( class_Groups_Ocancel__semigroup__add(T_a)
% 186.97/187.94 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_c_2)
% 186.97/187.94 <=> V_b_2 = V_c_2 ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_add__right__cancel,axiom,
% 186.97/187.94 ! [V_c_2,V_a_2,V_b_2,T_a] :
% 186.97/187.94 ( class_Groups_Ocancel__semigroup__add(T_a)
% 186.97/187.94 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_a_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_a_2)
% 186.97/187.94 <=> V_b_2 = V_c_2 ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_add__left__imp__eq,axiom,
% 186.97/187.94 ! [V_c,V_b,V_a,T_a] :
% 186.97/187.94 ( class_Groups_Ocancel__semigroup__add(T_a)
% 186.97/187.94 => ( 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)
% 186.97/187.94 => V_b = V_c ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_add__imp__eq,axiom,
% 186.97/187.94 ! [V_c,V_b,V_a,T_a] :
% 186.97/187.94 ( class_Groups_Ocancel__ab__semigroup__add(T_a)
% 186.97/187.94 => ( 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)
% 186.97/187.94 => V_b = V_c ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_add__right__imp__eq,axiom,
% 186.97/187.94 ! [V_c,V_a,V_b,T_a] :
% 186.97/187.94 ( class_Groups_Ocancel__semigroup__add(T_a)
% 186.97/187.94 => ( 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)
% 186.97/187.94 => V_b = V_c ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_add__le__cancel__right,axiom,
% 186.97/187.94 ! [V_b_2,V_c_2,V_a_2,T_a] :
% 186.97/187.94 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 186.97/187.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_c_2)))
% 186.97/187.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_add__le__cancel__left,axiom,
% 186.97/187.94 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 186.97/187.94 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 186.97/187.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_b_2)))
% 186.97/187.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_add__right__mono,axiom,
% 186.97/187.94 ! [V_c,V_b,V_a,T_a] :
% 186.97/187.94 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 186.97/187.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 186.97/187.94 => 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))) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_add__left__mono,axiom,
% 186.97/187.94 ! [V_c,V_b,V_a,T_a] :
% 186.97/187.94 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 186.97/187.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 186.97/187.94 => 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))) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_add__mono,axiom,
% 186.97/187.94 ! [V_d,V_c,V_b,V_a,T_a] :
% 186.97/187.94 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 186.97/187.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 186.97/187.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 186.97/187.94 => 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))) ) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_add__le__imp__le__right,axiom,
% 186.97/187.94 ! [V_b,V_c,V_a,T_a] :
% 186.97/187.94 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 186.97/187.94 => ( 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)))
% 186.97/187.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_add__le__imp__le__left,axiom,
% 186.97/187.94 ! [V_b,V_a,V_c,T_a] :
% 186.97/187.94 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 186.97/187.94 => ( 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)))
% 186.97/187.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_add__less__imp__less__left,axiom,
% 186.97/187.94 ! [V_b,V_a,V_c,T_a] :
% 186.97/187.94 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 186.97/187.94 => ( 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)))
% 186.97/187.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_add__less__imp__less__right,axiom,
% 186.97/187.94 ! [V_b,V_c,V_a,T_a] :
% 186.97/187.94 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 186.97/187.94 => ( 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)))
% 186.97/187.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_add__strict__mono,axiom,
% 186.97/187.94 ! [V_d,V_c,V_b,V_a,T_a] :
% 186.97/187.94 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 186.97/187.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 186.97/187.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 186.97/187.94 => 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))) ) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_add__strict__left__mono,axiom,
% 186.97/187.94 ! [V_c,V_b,V_a,T_a] :
% 186.97/187.94 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 186.97/187.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 186.97/187.94 => 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))) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_add__strict__right__mono,axiom,
% 186.97/187.94 ! [V_c,V_b,V_a,T_a] :
% 186.97/187.94 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 186.97/187.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 186.97/187.94 => 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))) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_add__less__cancel__left,axiom,
% 186.97/187.94 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 186.97/187.94 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 186.97/187.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_b_2)))
% 186.97/187.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_add__less__cancel__right,axiom,
% 186.97/187.94 ! [V_b_2,V_c_2,V_a_2,T_a] :
% 186.97/187.94 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 186.97/187.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_c_2)))
% 186.97/187.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_add__diff__cancel,axiom,
% 186.97/187.94 ! [V_b,V_a,T_a] :
% 186.97/187.94 ( class_Groups_Ogroup__add(T_a)
% 186.97/187.94 => 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 ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_diff__add__cancel,axiom,
% 186.97/187.94 ! [V_b,V_a,T_a] :
% 186.97/187.94 ( class_Groups_Ogroup__add(T_a)
% 186.97/187.94 => 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 ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_mult__1__left,axiom,
% 186.97/187.94 ! [V_a,T_a] :
% 186.97/187.94 ( class_Groups_Omonoid__mult(T_a)
% 186.97/187.94 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_mult__1,axiom,
% 186.97/187.94 ! [V_a,T_a] :
% 186.97/187.94 ( class_Groups_Ocomm__monoid__mult(T_a)
% 186.97/187.94 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_mult__1__right,axiom,
% 186.97/187.94 ! [V_a,T_a] :
% 186.97/187.94 ( class_Groups_Omonoid__mult(T_a)
% 186.97/187.94 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_mult_Ocomm__neutral,axiom,
% 186.97/187.94 ! [V_a,T_a] :
% 186.97/187.94 ( class_Groups_Ocomm__monoid__mult(T_a)
% 186.97/187.94 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_setsum__addf,axiom,
% 186.97/187.94 ! [V_A_2,V_g_2,V_f_2,T_b,T_a] :
% 186.97/187.94 ( class_Groups_Ocomm__monoid__add(T_a)
% 186.97/187.94 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBS(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Groups_Oplus__class_Oplus(T_a)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_g_2),V_A_2)) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_add__less__le__mono,axiom,
% 186.97/187.94 ! [V_d,V_c,V_b,V_a,T_a] :
% 186.97/187.94 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 186.97/187.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 186.97/187.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 186.97/187.94 => 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))) ) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_add__le__less__mono,axiom,
% 186.97/187.94 ! [V_d,V_c,V_b,V_a,T_a] :
% 186.97/187.94 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 186.97/187.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 186.97/187.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 186.97/187.94 => 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))) ) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_fold1__singleton,axiom,
% 186.97/187.94 ! [V_a_2,V_f_2,T_a] : hAPP(c_Finite__Set_Ofold1(T_a,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_a_2 ).
% 186.97/187.94
% 186.97/187.94 fof(fact_fold1__singleton__def,axiom,
% 186.97/187.94 ! [V_a_2,V_f_2,T_a,V_g_2] :
% 186.97/187.94 ( V_g_2 = c_Finite__Set_Ofold1(T_a,V_f_2)
% 186.97/187.94 => hAPP(V_g_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_a_2 ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_setsum_Odistrib,axiom,
% 186.97/187.94 ! [V_h_2,V_g_2,V_A_2,T_a,T_b] :
% 186.97/187.94 ( class_Groups_Ocomm__monoid__add(T_b)
% 186.97/187.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.94 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_Groups_Oplus__class_Oplus(T_b)),V_g_2)),V_h_2)),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_h_2),V_A_2)) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_folding__one_Oeq__fold,axiom,
% 186.97/187.94 ! [V_A_2,V_Fa_2,V_f_2,T_a] :
% 186.97/187.94 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_Fa_2)
% 186.97/187.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.94 => hAPP(V_Fa_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,V_f_2),V_A_2) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_setsum__Un__nat,axiom,
% 186.97/187.94 ! [V_f_2,V_B_2,V_A_2,T_a] :
% 186.97/187.94 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 186.97/187.94 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,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_a,tc_Nat_Onat),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_fold1__def,axiom,
% 186.97/187.94 ! [V_A_2,V_f_2,T_a] : hAPP(c_Finite__Set_Ofold1(T_a,V_f_2),V_A_2) = c_HOL_OThe(T_a,c_Finite__Set_Ofold1Set(T_a,V_f_2,V_A_2)) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_fold__image__distrib,axiom,
% 186.97/187.94 ! [V_h_2,V_g_2,V_A_2,T_a,T_b] :
% 186.97/187.94 ( class_Groups_Ocomm__monoid__mult(T_b)
% 186.97/187.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.94 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_COMBS(T_a,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_Groups_Otimes__class_Otimes(T_b)),V_g_2)),V_h_2)),c_Groups_Oone__class_Oone(T_b)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),c_Groups_Oone__class_Oone(T_b)),V_A_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_h_2),c_Groups_Oone__class_Oone(T_b)),V_A_2)) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_Sup__fin_OF__eq,axiom,
% 186.97/187.94 ! [V_A_2,T_a] :
% 186.97/187.94 ( class_Lattices_Olattice(T_a)
% 186.97/187.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.94 => c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)),V_A_2) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_Inf__fin_OF__eq,axiom,
% 186.97/187.94 ! [V_A_2,T_a] :
% 186.97/187.94 ( class_Lattices_Olattice(T_a)
% 186.97/187.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.94 => c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_A_2) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_setsum_Oinsert,axiom,
% 186.97/187.94 ! [V_g_2,V_x_2,V_A_2,T_a,T_b] :
% 186.97/187.94 ( class_Groups_Ocomm__monoid__add(T_b)
% 186.97/187.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.94 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 186.97/187.94 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2)) ) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_setsum__insert,axiom,
% 186.97/187.94 ! [V_f_2,V_a_2,V_Fa_2,T_a,T_b] :
% 186.97/187.94 ( class_Groups_Ocomm__monoid__add(T_b)
% 186.97/187.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_Fa_2))
% 186.97/187.94 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_Fa_2))
% 186.97/187.94 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_Fa_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_Fa_2)) ) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_setsum__Un__Int,axiom,
% 186.97/187.94 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] :
% 186.97/187.94 ( class_Groups_Ocomm__monoid__add(T_b)
% 186.97/187.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 186.97/187.94 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_B_2)) ) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_fold1__belowI,axiom,
% 186.97/187.94 ! [V_a_2,V_A_2,T_a] :
% 186.97/187.94 ( class_Lattices_Osemilattice__inf(T_a)
% 186.97/187.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.94 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 186.97/187.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Finite__Set_Ofold1(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_A_2)),V_a_2)) ) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_below__fold1__iff,axiom,
% 186.97/187.94 ! [V_x_2,V_A_2,T_a] :
% 186.97/187.94 ( class_Lattices_Osemilattice__inf(T_a)
% 186.97/187.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.94 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 186.97/187.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),hAPP(c_Finite__Set_Ofold1(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_A_2)))
% 186.97/187.94 <=> ! [B_x] :
% 186.97/187.94 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 186.97/187.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_x)) ) ) ) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_fold1__insert__idem,axiom,
% 186.97/187.94 ! [V_x_2,V_A_2,T_a] :
% 186.97/187.94 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 186.97/187.94 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 186.97/187.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.94 => hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),V_A_2)) ) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_fold1__Un2,axiom,
% 186.97/187.94 ! [V_B_2,V_A_2,T_a] :
% 186.97/187.94 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 186.97/187.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.94 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 186.97/187.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 186.97/187.94 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 186.97/187.94 => hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),V_A_2)),hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),V_B_2)) ) ) ) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_comm__monoid__big_Oinfinite,axiom,
% 186.97/187.94 ! [V_g_2,V_A_2,V_Fa_2,V_z_2,V_f_2,T_b,T_a] :
% 186.97/187.94 ( c_Big__Operators_Ocomm__monoid__big(T_a,T_b,V_f_2,V_z_2,V_Fa_2)
% 186.97/187.94 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 186.97/187.94 => hAPP(hAPP(V_Fa_2,V_g_2),V_A_2) = V_z_2 ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_setsum_Oinsert__remove,axiom,
% 186.97/187.94 ! [V_x_2,V_g_2,V_A_2,T_a,T_b] :
% 186.97/187.94 ( class_Groups_Ocomm__monoid__add(T_b)
% 186.97/187.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.94 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_setsum__Un__disjoint,axiom,
% 186.97/187.94 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] :
% 186.97/187.94 ( class_Groups_Ocomm__monoid__add(T_b)
% 186.97/187.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 186.97/187.94 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 186.97/187.94 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_B_2)) ) ) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_setsum__Un,axiom,
% 186.97/187.94 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] :
% 186.97/187.94 ( class_Groups_Oab__group__add(T_b)
% 186.97/187.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 186.97/187.94 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_fold__image__Un__Int,axiom,
% 186.97/187.94 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] :
% 186.97/187.94 ( class_Groups_Ocomm__monoid__mult(T_b)
% 186.97/187.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 186.97/187.94 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),c_Groups_Oone__class_Oone(T_b)),V_A_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),c_Groups_Oone__class_Oone(T_b)),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),c_Groups_Oone__class_Oone(T_b)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),c_Groups_Oone__class_Oone(T_b)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_semilattice__big_OF__eq,axiom,
% 186.97/187.94 ! [V_A_2,V_Fa_2,V_f_2,T_a] :
% 186.97/187.94 ( c_Big__Operators_Osemilattice__big(T_a,V_f_2,V_Fa_2)
% 186.97/187.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.94 => hAPP(V_Fa_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,V_f_2),V_A_2) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_less__add__iff2,axiom,
% 186.97/187.94 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] :
% 186.97/187.94 ( class_Rings_Oordered__ring(T_a)
% 186.97/187.94 => ( 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_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2)))
% 186.97/187.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b_2),V_a_2)),V_e_2)),V_d_2))) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_less__add__iff1,axiom,
% 186.97/187.94 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] :
% 186.97/187.94 ( class_Rings_Oordered__ring(T_a)
% 186.97/187.94 => ( 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_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2)))
% 186.97/187.94 <=> 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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2)),V_e_2)),V_c_2)),V_d_2)) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_le__add__iff2,axiom,
% 186.97/187.94 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] :
% 186.97/187.94 ( class_Rings_Oordered__ring(T_a)
% 186.97/187.94 => ( 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_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2)))
% 186.97/187.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b_2),V_a_2)),V_e_2)),V_d_2))) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_le__add__iff1,axiom,
% 186.97/187.94 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] :
% 186.97/187.94 ( class_Rings_Oordered__ring(T_a)
% 186.97/187.94 => ( 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_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2)))
% 186.97/187.94 <=> 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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2)),V_e_2)),V_c_2)),V_d_2)) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
% 186.97/187.94 ! [V_m,T_a] :
% 186.97/187.94 ( class_Rings_Ocomm__semiring__1(T_a)
% 186.97/187.94 => 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) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
% 186.97/187.94 ! [V_a,V_m,T_a] :
% 186.97/187.94 ( class_Rings_Ocomm__semiring__1(T_a)
% 186.97/187.94 => 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) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
% 186.97/187.94 ! [V_m,V_a,T_a] :
% 186.97/187.94 ( class_Rings_Ocomm__semiring__1(T_a)
% 186.97/187.94 => 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) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_eq__add__iff1,axiom,
% 186.97/187.94 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] :
% 186.97/187.94 ( class_Rings_Oring(T_a)
% 186.97/187.94 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2)
% 186.97/187.94 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2)),V_e_2)),V_c_2) = V_d_2 ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_linorder__neqE__linordered__idom,axiom,
% 186.97/187.94 ! [V_y,V_x,T_a] :
% 186.97/187.94 ( class_Rings_Olinordered__idom(T_a)
% 186.97/187.94 => ( V_x != V_y
% 186.97/187.94 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 186.97/187.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
% 186.97/187.94 ! [V_c,V_a,T_a] :
% 186.97/187.94 ( class_Rings_Ocomm__semiring__1(T_a)
% 186.97/187.94 => 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) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
% 186.97/187.94 ! [V_d,V_c,V_a,T_a] :
% 186.97/187.94 ( class_Rings_Ocomm__semiring__1(T_a)
% 186.97/187.94 => 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)) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
% 186.97/187.94 ! [V_d,V_c,V_a,T_a] :
% 186.97/187.94 ( class_Rings_Ocomm__semiring__1(T_a)
% 186.97/187.94 => 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) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
% 186.97/187.94 ! [V_c,V_b,V_a,T_a] :
% 186.97/187.94 ( class_Rings_Ocomm__semiring__1(T_a)
% 186.97/187.94 => 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)) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
% 186.97/187.94 ! [V_c,V_b,V_a,T_a] :
% 186.97/187.94 ( class_Rings_Ocomm__semiring__1(T_a)
% 186.97/187.94 => 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) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
% 186.97/187.94 ! [V_d,V_c,V_b,V_a,T_a] :
% 186.97/187.94 ( class_Rings_Ocomm__semiring__1(T_a)
% 186.97/187.94 => 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)) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
% 186.97/187.94 ! [V_b,V_a,T_a] :
% 186.97/187.94 ( class_Rings_Ocomm__semiring__1(T_a)
% 186.97/187.94 => 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) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
% 186.97/187.94 ! [V_ry,V_rx,V_lx,T_a] :
% 186.97/187.94 ( class_Rings_Ocomm__semiring__1(T_a)
% 186.97/187.94 => 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)) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
% 186.97/187.94 ! [V_ry,V_rx,V_lx,T_a] :
% 186.97/187.94 ( class_Rings_Ocomm__semiring__1(T_a)
% 186.97/187.94 => 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) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
% 186.97/187.94 ! [V_rx,V_ly,V_lx,T_a] :
% 186.97/187.94 ( class_Rings_Ocomm__semiring__1(T_a)
% 186.97/187.94 => 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)) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
% 186.97/187.94 ! [V_rx,V_ly,V_lx,T_a] :
% 186.97/187.94 ( class_Rings_Ocomm__semiring__1(T_a)
% 186.97/187.94 => 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) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
% 186.97/187.94 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 186.97/187.94 ( class_Rings_Ocomm__semiring__1(T_a)
% 186.97/187.94 => 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))) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
% 186.97/187.94 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 186.97/187.94 ( class_Rings_Ocomm__semiring__1(T_a)
% 186.97/187.94 => 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)) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
% 186.97/187.94 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 186.97/187.94 ( class_Rings_Ocomm__semiring__1(T_a)
% 186.97/187.94 => 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)) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
% 186.97/187.94 ! [V_z,V_y,V_x,T_a] :
% 186.97/187.94 ( class_Rings_Ocomm__semiring__1(T_a)
% 186.97/187.94 => 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)) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_crossproduct__noteq,axiom,
% 186.97/187.94 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
% 186.97/187.94 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 186.97/187.94 => ( ( V_a_2 != V_b_2
% 186.97/187.94 & V_c_2 != V_d_2 )
% 186.97/187.94 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_d_2)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_d_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_c_2)) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_comm__semiring__class_Odistrib,axiom,
% 186.97/187.94 ! [V_c,V_b,V_a,T_a] :
% 186.97/187.94 ( class_Rings_Ocomm__semiring(T_a)
% 186.97/187.94 => 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)) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
% 186.97/187.94 ! [V_c,V_b,V_a,T_a] :
% 186.97/187.94 ( class_Rings_Ocomm__semiring__1(T_a)
% 186.97/187.94 => 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)) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
% 186.97/187.94 ! [V_b,V_m,V_a,T_a] :
% 186.97/187.94 ( class_Rings_Ocomm__semiring__1(T_a)
% 186.97/187.94 => 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) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_combine__common__factor,axiom,
% 186.97/187.94 ! [V_c,V_b,V_e,V_a,T_a] :
% 186.97/187.94 ( class_Rings_Osemiring(T_a)
% 186.97/187.94 => 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) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_crossproduct__eq,axiom,
% 186.97/187.94 ! [V_z_2,V_x_2,V_y_2,V_w_2,T_a] :
% 186.97/187.94 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 186.97/187.94 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_y_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_z_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_z_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_y_2))
% 186.97/187.94 <=> ( V_w_2 = V_x_2
% 186.97/187.94 | V_y_2 = V_z_2 ) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
% 186.97/187.94 ! [V_a,T_a] :
% 186.97/187.94 ( class_Rings_Ocomm__semiring__1(T_a)
% 186.97/187.94 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
% 186.97/187.94 ! [V_a,T_a] :
% 186.97/187.94 ( class_Rings_Ocomm__semiring__1(T_a)
% 186.97/187.94 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_less__add__one,axiom,
% 186.97/187.94 ! [V_a,T_a] :
% 186.97/187.94 ( class_Rings_Olinordered__semidom(T_a)
% 186.97/187.94 => 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)))) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_less__1__mult,axiom,
% 186.97/187.94 ! [V_n,V_m,T_a] :
% 186.97/187.94 ( class_Rings_Olinordered__semidom(T_a)
% 186.97/187.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_m))
% 186.97/187.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_n))
% 186.97/187.94 => 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))) ) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_eq__add__iff2,axiom,
% 186.97/187.94 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] :
% 186.97/187.94 ( class_Rings_Oring(T_a)
% 186.97/187.94 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2)
% 186.97/187.94 <=> V_c_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b_2),V_a_2)),V_e_2)),V_d_2) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_fold__image__Un__one,axiom,
% 186.97/187.94 ! [V_f_2,V_T_2,V_S_2,T_a,T_b] :
% 186.97/187.94 ( class_Groups_Ocomm__monoid__mult(T_b)
% 186.97/187.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 186.97/187.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2))
% 186.97/187.94 => ( ! [B_x] :
% 186.97/187.94 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2)))
% 186.97/187.94 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) )
% 186.97/187.94 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_f_2),c_Groups_Oone__class_Oone(T_b)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_f_2),c_Groups_Oone__class_Oone(T_b)),V_S_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_f_2),c_Groups_Oone__class_Oone(T_b)),V_T_2)) ) ) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_fold1__in,axiom,
% 186.97/187.94 ! [V_A_2,T_a] :
% 186.97/187.94 ( class_Groups_Oab__semigroup__mult(T_a)
% 186.97/187.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.94 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 186.97/187.94 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),hAPP(hAPP(c_Set_Oinsert(T_a),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))
% 186.97/187.94 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),V_A_2)),V_A_2)) ) ) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_diff__add__inverse2,axiom,
% 186.97/187.94 ! [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 ).
% 186.97/187.94
% 186.97/187.94 fof(fact_diff__add__inverse,axiom,
% 186.97/187.94 ! [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 ).
% 186.97/187.94
% 186.97/187.94 fof(fact_diff__diff__left,axiom,
% 186.97/187.94 ! [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)) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_diff__cancel,axiom,
% 186.97/187.94 ! [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) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_diff__cancel2,axiom,
% 186.97/187.94 ! [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) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_diff__add__assoc2,axiom,
% 186.97/187.94 ! [V_i,V_j,V_k] :
% 186.97/187.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 186.97/187.94 => 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) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_add__diff__assoc2,axiom,
% 186.97/187.94 ! [V_i,V_j,V_k] :
% 186.97/187.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 186.97/187.94 => 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) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_nat__less__le,axiom,
% 186.97/187.94 ! [V_n_2,V_m_2] :
% 186.97/187.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 186.97/187.94 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 186.97/187.94 & V_m_2 != V_n_2 ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_le__eq__less__or__eq,axiom,
% 186.97/187.94 ! [V_n_2,V_m_2] :
% 186.97/187.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 186.97/187.94 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 186.97/187.94 | V_m_2 = V_n_2 ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_less__imp__le__nat,axiom,
% 186.97/187.94 ! [V_n,V_m] :
% 186.97/187.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 186.97/187.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_le__neq__implies__less,axiom,
% 186.97/187.94 ! [V_n,V_m] :
% 186.97/187.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 186.97/187.94 => ( V_m != V_n
% 186.97/187.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_less__or__eq__imp__le,axiom,
% 186.97/187.94 ! [V_n,V_m] :
% 186.97/187.94 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 186.97/187.94 | V_m = V_n )
% 186.97/187.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_mult__le__mono,axiom,
% 186.97/187.94 ! [V_l,V_k,V_j,V_i] :
% 186.97/187.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 186.97/187.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l))
% 186.97/187.94 => 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))) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_mult__le__mono2,axiom,
% 186.97/187.94 ! [V_k,V_j,V_i] :
% 186.97/187.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 186.97/187.94 => 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))) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_mult__le__mono1,axiom,
% 186.97/187.94 ! [V_k,V_j,V_i] :
% 186.97/187.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 186.97/187.94 => 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))) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_le__cube,axiom,
% 186.97/187.94 ! [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)))) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_le__square,axiom,
% 186.97/187.94 ! [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))) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_le__refl,axiom,
% 186.97/187.94 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_n)) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_nat__le__linear,axiom,
% 186.97/187.94 ! [V_n,V_m] :
% 186.97/187.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 186.97/187.94 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_eq__imp__le,axiom,
% 186.97/187.94 ! [V_n,V_m] :
% 186.97/187.94 ( V_m = V_n
% 186.97/187.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_le__trans,axiom,
% 186.97/187.94 ! [V_k,V_j,V_i] :
% 186.97/187.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 186.97/187.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_k))
% 186.97/187.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_k)) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_le__antisym,axiom,
% 186.97/187.94 ! [V_n,V_m] :
% 186.97/187.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 186.97/187.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 186.97/187.94 => V_m = V_n ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_nat__add__commute,axiom,
% 186.97/187.94 ! [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) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_nat__add__left__commute,axiom,
% 186.97/187.94 ! [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)) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_nat__add__assoc,axiom,
% 186.97/187.94 ! [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)) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_nat__add__left__cancel,axiom,
% 186.97/187.94 ! [V_n_2,V_m_2,V_k_2] :
% 186.97/187.94 ( 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)
% 186.97/187.94 <=> V_m_2 = V_n_2 ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_nat__add__right__cancel,axiom,
% 186.97/187.94 ! [V_n_2,V_k_2,V_m_2] :
% 186.97/187.94 ( 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)
% 186.97/187.94 <=> V_m_2 = V_n_2 ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_add__leE,axiom,
% 186.97/187.94 ! [V_n,V_k,V_m] :
% 186.97/187.94 ( 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))
% 186.97/187.94 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 186.97/187.94 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_add__leD1,axiom,
% 186.97/187.94 ! [V_n,V_k,V_m] :
% 186.97/187.94 ( 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))
% 186.97/187.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_add__leD2,axiom,
% 186.97/187.94 ! [V_n,V_k,V_m] :
% 186.97/187.94 ( 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))
% 186.97/187.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_add__le__mono,axiom,
% 186.97/187.94 ! [V_l,V_k,V_j,V_i] :
% 186.97/187.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 186.97/187.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l))
% 186.97/187.94 => 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))) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_add__le__mono1,axiom,
% 186.97/187.94 ! [V_k,V_j,V_i] :
% 186.97/187.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 186.97/187.94 => 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))) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_trans__le__add2,axiom,
% 186.97/187.94 ! [V_m,V_j,V_i] :
% 186.97/187.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 186.97/187.94 => 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))) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_trans__le__add1,axiom,
% 186.97/187.94 ! [V_m,V_j,V_i] :
% 186.97/187.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 186.97/187.94 => 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))) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_nat__add__left__cancel__le,axiom,
% 186.97/187.94 ! [V_n_2,V_m_2,V_k_2] :
% 186.97/187.94 ( 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)))
% 186.97/187.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_le__iff__add,axiom,
% 186.97/187.94 ! [V_n_2,V_m_2] :
% 186.97/187.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 186.97/187.94 <=> ? [B_k] : V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_le__add1,axiom,
% 186.97/187.94 ! [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))) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_le__add2,axiom,
% 186.97/187.94 ! [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))) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_add__mult__distrib,axiom,
% 186.97/187.94 ! [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)) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_add__mult__distrib2,axiom,
% 186.97/187.94 ! [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)) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_not__add__less1,axiom,
% 186.97/187.94 ! [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)) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_not__add__less2,axiom,
% 186.97/187.94 ! [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)) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_nat__add__left__cancel__less,axiom,
% 186.97/187.94 ! [V_n_2,V_m_2,V_k_2] :
% 186.97/187.94 ( 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)))
% 186.97/187.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_trans__less__add1,axiom,
% 186.97/187.94 ! [V_m,V_j,V_i] :
% 186.97/187.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 186.97/187.94 => 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))) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_trans__less__add2,axiom,
% 186.97/187.94 ! [V_m,V_j,V_i] :
% 186.97/187.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 186.97/187.94 => 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))) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_add__less__mono1,axiom,
% 186.97/187.94 ! [V_k,V_j,V_i] :
% 186.97/187.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 186.97/187.94 => 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))) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_add__less__mono,axiom,
% 186.97/187.94 ! [V_l,V_k,V_j,V_i] :
% 186.97/187.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 186.97/187.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l))
% 186.97/187.94 => 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))) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_less__add__eq__less,axiom,
% 186.97/187.94 ! [V_n,V_m,V_l,V_k] :
% 186.97/187.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l))
% 186.97/187.94 => ( 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)
% 186.97/187.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_add__lessD1,axiom,
% 186.97/187.94 ! [V_k,V_j,V_i] :
% 186.97/187.94 ( 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))
% 186.97/187.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_k)) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_diff__mult__distrib2,axiom,
% 186.97/187.94 ! [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)) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_diff__mult__distrib,axiom,
% 186.97/187.94 ! [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)) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_less__imp__diff__less,axiom,
% 186.97/187.94 ! [V_n,V_k,V_j] :
% 186.97/187.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k))
% 186.97/187.94 => 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)) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_diff__less__mono2,axiom,
% 186.97/187.94 ! [V_l,V_n,V_m] :
% 186.97/187.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 186.97/187.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_l))
% 186.97/187.94 => 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))) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_less__diff__iff,axiom,
% 186.97/187.94 ! [V_n_2,V_m_2,V_k_2] :
% 186.97/187.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
% 186.97/187.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
% 186.97/187.94 => ( 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)))
% 186.97/187.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_diff__less__mono,axiom,
% 186.97/187.94 ! [V_c,V_b,V_a] :
% 186.97/187.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a),V_b))
% 186.97/187.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_c),V_a))
% 186.97/187.94 => 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))) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_diff__le__self,axiom,
% 186.97/187.94 ! [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)) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_diff__le__mono2,axiom,
% 186.97/187.94 ! [V_l,V_n,V_m] :
% 186.97/187.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 186.97/187.94 => 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))) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_diff__le__mono,axiom,
% 186.97/187.94 ! [V_l,V_n,V_m] :
% 186.97/187.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 186.97/187.94 => 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))) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_diff__diff__cancel,axiom,
% 186.97/187.94 ! [V_n,V_i] :
% 186.97/187.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_n))
% 186.97/187.94 => 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 ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_eq__diff__iff,axiom,
% 186.97/187.94 ! [V_n_2,V_m_2,V_k_2] :
% 186.97/187.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
% 186.97/187.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
% 186.97/187.94 => ( 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)
% 186.97/187.94 <=> V_m_2 = V_n_2 ) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_Nat_Odiff__diff__eq,axiom,
% 186.97/187.94 ! [V_n,V_m,V_k] :
% 186.97/187.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_m))
% 186.97/187.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n))
% 186.97/187.94 => 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) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_le__diff__iff,axiom,
% 186.97/187.94 ! [V_n_2,V_m_2,V_k_2] :
% 186.97/187.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
% 186.97/187.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
% 186.97/187.94 => ( 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)))
% 186.97/187.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_diff__commute,axiom,
% 186.97/187.94 ! [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) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_less__diff__conv,axiom,
% 186.97/187.94 ! [V_k_2,V_j_2,V_i_2] :
% 186.97/187.94 ( 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)))
% 186.97/187.94 <=> 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)) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_add__diff__inverse,axiom,
% 186.97/187.94 ! [V_n,V_m] :
% 186.97/187.94 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 186.97/187.94 => 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 ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_diff__diff__right,axiom,
% 186.97/187.94 ! [V_i,V_j,V_k] :
% 186.97/187.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 186.97/187.94 => 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) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_le__diff__conv,axiom,
% 186.97/187.94 ! [V_i_2,V_k_2,V_j_2] :
% 186.97/187.94 ( 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))
% 186.97/187.94 <=> 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))) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_le__add__diff,axiom,
% 186.97/187.94 ! [V_m,V_n,V_k] :
% 186.97/187.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n))
% 186.97/187.94 => 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))) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_le__add__diff__inverse,axiom,
% 186.97/187.94 ! [V_m,V_n] :
% 186.97/187.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 186.97/187.94 => 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 ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_add__diff__assoc,axiom,
% 186.97/187.94 ! [V_i,V_j,V_k] :
% 186.97/187.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 186.97/187.94 => 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) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_le__diff__conv2,axiom,
% 186.97/187.94 ! [V_i_2,V_j_2,V_k_2] :
% 186.97/187.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_j_2))
% 186.97/187.94 => ( 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)))
% 186.97/187.94 <=> 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)) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_le__add__diff__inverse2,axiom,
% 186.97/187.94 ! [V_m,V_n] :
% 186.97/187.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 186.97/187.94 => 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 ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_le__imp__diff__is__add,axiom,
% 186.97/187.94 ! [V_k_2,V_j_2,V_i_2] :
% 186.97/187.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 186.97/187.94 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2) = V_k_2
% 186.97/187.94 <=> V_j_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_i_2) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_diff__add__assoc,axiom,
% 186.97/187.94 ! [V_i,V_j,V_k] :
% 186.97/187.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 186.97/187.94 => 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)) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_nat__le__add__iff1,axiom,
% 186.97/187.94 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 186.97/187.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
% 186.97/187.94 => ( 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)))
% 186.97/187.94 <=> 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)) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_nat__less__add__iff1,axiom,
% 186.97/187.94 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 186.97/187.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
% 186.97/187.94 => ( 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)))
% 186.97/187.94 <=> 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)) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_nat__diff__add__eq1,axiom,
% 186.97/187.94 ! [V_n,V_m,V_u,V_i,V_j] :
% 186.97/187.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i))
% 186.97/187.94 => 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) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_nat__eq__add__iff1,axiom,
% 186.97/187.94 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 186.97/187.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
% 186.97/187.94 => ( 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)
% 186.97/187.94 <=> 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 ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_nat__le__add__iff2,axiom,
% 186.97/187.94 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 186.97/187.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 186.97/187.94 => ( 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)))
% 186.97/187.94 <=> 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))) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_nat__less__add__iff2,axiom,
% 186.97/187.94 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 186.97/187.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 186.97/187.94 => ( 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)))
% 186.97/187.94 <=> 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))) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_nat__diff__add__eq2,axiom,
% 186.97/187.94 ! [V_n,V_m,V_u,V_j,V_i] :
% 186.97/187.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 186.97/187.94 => 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)) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_nat__eq__add__iff2,axiom,
% 186.97/187.94 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 186.97/187.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 186.97/187.94 => ( 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)
% 186.97/187.94 <=> 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) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_termination__basic__simps_I4_J,axiom,
% 186.97/187.94 ! [V_y,V_z,V_x] :
% 186.97/187.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_z))
% 186.97/187.94 => 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))) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_nat__less__cases,axiom,
% 186.97/187.94 ! [V_P_2,V_n_2,V_m_2] :
% 186.97/187.94 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 186.97/187.94 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
% 186.97/187.94 => ( ( V_m_2 = V_n_2
% 186.97/187.94 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
% 186.97/187.94 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 186.97/187.94 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
% 186.97/187.94 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_less__not__refl3,axiom,
% 186.97/187.94 ! [V_t,V_s] :
% 186.97/187.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s),V_t))
% 186.97/187.94 => V_s != V_t ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_less__not__refl2,axiom,
% 186.97/187.94 ! [V_m,V_n] :
% 186.97/187.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m))
% 186.97/187.94 => V_m != V_n ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_less__irrefl__nat,axiom,
% 186.97/187.94 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_linorder__neqE__nat,axiom,
% 186.97/187.94 ! [V_y,V_x] :
% 186.97/187.94 ( V_x != V_y
% 186.97/187.94 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
% 186.97/187.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y),V_x)) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_nat__neq__iff,axiom,
% 186.97/187.94 ! [V_n_2,V_m_2] :
% 186.97/187.94 ( V_m_2 != V_n_2
% 186.97/187.94 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 186.97/187.94 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_less__not__refl,axiom,
% 186.97/187.94 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_nat__mult__commute,axiom,
% 186.97/187.94 ! [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) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_nat__mult__assoc,axiom,
% 186.97/187.94 ! [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)) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_nat__mult__eq__1__iff,axiom,
% 186.97/187.94 ! [V_n_2,V_m_2] :
% 186.97/187.94 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 186.97/187.94 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 186.97/187.94 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_nat__mult__1__right,axiom,
% 186.97/187.94 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n ).
% 186.97/187.94
% 186.97/187.94 fof(fact_nat__1__eq__mult__iff,axiom,
% 186.97/187.94 ! [V_n_2,V_m_2] :
% 186.97/187.94 ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)
% 186.97/187.94 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 186.97/187.94 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_nat__mult__1,axiom,
% 186.97/187.94 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) = V_n ).
% 186.97/187.94
% 186.97/187.94 fof(fact_termination__basic__simps_I2_J,axiom,
% 186.97/187.94 ! [V_y,V_z,V_x] :
% 186.97/187.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_z))
% 186.97/187.94 => 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))) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_termination__basic__simps_I1_J,axiom,
% 186.97/187.94 ! [V_z,V_y,V_x] :
% 186.97/187.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
% 186.97/187.94 => 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))) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_left__add__mult__distrib,axiom,
% 186.97/187.94 ! [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) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_termination__basic__simps_I5_J,axiom,
% 186.97/187.94 ! [V_y,V_x] :
% 186.97/187.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
% 186.97/187.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y)) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_termination__basic__simps_I3_J,axiom,
% 186.97/187.94 ! [V_z,V_y,V_x] :
% 186.97/187.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y))
% 186.97/187.94 => 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))) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_hom__fold1__commute,axiom,
% 186.97/187.94 ! [V_N_2,V_h_2,T_a] :
% 186.97/187.94 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 186.97/187.94 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_x),B_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
% 186.97/187.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
% 186.97/187.94 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 186.97/187.94 => hAPP(V_h_2,hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),V_N_2)) = hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),hAPP(c_Set_Oimage(T_a,T_a,V_h_2),V_N_2)) ) ) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_card__Diff__singleton,axiom,
% 186.97/187.94 ! [V_x_2,V_A_2,T_a] :
% 186.97/187.94 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.94 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 186.97/187.94 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_card__Diff__singleton__if,axiom,
% 186.97/187.94 ! [V_x_2,V_A_2,T_a] :
% 186.97/187.94 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.94 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 186.97/187.94 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
% 186.97/187.94 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 186.97/187.94 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(T_a),V_A_2) ) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_card_Oremove,axiom,
% 186.97/187.94 ! [V_x_2,V_A_2,T_a] :
% 186.97/187.94 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.94 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 186.97/187.94 => hAPP(c_Finite__Set_Ocard(T_a),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_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_card__Diff2__less,axiom,
% 186.97/187.94 ! [V_y_2,V_x_2,V_A_2,T_a] :
% 186.97/187.94 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.94 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 186.97/187.94 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2))
% 186.97/187.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(T_a),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(T_a),V_A_2))) ) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_card__Diff1__less,axiom,
% 186.97/187.94 ! [V_x_2,V_A_2,T_a] :
% 186.97/187.94 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.94 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 186.97/187.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(T_a),V_A_2))) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_setprod_Oremove,axiom,
% 186.97/187.94 ! [V_g_2,V_x_2,V_A_2,T_a,T_b] :
% 186.97/187.94 ( class_Groups_Ocomm__monoid__mult(T_b)
% 186.97/187.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.94 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 186.97/187.94 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_convex__bound__lt,axiom,
% 186.97/187.94 ! [V_v,V_u,V_y,V_a,V_x,T_a] :
% 186.97/187.94 ( class_Rings_Olinordered__semiring__1__strict(T_a)
% 186.97/187.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
% 186.97/187.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_a))
% 186.97/187.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u))
% 186.97/187.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v))
% 186.97/187.94 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a)
% 186.97/187.94 => 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)) ) ) ) ) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_fold__image__1,axiom,
% 186.97/187.94 ! [V_f_2,V_S_2,T_a,T_b] :
% 186.97/187.94 ( class_Groups_Ocomm__monoid__mult(T_b)
% 186.97/187.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 186.97/187.94 => ( ! [B_x] :
% 186.97/187.94 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2))
% 186.97/187.94 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) )
% 186.97/187.94 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_f_2),c_Groups_Oone__class_Oone(T_b)),V_S_2) = c_Groups_Oone__class_Oone(T_b) ) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_less__zeroE,axiom,
% 186.97/187.94 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_le0,axiom,
% 186.97/187.94 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_card__infinite,axiom,
% 186.97/187.94 ! [V_A_2,T_a] :
% 186.97/187.94 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.94 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_card_Oempty,axiom,
% 186.97/187.94 ! [T_a] : hAPP(c_Finite__Set_Ocard(T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_setprod__zero__iff,axiom,
% 186.97/187.94 ! [V_f_2,V_A_2,T_a,T_b] :
% 186.97/187.94 ( ( class_Rings_Ocomm__semiring__1(T_b)
% 186.97/187.94 & class_Rings_Ono__zero__divisors(T_b) )
% 186.97/187.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.94 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_b)
% 186.97/187.94 <=> ? [B_x] :
% 186.97/187.94 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 186.97/187.94 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_setprod__zero,axiom,
% 186.97/187.94 ! [V_f_2,V_A_2,T_a,T_b] :
% 186.97/187.94 ( class_Rings_Ocomm__semiring__1(T_b)
% 186.97/187.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.94 => ( ? [B_x] :
% 186.97/187.94 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 186.97/187.94 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) )
% 186.97/187.94 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_zero__reorient,axiom,
% 186.97/187.94 ! [V_x_2,T_a] :
% 186.97/187.94 ( class_Groups_Ozero(T_a)
% 186.97/187.94 => ( c_Groups_Ozero__class_Ozero(T_a) = V_x_2
% 186.97/187.94 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_setprod__pos__nat__iff,axiom,
% 186.97/187.94 ! [V_f_2,V_S_2,T_a] :
% 186.97/187.94 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 186.97/187.94 => ( 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_a,tc_Nat_Onat),V_f_2),V_S_2)))
% 186.97/187.94 <=> ! [B_x] :
% 186.97/187.94 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2))
% 186.97/187.94 => 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))) ) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_card__eq__0__iff,axiom,
% 186.97/187.94 ! [V_A_2,T_a] :
% 186.97/187.94 ( hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 186.97/187.94 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 186.97/187.94 | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_card__ge__0__finite,axiom,
% 186.97/187.94 ! [V_A_2,T_a] :
% 186.97/187.94 ( 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_a),V_A_2)))
% 186.97/187.94 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_setprod__eq__1__iff,axiom,
% 186.97/187.94 ! [V_f_2,V_Fa_2,T_a] :
% 186.97/187.94 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_Fa_2))
% 186.97/187.94 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,tc_Nat_Onat),V_f_2),V_Fa_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 186.97/187.94 <=> ! [B_x] :
% 186.97/187.94 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_Fa_2))
% 186.97/187.94 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_card__def,axiom,
% 186.97/187.94 ! [V_A_2,T_a] :
% 186.97/187.94 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.94 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,T_a,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,T_a),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2) )
% 186.97/187.94 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.94 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_card_Oeq__fold__g,axiom,
% 186.97/187.94 ! [V_A_2,T_a] :
% 186.97/187.94 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.94 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,T_a,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,T_a),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_add__0__left,axiom,
% 186.97/187.94 ! [V_a,T_a] :
% 186.97/187.94 ( class_Groups_Omonoid__add(T_a)
% 186.97/187.94 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_add__0,axiom,
% 186.97/187.94 ! [V_a,T_a] :
% 186.97/187.94 ( class_Groups_Ocomm__monoid__add(T_a)
% 186.97/187.94 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_double__zero__sym,axiom,
% 186.97/187.94 ! [V_a_2,T_a] :
% 186.97/187.94 ( class_Groups_Olinordered__ab__group__add(T_a)
% 186.97/187.94 => ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)
% 186.97/187.94 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_add__0__right,axiom,
% 186.97/187.94 ! [V_a,T_a] :
% 186.97/187.94 ( class_Groups_Omonoid__add(T_a)
% 186.97/187.94 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_add_Ocomm__neutral,axiom,
% 186.97/187.94 ! [V_a,T_a] :
% 186.97/187.94 ( class_Groups_Ocomm__monoid__add(T_a)
% 186.97/187.94 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_add__0__iff,axiom,
% 186.97/187.94 ! [V_a_2,V_b_2,T_a] :
% 186.97/187.94 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 186.97/187.94 => ( V_b_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_a_2)
% 186.97/187.94 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 186.97/187.94
% 186.97/187.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
% 186.97/187.94 ! [V_a,T_a] :
% 186.97/187.95 ( class_Rings_Ocomm__semiring__1(T_a)
% 186.97/187.95 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
% 186.97/187.95 ! [V_a,T_a] :
% 186.97/187.95 ( class_Rings_Ocomm__semiring__1(T_a)
% 186.97/187.95 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_divisors__zero,axiom,
% 186.97/187.95 ! [V_b,V_a,T_a] :
% 186.97/187.95 ( class_Rings_Ono__zero__divisors(T_a)
% 186.97/187.95 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a)
% 186.97/187.95 => ( V_a = c_Groups_Ozero__class_Ozero(T_a)
% 186.97/187.95 | V_b = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_no__zero__divisors,axiom,
% 186.97/187.95 ! [V_b,V_a,T_a] :
% 186.97/187.95 ( class_Rings_Ono__zero__divisors(T_a)
% 186.97/187.95 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 186.97/187.95 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 186.97/187.95 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_mult__eq__0__iff,axiom,
% 186.97/187.95 ! [V_b_2,V_a_2,T_a] :
% 186.97/187.95 ( class_Rings_Oring__no__zero__divisors(T_a)
% 186.97/187.95 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a)
% 186.97/187.95 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
% 186.97/187.95 | V_b_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
% 186.97/187.95 ! [V_a,T_a] :
% 186.97/187.95 ( class_Rings_Ocomm__semiring__1(T_a)
% 186.97/187.95 => 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) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_mult__zero__right,axiom,
% 186.97/187.95 ! [V_a,T_a] :
% 186.97/187.95 ( class_Rings_Omult__zero(T_a)
% 186.97/187.95 => 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) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
% 186.97/187.95 ! [V_a,T_a] :
% 186.97/187.95 ( class_Rings_Ocomm__semiring__1(T_a)
% 186.97/187.95 => 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) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_mult__zero__left,axiom,
% 186.97/187.95 ! [V_a,T_a] :
% 186.97/187.95 ( class_Rings_Omult__zero(T_a)
% 186.97/187.95 => 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) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_right__minus__eq,axiom,
% 186.97/187.95 ! [V_b_2,V_a_2,T_a] :
% 186.97/187.95 ( class_Groups_Ogroup__add(T_a)
% 186.97/187.95 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a)
% 186.97/187.95 <=> V_a_2 = V_b_2 ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_eq__iff__diff__eq__0,axiom,
% 186.97/187.95 ! [V_b_2,V_a_2,T_a] :
% 186.97/187.95 ( class_Groups_Oab__group__add(T_a)
% 186.97/187.95 => ( V_a_2 = V_b_2
% 186.97/187.95 <=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_diff__self,axiom,
% 186.97/187.95 ! [V_a,T_a] :
% 186.97/187.95 ( class_Groups_Ogroup__add(T_a)
% 186.97/187.95 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_diff__0__right,axiom,
% 186.97/187.95 ! [V_a,T_a] :
% 186.97/187.95 ( class_Groups_Ogroup__add(T_a)
% 186.97/187.95 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_zero__neq__one,axiom,
% 186.97/187.95 ! [T_a] :
% 186.97/187.95 ( class_Rings_Ozero__neq__one(T_a)
% 186.97/187.95 => c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_one__neq__zero,axiom,
% 186.97/187.95 ! [T_a] :
% 186.97/187.95 ( class_Rings_Ozero__neq__one(T_a)
% 186.97/187.95 => c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_not__less0,axiom,
% 186.97/187.95 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_neq0__conv,axiom,
% 186.97/187.95 ! [V_n_2] :
% 186.97/187.95 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 186.97/187.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_less__nat__zero__code,axiom,
% 186.97/187.95 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_gr__implies__not0,axiom,
% 186.97/187.95 ! [V_n,V_m] :
% 186.97/187.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 186.97/187.95 => V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_gr0I,axiom,
% 186.97/187.95 ! [V_n] :
% 186.97/187.95 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 186.97/187.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_plus__nat_Oadd__0,axiom,
% 186.97/187.95 ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ).
% 186.97/187.95
% 186.97/187.95 fof(fact_Nat_Oadd__0__right,axiom,
% 186.97/187.95 ! [V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 186.97/187.95
% 186.97/187.95 fof(fact_add__is__0,axiom,
% 186.97/187.95 ! [V_n_2,V_m_2] :
% 186.97/187.95 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 186.97/187.95 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 186.97/187.95 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_add__eq__self__zero,axiom,
% 186.97/187.95 ! [V_n,V_m] :
% 186.97/187.95 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_m
% 186.97/187.95 => V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_less__eq__nat_Osimps_I1_J,axiom,
% 186.97/187.95 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_le__0__eq,axiom,
% 186.97/187.95 ! [V_n_2] :
% 186.97/187.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 186.97/187.95 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_setprod__timesf,axiom,
% 186.97/187.95 ! [V_A_2,V_g_2,V_f_2,T_b,T_a] :
% 186.97/187.95 ( class_Groups_Ocomm__monoid__mult(T_a)
% 186.97/187.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),hAPP(hAPP(c_COMBS(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Groups_Otimes__class_Otimes(T_a)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),V_g_2),V_A_2)) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_diffs0__imp__equal,axiom,
% 186.97/187.95 ! [V_n,V_m] :
% 186.97/187.95 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 186.97/187.95 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 186.97/187.95 => V_m = V_n ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_diff__self__eq__0,axiom,
% 186.97/187.95 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_minus__nat_Odiff__0,axiom,
% 186.97/187.95 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 186.97/187.95
% 186.97/187.95 fof(fact_diff__0__eq__0,axiom,
% 186.97/187.95 ! [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) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_nat__mult__eq__cancel__disj,axiom,
% 186.97/187.95 ! [V_n_2,V_m_2,V_k_2] :
% 186.97/187.95 ( 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)
% 186.97/187.95 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 186.97/187.95 | V_m_2 = V_n_2 ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_mult__eq__self__implies__10,axiom,
% 186.97/187.95 ! [V_n,V_m] :
% 186.97/187.95 ( V_m = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)
% 186.97/187.95 => ( V_n = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 186.97/187.95 | V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_mult__cancel2,axiom,
% 186.97/187.95 ! [V_n_2,V_k_2,V_m_2] :
% 186.97/187.95 ( 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)
% 186.97/187.95 <=> ( V_m_2 = V_n_2
% 186.97/187.95 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_mult__cancel1,axiom,
% 186.97/187.95 ! [V_n_2,V_m_2,V_k_2] :
% 186.97/187.95 ( 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)
% 186.97/187.95 <=> ( V_m_2 = V_n_2
% 186.97/187.95 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_mult__is__0,axiom,
% 186.97/187.95 ! [V_n_2,V_m_2] :
% 186.97/187.95 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 186.97/187.95 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 186.97/187.95 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_mult__0__right,axiom,
% 186.97/187.95 ! [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) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_mult__0,axiom,
% 186.97/187.95 ! [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) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_setprod__1,axiom,
% 186.97/187.95 ! [V_A_2,T_b,T_a] :
% 186.97/187.95 ( class_Groups_Ocomm__monoid__mult(T_a)
% 186.97/187.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),hAPP(c_COMBK(T_a,T_b),c_Groups_Oone__class_Oone(T_a))),V_A_2) = c_Groups_Oone__class_Oone(T_a) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_card__gt__0__iff,axiom,
% 186.97/187.95 ! [V_A_2,T_a] :
% 186.97/187.95 ( 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_a),V_A_2)))
% 186.97/187.95 <=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 186.97/187.95 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_card__eq__setsum,axiom,
% 186.97/187.95 ! [V_A_2,T_a] : hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,T_a),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_A_2) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_setsum__0,axiom,
% 186.97/187.95 ! [V_A_2,T_b,T_a] :
% 186.97/187.95 ( class_Groups_Ocomm__monoid__add(T_a)
% 186.97/187.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(c_COMBK(T_a,T_b),c_Groups_Ozero__class_Ozero(T_a))),V_A_2) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_setprod__empty,axiom,
% 186.97/187.95 ! [V_f_2,T_b,T_a] :
% 186.97/187.95 ( class_Groups_Ocomm__monoid__mult(T_a)
% 186.97/187.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(T_a) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_setprod_Oempty,axiom,
% 186.97/187.95 ! [V_g_2,T_b,T_a] :
% 186.97/187.95 ( class_Groups_Ocomm__monoid__mult(T_a)
% 186.97/187.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),V_g_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(T_a) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_setprod__infinite,axiom,
% 186.97/187.95 ! [V_f_2,V_A_2,T_a,T_b] :
% 186.97/187.95 ( class_Groups_Ocomm__monoid__mult(T_b)
% 186.97/187.95 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_A_2) = c_Groups_Oone__class_Oone(T_b) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_setprod_Oinfinite,axiom,
% 186.97/187.95 ! [V_g_2,V_A_2,T_a,T_b] :
% 186.97/187.95 ( class_Groups_Ocomm__monoid__mult(T_b)
% 186.97/187.95 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2) = c_Groups_Oone__class_Oone(T_b) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_setprod_Odistrib,axiom,
% 186.97/187.95 ! [V_h_2,V_g_2,V_A_2,T_a,T_b] :
% 186.97/187.95 ( class_Groups_Ocomm__monoid__mult(T_b)
% 186.97/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_Groups_Otimes__class_Otimes(T_b)),V_g_2)),V_h_2)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_h_2),V_A_2)) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_add__nonpos__nonpos,axiom,
% 186.97/187.95 ! [V_b,V_a,T_a] :
% 186.97/187.95 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 186.97/187.95 => 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))) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_add__increasing2,axiom,
% 186.97/187.95 ! [V_a,V_b,V_c,T_a] :
% 186.97/187.95 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 186.97/187.95 => 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))) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_add__increasing,axiom,
% 186.97/187.95 ! [V_c,V_b,V_a,T_a] :
% 186.97/187.95 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
% 186.97/187.95 => 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))) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_add__nonneg__eq__0__iff,axiom,
% 186.97/187.95 ! [V_y_2,V_x_2,T_a] :
% 186.97/187.95 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x_2))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y_2))
% 186.97/187.95 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x_2),V_y_2) = c_Groups_Ozero__class_Ozero(T_a)
% 186.97/187.95 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 186.97/187.95 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_add__nonneg__nonneg,axiom,
% 186.97/187.95 ! [V_b,V_a,T_a] :
% 186.97/187.95 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 186.97/187.95 => 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))) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom,
% 186.97/187.95 ! [V_a_2,T_a] :
% 186.97/187.95 ( class_Groups_Olinordered__ab__group__add(T_a)
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_a)))
% 186.97/187.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom,
% 186.97/187.95 ! [V_a_2,T_a] :
% 186.97/187.95 ( class_Groups_Olinordered__ab__group__add(T_a)
% 186.97/187.95 => ( 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_2),V_a_2)))
% 186.97/187.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_zero__le__square,axiom,
% 186.97/187.95 ! [V_a,T_a] :
% 186.97/187.95 ( class_Rings_Olinordered__ring(T_a)
% 186.97/187.95 => 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))) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_zero__le__mult__iff,axiom,
% 186.97/187.95 ! [V_b_2,V_a_2,T_a] :
% 186.97/187.95 ( class_Rings_Olinordered__ring__strict(T_a)
% 186.97/187.95 => ( 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_2),V_b_2)))
% 186.97/187.95 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2))
% 186.97/187.95 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) )
% 186.97/187.95 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a)))
% 186.97/187.95 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_mult__le__0__iff,axiom,
% 186.97/187.95 ! [V_b_2,V_a_2,T_a] :
% 186.97/187.95 ( class_Rings_Olinordered__ring__strict(T_a)
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_a)))
% 186.97/187.95 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2))
% 186.97/187.95 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) )
% 186.97/187.95 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a)))
% 186.97/187.95 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_mult__nonneg__nonneg,axiom,
% 186.97/187.95 ! [V_b,V_a,T_a] :
% 186.97/187.95 ( class_Rings_Oordered__cancel__semiring(T_a)
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 186.97/187.95 => 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))) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_mult__nonneg__nonpos,axiom,
% 186.97/187.95 ! [V_b,V_a,T_a] :
% 186.97/187.95 ( class_Rings_Oordered__cancel__semiring(T_a)
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 186.97/187.95 => 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))) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_mult__nonneg__nonpos2,axiom,
% 186.97/187.95 ! [V_b,V_a,T_a] :
% 186.97/187.95 ( class_Rings_Oordered__cancel__semiring(T_a)
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 186.97/187.95 => 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))) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_mult__nonpos__nonneg,axiom,
% 186.97/187.95 ! [V_b,V_a,T_a] :
% 186.97/187.95 ( class_Rings_Oordered__cancel__semiring(T_a)
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 186.97/187.95 => 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))) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_mult__nonpos__nonpos,axiom,
% 186.97/187.95 ! [V_b,V_a,T_a] :
% 186.97/187.95 ( class_Rings_Oordered__ring(T_a)
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 186.97/187.95 => 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))) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_mult__right__mono,axiom,
% 186.97/187.95 ! [V_c,V_b,V_a,T_a] :
% 186.97/187.95 ( class_Rings_Oordered__semiring(T_a)
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 186.97/187.95 => 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))) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_mult__left__mono,axiom,
% 186.97/187.95 ! [V_c,V_b,V_a,T_a] :
% 186.97/187.95 ( class_Rings_Oordered__semiring(T_a)
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 186.97/187.95 => 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))) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_comm__mult__left__mono,axiom,
% 186.97/187.95 ! [V_c,V_b,V_a,T_a] :
% 186.97/187.95 ( class_Rings_Oordered__comm__semiring(T_a)
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 186.97/187.95 => 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))) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_mult__right__mono__neg,axiom,
% 186.97/187.95 ! [V_c,V_a,V_b,T_a] :
% 186.97/187.95 ( class_Rings_Oordered__ring(T_a)
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 186.97/187.95 => 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))) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_mult__left__mono__neg,axiom,
% 186.97/187.95 ! [V_c,V_a,V_b,T_a] :
% 186.97/187.95 ( class_Rings_Oordered__ring(T_a)
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 186.97/187.95 => 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))) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_mult__mono_H,axiom,
% 186.97/187.95 ! [V_d,V_c,V_b,V_a,T_a] :
% 186.97/187.95 ( class_Rings_Oordered__semiring(T_a)
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 186.97/187.95 => 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))) ) ) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_mult__mono,axiom,
% 186.97/187.95 ! [V_d,V_c,V_b,V_a,T_a] :
% 186.97/187.95 ( class_Rings_Oordered__semiring(T_a)
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 186.97/187.95 => 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))) ) ) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_split__mult__pos__le,axiom,
% 186.97/187.95 ! [V_b,V_a,T_a] :
% 186.97/187.95 ( class_Rings_Oordered__ring(T_a)
% 186.97/187.95 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 186.97/187.95 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) )
% 186.97/187.95 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 186.97/187.95 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) )
% 186.97/187.95 => 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))) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_split__mult__neg__le,axiom,
% 186.97/187.95 ! [V_b,V_a,T_a] :
% 186.97/187.95 ( class_Rings_Oordered__cancel__semiring(T_a)
% 186.97/187.95 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 186.97/187.95 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) )
% 186.97/187.95 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 186.97/187.95 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) )
% 186.97/187.95 => 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))) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_add__neg__neg,axiom,
% 186.97/187.95 ! [V_b,V_a,T_a] :
% 186.97/187.95 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 186.97/187.95 => 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))) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_add__pos__pos,axiom,
% 186.97/187.95 ! [V_b,V_a,T_a] :
% 186.97/187.95 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 186.97/187.95 => 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))) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom,
% 186.97/187.95 ! [V_a_2,T_a] :
% 186.97/187.95 ( class_Groups_Olinordered__ab__group__add(T_a)
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_a)))
% 186.97/187.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom,
% 186.97/187.95 ! [V_a_2,T_a] :
% 186.97/187.95 ( class_Groups_Olinordered__ab__group__add(T_a)
% 186.97/187.95 => ( 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_2),V_a_2)))
% 186.97/187.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_pos__add__strict,axiom,
% 186.97/187.95 ! [V_c,V_b,V_a,T_a] :
% 186.97/187.95 ( class_Rings_Olinordered__semidom(T_a)
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
% 186.97/187.95 => 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))) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_not__square__less__zero,axiom,
% 186.97/187.95 ! [V_a,T_a] :
% 186.97/187.95 ( class_Rings_Olinordered__ring(T_a)
% 186.97/187.95 => ~ 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))) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_mult__less__cancel__right__disj,axiom,
% 186.97/187.95 ! [V_b_2,V_c_2,V_a_2,T_a] :
% 186.97/187.95 ( class_Rings_Olinordered__ring__strict(T_a)
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_c_2)))
% 186.97/187.95 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
% 186.97/187.95 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) )
% 186.97/187.95 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a)))
% 186.97/187.95 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_a_2)) ) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_mult__less__cancel__left__disj,axiom,
% 186.97/187.95 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 186.97/187.95 ( class_Rings_Olinordered__ring__strict(T_a)
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2)))
% 186.97/187.95 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
% 186.97/187.95 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) )
% 186.97/187.95 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a)))
% 186.97/187.95 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_a_2)) ) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_mult__less__cancel__left__pos,axiom,
% 186.97/187.95 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 186.97/187.95 ( class_Rings_Olinordered__ring__strict(T_a)
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2)))
% 186.97/187.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_mult__pos__pos,axiom,
% 186.97/187.95 ! [V_b,V_a,T_a] :
% 186.97/187.95 ( class_Rings_Olinordered__semiring__strict(T_a)
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 186.97/187.95 => 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))) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_mult__pos__neg,axiom,
% 186.97/187.95 ! [V_b,V_a,T_a] :
% 186.97/187.95 ( class_Rings_Olinordered__semiring__strict(T_a)
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 186.97/187.95 => 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))) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_mult__pos__neg2,axiom,
% 186.97/187.95 ! [V_b,V_a,T_a] :
% 186.97/187.95 ( class_Rings_Olinordered__semiring__strict(T_a)
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 186.97/187.95 => 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))) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_zero__less__mult__pos,axiom,
% 186.97/187.95 ! [V_b,V_a,T_a] :
% 186.97/187.95 ( class_Rings_Olinordered__semiring__strict(T_a)
% 186.97/187.95 => ( 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)))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 186.97/187.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_zero__less__mult__pos2,axiom,
% 186.97/187.95 ! [V_a,V_b,T_a] :
% 186.97/187.95 ( class_Rings_Olinordered__semiring__strict(T_a)
% 186.97/187.95 => ( 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)))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 186.97/187.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_mult__less__cancel__left__neg,axiom,
% 186.97/187.95 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 186.97/187.95 ( class_Rings_Olinordered__ring__strict(T_a)
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a)))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2)))
% 186.97/187.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_a_2)) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_mult__neg__pos,axiom,
% 186.97/187.95 ! [V_b,V_a,T_a] :
% 186.97/187.95 ( class_Rings_Olinordered__semiring__strict(T_a)
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 186.97/187.95 => 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))) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_mult__neg__neg,axiom,
% 186.97/187.95 ! [V_b,V_a,T_a] :
% 186.97/187.95 ( class_Rings_Olinordered__ring__strict(T_a)
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 186.97/187.95 => 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))) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_mult__strict__right__mono,axiom,
% 186.97/187.95 ! [V_c,V_b,V_a,T_a] :
% 186.97/187.95 ( class_Rings_Olinordered__semiring__strict(T_a)
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 186.97/187.95 => 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))) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_mult__strict__left__mono,axiom,
% 186.97/187.95 ! [V_c,V_b,V_a,T_a] :
% 186.97/187.95 ( class_Rings_Olinordered__semiring__strict(T_a)
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 186.97/187.95 => 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))) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_comm__mult__strict__left__mono,axiom,
% 186.97/187.95 ! [V_c,V_b,V_a,T_a] :
% 186.97/187.95 ( class_Rings_Olinordered__comm__semiring__strict(T_a)
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 186.97/187.95 => 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))) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_mult__strict__right__mono__neg,axiom,
% 186.97/187.95 ! [V_c,V_a,V_b,T_a] :
% 186.97/187.95 ( class_Rings_Olinordered__ring__strict(T_a)
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 186.97/187.95 => 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))) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_mult__strict__left__mono__neg,axiom,
% 186.97/187.95 ! [V_c,V_a,V_b,T_a] :
% 186.97/187.95 ( class_Rings_Olinordered__ring__strict(T_a)
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 186.97/187.95 => 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))) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_le__iff__diff__le__0,axiom,
% 186.97/187.95 ! [V_b_2,V_a_2,T_a] :
% 186.97/187.95 ( class_Groups_Oordered__ab__group__add(T_a)
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2))
% 186.97/187.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_less__iff__diff__less__0,axiom,
% 186.97/187.95 ! [V_b_2,V_a_2,T_a] :
% 186.97/187.95 ( class_Groups_Oordered__ab__group__add(T_a)
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2))
% 186.97/187.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_add__scale__eq__noteq,axiom,
% 186.97/187.95 ! [V_d,V_c,V_b,V_a,V_r,T_a] :
% 186.97/187.95 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 186.97/187.95 => ( V_r != c_Groups_Ozero__class_Ozero(T_a)
% 186.97/187.95 => ( ( V_a = V_b
% 186.97/187.95 & V_c != V_d )
% 186.97/187.95 => 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)) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_not__one__le__zero,axiom,
% 186.97/187.95 ! [T_a] :
% 186.97/187.95 ( class_Rings_Olinordered__semidom(T_a)
% 186.97/187.95 => ~ 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))) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_zero__le__one,axiom,
% 186.97/187.95 ! [T_a] :
% 186.97/187.95 ( class_Rings_Olinordered__semidom(T_a)
% 186.97/187.95 => 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))) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_zero__less__one,axiom,
% 186.97/187.95 ! [T_a] :
% 186.97/187.95 ( class_Rings_Olinordered__semidom(T_a)
% 186.97/187.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_not__one__less__zero,axiom,
% 186.97/187.95 ! [T_a] :
% 186.97/187.95 ( class_Rings_Olinordered__semidom(T_a)
% 186.97/187.95 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_setsum__empty,axiom,
% 186.97/187.95 ! [V_f_2,T_b,T_a] :
% 186.97/187.95 ( class_Groups_Ocomm__monoid__add(T_a)
% 186.97/187.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_setsum_Oempty,axiom,
% 186.97/187.95 ! [V_g_2,T_b,T_a] :
% 186.97/187.95 ( class_Groups_Ocomm__monoid__add(T_a)
% 186.97/187.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_g_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_setsum__infinite,axiom,
% 186.97/187.95 ! [V_f_2,V_A_2,T_a,T_b] :
% 186.97/187.95 ( class_Groups_Ocomm__monoid__add(T_b)
% 186.97/187.95 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_setsum_Oinfinite,axiom,
% 186.97/187.95 ! [V_g_2,V_A_2,T_a,T_b] :
% 186.97/187.95 ( class_Groups_Ocomm__monoid__add(T_b)
% 186.97/187.95 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_add__gr__0,axiom,
% 186.97/187.95 ! [V_n_2,V_m_2] :
% 186.97/187.95 ( 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)))
% 186.97/187.95 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))
% 186.97/187.95 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_zero__less__diff,axiom,
% 186.97/187.95 ! [V_m_2,V_n_2] :
% 186.97/187.95 ( 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)))
% 186.97/187.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_diff__less,axiom,
% 186.97/187.95 ! [V_m,V_n] :
% 186.97/187.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 186.97/187.95 => 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)) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_nat__mult__less__cancel1,axiom,
% 186.97/187.95 ! [V_n_2,V_m_2,V_k_2] :
% 186.97/187.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 186.97/187.95 => ( 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)))
% 186.97/187.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_nat__mult__eq__cancel1,axiom,
% 186.97/187.95 ! [V_n_2,V_m_2,V_k_2] :
% 186.97/187.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 186.97/187.95 => ( 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)
% 186.97/187.95 <=> V_m_2 = V_n_2 ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_nat__0__less__mult__iff,axiom,
% 186.97/187.95 ! [V_n_2,V_m_2] :
% 186.97/187.95 ( 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)))
% 186.97/187.95 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))
% 186.97/187.95 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_mult__less__cancel1,axiom,
% 186.97/187.95 ! [V_n_2,V_m_2,V_k_2] :
% 186.97/187.95 ( 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)))
% 186.97/187.95 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 186.97/187.95 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_mult__less__cancel2,axiom,
% 186.97/187.95 ! [V_n_2,V_k_2,V_m_2] :
% 186.97/187.95 ( 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)))
% 186.97/187.95 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 186.97/187.95 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_mult__less__mono1,axiom,
% 186.97/187.95 ! [V_k,V_j,V_i] :
% 186.97/187.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 186.97/187.95 => 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))) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_mult__less__mono2,axiom,
% 186.97/187.95 ! [V_k,V_j,V_i] :
% 186.97/187.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 186.97/187.95 => 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))) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_diff__add__0,axiom,
% 186.97/187.95 ! [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) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_diff__is__0__eq,axiom,
% 186.97/187.95 ! [V_n_2,V_m_2] :
% 186.97/187.95 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 186.97/187.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_diff__is__0__eq_H,axiom,
% 186.97/187.95 ! [V_n,V_m] :
% 186.97/187.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 186.97/187.95 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_setsum__eq__1__iff,axiom,
% 186.97/187.95 ! [V_f_2,V_A_2,T_a] :
% 186.97/187.95 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.95 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_A_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 186.97/187.95 <=> ? [B_x] :
% 186.97/187.95 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 186.97/187.95 & hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 186.97/187.95 & ! [B_xa] :
% 186.97/187.95 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2))
% 186.97/187.95 => ( B_x != B_xa
% 186.97/187.95 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_setsum__eq__0__iff,axiom,
% 186.97/187.95 ! [V_f_2,V_Fa_2,T_a] :
% 186.97/187.95 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_Fa_2))
% 186.97/187.95 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_Fa_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 186.97/187.95 <=> ! [B_x] :
% 186.97/187.95 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_Fa_2))
% 186.97/187.95 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_card__insert__le,axiom,
% 186.97/187.95 ! [V_x_2,V_A_2,T_a] :
% 186.97/187.95 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)))) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_card__mono,axiom,
% 186.97/187.95 ! [V_A_2,V_B_2,T_a] :
% 186.97/187.95 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 186.97/187.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),V_B_2))) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_card__seteq,axiom,
% 186.97/187.95 ! [V_A_2,V_B_2,T_a] :
% 186.97/187.95 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_B_2)),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)))
% 186.97/187.95 => V_A_2 = V_B_2 ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_card__image__le,axiom,
% 186.97/187.95 ! [V_f_2,T_b,V_A_2,T_a] :
% 186.97/187.95 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))),hAPP(c_Finite__Set_Ocard(T_a),V_A_2))) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_setprod__delta,axiom,
% 186.97/187.95 ! [V_b_2,V_a_2,V_S_2,T_a,T_b] :
% 186.97/187.95 ( class_Groups_Ocomm__monoid__mult(T_b)
% 186.97/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 186.97/187.95 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2))
% 186.97/187.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,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_a),c_If(T_b)),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_b))),V_S_2) = hAPP(V_b_2,V_a_2) )
% 186.97/187.95 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2))
% 186.97/187.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,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_a),c_If(T_b)),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_b))),V_S_2) = c_Groups_Oone__class_Oone(T_b) ) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_setprod__delta_H,axiom,
% 186.97/187.95 ! [V_b_2,V_a_2,V_S_2,T_a,T_b] :
% 186.97/187.95 ( class_Groups_Ocomm__monoid__mult(T_b)
% 186.97/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 186.97/187.95 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2))
% 186.97/187.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,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_a),c_If(T_b)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_b))),V_S_2) = hAPP(V_b_2,V_a_2) )
% 186.97/187.95 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2))
% 186.97/187.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,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_a),c_If(T_b)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_b))),V_S_2) = c_Groups_Oone__class_Oone(T_b) ) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_psubset__card__mono,axiom,
% 186.97/187.95 ! [V_A_2,V_B_2,T_a] :
% 186.97/187.95 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 186.97/187.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),V_B_2))) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_add__pos__nonneg,axiom,
% 186.97/187.95 ! [V_b,V_a,T_a] :
% 186.97/187.95 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 186.97/187.95 => 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))) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_add__nonneg__pos,axiom,
% 186.97/187.95 ! [V_b,V_a,T_a] :
% 186.97/187.95 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 186.97/187.95 => 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))) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_add__strict__increasing,axiom,
% 186.97/187.95 ! [V_c,V_b,V_a,T_a] :
% 186.97/187.95 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
% 186.97/187.95 => 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))) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_add__strict__increasing2,axiom,
% 186.97/187.95 ! [V_c,V_b,V_a,T_a] :
% 186.97/187.95 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
% 186.97/187.95 => 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))) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_add__neg__nonpos,axiom,
% 186.97/187.95 ! [V_b,V_a,T_a] :
% 186.97/187.95 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 186.97/187.95 => 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))) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_add__nonpos__neg,axiom,
% 186.97/187.95 ! [V_b,V_a,T_a] :
% 186.97/187.95 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 186.97/187.95 => 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))) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_mult__le__cancel__left__pos,axiom,
% 186.97/187.95 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 186.97/187.95 ( class_Rings_Olinordered__ring__strict(T_a)
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2)))
% 186.97/187.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_mult__le__cancel__left__neg,axiom,
% 186.97/187.95 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 186.97/187.95 ( class_Rings_Olinordered__ring__strict(T_a)
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a)))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2)))
% 186.97/187.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_a_2)) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_mult__strict__mono,axiom,
% 186.97/187.95 ! [V_d,V_c,V_b,V_a,T_a] :
% 186.97/187.95 ( class_Rings_Olinordered__semiring__strict(T_a)
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 186.97/187.95 => 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))) ) ) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_mult__strict__mono_H,axiom,
% 186.97/187.95 ! [V_d,V_c,V_b,V_a,T_a] :
% 186.97/187.95 ( class_Rings_Olinordered__semiring__strict(T_a)
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 186.97/187.95 => 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))) ) ) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_mult__less__le__imp__less,axiom,
% 186.97/187.95 ! [V_d,V_c,V_b,V_a,T_a] :
% 186.97/187.95 ( class_Rings_Olinordered__semiring__strict(T_a)
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 186.97/187.95 => 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))) ) ) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_mult__le__less__imp__less,axiom,
% 186.97/187.95 ! [V_d,V_c,V_b,V_a,T_a] :
% 186.97/187.95 ( class_Rings_Olinordered__semiring__strict(T_a)
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 186.97/187.95 => 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))) ) ) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_mult__right__less__imp__less,axiom,
% 186.97/187.95 ! [V_b,V_c,V_a,T_a] :
% 186.97/187.95 ( class_Rings_Olinordered__semiring(T_a)
% 186.97/187.95 => ( 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)))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 186.97/187.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_mult__less__imp__less__right,axiom,
% 186.97/187.95 ! [V_b,V_c,V_a,T_a] :
% 186.97/187.95 ( class_Rings_Olinordered__semiring__strict(T_a)
% 186.97/187.95 => ( 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)))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 186.97/187.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_mult__left__less__imp__less,axiom,
% 186.97/187.95 ! [V_b,V_a,V_c,T_a] :
% 186.97/187.95 ( class_Rings_Olinordered__semiring(T_a)
% 186.97/187.95 => ( 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)))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 186.97/187.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_mult__less__imp__less__left,axiom,
% 186.97/187.95 ! [V_b,V_a,V_c,T_a] :
% 186.97/187.95 ( class_Rings_Olinordered__semiring__strict(T_a)
% 186.97/187.95 => ( 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)))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 186.97/187.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_mult__right__le__imp__le,axiom,
% 186.97/187.95 ! [V_b,V_c,V_a,T_a] :
% 186.97/187.95 ( class_Rings_Olinordered__semiring__strict(T_a)
% 186.97/187.95 => ( 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)))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 186.97/187.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_mult__left__le__imp__le,axiom,
% 186.97/187.95 ! [V_b,V_a,V_c,T_a] :
% 186.97/187.95 ( class_Rings_Olinordered__semiring__strict(T_a)
% 186.97/187.95 => ( 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)))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 186.97/187.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_mult__right__le__one__le,axiom,
% 186.97/187.95 ! [V_y,V_x,T_a] :
% 186.97/187.95 ( class_Rings_Olinordered__idom(T_a)
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a)))
% 186.97/187.95 => 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)) ) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_mult__left__le__one__le,axiom,
% 186.97/187.95 ! [V_y,V_x,T_a] :
% 186.97/187.95 ( class_Rings_Olinordered__idom(T_a)
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a)))
% 186.97/187.95 => 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)) ) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_zero__less__two,axiom,
% 186.97/187.95 ! [T_a] :
% 186.97/187.95 ( class_Rings_Olinordered__semidom(T_a)
% 186.97/187.95 => 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)))) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_nat__diff__split__asm,axiom,
% 186.97/187.95 ! [V_b_2,V_a_2,V_P_2] :
% 186.97/187.95 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))
% 186.97/187.95 <=> ~ ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 186.97/187.95 & ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 186.97/187.95 | ? [B_d] :
% 186.97/187.95 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d)
% 186.97/187.95 & ~ hBOOL(hAPP(V_P_2,B_d)) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_nat__diff__split,axiom,
% 186.97/187.95 ! [V_b_2,V_a_2,V_P_2] :
% 186.97/187.95 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))
% 186.97/187.95 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 186.97/187.95 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 186.97/187.95 & ! [B_d] :
% 186.97/187.95 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d)
% 186.97/187.95 => hBOOL(hAPP(V_P_2,B_d)) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_mult__le__cancel1,axiom,
% 186.97/187.95 ! [V_n_2,V_m_2,V_k_2] :
% 186.97/187.95 ( 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)))
% 186.97/187.95 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 186.97/187.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_mult__le__cancel2,axiom,
% 186.97/187.95 ! [V_n_2,V_k_2,V_m_2] :
% 186.97/187.95 ( 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)))
% 186.97/187.95 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 186.97/187.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_nat__mult__le__cancel1,axiom,
% 186.97/187.95 ! [V_n_2,V_m_2,V_k_2] :
% 186.97/187.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 186.97/187.95 => ( 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)))
% 186.97/187.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_setprod__insert,axiom,
% 186.97/187.95 ! [V_f_2,V_a_2,V_A_2,T_a,T_b] :
% 186.97/187.95 ( class_Groups_Ocomm__monoid__mult(T_b)
% 186.97/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.95 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 186.97/187.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_A_2)) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_setprod_Oinsert,axiom,
% 186.97/187.95 ! [V_g_2,V_x_2,V_A_2,T_a,T_b] :
% 186.97/187.95 ( class_Groups_Ocomm__monoid__mult(T_b)
% 186.97/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.95 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 186.97/187.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2)) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_setprod_Ounion__inter,axiom,
% 186.97/187.95 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] :
% 186.97/187.95 ( class_Groups_Ocomm__monoid__mult(T_b)
% 186.97/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 186.97/187.95 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_B_2)) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_setprod__Un__Int,axiom,
% 186.97/187.95 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] :
% 186.97/187.95 ( class_Groups_Ocomm__monoid__mult(T_b)
% 186.97/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 186.97/187.95 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_B_2)) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_setsum__delta,axiom,
% 186.97/187.95 ! [V_b_2,V_a_2,V_S_2,T_a,T_b] :
% 186.97/187.95 ( class_Groups_Ocomm__monoid__add(T_b)
% 186.97/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 186.97/187.95 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2))
% 186.97/187.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,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_a),c_If(T_b)),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))),V_S_2) = hAPP(V_b_2,V_a_2) )
% 186.97/187.95 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2))
% 186.97/187.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,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_a),c_If(T_b)),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))),V_S_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_setsum__delta_H,axiom,
% 186.97/187.95 ! [V_b_2,V_a_2,V_S_2,T_a,T_b] :
% 186.97/187.95 ( class_Groups_Ocomm__monoid__add(T_b)
% 186.97/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 186.97/187.95 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2))
% 186.97/187.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,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_a),c_If(T_b)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))),V_S_2) = hAPP(V_b_2,V_a_2) )
% 186.97/187.95 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2))
% 186.97/187.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,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_a),c_If(T_b)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))),V_S_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_setprod_OF__eq,axiom,
% 186.97/187.95 ! [V_g_2,V_A_2,T_a,T_b] :
% 186.97/187.95 ( class_Groups_Ocomm__monoid__mult(T_b)
% 186.97/187.95 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),c_Groups_Oone__class_Oone(T_b)),V_A_2) )
% 186.97/187.95 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2) = c_Groups_Oone__class_Oone(T_b) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_setprod_Oeq__fold,axiom,
% 186.97/187.95 ! [V_g_2,V_A_2,T_a,T_b] :
% 186.97/187.95 ( class_Groups_Ocomm__monoid__mult(T_b)
% 186.97/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),c_Groups_Oone__class_Oone(T_b)),V_A_2) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_card_Oinsert,axiom,
% 186.97/187.95 ! [V_x_2,V_A_2,T_a] :
% 186.97/187.95 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.95 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 186.97/187.95 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),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_a),V_A_2)) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_card__Un__Int,axiom,
% 186.97/187.95 ! [V_B_2,V_A_2,T_a] :
% 186.97/187.95 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 186.97/187.95 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_card_Ounion__inter,axiom,
% 186.97/187.95 ! [V_B_2,V_A_2,T_a] :
% 186.97/187.95 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 186.97/187.95 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,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_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),V_B_2)) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_card__Diff__subset,axiom,
% 186.97/187.95 ! [V_A_2,V_B_2,T_a] :
% 186.97/187.95 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 186.97/187.95 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,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_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),V_B_2)) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_card__Diff__subset__Int,axiom,
% 186.97/187.95 ! [V_B_2,V_A_2,T_a] :
% 186.97/187.95 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
% 186.97/187.95 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,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_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_diff__card__le__card__Diff,axiom,
% 186.97/187.95 ! [V_A_2,V_B_2,T_a] :
% 186.97/187.95 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 186.97/187.95 => 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_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),V_B_2))),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_card__psubset,axiom,
% 186.97/187.95 ! [V_A_2,V_B_2,T_a] :
% 186.97/187.95 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),V_B_2)))
% 186.97/187.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_convex__bound__le,axiom,
% 186.97/187.95 ! [V_v,V_u,V_y,V_a,V_x,T_a] :
% 186.97/187.95 ( class_Rings_Olinordered__semiring__1(T_a)
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_a))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v))
% 186.97/187.95 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a)
% 186.97/187.95 => 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)) ) ) ) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_setprod_Oinsert__remove,axiom,
% 186.97/187.95 ! [V_x_2,V_g_2,V_A_2,T_a,T_b] :
% 186.97/187.95 ( class_Groups_Ocomm__monoid__mult(T_b)
% 186.97/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_setprod__Un__disjoint,axiom,
% 186.97/187.95 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] :
% 186.97/187.95 ( class_Groups_Ocomm__monoid__mult(T_b)
% 186.97/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 186.97/187.95 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 186.97/187.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_B_2)) ) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_setprod_Ounion__disjoint,axiom,
% 186.97/187.95 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] :
% 186.97/187.95 ( class_Groups_Ocomm__monoid__mult(T_b)
% 186.97/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 186.97/187.95 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 186.97/187.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_B_2)) ) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_setsum_OF__eq,axiom,
% 186.97/187.95 ! [V_g_2,V_A_2,T_a,T_b] :
% 186.97/187.95 ( class_Groups_Ocomm__monoid__add(T_b)
% 186.97/187.95 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Oplus__class_Oplus(T_b)),V_g_2),c_Groups_Ozero__class_Ozero(T_b)),V_A_2) )
% 186.97/187.95 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_setsum_Oeq__fold,axiom,
% 186.97/187.95 ! [V_g_2,V_A_2,T_a,T_b] :
% 186.97/187.95 ( class_Groups_Ocomm__monoid__add(T_b)
% 186.97/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Oplus__class_Oplus(T_b)),V_g_2),c_Groups_Ozero__class_Ozero(T_b)),V_A_2) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_setsum__restrict__set,axiom,
% 186.97/187.95 ! [V_B_2,V_f_2,V_A_2,T_a,T_b] :
% 186.97/187.95 ( class_Groups_Ocomm__monoid__add(T_b)
% 186.97/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,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_a),c_If(T_b)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))),V_f_2)),c_Groups_Ozero__class_Ozero(T_b))),V_A_2) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_card__Diff__insert,axiom,
% 186.97/187.95 ! [V_B_2,V_a_2,V_A_2,T_a] :
% 186.97/187.95 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 186.97/187.95 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_B_2))
% 186.97/187.95 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_card_Oinsert__remove,axiom,
% 186.97/187.95 ! [V_x_2,V_A_2,T_a] :
% 186.97/187.95 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.95 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),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_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_card__Un__disjoint,axiom,
% 186.97/187.95 ! [V_B_2,V_A_2,T_a] :
% 186.97/187.95 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 186.97/187.95 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 186.97/187.95 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,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_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),V_B_2)) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_card__Diff1__le,axiom,
% 186.97/187.95 ! [V_x_2,V_A_2,T_a] :
% 186.97/187.95 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(T_a),V_A_2))) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_mult__eq__if,axiom,
% 186.97/187.95 ! [V_n,V_m] :
% 186.97/187.95 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 186.97/187.95 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 186.97/187.95 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 186.97/187.95 => 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)) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_not__sum__squares__lt__zero,axiom,
% 186.97/187.95 ! [V_y,V_x,T_a] :
% 186.97/187.95 ( class_Rings_Olinordered__ring(T_a)
% 186.97/187.95 => ~ 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))) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_sum__squares__gt__zero__iff,axiom,
% 186.97/187.95 ! [V_y_2,V_x_2,T_a] :
% 186.97/187.95 ( class_Rings_Olinordered__ring__strict(T_a)
% 186.97/187.95 => ( 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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2))))
% 186.97/187.95 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_a)
% 186.97/187.95 | V_y_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_sum__squares__ge__zero,axiom,
% 186.97/187.95 ! [V_y,V_x,T_a] :
% 186.97/187.95 ( class_Rings_Olinordered__ring(T_a)
% 186.97/187.95 => 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)))) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_sum__squares__le__zero__iff,axiom,
% 186.97/187.95 ! [V_y_2,V_x_2,T_a] :
% 186.97/187.95 ( class_Rings_Olinordered__ring__strict(T_a)
% 186.97/187.95 => ( 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_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2))),c_Groups_Ozero__class_Ozero(T_a)))
% 186.97/187.95 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 186.97/187.95 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_sum__squares__eq__zero__iff,axiom,
% 186.97/187.95 ! [V_y_2,V_x_2,T_a] :
% 186.97/187.95 ( class_Rings_Olinordered__ring__strict(T_a)
% 186.97/187.95 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)) = c_Groups_Ozero__class_Ozero(T_a)
% 186.97/187.95 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 186.97/187.95 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_even__less__0__iff,axiom,
% 186.97/187.95 ! [V_a_2,T_a] :
% 186.97/187.95 ( class_Rings_Olinordered__idom(T_a)
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_a)))
% 186.97/187.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_setsum__mono2,axiom,
% 186.97/187.95 ! [V_f_2,V_A_2,V_B_2,T_a,T_b] :
% 186.97/187.95 ( class_Groups_Oordered__comm__monoid__add(T_b)
% 186.97/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 186.97/187.95 => ( ! [B_b] :
% 186.97/187.95 ( hBOOL(hAPP(hAPP(c_member(T_a),B_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)))
% 186.97/187.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_b))) )
% 186.97/187.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_B_2))) ) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_triple_Osize_I1_J,axiom,
% 186.97/187.95 ! [V_fun2_2,V_com_2,V_fun1_2,V_fa_2,T_a] : c_Hoare__Mirabelle_Otriple_Otriple__size(T_a,V_fa_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_fun1_2),V_com_2),V_fun2_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_bot__nat__def,axiom,
% 186.97/187.95 c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_double__eq__0__iff,axiom,
% 186.97/187.95 ! [V_a_2,T_a] :
% 186.97/187.95 ( class_Groups_Olinordered__ab__group__add(T_a)
% 186.97/187.95 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
% 186.97/187.95 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_triple_Osize_I2_J,axiom,
% 186.97/187.95 ! [V_fun2_2,V_com_2,V_fun1_2,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_fun1_2),V_com_2),V_fun2_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_card_Ounion__inter__neutral,axiom,
% 186.97/187.95 ! [V_B_2,V_A_2,T_a] :
% 186.97/187.95 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 186.97/187.95 => ( ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
% 186.97/187.95 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 186.97/187.95 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,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_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),V_B_2)) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_setprod__Un__one,axiom,
% 186.97/187.95 ! [V_f_2,V_T_2,V_S_2,T_a,T_b] :
% 186.97/187.95 ( class_Groups_Ocomm__monoid__mult(T_b)
% 186.97/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 186.97/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2))
% 186.97/187.95 => ( ! [B_x] :
% 186.97/187.95 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2)))
% 186.97/187.95 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) )
% 186.97/187.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_S_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_T_2)) ) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_setprod_Ounion__inter__neutral,axiom,
% 186.97/187.95 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] :
% 186.97/187.95 ( class_Groups_Ocomm__monoid__mult(T_b)
% 186.97/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 186.97/187.95 => ( ! [B_x] :
% 186.97/187.95 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
% 186.97/187.95 => hAPP(V_g_2,B_x) = c_Groups_Oone__class_Oone(T_b) )
% 186.97/187.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_B_2)) ) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_setsum__Un__zero,axiom,
% 186.97/187.95 ! [V_f_2,V_T_2,V_S_2,T_a,T_b] :
% 186.97/187.95 ( class_Groups_Ocomm__monoid__add(T_b)
% 186.97/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 186.97/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2))
% 186.97/187.95 => ( ! [B_x] :
% 186.97/187.95 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2)))
% 186.97/187.95 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) )
% 186.97/187.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_S_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_T_2)) ) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_setsum_Ounion__inter__neutral,axiom,
% 186.97/187.95 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] :
% 186.97/187.95 ( class_Groups_Ocomm__monoid__add(T_b)
% 186.97/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 186.97/187.95 => ( ! [B_x] :
% 186.97/187.95 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
% 186.97/187.95 => hAPP(V_g_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) )
% 186.97/187.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_B_2)) ) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_setsum__mono3,axiom,
% 186.97/187.95 ! [V_f_2,V_A_2,V_B_2,T_a,T_b] :
% 186.97/187.95 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 186.97/187.95 & class_Groups_Oordered__ab__semigroup__add(T_b) )
% 186.97/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 186.97/187.95 => ( ! [B_x] :
% 186.97/187.95 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)))
% 186.97/187.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_x))) )
% 186.97/187.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_B_2))) ) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_setprod__gen__delta,axiom,
% 186.97/187.95 ! [V_c_2,V_b_2,V_a_2,V_S_2,T_a,T_b] :
% 186.97/187.95 ( class_Groups_Ocomm__monoid__mult(T_b)
% 186.97/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 186.97/187.95 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2))
% 186.97/187.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,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_a),c_If(T_b)),hAPP(hAPP(c_COMBC(T_a,T_a,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_b),hAPP(V_b_2,V_a_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_S_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
% 186.97/187.95 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2))
% 186.97/187.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,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_a),c_If(T_b)),hAPP(hAPP(c_COMBC(T_a,T_a,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_b),V_c_2),hAPP(c_Finite__Set_Ocard(T_a),V_S_2)) ) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom,
% 186.97/187.95 ! [V_q,V_y,V_x,T_a] :
% 186.97/187.95 ( class_Rings_Ocomm__semiring__1(T_a)
% 186.97/187.95 => 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)) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_zpower__zadd__distrib,axiom,
% 186.97/187.95 ! [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)) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom,
% 186.97/187.95 ! [V_q,V_p,V_x,T_a] :
% 186.97/187.95 ( class_Rings_Ocomm__semiring__1(T_a)
% 186.97/187.95 => 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)) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_zpower__zpower,axiom,
% 186.97/187.95 ! [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)) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
% 186.97/187.95 ! [V_x,T_a] :
% 186.97/187.95 ( class_Rings_Ocomm__semiring__1(T_a)
% 186.97/187.95 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_x ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom,
% 186.97/187.95 ! [V_x,T_a] :
% 186.97/187.95 ( class_Rings_Ocomm__semiring__1(T_a)
% 186.97/187.95 => 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) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom,
% 186.97/187.95 ! [V_q,V_p,V_x,T_a] :
% 186.97/187.95 ( class_Rings_Ocomm__semiring__1(T_a)
% 186.97/187.95 => 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)) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_setprod__constant,axiom,
% 186.97/187.95 ! [V_y_2,V_A_2,T_a,T_b] :
% 186.97/187.95 ( class_Groups_Ocomm__monoid__mult(T_b)
% 186.97/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(c_COMBK(T_b,T_a),V_y_2)),V_A_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_y_2),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_power__eq__if,axiom,
% 186.97/187.95 ! [V_p,V_m] :
% 186.97/187.95 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 186.97/187.95 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
% 186.97/187.95 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 186.97/187.95 => 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)))) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_power__strict__mono,axiom,
% 186.97/187.95 ! [V_n,V_b,V_a,T_a] :
% 186.97/187.95 ( class_Rings_Olinordered__semidom(T_a)
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 186.97/187.95 => 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))) ) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_one__less__power,axiom,
% 186.97/187.95 ! [V_n,V_a,T_a] :
% 186.97/187.95 ( class_Rings_Olinordered__semidom(T_a)
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 186.97/187.95 => 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))) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_power__increasing__iff,axiom,
% 186.97/187.95 ! [V_y_2,V_x_2,V_b_2,T_a] :
% 186.97/187.95 ( class_Rings_Olinordered__semidom(T_a)
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_b_2))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_y_2)))
% 186.97/187.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_power__le__imp__le__exp,axiom,
% 186.97/187.95 ! [V_n,V_m,V_a,T_a] :
% 186.97/187.95 ( class_Rings_Olinordered__semidom(T_a)
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 186.97/187.95 => ( 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)))
% 186.97/187.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_power__decreasing,axiom,
% 186.97/187.95 ! [V_a,V_N,V_n,T_a] :
% 186.97/187.95 ( class_Rings_Olinordered__semidom(T_a)
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 186.97/187.95 => 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))) ) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_power__strict__decreasing,axiom,
% 186.97/187.95 ! [V_a,V_N,V_n,T_a] :
% 186.97/187.95 ( class_Rings_Olinordered__semidom(T_a)
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 186.97/187.95 => 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))) ) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_power__eq__imp__eq__base,axiom,
% 186.97/187.95 ! [V_b,V_n,V_a,T_a] :
% 186.97/187.95 ( class_Rings_Olinordered__semidom(T_a)
% 186.97/187.95 => ( 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)
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 186.97/187.95 => V_a = V_b ) ) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_power__Suc__less,axiom,
% 186.97/187.95 ! [V_n,V_a,T_a] :
% 186.97/187.95 ( class_Rings_Olinordered__semidom(T_a)
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 186.97/187.95 => 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))) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_zdiff__zmult__distrib2,axiom,
% 186.97/187.95 ! [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)) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_zdiff__zmult__distrib,axiom,
% 186.97/187.95 ! [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)) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_zmult__assoc,axiom,
% 186.97/187.95 ! [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)) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_zmult__commute,axiom,
% 186.97/187.95 ! [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) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_zadd__zmult__distrib,axiom,
% 186.97/187.95 ! [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)) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_zadd__zmult__distrib2,axiom,
% 186.97/187.95 ! [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)) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_zmult__zless__mono2,axiom,
% 186.97/187.95 ! [V_k,V_j,V_i] :
% 186.97/187.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 186.97/187.95 => 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))) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_zmult__1__right,axiom,
% 186.97/187.95 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint)) = V_z ).
% 186.97/187.95
% 186.97/187.95 fof(fact_zmult__1,axiom,
% 186.97/187.95 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) = V_z ).
% 186.97/187.95
% 186.97/187.95 fof(fact_pos__zmult__eq__1__iff,axiom,
% 186.97/187.95 ! [V_n_2,V_m_2] :
% 186.97/187.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m_2))
% 186.97/187.95 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 186.97/187.95 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 186.97/187.95 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_field__power__not__zero,axiom,
% 186.97/187.95 ! [V_n,V_a,T_a] :
% 186.97/187.95 ( class_Rings_Oring__1__no__zero__divisors(T_a)
% 186.97/187.95 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 186.97/187.95 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_nat__zero__less__power__iff,axiom,
% 186.97/187.95 ! [V_n_2,V_x_2] :
% 186.97/187.95 ( 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)))
% 186.97/187.95 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x_2))
% 186.97/187.95 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_nat__power__less__imp__less,axiom,
% 186.97/187.95 ! [V_n,V_m,V_i] :
% 186.97/187.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i))
% 186.97/187.95 => ( 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)))
% 186.97/187.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_power__commutes,axiom,
% 186.97/187.95 ! [V_n,V_a,T_a] :
% 186.97/187.95 ( class_Groups_Omonoid__mult(T_a)
% 186.97/187.95 => 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)) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_power__mult__distrib,axiom,
% 186.97/187.95 ! [V_n,V_b,V_a,T_a] :
% 186.97/187.95 ( class_Groups_Ocomm__monoid__mult(T_a)
% 186.97/187.95 => 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)) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_power__one,axiom,
% 186.97/187.95 ! [V_n,T_a] :
% 186.97/187.95 ( class_Groups_Omonoid__mult(T_a)
% 186.97/187.95 => 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) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_power__mult,axiom,
% 186.97/187.95 ! [V_n,V_m,V_a,T_a] :
% 186.97/187.95 ( class_Groups_Omonoid__mult(T_a)
% 186.97/187.95 => 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) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_power__one__right,axiom,
% 186.97/187.95 ! [V_a,T_a] :
% 186.97/187.95 ( class_Groups_Omonoid__mult(T_a)
% 186.97/187.95 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_a ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_zero__le__power,axiom,
% 186.97/187.95 ! [V_n,V_a,T_a] :
% 186.97/187.95 ( class_Rings_Olinordered__semidom(T_a)
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 186.97/187.95 => 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))) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_power__mono,axiom,
% 186.97/187.95 ! [V_n,V_b,V_a,T_a] :
% 186.97/187.95 ( class_Rings_Olinordered__semidom(T_a)
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 186.97/187.95 => 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))) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_zero__less__power,axiom,
% 186.97/187.95 ! [V_n,V_a,T_a] :
% 186.97/187.95 ( class_Rings_Olinordered__semidom(T_a)
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 186.97/187.95 => 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))) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_power__eq__0__iff,axiom,
% 186.97/187.95 ! [V_n_2,V_a_2,T_a] :
% 186.97/187.95 ( ( class_Power_Opower(T_a)
% 186.97/187.95 & class_Rings_Omult__zero(T_a)
% 186.97/187.95 & class_Rings_Ono__zero__divisors(T_a)
% 186.97/187.95 & class_Rings_Ozero__neq__one(T_a) )
% 186.97/187.95 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a)
% 186.97/187.95 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
% 186.97/187.95 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_one__le__power,axiom,
% 186.97/187.95 ! [V_n,V_a,T_a] :
% 186.97/187.95 ( class_Rings_Olinordered__semidom(T_a)
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 186.97/187.95 => 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))) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_power__inject__exp,axiom,
% 186.97/187.95 ! [V_n_2,V_m_2,V_a_2,T_a] :
% 186.97/187.95 ( class_Rings_Olinordered__semidom(T_a)
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a_2))
% 186.97/187.95 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_m_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2)
% 186.97/187.95 <=> V_m_2 = V_n_2 ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_power__0,axiom,
% 186.97/187.95 ! [V_a,T_a] :
% 186.97/187.95 ( class_Power_Opower(T_a)
% 186.97/187.95 => 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) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_power__add,axiom,
% 186.97/187.95 ! [V_n,V_m,V_a,T_a] :
% 186.97/187.95 ( class_Groups_Omonoid__mult(T_a)
% 186.97/187.95 => 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)) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_power__less__imp__less__base,axiom,
% 186.97/187.95 ! [V_b,V_n,V_a,T_a] :
% 186.97/187.95 ( class_Rings_Olinordered__semidom(T_a)
% 186.97/187.95 => ( 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)))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 186.97/187.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_power__less__power__Suc,axiom,
% 186.97/187.95 ! [V_n,V_a,T_a] :
% 186.97/187.95 ( class_Rings_Olinordered__semidom(T_a)
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 186.97/187.95 => 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)))) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_power__gt1__lemma,axiom,
% 186.97/187.95 ! [V_n,V_a,T_a] :
% 186.97/187.95 ( class_Rings_Olinordered__semidom(T_a)
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 186.97/187.95 => 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)))) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_power__0__left,axiom,
% 186.97/187.95 ! [V_n,T_a] :
% 186.97/187.95 ( ( class_Power_Opower(T_a)
% 186.97/187.95 & class_Rings_Osemiring__0(T_a) )
% 186.97/187.95 => ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 186.97/187.95 => 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) )
% 186.97/187.95 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 186.97/187.95 => 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) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_power__strict__increasing__iff,axiom,
% 186.97/187.95 ! [V_y_2,V_x_2,V_b_2,T_a] :
% 186.97/187.95 ( class_Rings_Olinordered__semidom(T_a)
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_b_2))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_y_2)))
% 186.97/187.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_power__less__imp__less__exp,axiom,
% 186.97/187.95 ! [V_n,V_m,V_a,T_a] :
% 186.97/187.95 ( class_Rings_Olinordered__semidom(T_a)
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 186.97/187.95 => ( 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)))
% 186.97/187.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_power__strict__increasing,axiom,
% 186.97/187.95 ! [V_a,V_N,V_n,T_a] :
% 186.97/187.95 ( class_Rings_Olinordered__semidom(T_a)
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 186.97/187.95 => 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))) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_power__increasing,axiom,
% 186.97/187.95 ! [V_a,V_N,V_n,T_a] :
% 186.97/187.95 ( class_Rings_Olinordered__semidom(T_a)
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 186.97/187.95 => 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))) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_power__power__power,axiom,
% 186.97/187.95 ! [T_a] :
% 186.97/187.95 ( class_Power_Opower(T_a)
% 186.97/187.95 => c_Power_Opower__class_Opower(T_a) = c_Power_Opower_Opower(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Otimes__class_Otimes(T_a)) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_Ints__odd__less__0,axiom,
% 186.97/187.95 ! [V_a_2,T_a] :
% 186.97/187.95 ( class_Rings_Olinordered__idom(T_a)
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a)))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),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)),V_a_2)),V_a_2)),c_Groups_Ozero__class_Ozero(T_a)))
% 186.97/187.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_card__Plus__conv__if,axiom,
% 186.97/187.95 ! [V_B_2,T_b,V_A_2,T_a] :
% 186.97/187.95 ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.95 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) )
% 186.97/187.95 => hAPP(c_Finite__Set_Ocard(tc_sum(T_a,T_b)),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) )
% 186.97/187.95 & ( ~ ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.95 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) )
% 186.97/187.95 => hAPP(c_Finite__Set_Ocard(tc_sum(T_a,T_b)),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_setprod__diff1,axiom,
% 186.97/187.95 ! [V_a_2,V_f_2,V_A_2,T_a,T_b] :
% 186.97/187.95 ( class_Fields_Ofield(T_b)
% 186.97/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.95 => ( hAPP(V_f_2,V_a_2) != c_Groups_Ozero__class_Ozero(T_b)
% 186.97/187.95 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 186.97/187.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)) )
% 186.97/187.95 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 186.97/187.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_A_2) ) ) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_setsum__nonneg__0,axiom,
% 186.97/187.95 ! [V_i_2,V_f_2,V_s_2,T_a,T_b] :
% 186.97/187.95 ( class_Groups_Oordered__ab__group__add(T_b)
% 186.97/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_s_2))
% 186.97/187.95 => ( ! [B_i] :
% 186.97/187.95 ( hBOOL(hAPP(hAPP(c_member(T_a),B_i),V_s_2))
% 186.97/187.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_i))) )
% 186.97/187.95 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_s_2) = c_Groups_Ozero__class_Ozero(T_b)
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),V_s_2))
% 186.97/187.95 => hAPP(V_f_2,V_i_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_setsum__nonneg__leq__bound,axiom,
% 186.97/187.95 ! [V_i_2,V_B_2,V_f_2,V_s_2,T_a,T_b] :
% 186.97/187.95 ( class_Groups_Oordered__ab__group__add(T_b)
% 186.97/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_s_2))
% 186.97/187.95 => ( ! [B_i] :
% 186.97/187.95 ( hBOOL(hAPP(hAPP(c_member(T_a),B_i),V_s_2))
% 186.97/187.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_i))) )
% 186.97/187.95 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_s_2) = V_B_2
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),V_s_2))
% 186.97/187.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_i_2)),V_B_2)) ) ) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_ex__least__nat__less,axiom,
% 186.97/187.95 ! [V_n_2,V_P_2] :
% 186.97/187.95 ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 186.97/187.95 => ( hBOOL(hAPP(V_P_2,V_n_2))
% 186.97/187.95 => ? [B_k] :
% 186.97/187.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_k),V_n_2))
% 186.97/187.95 & ! [B_i] :
% 186.97/187.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_k))
% 186.97/187.95 => ~ hBOOL(hAPP(V_P_2,B_i)) )
% 186.97/187.95 & 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)))) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_setprod__mono__one__left,axiom,
% 186.97/187.95 ! [V_f_2,V_S_2,V_T_2,T_a,T_b] :
% 186.97/187.95 ( class_Groups_Ocomm__monoid__mult(T_b)
% 186.97/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2))
% 186.97/187.95 => ( ! [B_x] :
% 186.97/187.95 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_T_2),V_S_2)))
% 186.97/187.95 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) )
% 186.97/187.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_T_2) ) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_zle__add1__eq__le,axiom,
% 186.97/187.95 ! [V_z_2,V_w_2] :
% 186.97/187.95 ( 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))))
% 186.97/187.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_add1__zle__eq,axiom,
% 186.97/187.95 ! [V_z_2,V_w_2] :
% 186.97/187.95 ( 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))
% 186.97/187.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_le__imp__0__less,axiom,
% 186.97/187.95 ! [V_z] :
% 186.97/187.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 186.97/187.95 => 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))) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_zless__imp__add1__zle,axiom,
% 186.97/187.95 ! [V_z,V_w] :
% 186.97/187.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w),V_z))
% 186.97/187.95 => 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)) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_int__one__le__iff__zero__less,axiom,
% 186.97/187.95 ! [V_z_2] :
% 186.97/187.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2))
% 186.97/187.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_zle__diff1__eq,axiom,
% 186.97/187.95 ! [V_z_2,V_w_2] :
% 186.97/187.95 ( 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))))
% 186.97/187.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_less__bin__lemma,axiom,
% 186.97/187.95 ! [V_l_2,V_k_2] :
% 186.97/187.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2))
% 186.97/187.95 <=> 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))) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_int__0__less__1,axiom,
% 186.97/187.95 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))) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_zless__add1__eq,axiom,
% 186.97/187.95 ! [V_z_2,V_w_2] :
% 186.97/187.95 ( 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))))
% 186.97/187.95 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
% 186.97/187.95 | V_w_2 = V_z_2 ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_odd__less__0,axiom,
% 186.97/187.95 ! [V_z_2] :
% 186.97/187.95 ( 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)))
% 186.97/187.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_zadd__0__right,axiom,
% 186.97/187.95 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z ).
% 186.97/187.95
% 186.97/187.95 fof(fact_zadd__0,axiom,
% 186.97/187.95 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z) = V_z ).
% 186.97/187.95
% 186.97/187.95 fof(fact_odd__nonzero,axiom,
% 186.97/187.95 ! [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) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_int__0__neq__1,axiom,
% 186.97/187.95 c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_zadd__left__mono,axiom,
% 186.97/187.95 ! [V_k,V_j,V_i] :
% 186.97/187.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 186.97/187.95 => 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))) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_zadd__commute,axiom,
% 186.97/187.95 ! [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) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_zadd__left__commute,axiom,
% 186.97/187.95 ! [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)) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_zadd__assoc,axiom,
% 186.97/187.95 ! [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)) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_zadd__strict__right__mono,axiom,
% 186.97/187.95 ! [V_k,V_j,V_i] :
% 186.97/187.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
% 186.97/187.95 => 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))) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_zless__linear,axiom,
% 186.97/187.95 ! [V_y,V_x] :
% 186.97/187.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),V_y))
% 186.97/187.95 | V_x = V_y
% 186.97/187.95 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_x)) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_zless__le,axiom,
% 186.97/187.95 ! [V_w_2,V_z_2] :
% 186.97/187.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),V_w_2))
% 186.97/187.95 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),V_w_2))
% 186.97/187.95 & V_z_2 != V_w_2 ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_zadd__zless__mono,axiom,
% 186.97/187.95 ! [V_z,V_z_H,V_w,V_w_H] :
% 186.97/187.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_H),V_w))
% 186.97/187.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z))
% 186.97/187.95 => 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))) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_divide__zero__left,axiom,
% 186.97/187.95 ! [V_a,T_a] :
% 186.97/187.95 ( class_Rings_Odivision__ring(T_a)
% 186.97/187.95 => 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) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_divide__zero,axiom,
% 186.97/187.95 ! [V_a,T_a] :
% 186.97/187.95 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 186.97/187.95 => 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) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_add__divide__distrib,axiom,
% 186.97/187.95 ! [V_c,V_b,V_a,T_a] :
% 186.97/187.95 ( class_Rings_Odivision__ring(T_a)
% 186.97/187.95 => 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)) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_times__divide__eq__right,axiom,
% 186.97/187.95 ! [V_c,V_b,V_a,T_a] :
% 186.97/187.95 ( class_Rings_Odivision__ring(T_a)
% 186.97/187.95 => 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) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_diff__divide__distrib,axiom,
% 186.97/187.95 ! [V_c,V_b,V_a,T_a] :
% 186.97/187.95 ( class_Rings_Odivision__ring(T_a)
% 186.97/187.95 => 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)) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_divide__1,axiom,
% 186.97/187.95 ! [V_a,T_a] :
% 186.97/187.95 ( class_Rings_Odivision__ring(T_a)
% 186.97/187.95 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_power__divide,axiom,
% 186.97/187.95 ! [V_n,V_b,V_a,T_a] :
% 186.97/187.95 ( class_Fields_Ofield__inverse__zero(T_a)
% 186.97/187.95 => 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)) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_setsum__divide__distrib,axiom,
% 186.97/187.95 ! [V_r_2,V_A_2,V_f_2,T_b,T_a] :
% 186.97/187.95 ( class_Fields_Ofield(T_a)
% 186.97/187.95 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_f_2),V_A_2)),V_r_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Rings_Oinverse__class_Odivide(T_a)),V_f_2)),V_r_2)),V_A_2) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_nonzero__eq__divide__eq,axiom,
% 186.97/187.95 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 186.97/187.95 ( class_Rings_Odivision__ring(T_a)
% 186.97/187.95 => ( V_c_2 != c_Groups_Ozero__class_Ozero(T_a)
% 186.97/187.95 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)
% 186.97/187.95 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2) = V_b_2 ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_nonzero__divide__eq__eq,axiom,
% 186.97/187.95 ! [V_a_2,V_b_2,V_c_2,T_a] :
% 186.97/187.95 ( class_Rings_Odivision__ring(T_a)
% 186.97/187.95 => ( V_c_2 != c_Groups_Ozero__class_Ozero(T_a)
% 186.97/187.95 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2) = V_a_2
% 186.97/187.95 <=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_divide__eq__imp,axiom,
% 186.97/187.95 ! [V_a,V_b,V_c,T_a] :
% 186.97/187.95 ( class_Rings_Odivision__ring(T_a)
% 186.97/187.95 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 186.97/187.95 => ( V_b = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)
% 186.97/187.95 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) = V_a ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_eq__divide__imp,axiom,
% 186.97/187.95 ! [V_b,V_a,V_c,T_a] :
% 186.97/187.95 ( class_Rings_Odivision__ring(T_a)
% 186.97/187.95 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 186.97/187.95 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) = V_b
% 186.97/187.95 => V_a = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) ) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_finite__Plus__iff,axiom,
% 186.97/187.95 ! [V_B_2,V_A_2,T_b,T_a] :
% 186.97/187.95 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_a,T_b)),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2)))
% 186.97/187.95 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.95 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_finite__Plus,axiom,
% 186.97/187.95 ! [V_B_2,T_b,V_A_2,T_a] :
% 186.97/187.95 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 186.97/187.95 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_a,T_b)),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2))) ) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_finite__PlusD_I1_J,axiom,
% 186.97/187.95 ! [V_B_2,V_A_2,T_b,T_a] :
% 186.97/187.95 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_a,T_b)),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2)))
% 186.97/187.95 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ).
% 186.97/187.95
% 186.97/187.95 fof(fact_finite__PlusD_I2_J,axiom,
% 186.97/187.95 ! [V_B_2,V_A_2,T_b,T_a] :
% 186.97/187.95 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_a,T_b)),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2)))
% 186.97/187.96 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_right__inverse__eq,axiom,
% 186.97/187.96 ! [V_a_2,V_b_2,T_a] :
% 186.97/187.96 ( class_Rings_Odivision__ring(T_a)
% 186.97/187.96 => ( V_b_2 != c_Groups_Ozero__class_Ozero(T_a)
% 186.97/187.96 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a_2),V_b_2) = c_Groups_Oone__class_Oone(T_a)
% 186.97/187.96 <=> V_a_2 = V_b_2 ) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_divide__self,axiom,
% 186.97/187.96 ! [V_a,T_a] :
% 186.97/187.96 ( class_Rings_Odivision__ring(T_a)
% 186.97/187.96 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 186.97/187.96 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_divide__self__if,axiom,
% 186.97/187.96 ! [V_a,T_a] :
% 186.97/187.96 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 186.97/187.96 => ( ( V_a = c_Groups_Ozero__class_Ozero(T_a)
% 186.97/187.96 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) )
% 186.97/187.96 & ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 186.97/187.96 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_nonzero__power__divide,axiom,
% 186.97/187.96 ! [V_n,V_a,V_b,T_a] :
% 186.97/187.96 ( class_Fields_Ofield(T_a)
% 186.97/187.96 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 186.97/187.96 => 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)) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_power__one__over,axiom,
% 186.97/187.96 ! [V_n,V_a,T_a] :
% 186.97/187.96 ( class_Fields_Ofield__inverse__zero(T_a)
% 186.97/187.96 => 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) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_setprod__dividef,axiom,
% 186.97/187.96 ! [V_g_2,V_f_2,V_A_2,T_a,T_b] :
% 186.97/187.96 ( class_Fields_Ofield__inverse__zero(T_b)
% 186.97/187.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.96 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_Rings_Oinverse__class_Odivide(T_b)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2)) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_Ints__0,axiom,
% 186.97/187.96 ! [T_a] :
% 186.97/187.96 ( class_Rings_Oring__1(T_a)
% 186.97/187.96 => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Int_Oring__1__class_OInts(T_a))) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_Ints__add,axiom,
% 186.97/187.96 ! [V_b_2,V_a_2,T_a] :
% 186.97/187.96 ( class_Rings_Oring__1(T_a)
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a)))
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Int_Oring__1__class_OInts(T_a)))
% 186.97/187.96 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_a))) ) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_Ints__mult,axiom,
% 186.97/187.96 ! [V_b_2,V_a_2,T_a] :
% 186.97/187.96 ( class_Rings_Oring__1(T_a)
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a)))
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Int_Oring__1__class_OInts(T_a)))
% 186.97/187.96 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_a))) ) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_Ints__diff,axiom,
% 186.97/187.96 ! [V_b_2,V_a_2,T_a] :
% 186.97/187.96 ( class_Rings_Oring__1(T_a)
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a)))
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Int_Oring__1__class_OInts(T_a)))
% 186.97/187.96 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_a))) ) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_Ints__1,axiom,
% 186.97/187.96 ! [T_a] :
% 186.97/187.96 ( class_Rings_Oring__1(T_a)
% 186.97/187.96 => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Oone__class_Oone(T_a)),c_Int_Oring__1__class_OInts(T_a))) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_Ints__power,axiom,
% 186.97/187.96 ! [V_n_2,V_a_2,T_a] :
% 186.97/187.96 ( class_Rings_Oring__1(T_a)
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a)))
% 186.97/187.96 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2)),c_Int_Oring__1__class_OInts(T_a))) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_power_Opower_Opower__0,axiom,
% 186.97/187.96 ! [V_a_2,V_times_2,V_one_2,T_a] : hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_a_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_one_2 ).
% 186.97/187.96
% 186.97/187.96 fof(fact_power__diff,axiom,
% 186.97/187.96 ! [V_m,V_n,V_a,T_a] :
% 186.97/187.96 ( class_Fields_Ofield(T_a)
% 186.97/187.96 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 186.97/187.96 => 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)) ) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_Ints__double__eq__0__iff,axiom,
% 186.97/187.96 ! [V_a_2,T_a] :
% 186.97/187.96 ( class_Int_Oring__char__0(T_a)
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a)))
% 186.97/187.96 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
% 186.97/187.96 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_card__Plus,axiom,
% 186.97/187.96 ! [V_B_2,T_b,V_A_2,T_a] :
% 186.97/187.96 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 186.97/187.96 => hAPP(c_Finite__Set_Ocard(tc_sum(T_a,T_b)),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_Ints__odd__nonzero,axiom,
% 186.97/187.96 ! [V_a_2,T_a] :
% 186.97/187.96 ( class_Int_Oring__char__0(T_a)
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a)))
% 186.97/187.96 => 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)),V_a_2)),V_a_2) != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_self__quotient__aux2,axiom,
% 186.97/187.96 ! [V_q,V_r,V_a] :
% 186.97/187.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 186.97/187.96 => ( 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))
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 186.97/187.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_self__quotient__aux1,axiom,
% 186.97/187.96 ! [V_q,V_r,V_a] :
% 186.97/187.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 186.97/187.96 => ( 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))
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_a))
% 186.97/187.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_q)) ) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_divide__left__mono__neg,axiom,
% 186.97/187.96 ! [V_c,V_b,V_a,T_a] :
% 186.97/187.96 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 186.97/187.96 => ( 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)))
% 186.97/187.96 => 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))) ) ) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_divide__left__mono,axiom,
% 186.97/187.96 ! [V_c,V_a,V_b,T_a] :
% 186.97/187.96 ( class_Fields_Olinordered__field(T_a)
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 186.97/187.96 => ( 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)))
% 186.97/187.96 => 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))) ) ) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_neg__divide__le__eq,axiom,
% 186.97/187.96 ! [V_a_2,V_b_2,V_c_2,T_a] :
% 186.97/187.96 ( class_Fields_Olinordered__field(T_a)
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a)))
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)),V_a_2))
% 186.97/187.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),V_b_2)) ) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_neg__le__divide__eq,axiom,
% 186.97/187.96 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 186.97/187.96 ( class_Fields_Olinordered__field(T_a)
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a)))
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)))
% 186.97/187.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2))) ) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_mult__imp__le__div__pos,axiom,
% 186.97/187.96 ! [V_x,V_z,V_y,T_a] :
% 186.97/187.96 ( class_Fields_Olinordered__field(T_a)
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 186.97/187.96 => ( 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))
% 186.97/187.96 => 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))) ) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_zle__antisym,axiom,
% 186.97/187.96 ! [V_w,V_z] :
% 186.97/187.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w))
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z))
% 186.97/187.96 => V_z = V_w ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_zle__trans,axiom,
% 186.97/187.96 ! [V_k,V_j,V_i] :
% 186.97/187.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_j),V_k))
% 186.97/187.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_k)) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_zle__linear,axiom,
% 186.97/187.96 ! [V_w,V_z] :
% 186.97/187.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w))
% 186.97/187.96 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z)) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_zle__refl,axiom,
% 186.97/187.96 ! [V_w] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_w)) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_times__divide__times__eq,axiom,
% 186.97/187.96 ! [V_w,V_z,V_y,V_x,T_a] :
% 186.97/187.96 ( class_Fields_Ofield__inverse__zero(T_a)
% 186.97/187.96 => 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)) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_zero__le__divide__iff,axiom,
% 186.97/187.96 ! [V_b_2,V_a_2,T_a] :
% 186.97/187.96 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 186.97/187.96 => ( 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_a_2),V_b_2)))
% 186.97/187.96 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2))
% 186.97/187.96 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) )
% 186.97/187.96 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a)))
% 186.97/187.96 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_divide__le__0__iff,axiom,
% 186.97/187.96 ! [V_b_2,V_a_2,T_a] :
% 186.97/187.96 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_a)))
% 186.97/187.96 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2))
% 186.97/187.96 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) )
% 186.97/187.96 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a)))
% 186.97/187.96 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) ) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_divide__right__mono,axiom,
% 186.97/187.96 ! [V_c,V_b,V_a,T_a] :
% 186.97/187.96 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 186.97/187.96 => 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))) ) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_divide__right__mono__neg,axiom,
% 186.97/187.96 ! [V_c,V_b,V_a,T_a] :
% 186.97/187.96 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 186.97/187.96 => 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))) ) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_divide__strict__right__mono__neg,axiom,
% 186.97/187.96 ! [V_c,V_a,V_b,T_a] :
% 186.97/187.96 ( class_Fields_Olinordered__field(T_a)
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 186.97/187.96 => 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))) ) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_divide__strict__right__mono,axiom,
% 186.97/187.96 ! [V_c,V_b,V_a,T_a] :
% 186.97/187.96 ( class_Fields_Olinordered__field(T_a)
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 186.97/187.96 => 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))) ) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_divide__neg__neg,axiom,
% 186.97/187.96 ! [V_y,V_x,T_a] :
% 186.97/187.96 ( class_Fields_Olinordered__field(T_a)
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 186.97/187.96 => 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))) ) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_divide__neg__pos,axiom,
% 186.97/187.96 ! [V_y,V_x,T_a] :
% 186.97/187.96 ( class_Fields_Olinordered__field(T_a)
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 186.97/187.96 => 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))) ) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_divide__pos__neg,axiom,
% 186.97/187.96 ! [V_y,V_x,T_a] :
% 186.97/187.96 ( class_Fields_Olinordered__field(T_a)
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 186.97/187.96 => 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))) ) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_divide__pos__pos,axiom,
% 186.97/187.96 ! [V_y,V_x,T_a] :
% 186.97/187.96 ( class_Fields_Olinordered__field(T_a)
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 186.97/187.96 => 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))) ) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_divide__less__0__iff,axiom,
% 186.97/187.96 ! [V_b_2,V_a_2,T_a] :
% 186.97/187.96 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_a)))
% 186.97/187.96 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2))
% 186.97/187.96 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) )
% 186.97/187.96 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a)))
% 186.97/187.96 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) ) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_zero__less__divide__iff,axiom,
% 186.97/187.96 ! [V_b_2,V_a_2,T_a] :
% 186.97/187.96 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 186.97/187.96 => ( 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_a_2),V_b_2)))
% 186.97/187.96 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2))
% 186.97/187.96 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) )
% 186.97/187.96 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a)))
% 186.97/187.96 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_eq__divide__eq,axiom,
% 186.97/187.96 ! [V_c_2,V_b_2,V_a_2,T_a] :
% 186.97/187.96 ( class_Fields_Ofield__inverse__zero(T_a)
% 186.97/187.96 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)
% 186.97/187.96 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_a)
% 186.97/187.96 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2) = V_b_2 )
% 186.97/187.96 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_a)
% 186.97/187.96 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_divide__eq__eq,axiom,
% 186.97/187.96 ! [V_a_2,V_c_2,V_b_2,T_a] :
% 186.97/187.96 ( class_Fields_Ofield__inverse__zero(T_a)
% 186.97/187.96 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2) = V_a_2
% 186.97/187.96 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_a)
% 186.97/187.96 => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2) )
% 186.97/187.96 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_a)
% 186.97/187.96 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_mult__divide__mult__cancel__right,axiom,
% 186.97/187.96 ! [V_b,V_a,V_c,T_a] :
% 186.97/187.96 ( class_Fields_Ofield__inverse__zero(T_a)
% 186.97/187.96 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 186.97/187.96 => 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) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_mult__divide__mult__cancel__left,axiom,
% 186.97/187.96 ! [V_b,V_a,V_c,T_a] :
% 186.97/187.96 ( class_Fields_Ofield__inverse__zero(T_a)
% 186.97/187.96 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 186.97/187.96 => 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) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_frac__eq__eq,axiom,
% 186.97/187.96 ! [V_w_2,V_x_2,V_z_2,V_y_2,T_a] :
% 186.97/187.96 ( class_Fields_Ofield(T_a)
% 186.97/187.96 => ( V_y_2 != c_Groups_Ozero__class_Ozero(T_a)
% 186.97/187.96 => ( V_z_2 != c_Groups_Ozero__class_Ozero(T_a)
% 186.97/187.96 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x_2),V_y_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_w_2),V_z_2)
% 186.97/187.96 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_z_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_y_2) ) ) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_divide__nonpos__neg,axiom,
% 186.97/187.96 ! [V_y,V_x,T_a] :
% 186.97/187.96 ( class_Fields_Olinordered__field(T_a)
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 186.97/187.96 => 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))) ) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_divide__nonpos__pos,axiom,
% 186.97/187.96 ! [V_y,V_x,T_a] :
% 186.97/187.96 ( class_Fields_Olinordered__field(T_a)
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 186.97/187.96 => 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))) ) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_frac__le,axiom,
% 186.97/187.96 ! [V_z,V_w,V_y,V_x,T_a] :
% 186.97/187.96 ( class_Fields_Olinordered__field(T_a)
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z))
% 186.97/187.96 => 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))) ) ) ) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_frac__less,axiom,
% 186.97/187.96 ! [V_z,V_w,V_y,V_x,T_a] :
% 186.97/187.96 ( class_Fields_Olinordered__field(T_a)
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z))
% 186.97/187.96 => 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))) ) ) ) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_frac__less2,axiom,
% 186.97/187.96 ! [V_z,V_w,V_y,V_x,T_a] :
% 186.97/187.96 ( class_Fields_Olinordered__field(T_a)
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_w),V_z))
% 186.97/187.96 => 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))) ) ) ) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_divide__nonneg__neg,axiom,
% 186.97/187.96 ! [V_y,V_x,T_a] :
% 186.97/187.96 ( class_Fields_Olinordered__field(T_a)
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 186.97/187.96 => 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))) ) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_divide__nonneg__pos,axiom,
% 186.97/187.96 ! [V_y,V_x,T_a] :
% 186.97/187.96 ( class_Fields_Olinordered__field(T_a)
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 186.97/187.96 => 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))) ) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_divide__strict__left__mono__neg,axiom,
% 186.97/187.96 ! [V_c,V_b,V_a,T_a] :
% 186.97/187.96 ( class_Fields_Olinordered__field(T_a)
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 186.97/187.96 => ( 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)))
% 186.97/187.96 => 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))) ) ) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_divide__strict__left__mono,axiom,
% 186.97/187.96 ! [V_c,V_a,V_b,T_a] :
% 186.97/187.96 ( class_Fields_Olinordered__field(T_a)
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 186.97/187.96 => ( 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)))
% 186.97/187.96 => 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))) ) ) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_neg__divide__less__eq,axiom,
% 186.97/187.96 ! [V_a_2,V_b_2,V_c_2,T_a] :
% 186.97/187.96 ( class_Fields_Olinordered__field(T_a)
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a)))
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)),V_a_2))
% 186.97/187.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),V_b_2)) ) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_neg__less__divide__eq,axiom,
% 186.97/187.96 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 186.97/187.96 ( class_Fields_Olinordered__field(T_a)
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a)))
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)))
% 186.97/187.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2))) ) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_mult__imp__less__div__pos,axiom,
% 186.97/187.96 ! [V_x,V_z,V_y,T_a] :
% 186.97/187.96 ( class_Fields_Olinordered__field(T_a)
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 186.97/187.96 => ( 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))
% 186.97/187.96 => 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))) ) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_mult__imp__div__pos__less,axiom,
% 186.97/187.96 ! [V_z,V_x,V_y,T_a] :
% 186.97/187.96 ( class_Fields_Olinordered__field(T_a)
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 186.97/187.96 => ( 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)))
% 186.97/187.96 => 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)) ) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_pos__divide__less__eq,axiom,
% 186.97/187.96 ! [V_a_2,V_b_2,V_c_2,T_a] :
% 186.97/187.96 ( class_Fields_Olinordered__field(T_a)
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)),V_a_2))
% 186.97/187.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2))) ) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_pos__less__divide__eq,axiom,
% 186.97/187.96 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 186.97/187.96 ( class_Fields_Olinordered__field(T_a)
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)))
% 186.97/187.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),V_b_2)) ) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_divide__less__eq,axiom,
% 186.97/187.96 ! [V_a_2,V_c_2,V_b_2,T_a] :
% 186.97/187.96 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)),V_a_2))
% 186.97/187.96 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
% 186.97/187.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2))) )
% 186.97/187.96 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
% 186.97/187.96 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a)))
% 186.97/187.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),V_b_2)) )
% 186.97/187.96 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a)))
% 186.97/187.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ) ) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_less__divide__eq,axiom,
% 186.97/187.96 ! [V_c_2,V_b_2,V_a_2,T_a] :
% 186.97/187.96 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)))
% 186.97/187.96 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
% 186.97/187.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),V_b_2)) )
% 186.97/187.96 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
% 186.97/187.96 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a)))
% 186.97/187.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2))) )
% 186.97/187.96 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a)))
% 186.97/187.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_add__frac__eq,axiom,
% 186.97/187.96 ! [V_w,V_x,V_z,V_y,T_a] :
% 186.97/187.96 ( class_Fields_Ofield(T_a)
% 186.97/187.96 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 186.97/187.96 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 186.97/187.96 => 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)) ) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_divide__add__eq__iff,axiom,
% 186.97/187.96 ! [V_y,V_x,V_z,T_a] :
% 186.97/187.96 ( class_Fields_Ofield(T_a)
% 186.97/187.96 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 186.97/187.96 => 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) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_add__frac__num,axiom,
% 186.97/187.96 ! [V_z,V_x,V_y,T_a] :
% 186.97/187.96 ( class_Fields_Ofield__inverse__zero(T_a)
% 186.97/187.96 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 186.97/187.96 => 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) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_add__divide__eq__iff,axiom,
% 186.97/187.96 ! [V_y,V_x,V_z,T_a] :
% 186.97/187.96 ( class_Fields_Ofield(T_a)
% 186.97/187.96 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 186.97/187.96 => 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) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_add__num__frac,axiom,
% 186.97/187.96 ! [V_x,V_z,V_y,T_a] :
% 186.97/187.96 ( class_Fields_Ofield__inverse__zero(T_a)
% 186.97/187.96 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 186.97/187.96 => 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) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_diff__divide__eq__iff,axiom,
% 186.97/187.96 ! [V_y,V_x,V_z,T_a] :
% 186.97/187.96 ( class_Fields_Ofield(T_a)
% 186.97/187.96 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 186.97/187.96 => 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) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_divide__diff__eq__iff,axiom,
% 186.97/187.96 ! [V_y,V_x,V_z,T_a] :
% 186.97/187.96 ( class_Fields_Ofield(T_a)
% 186.97/187.96 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 186.97/187.96 => 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) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_diff__frac__eq,axiom,
% 186.97/187.96 ! [V_w,V_x,V_z,V_y,T_a] :
% 186.97/187.96 ( class_Fields_Ofield(T_a)
% 186.97/187.96 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 186.97/187.96 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 186.97/187.96 => 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)) ) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_less__half__sum,axiom,
% 186.97/187.96 ! [V_b,V_a,T_a] :
% 186.97/187.96 ( class_Fields_Olinordered__field(T_a)
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 186.97/187.96 => 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))))) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_gt__half__sum,axiom,
% 186.97/187.96 ! [V_b,V_a,T_a] :
% 186.97/187.96 ( class_Fields_Olinordered__field(T_a)
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 186.97/187.96 => 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)) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_zdiv__mono2__neg__lemma,axiom,
% 186.97/187.96 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
% 186.97/187.96 ( 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)
% 186.97/187.96 => ( 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)))
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 186.97/187.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_unique__quotient__lemma__neg,axiom,
% 186.97/187.96 ! [V_r,V_q,V_r_H,V_q_H,V_b] :
% 186.97/187.96 ( 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)))
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r_H))
% 186.97/187.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_zdiv__mono2__lemma,axiom,
% 186.97/187.96 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
% 186.97/187.96 ( 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)
% 186.97/187.96 => ( 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)))
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H))
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 186.97/187.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_unique__quotient__lemma,axiom,
% 186.97/187.96 ! [V_r,V_q,V_r_H,V_q_H,V_b] :
% 186.97/187.96 ( 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)))
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b))
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 186.97/187.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_q__neg__lemma,axiom,
% 186.97/187.96 ! [V_r_H,V_q_H,V_b_H] :
% 186.97/187.96 ( 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)))
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 186.97/187.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_q__pos__lemma,axiom,
% 186.97/187.96 ! [V_r_H,V_q_H,V_b_H] :
% 186.97/187.96 ( 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)))
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H))
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 186.97/187.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_q_H)) ) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_le__divide__eq,axiom,
% 186.97/187.96 ! [V_c_2,V_b_2,V_a_2,T_a] :
% 186.97/187.96 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)))
% 186.97/187.96 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
% 186.97/187.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),V_b_2)) )
% 186.97/187.96 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
% 186.97/187.96 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a)))
% 186.97/187.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2))) )
% 186.97/187.96 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a)))
% 186.97/187.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_divide__le__eq,axiom,
% 186.97/187.96 ! [V_a_2,V_c_2,V_b_2,T_a] :
% 186.97/187.96 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)),V_a_2))
% 186.97/187.96 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
% 186.97/187.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2))) )
% 186.97/187.96 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
% 186.97/187.96 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a)))
% 186.97/187.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),V_b_2)) )
% 186.97/187.96 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a)))
% 186.97/187.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ) ) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_pos__le__divide__eq,axiom,
% 186.97/187.96 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 186.97/187.96 ( class_Fields_Olinordered__field(T_a)
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)))
% 186.97/187.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),V_b_2)) ) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_pos__divide__le__eq,axiom,
% 186.97/187.96 ! [V_a_2,V_b_2,V_c_2,T_a] :
% 186.97/187.96 ( class_Fields_Olinordered__field(T_a)
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)),V_a_2))
% 186.97/187.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2))) ) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_mult__imp__div__pos__le,axiom,
% 186.97/187.96 ! [V_z,V_x,V_y,T_a] :
% 186.97/187.96 ( class_Fields_Olinordered__field(T_a)
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 186.97/187.96 => ( 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)))
% 186.97/187.96 => 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)) ) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom,
% 186.97/187.96 ! [V_n,V_x] :
% 186.97/187.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 186.97/187.96 => 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))) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom,
% 186.97/187.96 ! [V_y,V_x] :
% 186.97/187.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 186.97/187.96 => 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))) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom,
% 186.97/187.96 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))) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom,
% 186.97/187.96 ! [V_y,V_x] :
% 186.97/187.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 186.97/187.96 => 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))) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_setprod__Un,axiom,
% 186.97/187.96 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] :
% 186.97/187.96 ( class_Fields_Ofield(T_b)
% 186.97/187.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 186.97/187.96 => ( ! [B_x] :
% 186.97/187.96 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
% 186.97/187.96 => hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_b) )
% 186.97/187.96 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_Plus__eq__empty__conv,axiom,
% 186.97/187.96 ! [V_B_2,V_A_2,T_b,T_a] :
% 186.97/187.96 ( c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(T_a,T_b),tc_HOL_Obool))
% 186.97/187.96 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 186.97/187.96 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom,
% 186.97/187.96 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))) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_tsub__def,axiom,
% 186.97/187.96 ! [V_x,V_y] :
% 186.97/187.96 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
% 186.97/187.96 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) )
% 186.97/187.96 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
% 186.97/187.96 => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_setprod__mono__one__right,axiom,
% 186.97/187.96 ! [V_f_2,V_S_2,V_T_2,T_a,T_b] :
% 186.97/187.96 ( class_Groups_Ocomm__monoid__mult(T_b)
% 186.97/187.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2))
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2))
% 186.97/187.96 => ( ! [B_x] :
% 186.97/187.96 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_T_2),V_S_2)))
% 186.97/187.96 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) )
% 186.97/187.96 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_T_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_S_2) ) ) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_setsum__mono__zero__right,axiom,
% 186.97/187.96 ! [V_f_2,V_S_2,V_T_2,T_a,T_b] :
% 186.97/187.96 ( class_Groups_Ocomm__monoid__add(T_b)
% 186.97/187.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2))
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2))
% 186.97/187.96 => ( ! [B_x] :
% 186.97/187.96 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_T_2),V_S_2)))
% 186.97/187.96 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) )
% 186.97/187.96 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_T_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_S_2) ) ) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_setsum__mono__zero__left,axiom,
% 186.97/187.96 ! [V_f_2,V_S_2,V_T_2,T_a,T_b] :
% 186.97/187.96 ( class_Groups_Ocomm__monoid__add(T_b)
% 186.97/187.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2))
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2))
% 186.97/187.96 => ( ! [B_x] :
% 186.97/187.96 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_T_2),V_S_2)))
% 186.97/187.96 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) )
% 186.97/187.96 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_T_2) ) ) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_field__le__mult__one__interval,axiom,
% 186.97/187.96 ! [V_y,V_x,T_a] :
% 186.97/187.96 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 186.97/187.96 => ( ! [B_z] :
% 186.97/187.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_z))
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_z),c_Groups_Oone__class_Oone(T_a)))
% 186.97/187.96 => 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)) ) )
% 186.97/187.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_card__Suc__Diff1,axiom,
% 186.97/187.96 ! [V_x_2,V_A_2,T_a] :
% 186.97/187.96 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 186.97/187.96 => hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(T_a),V_A_2) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_Body__triple__valid__0,axiom,
% 186.97/187.96 ! [V_Q_2,V_pn_2,V_P_2,T_a] : c_Hoare__Mirabelle_Otriple__valid(T_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Q_2)) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_Suc__mono,axiom,
% 186.97/187.96 ! [V_n,V_m] :
% 186.97/187.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 186.97/187.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_lessI,axiom,
% 186.97/187.96 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_n))) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_zero__less__Suc,axiom,
% 186.97/187.96 ! [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))) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_Suc__inject,axiom,
% 186.97/187.96 ! [V_y,V_x] :
% 186.97/187.96 ( hAPP(c_Nat_OSuc,V_x) = hAPP(c_Nat_OSuc,V_y)
% 186.97/187.96 => V_x = V_y ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_nat_Oinject,axiom,
% 186.97/187.96 ! [V_nat_H_2,V_nat_2] :
% 186.97/187.96 ( hAPP(c_Nat_OSuc,V_nat_2) = hAPP(c_Nat_OSuc,V_nat_H_2)
% 186.97/187.96 <=> V_nat_2 = V_nat_H_2 ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_Suc__n__not__n,axiom,
% 186.97/187.96 ! [V_n] : hAPP(c_Nat_OSuc,V_n) != V_n ).
% 186.97/187.96
% 186.97/187.96 fof(fact_n__not__Suc__n,axiom,
% 186.97/187.96 ! [V_n] : V_n != hAPP(c_Nat_OSuc,V_n) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_triple__valid__Suc,axiom,
% 186.97/187.96 ! [V_t,V_n,T_a] :
% 186.97/187.96 ( c_Hoare__Mirabelle_Otriple__valid(T_a,hAPP(c_Nat_OSuc,V_n),V_t)
% 186.97/187.96 => c_Hoare__Mirabelle_Otriple__valid(T_a,V_n,V_t) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_Zero__not__Suc,axiom,
% 186.97/187.96 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_nat_Osimps_I2_J,axiom,
% 186.97/187.96 ! [V_nat_H] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_nat_H) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_Suc__not__Zero,axiom,
% 186.97/187.96 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_nat_Osimps_I3_J,axiom,
% 186.97/187.96 ! [V_nat_H_1] : hAPP(c_Nat_OSuc,V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_Zero__neq__Suc,axiom,
% 186.97/187.96 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_Suc__neq__Zero,axiom,
% 186.97/187.96 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_Suc__less__SucD,axiom,
% 186.97/187.96 ! [V_n,V_m] :
% 186.97/187.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)))
% 186.97/187.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_Suc__lessD,axiom,
% 186.97/187.96 ! [V_n,V_m] :
% 186.97/187.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
% 186.97/187.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_less__SucE,axiom,
% 186.97/187.96 ! [V_n,V_m] :
% 186.97/187.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)))
% 186.97/187.96 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 186.97/187.96 => V_m = V_n ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_less__trans__Suc,axiom,
% 186.97/187.96 ! [V_k,V_j,V_i] :
% 186.97/187.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k))
% 186.97/187.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_i)),V_k)) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_Suc__lessI,axiom,
% 186.97/187.96 ! [V_n,V_m] :
% 186.97/187.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 186.97/187.96 => ( hAPP(c_Nat_OSuc,V_m) != V_n
% 186.97/187.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_less__SucI,axiom,
% 186.97/187.96 ! [V_n,V_m] :
% 186.97/187.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 186.97/187.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_less__antisym,axiom,
% 186.97/187.96 ! [V_m,V_n] :
% 186.97/187.96 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m))
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_m)))
% 186.97/187.96 => V_m = V_n ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_not__less__less__Suc__eq,axiom,
% 186.97/187.96 ! [V_m_2,V_n_2] :
% 186.97/187.96 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2)))
% 186.97/187.96 <=> V_n_2 = V_m_2 ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_Suc__less__eq,axiom,
% 186.97/187.96 ! [V_n_2,V_m_2] :
% 186.97/187.96 ( 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)))
% 186.97/187.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_less__Suc__eq,axiom,
% 186.97/187.96 ! [V_n_2,V_m_2] :
% 186.97/187.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 186.97/187.96 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 186.97/187.96 | V_m_2 = V_n_2 ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_not__less__eq,axiom,
% 186.97/187.96 ! [V_n_2,V_m_2] :
% 186.97/187.96 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 186.97/187.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_add__Suc__shift,axiom,
% 186.97/187.96 ! [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)) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_add__Suc,axiom,
% 186.97/187.96 ! [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)) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_add__Suc__right,axiom,
% 186.97/187.96 ! [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)) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_Suc__leD,axiom,
% 186.97/187.96 ! [V_n,V_m] :
% 186.97/187.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
% 186.97/187.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_le__SucE,axiom,
% 186.97/187.96 ! [V_n,V_m] :
% 186.97/187.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)))
% 186.97/187.96 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 186.97/187.96 => V_m = hAPP(c_Nat_OSuc,V_n) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_le__SucI,axiom,
% 186.97/187.96 ! [V_n,V_m] :
% 186.97/187.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 186.97/187.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_Suc__le__mono,axiom,
% 186.97/187.96 ! [V_m_2,V_n_2] :
% 186.97/187.96 ( 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)))
% 186.97/187.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_le__Suc__eq,axiom,
% 186.97/187.96 ! [V_n_2,V_m_2] :
% 186.97/187.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 186.97/187.96 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 186.97/187.96 | V_m_2 = hAPP(c_Nat_OSuc,V_n_2) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_not__less__eq__eq,axiom,
% 186.97/187.96 ! [V_n_2,V_m_2] :
% 186.97/187.96 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 186.97/187.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_Suc__n__not__le__n,axiom,
% 186.97/187.96 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n)),V_n)) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_diff__Suc__Suc,axiom,
% 186.97/187.96 ! [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) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_Suc__diff__diff,axiom,
% 186.97/187.96 ! [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) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_Suc__mult__cancel1,axiom,
% 186.97/187.96 ! [V_n_2,V_m_2,V_k_2] :
% 186.97/187.96 ( 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)
% 186.97/187.96 <=> V_m_2 = V_n_2 ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_power_Opower_Opower__Suc,axiom,
% 186.97/187.96 ! [V_n_2,V_a_2,V_times_2,V_one_2,T_a] : hAPP(hAPP(c_Power_Opower_Opower(T_a,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_a,V_one_2,V_times_2),V_a_2),V_n_2)) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_power__0__Suc,axiom,
% 186.97/187.96 ! [V_n,T_a] :
% 186.97/187.96 ( ( class_Power_Opower(T_a)
% 186.97/187.96 & class_Rings_Osemiring__0(T_a) )
% 186.97/187.96 => 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) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_gr0__conv__Suc,axiom,
% 186.97/187.96 ! [V_n_2] :
% 186.97/187.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 186.97/187.96 <=> ? [B_m] : V_n_2 = hAPP(c_Nat_OSuc,B_m) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_less__Suc0,axiom,
% 186.97/187.96 ! [V_n_2] :
% 186.97/187.96 ( 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))))
% 186.97/187.96 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_less__Suc__eq__0__disj,axiom,
% 186.97/187.96 ! [V_n_2,V_m_2] :
% 186.97/187.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 186.97/187.96 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 186.97/187.96 | ? [B_j] :
% 186.97/187.96 ( V_m_2 = hAPP(c_Nat_OSuc,B_j)
% 186.97/187.96 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_n_2)) ) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_power__Suc,axiom,
% 186.97/187.96 ! [V_n,V_a,T_a] :
% 186.97/187.96 ( class_Power_Opower(T_a)
% 186.97/187.96 => 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)) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_power__Suc2,axiom,
% 186.97/187.96 ! [V_n,V_a,T_a] :
% 186.97/187.96 ( class_Groups_Omonoid__mult(T_a)
% 186.97/187.96 => 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) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J,axiom,
% 186.97/187.96 ! [V_q,V_x,T_a] :
% 186.97/187.96 ( class_Rings_Ocomm__semiring__1(T_a)
% 186.97/187.96 => 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)) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J,axiom,
% 186.97/187.96 ! [V_q,V_x,T_a] :
% 186.97/187.96 ( class_Rings_Ocomm__semiring__1(T_a)
% 186.97/187.96 => 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)) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J,axiom,
% 186.97/187.96 ! [V_q,V_x,T_a] :
% 186.97/187.96 ( class_Rings_Ocomm__semiring__1(T_a)
% 186.97/187.96 => 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)) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_add__is__1,axiom,
% 186.97/187.96 ! [V_n_2,V_m_2] :
% 186.97/187.96 ( 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))
% 186.97/187.96 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 186.97/187.96 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 186.97/187.96 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 186.97/187.96 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_one__is__add,axiom,
% 186.97/187.96 ! [V_n_2,V_m_2] :
% 186.97/187.96 ( 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)
% 186.97/187.96 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 186.97/187.96 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 186.97/187.96 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 186.97/187.96 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_less__iff__Suc__add,axiom,
% 186.97/187.96 ! [V_n_2,V_m_2] :
% 186.97/187.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 186.97/187.96 <=> ? [B_k] : V_n_2 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k)) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_less__add__Suc2,axiom,
% 186.97/187.96 ! [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)))) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_less__add__Suc1,axiom,
% 186.97/187.96 ! [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)))) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_Suc__le__lessD,axiom,
% 186.97/187.96 ! [V_n,V_m] :
% 186.97/187.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
% 186.97/187.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_le__less__Suc__eq,axiom,
% 186.97/187.96 ! [V_n_2,V_m_2] :
% 186.97/187.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2)))
% 186.97/187.96 <=> V_n_2 = V_m_2 ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_Suc__leI,axiom,
% 186.97/187.96 ! [V_n,V_m] :
% 186.97/187.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 186.97/187.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_le__imp__less__Suc,axiom,
% 186.97/187.96 ! [V_n,V_m] :
% 186.97/187.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 186.97/187.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_Suc__le__eq,axiom,
% 186.97/187.96 ! [V_n_2,V_m_2] :
% 186.97/187.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2))
% 186.97/187.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_less__Suc__eq__le,axiom,
% 186.97/187.96 ! [V_n_2,V_m_2] :
% 186.97/187.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 186.97/187.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_less__eq__Suc__le,axiom,
% 186.97/187.96 ! [V_m_2,V_n_2] :
% 186.97/187.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 186.97/187.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_mult__eq__1__iff,axiom,
% 186.97/187.96 ! [V_n_2,V_m_2] :
% 186.97/187.96 ( 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))
% 186.97/187.96 <=> ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 186.97/187.96 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_diff__less__Suc,axiom,
% 186.97/187.96 ! [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))) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_Suc__mult__less__cancel1,axiom,
% 186.97/187.96 ! [V_n_2,V_m_2,V_k_2] :
% 186.97/187.96 ( 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)))
% 186.97/187.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_mult__Suc__right,axiom,
% 186.97/187.96 ! [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)) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_mult__Suc,axiom,
% 186.97/187.96 ! [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)) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_Suc__diff__le,axiom,
% 186.97/187.96 ! [V_m,V_n] :
% 186.97/187.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 186.97/187.96 => 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)) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_Suc__mult__le__cancel1,axiom,
% 186.97/187.96 ! [V_n_2,V_m_2,V_k_2] :
% 186.97/187.96 ( 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)))
% 186.97/187.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_One__nat__def,axiom,
% 186.97/187.96 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_Suc__eq__plus1__left,axiom,
% 186.97/187.96 ! [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) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_Suc__eq__plus1,axiom,
% 186.97/187.96 ! [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)) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_diff__Suc__eq__diff__pred,axiom,
% 186.97/187.96 ! [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) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_diff__Suc__1,axiom,
% 186.97/187.96 ! [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 ).
% 186.97/187.96
% 186.97/187.96 fof(fact_nat__power__eq__Suc__0__iff,axiom,
% 186.97/187.96 ! [V_m_2,V_x_2] :
% 186.97/187.96 ( 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))
% 186.97/187.96 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 186.97/187.96 | V_x_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_power__Suc__0,axiom,
% 186.97/187.96 ! [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)) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_less__eq__Suc__le__raw,axiom,
% 186.97/187.96 ! [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)) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_Body__triple__valid__Suc,axiom,
% 186.97/187.96 ! [V_Q_2,V_pn_2,V_P_2,V_n_2,T_a] :
% 186.97/187.96 ( c_Hoare__Mirabelle_Otriple__valid(T_a,V_n_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn_2))),V_Q_2))
% 186.97/187.96 <=> c_Hoare__Mirabelle_Otriple__valid(T_a,hAPP(c_Nat_OSuc,V_n_2),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Q_2)) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_power__le__imp__le__base,axiom,
% 186.97/187.96 ! [V_b,V_n,V_a,T_a] :
% 186.97/187.96 ( class_Rings_Olinordered__semidom(T_a)
% 186.97/187.96 => ( 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))))
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 186.97/187.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_power__inject__base,axiom,
% 186.97/187.96 ! [V_b,V_n,V_a,T_a] :
% 186.97/187.96 ( class_Rings_Olinordered__semidom(T_a)
% 186.97/187.96 => ( 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))
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 186.97/187.96 => V_a = V_b ) ) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_power__gt1,axiom,
% 186.97/187.96 ! [V_n,V_a,T_a] :
% 186.97/187.96 ( class_Rings_Olinordered__semidom(T_a)
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 186.97/187.96 => 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)))) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_diff__Suc__less,axiom,
% 186.97/187.96 ! [V_i,V_n] :
% 186.97/187.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 186.97/187.96 => 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)) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_Suc__pred,axiom,
% 186.97/187.96 ! [V_n] :
% 186.97/187.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 186.97/187.96 => 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 ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_one__less__mult,axiom,
% 186.97/187.96 ! [V_m,V_n] :
% 186.97/187.96 ( 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))
% 186.97/187.96 => ( 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))
% 186.97/187.96 => 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))) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_n__less__n__mult__m,axiom,
% 186.97/187.96 ! [V_m,V_n] :
% 186.97/187.96 ( 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))
% 186.97/187.96 => ( 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))
% 186.97/187.96 => 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))) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_n__less__m__mult__n,axiom,
% 186.97/187.96 ! [V_m,V_n] :
% 186.97/187.96 ( 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))
% 186.97/187.96 => ( 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))
% 186.97/187.96 => 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))) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_one__le__mult__iff,axiom,
% 186.97/187.96 ! [V_n_2,V_m_2] :
% 186.97/187.96 ( 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)))
% 186.97/187.96 <=> ( 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))
% 186.97/187.96 & 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)) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_diff__Suc__diff__eq2,axiom,
% 186.97/187.96 ! [V_m,V_j,V_k] :
% 186.97/187.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 186.97/187.96 => 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)) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_diff__Suc__diff__eq1,axiom,
% 186.97/187.96 ! [V_m,V_j,V_k] :
% 186.97/187.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 186.97/187.96 => 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)) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_setsum__eq__Suc0__iff,axiom,
% 186.97/187.96 ! [V_f_2,V_A_2,T_a] :
% 186.97/187.96 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.96 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 186.97/187.96 <=> ? [B_x] :
% 186.97/187.96 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 186.97/187.96 & hAPP(V_f_2,B_x) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 186.97/187.96 & ! [B_xa] :
% 186.97/187.96 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2))
% 186.97/187.96 => ( B_x != B_xa
% 186.97/187.96 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_nat__one__le__power,axiom,
% 186.97/187.96 ! [V_n,V_i] :
% 186.97/187.96 ( 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))
% 186.97/187.96 => 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))) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_power__Suc__less__one,axiom,
% 186.97/187.96 ! [V_n,V_a,T_a] :
% 186.97/187.96 ( class_Rings_Olinordered__semidom(T_a)
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 186.97/187.96 => 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))) ) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_card__insert__disjoint,axiom,
% 186.97/187.96 ! [V_x_2,V_A_2,T_a] :
% 186.97/187.96 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.96 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 186.97/187.96 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_a),V_A_2)) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_card__insert__if,axiom,
% 186.97/187.96 ! [V_x_2,V_A_2,T_a] :
% 186.97/187.96 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.96 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 186.97/187.96 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_a),V_A_2) )
% 186.97/187.96 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 186.97/187.96 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_a),V_A_2)) ) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_Suc__pred_H,axiom,
% 186.97/187.96 ! [V_n] :
% 186.97/187.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 186.97/187.96 => 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))) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_Suc__diff__1,axiom,
% 186.97/187.96 ! [V_n] :
% 186.97/187.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 186.97/187.96 => 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 ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_add__eq__if,axiom,
% 186.97/187.96 ! [V_n,V_m] :
% 186.97/187.96 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 186.97/187.96 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_n )
% 186.97/187.96 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 186.97/187.96 => 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)) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,axiom,
% 186.97/187.96 ! [V_y,V_x] :
% 186.97/187.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 186.97/187.96 => 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))) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_tsub__eq,axiom,
% 186.97/187.96 ! [V_x,V_y] :
% 186.97/187.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
% 186.97/187.96 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_card__insert,axiom,
% 186.97/187.96 ! [V_x_2,V_A_2,T_a] :
% 186.97/187.96 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.96 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_card__Suc__eq,axiom,
% 186.97/187.96 ! [V_k_2,V_A_2,T_a] :
% 186.97/187.96 ( hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = hAPP(c_Nat_OSuc,V_k_2)
% 186.97/187.96 <=> ? [B_b,B_B] :
% 186.97/187.96 ( V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_a),B_b),B_B)
% 186.97/187.96 & ~ hBOOL(hAPP(hAPP(c_member(T_a),B_b),B_B))
% 186.97/187.96 & hAPP(c_Finite__Set_Ocard(T_a),B_B) = V_k_2
% 186.97/187.96 & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 186.97/187.96 => B_B = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_int__power__div__base,axiom,
% 186.97/187.96 ! [V_k,V_m] :
% 186.97/187.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 186.97/187.96 => 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)))) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_com_Osize_I4_J,axiom,
% 186.97/187.96 ! [V_com2,V_com1] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(V_com1,V_com2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(V_com1)),c_Com_Ocom_Ocom__size(V_com2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_com_Osize_I6_J,axiom,
% 186.97/187.96 ! [V_com_2,V_fun_2] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OWhile(V_fun_2,V_com_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(V_com_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_com_Osize_I12_J,axiom,
% 186.97/187.96 ! [V_com2,V_com1] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSemi(V_com1,V_com2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com1)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_com_Osize_I14_J,axiom,
% 186.97/187.96 ! [V_com_2,V_fun_2] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OWhile(V_fun_2,V_com_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_card__Pow,axiom,
% 186.97/187.96 ! [V_A_2,T_a] :
% 186.97/187.96 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 186.97/187.96 => hAPP(c_Finite__Set_Ocard(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OPow(T_a),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_a),V_A_2)) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_PowI,axiom,
% 186.97/187.96 ! [V_B_2,V_A_2,T_a] :
% 186.97/187.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 186.97/187.96 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_a),V_B_2))) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_Cantors__paradox,axiom,
% 186.97/187.96 ! [V_A_2,T_a] :
% 186.97/187.96 ~ ? [B_f] : hAPP(c_Set_Oimage(T_a,tc_fun(T_a,tc_HOL_Obool),B_f),V_A_2) = hAPP(c_Set_OPow(T_a),V_A_2) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_Pow__top,axiom,
% 186.97/187.96 ! [V_A_2,T_a] : hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_a),V_A_2))) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_Pow__not__empty,axiom,
% 186.97/187.96 ! [V_A_2,T_a] : hAPP(c_Set_OPow(T_a),V_A_2) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_zdiv__zero,axiom,
% 186.97/187.96 ! [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) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_div__0,axiom,
% 186.97/187.96 ! [V_a,T_a] :
% 186.97/187.96 ( class_Divides_Osemiring__div(T_a)
% 186.97/187.96 => 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) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_div__by__0,axiom,
% 186.97/187.96 ! [V_a,T_a] :
% 186.97/187.96 ( class_Divides_Osemiring__div(T_a)
% 186.97/187.96 => 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) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_div__by__1,axiom,
% 186.97/187.96 ! [V_a,T_a] :
% 186.97/187.96 ( class_Divides_Osemiring__div(T_a)
% 186.97/187.96 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_Pow__bottom,axiom,
% 186.97/187.96 ! [V_B_2,T_a] : hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),hAPP(c_Set_OPow(T_a),V_B_2))) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_Pow__empty,axiom,
% 186.97/187.96 ! [T_a] : hAPP(c_Set_OPow(T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_finite__Pow__iff,axiom,
% 186.97/187.96 ! [V_A_2,T_a] :
% 186.97/187.96 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OPow(T_a),V_A_2)))
% 186.97/187.96 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_Pow__insert,axiom,
% 186.97/187.96 ! [V_A_2,V_a_2,T_a] : hAPP(c_Set_OPow(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_a),V_A_2)),hAPP(c_Set_Oimage(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oinsert(T_a),V_a_2)),hAPP(c_Set_OPow(T_a),V_A_2))) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_PowD,axiom,
% 186.97/187.96 ! [V_B_2,V_A_2,T_a] :
% 186.97/187.96 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_a),V_B_2)))
% 186.97/187.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_Pow__iff,axiom,
% 186.97/187.96 ! [V_B_2,V_A_2,T_a] :
% 186.97/187.96 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_a),V_B_2)))
% 186.97/187.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_Pow__mono,axiom,
% 186.97/187.96 ! [V_B_2,V_A_2,T_a] :
% 186.97/187.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 186.97/187.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_a),V_A_2)),hAPP(c_Set_OPow(T_a),V_B_2))) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_image__Pow__surj,axiom,
% 186.97/187.96 ! [V_B_2,V_A_2,V_f_2,T_a,T_b] :
% 186.97/187.96 ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2) = V_B_2
% 186.97/187.96 => hAPP(c_Set_Oimage(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),c_Set_Oimage(T_b,T_a,V_f_2)),hAPP(c_Set_OPow(T_b),V_A_2)) = hAPP(c_Set_OPow(T_a),V_B_2) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_Un__Pow__subset,axiom,
% 186.97/187.96 ! [V_B_2,V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_a),V_A_2)),hAPP(c_Set_OPow(T_a),V_B_2))),hAPP(c_Set_OPow(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_Pow__Int__eq,axiom,
% 186.97/187.96 ! [V_B_2,V_A_2,T_a] : hAPP(c_Set_OPow(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_a),V_A_2)),hAPP(c_Set_OPow(T_a),V_B_2)) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_Divides_Otransfer__nat__int__function__closures_I1_J,axiom,
% 186.97/187.96 ! [V_y,V_x] :
% 186.97/187.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 186.97/187.96 => 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))) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_pos__imp__zdiv__neg__iff,axiom,
% 186.97/187.96 ! [V_a_2,V_b_2] :
% 186.97/187.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))
% 186.97/187.96 => ( 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)))
% 186.97/187.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_neg__imp__zdiv__neg__iff,axiom,
% 186.97/187.96 ! [V_a_2,V_b_2] :
% 186.97/187.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 186.97/187.96 => ( 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)))
% 186.97/187.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_div__neg__pos__less0,axiom,
% 186.97/187.96 ! [V_b,V_a] :
% 186.97/187.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 186.97/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 186.97/187.96 => 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))) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_zdiv__self,axiom,
% 186.97/187.96 ! [V_a] :
% 186.97/187.96 ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 186.97/187.96 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_a) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_div__mult__mult1,axiom,
% 186.97/187.96 ! [V_b,V_a,V_c,T_a] :
% 186.97/187.96 ( class_Divides_Osemiring__div(T_a)
% 186.97/187.96 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 186.97/187.96 => 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) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_div__mult__mult2,axiom,
% 186.97/187.96 ! [V_b,V_a,V_c,T_a] :
% 186.97/187.96 ( class_Divides_Osemiring__div(T_a)
% 186.97/187.96 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 186.97/187.96 => 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) ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_div__mult__self1__is__id,axiom,
% 186.97/187.96 ! [V_a,V_b,T_a] :
% 186.97/187.96 ( class_Divides_Osemiring__div(T_a)
% 186.97/187.96 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 186.97/187.96 => 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 ) ) ).
% 186.97/187.96
% 186.97/187.96 fof(fact_div__mult__self2__is__id,axiom,
% 186.97/187.96 ! [V_a,V_b,T_a] :
% 186.97/187.96 ( class_Divides_Osemiring__div(T_a)
% 186.97/187.96 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 187.18/187.96 => 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 ) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_div__mult__mult1__if,axiom,
% 187.18/187.96 ! [V_b,V_a,V_c,T_a] :
% 187.18/187.96 ( class_Divides_Osemiring__div(T_a)
% 187.18/187.96 => ( ( V_c = c_Groups_Ozero__class_Ozero(T_a)
% 187.18/187.96 => 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) )
% 187.18/187.96 & ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 187.18/187.96 => 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) ) ) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_div__self,axiom,
% 187.18/187.96 ! [V_a,T_a] :
% 187.18/187.96 ( class_Divides_Osemiring__div(T_a)
% 187.18/187.96 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 187.18/187.96 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_image__Pow__mono,axiom,
% 187.18/187.96 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 187.18/187.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2)),V_B_2))
% 187.18/187.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),c_Set_Oimage(T_b,T_a,V_f_2)),hAPP(c_Set_OPow(T_b),V_A_2))),hAPP(c_Set_OPow(T_a),V_B_2))) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_zdiv__eq__0__iff,axiom,
% 187.18/187.96 ! [V_k_2,V_i_2] :
% 187.18/187.96 ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_i_2),V_k_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.18/187.96 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.18/187.96 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i_2))
% 187.18/187.96 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),V_k_2)) )
% 187.18/187.96 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.18/187.96 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_i_2)) ) ) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_pos__imp__zdiv__nonneg__iff,axiom,
% 187.18/187.96 ! [V_a_2,V_b_2] :
% 187.18/187.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))
% 187.18/187.96 => ( 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)))
% 187.18/187.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_pos__imp__zdiv__pos__iff,axiom,
% 187.18/187.96 ! [V_i_2,V_k_2] :
% 187.18/187.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 187.18/187.96 => ( 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)))
% 187.18/187.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_i_2)) ) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_nonneg1__imp__zdiv__pos__iff,axiom,
% 187.18/187.96 ! [V_b_2,V_a_2] :
% 187.18/187.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2))
% 187.18/187.96 => ( 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)))
% 187.18/187.96 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),V_a_2))
% 187.18/187.96 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) ) ) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_zdiv__mono2,axiom,
% 187.18/187.96 ! [V_b,V_b_H,V_a] :
% 187.18/187.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 187.18/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 187.18/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 187.18/187.96 => 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))) ) ) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_div__nonneg__neg__le0,axiom,
% 187.18/187.96 ! [V_b,V_a] :
% 187.18/187.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 187.18/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.18/187.96 => 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))) ) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_div__pos__pos__trivial,axiom,
% 187.18/187.96 ! [V_b,V_a] :
% 187.18/187.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 187.18/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 187.18/187.96 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_neg__imp__zdiv__nonneg__iff,axiom,
% 187.18/187.96 ! [V_a_2,V_b_2] :
% 187.18/187.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.18/187.96 => ( 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)))
% 187.18/187.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_div__nonpos__pos__le0,axiom,
% 187.18/187.96 ! [V_b,V_a] :
% 187.18/187.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.18/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 187.18/187.96 => 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))) ) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_zdiv__mono2__neg,axiom,
% 187.18/187.96 ! [V_b,V_b_H,V_a] :
% 187.18/187.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.18/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 187.18/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 187.18/187.96 => 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))) ) ) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_div__neg__neg__trivial,axiom,
% 187.18/187.96 ! [V_b,V_a] :
% 187.18/187.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.18/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a))
% 187.18/187.96 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_zdiv__mono1,axiom,
% 187.18/187.96 ! [V_b,V_a_H,V_a] :
% 187.18/187.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H))
% 187.18/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 187.18/187.96 => 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))) ) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_zdiv__mono1__neg,axiom,
% 187.18/187.96 ! [V_b,V_a_H,V_a] :
% 187.18/187.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H))
% 187.18/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.18/187.96 => 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))) ) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_int__div__less__self,axiom,
% 187.18/187.96 ! [V_k,V_x] :
% 187.18/187.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 187.18/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k))
% 187.18/187.96 => 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)) ) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_zdiv__zmult2__eq,axiom,
% 187.18/187.96 ! [V_b,V_a,V_c] :
% 187.18/187.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 187.18/187.96 => 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) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_div__mult__self2,axiom,
% 187.18/187.96 ! [V_c,V_a,V_b,T_a] :
% 187.18/187.96 ( class_Divides_Osemiring__div(T_a)
% 187.18/187.96 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 187.18/187.96 => 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)) ) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_div__mult__self1,axiom,
% 187.18/187.96 ! [V_c,V_a,V_b,T_a] :
% 187.18/187.96 ( class_Divides_Osemiring__div(T_a)
% 187.18/187.96 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 187.18/187.96 => 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)) ) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_div__add__self1,axiom,
% 187.18/187.96 ! [V_a,V_b,T_a] :
% 187.18/187.96 ( class_Divides_Osemiring__div(T_a)
% 187.18/187.96 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 187.18/187.96 => 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)) ) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_div__add__self2,axiom,
% 187.18/187.96 ! [V_a,V_b,T_a] :
% 187.18/187.96 ( class_Divides_Osemiring__div(T_a)
% 187.18/187.96 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 187.18/187.96 => 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)) ) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_com_Osize_I15_J,axiom,
% 187.18/187.96 ! [V_pname] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),hAPP(c_Com_Ocom_OBODY,V_pname)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_com_Osize_I7_J,axiom,
% 187.18/187.96 ! [V_pname] : c_Com_Ocom_Ocom__size(hAPP(c_Com_Ocom_OBODY,V_pname)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_com_Osize_I9_J,axiom,
% 187.18/187.96 hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_com_Osize_I1_J,axiom,
% 187.18/187.96 c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_divmod__int__rel__div__eq,axiom,
% 187.18/187.96 ! [V_r_1,V_y,V_b_1,V_a_1] :
% 187.18/187.96 ( 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)
% 187.18/187.96 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 187.18/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_1))
% 187.18/187.96 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_1),V_b_1)) ) )
% 187.18/187.96 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 187.18/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_r_1))
% 187.18/187.96 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r_1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
% 187.18/187.96 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.18/187.96 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_1),V_b_1) = V_y ) ) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_split__zdiv,axiom,
% 187.18/187.96 ! [V_k_2,V_n_2,V_P_2] :
% 187.18/187.96 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)))
% 187.18/187.96 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.18/187.96 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 187.18/187.96 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 187.18/187.96 => ! [B_i] :
% 187.18/187.96 ( ? [B_j] :
% 187.18/187.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))
% 187.18/187.96 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
% 187.18/187.96 & 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) )
% 187.18/187.96 => hBOOL(hAPP(V_P_2,B_i)) ) )
% 187.18/187.96 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.18/187.96 => ! [B_i] :
% 187.18/187.96 ( ? [B_j] :
% 187.18/187.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j))
% 187.18/187.96 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.18/187.96 & 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) )
% 187.18/187.96 => hBOOL(hAPP(V_P_2,B_i)) ) ) ) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_Powp__Pow__eq,axiom,
% 187.18/187.96 ! [V_x_2,V_A_2,T_a] :
% 187.18/187.96 ( hBOOL(hAPP(c_Predicate_OPowp(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)),V_x_2))
% 187.18/187.96 <=> hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_x_2),hAPP(c_Set_OPow(T_a),V_A_2))) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_split__neg__lemma,axiom,
% 187.18/187.96 ! [V_n_2,V_P_2,V_k_2] :
% 187.18/187.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.18/187.96 => ( 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)))
% 187.18/187.96 <=> ! [B_i,B_j] :
% 187.18/187.96 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j))
% 187.18/187.96 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.18/187.96 & 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) )
% 187.18/187.96 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) ) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_split__pos__lemma,axiom,
% 187.18/187.96 ! [V_n_2,V_P_2,V_k_2] :
% 187.18/187.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 187.18/187.96 => ( 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)))
% 187.18/187.96 <=> ! [B_i,B_j] :
% 187.18/187.96 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))
% 187.18/187.96 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
% 187.18/187.96 & 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) )
% 187.18/187.96 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) ) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_diff__Suc,axiom,
% 187.18/187.96 ! [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)) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_setprod__pos__nat,axiom,
% 187.18/187.96 ! [V_f_2,V_S_2,T_a] :
% 187.18/187.96 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 187.18/187.96 => ( ! [B_x] :
% 187.18/187.96 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2))
% 187.18/187.96 => 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))) )
% 187.18/187.96 => 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_a,tc_Nat_Onat),V_f_2),V_S_2))) ) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_evaln_OBody,axiom,
% 187.18/187.96 ! [V_s1,V_n,V_s0,V_pn] :
% 187.18/187.96 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn))),V_s0),V_n),V_s1))
% 187.18/187.96 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Com_Ocom_OBODY,V_pn)),V_s0),hAPP(c_Nat_OSuc,V_n)),V_s1)) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_arith__series__nat,axiom,
% 187.18/187.96 ! [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)))) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_finite__lessThan,axiom,
% 187.18/187.96 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_k_2))) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_evaln_OWhileTrue,axiom,
% 187.18/187.96 ! [V_s2_2,V_s1_2,V_n_2,V_c_2,V_s0_2,V_b_2] :
% 187.18/187.96 ( hBOOL(hAPP(V_b_2,V_s0_2))
% 187.18/187.96 => ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c_2),V_s0_2),V_n_2),V_s1_2))
% 187.18/187.96 => ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(V_b_2,V_c_2)),V_s1_2),V_n_2),V_s2_2))
% 187.18/187.96 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(V_b_2,V_c_2)),V_s0_2),V_n_2),V_s2_2)) ) ) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_evaln_OWhileFalse,axiom,
% 187.18/187.96 ! [V_n_2,V_c_2,V_s_2,V_b_2] :
% 187.18/187.96 ( ~ hBOOL(hAPP(V_b_2,V_s_2))
% 187.18/187.96 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(V_b_2,V_c_2)),V_s_2),V_n_2),V_s_2)) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_evaln_OSemi,axiom,
% 187.18/187.96 ! [V_s2,V_c1,V_s1,V_n,V_s0,V_c0] :
% 187.18/187.96 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c0),V_s0),V_n),V_s1))
% 187.18/187.96 => ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c1),V_s1),V_n),V_s2))
% 187.18/187.96 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSemi(V_c0,V_c1)),V_s0),V_n),V_s2)) ) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_evaln__elim__cases_I1_J,axiom,
% 187.18/187.96 ! [V_t,V_n,V_s] :
% 187.18/187.96 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSKIP),V_s),V_n),V_t))
% 187.18/187.96 => V_t = V_s ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_evaln_OSkip,axiom,
% 187.18/187.96 ! [V_n,V_s] : hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSKIP),V_s),V_n),V_s)) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_card__lessThan,axiom,
% 187.18/187.96 ! [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 ).
% 187.18/187.96
% 187.18/187.96 fof(fact_lessThan__0,axiom,
% 187.18/187.96 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)) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_lessThan__eq__iff,axiom,
% 187.18/187.96 ! [V_y_2,V_x_2,T_a] :
% 187.18/187.96 ( class_Orderings_Olinorder(T_a)
% 187.18/187.96 => ( hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_x_2) = hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_y_2)
% 187.18/187.96 <=> V_x_2 = V_y_2 ) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_mod__mod__trivial,axiom,
% 187.18/187.96 ! [V_b,V_a,T_a] :
% 187.18/187.96 ( class_Divides_Osemiring__div(T_a)
% 187.18/187.96 => 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) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_lessThan__Suc,axiom,
% 187.18/187.96 ! [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)) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_mod__self,axiom,
% 187.18/187.96 ! [V_a,T_a] :
% 187.18/187.96 ( class_Divides_Osemiring__div(T_a)
% 187.18/187.96 => c_Divides_Odiv__class_Omod(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_mod__by__0,axiom,
% 187.18/187.96 ! [V_a,T_a] :
% 187.18/187.96 ( class_Divides_Osemiring__div(T_a)
% 187.18/187.96 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_mod__0,axiom,
% 187.18/187.96 ! [V_a,T_a] :
% 187.18/187.96 ( class_Divides_Osemiring__div(T_a)
% 187.18/187.96 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_mod__add__cong,axiom,
% 187.18/187.96 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 187.18/187.96 ( class_Divides_Osemiring__div(T_a)
% 187.18/187.96 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 187.18/187.96 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 187.18/187.96 => 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) ) ) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_zmod__simps_I1_J,axiom,
% 187.18/187.96 ! [V_b,V_c,V_a,T_a] :
% 187.18/187.96 ( class_Divides_Osemiring__div(T_a)
% 187.18/187.96 => 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) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_zmod__simps_I2_J,axiom,
% 187.18/187.96 ! [V_c,V_b,V_a,T_a] :
% 187.18/187.96 ( class_Divides_Osemiring__div(T_a)
% 187.18/187.96 => 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) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_mod__add__eq,axiom,
% 187.18/187.96 ! [V_c,V_b,V_a,T_a] :
% 187.18/187.96 ( class_Divides_Osemiring__div(T_a)
% 187.18/187.96 => 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) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_mod__add__left__eq,axiom,
% 187.18/187.96 ! [V_c,V_b,V_a,T_a] :
% 187.18/187.96 ( class_Divides_Osemiring__div(T_a)
% 187.18/187.96 => 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) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_mod__add__right__eq,axiom,
% 187.18/187.96 ! [V_c,V_b,V_a,T_a] :
% 187.18/187.96 ( class_Divides_Osemiring__div(T_a)
% 187.18/187.96 => 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) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_mod__add__self1,axiom,
% 187.18/187.96 ! [V_a,V_b,T_a] :
% 187.18/187.96 ( class_Divides_Osemiring__div(T_a)
% 187.18/187.96 => 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) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_mod__add__self2,axiom,
% 187.18/187.96 ! [V_b,V_a,T_a] :
% 187.18/187.96 ( class_Divides_Osemiring__div(T_a)
% 187.18/187.96 => 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) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_mod__mult__cong,axiom,
% 187.18/187.96 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 187.18/187.96 ( class_Divides_Osemiring__div(T_a)
% 187.18/187.96 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 187.18/187.96 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 187.18/187.96 => 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) ) ) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_zmod__simps_I4_J,axiom,
% 187.18/187.96 ! [V_b,V_c,V_a,T_a] :
% 187.18/187.96 ( class_Divides_Osemiring__div(T_a)
% 187.18/187.96 => 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) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_mod__mult__mult2,axiom,
% 187.18/187.96 ! [V_b,V_c,V_a,T_a] :
% 187.18/187.96 ( class_Divides_Osemiring__div(T_a)
% 187.18/187.96 => 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) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_mod__mult__mult1,axiom,
% 187.18/187.96 ! [V_b,V_a,V_c,T_a] :
% 187.18/187.96 ( class_Divides_Osemiring__div(T_a)
% 187.18/187.96 => 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)) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_mod__mult__eq,axiom,
% 187.18/187.96 ! [V_c,V_b,V_a,T_a] :
% 187.18/187.96 ( class_Divides_Osemiring__div(T_a)
% 187.18/187.96 => 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) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_mod__mult__left__eq,axiom,
% 187.18/187.96 ! [V_c,V_b,V_a,T_a] :
% 187.18/187.96 ( class_Divides_Osemiring__div(T_a)
% 187.18/187.96 => 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) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_mod__mult__right__eq,axiom,
% 187.18/187.96 ! [V_c,V_b,V_a,T_a] :
% 187.18/187.96 ( class_Divides_Osemiring__div(T_a)
% 187.18/187.96 => 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) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_mod__diff__cong,axiom,
% 187.18/187.96 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 187.18/187.96 ( class_Divides_Oring__div(T_a)
% 187.18/187.96 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 187.18/187.96 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 187.18/187.96 => 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) ) ) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_mod__diff__eq,axiom,
% 187.18/187.96 ! [V_c,V_b,V_a,T_a] :
% 187.18/187.96 ( class_Divides_Oring__div(T_a)
% 187.18/187.96 => 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) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_mod__diff__left__eq,axiom,
% 187.18/187.96 ! [V_c,V_b,V_a,T_a] :
% 187.18/187.96 ( class_Divides_Oring__div(T_a)
% 187.18/187.96 => 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) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_mod__diff__right__eq,axiom,
% 187.18/187.96 ! [V_c,V_b,V_a,T_a] :
% 187.18/187.96 ( class_Divides_Oring__div(T_a)
% 187.18/187.96 => 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) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_div__le__dividend,axiom,
% 187.18/187.96 ! [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)) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_div__le__mono,axiom,
% 187.18/187.96 ! [V_k,V_n,V_m] :
% 187.18/187.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 187.18/187.96 => 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))) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_div__mult2__eq,axiom,
% 187.18/187.96 ! [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) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_zmod__self,axiom,
% 187.18/187.96 ! [V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_a) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_zmod__zero,axiom,
% 187.18/187.96 ! [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) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_evaln__Suc,axiom,
% 187.18/187.96 ! [V_s_H,V_n,V_s,V_c] :
% 187.18/187.96 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),V_n),V_s_H))
% 187.18/187.96 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),hAPP(c_Nat_OSuc,V_n)),V_s_H)) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_zmod__simps_I3_J,axiom,
% 187.18/187.96 ! [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) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_zmod__zmult1__eq,axiom,
% 187.18/187.96 ! [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) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_evaln__nonstrict,axiom,
% 187.18/187.96 ! [V_m,V_t,V_n,V_s,V_c] :
% 187.18/187.96 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),V_n),V_t))
% 187.18/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 187.18/187.96 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),V_m),V_t)) ) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_zdiff__zmod__right,axiom,
% 187.18/187.96 ! [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) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_zdiff__zmod__left,axiom,
% 187.18/187.96 ! [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) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_eval__eq,axiom,
% 187.18/187.96 ! [V_t_2,V_s_2,V_c_2] :
% 187.18/187.96 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c_2),V_s_2),V_t_2))
% 187.18/187.96 <=> ? [B_n] : hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c_2),V_s_2),B_n),V_t_2)) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_evaln__evalc,axiom,
% 187.18/187.96 ! [V_t,V_n,V_s,V_c] :
% 187.18/187.96 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),V_n),V_t))
% 187.18/187.96 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_t)) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_evaln_Oequations_I8_J,axiom,
% 187.18/187.96 ! [V_a6_2,V_a4_2,V_a2_2,V_a3_2,V_a1_2] :
% 187.18/187.96 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),V_a2_2),V_a4_2),V_a6_2))
% 187.18/187.96 <=> ( ( V_a6_2 = V_a2_2
% 187.18/187.96 & ~ hBOOL(hAPP(V_a1_2,V_a2_2)) )
% 187.18/187.96 | ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 187.18/187.96 & ? [B_s1] :
% 187.18/187.96 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a3_2),V_a2_2),V_a4_2),B_s1))
% 187.18/187.96 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),B_s1),V_a4_2),V_a6_2)) ) ) ) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_evaln_Oequations_I7_J,axiom,
% 187.18/187.96 ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2] :
% 187.18/187.96 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),V_a2_2),V_a4_2),V_a2_2))
% 187.18/187.96 <=> ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 187.18/187.96 => ? [B_s1] :
% 187.18/187.96 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a3_2),V_a2_2),V_a4_2),B_s1))
% 187.18/187.96 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),B_s1),V_a4_2),V_a2_2)) ) ) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_zpower__zmod,axiom,
% 187.18/187.96 ! [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) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_evaln_Oequations_I4_J,axiom,
% 187.18/187.96 ! [V_a6_2,V_a3_2,V_a2_2,V_a5_2,V_a1_2] :
% 187.18/187.96 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSemi(V_a1_2,V_a5_2)),V_a2_2),V_a3_2),V_a6_2))
% 187.18/187.96 <=> ? [B_s1] :
% 187.18/187.96 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a1_2),V_a2_2),V_a3_2),B_s1))
% 187.18/187.96 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a5_2),B_s1),V_a3_2),V_a6_2)) ) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_evaln_Oequations_I1_J,axiom,
% 187.18/187.96 ! [V_a2,V_a1] : hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSKIP),V_a1),V_a2),V_a1)) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_lessThan__Suc__eq__insert__0,axiom,
% 187.18/187.96 ! [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))) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_lessThan__iff,axiom,
% 187.18/187.96 ! [V_k_2,V_i_2,T_a] :
% 187.18/187.96 ( class_Orderings_Oord(T_a)
% 187.18/187.96 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_k_2)))
% 187.18/187.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_i_2),V_k_2)) ) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_lessThan__subset__iff,axiom,
% 187.18/187.96 ! [V_y_2,V_x_2,T_a] :
% 187.18/187.96 ( class_Orderings_Olinorder(T_a)
% 187.18/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_x_2)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_y_2)))
% 187.18/187.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) ) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_setsum__lessThan__Suc,axiom,
% 187.18/187.96 ! [V_n_2,V_f_2,T_a] :
% 187.18/187.96 ( class_Groups_Ocomm__monoid__add(T_a)
% 187.18/187.96 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))),hAPP(V_f_2,V_n_2)) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_mod__mult__self2__is__0,axiom,
% 187.18/187.96 ! [V_b,V_a,T_a] :
% 187.18/187.96 ( class_Divides_Osemiring__div(T_a)
% 187.18/187.96 => 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) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_mod__mult__self1__is__0,axiom,
% 187.18/187.96 ! [V_a,V_b,T_a] :
% 187.18/187.96 ( class_Divides_Osemiring__div(T_a)
% 187.18/187.96 => 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) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_mod__mult__self1,axiom,
% 187.18/187.96 ! [V_b,V_c,V_a,T_a] :
% 187.18/187.96 ( class_Divides_Osemiring__div(T_a)
% 187.18/187.96 => 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) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_mod__mult__self2,axiom,
% 187.18/187.96 ! [V_c,V_b,V_a,T_a] :
% 187.18/187.96 ( class_Divides_Osemiring__div(T_a)
% 187.18/187.96 => 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) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_mod__by__1,axiom,
% 187.18/187.96 ! [V_a,T_a] :
% 187.18/187.96 ( class_Divides_Osemiring__div(T_a)
% 187.18/187.96 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_mod__div__trivial,axiom,
% 187.18/187.96 ! [V_b,V_a,T_a] :
% 187.18/187.96 ( class_Divides_Osemiring__div(T_a)
% 187.18/187.96 => 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) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_div__1,axiom,
% 187.18/187.96 ! [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 ).
% 187.18/187.96
% 187.18/187.96 fof(fact_lessThan__strict__subset__iff,axiom,
% 187.18/187.96 ! [V_n_2,V_m_2,T_a] :
% 187.18/187.96 ( class_Orderings_Olinorder(T_a)
% 187.18/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_m_2)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_n_2)))
% 187.18/187.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_m_2),V_n_2)) ) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_div__less,axiom,
% 187.18/187.96 ! [V_n,V_m] :
% 187.18/187.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 187.18/187.96 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_nat__mult__div__cancel__disj,axiom,
% 187.18/187.96 ! [V_n,V_m,V_k] :
% 187.18/187.96 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.18/187.96 => 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) )
% 187.18/187.96 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.18/187.96 => 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) ) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_Divides_Otransfer__nat__int__function__closures_I2_J,axiom,
% 187.18/187.96 ! [V_y,V_x] :
% 187.18/187.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 187.18/187.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 187.18/187.96 => 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))) ) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_zmod__le__nonneg__dividend,axiom,
% 187.18/187.96 ! [V_k,V_m] :
% 187.18/187.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m))
% 187.18/187.96 => 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)) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_neg__mod__bound,axiom,
% 187.18/187.96 ! [V_a,V_b] :
% 187.18/187.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.18/187.96 => 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))) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_pos__mod__bound,axiom,
% 187.18/187.96 ! [V_a,V_b] :
% 187.18/187.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 187.18/187.96 => 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)) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_zmod__eq__0__iff,axiom,
% 187.18/187.96 ! [V_d_2,V_m_2] :
% 187.18/187.96 ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.18/187.96 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_d_2),B_q) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_DIVISION__BY__ZERO,axiom,
% 187.18/187.96 ! [V_a] :
% 187.18/187.96 ( 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)
% 187.18/187.96 & c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_a ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_zmod__zdiv__trivial,axiom,
% 187.18/187.96 ! [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) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_zdiv__zadd1__eq,axiom,
% 187.18/187.96 ! [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)) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_triple__valid__def2,axiom,
% 187.18/187.96 ! [V_Q_2,V_c_2,V_P_2,V_n_2,T_a] :
% 187.18/187.96 ( c_Hoare__Mirabelle_Otriple__valid(T_a,V_n_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),V_c_2),V_Q_2))
% 187.18/187.96 <=> ! [B_Z,B_s] :
% 187.18/187.96 ( hBOOL(hAPP(hAPP(V_P_2,B_Z),B_s))
% 187.18/187.96 => ! [B_s_H] :
% 187.18/187.96 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c_2),B_s),V_n_2),B_s_H))
% 187.18/187.96 => hBOOL(hAPP(hAPP(V_Q_2,B_Z),B_s_H)) ) ) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_nat__case__0,axiom,
% 187.18/187.96 ! [V_f2_2,V_f1_2,T_a] : c_Nat_Onat_Onat__case(T_a,V_f1_2,V_f2_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_f1_2 ).
% 187.18/187.96
% 187.18/187.96 fof(fact_nat__case__Suc,axiom,
% 187.18/187.96 ! [V_nat_2,V_f2_2,V_f1_2,T_a] : c_Nat_Onat_Onat__case(T_a,V_f1_2,V_f2_2,hAPP(c_Nat_OSuc,V_nat_2)) = hAPP(V_f2_2,V_nat_2) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_single__Diff__lessThan,axiom,
% 187.18/187.96 ! [V_k_2,T_a] :
% 187.18/187.96 ( class_Orderings_Oorder(T_a)
% 187.18/187.96 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_k_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_k_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_k_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_semiring__div__class_Omod__div__equality_H,axiom,
% 187.18/187.96 ! [V_b,V_a,T_a] :
% 187.18/187.96 ( class_Divides_Osemiring__div(T_a)
% 187.18/187.96 => 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 ) ).
% 187.18/187.96
% 187.18/187.96 fof(fact_mod__div__equality2,axiom,
% 187.18/187.96 ! [V_a,V_b,T_a] :
% 187.18/187.96 ( class_Divides_Osemiring__div(T_a)
% 187.18/187.97 => 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 ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_mod__div__equality,axiom,
% 187.18/187.97 ! [V_b,V_a,T_a] :
% 187.18/187.97 ( class_Divides_Osemiring__div(T_a)
% 187.18/187.97 => 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 ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_div__mod__equality2,axiom,
% 187.18/187.97 ! [V_c,V_a,V_b,T_a] :
% 187.18/187.97 ( class_Divides_Osemiring__div(T_a)
% 187.18/187.97 => 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) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_div__mod__equality,axiom,
% 187.18/187.97 ! [V_c,V_b,V_a,T_a] :
% 187.18/187.97 ( class_Divides_Osemiring__div(T_a)
% 187.18/187.97 => 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) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_div__le__mono2,axiom,
% 187.18/187.97 ! [V_k,V_n,V_m] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 187.18/187.97 => 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))) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_div__mult__self__is__m,axiom,
% 187.18/187.97 ! [V_m,V_n] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 187.18/187.97 => 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 ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_div__mult__self1__is__m,axiom,
% 187.18/187.97 ! [V_m,V_n] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 187.18/187.97 => 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 ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_nat__mult__div__cancel1,axiom,
% 187.18/187.97 ! [V_n,V_m,V_k] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 187.18/187.97 => 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) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_div__less__dividend,axiom,
% 187.18/187.97 ! [V_m,V_n] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n))
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 187.18/187.97 => 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)) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_mod__neg__neg__trivial,axiom,
% 187.18/187.97 ! [V_b,V_a] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a))
% 187.18/187.97 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_neg__mod__conj,axiom,
% 187.18/187.97 ! [V_a,V_b] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.18/187.97 => ( 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)))
% 187.18/187.97 & 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))) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_neg__mod__sign,axiom,
% 187.18/187.97 ! [V_a,V_b] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.18/187.97 => 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))) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_mod__pos__pos__trivial,axiom,
% 187.18/187.97 ! [V_b,V_a] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 187.18/187.97 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_pos__mod__conj,axiom,
% 187.18/187.97 ! [V_a,V_b] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 187.18/187.97 => ( 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)))
% 187.18/187.97 & 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)) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_pos__mod__sign,axiom,
% 187.18/187.97 ! [V_a,V_b] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 187.18/187.97 => 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))) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_zmod__zdiv__equality,axiom,
% 187.18/187.97 ! [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)) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_zdiv__zmult1__eq,axiom,
% 187.18/187.97 ! [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)) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_zdiv__zmod__equality,axiom,
% 187.18/187.97 ! [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) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_zdiv__zmod__equality2,axiom,
% 187.18/187.97 ! [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) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_zmult__div__cancel,axiom,
% 187.18/187.97 ! [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)) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_zmod__zdiv__equality_H,axiom,
% 187.18/187.97 ! [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)) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_Powp__mono,axiom,
% 187.18/187.97 ! [V_B_2,V_A_2,T_a] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 187.18/187.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),c_Predicate_OPowp(T_a,V_A_2)),c_Predicate_OPowp(T_a,V_B_2))) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_finite__nat__set__iff__bounded,axiom,
% 187.18/187.97 ! [V_N_2] :
% 187.18/187.97 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2))
% 187.18/187.97 <=> ? [B_m] :
% 187.18/187.97 ! [B_x] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
% 187.18/187.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_x),B_m)) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_finite__nat__set__iff__bounded__le,axiom,
% 187.18/187.97 ! [V_N_2] :
% 187.18/187.97 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2))
% 187.18/187.97 <=> ? [B_m] :
% 187.18/187.97 ! [B_x] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
% 187.18/187.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_x),B_m)) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_div__geq,axiom,
% 187.18/187.97 ! [V_m,V_n] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 187.18/187.97 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 187.18/187.97 => 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)) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_div__if,axiom,
% 187.18/187.97 ! [V_m,V_n] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 187.18/187.97 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 187.18/187.97 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 187.18/187.97 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 187.18/187.97 => 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)) ) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_split__div,axiom,
% 187.18/187.97 ! [V_k_2,V_n_2,V_P_2] :
% 187.18/187.97 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n_2),V_k_2)))
% 187.18/187.97 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.18/187.97 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 187.18/187.97 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.18/187.97 => ! [B_i,B_j] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2))
% 187.18/187.97 => ( 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)
% 187.18/187.97 => hBOOL(hAPP(V_P_2,B_i)) ) ) ) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_mod__pos__neg__trivial,axiom,
% 187.18/187.97 ! [V_b,V_a] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 187.18/187.97 => ( 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)))
% 187.18/187.97 => 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) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_triple__valid__def,axiom,
% 187.18/187.97 ! [V_t_2,V_n_2,T_a] :
% 187.18/187.97 ( c_Hoare__Mirabelle_Otriple__valid(T_a,V_n_2,V_t_2)
% 187.18/187.97 <=> hBOOL(c_Hoare__Mirabelle_Otriple_Otriple__case(T_a,tc_HOL_Obool,hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_HOL_Obool),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_HOL_OAll(T_a)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OAll(tc_Com_Ostate))))),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))))),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_COMBB(tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_COMBS(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_a),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fimplies))))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_HOL_Obool,tc_Com_Ostate),c_HOL_OAll(tc_Com_Ostate))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_Com_Ocom),c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_a)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),c_COMBC(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(tc_Com_Ostate,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Com_Ostate),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Com_Ostate),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fimplies))),hAPP(hAPP(c_COMBC(tc_Com_Ocom,tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),c_COMBC(tc_Com_Ostate,tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_Natural_Oevaln)),V_n_2))))))))),V_t_2)) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_evaln_Oequations_I9_J,axiom,
% 187.18/187.97 ! [V_a4_2,V_a3_2,V_a2_2,V_a1_2] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Com_Ocom_OBODY,V_a1_2)),V_a2_2),hAPP(c_Nat_OSuc,V_a3_2)),V_a4_2))
% 187.18/187.97 <=> hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_a1_2))),V_a2_2),V_a3_2),V_a4_2)) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_le__div__geq,axiom,
% 187.18/187.97 ! [V_m,V_n] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 187.18/187.97 => 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)) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_split__div_H,axiom,
% 187.18/187.97 ! [V_n_2,V_m_2,V_P_2] :
% 187.18/187.97 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2)))
% 187.18/187.97 <=> ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.18/187.97 & hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 187.18/187.97 | ? [B_q] :
% 187.18/187.97 ( 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))
% 187.18/187.97 & 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))))
% 187.18/187.97 & hBOOL(hAPP(V_P_2,B_q)) ) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_split__div__lemma,axiom,
% 187.18/187.97 ! [V_m_2,V_q_2,V_n_2] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 187.18/187.97 => ( ( 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))
% 187.18/187.97 & 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)))) )
% 187.18/187.97 <=> V_q_2 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_split__zmod,axiom,
% 187.18/187.97 ! [V_k_2,V_n_2,V_P_2] :
% 187.18/187.97 ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))
% 187.18/187.97 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.18/187.97 => hBOOL(hAPP(V_P_2,V_n_2)) )
% 187.18/187.97 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 187.18/187.97 => ! [B_i,B_j] :
% 187.18/187.97 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))
% 187.18/187.97 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
% 187.18/187.97 & 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) )
% 187.18/187.97 => hBOOL(hAPP(V_P_2,B_j)) ) )
% 187.18/187.97 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.18/187.97 => ! [B_i,B_j] :
% 187.18/187.97 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j))
% 187.18/187.97 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.18/187.97 & 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) )
% 187.18/187.97 => hBOOL(hAPP(V_P_2,B_j)) ) ) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_zmult2__lemma__aux3,axiom,
% 187.18/187.97 ! [V_q,V_b,V_r,V_c] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 187.18/187.97 => 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))) ) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_zmult2__lemma__aux4,axiom,
% 187.18/187.97 ! [V_q,V_b,V_r,V_c] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 187.18/187.97 => 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))) ) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_zmult2__lemma__aux1,axiom,
% 187.18/187.97 ! [V_q,V_r,V_b,V_c] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.18/187.97 => 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))) ) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_zmult2__lemma__aux2,axiom,
% 187.18/187.97 ! [V_q,V_r,V_b,V_c] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.18/187.97 => 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))) ) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_divmod__int__rel__mod__eq,axiom,
% 187.18/187.97 ! [V_y,V_q_1,V_b_1,V_a_1] :
% 187.18/187.97 ( 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)
% 187.18/187.97 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 187.18/187.97 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_b_1)) ) )
% 187.18/187.97 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_y))
% 187.18/187.97 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
% 187.18/187.97 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.18/187.97 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a_1,V_b_1) = V_y ) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_zmod__zmult2__eq,axiom,
% 187.18/187.97 ! [V_b,V_a,V_c] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 187.18/187.97 => 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)) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_evaln__elim__cases_I6_J,axiom,
% 187.18/187.97 ! [V_s1,V_n,V_s,V_P] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Com_Ocom_OBODY,V_P)),V_s),V_n),V_s1))
% 187.18/187.97 => ~ ! [B_n] :
% 187.18/187.97 ( V_n = hAPP(c_Nat_OSuc,B_n)
% 187.18/187.97 => ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_P))),V_s),B_n),V_s1)) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_arith__series__general,axiom,
% 187.18/187.97 ! [V_n_2,V_d_2,V_a_2,T_a] :
% 187.18/187.97 ( class_Rings_Ocomm__semiring__1(T_a)
% 187.18/187.97 => 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(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(T_a)),c_Nat_Osemiring__1__class_Oof__nat(T_a))),V_d_2))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),V_d_2)))) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_ord_OatMost__iff,axiom,
% 187.18/187.97 ! [V_k_2,V_less__eq_2,V_i_2,T_a] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OatMost(T_a,V_less__eq_2,V_k_2)))
% 187.18/187.97 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_k_2)) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_ord_OatLeast__iff,axiom,
% 187.18/187.97 ! [V_k_2,V_less__eq_2,V_i_2,T_a] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OatLeast(T_a,V_less__eq_2,V_k_2)))
% 187.18/187.97 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_k_2),V_i_2)) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_ord_OlessThan__iff,axiom,
% 187.18/187.97 ! [V_k_2,V_less_2,V_i_2,T_a] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OlessThan(T_a,V_less_2,V_k_2)))
% 187.18/187.97 <=> hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_k_2)) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_ord_OgreaterThan__iff,axiom,
% 187.18/187.97 ! [V_k_2,V_less_2,V_i_2,T_a] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OgreaterThan(T_a,V_less_2,V_k_2)))
% 187.18/187.97 <=> hBOOL(hAPP(hAPP(V_less_2,V_k_2),V_i_2)) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_ord_OatLeastAtMost__iff,axiom,
% 187.18/187.97 ! [V_u_2,V_l_2,V_less__eq_2,V_i_2,T_a] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OatLeastAtMost(T_a,V_less__eq_2,V_l_2,V_u_2)))
% 187.18/187.97 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2))
% 187.18/187.97 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J,axiom,
% 187.18/187.97 ! [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)) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_transfer__nat__int__set__relations_I1_J,axiom,
% 187.18/187.97 ! [V_A_2] :
% 187.18/187.97 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_A_2))
% 187.18/187.97 <=> 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))) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J,axiom,
% 187.18/187.97 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))) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_Divides_Otransfer__int__nat__functions_I2_J,axiom,
% 187.18/187.97 ! [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)) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_zmod__int,axiom,
% 187.18/187.97 ! [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)) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_of__nat__eq__iff,axiom,
% 187.18/187.97 ! [V_n_2,V_m_2,T_a] :
% 187.18/187.97 ( class_Nat_Osemiring__char__0(T_a)
% 187.18/187.97 => ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2)
% 187.18/187.97 <=> V_m_2 = V_n_2 ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_mod__Suc__eq__Suc__mod,axiom,
% 187.18/187.97 ! [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) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_mod__less,axiom,
% 187.18/187.97 ! [V_n,V_m] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 187.18/187.97 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_div__add1__eq,axiom,
% 187.18/187.97 ! [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)) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_mod__less__eq__dividend,axiom,
% 187.18/187.97 ! [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)) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_mod__mult__distrib2,axiom,
% 187.18/187.97 ! [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)) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_mod__mult__distrib,axiom,
% 187.18/187.97 ! [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)) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_Divides_Otransfer__int__nat__functions_I1_J,axiom,
% 187.18/187.97 ! [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)) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_zdiv__int,axiom,
% 187.18/187.97 ! [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)) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_int__setsum,axiom,
% 187.18/187.97 ! [V_A_2,V_f_2,T_a] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_a),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_int__setprod,axiom,
% 187.18/187.97 ! [V_A_2,V_f_2,T_a] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_a),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_mod__Suc,axiom,
% 187.18/187.97 ! [V_n,V_m] :
% 187.18/187.97 ( ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) = V_n
% 187.18/187.97 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 187.18/187.97 & ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) != V_n
% 187.18/187.97 => 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)) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_mod__1,axiom,
% 187.18/187.97 ! [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) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_mod__less__divisor,axiom,
% 187.18/187.97 ! [V_m,V_n] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 187.18/187.97 => 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)) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_transfer__int__nat__numerals_I1_J,axiom,
% 187.18/187.97 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)) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_int__0,axiom,
% 187.18/187.97 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) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_int__eq__0__conv,axiom,
% 187.18/187.97 ! [V_n_2] :
% 187.18/187.97 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.18/187.97 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_mod__eq__0__iff,axiom,
% 187.18/187.97 ! [V_d_2,V_m_2] :
% 187.18/187.97 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.18/187.97 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_d_2),B_q) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_mod__geq,axiom,
% 187.18/187.97 ! [V_n,V_m] :
% 187.18/187.97 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 187.18/187.97 => 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) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_mod__if,axiom,
% 187.18/187.97 ! [V_n,V_m] :
% 187.18/187.97 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 187.18/187.97 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m )
% 187.18/187.97 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 187.18/187.97 => 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) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J,axiom,
% 187.18/187.97 ! [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))) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_transfer__int__nat__quantifiers_I2_J,axiom,
% 187.18/187.97 ! [V_P_2] :
% 187.18/187.97 ( ? [B_x] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 187.18/187.97 & hBOOL(hAPP(V_P_2,B_x)) )
% 187.18/187.97 <=> ? [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_transfer__int__nat__quantifiers_I1_J,axiom,
% 187.18/187.97 ! [V_P_2] :
% 187.18/187.97 ( ! [B_x] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 187.18/187.97 => hBOOL(hAPP(V_P_2,B_x)) )
% 187.18/187.97 <=> ! [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_zero__zle__int,axiom,
% 187.18/187.97 ! [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))) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_int__less__0__conv,axiom,
% 187.18/187.97 ! [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))) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_mod__mult__self3,axiom,
% 187.18/187.97 ! [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) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_div__mult1__eq,axiom,
% 187.18/187.97 ! [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)) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_mod__mult2__eq,axiom,
% 187.18/187.97 ! [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)) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_transfer__int__nat__relations_I2_J,axiom,
% 187.18/187.97 ! [V_y_2,V_x_2] :
% 187.18/187.97 ( 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)))
% 187.18/187.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_zless__int,axiom,
% 187.18/187.97 ! [V_n_2,V_m_2] :
% 187.18/187.97 ( 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)))
% 187.18/187.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_le__mod__geq,axiom,
% 187.18/187.97 ! [V_m,V_n] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 187.18/187.97 => 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) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_transfer__int__nat__relations_I3_J,axiom,
% 187.18/187.97 ! [V_y_2,V_x_2] :
% 187.18/187.97 ( 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)))
% 187.18/187.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_zle__int,axiom,
% 187.18/187.97 ! [V_n_2,V_m_2] :
% 187.18/187.97 ( 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)))
% 187.18/187.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_Divides_Omod__div__equality_H,axiom,
% 187.18/187.97 ! [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)) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_mult__div__cancel,axiom,
% 187.18/187.97 ! [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)) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_div__mod__equality_H,axiom,
% 187.18/187.97 ! [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)) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J,axiom,
% 187.18/187.97 ! [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)) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_zadd__int__left,axiom,
% 187.18/187.97 ! [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) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_zadd__int,axiom,
% 187.18/187.97 ! [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)) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_zle__iff__zadd,axiom,
% 187.18/187.97 ! [V_z_2,V_w_2] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2))
% 187.18/187.97 <=> ? [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)) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_of__nat__0__le__iff,axiom,
% 187.18/187.97 ! [V_n,T_a] :
% 187.18/187.97 ( class_Rings_Olinordered__semidom(T_a)
% 187.18/187.97 => 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))) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_zero__le__imp__of__nat,axiom,
% 187.18/187.97 ! [V_m,T_a] :
% 187.18/187.97 ( class_Rings_Olinordered__semidom(T_a)
% 187.18/187.97 => 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))) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_of__nat__less__0__iff,axiom,
% 187.18/187.97 ! [V_m,T_a] :
% 187.18/187.97 ( class_Rings_Olinordered__semidom(T_a)
% 187.18/187.97 => ~ 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))) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J,axiom,
% 187.18/187.97 ! [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)) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_zmult__int,axiom,
% 187.18/187.97 ! [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)) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_int__mult,axiom,
% 187.18/187.97 ! [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)) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_of__nat__0,axiom,
% 187.18/187.97 ! [T_a] :
% 187.18/187.97 ( class_Rings_Osemiring__1(T_a)
% 187.18/187.97 => 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) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_of__nat__less__iff,axiom,
% 187.18/187.97 ! [V_n_2,V_m_2,T_a] :
% 187.18/187.97 ( class_Rings_Olinordered__semidom(T_a)
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2)))
% 187.18/187.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_less__imp__of__nat__less,axiom,
% 187.18/187.97 ! [V_n,V_m,T_a] :
% 187.18/187.97 ( class_Rings_Olinordered__semidom(T_a)
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 187.18/187.97 => 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))) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_of__nat__less__imp__less,axiom,
% 187.18/187.97 ! [V_n,V_m,T_a] :
% 187.18/187.97 ( class_Rings_Olinordered__semidom(T_a)
% 187.18/187.97 => ( 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)))
% 187.18/187.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_transfer__int__nat__numerals_I2_J,axiom,
% 187.18/187.97 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)) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_int__1,axiom,
% 187.18/187.97 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) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_of__nat__le__iff,axiom,
% 187.18/187.97 ! [V_n_2,V_m_2,T_a] :
% 187.18/187.97 ( class_Rings_Olinordered__semidom(T_a)
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2)))
% 187.18/187.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_of__nat__add,axiom,
% 187.18/187.97 ! [V_n,V_m,T_a] :
% 187.18/187.97 ( class_Rings_Osemiring__1(T_a)
% 187.18/187.97 => 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)) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_of__nat__mult,axiom,
% 187.18/187.97 ! [V_n,V_m,T_a] :
% 187.18/187.97 ( class_Rings_Osemiring__1(T_a)
% 187.18/187.97 => 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)) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_of__nat__1,axiom,
% 187.18/187.97 ! [T_a] :
% 187.18/187.97 ( class_Rings_Osemiring__1(T_a)
% 187.18/187.97 => 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) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_Ints__of__nat,axiom,
% 187.18/187.97 ! [V_n_2,T_a] :
% 187.18/187.97 ( class_Rings_Oring__1(T_a)
% 187.18/187.97 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2)),c_Int_Oring__1__class_OInts(T_a))) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_of__nat__power,axiom,
% 187.18/187.97 ! [V_n,V_m,T_a] :
% 187.18/187.97 ( class_Rings_Osemiring__1(T_a)
% 187.18/187.97 => 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) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J,axiom,
% 187.18/187.97 ! [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)) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_zpower__int,axiom,
% 187.18/187.97 ! [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)) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_int__power,axiom,
% 187.18/187.97 ! [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) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J,axiom,
% 187.18/187.97 ! [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)) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_of__nat__setsum,axiom,
% 187.18/187.97 ! [V_A_2,V_f_2,T_b,T_a] :
% 187.18/187.97 ( class_Rings_Osemiring__1(T_a)
% 187.18/187.97 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),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,T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,T_b),c_Nat_Osemiring__1__class_Oof__nat(T_a)),V_f_2)),V_A_2) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_mod__le__divisor,axiom,
% 187.18/187.97 ! [V_m,V_n] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 187.18/187.97 => 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)) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_mod__mult__self4,axiom,
% 187.18/187.97 ! [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) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_int__le__0__conv,axiom,
% 187.18/187.97 ! [V_n_2] :
% 187.18/187.97 ( 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)))
% 187.18/187.97 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_int__Suc0__eq__1,axiom,
% 187.18/187.97 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) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_zless__iff__Suc__zadd,axiom,
% 187.18/187.97 ! [V_z_2,V_w_2] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
% 187.18/187.97 <=> ? [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))) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_int__Suc,axiom,
% 187.18/187.97 ! [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)) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_zdiff__int,axiom,
% 187.18/187.97 ! [V_m,V_n] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 187.18/187.97 => 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)) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_of__nat__setprod,axiom,
% 187.18/187.97 ! [V_A_2,V_f_2,T_b,T_a] :
% 187.18/187.97 ( ( class_Groups_Ocomm__monoid__mult(T_a)
% 187.18/187.97 & class_Rings_Osemiring__1(T_a) )
% 187.18/187.97 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),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,T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,T_b),c_Nat_Osemiring__1__class_Oof__nat(T_a)),V_f_2)),V_A_2) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_of__nat__Suc,axiom,
% 187.18/187.97 ! [V_m,T_a] :
% 187.18/187.97 ( class_Rings_Osemiring__1(T_a)
% 187.18/187.97 => 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)) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_of__nat__diff,axiom,
% 187.18/187.97 ! [V_m,V_n,T_a] :
% 187.18/187.97 ( class_Rings_Oring__1(T_a)
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 187.18/187.97 => 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)) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_setsum__constant,axiom,
% 187.18/187.97 ! [V_A_2,V_y_2,T_b,T_a] :
% 187.18/187.97 ( class_Rings_Osemiring__1(T_a)
% 187.18/187.97 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(c_COMBK(T_a,T_b),V_y_2)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))),V_y_2) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_mod__lemma,axiom,
% 187.18/187.97 ! [V_q,V_b,V_r,V_c] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_r),V_b))
% 187.18/187.97 => 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))) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_split__mod,axiom,
% 187.18/187.97 ! [V_k_2,V_n_2,V_P_2] :
% 187.18/187.97 ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2)))
% 187.18/187.97 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.18/187.97 => hBOOL(hAPP(V_P_2,V_n_2)) )
% 187.18/187.97 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.18/187.97 => ! [B_i,B_j] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2))
% 187.18/187.97 => ( 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)
% 187.18/187.97 => hBOOL(hAPP(V_P_2,B_j)) ) ) ) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_zero__less__int__conv,axiom,
% 187.18/187.97 ! [V_n_2] :
% 187.18/187.97 ( 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)))
% 187.18/187.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_Suc__times__mod__eq,axiom,
% 187.18/187.97 ! [V_m,V_k] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_k))
% 187.18/187.97 => 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) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_zmult__zless__mono2__lemma,axiom,
% 187.18/187.97 ! [V_k,V_j,V_i] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 187.18/187.97 => 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))) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_of__nat__0__less__iff,axiom,
% 187.18/187.97 ! [V_n_2,T_a] :
% 187.18/187.97 ( class_Rings_Olinordered__semidom(T_a)
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2)))
% 187.18/187.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_less__eq__nat_Osimps_I2_J,axiom,
% 187.18/187.97 ! [V_n_2,V_m_2] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2))
% 187.18/187.97 <=> 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)) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_zdiff__int__split,axiom,
% 187.18/187.97 ! [V_y_2,V_x_2,V_P_2] :
% 187.18/187.97 ( 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))))
% 187.18/187.97 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),V_x_2))
% 187.18/187.97 => 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)))) )
% 187.18/187.97 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
% 187.18/187.97 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_semiring__1__class_Oof__nat__code,axiom,
% 187.18/187.97 ! [V_n_2,T_a] :
% 187.18/187.97 ( class_Rings_Osemiring__1(T_a)
% 187.18/187.97 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2) = c_Nat_Osemiring__1__class_Oof__nat__aux(T_a,hAPP(hAPP(c_COMBC(T_a,T_a,T_a),c_Groups_Oplus__class_Oplus(T_a)),c_Groups_Oone__class_Oone(T_a)),V_n_2,c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_setsum__bounded,axiom,
% 187.18/187.97 ! [V_K_2,V_f_2,V_A_2,T_a,T_b] :
% 187.18/187.97 ( ( class_Groups_Oordered__ab__semigroup__add(T_b)
% 187.18/187.97 & class_Rings_Osemiring__1(T_b) )
% 187.18/187.97 => ( ! [B_i] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_member(T_a),B_i),V_A_2))
% 187.18/187.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,B_i)),V_K_2)) )
% 187.18/187.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_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_a),V_A_2))),V_K_2))) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_ord_OgreaterThanAtMost__iff,axiom,
% 187.18/187.97 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_a] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OgreaterThanAtMost(T_a,V_less__eq_2,V_less_2,V_l_2,V_u_2)))
% 187.18/187.97 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2))
% 187.18/187.97 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_ord_OatLeastLessThan__iff,axiom,
% 187.18/187.97 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_a] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OatLeastLessThan(T_a,V_less__eq_2,V_less_2,V_l_2,V_u_2)))
% 187.18/187.97 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2))
% 187.18/187.97 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_ord_OgreaterThanLessThan__iff,axiom,
% 187.18/187.97 ! [V_u_2,V_l_2,V_less_2,V_i_2,T_a] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OgreaterThanLessThan(T_a,V_less_2,V_l_2,V_u_2)))
% 187.18/187.97 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2))
% 187.18/187.97 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_transfer__nat__int__set__relations_I5_J,axiom,
% 187.18/187.97 ! [V_B_2,V_A_2] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2))
% 187.18/187.97 <=> 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))) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_transfer__nat__int__set__relations_I3_J,axiom,
% 187.18/187.97 ! [V_B_2,V_A_2] :
% 187.18/187.97 ( V_A_2 = V_B_2
% 187.18/187.97 <=> 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) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_transfer__nat__int__set__relations_I2_J,axiom,
% 187.18/187.97 ! [V_A_2,V_x_2] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),V_A_2))
% 187.18/187.97 <=> 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))) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_transfer__nat__int__set__relations_I4_J,axiom,
% 187.18/187.97 ! [V_B_2,V_A_2] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2))
% 187.18/187.97 <=> 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))) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_int__int__eq,axiom,
% 187.18/187.97 ! [V_n_2,V_m_2] :
% 187.18/187.97 ( 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)
% 187.18/187.97 <=> V_m_2 = V_n_2 ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_transfer__int__nat__relations_I1_J,axiom,
% 187.18/187.97 ! [V_y_2,V_x_2] :
% 187.18/187.97 ( 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)
% 187.18/187.97 <=> V_x_2 = V_y_2 ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_of__nat__aux_Osimps_I1_J,axiom,
% 187.18/187.97 ! [V_i_2,V_inc_2,T_a] :
% 187.18/187.97 ( class_Rings_Osemiring__1(T_a)
% 187.18/187.97 => c_Nat_Osemiring__1__class_Oof__nat__aux(T_a,V_inc_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i_2) = V_i_2 ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_of__nat__aux_Osimps_I2_J,axiom,
% 187.18/187.97 ! [V_i_2,V_n_2,V_inc_2,T_a] :
% 187.18/187.97 ( class_Rings_Osemiring__1(T_a)
% 187.18/187.97 => c_Nat_Osemiring__1__class_Oof__nat__aux(T_a,V_inc_2,hAPP(c_Nat_OSuc,V_n_2),V_i_2) = c_Nat_Osemiring__1__class_Oof__nat__aux(T_a,V_inc_2,V_n_2,hAPP(V_inc_2,V_i_2)) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_image__minus__const__atLeastLessThan__nat,axiom,
% 187.18/187.97 ! [V_x_2,V_y_2,V_c_2] :
% 187.18/187.97 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_c_2),V_y_2))
% 187.18/187.97 => 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)) )
% 187.18/187.97 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_c_2),V_y_2))
% 187.18/187.97 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
% 187.18/187.97 => 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))) )
% 187.18/187.97 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
% 187.18/187.97 => 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)) ) ) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_sum__diff__distrib,axiom,
% 187.18/187.97 ! [V_n_2,V_P_2,V_Q_2] :
% 187.18/187.97 ( ! [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)))
% 187.18/187.97 => 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)) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_setsum__natinterval__difff,axiom,
% 187.18/187.97 ! [V_f_2,V_n_2,V_m_2,T_a] :
% 187.18/187.97 ( class_Groups_Oab__group__add(T_a)
% 187.18/187.97 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 187.18/187.97 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(T_a)),V_f_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,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_a),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)))) )
% 187.18/187.97 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 187.18/187.97 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(T_a)),V_f_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,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_a) ) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_gauss__sum,axiom,
% 187.18/187.97 ! [V_n_2,T_a] :
% 187.18/187.97 ( class_Rings_Ocomm__semiring__1(T_a)
% 187.18/187.97 => 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(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),c_Nat_Osemiring__1__class_Oof__nat(T_a)),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_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2)),c_Groups_Oone__class_Oone(T_a))) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_decr__mult__lemma,axiom,
% 187.18/187.97 ! [V_k_2,V_P_2,V_d_2] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
% 187.18/187.97 => ( ! [B_x] :
% 187.18/187.97 ( hBOOL(hAPP(V_P_2,B_x))
% 187.18/187.97 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_d_2))) )
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 187.18/187.97 => ! [B_x] :
% 187.18/187.97 ( hBOOL(hAPP(V_P_2,B_x))
% 187.18/187.97 => 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)))) ) ) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_incr__mult__lemma,axiom,
% 187.18/187.97 ! [V_k_2,V_P_2,V_d_2] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
% 187.18/187.97 => ( ! [B_x] :
% 187.18/187.97 ( hBOOL(hAPP(V_P_2,B_x))
% 187.18/187.97 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_d_2))) )
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 187.18/187.97 => ! [B_x] :
% 187.18/187.97 ( hBOOL(hAPP(V_P_2,B_x))
% 187.18/187.97 => 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)))) ) ) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_finite__atLeastLessThan,axiom,
% 187.18/187.97 ! [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))) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_finite__atLeastAtMost,axiom,
% 187.18/187.97 ! [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))) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_atLeastLessThanSuc__atLeastAtMost,axiom,
% 187.18/187.97 ! [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) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_ivl__disj__un_I21_J,axiom,
% 187.18/187.97 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 187.18/187.97 ( class_Orderings_Olinorder(T_a)
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2))
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2))
% 187.18/187.97 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2) ) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_ivl__disj__int_I15_J,axiom,
% 187.18/187.97 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 187.18/187.97 ( class_Orderings_Oorder(T_a)
% 187.18/187.97 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_atLeastLessThan__inj_I2_J,axiom,
% 187.18/187.97 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
% 187.18/187.97 ( class_Orderings_Olinorder(T_a)
% 187.18/187.97 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_c_2),V_d_2)
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2))
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),V_d_2))
% 187.18/187.97 => V_b_2 = V_d_2 ) ) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_atLeastLessThan__inj_I1_J,axiom,
% 187.18/187.97 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
% 187.18/187.97 ( class_Orderings_Olinorder(T_a)
% 187.18/187.97 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_c_2),V_d_2)
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2))
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),V_d_2))
% 187.18/187.97 => V_a_2 = V_c_2 ) ) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_atLeastLessThan__eq__iff,axiom,
% 187.18/187.97 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
% 187.18/187.97 ( class_Orderings_Olinorder(T_a)
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2))
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),V_d_2))
% 187.18/187.97 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_c_2),V_d_2)
% 187.18/187.97 <=> ( V_a_2 = V_c_2
% 187.18/187.97 & V_b_2 = V_d_2 ) ) ) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_atLeastLessThan__add__Un,axiom,
% 187.18/187.97 ! [V_k_2,V_j_2,V_i_2] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 187.18/187.97 => 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))) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_atLeastLessThan0,axiom,
% 187.18/187.97 ! [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)) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_atLeast0LessThan,axiom,
% 187.18/187.97 ! [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) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_ivl__disj__un_I6_J,axiom,
% 187.18/187.97 ! [V_u_2,V_l_2,T_a] :
% 187.18/187.97 ( class_Orderings_Olinorder(T_a)
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2))
% 187.18/187.97 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_subset__card__intvl__is__intvl,axiom,
% 187.18/187.97 ! [V_k_2,V_A_2] :
% 187.18/187.97 ( 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)))))
% 187.18/187.97 => 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))) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_card__atLeastLessThan,axiom,
% 187.18/187.97 ! [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) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_atLeastatMost__empty__iff2,axiom,
% 187.18/187.97 ! [V_b_2,V_a_2,T_a] :
% 187.18/187.97 ( class_Orderings_Oorder(T_a)
% 187.18/187.97 => ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2)
% 187.18/187.97 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_atLeastatMost__empty__iff,axiom,
% 187.18/187.97 ! [V_b_2,V_a_2,T_a] :
% 187.18/187.97 ( class_Orderings_Oorder(T_a)
% 187.18/187.97 => ( c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.97 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_atLeastatMost__empty,axiom,
% 187.18/187.97 ! [V_a_2,V_b_2,T_a] :
% 187.18/187.97 ( class_Orderings_Oorder(T_a)
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_a_2))
% 187.18/187.97 => c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_atLeastatMost__subset__iff,axiom,
% 187.18/187.97 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
% 187.18/187.97 ( class_Orderings_Oorder(T_a)
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_c_2,V_d_2)))
% 187.18/187.97 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2))
% 187.18/187.97 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c_2),V_a_2))
% 187.18/187.97 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_d_2)) ) ) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_image__Suc__atLeastLessThan,axiom,
% 187.18/187.97 ! [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)) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_atLeastLessThan__empty,axiom,
% 187.18/187.97 ! [V_a_2,V_b_2,T_a] :
% 187.18/187.97 ( class_Orderings_Oorder(T_a)
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_a_2))
% 187.18/187.97 => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_atLeastAtMost__singleton_H,axiom,
% 187.18/187.97 ! [V_b_2,V_a_2,T_a] :
% 187.18/187.97 ( class_Orderings_Oorder(T_a)
% 187.18/187.97 => ( V_a_2 = V_b_2
% 187.18/187.97 => c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_atLeastAtMost__singleton__iff,axiom,
% 187.18/187.97 ! [V_c_2,V_b_2,V_a_2,T_a] :
% 187.18/187.97 ( class_Orderings_Oorder(T_a)
% 187.18/187.97 => ( c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))
% 187.18/187.97 <=> ( V_a_2 = V_b_2
% 187.18/187.97 & V_b_2 = V_c_2 ) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_atLeastAtMost__singleton,axiom,
% 187.18/187.97 ! [V_a_2,T_a] :
% 187.18/187.97 ( class_Orderings_Oorder(T_a)
% 187.18/187.97 => c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_a_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_atLeastLessThan__empty__iff,axiom,
% 187.18/187.97 ! [V_b_2,V_a_2,T_a] :
% 187.18/187.97 ( class_Orderings_Oorder(T_a)
% 187.18/187.97 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.97 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_atLeastLessThan__empty__iff2,axiom,
% 187.18/187.97 ! [V_b_2,V_a_2,T_a] :
% 187.18/187.97 ( class_Orderings_Oorder(T_a)
% 187.18/187.97 => ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2)
% 187.18/187.97 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_atLeastLessThan__subset__iff,axiom,
% 187.18/187.97 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
% 187.18/187.97 ( class_Orderings_Olinorder(T_a)
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_c_2),V_d_2)))
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_a_2))
% 187.18/187.97 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c_2),V_a_2))
% 187.18/187.97 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_d_2)) ) ) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_setsum__shift__bounds__Suc__ivl,axiom,
% 187.18/187.97 ! [V_n_2,V_m_2,V_f_2,T_a] :
% 187.18/187.97 ( class_Groups_Ocomm__monoid__add(T_a)
% 187.18/187.97 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,tc_Nat_Onat),V_f_2),c_Nat_OSuc)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2)) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_ivl__disj__un_I17_J,axiom,
% 187.18/187.97 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 187.18/187.97 ( class_Orderings_Olinorder(T_a)
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2))
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2))
% 187.18/187.97 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_m_2),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_u_2) ) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_setsum__shift__bounds__nat__ivl,axiom,
% 187.18/187.97 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_a] :
% 187.18/187.97 ( class_Groups_Ocomm__monoid__add(T_a)
% 187.18/187.97 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,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)) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_ivl__diff,axiom,
% 187.18/187.97 ! [V_m_2,V_n_2,V_i_2,T_a] :
% 187.18/187.97 ( class_Orderings_Olinorder(T_a)
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_i_2),V_n_2))
% 187.18/187.97 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_i_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_i_2),V_n_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_n_2),V_m_2) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_ivl__disj__int_I11_J,axiom,
% 187.18/187.97 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 187.18/187.97 ( class_Orderings_Oorder(T_a)
% 187.18/187.97 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_m_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_image__Suc__atLeastAtMost,axiom,
% 187.18/187.97 ! [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)) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_setsum__shift__bounds__cl__Suc__ivl,axiom,
% 187.18/187.97 ! [V_n_2,V_m_2,V_f_2,T_a] :
% 187.18/187.97 ( class_Groups_Ocomm__monoid__add(T_a)
% 187.18/187.97 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,tc_Nat_Onat),V_f_2),c_Nat_OSuc)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_setsum__shift__bounds__cl__nat__ivl,axiom,
% 187.18/187.97 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_a] :
% 187.18/187.97 ( class_Groups_Ocomm__monoid__add(T_a)
% 187.18/187.97 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,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)) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_image__add__atLeastLessThan,axiom,
% 187.18/187.97 ! [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)) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_image__add__atLeastAtMost,axiom,
% 187.18/187.97 ! [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)) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_setsum__add__nat__ivl,axiom,
% 187.18/187.97 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_a] :
% 187.18/187.97 ( class_Groups_Ocomm__monoid__add(T_a)
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2))
% 187.18/187.97 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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_a),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_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_p_2)) ) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_setsum__diff__nat__ivl,axiom,
% 187.18/187.97 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_a] :
% 187.18/187.97 ( class_Groups_Oab__group__add(T_a)
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2))
% 187.18/187.97 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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_a),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_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_n_2),V_p_2)) ) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_card__atLeastAtMost,axiom,
% 187.18/187.97 ! [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) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_atLeastAtMostSuc__conv,axiom,
% 187.18/187.97 ! [V_n_2,V_m_2] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 187.18/187.97 => 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)) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_atLeastLessThan__singleton,axiom,
% 187.18/187.97 ! [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))) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_setsum__shift__lb__Suc0__0,axiom,
% 187.18/187.97 ! [V_k_2,V_f_2] :
% 187.18/187.97 ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.18/187.97 => 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)) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_atLeastatMost__psubset__iff,axiom,
% 187.18/187.97 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
% 187.18/187.97 ( class_Orderings_Oorder(T_a)
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_c_2,V_d_2)))
% 187.18/187.97 <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2))
% 187.18/187.97 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c_2),V_a_2))
% 187.18/187.97 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_d_2))
% 187.18/187.97 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),V_a_2))
% 187.18/187.97 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_d_2)) ) ) )
% 187.18/187.97 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c_2),V_d_2)) ) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_ivl__disj__int_I4_J,axiom,
% 187.18/187.97 ! [V_u_2,V_l_2,T_a] :
% 187.18/187.97 ( class_Orderings_Oorder(T_a)
% 187.18/187.97 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_l_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_ivl__disj__un_I8_J,axiom,
% 187.18/187.97 ! [V_u_2,V_l_2,T_a] :
% 187.18/187.97 ( class_Orderings_Olinorder(T_a)
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2))
% 187.18/187.97 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_l_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_u_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_u_2) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_ivl__disj__int_I2_J,axiom,
% 187.18/187.97 ! [V_u_2,V_l_2,T_a] :
% 187.18/187.97 ( class_Orderings_Oorder(T_a)
% 187.18/187.97 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_l_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_setsum__shift__lb__Suc0__0__upt,axiom,
% 187.18/187.97 ! [V_k_2,V_f_2,T_a] :
% 187.18/187.97 ( class_Groups_Ocomm__monoid__add(T_a)
% 187.18/187.97 => ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(T_a)
% 187.18/187.97 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_setsum__head__upt__Suc,axiom,
% 187.18/187.97 ! [V_f_2,V_n_2,V_m_2,T_a] :
% 187.18/187.97 ( class_Groups_Ocomm__monoid__add(T_a)
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 187.18/187.97 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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_a),hAPP(V_f_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2)),V_n_2))) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_setsum__head__Suc,axiom,
% 187.18/187.97 ! [V_f_2,V_n_2,V_m_2,T_a] :
% 187.18/187.97 ( class_Groups_Ocomm__monoid__add(T_a)
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 187.18/187.97 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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_a),hAPP(V_f_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2),V_n_2))) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_atLeastLessThanSuc,axiom,
% 187.18/187.97 ! [V_n_2,V_m_2] :
% 187.18/187.97 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 187.18/187.97 => 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)) )
% 187.18/187.97 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 187.18/187.97 => 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)) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_setsum__op__ivl__Suc,axiom,
% 187.18/187.97 ! [V_f_2,V_m_2,V_n_2,T_a] :
% 187.18/187.97 ( class_Groups_Ocomm__monoid__add(T_a)
% 187.18/187.97 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 187.18/187.97 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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_a) )
% 187.18/187.97 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 187.18/187.97 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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)) ) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_setsum__cl__ivl__Suc,axiom,
% 187.18/187.97 ! [V_f_2,V_m_2,V_n_2,T_a] :
% 187.18/187.97 ( class_Groups_Ocomm__monoid__add(T_a)
% 187.18/187.97 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2))
% 187.18/187.97 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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_a) )
% 187.18/187.97 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2))
% 187.18/187.97 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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))) ) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_setsum__ub__add__nat,axiom,
% 187.18/187.97 ! [V_p_2,V_f_2,V_n_2,V_m_2,T_a] :
% 187.18/187.97 ( class_Groups_Ocomm__monoid__add(T_a)
% 187.18/187.97 => ( 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))))
% 187.18/187.97 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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_a),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)))) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_geometric__sum,axiom,
% 187.18/187.97 ! [V_n_2,V_x_2,T_a] :
% 187.18/187.97 ( class_Fields_Ofield(T_a)
% 187.18/187.97 => ( V_x_2 != c_Groups_Oone__class_Oone(T_a)
% 187.18/187.97 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),hAPP(c_Power_Opower__class_Opower(T_a),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_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x_2),V_n_2)),c_Groups_Oone__class_Oone(T_a))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x_2),c_Groups_Oone__class_Oone(T_a))) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_ex__nat__less,axiom,
% 187.18/187.97 ! [V_P_2,V_n_2] :
% 187.18/187.97 ( ? [B_m] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2))
% 187.18/187.97 & hBOOL(hAPP(V_P_2,B_m)) )
% 187.18/187.97 <=> ? [B_x] :
% 187.18/187.97 ( 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)))
% 187.18/187.97 & hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_all__nat__less,axiom,
% 187.18/187.97 ! [V_P_2,V_n_2] :
% 187.18/187.97 ( ! [B_m] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2))
% 187.18/187.97 => hBOOL(hAPP(V_P_2,B_m)) )
% 187.18/187.97 <=> ! [B_x] :
% 187.18/187.97 ( 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)))
% 187.18/187.97 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_all__nat__less__eq,axiom,
% 187.18/187.97 ! [V_P_2,V_n_2] :
% 187.18/187.97 ( ! [B_m] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2))
% 187.18/187.97 => hBOOL(hAPP(V_P_2,B_m)) )
% 187.18/187.97 <=> ! [B_x] :
% 187.18/187.97 ( 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)))
% 187.18/187.97 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_ex__nat__less__eq,axiom,
% 187.18/187.97 ! [V_P_2,V_n_2] :
% 187.18/187.97 ( ? [B_m] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2))
% 187.18/187.97 & hBOOL(hAPP(V_P_2,B_m)) )
% 187.18/187.97 <=> ? [B_x] :
% 187.18/187.97 ( 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)))
% 187.18/187.97 & hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_ivl__disj__un_I18_J,axiom,
% 187.18/187.97 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 187.18/187.97 ( class_Orderings_Olinorder(T_a)
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2))
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_m_2),V_u_2))
% 187.18/187.97 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_m_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_u_2) ) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_ivl__disj__un_I3_J,axiom,
% 187.18/187.97 ! [V_u_2,V_l_2,T_a] :
% 187.18/187.97 ( class_Orderings_Olinorder(T_a)
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_u_2))
% 187.18/187.97 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_u_2) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_finite__greaterThanLessThan,axiom,
% 187.18/187.97 ! [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))) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_finite__atLeastAtMost__int,axiom,
% 187.18/187.97 ! [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))) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_finite__atLeastLessThan__int,axiom,
% 187.18/187.97 ! [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))) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_finite__greaterThanLessThan__int,axiom,
% 187.18/187.97 ! [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))) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_atLeastLessThanPlusOne__atLeastAtMost__int,axiom,
% 187.18/187.97 ! [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) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom,
% 187.18/187.97 ! [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) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_finite__atLeastZeroLessThan__int,axiom,
% 187.18/187.97 ! [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))) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_greaterThanLessThan__empty,axiom,
% 187.18/187.97 ! [V_k_2,V_l_2,T_a] :
% 187.18/187.97 ( class_Orderings_Oorder(T_a)
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_k_2))
% 187.18/187.97 => c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_atLeastSucLessThan__greaterThanLessThan,axiom,
% 187.18/187.97 ! [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) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_image__add__int__atLeastLessThan,axiom,
% 187.18/187.97 ! [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) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_ivl__disj__int_I12_J,axiom,
% 187.18/187.97 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 187.18/187.97 ( class_Orderings_Oorder(T_a)
% 187.18/187.97 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_ivl__disj__int_I13_J,axiom,
% 187.18/187.97 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 187.18/187.97 ( class_Orderings_Oorder(T_a)
% 187.18/187.97 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_ivl__disj__int_I9_J,axiom,
% 187.18/187.97 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 187.18/187.97 ( class_Orderings_Oorder(T_a)
% 187.18/187.97 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_m_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_card__greaterThanLessThan,axiom,
% 187.18/187.97 ! [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)) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_simp__from__to,axiom,
% 187.18/187.97 ! [V_i_2,V_j_2] :
% 187.18/187.97 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2))
% 187.18/187.97 => 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)) )
% 187.18/187.97 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2))
% 187.18/187.97 => 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)) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_ivl__disj__un_I15_J,axiom,
% 187.18/187.97 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 187.18/187.97 ( class_Orderings_Olinorder(T_a)
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_m_2))
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2))
% 187.18/187.97 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_m_2),V_u_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2) ) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_bset_I8_J,axiom,
% 187.18/187.97 ! [V_B_2,V_t_2,V_D_2] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 187.18/187.97 => ( 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))
% 187.18/187.97 => ! [B_x] :
% 187.18/187.97 ( ! [B_xa] :
% 187.18/187.97 ( 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)))
% 187.18/187.97 => ! [B_xb] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 187.18/187.97 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x))
% 187.18/187.97 => 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))) ) ) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_aset_I6_J,axiom,
% 187.18/187.97 ! [V_A_2,V_t_2,V_D_2] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 187.18/187.97 => ( 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))
% 187.18/187.97 => ! [B_x] :
% 187.18/187.97 ( ! [B_xa] :
% 187.18/187.97 ( 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)))
% 187.18/187.97 => ! [B_xb] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 187.18/187.97 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2))
% 187.18/187.97 => 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)) ) ) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_aset_I4_J,axiom,
% 187.18/187.97 ! [V_A_2,V_t_2,V_D_2] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2))
% 187.18/187.97 => ! [B_x] :
% 187.18/187.97 ( ! [B_xa] :
% 187.18/187.97 ( 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)))
% 187.18/187.97 => ! [B_xb] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 187.18/187.97 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 187.18/187.97 => ( B_x != V_t_2
% 187.18/187.97 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_bset_I4_J,axiom,
% 187.18/187.97 ! [V_B_2,V_t_2,V_D_2] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2))
% 187.18/187.97 => ! [B_x] :
% 187.18/187.97 ( ! [B_xa] :
% 187.18/187.97 ( 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)))
% 187.18/187.97 => ! [B_xb] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 187.18/187.97 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 187.18/187.97 => ( B_x != V_t_2
% 187.18/187.97 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_bset_I7_J,axiom,
% 187.18/187.97 ! [V_B_2,V_t_2,V_D_2] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2))
% 187.18/187.97 => ! [B_x] :
% 187.18/187.97 ( ! [B_xa] :
% 187.18/187.97 ( 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)))
% 187.18/187.97 => ! [B_xb] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 187.18/187.97 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x))
% 187.18/187.97 => 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))) ) ) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_aset_I5_J,axiom,
% 187.18/187.97 ! [V_A_2,V_t_2,V_D_2] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2))
% 187.18/187.97 => ! [B_x] :
% 187.18/187.97 ( ! [B_xa] :
% 187.18/187.97 ( 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)))
% 187.18/187.97 => ! [B_xb] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 187.18/187.97 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2))
% 187.18/187.97 => 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)) ) ) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_bset_I3_J,axiom,
% 187.18/187.97 ! [V_B_2,V_t_2,V_D_2] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 187.18/187.97 => ( 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))
% 187.18/187.97 => ( ! [B_x] :
% 187.18/187.97 ( 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)))
% 187.18/187.97 => ! [B_xa] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_B_2))
% 187.18/187.97 => V_t_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xa),B_x) ) )
% 187.18/187.97 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_aset_I3_J,axiom,
% 187.18/187.97 ! [V_A_2,V_t_2,V_D_2] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 187.18/187.97 => ( 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))
% 187.18/187.97 => ( ! [B_x] :
% 187.18/187.97 ( 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)))
% 187.18/187.97 => ! [B_xa] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_A_2))
% 187.18/187.97 => V_t_2 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xa),B_x) ) )
% 187.18/187.97 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_bset_I6_J,axiom,
% 187.18/187.97 ! [V_t_2,V_B_2,V_D_2] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 187.18/187.97 => ! [B_x] :
% 187.18/187.97 ( ! [B_xa] :
% 187.18/187.97 ( 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)))
% 187.18/187.97 => ! [B_xb] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 187.18/187.97 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2))
% 187.18/187.97 => 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)) ) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_aset_I8_J,axiom,
% 187.18/187.97 ! [V_t_2,V_A_2,V_D_2] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 187.18/187.97 => ! [B_x] :
% 187.18/187.97 ( ! [B_xa] :
% 187.18/187.97 ( 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)))
% 187.18/187.97 => ! [B_xb] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 187.18/187.97 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x))
% 187.18/187.97 => 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))) ) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_periodic__finite__ex,axiom,
% 187.18/187.97 ! [V_P_2,V_d_2] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
% 187.18/187.97 => ( ! [B_x,B_k] :
% 187.18/187.97 ( hBOOL(hAPP(V_P_2,B_x))
% 187.18/187.97 <=> 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)))) )
% 187.18/187.97 => ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 187.18/187.97 <=> ? [B_x] :
% 187.18/187.97 ( 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)))
% 187.18/187.97 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_bset_I5_J,axiom,
% 187.18/187.97 ! [V_t_2,V_B_2,V_D_2] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 187.18/187.97 => ! [B_x] :
% 187.18/187.97 ( ! [B_xa] :
% 187.18/187.97 ( 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)))
% 187.18/187.97 => ! [B_xb] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 187.18/187.97 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2))
% 187.18/187.97 => 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)) ) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_aset_I7_J,axiom,
% 187.18/187.97 ! [V_t_2,V_A_2,V_D_2] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 187.18/187.97 => ! [B_x] :
% 187.18/187.97 ( ! [B_xa] :
% 187.18/187.97 ( 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)))
% 187.18/187.97 => ! [B_xb] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 187.18/187.97 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x))
% 187.18/187.97 => 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))) ) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_ivl__disj__un_I19_J,axiom,
% 187.18/187.97 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 187.18/187.97 ( class_Orderings_Olinorder(T_a)
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_m_2))
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2))
% 187.18/187.97 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2) ) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_ivl__disj__un_I4_J,axiom,
% 187.18/187.97 ! [V_u_2,V_l_2,T_a] :
% 187.18/187.97 ( class_Orderings_Olinorder(T_a)
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_u_2))
% 187.18/187.97 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_ivl__disj__un_I5_J,axiom,
% 187.18/187.97 ! [V_u_2,V_l_2,T_a] :
% 187.18/187.97 ( class_Orderings_Olinorder(T_a)
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2))
% 187.18/187.97 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_image__atLeastZeroLessThan__int,axiom,
% 187.18/187.97 ! [V_u_2] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2))
% 187.18/187.97 => 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))) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_zero__less__imp__eq__int,axiom,
% 187.18/187.97 ! [V_k] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 187.18/187.97 => ? [B_n] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n))
% 187.18/187.97 & V_k = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_finite__greaterThanAtMost,axiom,
% 187.18/187.97 ! [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))) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_finite__greaterThanAtMost__int,axiom,
% 187.18/187.97 ! [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))) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_nat__int,axiom,
% 187.18/187.97 ! [V_n] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = V_n ).
% 187.18/187.97
% 187.18/187.97 fof(fact_card__greaterThanAtMost__int,axiom,
% 187.18/187.97 ! [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)) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_transfer__nat__int__numerals_I1_J,axiom,
% 187.18/187.97 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_nat__0,axiom,
% 187.18/187.97 hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_ex__nat,axiom,
% 187.18/187.97 ! [V_P_2] :
% 187.18/187.97 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 187.18/187.97 <=> ? [B_x] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 187.18/187.97 & hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x))) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_all__nat,axiom,
% 187.18/187.97 ! [V_P_2] :
% 187.18/187.97 ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 187.18/187.97 <=> ! [B_x] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 187.18/187.97 => hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x))) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_transfer__nat__int__relations_I1_J,axiom,
% 187.18/187.97 ! [V_y_2,V_x_2] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 187.18/187.97 => ( hAPP(c_Int_Onat,V_x_2) = hAPP(c_Int_Onat,V_y_2)
% 187.18/187.97 <=> V_x_2 = V_y_2 ) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_eq__nat__nat__iff,axiom,
% 187.18/187.97 ! [V_z_H_2,V_z_2] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H_2))
% 187.18/187.97 => ( hAPP(c_Int_Onat,V_z_2) = hAPP(c_Int_Onat,V_z_H_2)
% 187.18/187.97 <=> V_z_2 = V_z_H_2 ) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_transfer__nat__int__numerals_I2_J,axiom,
% 187.18/187.97 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I4_J,axiom,
% 187.18/187.97 ! [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))) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_transfer__int__nat__set__return__embed,axiom,
% 187.18/187.97 ! [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 ).
% 187.18/187.97
% 187.18/187.97 fof(fact_transfer__nat__int__sum__prod_I2_J,axiom,
% 187.18/187.97 ! [V_A_2,V_f_2,T_a] :
% 187.18/187.97 ( ( class_Groups_Ocomm__monoid__add(T_a)
% 187.18/187.97 & class_Groups_Ocomm__monoid__mult(T_a) )
% 187.18/187.97 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,T_a),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,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)) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_greaterThanAtMost__empty,axiom,
% 187.18/187.97 ! [V_k_2,V_l_2,T_a] :
% 187.18/187.97 ( class_Orderings_Oorder(T_a)
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_k_2))
% 187.18/187.97 => c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_greaterThanAtMost__empty__iff,axiom,
% 187.18/187.97 ! [V_l_2,V_k_2,T_a] :
% 187.18/187.97 ( class_Orderings_Oorder(T_a)
% 187.18/187.97 => ( c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.97 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_k_2),V_l_2)) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_greaterThanAtMost__empty__iff2,axiom,
% 187.18/187.97 ! [V_l_2,V_k_2,T_a] :
% 187.18/187.97 ( class_Orderings_Oorder(T_a)
% 187.18/187.97 => ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_k_2,V_l_2)
% 187.18/187.97 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_k_2),V_l_2)) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_ivl__disj__un_I20_J,axiom,
% 187.18/187.97 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 187.18/187.97 ( class_Orderings_Olinorder(T_a)
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2))
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2))
% 187.18/187.97 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2) ) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I2_J,axiom,
% 187.18/187.97 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))) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_ivl__disj__int_I14_J,axiom,
% 187.18/187.97 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 187.18/187.97 ( class_Orderings_Oorder(T_a)
% 187.18/187.97 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_atLeastSucAtMost__greaterThanAtMost,axiom,
% 187.18/187.97 ! [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) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_nat__0__iff,axiom,
% 187.18/187.97 ! [V_i_2] :
% 187.18/187.97 ( hAPP(c_Int_Onat,V_i_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.18/187.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_nat__le__0,axiom,
% 187.18/187.97 ! [V_z] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.18/187.97 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_nat__mono__iff,axiom,
% 187.18/187.97 ! [V_w_2,V_z_2] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 187.18/187.97 => ( 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)))
% 187.18/187.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_zless__nat__conj,axiom,
% 187.18/187.97 ! [V_z_2,V_w_2] :
% 187.18/187.97 ( 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)))
% 187.18/187.97 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 187.18/187.97 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_transfer__nat__int__relations_I3_J,axiom,
% 187.18/187.97 ! [V_y_2,V_x_2] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 187.18/187.97 => ( 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)))
% 187.18/187.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_nat__1,axiom,
% 187.18/187.97 hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_int__nat__eq,axiom,
% 187.18/187.97 ! [V_z] :
% 187.18/187.97 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 187.18/187.97 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z )
% 187.18/187.97 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 187.18/187.97 => 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) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_int__eq__iff,axiom,
% 187.18/187.97 ! [V_z_2,V_m_2] :
% 187.18/187.97 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = V_z_2
% 187.18/187.97 <=> ( V_m_2 = hAPP(c_Int_Onat,V_z_2)
% 187.18/187.97 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_nat__0__le,axiom,
% 187.18/187.97 ! [V_z] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 187.18/187.97 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_zless__nat__eq__int__zless,axiom,
% 187.18/187.97 ! [V_z_2,V_m_2] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Int_Onat,V_z_2)))
% 187.18/187.97 <=> 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)) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_card__greaterThanAtMost,axiom,
% 187.18/187.97 ! [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) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I2_J,axiom,
% 187.18/187.97 ! [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))) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_transfer__nat__int__sum__prod_I1_J,axiom,
% 187.18/187.97 ! [V_A_2,V_f_2,T_a] :
% 187.18/187.97 ( ( class_Groups_Ocomm__monoid__add(T_a)
% 187.18/187.97 & class_Groups_Ocomm__monoid__mult(T_a) )
% 187.18/187.97 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,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)) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_card__atLeastZeroLessThan__int,axiom,
% 187.18/187.97 ! [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) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_card__atLeastLessThan__int,axiom,
% 187.18/187.97 ! [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)) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_zero__less__nat__eq,axiom,
% 187.18/187.97 ! [V_z_2] :
% 187.18/187.97 ( 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)))
% 187.18/187.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_transfer__nat__int__relations_I2_J,axiom,
% 187.18/187.97 ! [V_y_2,V_x_2] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 187.18/187.97 => ( 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)))
% 187.18/187.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_nat__less__eq__zless,axiom,
% 187.18/187.97 ! [V_z_2,V_w_2] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 187.18/187.97 => ( 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)))
% 187.18/187.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_nat__eq__iff,axiom,
% 187.18/187.97 ! [V_m_2,V_w_2] :
% 187.18/187.97 ( hAPP(c_Int_Onat,V_w_2) = V_m_2
% 187.18/187.97 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 187.18/187.97 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) )
% 187.18/187.97 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 187.18/187.97 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_nat__eq__iff2,axiom,
% 187.18/187.97 ! [V_w_2,V_m_2] :
% 187.18/187.97 ( V_m_2 = hAPP(c_Int_Onat,V_w_2)
% 187.18/187.97 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 187.18/187.97 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) )
% 187.18/187.97 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 187.18/187.97 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_nat__le__eq__zle,axiom,
% 187.18/187.97 ! [V_z_2,V_w_2] :
% 187.18/187.97 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 187.18/187.97 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) )
% 187.18/187.97 => ( 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)))
% 187.18/187.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_split__nat,axiom,
% 187.18/187.97 ! [V_i_2,V_P_2] :
% 187.18/187.97 ( hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,V_i_2)))
% 187.18/187.97 <=> ( ! [B_n] :
% 187.18/187.97 ( V_i_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n)
% 187.18/187.97 => hBOOL(hAPP(V_P_2,B_n)) )
% 187.18/187.97 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.18/187.97 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I1_J,axiom,
% 187.18/187.97 ! [V_y,V_x] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 187.18/187.97 => 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)) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_nat__add__distrib,axiom,
% 187.18/187.97 ! [V_z_H,V_z] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H))
% 187.18/187.97 => 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)) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I2_J,axiom,
% 187.18/187.97 ! [V_y,V_x] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 187.18/187.97 => 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)) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_nat__mult__distrib,axiom,
% 187.18/187.97 ! [V_z_H,V_z] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 187.18/187.97 => 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)) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I3_J,axiom,
% 187.18/187.97 ! [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))) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_nat__diff__distrib,axiom,
% 187.18/187.97 ! [V_z,V_z_H] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H))
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z))
% 187.18/187.97 => 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)) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_transfer__nat__int__sum__prod2_I1_J,axiom,
% 187.18/187.97 ! [V_A_2,V_f_2,T_a] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_a),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2)) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_Divides_Otransfer__nat__int__functions_I2_J,axiom,
% 187.18/187.97 ! [V_y,V_x] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 187.18/187.97 => 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)) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_nat__mod__distrib,axiom,
% 187.18/187.97 ! [V_y,V_x] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 187.18/187.97 => 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)) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_Divides_Otransfer__nat__int__functions_I1_J,axiom,
% 187.18/187.97 ! [V_y,V_x] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 187.18/187.97 => 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)) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_nat__div__distrib,axiom,
% 187.18/187.97 ! [V_y,V_x] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 187.18/187.97 => 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)) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_ivl__disj__un_I22_J,axiom,
% 187.18/187.97 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 187.18/187.97 ( class_Orderings_Olinorder(T_a)
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2))
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2))
% 187.18/187.97 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2) ) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom,
% 187.18/187.97 ! [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) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_ivl__disj__int_I16_J,axiom,
% 187.18/187.97 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 187.18/187.97 ( class_Orderings_Oorder(T_a)
% 187.18/187.97 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J,axiom,
% 187.18/187.97 ! [V_n,V_x] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 187.18/187.97 => 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)) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_nat__power__eq,axiom,
% 187.18/187.97 ! [V_n,V_z] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 187.18/187.97 => 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) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_transfer__nat__int__sum__prod2_I2_J,axiom,
% 187.18/187.97 ! [V_A_2,V_f_2,T_a] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_a),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2)) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_ivl__disj__int_I10_J,axiom,
% 187.18/187.97 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 187.18/187.97 ( class_Orderings_Oorder(T_a)
% 187.18/187.97 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J,axiom,
% 187.18/187.97 ! [V_y,V_x] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 187.18/187.97 => 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)) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_one__less__nat__eq,axiom,
% 187.18/187.97 ! [V_z_2] :
% 187.18/187.97 ( 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)))
% 187.18/187.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_nat__less__iff,axiom,
% 187.18/187.97 ! [V_m_2,V_w_2] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),V_m_2))
% 187.18/187.97 <=> 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))) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_Suc__nat__eq__nat__zadd1,axiom,
% 187.18/187.97 ! [V_z] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 187.18/187.97 => 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)) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_card__atLeastAtMost__int,axiom,
% 187.18/187.97 ! [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))) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_ivl__disj__un_I16_J,axiom,
% 187.18/187.97 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 187.18/187.97 ( class_Orderings_Olinorder(T_a)
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2))
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_m_2),V_u_2))
% 187.18/187.97 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2) ) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_setsum__head,axiom,
% 187.18/187.97 ! [V_P_2,V_n_2,V_m_2,T_a] :
% 187.18/187.97 ( class_Groups_Ocomm__monoid__add(T_a)
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 187.18/187.97 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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_a),hAPP(V_P_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_P_2),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_m_2,V_n_2))) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_card__greaterThanLessThan__int,axiom,
% 187.18/187.97 ! [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)))) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_nat__aux__def,axiom,
% 187.18/187.97 ! [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) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_transfer__morphism__nat__int,axiom,
% 187.18/187.97 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))) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_SetInterval_Otransfer__int__nat__set__functions,axiom,
% 187.18/187.97 ! [V_n_2,V_m_2] :
% 187.18/187.97 ( c_Nat__Transfer_Ois__nat(V_m_2)
% 187.18/187.97 => ( c_Nat__Transfer_Ois__nat(V_n_2)
% 187.18/187.97 => 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))) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I3_J,axiom,
% 187.18/187.97 ! [V_B_2,V_A_2] :
% 187.18/187.97 ( c_Nat__Transfer_Onat__set(V_A_2)
% 187.18/187.97 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 187.18/187.97 => 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))) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_transfer__int__nat__set__relations_I4_J,axiom,
% 187.18/187.97 ! [V_B_2,V_A_2] :
% 187.18/187.97 ( c_Nat__Transfer_Onat__set(V_A_2)
% 187.18/187.97 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2))
% 187.18/187.97 <=> 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))) ) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_ivl__disj__un_I7_J,axiom,
% 187.18/187.97 ! [V_u_2,V_l_2,T_a] :
% 187.18/187.97 ( class_Orderings_Olinorder(T_a)
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_u_2))
% 187.18/187.97 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_l_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_u_2) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_finite__atMost,axiom,
% 187.18/187.97 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2))) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_SetInterval_Otransfer__int__nat__set__function__closures,axiom,
% 187.18/187.97 ! [V_y_2,V_x_2] :
% 187.18/187.97 ( c_Nat__Transfer_Ois__nat(V_x_2)
% 187.18/187.97 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J,axiom,
% 187.18/187.97 ! [V_x_2,V_A_2] :
% 187.18/187.97 ( c_Nat__Transfer_Onat__set(V_A_2)
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
% 187.18/187.97 => c_Nat__Transfer_Ois__nat(V_x_2) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_atMost__eq__iff,axiom,
% 187.18/187.97 ! [V_y_2,V_x_2,T_a] :
% 187.18/187.97 ( class_Orderings_Olinorder(T_a)
% 187.18/187.97 => ( hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_x_2) = hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_y_2)
% 187.18/187.97 <=> V_x_2 = V_y_2 ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I3_J,axiom,
% 187.18/187.97 ! [V_B_2,V_A_2] :
% 187.18/187.97 ( c_Nat__Transfer_Onat__set(V_A_2)
% 187.18/187.97 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 187.18/187.97 => 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)) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I2_J,axiom,
% 187.18/187.97 ! [V_B_2,V_A_2] :
% 187.18/187.97 ( c_Nat__Transfer_Onat__set(V_A_2)
% 187.18/187.97 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 187.18/187.97 => 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)) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_transfer__int__nat__set__relations_I3_J,axiom,
% 187.18/187.97 ! [V_B_2,V_A_2] :
% 187.18/187.97 ( c_Nat__Transfer_Onat__set(V_A_2)
% 187.18/187.97 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 187.18/187.97 => ( V_A_2 = V_B_2
% 187.18/187.97 <=> 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) ) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I5_J,axiom,
% 187.18/187.97 c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J,axiom,
% 187.18/187.97 ! [V_y,V_x] :
% 187.18/187.97 ( c_Nat__Transfer_Ois__nat(V_x)
% 187.18/187.97 => ( c_Nat__Transfer_Ois__nat(V_y)
% 187.18/187.97 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y)) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J,axiom,
% 187.18/187.97 ! [V_z] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_z)) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J,axiom,
% 187.18/187.97 c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J,axiom,
% 187.18/187.97 ! [V_y,V_x] :
% 187.18/187.97 ( c_Nat__Transfer_Ois__nat(V_x)
% 187.18/187.97 => ( c_Nat__Transfer_Ois__nat(V_y)
% 187.18/187.97 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_Divides_Otransfer__int__nat__function__closures_I2_J,axiom,
% 187.18/187.97 ! [V_y,V_x] :
% 187.18/187.97 ( c_Nat__Transfer_Ois__nat(V_x)
% 187.18/187.97 => ( c_Nat__Transfer_Ois__nat(V_y)
% 187.18/187.97 => c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_Divides_Otransfer__int__nat__function__closures_I1_J,axiom,
% 187.18/187.97 ! [V_y,V_x] :
% 187.18/187.97 ( c_Nat__Transfer_Ois__nat(V_x)
% 187.18/187.97 => ( c_Nat__Transfer_Ois__nat(V_y)
% 187.18/187.97 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J,axiom,
% 187.18/187.97 ! [V_n,V_x] :
% 187.18/187.97 ( c_Nat__Transfer_Ois__nat(V_x)
% 187.18/187.97 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n)) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J,axiom,
% 187.18/187.97 ! [V_y,V_x] :
% 187.18/187.97 ( c_Nat__Transfer_Ois__nat(V_x)
% 187.18/187.97 => ( c_Nat__Transfer_Ois__nat(V_y)
% 187.18/187.97 => c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(V_x,V_y)) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_transfer__int__nat__set__relations_I2_J,axiom,
% 187.18/187.97 ! [V_A_2,V_x_2] :
% 187.18/187.97 ( c_Nat__Transfer_Ois__nat(V_x_2)
% 187.18/187.97 => ( c_Nat__Transfer_Onat__set(V_A_2)
% 187.18/187.97 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
% 187.18/187.97 <=> 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))) ) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I1_J,axiom,
% 187.18/187.97 c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_nat__set__def,axiom,
% 187.18/187.97 ! [V_S_2] :
% 187.18/187.97 ( c_Nat__Transfer_Onat__set(V_S_2)
% 187.18/187.97 <=> ! [B_x] :
% 187.18/187.97 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),V_S_2))
% 187.18/187.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) ) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_atLeast0AtMost,axiom,
% 187.18/187.97 ! [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) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_is__nat__def,axiom,
% 187.18/187.97 ! [V_x_2] :
% 187.18/187.97 ( c_Nat__Transfer_Ois__nat(V_x_2)
% 187.18/187.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_lessThan__Suc__atMost,axiom,
% 187.18/187.97 ! [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) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_card__atMost,axiom,
% 187.18/187.97 ! [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) ).
% 187.18/187.97
% 187.18/187.97 fof(fact_atMost__Suc,axiom,
% 187.18/187.97 ! [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)) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_atMost__iff,axiom,
% 187.18/187.98 ! [V_k_2,V_i_2,T_a] :
% 187.18/187.98 ( class_Orderings_Oord(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_k_2)))
% 187.18/187.98 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_i_2),V_k_2)) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J,axiom,
% 187.18/187.98 ! [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)) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_atMost__subset__iff,axiom,
% 187.18/187.98 ! [V_y_2,V_x_2,T_a] :
% 187.18/187.98 ( class_Orderings_Oorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_x_2)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_y_2)))
% 187.18/187.98 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_transfer__int__nat__sum__prod_I2_J,axiom,
% 187.18/187.98 ! [V_f_2,V_A_2,T_a] :
% 187.18/187.98 ( ( class_Groups_Ocomm__monoid__add(T_a)
% 187.18/187.98 & class_Groups_Ocomm__monoid__mult(T_a) )
% 187.18/187.98 => ( c_Nat__Transfer_Onat__set(V_A_2)
% 187.18/187.98 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_a),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,T_a),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_a,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)) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_SetInterval_Otransfer__nat__int__set__function__closures,axiom,
% 187.18/187.98 ! [V_y_2,V_x_2] :
% 187.18/187.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 187.18/187.98 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_transfer__nat__int__set__return__embed,axiom,
% 187.18/187.98 ! [V_A_2] :
% 187.18/187.98 ( c_Nat__Transfer_Onat__set(V_A_2)
% 187.18/187.98 => 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 ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I4_J,axiom,
% 187.18/187.98 ! [V_B_2,V_A_2] :
% 187.18/187.98 ( c_Nat__Transfer_Onat__set(V_A_2)
% 187.18/187.98 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 187.18/187.98 => 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))) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J,axiom,
% 187.18/187.98 ! [V_x_2,V_A_2] :
% 187.18/187.98 ( c_Nat__Transfer_Onat__set(V_A_2)
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
% 187.18/187.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_setsum__atMost__Suc,axiom,
% 187.18/187.98 ! [V_n_2,V_f_2,T_a] :
% 187.18/187.98 ( class_Groups_Ocomm__monoid__add(T_a)
% 187.18/187.98 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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))) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_atMost__0,axiom,
% 187.18/187.98 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))) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_transfer__int__nat__sum__prod_I1_J,axiom,
% 187.18/187.98 ! [V_f_2,V_A_2,T_a] :
% 187.18/187.98 ( ( class_Groups_Ocomm__monoid__add(T_a)
% 187.18/187.98 & class_Groups_Ocomm__monoid__mult(T_a) )
% 187.18/187.98 => ( c_Nat__Transfer_Onat__set(V_A_2)
% 187.18/187.98 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_a),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_a,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)) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_ivl__disj__un_I9_J,axiom,
% 187.18/187.98 ! [V_u_2,V_l_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2))
% 187.18/187.98 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_l_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_u_2) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_ivl__disj__int_I3_J,axiom,
% 187.18/187.98 ! [V_u_2,V_l_2,T_a] :
% 187.18/187.98 ( class_Orderings_Oorder(T_a)
% 187.18/187.98 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_l_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_ivl__disj__int_I1_J,axiom,
% 187.18/187.98 ! [V_u_2,V_l_2,T_a] :
% 187.18/187.98 ( class_Orderings_Oorder(T_a)
% 187.18/187.98 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_l_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_transfer__int__nat__set__relations_I1_J,axiom,
% 187.18/187.98 ! [V_A_2] :
% 187.18/187.98 ( c_Nat__Transfer_Onat__set(V_A_2)
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),V_A_2))
% 187.18/187.98 <=> 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))) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J,axiom,
% 187.18/187.98 ! [V_A_2] :
% 187.18/187.98 ( c_Nat__Transfer_Onat__set(V_A_2)
% 187.18/187.98 => 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)) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I1_J,axiom,
% 187.18/187.98 ! [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))) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_ivl__disj__un_I2_J,axiom,
% 187.18/187.98 ! [V_u_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_u_2) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_ivl__disj__un_I10_J,axiom,
% 187.18/187.98 ! [V_u_2,V_l_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2))
% 187.18/187.98 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_l_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_u_2) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_transfer__int__nat__set__relations_I5_J,axiom,
% 187.18/187.98 ! [V_B_2,V_A_2] :
% 187.18/187.98 ( c_Nat__Transfer_Onat__set(V_A_2)
% 187.18/187.98 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2))
% 187.18/187.98 <=> 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))) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_transfer__int__nat__sum__prod2_I2_J,axiom,
% 187.18/187.98 ! [V_f_2,V_A_2,T_a] :
% 187.18/187.98 ( ! [B_x] :
% 187.18/187.98 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 187.18/187.98 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) )
% 187.18/187.98 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,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_a,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,T_a),c_Int_Onat),V_f_2)),V_A_2)) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_transfer__int__nat__sum__prod2_I1_J,axiom,
% 187.18/187.98 ! [V_f_2,V_A_2,T_a] :
% 187.18/187.98 ( ! [B_x] :
% 187.18/187.98 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 187.18/187.98 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) )
% 187.18/187.98 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,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_a,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,T_a),c_Int_Onat),V_f_2)),V_A_2)) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_atMost__Int__atLeast,axiom,
% 187.18/187.98 ! [V_n_2,T_a] :
% 187.18/187.98 ( class_Orderings_Oorder(T_a)
% 187.18/187.98 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_n_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_n_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_n_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_transfer__nat__int__sum__prod__cong_I2_J,axiom,
% 187.18/187.98 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_a] :
% 187.18/187.98 ( ( class_Groups_Ocomm__monoid__add(T_a)
% 187.18/187.98 & class_Groups_Ocomm__monoid__mult(T_a) )
% 187.18/187.98 => ( V_A_2 = V_B_2
% 187.18/187.98 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 187.18/187.98 => ( ! [B_x] :
% 187.18/187.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 187.18/187.98 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) )
% 187.18/187.98 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_a),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_a),V_g_2),V_B_2) ) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_decr__lemma,axiom,
% 187.18/187.98 ! [V_z,V_x,V_d] :
% 187.18/187.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d))
% 187.18/187.98 => 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)) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_setsum__abs,axiom,
% 187.18/187.98 ! [V_A_2,V_f_2,T_b,T_a] :
% 187.18/187.98 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 187.18/187.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_f_2),V_A_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,T_b),c_Groups_Oabs__class_Oabs(T_a)),V_f_2)),V_A_2))) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_setsum__abs__ge__zero,axiom,
% 187.18/187.98 ! [V_A_2,V_f_2,T_b,T_a] :
% 187.18/187.98 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 187.18/187.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,T_b),c_Groups_Oabs__class_Oabs(T_a)),V_f_2)),V_A_2))) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_abs__add__abs,axiom,
% 187.18/187.98 ! [V_b,V_a,T_a] :
% 187.18/187.98 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 187.18/187.98 => 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)) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_abs__mult__self,axiom,
% 187.18/187.98 ! [V_a,T_a] :
% 187.18/187.98 ( class_Rings_Olinordered__idom(T_a)
% 187.18/187.98 => 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) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_abs__mult,axiom,
% 187.18/187.98 ! [V_b,V_a,T_a] :
% 187.18/187.98 ( class_Rings_Olinordered__idom(T_a)
% 187.18/187.98 => 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)) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_abs__minus__commute,axiom,
% 187.18/187.98 ! [V_b,V_a,T_a] :
% 187.18/187.98 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 187.18/187.98 => 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)) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_abs__one,axiom,
% 187.18/187.98 ! [T_a] :
% 187.18/187.98 ( class_Rings_Olinordered__idom(T_a)
% 187.18/187.98 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_atLeast__eq__iff,axiom,
% 187.18/187.98 ! [V_y_2,V_x_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_x_2) = hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_y_2)
% 187.18/187.98 <=> V_x_2 = V_y_2 ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_abs__idempotent,axiom,
% 187.18/187.98 ! [V_a,T_a] :
% 187.18/187.98 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 187.18/187.98 => 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) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_abs__eq__0,axiom,
% 187.18/187.98 ! [V_a_2,T_a] :
% 187.18/187.98 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 187.18/187.98 => ( hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
% 187.18/187.98 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_abs__zero,axiom,
% 187.18/187.98 ! [T_a] :
% 187.18/187.98 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 187.18/187.98 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_abs__le__D1,axiom,
% 187.18/187.98 ! [V_b,V_a,T_a] :
% 187.18/187.98 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b))
% 187.18/187.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_abs__ge__self,axiom,
% 187.18/187.98 ! [V_a,T_a] :
% 187.18/187.98 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 187.18/187.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_abs__of__nat,axiom,
% 187.18/187.98 ! [V_n,T_a] :
% 187.18/187.98 ( class_Rings_Olinordered__idom(T_a)
% 187.18/187.98 => 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) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_power__abs,axiom,
% 187.18/187.98 ! [V_n,V_a,T_a] :
% 187.18/187.98 ( class_Rings_Olinordered__idom(T_a)
% 187.18/187.98 => 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) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_abs__divide,axiom,
% 187.18/187.98 ! [V_b,V_a,T_a] :
% 187.18/187.98 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 187.18/187.98 => 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)) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_abs__int__eq,axiom,
% 187.18/187.98 ! [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) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_abs__setsum__abs,axiom,
% 187.18/187.98 ! [V_A_2,V_f_2,T_b,T_a] :
% 187.18/187.98 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 187.18/187.98 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,T_b),c_Groups_Oabs__class_Oabs(T_a)),V_f_2)),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,T_b),c_Groups_Oabs__class_Oabs(T_a)),V_f_2)),V_A_2) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_abs__setprod,axiom,
% 187.18/187.98 ! [V_A_2,V_f_2,T_b,T_a] :
% 187.18/187.98 ( class_Fields_Olinordered__field(T_a)
% 187.18/187.98 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,T_b),c_Groups_Oabs__class_Oabs(T_a)),V_f_2)),V_A_2) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_abs__ge__zero,axiom,
% 187.18/187.98 ! [V_a,T_a] :
% 187.18/187.98 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 187.18/187.98 => 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))) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_abs__le__zero__iff,axiom,
% 187.18/187.98 ! [V_a_2,T_a] :
% 187.18/187.98 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a_2)),c_Groups_Ozero__class_Ozero(T_a)))
% 187.18/187.98 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_abs__of__nonneg,axiom,
% 187.18/187.98 ! [V_a,T_a] :
% 187.18/187.98 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 187.18/187.98 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_abs__not__less__zero,axiom,
% 187.18/187.98 ! [V_a,T_a] :
% 187.18/187.98 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 187.18/187.98 => ~ 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))) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_zero__less__abs__iff,axiom,
% 187.18/187.98 ! [V_a_2,T_a] :
% 187.18/187.98 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a_2)))
% 187.18/187.98 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_abs__of__pos,axiom,
% 187.18/187.98 ! [V_a,T_a] :
% 187.18/187.98 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 187.18/187.98 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_abs__triangle__ineq,axiom,
% 187.18/187.98 ! [V_b,V_a,T_a] :
% 187.18/187.98 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 187.18/187.98 => 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)))) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_abs__mult__less,axiom,
% 187.18/187.98 ! [V_d,V_b,V_c,V_a,T_a] :
% 187.18/187.98 ( class_Rings_Olinordered__idom(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_c))
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)),V_d))
% 187.18/187.98 => 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))) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_abs__triangle__ineq3,axiom,
% 187.18/187.98 ! [V_b,V_a,T_a] :
% 187.18/187.98 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 187.18/187.98 => 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)))) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_abs__triangle__ineq2,axiom,
% 187.18/187.98 ! [V_b,V_a,T_a] :
% 187.18/187.98 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 187.18/187.98 => 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)))) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_abs__triangle__ineq2__sym,axiom,
% 187.18/187.98 ! [V_b,V_a,T_a] :
% 187.18/187.98 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 187.18/187.98 => 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)))) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_nonzero__abs__divide,axiom,
% 187.18/187.98 ! [V_a,V_b,T_a] :
% 187.18/187.98 ( class_Fields_Olinordered__field(T_a)
% 187.18/187.98 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 187.18/187.98 => 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)) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_abs__zmult__eq__1,axiom,
% 187.18/187.98 ! [V_n,V_m] :
% 187.18/187.98 ( 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)
% 187.18/187.98 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_m) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_abs__mult__pos,axiom,
% 187.18/187.98 ! [V_y,V_x,T_a] :
% 187.18/187.98 ( class_Rings_Olinordered__idom(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 187.18/187.98 => 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)) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_abs__eq__mult,axiom,
% 187.18/187.98 ! [V_b,V_a,T_a] :
% 187.18/187.98 ( class_Rings_Oordered__ring__abs(T_a)
% 187.18/187.98 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 187.18/187.98 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) )
% 187.18/187.98 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 187.18/187.98 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) )
% 187.18/187.98 => 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)) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_abs__triangle__ineq4,axiom,
% 187.18/187.98 ! [V_b,V_a,T_a] :
% 187.18/187.98 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 187.18/187.98 => 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)))) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_abs__diff__triangle__ineq,axiom,
% 187.18/187.98 ! [V_d,V_c,V_b,V_a,T_a] :
% 187.18/187.98 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 187.18/187.98 => 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))))) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_zero__le__power__abs,axiom,
% 187.18/187.98 ! [V_n,V_a,T_a] :
% 187.18/187.98 ( class_Rings_Olinordered__idom(T_a)
% 187.18/187.98 => 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))) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_abs__div__pos,axiom,
% 187.18/187.98 ! [V_x,V_y,T_a] :
% 187.18/187.98 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 187.18/187.98 => 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)) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_atLeast__iff,axiom,
% 187.18/187.98 ! [V_k_2,V_i_2,T_a] :
% 187.18/187.98 ( class_Orderings_Oord(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_k_2)))
% 187.18/187.98 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_k_2),V_i_2)) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_zabs__less__one__iff,axiom,
% 187.18/187.98 ! [V_z_2] :
% 187.18/187.98 ( 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)))
% 187.18/187.98 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_nat__abs__mult__distrib,axiom,
% 187.18/187.98 ! [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))) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_atLeast__subset__iff,axiom,
% 187.18/187.98 ! [V_y_2,V_x_2,T_a] :
% 187.18/187.98 ( class_Orderings_Oorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_x_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_y_2)))
% 187.18/187.98 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_zero__le__zpower__abs,axiom,
% 187.18/187.98 ! [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))) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_zero__less__zpower__abs__iff,axiom,
% 187.18/187.98 ! [V_n_2,V_x_2] :
% 187.18/187.98 ( 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)))
% 187.18/187.98 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.18/187.98 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_ivl__disj__un_I14_J,axiom,
% 187.18/187.98 ! [V_u_2,V_l_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2))
% 187.18/187.98 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_l_2) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_ivl__disj__int_I8_J,axiom,
% 187.18/187.98 ! [V_u_2,V_l_2,T_a] :
% 187.18/187.98 ( class_Orderings_Oorder(T_a)
% 187.18/187.98 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_ivl__disj__int_I6_J,axiom,
% 187.18/187.98 ! [V_u_2,V_l_2,T_a] :
% 187.18/187.98 ( class_Orderings_Oorder(T_a)
% 187.18/187.98 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_atLeast__Suc,axiom,
% 187.18/187.98 ! [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)))) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_incr__lemma,axiom,
% 187.18/187.98 ! [V_x,V_z,V_d] :
% 187.18/187.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d))
% 187.18/187.98 => 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)))) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_ivl__disj__un_I12_J,axiom,
% 187.18/187.98 ! [V_u_2,V_l_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_u_2))
% 187.18/187.98 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_u_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_l_2) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_Nitpick_Oint__lcm__def,axiom,
% 187.18/187.98 ! [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)))) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_ivl__disj__un_I13_J,axiom,
% 187.18/187.98 ! [V_u_2,V_l_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2))
% 187.18/187.98 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_l_2) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_ivl__disj__un_I1_J,axiom,
% 187.18/187.98 ! [V_l_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_l_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_l_2) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_transfer__nat__int__sum__prod__cong_I1_J,axiom,
% 187.18/187.98 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_a] :
% 187.18/187.98 ( ( class_Groups_Ocomm__monoid__add(T_a)
% 187.18/187.98 & class_Groups_Ocomm__monoid__mult(T_a) )
% 187.18/187.98 => ( V_A_2 = V_B_2
% 187.18/187.98 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 187.18/187.98 => ( ! [B_x] :
% 187.18/187.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 187.18/187.98 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) )
% 187.18/187.98 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_a),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_a),V_g_2),V_B_2) ) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_greaterThan__eq__iff,axiom,
% 187.18/187.98 ! [V_y_2,V_x_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_x_2) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_y_2)
% 187.18/187.98 <=> V_x_2 = V_y_2 ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_atLeast__Suc__greaterThan,axiom,
% 187.18/187.98 ! [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) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_greaterThan__iff,axiom,
% 187.18/187.98 ! [V_k_2,V_i_2,T_a] :
% 187.18/187.98 ( class_Orderings_Oord(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_k_2)))
% 187.18/187.98 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_k_2),V_i_2)) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_greaterThan__subset__iff,axiom,
% 187.18/187.98 ! [V_y_2,V_x_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_x_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_y_2)))
% 187.18/187.98 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_ivl__disj__int_I7_J,axiom,
% 187.18/187.98 ! [V_u_2,V_l_2,T_a] :
% 187.18/187.98 ( class_Orderings_Oorder(T_a)
% 187.18/187.98 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_ivl__disj__un_I11_J,axiom,
% 187.18/187.98 ! [V_u_2,V_l_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2))
% 187.18/187.98 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_u_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_l_2) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_ivl__disj__int_I5_J,axiom,
% 187.18/187.98 ! [V_u_2,V_l_2,T_a] :
% 187.18/187.98 ( class_Orderings_Oorder(T_a)
% 187.18/187.98 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_greaterThan__Suc,axiom,
% 187.18/187.98 ! [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)))) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_Nitpick_Onat__lcm__def,axiom,
% 187.18/187.98 ! [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)) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_int__val__lemma,axiom,
% 187.18/187.98 ! [V_k_2,V_f_2,V_n_2] :
% 187.18/187.98 ( ! [B_i] :
% 187.18/187.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
% 187.18/187.98 => 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))) )
% 187.18/187.98 => ( 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))
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
% 187.18/187.98 => ? [B_i] :
% 187.18/187.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2))
% 187.18/187.98 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_nat0__intermed__int__val,axiom,
% 187.18/187.98 ! [V_k_2,V_f_2,V_n_2] :
% 187.18/187.98 ( ! [B_i] :
% 187.18/187.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
% 187.18/187.98 => 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))) )
% 187.18/187.98 => ( 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))
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
% 187.18/187.98 => ? [B_i] :
% 187.18/187.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2))
% 187.18/187.98 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_card__less__Suc2,axiom,
% 187.18/187.98 ! [V_i_2,V_M_2] :
% 187.18/187.98 ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
% 187.18/187.98 => 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))))) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_card__less,axiom,
% 187.18/187.98 ! [V_i_2,V_M_2] :
% 187.18/187.98 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
% 187.18/187.98 => 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) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_CollectI,axiom,
% 187.18/187.98 ! [T_a,V_a_2,V_P_2] :
% 187.18/187.98 ( hBOOL(hAPP(V_P_2,V_a_2))
% 187.18/187.98 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2))) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_finite__Collect__conjI,axiom,
% 187.18/187.98 ! [V_Q_2,V_P_2,T_a] :
% 187.18/187.98 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2)))
% 187.18/187.98 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_Q_2))) )
% 187.18/187.98 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),V_P_2)),V_Q_2)))) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_finite__Collect__less__nat,axiom,
% 187.18/187.98 ! [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)))) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_finite__Collect__le__nat,axiom,
% 187.18/187.98 ! [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)))) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_Collect__empty__eq,axiom,
% 187.18/187.98 ! [V_P_2,T_a] :
% 187.18/187.98 ( hAPP(c_Set_OCollect(T_a),V_P_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 <=> ! [B_x] : ~ hBOOL(hAPP(V_P_2,B_x)) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_empty__Collect__eq,axiom,
% 187.18/187.98 ! [V_P_2,T_a] :
% 187.18/187.98 ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_a),V_P_2)
% 187.18/187.98 <=> ! [B_x] : ~ hBOOL(hAPP(V_P_2,B_x)) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_Collect__def,axiom,
% 187.18/187.98 ! [V_P_2,T_a] : hAPP(c_Set_OCollect(T_a),V_P_2) = V_P_2 ).
% 187.18/187.98
% 187.18/187.98 fof(fact_Collect__mem__eq,axiom,
% 187.18/187.98 ! [V_A_2,T_a] : hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)) = V_A_2 ).
% 187.18/187.98
% 187.18/187.98 fof(fact_mem__Collect__eq,axiom,
% 187.18/187.98 ! [V_P_2,V_a_2,T_a] :
% 187.18/187.98 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2)))
% 187.18/187.98 <=> hBOOL(hAPP(V_P_2,V_a_2)) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_CollectD,axiom,
% 187.18/187.98 ! [V_P_2,V_a_2,T_a] :
% 187.18/187.98 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2)))
% 187.18/187.98 => hBOOL(hAPP(V_P_2,V_a_2)) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_CollectE,axiom,
% 187.18/187.98 ! [V_P_2,V_a_2,T_a] :
% 187.18/187.98 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2)))
% 187.18/187.98 => hBOOL(hAPP(V_P_2,V_a_2)) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_empty__def,axiom,
% 187.18/187.98 ! [T_a] : c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_a),hAPP(c_COMBK(tc_HOL_Obool,T_a),c_fFalse)) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_finite__Collect__disjI,axiom,
% 187.18/187.98 ! [V_Q_2,V_P_2,T_a] :
% 187.18/187.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fdisj),V_P_2)),V_Q_2))))
% 187.18/187.98 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2)))
% 187.18/187.98 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_Q_2))) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_insert__Collect,axiom,
% 187.18/187.98 ! [V_P_2,V_a_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2)) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2)))),V_P_2)) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_Collect__disj__eq,axiom,
% 187.18/187.98 ! [V_Q_2,V_P_2,T_a] : hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fdisj),V_P_2)),V_Q_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_a),V_P_2)),hAPP(c_Set_OCollect(T_a),V_Q_2)) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_Collect__conj__eq,axiom,
% 187.18/187.98 ! [V_Q_2,V_P_2,T_a] : hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),V_P_2)),V_Q_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_a),V_P_2)),hAPP(c_Set_OCollect(T_a),V_Q_2)) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_insert__compr,axiom,
% 187.18/187.98 ! [V_B_2,V_a_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fdisj),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_insert__compr__raw,axiom,
% 187.18/187.98 ! [V_B_2,V_a_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fdisj),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_Un__def,axiom,
% 187.18/187.98 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fdisj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_Int__def,axiom,
% 187.18/187.98 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_Int__Collect,axiom,
% 187.18/187.98 ! [V_P_2,V_A_2,V_x_2,T_a] :
% 187.18/187.98 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_a),V_P_2))))
% 187.18/187.98 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 187.18/187.98 & hBOOL(hAPP(V_P_2,V_x_2)) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_singleton__conv2,axiom,
% 187.18/187.98 ! [V_a_2,T_a] : hAPP(c_Set_OCollect(T_a),hAPP(c_fequal,V_a_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_singleton__conv,axiom,
% 187.18/187.98 ! [V_a_2,T_a] : hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_Collect__conv__if2,axiom,
% 187.18/187.98 ! [T_a,V_a_2,V_P_2] :
% 187.18/187.98 ( ( hBOOL(hAPP(V_P_2,V_a_2))
% 187.18/187.98 => hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(c_fequal,V_a_2))),V_P_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) )
% 187.18/187.98 & ( ~ hBOOL(hAPP(V_P_2,V_a_2))
% 187.18/187.98 => hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(c_fequal,V_a_2))),V_P_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_Collect__conv__if,axiom,
% 187.18/187.98 ! [T_a,V_a_2,V_P_2] :
% 187.18/187.98 ( ( hBOOL(hAPP(V_P_2,V_a_2))
% 187.18/187.98 => hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2))),V_P_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) )
% 187.18/187.98 & ( ~ hBOOL(hAPP(V_P_2,V_a_2))
% 187.18/187.98 => hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2))),V_P_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_set__diff__eq,axiom,
% 187.18/187.98 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2)))) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_insert__def,axiom,
% 187.18/187.98 ! [V_B_2,V_a_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2))),V_B_2) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_finite__M__bounded__by__nat,axiom,
% 187.18/187.98 ! [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))))) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_setsum__setsum__restrict,axiom,
% 187.18/187.98 ! [V_R_2,V_f_2,V_T_2,T_b,V_S_2,T_a,T_c] :
% 187.18/187.98 ( class_Groups_Ocomm__monoid__add(T_c)
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 187.18/187.98 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_c),hAPP(hAPP(c_COMBS(T_a,tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_c),tc_fun(tc_fun(T_b,tc_HOL_Obool),T_c),T_a),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c)),V_f_2)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),c_Set_OCollect(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),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_T_2)))),V_R_2)))),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_a,tc_HOL_Obool),T_c),hAPP(hAPP(c_COMBB(tc_fun(T_a,T_c),tc_fun(tc_fun(T_a,tc_HOL_Obool),T_c),T_b),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_c)),hAPP(c_COMBC(T_a,T_b,T_c),V_f_2))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),c_Set_OCollect(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_S_2)))),hAPP(c_COMBC(T_a,T_b,tc_HOL_Obool),V_R_2))))),V_T_2) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_if__image__distrib,axiom,
% 187.18/187.98 ! [V_S_2,V_g_2,V_f_2,V_P_2,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,hAPP(hAPP(c_COMBS(T_b,T_a,T_a),hAPP(hAPP(c_COMBS(T_b,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),T_b),c_If(T_a)),V_P_2)),V_f_2)),V_g_2)),V_S_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_S_2),hAPP(c_Set_OCollect(T_b),V_P_2)))),hAPP(c_Set_Oimage(T_b,T_a,V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_S_2),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_P_2))))) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_nat__seg__image__imp__finite,axiom,
% 187.18/187.98 ! [V_n_2,V_f_2,T_a,V_A_2] :
% 187.18/187.98 ( V_A_2 = hAPP(c_Set_Oimage(tc_Nat_Onat,T_a,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)))
% 187.18/187.98 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_setsum__restrict__set_H,axiom,
% 187.18/187.98 ! [V_B_2,V_f_2,V_A_2,T_a,T_b] :
% 187.18/187.98 ( class_Groups_Ocomm__monoid__add(T_b)
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/187.98 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,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_a),c_If(T_b)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))),V_f_2)),c_Groups_Ozero__class_Ozero(T_b))),V_A_2) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_setsum__image__gen,axiom,
% 187.18/187.98 ! [V_f_2,T_c,V_g_2,V_S_2,T_a,T_b] :
% 187.18/187.98 ( class_Groups_Ocomm__monoid__add(T_b)
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 187.18/187.98 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),T_b,T_c),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c),c_Set_OCollect(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c),hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_S_2)))),hAPP(c_COMBC(T_a,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_a),c_fequal),V_f_2)))))),hAPP(c_Set_Oimage(T_a,T_c,V_f_2),V_S_2)) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_nat__gcd_Osimps,axiom,
% 187.18/187.98 ! [V_x,V_y] :
% 187.18/187.98 ( ( V_y = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.18/187.98 => c_Nitpick_Onat__gcd(V_x,V_y) = V_x )
% 187.18/187.98 & ( V_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.18/187.98 => 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)) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_card__less__Suc,axiom,
% 187.18/187.98 ! [V_i_2,V_M_2] :
% 187.18/187.98 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
% 187.18/187.98 => 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))))) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_dom__if,axiom,
% 187.18/187.98 ! [V_g_2,V_f_2,V_P_2,T_b,T_a] : c_Map_Odom(T_a,T_b,hAPP(hAPP(c_COMBS(T_a,tc_Option_Ooption(T_b),tc_Option_Ooption(T_b)),hAPP(hAPP(c_COMBS(T_a,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_a),c_If(tc_Option_Ooption(T_b))),V_P_2)),V_f_2)),V_g_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Map_Odom(T_a,T_b,V_f_2)),hAPP(c_Set_OCollect(T_a),V_P_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Map_Odom(T_a,T_b,V_g_2)),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),V_P_2)))) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_Nitpick_Oint__gcd__def,axiom,
% 187.18/187.98 ! [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)))) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_dom__override__on,axiom,
% 187.18/187.98 ! [V_A_2,V_g_2,V_f_2,T_b,T_a] : c_Map_Odom(T_a,T_b,c_Fun_Ooverride__on(T_a,tc_Option_Ooption(T_b),V_f_2,V_g_2,V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),c_Map_Odom(T_a,T_b,V_f_2)),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Map_Odom(T_a,T_b,V_g_2)))))),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Map_Odom(T_a,T_b,V_g_2))))) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_setsum__multicount,axiom,
% 187.18/187.98 ! [V_k_2,V_R_2,V_T_2,T_b,V_S_2,T_a] :
% 187.18/187.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 187.18/187.98 => ( ! [B_x] :
% 187.18/187.98 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_T_2))
% 187.18/187.98 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_S_2))),hAPP(hAPP(c_COMBC(T_a,T_b,tc_HOL_Obool),V_R_2),B_x)))) = V_k_2 )
% 187.18/187.98 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_Nat_Onat,T_a),c_Finite__Set_Ocard(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),c_Set_OCollect(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),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_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_b),V_T_2)) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_setsum__multicount__gen,axiom,
% 187.18/187.98 ! [V_k_2,V_R_2,V_t_2,T_b,V_s_2,T_a] :
% 187.18/187.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_s_2))
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_t_2))
% 187.18/187.98 => ( ! [B_x] :
% 187.18/187.98 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_t_2))
% 187.18/187.98 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_s_2))),hAPP(hAPP(c_COMBC(T_a,T_b,tc_HOL_Obool),V_R_2),B_x)))) = hAPP(V_k_2,B_x) )
% 187.18/187.98 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_Nat_Onat,T_a),c_Finite__Set_Ocard(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),c_Set_OCollect(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),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_t_2)))),V_R_2)))),V_s_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_k_2),V_t_2) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_finite__Collect__subsets,axiom,
% 187.18/187.98 ! [V_A_2,T_a] :
% 187.18/187.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/187.98 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool))),V_A_2)))) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_Pow__def,axiom,
% 187.18/187.98 ! [V_A_2,T_a] : hAPP(c_Set_OPow(T_a),V_A_2) = hAPP(c_Set_OCollect(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool))),V_A_2)) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_override__on__apply__in,axiom,
% 187.18/187.98 ! [V_g_2,V_f_2,T_b,V_A_2,V_a_2,T_a] :
% 187.18/187.98 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 187.18/187.98 => hAPP(c_Fun_Ooverride__on(T_a,T_b,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_g_2,V_a_2) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_override__on__apply__notin,axiom,
% 187.18/187.98 ! [V_g_2,V_f_2,T_b,V_A_2,V_a_2,T_a] :
% 187.18/187.98 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 187.18/187.98 => hAPP(c_Fun_Ooverride__on(T_a,T_b,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_f_2,V_a_2) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_override__on__emptyset,axiom,
% 187.18/187.98 ! [V_g_2,V_f_2,T_b,T_a] : c_Fun_Ooverride__on(T_a,T_b,V_f_2,V_g_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = V_f_2 ).
% 187.18/187.98
% 187.18/187.98 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J,axiom,
% 187.18/187.98 ! [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))) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_override__on__def,axiom,
% 187.18/187.98 ! [V_g_2,V_f_2,T_b,V_A_2,V_a_2,T_a] :
% 187.18/187.98 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 187.18/187.98 => hAPP(c_Fun_Ooverride__on(T_a,T_b,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_g_2,V_a_2) )
% 187.18/187.98 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 187.18/187.98 => hAPP(c_Fun_Ooverride__on(T_a,T_b,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_f_2,V_a_2) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J,axiom,
% 187.18/187.98 ! [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)))) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J,axiom,
% 187.18/187.98 ! [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)))) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_inf__Sup1__distrib,axiom,
% 187.18/187.98 ! [V_x_2,V_A_2,T_a] :
% 187.18/187.98 ( class_Lattices_Odistrib__lattice(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/187.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal)),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))))) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_inf__Sup2__distrib,axiom,
% 187.18/187.98 ! [V_B_2,V_A_2,T_a] :
% 187.18/187.98 ( class_Lattices_Odistrib__lattice(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/187.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 187.18/187.98 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_B_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),T_a),c_COMBS(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),T_a),c_COMBB(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool),T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal))),c_Lattices_Osemilattice__inf__class_Oinf(T_a)))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))))))) ) ) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_sup__Inf2__distrib,axiom,
% 187.18/187.98 ! [V_B_2,V_A_2,T_a] :
% 187.18/187.98 ( class_Lattices_Odistrib__lattice(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/187.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 187.18/187.98 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_B_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),T_a),c_COMBS(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),T_a),c_COMBB(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool),T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal))),c_Lattices_Osemilattice__sup__class_Osup(T_a)))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))))))) ) ) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_sup__Inf1__distrib,axiom,
% 187.18/187.98 ! [V_x_2,V_A_2,T_a] :
% 187.18/187.98 ( class_Lattices_Odistrib__lattice(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/187.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal)),hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))))) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_finite__conv__nat__seg__image,axiom,
% 187.18/187.98 ! [V_A_2,T_a] :
% 187.18/187.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/187.98 <=> ? [B_n,B_f] : V_A_2 = hAPP(c_Set_Oimage(tc_Nat_Onat,T_a,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))) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_finite__Collect__bounded__ex,axiom,
% 187.18/187.98 ! [V_Q_2,T_b,V_P_2,T_a] :
% 187.18/187.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2)))
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),V_P_2))),V_Q_2)))))
% 187.18/187.98 <=> ! [B_y] :
% 187.18/187.98 ( hBOOL(hAPP(V_P_2,B_y))
% 187.18/187.98 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,T_a,tc_HOL_Obool),V_Q_2),B_y)))) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_finite__image__set,axiom,
% 187.18/187.98 ! [V_f_2,T_b,V_P_2,T_a] :
% 187.18/187.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2)))
% 187.18/187.98 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,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_a),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_a,T_b),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_b),tc_fun(T_a,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_a)),c_fequal)),V_f_2)))),V_P_2))))) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_add__Min__commute,axiom,
% 187.18/187.98 ! [V_k_2,V_N_2,T_a] :
% 187.18/187.98 ( class_Groups_Olinordered__ab__semigroup__add(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
% 187.18/187.98 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_k_2),c_Big__Operators_Olinorder__class_OMin(T_a,V_N_2)) = c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(T_a),V_k_2))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_N_2))))) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_add__Max__commute,axiom,
% 187.18/187.98 ! [V_k_2,V_N_2,T_a] :
% 187.18/187.98 ( class_Groups_Olinordered__ab__semigroup__add(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
% 187.18/187.98 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_k_2),c_Big__Operators_Olinorder__class_OMax(T_a,V_N_2)) = c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(T_a),V_k_2))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_N_2))))) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_pigeonhole__infinite,axiom,
% 187.18/187.98 ! [V_f_2,T_b,V_A_2,T_a] :
% 187.18/187.98 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)))
% 187.18/187.98 => ? [B_x] :
% 187.18/187.98 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 187.18/187.98 & ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))),hAPP(hAPP(c_COMBC(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),c_fequal),V_f_2)),hAPP(V_f_2,B_x)))))) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_UN__le__eq__Un0,axiom,
% 187.18/187.98 ! [V_M_2,V_n_2,T_a] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,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_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,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))) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_greaterThan__0,axiom,
% 187.18/187.98 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))) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_top1I,axiom,
% 187.18/187.98 ! [V_x_2,T_a] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_x_2)) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_UNIV__I,axiom,
% 187.18/187.98 ! [V_x_2,T_a] : hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_SUP1__I,axiom,
% 187.18/187.98 ! [T_b,V_b_2,V_B_2,V_A_2,V_a_2,T_a] :
% 187.18/187.98 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2))
% 187.18/187.98 => hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2)) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_UN__atMost__UNIV,axiom,
% 187.18/187.98 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)) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_finite__UN,axiom,
% 187.18/187.98 ! [V_B_2,T_b,V_A_2,T_a] :
% 187.18/187.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 187.18/187.98 <=> ! [B_x] :
% 187.18/187.98 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 187.18/187.98 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_SUP__UN__eq,axiom,
% 187.18/187.98 ! [V_x_2,V_r_2,T_b,T_a] :
% 187.18/187.98 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b))),V_r_2)),V_x_2))
% 187.18/187.98 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),V_r_2))) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_UN__lessThan__UNIV,axiom,
% 187.18/187.98 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)) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_SUP1__iff,axiom,
% 187.18/187.98 ! [V_b_2,V_B_2,V_A_2,T_b,T_a] :
% 187.18/187.98 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2))
% 187.18/187.98 <=> ? [B_x] :
% 187.18/187.98 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 187.18/187.98 & hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_Pow__UNIV,axiom,
% 187.18/187.98 ! [T_a] : hAPP(c_Set_OPow(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_UNIV__Plus__UNIV,axiom,
% 187.18/187.98 ! [T_b,T_a] : c_Sum__Type_OPlus(T_a,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(T_a,T_b),tc_HOL_Obool)) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_top__apply,axiom,
% 187.18/187.98 ! [V_x_2,T_b,T_a] :
% 187.18/187.98 ( class_Orderings_Otop(T_a)
% 187.18/187.98 => hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_b,T_a)),V_x_2) = c_Orderings_Otop__class_Otop(T_a) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_finite__option__UNIV,axiom,
% 187.18/187.98 ! [T_a] :
% 187.18/187.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_a)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(T_a),tc_HOL_Obool))))
% 187.18/187.98 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_finite__Prod__UNIV,axiom,
% 187.18/187.98 ! [T_b,T_a] :
% 187.18/187.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 187.18/187.98 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)))) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_UN__atLeast__UNIV,axiom,
% 187.18/187.98 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)) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_finite__fun__UNIVD2,axiom,
% 187.18/187.98 ! [T_b,T_a] :
% 187.18/187.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,T_b)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_a,T_b),tc_HOL_Obool))))
% 187.18/187.98 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_UN__UN__finite__eq,axiom,
% 187.18/187.98 ! [V_A_2,T_a] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,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_a,tc_HOL_Obool)),tc_fun(T_a,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_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),tc_Nat_Onat),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,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_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_UNIV__not__empty,axiom,
% 187.18/187.98 ! [T_a] : c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_finite__UNIV,axiom,
% 187.18/187.98 ! [T_a] :
% 187.18/187.98 ( class_Finite__Set_Ofinite(T_a)
% 187.18/187.98 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_subset__UNIV,axiom,
% 187.18/187.98 ! [V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_Un__UNIV__right,axiom,
% 187.18/187.98 ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_Un__UNIV__left,axiom,
% 187.18/187.98 ! [V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),V_B_2) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_Int__UNIV__right,axiom,
% 187.18/187.98 ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = V_A_2 ).
% 187.18/187.98
% 187.18/187.98 fof(fact_Int__UNIV__left,axiom,
% 187.18/187.98 ! [V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),V_B_2) = V_B_2 ).
% 187.18/187.98
% 187.18/187.98 fof(fact_finite__Plus__UNIV__iff,axiom,
% 187.18/187.98 ! [T_b,T_a] :
% 187.18/187.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_a,T_b)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(T_a,T_b),tc_HOL_Obool))))
% 187.18/187.98 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))
% 187.18/187.98 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_infinite__UNIV__nat,axiom,
% 187.18/187.98 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_UNIV__def,axiom,
% 187.18/187.98 ! [T_a] : c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_a),hAPP(c_COMBK(tc_HOL_Obool,T_a),c_fTrue)) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_range__composition,axiom,
% 187.18/187.98 ! [V_g_2,V_f_2,T_c,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,hAPP(hAPP(c_COMBB(T_c,T_a,T_b),V_f_2),V_g_2)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = hAPP(c_Set_Oimage(T_c,T_a,V_f_2),hAPP(c_Set_Oimage(T_b,T_c,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_top__greatest,axiom,
% 187.18/187.98 ! [V_x,T_a] :
% 187.18/187.98 ( class_Orderings_Otop(T_a)
% 187.18/187.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Orderings_Otop__class_Otop(T_a))) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_sup__top__left,axiom,
% 187.18/187.98 ! [V_x,T_a] :
% 187.18/187.98 ( class_Lattices_Obounded__lattice__top(T_a)
% 187.18/187.98 => 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) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_sup__top__right,axiom,
% 187.18/187.98 ! [V_x,T_a] :
% 187.18/187.98 ( class_Lattices_Obounded__lattice__top(T_a)
% 187.18/187.98 => 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) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_inf__eq__top__iff,axiom,
% 187.18/187.98 ! [V_y_2,V_x_2,T_a] :
% 187.18/187.98 ( class_Lattices_Obounded__lattice__top(T_a)
% 187.18/187.98 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),V_y_2) = c_Orderings_Otop__class_Otop(T_a)
% 187.18/187.98 <=> ( V_x_2 = c_Orderings_Otop__class_Otop(T_a)
% 187.18/187.98 & V_y_2 = c_Orderings_Otop__class_Otop(T_a) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_inf__top__right,axiom,
% 187.18/187.98 ! [V_x,T_a] :
% 187.18/187.98 ( class_Lattices_Obounded__lattice__top(T_a)
% 187.18/187.98 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),c_Orderings_Otop__class_Otop(T_a)) = V_x ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_inf__top__left,axiom,
% 187.18/187.98 ! [V_x,T_a] :
% 187.18/187.98 ( class_Lattices_Obounded__lattice__top(T_a)
% 187.18/187.98 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Orderings_Otop__class_Otop(T_a)),V_x) = V_x ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_rangeI,axiom,
% 187.18/187.98 ! [T_b,V_x_2,V_f_2,T_a] : hBOOL(hAPP(hAPP(c_member(T_a),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_range__eqI,axiom,
% 187.18/187.98 ! [T_b,T_a,V_x_2,V_f_2,V_b_2] :
% 187.18/187.98 ( V_b_2 = hAPP(V_f_2,V_x_2)
% 187.18/187.98 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_Diff__UNIV,axiom,
% 187.18/187.98 ! [V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_card__eq__UNIV__imp__eq__UNIV,axiom,
% 187.18/187.98 ! [V_A_2,T_a] :
% 187.18/187.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))
% 187.18/187.98 => ( hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = hAPP(c_Finite__Set_Ocard(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 187.18/187.98 => V_A_2 = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_Max_Osingleton,axiom,
% 187.18/187.98 ! [V_x_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_x_2 ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_Min_Osingleton,axiom,
% 187.18/187.98 ! [V_x_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_x_2 ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_finite__Collect__not,axiom,
% 187.18/187.98 ! [V_P_2,T_a] :
% 187.18/187.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2)))
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),V_P_2))))
% 187.18/187.98 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_finite__range__imageI,axiom,
% 187.18/187.98 ! [V_f_2,T_c,V_g_2,T_b,T_a] :
% 187.18/187.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_Oimage(T_b,T_a,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))))
% 187.18/187.98 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,hAPP(hAPP(c_COMBB(T_a,T_c,T_b),V_f_2),V_g_2)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_atLeast__0,axiom,
% 187.18/187.98 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)) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_Min__le,axiom,
% 187.18/187.98 ! [V_x_2,V_A_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 187.18/187.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)),V_x_2)) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_Max__ge,axiom,
% 187.18/187.98 ! [V_x_2,V_A_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 187.18/187.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2))) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_Min__in,axiom,
% 187.18/187.98 ! [V_A_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/187.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)),V_A_2)) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_Max__in,axiom,
% 187.18/187.98 ! [V_A_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/187.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)),V_A_2)) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_UN__le__add__shift,axiom,
% 187.18/187.98 ! [V_k_2,V_M_2,V_n_2,T_a] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,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_a,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_a,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) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_finite__UNIV__card__ge__0,axiom,
% 187.18/187.98 ! [T_a] :
% 187.18/187.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))
% 187.18/187.98 => 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_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_Min__antimono,axiom,
% 187.18/187.98 ! [V_N_2,V_M_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_M_2),V_N_2))
% 187.18/187.98 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
% 187.18/187.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_N_2)),c_Big__Operators_Olinorder__class_OMin(T_a,V_M_2))) ) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_Max__mono,axiom,
% 187.18/187.98 ! [V_N_2,V_M_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_M_2),V_N_2))
% 187.18/187.98 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
% 187.18/187.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_M_2)),c_Big__Operators_Olinorder__class_OMax(T_a,V_N_2))) ) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_finite__fun__UNIVD1,axiom,
% 187.18/187.98 ! [T_b,T_a] :
% 187.18/187.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,T_b)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_a,T_b),tc_HOL_Obool))))
% 187.18/187.98 => ( hAPP(c_Finite__Set_Ocard(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 187.18/187.98 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_UN__I,axiom,
% 187.18/187.98 ! [V_B_2,V_b_2,T_b,V_A_2,V_a_2,T_a] :
% 187.18/187.98 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2)))
% 187.18/187.98 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_image__eq__UN,axiom,
% 187.18/187.98 ! [V_A_2,V_f_2,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Set_Oinsert(T_a)),V_f_2)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_UN__Pow__subset,axiom,
% 187.18/187.98 ! [V_B_2,V_A_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),T_b),c_Set_OPow(T_a)),V_B_2))),hAPP(c_Set_OPow(T_a),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_UN__insert,axiom,
% 187.18/187.98 ! [V_B_2,V_A_2,V_a_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(V_B_2,V_a_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_card__UNIV__unit,axiom,
% 187.18/187.98 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) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_infinite__UNIV__int,axiom,
% 187.18/187.98 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool)))) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_ball__UN,axiom,
% 187.18/187.98 ! [V_P_2,V_B_2,V_A_2,T_b,T_a] :
% 187.18/187.98 ( ! [B_x] :
% 187.18/187.98 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
% 187.18/187.98 => hBOOL(hAPP(V_P_2,B_x)) )
% 187.18/187.98 <=> ! [B_x] :
% 187.18/187.98 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 187.18/187.98 => ! [B_xa] :
% 187.18/187.98 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),hAPP(V_B_2,B_x)))
% 187.18/187.98 => hBOOL(hAPP(V_P_2,B_xa)) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_SUP__commute,axiom,
% 187.18/187.98 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_a] :
% 187.18/187.98 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 187.18/187.98 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_a),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_a),T_a,T_b),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_a),V_B_2)),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_a),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_a),T_a,T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_a),V_A_2)),hAPP(c_COMBC(T_b,T_c,T_a),V_f_2))) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_UN__extend__simps_I9_J,axiom,
% 187.18/187.98 ! [V_C_2,V_B_2,T_c,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool))),V_B_2)),V_C_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_UN__simps_I9_J,axiom,
% 187.18/187.98 ! [V_C_2,V_B_2,V_A_2,T_c,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,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)),V_C_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),T_c),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool))),V_B_2)),V_C_2)) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_UN__UN__flatten,axiom,
% 187.18/187.98 ! [V_C_2,V_B_2,V_A_2,T_c,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,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)),V_C_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),T_c),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool))),V_B_2)),V_C_2)) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_SUP__le__iff,axiom,
% 187.18/187.98 ! [V_u_2,V_M_2,V_A_2,T_b,T_a] :
% 187.18/187.98 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_a),V_A_2),V_M_2)),V_u_2))
% 187.18/187.98 <=> ! [B_x] :
% 187.18/187.98 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 187.18/187.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(V_M_2,B_x)),V_u_2)) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_less__SUP__iff,axiom,
% 187.18/187.98 ! [V_f_2,V_A_2,T_b,V_a_2,T_a] :
% 187.18/187.98 ( ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 187.18/187.98 & class_Orderings_Olinorder(T_a) )
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_a),V_A_2),V_f_2)))
% 187.18/187.98 <=> ? [B_x] :
% 187.18/187.98 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 187.18/187.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(V_f_2,B_x))) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_UN__iff,axiom,
% 187.18/187.98 ! [V_B_2,V_A_2,T_b,V_b_2,T_a] :
% 187.18/187.98 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
% 187.18/187.98 <=> ? [B_x] :
% 187.18/187.98 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 187.18/187.98 & hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(V_B_2,B_x))) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_SUP__const,axiom,
% 187.18/187.98 ! [V_M_2,T_a,V_A_2,T_b] :
% 187.18/187.98 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 187.18/187.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,T_b),V_A_2),hAPP(c_COMBK(T_b,T_a),V_M_2)) = V_M_2 ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_UNION__empty__conv_I2_J,axiom,
% 187.18/187.98 ! [V_B_2,V_A_2,T_a,T_b] :
% 187.18/187.98 ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 <=> ! [B_x] :
% 187.18/187.98 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 187.18/187.98 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_UN__constant,axiom,
% 187.18/187.98 ! [V_c_2,T_b,T_a,V_A_2] :
% 187.18/187.98 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_c_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
% 187.18/187.98 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_c_2)) = V_c_2 ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_UN__empty2,axiom,
% 187.18/187.98 ! [V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_b),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_UNION__empty__conv_I1_J,axiom,
% 187.18/187.98 ! [V_B_2,V_A_2,T_b,T_a] :
% 187.18/187.98 ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)
% 187.18/187.98 <=> ! [B_x] :
% 187.18/187.98 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 187.18/187.98 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_UN__subset__iff,axiom,
% 187.18/187.98 ! [V_B_2,V_A_2,V_I_2,T_b,T_a] :
% 187.18/187.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2)),V_B_2))
% 187.18/187.98 <=> ! [B_x] :
% 187.18/187.98 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2))
% 187.18/187.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(V_A_2,B_x)),V_B_2)) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_UN__simps_I10_J,axiom,
% 187.18/187.98 ! [V_B_2,V_A_2,V_f_2,T_c,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_a,tc_HOL_Obool),T_c),V_B_2),V_f_2)) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_image__UN,axiom,
% 187.18/187.98 ! [V_B_2,V_A_2,T_c,V_f_2,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,V_f_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)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c),c_Set_Oimage(T_b,T_a,V_f_2)),V_B_2)) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_UN__extend__simps_I10_J,axiom,
% 187.18/187.98 ! [V_f_2,V_B_2,T_c,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_a,tc_HOL_Obool),T_b),V_B_2),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),V_B_2) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_UN__Un__distrib,axiom,
% 187.18/187.98 ! [V_B_2,V_A_2,V_I_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_B_2)) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_UN__Un,axiom,
% 187.18/187.98 ! [V_M_2,V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,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_M_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_M_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_M_2)) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_Int__UN__distrib2,axiom,
% 187.18/187.98 ! [V_B_2,V_J_2,T_c,V_A_2,V_I_2,T_b,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),V_J_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),V_J_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_fun(tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool))),V_A_2))),V_B_2))) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_UN__extend__simps_I4_J,axiom,
% 187.18/187.98 ! [V_B_2,V_A_2,V_C_2,T_b,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,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_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_Int__UN__distrib,axiom,
% 187.18/187.98 ! [V_A_2,V_I_2,T_b,V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2)),V_A_2)) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_UN__extend__simps_I5_J,axiom,
% 187.18/187.98 ! [V_B_2,V_C_2,T_b,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),V_B_2)) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_UN__simps_I4_J,axiom,
% 187.18/187.98 ! [V_B_2,V_A_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_UN__simps_I5_J,axiom,
% 187.18/187.98 ! [V_B_2,V_A_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_SUPR__apply,axiom,
% 187.18/187.98 ! [V_x_2,V_f_2,V_A_2,T_c,T_b,T_a] :
% 187.18/187.98 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 187.18/187.98 => hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,T_a)),V_A_2),V_f_2),V_x_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_a),V_A_2),hAPP(hAPP(c_COMBC(T_b,T_c,T_a),V_f_2),V_x_2)) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_UN__simps_I6_J,axiom,
% 187.18/187.98 ! [V_B_2,V_A_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_UN__extend__simps_I6_J,axiom,
% 187.18/187.98 ! [V_B_2,V_A_2,V_C_2,T_b,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,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_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_SUP__subset,axiom,
% 187.18/187.98 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] :
% 187.18/187.98 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 187.18/187.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,T_b),V_A_2),V_f_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,T_b),V_B_2),V_f_2))) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_le__SUPI,axiom,
% 187.18/187.98 ! [V_M_2,V_A_2,V_i_2,T_a,T_b] :
% 187.18/187.98 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),V_A_2))
% 187.18/187.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_M_2,V_i_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,T_b),V_A_2),V_M_2))) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_UN__insert__distrib,axiom,
% 187.18/187.98 ! [V_B_2,V_a_2,T_b,V_A_2,V_u_2,T_a] :
% 187.18/187.98 ( hBOOL(hAPP(hAPP(c_member(T_a),V_u_2),V_A_2))
% 187.18/187.98 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,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_a),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_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_UN__upper,axiom,
% 187.18/187.98 ! [V_B_2,T_b,V_A_2,V_a_2,T_a] :
% 187.18/187.98 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 187.18/187.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_B_2,V_a_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_UN__absorb,axiom,
% 187.18/187.98 ! [V_A_2,T_b,V_I_2,V_k_2,T_a] :
% 187.18/187.98 ( hBOOL(hAPP(hAPP(c_member(T_a),V_k_2),V_I_2))
% 187.18/187.98 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_A_2,V_k_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_UN__extend__simps_I1_J,axiom,
% 187.18/187.98 ! [V_B_2,V_a_2,T_b,T_a,V_C_2] :
% 187.18/187.98 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_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))) )
% 187.18/187.98 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,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_a),hAPP(c_Set_Oinsert(T_b),V_a_2)),V_B_2)) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_UN__singleton,axiom,
% 187.18/187.98 ! [V_A_2,T_a] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_A_2 ).
% 187.18/187.98
% 187.18/187.98 fof(fact_UN__simps_I1_J,axiom,
% 187.18/187.98 ! [V_B_2,V_a_2,T_b,T_a,V_C_2] :
% 187.18/187.98 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,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_a),hAPP(c_Set_Oinsert(T_b),V_a_2)),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
% 187.18/187.98 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,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_a),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_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_UN__extend__simps_I2_J,axiom,
% 187.18/187.98 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
% 187.18/187.98 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => 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_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = V_B_2 )
% 187.18/187.98 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => 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_a,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_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,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_a),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_UN__extend__simps_I3_J,axiom,
% 187.18/187.98 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
% 187.18/187.98 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => 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_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = V_A_2 )
% 187.18/187.98 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => 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_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,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_a),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_UN__simps_I2_J,axiom,
% 187.18/187.98 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
% 187.18/187.98 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,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_a),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)) )
% 187.18/187.98 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,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_a),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_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_UN__simps_I3_J,axiom,
% 187.18/187.98 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
% 187.18/187.98 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,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_a),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)) )
% 187.18/187.98 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,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_a),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_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_UN__finite2__subset,axiom,
% 187.18/187.98 ! [V_B_2,V_k_2,V_A_2,T_a] :
% 187.18/187.98 ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,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_a,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)))
% 187.18/187.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,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_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_B_2))) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_UN__finite2__eq,axiom,
% 187.18/187.98 ! [V_B_2,V_k_2,V_A_2,T_a] :
% 187.18/187.98 ( ! [B_n] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,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_a,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)
% 187.18/187.98 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,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_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_B_2) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_UN__finite__subset,axiom,
% 187.18/187.98 ! [V_C_2,V_A_2,T_a] :
% 187.18/187.98 ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,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))
% 187.18/187.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2)),V_C_2)) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_iso__tuple__UNIV__I,axiom,
% 187.18/187.98 ! [V_x_2,T_a] : hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_Min_Oremove,axiom,
% 187.18/187.98 ! [V_x_2,V_A_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 187.18/187.98 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2) = V_x_2 )
% 187.18/187.98 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_SUP2__I,axiom,
% 187.18/187.98 ! [T_c,T_b,V_c_2,V_b_2,V_B_2,V_A_2,V_a_2,T_a] :
% 187.18/187.98 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2))
% 187.18/187.98 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2)) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__add__distrib__left,axiom,
% 187.18/187.98 ! [V_z,V_y,V_x,T_a] :
% 187.18/187.98 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 187.18/187.98 => 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)) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_Min_Oidem,axiom,
% 187.18/187.98 ! [V_x,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_x) = V_x ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_Oinf__assoc,axiom,
% 187.18/187.98 ! [V_z,V_y,V_x,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => 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)) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_Oinf_Oassoc,axiom,
% 187.18/187.98 ! [V_c,V_b,V_a,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => 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)) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_Oinf__left__commute,axiom,
% 187.18/187.98 ! [V_z,V_y,V_x,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => 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)) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_Oinf_Oleft__commute,axiom,
% 187.18/187.98 ! [V_c,V_a,V_b,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => 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)) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_Oinf__left__idem,axiom,
% 187.18/187.98 ! [V_y,V_x,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => 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) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_Oinf_Oleft__idem,axiom,
% 187.18/187.98 ! [V_b,V_a,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => 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) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_Oinf__commute,axiom,
% 187.18/187.98 ! [V_y,V_x,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => 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) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_Oinf_Ocommute,axiom,
% 187.18/187.98 ! [V_b,V_a,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => 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) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_Oinf_Oidem,axiom,
% 187.18/187.98 ! [V_a,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_a) = V_a ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_Oless__infI1,axiom,
% 187.18/187.98 ! [V_b,V_x,V_a,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x))
% 187.18/187.98 => 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)) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_Oless__infI2,axiom,
% 187.18/187.98 ! [V_a,V_x,V_b,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x))
% 187.18/187.98 => 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)) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__less__iff__conj,axiom,
% 187.18/187.98 ! [V_y_2,V_x_2,V_z_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),V_y_2)))
% 187.18/187.98 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),V_x_2))
% 187.18/187.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),V_y_2)) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__less__iff__disj,axiom,
% 187.18/187.98 ! [V_z_2,V_y_2,V_x_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),V_y_2)),V_z_2))
% 187.18/187.98 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_z_2))
% 187.18/187.98 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_z_2)) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__le__iff__disj,axiom,
% 187.18/187.98 ! [V_z_2,V_y_2,V_x_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),V_y_2)),V_z_2))
% 187.18/187.98 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2))
% 187.18/187.98 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_z_2)) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_Oinf__le1,axiom,
% 187.18/187.98 ! [V_y,V_x,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => 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)) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_Oinf__le2,axiom,
% 187.18/187.98 ! [V_y,V_x,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => 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)) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_Ole__iff__inf,axiom,
% 187.18/187.98 ! [V_y_2,V_x_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 187.18/187.98 <=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),V_y_2) = V_x_2 ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_Ole__inf__iff,axiom,
% 187.18/187.98 ! [V_z_2,V_y_2,V_x_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y_2),V_z_2)))
% 187.18/187.98 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 187.18/187.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2)) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_Ole__infI1,axiom,
% 187.18/187.98 ! [V_b,V_x,V_a,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 187.18/187.98 => 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)) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_Ole__infI2,axiom,
% 187.18/187.98 ! [V_a,V_x,V_b,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 187.18/187.98 => 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)) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_Oinf__absorb1,axiom,
% 187.18/187.98 ! [V_y,V_x,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 187.18/187.98 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_x ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_Oinf__absorb2,axiom,
% 187.18/187.98 ! [V_x,V_y,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 187.18/187.98 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_y ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_Ole__infI,axiom,
% 187.18/187.98 ! [V_b,V_a,V_x,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 187.18/187.98 => 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))) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_Oinf__greatest,axiom,
% 187.18/187.98 ! [V_z,V_y,V_x,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z))
% 187.18/187.98 => 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))) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_Oinf__mono,axiom,
% 187.18/187.98 ! [V_d,V_b,V_c,V_a,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 187.18/187.98 => 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))) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_Ole__infE,axiom,
% 187.18/187.98 ! [V_b,V_a,V_x,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( 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)))
% 187.18/187.98 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 187.18/187.98 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__Suc__Suc,axiom,
% 187.18/187.98 ! [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)) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__0R,axiom,
% 187.18/187.98 ! [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) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__0L,axiom,
% 187.18/187.98 ! [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) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_inf__min,axiom,
% 187.18/187.98 ! [T_a] :
% 187.18/187.98 ( ( class_Lattices_Osemilattice__inf(T_a)
% 187.18/187.98 & class_Orderings_Olinorder(T_a) )
% 187.18/187.98 => c_Lattices_Osemilattice__inf__class_Oinf(T_a) = c_Orderings_Oord__class_Omin(T_a) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__diff__distrib__left,axiom,
% 187.18/187.98 ! [V_z,V_y,V_x,T_a] :
% 187.18/187.98 ( class_Groups_Oordered__ab__group__add(T_a)
% 187.18/187.98 => 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)) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__diff,axiom,
% 187.18/187.98 ! [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) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_Ofun__left__comm__idem__inf,axiom,
% 187.18/187.98 ! [T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Orderings_Oord__class_Omin(T_a)) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_Min_Oin__idem,axiom,
% 187.18/187.98 ! [V_x_2,V_A_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 187.18/187.98 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)) = c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_Int__atLeastAtMostL1,axiom,
% 187.18/187.98 ! [V_d_2,V_b_2,V_a_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b_2),V_d_2)) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_Int__atLeastAtMostR1,axiom,
% 187.18/187.98 ! [V_d_2,V_c_2,V_b_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_c_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b_2),V_d_2)) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_Min_OF__eq,axiom,
% 187.18/187.98 ! [V_A_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/187.98 => c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omin(T_a)),V_A_2) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__Suc2,axiom,
% 187.18/187.98 ! [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) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__Suc1,axiom,
% 187.18/187.98 ! [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) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_Ofold1__belowI,axiom,
% 187.18/187.98 ! [V_a_2,V_A_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 187.18/187.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omin(T_a)),V_A_2)),V_a_2)) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_fold1__below__iff,axiom,
% 187.18/187.98 ! [V_x_2,V_A_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/187.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omin(T_a)),V_A_2)),V_x_2))
% 187.18/187.98 <=> ? [B_x] :
% 187.18/187.98 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 187.18/187.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),V_x_2)) ) ) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_Obelow__fold1__iff,axiom,
% 187.18/187.98 ! [V_x_2,V_A_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/187.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omin(T_a)),V_A_2)))
% 187.18/187.98 <=> ! [B_x] :
% 187.18/187.98 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 187.18/187.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_x)) ) ) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_strict__below__fold1__iff,axiom,
% 187.18/187.98 ! [V_x_2,V_A_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/187.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omin(T_a)),V_A_2)))
% 187.18/187.98 <=> ! [B_x] :
% 187.18/187.98 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 187.18/187.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),B_x)) ) ) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_fold1__strict__below__iff,axiom,
% 187.18/187.98 ! [V_x_2,V_A_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/187.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omin(T_a)),V_A_2)),V_x_2))
% 187.18/187.98 <=> ? [B_x] :
% 187.18/187.98 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 187.18/187.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_x),V_x_2)) ) ) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_Min__insert,axiom,
% 187.18/187.98 ! [V_x_2,V_A_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/187.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_Min_Osubset__idem,axiom,
% 187.18/187.98 ! [V_B_2,V_A_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/187.98 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 187.18/187.98 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_B_2)),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)) = c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2) ) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_Min__Un,axiom,
% 187.18/187.98 ! [V_B_2,V_A_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/187.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 187.18/187.98 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)),c_Big__Operators_Olinorder__class_OMin(T_a,V_B_2)) ) ) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_Min_Oinsert,axiom,
% 187.18/187.98 ! [V_x_2,V_A_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/187.98 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 187.18/187.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)) ) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_fold1__antimono,axiom,
% 187.18/187.98 ! [V_B_2,V_A_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 187.18/187.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omin(T_a)),V_B_2)),hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omin(T_a)),V_A_2))) ) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_Min_Oinsert__remove,axiom,
% 187.18/187.98 ! [V_x_2,V_A_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/187.98 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 )
% 187.18/187.98 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_Min_Ounion__disjoint,axiom,
% 187.18/187.98 ! [V_B_2,V_A_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/187.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 187.18/187.98 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)),c_Big__Operators_Olinorder__class_OMin(T_a,V_B_2)) ) ) ) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_Min_Ounion__inter,axiom,
% 187.18/187.98 ! [V_B_2,V_A_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 187.18/187.98 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)),c_Big__Operators_Olinorder__class_OMin(T_a,V_B_2)) ) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_dual__max,axiom,
% 187.18/187.98 ! [T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => c_Orderings_Oord_Omax(T_a,hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_a))) = c_Orderings_Oord__class_Omin(T_a) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__ord__min,axiom,
% 187.18/187.98 ! [T_a] :
% 187.18/187.98 ( class_Orderings_Oord(T_a)
% 187.18/187.98 => c_Orderings_Oord__class_Omin(T_a) = c_Orderings_Oord_Omin(T_a,c_Orderings_Oord__class_Oless__eq(T_a)) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_Min_Oclosed,axiom,
% 187.18/187.98 ! [V_A_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/187.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),hAPP(hAPP(c_Set_Oinsert(T_a),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))
% 187.18/187.98 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)),V_A_2)) ) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_OInf__fin_Oremove,axiom,
% 187.18/187.98 ! [V_x_2,V_A_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 187.18/187.98 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2) = V_x_2 )
% 187.18/187.98 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_Min_Ohom__commute,axiom,
% 187.18/187.98 ! [V_N_2,V_h_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
% 187.18/187.98 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => hAPP(V_h_2,c_Big__Operators_Olinorder__class_OMin(T_a,V_N_2)) = c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(c_Set_Oimage(T_a,T_a,V_h_2),V_N_2)) ) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_SUP2__iff,axiom,
% 187.18/187.98 ! [V_c_2,V_b_2,V_B_2,V_A_2,T_c,T_b,T_a] :
% 187.18/187.98 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2))
% 187.18/187.98 <=> ? [B_x] :
% 187.18/187.98 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 187.18/187.98 & hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2)) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_inf__nat__def,axiom,
% 187.18/187.98 c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_OInf__fin_Oin__idem,axiom,
% 187.18/187.98 ! [V_x_2,V_A_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 187.18/187.98 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_OInf__fin_Osingleton,axiom,
% 187.18/187.98 ! [V_x_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_x_2 ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_OInf__fin_OF__eq,axiom,
% 187.18/187.98 ! [V_A_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/187.98 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omin(T_a)),V_A_2) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_OInf__fin_Oinsert__idem,axiom,
% 187.18/187.98 ! [V_x_2,V_A_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/187.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_OInf__fin_Osubset__idem,axiom,
% 187.18/187.98 ! [V_B_2,V_A_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/187.98 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 187.18/187.98 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_B_2)),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2) ) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_OInf__fin_Ounion__idem,axiom,
% 187.18/187.98 ! [V_B_2,V_A_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/187.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 187.18/187.98 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_B_2)) ) ) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_OInf__fin_Oinsert,axiom,
% 187.18/187.98 ! [V_x_2,V_A_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/187.98 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 187.18/187.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)) ) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_OInf__fin_Oinsert__remove,axiom,
% 187.18/187.98 ! [V_x_2,V_A_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/187.98 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 )
% 187.18/187.98 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_OInf__fin_Ounion__inter,axiom,
% 187.18/187.98 ! [V_B_2,V_A_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 187.18/187.98 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_B_2)) ) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_OInf__fin_Ounion__disjoint,axiom,
% 187.18/187.98 ! [V_B_2,V_A_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/187.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 187.18/187.98 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_B_2)) ) ) ) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_OInf__fin_Oclosed,axiom,
% 187.18/187.98 ! [V_A_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/187.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),hAPP(hAPP(c_Set_Oinsert(T_a),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))
% 187.18/187.98 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)),V_A_2)) ) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_Osup__Inf1__distrib,axiom,
% 187.18/187.98 ! [V_x_2,V_A_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/187.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal)),hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))))) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_Osup__Inf2__distrib,axiom,
% 187.18/187.98 ! [V_B_2,V_A_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/187.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 187.18/187.98 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_B_2)) = c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),T_a),c_COMBS(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),T_a),c_COMBB(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool),T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal))),c_Orderings_Oord__class_Omax(T_a)))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))))))) ) ) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_OInf__fin_Ohom__commute,axiom,
% 187.18/187.98 ! [V_N_2,V_h_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
% 187.18/187.98 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => hAPP(V_h_2,c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_N_2)) = c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(c_Set_Oimage(T_a,T_a,V_h_2),V_N_2)) ) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_Max_Oremove,axiom,
% 187.18/187.98 ! [V_x_2,V_A_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 187.18/187.98 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2) = V_x_2 )
% 187.18/187.98 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_Oinf__sup__distrib2,axiom,
% 187.18/187.98 ! [V_x,V_z,V_y,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => 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)) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_Osup__inf__distrib2,axiom,
% 187.18/187.98 ! [V_x,V_z,V_y,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => 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)) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_Oinf__sup__distrib1,axiom,
% 187.18/187.98 ! [V_z,V_y,V_x,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => 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)) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_Osup__inf__distrib1,axiom,
% 187.18/187.98 ! [V_z,V_y,V_x,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => 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)) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_Oinf__sup__absorb,axiom,
% 187.18/187.98 ! [V_y,V_x,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => 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 ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_Osup__inf__absorb,axiom,
% 187.18/187.98 ! [V_y,V_x,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => 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 ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_max__add__distrib__left,axiom,
% 187.18/187.98 ! [V_z,V_y,V_x,T_a] :
% 187.18/187.98 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 187.18/187.98 => 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)) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_Max_Oidem,axiom,
% 187.18/187.98 ! [V_x,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_x) = V_x ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_Osup__assoc,axiom,
% 187.18/187.98 ! [V_z,V_y,V_x,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => 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)) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_Osup_Oassoc,axiom,
% 187.18/187.98 ! [V_c,V_b,V_a,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => 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)) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_Osup__left__commute,axiom,
% 187.18/187.98 ! [V_z,V_y,V_x,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => 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)) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_Osup_Oleft__commute,axiom,
% 187.18/187.98 ! [V_c,V_a,V_b,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => 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)) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_Osup__left__idem,axiom,
% 187.18/187.98 ! [V_y,V_x,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => 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) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_Osup_Oleft__idem,axiom,
% 187.18/187.98 ! [V_b,V_a,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => 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) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_Osup__commute,axiom,
% 187.18/187.98 ! [V_y,V_x,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => 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) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_Osup_Ocommute,axiom,
% 187.18/187.98 ! [V_b,V_a,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => 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) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_Osup_Oidem,axiom,
% 187.18/187.98 ! [V_a,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_a) = V_a ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_Oless__supI1,axiom,
% 187.18/187.98 ! [V_b,V_a,V_x,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
% 187.18/187.98 => 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))) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_Oless__supI2,axiom,
% 187.18/187.98 ! [V_a,V_b,V_x,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b))
% 187.18/187.98 => 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))) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_less__max__iff__disj,axiom,
% 187.18/187.98 ! [V_y_2,V_x_2,V_z_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),V_y_2)))
% 187.18/187.98 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),V_x_2))
% 187.18/187.98 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),V_y_2)) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_max__less__iff__conj,axiom,
% 187.18/187.98 ! [V_z_2,V_y_2,V_x_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),V_y_2)),V_z_2))
% 187.18/187.98 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_z_2))
% 187.18/187.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_z_2)) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_le__max__iff__disj,axiom,
% 187.18/187.98 ! [V_y_2,V_x_2,V_z_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),V_y_2)))
% 187.18/187.98 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z_2),V_x_2))
% 187.18/187.98 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z_2),V_y_2)) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_le__maxI1,axiom,
% 187.18/187.98 ! [V_y,V_x,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => 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))) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_le__maxI2,axiom,
% 187.18/187.98 ! [V_x,V_y,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => 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))) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_Ole__iff__sup,axiom,
% 187.18/187.98 ! [V_y_2,V_x_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 187.18/187.98 <=> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),V_y_2) = V_y_2 ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_Ole__sup__iff,axiom,
% 187.18/187.98 ! [V_z_2,V_y_2,V_x_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),V_y_2)),V_z_2))
% 187.18/187.98 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2))
% 187.18/187.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_z_2)) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_Ole__supI1,axiom,
% 187.18/187.98 ! [V_b,V_a,V_x,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 187.18/187.98 => 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))) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_Ole__supI2,axiom,
% 187.18/187.98 ! [V_a,V_b,V_x,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 187.18/187.98 => 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))) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_Osup__absorb2,axiom,
% 187.18/187.98 ! [V_y,V_x,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 187.18/187.98 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_y ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_Osup__absorb1,axiom,
% 187.18/187.98 ! [V_x,V_y,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 187.18/187.98 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_x ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_Ole__supI,axiom,
% 187.18/187.98 ! [V_b,V_x,V_a,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 187.18/187.98 => 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)) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_Osup__least,axiom,
% 187.18/187.98 ! [V_z,V_x,V_y,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x))
% 187.18/187.98 => 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)) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_Osup__mono,axiom,
% 187.18/187.98 ! [V_d,V_b,V_c,V_a,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 187.18/187.98 => 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))) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_Ole__supE,axiom,
% 187.18/187.98 ! [V_x,V_b,V_a,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( 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))
% 187.18/187.98 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 187.18/187.98 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_max__Suc__Suc,axiom,
% 187.18/187.98 ! [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)) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_max__0R,axiom,
% 187.18/187.98 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_n ).
% 187.18/187.98
% 187.18/187.98 fof(fact_max__0L,axiom,
% 187.18/187.98 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ).
% 187.18/187.98
% 187.18/187.98 fof(fact_sup__max,axiom,
% 187.18/187.98 ! [T_a] :
% 187.18/187.98 ( ( class_Lattices_Osemilattice__sup(T_a)
% 187.18/187.98 & class_Orderings_Olinorder(T_a) )
% 187.18/187.98 => c_Lattices_Osemilattice__sup__class_Osup(T_a) = c_Orderings_Oord__class_Omax(T_a) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_max__diff__distrib__left,axiom,
% 187.18/187.98 ! [V_z,V_y,V_x,T_a] :
% 187.18/187.98 ( class_Groups_Oordered__ab__group__add(T_a)
% 187.18/187.98 => 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)) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_Ofun__left__comm__idem__sup,axiom,
% 187.18/187.98 ! [T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Orderings_Oord__class_Omax(T_a)) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_Odistrib__sup__le,axiom,
% 187.18/187.98 ! [V_z,V_y,V_x,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => 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)))) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_Odistrib__inf__le,axiom,
% 187.18/187.98 ! [V_z,V_y,V_x,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => 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)))) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_nat__minus__add__max,axiom,
% 187.18/187.98 ! [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) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_max__Suc1,axiom,
% 187.18/187.98 ! [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) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_max__Suc2,axiom,
% 187.18/187.98 ! [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) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_max__ord__max,axiom,
% 187.18/187.98 ! [T_a] :
% 187.18/187.98 ( class_Orderings_Oord(T_a)
% 187.18/187.98 => c_Orderings_Oord__class_Omax(T_a) = c_Orderings_Oord_Omax(T_a,c_Orderings_Oord__class_Oless__eq(T_a)) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_Max_Oin__idem,axiom,
% 187.18/187.98 ! [V_x_2,V_A_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 187.18/187.98 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)) = c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_Int__atLeastAtMost,axiom,
% 187.18/187.98 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b_2),V_d_2)) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_Int__atLeastLessThan,axiom,
% 187.18/187.98 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_c_2),V_d_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b_2),V_d_2)) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_Int__greaterThanAtMost,axiom,
% 187.18/187.98 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_a_2,V_b_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b_2),V_d_2)) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_Int__greaterThanLessThan,axiom,
% 187.18/187.98 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_a_2,V_b_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b_2),V_d_2)) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_Int__atLeastAtMostL2,axiom,
% 187.18/187.98 ! [V_c_2,V_b_2,V_a_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_c_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),V_c_2),V_b_2) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_Int__atLeastAtMostR2,axiom,
% 187.18/187.98 ! [V_d_2,V_c_2,V_a_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_a_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),V_c_2),V_d_2) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_Max_OF__eq,axiom,
% 187.18/187.98 ! [V_A_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/187.98 => c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omax(T_a)),V_A_2) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_dual__min,axiom,
% 187.18/187.98 ! [T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => c_Orderings_Oord_Omin(T_a,hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_a))) = c_Orderings_Oord__class_Omax(T_a) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_Max__insert,axiom,
% 187.18/187.98 ! [V_x_2,V_A_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/187.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_Max_Osubset__idem,axiom,
% 187.18/187.98 ! [V_B_2,V_A_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/187.98 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 187.18/187.98 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_B_2)),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)) = c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2) ) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_Osup__Inf__absorb,axiom,
% 187.18/187.98 ! [V_a_2,V_A_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 187.18/187.98 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)) = V_a_2 ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_Max__Un,axiom,
% 187.18/187.98 ! [V_B_2,V_A_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/187.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 187.18/187.98 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)),c_Big__Operators_Olinorder__class_OMax(T_a,V_B_2)) ) ) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_Max_Oinsert,axiom,
% 187.18/187.98 ! [V_x_2,V_A_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/187.98 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 187.18/187.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)) ) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_Max_Oinsert__remove,axiom,
% 187.18/187.98 ! [V_x_2,V_A_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/187.98 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 )
% 187.18/187.98 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_Max_Ounion__disjoint,axiom,
% 187.18/187.98 ! [V_B_2,V_A_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/187.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 187.18/187.98 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)),c_Big__Operators_Olinorder__class_OMax(T_a,V_B_2)) ) ) ) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_Max_Ounion__inter,axiom,
% 187.18/187.98 ! [V_B_2,V_A_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 187.18/187.98 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)),c_Big__Operators_Olinorder__class_OMax(T_a,V_B_2)) ) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_Oinf__Sup2__distrib,axiom,
% 187.18/187.98 ! [V_B_2,V_A_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/187.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 187.18/187.98 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_B_2)) = c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),T_a),c_COMBS(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),T_a),c_COMBB(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool),T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal))),c_Orderings_Oord__class_Omin(T_a)))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))))))) ) ) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_Oinf__Sup1__distrib,axiom,
% 187.18/187.98 ! [V_x_2,V_A_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/187.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal)),hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))))) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_Max_Oclosed,axiom,
% 187.18/187.98 ! [V_A_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/187.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),hAPP(hAPP(c_Set_Oinsert(T_a),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))
% 187.18/187.98 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)),V_A_2)) ) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_OInf__le__Sup,axiom,
% 187.18/187.98 ! [V_A_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/187.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2))) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_OSup__fin_Oremove,axiom,
% 187.18/187.98 ! [V_x_2,V_A_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 187.18/187.98 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2) = V_x_2 )
% 187.18/187.98 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_sup__nat__def,axiom,
% 187.18/187.98 c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_OSup__fin_Oin__idem,axiom,
% 187.18/187.98 ! [V_x_2,V_A_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 187.18/187.98 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_OSup__fin_Osingleton,axiom,
% 187.18/187.98 ! [V_x_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_x_2 ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_OSup__fin_OF__eq,axiom,
% 187.18/187.98 ! [V_A_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/187.98 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omax(T_a)),V_A_2) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_OSup__fin_Oinsert__idem,axiom,
% 187.18/187.98 ! [V_x_2,V_A_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/187.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_OSup__fin_Osubset__idem,axiom,
% 187.18/187.98 ! [V_B_2,V_A_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/187.98 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 187.18/187.98 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_B_2)),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2) ) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_Oinf__Sup__absorb,axiom,
% 187.18/187.98 ! [V_a_2,V_A_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 187.18/187.98 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a_2),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)) = V_a_2 ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_OSup__fin_Ounion__idem,axiom,
% 187.18/187.98 ! [V_B_2,V_A_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/187.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 187.18/187.98 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_B_2)) ) ) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_OSup__fin_Oinsert,axiom,
% 187.18/187.98 ! [V_x_2,V_A_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/187.98 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 187.18/187.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)) ) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_OSup__fin_Oinsert__remove,axiom,
% 187.18/187.98 ! [V_x_2,V_A_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/187.98 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 )
% 187.18/187.98 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_OSup__fin_Ounion__inter,axiom,
% 187.18/187.98 ! [V_B_2,V_A_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 187.18/187.98 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_B_2)) ) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_OSup__fin_Ounion__disjoint,axiom,
% 187.18/187.98 ! [V_B_2,V_A_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/187.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 187.18/187.98 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_B_2)) ) ) ) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_OSup__fin_Oclosed,axiom,
% 187.18/187.98 ! [V_A_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/187.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),hAPP(hAPP(c_Set_Oinsert(T_a),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))
% 187.18/187.98 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)),V_A_2)) ) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_min__max_OSup__fin_Ohom__commute,axiom,
% 187.18/187.98 ! [V_N_2,V_h_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
% 187.18/187.98 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => hAPP(V_h_2,c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_N_2)) = c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(c_Set_Oimage(T_a,T_a,V_h_2),V_N_2)) ) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_Max_Ohom__commute,axiom,
% 187.18/187.98 ! [V_N_2,V_h_2,T_a] :
% 187.18/187.98 ( class_Orderings_Olinorder(T_a)
% 187.18/187.98 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
% 187.18/187.98 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.98 => hAPP(V_h_2,c_Big__Operators_Olinorder__class_OMax(T_a,V_N_2)) = c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(c_Set_Oimage(T_a,T_a,V_h_2),V_N_2)) ) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_finite__UN__I,axiom,
% 187.18/187.98 ! [V_B_2,T_b,V_A_2,T_a] :
% 187.18/187.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/187.98 => ( ! [B_a] :
% 187.18/187.98 ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2))
% 187.18/187.98 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_a))) )
% 187.18/187.98 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_diff__nat__eq__if,axiom,
% 187.18/187.98 ! [V_z_2,V_z_H_2] :
% 187.18/187.98 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2))
% 187.18/187.98 => 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) )
% 187.18/187.98 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2))
% 187.18/187.98 => 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)) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_not__neg__0,axiom,
% 187.18/187.98 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_not__neg__int,axiom,
% 187.18/187.98 ! [V_n] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_not__neg__1,axiom,
% 187.18/187.98 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_not__neg__eq__ge__0,axiom,
% 187.18/187.98 ! [V_x_2] :
% 187.18/187.98 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_x_2))
% 187.18/187.98 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_neg__def,axiom,
% 187.18/187.98 ! [V_Z_2] :
% 187.18/187.98 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_Z_2))
% 187.18/187.98 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_Z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_neg__nat,axiom,
% 187.18/187.98 ! [V_z] :
% 187.18/187.98 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z))
% 187.18/187.98 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_not__neg__nat,axiom,
% 187.18/187.98 ! [V_z] :
% 187.18/187.98 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z))
% 187.18/187.98 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_setsum__SucD,axiom,
% 187.18/187.98 ! [V_n_2,V_A_2,V_f_2,T_a] :
% 187.18/187.98 ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Nat_OSuc,V_n_2)
% 187.18/187.98 => ? [B_x] :
% 187.18/187.98 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 187.18/187.98 & 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))) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_setsum__cases,axiom,
% 187.18/187.98 ! [V_g_2,V_f_2,V_P_2,V_A_2,T_a,T_b] :
% 187.18/187.98 ( class_Groups_Ocomm__monoid__add(T_b)
% 187.18/187.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/187.98 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,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_a),c_If(T_b)),V_P_2)),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_a,T_b),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_a),V_P_2)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_a),V_P_2))))) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_nat__mod__eq__lemma,axiom,
% 187.18/187.98 ! [V_y,V_n,V_x] :
% 187.18/187.98 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_y,V_n)
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y),V_x))
% 187.18/187.98 => ? [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)) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_zdiv__zminus2__eq__if,axiom,
% 187.18/187.98 ! [V_a,V_b] :
% 187.18/187.98 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.18/187.98 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.18/187.98 => 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)) )
% 187.18/187.98 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.18/187.98 => 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)) ) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_ComplI,axiom,
% 187.18/187.98 ! [V_A_2,V_c_2,T_a] :
% 187.18/187.98 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2))
% 187.18/187.98 => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2))) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_negative__zle,axiom,
% 187.18/187.98 ! [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))) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_negative__zless,axiom,
% 187.18/187.98 ! [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))) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_zminus__zmod,axiom,
% 187.18/187.98 ! [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) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_zmod__zminus__zminus,axiom,
% 187.18/187.98 ! [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)) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_zmod__zminus2,axiom,
% 187.18/187.98 ! [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)) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_zdiv__zminus__zminus,axiom,
% 187.18/187.98 ! [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) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_zdiv__zminus2,axiom,
% 187.18/187.98 ! [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) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_abs__minus__cancel,axiom,
% 187.18/187.98 ! [V_a,T_a] :
% 187.18/187.98 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 187.18/187.98 => 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) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_Compl__anti__mono,axiom,
% 187.18/187.98 ! [V_B_2,V_A_2,T_a] :
% 187.18/187.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 187.18/187.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2))) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_Compl__subset__Compl__iff,axiom,
% 187.18/187.98 ! [V_B_2,V_A_2,T_a] :
% 187.18/187.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2)))
% 187.18/187.98 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_zminus__0,axiom,
% 187.18/187.98 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) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_minus__diff__eq,axiom,
% 187.18/187.98 ! [V_b,V_a,T_a] :
% 187.18/187.98 ( class_Groups_Oab__group__add(T_a)
% 187.18/187.98 => 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) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_mod__minus__cong,axiom,
% 187.18/187.98 ! [V_a_H,V_b,V_a,T_a] :
% 187.18/187.98 ( class_Divides_Oring__div(T_a)
% 187.18/187.98 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_b) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_b)
% 187.18/187.98 => 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) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_mod__minus__eq,axiom,
% 187.18/187.98 ! [V_b,V_a,T_a] :
% 187.18/187.98 ( class_Divides_Oring__div(T_a)
% 187.18/187.98 => 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) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_compl__mono,axiom,
% 187.18/187.98 ! [V_y,V_x,T_a] :
% 187.18/187.98 ( class_Lattices_Oboolean__algebra(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 187.18/187.98 => 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))) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_compl__le__compl__iff,axiom,
% 187.18/187.98 ! [V_y_2,V_x_2,T_a] :
% 187.18/187.98 ( class_Lattices_Oboolean__algebra(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y_2)))
% 187.18/187.98 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_le__imp__neg__le,axiom,
% 187.18/187.98 ! [V_b,V_a,T_a] :
% 187.18/187.98 ( class_Groups_Oordered__ab__group__add(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 187.18/187.98 => 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))) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_neg__le__iff__le,axiom,
% 187.18/187.98 ! [V_a_2,V_b_2,T_a] :
% 187.18/187.98 ( class_Groups_Oordered__ab__group__add(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)))
% 187.18/187.98 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_minus__le__iff,axiom,
% 187.18/187.98 ! [V_b_2,V_a_2,T_a] :
% 187.18/187.98 ( class_Groups_Oordered__ab__group__add(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_b_2))
% 187.18/187.98 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)),V_a_2)) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_le__minus__iff,axiom,
% 187.18/187.98 ! [V_b_2,V_a_2,T_a] :
% 187.18/187.98 ( class_Groups_Oordered__ab__group__add(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)))
% 187.18/187.98 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_neg__equal__zero,axiom,
% 187.18/187.98 ! [V_a_2,T_a] :
% 187.18/187.98 ( class_Groups_Olinordered__ab__group__add(T_a)
% 187.18/187.98 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) = V_a_2
% 187.18/187.98 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_neg__equal__0__iff__equal,axiom,
% 187.18/187.98 ! [V_a_2,T_a] :
% 187.18/187.98 ( class_Groups_Ogroup__add(T_a)
% 187.18/187.98 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
% 187.18/187.98 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_equal__neg__zero,axiom,
% 187.18/187.98 ! [V_a_2,T_a] :
% 187.18/187.98 ( class_Groups_Olinordered__ab__group__add(T_a)
% 187.18/187.98 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)
% 187.18/187.98 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_neg__0__equal__iff__equal,axiom,
% 187.18/187.98 ! [V_a_2,T_a] :
% 187.18/187.98 ( class_Groups_Ogroup__add(T_a)
% 187.18/187.98 => ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)
% 187.18/187.98 <=> c_Groups_Ozero__class_Ozero(T_a) = V_a_2 ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_minus__zero,axiom,
% 187.18/187.98 ! [T_a] :
% 187.18/187.98 ( class_Groups_Ogroup__add(T_a)
% 187.18/187.98 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_less__minus__iff,axiom,
% 187.18/187.98 ! [V_b_2,V_a_2,T_a] :
% 187.18/187.98 ( class_Groups_Oordered__ab__group__add(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)))
% 187.18/187.98 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_minus__less__iff,axiom,
% 187.18/187.98 ! [V_b_2,V_a_2,T_a] :
% 187.18/187.98 ( class_Groups_Oordered__ab__group__add(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_b_2))
% 187.18/187.98 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)),V_a_2)) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_neg__less__iff__less,axiom,
% 187.18/187.98 ! [V_a_2,V_b_2,T_a] :
% 187.18/187.98 ( class_Groups_Oordered__ab__group__add(T_a)
% 187.18/187.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)))
% 187.18/187.98 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_zminus__zminus,axiom,
% 187.18/187.98 ! [V_z] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)) = V_z ).
% 187.18/187.98
% 187.18/187.98 fof(fact_double__compl,axiom,
% 187.18/187.98 ! [V_x,T_a] :
% 187.18/187.98 ( class_Lattices_Oboolean__algebra(T_a)
% 187.18/187.98 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = V_x ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_uminus__apply,axiom,
% 187.18/187.98 ! [V_x_2,V_A_2,T_b,T_a] :
% 187.18/187.98 ( class_Groups_Ouminus(T_a)
% 187.18/187.98 => hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,T_a)),V_A_2),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(V_A_2,V_x_2)) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_compl__eq__compl__iff,axiom,
% 187.18/187.98 ! [V_y_2,V_x_2,T_a] :
% 187.18/187.98 ( class_Lattices_Oboolean__algebra(T_a)
% 187.18/187.98 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y_2)
% 187.18/187.98 <=> V_x_2 = V_y_2 ) ) ).
% 187.18/187.98
% 187.18/187.98 fof(fact_double__complement,axiom,
% 187.18/187.98 ! [V_A_2,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) = V_A_2 ).
% 187.18/187.98
% 187.18/187.98 fof(fact_Compl__eq__Compl__iff,axiom,
% 187.18/187.99 ! [V_B_2,V_A_2,T_a] :
% 187.18/187.99 ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2)
% 187.18/187.99 <=> V_A_2 = V_B_2 ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_minus__minus,axiom,
% 187.18/187.99 ! [V_a,T_a] :
% 187.18/187.99 ( class_Groups_Ogroup__add(T_a)
% 187.18/187.99 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = V_a ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_equation__minus__iff,axiom,
% 187.18/187.99 ! [V_b_2,V_a_2,T_a] :
% 187.18/187.99 ( class_Groups_Ogroup__add(T_a)
% 187.18/187.99 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)
% 187.18/187.99 <=> V_b_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_minus__equation__iff,axiom,
% 187.18/187.99 ! [V_b_2,V_a_2,T_a] :
% 187.18/187.99 ( class_Groups_Ogroup__add(T_a)
% 187.18/187.99 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) = V_b_2
% 187.18/187.99 <=> hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2) = V_a_2 ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_neg__equal__iff__equal,axiom,
% 187.18/187.99 ! [V_b_2,V_a_2,T_a] :
% 187.18/187.99 ( class_Groups_Ogroup__add(T_a)
% 187.18/187.99 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)
% 187.18/187.99 <=> V_a_2 = V_b_2 ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_fun__Compl__def,axiom,
% 187.18/187.99 ! [V_x_2,V_A_2,T_b,T_a] :
% 187.18/187.99 ( class_Groups_Ouminus(T_a)
% 187.18/187.99 => hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,T_a)),V_A_2),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(V_A_2,V_x_2)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_ComplE,axiom,
% 187.18/187.99 ! [V_A_2,V_c_2,T_a] :
% 187.18/187.99 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)))
% 187.18/187.99 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_ComplD,axiom,
% 187.18/187.99 ! [V_A_2,V_c_2,T_a] :
% 187.18/187.99 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)))
% 187.18/187.99 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_Compl__iff,axiom,
% 187.18/187.99 ! [V_A_2,V_c_2,T_a] :
% 187.18/187.99 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)))
% 187.18/187.99 <=> ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_square__eq__iff,axiom,
% 187.18/187.99 ! [V_b_2,V_a_2,T_a] :
% 187.18/187.99 ( class_Rings_Oidom(T_a)
% 187.18/187.99 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_a_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_b_2)
% 187.18/187.99 <=> ( V_a_2 = V_b_2
% 187.18/187.99 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2) ) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_minus__mult__minus,axiom,
% 187.18/187.99 ! [V_b,V_a,T_a] :
% 187.18/187.99 ( class_Rings_Oring(T_a)
% 187.18/187.99 => 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) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_minus__mult__commute,axiom,
% 187.18/187.99 ! [V_b,V_a,T_a] :
% 187.18/187.99 ( class_Rings_Oring(T_a)
% 187.18/187.99 => 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)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_minus__mult__left,axiom,
% 187.18/187.99 ! [V_b,V_a,T_a] :
% 187.18/187.99 ( class_Rings_Oring(T_a)
% 187.18/187.99 => 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) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_minus__mult__right,axiom,
% 187.18/187.99 ! [V_b,V_a,T_a] :
% 187.18/187.99 ( class_Rings_Oring(T_a)
% 187.18/187.99 => 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)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_minus__add__cancel,axiom,
% 187.18/187.99 ! [V_b,V_a,T_a] :
% 187.18/187.99 ( class_Groups_Ogroup__add(T_a)
% 187.18/187.99 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)) = V_b ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_add__minus__cancel,axiom,
% 187.18/187.99 ! [V_b,V_a,T_a] :
% 187.18/187.99 ( class_Groups_Ogroup__add(T_a)
% 187.18/187.99 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) = V_b ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_minus__add,axiom,
% 187.18/187.99 ! [V_b,V_a,T_a] :
% 187.18/187.99 ( class_Groups_Ogroup__add(T_a)
% 187.18/187.99 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_minus__add__distrib,axiom,
% 187.18/187.99 ! [V_b,V_a,T_a] :
% 187.18/187.99 ( class_Groups_Oab__group__add(T_a)
% 187.18/187.99 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_minus__divide__divide,axiom,
% 187.18/187.99 ! [V_b,V_a,T_a] :
% 187.18/187.99 ( class_Fields_Ofield__inverse__zero(T_a)
% 187.18/187.99 => 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) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_minus__divide__right,axiom,
% 187.18/187.99 ! [V_b,V_a,T_a] :
% 187.18/187.99 ( class_Fields_Ofield__inverse__zero(T_a)
% 187.18/187.99 => 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)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_minus__divide__left,axiom,
% 187.18/187.99 ! [V_b,V_a,T_a] :
% 187.18/187.99 ( class_Rings_Odivision__ring(T_a)
% 187.18/187.99 => 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) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_zmult__zminus,axiom,
% 187.18/187.99 ! [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)) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_zminus__zadd__distrib,axiom,
% 187.18/187.99 ! [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)) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_setsum__negf,axiom,
% 187.18/187.99 ! [V_A_2,V_f_2,T_b,T_a] :
% 187.18/187.99 ( class_Groups_Oab__group__add(T_a)
% 187.18/187.99 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,T_b),c_Groups_Ouminus__class_Ouminus(T_a)),V_f_2)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_f_2),V_A_2)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_Collect__neg__eq,axiom,
% 187.18/187.99 ! [V_P_2,T_a] : hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),V_P_2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_a),V_P_2)) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_neg__0__le__iff__le,axiom,
% 187.18/187.99 ! [V_a_2,T_a] :
% 187.18/187.99 ( class_Groups_Oordered__ab__group__add(T_a)
% 187.18/187.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)))
% 187.18/187.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_le__minus__self__iff,axiom,
% 187.18/187.99 ! [V_a_2,T_a] :
% 187.18/187.99 ( class_Groups_Olinordered__ab__group__add(T_a)
% 187.18/187.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)))
% 187.18/187.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_neg__le__0__iff__le,axiom,
% 187.18/187.99 ! [V_a_2,T_a] :
% 187.18/187.99 ( class_Groups_Oordered__ab__group__add(T_a)
% 187.18/187.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),c_Groups_Ozero__class_Ozero(T_a)))
% 187.18/187.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_minus__le__self__iff,axiom,
% 187.18/187.99 ! [V_a_2,T_a] :
% 187.18/187.99 ( class_Groups_Olinordered__ab__group__add(T_a)
% 187.18/187.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_a_2))
% 187.18/187.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_neg__0__less__iff__less,axiom,
% 187.18/187.99 ! [V_a_2,T_a] :
% 187.18/187.99 ( class_Groups_Oordered__ab__group__add(T_a)
% 187.18/187.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)))
% 187.18/187.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_neg__less__0__iff__less,axiom,
% 187.18/187.99 ! [V_a_2,T_a] :
% 187.18/187.99 ( class_Groups_Oordered__ab__group__add(T_a)
% 187.18/187.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),c_Groups_Ozero__class_Ozero(T_a)))
% 187.18/187.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_neg__less__nonneg,axiom,
% 187.18/187.99 ! [V_a_2,T_a] :
% 187.18/187.99 ( class_Groups_Olinordered__ab__group__add(T_a)
% 187.18/187.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_a_2))
% 187.18/187.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_less__minus__self__iff,axiom,
% 187.18/187.99 ! [V_a_2,T_a] :
% 187.18/187.99 ( class_Rings_Olinordered__idom(T_a)
% 187.18/187.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)))
% 187.18/187.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_right__minus,axiom,
% 187.18/187.99 ! [V_a,T_a] :
% 187.18/187.99 ( class_Groups_Ogroup__add(T_a)
% 187.18/187.99 => 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) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_eq__neg__iff__add__eq__0,axiom,
% 187.18/187.99 ! [V_b_2,V_a_2,T_a] :
% 187.18/187.99 ( class_Groups_Ogroup__add(T_a)
% 187.18/187.99 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)
% 187.18/187.99 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_left__minus,axiom,
% 187.18/187.99 ! [V_a,T_a] :
% 187.18/187.99 ( class_Groups_Ogroup__add(T_a)
% 187.18/187.99 => 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) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_ab__left__minus,axiom,
% 187.18/187.99 ! [V_a,T_a] :
% 187.18/187.99 ( class_Groups_Oab__group__add(T_a)
% 187.18/187.99 => 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) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_minus__unique,axiom,
% 187.18/187.99 ! [V_b,V_a,T_a] :
% 187.18/187.99 ( class_Groups_Ogroup__add(T_a)
% 187.18/187.99 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a)
% 187.18/187.99 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) = V_b ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_diff__0,axiom,
% 187.18/187.99 ! [V_a,T_a] :
% 187.18/187.99 ( class_Groups_Ogroup__add(T_a)
% 187.18/187.99 => 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) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_diff__minus__eq__add,axiom,
% 187.18/187.99 ! [V_b,V_a,T_a] :
% 187.18/187.99 ( class_Groups_Ogroup__add(T_a)
% 187.18/187.99 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_ab__diff__minus,axiom,
% 187.18/187.99 ! [V_b,V_a,T_a] :
% 187.18/187.99 ( class_Groups_Oab__group__add(T_a)
% 187.18/187.99 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_diff__def,axiom,
% 187.18/187.99 ! [V_b,V_a,T_a] :
% 187.18/187.99 ( class_Groups_Ogroup__add(T_a)
% 187.18/187.99 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J,axiom,
% 187.18/187.99 ! [V_y,V_x,T_a] :
% 187.18/187.99 ( class_Rings_Ocomm__ring__1(T_a)
% 187.18/187.99 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_y) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J,axiom,
% 187.18/187.99 ! [V_x,T_a] :
% 187.18/187.99 ( class_Rings_Ocomm__ring__1(T_a)
% 187.18/187.99 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),V_x) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_square__eq__1__iff,axiom,
% 187.18/187.99 ! [V_x_2,T_a] :
% 187.18/187.99 ( class_Rings_Oring__1__no__zero__divisors(T_a)
% 187.18/187.99 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2) = c_Groups_Oone__class_Oone(T_a)
% 187.18/187.99 <=> ( V_x_2 = c_Groups_Oone__class_Oone(T_a)
% 187.18/187.99 | V_x_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_inf__compl__bot,axiom,
% 187.18/187.99 ! [V_x,T_a] :
% 187.18/187.99 ( class_Lattices_Oboolean__algebra(T_a)
% 187.18/187.99 => 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) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_compl__inf__bot,axiom,
% 187.18/187.99 ! [V_x,T_a] :
% 187.18/187.99 ( class_Lattices_Oboolean__algebra(T_a)
% 187.18/187.99 => 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) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_diff__eq,axiom,
% 187.18/187.99 ! [V_y,V_x,T_a] :
% 187.18/187.99 ( class_Lattices_Oboolean__algebra(T_a)
% 187.18/187.99 => 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)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_compl__bot__eq,axiom,
% 187.18/187.99 ! [T_a] :
% 187.18/187.99 ( class_Lattices_Oboolean__algebra(T_a)
% 187.18/187.99 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Obot__class_Obot(T_a)) = c_Orderings_Otop__class_Otop(T_a) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_compl__top__eq,axiom,
% 187.18/187.99 ! [T_a] :
% 187.18/187.99 ( class_Lattices_Oboolean__algebra(T_a)
% 187.18/187.99 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Otop__class_Otop(T_a)) = c_Orderings_Obot__class_Obot(T_a) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_compl__inf,axiom,
% 187.18/187.99 ! [V_y,V_x,T_a] :
% 187.18/187.99 ( class_Lattices_Oboolean__algebra(T_a)
% 187.18/187.99 => 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)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_compl__sup,axiom,
% 187.18/187.99 ! [V_y,V_x,T_a] :
% 187.18/187.99 ( class_Lattices_Oboolean__algebra(T_a)
% 187.18/187.99 => 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)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_sup__compl__top,axiom,
% 187.18/187.99 ! [V_x,T_a] :
% 187.18/187.99 ( class_Lattices_Oboolean__algebra(T_a)
% 187.18/187.99 => 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) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_compl__sup__top,axiom,
% 187.18/187.99 ! [V_x,T_a] :
% 187.18/187.99 ( class_Lattices_Oboolean__algebra(T_a)
% 187.18/187.99 => 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) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_nonzero__minus__divide__right,axiom,
% 187.18/187.99 ! [V_a,V_b,T_a] :
% 187.18/187.99 ( class_Rings_Odivision__ring(T_a)
% 187.18/187.99 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 187.18/187.99 => 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)) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_nonzero__minus__divide__divide,axiom,
% 187.18/187.99 ! [V_a,V_b,T_a] :
% 187.18/187.99 ( class_Rings_Odivision__ring(T_a)
% 187.18/187.99 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 187.18/187.99 => 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) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_abs__le__D2,axiom,
% 187.18/187.99 ! [V_b,V_a,T_a] :
% 187.18/187.99 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 187.18/187.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b))
% 187.18/187.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_abs__leI,axiom,
% 187.18/187.99 ! [V_b,V_a,T_a] :
% 187.18/187.99 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 187.18/187.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 187.18/187.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b))
% 187.18/187.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) ) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_abs__le__iff,axiom,
% 187.18/187.99 ! [V_b_2,V_a_2,T_a] :
% 187.18/187.99 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 187.18/187.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a_2)),V_b_2))
% 187.18/187.99 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2))
% 187.18/187.99 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_b_2)) ) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_abs__ge__minus__self,axiom,
% 187.18/187.99 ! [V_a,T_a] :
% 187.18/187.99 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 187.18/187.99 => 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))) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_abs__less__iff,axiom,
% 187.18/187.99 ! [V_b_2,V_a_2,T_a] :
% 187.18/187.99 ( class_Rings_Olinordered__idom(T_a)
% 187.18/187.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a_2)),V_b_2))
% 187.18/187.99 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2))
% 187.18/187.99 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_b_2)) ) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_subset__Compl__self__eq,axiom,
% 187.18/187.99 ! [V_A_2,T_a] :
% 187.18/187.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)))
% 187.18/187.99 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_Compl__empty__eq,axiom,
% 187.18/187.99 ! [T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_Compl__UNIV__eq,axiom,
% 187.18/187.99 ! [T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_finite__compl,axiom,
% 187.18/187.99 ! [V_A_2,T_a] :
% 187.18/187.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/187.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)))
% 187.18/187.99 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_Compl__disjoint,axiom,
% 187.18/187.99 ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_Compl__disjoint2,axiom,
% 187.18/187.99 ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_Compl__partition,axiom,
% 187.18/187.99 ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_Compl__partition2,axiom,
% 187.18/187.99 ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_Compl__Int,axiom,
% 187.18/187.99 ! [V_B_2,V_A_2,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2)) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_Compl__Un,axiom,
% 187.18/187.99 ! [V_B_2,V_A_2,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2)) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_minus__max__eq__min,axiom,
% 187.18/187.99 ! [V_y,V_x,T_a] :
% 187.18/187.99 ( class_Groups_Olinordered__ab__group__add(T_a)
% 187.18/187.99 => 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)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_minus__min__eq__max,axiom,
% 187.18/187.99 ! [V_y,V_x,T_a] :
% 187.18/187.99 ( class_Groups_Olinordered__ab__group__add(T_a)
% 187.18/187.99 => 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)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_image__uminus__atLeastAtMost,axiom,
% 187.18/187.99 ! [V_y_2,V_x_2,T_a] :
% 187.18/187.99 ( class_Groups_Oordered__ab__group__add(T_a)
% 187.18/187.99 => hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_x_2,V_y_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_Compl__eq__Diff__UNIV,axiom,
% 187.18/187.99 ! [V_A_2,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),V_A_2) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_abs__power__minus,axiom,
% 187.18/187.99 ! [V_n,V_a,T_a] :
% 187.18/187.99 ( class_Rings_Olinordered__idom(T_a)
% 187.18/187.99 => 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)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_zadd__zminus__inverse2,axiom,
% 187.18/187.99 ! [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) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_Compl__Diff__eq,axiom,
% 187.18/187.99 ! [V_B_2,V_A_2,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),V_B_2) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_Diff__eq,axiom,
% 187.18/187.99 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2)) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_Diff__Compl,axiom,
% 187.18/187.99 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_negative__eq__positive,axiom,
% 187.18/187.99 ! [V_m_2,V_n_2] :
% 187.18/187.99 ( 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)
% 187.18/187.99 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.18/187.99 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_not__int__zless__negative,axiom,
% 187.18/187.99 ! [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)))) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_zmod__zminus1__not__zero,axiom,
% 187.18/187.99 ! [V_l,V_k] :
% 187.18/187.99 ( 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)
% 187.18/187.99 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_zmod__zminus2__not__zero,axiom,
% 187.18/187.99 ! [V_l,V_k] :
% 187.18/187.99 ( 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)
% 187.18/187.99 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_diff__int__def,axiom,
% 187.18/187.99 ! [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)) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_diff__int__def__symmetric,axiom,
% 187.18/187.99 ! [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) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_Ints__minus,axiom,
% 187.18/187.99 ! [V_a_2,T_a] :
% 187.18/187.99 ( class_Rings_Oring__1(T_a)
% 187.18/187.99 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a)))
% 187.18/187.99 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),c_Int_Oring__1__class_OInts(T_a))) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_image__uminus__greaterThanLessThan,axiom,
% 187.18/187.99 ! [V_y_2,V_x_2,T_a] :
% 187.18/187.99 ( class_Groups_Oordered__ab__group__add(T_a)
% 187.18/187.99 => hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_x_2,V_y_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_Compl__eq,axiom,
% 187.18/187.99 ! [V_A_2,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_Compl__lessThan,axiom,
% 187.18/187.99 ! [V_k_2,T_a] :
% 187.18/187.99 ( class_Orderings_Olinorder(T_a)
% 187.18/187.99 => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_k_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_k_2) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_Compl__atLeast,axiom,
% 187.18/187.99 ! [V_k_2,T_a] :
% 187.18/187.99 ( class_Orderings_Olinorder(T_a)
% 187.18/187.99 => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_k_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_k_2) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_Collect__imp__eq,axiom,
% 187.18/187.99 ! [V_Q_2,V_P_2,T_a] : hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fimplies),V_P_2)),V_Q_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_a),V_P_2))),hAPP(c_Set_OCollect(T_a),V_Q_2)) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_Compl__atMost,axiom,
% 187.18/187.99 ! [V_k_2,T_a] :
% 187.18/187.99 ( class_Orderings_Olinorder(T_a)
% 187.18/187.99 => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_k_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_k_2) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_Compl__greaterThan,axiom,
% 187.18/187.99 ! [V_k_2,T_a] :
% 187.18/187.99 ( class_Orderings_Olinorder(T_a)
% 187.18/187.99 => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_k_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_k_2) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_abs__minus__le__zero,axiom,
% 187.18/187.99 ! [V_a,T_a] :
% 187.18/187.99 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 187.18/187.99 => 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))) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_abs__of__nonpos,axiom,
% 187.18/187.99 ! [V_a,T_a] :
% 187.18/187.99 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 187.18/187.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 187.18/187.99 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_abs__if,axiom,
% 187.18/187.99 ! [V_a,T_a] :
% 187.18/187.99 ( class_Groups_Oabs__if(T_a)
% 187.18/187.99 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 187.18/187.99 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) )
% 187.18/187.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 187.18/187.99 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_abs__of__neg,axiom,
% 187.18/187.99 ! [V_a,T_a] :
% 187.18/187.99 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 187.18/187.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 187.18/187.99 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_power__minus,axiom,
% 187.18/187.99 ! [V_n,V_a,T_a] :
% 187.18/187.99 ( class_Rings_Oring__1(T_a)
% 187.18/187.99 => 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)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_disjoint__eq__subset__Compl,axiom,
% 187.18/187.99 ! [V_B_2,V_A_2,T_a] :
% 187.18/187.99 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2))) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_surj__Compl__image__subset,axiom,
% 187.18/187.99 ! [V_A_2,V_f_2,T_a,T_b] :
% 187.18/187.99 ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2))),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_int__zle__neg,axiom,
% 187.18/187.99 ! [V_m_2,V_n_2] :
% 187.18/187.99 ( 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))))
% 187.18/187.99 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.18/187.99 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_negative__zle__0,axiom,
% 187.18/187.99 ! [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))) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_nat__zminus__int,axiom,
% 187.18/187.99 ! [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) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_zmod__zminus1__eq__if,axiom,
% 187.18/187.99 ! [V_b,V_a] :
% 187.18/187.99 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.18/187.99 => 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) )
% 187.18/187.99 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.18/187.99 => 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)) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_zmod__zminus2__eq__if,axiom,
% 187.18/187.99 ! [V_b,V_a] :
% 187.18/187.99 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.18/187.99 => 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) )
% 187.18/187.99 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.18/187.99 => 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) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_zabs__def,axiom,
% 187.18/187.99 ! [V_i] :
% 187.18/187.99 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.18/187.99 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_i) )
% 187.18/187.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.18/187.99 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = V_i ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_image__uminus__greaterThanAtMost,axiom,
% 187.18/187.99 ! [V_y_2,V_x_2,T_a] :
% 187.18/187.99 ( class_Groups_Oordered__ab__group__add(T_a)
% 187.18/187.99 => hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_x_2,V_y_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_image__uminus__atLeastLessThan,axiom,
% 187.18/187.99 ! [V_y_2,V_x_2,T_a] :
% 187.18/187.99 ( class_Groups_Oordered__ab__group__add(T_a)
% 187.18/187.99 => hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_x_2),V_y_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_neg__zminus__int,axiom,
% 187.18/187.99 ! [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))))) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_image__uminus__lessThan,axiom,
% 187.18/187.99 ! [V_x_2,T_a] :
% 187.18/187.99 ( class_Groups_Oordered__ab__group__add(T_a)
% 187.18/187.99 => hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_x_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_image__uminus__greaterThan,axiom,
% 187.18/187.99 ! [V_x_2,T_a] :
% 187.18/187.99 ( class_Groups_Oordered__ab__group__add(T_a)
% 187.18/187.99 => hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_x_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_image__uminus__atMost,axiom,
% 187.18/187.99 ! [V_x_2,T_a] :
% 187.18/187.99 ( class_Groups_Oordered__ab__group__add(T_a)
% 187.18/187.99 => hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_x_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_image__uminus__atLeast,axiom,
% 187.18/187.99 ! [V_x_2,T_a] :
% 187.18/187.99 ( class_Groups_Oordered__ab__group__add(T_a)
% 187.18/187.99 => hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_x_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_Pow__Compl,axiom,
% 187.18/187.99 ! [V_A_2,T_a] : hAPP(c_Set_OPow(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) = hAPP(c_Set_OCollect(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_a,tc_HOL_Obool)),c_HOL_OEx(tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),c_COMBS(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_fconj)),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_a,tc_HOL_Obool))),c_fequal)),c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),c_Set_OPow(T_a))))) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_compl__unique,axiom,
% 187.18/187.99 ! [V_y,V_x,T_a] :
% 187.18/187.99 ( class_Lattices_Oboolean__algebra(T_a)
% 187.18/187.99 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = c_Orderings_Obot__class_Obot(T_a)
% 187.18/187.99 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = c_Orderings_Otop__class_Otop(T_a)
% 187.18/187.99 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x) = V_y ) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_not__zle__0__negative,axiom,
% 187.18/187.99 ! [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))))) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_negative__zless__0,axiom,
% 187.18/187.99 ! [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))) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_nat__mult__distrib__neg,axiom,
% 187.18/187.99 ! [V_z_H,V_z] :
% 187.18/187.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.18/187.99 => 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))) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_minus__Max__eq__Min,axiom,
% 187.18/187.99 ! [V_S_2,T_a] :
% 187.18/187.99 ( class_Groups_Olinordered__ab__group__add(T_a)
% 187.18/187.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 187.18/187.99 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.99 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_S_2)) = c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),V_S_2)) ) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_minus__Min__eq__Max,axiom,
% 187.18/187.99 ! [V_S_2,T_a] :
% 187.18/187.99 ( class_Groups_Olinordered__ab__group__add(T_a)
% 187.18/187.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 187.18/187.99 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/187.99 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_S_2)) = c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),V_S_2)) ) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_zdiv__zminus1__eq__if,axiom,
% 187.18/187.99 ! [V_a,V_b] :
% 187.18/187.99 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.18/187.99 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.18/187.99 => 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)) )
% 187.18/187.99 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.18/187.99 => 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)) ) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_z3div__def,axiom,
% 187.18/187.99 ! [V_k,V_l] :
% 187.18/187.99 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 187.18/187.99 => c_SMT_Oz3div(V_k,V_l) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l) )
% 187.18/187.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 187.18/187.99 => 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))) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_z3mod__def,axiom,
% 187.18/187.99 ! [V_k,V_l] :
% 187.18/187.99 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 187.18/187.99 => c_SMT_Oz3mod(V_k,V_l) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) )
% 187.18/187.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 187.18/187.99 => 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)) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_of__int__of__nat,axiom,
% 187.18/187.99 ! [V_k,T_a] :
% 187.18/187.99 ( class_Rings_Oring__1(T_a)
% 187.18/187.99 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.18/187.99 => 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)))) )
% 187.18/187.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.18/187.99 => 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)) ) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_negD,axiom,
% 187.18/187.99 ! [V_x] :
% 187.18/187.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.18/187.99 => ? [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))) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_of__int__eq__iff,axiom,
% 187.18/187.99 ! [V_z_2,V_w_2,T_a] :
% 187.18/187.99 ( class_Int_Oring__char__0(T_a)
% 187.18/187.99 => ( hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_w_2) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2)
% 187.18/187.99 <=> V_w_2 = V_z_2 ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_of__int__int__eq,axiom,
% 187.18/187.99 ! [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) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_of__int__eq__0__iff,axiom,
% 187.18/187.99 ! [V_z_2,T_a] :
% 187.18/187.99 ( class_Int_Oring__char__0(T_a)
% 187.18/187.99 => ( hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2) = c_Groups_Ozero__class_Ozero(T_a)
% 187.18/187.99 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_of__int__0__eq__iff,axiom,
% 187.18/187.99 ! [V_z_2,T_a] :
% 187.18/187.99 ( class_Int_Oring__char__0(T_a)
% 187.18/187.99 => ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2)
% 187.18/187.99 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_of__int__0,axiom,
% 187.18/187.99 ! [T_a] :
% 187.18/187.99 ( class_Rings_Oring__1(T_a)
% 187.18/187.99 => 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) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_of__int__le__iff,axiom,
% 187.18/187.99 ! [V_z_2,V_w_2,T_a] :
% 187.18/187.99 ( class_Rings_Olinordered__idom(T_a)
% 187.18/187.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_w_2)),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2)))
% 187.18/187.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_of__int__less__iff,axiom,
% 187.18/187.99 ! [V_z_2,V_w_2,T_a] :
% 187.18/187.99 ( class_Rings_Olinordered__idom(T_a)
% 187.18/187.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_w_2)),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2)))
% 187.18/187.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_of__int__add,axiom,
% 187.18/187.99 ! [V_z,V_w,T_a] :
% 187.18/187.99 ( class_Rings_Oring__1(T_a)
% 187.18/187.99 => 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)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_of__int__mult,axiom,
% 187.18/187.99 ! [V_z,V_w,T_a] :
% 187.18/187.99 ( class_Rings_Oring__1(T_a)
% 187.18/187.99 => 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)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_of__int__1,axiom,
% 187.18/187.99 ! [T_a] :
% 187.18/187.99 ( class_Rings_Oring__1(T_a)
% 187.18/187.99 => 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) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_of__int__diff,axiom,
% 187.18/187.99 ! [V_z,V_w,T_a] :
% 187.18/187.99 ( class_Rings_Oring__1(T_a)
% 187.18/187.99 => 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)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_of__int__of__nat__eq,axiom,
% 187.18/187.99 ! [V_n,T_a] :
% 187.18/187.99 ( class_Rings_Oring__1(T_a)
% 187.18/187.99 => 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) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_of__int__minus,axiom,
% 187.18/187.99 ! [V_z,T_a] :
% 187.18/187.99 ( class_Rings_Oring__1(T_a)
% 187.18/187.99 => 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)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_Ints__of__int,axiom,
% 187.18/187.99 ! [V_z_2,T_a] :
% 187.18/187.99 ( class_Rings_Oring__1(T_a)
% 187.18/187.99 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2)),c_Int_Oring__1__class_OInts(T_a))) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_of__int__power,axiom,
% 187.18/187.99 ! [V_n,V_z,T_a] :
% 187.18/187.99 ( class_Rings_Oring__1(T_a)
% 187.18/187.99 => 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) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_of__int__setsum,axiom,
% 187.18/187.99 ! [V_A_2,V_f_2,T_b,T_a] :
% 187.18/187.99 ( class_Rings_Oring__1(T_a)
% 187.18/187.99 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Int_Oint),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_a,T_b),c_Int_Oring__1__class_Oof__int(T_a)),V_f_2)),V_A_2) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_of__int__setprod,axiom,
% 187.18/187.99 ! [V_A_2,V_f_2,T_b,T_a] :
% 187.18/187.99 ( ( class_Groups_Ocomm__monoid__mult(T_a)
% 187.18/187.99 & class_Rings_Oring__1(T_a) )
% 187.18/187.99 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Int_Oint),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_a,T_b),c_Int_Oring__1__class_Oof__int(T_a)),V_f_2)),V_A_2) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_of__int__0__le__iff,axiom,
% 187.18/187.99 ! [V_z_2,T_a] :
% 187.18/187.99 ( class_Rings_Olinordered__idom(T_a)
% 187.18/187.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2)))
% 187.18/187.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_of__int__le__0__iff,axiom,
% 187.18/187.99 ! [V_z_2,T_a] :
% 187.18/187.99 ( class_Rings_Olinordered__idom(T_a)
% 187.18/187.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2)),c_Groups_Ozero__class_Ozero(T_a)))
% 187.18/187.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_of__int__less__0__iff,axiom,
% 187.18/187.99 ! [V_z_2,T_a] :
% 187.18/187.99 ( class_Rings_Olinordered__idom(T_a)
% 187.18/187.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2)),c_Groups_Ozero__class_Ozero(T_a)))
% 187.18/187.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_of__int__0__less__iff,axiom,
% 187.18/187.99 ! [V_z_2,T_a] :
% 187.18/187.99 ( class_Rings_Olinordered__idom(T_a)
% 187.18/187.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2)))
% 187.18/187.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_of__nat__nat,axiom,
% 187.18/187.99 ! [V_z,T_a] :
% 187.18/187.99 ( class_Rings_Oring__1(T_a)
% 187.18/187.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 187.18/187.99 => 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) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_sgn__neg,axiom,
% 187.18/187.99 ! [V_a,T_a] :
% 187.18/187.99 ( class_Rings_Olinordered__idom(T_a)
% 187.18/187.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 187.18/187.99 => c_Groups_Osgn__class_Osgn(T_a,V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_sgn__1__neg,axiom,
% 187.18/187.99 ! [V_a_2,T_a] :
% 187.18/187.99 ( class_Rings_Olinordered__idom(T_a)
% 187.18/187.99 => ( c_Groups_Osgn__class_Osgn(T_a,V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))
% 187.18/187.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_sgn__if,axiom,
% 187.18/187.99 ! [V_x,T_a] :
% 187.18/187.99 ( class_Groups_Osgn__if(T_a)
% 187.18/187.99 => ( ( V_x = c_Groups_Ozero__class_Ozero(T_a)
% 187.18/187.99 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ozero__class_Ozero(T_a) )
% 187.18/187.99 & ( V_x != c_Groups_Ozero__class_Ozero(T_a)
% 187.18/187.99 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 187.18/187.99 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Oone__class_Oone(T_a) )
% 187.18/187.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 187.18/187.99 => c_Groups_Osgn__class_Osgn(T_a,V_x) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_zsgn__def,axiom,
% 187.18/187.99 ! [V_i] :
% 187.18/187.99 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.18/187.99 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 187.18/187.99 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.18/187.99 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i))
% 187.18/187.99 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Oone__class_Oone(tc_Int_Oint) )
% 187.18/187.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i))
% 187.18/187.99 => 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)) ) ) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_sgn__sgn,axiom,
% 187.18/187.99 ! [V_a,T_a] :
% 187.18/187.99 ( class_Rings_Olinordered__idom(T_a)
% 187.18/187.99 => 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) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_sgn__0__0,axiom,
% 187.18/187.99 ! [V_a_2,T_a] :
% 187.18/187.99 ( class_Rings_Olinordered__idom(T_a)
% 187.18/187.99 => ( c_Groups_Osgn__class_Osgn(T_a,V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
% 187.18/187.99 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_sgn0,axiom,
% 187.18/187.99 ! [T_a] :
% 187.18/187.99 ( class_Groups_Osgn__if(T_a)
% 187.18/187.99 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_sgn__times,axiom,
% 187.18/187.99 ! [V_b,V_a,T_a] :
% 187.18/187.99 ( class_Rings_Olinordered__idom(T_a)
% 187.18/187.99 => 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)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_sgn__greater,axiom,
% 187.18/187.99 ! [V_a_2,T_a] :
% 187.18/187.99 ( class_Rings_Olinordered__idom(T_a)
% 187.18/187.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Osgn__class_Osgn(T_a,V_a_2)))
% 187.18/187.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_sgn__less,axiom,
% 187.18/187.99 ! [V_a_2,T_a] :
% 187.18/187.99 ( class_Rings_Olinordered__idom(T_a)
% 187.18/187.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Osgn__class_Osgn(T_a,V_a_2)),c_Groups_Ozero__class_Ozero(T_a)))
% 187.18/187.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_mult__sgn__abs,axiom,
% 187.18/187.99 ! [V_x,T_a] :
% 187.18/187.99 ( class_Rings_Olinordered__idom(T_a)
% 187.18/187.99 => 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 ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_abs__sgn,axiom,
% 187.18/187.99 ! [V_k,T_a] :
% 187.18/187.99 ( class_Rings_Olinordered__idom(T_a)
% 187.18/187.99 => 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)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_sgn__pos,axiom,
% 187.18/187.99 ! [V_a,T_a] :
% 187.18/187.99 ( class_Rings_Olinordered__idom(T_a)
% 187.18/187.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 187.18/187.99 => c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_sgn__1__pos,axiom,
% 187.18/187.99 ! [V_a_2,T_a] :
% 187.18/187.99 ( class_Rings_Olinordered__idom(T_a)
% 187.18/187.99 => ( c_Groups_Osgn__class_Osgn(T_a,V_a_2) = c_Groups_Oone__class_Oone(T_a)
% 187.18/187.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_com_Osize_I13_J,axiom,
% 187.18/187.99 ! [V_com2_2,V_com1_2,V_fun_2] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com1_2)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com2_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_com_Osize_I5_J,axiom,
% 187.18/187.99 ! [V_com2_2,V_com1_2,V_fun_2] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(V_com1_2)),c_Com_Ocom_Ocom__size(V_com2_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_card_Oneutral,axiom,
% 187.18/187.99 ! [V_A_2,T_a] :
% 187.18/187.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/187.99 => ( ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 187.18/187.99 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 187.18/187.99 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_mod__induct__0,axiom,
% 187.18/187.99 ! [V_i_2,V_P_2,V_p_2] :
% 187.18/187.99 ( ! [B_i] :
% 187.18/187.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_p_2))
% 187.18/187.99 => ( hBOOL(hAPP(V_P_2,B_i))
% 187.18/187.99 => hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,B_i),V_p_2))) ) )
% 187.18/187.99 => ( hBOOL(hAPP(V_P_2,V_i_2))
% 187.18/187.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_p_2))
% 187.18/187.99 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_evaln__elim__cases_I5_J,axiom,
% 187.18/187.99 ! [V_t_2,V_n_2,V_s_2,V_c2_2,V_c1_2,V_b_2] :
% 187.18/187.99 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OCond(V_b_2,V_c1_2,V_c2_2)),V_s_2),V_n_2),V_t_2))
% 187.18/187.99 => ( ( hBOOL(hAPP(V_b_2,V_s_2))
% 187.18/187.99 => ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c1_2),V_s_2),V_n_2),V_t_2)) )
% 187.18/187.99 => ~ ( ~ hBOOL(hAPP(V_b_2,V_s_2))
% 187.18/187.99 => ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c2_2),V_s_2),V_n_2),V_t_2)) ) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_evaln_OIfTrue,axiom,
% 187.18/187.99 ! [V_c1_2,V_s1_2,V_n_2,V_c0_2,V_s_2,V_b_2] :
% 187.18/187.99 ( hBOOL(hAPP(V_b_2,V_s_2))
% 187.18/187.99 => ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c0_2),V_s_2),V_n_2),V_s1_2))
% 187.18/187.99 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OCond(V_b_2,V_c0_2,V_c1_2)),V_s_2),V_n_2),V_s1_2)) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_evaln_OIfFalse,axiom,
% 187.18/187.99 ! [V_c0_2,V_s1_2,V_n_2,V_c1_2,V_s_2,V_b_2] :
% 187.18/187.99 ( ~ hBOOL(hAPP(V_b_2,V_s_2))
% 187.18/187.99 => ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c1_2),V_s_2),V_n_2),V_s1_2))
% 187.18/187.99 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OCond(V_b_2,V_c0_2,V_c1_2)),V_s_2),V_n_2),V_s1_2)) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_evalc_OIfFalse,axiom,
% 187.18/187.99 ! [V_c0_2,V_s1_2,V_c1_2,V_s_2,V_b_2] :
% 187.18/187.99 ( ~ hBOOL(hAPP(V_b_2,V_s_2))
% 187.18/187.99 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1_2),V_s_2),V_s1_2))
% 187.18/187.99 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(V_b_2,V_c0_2,V_c1_2)),V_s_2),V_s1_2)) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_evalc_OIfTrue,axiom,
% 187.18/187.99 ! [V_c1_2,V_s1_2,V_c0_2,V_s_2,V_b_2] :
% 187.18/187.99 ( hBOOL(hAPP(V_b_2,V_s_2))
% 187.18/187.99 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c0_2),V_s_2),V_s1_2))
% 187.18/187.99 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(V_b_2,V_c0_2,V_c1_2)),V_s_2),V_s1_2)) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_evalc__elim__cases_I5_J,axiom,
% 187.18/187.99 ! [V_t_2,V_s_2,V_c2_2,V_c1_2,V_b_2] :
% 187.18/187.99 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(V_b_2,V_c1_2,V_c2_2)),V_s_2),V_t_2))
% 187.18/187.99 => ( ( hBOOL(hAPP(V_b_2,V_s_2))
% 187.18/187.99 => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1_2),V_s_2),V_t_2)) )
% 187.18/187.99 => ~ ( ~ hBOOL(hAPP(V_b_2,V_s_2))
% 187.18/187.99 => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c2_2),V_s_2),V_t_2)) ) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_WTs__elim__cases_I5_J,axiom,
% 187.18/187.99 ! [V_c2_2,V_c1_2,V_b_2] :
% 187.18/187.99 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(V_b_2,V_c1_2,V_c2_2)))
% 187.18/187.99 => ~ ( hBOOL(hAPP(c_Com_OWT,V_c1_2))
% 187.18/187.99 => ~ hBOOL(hAPP(c_Com_OWT,V_c2_2)) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_com_Osimps_I4_J,axiom,
% 187.18/187.99 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_com2_2,V_com1_2,V_fun_2] :
% 187.18/187.99 ( c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2) = c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2)
% 187.18/187.99 <=> ( V_fun_2 = V_fun_H_2
% 187.18/187.99 & V_com1_2 = V_com1_H_2
% 187.18/187.99 & V_com2_2 = V_com2_H_2 ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_evaln_Oequations_I6_J,axiom,
% 187.18/187.99 ! [V_a5_2,V_a4_2,V_a2_2,V_a3_2,V_a6_2,V_a1_2] :
% 187.18/187.99 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OCond(V_a1_2,V_a6_2,V_a3_2)),V_a2_2),V_a4_2),V_a5_2))
% 187.18/187.99 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 187.18/187.99 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a6_2),V_a2_2),V_a4_2),V_a5_2)) )
% 187.18/187.99 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2))
% 187.18/187.99 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a3_2),V_a2_2),V_a4_2),V_a5_2)) ) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_evaln_Oequations_I5_J,axiom,
% 187.18/187.99 ! [V_a5_2,V_a4_2,V_a2_2,V_a6_2,V_a3_2,V_a1_2] :
% 187.18/187.99 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OCond(V_a1_2,V_a3_2,V_a6_2)),V_a2_2),V_a4_2),V_a5_2))
% 187.18/187.99 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 187.18/187.99 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a3_2),V_a2_2),V_a4_2),V_a5_2)) )
% 187.18/187.99 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2))
% 187.18/187.99 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a6_2),V_a2_2),V_a4_2),V_a5_2)) ) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_evalc_Oequations_I5_J,axiom,
% 187.18/187.99 ! [V_a4_2,V_a2_2,V_a5_2,V_a3_2,V_a1_2] :
% 187.18/187.99 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(V_a1_2,V_a3_2,V_a5_2)),V_a2_2),V_a4_2))
% 187.18/187.99 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 187.18/187.99 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),V_a4_2)) )
% 187.18/187.99 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2))
% 187.18/187.99 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a5_2),V_a2_2),V_a4_2)) ) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_evalc_Oequations_I6_J,axiom,
% 187.18/187.99 ! [V_a4_2,V_a2_2,V_a3_2,V_a5_2,V_a1_2] :
% 187.18/187.99 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(V_a1_2,V_a5_2,V_a3_2)),V_a2_2),V_a4_2))
% 187.18/187.99 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 187.18/187.99 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a5_2),V_a2_2),V_a4_2)) )
% 187.18/187.99 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2))
% 187.18/187.99 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),V_a4_2)) ) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_com_Osimps_I54_J,axiom,
% 187.18/187.99 ! [V_pname_H_2,V_com2_2,V_com1_2,V_fun_2] : c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2) != hAPP(c_Com_Ocom_OBODY,V_pname_H_2) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_com_Osimps_I55_J,axiom,
% 187.18/187.99 ! [V_com2_2,V_com1_2,V_fun_2,V_pname_H_2] : hAPP(c_Com_Ocom_OBODY,V_pname_H_2) != c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_WT_OIf,axiom,
% 187.18/187.99 ! [V_b_2,V_c1_2,V_c0_2] :
% 187.18/187.99 ( hBOOL(hAPP(c_Com_OWT,V_c0_2))
% 187.18/187.99 => ( hBOOL(hAPP(c_Com_OWT,V_c1_2))
% 187.18/187.99 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(V_b_2,V_c0_2,V_c1_2))) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_WT_Oequations_I5_J,axiom,
% 187.18/187.99 ! [V_a2_2,V_a1_2,V_a3_2] :
% 187.18/187.99 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(V_a3_2,V_a1_2,V_a2_2)))
% 187.18/187.99 <=> ( hBOOL(hAPP(c_Com_OWT,V_a1_2))
% 187.18/187.99 & hBOOL(hAPP(c_Com_OWT,V_a2_2)) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_com_Osimps_I52_J,axiom,
% 187.18/187.99 ! [V_com_H_2,V_fun_H_2,V_com2_2,V_com1_2,V_fun_2] : c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2) != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_com_Osimps_I53_J,axiom,
% 187.18/187.99 ! [V_com2_2,V_com1_2,V_fun_2,V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_com_Osimps_I45_J,axiom,
% 187.18/187.99 ! [V_com2_2,V_com1_2,V_com2_H_2,V_com1_H_2,V_fun_H_2] : c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OSemi(V_com1_2,V_com2_2) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_com_Osimps_I44_J,axiom,
% 187.18/187.99 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_com2_2,V_com1_2] : c_Com_Ocom_OSemi(V_com1_2,V_com2_2) != c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_com_Osimps_I15_J,axiom,
% 187.18/187.99 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2] : c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OSKIP ).
% 187.18/187.99
% 187.18/187.99 fof(fact_com_Osimps_I14_J,axiom,
% 187.18/187.99 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_fold__image__cong,axiom,
% 187.18/187.99 ! [V_z_2,V_h_2,V_g_2,V_A_2,T_a,T_b] :
% 187.18/187.99 ( class_Groups_Oab__semigroup__mult(T_b)
% 187.18/187.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/187.99 => ( ! [B_x] :
% 187.18/187.99 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 187.18/187.99 => hAPP(V_g_2,B_x) = hAPP(V_h_2,B_x) )
% 187.18/187.99 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),V_z_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_h_2),V_z_2),V_A_2) ) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_Max__eqI,axiom,
% 187.18/187.99 ! [V_x_2,V_A_2,T_a] :
% 187.18/187.99 ( class_Orderings_Olinorder(T_a)
% 187.18/187.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/187.99 => ( ! [B_y] :
% 187.18/187.99 ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),V_A_2))
% 187.18/187.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_y),V_x_2)) )
% 187.18/187.99 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 187.18/187.99 => c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2) = V_x_2 ) ) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_Min__eqI,axiom,
% 187.18/187.99 ! [V_x_2,V_A_2,T_a] :
% 187.18/187.99 ( class_Orderings_Olinorder(T_a)
% 187.18/187.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/187.99 => ( ! [B_y] :
% 187.18/187.99 ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),V_A_2))
% 187.18/187.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_y)) )
% 187.18/187.99 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 187.18/187.99 => c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2) = V_x_2 ) ) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_expand__Suc,axiom,
% 187.18/187.99 ! [V_v] :
% 187.18/187.99 ( 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)))
% 187.18/187.99 => 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))) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_of__nat__number__of__eq,axiom,
% 187.18/187.99 ! [V_v,T_a] :
% 187.18/187.99 ( class_Int_Onumber__ring(T_a)
% 187.18/187.99 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 187.18/187.99 => 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) )
% 187.18/187.99 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 187.18/187.99 => 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) ) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_number__of__reorient,axiom,
% 187.18/187.99 ! [V_x_2,V_w_2,T_a] :
% 187.18/187.99 ( class_Int_Onumber(T_a)
% 187.18/187.99 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = V_x_2
% 187.18/187.99 <=> V_x_2 = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_eq__number__of,axiom,
% 187.18/187.99 ! [V_y_2,V_x_2,T_a] :
% 187.18/187.99 ( ( class_Int_Onumber__ring(T_a)
% 187.18/187.99 & class_Int_Oring__char__0(T_a) )
% 187.18/187.99 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2)
% 187.18/187.99 <=> V_x_2 = V_y_2 ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_of__nat__number__of__lemma,axiom,
% 187.18/187.99 ! [V_v,T_a] :
% 187.18/187.99 ( class_Int_Onumber__ring(T_a)
% 187.18/187.99 => ( ( 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)))
% 187.18/187.99 => 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) )
% 187.18/187.99 & ( ~ 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)))
% 187.18/187.99 => 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) ) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_number__of__eq,axiom,
% 187.18/187.99 ! [V_k,T_a] :
% 187.18/187.99 ( class_Int_Onumber__ring(T_a)
% 187.18/187.99 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_k) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_of__int__number__of__eq,axiom,
% 187.18/187.99 ! [V_v,T_a] :
% 187.18/187.99 ( class_Int_Onumber__ring(T_a)
% 187.18/187.99 => 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) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_le__number__of__eq__not__less,axiom,
% 187.18/187.99 ! [V_w_2,V_v_2,T_a] :
% 187.18/187.99 ( ( class_Int_Onumber(T_a)
% 187.18/187.99 & class_Orderings_Olinorder(T_a) )
% 187.18/187.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)))
% 187.18/187.99 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v_2))) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_right__distrib__number__of,axiom,
% 187.18/187.99 ! [V_c,V_b,V_v,T_b] :
% 187.18/187.99 ( ( class_Int_Onumber(T_b)
% 187.18/187.99 & class_Rings_Osemiring(T_b) )
% 187.18/187.99 => 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)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_left__distrib__number__of,axiom,
% 187.18/187.99 ! [V_v,V_b,V_a,T_b] :
% 187.18/187.99 ( ( class_Int_Onumber(T_b)
% 187.18/187.99 & class_Rings_Osemiring(T_b) )
% 187.18/187.99 => 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))) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_left__diff__distrib__number__of,axiom,
% 187.18/187.99 ! [V_v,V_b,V_a,T_b] :
% 187.18/187.99 ( ( class_Int_Onumber(T_b)
% 187.18/187.99 & class_Rings_Oring(T_b) )
% 187.18/187.99 => 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))) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_right__diff__distrib__number__of,axiom,
% 187.18/187.99 ! [V_c,V_b,V_v,T_b] :
% 187.18/187.99 ( ( class_Int_Onumber(T_b)
% 187.18/187.99 & class_Rings_Oring(T_b) )
% 187.18/187.99 => 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)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_le__number__of,axiom,
% 187.18/187.99 ! [V_y_2,V_x_2,T_a] :
% 187.18/187.99 ( ( class_Int_Onumber__ring(T_a)
% 187.18/187.99 & class_Rings_Olinordered__idom(T_a) )
% 187.18/187.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2)))
% 187.18/187.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_less__number__of,axiom,
% 187.18/187.99 ! [V_y_2,V_x_2,T_a] :
% 187.18/187.99 ( ( class_Int_Onumber__ring(T_a)
% 187.18/187.99 & class_Rings_Olinordered__idom(T_a) )
% 187.18/187.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2)))
% 187.18/187.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_min__number__of,axiom,
% 187.18/187.99 ! [V_v,V_u,T_b] :
% 187.18/187.99 ( ( class_Int_Onumber(T_b)
% 187.18/187.99 & class_Orderings_Oord(T_b) )
% 187.18/187.99 => ( ( 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)))
% 187.18/187.99 => 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) )
% 187.18/187.99 & ( ~ 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)))
% 187.18/187.99 => 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) ) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_max__number__of,axiom,
% 187.18/187.99 ! [V_v,V_u,T_b] :
% 187.18/187.99 ( ( class_Int_Onumber(T_b)
% 187.18/187.99 & class_Orderings_Oord(T_b) )
% 187.18/187.99 => ( ( 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)))
% 187.18/187.99 => 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) )
% 187.18/187.99 & ( ~ 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)))
% 187.18/187.99 => 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) ) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_add__number__of__left,axiom,
% 187.18/187.99 ! [V_z,V_w,V_v,T_a] :
% 187.18/187.99 ( class_Int_Onumber__ring(T_a)
% 187.18/187.99 => 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) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_add__number__of__eq,axiom,
% 187.18/187.99 ! [V_w,V_v,T_a] :
% 187.18/187.99 ( class_Int_Onumber__ring(T_a)
% 187.18/187.99 => 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)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_number__of__add,axiom,
% 187.18/187.99 ! [V_w,V_v,T_a] :
% 187.18/187.99 ( class_Int_Onumber__ring(T_a)
% 187.18/187.99 => 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)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_mult__number__of__left,axiom,
% 187.18/187.99 ! [V_z,V_w,V_v,T_a] :
% 187.18/187.99 ( class_Int_Onumber__ring(T_a)
% 187.18/187.99 => 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) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_arith__simps_I32_J,axiom,
% 187.18/187.99 ! [V_w,V_v,T_a] :
% 187.18/187.99 ( class_Int_Onumber__ring(T_a)
% 187.18/187.99 => 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)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_number__of__mult,axiom,
% 187.18/187.99 ! [V_w,V_v,T_a] :
% 187.18/187.99 ( class_Int_Onumber__ring(T_a)
% 187.18/187.99 => 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)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_number__of__diff,axiom,
% 187.18/187.99 ! [V_w,V_v,T_a] :
% 187.18/187.99 ( class_Int_Onumber__ring(T_a)
% 187.18/187.99 => 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)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_arith__simps_I30_J,axiom,
% 187.18/187.99 ! [V_w,T_a] :
% 187.18/187.99 ( class_Int_Onumber__ring(T_a)
% 187.18/187.99 => 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)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_number__of__minus,axiom,
% 187.18/187.99 ! [V_w,T_a] :
% 187.18/187.99 ( class_Int_Onumber__ring(T_a)
% 187.18/187.99 => 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)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_Ints__number__of,axiom,
% 187.18/187.99 ! [V_w_2,T_a] :
% 187.18/187.99 ( class_Int_Onumber__ring(T_a)
% 187.18/187.99 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Int_Oring__1__class_OInts(T_a))) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_eq__divide__eq__number__of1,axiom,
% 187.18/187.99 ! [V_w_2,V_b_2,V_a_2,T_a] :
% 187.18/187.99 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 187.18/187.99 & class_Int_Onumber(T_a) )
% 187.18/187.99 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))
% 187.18/187.99 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) != c_Groups_Ozero__class_Ozero(T_a)
% 187.18/187.99 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)) = V_b_2 )
% 187.18/187.99 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = c_Groups_Ozero__class_Ozero(T_a)
% 187.18/187.99 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_eq__divide__eq__number__of,axiom,
% 187.18/187.99 ! [V_c_2,V_b_2,V_w_2,T_a] :
% 187.18/187.99 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 187.18/187.99 & class_Int_Onumber(T_a) )
% 187.18/187.99 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)
% 187.18/187.99 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_a)
% 187.18/187.99 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_c_2) = V_b_2 )
% 187.18/187.99 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_a)
% 187.18/187.99 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_divide__eq__eq__number__of,axiom,
% 187.18/187.99 ! [V_w_2,V_c_2,V_b_2,T_a] :
% 187.18/187.99 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 187.18/187.99 & class_Int_Onumber(T_a) )
% 187.18/187.99 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)
% 187.18/187.99 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_a)
% 187.18/187.99 => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_c_2) )
% 187.18/187.99 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_a)
% 187.18/187.99 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_divide__eq__eq__number__of1,axiom,
% 187.18/187.99 ! [V_a_2,V_w_2,V_b_2,T_a] :
% 187.18/187.99 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 187.18/187.99 & class_Int_Onumber(T_a) )
% 187.18/187.99 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)) = V_a_2
% 187.18/187.99 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) != c_Groups_Ozero__class_Ozero(T_a)
% 187.18/187.99 => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)) )
% 187.18/187.99 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = c_Groups_Ozero__class_Ozero(T_a)
% 187.18/187.99 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_add__number__of__diff1,axiom,
% 187.18/187.99 ! [V_c,V_w,V_v,T_a] :
% 187.18/187.99 ( class_Int_Onumber__ring(T_a)
% 187.18/187.99 => 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) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_minus__number__of__mult,axiom,
% 187.18/187.99 ! [V_z,V_w,T_a] :
% 187.18/187.99 ( class_Int_Onumber__ring(T_a)
% 187.18/187.99 => 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) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_diff__number__of__eq,axiom,
% 187.18/187.99 ! [V_w,V_v,T_a] :
% 187.18/187.99 ( class_Int_Onumber__ring(T_a)
% 187.18/187.99 => 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))) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_less__divide__eq__number__of1,axiom,
% 187.18/187.99 ! [V_w_2,V_b_2,V_a_2,T_a] :
% 187.18/187.99 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 187.18/187.99 & class_Int_Onumber(T_a) )
% 187.18/187.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))))
% 187.18/187.99 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)))
% 187.18/187.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))),V_b_2)) )
% 187.18/187.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)))
% 187.18/187.99 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Groups_Ozero__class_Ozero(T_a)))
% 187.18/187.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)))) )
% 187.18/187.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Groups_Ozero__class_Ozero(T_a)))
% 187.18/187.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_less__divide__eq__number__of,axiom,
% 187.18/187.99 ! [V_c_2,V_b_2,V_w_2,T_a] :
% 187.18/187.99 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 187.18/187.99 & class_Int_Onumber(T_a) )
% 187.18/187.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)))
% 187.18/187.99 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
% 187.18/187.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_c_2)),V_b_2)) )
% 187.18/187.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
% 187.18/187.99 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a)))
% 187.18/187.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_c_2))) )
% 187.18/187.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a)))
% 187.18/187.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_divide__less__eq__number__of,axiom,
% 187.18/187.99 ! [V_w_2,V_c_2,V_b_2,T_a] :
% 187.18/187.99 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 187.18/187.99 & class_Int_Onumber(T_a) )
% 187.18/187.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)))
% 187.18/187.99 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
% 187.18/187.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_c_2))) )
% 187.18/187.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
% 187.18/187.99 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a)))
% 187.18/187.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_c_2)),V_b_2)) )
% 187.18/187.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a)))
% 187.18/187.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) ) ) ) ) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_divide__less__eq__number__of1,axiom,
% 187.18/187.99 ! [V_a_2,V_w_2,V_b_2,T_a] :
% 187.18/187.99 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 187.18/187.99 & class_Int_Onumber(T_a) )
% 187.18/187.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))),V_a_2))
% 187.18/187.99 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)))
% 187.18/187.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)))) )
% 187.18/187.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)))
% 187.18/187.99 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Groups_Ozero__class_Ozero(T_a)))
% 187.18/187.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))),V_b_2)) )
% 187.18/187.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Groups_Ozero__class_Ozero(T_a)))
% 187.18/187.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ) ) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_abs__number__of,axiom,
% 187.18/187.99 ! [V_x,T_a] :
% 187.18/187.99 ( ( class_Int_Onumber__ring(T_a)
% 187.18/187.99 & class_Rings_Olinordered__idom(T_a) )
% 187.18/187.99 => ( ( 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)))
% 187.18/187.99 => 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)) )
% 187.18/187.99 & ( ~ 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)))
% 187.18/187.99 => 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) ) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_add__number__of__diff2,axiom,
% 187.18/187.99 ! [V_w,V_c,V_v,T_a] :
% 187.18/187.99 ( class_Int_Onumber__ring(T_a)
% 187.18/187.99 => 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) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_divide__le__eq__number__of1,axiom,
% 187.18/187.99 ! [V_a_2,V_w_2,V_b_2,T_a] :
% 187.18/187.99 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 187.18/187.99 & class_Int_Onumber(T_a) )
% 187.18/187.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))),V_a_2))
% 187.18/187.99 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)))
% 187.18/187.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)))) )
% 187.18/187.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)))
% 187.18/187.99 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Groups_Ozero__class_Ozero(T_a)))
% 187.18/187.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))),V_b_2)) )
% 187.18/187.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Groups_Ozero__class_Ozero(T_a)))
% 187.18/187.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ) ) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_divide__le__eq__number__of,axiom,
% 187.18/187.99 ! [V_w_2,V_c_2,V_b_2,T_a] :
% 187.18/187.99 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 187.18/187.99 & class_Int_Onumber(T_a) )
% 187.18/187.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)))
% 187.18/187.99 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
% 187.18/187.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_c_2))) )
% 187.18/187.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
% 187.18/187.99 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a)))
% 187.18/187.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_c_2)),V_b_2)) )
% 187.18/187.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a)))
% 187.18/187.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) ) ) ) ) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_le__divide__eq__number__of,axiom,
% 187.18/187.99 ! [V_c_2,V_b_2,V_w_2,T_a] :
% 187.18/187.99 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 187.18/187.99 & class_Int_Onumber(T_a) )
% 187.18/187.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)))
% 187.18/187.99 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
% 187.18/187.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_c_2)),V_b_2)) )
% 187.18/187.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
% 187.18/187.99 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a)))
% 187.18/187.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_c_2))) )
% 187.18/187.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a)))
% 187.18/187.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_le__divide__eq__number__of1,axiom,
% 187.18/187.99 ! [V_w_2,V_b_2,V_a_2,T_a] :
% 187.18/187.99 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 187.18/187.99 & class_Int_Onumber(T_a) )
% 187.18/187.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))))
% 187.18/187.99 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)))
% 187.18/187.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))),V_b_2)) )
% 187.18/187.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)))
% 187.18/187.99 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Groups_Ozero__class_Ozero(T_a)))
% 187.18/187.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)))) )
% 187.18/187.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Groups_Ozero__class_Ozero(T_a)))
% 187.18/187.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_one__mod__nat__number__of,axiom,
% 187.18/187.99 ! [V_v_H] :
% 187.18/187.99 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 187.18/187.99 => 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)) )
% 187.18/187.99 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 187.18/187.99 => 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))) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_one__div__nat__number__of,axiom,
% 187.18/187.99 ! [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))) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_power__number__of__odd__number__of,axiom,
% 187.18/187.99 ! [V_v_2,V_w_2,T_a] :
% 187.18/187.99 ( class_Int_Onumber__ring(T_a)
% 187.18/187.99 => ( ( 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)))
% 187.18/187.99 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),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_a,T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_a,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_a),c_Groups_Otimes__class_Otimes(T_a)),hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v_2)))),c_COMBI(T_a))) )
% 187.18/187.99 & ( ~ 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)))
% 187.18/187.99 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),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_a) ) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_power__nat__number__of__number__of,axiom,
% 187.18/187.99 ! [V_w,V_v] :
% 187.18/187.99 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 187.18/187.99 => 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)) )
% 187.18/187.99 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 187.18/187.99 => 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))) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_minus__numeral__code_I5_J,axiom,
% 187.18/187.99 ! [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)) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_neg__number__of__Bit1,axiom,
% 187.18/187.99 ! [V_w_2] :
% 187.18/187.99 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_w_2))))
% 187.18/187.99 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_times__numeral__code_I5_J,axiom,
% 187.18/187.99 ! [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)) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_number__of__is__id,axiom,
% 187.18/187.99 ! [V_k] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k) = V_k ).
% 187.18/187.99
% 187.18/187.99 fof(fact_plus__numeral__code_I9_J,axiom,
% 187.18/187.99 ! [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)) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_less__number__of__int__code,axiom,
% 187.18/187.99 ! [V_l_2,V_k_2] :
% 187.18/187.99 ( 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)))
% 187.18/187.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_less__eq__number__of__int__code,axiom,
% 187.18/187.99 ! [V_l_2,V_k_2] :
% 187.18/187.99 ( 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)))
% 187.18/187.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_rel__simps_I51_J,axiom,
% 187.18/187.99 ! [V_l_2,V_k_2] :
% 187.18/187.99 ( c_Int_OBit1(V_k_2) = c_Int_OBit1(V_l_2)
% 187.18/187.99 <=> V_k_2 = V_l_2 ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_less__int__code_I16_J,axiom,
% 187.18/187.99 ! [V_k2_2,V_k1_2] :
% 187.18/187.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 187.18/187.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_rel__simps_I17_J,axiom,
% 187.18/187.99 ! [V_l_2,V_k_2] :
% 187.18/187.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2)))
% 187.18/187.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_rel__simps_I34_J,axiom,
% 187.18/187.99 ! [V_l_2,V_k_2] :
% 187.18/187.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2)))
% 187.18/187.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_less__eq__int__code_I16_J,axiom,
% 187.18/187.99 ! [V_k2_2,V_k1_2] :
% 187.18/187.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 187.18/187.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_int__number__of__def,axiom,
% 187.18/187.99 ! [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) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_bin__less__0__simps_I4_J,axiom,
% 187.18/187.99 ! [V_w_2] :
% 187.18/187.99 ( 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)))
% 187.18/187.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_Bit1__def,axiom,
% 187.18/187.99 ! [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) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_nat__number__of__def,axiom,
% 187.18/187.99 ! [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)) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_nat__number__of,axiom,
% 187.18/187.99 ! [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) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_nat__number__of__Bit1,axiom,
% 187.18/187.99 ! [V_w_2] :
% 187.18/187.99 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 187.18/187.99 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 187.18/187.99 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 187.18/187.99 => 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)))) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_number__of__Bit1,axiom,
% 187.18/187.99 ! [V_w,T_a] :
% 187.18/187.99 ( class_Int_Onumber__ring(T_a)
% 187.18/187.99 => 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)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_power__number__of__odd,axiom,
% 187.18/187.99 ! [V_z_2,V_w_2,T_a] :
% 187.18/187.99 ( class_Int_Onumber__ring(T_a)
% 187.18/187.99 => ( ( 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)))
% 187.18/187.99 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),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_a,T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_a,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_a),c_Groups_Otimes__class_Otimes(T_a)),hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z_2))),c_COMBI(T_a))) )
% 187.18/187.99 & ( ~ 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)))
% 187.18/187.99 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),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_a) ) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_zpower__number__of__odd,axiom,
% 187.18/187.99 ! [V_z_2,V_w_2] :
% 187.18/187.99 ( ( 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)))
% 187.18/187.99 => 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))) )
% 187.18/187.99 & ( ~ 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)))
% 187.18/187.99 => 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) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_minus__numeral__code_I6_J,axiom,
% 187.18/187.99 ! [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))) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_neg__imp__number__of__eq__0,axiom,
% 187.18/187.99 ! [V_v] :
% 187.18/187.99 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 187.18/187.99 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_int__eq__iff__number__of,axiom,
% 187.18/187.99 ! [V_v_2,V_m_2] :
% 187.18/187.99 ( 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)
% 187.18/187.99 <=> ( V_m_2 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))
% 187.18/187.99 & 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))) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_eq__nat__number__of,axiom,
% 187.18/187.99 ! [V_v_H_2,V_v_2] :
% 187.18/187.99 ( 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)
% 187.18/187.99 <=> ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)))
% 187.18/187.99 => 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))) )
% 187.18/187.99 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)))
% 187.18/187.99 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2)))
% 187.18/187.99 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 187.18/187.99 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2)))
% 187.18/187.99 => V_v_2 = V_v_H_2 ) ) ) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_nat__number__of__add__left,axiom,
% 187.18/187.99 ! [V_k,V_v_H,V_v] :
% 187.18/187.99 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 187.18/187.99 => 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) )
% 187.18/187.99 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 187.18/187.99 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 187.18/187.99 => 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) )
% 187.18/187.99 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 187.18/187.99 => 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) ) ) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_int__nat__number__of,axiom,
% 187.18/187.99 ! [V_v] :
% 187.18/187.99 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 187.18/187.99 => 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) )
% 187.18/187.99 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 187.18/187.99 => 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) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_mod__nat__number__of,axiom,
% 187.18/187.99 ! [V_v_H,V_v] :
% 187.18/187.99 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 187.18/187.99 => 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) )
% 187.18/187.99 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 187.18/187.99 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 187.18/187.99 => 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) )
% 187.18/187.99 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 187.18/187.99 => 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))) ) ) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_div__nat__number__of,axiom,
% 187.18/187.99 ! [V_v_H,V_v] :
% 187.18/187.99 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 187.18/187.99 => 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) )
% 187.18/187.99 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 187.18/187.99 => 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))) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_power__nat__number__of,axiom,
% 187.18/187.99 ! [V_n,V_v] :
% 187.18/187.99 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 187.18/187.99 => 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) )
% 187.18/187.99 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 187.18/187.99 => 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)) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_Suc__nat__number__of__add,axiom,
% 187.18/187.99 ! [V_n,V_v] :
% 187.18/187.99 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 187.18/187.99 => 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) )
% 187.18/187.99 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 187.18/187.99 => 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) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_diff__nat__number__of,axiom,
% 187.18/187.99 ! [V_v_2,V_v_H_2] :
% 187.18/187.99 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls))
% 187.18/187.99 => 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) )
% 187.18/187.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls))
% 187.18/187.99 => 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)) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_min__number__of__Suc,axiom,
% 187.18/187.99 ! [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)))) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_min__Suc__number__of,axiom,
% 187.18/187.99 ! [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)))) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_rel__simps_I46_J,axiom,
% 187.18/187.99 ! [V_k] : c_Int_OBit1(V_k) != c_Int_OPls ).
% 187.18/187.99
% 187.18/187.99 fof(fact_rel__simps_I39_J,axiom,
% 187.18/187.99 ! [V_l] : c_Int_OPls != c_Int_OBit1(V_l) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_succ__Pls,axiom,
% 187.18/187.99 c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_minus__Pls,axiom,
% 187.18/187.99 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) = c_Int_OPls ).
% 187.18/187.99
% 187.18/187.99 fof(fact_rel__simps_I19_J,axiom,
% 187.18/187.99 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_rel__simps_I2_J,axiom,
% 187.18/187.99 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_succ__pred,axiom,
% 187.18/187.99 ! [V_x] : c_Int_Osucc(c_Int_Opred(V_x)) = V_x ).
% 187.18/187.99
% 187.18/187.99 fof(fact_Pls__def,axiom,
% 187.18/187.99 c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_mult__Pls,axiom,
% 187.18/187.99 ! [V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),V_w) = c_Int_OPls ).
% 187.18/187.99
% 187.18/187.99 fof(fact_add__Pls__right,axiom,
% 187.18/187.99 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ).
% 187.18/187.99
% 187.18/187.99 fof(fact_add__Pls,axiom,
% 187.18/187.99 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),V_k) = V_k ).
% 187.18/187.99
% 187.18/187.99 fof(fact_diff__bin__simps_I1_J,axiom,
% 187.18/187.99 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ).
% 187.18/187.99
% 187.18/187.99 fof(fact_semiring__norm_I112_J,axiom,
% 187.18/187.99 ! [T_a] :
% 187.18/187.99 ( class_Int_Onumber__ring(T_a)
% 187.18/187.99 => c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_number__of__Pls,axiom,
% 187.18/187.99 ! [T_a] :
% 187.18/187.99 ( class_Int_Onumber__ring(T_a)
% 187.18/187.99 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_add__numeral__0,axiom,
% 187.18/187.99 ! [V_a,T_a] :
% 187.18/187.99 ( class_Int_Onumber__ring(T_a)
% 187.18/187.99 => 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 ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_add__numeral__0__right,axiom,
% 187.18/187.99 ! [V_a,T_a] :
% 187.18/187.99 ( class_Int_Onumber__ring(T_a)
% 187.18/187.99 => 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 ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_bin__less__0__simps_I1_J,axiom,
% 187.18/187.99 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_semiring__norm_I113_J,axiom,
% 187.18/187.99 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_nat__number__of__Pls,axiom,
% 187.18/187.99 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_zero__is__num__zero,axiom,
% 187.18/187.99 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_rel__simps_I22_J,axiom,
% 187.18/187.99 ! [V_k_2] :
% 187.18/187.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2)))
% 187.18/187.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_rel__simps_I12_J,axiom,
% 187.18/187.99 ! [V_k_2] :
% 187.18/187.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls))
% 187.18/187.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_Suc__diff__number__of,axiom,
% 187.18/187.99 ! [V_m,V_v] :
% 187.18/187.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v))
% 187.18/187.99 => 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))) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_not__neg__number__of__Pls,axiom,
% 187.18/187.99 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_nat__1__add__number__of,axiom,
% 187.18/187.99 ! [V_v] :
% 187.18/187.99 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 187.18/187.99 => 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) )
% 187.18/187.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 187.18/187.99 => 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)) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_nat__number__of__add__1,axiom,
% 187.18/187.99 ! [V_v] :
% 187.18/187.99 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 187.18/187.99 => 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) )
% 187.18/187.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 187.18/187.99 => 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)) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_le__iff__pred__less,axiom,
% 187.18/187.99 ! [V_l_2,V_k_2] :
% 187.18/187.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2))
% 187.18/187.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(V_k_2)),V_l_2)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_minus__Bit1,axiom,
% 187.18/187.99 ! [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))) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_pred__def,axiom,
% 187.18/187.99 ! [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)) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_nat__number__of__diff__1,axiom,
% 187.18/187.99 ! [V_v] :
% 187.18/187.99 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls))
% 187.18/187.99 => 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) )
% 187.18/187.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls))
% 187.18/187.99 => 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)) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_mult__numeral__1__right,axiom,
% 187.18/187.99 ! [V_a,T_a] :
% 187.18/187.99 ( class_Int_Onumber__ring(T_a)
% 187.18/187.99 => 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 ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_mult__numeral__1,axiom,
% 187.18/187.99 ! [V_a,T_a] :
% 187.18/187.99 ( class_Int_Onumber__ring(T_a)
% 187.18/187.99 => 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 ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_divide__Numeral0,axiom,
% 187.18/187.99 ! [V_x,T_a] :
% 187.18/187.99 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 187.18/187.99 & class_Int_Onumber__ring(T_a) )
% 187.18/187.99 => 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) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_semiring__norm_I110_J,axiom,
% 187.18/187.99 ! [T_a] :
% 187.18/187.99 ( class_Int_Onumber__ring(T_a)
% 187.18/187.99 => c_Groups_Oone__class_Oone(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_numeral__1__eq__1,axiom,
% 187.18/187.99 ! [T_a] :
% 187.18/187.99 ( class_Int_Onumber__ring(T_a)
% 187.18/187.99 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_eq__number__of__0,axiom,
% 187.18/187.99 ! [V_v_2] :
% 187.18/187.99 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.18/187.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_eq__0__number__of,axiom,
% 187.18/187.99 ! [V_v_2] :
% 187.18/187.99 ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)
% 187.18/187.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_number__of2,axiom,
% 187.18/187.99 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))) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_rel__simps_I29_J,axiom,
% 187.18/187.99 ! [V_k_2] :
% 187.18/187.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls))
% 187.18/187.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_rel__simps_I5_J,axiom,
% 187.18/187.99 ! [V_k_2] :
% 187.18/187.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2)))
% 187.18/187.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_less__nat__number__of,axiom,
% 187.18/187.99 ! [V_v_H_2,V_v_2] :
% 187.18/187.99 ( 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)))
% 187.18/187.99 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2))
% 187.18/187.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_H_2)) )
% 187.18/187.99 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2)) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_divide__numeral__1,axiom,
% 187.18/187.99 ! [V_a,T_a] :
% 187.18/187.99 ( ( class_Fields_Ofield(T_a)
% 187.18/187.99 & class_Int_Onumber__ring(T_a) )
% 187.18/187.99 => 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 ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_divide__Numeral1,axiom,
% 187.18/187.99 ! [V_x,T_a] :
% 187.18/187.99 ( ( class_Fields_Ofield(T_a)
% 187.18/187.99 & class_Int_Onumber__ring(T_a) )
% 187.18/187.99 => 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 ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_le__nat__number__of,axiom,
% 187.18/187.99 ! [V_v_H_2,V_v_2] :
% 187.18/187.99 ( 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)))
% 187.18/187.99 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),V_v_H_2))
% 187.18/187.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_one__is__num__one,axiom,
% 187.18/187.99 c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_Numeral1__eq1__nat,axiom,
% 187.18/187.99 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_nat__numeral__1__eq__1,axiom,
% 187.18/187.99 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I8_J,axiom,
% 187.18/187.99 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_succ__def,axiom,
% 187.18/187.99 ! [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)) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_le__special_I3_J,axiom,
% 187.18/187.99 ! [V_x_2,T_a] :
% 187.18/187.99 ( ( class_Int_Onumber__ring(T_a)
% 187.18/187.99 & class_Rings_Olinordered__idom(T_a) )
% 187.18/187.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2)),c_Groups_Ozero__class_Ozero(T_a)))
% 187.18/187.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_le__special_I1_J,axiom,
% 187.18/187.99 ! [V_y_2,T_a] :
% 187.18/187.99 ( ( class_Int_Onumber__ring(T_a)
% 187.18/187.99 & class_Rings_Olinordered__idom(T_a) )
% 187.18/187.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2)))
% 187.18/187.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_less__special_I3_J,axiom,
% 187.18/187.99 ! [V_x_2,T_a] :
% 187.18/187.99 ( ( class_Int_Onumber__ring(T_a)
% 187.18/187.99 & class_Rings_Olinordered__idom(T_a) )
% 187.18/187.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2)),c_Groups_Ozero__class_Ozero(T_a)))
% 187.18/187.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_less__special_I1_J,axiom,
% 187.18/187.99 ! [V_y_2,T_a] :
% 187.18/187.99 ( ( class_Int_Onumber__ring(T_a)
% 187.18/187.99 & class_Rings_Olinordered__idom(T_a) )
% 187.18/187.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2)))
% 187.18/187.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_less__0__number__of,axiom,
% 187.18/187.99 ! [V_v_2] :
% 187.18/187.99 ( 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)))
% 187.18/187.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_2)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_numeral__3__eq__3,axiom,
% 187.18/187.99 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)))) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_numeral__1__eq__Suc__0,axiom,
% 187.18/187.99 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)) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_power3__eq__cube,axiom,
% 187.18/187.99 ! [V_a,T_a] :
% 187.18/187.99 ( class_Groups_Omonoid__mult(T_a)
% 187.18/187.99 => 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) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J,axiom,
% 187.18/187.99 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))))) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_Suc3__eq__add__3,axiom,
% 187.18/187.99 ! [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) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_add__nat__number__of,axiom,
% 187.18/187.99 ! [V_v_H,V_v] :
% 187.18/187.99 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 187.18/187.99 => 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) )
% 187.18/187.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 187.18/187.99 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls))
% 187.18/187.99 => 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) )
% 187.18/187.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls))
% 187.18/187.99 => 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)) ) ) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_transfer__int__nat__numerals_I4_J,axiom,
% 187.18/187.99 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)))) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_transfer__nat__int__numerals_I4_J,axiom,
% 187.18/187.99 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)))) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_number__of__succ,axiom,
% 187.18/187.99 ! [V_k,T_a] :
% 187.18/187.99 ( class_Int_Onumber__ring(T_a)
% 187.18/187.99 => 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)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_number__of__pred,axiom,
% 187.18/187.99 ! [V_w,T_a] :
% 187.18/187.99 ( class_Int_Onumber__ring(T_a)
% 187.18/187.99 => 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)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_le__special_I4_J,axiom,
% 187.18/187.99 ! [V_x_2,T_a] :
% 187.18/187.99 ( ( class_Int_Onumber__ring(T_a)
% 187.18/187.99 & class_Rings_Olinordered__idom(T_a) )
% 187.18/187.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2)),c_Groups_Oone__class_Oone(T_a)))
% 187.18/187.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_le__special_I2_J,axiom,
% 187.18/187.99 ! [V_y_2,T_a] :
% 187.18/187.99 ( ( class_Int_Onumber__ring(T_a)
% 187.18/187.99 & class_Rings_Olinordered__idom(T_a) )
% 187.18/187.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2)))
% 187.18/187.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_less__special_I4_J,axiom,
% 187.18/187.99 ! [V_x_2,T_a] :
% 187.18/187.99 ( ( class_Int_Onumber__ring(T_a)
% 187.18/187.99 & class_Rings_Olinordered__idom(T_a) )
% 187.18/187.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2)),c_Groups_Oone__class_Oone(T_a)))
% 187.18/187.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_less__special_I2_J,axiom,
% 187.18/187.99 ! [V_y_2,T_a] :
% 187.18/187.99 ( ( class_Int_Onumber__ring(T_a)
% 187.18/187.99 & class_Rings_Olinordered__idom(T_a) )
% 187.18/187.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2)))
% 187.18/187.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_add__special_I2_J,axiom,
% 187.18/187.99 ! [V_w,T_a] :
% 187.18/187.99 ( class_Int_Onumber__ring(T_a)
% 187.18/187.99 => 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)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_add__special_I3_J,axiom,
% 187.18/187.99 ! [V_v,T_a] :
% 187.18/187.99 ( class_Int_Onumber__ring(T_a)
% 187.18/187.99 => 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))) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_Suc__diff__eq__diff__pred,axiom,
% 187.18/187.99 ! [V_m,V_n] :
% 187.18/187.99 ( 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))
% 187.18/187.99 => 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)))) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_nat__number__of__mult__left,axiom,
% 187.18/187.99 ! [V_k,V_v_H,V_v] :
% 187.18/187.99 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 187.18/187.99 => 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) )
% 187.18/187.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 187.18/187.99 => 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) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_mult__nat__number__of,axiom,
% 187.18/187.99 ! [V_v_H,V_v] :
% 187.18/187.99 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 187.18/187.99 => 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) )
% 187.18/187.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 187.18/187.99 => 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)) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_neg__number__of__pred__iff__0,axiom,
% 187.18/187.99 ! [V_v_2] :
% 187.18/187.99 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))))
% 187.18/187.99 <=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_Suc__mod__eq__add3__mod__number__of,axiom,
% 187.18/187.99 ! [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)) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_Suc__mod__eq__add3__mod,axiom,
% 187.18/187.99 ! [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) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_mod__Suc__eq__mod__add3,axiom,
% 187.18/187.99 ! [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)) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_Suc__div__eq__add3__div__number__of,axiom,
% 187.18/187.99 ! [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)) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_Suc__div__eq__add3__div,axiom,
% 187.18/187.99 ! [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) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_div__Suc__eq__div__add3,axiom,
% 187.18/187.99 ! [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)) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_diff__special_I2_J,axiom,
% 187.18/187.99 ! [V_v,T_a] :
% 187.18/187.99 ( class_Int_Onumber__ring(T_a)
% 187.18/187.99 => 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)))) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_diff__special_I1_J,axiom,
% 187.18/187.99 ! [V_w,T_a] :
% 187.18/187.99 ( class_Int_Onumber__ring(T_a)
% 187.18/187.99 => 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))) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_Suc__eq__number__of,axiom,
% 187.18/187.99 ! [V_v_2,V_n_2] :
% 187.18/187.99 ( hAPP(c_Nat_OSuc,V_n_2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)
% 187.18/187.99 <=> 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))))) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_eq__number__of__Suc,axiom,
% 187.18/187.99 ! [V_n_2,V_v_2] :
% 187.18/187.99 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = hAPP(c_Nat_OSuc,V_n_2)
% 187.18/187.99 <=> 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))))) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_nat__case__number__of,axiom,
% 187.18/187.99 ! [V_v_2,V_f_2,V_a_2,T_a] : c_Nat_Onat_Onat__case(T_a,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_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_a,T_a),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),tc_Int_Oint),c_If(T_a)),c_Nat__Numeral_Oneg)),V_a_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,tc_Int_Oint),V_f_2),c_Int_Onat))) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_less__Suc__number__of,axiom,
% 187.18/187.99 ! [V_v_2,V_n_2] :
% 187.18/187.99 ( 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)))
% 187.18/187.99 <=> 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))))) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_less__number__of__Suc,axiom,
% 187.18/187.99 ! [V_n_2,V_v_2] :
% 187.18/187.99 ( 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)))
% 187.18/187.99 <=> 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)))) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_le__Suc__number__of,axiom,
% 187.18/187.99 ! [V_v_2,V_n_2] :
% 187.18/187.99 ( 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)))
% 187.18/187.99 <=> 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))))) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_le__number__of__Suc,axiom,
% 187.18/187.99 ! [V_n_2,V_v_2] :
% 187.18/187.99 ( 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)))
% 187.18/187.99 <=> 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)))) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_Suc__nat__number__of,axiom,
% 187.18/187.99 ! [V_v] :
% 187.18/187.99 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 187.18/187.99 => hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
% 187.18/187.99 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 187.18/187.99 => 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)) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_max__Suc__number__of,axiom,
% 187.18/187.99 ! [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)))) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_max__number__of__Suc,axiom,
% 187.18/187.99 ! [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)))) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_nat__case__add__eq__if,axiom,
% 187.18/187.99 ! [V_n_2,V_v_2,V_f_2,V_a_2,T_a] : c_Nat_Onat_Onat__case(T_a,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_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_a,T_a),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),tc_Int_Oint),c_If(T_a)),c_Nat__Numeral_Oneg)),c_Nat_Onat_Onat__case(T_a,V_a_2,V_f_2,V_n_2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,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)))) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_nat__rec__add__eq__if,axiom,
% 187.18/187.99 ! [V_n_2,V_v_2,V_f_2,V_a_2,T_a] : hAPP(c_Nat_Onat_Onat__rec(T_a,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_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_a,T_a),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),tc_Int_Oint),c_If(T_a)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_Onat_Onat__rec(T_a,V_a_2,V_f_2),V_n_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_a,T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_a,T_a),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_a,tc_Int_Oint),c_Nat_Onat_Onat__rec(T_a,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))))) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_eq__special_I2_J,axiom,
% 187.18/187.99 ! [V_y_2,T_a] :
% 187.18/187.99 ( class_Int_Onumber__ring(T_a)
% 187.18/187.99 => ( c_Groups_Oone__class_Oone(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2)
% 187.18/187.99 <=> c_Int_Oiszero(T_a,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_y_2)))) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_eq__special_I4_J,axiom,
% 187.18/187.99 ! [V_x_2,T_a] :
% 187.18/187.99 ( class_Int_Onumber__ring(T_a)
% 187.18/187.99 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2) = c_Groups_Oone__class_Oone(T_a)
% 187.18/187.99 <=> c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),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))))) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_nat__rec__number__of,axiom,
% 187.18/187.99 ! [V_v_2,V_f_2,V_a_2,T_a] : hAPP(c_Nat_Onat_Onat__rec(T_a,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_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_a,T_a),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),tc_Int_Oint),c_If(T_a)),c_Nat__Numeral_Oneg)),V_a_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_a,T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_a,T_a),tc_Int_Oint),V_f_2),c_Int_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,tc_Int_Oint),c_Nat_Onat_Onat__rec(T_a,V_a_2,V_f_2)),c_Int_Onat)))) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_iszero__0,axiom,
% 187.18/187.99 ! [T_a] :
% 187.18/187.99 ( class_Rings_Osemiring__1(T_a)
% 187.18/187.99 => c_Int_Oiszero(T_a,c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_iszero__def,axiom,
% 187.18/187.99 ! [V_z_2,T_a] :
% 187.18/187.99 ( class_Rings_Osemiring__1(T_a)
% 187.18/187.99 => ( c_Int_Oiszero(T_a,V_z_2)
% 187.18/187.99 <=> V_z_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_not__iszero__1,axiom,
% 187.18/187.99 ! [T_a] :
% 187.18/187.99 ( class_Rings_Osemiring__1(T_a)
% 187.18/187.99 => ~ c_Int_Oiszero(T_a,c_Groups_Oone__class_Oone(T_a)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_nat__rec__0,axiom,
% 187.18/187.99 ! [V_f2_2,V_f1_2,T_a] : hAPP(c_Nat_Onat_Onat__rec(T_a,V_f1_2,V_f2_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_f1_2 ).
% 187.18/187.99
% 187.18/187.99 fof(fact_nat__rec__Suc,axiom,
% 187.18/187.99 ! [V_nat_2,V_f2_2,V_f1_2,T_a] : hAPP(c_Nat_Onat_Onat__rec(T_a,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_a,V_f1_2,V_f2_2),V_nat_2)) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_iszero__Numeral0,axiom,
% 187.18/187.99 ! [T_a] :
% 187.18/187.99 ( class_Int_Onumber__ring(T_a)
% 187.18/187.99 => c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_iszero__number__of__Bit1,axiom,
% 187.18/187.99 ! [V_w,T_a] :
% 187.18/187.99 ( ( class_Int_Onumber__ring(T_a)
% 187.18/187.99 & class_Int_Oring__char__0(T_a) )
% 187.18/187.99 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(V_w))) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_not__iszero__Numeral1,axiom,
% 187.18/187.99 ! [T_a] :
% 187.18/187.99 ( class_Int_Onumber__ring(T_a)
% 187.18/187.99 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_eq__number__of__eq,axiom,
% 187.18/187.99 ! [V_y_2,V_x_2,T_a] :
% 187.18/187.99 ( class_Int_Onumber__ring(T_a)
% 187.18/187.99 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2)
% 187.18/187.99 <=> c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),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)))) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_eq__special_I3_J,axiom,
% 187.18/187.99 ! [V_x_2,T_a] :
% 187.18/187.99 ( class_Int_Onumber__ring(T_a)
% 187.18/187.99 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2) = c_Groups_Ozero__class_Ozero(T_a)
% 187.18/187.99 <=> c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),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)))) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_eq__special_I1_J,axiom,
% 187.18/187.99 ! [V_y_2,T_a] :
% 187.18/187.99 ( class_Int_Onumber__ring(T_a)
% 187.18/187.99 => ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2)
% 187.18/187.99 <=> c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),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)))) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_neg__zmod__mult__2,axiom,
% 187.18/187.99 ! [V_b,V_a] :
% 187.18/187.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.18/187.99 => 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)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_zmod__number__of__Bit1,axiom,
% 187.18/187.99 ! [V_v,V_w] :
% 187.18/187.99 ( ( 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)))
% 187.18/187.99 => 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)) )
% 187.18/187.99 & ( ~ 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)))
% 187.18/187.99 => 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)) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_arith__series__int,axiom,
% 187.18/187.99 ! [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)))) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_pos__zdiv__mult__2,axiom,
% 187.18/187.99 ! [V_b,V_a] :
% 187.18/187.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 187.18/187.99 => 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) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_rel__simps_I50_J,axiom,
% 187.18/187.99 ! [V_l,V_k] : c_Int_OBit1(V_k) != c_Int_OBit0(V_l) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_rel__simps_I49_J,axiom,
% 187.18/187.99 ! [V_l,V_k] : c_Int_OBit0(V_k) != c_Int_OBit1(V_l) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_minus__Bit0,axiom,
% 187.18/187.99 ! [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)) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_add__Bit0__Bit0,axiom,
% 187.18/187.99 ! [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)) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_Bit0__def,axiom,
% 187.18/187.99 ! [V_k] : c_Int_OBit0(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_k) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_rel__simps_I48_J,axiom,
% 187.18/187.99 ! [V_l_2,V_k_2] :
% 187.18/187.99 ( c_Int_OBit0(V_k_2) = c_Int_OBit0(V_l_2)
% 187.18/187.99 <=> V_k_2 = V_l_2 ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_rel__simps_I14_J,axiom,
% 187.18/187.99 ! [V_l_2,V_k_2] :
% 187.18/187.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2)))
% 187.18/187.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_less__int__code_I13_J,axiom,
% 187.18/187.99 ! [V_k2_2,V_k1_2] :
% 187.18/187.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 187.18/187.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_less__eq__int__code_I13_J,axiom,
% 187.18/187.99 ! [V_k2_2,V_k1_2] :
% 187.18/187.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 187.18/187.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_rel__simps_I31_J,axiom,
% 187.18/187.99 ! [V_l_2,V_k_2] :
% 187.18/187.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2)))
% 187.18/187.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_mult__Bit0,axiom,
% 187.18/187.99 ! [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)) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_diff__bin__simps_I7_J,axiom,
% 187.18/187.99 ! [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)) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_rel__simps_I44_J,axiom,
% 187.18/187.99 ! [V_k_2] :
% 187.18/187.99 ( c_Int_OBit0(V_k_2) = c_Int_OPls
% 187.18/187.99 <=> V_k_2 = c_Int_OPls ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_rel__simps_I38_J,axiom,
% 187.18/187.99 ! [V_l_2] :
% 187.18/187.99 ( c_Int_OPls = c_Int_OBit0(V_l_2)
% 187.18/187.99 <=> c_Int_OPls = V_l_2 ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_Bit0__Pls,axiom,
% 187.18/187.99 c_Int_OBit0(c_Int_OPls) = c_Int_OPls ).
% 187.18/187.99
% 187.18/187.99 fof(fact_bin__less__0__simps_I3_J,axiom,
% 187.18/187.99 ! [V_w_2] :
% 187.18/187.99 ( 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)))
% 187.18/187.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_rel__simps_I27_J,axiom,
% 187.18/187.99 ! [V_k_2] :
% 187.18/187.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls))
% 187.18/187.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_rel__simps_I21_J,axiom,
% 187.18/187.99 ! [V_k_2] :
% 187.18/187.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2)))
% 187.18/187.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_less__eq__int__code_I14_J,axiom,
% 187.18/187.99 ! [V_k2_2,V_k1_2] :
% 187.18/187.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 187.18/187.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_rel__simps_I32_J,axiom,
% 187.18/187.99 ! [V_l_2,V_k_2] :
% 187.18/187.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2)))
% 187.18/187.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_rel__simps_I10_J,axiom,
% 187.18/187.99 ! [V_k_2] :
% 187.18/187.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls))
% 187.18/187.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_rel__simps_I4_J,axiom,
% 187.18/187.99 ! [V_k_2] :
% 187.18/187.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2)))
% 187.18/187.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_less__int__code_I15_J,axiom,
% 187.18/187.99 ! [V_k2_2,V_k1_2] :
% 187.18/187.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 187.18/187.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_rel__simps_I16_J,axiom,
% 187.18/187.99 ! [V_l_2,V_k_2] :
% 187.18/187.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2)))
% 187.18/187.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_add__Bit1__Bit0,axiom,
% 187.18/187.99 ! [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)) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_add__Bit0__Bit1,axiom,
% 187.18/187.99 ! [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)) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_diff__bin__simps_I3_J,axiom,
% 187.18/187.99 ! [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)) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_diff__bin__simps_I10_J,axiom,
% 187.18/187.99 ! [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)) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_diff__bin__simps_I9_J,axiom,
% 187.18/187.99 ! [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)) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_zdiv__number__of__Bit0,axiom,
% 187.18/187.99 ! [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)) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_neg__number__of__Bit0,axiom,
% 187.18/187.99 ! [V_w_2] :
% 187.18/187.99 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w_2))))
% 187.18/187.99 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_pred__Bit0,axiom,
% 187.18/187.99 ! [V_k] : c_Int_Opred(c_Int_OBit0(V_k)) = c_Int_OBit1(c_Int_Opred(V_k)) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_pred__Bit1,axiom,
% 187.18/187.99 ! [V_k] : c_Int_Opred(c_Int_OBit1(V_k)) = c_Int_OBit0(V_k) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_iszero__number__of__Bit0,axiom,
% 187.18/187.99 ! [V_w_2,T_a] :
% 187.18/187.99 ( ( class_Int_Onumber__ring(T_a)
% 187.18/187.99 & class_Int_Oring__char__0(T_a) )
% 187.18/187.99 => ( c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(V_w_2)))
% 187.18/187.99 <=> c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_succ__Bit1,axiom,
% 187.18/187.99 ! [V_k] : c_Int_Osucc(c_Int_OBit1(V_k)) = c_Int_OBit0(c_Int_Osucc(V_k)) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_succ__Bit0,axiom,
% 187.18/187.99 ! [V_k] : c_Int_Osucc(c_Int_OBit0(V_k)) = c_Int_OBit1(V_k) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_nat__number__of__Bit0,axiom,
% 187.18/187.99 ! [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))) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_number__of__Bit0,axiom,
% 187.18/187.99 ! [V_w,T_a] :
% 187.18/187.99 ( class_Int_Onumber__ring(T_a)
% 187.18/187.99 => 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)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_rel__simps_I15_J,axiom,
% 187.18/187.99 ! [V_l_2,V_k_2] :
% 187.18/187.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2)))
% 187.18/187.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_less__int__code_I14_J,axiom,
% 187.18/187.99 ! [V_k2_2,V_k1_2] :
% 187.18/187.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 187.18/187.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_rel__simps_I33_J,axiom,
% 187.18/187.99 ! [V_l_2,V_k_2] :
% 187.18/187.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2)))
% 187.18/187.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_less__eq__int__code_I15_J,axiom,
% 187.18/187.99 ! [V_k2_2,V_k1_2] :
% 187.18/187.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 187.18/187.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_card__UNIV__bool,axiom,
% 187.18/187.99 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))) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_mult__Bit1,axiom,
% 187.18/187.99 ! [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) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_diff__bin__simps_I8_J,axiom,
% 187.18/187.99 ! [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)) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_add__Bit1__Bit1,axiom,
% 187.18/187.99 ! [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))) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_power__number__of__even,axiom,
% 187.18/187.99 ! [V_w_2,V_z_2,T_a] :
% 187.18/187.99 ( class_Int_Onumber__ring(T_a)
% 187.18/187.99 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),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_a,T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_a,T_a,T_a),c_Groups_Otimes__class_Otimes(T_a)),c_COMBI(T_a))) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_zpower__number__of__even,axiom,
% 187.18/187.99 ! [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))) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_double__number__of__Bit0,axiom,
% 187.18/187.99 ! [V_w,T_a] :
% 187.18/187.99 ( class_Int_Onumber__ring(T_a)
% 187.18/187.99 => 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)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_number__of1,axiom,
% 187.18/187.99 ! [V_n] :
% 187.18/187.99 ( 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)))
% 187.18/187.99 => ( 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))))
% 187.18/187.99 & 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)))) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I7_J,axiom,
% 187.18/187.99 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_power__number__of__even__number__of,axiom,
% 187.18/187.99 ! [V_w_2,V_v_2,T_a] :
% 187.18/187.99 ( class_Int_Onumber__ring(T_a)
% 187.18/187.99 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),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_a,T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_a,T_a,T_a),c_Groups_Otimes__class_Otimes(T_a)),c_COMBI(T_a))) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_mult__2,axiom,
% 187.18/187.99 ! [V_z,T_a] :
% 187.18/187.99 ( class_Int_Onumber__ring(T_a)
% 187.18/187.99 => 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) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_mult__2__right,axiom,
% 187.18/187.99 ! [V_z,T_a] :
% 187.18/187.99 ( class_Int_Onumber__ring(T_a)
% 187.18/187.99 => 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) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_one__add__one__is__two,axiom,
% 187.18/187.99 ! [T_a] :
% 187.18/187.99 ( class_Int_Onumber__ring(T_a)
% 187.18/187.99 => 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))) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_zero__eq__power2,axiom,
% 187.18/187.99 ! [V_a_2,T_a] :
% 187.18/187.99 ( class_Rings_Oring__1__no__zero__divisors(T_a)
% 187.18/187.99 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),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_a)
% 187.18/187.99 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_zero__power2,axiom,
% 187.18/187.99 ! [T_a] :
% 187.18/187.99 ( class_Rings_Osemiring__1(T_a)
% 187.18/187.99 => 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) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_semiring__norm_I115_J,axiom,
% 187.18/187.99 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))) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_numeral__2__eq__2,axiom,
% 187.18/187.99 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))) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom,
% 187.18/187.99 ! [V_x,T_a] :
% 187.18/187.99 ( class_Rings_Ocomm__semiring__1(T_a)
% 187.18/187.99 => 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)))) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_power2__eq__square,axiom,
% 187.18/187.99 ! [V_a,T_a] :
% 187.18/187.99 ( class_Groups_Omonoid__mult(T_a)
% 187.18/187.99 => 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) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J,axiom,
% 187.18/187.99 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))))) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_add__2__eq__Suc,axiom,
% 187.18/187.99 ! [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)) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_add__2__eq__Suc_H,axiom,
% 187.18/187.99 ! [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)) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_one__power2,axiom,
% 187.18/187.99 ! [T_a] :
% 187.18/187.99 ( class_Rings_Osemiring__1(T_a)
% 187.18/187.99 => 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) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_power2__minus,axiom,
% 187.18/187.99 ! [V_a,T_a] :
% 187.18/187.99 ( class_Rings_Oring__1(T_a)
% 187.18/187.99 => 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)))) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_nat__mult__2,axiom,
% 187.18/187.99 ! [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) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_nat__mult__2__right,axiom,
% 187.18/187.99 ! [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) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_power__even__eq,axiom,
% 187.18/187.99 ! [V_n,V_a,T_a] :
% 187.18/187.99 ( class_Groups_Omonoid__mult(T_a)
% 187.18/187.99 => 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)))) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_transfer__int__nat__numerals_I3_J,axiom,
% 187.18/187.99 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)))) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_transfer__nat__int__numerals_I3_J,axiom,
% 187.18/187.99 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)))) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_power2__abs,axiom,
% 187.18/187.99 ! [V_a,T_a] :
% 187.18/187.99 ( class_Rings_Olinordered__idom(T_a)
% 187.18/187.99 => 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)))) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_abs__power2,axiom,
% 187.18/187.99 ! [V_a,T_a] :
% 187.18/187.99 ( class_Rings_Olinordered__idom(T_a)
% 187.18/187.99 => 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)))) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_nat__1__add__1,axiom,
% 187.18/187.99 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))) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_mod2__Suc__Suc,axiom,
% 187.18/187.99 ! [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)))) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_div2__Suc__Suc,axiom,
% 187.18/187.99 ! [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))))) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_zmod__number__of__Bit0,axiom,
% 187.18/187.99 ! [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))) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_add__self__div__2,axiom,
% 187.18/187.99 ! [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 ).
% 187.18/187.99
% 187.18/187.99 fof(fact_half__gt__zero,axiom,
% 187.18/187.99 ! [V_r,T_a] :
% 187.18/187.99 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 187.18/187.99 & class_Int_Onumber__ring(T_a) )
% 187.18/187.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_r))
% 187.18/187.99 => 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)))))) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_half__gt__zero__iff,axiom,
% 187.18/187.99 ! [V_r_2,T_a] :
% 187.18/187.99 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 187.18/187.99 & class_Int_Onumber__ring(T_a) )
% 187.18/187.99 => ( 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_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
% 187.18/187.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_r_2)) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_zero__le__power2,axiom,
% 187.18/187.99 ! [V_a,T_a] :
% 187.18/187.99 ( class_Rings_Olinordered__idom(T_a)
% 187.18/187.99 => 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)))))) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_power2__le__imp__le,axiom,
% 187.18/187.99 ! [V_y,V_x,T_a] :
% 187.18/187.99 ( class_Rings_Olinordered__semidom(T_a)
% 187.18/187.99 => ( 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))))))
% 187.18/187.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 187.18/187.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_power2__eq__imp__eq,axiom,
% 187.18/187.99 ! [V_y,V_x,T_a] :
% 187.18/187.99 ( class_Rings_Olinordered__semidom(T_a)
% 187.18/187.99 => ( 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))))
% 187.18/187.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 187.18/187.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 187.18/187.99 => V_x = V_y ) ) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_zero__less__power2,axiom,
% 187.18/187.99 ! [V_a_2,T_a] :
% 187.18/187.99 ( class_Rings_Olinordered__idom(T_a)
% 187.18/187.99 => ( 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_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
% 187.18/187.99 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_power2__less__0,axiom,
% 187.18/187.99 ! [V_a,T_a] :
% 187.18/187.99 ( class_Rings_Olinordered__idom(T_a)
% 187.18/187.99 => ~ 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))) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_sum__power2__eq__zero__iff,axiom,
% 187.18/187.99 ! [V_y_2,V_x_2,T_a] :
% 187.18/187.99 ( class_Rings_Olinordered__idom(T_a)
% 187.18/187.99 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),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_a),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_a)
% 187.18/187.99 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 187.18/187.99 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_power2__eq__square__number__of,axiom,
% 187.18/187.99 ! [V_w,T_b] :
% 187.18/187.99 ( ( class_Groups_Omonoid__mult(T_b)
% 187.18/187.99 & class_Int_Onumber(T_b) )
% 187.18/187.99 => 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)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_less__2__cases,axiom,
% 187.18/187.99 ! [V_n] :
% 187.18/187.99 ( 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)))))
% 187.18/187.99 => ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.18/187.99 | V_n = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_nat__2,axiom,
% 187.18/187.99 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))) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_power2__eq__1__iff,axiom,
% 187.18/187.99 ! [V_a_2,T_a] :
% 187.18/187.99 ( class_Rings_Oring__1__no__zero__divisors(T_a)
% 187.18/187.99 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),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_a)
% 187.18/187.99 <=> ( V_a_2 = c_Groups_Oone__class_Oone(T_a)
% 187.18/187.99 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom,
% 187.18/187.99 ! [V_n,V_x,T_a] :
% 187.18/187.99 ( class_Rings_Ocomm__semiring__1(T_a)
% 187.18/187.99 => 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)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_power__minus__even,axiom,
% 187.18/187.99 ! [V_n,V_a,T_a] :
% 187.18/187.99 ( class_Rings_Oring__1(T_a)
% 187.18/187.99 => 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)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_power2__less__imp__less,axiom,
% 187.18/187.99 ! [V_y,V_x,T_a] :
% 187.18/187.99 ( class_Rings_Olinordered__semidom(T_a)
% 187.18/187.99 => ( 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))))))
% 187.18/187.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 187.18/187.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_sum__power2__ge__zero,axiom,
% 187.18/187.99 ! [V_y,V_x,T_a] :
% 187.18/187.99 ( class_Rings_Olinordered__idom(T_a)
% 187.18/187.99 => 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))))))) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_sum__power2__le__zero__iff,axiom,
% 187.18/187.99 ! [V_y_2,V_x_2,T_a] :
% 187.18/187.99 ( class_Rings_Olinordered__idom(T_a)
% 187.18/187.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),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_a),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_a)))
% 187.18/187.99 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 187.18/187.99 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_not__sum__power2__lt__zero,axiom,
% 187.18/187.99 ! [V_y,V_x,T_a] :
% 187.18/187.99 ( class_Rings_Olinordered__idom(T_a)
% 187.18/187.99 => ~ 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))) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_sum__power2__gt__zero__iff,axiom,
% 187.18/187.99 ! [V_y_2,V_x_2,T_a] :
% 187.18/187.99 ( class_Rings_Olinordered__idom(T_a)
% 187.18/187.99 => ( 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),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),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_a),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
% 187.18/187.99 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_a)
% 187.18/187.99 | V_y_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_power2__sum,axiom,
% 187.18/187.99 ! [V_y,V_x,T_a] :
% 187.18/187.99 ( class_Int_Onumber__ring(T_a)
% 187.18/187.99 => 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)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_zero__le__even__power_H,axiom,
% 187.18/187.99 ! [V_n,V_a,T_a] :
% 187.18/187.99 ( class_Rings_Olinordered__idom(T_a)
% 187.18/187.99 => 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)))) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J,axiom,
% 187.18/187.99 ! [V_n,V_x,T_a] :
% 187.18/187.99 ( class_Rings_Ocomm__semiring__1(T_a)
% 187.18/187.99 => 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))) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_power__odd__eq,axiom,
% 187.18/187.99 ! [V_n,V_a,T_a] :
% 187.18/187.99 ( class_Groups_Omonoid__mult(T_a)
% 187.18/187.99 => 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))))) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_power__minus1__even,axiom,
% 187.18/187.99 ! [V_n,T_a] :
% 187.18/187.99 ( class_Rings_Oring__1(T_a)
% 187.18/187.99 => 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) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_zdiv__number__of__Bit1,axiom,
% 187.18/187.99 ! [V_v,V_w] :
% 187.18/187.99 ( ( 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)))
% 187.18/187.99 => 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)) )
% 187.18/187.99 & ( ~ 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)))
% 187.18/187.99 => 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)) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_mod2__gr__0,axiom,
% 187.18/187.99 ! [V_m_2] :
% 187.18/187.99 ( 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))))))
% 187.18/187.99 <=> 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) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_div__2__gt__zero,axiom,
% 187.18/187.99 ! [V_n] :
% 187.18/187.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n))
% 187.18/187.99 => 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)))))) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_power2__diff,axiom,
% 187.18/187.99 ! [V_y,V_x,T_a] :
% 187.18/187.99 ( class_Int_Onumber__ring(T_a)
% 187.18/187.99 => 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)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_odd__0__le__power__imp__0__le,axiom,
% 187.18/187.99 ! [V_n,V_a,T_a] :
% 187.18/187.99 ( class_Rings_Olinordered__idom(T_a)
% 187.18/187.99 => ( 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)))))
% 187.18/187.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_odd__power__less__zero,axiom,
% 187.18/187.99 ! [V_n,V_a,T_a] :
% 187.18/187.99 ( class_Rings_Olinordered__idom(T_a)
% 187.18/187.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 187.18/187.99 => 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))) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_power__minus1__odd,axiom,
% 187.18/187.99 ! [V_n,T_a] :
% 187.18/187.99 ( class_Rings_Oring__1(T_a)
% 187.18/187.99 => 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)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_Suc__n__div__2__gt__zero,axiom,
% 187.18/187.99 ! [V_n] :
% 187.18/187.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 187.18/187.99 => 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)))))) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_of__nat__double,axiom,
% 187.18/187.99 ! [V_x,T_a] :
% 187.18/187.99 ( class_Rings_Osemiring__1(T_a)
% 187.18/187.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 187.18/187.99 => 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))) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_pos__zmod__mult__2,axiom,
% 187.18/187.99 ! [V_b,V_a] :
% 187.18/187.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 187.18/187.99 => 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))) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_neg__zdiv__mult__2,axiom,
% 187.18/187.99 ! [V_b,V_a] :
% 187.18/187.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.18/187.99 => 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) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_int__of__code,axiom,
% 187.18/187.99 ! [V_k] :
% 187.18/187.99 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 187.18/187.99 => hAPP(c_Code__Numeral_Oint__of,V_k) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 187.18/187.99 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 187.18/187.99 => ( ( 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)
% 187.18/187.99 => 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)))))) )
% 187.18/187.99 & ( 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)
% 187.18/187.99 => 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)) ) ) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_of__int__num,axiom,
% 187.18/187.99 ! [V_k_2,T_a] :
% 187.18/187.99 ( class_Rings_Oring__1(T_a)
% 187.18/187.99 => ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.18/187.99 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k_2) = c_Groups_Ozero__class_Ozero(T_a) )
% 187.18/187.99 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.18/187.99 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.18/187.99 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k_2))) )
% 187.18/187.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.18/187.99 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,T_a),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(T_a,T_a)),tc_fun(tc_Int_Oint,T_a)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,T_a),T_a),tc_fun(tc_fun(tc_Int_Oint,tc_fun(T_a,T_a)),tc_fun(tc_Int_Oint,T_a)),tc_Int_Oint),c_COMBB(tc_fun(T_a,T_a),T_a,tc_Int_Oint)),hAPP(hAPP(c_COMBB(T_a,tc_fun(tc_fun(T_a,T_a),T_a),tc_Int_Oint),c_HOL_OLet(T_a,T_a)),c_Int_Oring__1__class_Oof__int(T_a)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(T_a,T_a),tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,T_a)),tc_Int_Oint),c_COMBS(T_a,T_a,T_a)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(T_a,T_a),tc_fun(T_a,tc_fun(T_a,T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_fun(T_a,T_a))),tc_Int_Oint),c_COMBB(T_a,tc_fun(T_a,T_a),T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),tc_Int_Oint),c_If(T_a)),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_a,T_a,T_a),c_Groups_Oplus__class_Oplus(T_a)),c_COMBI(T_a))))),hAPP(hAPP(c_COMBC(T_a,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_a),c_Groups_Oplus__class_Oplus(T_a)),hAPP(hAPP(c_COMBS(T_a,T_a,T_a),c_Groups_Oplus__class_Oplus(T_a)),c_COMBI(T_a)))),c_Groups_Oone__class_Oone(T_a))))),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))))) ) ) ) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_power__m1__odd,axiom,
% 187.18/187.99 ! [V_n,T_a] :
% 187.18/187.99 ( class_Int_Onumber__ring(T_a)
% 187.18/187.99 => 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) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_power__m1__even,axiom,
% 187.18/187.99 ! [V_n,T_a] :
% 187.18/187.99 ( class_Int_Onumber__ring(T_a)
% 187.18/187.99 => 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) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_rel__simps_I42_J,axiom,
% 187.18/187.99 ! [V_l] : c_Int_OMin != c_Int_OBit0(V_l) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_rel__simps_I45_J,axiom,
% 187.18/187.99 ! [V_k] : c_Int_OBit0(V_k) != c_Int_OMin ).
% 187.18/187.99
% 187.18/187.99 fof(fact_rel__simps_I40_J,axiom,
% 187.18/187.99 c_Int_OMin != c_Int_OPls ).
% 187.18/187.99
% 187.18/187.99 fof(fact_rel__simps_I37_J,axiom,
% 187.18/187.99 c_Int_OPls != c_Int_OMin ).
% 187.18/187.99
% 187.18/187.99 fof(fact_rel__simps_I7_J,axiom,
% 187.18/187.99 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_code__numeral__zero__minus__one,axiom,
% 187.18/187.99 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) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_rel__simps_I24_J,axiom,
% 187.18/187.99 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_Bit1__Min,axiom,
% 187.18/187.99 c_Int_OBit1(c_Int_OMin) = c_Int_OMin ).
% 187.18/187.99
% 187.18/187.99 fof(fact_rel__simps_I43_J,axiom,
% 187.18/187.99 ! [V_l_2] :
% 187.18/187.99 ( c_Int_OMin = c_Int_OBit1(V_l_2)
% 187.18/187.99 <=> c_Int_OMin = V_l_2 ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_rel__simps_I47_J,axiom,
% 187.18/187.99 ! [V_k_2] :
% 187.18/187.99 ( c_Int_OBit1(V_k_2) = c_Int_OMin
% 187.18/187.99 <=> V_k_2 = c_Int_OMin ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_bin__less__0__simps_I2_J,axiom,
% 187.18/187.99 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_rel__simps_I23_J,axiom,
% 187.18/187.99 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_rel__simps_I20_J,axiom,
% 187.18/187.99 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_rel__simps_I26_J,axiom,
% 187.18/187.99 ! [V_k_2] :
% 187.18/187.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2)))
% 187.18/187.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_rel__simps_I30_J,axiom,
% 187.18/187.99 ! [V_k_2] :
% 187.18/187.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin))
% 187.18/187.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_rel__simps_I6_J,axiom,
% 187.18/187.99 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_rel__simps_I3_J,axiom,
% 187.18/187.99 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_rel__simps_I9_J,axiom,
% 187.18/187.99 ! [V_k_2] :
% 187.18/187.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2)))
% 187.18/187.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_rel__simps_I13_J,axiom,
% 187.18/187.99 ! [V_k_2] :
% 187.18/187.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin))
% 187.18/187.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_rel__simps_I28_J,axiom,
% 187.18/187.99 ! [V_k_2] :
% 187.18/187.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin))
% 187.18/187.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_rel__simps_I8_J,axiom,
% 187.18/187.99 ! [V_k_2] :
% 187.18/187.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2)))
% 187.18/187.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_eq__number__of__Pls__Min,axiom,
% 187.18/187.99 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) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_Int_OMin__def,axiom,
% 187.18/187.99 c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_mult__Min,axiom,
% 187.18/187.99 ! [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) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_neg__number__of__Min,axiom,
% 187.18/187.99 hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_pred__Pls,axiom,
% 187.18/187.99 c_Int_Opred(c_Int_OPls) = c_Int_OMin ).
% 187.18/187.99
% 187.18/187.99 fof(fact_add__Min,axiom,
% 187.18/187.99 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),V_k) = c_Int_Opred(V_k) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_add__Min__right,axiom,
% 187.18/187.99 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Opred(V_k) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_pred__Min,axiom,
% 187.18/187.99 c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_nonzero__number__of__Min,axiom,
% 187.18/187.99 ! [T_a] :
% 187.18/187.99 ( class_Int_Onumber__ring(T_a)
% 187.18/187.99 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_succ__Min,axiom,
% 187.18/187.99 c_Int_Osucc(c_Int_OMin) = c_Int_OPls ).
% 187.18/187.99
% 187.18/187.99 fof(fact_diff__bin__simps_I2_J,axiom,
% 187.18/187.99 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Osucc(V_k) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_mult__minus1__right,axiom,
% 187.18/187.99 ! [V_z,T_a] :
% 187.18/187.99 ( class_Int_Onumber__ring(T_a)
% 187.18/187.99 => 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) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_mult__minus1,axiom,
% 187.18/187.99 ! [V_z,T_a] :
% 187.18/187.99 ( class_Int_Onumber__ring(T_a)
% 187.18/187.99 => 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) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_arith__simps_I31_J,axiom,
% 187.18/187.99 ! [T_a] :
% 187.18/187.99 ( class_Int_Onumber__ring(T_a)
% 187.18/187.99 => 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) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_number__of__Min,axiom,
% 187.18/187.99 ! [T_a] :
% 187.18/187.99 ( class_Int_Onumber__ring(T_a)
% 187.18/187.99 => 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)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_abs__minus__one,axiom,
% 187.18/187.99 ! [T_a] :
% 187.18/187.99 ( ( class_Int_Onumber__ring(T_a)
% 187.18/187.99 & class_Rings_Olinordered__idom(T_a) )
% 187.18/187.99 => 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) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_divide__minus1,axiom,
% 187.18/187.99 ! [V_x,T_a] :
% 187.18/187.99 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 187.18/187.99 & class_Int_Onumber__ring(T_a) )
% 187.18/187.99 => 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) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_rel__simps_I11_J,axiom,
% 187.18/187.99 ! [V_k_2] :
% 187.18/187.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin))
% 187.18/187.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_rel__simps_I25_J,axiom,
% 187.18/187.99 ! [V_k_2] :
% 187.18/187.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2)))
% 187.18/187.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_zmod__minus1__right,axiom,
% 187.18/187.99 ! [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) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_diff__bin__simps_I4_J,axiom,
% 187.18/187.99 ! [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)) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_minus__Min,axiom,
% 187.18/187.99 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = c_Int_OBit1(c_Int_OPls) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_zmult__eq__1__iff,axiom,
% 187.18/187.99 ! [V_n_2,V_m_2] :
% 187.18/187.99 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 187.18/187.99 <=> ( ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 187.18/187.99 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
% 187.18/187.99 | ( V_m_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
% 187.18/187.99 & V_n_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_pos__zmult__eq__1__iff__lemma,axiom,
% 187.18/187.99 ! [V_n,V_m] :
% 187.18/187.99 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 187.18/187.99 => ( V_m = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 187.18/187.99 | V_m = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_diff__bin__simps_I6_J,axiom,
% 187.18/187.99 ! [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)) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_diff__bin__simps_I5_J,axiom,
% 187.18/187.99 ! [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)) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_of__int__m1,axiom,
% 187.18/187.99 ! [T_a] :
% 187.18/187.99 ( class_Int_Onumber__ring(T_a)
% 187.18/187.99 => 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) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_zdiv__minus1__right,axiom,
% 187.18/187.99 ! [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) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_zero__code__numeral__code,axiom,
% 187.18/187.99 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) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_minus1__divide,axiom,
% 187.18/187.99 ! [V_x,T_a] :
% 187.18/187.99 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 187.18/187.99 & class_Int_Onumber__ring(T_a) )
% 187.18/187.99 => 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)) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_abs__power__minus__one,axiom,
% 187.18/187.99 ! [V_n,T_a] :
% 187.18/187.99 ( ( class_Int_Onumber__ring(T_a)
% 187.18/187.99 & class_Rings_Olinordered__idom(T_a) )
% 187.18/187.99 => 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) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_div__eq__minus1,axiom,
% 187.18/187.99 ! [V_b] :
% 187.18/187.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 187.18/187.99 => 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) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_div__pos__neg__trivial,axiom,
% 187.18/187.99 ! [V_b,V_a] :
% 187.18/187.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 187.18/187.99 => ( 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)))
% 187.18/187.99 => 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) ) ) ).
% 187.18/187.99
% 187.18/187.99 fof(fact_zmod__minus1,axiom,
% 187.18/187.99 ! [V_b] :
% 187.18/187.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 187.18/187.99 => 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)) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_one__code__numeral__code,axiom,
% 187.18/188.00 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)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_Nitpick_OFrac__def,axiom,
% 187.18/188.00 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)))) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_int__ge__less__than__def,axiom,
% 187.18/188.00 ! [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)))) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_int__ge__less__than2__def,axiom,
% 187.18/188.00 ! [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)))) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_code__numeral_Osize_I1_J,axiom,
% 187.18/188.00 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) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_Nitpick_Oprod__def,axiom,
% 187.18/188.00 ! [V_B_2,V_A_2,T_b,T_a] : c_Nitpick_Oprod(T_a,T_b,V_A_2,V_B_2) = hAPP(c_Set_OCollect(tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,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_a),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_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),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)))) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_nat__of__aux__code,axiom,
% 187.18/188.00 ! [V_n,V_i] :
% 187.18/188.00 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 187.18/188.00 => c_Code__Numeral_Onat__of__aux(V_i,V_n) = V_n )
% 187.18/188.00 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 187.18/188.00 => 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)) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_divmod__int__rel__def,axiom,
% 187.18/188.00 ! [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))))))) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_divmod__int__correct,axiom,
% 187.18/188.00 ! [V_a,V_b] :
% 187.18/188.00 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.18/188.00 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_Odivmod__int(V_a,V_b))) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_code__numeral_Osize_I2_J,axiom,
% 187.18/188.00 ! [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))) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_zmult2__lemma,axiom,
% 187.18/188.00 ! [V_c,V_r,V_q,V_b,V_a] :
% 187.18/188.00 ( 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)))
% 187.18/188.00 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 187.18/188.00 => 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)))) ) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_Nats__number__of,axiom,
% 187.18/188.00 ! [V_w_2,T_a] :
% 187.18/188.00 ( class_Int_Onumber__ring(T_a)
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_w_2))
% 187.18/188.00 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Nat_Osemiring__1__class_ONats(T_a))) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_code__numeral_Oinject,axiom,
% 187.18/188.00 ! [V_code__numeral_H_2,V_code__numeral_2] :
% 187.18/188.00 ( c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2) = c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H_2)
% 187.18/188.00 <=> V_code__numeral_2 = V_code__numeral_H_2 ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_sup__Un__eq2,axiom,
% 187.18/188.00 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_b,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_R_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_S_2)),V_x_2),V_y_2))
% 187.18/188.00 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_R_2),V_S_2))) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_inf__Int__eq2,axiom,
% 187.18/188.00 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_b,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_R_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_S_2)),V_x_2),V_y_2))
% 187.18/188.00 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_R_2),V_S_2))) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_pred__equals__eq2,axiom,
% 187.18/188.00 ! [V_S_2,V_R_2,T_b,T_a] :
% 187.18/188.00 ( hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_R_2) = hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_S_2)
% 187.18/188.00 <=> V_R_2 = V_S_2 ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_pred__subset__eq2,axiom,
% 187.18/188.00 ! [V_S_2,V_R_2,T_b,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_R_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_S_2)))
% 187.18/188.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_R_2),V_S_2)) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_bot__empty__eq2,axiom,
% 187.18/188.00 ! [V_y_2,V_x_2,T_b,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_x_2),V_y_2))
% 187.18/188.00 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)))) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_code__numeral_Osimps_I2_J,axiom,
% 187.18/188.00 ! [V_code__numeral_H] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_code__numeral_Osimps_I3_J,axiom,
% 187.18/188.00 ! [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) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_divmod__int__rel__0,axiom,
% 187.18/188.00 ! [V_b] :
% 187.18/188.00 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.18/188.00 => 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)))) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_self__remainder,axiom,
% 187.18/188.00 ! [V_r,V_q,V_a] :
% 187.18/188.00 ( 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)))
% 187.18/188.00 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.18/188.00 => V_r = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_unique__quotient,axiom,
% 187.18/188.00 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] :
% 187.18/188.00 ( 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)))
% 187.18/188.00 => ( 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)))
% 187.18/188.00 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.18/188.00 => V_q = V_q_H ) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_unique__remainder,axiom,
% 187.18/188.00 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] :
% 187.18/188.00 ( 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)))
% 187.18/188.00 => ( 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)))
% 187.18/188.00 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.18/188.00 => V_r = V_r_H ) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_SUP__UN__eq2,axiom,
% 187.18/188.00 ! [V_y_2,V_x_2,V_r_2,T_c,T_b,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),T_a),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))
% 187.18/188.00 <=> 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_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),V_r_2))) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_self__quotient,axiom,
% 187.18/188.00 ! [V_r,V_q,V_a] :
% 187.18/188.00 ( 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)))
% 187.18/188.00 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.18/188.00 => V_q = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_divmod__int__rel__mod,axiom,
% 187.18/188.00 ! [V_r,V_q,V_b,V_a] :
% 187.18/188.00 ( 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)))
% 187.18/188.00 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.18/188.00 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_r ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_divmod__int__rel__div,axiom,
% 187.18/188.00 ! [V_r,V_q,V_b,V_a] :
% 187.18/188.00 ( 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)))
% 187.18/188.00 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.18/188.00 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = V_q ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_Nats__0,axiom,
% 187.18/188.00 ! [T_a] :
% 187.18/188.00 ( class_Rings_Osemiring__1(T_a)
% 187.18/188.00 => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Nat_Osemiring__1__class_ONats(T_a))) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_divmod__int__mod__div,axiom,
% 187.18/188.00 ! [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)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_Nats__add,axiom,
% 187.18/188.00 ! [V_b_2,V_a_2,T_a] :
% 187.18/188.00 ( class_Rings_Osemiring__1(T_a)
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Nat_Osemiring__1__class_ONats(T_a)))
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Nat_Osemiring__1__class_ONats(T_a)))
% 187.18/188.00 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_b_2)),c_Nat_Osemiring__1__class_ONats(T_a))) ) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_Nats__mult,axiom,
% 187.18/188.00 ! [V_b_2,V_a_2,T_a] :
% 187.18/188.00 ( class_Rings_Osemiring__1(T_a)
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Nat_Osemiring__1__class_ONats(T_a)))
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Nat_Osemiring__1__class_ONats(T_a)))
% 187.18/188.00 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2)),c_Nat_Osemiring__1__class_ONats(T_a))) ) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_Nats__1,axiom,
% 187.18/188.00 ! [T_a] :
% 187.18/188.00 ( class_Rings_Osemiring__1(T_a)
% 187.18/188.00 => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Oone__class_Oone(T_a)),c_Nat_Osemiring__1__class_ONats(T_a))) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_of__nat__in__Nats,axiom,
% 187.18/188.00 ! [V_n_2,T_a] :
% 187.18/188.00 ( class_Rings_Osemiring__1(T_a)
% 187.18/188.00 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2)),c_Nat_Osemiring__1__class_ONats(T_a))) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_Suc__code__numeral__minus__one,axiom,
% 187.18/188.00 ! [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 ).
% 187.18/188.00
% 187.18/188.00 fof(fact_divmod__int__rel__div__mod,axiom,
% 187.18/188.00 ! [V_a,V_b] :
% 187.18/188.00 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.18/188.00 => 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)))) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_zadd1__lemma,axiom,
% 187.18/188.00 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] :
% 187.18/188.00 ( 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)))
% 187.18/188.00 => ( 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)))
% 187.18/188.00 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.18/188.00 => 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)))) ) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_zminus1__lemma,axiom,
% 187.18/188.00 ! [V_r_2,V_q_2,V_b_2,V_a_2] :
% 187.18/188.00 ( 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)))
% 187.18/188.00 => 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))))) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_divmod__int__relI,axiom,
% 187.18/188.00 ! [V_r,V_q,V_b,V_a] :
% 187.18/188.00 ( 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)
% 187.18/188.00 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 187.18/188.00 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) ) )
% 187.18/188.00 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 187.18/188.00 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
% 187.18/188.00 => 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))) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_zmult1__lemma,axiom,
% 187.18/188.00 ! [V_a,V_r,V_q,V_c,V_b] :
% 187.18/188.00 ( 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)))
% 187.18/188.00 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.18/188.00 => 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)))) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_pair__imageI,axiom,
% 187.18/188.00 ! [V_f_2,T_c,V_A_2,V_b_2,V_a_2,T_b,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),V_A_2))
% 187.18/188.00 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(hAPP(V_f_2,V_a_2),V_b_2)),hAPP(c_Set_Oimage(tc_prod(T_a,T_b),T_c,hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),V_f_2)),V_A_2))) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_norm__frac_Osimps,axiom,
% 187.18/188.00 ! [V_a_2,V_b_2] :
% 187.18/188.00 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.18/188.00 => 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)) )
% 187.18/188.00 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.18/188.00 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.18/188.00 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 187.18/188.00 => 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)) )
% 187.18/188.00 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.18/188.00 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 187.18/188.00 => 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))) ) ) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_adjust__eq,axiom,
% 187.18/188.00 ! [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))) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_sup2E,axiom,
% 187.18/188.00 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2))
% 187.18/188.00 => ( ~ hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 187.18/188.00 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_sup2CI,axiom,
% 187.18/188.00 ! [T_b,T_a,V_A_2,V_y_2,V_x_2,V_B_2] :
% 187.18/188.00 ( ( ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
% 187.18/188.00 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) )
% 187.18/188.00 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_inf2I,axiom,
% 187.18/188.00 ! [T_b,T_a,V_B_2,V_y_2,V_x_2,V_A_2] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
% 187.18/188.00 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_inf2E,axiom,
% 187.18/188.00 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2))
% 187.18/188.00 => ~ ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 187.18/188.00 => ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_mem__splitI,axiom,
% 187.18/188.00 ! [T_c,T_b,V_b_2,V_a_2,V_c_2,V_z_2,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(hAPP(V_c_2,V_a_2),V_b_2)))
% 187.18/188.00 => hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(T_a,tc_HOL_Obool)),V_c_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)))) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_prod__caseI,axiom,
% 187.18/188.00 ! [T_b,T_a,V_b_2,V_a_2,V_f1_2] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(V_f1_2,V_a_2),V_b_2))
% 187.18/188.00 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_f1_2),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2))) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_splitI,axiom,
% 187.18/188.00 ! [T_b,T_a,V_b_2,V_a_2,V_f_2] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2))
% 187.18/188.00 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2))) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_bot2E,axiom,
% 187.18/188.00 ! [V_y_2,V_x_2,T_b,T_a] : ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_x_2),V_y_2)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_splitD_H,axiom,
% 187.18/188.00 ! [V_c_2,V_b_2,V_a_2,V_R_2,T_c,T_b,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_fun(T_c,tc_HOL_Obool)),V_R_2),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),V_c_2))
% 187.18/188.00 => hBOOL(hAPP(hAPP(hAPP(V_R_2,V_a_2),V_b_2),V_c_2)) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_less__by__empty,axiom,
% 187.18/188.00 ! [V_B_2,T_a,V_A_2] :
% 187.18/188.00 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))
% 187.18/188.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_predicate2D,axiom,
% 187.18/188.00 ! [V_y_2,V_x_2,V_Q_2,V_P_2,T_b,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_P_2),V_Q_2))
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
% 187.18/188.00 => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_rev__predicate2D,axiom,
% 187.18/188.00 ! [V_Q_2,T_b,T_a,V_y_2,V_x_2,V_P_2] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_P_2),V_Q_2))
% 187.18/188.00 => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_inf2D1,axiom,
% 187.18/188.00 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2))
% 187.18/188.00 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_inf2D2,axiom,
% 187.18/188.00 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2))
% 187.18/188.00 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_sup2I1,axiom,
% 187.18/188.00 ! [V_B_2,T_b,T_a,V_y_2,V_x_2,V_A_2] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 187.18/188.00 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_sup2I2,axiom,
% 187.18/188.00 ! [V_A_2,T_b,T_a,V_y_2,V_x_2,V_B_2] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
% 187.18/188.00 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_split__paired__All,axiom,
% 187.18/188.00 ! [T_b,T_a,V_P_2] :
% 187.18/188.00 ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 187.18/188.00 <=> ! [B_a,B_b] : hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_a),B_b))) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_Pair__eq,axiom,
% 187.18/188.00 ! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_b,T_a] :
% 187.18/188.00 ( hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_H_2),V_b_H_2)
% 187.18/188.00 <=> ( V_a_2 = V_a_H_2
% 187.18/188.00 & V_b_2 = V_b_H_2 ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_Pair__inject,axiom,
% 187.18/188.00 ! [V_b_H,V_a_H,V_b,V_a,T_b,T_a] :
% 187.18/188.00 ( 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)
% 187.18/188.00 => ~ ( V_a = V_a_H
% 187.18/188.00 => V_b != V_b_H ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_split__weak__cong,axiom,
% 187.18/188.00 ! [V_c_2,T_c,T_b,T_a,V_q_2,V_p_2] :
% 187.18/188.00 ( V_p_2 = V_q_2
% 187.18/188.00 => hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),V_c_2),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),V_c_2),V_q_2) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_split__twice,axiom,
% 187.18/188.00 ! [V_p_2,V_g_2,T_e,T_d,V_f_2,T_a,T_c,T_b] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),V_f_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,tc_prod(T_b,T_c)),V_g_2),V_p_2)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,T_a),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_prod(T_b,T_c)),tc_fun(T_e,T_a),T_d),hAPP(c_COMBB(tc_prod(T_b,T_c),T_a,T_e),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),V_f_2))),V_g_2)),V_p_2) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_prod_Osimps_I2_J,axiom,
% 187.18/188.00 ! [V_b_2,V_a_2,V_f1_2,T_a,T_c,T_b] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),V_f1_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_split__conv,axiom,
% 187.18/188.00 ! [V_b_2,V_a_2,V_f_2,T_a,T_c,T_b] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)) = hAPP(hAPP(V_f_2,V_a_2),V_b_2) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_splitD,axiom,
% 187.18/188.00 ! [V_b_2,V_a_2,V_f_2,T_b,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)))
% 187.18/188.00 => hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2)) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_split__eta,axiom,
% 187.18/188.00 ! [V_f_2,T_c,T_b,T_a] : hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,T_c),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),T_c,T_b),V_f_2)),c_Product__Type_OPair(T_a,T_b))) = V_f_2 ).
% 187.18/188.00
% 187.18/188.00 fof(fact_The__split__eq,axiom,
% 187.18/188.00 ! [V_y_2,V_x_2,T_b,T_a] : c_HOL_OThe(tc_prod(T_a,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,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_a),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_a),c_fconj),hAPP(c_fequal,V_x_2)))),hAPP(c_fequal,V_y_2)))) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_split__paired__The,axiom,
% 187.18/188.00 ! [V_P_2,T_b,T_a] : c_HOL_OThe(tc_prod(T_a,T_b),V_P_2) = c_HOL_OThe(tc_prod(T_a,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_HOL_Obool,T_b),V_P_2)),c_Product__Type_OPair(T_a,T_b)))) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_adjust__def,axiom,
% 187.18/188.00 ! [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))))))) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_in__rel__def,axiom,
% 187.18/188.00 ! [V_y_2,V_x_2,V_R_2,T_b,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(T_a,T_b,V_R_2),V_x_2),V_y_2))
% 187.18/188.00 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),V_R_2)) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_div__mod__code__numeral__def,axiom,
% 187.18/188.00 ! [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)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_negDivAlg__eqn__1__number__of,axiom,
% 187.18/188.00 ! [V_w] :
% 187.18/188.00 ( 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)))
% 187.18/188.00 => ( ( 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))))
% 187.18/188.00 => 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))) )
% 187.18/188.00 & ( ~ 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))))
% 187.18/188.00 => 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)))) ) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_negDivAlg__correct,axiom,
% 187.18/188.00 ! [V_b,V_a] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 187.18/188.00 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OnegDivAlg(V_a,V_b))) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_negDivAlg__div__mod,axiom,
% 187.18/188.00 ! [V_l,V_k] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 187.18/188.00 => 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)) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_negDivAlg__minus1,axiom,
% 187.18/188.00 ! [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))) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_negDivAlg_Osimps,axiom,
% 187.18/188.00 ! [V_b,V_a] :
% 187.18/188.00 ( ( ( 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)))
% 187.18/188.00 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 187.18/188.00 => 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)) )
% 187.18/188.00 & ( ~ ( 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)))
% 187.18/188.00 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 187.18/188.00 => 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))) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_negDivAlg__eqn__number__of,axiom,
% 187.18/188.00 ! [V_w,V_v] :
% 187.18/188.00 ( 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)))
% 187.18/188.00 => ( ( 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))))
% 187.18/188.00 => 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))) )
% 187.18/188.00 & ( ~ 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))))
% 187.18/188.00 => 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)))) ) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_negDivAlg__eqn,axiom,
% 187.18/188.00 ! [V_a,V_b] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 187.18/188.00 => ( ( 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)))
% 187.18/188.00 => 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)) )
% 187.18/188.00 & ( ~ 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)))
% 187.18/188.00 => 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))) ) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_Nitpick_Orefl_H__def,axiom,
% 187.18/188.00 ! [V_r_2,T_a] :
% 187.18/188.00 ( c_Nitpick_Orefl_H(T_a,V_r_2)
% 187.18/188.00 <=> ! [B_x] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),V_r_2)) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_posDivAlg__eqn__1__number__of,axiom,
% 187.18/188.00 ! [V_w] :
% 187.18/188.00 ( 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)))
% 187.18/188.00 => ( ( 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)))
% 187.18/188.00 => 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)) )
% 187.18/188.00 & ( ~ 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)))
% 187.18/188.00 => 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)))) ) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_posDivAlg_Osimps,axiom,
% 187.18/188.00 ! [V_b,V_a] :
% 187.18/188.00 ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 187.18/188.00 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 187.18/188.00 => 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) )
% 187.18/188.00 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 187.18/188.00 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 187.18/188.00 => 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))) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_posDivAlg__0,axiom,
% 187.18/188.00 ! [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)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_posDivAlg__correct,axiom,
% 187.18/188.00 ! [V_b,V_a] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 187.18/188.00 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OposDivAlg(V_a,V_b))) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_posDivAlg__div__mod,axiom,
% 187.18/188.00 ! [V_l,V_k] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 187.18/188.00 => 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)) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_posDivAlg__eqn__number__of,axiom,
% 187.18/188.00 ! [V_w,V_v] :
% 187.18/188.00 ( 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)))
% 187.18/188.00 => ( ( 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)))
% 187.18/188.00 => 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)) )
% 187.18/188.00 & ( ~ 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)))
% 187.18/188.00 => 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)))) ) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_posDivAlg__eqn,axiom,
% 187.18/188.00 ! [V_a,V_b] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 187.18/188.00 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 187.18/188.00 => 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) )
% 187.18/188.00 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 187.18/188.00 => 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))) ) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_divmod__int__def,axiom,
% 187.18/188.00 ! [V_b,V_a] :
% 187.18/188.00 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 187.18/188.00 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 187.18/188.00 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OposDivAlg(V_a,V_b) )
% 187.18/188.00 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 187.18/188.00 => ( ( V_a = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.18/188.00 => 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)) )
% 187.18/188.00 & ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.18/188.00 => 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))) ) ) ) ) )
% 187.18/188.00 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 187.18/188.00 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 187.18/188.00 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OnegDivAlg(V_a,V_b) )
% 187.18/188.00 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 187.18/188.00 => 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))) ) ) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_divmod__nat__step,axiom,
% 187.18/188.00 ! [V_m,V_n] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 187.18/188.00 => 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)) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_divmod__int__pdivmod,axiom,
% 187.18/188.00 ! [V_l_2,V_k_2] :
% 187.18/188.00 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.18/188.00 => 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)) )
% 187.18/188.00 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.18/188.00 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.18/188.00 => 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) )
% 187.18/188.00 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.18/188.00 => 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)))) ) ) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_negateSnd__def,axiom,
% 187.18/188.00 c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_apsnd__conv,axiom,
% 187.18/188.00 ! [V_y_2,V_x_2,V_f_2,T_a,T_b,T_c] : hAPP(c_Product__Type_Oapsnd(T_c,T_b,T_a,V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_a,T_c),V_x_2),V_y_2)) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),hAPP(V_f_2,V_y_2)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_divmod__nat__zero,axiom,
% 187.18/188.00 ! [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) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_divmod__nat__base,axiom,
% 187.18/188.00 ! [V_n,V_m] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 187.18/188.00 => 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) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_negateSnd__eq,axiom,
% 187.18/188.00 ! [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)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_divmod__nat__div__mod,axiom,
% 187.18/188.00 ! [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)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_divmod__int__rel__neg,axiom,
% 187.18/188.00 ! [V_qr,V_b,V_a] :
% 187.18/188.00 ( 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))
% 187.18/188.00 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(c_Divides_OnegateSnd,V_qr))) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_divmod__nat__if,axiom,
% 187.18/188.00 ! [V_m_2,V_n_2] :
% 187.18/188.00 ( ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.18/188.00 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) )
% 187.18/188.00 => 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) )
% 187.18/188.00 & ( ~ ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.18/188.00 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) )
% 187.18/188.00 => 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)) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_pdivmod__def,axiom,
% 187.18/188.00 ! [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))) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_pdivmod__posDivAlg,axiom,
% 187.18/188.00 ! [V_k,V_l] :
% 187.18/188.00 ( ( V_l = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.18/188.00 => 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)) )
% 187.18/188.00 & ( V_l != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.18/188.00 => 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)) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_divmod__int__code,axiom,
% 187.18/188.00 ! [V_l_2,V_k_2] :
% 187.18/188.00 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.18/188.00 => 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)) )
% 187.18/188.00 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.18/188.00 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.18/188.00 => 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) )
% 187.18/188.00 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.18/188.00 => 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)))) ) ) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_code__numeral_Osize_I4_J,axiom,
% 187.18/188.00 ! [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))) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_divmod__nat__rel__mult2__eq,axiom,
% 187.18/188.00 ! [V_c,V_r,V_q,V_b,V_a] :
% 187.18/188.00 ( 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)))
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_b))
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 187.18/188.00 => 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)))) ) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_divmod__nat__rel__mult1__eq,axiom,
% 187.18/188.00 ! [V_a,V_r,V_q,V_c,V_b] :
% 187.18/188.00 ( 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)))
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 187.18/188.00 => 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)))) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_divmod__nat__rel__unique,axiom,
% 187.18/188.00 ! [V_qr_H,V_qr,V_n,V_m] :
% 187.18/188.00 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr))
% 187.18/188.00 => ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr_H))
% 187.18/188.00 => V_qr = V_qr_H ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_divmod__nat__eq,axiom,
% 187.18/188.00 ! [V_qr,V_n,V_m] :
% 187.18/188.00 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr))
% 187.18/188.00 => c_Divides_Odivmod__nat(V_m,V_n) = V_qr ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_divmod__nat__rel__divmod__nat,axiom,
% 187.18/188.00 ! [V_n,V_m] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),c_Divides_Odivmod__nat(V_m,V_n))) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_divmod__nat__def,axiom,
% 187.18/188.00 ! [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)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_mod__eq,axiom,
% 187.18/188.00 ! [V_r,V_q,V_n,V_m] :
% 187.18/188.00 ( 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)))
% 187.18/188.00 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_r ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_div__eq,axiom,
% 187.18/188.00 ! [V_r,V_q,V_n,V_m] :
% 187.18/188.00 ( 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)))
% 187.18/188.00 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = V_q ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_divmod__nat__rel,axiom,
% 187.18/188.00 ! [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)))) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_code__numeral_Osize_I3_J,axiom,
% 187.18/188.00 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) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_divmod__nat__rel__add1__eq,axiom,
% 187.18/188.00 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] :
% 187.18/188.00 ( 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)))
% 187.18/188.00 => ( 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)))
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 187.18/188.00 => 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)))) ) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_negDivAlg_Opsimps,axiom,
% 187.18/188.00 ! [V_b_2,V_a_2] :
% 187.18/188.00 ( 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)))
% 187.18/188.00 => ( ( ( 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)))
% 187.18/188.00 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 187.18/188.00 => 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)) )
% 187.18/188.00 & ( ~ ( 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)))
% 187.18/188.00 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 187.18/188.00 => 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))) ) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_posDivAlg_Opsimps,axiom,
% 187.18/188.00 ! [V_b_2,V_a_2] :
% 187.18/188.00 ( 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)))
% 187.18/188.00 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2))
% 187.18/188.00 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 187.18/188.00 => 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) )
% 187.18/188.00 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2))
% 187.18/188.00 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 187.18/188.00 => 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))) ) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_mod__pos__neg__1__number__of,axiom,
% 187.18/188.00 ! [V_w] :
% 187.18/188.00 ( 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)))
% 187.18/188.00 => 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))))) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_snd__apsnd,axiom,
% 187.18/188.00 ! [V_x_2,V_f_2,T_c,T_a,T_b] : hAPP(c_Product__Type_Osnd(T_b,T_a),hAPP(c_Product__Type_Oapsnd(T_c,T_a,T_b,V_f_2),V_x_2)) = hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_b,T_c),V_x_2)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_apsnd__eq__conv,axiom,
% 187.18/188.00 ! [V_g_2,V_x_2,V_f_2,T_a,T_b,T_c] :
% 187.18/188.00 ( hAPP(c_Product__Type_Oapsnd(T_c,T_b,T_a,V_f_2),V_x_2) = hAPP(c_Product__Type_Oapsnd(T_c,T_b,T_a,V_g_2),V_x_2)
% 187.18/188.00 <=> hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_a,T_c),V_x_2)) = hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_a,T_c),V_x_2)) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_snd__eqD,axiom,
% 187.18/188.00 ! [V_a,V_y,V_x,T_a,T_b] :
% 187.18/188.00 ( 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
% 187.18/188.00 => V_y = V_a ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_snd__conv,axiom,
% 187.18/188.00 ! [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 ).
% 187.18/188.00
% 187.18/188.00 fof(fact_snd__def,axiom,
% 187.18/188.00 ! [V_p_2,T_a,T_b] : hAPP(c_Product__Type_Osnd(T_b,T_a),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_a,T_a),hAPP(c_COMBK(tc_fun(T_a,T_a),T_b),c_COMBI(T_a))),V_p_2) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_mod__int__def,axiom,
% 187.18/188.00 ! [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)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_mod__neg__pos,axiom,
% 187.18/188.00 ! [V_b,V_a] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 187.18/188.00 => 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)) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_mod__pos__pos,axiom,
% 187.18/188.00 ! [V_b,V_a] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 187.18/188.00 => 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)) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_mod__pos__pos__1__number__of,axiom,
% 187.18/188.00 ! [V_w] :
% 187.18/188.00 ( 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)))
% 187.18/188.00 => 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))) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_mod__pos__neg,axiom,
% 187.18/188.00 ! [V_b,V_a] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.18/188.00 => 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)))) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_mod__neg__neg,axiom,
% 187.18/188.00 ! [V_b,V_a] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.18/188.00 => 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)))) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_norm__frac_Opsimps,axiom,
% 187.18/188.00 ! [V_b_2,V_a_2] :
% 187.18/188.00 ( 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)))
% 187.18/188.00 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.18/188.00 => 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)) )
% 187.18/188.00 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.18/188.00 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.18/188.00 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 187.18/188.00 => 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)) )
% 187.18/188.00 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 187.18/188.00 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 187.18/188.00 => 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))) ) ) ) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_negDivAlg_Opinduct,axiom,
% 187.18/188.00 ! [V_P_2,V_a1_2,V_a0_2] :
% 187.18/188.00 ( 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)))
% 187.18/188.00 => ( ! [B_a,B_b] :
% 187.18/188.00 ( 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)))
% 187.18/188.00 => ( ( ~ ( 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)))
% 187.18/188.00 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 187.18/188.00 => 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))) )
% 187.18/188.00 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) )
% 187.18/188.00 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_posDivAlg_Opinduct,axiom,
% 187.18/188.00 ! [V_P_2,V_a1_2,V_a0_2] :
% 187.18/188.00 ( 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)))
% 187.18/188.00 => ( ! [B_a,B_b] :
% 187.18/188.00 ( 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)))
% 187.18/188.00 => ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_a),B_b))
% 187.18/188.00 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 187.18/188.00 => 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))) )
% 187.18/188.00 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) )
% 187.18/188.00 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_mod__nat__def,axiom,
% 187.18/188.00 ! [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)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_accp__subset,axiom,
% 187.18/188.00 ! [V_R2_2,V_R1_2,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),V_R1_2),V_R2_2))
% 187.18/188.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_Wellfounded_Oaccp(T_a,V_R2_2)),c_Wellfounded_Oaccp(T_a,V_R1_2))) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_norm__frac_Opinduct,axiom,
% 187.18/188.00 ! [V_P_2,V_a1_2,V_a0_2] :
% 187.18/188.00 ( 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)))
% 187.18/188.00 => ( ! [B_a,B_b] :
% 187.18/188.00 ( 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)))
% 187.18/188.00 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.18/188.00 => 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))) )
% 187.18/188.00 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) )
% 187.18/188.00 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_div__pos__neg__1__number__of,axiom,
% 187.18/188.00 ! [V_w] :
% 187.18/188.00 ( 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)))
% 187.18/188.00 => 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))))) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_Pair__fst__snd__eq,axiom,
% 187.18/188.00 ! [T_b,T_a,V_t_2,V_s_2] :
% 187.18/188.00 ( V_s_2 = V_t_2
% 187.18/188.00 <=> ( hAPP(c_Product__Type_Ofst(T_a,T_b),V_s_2) = hAPP(c_Product__Type_Ofst(T_a,T_b),V_t_2)
% 187.18/188.00 & hAPP(c_Product__Type_Osnd(T_a,T_b),V_s_2) = hAPP(c_Product__Type_Osnd(T_a,T_b),V_t_2) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_prod__eqI,axiom,
% 187.18/188.00 ! [V_q,V_p,T_b,T_a] :
% 187.18/188.00 ( hAPP(c_Product__Type_Ofst(T_a,T_b),V_p) = hAPP(c_Product__Type_Ofst(T_a,T_b),V_q)
% 187.18/188.00 => ( hAPP(c_Product__Type_Osnd(T_a,T_b),V_p) = hAPP(c_Product__Type_Osnd(T_a,T_b),V_q)
% 187.18/188.00 => V_p = V_q ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_fst__apsnd,axiom,
% 187.18/188.00 ! [V_x_2,V_f_2,T_c,T_b,T_a] : hAPP(c_Product__Type_Ofst(T_a,T_b),hAPP(c_Product__Type_Oapsnd(T_c,T_b,T_a,V_f_2),V_x_2)) = hAPP(c_Product__Type_Ofst(T_a,T_c),V_x_2) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_fst__def,axiom,
% 187.18/188.00 ! [V_p_2,T_b,T_a] : hAPP(c_Product__Type_Ofst(T_a,T_b),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_a),c_COMBK(T_a,T_b)),V_p_2) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_fst__eqD,axiom,
% 187.18/188.00 ! [V_a,V_y,V_x,T_b,T_a] :
% 187.18/188.00 ( 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
% 187.18/188.00 => V_x = V_a ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_fst__conv,axiom,
% 187.18/188.00 ! [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 ).
% 187.18/188.00
% 187.18/188.00 fof(fact_pair__collapse,axiom,
% 187.18/188.00 ! [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 ).
% 187.18/188.00
% 187.18/188.00 fof(fact_surjective__pairing,axiom,
% 187.18/188.00 ! [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)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_prod__case__beta,axiom,
% 187.18/188.00 ! [V_p_2,V_f_2,T_a,T_c,T_b] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),V_f_2),V_p_2) = hAPP(hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_b,T_c),V_p_2)),hAPP(c_Product__Type_Osnd(T_b,T_c),V_p_2)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_div__int__def,axiom,
% 187.18/188.00 ! [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)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_split__comp__eq,axiom,
% 187.18/188.00 ! [V_g_2,V_f_2,T_d,T_c,T_b,T_a] : hAPP(hAPP(c_COMBS(tc_prod(T_a,T_b),T_b,T_c),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_b,T_c),tc_prod(T_a,T_b)),V_f_2),hAPP(hAPP(c_COMBB(T_a,T_d,tc_prod(T_a,T_b)),V_g_2),c_Product__Type_Ofst(T_a,T_b)))),c_Product__Type_Osnd(T_a,T_b)) = hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_b,T_c),T_a),V_f_2),V_g_2)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_split__beta,axiom,
% 187.18/188.00 ! [V_z_2,V_P_2,T_a,T_c,T_b] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),V_P_2),V_z_2) = hAPP(hAPP(V_P_2,hAPP(c_Product__Type_Ofst(T_b,T_c),V_z_2)),hAPP(c_Product__Type_Osnd(T_b,T_c),V_z_2)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_split__def,axiom,
% 187.18/188.00 ! [V_p_2,V_c_2,T_a,T_c,T_b] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),V_c_2),V_p_2) = hAPP(hAPP(V_c_2,hAPP(c_Product__Type_Ofst(T_b,T_c),V_p_2)),hAPP(c_Product__Type_Osnd(T_b,T_c),V_p_2)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_accp__downward,axiom,
% 187.18/188.00 ! [V_a_2,V_b_2,V_r_2,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_b_2))
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 187.18/188.00 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_a_2)) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_accp_Oequations,axiom,
% 187.18/188.00 ! [V_a_2,V_r_2,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_a_2))
% 187.18/188.00 <=> ! [B_x] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2))
% 187.18/188.00 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),B_x)) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_accp_Osimps,axiom,
% 187.18/188.00 ! [V_a_2,V_r_2,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_a_2))
% 187.18/188.00 <=> ! [B_x] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2))
% 187.18/188.00 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),B_x)) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_The__split,axiom,
% 187.18/188.00 ! [V_P_2,T_b,T_a] : c_HOL_OThe(tc_prod(T_a,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_P_2)) = c_HOL_OThe(tc_prod(T_a,T_b),hAPP(hAPP(c_COMBS(tc_prod(T_a,T_b),T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_b,tc_HOL_Obool),tc_prod(T_a,T_b)),V_P_2),c_Product__Type_Ofst(T_a,T_b))),c_Product__Type_Osnd(T_a,T_b))) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_div__neg__pos,axiom,
% 187.18/188.00 ! [V_b,V_a] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 187.18/188.00 => 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)) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_div__pos__pos,axiom,
% 187.18/188.00 ! [V_b,V_a] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 187.18/188.00 => 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)) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_div__pos__pos__1__number__of,axiom,
% 187.18/188.00 ! [V_w] :
% 187.18/188.00 ( 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)))
% 187.18/188.00 => 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))) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_div__pos__neg,axiom,
% 187.18/188.00 ! [V_b,V_a] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.18/188.00 => 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)))) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_div__neg__neg,axiom,
% 187.18/188.00 ! [V_b,V_a] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 187.18/188.00 => 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)))) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_prod__size__simp,axiom,
% 187.18/188.00 ! [V_p_2,V_g_2,V_f_2,T_b,T_a] : c_Product__Type_Oprod_Oprod__size(T_a,T_b,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_a,T_b),V_p_2))),hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_a,T_b),V_p_2)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_nat__gcd_Opsimps,axiom,
% 187.18/188.00 ! [V_y_2,V_x_2] :
% 187.18/188.00 ( 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)))
% 187.18/188.00 => ( ( V_y_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.18/188.00 => c_Nitpick_Onat__gcd(V_x_2,V_y_2) = V_x_2 )
% 187.18/188.00 & ( V_y_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.18/188.00 => 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)) ) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_exI__realizer,axiom,
% 187.18/188.00 ! [T_a,T_b,V_x_2,V_y_2,V_P_2] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(V_P_2,V_y_2),V_x_2))
% 187.18/188.00 => hBOOL(hAPP(hAPP(V_P_2,hAPP(c_Product__Type_Osnd(T_b,T_a),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_x_2),V_y_2))),hAPP(c_Product__Type_Ofst(T_b,T_a),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_x_2),V_y_2)))) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_div__nat__def,axiom,
% 187.18/188.00 ! [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)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_divmod__nat__rel__def,axiom,
% 187.18/188.00 ! [V_qr_2,V_n_2,V_m_2] :
% 187.18/188.00 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m_2,V_n_2),V_qr_2))
% 187.18/188.00 <=> ( V_m_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(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))
% 187.18/188.00 & ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.18/188.00 => hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),V_qr_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 187.18/188.00 & ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.18/188.00 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 187.18/188.00 => ( 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)))
% 187.18/188.00 & 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)) ) )
% 187.18/188.00 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 187.18/188.00 => ( 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)))
% 187.18/188.00 & 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))) ) ) ) ) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_conjI__realizer,axiom,
% 187.18/188.00 ! [T_b,T_a,V_q_2,V_Q_2,V_p_2,V_P_2] :
% 187.18/188.00 ( hBOOL(hAPP(V_P_2,V_p_2))
% 187.18/188.00 => ( hBOOL(hAPP(V_Q_2,V_q_2))
% 187.18/188.00 => ( hBOOL(hAPP(V_P_2,hAPP(c_Product__Type_Ofst(T_a,T_b),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_p_2),V_q_2))))
% 187.18/188.00 & hBOOL(hAPP(V_Q_2,hAPP(c_Product__Type_Osnd(T_a,T_b),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_p_2),V_q_2)))) ) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_nat_Osize_I2_J,axiom,
% 187.18/188.00 ! [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))) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_in__measure,axiom,
% 187.18/188.00 ! [V_f_2,V_y_2,V_x_2,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),hAPP(c_Wellfounded_Omeasure(T_a),V_f_2)))
% 187.18/188.00 <=> 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))) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_nat__def,axiom,
% 187.18/188.00 ! [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)))))) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_Rep__Integ__inject,axiom,
% 187.18/188.00 ! [V_y_2,V_x_2] :
% 187.18/188.00 ( hAPP(c_Int_ORep__Integ,V_x_2) = hAPP(c_Int_ORep__Integ,V_y_2)
% 187.18/188.00 <=> V_x_2 = V_y_2 ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_nat_Osize_I1_J,axiom,
% 187.18/188.00 c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_nat__gcd_Opinduct,axiom,
% 187.18/188.00 ! [V_P_2,V_a1_2,V_a0_2] :
% 187.18/188.00 ( 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)))
% 187.18/188.00 => ( ! [B_x,B_y] :
% 187.18/188.00 ( 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)))
% 187.18/188.00 => ( ( B_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.18/188.00 => hBOOL(hAPP(hAPP(V_P_2,B_y),c_Divides_Odiv__class_Omod(tc_Nat_Onat,B_x,B_y))) )
% 187.18/188.00 => hBOOL(hAPP(hAPP(V_P_2,B_x),B_y)) ) )
% 187.18/188.00 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_mlex__leq,axiom,
% 187.18/188.00 ! [V_R_2,T_a,V_y_2,V_x_2,V_f_2] :
% 187.18/188.00 ( 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)))
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_R_2))
% 187.18/188.00 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Wellfounded_Omlex__prod(T_a,V_f_2,V_R_2))) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_mlex__less,axiom,
% 187.18/188.00 ! [V_R_2,T_a,V_y_2,V_x_2,V_f_2] :
% 187.18/188.00 ( 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)))
% 187.18/188.00 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Wellfounded_Omlex__prod(T_a,V_f_2,V_R_2))) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_finite__psubset__def,axiom,
% 187.18/188.00 ! [T_a] : c_Wellfounded_Ofinite__psubset(T_a) = hAPP(c_Set_OCollect(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),c_COMBS(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_fconj)),c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool))))),c_Finite__Set_Ofinite(T_a)))) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_nat_Osize_I4_J,axiom,
% 187.18/188.00 ! [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))) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_prod_Orecs,axiom,
% 187.18/188.00 ! [V_b_2,V_a_2,V_f1_2,T_a,T_c,T_b] : c_Product__Type_Oprod_Oprod__rec(T_b,T_c,T_a,V_f1_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_nat__size,axiom,
% 187.18/188.00 ! [V_n] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),V_n) = V_n ).
% 187.18/188.00
% 187.18/188.00 fof(fact_nat_Osize_I3_J,axiom,
% 187.18/188.00 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) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_in__finite__psubset,axiom,
% 187.18/188.00 ! [V_B_2,V_A_2,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),c_Wellfounded_Ofinite__psubset(T_a)))
% 187.18/188.00 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 187.18/188.00 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_in__lex__prod,axiom,
% 187.18/188.00 ! [V_s_2,V_r_2,V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_b,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_H_2),V_b_H_2))),c_Wellfounded_Olex__prod(T_a,T_b,V_r_2,V_s_2)))
% 187.18/188.00 <=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_a_H_2)),V_r_2))
% 187.18/188.00 | ( V_a_2 = V_a_H_2
% 187.18/188.00 & 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_b_H_2)),V_s_2)) ) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_apfst__apsnd,axiom,
% 187.18/188.00 ! [V_x_2,V_g_2,T_d,V_f_2,T_b,T_a,T_c] : hAPP(c_Product__Type_Oapfst(T_c,T_a,T_b,V_f_2),hAPP(c_Product__Type_Oapsnd(T_d,T_b,T_c,V_g_2),V_x_2)) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_x_2))),hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_c,T_d),V_x_2))) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_apsnd__apfst,axiom,
% 187.18/188.00 ! [V_x_2,V_g_2,T_d,V_f_2,T_a,T_b,T_c] : hAPP(c_Product__Type_Oapsnd(T_c,T_b,T_a,V_f_2),hAPP(c_Product__Type_Oapfst(T_d,T_a,T_c,V_g_2),V_x_2)) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_d,T_c),V_x_2))),hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_d,T_c),V_x_2))) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_apfst__conv,axiom,
% 187.18/188.00 ! [V_y_2,V_x_2,V_f_2,T_b,T_a,T_c] : hAPP(c_Product__Type_Oapfst(T_c,T_a,T_b,V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2),V_y_2)) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(V_f_2,V_x_2)),V_y_2) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_apfst__eq__conv,axiom,
% 187.18/188.00 ! [V_g_2,V_x_2,V_f_2,T_b,T_a,T_c] :
% 187.18/188.00 ( hAPP(c_Product__Type_Oapfst(T_c,T_a,T_b,V_f_2),V_x_2) = hAPP(c_Product__Type_Oapfst(T_c,T_a,T_b,V_g_2),V_x_2)
% 187.18/188.00 <=> hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_c,T_b),V_x_2)) = hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_c,T_b),V_x_2)) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_fst__apfst,axiom,
% 187.18/188.00 ! [V_x_2,V_f_2,T_c,T_b,T_a] : hAPP(c_Product__Type_Ofst(T_a,T_b),hAPP(c_Product__Type_Oapfst(T_c,T_a,T_b,V_f_2),V_x_2)) = hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_c,T_b),V_x_2)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_snd__apfst,axiom,
% 187.18/188.00 ! [V_x_2,V_f_2,T_c,T_a,T_b] : hAPP(c_Product__Type_Osnd(T_b,T_a),hAPP(c_Product__Type_Oapfst(T_c,T_b,T_a,V_f_2),V_x_2)) = hAPP(c_Product__Type_Osnd(T_c,T_a),V_x_2) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_apsnd__apfst__commute,axiom,
% 187.18/188.00 ! [V_p_2,V_g_2,T_d,V_f_2,T_a,T_b,T_c] : hAPP(c_Product__Type_Oapsnd(T_c,T_b,T_a,V_f_2),hAPP(c_Product__Type_Oapfst(T_d,T_a,T_c,V_g_2),V_p_2)) = hAPP(c_Product__Type_Oapfst(T_d,T_a,T_b,V_g_2),hAPP(c_Product__Type_Oapsnd(T_c,T_b,T_d,V_f_2),V_p_2)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_same__fstI,axiom,
% 187.18/188.00 ! [T_a,V_R_2,V_y_2,V_y_H_2,T_b,V_x_2,V_P_2] :
% 187.18/188.00 ( hBOOL(hAPP(V_P_2,V_x_2))
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_H_2),V_y_2)),hAPP(V_R_2,V_x_2)))
% 187.18/188.00 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_H_2)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2))),c_Recdef_Osame__fst(T_a,T_b,V_P_2,V_R_2))) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_pair__lessI2,axiom,
% 187.18/188.00 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2))
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s_2),V_t_2))
% 187.18/188.00 => 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)) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_max__ext__additive,axiom,
% 187.18/188.00 ! [V_D_2,V_C_2,V_R_2,V_B_2,V_A_2,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),c_Wellfounded_Omax__ext(T_a,V_R_2)))
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_D_2)),c_Wellfounded_Omax__ext(T_a,V_R_2)))
% 187.18/188.00 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_D_2))),c_Wellfounded_Omax__ext(T_a,V_R_2))) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_pair__lessI1,axiom,
% 187.18/188.00 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 187.18/188.00 => 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)) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_max__extp__max__ext__eq,axiom,
% 187.18/188.00 ! [V_xa_2,V_x_2,V_R_2,T_a] :
% 187.18/188.00 ( c_Wellfounded_Omax__extp(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a)))),c_Product__Type_OPair(T_a,T_a)))),V_R_2),V_x_2,V_xa_2)
% 187.18/188.00 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_x_2),V_xa_2)),c_Wellfounded_Omax__ext(T_a,V_R_2))) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_pair__leqI2,axiom,
% 187.18/188.00 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2))
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_s_2),V_t_2))
% 187.18/188.00 => 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)) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_smin__insertI,axiom,
% 187.18/188.00 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2))
% 187.18/188.00 => ( 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))
% 187.18/188.00 => ( 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))
% 187.18/188.00 => 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)) ) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_smin__emptyI,axiom,
% 187.18/188.00 ! [V_X_2] :
% 187.18/188.00 ( V_X_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
% 187.18/188.00 => 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)) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_pair__leqI1,axiom,
% 187.18/188.00 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 187.18/188.00 => 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)) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_wmax__insertI,axiom,
% 187.18/188.00 ! [V_XS_2,V_x_2,V_YS_2,V_y_2] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2))
% 187.18/188.00 => ( 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))
% 187.18/188.00 => ( 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))
% 187.18/188.00 => 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)) ) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_wmin__insertI,axiom,
% 187.18/188.00 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2))
% 187.18/188.00 => ( 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))
% 187.18/188.00 => ( 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))
% 187.18/188.00 => 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)) ) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_smax__insertI,axiom,
% 187.18/188.00 ! [V_X_2,V_x_2,V_Y_2,V_y_2] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_Y_2))
% 187.18/188.00 => ( 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))
% 187.18/188.00 => ( 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))
% 187.18/188.00 => 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)) ) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_max__strict__def,axiom,
% 187.18/188.00 c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_wmin__emptyI,axiom,
% 187.18/188.00 ! [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)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_wmax__emptyI,axiom,
% 187.18/188.00 ! [V_X_2] :
% 187.18/188.00 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_X_2))
% 187.18/188.00 => 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)) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_smax__emptyI,axiom,
% 187.18/188.00 ! [V_Y_2] :
% 187.18/188.00 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_Y_2))
% 187.18/188.00 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
% 187.18/188.00 => 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)) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_max__weak__def,axiom,
% 187.18/188.00 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)))) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_min__weak__def,axiom,
% 187.18/188.00 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)))) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_max__rpair__set,axiom,
% 187.18/188.00 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)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_min__rpair__set,axiom,
% 187.18/188.00 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)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_min__strict__def,axiom,
% 187.18/188.00 c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_less__than__iff,axiom,
% 187.18/188.00 ! [V_y_2,V_x_2] :
% 187.18/188.00 ( 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))
% 187.18/188.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_intrel__iff,axiom,
% 187.18/188.00 ! [V_v_2,V_u_2,V_y_2,V_x_2] :
% 187.18/188.00 ( 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))
% 187.18/188.00 <=> 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) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_rp__inv__image__rp,axiom,
% 187.18/188.00 ! [V_f_2,T_b,V_P_2,T_a] :
% 187.18/188.00 ( c_FunDef_Oreduction__pair(T_a,V_P_2)
% 187.18/188.00 => c_FunDef_Oreduction__pair(T_b,hAPP(hAPP(c_FunDef_Orp__inv__image(T_a,T_b),V_P_2),V_f_2)) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_pair__less__def,axiom,
% 187.18/188.00 c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_mlex__prod__def,axiom,
% 187.18/188.00 ! [V_R_2,V_f_2,T_a] : c_Wellfounded_Omlex__prod(T_a,V_f_2,V_R_2) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,T_a),T_a),c_Wellfounded_Olex__prod(tc_Nat_Onat,T_a,c_Wellfounded_Oless__than,V_R_2)),hAPP(hAPP(c_COMBS(T_a,T_a,tc_prod(tc_Nat_Onat,T_a)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_a,tc_prod(tc_Nat_Onat,T_a)),T_a),c_Product__Type_OPair(tc_Nat_Onat,T_a)),V_f_2)),c_COMBI(T_a))) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_rp__inv__image__def,axiom,
% 187.18/188.00 ! [T_b,T_a] : c_FunDef_Orp__inv__image(T_a,T_b) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_b,T_a),tc_prod(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_COMBC(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_b,T_a),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_b,T_a),tc_prod(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_fun(tc_fun(tc_fun(T_b,T_a),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),tc_fun(tc_fun(T_b,T_a),tc_prod(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(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_b,T_a),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_b,T_a),tc_prod(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_prod(T_a,T_a),tc_HOL_Obool)),c_COMBB(tc_fun(tc_fun(T_b,T_a),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),tc_fun(tc_fun(T_b,T_a),tc_prod(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_prod(T_a,T_a),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_a),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_prod(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(tc_fun(T_b,T_a),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),tc_fun(tc_fun(T_b,T_a),tc_prod(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_prod(T_a,T_a),tc_HOL_Obool)),c_COMBS(tc_fun(T_b,T_a),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_prod(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_fun(tc_fun(T_b,T_a),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),tc_fun(tc_fun(T_b,T_a),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_prod(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_prod(T_a,T_a),tc_HOL_Obool)),hAPP(c_COMBB(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_prod(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))),tc_fun(T_b,T_a)),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)))),c_Relation_Oinv__image(T_a,T_b))))),c_Relation_Oinv__image(T_a,T_b))) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_equiv__intrel__iff,axiom,
% 187.18/188.00 ! [V_y_2,V_x_2] :
% 187.18/188.00 ( 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))))
% 187.18/188.00 <=> 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)) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_measure__def,axiom,
% 187.18/188.00 ! [T_a] : c_Wellfounded_Omeasure(T_a) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,T_a),c_Wellfounded_Oless__than) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_Image__singleton,axiom,
% 187.18/188.00 ! [V_a_2,V_r_2,T_a,T_b] : hAPP(c_Relation_OImage(T_b,T_a,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_Set_OCollect(T_a),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(T_b,T_a),tc_fun(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_b,T_a))),hAPP(c_Product__Type_OPair(T_b,T_a),V_a_2))),V_r_2)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_Image__singleton__iff,axiom,
% 187.18/188.00 ! [V_a_2,V_r_2,T_b,V_b_2,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Relation_OImage(T_b,T_a,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))))))
% 187.18/188.00 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_a_2),V_b_2)),V_r_2)) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_inv__image__def,axiom,
% 187.18/188.00 ! [V_f_2,V_r_2,T_a,T_b] : hAPP(hAPP(c_Relation_Oinv__image(T_b,T_a),V_r_2),V_f_2) = hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,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_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_b,T_b)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),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_a),c_member(tc_prod(T_b,T_b)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_b),tc_fun(T_a,tc_prod(T_b,T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(tc_fun(T_a,T_b),tc_fun(T_a,tc_prod(T_b,T_b))),T_a),c_COMBB(T_b,tc_prod(T_b,T_b),T_a)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_prod(T_b,T_b)),T_a),c_Product__Type_OPair(T_b,T_b)),V_f_2))),V_f_2)))),V_r_2))) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_Image__empty,axiom,
% 187.18/188.00 ! [V_R_2,T_a,T_b] : hAPP(c_Relation_OImage(T_b,T_a,V_R_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_Image__Un,axiom,
% 187.18/188.00 ! [V_B_2,V_A_2,V_R_2,T_a,T_b] : hAPP(c_Relation_OImage(T_b,T_a,V_R_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_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_a,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_b,T_a,V_R_2),V_B_2)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_Image__UN,axiom,
% 187.18/188.00 ! [V_B_2,V_A_2,T_c,V_r_2,T_a,T_b] : hAPP(c_Relation_OImage(T_b,T_a,V_r_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)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c),c_Relation_OImage(T_b,T_a,V_r_2)),V_B_2)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_Image__Int__subset,axiom,
% 187.18/188.00 ! [V_B_2,V_A_2,V_R_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_a,V_R_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_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_a,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_b,T_a,V_R_2),V_B_2)))) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_Image__mono,axiom,
% 187.18/188.00 ! [V_A_2,V_A_H_2,V_r_2,V_r_H_2,T_b,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_r_H_2),V_r_2))
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_H_2),V_A_2))
% 187.18/188.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_b,V_r_H_2),V_A_H_2)),hAPP(c_Relation_OImage(T_a,T_b,V_r_2),V_A_2))) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_Un__Image,axiom,
% 187.18/188.00 ! [V_A_2,V_S_2,V_R_2,T_a,T_b] : hAPP(c_Relation_OImage(T_b,T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),V_R_2),V_S_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_a,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_b,T_a,V_S_2),V_A_2)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_in__inv__image,axiom,
% 187.18/188.00 ! [V_f_2,V_r_2,T_b,V_y_2,V_x_2,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),hAPP(hAPP(c_Relation_Oinv__image(T_b,T_a),V_r_2),V_f_2)))
% 187.18/188.00 <=> 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,V_x_2)),hAPP(V_f_2,V_y_2))),V_r_2)) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_Image__iff,axiom,
% 187.18/188.00 ! [V_A_2,V_r_2,T_b,V_b_2,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Relation_OImage(T_b,T_a,V_r_2),V_A_2)))
% 187.18/188.00 <=> ? [B_x] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 187.18/188.00 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),B_x),V_b_2)),V_r_2)) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_rev__ImageI,axiom,
% 187.18/188.00 ! [V_r_2,V_b_2,T_b,V_A_2,V_a_2,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),V_r_2))
% 187.18/188.00 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_a,T_b,V_r_2),V_A_2))) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_Image__eq__UN,axiom,
% 187.18/188.00 ! [V_B_2,V_r_2,T_a,T_b] : hAPP(c_Relation_OImage(T_b,T_a,V_r_2),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),c_Relation_OImage(T_b,T_a,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))))) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_of__int,axiom,
% 187.18/188.00 ! [V_j_2,V_i_2,T_a] :
% 187.18/188.00 ( class_Rings_Oring__1(T_a)
% 187.18/188.00 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),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_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_i_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_j_2)) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_One__int__def,axiom,
% 187.18/188.00 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))))) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_mult,axiom,
% 187.18/188.00 ! [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))))) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_Rep__Integ__inverse,axiom,
% 187.18/188.00 ! [V_x_2] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,V_x_2)) = V_x_2 ).
% 187.18/188.00
% 187.18/188.00 fof(fact_minus,axiom,
% 187.18/188.00 ! [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))))) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_Zero__int__def,axiom,
% 187.18/188.00 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))))) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_int__def,axiom,
% 187.18/188.00 ! [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))))) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_add,axiom,
% 187.18/188.00 ! [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))))) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_nat,axiom,
% 187.18/188.00 ! [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) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_minus__int__def,axiom,
% 187.18/188.00 ! [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))))))) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_less,axiom,
% 187.18/188.00 ! [V_v_2,V_u_2,V_y_2,V_x_2] :
% 187.18/188.00 ( 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)))))))
% 187.18/188.00 <=> 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))) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_le,axiom,
% 187.18/188.00 ! [V_v_2,V_u_2,V_y_2,V_x_2] :
% 187.18/188.00 ( 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)))))))
% 187.18/188.00 <=> 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))) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_irrefl__def,axiom,
% 187.18/188.00 ! [V_r_2,T_a] :
% 187.18/188.00 ( c_Relation_Oirrefl(T_a,V_r_2)
% 187.18/188.00 <=> ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),V_r_2)) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_eq__Abs__Integ,axiom,
% 187.18/188.00 ! [V_z_2] :
% 187.18/188.00 ~ ! [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))))) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_Field__insert,axiom,
% 187.18/188.00 ! [V_r_2,V_b_2,V_a_2,T_a] : hAPP(c_Relation_OField(T_a),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),hAPP(c_Relation_OField(T_a),V_r_2)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_Field__empty,axiom,
% 187.18/188.00 ! [T_a] : hAPP(c_Relation_OField(T_a),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_mono__Field,axiom,
% 187.18/188.00 ! [V_s_2,V_r_2,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2))
% 187.18/188.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OField(T_a),V_r_2)),hAPP(c_Relation_OField(T_a),V_s_2))) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_Field__Un,axiom,
% 187.18/188.00 ! [V_s_2,V_r_2,T_a] : hAPP(c_Relation_OField(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OField(T_a),V_r_2)),hAPP(c_Relation_OField(T_a),V_s_2)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_finite__Field,axiom,
% 187.18/188.00 ! [V_r_2,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2))
% 187.18/188.00 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Relation_OField(T_a),V_r_2))) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_Id__on__def,axiom,
% 187.18/188.00 ! [V_A_2,T_a] : c_Relation_OId__on(T_a,V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),T_a),c_Set_Oinsert(tc_prod(T_a,T_a))),hAPP(hAPP(c_COMBS(T_a,T_a,tc_prod(T_a,T_a)),c_Product__Type_OPair(T_a,T_a)),c_COMBI(T_a)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)))) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_quotient__def,axiom,
% 187.18/188.00 ! [V_r_2,V_A_2,T_a] : hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),T_a),c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_a),c_Relation_OImage(T_a,T_a,V_r_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)))) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_ImageE,axiom,
% 187.18/188.00 ! [V_A_2,V_r_2,T_b,V_b_2,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Relation_OImage(T_b,T_a,V_r_2),V_A_2)))
% 187.18/188.00 => ~ ! [B_x] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),B_x),V_b_2)),V_r_2))
% 187.18/188.00 => ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_quotient__is__empty,axiom,
% 187.18/188.00 ! [V_r_2,V_A_2,T_a] :
% 187.18/188.00 ( hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))
% 187.18/188.00 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_quotient__is__empty2,axiom,
% 187.18/188.00 ! [V_r_2,V_A_2,T_a] :
% 187.18/188.00 ( c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2)
% 187.18/188.00 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_quotient__empty,axiom,
% 187.18/188.00 ! [V_r_2,T_a] : hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_Id__on__def_H,axiom,
% 187.18/188.00 ! [V_A_2,T_a] : c_Relation_OId__on(T_a,V_A_2) = hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_HOL_Obool,tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj)),c_fequal))),V_A_2)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_Id__on__empty,axiom,
% 187.18/188.00 ! [T_a] : c_Relation_OId__on(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_Image__Id__on,axiom,
% 187.18/188.00 ! [V_B_2,V_A_2,T_a] : hAPP(c_Relation_OImage(T_a,T_a,c_Relation_OId__on(T_a,V_A_2)),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_quotientI,axiom,
% 187.18/188.00 ! [V_r_2,V_A_2,V_x_2,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 187.18/188.00 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2))) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_Id__on__iff,axiom,
% 187.18/188.00 ! [V_A_2,V_y_2,V_x_2,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Relation_OId__on(T_a,V_A_2)))
% 187.18/188.00 <=> ( V_x_2 = V_y_2
% 187.18/188.00 & hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_Id__on__eqI,axiom,
% 187.18/188.00 ! [V_A_2,T_a,V_b_2,V_a_2] :
% 187.18/188.00 ( V_a_2 = V_b_2
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 187.18/188.00 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Relation_OId__on(T_a,V_A_2))) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_singleton__quotient,axiom,
% 187.18/188.00 ! [V_r_2,V_x_2,T_a] : hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_r_2) = hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_equiv__class__nondisjoint,axiom,
% 187.18/188.00 ! [V_b_2,V_a_2,V_x_2,V_r_2,V_A_2,T_a] :
% 187.18/188.00 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))))
% 187.18/188.00 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2)) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_subset__equiv__class,axiom,
% 187.18/188.00 ! [V_a_2,V_b_2,V_r_2,V_A_2,T_a] :
% 187.18/188.00 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2))
% 187.18/188.00 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2)) ) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_quotientE,axiom,
% 187.18/188.00 ! [V_r_2,V_A_2,V_X_2,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2)))
% 187.18/188.00 => ~ ! [B_x] :
% 187.18/188.00 ( V_X_2 = hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))
% 187.18/188.00 => ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_equiv__intrel,axiom,
% 187.18/188.00 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) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_equiv__class__self,axiom,
% 187.18/188.00 ! [V_a_2,V_r_2,V_A_2,T_a] :
% 187.18/188.00 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 187.18/188.00 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_quotient__disj,axiom,
% 187.18/188.00 ! [V_Y_2,V_X_2,V_r_2,V_A_2,T_a] :
% 187.18/188.00 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2)))
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2)))
% 187.18/188.00 => ( V_X_2 = V_Y_2
% 187.18/188.00 | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_X_2),V_Y_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_equiv__class__eq,axiom,
% 187.18/188.00 ! [V_b_2,V_a_2,V_r_2,V_A_2,T_a] :
% 187.18/188.00 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2))
% 187.18/188.00 => hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_quotient__eqI,axiom,
% 187.18/188.00 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_a] :
% 187.18/188.00 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2)))
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2)))
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_X_2))
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_Y_2))
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2))
% 187.18/188.00 => V_X_2 = V_Y_2 ) ) ) ) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_quotient__eq__iff,axiom,
% 187.18/188.00 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_a] :
% 187.18/188.00 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2)))
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2)))
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_X_2))
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_Y_2))
% 187.18/188.00 => ( V_X_2 = V_Y_2
% 187.18/188.00 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) ) ) ) ) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_equiv__class__eq__iff,axiom,
% 187.18/188.00 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] :
% 187.18/188.00 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2))
% 187.18/188.00 <=> ( hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))
% 187.18/188.00 & hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 187.18/188.00 & hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) ) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_eq__equiv__class__iff,axiom,
% 187.18/188.00 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] :
% 187.18/188.00 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2))
% 187.18/188.00 => ( hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))
% 187.18/188.00 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) ) ) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_eq__equiv__class,axiom,
% 187.18/188.00 ! [V_A_2,V_b_2,V_a_2,V_r_2,T_a] :
% 187.18/188.00 ( hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))
% 187.18/188.00 => ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2))
% 187.18/188.00 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2)) ) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_equiv__class__subset,axiom,
% 187.18/188.00 ! [V_b_2,V_a_2,V_r_2,V_A_2,T_a] :
% 187.18/188.00 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2))
% 187.18/188.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_eq__equiv__class__iff2,axiom,
% 187.18/188.00 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] :
% 187.18/188.00 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2))
% 187.18/188.00 => ( hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_r_2) = hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_r_2)
% 187.18/188.00 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) ) ) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_UN__equiv__class,axiom,
% 187.18/188.00 ! [V_a_2,V_f_2,T_b,V_r_2,V_A_2,T_a] :
% 187.18/188.00 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 187.18/188.00 => ( c_Equiv__Relations_Ocongruent(T_a,tc_fun(T_b,tc_HOL_Obool),V_r_2,V_f_2)
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 187.18/188.00 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_f_2) = hAPP(V_f_2,V_a_2) ) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_UN__equiv__class2,axiom,
% 187.18/188.00 ! [V_a2_2,V_a1_2,V_f_2,T_c,V_r2_2,V_A2_2,T_b,V_r1_2,V_A1_2,T_a] :
% 187.18/188.00 ( c_Equiv__Relations_Oequiv(T_a,V_A1_2,V_r1_2)
% 187.18/188.00 => ( c_Equiv__Relations_Oequiv(T_b,V_A2_2,V_r2_2)
% 187.18/188.00 => ( c_Equiv__Relations_Ocongruent2(T_a,T_b,tc_fun(T_c,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a1_2),V_A1_2))
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a2_2),V_A2_2))
% 187.18/188.00 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_a,V_r1_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a1_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool),T_a),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_r2_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a2_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),V_f_2)) = hAPP(hAPP(V_f_2,V_a1_2),V_a2_2) ) ) ) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_equivp__equiv,axiom,
% 187.18/188.00 ! [V_A_2,T_a] :
% 187.18/188.00 ( c_Equiv__Relations_Oequiv(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_A_2)
% 187.18/188.00 <=> c_Equiv__Relations_Oequivp(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a)))),c_Product__Type_OPair(T_a,T_a)))),V_A_2)) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_equivp__transp,axiom,
% 187.18/188.00 ! [V_z_2,V_y_2,V_x_2,V_R_2,T_a] :
% 187.18/188.00 ( c_Equiv__Relations_Oequivp(T_a,V_R_2)
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_z_2))
% 187.18/188.00 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_z_2)) ) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_equivp__symp,axiom,
% 187.18/188.00 ! [V_y_2,V_x_2,V_R_2,T_a] :
% 187.18/188.00 ( c_Equiv__Relations_Oequivp(T_a,V_R_2)
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
% 187.18/188.00 => hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2)) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_equivp__reflp,axiom,
% 187.18/188.00 ! [V_x_2,V_R_2,T_a] :
% 187.18/188.00 ( c_Equiv__Relations_Oequivp(T_a,V_R_2)
% 187.18/188.00 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_equivp__def,axiom,
% 187.18/188.00 ! [V_R_2,T_a] :
% 187.18/188.00 ( c_Equiv__Relations_Oequivp(T_a,V_R_2)
% 187.18/188.00 <=> ! [B_x,B_y] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_y))
% 187.18/188.00 <=> hAPP(V_R_2,B_x) = hAPP(V_R_2,B_y) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_identity__equivp,axiom,
% 187.18/188.00 ! [T_a] : c_Equiv__Relations_Oequivp(T_a,c_fequal) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_congruent2__implies__congruent,axiom,
% 187.18/188.00 ! [V_a_2,V_f_2,V_r2_2,T_c,T_b,V_r1_2,V_A_2,T_a] :
% 187.18/188.00 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r1_2)
% 187.18/188.00 => ( c_Equiv__Relations_Ocongruent2(T_a,T_b,T_c,V_r1_2,V_r2_2,V_f_2)
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 187.18/188.00 => c_Equiv__Relations_Ocongruent(T_b,T_c,V_r2_2,hAPP(V_f_2,V_a_2)) ) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_congruent2D,axiom,
% 187.18/188.00 ! [V_z2_2,V_y2_2,V_z1_2,V_y1_2,V_f_2,V_r2_2,V_r1_2,T_c,T_b,T_a] :
% 187.18/188.00 ( c_Equiv__Relations_Ocongruent2(T_a,T_b,T_c,V_r1_2,V_r2_2,V_f_2)
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y1_2),V_z1_2)),V_r1_2))
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y2_2),V_z2_2)),V_r2_2))
% 187.18/188.00 => hAPP(hAPP(V_f_2,V_y1_2),V_y2_2) = hAPP(hAPP(V_f_2,V_z1_2),V_z2_2) ) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_congruentD,axiom,
% 187.18/188.00 ! [V_z_2,V_y_2,V_f_2,V_r_2,T_b,T_a] :
% 187.18/188.00 ( c_Equiv__Relations_Ocongruent(T_a,T_b,V_r_2,V_f_2)
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_z_2)),V_r_2))
% 187.18/188.00 => hAPP(V_f_2,V_y_2) = hAPP(V_f_2,V_z_2) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_congruent2__implies__congruent__UN,axiom,
% 187.18/188.00 ! [V_a_2,V_f_2,T_c,V_r2_2,V_A2_2,T_b,V_r1_2,V_A1_2,T_a] :
% 187.18/188.00 ( c_Equiv__Relations_Oequiv(T_a,V_A1_2,V_r1_2)
% 187.18/188.00 => ( c_Equiv__Relations_Oequiv(T_b,V_A2_2,V_r2_2)
% 187.18/188.00 => ( c_Equiv__Relations_Ocongruent2(T_a,T_b,tc_fun(T_c,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A2_2))
% 187.18/188.00 => c_Equiv__Relations_Ocongruent(T_a,tc_fun(T_c,tc_HOL_Obool),V_r1_2,hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool),T_a),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_r2_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)) ) ) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_UN__equiv__class__inject,axiom,
% 187.18/188.00 ! [V_Y_2,V_X_2,V_f_2,T_b,V_r_2,V_A_2,T_a] :
% 187.18/188.00 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 187.18/188.00 => ( c_Equiv__Relations_Ocongruent(T_a,tc_fun(T_b,tc_HOL_Obool),V_r_2,V_f_2)
% 187.18/188.00 => ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_f_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_Y_2),V_f_2)
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2)))
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2)))
% 187.18/188.00 => ( ! [B_x] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 187.18/188.00 => ! [B_y] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),V_A_2))
% 187.18/188.00 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y)
% 187.18/188.00 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_y)),V_r_2)) ) ) )
% 187.18/188.00 => V_X_2 = V_Y_2 ) ) ) ) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_UN__equiv__class__type2,axiom,
% 187.18/188.00 ! [V_B_2,V_X2_2,V_X1_2,V_f_2,T_c,V_r2_2,V_A2_2,T_b,V_r1_2,V_A1_2,T_a] :
% 187.18/188.00 ( c_Equiv__Relations_Oequiv(T_a,V_A1_2,V_r1_2)
% 187.18/188.00 => ( c_Equiv__Relations_Oequiv(T_b,V_A2_2,V_r2_2)
% 187.18/188.00 => ( c_Equiv__Relations_Ocongruent2(T_a,T_b,tc_fun(T_c,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X1_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A1_2),V_r1_2)))
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X2_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A2_2),V_r2_2)))
% 187.18/188.00 => ( ! [B_x1] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x1),V_A1_2))
% 187.18/188.00 => ! [B_x2] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x2),V_A2_2))
% 187.18/188.00 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(V_f_2,B_x1),B_x2)),V_B_2)) ) )
% 187.18/188.00 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_c,tc_HOL_Obool)),V_X1_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool),T_a),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_X2_2)),V_f_2))),V_B_2)) ) ) ) ) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_UN__equiv__class__type,axiom,
% 187.18/188.00 ! [V_B_2,V_X_2,V_f_2,T_b,V_r_2,V_A_2,T_a] :
% 187.18/188.00 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 187.18/188.00 => ( c_Equiv__Relations_Ocongruent(T_a,tc_fun(T_b,tc_HOL_Obool),V_r_2,V_f_2)
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2)))
% 187.18/188.00 => ( ! [B_x] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 187.18/188.00 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_f_2,B_x)),V_B_2)) )
% 187.18/188.00 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_f_2)),V_B_2)) ) ) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_Integ__def,axiom,
% 187.18/188.00 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) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_Id__onE,axiom,
% 187.18/188.00 ! [V_A_2,V_c_2,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_c_2),c_Relation_OId__on(T_a,V_A_2)))
% 187.18/188.00 => ~ ! [B_x] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 187.18/188.00 => V_c_2 != hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_card__quotient__disjoint,axiom,
% 187.18/188.00 ! [V_r_2,V_A_2,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.00 => ( c_Fun_Oinj__on(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),T_a),c_Equiv__Relations_Oquotient(T_a)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_r_2),V_A_2)
% 187.18/188.00 => hAPP(c_Finite__Set_Ocard(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2)) = hAPP(c_Finite__Set_Ocard(T_a),V_A_2) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_inj__on__empty,axiom,
% 187.18/188.00 ! [V_f_2,T_b,T_a] : c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_inj__uminus,axiom,
% 187.18/188.00 ! [V_A_2,T_a] :
% 187.18/188.00 ( class_Groups_Oordered__ab__group__add(T_a)
% 187.18/188.00 => c_Fun_Oinj__on(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a),V_A_2) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_inj__on__diff,axiom,
% 187.18/188.00 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 187.18/188.00 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 187.18/188.00 => c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_inj__on__id2,axiom,
% 187.18/188.00 ! [V_A_2,T_a] : c_Fun_Oinj__on(T_a,T_a,c_COMBI(T_a),V_A_2) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_inj__on__def,axiom,
% 187.18/188.00 ! [V_A_2,V_f_2,T_b,T_a] :
% 187.18/188.00 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 187.18/188.00 <=> ! [B_x] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 187.18/188.00 => ! [B_xa] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2))
% 187.18/188.00 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_xa)
% 187.18/188.00 => B_x = B_xa ) ) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_inj__on__Int,axiom,
% 187.18/188.00 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 187.18/188.00 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 187.18/188.00 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2)
% 187.18/188.00 => c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_subset__inj__on,axiom,
% 187.18/188.00 ! [V_A_2,V_B_2,V_f_2,T_b,T_a] :
% 187.18/188.00 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2)
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 187.18/188.00 => c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_inj__on__contraD,axiom,
% 187.18/188.00 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] :
% 187.18/188.00 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 187.18/188.00 => ( V_x_2 != V_y_2
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2))
% 187.18/188.00 => hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) ) ) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_inj__on__iff,axiom,
% 187.18/188.00 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] :
% 187.18/188.00 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2))
% 187.18/188.00 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 187.18/188.00 <=> V_x_2 = V_y_2 ) ) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_inj__onD,axiom,
% 187.18/188.00 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] :
% 187.18/188.00 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 187.18/188.00 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2))
% 187.18/188.00 => V_x_2 = V_y_2 ) ) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_inj__eq,axiom,
% 187.18/188.00 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] :
% 187.18/188.00 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 187.18/188.00 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 187.18/188.00 <=> V_x_2 = V_y_2 ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_injD,axiom,
% 187.18/188.00 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] :
% 187.18/188.00 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 187.18/188.00 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 187.18/188.00 => V_x_2 = V_y_2 ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_inj__fun,axiom,
% 187.18/188.00 ! [T_c,V_f_2,T_b,T_a] :
% 187.18/188.00 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 187.18/188.00 => c_Fun_Oinj__on(T_a,tc_fun(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,T_b),T_a),c_COMBK(T_b,T_c)),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_finite__imageD,axiom,
% 187.18/188.00 ! [V_A_2,V_f_2,T_b,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2)))
% 187.18/188.00 => ( c_Fun_Oinj__on(T_b,T_a,V_f_2,V_A_2)
% 187.18/188.00 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_inj__image__eq__iff,axiom,
% 187.18/188.00 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 187.18/188.00 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 187.18/188.00 => ( hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2) = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2)
% 187.18/188.00 <=> V_A_2 = V_B_2 ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_inj__on__Un__image__eq__iff,axiom,
% 187.18/188.00 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 187.18/188.00 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 187.18/188.00 => ( hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2) = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2)
% 187.18/188.00 <=> V_A_2 = V_B_2 ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_card__image,axiom,
% 187.18/188.00 ! [V_A_2,V_f_2,T_b,T_a] :
% 187.18/188.00 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 187.18/188.00 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_a),V_A_2) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_inj__on__strict__subset,axiom,
% 187.18/188.00 ! [V_A_2,V_B_2,V_f_2,T_b,T_a] :
% 187.18/188.00 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2)
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 187.18/188.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2))) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_range__ex1__eq,axiom,
% 187.18/188.00 ! [V_b_2,V_f_2,T_b,T_a] :
% 187.18/188.00 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))))
% 187.18/188.00 <=> ? [B_x] :
% 187.18/188.00 ( V_b_2 = hAPP(V_f_2,B_x)
% 187.18/188.00 & ! [B_y] :
% 187.18/188.00 ( V_b_2 = hAPP(V_f_2,B_y)
% 187.18/188.00 => B_y = B_x ) ) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_inj__image__mem__iff,axiom,
% 187.18/188.00 ! [V_A_2,V_a_2,V_f_2,T_b,T_a] :
% 187.18/188.00 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)))
% 187.18/188.00 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_inj__on__iff__surj,axiom,
% 187.18/188.00 ! [V_A_H_2,T_b,T_a,V_A_2] :
% 187.18/188.00 ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/188.00 => ( ? [B_f] :
% 187.18/188.00 ( c_Fun_Oinj__on(T_a,T_b,B_f,V_A_2)
% 187.18/188.00 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,B_f),V_A_2)),V_A_H_2)) )
% 187.18/188.00 <=> ? [B_g] : hAPP(c_Set_Oimage(T_b,T_a,B_g),V_A_H_2) = V_A_2 ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_endo__inj__surj,axiom,
% 187.18/188.00 ! [V_f_2,V_A_2,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_a,V_f_2),V_A_2)),V_A_2))
% 187.18/188.00 => ( c_Fun_Oinj__on(T_a,T_a,V_f_2,V_A_2)
% 187.18/188.00 => hAPP(c_Set_Oimage(T_a,T_a,V_f_2),V_A_2) = V_A_2 ) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_finite__surj__inj,axiom,
% 187.18/188.00 ! [V_f_2,V_A_2,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_Oimage(T_a,T_a,V_f_2),V_A_2)))
% 187.18/188.00 => c_Fun_Oinj__on(T_a,T_a,V_f_2,V_A_2) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_finite__UNIV__inj__surj,axiom,
% 187.18/188.00 ! [V_f_2,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))
% 187.18/188.00 => ( c_Fun_Oinj__on(T_a,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 187.18/188.00 => hAPP(c_Set_Oimage(T_a,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_finite__UNIV__surj__inj,axiom,
% 187.18/188.00 ! [V_f_2,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))
% 187.18/188.00 => ( hAPP(c_Set_Oimage(T_a,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))
% 187.18/188.00 => c_Fun_Oinj__on(T_a,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_inj__image__subset__iff,axiom,
% 187.18/188.00 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 187.18/188.00 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2)))
% 187.18/188.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_inj__on__image__Int,axiom,
% 187.18/188.00 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_b,T_a] :
% 187.18/188.00 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_C_2)
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2))
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))
% 187.18/188.00 => hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,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_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2)) ) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_image__Int,axiom,
% 187.18/188.00 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 187.18/188.00 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 187.18/188.00 => hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,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_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2)) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_eq__card__imp__inj__on,axiom,
% 187.18/188.00 ! [V_f_2,T_b,V_A_2,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.00 => ( hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_a),V_A_2)
% 187.18/188.00 => c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_inj__on__iff__eq__card,axiom,
% 187.18/188.00 ! [V_f_2,T_b,V_A_2,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.00 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 187.18/188.00 <=> hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_a),V_A_2) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_inj__on__image__set__diff,axiom,
% 187.18/188.00 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_b,T_a] :
% 187.18/188.00 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_C_2)
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2))
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))
% 187.18/188.00 => hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,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_Oimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2)) ) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_image__set__diff,axiom,
% 187.18/188.00 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 187.18/188.00 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 187.18/188.00 => hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,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_Oimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2)) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_pigeonhole,axiom,
% 187.18/188.00 ! [V_A_2,V_f_2,T_b,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)))
% 187.18/188.00 => ~ c_Fun_Oinj__on(T_b,T_a,V_f_2,V_A_2) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_inj__on__fun__updI,axiom,
% 187.18/188.00 ! [V_x_2,V_y_2,V_A_2,V_f_2,T_b,T_a] :
% 187.18/188.00 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 187.18/188.00 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)))
% 187.18/188.00 => c_Fun_Oinj__on(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_y_2),V_A_2) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_inj__singleton,axiom,
% 187.18/188.00 ! [T_a] : c_Fun_Oinj__on(T_a,tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_Rep__Integ,axiom,
% 187.18/188.00 ! [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)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_card__bij__eq,axiom,
% 187.18/188.00 ! [V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 187.18/188.00 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)),V_B_2))
% 187.18/188.00 => ( c_Fun_Oinj__on(T_b,T_a,V_g_2,V_B_2)
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_g_2),V_B_2)),V_A_2))
% 187.18/188.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 187.18/188.00 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = hAPP(c_Finite__Set_Ocard(T_b),V_B_2) ) ) ) ) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_inj__image__Compl__subset,axiom,
% 187.18/188.00 ! [V_A_2,V_f_2,T_b,T_a] :
% 187.18/188.00 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 187.18/188.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)))) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_inj__on__insert,axiom,
% 187.18/188.00 ! [V_A_2,V_a_2,V_f_2,T_b,T_a] :
% 187.18/188.00 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2))
% 187.18/188.00 <=> ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 187.18/188.00 & ~ hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_inj__on__Un,axiom,
% 187.18/188.00 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 187.18/188.00 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 187.18/188.00 <=> ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 187.18/188.00 & c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2)
% 187.18/188.00 & hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_inj__on__iff__card__le,axiom,
% 187.18/188.00 ! [V_B_2,T_b,V_A_2,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 187.18/188.00 => ( ? [B_f] :
% 187.18/188.00 ( c_Fun_Oinj__on(T_a,T_b,B_f,V_A_2)
% 187.18/188.00 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,B_f),V_A_2)),V_B_2)) )
% 187.18/188.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2))) ) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_card__inj__on__le,axiom,
% 187.18/188.00 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 187.18/188.00 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)),V_B_2))
% 187.18/188.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 187.18/188.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2))) ) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_quotient__diff1,axiom,
% 187.18/188.00 ! [V_a_2,V_A_2,V_r_2,T_a] :
% 187.18/188.00 ( c_Fun_Oinj__on(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),T_a),c_Equiv__Relations_Oquotient(T_a)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_r_2),V_A_2)
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 187.18/188.00 => hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_r_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_r_2)) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_type__definition__Integ,axiom,
% 187.18/188.00 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) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_the__inv__into__into,axiom,
% 187.18/188.00 ! [V_B_2,V_x_2,V_A_2,V_f_2,T_b,T_a] :
% 187.18/188.00 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)))
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 187.18/188.00 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),V_x_2)),V_B_2)) ) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_inj__vimage__singleton,axiom,
% 187.18/188.00 ! [V_a_2,V_f_2,T_b,T_a] :
% 187.18/188.00 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 187.18/188.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_a,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))))),hAPP(hAPP(c_Set_Oinsert(T_a),c_HOL_OThe(T_a,hAPP(hAPP(c_COMBC(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),c_fequal),V_f_2)),V_a_2))),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_vimageI,axiom,
% 187.18/188.00 ! [T_b,V_B_2,T_a,V_b_2,V_a_2,V_f_2] :
% 187.18/188.00 ( hAPP(V_f_2,V_a_2) = V_b_2
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_B_2))
% 187.18/188.00 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_B_2))) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_inj__Suc,axiom,
% 187.18/188.00 ! [V_N_2] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,V_N_2) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_inj__on__add__nat,axiom,
% 187.18/188.00 ! [V_N_2,V_k_2] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2),V_N_2) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_vimage__UNIV,axiom,
% 187.18/188.00 ! [V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,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_a,tc_HOL_Obool)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_vimage__empty,axiom,
% 187.18/188.00 ! [V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_vimage__Un,axiom,
% 187.18/188.00 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_vimageI2,axiom,
% 187.18/188.00 ! [T_b,V_A_2,V_a_2,V_f_2,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_member(T_a),hAPP(V_f_2,V_a_2)),V_A_2))
% 187.18/188.00 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_A_2))) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_vimageD,axiom,
% 187.18/188.00 ! [V_A_2,V_f_2,T_b,V_a_2,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_A_2)))
% 187.18/188.00 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),V_A_2)) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_vimage__eq,axiom,
% 187.18/188.00 ! [V_B_2,V_f_2,T_b,V_a_2,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2)))
% 187.18/188.00 <=> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),V_B_2)) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_vimage__mono,axiom,
% 187.18/188.00 ! [V_f_2,T_b,V_B_2,V_A_2,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 187.18/188.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_B_2))) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_vimage__Int,axiom,
% 187.18/188.00 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,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_a,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_vimage__Compl,axiom,
% 187.18/188.00 ! [V_A_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,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_a,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_A_2)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_vimage__code,axiom,
% 187.18/188.00 ! [V_x_2,V_A_2,V_f_2,T_b,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_A_2),V_x_2))
% 187.18/188.00 <=> hBOOL(hAPP(V_A_2,hAPP(V_f_2,V_x_2))) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_vimage__ident,axiom,
% 187.18/188.00 ! [V_Y_2,T_a] : hAPP(c_Set_Ovimage(T_a,T_a,c_COMBI(T_a)),V_Y_2) = V_Y_2 ).
% 187.18/188.00
% 187.18/188.00 fof(fact_vimage__Diff,axiom,
% 187.18/188.00 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,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_a,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_vimage__Collect__eq,axiom,
% 187.18/188.00 ! [V_P_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),hAPP(c_Set_OCollect(T_b),V_P_2)) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,T_a),V_P_2),V_f_2)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_vimage__UN,axiom,
% 187.18/188.00 ! [V_B_2,V_A_2,T_c,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_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)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c),c_Set_Ovimage(T_a,T_b,V_f_2)),V_B_2)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_inj__of__nat,axiom,
% 187.18/188.00 ! [T_a] :
% 187.18/188.00 ( class_Nat_Osemiring__char__0(T_a)
% 187.18/188.00 => c_Fun_Oinj__on(tc_Nat_Onat,T_a,c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_inj__int,axiom,
% 187.18/188.00 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))) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_image__vimage__subset,axiom,
% 187.18/188.00 ! [V_A_2,V_f_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_A_2))),V_A_2)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_surj__image__vimage__eq,axiom,
% 187.18/188.00 ! [V_A_2,V_f_2,T_a,T_b] :
% 187.18/188.00 ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))
% 187.18/188.00 => hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_A_2)) = V_A_2 ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_vimage__def,axiom,
% 187.18/188.00 ! [V_B_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(T_b)),V_f_2)),V_B_2)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_swap__inj__on,axiom,
% 187.18/188.00 ! [V_A_2,T_b,T_a] : c_Fun_Oinj__on(tc_prod(T_a,T_b),tc_prod(T_b,T_a),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_prod(T_b,T_a)),hAPP(c_COMBC(T_b,T_a,tc_prod(T_b,T_a)),c_Product__Type_OPair(T_b,T_a))),V_A_2) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_vimage__singleton__eq,axiom,
% 187.18/188.00 ! [V_b_2,V_f_2,T_b,V_a_2,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
% 187.18/188.00 <=> hAPP(V_f_2,V_a_2) = V_b_2 ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_vimage__insert,axiom,
% 187.18/188.00 ! [V_B_2,V_a_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_a,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))))),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_finite__vimageD,axiom,
% 187.18/188.00 ! [V_Fa_2,V_h_2,T_b,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_Ovimage(T_a,T_b,V_h_2),V_Fa_2)))
% 187.18/188.00 => ( hAPP(c_Set_Oimage(T_a,T_b,V_h_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
% 187.18/188.00 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Fa_2)) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_vimage__subsetD,axiom,
% 187.18/188.00 ! [V_A_2,V_B_2,V_f_2,T_a,T_b] :
% 187.18/188.00 ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_B_2)),V_A_2))
% 187.18/188.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2))) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_image__vimage__eq,axiom,
% 187.18/188.00 ! [V_A_2,V_f_2,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_finite__vimageI,axiom,
% 187.18/188.00 ! [V_h_2,T_b,V_Fa_2,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_Fa_2))
% 187.18/188.00 => ( c_Fun_Oinj__on(T_b,T_a,V_h_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 187.18/188.00 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Ovimage(T_b,T_a,V_h_2),V_Fa_2))) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_inj__vimage__image__eq,axiom,
% 187.18/188.00 ! [V_A_2,V_f_2,T_b,T_a] :
% 187.18/188.00 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 187.18/188.00 => hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)) = V_A_2 ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_vimage__const,axiom,
% 187.18/188.00 ! [T_b,V_A_2,V_c_2,T_a] :
% 187.18/188.00 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2))
% 187.18/188.00 => hAPP(c_Set_Ovimage(T_b,T_a,hAPP(c_COMBK(T_a,T_b),V_c_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) )
% 187.18/188.00 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2))
% 187.18/188.00 => hAPP(c_Set_Ovimage(T_b,T_a,hAPP(c_COMBK(T_a,T_b),V_c_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_vimage__eq__UN,axiom,
% 187.18/188.00 ! [V_B_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),c_Set_Ovimage(T_a,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))))) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_the__inv__into__f__eq,axiom,
% 187.18/188.00 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] :
% 187.18/188.00 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 187.18/188.00 => ( hAPP(V_f_2,V_x_2) = V_y_2
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 187.18/188.00 => hAPP(c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),V_y_2) = V_x_2 ) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_the__inv__into__f__f,axiom,
% 187.18/188.00 ! [V_x_2,V_A_2,V_f_2,T_b,T_a] :
% 187.18/188.00 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 187.18/188.00 => hAPP(c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2 ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_inj__on__the__inv__into,axiom,
% 187.18/188.00 ! [V_A_2,V_f_2,T_b,T_a] :
% 187.18/188.00 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 187.18/188.00 => c_Fun_Oinj__on(T_b,T_a,c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_the__inv__into__onto,axiom,
% 187.18/188.00 ! [V_A_2,V_f_2,T_b,T_a] :
% 187.18/188.00 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 187.18/188.00 => hAPP(c_Set_Oimage(T_b,T_a,c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)) = V_A_2 ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_the__inv__f__f,axiom,
% 187.18/188.00 ! [V_x_2,V_f_2,T_b,T_a] :
% 187.18/188.00 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 187.18/188.00 => hAPP(c_Fun_Othe__inv__into(T_a,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2 ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_inj__graph,axiom,
% 187.18/188.00 ! [T_b,T_a] : c_Fun_Oinj__on(tc_fun(T_a,T_b),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_a,T_b)),c_Set_OCollect(tc_prod(T_a,T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_a,T_b)),c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool)),hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal)))),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_a,T_b),tc_HOL_Obool))) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_vimage__subsetI,axiom,
% 187.18/188.00 ! [V_A_2,V_B_2,V_f_2,T_b,T_a] :
% 187.18/188.00 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)))
% 187.18/188.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2)),V_A_2)) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_the__inv__into__def,axiom,
% 187.18/188.00 ! [V_x_2,V_f_2,V_A_2,T_b,T_a] : hAPP(c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),V_x_2) = c_HOL_OThe(T_a,hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))),hAPP(hAPP(c_COMBC(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),c_fequal),V_f_2)),V_x_2))) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_vimage__if,axiom,
% 187.18/188.00 ! [V_B_2,T_b,V_d_2,V_A_2,V_c_2,T_a] :
% 187.18/188.00 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2))
% 187.18/188.00 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_d_2),V_A_2))
% 187.18/188.00 => hAPP(c_Set_Ovimage(T_b,T_a,hAPP(hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBC(T_b,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),T_b),c_If(T_a)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) )
% 187.18/188.00 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_d_2),V_A_2))
% 187.18/188.00 => hAPP(c_Set_Ovimage(T_b,T_a,hAPP(hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBC(T_b,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),T_b),c_If(T_a)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = V_B_2 ) ) )
% 187.18/188.00 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2))
% 187.18/188.00 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_d_2),V_A_2))
% 187.18/188.00 => hAPP(c_Set_Ovimage(T_b,T_a,hAPP(hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBC(T_b,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),T_b),c_If(T_a)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2) )
% 187.18/188.00 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_d_2),V_A_2))
% 187.18/188.00 => hAPP(c_Set_Ovimage(T_b,T_a,hAPP(hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBC(T_b,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),T_b),c_If(T_a)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_f__the__inv__into__f,axiom,
% 187.18/188.00 ! [V_y_2,V_A_2,V_f_2,T_b,T_a] :
% 187.18/188.00 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)))
% 187.18/188.00 => hAPP(V_f_2,hAPP(c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),V_y_2)) = V_y_2 ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_type__definition_ORep__range,axiom,
% 187.18/188.00 ! [V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] :
% 187.18/188.00 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2)
% 187.18/188.00 => hAPP(c_Set_Oimage(T_a,T_b,V_Rep_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = V_A_2 ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_type__definition_OAbs__image,axiom,
% 187.18/188.00 ! [V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] :
% 187.18/188.00 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2)
% 187.18/188.00 => hAPP(c_Set_Oimage(T_b,T_a,V_Abs_2),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_type__definition_OAbs__inject,axiom,
% 187.18/188.00 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] :
% 187.18/188.00 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2)
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 187.18/188.00 => ( hAPP(V_Abs_2,V_x_2) = hAPP(V_Abs_2,V_y_2)
% 187.18/188.00 <=> V_x_2 = V_y_2 ) ) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_type__definition_ORep__inverse,axiom,
% 187.18/188.00 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] :
% 187.18/188.00 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2)
% 187.18/188.00 => hAPP(V_Abs_2,hAPP(V_Rep_2,V_x_2)) = V_x_2 ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_type__definition_ORep__inject,axiom,
% 187.18/188.00 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] :
% 187.18/188.00 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2)
% 187.18/188.00 => ( hAPP(V_Rep_2,V_x_2) = hAPP(V_Rep_2,V_y_2)
% 187.18/188.00 <=> V_x_2 = V_y_2 ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_type__definition_ORep,axiom,
% 187.18/188.00 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] :
% 187.18/188.00 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2)
% 187.18/188.00 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_Rep_2,V_x_2)),V_A_2)) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_type__definition_OAbs__inverse,axiom,
% 187.18/188.00 ! [V_y_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] :
% 187.18/188.00 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2)
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 187.18/188.00 => hAPP(V_Rep_2,hAPP(V_Abs_2,V_y_2)) = V_y_2 ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_code__numeral_Osimps_I5_J,axiom,
% 187.18/188.00 ! [V_code__numeral_2,V_f2_2,V_f1_2,T_a] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(T_a,V_f1_2,V_f2_2,c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2)) = hAPP(V_f2_2,V_code__numeral_2) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_accp__acc__eq,axiom,
% 187.18/188.00 ! [V_x_2,V_r_2,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a)))),c_Product__Type_OPair(T_a,T_a)))),V_r_2)),V_x_2))
% 187.18/188.00 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_rel__comp__def,axiom,
% 187.18/188.00 ! [V_s_2,V_r_2,T_b,T_c,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_r_2),V_s_2) = hAPP(c_Set_OCollect(tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_a),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_a,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(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_a),c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b)),hAPP(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_a),c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_a),c_COMBC(T_c,tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_a,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_c),tc_fun(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_a,T_c)))),c_Product__Type_OPair(T_a,T_c)))),V_r_2))))),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_s_2))))) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_rel__compI,axiom,
% 187.18/188.00 ! [V_s_2,V_c_2,T_c,V_r_2,V_b_2,V_a_2,T_b,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),V_r_2))
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_b_2),V_c_2)),V_s_2))
% 187.18/188.00 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_c),V_a_2),V_c_2)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_b,T_c),V_r_2),V_s_2))) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_O__assoc,axiom,
% 187.18/188.00 ! [V_T_2,V_S_2,V_R_2,T_d,T_b,T_c,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_d,T_c),V_R_2),V_S_2)),V_T_2) = hAPP(hAPP(c_Relation_Orel__comp(T_a,T_d,T_b),V_R_2),hAPP(hAPP(c_Relation_Orel__comp(T_d,T_c,T_b),V_S_2),V_T_2)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_rel__comp__mono,axiom,
% 187.18/188.00 ! [V_s_2,V_s_H_2,T_c,V_r_2,V_r_H_2,T_b,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_r_H_2),V_r_2))
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_s_H_2),V_s_2))
% 187.18/188.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_b,T_c),V_r_H_2),V_s_H_2)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_b,T_c),V_r_2),V_s_2))) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_rel__comp__distrib,axiom,
% 187.18/188.00 ! [V_T_2,V_S_2,V_R_2,T_b,T_c,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_R_2),V_S_2)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_R_2),V_T_2)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_rel__comp__distrib2,axiom,
% 187.18/188.00 ! [V_R_2,V_T_2,V_S_2,T_b,T_c,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_c),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_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_S_2),V_R_2)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_T_2),V_R_2)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_rel__comp__empty1,axiom,
% 187.18/188.00 ! [V_R_2,T_b,T_c,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool))),V_R_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_rel__comp__empty2,axiom,
% 187.18/188.00 ! [V_R_2,T_b,T_c,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_R_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_rel__comp__UNION__distrib,axiom,
% 187.18/188.00 ! [V_r_2,V_I_2,T_d,V_s_2,T_b,T_c,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_s_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_I_2),V_r_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),T_d),hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_s_2)),V_r_2)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_rel__comp__UNION__distrib2,axiom,
% 187.18/188.00 ! [V_s_2,V_r_2,V_I_2,T_d,T_b,T_c,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool)),V_I_2),V_r_2)),V_s_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBC(T_d,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),T_d),c_Relation_Orel__comp(T_a,T_c,T_b)),V_r_2)),V_s_2)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_union__comp__emptyR,axiom,
% 187.18/188.00 ! [V_C_2,V_B_2,V_A_2,T_a] :
% 187.18/188.00 ( hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))
% 187.18/188.00 => ( hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_A_2),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))
% 187.18/188.00 => hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_B_2),V_C_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_union__comp__emptyL,axiom,
% 187.18/188.00 ! [V_B_2,V_C_2,V_A_2,T_a] :
% 187.18/188.00 ( hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_A_2),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))
% 187.18/188.00 => ( hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_B_2),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))
% 187.18/188.00 => hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_acc__subset,axiom,
% 187.18/188.00 ! [V_R2_2,V_R1_2,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R1_2),V_R2_2))
% 187.18/188.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_Wellfounded_Oacc(T_a,V_R2_2)),c_Wellfounded_Oacc(T_a,V_R1_2))) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_acc_Osimps,axiom,
% 187.18/188.00 ! [V_r_2,V_a_2,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Wellfounded_Oacc(T_a,V_r_2)))
% 187.18/188.00 <=> ! [B_x] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),V_a_2)),V_r_2))
% 187.18/188.00 => hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Wellfounded_Oacc(T_a,V_r_2))) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_acc__downward,axiom,
% 187.18/188.00 ! [V_a_2,V_r_2,V_b_2,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Wellfounded_Oacc(T_a,V_r_2)))
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2))
% 187.18/188.00 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_max__ext__compat,axiom,
% 187.18/188.00 ! [V_S_2,V_R_2,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_R_2),V_S_2)),V_R_2))
% 187.18/188.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Wellfounded_Omax__ext(T_a,V_R_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(T_a,V_S_2)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omax__ext(T_a,V_R_2))) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_min__ext__compat,axiom,
% 187.18/188.00 ! [V_S_2,V_R_2,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_R_2),V_S_2)),V_R_2))
% 187.18/188.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Wellfounded_Omin__ext(T_a,V_R_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(T_a,V_S_2)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omin__ext(T_a,V_R_2))) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_code__numeral_Osimps_I4_J,axiom,
% 187.18/188.00 ! [V_f2_2,V_f1_2,T_a] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(T_a,V_f1_2,V_f2_2,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = V_f1_2 ).
% 187.18/188.00
% 187.18/188.00 fof(fact_pred__comp__rel__comp__eq,axiom,
% 187.18/188.00 ! [V_y_2,V_x_2,V_s_2,V_r_2,T_c,T_b,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_a,T_b,T_c,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),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))
% 187.18/188.00 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_c),V_x_2),V_y_2)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_b,T_c),V_r_2),V_s_2))) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_reduction__pairI,axiom,
% 187.18/188.00 ! [V_S_2,V_R_2,T_a] :
% 187.18/188.00 ( c_Wellfounded_Owf(T_a,V_R_2)
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_R_2),V_S_2)),V_R_2))
% 187.18/188.00 => c_FunDef_Oreduction__pair(T_a,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),V_S_2)) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_max__extp_Oequations,axiom,
% 187.18/188.00 ! [V_a2_2,V_a1_2,V_R_2,T_a] :
% 187.18/188.00 ( c_Wellfounded_Omax__extp(T_a,V_R_2,V_a1_2,V_a2_2)
% 187.18/188.00 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a1_2))
% 187.18/188.00 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a2_2))
% 187.18/188.00 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/188.00 & ! [B_x] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_a1_2))
% 187.18/188.00 => ? [B_xa] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_a2_2))
% 187.18/188.00 & hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa)) ) ) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_wf__less__than,axiom,
% 187.18/188.00 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_pred__comp_Ointros,axiom,
% 187.18/188.00 ! [T_c,T_b,T_a,V_c_2,V_s_2,V_b_2,V_a_2,V_r_2] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(V_s_2,V_b_2),V_c_2))
% 187.18/188.00 => hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_a,T_b,T_c,V_r_2,V_s_2),V_a_2),V_c_2)) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_wf__empty,axiom,
% 187.18/188.00 ! [T_a] : c_Wellfounded_Owf(T_a,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_wf__inv__image,axiom,
% 187.18/188.00 ! [V_f_2,T_b,V_r_2,T_a] :
% 187.18/188.00 ( c_Wellfounded_Owf(T_a,V_r_2)
% 187.18/188.00 => c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Relation_Oinv__image(T_a,T_b),V_r_2),V_f_2)) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_wf__lex__prod,axiom,
% 187.18/188.00 ! [V_rb_2,T_b,V_ra_2,T_a] :
% 187.18/188.00 ( c_Wellfounded_Owf(T_a,V_ra_2)
% 187.18/188.00 => ( c_Wellfounded_Owf(T_b,V_rb_2)
% 187.18/188.00 => c_Wellfounded_Owf(tc_prod(T_a,T_b),c_Wellfounded_Olex__prod(T_a,T_b,V_ra_2,V_rb_2)) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_wf__measure,axiom,
% 187.18/188.00 ! [V_f_2,T_a] : c_Wellfounded_Owf(T_a,hAPP(c_Wellfounded_Omeasure(T_a),V_f_2)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_wf__comp__self,axiom,
% 187.18/188.00 ! [V_R_2,T_a] :
% 187.18/188.00 ( c_Wellfounded_Owf(T_a,V_R_2)
% 187.18/188.00 <=> c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_R_2),V_R_2)) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_wf__less,axiom,
% 187.18/188.00 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)))) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_wf__mlex,axiom,
% 187.18/188.00 ! [V_f_2,V_R_2,T_a] :
% 187.18/188.00 ( c_Wellfounded_Owf(T_a,V_R_2)
% 187.18/188.00 => c_Wellfounded_Owf(T_a,c_Wellfounded_Omlex__prod(T_a,V_f_2,V_R_2)) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_wf__pair__less,axiom,
% 187.18/188.00 c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_wf__subset,axiom,
% 187.18/188.00 ! [V_p_2,V_r_2,T_a] :
% 187.18/188.00 ( c_Wellfounded_Owf(T_a,V_r_2)
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_p_2),V_r_2))
% 187.18/188.00 => c_Wellfounded_Owf(T_a,V_p_2) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_wf__Int2,axiom,
% 187.18/188.00 ! [V_r_H_2,V_r_2,T_a] :
% 187.18/188.00 ( c_Wellfounded_Owf(T_a,V_r_2)
% 187.18/188.00 => c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_H_2),V_r_2)) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_wf__Int1,axiom,
% 187.18/188.00 ! [V_r_H_2,V_r_2,T_a] :
% 187.18/188.00 ( c_Wellfounded_Owf(T_a,V_r_2)
% 187.18/188.00 => c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_r_H_2)) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_pred__comp_Oequations,axiom,
% 187.18/188.00 ! [V_a3_2,V_a1_2,V_s_2,V_r_2,T_c,T_b,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_a,T_b,T_c,V_r_2,V_s_2),V_a1_2),V_a3_2))
% 187.18/188.00 <=> ? [B_b] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_b))
% 187.18/188.00 & hBOOL(hAPP(hAPP(V_s_2,B_b),V_a3_2)) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_min__ext__wf,axiom,
% 187.18/188.00 ! [V_r_2,T_a] :
% 187.18/188.00 ( c_Wellfounded_Owf(T_a,V_r_2)
% 187.18/188.00 => c_Wellfounded_Owf(tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Omin__ext(T_a,V_r_2)) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_max__ext__wf,axiom,
% 187.18/188.00 ! [V_r_2,T_a] :
% 187.18/188.00 ( c_Wellfounded_Owf(T_a,V_r_2)
% 187.18/188.00 => c_Wellfounded_Owf(tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Omax__ext(T_a,V_r_2)) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_wf__finite__psubset,axiom,
% 187.18/188.00 ! [T_a] : c_Wellfounded_Owf(tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(T_a)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_wf__not__refl,axiom,
% 187.18/188.00 ! [V_a_2,V_r_2,T_a] :
% 187.18/188.00 ( c_Wellfounded_Owf(T_a,V_r_2)
% 187.18/188.00 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_a_2)),V_r_2)) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_wf__not__sym,axiom,
% 187.18/188.00 ! [V_x_2,V_a_2,V_r_2,T_a] :
% 187.18/188.00 ( c_Wellfounded_Owf(T_a,V_r_2)
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_x_2)),V_r_2))
% 187.18/188.00 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_a_2)),V_r_2)) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_wf__asym,axiom,
% 187.18/188.00 ! [V_x_2,V_a_2,V_r_2,T_a] :
% 187.18/188.00 ( c_Wellfounded_Owf(T_a,V_r_2)
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_x_2)),V_r_2))
% 187.18/188.00 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_a_2)),V_r_2)) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_wf__irrefl,axiom,
% 187.18/188.00 ! [V_a_2,V_r_2,T_a] :
% 187.18/188.00 ( c_Wellfounded_Owf(T_a,V_r_2)
% 187.18/188.00 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_a_2)),V_r_2)) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_wf__int__ge__less__than2,axiom,
% 187.18/188.00 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(V_d_2)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_wf__int__ge__less__than,axiom,
% 187.18/188.00 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(V_d_2)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_wf__acc__iff,axiom,
% 187.18/188.00 ! [V_r_2,T_a] :
% 187.18/188.00 ( c_Wellfounded_Owf(T_a,V_r_2)
% 187.18/188.00 <=> ! [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Wellfounded_Oacc(T_a,V_r_2))) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_acc__wfD,axiom,
% 187.18/188.00 ! [V_x_2,V_r_2,T_a] :
% 187.18/188.00 ( c_Wellfounded_Owf(T_a,V_r_2)
% 187.18/188.00 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_wf__no__loop,axiom,
% 187.18/188.00 ! [V_R_2,T_a] :
% 187.18/188.00 ( hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_R_2),V_R_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))
% 187.18/188.00 => c_Wellfounded_Owf(T_a,V_R_2) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_wf__union__merge,axiom,
% 187.18/188.00 ! [V_S_2,V_R_2,T_a] :
% 187.18/188.00 ( c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),V_S_2))
% 187.18/188.00 <=> c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_R_2),V_R_2)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_S_2),V_R_2))),V_S_2)) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_wf__iff__no__infinite__down__chain,axiom,
% 187.18/188.00 ! [V_r_2,T_a] :
% 187.18/188.00 ( c_Wellfounded_Owf(T_a,V_r_2)
% 187.18/188.00 <=> ~ ? [B_f] :
% 187.18/188.00 ! [B_i] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),hAPP(B_f,hAPP(c_Nat_OSuc,B_i))),hAPP(B_f,B_i))),V_r_2)) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_wfE__pf,axiom,
% 187.18/188.00 ! [V_A_2,V_R_2,T_a] :
% 187.18/188.00 ( c_Wellfounded_Owf(T_a,V_R_2)
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Relation_OImage(T_a,T_a,V_R_2),V_A_2)))
% 187.18/188.00 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_wf__union__compatible,axiom,
% 187.18/188.00 ! [V_S_2,V_R_2,T_a] :
% 187.18/188.00 ( c_Wellfounded_Owf(T_a,V_R_2)
% 187.18/188.00 => ( c_Wellfounded_Owf(T_a,V_S_2)
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_R_2),V_S_2)),V_R_2))
% 187.18/188.00 => c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),V_S_2)) ) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_wf,axiom,
% 187.18/188.00 ! [T_a] :
% 187.18/188.00 ( class_Orderings_Owellorder(T_a)
% 187.18/188.00 => c_Wellfounded_Owf(T_a,hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),c_Orderings_Oord__class_Oless(T_a)))) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_reduction__pair__def,axiom,
% 187.18/188.00 ! [V_P_2,T_a] :
% 187.18/188.00 ( c_FunDef_Oreduction__pair(T_a,V_P_2)
% 187.18/188.00 <=> ( c_Wellfounded_Owf(T_a,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_P_2))
% 187.18/188.00 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_P_2)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_P_2))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_P_2))) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_reduction__pair__lemma,axiom,
% 187.18/188.00 ! [V_S_2,V_R_2,V_P_2,T_a] :
% 187.18/188.00 ( c_FunDef_Oreduction__pair(T_a,V_P_2)
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_P_2)))
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_S_2),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_P_2)))
% 187.18/188.00 => ( c_Wellfounded_Owf(T_a,V_S_2)
% 187.18/188.00 => c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),V_S_2)) ) ) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_wf__lenlex,axiom,
% 187.18/188.00 ! [V_r_2,T_a] :
% 187.18/188.00 ( c_Wellfounded_Owf(T_a,V_r_2)
% 187.18/188.00 => c_Wellfounded_Owf(tc_List_Olist(T_a),c_List_Olenlex(T_a,V_r_2)) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_wf__if__measure,axiom,
% 187.18/188.00 ! [T_a,V_g_2,V_f_2,V_P_2] :
% 187.18/188.00 ( ! [B_x] :
% 187.18/188.00 ( hBOOL(hAPP(V_P_2,B_x))
% 187.18/188.00 => 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))) )
% 187.18/188.00 => c_Wellfounded_Owf(T_a,hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),V_P_2))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal)),V_g_2))))) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_max__ext_Ointros,axiom,
% 187.18/188.00 ! [V_R_2,V_Y_2,V_X_2,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_X_2))
% 187.18/188.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_Y_2))
% 187.18/188.00 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/188.00 => ( ! [B_x] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_X_2))
% 187.18/188.00 => ? [B_xa] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_Y_2))
% 187.18/188.00 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_xa)),V_R_2)) ) )
% 187.18/188.00 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_X_2),V_Y_2)),c_Wellfounded_Omax__ext(T_a,V_R_2))) ) ) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_pred__nat__def,axiom,
% 187.18/188.00 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))) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_wf__lex,axiom,
% 187.18/188.00 ! [V_r_2,T_a] :
% 187.18/188.00 ( c_Wellfounded_Owf(T_a,V_r_2)
% 187.18/188.00 => c_Wellfounded_Owf(tc_List_Olist(T_a),c_List_Olex(T_a,V_r_2)) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_wf__lexn,axiom,
% 187.18/188.00 ! [V_n_2,V_r_2,T_a] :
% 187.18/188.00 ( c_Wellfounded_Owf(T_a,V_r_2)
% 187.18/188.00 => c_Wellfounded_Owf(tc_List_Olist(T_a),hAPP(c_List_Olexn(T_a,V_r_2),V_n_2)) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_lex__def,axiom,
% 187.18/188.00 ! [V_r_2,T_a] : c_List_Olex(T_a,V_r_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_List_Olexn(T_a,V_r_2)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_lexn_Osimps_I1_J,axiom,
% 187.18/188.00 ! [V_r_2,T_a] : hAPP(c_List_Olexn(T_a,V_r_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_wf__pred__nat,axiom,
% 187.18/188.00 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_wf__same__fst,axiom,
% 187.18/188.00 ! [T_a,V_R_2,T_b,V_P_2] :
% 187.18/188.00 ( ! [B_x] :
% 187.18/188.00 ( hBOOL(hAPP(V_P_2,B_x))
% 187.18/188.00 => c_Wellfounded_Owf(T_b,hAPP(V_R_2,B_x)) )
% 187.18/188.00 => c_Wellfounded_Owf(tc_prod(T_a,T_b),c_Recdef_Osame__fst(T_a,T_b,V_P_2,V_R_2)) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_Nitpick_Ozero__frac__def,axiom,
% 187.18/188.00 ! [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))) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_Range__Collect__split,axiom,
% 187.18/188.00 ! [V_P_2,T_a,T_b] : hAPP(c_Relation_ORange(T_b,T_a),hAPP(c_Set_OCollect(tc_prod(T_b,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_a,tc_HOL_Obool),V_P_2))) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_b)),hAPP(c_COMBC(T_b,T_a,tc_HOL_Obool),V_P_2))) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_RangeI,axiom,
% 187.18/188.00 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),V_r_2))
% 187.18/188.00 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_ORange(T_a,T_b),V_r_2))) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_Range__Id__on,axiom,
% 187.18/188.00 ! [V_A_2,T_a] : hAPP(c_Relation_ORange(T_a,T_a),c_Relation_OId__on(T_a,V_A_2)) = V_A_2 ).
% 187.18/188.00
% 187.18/188.00 fof(fact_Range__Diff__subset,axiom,
% 187.18/188.00 ! [V_B_2,V_A_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_b,T_a),V_A_2)),hAPP(c_Relation_ORange(T_b,T_a),V_B_2))),hAPP(c_Relation_ORange(T_b,T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),V_A_2),V_B_2)))) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_Range__empty,axiom,
% 187.18/188.00 ! [T_a,T_b] : hAPP(c_Relation_ORange(T_b,T_a),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_Range__empty__iff,axiom,
% 187.18/188.00 ! [V_r_2,T_a,T_b] :
% 187.18/188.00 ( hAPP(c_Relation_ORange(T_b,T_a),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/188.00 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_Range__Un__eq,axiom,
% 187.18/188.00 ! [V_B_2,V_A_2,T_a,T_b] : hAPP(c_Relation_ORange(T_b,T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_b,T_a),V_A_2)),hAPP(c_Relation_ORange(T_b,T_a),V_B_2)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_finite__Range,axiom,
% 187.18/188.00 ! [V_r_2,T_b,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),V_r_2))
% 187.18/188.00 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_ORange(T_a,T_b),V_r_2))) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_snd__eq__Range,axiom,
% 187.18/188.00 ! [V_R_2,T_a,T_b] : hAPP(c_Set_Oimage(tc_prod(T_b,T_a),T_a,c_Product__Type_Osnd(T_b,T_a)),V_R_2) = hAPP(c_Relation_ORange(T_b,T_a),V_R_2) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_Range__iff,axiom,
% 187.18/188.00 ! [V_r_2,T_b,V_a_2,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_ORange(T_b,T_a),V_r_2)))
% 187.18/188.00 <=> ? [B_y] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),B_y),V_a_2)),V_r_2)) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_Range__insert,axiom,
% 187.18/188.00 ! [V_r_2,V_b_2,V_a_2,T_a,T_b] : hAPP(c_Relation_ORange(T_b,T_a),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),hAPP(c_Relation_ORange(T_b,T_a),V_r_2)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_Range__Int__subset,axiom,
% 187.18/188.00 ! [V_B_2,V_A_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_b,T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_b,T_a),V_A_2)),hAPP(c_Relation_ORange(T_b,T_a),V_B_2)))) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_Nitpick_Oone__frac__def,axiom,
% 187.18/188.00 ! [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))) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_Nitpick_Onumber__of__frac__def,axiom,
% 187.18/188.00 ! [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))) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_RangeP__Range__eq,axiom,
% 187.18/188.00 ! [V_x_2,V_r_2,T_b,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(c_Predicate_ORangeP(T_a,T_b,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_r_2)),V_x_2))
% 187.18/188.00 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ORange(T_a,T_b),V_r_2))) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_RangeP_Ointros,axiom,
% 187.18/188.00 ! [T_b,T_a,V_b_2,V_a_2,V_r_2] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 187.18/188.00 => hBOOL(hAPP(c_Predicate_ORangeP(T_a,T_b,V_r_2),V_b_2)) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_RangeP_Oequations,axiom,
% 187.18/188.00 ! [V_a2_2,V_r_2,T_b,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(c_Predicate_ORangeP(T_a,T_b,V_r_2),V_a2_2))
% 187.18/188.00 <=> ? [B_a] : hBOOL(hAPP(hAPP(V_r_2,B_a),V_a2_2)) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_Nitpick_Ofrac__def,axiom,
% 187.18/188.00 ! [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)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_RangeE,axiom,
% 187.18/188.00 ! [V_r_2,T_b,V_b_2,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Relation_ORange(T_b,T_a),V_r_2)))
% 187.18/188.00 => ~ ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),B_x),V_b_2)),V_r_2)) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_wf__Un,axiom,
% 187.18/188.00 ! [V_s_2,V_r_2,T_a] :
% 187.18/188.00 ( c_Wellfounded_Owf(T_a,V_r_2)
% 187.18/188.00 => ( c_Wellfounded_Owf(T_a,V_s_2)
% 187.18/188.00 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_a,T_a),V_r_2)),hAPP(c_Relation_ORange(T_a,T_a),V_s_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/188.00 => c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2)) ) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_DomainI,axiom,
% 187.18/188.00 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),V_r_2))
% 187.18/188.00 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2))) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_Domain__Id__on,axiom,
% 187.18/188.00 ! [V_A_2,T_a] : hAPP(c_Relation_ODomain(T_a,T_a),c_Relation_OId__on(T_a,V_A_2)) = V_A_2 ).
% 187.18/188.00
% 187.18/188.00 fof(fact_Domain__empty,axiom,
% 187.18/188.00 ! [T_b,T_a] : hAPP(c_Relation_ODomain(T_a,T_b),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_Domain__empty__iff,axiom,
% 187.18/188.00 ! [V_r_2,T_b,T_a] :
% 187.18/188.00 ( hAPP(c_Relation_ODomain(T_a,T_b),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/188.00 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_Domain__mono,axiom,
% 187.18/188.00 ! [V_s_2,V_r_2,T_b,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
% 187.18/188.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2)),hAPP(c_Relation_ODomain(T_a,T_b),V_s_2))) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_Domain__Un__eq,axiom,
% 187.18/188.00 ! [V_B_2,V_A_2,T_b,T_a] : hAPP(c_Relation_ODomain(T_a,T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_a,T_b),V_A_2)),hAPP(c_Relation_ODomain(T_a,T_b),V_B_2)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_finite__Domain,axiom,
% 187.18/188.00 ! [V_r_2,T_b,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),V_r_2))
% 187.18/188.00 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2))) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_fst__eq__Domain,axiom,
% 187.18/188.00 ! [V_R_2,T_b,T_a] : hAPP(c_Set_Oimage(tc_prod(T_a,T_b),T_a,c_Product__Type_Ofst(T_a,T_b)),V_R_2) = hAPP(c_Relation_ODomain(T_a,T_b),V_R_2) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_Domain__iff,axiom,
% 187.18/188.00 ! [V_r_2,T_b,V_a_2,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2)))
% 187.18/188.00 <=> ? [B_y] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),B_y)),V_r_2)) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_Domain__insert,axiom,
% 187.18/188.00 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] : hAPP(c_Relation_ODomain(T_a,T_b),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_Domain__Int__subset,axiom,
% 187.18/188.00 ! [V_B_2,V_A_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_a,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_a,T_b),V_A_2)),hAPP(c_Relation_ODomain(T_a,T_b),V_B_2)))) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_Domain__Diff__subset,axiom,
% 187.18/188.00 ! [V_B_2,V_A_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_a,T_b),V_A_2)),hAPP(c_Relation_ODomain(T_a,T_b),V_B_2))),hAPP(c_Relation_ODomain(T_a,T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_A_2),V_B_2)))) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_Field__def,axiom,
% 187.18/188.00 ! [V_r_2,T_a] : hAPP(c_Relation_OField(T_a),V_r_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_a,T_a),V_r_2)),hAPP(c_Relation_ORange(T_a,T_a),V_r_2)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_Domain__Collect__split,axiom,
% 187.18/188.00 ! [V_P_2,T_b,T_a] : hAPP(c_Relation_ODomain(T_a,T_b),hAPP(c_Set_OCollect(tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_P_2))) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_b)),V_P_2)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_DomainP__Domain__eq,axiom,
% 187.18/188.00 ! [V_x_2,V_r_2,T_b,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(c_Predicate_ODomainP(T_a,T_b,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_r_2)),V_x_2))
% 187.18/188.00 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2))) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_DomainE,axiom,
% 187.18/188.00 ! [V_r_2,T_b,V_a_2,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2)))
% 187.18/188.00 => ~ ! [B_y] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),B_y)),V_r_2)) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_image__split__eq__Sigma,axiom,
% 187.18/188.00 ! [V_A_2,V_g_2,V_f_2,T_b,T_a,T_c] : hAPP(c_Set_Oimage(T_c,tc_prod(T_a,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_b,tc_prod(T_a,T_b)),T_c),c_Product__Type_OPair(T_a,T_b)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(c_Set_Oimage(T_c,T_a,V_f_2),V_A_2)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),c_Set_Oimage(T_c,T_b,V_g_2)),hAPP(hAPP(c_COMBC(T_a,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_a),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_a),c_Set_Ovimage(T_c,T_a,V_f_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),V_A_2))) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_DomainP_Ointros,axiom,
% 187.18/188.00 ! [T_b,T_a,V_b_2,V_a_2,V_r_2] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 187.18/188.00 => hBOOL(hAPP(c_Predicate_ODomainP(T_a,T_b,V_r_2),V_a_2)) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_SigmaI,axiom,
% 187.18/188.00 ! [V_B_2,V_b_2,T_b,V_A_2,V_a_2,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2)))
% 187.18/188.00 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2))) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_Sigma__empty1,axiom,
% 187.18/188.00 ! [V_B_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_Times__eq__cancel2,axiom,
% 187.18/188.00 ! [V_B_2,V_A_2,T_b,V_C_2,V_x_2,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_C_2))
% 187.18/188.00 => ( hAPP(hAPP(c_Product__Type_OSigma(T_b,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_b),V_C_2)) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_a),V_B_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_b),V_C_2))
% 187.18/188.00 <=> V_A_2 = V_B_2 ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_card__cartesian__product,axiom,
% 187.18/188.00 ! [V_B_2,V_A_2,T_b,T_a] : hAPP(c_Finite__Set_Ocard(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_setsum__cartesian__product,axiom,
% 187.18/188.00 ! [V_A_2,V_B_2,V_f_2,T_c,T_b,T_a] :
% 187.18/188.00 ( class_Groups_Ocomm__monoid__add(T_a)
% 187.18/188.00 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),T_a),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_a),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_a),T_b),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_a)),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_a),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),V_f_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))) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_Times__empty,axiom,
% 187.18/188.00 ! [V_B_2,V_A_2,T_b,T_a] :
% 187.18/188.00 ( hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))
% 187.18/188.00 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/188.00 | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_Sigma__empty2,axiom,
% 187.18/188.00 ! [V_A_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_Compl__Times__UNIV1,axiom,
% 187.18/188.00 ! [V_A_2,T_b,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_A_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_Compl__Times__UNIV2,axiom,
% 187.18/188.00 ! [V_A_2,T_b,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_setprod__cartesian__product,axiom,
% 187.18/188.00 ! [V_A_2,V_B_2,V_f_2,T_c,T_b,T_a] :
% 187.18/188.00 ( class_Groups_Ocomm__monoid__mult(T_a)
% 187.18/188.00 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),T_a),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_a),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_a),T_b),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_a)),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_a),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),V_f_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))) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_Sigma__Un__distrib2,axiom,
% 187.18/188.00 ! [V_B_2,V_A_2,V_I_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),hAPP(hAPP(c_COMBS(T_a,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_a),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_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),V_B_2)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_Times__Un__distrib1,axiom,
% 187.18/188.00 ! [V_C_2,V_B_2,V_A_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_B_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_C_2))) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_Sigma__Un__distrib1,axiom,
% 187.18/188.00 ! [V_C_2,V_J_2,V_I_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,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_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),V_C_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_J_2),V_C_2)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_rel__comp__subset__Sigma,axiom,
% 187.18/188.00 ! [V_C_2,V_s_2,T_c,V_B_2,V_A_2,V_r_2,T_b,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2))))
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_s_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))))
% 187.18/188.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_b,T_c),V_r_2),V_s_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_a),V_C_2)))) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_swap__product,axiom,
% 187.18/188.00 ! [V_B_2,V_A_2,T_a,T_b] : hAPP(c_Set_Oimage(tc_prod(T_b,T_a),tc_prod(T_a,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_a,tc_prod(T_a,T_b)),hAPP(c_COMBC(T_a,T_b,tc_prod(T_a,T_b)),c_Product__Type_OPair(T_a,T_b)))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_b),V_B_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_B_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_A_2)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_finite__cartesian__product,axiom,
% 187.18/188.00 ! [V_B_2,T_b,V_A_2,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 187.18/188.00 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2)))) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_equiv__type,axiom,
% 187.18/188.00 ! [V_r_2,V_A_2,T_a] :
% 187.18/188.00 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 187.18/188.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2)))) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_Sigma__Int__distrib1,axiom,
% 187.18/188.00 ! [V_C_2,V_J_2,V_I_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,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_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),V_C_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_J_2),V_C_2)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_Times__Int__distrib1,axiom,
% 187.18/188.00 ! [V_C_2,V_B_2,V_A_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_B_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_C_2))) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_Sigma__Int__distrib2,axiom,
% 187.18/188.00 ! [V_B_2,V_A_2,V_I_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),hAPP(hAPP(c_COMBS(T_a,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_a),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_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),V_B_2)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_Id__on__subset__Times,axiom,
% 187.18/188.00 ! [V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Relation_OId__on(T_a,V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2)))) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_Sigma__Diff__distrib2,axiom,
% 187.18/188.00 ! [V_B_2,V_A_2,V_I_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),hAPP(hAPP(c_COMBS(T_a,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_a),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(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),V_B_2)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_Times__Diff__distrib1,axiom,
% 187.18/188.00 ! [V_C_2,V_B_2,V_A_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_C_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_B_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_C_2))) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_Sigma__Diff__distrib1,axiom,
% 187.18/188.00 ! [V_C_2,V_J_2,V_I_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_J_2)),V_C_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),V_C_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_J_2),V_C_2)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_DomainP_Oequations,axiom,
% 187.18/188.00 ! [V_a1_2,V_r_2,T_b,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(c_Predicate_ODomainP(T_a,T_b,V_r_2),V_a1_2))
% 187.18/188.00 <=> ? [B_x1] : hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_x1)) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_UNIV__Times__UNIV,axiom,
% 187.18/188.00 ! [T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_SigmaE2,axiom,
% 187.18/188.00 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_b,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2)))
% 187.18/188.00 => ~ ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 187.18/188.00 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_SigmaD2,axiom,
% 187.18/188.00 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_b,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2)))
% 187.18/188.00 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_SigmaD1,axiom,
% 187.18/188.00 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_b,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2)))
% 187.18/188.00 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_mem__Sigma__iff,axiom,
% 187.18/188.00 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_b,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2)))
% 187.18/188.00 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 187.18/188.00 & hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_card__cartesian__product__singleton,axiom,
% 187.18/188.00 ! [V_A_2,V_x_2,T_b,T_a] : hAPP(c_Finite__Set_Ocard(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_A_2))) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_Times__subset__cancel2,axiom,
% 187.18/188.00 ! [V_B_2,V_A_2,T_b,V_C_2,V_x_2,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_C_2))
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_b),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_a),V_B_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_b),V_C_2))))
% 187.18/188.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_Image__subset,axiom,
% 187.18/188.00 ! [V_C_2,V_B_2,V_A_2,V_r_2,T_b,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2))))
% 187.18/188.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_b,V_r_2),V_C_2)),V_B_2)) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_finite__cartesian__productD1,axiom,
% 187.18/188.00 ! [V_B_2,V_A_2,T_b,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2))))
% 187.18/188.00 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 187.18/188.00 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_finite__cartesian__productD2,axiom,
% 187.18/188.00 ! [V_B_2,V_A_2,T_b,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2))))
% 187.18/188.00 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/188.00 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_SetCompr__Sigma__eq,axiom,
% 187.18/188.00 ! [V_Q_2,V_P_2,T_b,T_a] : hAPP(c_Set_OCollect(tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBS(T_a,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_a),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_a),c_fconj),V_P_2))),V_Q_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(c_Set_OCollect(T_a),V_P_2)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),c_Set_OCollect(T_b)),V_Q_2)) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_Collect__split,axiom,
% 187.18/188.00 ! [V_Q_2,V_P_2,T_b,T_a] : hAPP(c_Set_OCollect(tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,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_a),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_a),c_fconj),V_P_2))),V_Q_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(c_Set_OCollect(T_a),V_P_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Set_OCollect(T_b),V_Q_2))) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_fst__image__times,axiom,
% 187.18/188.00 ! [V_A_2,T_b,T_a,V_B_2] :
% 187.18/188.00 ( ( V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/188.00 => hAPP(c_Set_Oimage(tc_prod(T_b,T_a),T_b,c_Product__Type_Ofst(T_b,T_a)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_b),V_B_2))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
% 187.18/188.00 & ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/188.00 => hAPP(c_Set_Oimage(tc_prod(T_b,T_a),T_b,c_Product__Type_Ofst(T_b,T_a)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_b),V_B_2))) = V_A_2 ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_snd__image__times,axiom,
% 187.18/188.00 ! [V_B_2,T_b,T_a,V_A_2] :
% 187.18/188.00 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/188.00 => hAPP(c_Set_Oimage(tc_prod(T_a,T_b),T_b,c_Product__Type_Osnd(T_a,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
% 187.18/188.00 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/188.00 => hAPP(c_Set_Oimage(tc_prod(T_a,T_b),T_b,c_Product__Type_Osnd(T_a,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2))) = V_B_2 ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_insert__times__insert,axiom,
% 187.18/188.00 ! [V_B_2,V_b_2,V_A_2,V_a_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2)))),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2)))) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_finite__equiv__class,axiom,
% 187.18/188.00 ! [V_X_2,V_r_2,V_A_2,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2))))
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2)))
% 187.18/188.00 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_X_2)) ) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_UN__Times__distrib,axiom,
% 187.18/188.00 ! [V_Fa_2,V_E_2,V_B_2,V_A_2,T_b,T_a,T_d,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(T_c,T_d),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),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(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),tc_fun(T_d,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),tc_fun(tc_fun(T_d,tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),tc_fun(T_d,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))),T_c),c_COMBB(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),T_c),c_Product__Type_OSigma(T_a,T_b)),V_E_2))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),T_d),c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a)),V_Fa_2)))) = hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_E_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_Fa_2))) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_Sigma__def,axiom,
% 187.18/188.00 ! [V_B_2,V_A_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBS(T_a,tc_fun(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),T_a),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))),V_B_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),T_b),c_Set_Oinsert(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))))) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_finite__quotient,axiom,
% 187.18/188.00 ! [V_r_2,V_A_2,T_a] :
% 187.18/188.00 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2))))
% 187.18/188.00 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2))) ) ) ).
% 187.18/188.00
% 187.18/188.00 fof(fact_setsum__mult__setsum__if__inj,axiom,
% 187.18/188.01 ! [V_B_2,V_A_2,V_g_2,V_f_2,T_b,T_a,T_c] :
% 187.18/188.01 ( class_Rings_Osemiring__0(T_c)
% 187.18/188.01 => ( c_Fun_Oinj__on(tc_prod(T_a,T_b),T_c,hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,T_c),tc_fun(T_b,T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_c),tc_fun(tc_fun(T_b,T_c),tc_fun(T_b,T_c)),T_a),c_COMBB(T_c,T_c,T_b)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_a),c_Groups_Otimes__class_Otimes(T_c)),V_f_2))),V_g_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2)))
% 187.18/188.01 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,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_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_c),c_Fun_Oid(T_c)),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool),T_c),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_b))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),T_c),c_COMBS(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),T_c),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_a),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_c),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),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_a,tc_fun(T_b,T_c)),tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_fun(T_b,T_c)),tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),T_c),c_COMBB(tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool),T_a)),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))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,T_c),tc_fun(T_b,T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_c),tc_fun(tc_fun(T_b,T_c),tc_fun(T_b,T_c)),T_a),c_COMBB(T_c,T_c,T_b)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_a),c_Groups_Otimes__class_Otimes(T_c)),V_f_2))),V_g_2)))))),hAPP(hAPP(c_COMBC(T_a,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_a),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_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),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))))))) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Ex__inj__on__UNION__Sigma,axiom,
% 187.18/188.01 ! [V_A_2,V_I_2,T_b,T_a] :
% 187.18/188.01 ? [B_f] :
% 187.18/188.01 ( c_Fun_Oinj__on(T_a,tc_prod(T_b,T_a),B_f,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2))
% 187.18/188.01 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,tc_prod(T_b,T_a),B_f),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_a),V_I_2),V_A_2))) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_fold__image__Sigma,axiom,
% 187.18/188.01 ! [V_g_2,V_B_2,T_b,V_A_2,T_a,T_c] :
% 187.18/188.01 ( class_Groups_Ocomm__monoid__mult(T_c)
% 187.18/188.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.01 => ( ! [B_x] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 187.18/188.01 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) )
% 187.18/188.01 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_a,c_Groups_Otimes__class_Otimes(T_c)),hAPP(hAPP(c_COMBS(T_a,tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(hAPP(c_COMBC(T_a,T_c,tc_fun(tc_fun(T_b,tc_HOL_Obool),T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_c),tc_fun(T_c,tc_fun(tc_fun(T_b,tc_HOL_Obool),T_c)),T_a),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)),c_Groups_Oone__class_Oone(T_c)),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,tc_prod(T_a,T_b),c_Groups_Otimes__class_Otimes(T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),V_g_2)),c_Groups_Oone__class_Oone(T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2)) ) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_image__id,axiom,
% 187.18/188.01 ! [V_Y_2,T_a] : hAPP(c_Set_Oimage(T_a,T_a,c_Fun_Oid(T_a)),V_Y_2) = V_Y_2 ).
% 187.18/188.01
% 187.18/188.01 fof(fact_inj__on__id,axiom,
% 187.18/188.01 ! [V_A_2,T_a] : c_Fun_Oinj__on(T_a,T_a,c_Fun_Oid(T_a),V_A_2) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_apfst__id,axiom,
% 187.18/188.01 ! [T_b,T_a] : c_Product__Type_Oapfst(T_a,T_a,T_b,c_Fun_Oid(T_a)) = c_Fun_Oid(tc_prod(T_a,T_b)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_apsnd__id,axiom,
% 187.18/188.01 ! [T_a,T_b] : c_Product__Type_Oapsnd(T_b,T_b,T_a,c_Fun_Oid(T_b)) = c_Fun_Oid(tc_prod(T_a,T_b)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_id__apply,axiom,
% 187.18/188.01 ! [V_x,T_a] : hAPP(c_Fun_Oid(T_a),V_x) = V_x ).
% 187.18/188.01
% 187.18/188.01 fof(fact_id__def,axiom,
% 187.18/188.01 ! [V_x_1,T_a] : hAPP(c_Fun_Oid(T_a),V_x_1) = V_x_1 ).
% 187.18/188.01
% 187.18/188.01 fof(fact_vimage__id,axiom,
% 187.18/188.01 ! [V_A_2,T_a] : hAPP(c_Set_Ovimage(T_a,T_a,c_Fun_Oid(T_a)),V_A_2) = V_A_2 ).
% 187.18/188.01
% 187.18/188.01 fof(fact_of__int__eq__id,axiom,
% 187.18/188.01 c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_surj__id,axiom,
% 187.18/188.01 ! [T_a] : hAPP(c_Set_Oimage(T_a,T_a,c_Fun_Oid(T_a)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_split__Pair,axiom,
% 187.18/188.01 ! [T_b,T_a] : hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_prod(T_a,T_b)),c_Product__Type_OPair(T_a,T_b)) = c_Fun_Oid(tc_prod(T_a,T_b)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_setsum__reindex__id,axiom,
% 187.18/188.01 ! [V_B_2,V_f_2,T_a,T_b] :
% 187.18/188.01 ( class_Groups_Ocomm__monoid__add(T_b)
% 187.18/188.01 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2)
% 187.18/188.01 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_b),c_Fun_Oid(T_b)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2)) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_setprod__reindex__id,axiom,
% 187.18/188.01 ! [V_B_2,V_f_2,T_a,T_b] :
% 187.18/188.01 ( class_Groups_Ocomm__monoid__mult(T_b)
% 187.18/188.01 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2)
% 187.18/188.01 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_b),c_Fun_Oid(T_b)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2)) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_setprod__Sigma,axiom,
% 187.18/188.01 ! [V_f_2,V_B_2,T_b,V_A_2,T_a,T_c] :
% 187.18/188.01 ( class_Groups_Ocomm__monoid__mult(T_c)
% 187.18/188.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.01 => ( ! [B_x] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 187.18/188.01 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) )
% 187.18/188.01 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_c),hAPP(hAPP(c_COMBS(T_a,tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_c),tc_fun(tc_fun(T_b,tc_HOL_Obool),T_c),T_a),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(T_a,T_b),T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2)) ) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_setsum__Sigma,axiom,
% 187.18/188.01 ! [V_f_2,V_B_2,T_b,V_A_2,T_a,T_c] :
% 187.18/188.01 ( class_Groups_Ocomm__monoid__add(T_c)
% 187.18/188.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.01 => ( ! [B_x] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 187.18/188.01 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) )
% 187.18/188.01 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_c),hAPP(hAPP(c_COMBS(T_a,tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_c),tc_fun(tc_fun(T_b,tc_HOL_Obool),T_c),T_a),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(T_a,T_b),T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2)) ) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_card__SigmaI,axiom,
% 187.18/188.01 ! [V_B_2,T_b,V_A_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.01 => ( ! [B_x] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 187.18/188.01 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) )
% 187.18/188.01 => hAPP(c_Finite__Set_Ocard(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_Nat_Onat,T_a),c_Finite__Set_Ocard(T_b)),V_B_2)),V_A_2) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_finite__SigmaI,axiom,
% 187.18/188.01 ! [V_B_2,T_b,V_A_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.01 => ( ! [B_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2))
% 187.18/188.01 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_a))) )
% 187.18/188.01 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2))) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_SigmaE,axiom,
% 187.18/188.01 ! [V_B_2,V_A_2,V_c_2,T_b,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),V_c_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2)))
% 187.18/188.01 => ~ ! [B_x] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 187.18/188.01 => ! [B_y] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),hAPP(V_B_2,B_x)))
% 187.18/188.01 => V_c_2 != hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_x),B_y) ) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_map__pair__surj,axiom,
% 187.18/188.01 ! [V_g_2,T_c,T_d,V_f_2,T_a,T_b] :
% 187.18/188.01 ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))
% 187.18/188.01 => ( hAPP(c_Set_Oimage(T_d,T_c,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))
% 187.18/188.01 => hAPP(c_Set_Oimage(tc_prod(T_b,T_d),tc_prod(T_a,T_c),c_Product__Type_Omap__pair(T_b,T_a,T_d,T_c,V_f_2,V_g_2)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool)) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_map__pair__imageI,axiom,
% 187.18/188.01 ! [V_g_2,V_f_2,T_d,T_c,V_R_2,V_b_2,V_a_2,T_b,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),V_R_2))
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),hAPP(V_f_2,V_a_2)),hAPP(V_g_2,V_b_2))),hAPP(c_Set_Oimage(tc_prod(T_a,T_b),tc_prod(T_c,T_d),c_Product__Type_Omap__pair(T_a,T_c,T_b,T_d,V_f_2,V_g_2)),V_R_2))) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_map__pair__simp,axiom,
% 187.18/188.01 ! [V_b_2,V_a_2,V_g_2,V_f_2,T_b,T_d,T_a,T_c] : hAPP(c_Product__Type_Omap__pair(T_c,T_a,T_d,T_b,V_f_2,V_g_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(V_f_2,V_a_2)),hAPP(V_g_2,V_b_2)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_map__pair__ident,axiom,
% 187.18/188.01 ! [V_z_2,T_b,T_a] : hAPP(c_Product__Type_Omap__pair(T_a,T_a,T_b,T_b,c_COMBI(T_a),c_COMBI(T_b)),V_z_2) = V_z_2 ).
% 187.18/188.01
% 187.18/188.01 fof(fact_fst__map__pair,axiom,
% 187.18/188.01 ! [V_x_2,V_g_2,V_f_2,T_d,T_c,T_b,T_a] : hAPP(c_Product__Type_Ofst(T_a,T_b),hAPP(c_Product__Type_Omap__pair(T_c,T_a,T_d,T_b,V_f_2,V_g_2),V_x_2)) = hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_x_2)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_snd__prod__fun,axiom,
% 187.18/188.01 ! [V_x_2,V_g_2,V_f_2,T_d,T_c,T_a,T_b] : hAPP(c_Product__Type_Osnd(T_b,T_a),hAPP(c_Product__Type_Omap__pair(T_c,T_b,T_d,T_a,V_f_2,V_g_2),V_x_2)) = hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_c,T_d),V_x_2)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_map__pair_Oidentity,axiom,
% 187.18/188.01 ! [T_b,T_a] : c_Product__Type_Omap__pair(T_a,T_a,T_b,T_b,c_COMBI(T_a),c_COMBI(T_b)) = c_Fun_Oid(tc_prod(T_a,T_b)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_apfst__def,axiom,
% 187.18/188.01 ! [V_f_2,T_b,T_c,T_a] : c_Product__Type_Oapfst(T_a,T_c,T_b,V_f_2) = c_Product__Type_Omap__pair(T_a,T_c,T_b,T_b,V_f_2,c_Fun_Oid(T_b)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_apsnd__def,axiom,
% 187.18/188.01 ! [V_f_2,T_a,T_c,T_b] : c_Product__Type_Oapsnd(T_b,T_c,T_a,V_f_2) = c_Product__Type_Omap__pair(T_a,T_a,T_b,T_c,c_Fun_Oid(T_a),V_f_2) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_map__pair_Oid,axiom,
% 187.18/188.01 ! [T_b,T_a] : c_Product__Type_Omap__pair(T_a,T_a,T_b,T_b,c_Fun_Oid(T_a),c_Fun_Oid(T_b)) = c_Fun_Oid(tc_prod(T_a,T_b)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_map__pair__def,axiom,
% 187.18/188.01 ! [V_g_2,V_f_2,T_d,T_b,T_c,T_a] : c_Product__Type_Omap__pair(T_a,T_c,T_b,T_d,V_f_2,V_g_2) = hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_prod(T_c,T_d)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,T_d),tc_fun(T_b,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_b,T_d),tc_fun(T_b,tc_prod(T_c,T_d))),T_a),c_COMBB(T_d,tc_prod(T_c,T_d),T_b)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_d,tc_prod(T_c,T_d)),T_a),c_Product__Type_OPair(T_c,T_d)),V_f_2))),V_g_2)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_map__pair__surj__on,axiom,
% 187.18/188.01 ! [V_B_H_2,V_B_2,V_g_2,T_c,T_d,V_A_H_2,V_A_2,V_f_2,T_a,T_b] :
% 187.18/188.01 ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2) = V_A_H_2
% 187.18/188.01 => ( hAPP(c_Set_Oimage(T_d,T_c,V_g_2),V_B_2) = V_B_H_2
% 187.18/188.01 => hAPP(c_Set_Oimage(tc_prod(T_b,T_d),tc_prod(T_a,T_c),c_Product__Type_Omap__pair(T_b,T_a,T_d,T_c,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))) = hAPP(hAPP(c_Product__Type_OSigma(T_a,T_c),V_A_H_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_a),V_B_H_2)) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_wf__map__pair__image,axiom,
% 187.18/188.01 ! [V_f_2,T_b,V_r_2,T_a] :
% 187.18/188.01 ( c_Wellfounded_Owf(T_a,V_r_2)
% 187.18/188.01 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 187.18/188.01 => c_Wellfounded_Owf(T_b,hAPP(c_Set_Oimage(tc_prod(T_a,T_a),tc_prod(T_b,T_b),c_Product__Type_Omap__pair(T_a,T_b,T_a,T_b,V_f_2,V_f_2)),V_r_2)) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_map__pair__inj__on,axiom,
% 187.18/188.01 ! [V_B_2,V_g_2,T_d,T_c,V_A_2,V_f_2,T_b,T_a] :
% 187.18/188.01 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 187.18/188.01 => ( c_Fun_Oinj__on(T_c,T_d,V_g_2,V_B_2)
% 187.18/188.01 => c_Fun_Oinj__on(tc_prod(T_a,T_c),tc_prod(T_b,T_d),c_Product__Type_Omap__pair(T_a,T_b,T_c,T_d,V_f_2,V_g_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_a),V_B_2))) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_prod__fun__imageE,axiom,
% 187.18/188.01 ! [V_R_2,V_g_2,V_f_2,T_d,T_c,V_c_2,T_b,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),V_c_2),hAPP(c_Set_Oimage(tc_prod(T_c,T_d),tc_prod(T_a,T_b),c_Product__Type_Omap__pair(T_c,T_a,T_d,T_b,V_f_2,V_g_2)),V_R_2)))
% 187.18/188.01 => ~ ! [B_x,B_y] :
% 187.18/188.01 ( V_c_2 = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_y))
% 187.18/188.01 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),B_x),B_y)),V_R_2)) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_refl__on__def,axiom,
% 187.18/188.01 ! [V_r_2,V_A_2,T_a] :
% 187.18/188.01 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2)
% 187.18/188.01 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2))))
% 187.18/188.01 & ! [B_x] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),V_r_2)) ) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_wfP__def,axiom,
% 187.18/188.01 ! [V_r_2,T_a] :
% 187.18/188.01 ( c_Wellfounded_OwfP(T_a,V_r_2)
% 187.18/188.01 <=> c_Wellfounded_Owf(T_a,hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),V_r_2))) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_wfP__empty,axiom,
% 187.18/188.01 ! [T_a] : c_Wellfounded_OwfP(T_a,hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBK(tc_HOL_Obool,T_a),c_fFalse))) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_refl__on__Id__on,axiom,
% 187.18/188.01 ! [V_A_2,T_a] : c_Relation_Orefl__on(T_a,V_A_2,c_Relation_OId__on(T_a,V_A_2)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_wfP__accp__iff,axiom,
% 187.18/188.01 ! [V_r_2,T_a] :
% 187.18/188.01 ( c_Wellfounded_OwfP(T_a,V_r_2)
% 187.18/188.01 <=> ! [B_x1] : hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),B_x1)) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_accp__wfPD,axiom,
% 187.18/188.01 ! [V_x_2,V_r_2,T_a] :
% 187.18/188.01 ( c_Wellfounded_OwfP(T_a,V_r_2)
% 187.18/188.01 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_x_2)) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_wfP__subset,axiom,
% 187.18/188.01 ! [V_p_2,V_r_2,T_a] :
% 187.18/188.01 ( c_Wellfounded_OwfP(T_a,V_r_2)
% 187.18/188.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),V_p_2),V_r_2))
% 187.18/188.01 => c_Wellfounded_OwfP(T_a,V_p_2) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_refl__on__empty,axiom,
% 187.18/188.01 ! [T_a] : c_Relation_Orefl__on(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_refl__on__Un,axiom,
% 187.18/188.01 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_a] :
% 187.18/188.01 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2)
% 187.18/188.01 => ( c_Relation_Orefl__on(T_a,V_B_2,V_s_2)
% 187.18/188.01 => c_Relation_Orefl__on(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2)) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_refl__on__Int,axiom,
% 187.18/188.01 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_a] :
% 187.18/188.01 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2)
% 187.18/188.01 => ( c_Relation_Orefl__on(T_a,V_B_2,V_s_2)
% 187.18/188.01 => c_Relation_Orefl__on(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2)) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_refl__onD,axiom,
% 187.18/188.01 ! [V_a_2,V_r_2,V_A_2,T_a] :
% 187.18/188.01 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2)
% 187.18/188.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_a_2)),V_r_2)) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_refl__onD2,axiom,
% 187.18/188.01 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] :
% 187.18/188.01 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2)
% 187.18/188.01 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2))
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_refl__onD1,axiom,
% 187.18/188.01 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] :
% 187.18/188.01 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2)
% 187.18/188.01 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2))
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_wf__in__rel,axiom,
% 187.18/188.01 ! [V_R_2,T_a] :
% 187.18/188.01 ( c_Wellfounded_Owf(T_a,V_R_2)
% 187.18/188.01 => c_Wellfounded_OwfP(T_a,c_FunDef_Oin__rel(T_a,T_a,V_R_2)) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_wfP__wf__eq,axiom,
% 187.18/188.01 ! [V_r_2,T_a] :
% 187.18/188.01 ( c_Wellfounded_OwfP(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a)))),c_Product__Type_OPair(T_a,T_a)))),V_r_2))
% 187.18/188.01 <=> c_Wellfounded_Owf(T_a,V_r_2) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_reflp__def,axiom,
% 187.18/188.01 ! [V_r_2,T_a] :
% 187.18/188.01 ( c_Predicate_Oreflp(T_a,V_r_2)
% 187.18/188.01 <=> c_Relation_Orefl__on(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),V_r_2))) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_refl__onI,axiom,
% 187.18/188.01 ! [V_A_2,V_r_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2))))
% 187.18/188.01 => ( ! [B_x] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),V_r_2)) )
% 187.18/188.01 => c_Relation_Orefl__on(T_a,V_A_2,V_r_2) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_wfP__acyclicP,axiom,
% 187.18/188.01 ! [V_r_2,T_a] :
% 187.18/188.01 ( c_Wellfounded_OwfP(T_a,V_r_2)
% 187.18/188.01 => c_Wellfounded_Oacyclic(T_a,hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),V_r_2))) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_wf__acyclic,axiom,
% 187.18/188.01 ! [V_r_2,T_a] :
% 187.18/188.01 ( c_Wellfounded_Owf(T_a,V_r_2)
% 187.18/188.01 => c_Wellfounded_Oacyclic(T_a,V_r_2) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_reflpE,axiom,
% 187.18/188.01 ! [V_x_2,V_r_2,T_a] :
% 187.18/188.01 ( c_Predicate_Oreflp(T_a,V_r_2)
% 187.18/188.01 => hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_x_2)) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_acyclic__subset,axiom,
% 187.18/188.01 ! [V_r_2,V_s_2,T_a] :
% 187.18/188.01 ( c_Wellfounded_Oacyclic(T_a,V_s_2)
% 187.18/188.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2))
% 187.18/188.01 => c_Wellfounded_Oacyclic(T_a,V_r_2) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_wf__iff__acyclic__if__finite,axiom,
% 187.18/188.01 ! [V_r_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2))
% 187.18/188.01 => ( c_Wellfounded_Owf(T_a,V_r_2)
% 187.18/188.01 <=> c_Wellfounded_Oacyclic(T_a,V_r_2) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_finite__acyclic__wf,axiom,
% 187.18/188.01 ! [V_r_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2))
% 187.18/188.01 => ( c_Wellfounded_Oacyclic(T_a,V_r_2)
% 187.18/188.01 => c_Wellfounded_Owf(T_a,V_r_2) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Nitpick_Owf_H__def,axiom,
% 187.18/188.01 ! [V_r_2,T_a] :
% 187.18/188.01 ( c_Nitpick_Owf_H(T_a,V_r_2)
% 187.18/188.01 <=> ( c_Wellfounded_Oacyclic(T_a,V_r_2)
% 187.18/188.01 & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2))
% 187.18/188.01 | c_Nitpick_Ounknown(tc_HOL_Obool) ) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Rep__Integ__cases,axiom,
% 187.18/188.01 ! [V_y_2] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg))
% 187.18/188.01 => ~ ! [B_x] : V_y_2 != hAPP(c_Int_ORep__Integ,B_x) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Rep__Integ__induct,axiom,
% 187.18/188.01 ! [V_P_2,V_y_2] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg))
% 187.18/188.01 => ( ! [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Int_ORep__Integ,B_x)))
% 187.18/188.01 => hBOOL(hAPP(V_P_2,V_y_2)) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_refl__on__def_H,axiom,
% 187.18/188.01 ! [V_r_2,V_A_2,T_a] :
% 187.18/188.01 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2)
% 187.18/188.01 <=> ( ! [B_x] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),B_x),V_r_2))
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))),B_x)) )
% 187.18/188.01 & ! [B_x] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),V_r_2)) ) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Abs__Integ__cases,axiom,
% 187.18/188.01 ! [V_x_2] :
% 187.18/188.01 ~ ! [B_y] :
% 187.18/188.01 ( V_x_2 = hAPP(c_Int_OAbs__Integ,B_y)
% 187.18/188.01 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg)) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Abs__Integ__induct,axiom,
% 187.18/188.01 ! [V_x_2,V_P_2] :
% 187.18/188.01 ( ! [B_y] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg))
% 187.18/188.01 => hBOOL(hAPP(V_P_2,hAPP(c_Int_OAbs__Integ,B_y))) )
% 187.18/188.01 => hBOOL(hAPP(V_P_2,V_x_2)) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_ball__UNIV,axiom,
% 187.18/188.01 ! [V_P_2,T_a] :
% 187.18/188.01 ( ! [B_x] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))
% 187.18/188.01 => hBOOL(hAPP(V_P_2,B_x)) )
% 187.18/188.01 <=> ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_ball__empty,axiom,
% 187.18/188.01 ! [V_P_2,T_a,B_x] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))
% 187.18/188.01 => hBOOL(hAPP(V_P_2,B_x)) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Powp__def,axiom,
% 187.18/188.01 ! [V_B_2,V_A_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(c_Predicate_OPowp(T_a,V_A_2),V_B_2))
% 187.18/188.01 <=> ! [B_x] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_B_2))
% 187.18/188.01 => hBOOL(hAPP(V_A_2,B_x)) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_congruent__def,axiom,
% 187.18/188.01 ! [V_f_2,V_r_2,T_b,T_a] :
% 187.18/188.01 ( c_Equiv__Relations_Ocongruent(T_a,T_b,V_r_2,V_f_2)
% 187.18/188.01 <=> ! [B_x] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),B_x),V_r_2))
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_b),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_b),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_b,tc_HOL_Obool,T_a)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),c_fequal),V_f_2))),V_f_2)),B_x)) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_inj__on__diff__nat,axiom,
% 187.18/188.01 ! [V_k_2,V_N_2] :
% 187.18/188.01 ( ! [B_x] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),B_x)) )
% 187.18/188.01 => 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) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_wfP__SUP,axiom,
% 187.18/188.01 ! [T_a,V_r_2,T_b] :
% 187.18/188.01 ( ! [B_i] : c_Wellfounded_OwfP(T_b,hAPP(V_r_2,B_i))
% 187.18/188.01 => ( ! [B_i,B_j] :
% 187.18/188.01 ( hAPP(V_r_2,B_i) != hAPP(V_r_2,B_j)
% 187.18/188.01 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Predicate_ODomainP(T_b,T_b,hAPP(V_r_2,B_i))),c_Predicate_ORangeP(T_b,T_b,hAPP(V_r_2,B_j))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
% 187.18/188.01 => c_Wellfounded_OwfP(T_b,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),V_r_2)) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_mem__splitE,axiom,
% 187.18/188.01 ! [V_p_2,V_c_2,T_c,T_b,V_z_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(T_a,tc_HOL_Obool)),V_c_2),V_p_2)))
% 187.18/188.01 => ~ ! [B_x,B_y] :
% 187.18/188.01 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_y)
% 187.18/188.01 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(hAPP(V_c_2,B_x),B_y))) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_triples__valid__Suc,axiom,
% 187.18/188.01 ! [V_n_2,V_ts_2,T_a] :
% 187.18/188.01 ( ! [B_x] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_a)),B_x),V_ts_2))
% 187.18/188.01 => c_Hoare__Mirabelle_Otriple__valid(T_a,hAPP(c_Nat_OSuc,V_n_2),B_x) )
% 187.18/188.01 => ! [B_x] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_a)),B_x),V_ts_2))
% 187.18/188.01 => c_Hoare__Mirabelle_Otriple__valid(T_a,V_n_2,B_x) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_hoare__valids__def,axiom,
% 187.18/188.01 ! [V_ts_2,V_G_2,T_a] :
% 187.18/188.01 ( c_Hoare__Mirabelle_Ohoare__valids(T_a,V_G_2,V_ts_2)
% 187.18/188.01 <=> ! [B_n] :
% 187.18/188.01 ( ! [B_x] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_a)),B_x),V_G_2))
% 187.18/188.01 => c_Hoare__Mirabelle_Otriple__valid(T_a,B_n,B_x) )
% 187.18/188.01 => ! [B_x] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_a)),B_x),V_ts_2))
% 187.18/188.01 => c_Hoare__Mirabelle_Otriple__valid(T_a,B_n,B_x) ) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_mem__splitI2,axiom,
% 187.18/188.01 ! [V_c_2,V_z_2,T_c,T_b,T_a,V_p_2] :
% 187.18/188.01 ( ! [B_a,B_b] :
% 187.18/188.01 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_a),B_b)
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_member(T_c),V_z_2),hAPP(hAPP(V_c_2,B_a),B_b))) )
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_member(T_c),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_fun(T_c,tc_HOL_Obool)),V_c_2),V_p_2))) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_vimage__Times,axiom,
% 187.18/188.01 ! [V_B_2,V_A_2,V_f_2,T_c,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,tc_prod(T_b,T_c),V_f_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))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_a,T_b,hAPP(c_Fun_Ocomp(tc_prod(T_b,T_c),T_b,T_a,c_Product__Type_Ofst(T_b,T_c)),V_f_2)),V_A_2)),hAPP(c_Set_Ovimage(T_a,T_c,hAPP(c_Fun_Ocomp(tc_prod(T_b,T_c),T_c,T_a,c_Product__Type_Osnd(T_b,T_c)),V_f_2)),V_B_2)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Eps__split,axiom,
% 187.18/188.01 ! [V_P_2,T_b,T_a] : c_Hilbert__Choice_OEps(tc_prod(T_a,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_P_2)) = c_Hilbert__Choice_OEps(tc_prod(T_a,T_b),hAPP(hAPP(c_COMBS(tc_prod(T_a,T_b),T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_b,tc_HOL_Obool),tc_prod(T_a,T_b)),V_P_2),c_Product__Type_Ofst(T_a,T_b))),c_Product__Type_Osnd(T_a,T_b))) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_o__eq__id__dest,axiom,
% 187.18/188.01 ! [V_v_2,V_c_2,V_b_2,V_a_2,T_a,T_b,T_c] :
% 187.18/188.01 ( hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_a_2),V_b_2) = hAPP(c_Fun_Ocomp(T_b,T_b,T_a,c_Fun_Oid(T_b)),V_c_2)
% 187.18/188.01 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,V_v_2) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_id__o,axiom,
% 187.18/188.01 ! [V_g_2,T_a,T_b] : hAPP(c_Fun_Ocomp(T_b,T_b,T_a,c_Fun_Oid(T_b)),V_g_2) = V_g_2 ).
% 187.18/188.01
% 187.18/188.01 fof(fact_o__id,axiom,
% 187.18/188.01 ! [V_f_2,T_b,T_a] : hAPP(c_Fun_Ocomp(T_a,T_b,T_a,V_f_2),c_Fun_Oid(T_a)) = V_f_2 ).
% 187.18/188.01
% 187.18/188.01 fof(fact_apfst__compose,axiom,
% 187.18/188.01 ! [V_x_2,V_g_2,T_d,V_f_2,T_b,T_a,T_c] : hAPP(c_Product__Type_Oapfst(T_c,T_a,T_b,V_f_2),hAPP(c_Product__Type_Oapfst(T_d,T_c,T_b,V_g_2),V_x_2)) = hAPP(c_Product__Type_Oapfst(T_d,T_a,T_b,hAPP(c_Fun_Ocomp(T_c,T_a,T_d,V_f_2),V_g_2)),V_x_2) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_apsnd__compose,axiom,
% 187.18/188.01 ! [V_x_2,V_g_2,T_d,V_f_2,T_a,T_b,T_c] : hAPP(c_Product__Type_Oapsnd(T_c,T_b,T_a,V_f_2),hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_a,V_g_2),V_x_2)) = hAPP(c_Product__Type_Oapsnd(T_d,T_b,T_a,hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2)),V_x_2) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_fun__left__comm__idem_Ofun__comp__idem,axiom,
% 187.18/188.01 ! [V_x_2,V_f_2,T_b,T_a] :
% 187.18/188.01 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2)
% 187.18/188.01 => hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_x_2)) = hAPP(V_f_2,V_x_2) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_K__record__comp,axiom,
% 187.18/188.01 ! [V_x_2,V_f_2,V_c_2,T_c,T_a,T_b] : hAPP(hAPP(c_Fun_Ocomp(T_b,T_a,T_c,hAPP(c_COMBK(T_a,T_b),V_c_2)),V_f_2),V_x_2) = V_c_2 ).
% 187.18/188.01
% 187.18/188.01 fof(fact_o__eq__dest__lhs,axiom,
% 187.18/188.01 ! [V_v_2,V_c_2,V_b_2,V_a_2,T_a,T_b,T_c] :
% 187.18/188.01 ( hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_a_2),V_b_2) = V_c_2
% 187.18/188.01 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,V_v_2) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_fun__upd__comp,axiom,
% 187.18/188.01 ! [V_y_2,V_x_2,V_g_2,V_f_2,T_a,T_b,T_c] : hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_f_2),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_c),V_g_2),V_x_2),V_y_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_f_2),V_g_2)),V_x_2),hAPP(V_f_2,V_y_2)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_comp__cong,axiom,
% 187.18/188.01 ! [T_e,T_d,T_c,T_a,T_b,V_x_H_2,V_g_H_2,V_f_H_2,V_x_2,V_g_2,V_f_2] :
% 187.18/188.01 ( hAPP(V_f_2,hAPP(V_g_2,V_x_2)) = hAPP(V_f_H_2,hAPP(V_g_H_2,V_x_H_2))
% 187.18/188.01 => hAPP(hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Fun_Ocomp(T_d,T_a,T_e,V_f_H_2),V_g_H_2),V_x_H_2) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_o__assoc,axiom,
% 187.18/188.01 ! [V_h_2,V_g_2,T_d,V_f_2,T_a,T_b,T_c] : hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_f_2),hAPP(c_Fun_Ocomp(T_d,T_c,T_a,V_g_2),V_h_2)) = hAPP(c_Fun_Ocomp(T_d,T_b,T_a,hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2)),V_h_2) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_o__apply,axiom,
% 187.18/188.01 ! [V_x_2,V_g_2,V_f_2,T_c,T_a,T_b] : hAPP(hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_f_2),V_g_2),V_x_2) = hAPP(V_f_2,hAPP(V_g_2,V_x_2)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_o__eq__dest,axiom,
% 187.18/188.01 ! [V_v_2,V_d_2,V_c_2,T_d,V_b_2,V_a_2,T_a,T_b,T_c] :
% 187.18/188.01 ( hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_a_2),V_b_2) = hAPP(c_Fun_Ocomp(T_d,T_b,T_a,V_c_2),V_d_2)
% 187.18/188.01 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,hAPP(V_d_2,V_v_2)) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_o__eq__elim,axiom,
% 187.18/188.01 ! [V_d_2,V_c_2,T_d,V_b_2,V_a_2,T_a,T_b,T_c] :
% 187.18/188.01 ( hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_a_2),V_b_2) = hAPP(c_Fun_Ocomp(T_d,T_b,T_a,V_c_2),V_d_2)
% 187.18/188.01 => ! [B_v] : hAPP(V_a_2,hAPP(V_b_2,B_v)) = hAPP(V_c_2,hAPP(V_d_2,B_v)) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_o__def,axiom,
% 187.18/188.01 ! [V_x_2,V_g_2,V_f_2,T_c,T_a,T_b] : hAPP(hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_f_2),V_g_2),V_x_2) = hAPP(V_f_2,hAPP(V_g_2,V_x_2)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_someI__ex,axiom,
% 187.18/188.01 ! [T_a,V_P_2] :
% 187.18/188.01 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 187.18/188.01 => hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_a,V_P_2))) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_some__eq__ex,axiom,
% 187.18/188.01 ! [T_a,V_P_2] :
% 187.18/188.01 ( hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_a,V_P_2)))
% 187.18/188.01 <=> ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_some__eq__trivial,axiom,
% 187.18/188.01 ! [V_x_2,T_a] : c_Hilbert__Choice_OEps(T_a,hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_x_2)) = V_x_2 ).
% 187.18/188.01
% 187.18/188.01 fof(fact_some__sym__eq__trivial,axiom,
% 187.18/188.01 ! [V_x_2,T_a] : c_Hilbert__Choice_OEps(T_a,hAPP(c_fequal,V_x_2)) = V_x_2 ).
% 187.18/188.01
% 187.18/188.01 fof(fact_tfl__some,axiom,
% 187.18/188.01 ! [T_a,B_P] :
% 187.18/188.01 ( ? [B_x] : hBOOL(hAPP(B_P,B_x))
% 187.18/188.01 => hBOOL(hAPP(B_P,c_Hilbert__Choice_OEps(T_a,B_P))) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_someI,axiom,
% 187.18/188.01 ! [T_a,V_x_2,V_P_2] :
% 187.18/188.01 ( hBOOL(hAPP(V_P_2,V_x_2))
% 187.18/188.01 => hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_a,V_P_2))) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_exE__some,axiom,
% 187.18/188.01 ! [T_a,V_c_2,V_P_2] :
% 187.18/188.01 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 187.18/188.01 => ( V_c_2 = c_Hilbert__Choice_OEps(T_a,V_P_2)
% 187.18/188.01 => hBOOL(hAPP(V_P_2,V_c_2)) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_vimage__compose,axiom,
% 187.18/188.01 ! [V_x_2,V_f_2,V_g_2,T_c,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_g_2),V_f_2)),V_x_2) = hAPP(c_Set_Ovimage(T_a,T_c,V_f_2),hAPP(c_Set_Ovimage(T_c,T_b,V_g_2),V_x_2)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_inj__comp,axiom,
% 187.18/188.01 ! [V_g_2,T_c,V_f_2,T_b,T_a] :
% 187.18/188.01 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 187.18/188.01 => ( c_Fun_Oinj__on(T_c,T_a,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 187.18/188.01 => c_Fun_Oinj__on(T_c,T_b,hAPP(c_Fun_Ocomp(T_a,T_b,T_c,V_f_2),V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_inj__on__imageI2,axiom,
% 187.18/188.01 ! [V_A_2,V_f_2,V_f_H_2,T_c,T_b,T_a] :
% 187.18/188.01 ( c_Fun_Oinj__on(T_a,T_b,hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_f_H_2),V_f_2),V_A_2)
% 187.18/188.01 => c_Fun_Oinj__on(T_a,T_c,V_f_2,V_A_2) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_comp__surj,axiom,
% 187.18/188.01 ! [V_g_2,T_c,V_f_2,T_a,T_b] :
% 187.18/188.01 ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))
% 187.18/188.01 => ( hAPP(c_Set_Oimage(T_a,T_c,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))
% 187.18/188.01 => hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_Fun_Ocomp(T_a,T_c,T_b,V_g_2),V_f_2)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_image__compose,axiom,
% 187.18/188.01 ! [V_r_2,V_g_2,V_f_2,T_c,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,hAPP(c_Fun_Ocomp(T_c,T_a,T_b,V_f_2),V_g_2)),V_r_2) = hAPP(c_Set_Oimage(T_c,T_a,V_f_2),hAPP(c_Set_Oimage(T_b,T_c,V_g_2),V_r_2)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_inj__on__imageI,axiom,
% 187.18/188.01 ! [V_A_2,V_f_2,V_g_2,T_c,T_b,T_a] :
% 187.18/188.01 ( c_Fun_Oinj__on(T_a,T_b,hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_g_2),V_f_2),V_A_2)
% 187.18/188.01 => c_Fun_Oinj__on(T_c,T_b,V_g_2,hAPP(c_Set_Oimage(T_a,T_c,V_f_2),V_A_2)) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_comp__inj__on,axiom,
% 187.18/188.01 ! [V_g_2,T_c,V_A_2,V_f_2,T_b,T_a] :
% 187.18/188.01 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 187.18/188.01 => ( c_Fun_Oinj__on(T_b,T_c,V_g_2,hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))
% 187.18/188.01 => c_Fun_Oinj__on(T_a,T_c,hAPP(c_Fun_Ocomp(T_b,T_c,T_a,V_g_2),V_f_2),V_A_2) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_comp__inj__on__iff,axiom,
% 187.18/188.01 ! [V_f_H_2,T_c,V_A_2,V_f_2,T_b,T_a] :
% 187.18/188.01 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 187.18/188.01 => ( c_Fun_Oinj__on(T_b,T_c,V_f_H_2,hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))
% 187.18/188.01 <=> c_Fun_Oinj__on(T_a,T_c,hAPP(c_Fun_Ocomp(T_b,T_c,T_a,V_f_H_2),V_f_2),V_A_2) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_map__pair_Ocompositionality,axiom,
% 187.18/188.01 ! [V_prod_2,V_i_2,V_h_2,T_f,T_e,V_g_2,V_f_2,T_b,T_d,T_a,T_c] : hAPP(c_Product__Type_Omap__pair(T_c,T_a,T_d,T_b,V_f_2,V_g_2),hAPP(c_Product__Type_Omap__pair(T_e,T_c,T_f,T_d,V_h_2,V_i_2),V_prod_2)) = hAPP(c_Product__Type_Omap__pair(T_e,T_a,T_f,T_b,hAPP(c_Fun_Ocomp(T_c,T_a,T_e,V_f_2),V_h_2),hAPP(c_Fun_Ocomp(T_d,T_b,T_f,V_g_2),V_i_2)),V_prod_2) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_map__pair__compose,axiom,
% 187.18/188.01 ! [V_g2_2,V_g1_2,T_f,V_f2_2,V_f1_2,T_e,T_d,T_b,T_c,T_a] : c_Product__Type_Omap__pair(T_a,T_c,T_b,T_d,hAPP(c_Fun_Ocomp(T_e,T_c,T_a,V_f1_2),V_f2_2),hAPP(c_Fun_Ocomp(T_f,T_d,T_b,V_g1_2),V_g2_2)) = hAPP(c_Fun_Ocomp(tc_prod(T_e,T_f),tc_prod(T_c,T_d),tc_prod(T_a,T_b),c_Product__Type_Omap__pair(T_e,T_c,T_f,T_d,V_f1_2,V_g1_2)),c_Product__Type_Omap__pair(T_a,T_e,T_b,T_f,V_f2_2,V_g2_2)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_map__pair_Ocomp,axiom,
% 187.18/188.01 ! [V_i_2,V_h_2,V_g_2,V_f_2,T_b,T_a,T_d,T_c,T_f,T_e] : hAPP(c_Fun_Ocomp(tc_prod(T_e,T_f),tc_prod(T_c,T_d),tc_prod(T_a,T_b),c_Product__Type_Omap__pair(T_e,T_c,T_f,T_d,V_f_2,V_g_2)),c_Product__Type_Omap__pair(T_a,T_e,T_b,T_f,V_h_2,V_i_2)) = c_Product__Type_Omap__pair(T_a,T_c,T_b,T_d,hAPP(c_Fun_Ocomp(T_e,T_c,T_a,V_f_2),V_h_2),hAPP(c_Fun_Ocomp(T_f,T_d,T_b,V_g_2),V_i_2)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_setsum__reindex,axiom,
% 187.18/188.01 ! [V_h_2,V_B_2,V_f_2,T_b,T_a,T_c] :
% 187.18/188.01 ( class_Groups_Ocomm__monoid__add(T_c)
% 187.18/188.01 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2)
% 187.18/188.01 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_h_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_c),hAPP(c_Fun_Ocomp(T_b,T_c,T_a,V_h_2),V_f_2)),V_B_2) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_setprod__reindex__cong,axiom,
% 187.18/188.01 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a,T_c] :
% 187.18/188.01 ( class_Groups_Ocomm__monoid__mult(T_c)
% 187.18/188.01 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 187.18/188.01 => ( V_B_2 = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)
% 187.18/188.01 => ( V_g_2 = hAPP(c_Fun_Ocomp(T_b,T_c,T_a,V_h_2),V_f_2)
% 187.18/188.01 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_h_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_c),V_g_2),V_A_2) ) ) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_setprod__reindex,axiom,
% 187.18/188.01 ! [V_h_2,V_B_2,V_f_2,T_b,T_a,T_c] :
% 187.18/188.01 ( class_Groups_Ocomm__monoid__mult(T_c)
% 187.18/188.01 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2)
% 187.18/188.01 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_h_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_c),hAPP(c_Fun_Ocomp(T_b,T_c,T_a,V_h_2),V_f_2)),V_B_2) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_split__paired__Eps,axiom,
% 187.18/188.01 ! [V_P_2,T_b,T_a] : c_Hilbert__Choice_OEps(tc_prod(T_a,T_b),V_P_2) = c_Hilbert__Choice_OEps(tc_prod(T_a,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_HOL_Obool,T_b),V_P_2)),c_Product__Type_OPair(T_a,T_b)))) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Eps__split__eq,axiom,
% 187.18/188.01 ! [V_y_2,V_x_2,T_b,T_a] : c_Hilbert__Choice_OEps(tc_prod(T_a,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,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_a),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_a),c_fconj),hAPP(c_fequal,V_x_2)))),hAPP(c_fequal,V_y_2)))) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_setsum_Oreindex,axiom,
% 187.18/188.01 ! [V_g_2,V_h_2,V_A_2,T_a,T_b] :
% 187.18/188.01 ( class_Groups_Ocomm__monoid__add(T_b)
% 187.18/188.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.01 => ( c_Fun_Oinj__on(T_a,T_a,V_h_2,V_A_2)
% 187.18/188.01 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(c_Set_Oimage(T_a,T_a,V_h_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),hAPP(c_Fun_Ocomp(T_a,T_b,T_a,V_g_2),V_h_2)),V_A_2) ) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_setprod_Oreindex,axiom,
% 187.18/188.01 ! [V_g_2,V_h_2,V_A_2,T_a,T_b] :
% 187.18/188.01 ( class_Groups_Ocomm__monoid__mult(T_b)
% 187.18/188.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.01 => ( c_Fun_Oinj__on(T_a,T_a,V_h_2,V_A_2)
% 187.18/188.01 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(c_Set_Oimage(T_a,T_a,V_h_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(c_Fun_Ocomp(T_a,T_b,T_a,V_g_2),V_h_2)),V_A_2) ) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_the__inv__into__comp,axiom,
% 187.18/188.01 ! [V_x_2,V_A_2,V_g_2,T_c,V_f_2,T_b,T_a] :
% 187.18/188.01 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(c_Set_Oimage(T_c,T_a,V_g_2),V_A_2))
% 187.18/188.01 => ( c_Fun_Oinj__on(T_c,T_a,V_g_2,V_A_2)
% 187.18/188.01 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(c_Set_Oimage(T_c,T_a,V_g_2),V_A_2))))
% 187.18/188.01 => hAPP(c_Fun_Othe__inv__into(T_c,T_b,V_A_2,hAPP(c_Fun_Ocomp(T_a,T_b,T_c,V_f_2),V_g_2)),V_x_2) = hAPP(hAPP(c_Fun_Ocomp(T_a,T_c,T_b,c_Fun_Othe__inv__into(T_c,T_a,V_A_2,V_g_2)),c_Fun_Othe__inv__into(T_a,T_b,hAPP(c_Set_Oimage(T_c,T_a,V_g_2),V_A_2),V_f_2)),V_x_2) ) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_fold__image__reindex,axiom,
% 187.18/188.01 ! [V_z_2,V_g_2,V_h_2,T_b,V_A_2,T_a,T_c] :
% 187.18/188.01 ( class_Groups_Oab__semigroup__mult(T_c)
% 187.18/188.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.01 => ( c_Fun_Oinj__on(T_a,T_b,V_h_2,V_A_2)
% 187.18/188.01 => 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(c_Set_Oimage(T_a,T_b,V_h_2),V_A_2)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_a,c_Groups_Otimes__class_Otimes(T_c)),hAPP(c_Fun_Ocomp(T_b,T_c,T_a,V_g_2),V_h_2)),V_z_2),V_A_2) ) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_LeastM__def,axiom,
% 187.18/188.01 ! [V_P_2,V_m_2,T_a,T_b] :
% 187.18/188.01 ( class_Orderings_Oord(T_b)
% 187.18/188.01 => c_Hilbert__Choice_OLeastM(T_a,T_b,V_m_2,V_P_2) = c_Hilbert__Choice_OEps(T_a,hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),V_P_2)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OAll(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fimplies),V_P_2))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_b),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_b),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_b,tc_HOL_Obool,T_a)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),c_Orderings_Oord__class_Oless__eq(T_b)),V_m_2))),V_m_2))))) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_GreatestM__def,axiom,
% 187.18/188.01 ! [V_P_2,V_m_2,T_a,T_b] :
% 187.18/188.01 ( class_Orderings_Oord(T_b)
% 187.18/188.01 => hAPP(c_Hilbert__Choice_OGreatestM(T_a,T_b,V_m_2),V_P_2) = c_Hilbert__Choice_OEps(T_a,hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),V_P_2)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OAll(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fimplies),V_P_2))),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBC(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),c_Orderings_Oord__class_Oless__eq(T_b)),V_m_2))),V_m_2))))) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_folding_Oremove,axiom,
% 187.18/188.01 ! [V_x_2,V_A_2,V_Fa_2,V_f_2,T_b,T_a] :
% 187.18/188.01 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_Fa_2)
% 187.18/188.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 187.18/188.01 => hAPP(V_Fa_2,V_A_2) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_Fa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),hAPP(V_f_2,V_x_2)) ) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_folding_Ocommute__comps_I1_J,axiom,
% 187.18/188.01 ! [V_h_2,V_g_2,T_f,V_f_2,T_c,T_d,T_e,V_Fa_2,V_fa_2,T_b,T_a] :
% 187.18/188.01 ( c_Finite__Set_Ofolding(T_a,T_b,V_fa_2,V_Fa_2)
% 187.18/188.01 => hAPP(c_Fun_Ocomp(T_e,T_d,T_c,V_f_2),hAPP(c_Fun_Ocomp(T_f,T_e,T_c,V_g_2),V_h_2)) = hAPP(c_Fun_Ocomp(T_f,T_d,T_c,hAPP(c_Fun_Ocomp(T_e,T_d,T_f,V_f_2),V_g_2)),V_h_2) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_folding_Ocommute__comp,axiom,
% 187.18/188.01 ! [V_x_2,V_y_2,V_Fa_2,V_f_2,T_b,T_a] :
% 187.18/188.01 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_Fa_2)
% 187.18/188.01 => hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_f_2,V_y_2)),hAPP(V_f_2,V_x_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_folding_Ocommute__left__comp,axiom,
% 187.18/188.01 ! [V_g_2,V_x_2,V_y_2,T_c,V_Fa_2,V_f_2,T_b,T_a] :
% 187.18/188.01 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_Fa_2)
% 187.18/188.01 => hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_f_2,V_y_2)),hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_f_2,V_x_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_f_2,V_x_2)),hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_f_2,V_y_2)),V_g_2)) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_UN__o,axiom,
% 187.18/188.01 ! [V_f_2,V_g_2,T_c,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Fun_Ocomp(T_c,tc_fun(T_a,tc_HOL_Obool),T_b,V_g_2),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),V_g_2) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_fst__comp__map__pair,axiom,
% 187.18/188.01 ! [V_g_2,V_f_2,T_b,T_a,T_d,T_c] : hAPP(c_Fun_Ocomp(tc_prod(T_c,T_d),T_c,tc_prod(T_a,T_b),c_Product__Type_Ofst(T_c,T_d)),c_Product__Type_Omap__pair(T_a,T_c,T_b,T_d,V_f_2,V_g_2)) = hAPP(c_Fun_Ocomp(T_a,T_c,tc_prod(T_a,T_b),V_f_2),c_Product__Type_Ofst(T_a,T_b)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_snd__comp__map__pair,axiom,
% 187.18/188.01 ! [V_g_2,V_f_2,T_b,T_a,T_c,T_d] : hAPP(c_Fun_Ocomp(tc_prod(T_d,T_c),T_c,tc_prod(T_a,T_b),c_Product__Type_Osnd(T_d,T_c)),c_Product__Type_Omap__pair(T_a,T_d,T_b,T_c,V_f_2,V_g_2)) = hAPP(c_Fun_Ocomp(T_b,T_c,tc_prod(T_a,T_b),V_g_2),c_Product__Type_Osnd(T_a,T_b)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_LeastM__nat__lemma,axiom,
% 187.18/188.01 ! [V_m_2,T_a,V_k_2,V_P_2] :
% 187.18/188.01 ( hBOOL(hAPP(V_P_2,V_k_2))
% 187.18/188.01 => ( hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OLeastM(T_a,tc_Nat_Onat,V_m_2,V_P_2)))
% 187.18/188.01 & ! [B_y] :
% 187.18/188.01 ( hBOOL(hAPP(V_P_2,B_y))
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_m_2,c_Hilbert__Choice_OLeastM(T_a,tc_Nat_Onat,V_m_2,V_P_2))),hAPP(V_m_2,B_y))) ) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_LeastM__nat__le,axiom,
% 187.18/188.01 ! [T_a,V_m_2,V_x_2,V_P_2] :
% 187.18/188.01 ( hBOOL(hAPP(V_P_2,V_x_2))
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_m_2,c_Hilbert__Choice_OLeastM(T_a,tc_Nat_Onat,V_m_2,V_P_2))),hAPP(V_m_2,V_x_2))) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_split__comp,axiom,
% 187.18/188.01 ! [V_x_2,V_g_2,V_f_2,T_d,T_a,T_c,T_b] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),hAPP(c_Fun_Ocomp(T_d,tc_fun(T_c,T_a),T_b,V_f_2),V_g_2)),V_x_2) = hAPP(hAPP(V_f_2,hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_b,T_c),V_x_2))),hAPP(c_Product__Type_Osnd(T_b,T_c),V_x_2)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_folding_Ocommute__left__comp_H_H,axiom,
% 187.18/188.01 ! [V_g_2,T_c,V_B_2,V_A_2,V_Fa_2,V_f_2,T_b,T_a] :
% 187.18/188.01 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_Fa_2)
% 187.18/188.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 187.18/188.01 => hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_Fa_2,V_B_2)),hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_Fa_2,V_A_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_Fa_2,V_A_2)),hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_Fa_2,V_B_2)),V_g_2)) ) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_folding_Ocommute__comp_H_H,axiom,
% 187.18/188.01 ! [V_B_2,V_A_2,V_Fa_2,V_f_2,T_b,T_a] :
% 187.18/188.01 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_Fa_2)
% 187.18/188.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 187.18/188.01 => hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_Fa_2,V_B_2)),hAPP(V_Fa_2,V_A_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_Fa_2,V_A_2)),hAPP(V_Fa_2,V_B_2)) ) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_folding_Ocommute__left__comp_H,axiom,
% 187.18/188.01 ! [V_g_2,V_x_2,T_c,V_A_2,V_Fa_2,V_f_2,T_b,T_a] :
% 187.18/188.01 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_Fa_2)
% 187.18/188.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.01 => hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_f_2,V_x_2)),hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_Fa_2,V_A_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_Fa_2,V_A_2)),hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_f_2,V_x_2)),V_g_2)) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_folding_Ocommute__comp_H,axiom,
% 187.18/188.01 ! [V_x_2,V_A_2,V_Fa_2,V_f_2,T_b,T_a] :
% 187.18/188.01 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_Fa_2)
% 187.18/188.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.01 => hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_f_2,V_x_2)),hAPP(V_Fa_2,V_A_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_Fa_2,V_A_2)),hAPP(V_f_2,V_x_2)) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_folding_Oempty,axiom,
% 187.18/188.01 ! [V_Fa_2,V_f_2,T_b,T_a] :
% 187.18/188.01 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_Fa_2)
% 187.18/188.01 => hAPP(V_Fa_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Fun_Oid(T_b) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_folding_Oinsert,axiom,
% 187.18/188.01 ! [V_x_2,V_A_2,V_Fa_2,V_f_2,T_b,T_a] :
% 187.18/188.01 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_Fa_2)
% 187.18/188.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.01 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 187.18/188.01 => hAPP(V_Fa_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_Fa_2,V_A_2)),hAPP(V_f_2,V_x_2)) ) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_folding_Ounion__inter,axiom,
% 187.18/188.01 ! [V_B_2,V_A_2,V_Fa_2,V_f_2,T_b,T_a] :
% 187.18/188.01 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_Fa_2)
% 187.18/188.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 187.18/188.01 => hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_Fa_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(V_Fa_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_Fa_2,V_A_2)),hAPP(V_Fa_2,V_B_2)) ) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_folding_Oinsert__remove,axiom,
% 187.18/188.01 ! [V_x_2,V_A_2,V_Fa_2,V_f_2,T_b,T_a] :
% 187.18/188.01 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_Fa_2)
% 187.18/188.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.01 => hAPP(V_Fa_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_Fa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),hAPP(V_f_2,V_x_2)) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_folding_Ounion,axiom,
% 187.18/188.01 ! [V_B_2,V_A_2,V_Fa_2,V_f_2,T_b,T_a] :
% 187.18/188.01 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_Fa_2)
% 187.18/188.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 187.18/188.01 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/188.01 => hAPP(V_Fa_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_Fa_2,V_A_2)),hAPP(V_Fa_2,V_B_2)) ) ) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Loop__sound__lemma,axiom,
% 187.18/188.01 ! [V_c_2,V_b_2,V_P_2,V_G_2,T_a] :
% 187.18/188.01 ( c_Hoare__Mirabelle_Ohoare__valids(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),c_Hoare__Mirabelle_Opeek__and(T_a,V_P_2,V_b_2)),V_c_2),V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))))
% 187.18/188.01 => c_Hoare__Mirabelle_Ohoare__valids(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),c_Com_Ocom_OWhile(V_b_2,V_c_2)),c_Hoare__Mirabelle_Opeek__and(T_a,V_P_2,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),V_b_2)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_hoare__derivs_OIf,axiom,
% 187.18/188.01 ! [V_d_2,V_Q_2,V_c_2,V_b_2,V_P_2,V_G_2,T_a] :
% 187.18/188.01 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),c_Hoare__Mirabelle_Opeek__and(T_a,V_P_2,V_b_2)),V_c_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))))
% 187.18/188.01 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),c_Hoare__Mirabelle_Opeek__and(T_a,V_P_2,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),V_b_2))),V_d_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))))
% 187.18/188.01 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),c_Com_Ocom_OCond(V_b_2,V_c_2,V_d_2)),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Loop,axiom,
% 187.18/188.01 ! [V_c_2,V_b_2,V_P_2,V_G_2,T_a] :
% 187.18/188.01 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),c_Hoare__Mirabelle_Opeek__and(T_a,V_P_2,V_b_2)),V_c_2),V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))))
% 187.18/188.01 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),c_Com_Ocom_OWhile(V_b_2,V_c_2)),c_Hoare__Mirabelle_Opeek__and(T_a,V_P_2,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),V_b_2)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_LeastM__natI,axiom,
% 187.18/188.01 ! [V_m_2,T_a,V_k_2,V_P_2] :
% 187.18/188.01 ( hBOOL(hAPP(V_P_2,V_k_2))
% 187.18/188.01 => hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OLeastM(T_a,tc_Nat_Onat,V_m_2,V_P_2))) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_peek__and__def,axiom,
% 187.18/188.01 ! [V_s_2,V_Z_2,V_p_2,V_P_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(T_a,V_P_2,V_p_2),V_Z_2),V_s_2))
% 187.18/188.01 <=> ( hBOOL(hAPP(hAPP(V_P_2,V_Z_2),V_s_2))
% 187.18/188.01 & hBOOL(hAPP(V_p_2,V_s_2)) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Greatest__def,axiom,
% 187.18/188.01 ! [T_a] :
% 187.18/188.01 ( class_Orderings_Oord(T_a)
% 187.18/188.01 => c_Hilbert__Choice_OGreatest(T_a) = c_Hilbert__Choice_OGreatestM(T_a,T_a,c_COMBI(T_a)) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_folding__image_Oreindex,axiom,
% 187.18/188.01 ! [V_g_2,V_h_2,V_A_2,V_Fa_2,V_z_2,V_f_2,T_b,T_a] :
% 187.18/188.01 ( c_Finite__Set_Ofolding__image(T_a,T_b,V_f_2,V_z_2,V_Fa_2)
% 187.18/188.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.18/188.01 => ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2)
% 187.18/188.01 => hAPP(hAPP(V_Fa_2,V_g_2),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_A_2)) = hAPP(hAPP(V_Fa_2,hAPP(c_Fun_Ocomp(T_b,T_a,T_b,V_g_2),V_h_2)),V_A_2) ) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_setsum__reindex__nonzero,axiom,
% 187.18/188.01 ! [T_b,V_h_2,V_f_2,V_S_2,T_a,T_c] :
% 187.18/188.01 ( class_Groups_Ocomm__monoid__add(T_c)
% 187.18/188.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 187.18/188.01 => ( ! [B_x] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2))
% 187.18/188.01 => ! [B_y] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),V_S_2))
% 187.18/188.01 => ( B_x != B_y
% 187.18/188.01 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y)
% 187.18/188.01 => hAPP(V_h_2,hAPP(V_f_2,B_x)) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) )
% 187.18/188.01 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_h_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_S_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_c),hAPP(c_Fun_Ocomp(T_b,T_c,T_a,V_h_2),V_f_2)),V_S_2) ) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_folding__image_Odistrib,axiom,
% 187.18/188.01 ! [V_h_2,V_g_2,V_A_2,V_Fa_2,V_z_2,V_f_2,T_b,T_a] :
% 187.18/188.01 ( c_Finite__Set_Ofolding__image(T_a,T_b,V_f_2,V_z_2,V_Fa_2)
% 187.18/188.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.18/188.01 => hAPP(hAPP(V_Fa_2,hAPP(hAPP(c_COMBS(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),V_f_2),V_g_2)),V_h_2)),V_A_2) = hAPP(hAPP(V_f_2,hAPP(hAPP(V_Fa_2,V_g_2),V_A_2)),hAPP(hAPP(V_Fa_2,V_h_2),V_A_2)) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_folding__image_Oeq__fold,axiom,
% 187.18/188.01 ! [V_g_2,V_A_2,V_Fa_2,V_z_2,V_f_2,T_b,T_a] :
% 187.18/188.01 ( c_Finite__Set_Ofolding__image(T_a,T_b,V_f_2,V_z_2,V_Fa_2)
% 187.18/188.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 187.18/188.01 => hAPP(hAPP(V_Fa_2,V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_a,T_b,V_f_2),V_g_2),V_z_2),V_A_2) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_folding__idem_Ounion__idem,axiom,
% 187.18/188.01 ! [V_B_2,V_A_2,V_Fa_2,V_f_2,T_b,T_a] :
% 187.18/188.01 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_Fa_2)
% 187.18/188.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 187.18/188.01 => hAPP(V_Fa_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_Fa_2,V_A_2)),hAPP(V_Fa_2,V_B_2)) ) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_folding__idem_Osubset__comp__idem,axiom,
% 187.18/188.01 ! [V_B_2,V_A_2,V_Fa_2,V_f_2,T_b,T_a] :
% 187.18/188.01 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_Fa_2)
% 187.18/188.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 187.18/188.01 => hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_Fa_2,V_A_2)),hAPP(V_Fa_2,V_B_2)) = hAPP(V_Fa_2,V_A_2) ) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_folding__idem_Oinsert__idem,axiom,
% 187.18/188.01 ! [V_x_2,V_A_2,V_Fa_2,V_f_2,T_b,T_a] :
% 187.18/188.01 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_Fa_2)
% 187.18/188.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.01 => hAPP(V_Fa_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_Fa_2,V_A_2)),hAPP(V_f_2,V_x_2)) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_folding__idem_Oidem__comp,axiom,
% 187.18/188.01 ! [V_x_2,V_Fa_2,V_f_2,T_b,T_a] :
% 187.18/188.01 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_Fa_2)
% 187.18/188.01 => hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_x_2)) = hAPP(V_f_2,V_x_2) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_folding__idem_Oidem__left__comp,axiom,
% 187.18/188.01 ! [V_g_2,V_x_2,T_c,V_Fa_2,V_f_2,T_b,T_a] :
% 187.18/188.01 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_Fa_2)
% 187.18/188.01 => hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_f_2,V_x_2)),hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_f_2,V_x_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_f_2,V_x_2)),V_g_2) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_folding__idem_Oin__comp__idem,axiom,
% 187.18/188.01 ! [V_x_2,V_A_2,V_Fa_2,V_f_2,T_b,T_a] :
% 187.18/188.01 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_Fa_2)
% 187.18/188.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 187.18/188.01 => hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_Fa_2,V_A_2)),hAPP(V_f_2,V_x_2)) = hAPP(V_Fa_2,V_A_2) ) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_strong__setprod__reindex__cong,axiom,
% 187.18/188.01 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a,T_c] :
% 187.18/188.01 ( class_Groups_Ocomm__monoid__mult(T_c)
% 187.18/188.01 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 187.18/188.01 => ( V_B_2 = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)
% 187.18/188.01 => ( ! [B_x] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 187.18/188.01 => hAPP(V_g_2,B_x) = hAPP(hAPP(c_Fun_Ocomp(T_b,T_c,T_a,V_h_2),V_f_2),B_x) )
% 187.18/188.01 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_h_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_c),V_g_2),V_A_2) ) ) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_wfI__pf,axiom,
% 187.18/188.01 ! [V_R_2,T_a] :
% 187.18/188.01 ( ! [B_A] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),B_A),hAPP(c_Relation_OImage(T_a,T_a,V_R_2),B_A)))
% 187.18/188.01 => B_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) )
% 187.18/188.01 => c_Wellfounded_Owf(T_a,V_R_2) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Sigma__mono,axiom,
% 187.18/188.01 ! [V_D_2,V_B_2,T_b,V_C_2,V_A_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2))
% 187.18/188.01 => ( ! [B_x] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_B_2,B_x)),hAPP(V_D_2,B_x))) )
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_C_2),V_D_2))) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_acc_OaccI,axiom,
% 187.18/188.01 ! [V_r_2,V_x_2,T_a] :
% 187.18/188.01 ( ! [B_y] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),V_x_2)),V_r_2))
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_member(T_a),B_y),c_Wellfounded_Oacc(T_a,V_r_2))) )
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_not__acc__down,axiom,
% 187.18/188.01 ! [V_R_2,V_x_2,T_a] :
% 187.18/188.01 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_R_2)))
% 187.18/188.01 => ~ ! [B_z] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_z),V_x_2)),V_R_2))
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_member(T_a),B_z),c_Wellfounded_Oacc(T_a,V_R_2))) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_max__ext_Osimps,axiom,
% 187.18/188.01 ! [V_R_2,V_a2_2,V_a1_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_a1_2),V_a2_2)),c_Wellfounded_Omax__ext(T_a,V_R_2)))
% 187.18/188.01 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a1_2))
% 187.18/188.01 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a2_2))
% 187.18/188.01 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/188.01 & ! [B_x] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_a1_2))
% 187.18/188.01 => ? [B_xa] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_a2_2))
% 187.18/188.01 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_xa)),V_R_2)) ) ) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_wf__no__infinite__down__chainE,axiom,
% 187.18/188.01 ! [V_f_2,V_r_2,T_a] :
% 187.18/188.01 ( c_Wellfounded_Owf(T_a,V_r_2)
% 187.18/188.01 => ~ ! [B_k] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),hAPP(V_f_2,hAPP(c_Nat_OSuc,B_k))),hAPP(V_f_2,B_k))),V_r_2)) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_com_Osize_I11_J,axiom,
% 187.18/188.01 ! [V_com_2,V_fun_2,V_loc_2] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_com_Osize_I3_J,axiom,
% 187.18/188.01 ! [V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(V_com_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_WTs__elim__cases_I3_J,axiom,
% 187.18/188.01 ! [V_c_2,V_a_2,V_Y_2] :
% 187.18/188.01 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_c_2)))
% 187.18/188.01 => hBOOL(hAPP(c_Com_OWT,V_c_2)) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_com_Osimps_I2_J,axiom,
% 187.18/188.01 ! [V_com_H_2,V_fun_H_2,V_loc_H_2,V_com_2,V_fun_2,V_loc_2] :
% 187.18/188.01 ( c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) = c_Com_Ocom_OLocal(V_loc_H_2,V_fun_H_2,V_com_H_2)
% 187.18/188.01 <=> ( V_loc_2 = V_loc_H_2
% 187.18/188.01 & V_fun_2 = V_fun_H_2
% 187.18/188.01 & V_com_2 = V_com_H_2 ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_com_Osimps_I39_J,axiom,
% 187.18/188.01 ! [V_com_2,V_fun_2,V_loc_2,V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_com_Osimps_I38_J,axiom,
% 187.18/188.01 ! [V_com_H_2,V_fun_H_2,V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_WT_Oequations_I3_J,axiom,
% 187.18/188.01 ! [V_a1_2,V_a3_2,V_a2_2] :
% 187.18/188.01 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(V_a2_2,V_a3_2,V_a1_2)))
% 187.18/188.01 <=> hBOOL(hAPP(c_Com_OWT,V_a1_2)) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_WT_OLocal,axiom,
% 187.18/188.01 ! [V_a_2,V_Y_2,V_c_2] :
% 187.18/188.01 ( hBOOL(hAPP(c_Com_OWT,V_c_2))
% 187.18/188.01 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_c_2))) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_com_Osimps_I41_J,axiom,
% 187.18/188.01 ! [V_com_2,V_fun_2,V_loc_2,V_pname_H_2] : hAPP(c_Com_Ocom_OBODY,V_pname_H_2) != c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_com_Osimps_I40_J,axiom,
% 187.18/188.01 ! [V_pname_H_2,V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) != hAPP(c_Com_Ocom_OBODY,V_pname_H_2) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_com_Osimps_I10_J,axiom,
% 187.18/188.01 ! [V_com_H_2,V_fun_H_2,V_loc_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OLocal(V_loc_H_2,V_fun_H_2,V_com_H_2) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_com_Osimps_I11_J,axiom,
% 187.18/188.01 ! [V_com_H_2,V_fun_H_2,V_loc_H_2] : c_Com_Ocom_OLocal(V_loc_H_2,V_fun_H_2,V_com_H_2) != c_Com_Ocom_OSKIP ).
% 187.18/188.01
% 187.18/188.01 fof(fact_com_Osimps_I35_J,axiom,
% 187.18/188.01 ! [V_com_2,V_fun_2,V_loc_2,V_com2_H_2,V_com1_H_2] : c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_com_Osimps_I34_J,axiom,
% 187.18/188.01 ! [V_com2_H_2,V_com1_H_2,V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) != c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_com_Osimps_I37_J,axiom,
% 187.18/188.01 ! [V_com_2,V_fun_2,V_loc_2,V_com2_H_2,V_com1_H_2,V_fun_H_2] : c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_com_Osimps_I36_J,axiom,
% 187.18/188.01 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) != c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_setsum__reindex__cong,axiom,
% 187.18/188.01 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a,T_c] :
% 187.18/188.01 ( class_Groups_Ocomm__monoid__add(T_c)
% 187.18/188.01 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 187.18/188.01 => ( V_B_2 = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)
% 187.18/188.01 => ( ! [B_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2))
% 187.18/188.01 => hAPP(V_g_2,B_a) = hAPP(V_h_2,hAPP(V_f_2,B_a)) )
% 187.18/188.01 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_h_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_c),V_g_2),V_A_2) ) ) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_scomp__unfold,axiom,
% 187.18/188.01 ! [V_x_2,V_g_2,V_f_2,T_a,T_d,T_c,T_b] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_c,T_d,T_a),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_c,T_d),hAPP(V_f_2,V_x_2))),hAPP(c_Product__Type_Osnd(T_c,T_d),hAPP(V_f_2,V_x_2))) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_setsum__ivl__cong,axiom,
% 187.18/188.01 ! [V_g_2,V_f_2,V_d_2,V_b_2,V_c_2,V_a_2,T_a,T_b] :
% 187.18/188.01 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 187.18/188.01 & class_Orderings_Oord(T_a) )
% 187.18/188.01 => ( V_a_2 = V_c_2
% 187.18/188.01 => ( V_b_2 = V_d_2
% 187.18/188.01 => ( ! [B_x] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c_2),B_x))
% 187.18/188.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_x),V_d_2))
% 187.18/188.01 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) )
% 187.18/188.01 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_c_2),V_d_2)) ) ) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_scomp__apply,axiom,
% 187.18/188.01 ! [V_x_2,V_g_2,V_f_2,T_a,T_d,T_c,T_b] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_c,T_d,T_a),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_a),V_g_2),hAPP(V_f_2,V_x_2)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_scomp__Pair,axiom,
% 187.18/188.01 ! [V_x_2,T_c,T_b,T_a] : hAPP(hAPP(c_Product__Type_Oscomp(T_a,T_b,T_c,tc_prod(T_b,T_c)),V_x_2),c_Product__Type_OPair(T_b,T_c)) = V_x_2 ).
% 187.18/188.01
% 187.18/188.01 fof(fact_scomp__scomp,axiom,
% 187.18/188.01 ! [V_h_2,V_g_2,V_f_2,T_f,T_e,T_b,T_d,T_c,T_a] : hAPP(hAPP(c_Product__Type_Oscomp(T_a,T_c,T_d,T_b),hAPP(hAPP(c_Product__Type_Oscomp(T_a,T_e,T_f,tc_prod(T_c,T_d)),V_f_2),V_g_2)),V_h_2) = hAPP(hAPP(c_Product__Type_Oscomp(T_a,T_e,T_f,T_b),V_f_2),hAPP(hAPP(c_COMBC(T_e,tc_fun(T_c,tc_fun(T_d,T_b)),tc_fun(T_f,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_f,tc_prod(T_c,T_d)),tc_fun(tc_fun(T_c,tc_fun(T_d,T_b)),tc_fun(T_f,T_b)),T_e),c_Product__Type_Oscomp(T_f,T_c,T_d,T_b)),V_g_2)),V_h_2)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Pair__scomp,axiom,
% 187.18/188.01 ! [V_f_2,V_x_2,T_b,T_c,T_a] : hAPP(hAPP(c_Product__Type_Oscomp(T_a,T_c,T_a,T_b),hAPP(c_Product__Type_OPair(T_c,T_a),V_x_2)),V_f_2) = hAPP(V_f_2,V_x_2) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_scomp__def,axiom,
% 187.18/188.01 ! [V_x_2,V_g_2,V_f_2,T_a,T_d,T_c,T_b] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_c,T_d,T_a),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_a),V_g_2),hAPP(V_f_2,V_x_2)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_iterate_Osimps,axiom,
% 187.18/188.01 ! [V_x_2,V_f_2,T_a,T_b,V_k_2] :
% 187.18/188.01 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 187.18/188.01 => hAPP(c_Random_Oiterate(T_b,T_a,V_k_2,V_f_2),V_x_2) = hAPP(c_Product__Type_OPair(T_b,T_a),V_x_2) )
% 187.18/188.01 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 187.18/188.01 => hAPP(c_Random_Oiterate(T_b,T_a,V_k_2,V_f_2),V_x_2) = hAPP(hAPP(c_Product__Type_Oscomp(T_a,T_b,T_a,tc_prod(T_b,T_a)),hAPP(V_f_2,V_x_2)),c_Random_Oiterate(T_b,T_a,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)) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_less__eq,axiom,
% 187.18/188.01 ! [V_n_2,V_m_2] :
% 187.18/188.01 ( 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)))
% 187.18/188.01 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_nat__intermed__int__val,axiom,
% 187.18/188.01 ! [V_k_2,V_f_2,V_n_2,V_m_2] :
% 187.18/188.01 ( ! [B_i] :
% 187.18/188.01 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i))
% 187.18/188.01 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) )
% 187.18/188.01 => 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))) )
% 187.18/188.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 187.18/188.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,V_m_2)),V_k_2))
% 187.18/188.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
% 187.18/188.01 => ? [B_i] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i))
% 187.18/188.01 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2))
% 187.18/188.01 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_wf__trancl,axiom,
% 187.18/188.01 ! [V_r_2,T_a] :
% 187.18/188.01 ( c_Wellfounded_Owf(T_a,V_r_2)
% 187.18/188.01 => c_Wellfounded_Owf(T_a,c_Transitive__Closure_Otrancl(T_a,V_r_2)) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_less__than__def,axiom,
% 187.18/188.01 c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_acyclic__def,axiom,
% 187.18/188.01 ! [V_r_2,T_a] :
% 187.18/188.01 ( c_Wellfounded_Oacyclic(T_a,V_r_2)
% 187.18/188.01 <=> ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_trancl_Or__into__trancl,axiom,
% 187.18/188.01 ! [V_r_2,V_b_2,V_a_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2))
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_trancl__subset__Field2,axiom,
% 187.18/188.01 ! [V_r_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_a,V_r_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),hAPP(c_Relation_OField(T_a),V_r_2)),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_Relation_OField(T_a),V_r_2))))) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_trancl__Int__subset,axiom,
% 187.18/188.01 ! [V_s_2,V_r_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2))
% 187.18/188.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_a,V_r_2)),V_s_2)),V_r_2)),V_s_2))
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_a,V_r_2)),V_s_2)) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_r__into__trancl_H,axiom,
% 187.18/188.01 ! [V_r_2,V_p_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),V_r_2))
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_trancl__empty,axiom,
% 187.18/188.01 ! [T_a] : c_Transitive__Closure_Otrancl(T_a,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_trancl__domain,axiom,
% 187.18/188.01 ! [V_r_2,T_a] : hAPP(c_Relation_ODomain(T_a,T_a),c_Transitive__Closure_Otrancl(T_a,V_r_2)) = hAPP(c_Relation_ODomain(T_a,T_a),V_r_2) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_trancl__range,axiom,
% 187.18/188.01 ! [V_r_2,T_a] : hAPP(c_Relation_ORange(T_a,T_a),c_Transitive__Closure_Otrancl(T_a,V_r_2)) = hAPP(c_Relation_ORange(T_a,T_a),V_r_2) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_finite__trancl,axiom,
% 187.18/188.01 ! [V_r_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
% 187.18/188.01 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2)) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_trancl__trans,axiom,
% 187.18/188.01 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
% 187.18/188.01 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_c_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Transitive__Closure_Otrancl__into__trancl,axiom,
% 187.18/188.01 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
% 187.18/188.01 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_c_2)),V_r_2))
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_trancl__into__trancl2,axiom,
% 187.18/188.01 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2))
% 187.18/188.01 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_c_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_r__r__into__trancl,axiom,
% 187.18/188.01 ! [V_c_2,V_R_2,V_b_2,V_a_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_R_2))
% 187.18/188.01 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_c_2)),V_R_2))
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_a,V_R_2))) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_trancl__mono,axiom,
% 187.18/188.01 ! [V_s_2,V_r_2,V_p_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
% 187.18/188.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2))
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_s_2))) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_trancl__unfold,axiom,
% 187.18/188.01 ! [V_r_2,T_a] : c_Transitive__Closure_Otrancl(T_a,V_r_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),c_Transitive__Closure_Otrancl(T_a,V_r_2)),V_r_2)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_trancl__subset__Sigma,axiom,
% 187.18/188.01 ! [V_A_2,V_r_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2))))
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_a,V_r_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2)))) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_log_Osimps,axiom,
% 187.18/188.01 ! [V_i,V_b] :
% 187.18/188.01 ( ( ( 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)))
% 187.18/188.01 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) )
% 187.18/188.01 => c_Random_Olog(V_b,V_i) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) )
% 187.18/188.01 & ( ~ ( 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)))
% 187.18/188.01 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) )
% 187.18/188.01 => 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))) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_minus__shift__def,axiom,
% 187.18/188.01 ! [V_r,V_l,V_k] :
% 187.18/188.01 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 187.18/188.01 => 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) )
% 187.18/188.01 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 187.18/188.01 => 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) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_inc__shift__def,axiom,
% 187.18/188.01 ! [V_k,V_v] :
% 187.18/188.01 ( ( V_v = V_k
% 187.18/188.01 => c_Random_Oinc__shift(V_v,V_k) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) )
% 187.18/188.01 & ( V_v != V_k
% 187.18/188.01 => 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)) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_range,axiom,
% 187.18/188.01 ! [V_s,V_k] :
% 187.18/188.01 ( 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))
% 187.18/188.01 => 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)) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_trancl__insert,axiom,
% 187.18/188.01 ! [V_r_2,V_x_2,V_y_2,T_a] : c_Transitive__Closure_Otrancl(T_a,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_x_2)),V_r_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_a,V_r_2)),hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a))),hAPP(hAPP(c_COMBC(T_a,T_a,tc_prod(T_a,T_a)),c_Product__Type_OPair(T_a,T_a)),V_y_2))),c_Transitive__Closure_Ortrancl(T_a,V_r_2))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a))),hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2))),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))))) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_reflcl__set__eq,axiom,
% 187.18/188.01 ! [V_y_2,V_x_2,V_r_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a)))),c_Product__Type_OPair(T_a,T_a)))),V_r_2)),c_fequal),V_x_2),V_y_2))
% 187.18/188.01 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_a)))) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_r__into__rtrancl,axiom,
% 187.18/188.01 ! [V_r_2,V_p_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),V_r_2))
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_rtrancl_Ortrancl__refl,axiom,
% 187.18/188.01 ! [V_r_2,V_a_2,T_a] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_a_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_IdI,axiom,
% 187.18/188.01 ! [V_a_2,T_a] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_a_2)),c_Relation_OId(T_a))) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_trancl__into__rtrancl,axiom,
% 187.18/188.01 ! [V_r_2,V_b_2,V_a_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_rtrancl__Int__subset,axiom,
% 187.18/188.01 ! [V_r_2,V_s_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Relation_OId(T_a)),V_s_2))
% 187.18/188.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)),V_s_2)),V_r_2)),V_s_2))
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)),V_s_2)) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Image__closed__trancl,axiom,
% 187.18/188.01 ! [V_X_2,V_r_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),V_X_2)),V_X_2))
% 187.18/188.01 => hAPP(c_Relation_OImage(T_a,T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)),V_X_2) = V_X_2 ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_rtrancl__mono,axiom,
% 187.18/188.01 ! [V_s_2,V_r_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2))
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)),c_Transitive__Closure_Ortrancl(T_a,V_s_2))) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_rtrancl__subset,axiom,
% 187.18/188.01 ! [V_S_2,V_R_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),V_S_2))
% 187.18/188.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_S_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2)))
% 187.18/188.01 => c_Transitive__Closure_Ortrancl(T_a,V_S_2) = c_Transitive__Closure_Ortrancl(T_a,V_R_2) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_rtrancl__subset__rtrancl,axiom,
% 187.18/188.01 ! [V_s_2,V_r_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),c_Transitive__Closure_Ortrancl(T_a,V_s_2)))
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)),c_Transitive__Closure_Ortrancl(T_a,V_s_2))) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_rtrancl__Un__subset,axiom,
% 187.18/188.01 ! [V_S_2,V_R_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_a,V_R_2)),c_Transitive__Closure_Ortrancl(T_a,V_S_2))),c_Transitive__Closure_Ortrancl(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),V_S_2)))) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Id__O__R,axiom,
% 187.18/188.01 ! [V_R_2,T_b,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_b),c_Relation_OId(T_a)),V_R_2) = V_R_2 ).
% 187.18/188.01
% 187.18/188.01 fof(fact_R__O__Id,axiom,
% 187.18/188.01 ! [V_R_2,T_b,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_b,T_b),V_R_2),c_Relation_OId(T_b)) = V_R_2 ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Image__Id,axiom,
% 187.18/188.01 ! [V_A_2,T_a] : hAPP(c_Relation_OImage(T_a,T_a,c_Relation_OId(T_a)),V_A_2) = V_A_2 ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Domain__rtrancl,axiom,
% 187.18/188.01 ! [V_R_2,T_a] : hAPP(c_Relation_ODomain(T_a,T_a),c_Transitive__Closure_Ortrancl(T_a,V_R_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_rtrancl__empty,axiom,
% 187.18/188.01 ! [T_a] : c_Transitive__Closure_Ortrancl(T_a,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))) = c_Relation_OId(T_a) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Range__rtrancl,axiom,
% 187.18/188.01 ! [V_R_2,T_a] : hAPP(c_Relation_ORange(T_a,T_a),c_Transitive__Closure_Ortrancl(T_a,V_R_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_converse__rtrancl__into__rtrancl,axiom,
% 187.18/188.01 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2))
% 187.18/188.01 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_rtrancl_Ortrancl__into__rtrancl,axiom,
% 187.18/188.01 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
% 187.18/188.01 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_c_2)),V_r_2))
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_rtrancl__trans,axiom,
% 187.18/188.01 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
% 187.18/188.01 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_rtrancl__idemp,axiom,
% 187.18/188.01 ! [V_r_2,T_a] : c_Transitive__Closure_Ortrancl(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)) = c_Transitive__Closure_Ortrancl(T_a,V_r_2) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_rtrancl__reflcl__absorb,axiom,
% 187.18/188.01 ! [V_R_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_a,V_R_2)),c_Relation_OId(T_a)) = c_Transitive__Closure_Ortrancl(T_a,V_R_2) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_rtrancl__Un__rtrancl,axiom,
% 187.18/188.01 ! [V_S_2,V_R_2,T_a] : c_Transitive__Closure_Ortrancl(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_a,V_R_2)),c_Transitive__Closure_Ortrancl(T_a,V_S_2))) = c_Transitive__Closure_Ortrancl(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),V_S_2)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_rtrancl__reflcl,axiom,
% 187.18/188.01 ! [V_R_2,T_a] : c_Transitive__Closure_Ortrancl(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),c_Relation_OId(T_a))) = c_Transitive__Closure_Ortrancl(T_a,V_R_2) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_in__rtrancl__UnI,axiom,
% 187.18/188.01 ! [V_S_2,V_R_2,V_x_2,T_a] :
% 187.18/188.01 ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_x_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2)))
% 187.18/188.01 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_x_2),c_Transitive__Closure_Ortrancl(T_a,V_S_2))) )
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_x_2),c_Transitive__Closure_Ortrancl(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),V_S_2)))) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_r__comp__rtrancl__eq,axiom,
% 187.18/188.01 ! [V_r_2,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_r_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)) = hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),c_Transitive__Closure_Ortrancl(T_a,V_r_2)),V_r_2) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_rtrancl__idemp__self__comp,axiom,
% 187.18/188.01 ! [V_R_2,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),c_Transitive__Closure_Ortrancl(T_a,V_R_2)),c_Transitive__Closure_Ortrancl(T_a,V_R_2)) = c_Transitive__Closure_Ortrancl(T_a,V_R_2) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_rtrancl__unfold,axiom,
% 187.18/188.01 ! [V_r_2,T_a] : c_Transitive__Closure_Ortrancl(T_a,V_r_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Relation_OId(T_a)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),c_Transitive__Closure_Ortrancl(T_a,V_r_2)),V_r_2)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_rtrancl__r__diff__Id,axiom,
% 187.18/188.01 ! [V_r_2,T_a] : c_Transitive__Closure_Ortrancl(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_a))) = c_Transitive__Closure_Ortrancl(T_a,V_r_2) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_refl__rtrancl,axiom,
% 187.18/188.01 ! [V_r_2,T_a] : c_Relation_Orefl__on(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_trancl__unfold__right,axiom,
% 187.18/188.01 ! [V_r_2,T_a] : c_Transitive__Closure_Otrancl(T_a,V_r_2) = hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),c_Transitive__Closure_Ortrancl(T_a,V_r_2)),V_r_2) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_trancl__unfold__left,axiom,
% 187.18/188.01 ! [V_r_2,T_a] : c_Transitive__Closure_Otrancl(T_a,V_r_2) = hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_r_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_trancl__reflcl,axiom,
% 187.18/188.01 ! [V_r_2,T_a] : c_Transitive__Closure_Otrancl(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_a))) = c_Transitive__Closure_Ortrancl(T_a,V_r_2) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_reflcl__trancl,axiom,
% 187.18/188.01 ! [V_r_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_a,V_r_2)),c_Relation_OId(T_a)) = c_Transitive__Closure_Ortrancl(T_a,V_r_2) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_trancl__rtrancl__absorb,axiom,
% 187.18/188.01 ! [V_R_2,T_a] : c_Transitive__Closure_Ortrancl(T_a,c_Transitive__Closure_Otrancl(T_a,V_R_2)) = c_Transitive__Closure_Ortrancl(T_a,V_R_2) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_rtrancl__trancl__absorb,axiom,
% 187.18/188.01 ! [V_R_2,T_a] : c_Transitive__Closure_Otrancl(T_a,c_Transitive__Closure_Ortrancl(T_a,V_R_2)) = c_Transitive__Closure_Ortrancl(T_a,V_R_2) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_pair__in__Id__conv,axiom,
% 187.18/188.01 ! [V_b_2,V_a_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Relation_OId(T_a)))
% 187.18/188.01 <=> V_a_2 = V_b_2 ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_rtrancl__eq__or__trancl,axiom,
% 187.18/188.01 ! [V_R_2,V_y_2,V_x_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_R_2)))
% 187.18/188.01 <=> ( V_x_2 = V_y_2
% 187.18/188.01 | ( V_x_2 != V_y_2
% 187.18/188.01 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_a,V_R_2))) ) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_rtrancl__into__trancl2,axiom,
% 187.18/188.01 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2))
% 187.18/188.01 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_rtranclD,axiom,
% 187.18/188.01 ! [V_R_2,V_b_2,V_a_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,V_R_2)))
% 187.18/188.01 => ( V_a_2 = V_b_2
% 187.18/188.01 | ( V_a_2 != V_b_2
% 187.18/188.01 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_a,V_R_2))) ) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_rtrancl__into__trancl1,axiom,
% 187.18/188.01 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
% 187.18/188.01 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_c_2)),V_r_2))
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_trancl__rtrancl__trancl,axiom,
% 187.18/188.01 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
% 187.18/188.01 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_rtrancl__trancl__trancl,axiom,
% 187.18/188.01 ! [V_z_2,V_r_2,V_y_2,V_x_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
% 187.18/188.01 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_z_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Domain__Id,axiom,
% 187.18/188.01 ! [T_a] : hAPP(c_Relation_ODomain(T_a,T_a),c_Relation_OId(T_a)) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Range__Id,axiom,
% 187.18/188.01 ! [T_a] : hAPP(c_Relation_ORange(T_a,T_a),c_Relation_OId(T_a)) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_refl__Id,axiom,
% 187.18/188.01 ! [T_a] : c_Relation_Orefl__on(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),c_Relation_OId(T_a)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_pair__leq__def,axiom,
% 187.18/188.01 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))) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Not__Domain__rtrancl,axiom,
% 187.18/188.01 ! [V_y_2,V_R_2,V_x_2,T_a] :
% 187.18/188.01 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_Relation_ODomain(T_a,T_a),V_R_2)))
% 187.18/188.01 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_R_2)))
% 187.18/188.01 <=> V_x_2 = V_y_2 ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_acc__downwards,axiom,
% 187.18/188.01 ! [V_b_2,V_r_2,V_a_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Wellfounded_Oacc(T_a,V_r_2)))
% 187.18/188.01 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_a_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_acc__downwards__aux,axiom,
% 187.18/188.01 ! [V_r_2,V_a_2,V_b_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_a_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
% 187.18/188.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Wellfounded_Oacc(T_a,V_r_2)))
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_wf__insert,axiom,
% 187.18/188.01 ! [V_r_2,V_x_2,V_y_2,T_a] :
% 187.18/188.01 ( c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_x_2)),V_r_2))
% 187.18/188.01 <=> ( c_Wellfounded_Owf(T_a,V_r_2)
% 187.18/188.01 & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_acyclic__insert,axiom,
% 187.18/188.01 ! [V_r_2,V_x_2,V_y_2,T_a] :
% 187.18/188.01 ( c_Wellfounded_Oacyclic(T_a,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_x_2)),V_r_2))
% 187.18/188.01 <=> ( c_Wellfounded_Oacyclic(T_a,V_r_2)
% 187.18/188.01 & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_refl__reflcl,axiom,
% 187.18/188.01 ! [V_r_2,T_a] : c_Relation_Orefl__on(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_a))) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Id__def,axiom,
% 187.18/188.01 ! [T_a] : c_Relation_OId(T_a) = hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,tc_prod(T_a,T_a)),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBC(tc_prod(T_a,T_a),tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_HOL_Obool)),tc_prod(T_a,T_a)),c_COMBB(tc_prod(T_a,T_a),tc_HOL_Obool,T_a)),c_fequal)),hAPP(hAPP(c_COMBS(T_a,T_a,tc_prod(T_a,T_a)),c_Product__Type_OPair(T_a,T_a)),c_COMBI(T_a))))) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_irrefl__diff__Id,axiom,
% 187.18/188.01 ! [V_r_2,T_a] : c_Relation_Oirrefl(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_a))) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_pred__nat__trancl__eq__le,axiom,
% 187.18/188.01 ! [V_n_2,V_m_2] :
% 187.18/188.01 ( 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)))
% 187.18/188.01 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_trancl__subset__Sigma__aux,axiom,
% 187.18/188.01 ! [V_A_2,V_r_2,V_b_2,V_a_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
% 187.18/188.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2))))
% 187.18/188.01 => ( V_a_2 = V_b_2
% 187.18/188.01 | hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_irrefl__tranclI,axiom,
% 187.18/188.01 ! [V_x_2,V_r_2,T_a] :
% 187.18/188.01 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))
% 187.18/188.01 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_x_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_sequence__trans,axiom,
% 187.18/188.01 ! [V_k_2,V_i_2,V_r_2,V_f_2,T_a] :
% 187.18/188.01 ( ! [B_i] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),hAPP(V_f_2,hAPP(c_Nat_OSuc,B_i))),hAPP(V_f_2,B_i))),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),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_a,V_r_2))) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_total__on__diff__Id,axiom,
% 187.18/188.01 ! [V_r_2,V_A_2,T_a] :
% 187.18/188.01 ( c_Relation_Ototal__on(T_a,V_A_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_a)))
% 187.18/188.01 <=> c_Relation_Ototal__on(T_a,V_A_2,V_r_2) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_converse__Id,axiom,
% 187.18/188.01 ! [T_a] : hAPP(c_Relation_Oconverse(T_a,T_a),c_Relation_OId(T_a)) = c_Relation_OId(T_a) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_rtrancl__converse,axiom,
% 187.18/188.01 ! [V_r_2,T_a] : c_Transitive__Closure_Ortrancl(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) = hAPP(c_Relation_Oconverse(T_a,T_a),c_Transitive__Closure_Ortrancl(T_a,V_r_2)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_trancl__converse,axiom,
% 187.18/188.01 ! [V_r_2,T_a] : c_Transitive__Closure_Otrancl(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) = hAPP(c_Relation_Oconverse(T_a,T_a),c_Transitive__Closure_Otrancl(T_a,V_r_2)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_converse__iff,axiom,
% 187.18/188.01 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2)))
% 187.18/188.01 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_b_2),V_a_2)),V_r_2)) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_converseI,axiom,
% 187.18/188.01 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),V_r_2))
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_b_2),V_a_2)),hAPP(c_Relation_Oconverse(T_a,T_b),V_r_2))) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_converseD,axiom,
% 187.18/188.01 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2)))
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_b_2),V_a_2)),V_r_2)) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_acyclic__converse,axiom,
% 187.18/188.01 ! [V_r_2,T_a] :
% 187.18/188.01 ( c_Wellfounded_Oacyclic(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2))
% 187.18/188.01 <=> c_Wellfounded_Oacyclic(T_a,V_r_2) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_converse__UNION,axiom,
% 187.18/188.01 ! [V_r_2,V_S_2,T_c,T_a,T_b] : hAPP(c_Relation_Oconverse(T_b,T_a),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),V_S_2),V_r_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_S_2),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),T_c),c_Relation_Oconverse(T_b,T_a)),V_r_2)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Field__converse,axiom,
% 187.18/188.01 ! [V_r_2,T_a] : hAPP(c_Relation_OField(T_a),hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) = hAPP(c_Relation_OField(T_a),V_r_2) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_converse__inv__image,axiom,
% 187.18/188.01 ! [V_f_2,V_R_2,T_b,T_a] : hAPP(c_Relation_Oconverse(T_a,T_a),hAPP(hAPP(c_Relation_Oinv__image(T_b,T_a),V_R_2),V_f_2)) = hAPP(hAPP(c_Relation_Oinv__image(T_b,T_a),hAPP(c_Relation_Oconverse(T_b,T_b),V_R_2)),V_f_2) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_finite__converse,axiom,
% 187.18/188.01 ! [V_r_2,T_b,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2)))
% 187.18/188.01 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_a)),V_r_2)) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_converse__Int,axiom,
% 187.18/188.01 ! [V_s_2,V_r_2,T_a,T_b] : hAPP(c_Relation_Oconverse(T_b,T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2)),hAPP(c_Relation_Oconverse(T_b,T_a),V_s_2)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_total__on__converse,axiom,
% 187.18/188.01 ! [V_r_2,V_A_2,T_a] :
% 187.18/188.01 ( c_Relation_Ototal__on(T_a,V_A_2,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2))
% 187.18/188.01 <=> c_Relation_Ototal__on(T_a,V_A_2,V_r_2) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_converse__converse,axiom,
% 187.18/188.01 ! [V_r_2,T_a,T_b] : hAPP(c_Relation_Oconverse(T_b,T_a),hAPP(c_Relation_Oconverse(T_a,T_b),V_r_2)) = V_r_2 ).
% 187.18/188.01
% 187.18/188.01 fof(fact_converse__Id__on,axiom,
% 187.18/188.01 ! [V_A_2,T_a] : hAPP(c_Relation_Oconverse(T_a,T_a),c_Relation_OId__on(T_a,V_A_2)) = c_Relation_OId__on(T_a,V_A_2) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_converse__Un,axiom,
% 187.18/188.01 ! [V_s_2,V_r_2,T_a,T_b] : hAPP(c_Relation_Oconverse(T_b,T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2)),hAPP(c_Relation_Oconverse(T_b,T_a),V_s_2)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_converse__rel__comp,axiom,
% 187.18/188.01 ! [V_s_2,V_r_2,T_c,T_a,T_b] : hAPP(c_Relation_Oconverse(T_b,T_a),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_a),V_r_2),V_s_2)) = hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),hAPP(c_Relation_Oconverse(T_c,T_a),V_s_2)),hAPP(c_Relation_Oconverse(T_b,T_c),V_r_2)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_refl__on__converse,axiom,
% 187.18/188.01 ! [V_r_2,V_A_2,T_a] :
% 187.18/188.01 ( c_Relation_Orefl__on(T_a,V_A_2,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2))
% 187.18/188.01 <=> c_Relation_Orefl__on(T_a,V_A_2,V_r_2) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_wf__converse__trancl,axiom,
% 187.18/188.01 ! [V_r_2,T_a] :
% 187.18/188.01 ( c_Wellfounded_Owf(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2))
% 187.18/188.01 => c_Wellfounded_Owf(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_equiv__comp__eq,axiom,
% 187.18/188.01 ! [V_r_2,V_A_2,T_a] :
% 187.18/188.01 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 187.18/188.01 => hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)),V_r_2) = V_r_2 ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Range__converse,axiom,
% 187.18/188.01 ! [V_r_2,T_a,T_b] : hAPP(c_Relation_ORange(T_b,T_a),hAPP(c_Relation_Oconverse(T_a,T_b),V_r_2)) = hAPP(c_Relation_ODomain(T_a,T_b),V_r_2) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Domain__converse,axiom,
% 187.18/188.01 ! [V_r_2,T_b,T_a] : hAPP(c_Relation_ODomain(T_a,T_b),hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2)) = hAPP(c_Relation_ORange(T_b,T_a),V_r_2) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Range__def,axiom,
% 187.18/188.01 ! [V_r_2,T_a,T_b] : hAPP(c_Relation_ORange(T_b,T_a),V_r_2) = hAPP(c_Relation_ODomain(T_a,T_b),hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_total__on__empty,axiom,
% 187.18/188.01 ! [V_r_2,T_a] : c_Relation_Ototal__on(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_r_2) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_rtrancl__converseD,axiom,
% 187.18/188.01 ! [V_r_2,V_y_2,V_x_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2))))
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_x_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_rtrancl__converseI,axiom,
% 187.18/188.01 ! [V_r_2,V_x_2,V_y_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_x_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)))) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_trancl__converseI,axiom,
% 187.18/188.01 ! [V_r_2,V_y_2,V_x_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_a,T_a),c_Transitive__Closure_Otrancl(T_a,V_r_2))))
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)))) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_trancl__converseD,axiom,
% 187.18/188.01 ! [V_r_2,V_y_2,V_x_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2))))
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_a,T_a),c_Transitive__Closure_Otrancl(T_a,V_r_2)))) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Image__subset__eq,axiom,
% 187.18/188.01 ! [V_B_2,V_A_2,V_r_2,T_b,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_a,V_r_2),V_A_2)),V_B_2))
% 187.18/188.01 <=> 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)),hAPP(c_Relation_OImage(T_a,T_b,hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2))))) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_refl__on__comp__subset,axiom,
% 187.18/188.01 ! [V_r_2,V_A_2,T_a] :
% 187.18/188.01 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2)
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)),V_r_2))) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_comp__equivI,axiom,
% 187.18/188.01 ! [V_A_2,V_r_2,T_a] :
% 187.18/188.01 ( hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)),V_r_2) = V_r_2
% 187.18/188.01 => ( hAPP(c_Relation_ODomain(T_a,T_a),V_r_2) = V_A_2
% 187.18/188.01 => c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_finite__acyclic__wf__converse,axiom,
% 187.18/188.01 ! [V_r_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2))
% 187.18/188.01 => ( c_Wellfounded_Oacyclic(T_a,V_r_2)
% 187.18/188.01 => c_Wellfounded_Owf(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_total__on__def,axiom,
% 187.18/188.01 ! [V_r_2,V_A_2,T_a] :
% 187.18/188.01 ( c_Relation_Ototal__on(T_a,V_A_2,V_r_2)
% 187.18/188.01 <=> ! [B_x] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 187.18/188.01 => ! [B_xa] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2))
% 187.18/188.01 => ( B_x != B_xa
% 187.18/188.01 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_xa)),V_r_2))
% 187.18/188.01 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_xa),B_x)),V_r_2)) ) ) ) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_converse__def,axiom,
% 187.18/188.01 ! [V_r_2,T_a,T_b] : hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2) = hAPP(c_Set_OCollect(tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_b,T_a),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_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_a)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_b,T_a),tc_fun(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_a)))),hAPP(c_COMBC(T_b,T_a,tc_prod(T_b,T_a)),c_Product__Type_OPair(T_b,T_a))))),V_r_2))) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_rtrancl__imp__UN__rel__pow,axiom,
% 187.18/188.01 ! [V_R_2,V_p_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2)))
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(T_a,T_a),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_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2)))) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_acyclicI,axiom,
% 187.18/188.01 ! [V_r_2,T_a] :
% 187.18/188.01 ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
% 187.18/188.01 => c_Wellfounded_Oacyclic(T_a,V_r_2) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Image__Int__eq,axiom,
% 187.18/188.01 ! [V_B_2,V_A_2,V_R_2,T_b,T_a] :
% 187.18/188.01 ( c_Relation_Osingle__valued(T_a,T_b,hAPP(c_Relation_Oconverse(T_b,T_a),V_R_2))
% 187.18/188.01 => hAPP(c_Relation_OImage(T_b,T_a,V_R_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_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_a,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_b,T_a,V_R_2),V_B_2)) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_single__valued__subset,axiom,
% 187.18/188.01 ! [V_s_2,V_r_2,T_b,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
% 187.18/188.01 => ( c_Relation_Osingle__valued(T_a,T_b,V_s_2)
% 187.18/188.01 => c_Relation_Osingle__valued(T_a,T_b,V_r_2) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_single__valued__rel__comp,axiom,
% 187.18/188.01 ! [V_s_2,T_c,V_r_2,T_b,T_a] :
% 187.18/188.01 ( c_Relation_Osingle__valued(T_a,T_b,V_r_2)
% 187.18/188.01 => ( c_Relation_Osingle__valued(T_b,T_c,V_s_2)
% 187.18/188.01 => c_Relation_Osingle__valued(T_a,T_c,hAPP(hAPP(c_Relation_Orel__comp(T_a,T_b,T_c),V_r_2),V_s_2)) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_funpow__mult,axiom,
% 187.18/188.01 ! [V_f_2,V_m_2,V_n_2,T_a] : hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),V_n_2),hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),V_m_2),V_f_2)) = hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)),V_f_2) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_funpow__swap1,axiom,
% 187.18/188.01 ! [V_x_2,V_n_2,T_a,V_f_2] : hAPP(V_f_2,hAPP(hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),V_n_2),V_f_2),V_x_2)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),V_n_2),V_f_2),hAPP(V_f_2,V_x_2)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_wf__exp,axiom,
% 187.18/188.01 ! [V_R_2,V_n_2,T_a] :
% 187.18/188.01 ( c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2))
% 187.18/188.01 => c_Wellfounded_Owf(T_a,V_R_2) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_comp__funpow,axiom,
% 187.18/188.01 ! [V_f_2,V_n_2,T_b,T_a] : hAPP(hAPP(c_Nat_Ocompow(tc_fun(T_a,T_b),tc_fun(T_a,T_b)),V_n_2),c_Fun_Ocomp(T_b,T_b,T_a,V_f_2)) = c_Fun_Ocomp(T_b,T_b,T_a,hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),V_f_2)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_rel__pow__1,axiom,
% 187.18/188.01 ! [V_R_2,T_a] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_R_2) = V_R_2 ).
% 187.18/188.01
% 187.18/188.01 fof(fact_single__valued__rel__pow,axiom,
% 187.18/188.01 ! [V_n_2,V_R_2,T_a] :
% 187.18/188.01 ( c_Relation_Osingle__valued(T_a,T_a,V_R_2)
% 187.18/188.01 => c_Relation_Osingle__valued(T_a,T_a,hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2)) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_rel__pow__commute,axiom,
% 187.18/188.01 ! [V_n_2,V_R_2,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_R_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2)) = hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2)),V_R_2) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_single__valued__Id,axiom,
% 187.18/188.01 ! [T_a] : c_Relation_Osingle__valued(T_a,T_a,c_Relation_OId(T_a)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_rel__pow__imp__rtrancl,axiom,
% 187.18/188.01 ! [V_R_2,V_n_2,V_p_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2)))
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_rtrancl__power,axiom,
% 187.18/188.01 ! [V_R_2,V_p_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2)))
% 187.18/188.01 <=> ? [B_n] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),B_n),V_R_2))) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_single__valued__Id__on,axiom,
% 187.18/188.01 ! [V_A_2,T_a] : c_Relation_Osingle__valued(T_a,T_a,c_Relation_OId__on(T_a,V_A_2)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_relpow_Osimps_I2_J,axiom,
% 187.18/188.01 ! [V_R_2,V_n_2,T_a] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2) = hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2)),V_R_2) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_rel__pow__add,axiom,
% 187.18/188.01 ! [V_R_2,V_n_2,V_m_2,T_a] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),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_a,T_a,T_a),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_m_2),V_R_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_relpow_Osimps_I1_J,axiom,
% 187.18/188.01 ! [V_R_2,T_a] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_R_2) = c_Relation_OId(T_a) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_rel__pow__0__I,axiom,
% 187.18/188.01 ! [V_R_2,V_x_2,T_a] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_x_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_R_2))) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_rel__pow__0__E,axiom,
% 187.18/188.01 ! [V_R_2,V_y_2,V_x_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_R_2)))
% 187.18/188.01 => V_x_2 = V_y_2 ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_rel__pow__Suc__I,axiom,
% 187.18/188.01 ! [V_z_2,V_R_2,V_n_2,V_y_2,V_x_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2)))
% 187.18/188.01 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_z_2)),V_R_2))
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2))) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_rel__pow__Suc__I2,axiom,
% 187.18/188.01 ! [V_n_2,V_z_2,V_R_2,V_y_2,V_x_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_R_2))
% 187.18/188.01 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2)))
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2))) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_funpow_Osimps_I2_J,axiom,
% 187.18/188.01 ! [V_f_2,V_n_2,T_a] : hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),hAPP(c_Nat_OSuc,V_n_2)),V_f_2) = hAPP(c_Fun_Ocomp(T_a,T_a,T_a,V_f_2),hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),V_n_2),V_f_2)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_funpow__add,axiom,
% 187.18/188.01 ! [V_f_2,V_n_2,V_m_2,T_a] : hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)),V_f_2) = hAPP(c_Fun_Ocomp(T_a,T_a,T_a,hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),V_m_2),V_f_2)),hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),V_n_2),V_f_2)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_single__valued__def,axiom,
% 187.18/188.01 ! [V_r_2,T_b,T_a] :
% 187.18/188.01 ( c_Relation_Osingle__valued(T_a,T_b,V_r_2)
% 187.18/188.01 <=> ! [B_x,B_y] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_x),B_y)),V_r_2))
% 187.18/188.01 => ! [B_z] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_x),B_z)),V_r_2))
% 187.18/188.01 => B_y = B_z ) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_single__valuedD,axiom,
% 187.18/188.01 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_b,T_a] :
% 187.18/188.01 ( c_Relation_Osingle__valued(T_a,T_b,V_r_2)
% 187.18/188.01 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),V_r_2))
% 187.18/188.01 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_z_2)),V_r_2))
% 187.18/188.01 => V_y_2 = V_z_2 ) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_funpow_Osimps_I1_J,axiom,
% 187.18/188.01 ! [V_f_2,T_a] : hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_f_2) = c_Fun_Oid(T_a) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_trancl__power,axiom,
% 187.18/188.01 ! [V_R_2,V_p_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_R_2)))
% 187.18/188.01 <=> ? [B_n] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n))
% 187.18/188.01 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),B_n),V_R_2))) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_rtrancl__is__UN__rel__pow,axiom,
% 187.18/188.01 ! [V_R_2,T_a] : c_Transitive__Closure_Ortrancl(T_a,V_R_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(T_a,T_a),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_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_single__valued__confluent,axiom,
% 187.18/188.01 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_a] :
% 187.18/188.01 ( c_Relation_Osingle__valued(T_a,T_a,V_r_2)
% 187.18/188.01 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
% 187.18/188.01 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
% 187.18/188.01 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_z_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
% 187.18/188.01 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_z_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_funpow__code__def,axiom,
% 187.18/188.01 ! [T_a] : c_Nat_Ofunpow(T_a) = c_Nat_Ocompow(T_a,T_a) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_rel__pow__E,axiom,
% 187.18/188.01 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2)))
% 187.18/188.01 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.18/188.01 => V_x_2 != V_z_2 )
% 187.18/188.01 => ~ ! [B_y,B_m] :
% 187.18/188.01 ( V_n_2 = hAPP(c_Nat_OSuc,B_m)
% 187.18/188.01 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),B_y)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),B_m),V_R_2)))
% 187.18/188.01 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),V_z_2)),V_R_2)) ) ) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_rel__pow__E2,axiom,
% 187.18/188.01 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2)))
% 187.18/188.01 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.18/188.01 => V_x_2 != V_z_2 )
% 187.18/188.01 => ~ ! [B_y,B_m] :
% 187.18/188.01 ( V_n_2 = hAPP(c_Nat_OSuc,B_m)
% 187.18/188.01 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),B_y)),V_R_2))
% 187.18/188.01 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),B_m),V_R_2))) ) ) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_rtrancl__Un__separatorE,axiom,
% 187.18/188.01 ! [V_Q_2,V_P_2,V_b_2,V_a_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_P_2),V_Q_2))))
% 187.18/188.01 => ( ! [B_x] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),B_x)),c_Transitive__Closure_Ortrancl(T_a,V_P_2)))
% 187.18/188.01 => ! [B_y] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_y)),V_Q_2))
% 187.18/188.01 => B_x = B_y ) )
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,V_P_2))) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_rtrancl__Un__separator__converseE,axiom,
% 187.18/188.01 ! [V_Q_2,V_P_2,V_b_2,V_a_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_P_2),V_Q_2))))
% 187.18/188.01 => ( ! [B_x] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,V_P_2)))
% 187.18/188.01 => ! [B_y] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),B_x)),V_Q_2))
% 187.18/188.01 => B_y = B_x ) )
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,V_P_2))) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_rel__pow__Suc__E,axiom,
% 187.18/188.01 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2)))
% 187.18/188.01 => ~ ! [B_y] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),B_y)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2)))
% 187.18/188.01 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),V_z_2)),V_R_2)) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_rel__pow__Suc__D2,axiom,
% 187.18/188.01 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2)))
% 187.18/188.01 => ? [B_y] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),B_y)),V_R_2))
% 187.18/188.01 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2))) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_rel__pow__Suc__E2,axiom,
% 187.18/188.01 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2)))
% 187.18/188.01 => ~ ! [B_y] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),B_y)),V_R_2))
% 187.18/188.01 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2))) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_tranclD2,axiom,
% 187.18/188.01 ! [V_R_2,V_y_2,V_x_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_a,V_R_2)))
% 187.18/188.01 => ? [B_z] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),B_z)),c_Transitive__Closure_Ortrancl(T_a,V_R_2)))
% 187.18/188.01 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_z),V_y_2)),V_R_2)) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_tranclD,axiom,
% 187.18/188.01 ! [V_R_2,V_y_2,V_x_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_a,V_R_2)))
% 187.18/188.01 => ? [B_z] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),B_z)),V_R_2))
% 187.18/188.01 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_z),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_IdE,axiom,
% 187.18/188.01 ! [V_p_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Relation_OId(T_a)))
% 187.18/188.01 => ~ ! [B_x] : V_p_2 != hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_mod__div__decomp,axiom,
% 187.18/188.01 ! [V_b,V_a,T_a] :
% 187.18/188.01 ( class_Divides_Osemiring__div(T_a)
% 187.18/188.01 => 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)) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_min__max_OSup__fin_Oeq__fold_H,axiom,
% 187.18/188.01 ! [V_x_2,V_A_2,T_a] :
% 187.18/188.01 ( class_Orderings_Olinorder(T_a)
% 187.18/188.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.01 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 187.18/188.01 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omax(T_a)),V_x_2),V_A_2) ) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_min__max_OInf__fin_Oeq__fold_H,axiom,
% 187.18/188.01 ! [V_x_2,V_A_2,T_a] :
% 187.18/188.01 ( class_Orderings_Olinorder(T_a)
% 187.18/188.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.01 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 187.18/188.01 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omin(T_a)),V_x_2),V_A_2) ) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_fold__image__def,axiom,
% 187.18/188.01 ! [V_g_2,V_f_2,T_b,T_a] : hAPP(c_Finite__Set_Ofold__image(T_a,T_b,V_f_2),V_g_2) = c_Finite__Set_Ofold(T_b,T_a,hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),V_f_2),V_g_2)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_fold__empty,axiom,
% 187.18/188.01 ! [V_z_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_a,V_f_2),V_z_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = V_z_2 ).
% 187.18/188.01
% 187.18/188.01 fof(fact_folding_Oeq__fold,axiom,
% 187.18/188.01 ! [V_s_2,V_A_2,V_Fa_2,V_f_2,T_b,T_a] :
% 187.18/188.01 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_Fa_2)
% 187.18/188.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.01 => hAPP(hAPP(V_Fa_2,V_A_2),V_s_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_s_2),V_A_2) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_fold__def,axiom,
% 187.18/188.01 ! [V_A_2,V_z_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_a,V_f_2),V_z_2),V_A_2) = c_HOL_OThe(T_a,c_Finite__Set_Ofold__graph(T_b,T_a,V_f_2,V_z_2,V_A_2)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_union__fold__insert,axiom,
% 187.18/188.01 ! [V_B_2,V_A_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.01 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a)),V_B_2),V_A_2) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_fold__sup__insert,axiom,
% 187.18/188.01 ! [V_a_2,V_b_2,V_A_2,T_a] :
% 187.18/188.01 ( class_Lattices_Osemilattice__sup(T_a)
% 187.18/188.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.01 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)),V_b_2),V_A_2)) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_fold__inf__insert,axiom,
% 187.18/188.01 ! [V_a_2,V_b_2,V_A_2,T_a] :
% 187.18/188.01 ( class_Lattices_Osemilattice__inf(T_a)
% 187.18/188.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.01 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_b_2),V_A_2)) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_min__max_Ofold__inf__insert,axiom,
% 187.18/188.01 ! [V_a_2,V_b_2,V_A_2,T_a] :
% 187.18/188.01 ( class_Orderings_Olinorder(T_a)
% 187.18/188.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.01 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omin(T_a)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omin(T_a)),V_b_2),V_A_2)) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_min__max_Ofold__sup__insert,axiom,
% 187.18/188.01 ! [V_a_2,V_b_2,V_A_2,T_a] :
% 187.18/188.01 ( class_Orderings_Olinorder(T_a)
% 187.18/188.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.01 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omax(T_a)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omax(T_a)),V_b_2),V_A_2)) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_fun__left__comm__idem_Ofold__insert__idem2,axiom,
% 187.18/188.01 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_b,T_a] :
% 187.18/188.01 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2)
% 187.18/188.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.01 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)),V_A_2) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_fun__left__comm__idem_Ofold__insert__idem,axiom,
% 187.18/188.01 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_b,T_a] :
% 187.18/188.01 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2)
% 187.18/188.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.01 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),V_A_2)) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_sup__SUPR__fold__sup,axiom,
% 187.18/188.01 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] :
% 187.18/188.01 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 187.18/188.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.01 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,T_b),V_A_2),V_f_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_f_2)),V_B_2),V_A_2) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_folding__one__idem_Oeq__fold__idem_H,axiom,
% 187.18/188.01 ! [V_a_2,V_A_2,V_Fa_2,V_f_2,T_a] :
% 187.18/188.01 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_Fa_2)
% 187.18/188.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.01 => hAPP(V_Fa_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,V_f_2),V_a_2),V_A_2) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_sup__le__fold__sup,axiom,
% 187.18/188.01 ! [V_b_2,V_a_2,V_A_2,T_a] :
% 187.18/188.01 ( class_Lattices_Osemilattice__sup(T_a)
% 187.18/188.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a_2),V_b_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)),V_b_2),V_A_2))) ) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_fold__inf__le__inf,axiom,
% 187.18/188.01 ! [V_b_2,V_a_2,V_A_2,T_a] :
% 187.18/188.01 ( class_Lattices_Osemilattice__inf(T_a)
% 187.18/188.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_b_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a_2),V_b_2))) ) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_min__max_Ofold__inf__le__inf,axiom,
% 187.18/188.01 ! [V_b_2,V_a_2,V_A_2,T_a] :
% 187.18/188.01 ( class_Orderings_Olinorder(T_a)
% 187.18/188.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omin(T_a)),V_b_2),V_A_2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a_2),V_b_2))) ) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_min__max_Osup__le__fold__sup,axiom,
% 187.18/188.01 ! [V_b_2,V_a_2,V_A_2,T_a] :
% 187.18/188.01 ( class_Orderings_Olinorder(T_a)
% 187.18/188.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),V_b_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omax(T_a)),V_b_2),V_A_2))) ) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_fold1__eq__fold__idem,axiom,
% 187.18/188.01 ! [V_a_2,V_A_2,T_a] :
% 187.18/188.01 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 187.18/188.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.01 => hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a)),V_a_2),V_A_2) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Sup__fin_Oeq__fold__idem_H,axiom,
% 187.18/188.01 ! [V_a_2,V_A_2,T_a] :
% 187.18/188.01 ( class_Lattices_Olattice(T_a)
% 187.18/188.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.01 => c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)),V_a_2),V_A_2) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Inf__fin_Oeq__fold__idem_H,axiom,
% 187.18/188.01 ! [V_a_2,V_A_2,T_a] :
% 187.18/188.01 ( class_Lattices_Olattice(T_a)
% 187.18/188.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.01 => c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_a_2),V_A_2) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Min_Oeq__fold__idem_H,axiom,
% 187.18/188.01 ! [V_a_2,V_A_2,T_a] :
% 187.18/188.01 ( class_Orderings_Olinorder(T_a)
% 187.18/188.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.01 => c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omin(T_a)),V_a_2),V_A_2) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Max_Oeq__fold__idem_H,axiom,
% 187.18/188.01 ! [V_a_2,V_A_2,T_a] :
% 187.18/188.01 ( class_Orderings_Olinorder(T_a)
% 187.18/188.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.01 => c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omax(T_a)),V_a_2),V_A_2) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_min__max_OInf__fin_Oeq__fold__idem_H,axiom,
% 187.18/188.01 ! [V_a_2,V_A_2,T_a] :
% 187.18/188.01 ( class_Orderings_Olinorder(T_a)
% 187.18/188.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.01 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omin(T_a)),V_a_2),V_A_2) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_min__max_OSup__fin_Oeq__fold__idem_H,axiom,
% 187.18/188.01 ! [V_a_2,V_A_2,T_a] :
% 187.18/188.01 ( class_Orderings_Olinorder(T_a)
% 187.18/188.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.01 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omax(T_a)),V_a_2),V_A_2) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_minus__fold__remove,axiom,
% 187.18/188.01 ! [V_B_2,V_A_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.01 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_B_2),V_A_2) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_folding__one_Oeq__fold_H,axiom,
% 187.18/188.01 ! [V_x_2,V_A_2,V_Fa_2,V_f_2,T_a] :
% 187.18/188.01 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_Fa_2)
% 187.18/188.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.01 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 187.18/188.01 => hAPP(V_Fa_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,V_f_2),V_x_2),V_A_2) ) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_SUPR__fold__sup,axiom,
% 187.18/188.01 ! [V_f_2,V_A_2,T_a,T_b] :
% 187.18/188.01 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 187.18/188.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.01 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,T_b),V_A_2),V_f_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_f_2)),c_Orderings_Obot__class_Obot(T_b)),V_A_2) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_fold1__eq__fold,axiom,
% 187.18/188.01 ! [V_a_2,V_A_2,T_a] :
% 187.18/188.01 ( class_Groups_Oab__semigroup__mult(T_a)
% 187.18/188.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.01 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 187.18/188.01 => hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a)),V_a_2),V_A_2) ) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Sup__fin_Oeq__fold_H,axiom,
% 187.18/188.01 ! [V_x_2,V_A_2,T_a] :
% 187.18/188.01 ( class_Lattices_Olattice(T_a)
% 187.18/188.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.01 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 187.18/188.01 => c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)),V_x_2),V_A_2) ) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Inf__fin_Oeq__fold_H,axiom,
% 187.18/188.01 ! [V_x_2,V_A_2,T_a] :
% 187.18/188.01 ( class_Lattices_Olattice(T_a)
% 187.18/188.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.01 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 187.18/188.01 => c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_x_2),V_A_2) ) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Min_Oeq__fold_H,axiom,
% 187.18/188.01 ! [V_x_2,V_A_2,T_a] :
% 187.18/188.01 ( class_Orderings_Olinorder(T_a)
% 187.18/188.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.01 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 187.18/188.01 => c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omin(T_a)),V_x_2),V_A_2) ) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Max_Oeq__fold_H,axiom,
% 187.18/188.01 ! [V_x_2,V_A_2,T_a] :
% 187.18/188.01 ( class_Orderings_Olinorder(T_a)
% 187.18/188.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.01 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 187.18/188.01 => c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omax(T_a)),V_x_2),V_A_2) ) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_fun__left__comm_Ofold__rec,axiom,
% 187.18/188.01 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_b,T_a] :
% 187.18/188.01 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2)
% 187.18/188.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 187.18/188.01 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),V_A_2) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_fun__left__comm_Ofold__insert__remove,axiom,
% 187.18/188.01 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_b,T_a] :
% 187.18/188.01 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2)
% 187.18/188.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.01 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_fun__left__comm_Ofold__graph__determ,axiom,
% 187.18/188.01 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_b,T_a] :
% 187.18/188.01 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2)
% 187.18/188.01 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_x_2))
% 187.18/188.01 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_y_2))
% 187.18/188.01 => V_y_2 = V_x_2 ) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_fun__left__comm_Ofun__left__comm,axiom,
% 187.18/188.01 ! [V_z_2,V_y_2,V_x_2,V_f_2,T_b,T_a] :
% 187.18/188.01 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2)
% 187.18/188.01 => 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)) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_fun__left__comm_Ofun__left__comm__apply,axiom,
% 187.18/188.01 ! [V_g_2,T_c,V_f_2,T_b,T_a] :
% 187.18/188.01 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2)
% 187.18/188.01 => c_Finite__Set_Ofun__left__comm(T_c,T_b,hAPP(hAPP(c_COMBB(T_a,tc_fun(T_b,T_b),T_c),V_f_2),V_g_2)) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_fun__left__comm,axiom,
% 187.18/188.01 ! [T_a] :
% 187.18/188.01 ( class_Groups_Oab__semigroup__mult(T_a)
% 187.18/188.01 => c_Finite__Set_Ofun__left__comm(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a)) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_fun__left__comm_Ofun__comp__comm,axiom,
% 187.18/188.01 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] :
% 187.18/188.01 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2)
% 187.18/188.01 => hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_f_2,V_y_2)),hAPP(V_f_2,V_x_2)) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_fun__left__comm_Ofold__fun__comm,axiom,
% 187.18/188.01 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_b,T_a] :
% 187.18/188.01 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2)
% 187.18/188.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.01 => hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)),V_A_2) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_fun__left__comm_Ofold__equality,axiom,
% 187.18/188.01 ! [V_y_2,V_A_2,V_z_2,V_f_2,T_b,T_a] :
% 187.18/188.01 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2)
% 187.18/188.01 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_y_2))
% 187.18/188.01 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),V_A_2) = V_y_2 ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_fun__left__comm_Ofold__graph__fold,axiom,
% 187.18/188.01 ! [V_z_2,V_A_2,V_f_2,T_b,T_a] :
% 187.18/188.01 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2)
% 187.18/188.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.01 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),V_A_2))) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_fun__left__comm_Ofold__insert,axiom,
% 187.18/188.01 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_b,T_a] :
% 187.18/188.01 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2)
% 187.18/188.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.01 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 187.18/188.01 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),V_A_2)) ) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_fun__left__comm_Ofold__insert2,axiom,
% 187.18/188.01 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_b,T_a] :
% 187.18/188.01 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2)
% 187.18/188.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.01 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 187.18/188.01 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)),V_A_2) ) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_fun__left__comm_Ofold__graph__insertE__aux,axiom,
% 187.18/188.01 ! [V_a_2,V_y_2,V_A_2,V_z_2,V_f_2,T_b,T_a] :
% 187.18/188.01 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2)
% 187.18/188.01 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_y_2))
% 187.18/188.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 187.18/188.01 => ? [B_y_H] :
% 187.18/188.01 ( V_y_2 = hAPP(hAPP(V_f_2,V_a_2),B_y_H)
% 187.18/188.01 & hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),B_y_H)) ) ) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_INFI__fold__inf,axiom,
% 187.18/188.01 ! [V_f_2,V_A_2,T_a,T_b] :
% 187.18/188.01 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 187.18/188.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.01 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,T_b),V_A_2),V_f_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_f_2)),c_Orderings_Otop__class_Otop(T_b)),V_A_2) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_INF1__E,axiom,
% 187.18/188.01 ! [V_a_2,V_b_2,V_B_2,V_A_2,T_b,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2))
% 187.18/188.01 => ( ~ hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2))
% 187.18/188.01 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_INF1__D,axiom,
% 187.18/188.01 ! [V_a_2,V_b_2,V_B_2,V_A_2,T_b,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2))
% 187.18/188.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 187.18/188.01 => hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2)) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_INT__E,axiom,
% 187.18/188.01 ! [V_a_2,V_B_2,V_A_2,T_b,V_b_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
% 187.18/188.01 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(V_B_2,V_a_2)))
% 187.18/188.01 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_INT__D,axiom,
% 187.18/188.01 ! [V_a_2,V_B_2,V_A_2,T_b,V_b_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
% 187.18/188.01 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_INF2__E,axiom,
% 187.18/188.01 ! [V_a_2,V_c_2,V_b_2,V_B_2,V_A_2,T_c,T_b,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2))
% 187.18/188.01 => ( ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2))
% 187.18/188.01 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_INF2__D,axiom,
% 187.18/188.01 ! [V_a_2,V_c_2,V_b_2,V_B_2,V_A_2,T_c,T_b,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2))
% 187.18/188.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 187.18/188.01 => hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2)) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_finite__INT,axiom,
% 187.18/188.01 ! [V_A_2,T_b,V_I_2,T_a] :
% 187.18/188.01 ( ? [B_x] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_I_2))
% 187.18/188.01 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_A_2,B_x))) )
% 187.18/188.01 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2))) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Compl__INT,axiom,
% 187.18/188.01 ! [V_B_2,V_A_2,T_b,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool))),V_B_2)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Compl__UN,axiom,
% 187.18/188.01 ! [V_B_2,V_A_2,T_b,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool))),V_B_2)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_INT__simps_I9_J,axiom,
% 187.18/188.01 ! [V_C_2,V_B_2,V_A_2,T_c,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,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)),V_C_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),T_c),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool))),V_B_2)),V_C_2)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_INT__extend__simps_I9_J,axiom,
% 187.18/188.01 ! [V_C_2,V_B_2,T_c,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool))),V_B_2)),V_C_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_UN__extend__simps_I7_J,axiom,
% 187.18/188.01 ! [V_B_2,V_C_2,T_b,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),V_B_2)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_UN__simps_I7_J,axiom,
% 187.18/188.01 ! [V_B_2,V_A_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_INF__INT__eq,axiom,
% 187.18/188.01 ! [V_x_2,V_r_2,T_b,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b))),V_r_2)),V_x_2))
% 187.18/188.01 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),V_r_2))) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_INT__absorb,axiom,
% 187.18/188.01 ! [V_A_2,T_b,V_I_2,V_k_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(T_a),V_k_2),V_I_2))
% 187.18/188.01 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_A_2,V_k_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_INF__const,axiom,
% 187.18/188.01 ! [V_M_2,T_a,V_A_2,T_b] :
% 187.18/188.01 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 187.18/188.01 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/188.01 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,T_b),V_A_2),hAPP(c_COMBK(T_b,T_a),V_M_2)) = V_M_2 ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_INT__insert__distrib,axiom,
% 187.18/188.01 ! [V_B_2,V_a_2,T_b,V_A_2,V_u_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(T_a),V_u_2),V_A_2))
% 187.18/188.01 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,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_a),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_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_INFI__bool__eq,axiom,
% 187.18/188.01 ! [T_a] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_HOL_Obool) = c_Set_OBall(T_a) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_vimage__INT,axiom,
% 187.18/188.01 ! [V_B_2,V_A_2,T_c,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_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)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c),c_Set_Ovimage(T_a,T_b,V_f_2)),V_B_2)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_INT__extend__simps_I10_J,axiom,
% 187.18/188.01 ! [V_f_2,V_B_2,T_c,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_a,tc_HOL_Obool),T_b),V_B_2),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),V_B_2) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_INT__simps_I10_J,axiom,
% 187.18/188.01 ! [V_B_2,V_A_2,V_f_2,T_c,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_a,tc_HOL_Obool),T_c),V_B_2),V_f_2)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_INF__INT__eq2,axiom,
% 187.18/188.01 ! [V_y_2,V_x_2,V_r_2,T_c,T_b,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),T_a),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))
% 187.18/188.01 <=> 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_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),V_r_2))) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_INT__iff,axiom,
% 187.18/188.01 ! [V_B_2,V_A_2,T_b,V_b_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
% 187.18/188.01 <=> ! [B_x] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(V_B_2,B_x))) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Pow__INT__eq,axiom,
% 187.18/188.01 ! [V_B_2,V_A_2,T_b,T_a] : hAPP(c_Set_OPow(T_a),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),T_b),c_Set_OPow(T_a)),V_B_2)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_INF__commute,axiom,
% 187.18/188.01 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_a] :
% 187.18/188.01 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 187.18/188.01 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_a),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_a),T_a,T_b),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_a),V_B_2)),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_a),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_a),T_a,T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_a),V_A_2)),hAPP(c_COMBC(T_b,T_c,T_a),V_f_2))) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_INFI__apply,axiom,
% 187.18/188.01 ! [V_x_2,V_f_2,V_A_2,T_c,T_b,T_a] :
% 187.18/188.01 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 187.18/188.01 => hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,T_a)),V_A_2),V_f_2),V_x_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_a),V_A_2),hAPP(hAPP(c_COMBC(T_b,T_c,T_a),V_f_2),V_x_2)) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_INT__Int__distrib,axiom,
% 187.18/188.01 ! [V_B_2,V_A_2,V_I_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_B_2)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_INTER__UNIV__conv_I2_J,axiom,
% 187.18/188.01 ! [V_B_2,V_A_2,T_a,T_b] :
% 187.18/188.01 ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))
% 187.18/188.01 <=> ! [B_x] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 187.18/188.01 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_INTER__UNIV__conv_I1_J,axiom,
% 187.18/188.01 ! [V_B_2,V_A_2,T_b,T_a] :
% 187.18/188.01 ( c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)
% 187.18/188.01 <=> ! [B_x] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 187.18/188.01 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_INT__extend__simps_I5_J,axiom,
% 187.18/188.01 ! [V_B_2,V_C_2,T_b,V_a_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_a),V_a_2)),V_B_2)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_INT__simps_I5_J,axiom,
% 187.18/188.01 ! [V_B_2,V_a_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_a),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_INT__extend__simps_I1_J,axiom,
% 187.18/188.01 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
% 187.18/188.01 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/188.01 => 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_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = V_B_2 )
% 187.18/188.01 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/188.01 => 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_a,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_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,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_a),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_INT__extend__simps_I2_J,axiom,
% 187.18/188.01 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
% 187.18/188.01 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/188.01 => 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_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = V_A_2 )
% 187.18/188.01 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/188.01 => 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_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,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_a),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_INT__empty,axiom,
% 187.18/188.01 ! [V_B_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_INT__constant,axiom,
% 187.18/188.01 ! [V_c_2,T_b,T_a,V_A_2] :
% 187.18/188.01 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/188.01 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_c_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) )
% 187.18/188.01 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/188.01 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_c_2)) = V_c_2 ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_INT__lower,axiom,
% 187.18/188.01 ! [V_B_2,T_b,V_A_2,V_a_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(V_B_2,V_a_2))) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_INF__less__iff,axiom,
% 187.18/188.01 ! [V_a_2,V_f_2,V_A_2,T_b,T_a] :
% 187.18/188.01 ( ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 187.18/188.01 & class_Orderings_Olinorder(T_a) )
% 187.18/188.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_a),V_A_2),V_f_2)),V_a_2))
% 187.18/188.01 <=> ? [B_x] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 187.18/188.01 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(V_f_2,B_x)),V_a_2)) ) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_INT__subset__iff,axiom,
% 187.18/188.01 ! [V_A_2,V_I_2,T_b,V_B_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2)))
% 187.18/188.01 <=> ! [B_x] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2))
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(V_A_2,B_x))) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_le__INF__iff,axiom,
% 187.18/188.01 ! [V_M_2,V_A_2,T_b,V_u_2,T_a] :
% 187.18/188.01 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 187.18/188.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_u_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_a),V_A_2),V_M_2)))
% 187.18/188.01 <=> ! [B_x] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_u_2),hAPP(V_M_2,B_x))) ) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_INT__Un,axiom,
% 187.18/188.01 ! [V_M_2,V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,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_M_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_M_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_M_2)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Collect__ball__eq,axiom,
% 187.18/188.01 ! [V_P_2,V_A_2,T_b,T_a] : hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OAll(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),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)))),V_P_2))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),c_Set_OCollect(T_a)),hAPP(c_COMBC(T_a,T_b,tc_HOL_Obool),V_P_2))) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_INT__insert,axiom,
% 187.18/188.01 ! [V_B_2,V_A_2,V_a_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(V_B_2,V_a_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_INT__simps_I7_J,axiom,
% 187.18/188.01 ! [V_B_2,V_A_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_INT__simps_I6_J,axiom,
% 187.18/188.01 ! [V_B_2,V_A_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_INT__extend__simps_I7_J,axiom,
% 187.18/188.01 ! [V_B_2,V_C_2,T_b,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),V_B_2)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Un__INT__distrib,axiom,
% 187.18/188.01 ! [V_A_2,V_I_2,T_b,V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2)),V_A_2)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_INT__extend__simps_I6_J,axiom,
% 187.18/188.01 ! [V_B_2,V_A_2,V_C_2,T_b,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,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_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Un__INT__distrib2,axiom,
% 187.18/188.01 ! [V_B_2,V_J_2,T_c,V_A_2,V_I_2,T_b,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),V_J_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),V_J_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_fun(tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool))),V_A_2))),V_B_2))) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_converse__INTER,axiom,
% 187.18/188.01 ! [V_r_2,V_S_2,T_c,T_a,T_b] : hAPP(c_Relation_Oconverse(T_b,T_a),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),V_S_2),V_r_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_S_2),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),T_c),c_Relation_Oconverse(T_b,T_a)),V_r_2)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Image__INT__subset,axiom,
% 187.18/188.01 ! [V_B_2,V_A_2,T_c,V_r_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_a,V_r_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))),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c),c_Relation_OImage(T_b,T_a,V_r_2)),V_B_2)))) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_INF__subset,axiom,
% 187.18/188.01 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] :
% 187.18/188.01 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 187.18/188.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,T_b),V_B_2),V_f_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,T_b),V_A_2),V_f_2))) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_INTER__def,axiom,
% 187.18/188.01 ! [V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OAll(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),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(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_b)),c_member(T_a))),V_B_2)))) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_INT__simps_I1_J,axiom,
% 187.18/188.01 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
% 187.18/188.01 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/188.01 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,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_a),c_Lattices_Osemilattice__inf__class_Oinf(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)) )
% 187.18/188.01 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/188.01 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,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_a),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_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_INT__simps_I2_J,axiom,
% 187.18/188.01 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
% 187.18/188.01 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/188.01 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,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_a),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(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)) )
% 187.18/188.01 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/188.01 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,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_a),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_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Collect__all__eq,axiom,
% 187.18/188.01 ! [V_P_2,T_b,T_a] : hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OAll(T_b)),V_P_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),c_Set_OCollect(T_a)),hAPP(c_COMBC(T_a,T_b,tc_HOL_Obool),V_P_2))) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_INT__extend__simps_I3_J,axiom,
% 187.18/188.01 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
% 187.18/188.01 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/188.01 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_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_B_2) )
% 187.18/188.01 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/188.01 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,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_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,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_a),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_INT__simps_I3_J,axiom,
% 187.18/188.01 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
% 187.18/188.01 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/188.01 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,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_a),c_Groups_Ominus__class_Ominus(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)) )
% 187.18/188.01 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/188.01 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,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_a),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_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_INT__extend__simps_I4_J,axiom,
% 187.18/188.01 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
% 187.18/188.01 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/188.01 => 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_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = V_A_2 )
% 187.18/188.01 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/188.01 => 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_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,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_a),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_INF__leI,axiom,
% 187.18/188.01 ! [V_M_2,V_A_2,V_i_2,T_a,T_b] :
% 187.18/188.01 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 187.18/188.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),V_A_2))
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,T_b),V_A_2),V_M_2)),hAPP(V_M_2,V_i_2))) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_INT__greaterThan__UNIV,axiom,
% 187.18/188.01 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)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_INT__simps_I4_J,axiom,
% 187.18/188.01 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
% 187.18/188.01 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/188.01 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,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_a),hAPP(c_Groups_Ominus__class_Ominus(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)) )
% 187.18/188.01 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/188.01 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,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_a),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_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Image__INT__eq,axiom,
% 187.18/188.01 ! [V_B_2,T_c,V_A_2,V_r_2,T_b,T_a] :
% 187.18/188.01 ( c_Relation_Osingle__valued(T_a,T_b,hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2))
% 187.18/188.01 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
% 187.18/188.01 => hAPP(c_Relation_OImage(T_b,T_a,V_r_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)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c),c_Relation_OImage(T_b,T_a,V_r_2)),V_B_2)) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_inf__INFI__fold__inf,axiom,
% 187.18/188.01 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] :
% 187.18/188.01 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 187.18/188.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.01 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,T_b),V_A_2),V_f_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_f_2)),V_B_2),V_A_2) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Inf__fold__inf,axiom,
% 187.18/188.01 ! [V_A_2,T_a] :
% 187.18/188.01 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 187.18/188.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.01 => c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),c_Orderings_Otop__class_Otop(T_a)),V_A_2) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Sup__fold__sup,axiom,
% 187.18/188.01 ! [V_A_2,T_a] :
% 187.18/188.01 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 187.18/188.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.01 => c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)),c_Orderings_Obot__class_Obot(T_a)),V_A_2) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_finite__Inter,axiom,
% 187.18/188.01 ! [V_M_2,T_a] :
% 187.18/188.01 ( ? [B_x] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_x),V_M_2))
% 187.18/188.01 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_x)) )
% 187.18/188.01 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_M_2))) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_UnionI,axiom,
% 187.18/188.01 ! [V_A_2,V_C_2,V_X_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),V_C_2))
% 187.18/188.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),V_X_2))
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_C_2))) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_InterD,axiom,
% 187.18/188.01 ! [V_X_2,V_C_2,V_A_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_C_2)))
% 187.18/188.01 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),V_C_2))
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),V_X_2)) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_InterE,axiom,
% 187.18/188.01 ! [V_X_2,V_C_2,V_A_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_C_2)))
% 187.18/188.01 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),V_C_2))
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),V_X_2)) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_INTER__eq__Inter__image,axiom,
% 187.18/188.01 ! [V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,tc_HOL_Obool),V_B_2),V_A_2)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Inter__image__eq,axiom,
% 187.18/188.01 ! [V_A_2,V_B_2,T_b,T_a] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,tc_HOL_Obool),V_B_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_INT__extend__simps_I8_J,axiom,
% 187.18/188.01 ! [V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool))),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),V_B_2) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_INT__simps_I8_J,axiom,
% 187.18/188.01 ! [V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool))),V_B_2)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_INF2__iff,axiom,
% 187.18/188.01 ! [V_c_2,V_b_2,V_B_2,V_A_2,T_c,T_b,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2))
% 187.18/188.01 <=> ! [B_x] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 187.18/188.01 => hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2)) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_INF1__iff,axiom,
% 187.18/188.01 ! [V_b_2,V_B_2,V_A_2,T_b,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2))
% 187.18/188.01 <=> ! [B_x] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 187.18/188.01 => hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Un__Inter,axiom,
% 187.18/188.01 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Inf__less__iff,axiom,
% 187.18/188.01 ! [V_a_2,V_S_2,T_a] :
% 187.18/188.01 ( ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 187.18/188.01 & class_Orderings_Olinorder(T_a) )
% 187.18/188.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Complete__Lattice_OInf__class_OInf(T_a,V_S_2)),V_a_2))
% 187.18/188.01 <=> ? [B_x] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2))
% 187.18/188.01 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_x),V_a_2)) ) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_less__Sup__iff,axiom,
% 187.18/188.01 ! [V_S_2,V_a_2,T_a] :
% 187.18/188.01 ( ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 187.18/188.01 & class_Orderings_Olinorder(T_a) )
% 187.18/188.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_a,V_S_2)))
% 187.18/188.01 <=> ? [B_x] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2))
% 187.18/188.01 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),B_x)) ) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_le__Inf__iff,axiom,
% 187.18/188.01 ! [V_A_2,V_b_2,T_a] :
% 187.18/188.01 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 187.18/188.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2)))
% 187.18/188.01 <=> ! [B_x] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),B_x)) ) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Sup__le__iff,axiom,
% 187.18/188.01 ! [V_b_2,V_A_2,T_a] :
% 187.18/188.01 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 187.18/188.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2)),V_b_2))
% 187.18/188.01 <=> ! [B_x] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),V_b_2)) ) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Union__upper,axiom,
% 187.18/188.01 ! [V_A_2,V_B_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2))) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Union__disjoint,axiom,
% 187.18/188.01 ! [V_A_2,V_C_2,T_a] :
% 187.18/188.01 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_C_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/188.01 <=> ! [B_x] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_x),V_C_2))
% 187.18/188.01 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),B_x),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Union__Pow__eq,axiom,
% 187.18/188.01 ! [V_A_2,T_a] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_OPow(T_a),V_A_2)) = V_A_2 ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Field__Union,axiom,
% 187.18/188.01 ! [V_R_2,T_a] : hAPP(c_Relation_OField(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_R_2)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),c_Relation_OField(T_a)),V_R_2)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_vimage__Union,axiom,
% 187.18/188.01 ! [V_A_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Set_Ovimage(T_a,T_b,V_f_2)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Sigma__Union,axiom,
% 187.18/188.01 ! [V_B_2,V_X_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_X_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),c_Product__Type_OSigma(T_a,T_b)),V_B_2)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_image__Union,axiom,
% 187.18/188.01 ! [V_S_2,V_f_2,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,V_f_2),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_a,tc_HOL_Obool)),V_S_2),c_Set_Oimage(T_b,T_a,V_f_2)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Int__Union,axiom,
% 187.18/188.01 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Int__Union2,axiom,
% 187.18/188.01 ! [V_A_2,V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_B_2)),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool))),V_A_2)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_UN__extend__simps_I8_J,axiom,
% 187.18/188.01 ! [V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool))),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),V_B_2) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_UN__simps_I8_J,axiom,
% 187.18/188.01 ! [V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool))),V_B_2)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Range__Union,axiom,
% 187.18/188.01 ! [V_S_2,T_a,T_b] : hAPP(c_Relation_ORange(T_b,T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_S_2),c_Relation_ORange(T_b,T_a)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Domain__Union,axiom,
% 187.18/188.01 ! [V_S_2,T_b,T_a] : hAPP(c_Relation_ODomain(T_a,T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_S_2),c_Relation_ODomain(T_a,T_b)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Inter__lower,axiom,
% 187.18/188.01 ! [V_A_2,V_B_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_A_2)),V_B_2)) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Inf__Sup,axiom,
% 187.18/188.01 ! [V_A_2,T_a] :
% 187.18/188.01 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 187.18/188.01 => c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_a,hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OAll(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fimplies),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)))),c_Orderings_Oord__class_Oless__eq(T_a))))) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Sup__Inf,axiom,
% 187.18/188.01 ! [V_A_2,T_a] :
% 187.18/188.01 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 187.18/188.01 => c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_a,hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OAll(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fimplies),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)))),hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_a)))))) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Union__empty,axiom,
% 187.18/188.01 ! [T_a] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Union__mono,axiom,
% 187.18/188.01 ! [V_B_2,V_A_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2))
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_B_2))) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Union__insert,axiom,
% 187.18/188.01 ! [V_B_2,V_a_2,T_a] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_a_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_B_2)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Union__quotient,axiom,
% 187.18/188.01 ! [V_r_2,V_A_2,T_a] :
% 187.18/188.01 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 187.18/188.01 => c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2)) = V_A_2 ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_finite__UnionD,axiom,
% 187.18/188.01 ! [V_A_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2)))
% 187.18/188.01 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_subset__Pow__Union,axiom,
% 187.18/188.01 ! [V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2)))) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Inter__anti__mono,axiom,
% 187.18/188.01 ! [V_A_2,V_B_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_B_2),V_A_2))
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_B_2))) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Inter__empty,axiom,
% 187.18/188.01 ! [T_a] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Inter__eq,axiom,
% 187.18/188.01 ! [V_A_2,T_a] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_A_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OAll(tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),T_a),hAPP(c_COMBS(tc_fun(T_a,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_a,tc_HOL_Obool)),c_fimplies),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_a,tc_HOL_Obool))),V_A_2)))),c_member(T_a)))) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Union__UNIV,axiom,
% 187.18/188.01 ! [T_a] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Union__Un__distrib,axiom,
% 187.18/188.01 ! [V_B_2,V_A_2,T_a] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_B_2)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Inter__insert,axiom,
% 187.18/188.01 ! [V_B_2,V_a_2,T_a] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_a_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_B_2)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Union__image__eq,axiom,
% 187.18/188.01 ! [V_A_2,V_B_2,T_b,T_a] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,tc_HOL_Obool),V_B_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_UNION__eq__Union__image,axiom,
% 187.18/188.01 ! [V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,tc_HOL_Obool),V_B_2),V_A_2)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Sup__upper,axiom,
% 187.18/188.01 ! [V_A_2,V_x_2,T_a] :
% 187.18/188.01 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 187.18/188.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2))) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Inter__UNIV,axiom,
% 187.18/188.01 ! [T_a] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Inf__lower,axiom,
% 187.18/188.01 ! [V_A_2,V_x_2,T_a] :
% 187.18/188.01 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 187.18/188.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2)),V_x_2)) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Sup__empty,axiom,
% 187.18/188.01 ! [T_a] :
% 187.18/188.01 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 187.18/188.01 => c_Complete__Lattice_OSup__class_OSup(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(T_a) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Inter__Un__distrib,axiom,
% 187.18/188.01 ! [V_B_2,V_A_2,T_a] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_B_2)) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Sup__singleton,axiom,
% 187.18/188.01 ! [V_a_2,T_a] :
% 187.18/188.01 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 187.18/188.01 => c_Complete__Lattice_OSup__class_OSup(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_a_2 ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Sup__insert,axiom,
% 187.18/188.01 ! [V_A_2,V_a_2,T_a] :
% 187.18/188.01 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 187.18/188.01 => c_Complete__Lattice_OSup__class_OSup(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2)) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Int__Inter__image,axiom,
% 187.18/188.01 ! [V_B_2,V_A_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,tc_HOL_Obool),V_A_2),V_C_2))),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,tc_HOL_Obool),V_B_2),V_C_2))) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Inf__singleton,axiom,
% 187.18/188.01 ! [V_a_2,T_a] :
% 187.18/188.01 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 187.18/188.01 => c_Complete__Lattice_OInf__class_OInf(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_a_2 ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Sup__UNIV,axiom,
% 187.18/188.01 ! [T_a] :
% 187.18/188.01 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 187.18/188.01 => c_Complete__Lattice_OSup__class_OSup(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(T_a) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Inf__empty,axiom,
% 187.18/188.01 ! [T_a] :
% 187.18/188.01 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 187.18/188.01 => c_Complete__Lattice_OInf__class_OInf(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(T_a) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Inf__UNIV,axiom,
% 187.18/188.01 ! [T_a] :
% 187.18/188.01 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 187.18/188.01 => c_Complete__Lattice_OInf__class_OInf(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(T_a) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Inf__insert,axiom,
% 187.18/188.01 ! [V_A_2,V_a_2,T_a] :
% 187.18/188.01 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 187.18/188.01 => c_Complete__Lattice_OInf__class_OInf(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a_2),c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2)) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Un__eq__Union,axiom,
% 187.18/188.01 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),V_B_2),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))))) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Un__Union__image,axiom,
% 187.18/188.01 ! [V_B_2,V_A_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,tc_HOL_Obool),V_A_2),V_C_2))),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,tc_HOL_Obool),V_B_2),V_C_2))) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Union__Int__subset,axiom,
% 187.18/188.01 ! [V_B_2,V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_B_2)))) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Int__eq__Inter,axiom,
% 187.18/188.01 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),V_B_2),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))))) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Inter__Un__subset,axiom,
% 187.18/188.01 ! [V_B_2,V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_B_2))),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)))) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Sup__binary,axiom,
% 187.18/188.01 ! [V_b_2,V_a_2,T_a] :
% 187.18/188.01 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 187.18/188.01 => c_Complete__Lattice_OSup__class_OSup(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a_2),V_b_2) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Inf__binary,axiom,
% 187.18/188.01 ! [V_b_2,V_a_2,T_a] :
% 187.18/188.01 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 187.18/188.01 => c_Complete__Lattice_OInf__class_OInf(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a_2),V_b_2) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_sup__Sup__fold__sup,axiom,
% 187.18/188.01 ! [V_B_2,V_A_2,T_a] :
% 187.18/188.01 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 187.18/188.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.01 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_B_2),c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)),V_B_2),V_A_2) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Sup__fin__Sup,axiom,
% 187.18/188.01 ! [V_A_2,T_a] :
% 187.18/188.01 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 187.18/188.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.01 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/188.01 => c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2) ) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_inf__Inf__fold__inf,axiom,
% 187.18/188.01 ! [V_B_2,V_A_2,T_a] :
% 187.18/188.01 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 187.18/188.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.01 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_B_2),c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_B_2),V_A_2) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Inf__fin__Inf,axiom,
% 187.18/188.01 ! [V_A_2,T_a] :
% 187.18/188.01 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 187.18/188.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.01 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/188.01 => c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2) ) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_image__INT,axiom,
% 187.18/188.01 ! [V_j_2,V_B_2,V_A_2,T_c,V_C_2,V_f_2,T_b,T_a] :
% 187.18/188.01 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_C_2)
% 187.18/188.01 => ( ! [B_x] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(V_B_2,B_x)),V_C_2)) )
% 187.18/188.01 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_j_2),V_A_2))
% 187.18/188.01 => hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,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_a,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Set_Oimage(T_a,T_b,V_f_2)),V_B_2)) ) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_card__partition,axiom,
% 187.18/188.01 ! [V_k_2,V_C_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),V_C_2))
% 187.18/188.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_C_2)))
% 187.18/188.01 => ( ! [B_c] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_c),V_C_2))
% 187.18/188.01 => hAPP(c_Finite__Set_Ocard(T_a),B_c) = V_k_2 )
% 187.18/188.01 => ( ! [B_c1] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_c1),V_C_2))
% 187.18/188.01 => ! [B_c2] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_c2),V_C_2))
% 187.18/188.01 => ( B_c1 != B_c2
% 187.18/188.01 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),B_c1),B_c2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) )
% 187.18/188.01 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(tc_fun(T_a,tc_HOL_Obool)),V_C_2)) = hAPP(c_Finite__Set_Ocard(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_C_2)) ) ) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Inter__def,axiom,
% 187.18/188.01 ! [V_S_2,T_a] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_S_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_S_2),c_COMBI(tc_fun(T_a,tc_HOL_Obool))) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Union__def,axiom,
% 187.18/188.01 ! [V_S_2,T_a] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_S_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_S_2),c_COMBI(tc_fun(T_a,tc_HOL_Obool))) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_finite__Union,axiom,
% 187.18/188.01 ! [V_A_2,T_a] :
% 187.18/188.01 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),V_A_2))
% 187.18/188.01 => ( ! [B_M] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_M),V_A_2))
% 187.18/188.01 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_M)) )
% 187.18/188.01 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2))) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_insert__partition,axiom,
% 187.18/188.01 ! [V_Fa_2,V_x_2,T_a] :
% 187.18/188.01 ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_x_2),V_Fa_2))
% 187.18/188.01 => ( ! [B_x] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_x),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),V_x_2),V_Fa_2)))
% 187.18/188.01 => ! [B_xa] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_xa),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),V_x_2),V_Fa_2)))
% 187.18/188.01 => ( B_x != B_xa
% 187.18/188.01 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),B_x),B_xa) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) )
% 187.18/188.01 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_x_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_Fa_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_inj__on__Inter,axiom,
% 187.18/188.01 ! [V_f_2,T_b,T_a,V_S_2] :
% 187.18/188.01 ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))
% 187.18/188.01 => ( ! [B_A] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_A),V_S_2))
% 187.18/188.01 => c_Fun_Oinj__on(T_a,T_b,V_f_2,B_A) )
% 187.18/188.01 => c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_S_2)) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_Inter__subset,axiom,
% 187.18/188.01 ! [V_B_2,V_A_2,T_a] :
% 187.18/188.01 ( ! [B_X] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_X),V_A_2))
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),B_X),V_B_2)) )
% 187.18/188.01 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_A_2)),V_B_2)) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_inj__on__INTER,axiom,
% 187.18/188.01 ! [V_A_2,V_f_2,T_c,T_b,T_a,V_I_2] :
% 187.18/188.01 ( V_I_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/188.01 => ( ! [B_i] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_i),V_I_2))
% 187.18/188.01 => c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(V_A_2,B_i)) )
% 187.18/188.01 => c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_fun__left__comm_Ofold__graph__insertE,axiom,
% 187.18/188.01 ! [V_v_2,V_A_2,V_x_2,V_z_2,V_f_2,T_b,T_a] :
% 187.18/188.01 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2)
% 187.18/188.01 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)),V_v_2))
% 187.18/188.01 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 187.18/188.01 => ~ ! [B_y] :
% 187.18/188.01 ( V_v_2 = hAPP(hAPP(V_f_2,V_x_2),B_y)
% 187.18/188.01 => ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),B_y)) ) ) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_min__max_Ofold__sup__le__sup,axiom,
% 187.18/188.01 ! [V_c_2,V_b_2,V_A_2,T_a] :
% 187.18/188.01 ( class_Orderings_Olinorder(T_a)
% 187.18/188.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.01 => ( ! [B_x] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),V_b_2)) )
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omax(T_a)),V_c_2),V_A_2)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_b_2),V_c_2))) ) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_min__max_Oinf__le__fold__inf,axiom,
% 187.18/188.01 ! [V_c_2,V_b_2,V_A_2,T_a] :
% 187.18/188.01 ( class_Orderings_Olinorder(T_a)
% 187.18/188.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.01 => ( ! [B_x] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),B_x)) )
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b_2),V_c_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omin(T_a)),V_c_2),V_A_2))) ) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_InterI,axiom,
% 187.18/188.01 ! [V_A_2,V_C_2,T_a] :
% 187.18/188.01 ( ! [B_X] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_X),V_C_2))
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),B_X)) )
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_C_2))) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_inf__le__fold__inf,axiom,
% 187.18/188.01 ! [V_c_2,V_b_2,V_A_2,T_a] :
% 187.18/188.01 ( class_Lattices_Osemilattice__inf(T_a)
% 187.18/188.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.01 => ( ! [B_x] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),B_x)) )
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_b_2),V_c_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_c_2),V_A_2))) ) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_fold__sup__le__sup,axiom,
% 187.18/188.01 ! [V_c_2,V_b_2,V_A_2,T_a] :
% 187.18/188.01 ( class_Lattices_Osemilattice__sup(T_a)
% 187.18/188.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.01 => ( ! [B_x] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),V_b_2)) )
% 187.18/188.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)),V_c_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_b_2),V_c_2))) ) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_wf__eq__minimal,axiom,
% 187.18/188.01 ! [V_r_2,T_a] :
% 187.18/188.01 ( c_Wellfounded_Owf(T_a,V_r_2)
% 187.18/188.01 <=> ! [B_Q] :
% 187.18/188.01 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),B_Q))
% 187.18/188.01 => ? [B_x] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),B_Q))
% 187.18/188.01 & ! [B_y] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),B_x)),V_r_2))
% 187.18/188.01 => ~ hBOOL(hAPP(hAPP(c_member(T_a),B_y),B_Q)) ) ) ) ) ).
% 187.18/188.01
% 187.18/188.01 fof(fact_transfer__nat__int__set__cong,axiom,
% 187.18/188.01 ! [V_P_H_2,V_P_2] :
% 187.18/188.01 ( ! [B_x] :
% 187.18/188.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 187.18/188.01 => ( hBOOL(hAPP(V_P_2,B_x))
% 187.18/188.01 <=> hBOOL(hAPP(V_P_H_2,B_x)) ) )
% 187.18/188.01 => 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)) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_Int__Collect__mono,axiom,
% 187.18/188.02 ! [V_Q_2,V_P_2,V_B_2,V_A_2,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 187.18/188.02 => ( ! [B_x] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 187.18/188.02 => ( hBOOL(hAPP(V_P_2,B_x))
% 187.18/188.02 => hBOOL(hAPP(V_Q_2,B_x)) ) )
% 187.18/188.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_a),V_P_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(c_Set_OCollect(T_a),V_Q_2)))) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_UnionE,axiom,
% 187.18/188.02 ! [V_C_2,V_A_2,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_C_2)))
% 187.18/188.02 => ~ ! [B_X] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),B_X))
% 187.18/188.02 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_X),V_C_2)) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_rel__compE,axiom,
% 187.18/188.02 ! [V_s_2,V_r_2,T_c,V_xz_2,T_b,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),V_xz_2),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_r_2),V_s_2)))
% 187.18/188.02 => ~ ! [B_x,B_y,B_z] :
% 187.18/188.02 ( V_xz_2 = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_x),B_z)
% 187.18/188.02 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_c),B_x),B_y)),V_r_2))
% 187.18/188.02 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_y),B_z)),V_s_2)) ) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_converseE,axiom,
% 187.18/188.02 ! [V_r_2,V_yx_2,T_b,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),V_yx_2),hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2)))
% 187.18/188.02 => ~ ! [B_x,B_y] :
% 187.18/188.02 ( V_yx_2 = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_y),B_x)
% 187.18/188.02 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),B_x),B_y)),V_r_2)) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_Nitpick_Oplus__frac__def,axiom,
% 187.18/188.02 ! [V_r_2,V_q_2,T_a] : c_Nitpick_Oplus__frac(T_a,V_q_2,V_r_2) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_a),c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(T_a),V_q_2),hAPP(c_Nitpick_Odenom(T_a),V_r_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,T_a),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,T_a),tc_Int_Oint),c_Nitpick_Ofrac(T_a)),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_a),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_a),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_a),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_a),V_r_2)))))),c_COMBI(tc_Int_Oint))) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_Nitpick_Otimes__frac__def,axiom,
% 187.18/188.02 ! [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))) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_Nitpick_Oof__frac__def,axiom,
% 187.18/188.02 ! [V_q,T_a,T_b] :
% 187.18/188.02 ( ( class_Rings_Oinverse(T_b)
% 187.18/188.02 & class_Rings_Oring__1(T_b) )
% 187.18/188.02 => 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))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_Nitpick_Oinverse__frac__def,axiom,
% 187.18/188.02 ! [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)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_Nitpick_Ouminus__frac__def,axiom,
% 187.18/188.02 ! [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))) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_Nitpick_Oless__frac__def,axiom,
% 187.18/188.02 ! [V_r_2,V_q_2,T_a] :
% 187.18/188.02 ( c_Nitpick_Oless__frac(T_a,V_q_2,V_r_2)
% 187.18/188.02 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_a),c_Nitpick_Oplus__frac(T_a,V_q_2,c_Nitpick_Ouminus__frac(T_a,V_r_2)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_Nitpick_Oless__eq__frac__def,axiom,
% 187.18/188.02 ! [V_r_2,V_q_2,T_a] :
% 187.18/188.02 ( c_Nitpick_Oless__eq__frac(T_a,V_q_2,V_r_2)
% 187.18/188.02 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_a),c_Nitpick_Oplus__frac(T_a,V_q_2,c_Nitpick_Ouminus__frac(T_a,V_r_2)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_Nitpick_Onum__def,axiom,
% 187.18/188.02 ! [T_a] : c_Nitpick_Onum(T_a) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,T_a,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(T_a)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_Nitpick_Odenom__def,axiom,
% 187.18/188.02 ! [T_a] : c_Nitpick_Odenom(T_a) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,T_a,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(T_a)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_setprod__pos,axiom,
% 187.18/188.02 ! [V_f_2,V_A_2,T_a,T_b] :
% 187.18/188.02 ( class_Rings_Olinordered__semidom(T_b)
% 187.18/188.02 => ( ! [B_x] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 187.18/188.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_x))) )
% 187.18/188.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_A_2))) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_internal__split__def,axiom,
% 187.18/188.02 ! [T_c,T_b,T_a] : c_Product__Type_Ointernal__split(T_a,T_b,T_c) = c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_internal__split__conv,axiom,
% 187.18/188.02 ! [V_b_2,V_a_2,V_c_2,T_a,T_c,T_b] : hAPP(hAPP(c_Product__Type_Ointernal__split(T_b,T_c,T_a),V_c_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)) = hAPP(hAPP(V_c_2,V_a_2),V_b_2) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_setprod__nonneg,axiom,
% 187.18/188.02 ! [V_f_2,V_A_2,T_a,T_b] :
% 187.18/188.02 ( class_Rings_Olinordered__semidom(T_b)
% 187.18/188.02 => ( ! [B_x] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 187.18/188.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_x))) )
% 187.18/188.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_A_2))) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_bool_Osize_I1_J,axiom,
% 187.18/188.02 c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_bool_Osize_I2_J,axiom,
% 187.18/188.02 c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_finite__less__ub,axiom,
% 187.18/188.02 ! [V_u_2,V_f_2] :
% 187.18/188.02 ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_n),hAPP(V_f_2,B_n)))
% 187.18/188.02 => 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)))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_lenlex__def,axiom,
% 187.18/188.02 ! [V_r_2,T_a] : c_List_Olenlex(T_a,V_r_2) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,tc_List_Olist(T_a)),tc_List_Olist(T_a)),c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_List_Olist(T_a),c_Wellfounded_Oless__than,c_List_Olex(T_a,V_r_2))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_prod(tc_Nat_Onat,tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_List_Olist(T_a),tc_prod(tc_Nat_Onat,tc_List_Olist(T_a))),tc_List_Olist(T_a)),c_Product__Type_OPair(tc_Nat_Onat,tc_List_Olist(T_a))),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),c_COMBI(tc_List_Olist(T_a)))) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_neq__if__length__neq,axiom,
% 187.18/188.02 ! [V_ys,V_xs,T_a] :
% 187.18/188.02 ( 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)
% 187.18/188.02 => V_xs != V_ys ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_lexn__length,axiom,
% 187.18/188.02 ! [V_n_2,V_r_2,V_ys_2,V_xs_2,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),hAPP(c_List_Olexn(T_a,V_r_2),V_n_2)))
% 187.18/188.02 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = V_n_2
% 187.18/188.02 & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) = V_n_2 ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_lenlex__conv,axiom,
% 187.18/188.02 ! [V_r_2,T_a] : c_List_Olenlex(T_a,V_r_2) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_List_Olist(T_a)),c_COMBS(tc_List_Olist(T_a),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(T_a)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_a)),c_fdisj)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_Nat_Onat),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_a),tc_Nat_Onat),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_List_Olist(T_a)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_a)),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_List_Olist(T_a)),c_COMBS(tc_List_Olist(T_a),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(T_a)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_a)),c_fconj)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_Nat_Onat),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_a),tc_Nat_Onat),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_List_Olist(T_a)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_a)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_List_Olist(T_a)),c_COMBC(tc_List_Olist(T_a),tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_fun(tc_List_Olist(T_a),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool),tc_HOL_Obool)),tc_List_Olist(T_a)),hAPP(c_COMBB(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_a)),c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))))),c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a))))),c_List_Olex(T_a,V_r_2)))))) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_length__sublist,axiom,
% 187.18/188.02 ! [V_I_2,V_xs_2,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Osublist(T_a,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_a)),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)))) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_lexn_Osimps_I2_J,axiom,
% 187.18/188.02 ! [V_n_2,V_r_2,T_a] : hAPP(c_List_Olexn(T_a,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_a),tc_List_Olist(T_a)),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_prod(tc_prod(T_a,tc_List_Olist(T_a)),tc_prod(T_a,tc_List_Olist(T_a))),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_Product__Type_Omap__pair(tc_prod(T_a,tc_List_Olist(T_a)),tc_List_Olist(T_a),tc_prod(T_a,tc_List_Olist(T_a)),tc_List_Olist(T_a),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)))),c_Wellfounded_Olex__prod(T_a,tc_List_Olist(T_a),V_r_2,hAPP(c_List_Olexn(T_a,V_r_2),V_n_2)))),hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_List_Olist(T_a)),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_a)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),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_a)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),hAPP(c_Nat_OSuc,V_n_2))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),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_a)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),hAPP(c_Nat_OSuc,V_n_2)))))) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_impossible__Cons,axiom,
% 187.18/188.02 ! [V_x,V_ys,V_xs,T_a] :
% 187.18/188.02 ( 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)))
% 187.18/188.02 => V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_not__Cons__self,axiom,
% 187.18/188.02 ! [V_x,T_a,V_xs] : V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_not__Cons__self2,axiom,
% 187.18/188.02 ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) != V_xs ).
% 187.18/188.02
% 187.18/188.02 fof(fact_list_Oinject,axiom,
% 187.18/188.02 ! [V_list_H_2,V_a_H_2,V_list_2,V_a_2,T_a] :
% 187.18/188.02 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_2),V_list_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_H_2),V_list_H_2)
% 187.18/188.02 <=> ( V_a_2 = V_a_H_2
% 187.18/188.02 & V_list_2 = V_list_H_2 ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_list_Osize_I4_J,axiom,
% 187.18/188.02 ! [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))) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_Cons__in__lex,axiom,
% 187.18/188.02 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2))),c_List_Olex(T_a,V_r_2)))
% 187.18/188.02 <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2))
% 187.18/188.02 & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) )
% 187.18/188.02 | ( V_x_2 = V_y_2
% 187.18/188.02 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olex(T_a,V_r_2))) ) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_set__Cons__def,axiom,
% 187.18/188.02 ! [V_XS_2,V_A_2,T_a] : c_List_Oset__Cons(T_a,V_A_2,V_XS_2) = hAPP(c_Set_OCollect(tc_List_Olist(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,tc_List_Olist(T_a)),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool),tc_List_Olist(T_a)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(tc_List_Olist(T_a)))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))),tc_List_Olist(T_a)),c_COMBS(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))),tc_List_Olist(T_a)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),T_a),c_COMBS(tc_List_Olist(T_a),tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_List_Olist(T_a)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_a)),c_fconj))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))),tc_List_Olist(T_a)),c_COMBB(tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),T_a)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_List_Olist(T_a)),c_COMBB(tc_List_Olist(T_a),tc_HOL_Obool,tc_List_Olist(T_a))),c_fequal))),c_List_Olist_OCons(T_a)))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(T_a))),V_XS_2)))))) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_pick_Osimps,axiom,
% 187.18/188.02 ! [V_xs,V_x,T_a,V_i] :
% 187.18/188.02 ( ( 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)))
% 187.18/188.02 => 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) )
% 187.18/188.02 & ( ~ 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)))
% 187.18/188.02 => 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))) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_select__weight__cons__zero,axiom,
% 187.18/188.02 ! [V_xs_2,V_x_2,T_a] : c_Random_Oselect__weight(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a)),hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_a),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),V_x_2)),V_xs_2)) = c_Random_Oselect__weight(T_a,V_xs_2) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_lexord__cons__cons,axiom,
% 187.18/188.02 ! [V_r_2,V_y_2,V_b_2,V_x_2,V_a_2,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_2),V_x_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_b_2),V_y_2))),c_List_Olexord(T_a,V_r_2)))
% 187.18/188.02 <=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2))
% 187.18/188.02 | ( V_a_2 = V_b_2
% 187.18/188.02 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_y_2)),c_List_Olexord(T_a,V_r_2))) ) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_lexord__lex,axiom,
% 187.18/188.02 ! [V_r_2,V_y_2,V_x_2,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_y_2)),c_List_Olex(T_a,V_r_2)))
% 187.18/188.02 <=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_y_2)),c_List_Olexord(T_a,V_r_2)))
% 187.18/188.02 & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_x_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_y_2) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_rtrancl__listrel1__ConsI2,axiom,
% 187.18/188.02 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
% 187.18/188.02 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2))))
% 187.18/188.02 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_list_Osize_I2_J,axiom,
% 187.18/188.02 ! [V_list_2,V_a_2,V_fa_2,T_a] : c_List_Olist_Olist__size(T_a,V_fa_2,hAPP(hAPP(c_List_Olist_OCons(T_a),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_a,V_fa_2,V_list_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_Cons__acc__listrel1I,axiom,
% 187.18/188.02 ! [V_xs_2,V_r_2,V_x_2,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2)))
% 187.18/188.02 => ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2))))
% 187.18/188.02 => hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),c_Wellfounded_Oacc(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_listrel1__mono,axiom,
% 187.18/188.02 ! [V_s_2,V_r_2,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2))
% 187.18/188.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool)),c_List_Olistrel1(T_a,V_r_2)),c_List_Olistrel1(T_a,V_s_2))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_listrel1__converse,axiom,
% 187.18/188.02 ! [V_r_2,T_a] : c_List_Olistrel1(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) = hAPP(c_Relation_Oconverse(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olistrel1(T_a,V_r_2)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_listrel1__rtrancl__subset__rtrancl__listrel1,axiom,
% 187.18/188.02 ! [V_r_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool)),c_List_Olistrel1(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_rtrancl__listrel1__ConsI1,axiom,
% 187.18/188.02 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2))))
% 187.18/188.02 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_ys_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_listrel1I2,axiom,
% 187.18/188.02 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2)))
% 187.18/188.02 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_ys_2))),c_List_Olistrel1(T_a,V_r_2))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_rtrancl__listrel1__eq__len,axiom,
% 187.18/188.02 ! [V_r_2,V_y_2,V_x_2,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2))))
% 187.18/188.02 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_x_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_y_2) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_listrel1__eq__len,axiom,
% 187.18/188.02 ! [V_r_2,V_ys_2,V_xs_2,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2)))
% 187.18/188.02 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_in__listrel1__converse,axiom,
% 187.18/188.02 ! [V_r_2,V_y_2,V_x_2,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_y_2)),c_List_Olistrel1(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2))))
% 187.18/188.02 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olistrel1(T_a,V_r_2)))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_Cons__listrel1__Cons,axiom,
% 187.18/188.02 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2))),c_List_Olistrel1(T_a,V_r_2)))
% 187.18/188.02 <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2))
% 187.18/188.02 & V_xs_2 = V_ys_2 )
% 187.18/188.02 | ( V_x_2 = V_y_2
% 187.18/188.02 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2))) ) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_listrel1I1,axiom,
% 187.18/188.02 ! [V_xs_2,V_r_2,V_y_2,V_x_2,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2))
% 187.18/188.02 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_xs_2))),c_List_Olistrel1(T_a,V_r_2))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_listrel__Cons,axiom,
% 187.18/188.02 ! [V_xs_2,V_x_2,V_r_2,T_a] : hAPP(c_Relation_OImage(tc_List_Olist(T_a),tc_List_Olist(T_a),c_List_Olistrel(T_a,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)))) = c_List_Oset__Cons(T_a,hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),hAPP(c_Relation_OImage(tc_List_Olist(T_a),tc_List_Olist(T_a),c_List_Olistrel(T_a,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_a)),V_xs_2),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))))) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_lexord__linear,axiom,
% 187.18/188.02 ! [V_y_2,V_x_2,V_r_2,T_a] :
% 187.18/188.02 ( ! [B_a,B_b] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_a),B_b)),V_r_2))
% 187.18/188.02 | B_a = B_b
% 187.18/188.02 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_b),B_a)),V_r_2)) )
% 187.18/188.02 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_y_2)),c_List_Olexord(T_a,V_r_2)))
% 187.18/188.02 | V_x_2 = V_y_2
% 187.18/188.02 | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_y_2),V_x_2)),c_List_Olexord(T_a,V_r_2))) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_listrel__rtrancl__refl,axiom,
% 187.18/188.02 ! [V_r_2,V_xs_2,T_a] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_xs_2)),c_List_Olistrel(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)))) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_listrel__mono,axiom,
% 187.18/188.02 ! [V_s_2,V_r_2,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2))
% 187.18/188.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool)),c_List_Olistrel(T_a,V_r_2)),c_List_Olistrel(T_a,V_s_2))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_listrel__subset__rtrancl__listrel1,axiom,
% 187.18/188.02 ! [V_r_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool)),c_List_Olistrel(T_a,V_r_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_listrel__eq__len,axiom,
% 187.18/188.02 ! [V_r_2,V_ys_2,V_xs_2,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel(T_a,V_r_2)))
% 187.18/188.02 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_listrel__rtrancl__trans,axiom,
% 187.18/188.02 ! [V_zs_2,V_r_2,V_ys_2,V_xs_2,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2))))
% 187.18/188.02 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_ys_2),V_zs_2)),c_List_Olistrel(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2))))
% 187.18/188.02 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_zs_2)),c_List_Olistrel(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)))) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_listrel__rtrancl__eq__rtrancl__listrel1,axiom,
% 187.18/188.02 ! [V_r_2,T_a] : c_List_Olistrel(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_listrel__reflcl__if__listrel1,axiom,
% 187.18/188.02 ! [V_r_2,V_ys_2,V_xs_2,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2)))
% 187.18/188.02 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_listrel1__subset__listrel,axiom,
% 187.18/188.02 ! [V_r_H_2,V_r_2,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_r_H_2))
% 187.18/188.02 => ( c_Relation_Orefl__on(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_r_H_2)
% 187.18/188.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool)),c_List_Olistrel1(T_a,V_r_2)),c_List_Olistrel(T_a,V_r_H_2))) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_rtrancl__listrel1__if__listrel,axiom,
% 187.18/188.02 ! [V_r_2,V_ys_2,V_xs_2,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel(T_a,V_r_2)))
% 187.18/188.02 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_listrel_OCons,axiom,
% 187.18/188.02 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2))
% 187.18/188.02 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel(T_a,V_r_2)))
% 187.18/188.02 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2))),c_List_Olistrel(T_a,V_r_2))) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_listrelp__listrel__eq,axiom,
% 187.18/188.02 ! [V_xa_2,V_x_2,V_r_2,T_a] :
% 187.18/188.02 ( c_List_Olistrelp(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a)))),c_Product__Type_OPair(T_a,T_a)))),V_r_2),V_x_2,V_xa_2)
% 187.18/188.02 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_xa_2)),c_List_Olistrel(T_a,V_r_2))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_listrel__Cons1,axiom,
% 187.18/188.02 ! [V_r_2,V_xs_2,V_ys_2,V_y_2,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2)),V_xs_2)),c_List_Olistrel(T_a,V_r_2)))
% 187.18/188.02 => ~ ! [B_y,B_ys] :
% 187.18/188.02 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_y),B_ys)
% 187.18/188.02 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),B_y)),V_r_2))
% 187.18/188.02 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_ys_2),B_ys)),c_List_Olistrel(T_a,V_r_2))) ) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_listrelp_OCons,axiom,
% 187.18/188.02 ! [V_ys_2,V_xs_2,T_a,V_y_2,V_x_2,V_r_2] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2))
% 187.18/188.02 => ( c_List_Olistrelp(T_a,V_r_2,V_xs_2,V_ys_2)
% 187.18/188.02 => c_List_Olistrelp(T_a,V_r_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2)) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_listrelp_Oequations_I2_J,axiom,
% 187.18/188.02 ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2,V_r_2,T_a] :
% 187.18/188.02 ( c_List_Olistrelp(T_a,V_r_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_a1_2),V_a3_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a2_2),V_a4_2))
% 187.18/188.02 <=> ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2))
% 187.18/188.02 & c_List_Olistrelp(T_a,V_r_2,V_a3_2,V_a4_2) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_listrel__Cons2,axiom,
% 187.18/188.02 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2))),c_List_Olistrel(T_a,V_r_2)))
% 187.18/188.02 => ~ ! [B_x,B_xs] :
% 187.18/188.02 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_x),B_xs)
% 187.18/188.02 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),V_y_2)),V_r_2))
% 187.18/188.02 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),B_xs),V_ys_2)),c_List_Olistrel(T_a,V_r_2))) ) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_listrel__subset,axiom,
% 187.18/188.02 ! [V_A_2,V_r_2,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2))))
% 187.18/188.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool)),c_List_Olistrel(T_a,V_r_2)),hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olists(T_a,V_A_2)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_List_Olist(T_a)),c_List_Olists(T_a,V_A_2))))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_lists__UNIV,axiom,
% 187.18/188.02 ! [T_a] : c_List_Olists(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_lists__mono,axiom,
% 187.18/188.02 ! [V_B_2,V_A_2,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 187.18/188.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),c_List_Olists(T_a,V_A_2)),c_List_Olists(T_a,V_B_2))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_equiv__listrel,axiom,
% 187.18/188.02 ! [V_r_2,V_A_2,T_a] :
% 187.18/188.02 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 187.18/188.02 => c_Equiv__Relations_Oequiv(tc_List_Olist(T_a),c_List_Olists(T_a,V_A_2),c_List_Olistrel(T_a,V_r_2)) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_listrel__refl__on,axiom,
% 187.18/188.02 ! [V_r_2,V_A_2,T_a] :
% 187.18/188.02 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2)
% 187.18/188.02 => c_Relation_Orefl__on(tc_List_Olist(T_a),c_List_Olists(T_a,V_A_2),c_List_Olistrel(T_a,V_r_2)) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_Cons__in__lists__iff,axiom,
% 187.18/188.02 ! [V_A_2,V_xs_2,V_x_2,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),c_List_Olists(T_a,V_A_2)))
% 187.18/188.02 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 187.18/188.02 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_List_Olists(T_a,V_A_2))) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_lists__accD,axiom,
% 187.18/188.02 ! [V_r_2,V_xs_2,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_List_Olists(T_a,c_Wellfounded_Oacc(T_a,V_r_2))))
% 187.18/188.02 => hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_lists__accI,axiom,
% 187.18/188.02 ! [V_r_2,V_xs_2,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2))))
% 187.18/188.02 => hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_List_Olists(T_a,c_Wellfounded_Oacc(T_a,V_r_2)))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_listrel__iff__nth,axiom,
% 187.18/188.02 ! [V_r_2,V_ys_2,V_xs_2,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel(T_a,V_r_2)))
% 187.18/188.02 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2)
% 187.18/188.02 & ! [B_n] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))
% 187.18/188.02 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_n)),hAPP(hAPP(c_List_Onth(T_a),V_ys_2),B_n))),V_r_2)) ) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_lexord__irreflexive,axiom,
% 187.18/188.02 ! [V_y_2,V_r_2,T_a] :
% 187.18/188.02 ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),V_r_2))
% 187.18/188.02 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_y_2),V_y_2)),c_List_Olexord(T_a,V_r_2))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_infinite__UNIV__listI,axiom,
% 187.18/188.02 ! [T_a] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_a)),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)))) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_list__eq__iff__nth__eq,axiom,
% 187.18/188.02 ! [T_a,V_ys_2,V_xs_2] :
% 187.18/188.02 ( V_xs_2 = V_ys_2
% 187.18/188.02 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2)
% 187.18/188.02 & ! [B_i] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))
% 187.18/188.02 => hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i) = hAPP(hAPP(c_List_Onth(T_a),V_ys_2),B_i) ) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_nth__Cons__Suc,axiom,
% 187.18/188.02 ! [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) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_nth__Cons__0,axiom,
% 187.18/188.02 ! [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 ).
% 187.18/188.02
% 187.18/188.02 fof(fact_nth_Osimps,axiom,
% 187.18/188.02 ! [V_n_2,V_xs_2,V_x_2,T_a] : hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),V_n_2) = c_Nat_Onat_Onat__case(T_a,V_x_2,hAPP(c_List_Onth(T_a),V_xs_2),V_n_2) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_nth__Cons_H,axiom,
% 187.18/188.02 ! [V_xs,V_x,T_a,V_n] :
% 187.18/188.02 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.18/188.02 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_n) = V_x )
% 187.18/188.02 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.18/188.02 => 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))) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_nth__Cons__number__of,axiom,
% 187.18/188.02 ! [V_xs,V_x,T_a,V_v] :
% 187.18/188.02 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.18/188.02 => 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 )
% 187.18/188.02 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.18/188.02 => 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))) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_lexord__take__index__conv,axiom,
% 187.18/188.02 ! [V_r_2,V_y_2,V_x_2,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_y_2)),c_List_Olexord(T_a,V_r_2)))
% 187.18/188.02 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_x_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_y_2)))
% 187.18/188.02 & hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_x_2)),V_y_2) = V_x_2 )
% 187.18/188.02 | ? [B_i] :
% 187.18/188.02 ( 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_a)),V_x_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_y_2))))
% 187.18/188.02 & hAPP(hAPP(c_List_Otake(T_a),B_i),V_x_2) = hAPP(hAPP(c_List_Otake(T_a),B_i),V_y_2)
% 187.18/188.02 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),hAPP(hAPP(c_List_Onth(T_a),V_x_2),B_i)),hAPP(hAPP(c_List_Onth(T_a),V_y_2),B_i))),V_r_2)) ) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_set__sublist,axiom,
% 187.18/188.02 ! [V_I_2,V_xs_2,T_a] : hAPP(c_List_Oset(T_a),c_List_Osublist(T_a,V_xs_2,V_I_2)) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(T_a,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_a),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_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_Nat_Onat,T_a),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,T_a),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(T_a),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_a)),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))))) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_finite__set,axiom,
% 187.18/188.02 ! [V_xs_2,T_a] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_List_Oset(T_a),V_xs_2))) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_set__subset__Cons,axiom,
% 187.18/188.02 ! [V_x_2,V_xs_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)))) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_take__all,axiom,
% 187.18/188.02 ! [V_n,V_xs,T_a] :
% 187.18/188.02 ( 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))
% 187.18/188.02 => hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs) = V_xs ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_set__take__subset,axiom,
% 187.18/188.02 ! [V_xs_2,V_n_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_xs_2))),hAPP(c_List_Oset(T_a),V_xs_2))) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_set__take__subset__set__take,axiom,
% 187.18/188.02 ! [V_xs_2,T_a,V_n_2,V_m_2] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 187.18/188.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Otake(T_a),V_m_2),V_xs_2))),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_xs_2)))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_set__sublist__subset,axiom,
% 187.18/188.02 ! [V_I_2,V_xs_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),c_List_Osublist(T_a,V_xs_2,V_I_2))),hAPP(c_List_Oset(T_a),V_xs_2))) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_nth__take,axiom,
% 187.18/188.02 ! [V_xs,T_a,V_n,V_i] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n))
% 187.18/188.02 => 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) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_take__Suc__Cons,axiom,
% 187.18/188.02 ! [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)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_set__ConsD,axiom,
% 187.18/188.02 ! [V_xs_2,V_x_2,V_y_2,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))))
% 187.18/188.02 => ( V_y_2 = V_x_2
% 187.18/188.02 | hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_in__set__sublistD,axiom,
% 187.18/188.02 ! [V_I_2,V_xs_2,V_x_2,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Osublist(T_a,V_xs_2,V_I_2))))
% 187.18/188.02 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_in__set__takeD,axiom,
% 187.18/188.02 ! [V_xs_2,V_n_2,V_x_2,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_xs_2))))
% 187.18/188.02 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_notin__set__sublistI,axiom,
% 187.18/188.02 ! [V_I_2,V_xs_2,V_x_2,T_a] :
% 187.18/188.02 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 187.18/188.02 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Osublist(T_a,V_xs_2,V_I_2)))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_length__take,axiom,
% 187.18/188.02 ! [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) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_take__take,axiom,
% 187.18/188.02 ! [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) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_sublist__upt__eq__take,axiom,
% 187.18/188.02 ! [V_n_2,V_l_2,T_a] : c_List_Osublist(T_a,V_l_2,hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2)) = hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_l_2) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_List_Oset_Osimps_I2_J,axiom,
% 187.18/188.02 ! [V_xs_2,V_x_2,T_a] : hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_card__length,axiom,
% 187.18/188.02 ! [V_xs_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),hAPP(c_List_Oset(T_a),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_all__set__conv__all__nth,axiom,
% 187.18/188.02 ! [V_P_2,V_xs_2,T_a] :
% 187.18/188.02 ( ! [B_x] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 187.18/188.02 => hBOOL(hAPP(V_P_2,B_x)) )
% 187.18/188.02 <=> ! [B_i] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))
% 187.18/188.02 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i))) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_list__size__estimation,axiom,
% 187.18/188.02 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 187.18/188.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2)))
% 187.18/188.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y_2),c_List_Olist_Olist__size(T_a,V_f_2,V_xs_2))) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_list__size__estimation_H,axiom,
% 187.18/188.02 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 187.18/188.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2)))
% 187.18/188.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),c_List_Olist_Olist__size(T_a,V_f_2,V_xs_2))) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_in__lists__conv__set,axiom,
% 187.18/188.02 ! [V_A_2,V_xs_2,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_List_Olists(T_a,V_A_2)))
% 187.18/188.02 <=> ! [B_x] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 187.18/188.02 => hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_length__pos__if__in__set,axiom,
% 187.18/188.02 ! [V_xs_2,V_x_2,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 187.18/188.02 => 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_a)),V_xs_2))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_nth__mem,axiom,
% 187.18/188.02 ! [V_xs_2,T_a,V_n_2] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))
% 187.18/188.02 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_n_2)),hAPP(c_List_Oset(T_a),V_xs_2))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_in__set__conv__nth,axiom,
% 187.18/188.02 ! [V_xs_2,V_x_2,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 187.18/188.02 <=> ? [B_i] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))
% 187.18/188.02 & hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i) = V_x_2 ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_lists__eq__set,axiom,
% 187.18/188.02 ! [V_A_2,T_a] : c_List_Olists(T_a,V_A_2) = hAPP(c_Set_OCollect(tc_List_Olist(T_a)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_a)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool))),c_List_Oset(T_a))),V_A_2)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_set__conv__nth,axiom,
% 187.18/188.02 ! [V_xs_2,T_a] : hAPP(c_List_Oset(T_a),V_xs_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(T_a,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_a),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_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_Nat_Onat,T_a),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,T_a),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(T_a),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_a)),V_xs_2))))) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_finite__lists__length__eq,axiom,
% 187.18/188.02 ! [V_n_2,V_A_2,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.02 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_a)),hAPP(c_Set_OCollect(tc_List_Olist(T_a)),hAPP(hAPP(c_COMBS(tc_List_Olist(T_a),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_a)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_a)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool))),c_List_Oset(T_a))),V_A_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),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_a)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),V_n_2))))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_finite__lists__length__le,axiom,
% 187.18/188.02 ! [V_n_2,V_A_2,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.02 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_a)),hAPP(c_Set_OCollect(tc_List_Olist(T_a)),hAPP(hAPP(c_COMBS(tc_List_Olist(T_a),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_a)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_a)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool))),c_List_Oset(T_a))),V_A_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),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_a)),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),V_n_2))))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_WT__bodies__def,axiom,
% 187.18/188.02 ( c_Com_OWT__bodies
% 187.18/188.02 <=> ! [B_x] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname,tc_Com_Ocom)),B_x),hAPP(c_List_Oset(tc_prod(tc_Com_Opname,tc_Com_Ocom)),c_Com_Obodies)))
% 187.18/188.02 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)),B_x)) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_listrel__iff__zip,axiom,
% 187.18/188.02 ! [V_r_2,V_ys_2,V_xs_2,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel(T_a,V_r_2)))
% 187.18/188.02 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2)
% 187.18/188.02 & ! [B_x] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),B_x),hAPP(c_List_Oset(tc_prod(T_a,T_a)),hAPP(hAPP(c_List_Ozip(T_a,T_a),V_xs_2),V_ys_2))))
% 187.18/188.02 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a)))),c_Product__Type_OPair(T_a,T_a)))),V_r_2)),B_x)) ) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_take__zip,axiom,
% 187.18/188.02 ! [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)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_length__zip,axiom,
% 187.18/188.02 ! [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)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_zip__Cons__Cons,axiom,
% 187.18/188.02 ! [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)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_list__eq__iff__zip__eq,axiom,
% 187.18/188.02 ! [T_a,V_ys_2,V_xs_2] :
% 187.18/188.02 ( V_xs_2 = V_ys_2
% 187.18/188.02 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2)
% 187.18/188.02 & ! [B_x] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),B_x),hAPP(c_List_Oset(tc_prod(T_a,T_a)),hAPP(hAPP(c_List_Ozip(T_a,T_a),V_xs_2),V_ys_2))))
% 187.18/188.02 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),c_fequal),B_x)) ) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_in__set__zipE,axiom,
% 187.18/188.02 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_b,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2))))
% 187.18/188.02 => ~ ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 187.18/188.02 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_ys_2))) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_set__zip__rightD,axiom,
% 187.18/188.02 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_b,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2))))
% 187.18/188.02 => hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_ys_2))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_set__zip__leftD,axiom,
% 187.18/188.02 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_b,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2))))
% 187.18/188.02 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_zip__same,axiom,
% 187.18/188.02 ! [V_xs_2,V_b_2,V_a_2,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),hAPP(c_List_Oset(tc_prod(T_a,T_a)),hAPP(hAPP(c_List_Ozip(T_a,T_a),V_xs_2),V_xs_2))))
% 187.18/188.02 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 187.18/188.02 & V_a_2 = V_b_2 ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_nth__zip,axiom,
% 187.18/188.02 ! [V_ys,T_b,V_xs,T_a,V_i] :
% 187.18/188.02 ( 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)))
% 187.18/188.02 => ( 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)))
% 187.18/188.02 => 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)) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_set__zip,axiom,
% 187.18/188.02 ! [V_ys_2,V_xs_2,T_b,T_a] : hAPP(c_List_Oset(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)) = hAPP(c_Set_OCollect(tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,tc_prod(T_a,T_b)),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(T_a,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)),tc_prod(T_a,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)),tc_prod(T_a,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(tc_prod(T_a,T_b),tc_fun(tc_Nat_Onat,tc_prod(T_a,T_b)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_prod(T_a,T_b)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(T_a,T_b)),c_COMBB(tc_prod(T_a,T_b),tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_b,tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_b,tc_prod(T_a,T_b)),tc_Nat_Onat),c_Product__Type_OPair(T_a,T_b)),hAPP(c_List_Onth(T_a),V_xs_2))),hAPP(c_List_Onth(T_b),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_a)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)))))) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_greaterThanLessThan__upto,axiom,
% 187.18/188.02 ! [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)))) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_listsum__setsum__nth,axiom,
% 187.18/188.02 ! [V_xs_2,T_a] :
% 187.18/188.02 ( class_Groups_Ocomm__monoid__add(T_a)
% 187.18/188.02 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_xs_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),hAPP(c_List_Onth(T_a),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_a)),V_xs_2))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_listsum__eq__0__nat__iff__nat,axiom,
% 187.18/188.02 ! [V_ns_2] :
% 187.18/188.02 ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.18/188.02 <=> ! [B_x] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
% 187.18/188.02 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_set__upto,axiom,
% 187.18/188.02 ! [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) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_atLeastAtMost__upto,axiom,
% 187.18/188.02 ! [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)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_elem__le__listsum__nat,axiom,
% 187.18/188.02 ! [V_ns,V_k] :
% 187.18/188.02 ( 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)))
% 187.18/188.02 => 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))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_listsum__simps_I2_J,axiom,
% 187.18/188.02 ! [V_xs,V_x,T_a] :
% 187.18/188.02 ( class_Groups_Omonoid__add(T_a)
% 187.18/188.02 => 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)) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_atLeastLessThan__upto,axiom,
% 187.18/188.02 ! [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)))) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_greaterThanAtMost__upto,axiom,
% 187.18/188.02 ! [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)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_nat__list__def,axiom,
% 187.18/188.02 ! [V_l_2] :
% 187.18/188.02 ( c_List_Onat__list(V_l_2)
% 187.18/188.02 <=> c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),V_l_2)) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_list__size__pointwise,axiom,
% 187.18/188.02 ! [V_g_2,V_f_2,V_xs_2,T_a] :
% 187.18/188.02 ( ! [B_x] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 187.18/188.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 187.18/188.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_List_Olist_Olist__size(T_a,V_f_2,V_xs_2)),c_List_Olist_Olist__size(T_a,V_g_2,V_xs_2))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_listsum__update__nat,axiom,
% 187.18/188.02 ! [V_n,V_ns,V_k] :
% 187.18/188.02 ( 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)))
% 187.18/188.02 => 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)) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_butlast__take,axiom,
% 187.18/188.02 ! [V_xs,T_a,V_n] :
% 187.18/188.02 ( 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)))
% 187.18/188.02 => 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) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_list__update__beyond,axiom,
% 187.18/188.02 ! [V_x,V_i,V_xs,T_a] :
% 187.18/188.02 ( 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))
% 187.18/188.02 => hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x) = V_xs ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_nth__list__update__neq,axiom,
% 187.18/188.02 ! [V_x,V_xs,T_a,V_j,V_i] :
% 187.18/188.02 ( V_i != V_j
% 187.18/188.02 => 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) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_list__update__id,axiom,
% 187.18/188.02 ! [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 ).
% 187.18/188.02
% 187.18/188.02 fof(fact_length__list__update,axiom,
% 187.18/188.02 ! [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) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_butlast__list__update,axiom,
% 187.18/188.02 ! [V_x,V_xs,T_a,V_k] :
% 187.18/188.02 ( ( 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))
% 187.18/188.02 => 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) )
% 187.18/188.02 & ( 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))
% 187.18/188.02 => 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) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_zip__update,axiom,
% 187.18/188.02 ! [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)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_update__zip,axiom,
% 187.18/188.02 ! [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))) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_list__update__overwrite,axiom,
% 187.18/188.02 ! [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) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_list__update__swap,axiom,
% 187.18/188.02 ! [V_x_H,V_x,V_xs,T_a,V_i_H,V_i] :
% 187.18/188.02 ( V_i != V_i_H
% 187.18/188.02 => 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) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_list__update_Osimps_I2_J,axiom,
% 187.18/188.02 ! [V_v_2,V_i_2,V_xs_2,V_x_2,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),V_i_2),V_v_2) = c_Nat_Onat_Onat__case(tc_List_Olist(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_v_2),V_xs_2),hAPP(hAPP(c_COMBB(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_Nat_Onat),hAPP(c_List_Olist_OCons(T_a),V_x_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,T_a,tc_List_Olist(T_a)),c_List_Olist__update(T_a,V_xs_2)),V_v_2)),V_i_2) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_list__update__code_I3_J,axiom,
% 187.18/188.02 ! [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)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_list__update__code_I2_J,axiom,
% 187.18/188.02 ! [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) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_in__set__butlastD,axiom,
% 187.18/188.02 ! [V_xs_2,V_x_2,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Obutlast(T_a,V_xs_2))))
% 187.18/188.02 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_set__update__subsetI,axiom,
% 187.18/188.02 ! [V_i_2,V_x_2,V_A_2,V_xs_2,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),V_A_2))
% 187.18/188.02 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 187.18/188.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_i_2),V_x_2))),V_A_2)) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_set__update__subset__insert,axiom,
% 187.18/188.02 ! [V_x_2,V_i_2,V_xs_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_i_2),V_x_2))),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_nth__list__update,axiom,
% 187.18/188.02 ! [V_x,V_j,V_xs,T_a,V_i] :
% 187.18/188.02 ( 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)))
% 187.18/188.02 => ( ( V_i = V_j
% 187.18/188.02 => 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 )
% 187.18/188.02 & ( V_i != V_j
% 187.18/188.02 => 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) ) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_list__update__same__conv,axiom,
% 187.18/188.02 ! [V_x_2,V_xs_2,T_a,V_i_2] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))
% 187.18/188.02 => ( hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_i_2),V_x_2) = V_xs_2
% 187.18/188.02 <=> hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_i_2) = V_x_2 ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_nth__list__update__eq,axiom,
% 187.18/188.02 ! [V_x,V_xs,T_a,V_i] :
% 187.18/188.02 ( 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)))
% 187.18/188.02 => 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 ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_take__butlast,axiom,
% 187.18/188.02 ! [V_xs,T_a,V_n] :
% 187.18/188.02 ( 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)))
% 187.18/188.02 => 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) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_length__butlast,axiom,
% 187.18/188.02 ! [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)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_set__update__memI,axiom,
% 187.18/188.02 ! [V_x_2,V_xs_2,T_a,V_n_2] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))
% 187.18/188.02 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_n_2),V_x_2)))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_butlast__conv__take,axiom,
% 187.18/188.02 ! [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) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_listrel1__iff__update,axiom,
% 187.18/188.02 ! [V_r_2,V_ys_2,V_xs_2,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2)))
% 187.18/188.02 <=> ? [B_y,B_n] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_n)),B_y)),V_r_2))
% 187.18/188.02 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))
% 187.18/188.02 & V_ys_2 = hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),B_n),B_y) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_distinct__list__update,axiom,
% 187.18/188.02 ! [V_i_2,V_a_2,V_xs_2,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 187.18/188.02 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_i_2)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))
% 187.18/188.02 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_i_2),V_a_2))) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_distinct__upto,axiom,
% 187.18/188.02 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(V_i,V_j))) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_distinct__take,axiom,
% 187.18/188.02 ! [V_i,V_xs,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 187.18/188.02 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_distinct__sublistI,axiom,
% 187.18/188.02 ! [V_I_2,V_xs_2,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 187.18/188.02 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Osublist(T_a,V_xs_2,V_I_2))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_distinct__zipI1,axiom,
% 187.18/188.02 ! [V_ys,T_b,V_xs,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 187.18/188.02 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_distinct__zipI2,axiom,
% 187.18/188.02 ! [V_xs,T_b,V_ys,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_ys))
% 187.18/188.02 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_b,T_a)),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs),V_ys))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_distinct_Osimps_I2_J,axiom,
% 187.18/188.02 ! [V_xs_2,V_x_2,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)))
% 187.18/188.02 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 187.18/188.02 & hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_card__distinct,axiom,
% 187.18/188.02 ! [V_xs_2,T_a] :
% 187.18/188.02 ( hAPP(c_Finite__Set_Ocard(T_a),hAPP(c_List_Oset(T_a),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)
% 187.18/188.02 => hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_distinct__card,axiom,
% 187.18/188.02 ! [V_xs_2,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 187.18/188.02 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(c_List_Oset(T_a),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_distinct__conv__nth,axiom,
% 187.18/188.02 ! [V_xs_2,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 187.18/188.02 <=> ! [B_i] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))
% 187.18/188.02 => ! [B_j] :
% 187.18/188.02 ( 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_2)))
% 187.18/188.02 => ( B_i != B_j
% 187.18/188.02 => hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i) != hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_j) ) ) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_nth__eq__iff__index__eq,axiom,
% 187.18/188.02 ! [V_j_2,V_i_2,V_xs_2,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 187.18/188.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))
% 187.18/188.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))
% 187.18/188.02 => ( hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_i_2) = hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_j_2)
% 187.18/188.02 <=> V_i_2 = V_j_2 ) ) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_distinct__listsum__conv__Setsum,axiom,
% 187.18/188.02 ! [V_xs_2,T_a] :
% 187.18/188.02 ( class_Groups_Ocomm__monoid__add(T_a)
% 187.18/188.02 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 187.18/188.02 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_xs_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_a),c_COMBI(T_a)),hAPP(c_List_Oset(T_a),V_xs_2)) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_Nitpick_Ocard_H__def,axiom,
% 187.18/188.02 ! [V_A_2,T_a] :
% 187.18/188.02 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.02 => c_Nitpick_Ocard_H(T_a,V_A_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_Hilbert__Choice_OEps(tc_List_Olist(T_a),hAPP(hAPP(c_COMBS(tc_List_Olist(T_a),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_a)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_a)),c_fequal),c_List_Oset(T_a))),V_A_2))),c_List_Odistinct(T_a)))) )
% 187.18/188.02 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.02 => c_Nitpick_Ocard_H(T_a,V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_dom__map__upds,axiom,
% 187.18/188.02 ! [V_ys_2,V_xs_2,V_m_2,T_b,T_a] : c_Map_Odom(T_a,T_b,c_Map_Omap__upds(T_a,T_b,V_m_2,V_xs_2,V_ys_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)),V_xs_2))),c_Map_Odom(T_a,T_b,V_m_2)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_map__upds__apply__nontin,axiom,
% 187.18/188.02 ! [V_ys_2,V_f_2,T_b,V_xs_2,V_x_2,T_a] :
% 187.18/188.02 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 187.18/188.02 => hAPP(c_Map_Omap__upds(T_a,T_b,V_f_2,V_xs_2,V_ys_2),V_x_2) = hAPP(V_f_2,V_x_2) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_map__upds__list__update2__drop,axiom,
% 187.18/188.02 ! [V_y_2,V_m_2,V_ys_2,T_b,V_i_2,V_xs_2,T_a] :
% 187.18/188.02 ( 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_2)),V_i_2))
% 187.18/188.02 => ( 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_ys_2)))
% 187.18/188.02 => c_Map_Omap__upds(T_a,T_b,V_m_2,V_xs_2,hAPP(hAPP(c_List_Olist__update(T_b,V_ys_2),V_i_2),V_y_2)) = c_Map_Omap__upds(T_a,T_b,V_m_2,V_xs_2,V_ys_2) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_nth__take__lemma,axiom,
% 187.18/188.02 ! [V_ys,V_xs,T_a,V_k] :
% 187.18/188.02 ( 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)))
% 187.18/188.02 => ( 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)))
% 187.18/188.02 => ( ! [B_i] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_k))
% 187.18/188.02 => hAPP(hAPP(c_List_Onth(T_a),V_xs),B_i) = hAPP(hAPP(c_List_Onth(T_a),V_ys),B_i) )
% 187.18/188.02 => hAPP(hAPP(c_List_Otake(T_a),V_k),V_xs) = hAPP(hAPP(c_List_Otake(T_a),V_k),V_ys) ) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_restrict__map__upds,axiom,
% 187.18/188.02 ! [V_m_2,V_D_2,V_ys_2,T_b,V_xs_2,T_a] :
% 187.18/188.02 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)
% 187.18/188.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),V_D_2))
% 187.18/188.02 => c_Map_Orestrict__map(T_a,T_b,c_Map_Omap__upds(T_a,T_b,V_m_2,V_xs_2,V_ys_2),V_D_2) = c_Map_Omap__upds(T_a,T_b,c_Map_Orestrict__map(T_a,T_b,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_D_2),hAPP(c_List_Oset(T_a),V_xs_2))),V_xs_2,V_ys_2) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_restrict__map__insert,axiom,
% 187.18/188.02 ! [V_A_2,V_a_2,V_f_2,T_b,T_a] : c_Map_Orestrict__map(T_a,T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_f_2,V_A_2)),V_a_2),hAPP(V_f_2,V_a_2)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_restrict__restrict,axiom,
% 187.18/188.02 ! [V_B_2,V_A_2,V_m_2,T_b,T_a] : c_Map_Orestrict__map(T_a,T_b,c_Map_Orestrict__map(T_a,T_b,V_m_2,V_A_2),V_B_2) = c_Map_Orestrict__map(T_a,T_b,V_m_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_restrict__in,axiom,
% 187.18/188.02 ! [V_m_2,T_b,V_A_2,V_x_2,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 187.18/188.02 => hAPP(c_Map_Orestrict__map(T_a,T_b,V_m_2,V_A_2),V_x_2) = hAPP(V_m_2,V_x_2) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_dom__restrict,axiom,
% 187.18/188.02 ! [V_A_2,V_m_2,T_b,T_a] : c_Map_Odom(T_a,T_b,c_Map_Orestrict__map(T_a,T_b,V_m_2,V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Map_Odom(T_a,T_b,V_m_2)),V_A_2) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_fun__upd__restrict,axiom,
% 187.18/188.02 ! [V_y_2,V_x_2,V_D_2,V_m_2,T_b,T_a] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_m_2,V_D_2)),V_x_2),V_y_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_D_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),V_x_2),V_y_2) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_fun__upd__restrict__conv,axiom,
% 187.18/188.02 ! [V_y_2,V_m_2,T_b,V_D_2,V_x_2,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2))
% 187.18/188.02 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_m_2,V_D_2)),V_x_2),V_y_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_D_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),V_x_2),V_y_2) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_restrict__fun__upd,axiom,
% 187.18/188.02 ! [V_y_2,V_m_2,T_b,V_D_2,V_x_2,T_a] :
% 187.18/188.02 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2))
% 187.18/188.02 => c_Map_Orestrict__map(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_m_2),V_x_2),V_y_2),V_D_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_D_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),V_x_2),V_y_2) )
% 187.18/188.02 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2))
% 187.18/188.02 => c_Map_Orestrict__map(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_m_2),V_x_2),V_y_2),V_D_2) = c_Map_Orestrict__map(T_a,T_b,V_m_2,V_D_2) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_set__remove1__eq,axiom,
% 187.18/188.02 ! [V_x_2,V_xs_2,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 187.18/188.02 => hAPP(c_List_Oset(T_a),c_List_Oremove1(T_a,V_x_2,V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_take__Cons__number__of,axiom,
% 187.18/188.02 ! [V_xs,V_x,T_a,V_v] :
% 187.18/188.02 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.18/188.02 => 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) )
% 187.18/188.02 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.18/188.02 => 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)) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_lists_ONil,axiom,
% 187.18/188.02 ! [V_A_2,T_a] : hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_List_Olists(T_a,V_A_2))) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_listrel__Nil1,axiom,
% 187.18/188.02 ! [V_r_2,V_xs_2,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),V_xs_2)),c_List_Olistrel(T_a,V_r_2)))
% 187.18/188.02 => V_xs_2 = c_List_Olist_ONil(T_a) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_listrel__Nil2,axiom,
% 187.18/188.02 ! [V_r_2,V_xs_2,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),c_List_Olist_ONil(T_a))),c_List_Olistrel(T_a,V_r_2)))
% 187.18/188.02 => V_xs_2 = c_List_Olist_ONil(T_a) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_list__update__nonempty,axiom,
% 187.18/188.02 ! [V_x_2,V_k_2,V_xs_2,T_a] :
% 187.18/188.02 ( hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_k_2),V_x_2) = c_List_Olist_ONil(T_a)
% 187.18/188.02 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_list__update_Osimps_I1_J,axiom,
% 187.18/188.02 ! [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) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_list__update__code_I1_J,axiom,
% 187.18/188.02 ! [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) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_set__empty,axiom,
% 187.18/188.02 ! [V_xs_2,T_a] :
% 187.18/188.02 ( hAPP(c_List_Oset(T_a),V_xs_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/188.02 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_set__empty2,axiom,
% 187.18/188.02 ! [V_xs_2,T_a] :
% 187.18/188.02 ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = hAPP(c_List_Oset(T_a),V_xs_2)
% 187.18/188.02 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_List_Oset_Osimps_I1_J,axiom,
% 187.18/188.02 ! [T_a] : hAPP(c_List_Oset(T_a),c_List_Olist_ONil(T_a)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_length__0__conv,axiom,
% 187.18/188.02 ! [V_xs_2,T_a] :
% 187.18/188.02 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.18/188.02 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_list_Osize_I3_J,axiom,
% 187.18/188.02 ! [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) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_listsum__simps_I1_J,axiom,
% 187.18/188.02 ! [T_a] :
% 187.18/188.02 ( class_Groups_Omonoid__add(T_a)
% 187.18/188.02 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),c_List_Olist_ONil(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_zip_Osimps_I1_J,axiom,
% 187.18/188.02 ! [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)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_zip__Nil,axiom,
% 187.18/188.02 ! [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)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_listrelp_ONil,axiom,
% 187.18/188.02 ! [V_r_2,T_a] : c_List_Olistrelp(T_a,V_r_2,c_List_Olist_ONil(T_a),c_List_Olist_ONil(T_a)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_listrelp_Oequations_I1_J,axiom,
% 187.18/188.02 ! [V_r_2,T_a] : c_List_Olistrelp(T_a,V_r_2,c_List_Olist_ONil(T_a),c_List_Olist_ONil(T_a)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_list_Osize_I1_J,axiom,
% 187.18/188.02 ! [V_fa_2,T_a] : c_List_Olist_Olist__size(T_a,V_fa_2,c_List_Olist_ONil(T_a)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_remove1_Osimps_I1_J,axiom,
% 187.18/188.02 ! [V_x,T_a] : c_List_Oremove1(T_a,V_x,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_remove1__commute,axiom,
% 187.18/188.02 ! [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)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_sublist__nil,axiom,
% 187.18/188.02 ! [V_A_2,T_a] : c_List_Osublist(T_a,c_List_Olist_ONil(T_a),V_A_2) = c_List_Olist_ONil(T_a) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_take__0,axiom,
% 187.18/188.02 ! [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) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_take__eq__Nil,axiom,
% 187.18/188.02 ! [V_xs_2,V_n_2,T_a] :
% 187.18/188.02 ( hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_xs_2) = c_List_Olist_ONil(T_a)
% 187.18/188.02 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.18/188.02 | V_xs_2 = c_List_Olist_ONil(T_a) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_take__Nil,axiom,
% 187.18/188.02 ! [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) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_upto__empty,axiom,
% 187.18/188.02 ! [V_i,V_j] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j),V_i))
% 187.18/188.02 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_remove1_Osimps_I2_J,axiom,
% 187.18/188.02 ! [V_xs,T_a,V_y,V_x] :
% 187.18/188.02 ( ( V_x = V_y
% 187.18/188.02 => c_List_Oremove1(T_a,V_x,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = V_xs )
% 187.18/188.02 & ( V_x != V_y
% 187.18/188.02 => 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)) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_list_Osimps_I3_J,axiom,
% 187.18/188.02 ! [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) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_list_Osimps_I2_J,axiom,
% 187.18/188.02 ! [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) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_butlast_Osimps_I2_J,axiom,
% 187.18/188.02 ! [V_x,T_a,V_xs] :
% 187.18/188.02 ( ( V_xs = c_List_Olist_ONil(T_a)
% 187.18/188.02 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olist_ONil(T_a) )
% 187.18/188.02 & ( V_xs != c_List_Olist_ONil(T_a)
% 187.18/188.02 => 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)) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_butlast_Osimps_I1_J,axiom,
% 187.18/188.02 ! [T_a] : c_List_Obutlast(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_in__set__remove1,axiom,
% 187.18/188.02 ! [V_xs_2,T_a,V_b_2,V_a_2] :
% 187.18/188.02 ( V_a_2 != V_b_2
% 187.18/188.02 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),c_List_Oremove1(T_a,V_b_2,V_xs_2))))
% 187.18/188.02 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_notin__set__remove1,axiom,
% 187.18/188.02 ! [V_y_2,V_xs_2,V_x_2,T_a] :
% 187.18/188.02 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 187.18/188.02 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Oremove1(T_a,V_y_2,V_xs_2)))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_remove1__idem,axiom,
% 187.18/188.02 ! [V_xs_2,V_x_2,T_a] :
% 187.18/188.02 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 187.18/188.02 => c_List_Oremove1(T_a,V_x_2,V_xs_2) = V_xs_2 ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_map__upds__Nil2,axiom,
% 187.18/188.02 ! [V_as_2,V_m_2,T_b,T_a] : c_Map_Omap__upds(T_a,T_b,V_m_2,V_as_2,c_List_Olist_ONil(T_b)) = V_m_2 ).
% 187.18/188.02
% 187.18/188.02 fof(fact_map__upds__Nil1,axiom,
% 187.18/188.02 ! [V_bs_2,V_m_2,T_b,T_a] : c_Map_Omap__upds(T_a,T_b,V_m_2,c_List_Olist_ONil(T_a),V_bs_2) = V_m_2 ).
% 187.18/188.02
% 187.18/188.02 fof(fact_distinct_Osimps_I1_J,axiom,
% 187.18/188.02 ! [T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olist_ONil(T_a))) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_distinct__remove1,axiom,
% 187.18/188.02 ! [V_x,V_xs,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 187.18/188.02 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremove1(T_a,V_x,V_xs))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_distinct__butlast,axiom,
% 187.18/188.02 ! [T_a,V_xs] :
% 187.18/188.02 ( V_xs != c_List_Olist_ONil(T_a)
% 187.18/188.02 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 187.18/188.02 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Obutlast(T_a,V_xs))) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_sublist__empty,axiom,
% 187.18/188.02 ! [V_xs_2,T_a] : c_List_Osublist(T_a,V_xs_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) = c_List_Olist_ONil(T_a) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_set__remove1__subset,axiom,
% 187.18/188.02 ! [V_xs_2,V_x_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),c_List_Oremove1(T_a,V_x_2,V_xs_2))),hAPP(c_List_Oset(T_a),V_xs_2))) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_length__greater__0__conv,axiom,
% 187.18/188.02 ! [V_xs_2,T_a] :
% 187.18/188.02 ( 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_a)),V_xs_2)))
% 187.18/188.02 <=> V_xs_2 != c_List_Olist_ONil(T_a) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_take__1__Cons,axiom,
% 187.18/188.02 ! [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)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_not__Nil__listrel1,axiom,
% 187.18/188.02 ! [V_r_2,V_xs_2,T_a] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),V_xs_2)),c_List_Olistrel1(T_a,V_r_2))) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_not__listrel1__Nil,axiom,
% 187.18/188.02 ! [V_r_2,V_xs_2,T_a] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),c_List_Olist_ONil(T_a))),c_List_Olistrel1(T_a,V_r_2))) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_listrel_ONil,axiom,
% 187.18/188.02 ! [V_r_2,T_a] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_List_Olist_ONil(T_a))),c_List_Olistrel(T_a,V_r_2))) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_lexord__Nil__right,axiom,
% 187.18/188.02 ! [V_r_2,V_x_2,T_a] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),c_List_Olist_ONil(T_a))),c_List_Olexord(T_a,V_r_2))) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_Nil__notin__lex,axiom,
% 187.18/188.02 ! [V_r_2,V_ys_2,T_a] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),V_ys_2)),c_List_Olex(T_a,V_r_2))) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_Nil2__notin__lex,axiom,
% 187.18/188.02 ! [V_r_2,V_xs_2,T_a] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),c_List_Olist_ONil(T_a))),c_List_Olex(T_a,V_r_2))) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_take__Cons,axiom,
% 187.18/188.02 ! [V_xs_2,V_x_2,V_n_2,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_n_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = c_Nat_Onat_Onat__case(tc_List_Olist(T_a),c_List_Olist_ONil(T_a),hAPP(hAPP(c_COMBB(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_Nat_Onat),hAPP(c_List_Olist_OCons(T_a),V_x_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Otake(T_a)),V_xs_2)),V_n_2) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_upto_Osimps,axiom,
% 187.18/188.02 ! [V_j,V_i] :
% 187.18/188.02 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 187.18/188.02 => 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)) )
% 187.18/188.02 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 187.18/188.02 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_sublist__singleton,axiom,
% 187.18/188.02 ! [V_x_2,T_a,V_A_2] :
% 187.18/188.02 ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2))
% 187.18/188.02 => c_List_Osublist(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)),V_A_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)) )
% 187.18/188.02 & ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2))
% 187.18/188.02 => c_List_Osublist(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)),V_A_2) = c_List_Olist_ONil(T_a) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_lists__empty,axiom,
% 187.18/188.02 ! [T_a] : c_List_Olists(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_take__Cons_H,axiom,
% 187.18/188.02 ! [V_xs,V_x,T_a,V_n] :
% 187.18/188.02 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.18/188.02 => 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) )
% 187.18/188.02 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.18/188.02 => 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)) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_upto__rec__number__of,axiom,
% 187.18/188.02 ! [V_n,V_m] :
% 187.18/188.02 ( ( 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)))
% 187.18/188.02 => 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))) )
% 187.18/188.02 & ( ~ 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)))
% 187.18/188.02 => 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) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_listrel__Nil,axiom,
% 187.18/188.02 ! [V_r_2,T_a] : hAPP(c_Relation_OImage(tc_List_Olist(T_a),tc_List_Olist(T_a),c_List_Olistrel(T_a,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_set__Cons__sing__Nil,axiom,
% 187.18/188.02 ! [V_A_2,T_a] : c_List_Oset__Cons(T_a,V_A_2,hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)))) = hAPP(c_Set_Oimage(T_a,tc_List_Olist(T_a),hAPP(hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)),c_List_Olist_ONil(T_a))),V_A_2) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_length__remove1,axiom,
% 187.18/188.02 ! [V_xs_2,V_x_2,T_a] :
% 187.18/188.02 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 187.18/188.02 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oremove1(T_a,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_a)),V_xs_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
% 187.18/188.02 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 187.18/188.02 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oremove1(T_a,V_x_2,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_upto_Opsimps,axiom,
% 187.18/188.02 ! [V_j_2,V_i_2] :
% 187.18/188.02 ( 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)))
% 187.18/188.02 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2))
% 187.18/188.02 => 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)) )
% 187.18/188.02 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2))
% 187.18/188.02 => c_List_Oupto(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Int_Oint) ) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_select,axiom,
% 187.18/188.02 ! [V_s_2,T_a,V_xs_2] :
% 187.18/188.02 ( V_xs_2 != c_List_Olist_ONil(T_a)
% 187.18/188.02 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Product__Type_Ofst(T_a,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect(T_a,V_xs_2),V_s_2))),hAPP(c_List_Oset(T_a),V_xs_2))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_listset_Osimps_I1_J,axiom,
% 187.18/188.02 ! [T_a] : c_List_Olistset(T_a,c_List_Olist_ONil(tc_fun(T_a,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_zip__Cons1,axiom,
% 187.18/188.02 ! [V_ys_2,V_xs_2,V_x_2,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),V_ys_2) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(T_a,T_b)),T_b,c_List_Olist_ONil(tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_a,T_b))),tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_a,T_b)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(T_a,T_b)),tc_List_Olist(tc_prod(T_a,T_b))),tc_fun(tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_a,T_b))),tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_a,T_b)))),T_b),c_COMBB(tc_List_Olist(tc_prod(T_a,T_b)),tc_List_Olist(tc_prod(T_a,T_b)),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_List_Olist(tc_prod(T_a,T_b)),tc_List_Olist(tc_prod(T_a,T_b))),T_b),c_List_Olist_OCons(tc_prod(T_a,T_b))),hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2)))),hAPP(c_List_Ozip(T_a,T_b),V_xs_2))),V_ys_2) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_list_Osimps_I5_J,axiom,
% 187.18/188.02 ! [V_list_2,V_a_2,V_f2_2,V_f1_2,T_b,T_a] : hAPP(c_List_Olist_Olist__case(T_a,T_b,V_f1_2,V_f2_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_list_2)) = hAPP(hAPP(V_f2_2,V_a_2),V_list_2) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_list_Osimps_I4_J,axiom,
% 187.18/188.02 ! [V_f2_2,V_f1_2,T_b,T_a] : hAPP(c_List_Olist_Olist__case(T_a,T_b,V_f1_2,V_f2_2),c_List_Olist_ONil(T_b)) = V_f1_2 ).
% 187.18/188.02
% 187.18/188.02 fof(fact_listset_Osimps_I2_J,axiom,
% 187.18/188.02 ! [V_As_2,V_A_2,T_a] : c_List_Olistset(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_As_2)) = c_List_Oset__Cons(T_a,V_A_2,c_List_Olistset(T_a,V_As_2)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_zip__Cons,axiom,
% 187.18/188.02 ! [V_ys_2,V_y_2,V_xs_2,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(T_a,T_b)),T_a,c_List_Olist_ONil(tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_List_Olist(T_a),tc_List_Olist(tc_prod(T_a,T_b))),tc_fun(tc_List_Olist(T_a),tc_List_Olist(tc_prod(T_a,T_b)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(T_a,T_b)),tc_List_Olist(tc_prod(T_a,T_b))),tc_fun(tc_fun(tc_List_Olist(T_a),tc_List_Olist(tc_prod(T_a,T_b))),tc_fun(tc_List_Olist(T_a),tc_List_Olist(tc_prod(T_a,T_b)))),T_a),c_COMBB(tc_List_Olist(tc_prod(T_a,T_b)),tc_List_Olist(tc_prod(T_a,T_b)),tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_List_Olist(tc_prod(T_a,T_b)),tc_List_Olist(tc_prod(T_a,T_b))),T_a),c_List_Olist_OCons(tc_prod(T_a,T_b))),hAPP(hAPP(c_COMBC(T_a,T_b,tc_prod(T_a,T_b)),c_Product__Type_OPair(T_a,T_b)),V_y_2)))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_a,T_b))),c_List_Ozip(T_a,T_b)),V_ys_2))),V_xs_2) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_sorted__list__of__set__remove,axiom,
% 187.18/188.02 ! [V_x_2,V_A_2,T_a] :
% 187.18/188.02 ( class_Orderings_Olinorder(T_a)
% 187.18/188.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.02 => c_List_Olinorder__class_Osorted__list__of__set(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = c_List_Oremove1(T_a,V_x_2,c_List_Olinorder__class_Osorted__list__of__set(T_a,V_A_2)) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_upto_Opinduct,axiom,
% 187.18/188.02 ! [V_P_2,V_a1_2,V_a0_2] :
% 187.18/188.02 ( 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)))
% 187.18/188.02 => ( ! [B_i,B_j] :
% 187.18/188.02 ( 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)))
% 187.18/188.02 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_i),B_j))
% 187.18/188.02 => 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)) )
% 187.18/188.02 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) )
% 187.18/188.02 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_sorted__list__of__set__empty,axiom,
% 187.18/188.02 ! [T_a] :
% 187.18/188.02 ( class_Orderings_Olinorder(T_a)
% 187.18/188.02 => c_List_Olinorder__class_Osorted__list__of__set(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_List_Olist_ONil(T_a) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_anamorph_Osimps,axiom,
% 187.18/188.02 ! [V_x_2,V_f_2,T_a,T_b,V_k_2] :
% 187.18/188.02 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 187.18/188.02 => hAPP(hAPP(c_Lazy__Sequence_Oanamorph(T_b,T_a,V_f_2),V_k_2),V_x_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),T_b),c_List_Olist_ONil(T_a)),V_x_2) )
% 187.18/188.02 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 187.18/188.02 => hAPP(hAPP(c_Lazy__Sequence_Oanamorph(T_b,T_a,V_f_2),V_k_2),V_x_2) = hAPP(c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(T_a),T_b),tc_prod(T_a,T_b),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),T_b),c_List_Olist_ONil(T_a)),V_x_2),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_prod(tc_List_Olist(T_a),T_b)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_prod(tc_List_Olist(T_a),T_b)),tc_fun(T_b,tc_prod(tc_List_Olist(T_a),T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(T_a),T_b),tc_prod(tc_List_Olist(T_a),T_b)),tc_fun(tc_fun(T_b,tc_prod(tc_List_Olist(T_a),T_b)),tc_fun(T_b,tc_prod(tc_List_Olist(T_a),T_b))),T_a),c_COMBB(tc_prod(tc_List_Olist(T_a),T_b),tc_prod(tc_List_Olist(T_a),T_b),T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_fun(T_b,tc_prod(tc_List_Olist(T_a),T_b))),tc_fun(tc_prod(tc_List_Olist(T_a),T_b),tc_prod(tc_List_Olist(T_a),T_b)),T_a),c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_a),T_b,tc_prod(tc_List_Olist(T_a),T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_fun(tc_List_Olist(T_a),tc_fun(T_b,tc_prod(tc_List_Olist(T_a),T_b))),T_a),hAPP(c_COMBB(tc_List_Olist(T_a),tc_fun(T_b,tc_prod(tc_List_Olist(T_a),T_b)),tc_List_Olist(T_a)),c_Product__Type_OPair(tc_List_Olist(T_a),T_b))),c_List_Olist_OCons(T_a))))),hAPP(c_Lazy__Sequence_Oanamorph(T_b,T_a,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)) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_sublist__Cons,axiom,
% 187.18/188.02 ! [V_A_2,V_l_2,V_x_2,T_a] : c_List_Osublist(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_l_2),V_A_2) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(hAPP(c_If(tc_List_Olist(T_a)),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_a),V_x_2),c_List_Olist_ONil(T_a))),c_List_Olist_ONil(T_a))),c_List_Osublist(T_a,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)))) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_append1__eq__conv,axiom,
% 187.18/188.02 ! [V_y_2,V_ys_2,V_x_2,V_xs_2,T_a] :
% 187.18/188.02 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a))) = hAPP(hAPP(c_List_Oappend(T_a),V_ys_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),c_List_Olist_ONil(T_a)))
% 187.18/188.02 <=> ( V_xs_2 = V_ys_2
% 187.18/188.02 & V_x_2 = V_y_2 ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_Cons__eq__append__conv,axiom,
% 187.18/188.02 ! [V_zs_2,V_ys_2,V_xs_2,V_x_2,T_a] :
% 187.18/188.02 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) = hAPP(hAPP(c_List_Oappend(T_a),V_ys_2),V_zs_2)
% 187.18/188.02 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_a)
% 187.18/188.02 & hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) = V_zs_2 )
% 187.18/188.02 | ? [B_ys_H] :
% 187.18/188.02 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_ys_H) = V_ys_2
% 187.18/188.02 & V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),B_ys_H),V_zs_2) ) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_append__eq__Cons__conv,axiom,
% 187.18/188.02 ! [V_xs_2,V_x_2,V_zs_2,V_ys_2,T_a] :
% 187.18/188.02 ( hAPP(hAPP(c_List_Oappend(T_a),V_ys_2),V_zs_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)
% 187.18/188.02 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_a)
% 187.18/188.02 & V_zs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) )
% 187.18/188.02 | ? [B_ys_H] :
% 187.18/188.02 ( V_ys_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_ys_H)
% 187.18/188.02 & hAPP(hAPP(c_List_Oappend(T_a),B_ys_H),V_zs_2) = V_xs_2 ) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_Cons__eq__appendI,axiom,
% 187.18/188.02 ! [V_zs,V_xs,V_ys,V_xs1,V_x,T_a] :
% 187.18/188.02 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs1) = V_ys
% 187.18/188.02 => ( V_xs = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_zs)
% 187.18/188.02 => hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),V_ys),V_zs) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_append__Cons,axiom,
% 187.18/188.02 ! [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)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_set__append,axiom,
% 187.18/188.02 ! [V_ys_2,V_xs_2,T_a] : hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(c_List_Oset(T_a),V_ys_2)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_zip__append,axiom,
% 187.18/188.02 ! [V_vs,V_ys,V_us,T_b,V_xs,T_a] :
% 187.18/188.02 ( 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)
% 187.18/188.02 => ( 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)
% 187.18/188.02 => 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)) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_length__append,axiom,
% 187.18/188.02 ! [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)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_listsum__append,axiom,
% 187.18/188.02 ! [V_ys,V_xs,T_a] :
% 187.18/188.02 ( class_Groups_Omonoid__add(T_a)
% 187.18/188.02 => 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)) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_append__assoc,axiom,
% 187.18/188.02 ! [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)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_append__eq__append__conv2,axiom,
% 187.18/188.02 ! [V_ts_2,V_zs_2,V_ys_2,V_xs_2,T_a] :
% 187.18/188.02 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(T_a),V_zs_2),V_ts_2)
% 187.18/188.02 <=> ? [B_us] :
% 187.18/188.02 ( ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),V_zs_2),B_us)
% 187.18/188.02 & hAPP(hAPP(c_List_Oappend(T_a),B_us),V_ys_2) = V_ts_2 )
% 187.18/188.02 | ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),B_us) = V_zs_2
% 187.18/188.02 & V_ys_2 = hAPP(hAPP(c_List_Oappend(T_a),B_us),V_ts_2) ) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_same__append__eq,axiom,
% 187.18/188.02 ! [V_zs_2,V_ys_2,V_xs_2,T_a] :
% 187.18/188.02 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_zs_2)
% 187.18/188.02 <=> V_ys_2 = V_zs_2 ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_append__same__eq,axiom,
% 187.18/188.02 ! [V_zs_2,V_xs_2,V_ys_2,T_a] :
% 187.18/188.02 ( hAPP(hAPP(c_List_Oappend(T_a),V_ys_2),V_xs_2) = hAPP(hAPP(c_List_Oappend(T_a),V_zs_2),V_xs_2)
% 187.18/188.02 <=> V_ys_2 = V_zs_2 ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_append__eq__appendI,axiom,
% 187.18/188.02 ! [V_us,V_ys,V_zs,V_xs1,V_xs,T_a] :
% 187.18/188.02 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_xs1) = V_zs
% 187.18/188.02 => ( V_ys = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_us)
% 187.18/188.02 => hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys) = hAPP(hAPP(c_List_Oappend(T_a),V_zs),V_us) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_append__in__lists__conv,axiom,
% 187.18/188.02 ! [V_A_2,V_ys_2,V_xs_2,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)),c_List_Olists(T_a,V_A_2)))
% 187.18/188.02 <=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_List_Olists(T_a,V_A_2)))
% 187.18/188.02 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_ys_2),c_List_Olists(T_a,V_A_2))) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_fun__upds__append2__drop,axiom,
% 187.18/188.02 ! [V_zs_2,V_m_2,V_ys_2,T_b,V_xs_2,T_a] :
% 187.18/188.02 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)
% 187.18/188.02 => c_Map_Omap__upds(T_a,T_b,V_m_2,V_xs_2,hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_zs_2)) = c_Map_Omap__upds(T_a,T_b,V_m_2,V_xs_2,V_ys_2) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_fun__upds__append__drop,axiom,
% 187.18/188.02 ! [V_zs_2,V_m_2,V_ys_2,T_b,V_xs_2,T_a] :
% 187.18/188.02 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)
% 187.18/188.02 => c_Map_Omap__upds(T_a,T_b,V_m_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_zs_2),V_ys_2) = c_Map_Omap__upds(T_a,T_b,V_m_2,V_xs_2,V_ys_2) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_butlast__append,axiom,
% 187.18/188.02 ! [V_xs,T_a,V_ys] :
% 187.18/188.02 ( ( V_ys = c_List_Olist_ONil(T_a)
% 187.18/188.02 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Obutlast(T_a,V_xs) )
% 187.18/188.02 & ( V_ys != c_List_Olist_ONil(T_a)
% 187.18/188.02 => 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)) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_eq__Nil__appendI,axiom,
% 187.18/188.02 ! [T_a,V_ys,V_xs] :
% 187.18/188.02 ( V_xs = V_ys
% 187.18/188.02 => V_xs = hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_append__self__conv2,axiom,
% 187.18/188.02 ! [V_ys_2,V_xs_2,T_a] :
% 187.18/188.02 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = V_ys_2
% 187.18/188.02 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_append__self__conv,axiom,
% 187.18/188.02 ! [V_ys_2,V_xs_2,T_a] :
% 187.18/188.02 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = V_xs_2
% 187.18/188.02 <=> V_ys_2 = c_List_Olist_ONil(T_a) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_append__is__Nil__conv,axiom,
% 187.18/188.02 ! [V_ys_2,V_xs_2,T_a] :
% 187.18/188.02 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = c_List_Olist_ONil(T_a)
% 187.18/188.02 <=> ( V_xs_2 = c_List_Olist_ONil(T_a)
% 187.18/188.02 & V_ys_2 = c_List_Olist_ONil(T_a) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_self__append__conv2,axiom,
% 187.18/188.02 ! [V_xs_2,T_a,V_ys_2] :
% 187.18/188.02 ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)
% 187.18/188.02 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_self__append__conv,axiom,
% 187.18/188.02 ! [V_ys_2,T_a,V_xs_2] :
% 187.18/188.02 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)
% 187.18/188.02 <=> V_ys_2 = c_List_Olist_ONil(T_a) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_append__Nil2,axiom,
% 187.18/188.02 ! [V_xs,T_a] : hAPP(hAPP(c_List_Oappend(T_a),V_xs),c_List_Olist_ONil(T_a)) = V_xs ).
% 187.18/188.02
% 187.18/188.02 fof(fact_Nil__is__append__conv,axiom,
% 187.18/188.02 ! [V_ys_2,V_xs_2,T_a] :
% 187.18/188.02 ( c_List_Olist_ONil(T_a) = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)
% 187.18/188.02 <=> ( V_xs_2 = c_List_Olist_ONil(T_a)
% 187.18/188.02 & V_ys_2 = c_List_Olist_ONil(T_a) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_append__Nil,axiom,
% 187.18/188.02 ! [V_ys,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) = V_ys ).
% 187.18/188.02
% 187.18/188.02 fof(fact_nth__append__length,axiom,
% 187.18/188.02 ! [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 ).
% 187.18/188.02
% 187.18/188.02 fof(fact_nth__append__length__plus,axiom,
% 187.18/188.02 ! [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) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_take__append,axiom,
% 187.18/188.02 ! [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)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_list__update__append1,axiom,
% 187.18/188.02 ! [V_x,V_ys,V_xs,T_a,V_i] :
% 187.18/188.02 ( 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)))
% 187.18/188.02 => 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) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_list__update__length,axiom,
% 187.18/188.02 ! [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)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_remove1__append,axiom,
% 187.18/188.02 ! [V_ys_2,V_xs_2,V_x_2,T_a] :
% 187.18/188.02 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 187.18/188.02 => c_List_Oremove1(T_a,V_x_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_a),c_List_Oremove1(T_a,V_x_2,V_xs_2)),V_ys_2) )
% 187.18/188.02 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 187.18/188.02 => c_List_Oremove1(T_a,V_x_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),c_List_Oremove1(T_a,V_x_2,V_ys_2)) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_in__set__butlast__appendI,axiom,
% 187.18/188.02 ! [V_ys_2,V_xs_2,V_x_2,T_a] :
% 187.18/188.02 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Obutlast(T_a,V_xs_2))))
% 187.18/188.02 | hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Obutlast(T_a,V_ys_2)))) )
% 187.18/188.02 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2))))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_butlast__snoc,axiom,
% 187.18/188.02 ! [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 ).
% 187.18/188.02
% 187.18/188.02 fof(fact_append__listrel1I,axiom,
% 187.18/188.02 ! [V_vs_2,V_us_2,V_r_2,V_ys_2,V_xs_2,T_a] :
% 187.18/188.02 ( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2)))
% 187.18/188.02 & V_us_2 = V_vs_2 )
% 187.18/188.02 | ( V_xs_2 = V_ys_2
% 187.18/188.02 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_us_2),V_vs_2)),c_List_Olistrel1(T_a,V_r_2))) ) )
% 187.18/188.02 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_us_2)),hAPP(hAPP(c_List_Oappend(T_a),V_ys_2),V_vs_2))),c_List_Olistrel1(T_a,V_r_2))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_lexord__append__leftI,axiom,
% 187.18/188.02 ! [V_x_2,V_r_2,V_v_2,V_u_2,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_u_2),V_v_2)),c_List_Olexord(T_a,V_r_2)))
% 187.18/188.02 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Oappend(T_a),V_x_2),V_u_2)),hAPP(hAPP(c_List_Oappend(T_a),V_x_2),V_v_2))),c_List_Olexord(T_a,V_r_2))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_distinct__append,axiom,
% 187.18/188.02 ! [V_ys_2,V_xs_2,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)))
% 187.18/188.02 <=> ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 187.18/188.02 & hBOOL(hAPP(c_List_Odistinct(T_a),V_ys_2))
% 187.18/188.02 & hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(c_List_Oset(T_a),V_ys_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_nth__append,axiom,
% 187.18/188.02 ! [V_ys,V_xs,T_a,V_n] :
% 187.18/188.02 ( ( 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)))
% 187.18/188.02 => 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) )
% 187.18/188.02 & ( ~ 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)))
% 187.18/188.02 => 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))) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_list__update__append,axiom,
% 187.18/188.02 ! [V_x,V_ys,V_xs,T_a,V_n] :
% 187.18/188.02 ( ( 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)))
% 187.18/188.02 => 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) )
% 187.18/188.02 & ( ~ 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)))
% 187.18/188.02 => 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)) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_sublist__append,axiom,
% 187.18/188.02 ! [V_A_2,V_l_H_2,V_l_2,T_a] : c_List_Osublist(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_l_2),V_l_H_2),V_A_2) = hAPP(hAPP(c_List_Oappend(T_a),c_List_Osublist(T_a,V_l_2,V_A_2)),c_List_Osublist(T_a,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_a)),V_l_2)))),V_A_2)))) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_listrel1I,axiom,
% 187.18/188.02 ! [V_ys_2,V_vs_2,V_us_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2))
% 187.18/188.02 => ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),V_us_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_vs_2))
% 187.18/188.02 => ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_a),V_us_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_vs_2))
% 187.18/188.02 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2))) ) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_lexord__append__left__rightI,axiom,
% 187.18/188.02 ! [V_y_2,V_x_2,V_u_2,V_r_2,V_b_2,V_a_2,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2))
% 187.18/188.02 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Oappend(T_a),V_u_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_2),V_x_2))),hAPP(hAPP(c_List_Oappend(T_a),V_u_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_b_2),V_y_2)))),c_List_Olexord(T_a,V_r_2))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_take__Suc__conv__app__nth,axiom,
% 187.18/188.02 ! [V_xs,T_a,V_i] :
% 187.18/188.02 ( 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)))
% 187.18/188.02 => 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))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_snoc__listrel1__snoc__iff,axiom,
% 187.18/188.02 ! [V_r_2,V_y_2,V_ys_2,V_x_2,V_xs_2,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)))),hAPP(hAPP(c_List_Oappend(T_a),V_ys_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),c_List_Olist_ONil(T_a))))),c_List_Olistrel1(T_a,V_r_2)))
% 187.18/188.02 <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2)))
% 187.18/188.02 & V_x_2 = V_y_2 )
% 187.18/188.02 | ( V_xs_2 = V_ys_2
% 187.18/188.02 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) ) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_listrel1E,axiom,
% 187.18/188.02 ! [V_r_2,V_ys_2,V_xs_2,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2)))
% 187.18/188.02 => ~ ! [B_x,B_y] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_y)),V_r_2))
% 187.18/188.02 => ! [B_us,B_vs] :
% 187.18/188.02 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),B_us),hAPP(hAPP(c_List_Olist_OCons(T_a),B_x),B_vs))
% 187.18/188.02 => V_ys_2 != hAPP(hAPP(c_List_Oappend(T_a),B_us),hAPP(hAPP(c_List_Olist_OCons(T_a),B_y),B_vs)) ) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_lexord__append__leftD,axiom,
% 187.18/188.02 ! [V_r_2,V_v_2,V_u_2,V_x_2,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Oappend(T_a),V_x_2),V_u_2)),hAPP(hAPP(c_List_Oappend(T_a),V_x_2),V_v_2))),c_List_Olexord(T_a,V_r_2)))
% 187.18/188.02 => ( ! [B_a] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_a),B_a)),V_r_2))
% 187.18/188.02 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_u_2),V_v_2)),c_List_Olexord(T_a,V_r_2))) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_rotate1__def,axiom,
% 187.18/188.02 ! [V_xs_2,T_a] : hAPP(c_List_Orotate1(T_a),V_xs_2) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(T_a),T_a,c_List_Olist_ONil(T_a),hAPP(hAPP(c_COMBB(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),T_a),hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Oappend(T_a))),hAPP(hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)),c_List_Olist_ONil(T_a)))),V_xs_2) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_map__upds__append1,axiom,
% 187.18/188.02 ! [V_x_2,V_m_2,V_ys_2,T_b,V_xs_2,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)))
% 187.18/188.02 => c_Map_Omap__upds(T_a,T_b,V_m_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a))),V_ys_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Omap__upds(T_a,T_b,V_m_2,V_xs_2,V_ys_2)),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),hAPP(hAPP(c_List_Onth(T_b),V_ys_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_image__map__upd,axiom,
% 187.18/188.02 ! [V_y_2,V_m_2,T_b,V_A_2,V_x_2,T_a] :
% 187.18/188.02 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 187.18/188.02 => hAPP(c_Set_Oimage(T_a,tc_Option_Ooption(T_b),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_m_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2))),V_A_2) = hAPP(c_Set_Oimage(T_a,tc_Option_Ooption(T_b),V_m_2),V_A_2) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_set__rotate1,axiom,
% 187.18/188.02 ! [V_xs_2,T_a] : hAPP(c_List_Oset(T_a),hAPP(c_List_Orotate1(T_a),V_xs_2)) = hAPP(c_List_Oset(T_a),V_xs_2) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_length__rotate1,axiom,
% 187.18/188.02 ! [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) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_dom__const,axiom,
% 187.18/188.02 ! [V_f_2,T_b,T_a] : c_Map_Odom(T_a,T_b,hAPP(hAPP(c_COMBB(T_b,tc_Option_Ooption(T_b),T_a),c_Option_Ooption_OSome(T_b)),V_f_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_domI,axiom,
% 187.18/188.02 ! [T_b,V_b_2,T_a,V_a_2,V_m_2] :
% 187.18/188.02 ( hAPP(V_m_2,V_a_2) = hAPP(c_Option_Ooption_OSome(T_a),V_b_2)
% 187.18/188.02 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Map_Odom(T_b,T_a,V_m_2))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_insert__dom,axiom,
% 187.18/188.02 ! [T_b,V_y_2,T_a,V_x_2,V_f_2] :
% 187.18/188.02 ( hAPP(V_f_2,V_x_2) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2)
% 187.18/188.02 => hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Map_Odom(T_b,T_a,V_f_2)) = c_Map_Odom(T_b,T_a,V_f_2) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_distinct1__rotate,axiom,
% 187.18/188.02 ! [V_xs_2,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Orotate1(T_a),V_xs_2)))
% 187.18/188.02 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_map__upd__Some__unfold,axiom,
% 187.18/188.02 ! [V_y_2,V_x_2,V_b_2,V_a_2,V_m_2,T_a,T_b] :
% 187.18/188.02 ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_a),V_b_2)),V_x_2) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2)
% 187.18/188.02 <=> ( ( V_x_2 = V_a_2
% 187.18/188.02 & V_b_2 = V_y_2 )
% 187.18/188.02 | ( V_x_2 != V_a_2
% 187.18/188.02 & hAPP(V_m_2,V_x_2) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2) ) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_map__upd__triv,axiom,
% 187.18/188.02 ! [T_b,V_x_2,T_a,V_k_2,V_t_2] :
% 187.18/188.02 ( hAPP(V_t_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2)
% 187.18/188.02 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),V_t_2),V_k_2),hAPP(c_Option_Ooption_OSome(T_a),V_x_2)) = V_t_2 ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_map__upd__eqD1,axiom,
% 187.18/188.02 ! [V_y_2,V_n_2,V_x_2,V_a_2,V_m_2,T_b,T_a] :
% 187.18/188.02 ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_b),V_x_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_n_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2))
% 187.18/188.02 => V_x_2 = V_y_2 ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_rotate1__is__Nil__conv,axiom,
% 187.18/188.02 ! [V_xs_2,T_a] :
% 187.18/188.02 ( hAPP(c_List_Orotate1(T_a),V_xs_2) = c_List_Olist_ONil(T_a)
% 187.18/188.02 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_map__upds__Cons,axiom,
% 187.18/188.02 ! [V_bs_2,V_b_2,V_as_2,V_a_2,V_m_2,T_b,T_a] : c_Map_Omap__upds(T_a,T_b,V_m_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_2),V_as_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_b_2),V_bs_2)) = c_Map_Omap__upds(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_b),V_b_2)),V_as_2,V_bs_2) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_WT_Oequations_I7_J,axiom,
% 187.18/188.02 ! [V_a_2] :
% 187.18/188.02 ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_a_2)))
% 187.18/188.02 <=> ? [B_y] : hAPP(c_Com_Obody,V_a_2) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),B_y) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_finite__range__updI,axiom,
% 187.18/188.02 ! [V_b_2,V_a_2,V_f_2,T_b,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_a)),hAPP(c_Set_Oimage(T_b,tc_Option_Ooption(T_a),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))))
% 187.18/188.02 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_a)),hAPP(c_Set_Oimage(T_b,tc_Option_Ooption(T_a),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),V_f_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_a),V_b_2))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_WT__bodiesD,axiom,
% 187.18/188.02 ! [V_b,V_pn] :
% 187.18/188.02 ( c_Com_OWT__bodies
% 187.18/188.02 => ( hAPP(c_Com_Obody,V_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b)
% 187.18/188.02 => hBOOL(hAPP(c_Com_OWT,V_b)) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_map__upds__twist,axiom,
% 187.18/188.02 ! [V_bs_2,V_b_2,V_m_2,T_b,V_as_2,V_a_2,T_a] :
% 187.18/188.02 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_as_2)))
% 187.18/188.02 => c_Map_Omap__upds(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_b),V_b_2)),V_as_2,V_bs_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Omap__upds(T_a,T_b,V_m_2,V_as_2,V_bs_2)),V_a_2),hAPP(c_Option_Ooption_OSome(T_b),V_b_2)) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_restrict__upd__same,axiom,
% 187.18/188.02 ! [V_y_2,V_x_2,V_m_2,T_b,T_a] : c_Map_Orestrict__map(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_m_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = c_Map_Orestrict__map(T_a,T_b,V_m_2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_rotate__simps,axiom,
% 187.18/188.02 ! [V_xs,V_x,T_b,T_a] :
% 187.18/188.02 ( hAPP(c_List_Orotate1(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a)
% 187.18/188.02 & 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))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_rotate1__length01,axiom,
% 187.18/188.02 ! [V_xs,T_a] :
% 187.18/188.02 ( 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)))
% 187.18/188.02 => hAPP(c_List_Orotate1(T_a),V_xs) = V_xs ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_map__upd__upds__conv__if,axiom,
% 187.18/188.02 ! [V_y_2,V_f_2,V_xs_2,V_ys_2,T_b,V_x_2,T_a] :
% 187.18/188.02 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)),V_xs_2))))
% 187.18/188.02 => c_Map_Omap__upds(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_f_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2)),V_xs_2,V_ys_2) = c_Map_Omap__upds(T_a,T_b,V_f_2,V_xs_2,V_ys_2) )
% 187.18/188.02 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)),V_xs_2))))
% 187.18/188.02 => c_Map_Omap__upds(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_f_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2)),V_xs_2,V_ys_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Omap__upds(T_a,T_b,V_f_2,V_xs_2,V_ys_2)),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2)) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_option_Osize_I2_J,axiom,
% 187.18/188.02 ! [V_a_2,V_fa_2,T_a] : c_Option_Ooption_Ooption__size(T_a,V_fa_2,hAPP(c_Option_Ooption_OSome(T_a),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))) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_option_Osimps_I5_J,axiom,
% 187.18/188.02 ! [V_a_2,V_f2_2,V_f1_2,T_b,T_a] : hAPP(c_Option_Ooption_Ooption__case(T_a,T_b,V_f1_2,V_f2_2),hAPP(c_Option_Ooption_OSome(T_b),V_a_2)) = hAPP(V_f2_2,V_a_2) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_inj__Some,axiom,
% 187.18/188.02 ! [V_A_2,T_a] : c_Fun_Oinj__on(T_a,tc_Option_Ooption(T_a),c_Option_Ooption_OSome(T_a),V_A_2) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_option_Oinject,axiom,
% 187.18/188.02 ! [V_a_H_2,V_a_2,T_a] :
% 187.18/188.02 ( hAPP(c_Option_Ooption_OSome(T_a),V_a_2) = hAPP(c_Option_Ooption_OSome(T_a),V_a_H_2)
% 187.18/188.02 <=> V_a_2 = V_a_H_2 ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_the_Osimps,axiom,
% 187.18/188.02 ! [V_x,T_a] : hAPP(c_Option_Othe(T_a),hAPP(c_Option_Ooption_OSome(T_a),V_x)) = V_x ).
% 187.18/188.02
% 187.18/188.02 fof(fact_WTs__elim__cases_I7_J,axiom,
% 187.18/188.02 ! [V_P] :
% 187.18/188.02 ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_P)))
% 187.18/188.02 => ~ ! [B_y] : hAPP(c_Com_Obody,V_P) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),B_y) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_Option_Oset_Osimps_I2_J,axiom,
% 187.18/188.02 ! [V_x_2,T_a] : c_Option_Oset(T_a,hAPP(c_Option_Ooption_OSome(T_a),V_x_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_elem__set,axiom,
% 187.18/188.02 ! [V_xo_2,V_x_2,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Option_Oset(T_a,V_xo_2)))
% 187.18/188.02 <=> V_xo_2 = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_upd__conv__take__nth__drop,axiom,
% 187.18/188.02 ! [V_a,V_xs,T_a,V_i] :
% 187.18/188.02 ( 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)))
% 187.18/188.02 => 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))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_id__take__nth__drop,axiom,
% 187.18/188.02 ! [V_xs,T_a,V_i] :
% 187.18/188.02 ( 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)))
% 187.18/188.02 => 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))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_drop__Nil,axiom,
% 187.18/188.02 ! [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) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_distinct__drop,axiom,
% 187.18/188.02 ! [V_i,V_xs,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 187.18/188.02 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_butlast__drop,axiom,
% 187.18/188.02 ! [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)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_drop__butlast,axiom,
% 187.18/188.02 ! [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)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_drop__take,axiom,
% 187.18/188.02 ! [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)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_take__drop,axiom,
% 187.18/188.02 ! [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)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_drop__0,axiom,
% 187.18/188.02 ! [V_xs,T_a] : hAPP(hAPP(c_List_Odrop(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_xs) = V_xs ).
% 187.18/188.02
% 187.18/188.02 fof(fact_drop__drop,axiom,
% 187.18/188.02 ! [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) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_drop__zip,axiom,
% 187.18/188.02 ! [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)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_length__drop,axiom,
% 187.18/188.02 ! [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) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_in__set__dropD,axiom,
% 187.18/188.02 ! [V_xs_2,V_n_2,V_x_2,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n_2),V_xs_2))))
% 187.18/188.02 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_set__drop__subset,axiom,
% 187.18/188.02 ! [V_xs_2,V_n_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n_2),V_xs_2))),hAPP(c_List_Oset(T_a),V_xs_2))) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_drop__Suc__Cons,axiom,
% 187.18/188.02 ! [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) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_drop__1__Cons,axiom,
% 187.18/188.02 ! [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 ).
% 187.18/188.02
% 187.18/188.02 fof(fact_nth__via__drop,axiom,
% 187.18/188.02 ! [V_ys,V_y,V_xs,V_n,T_a] :
% 187.18/188.02 ( hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys)
% 187.18/188.02 => hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) = V_y ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_append__take__drop__id,axiom,
% 187.18/188.02 ! [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 ).
% 187.18/188.02
% 187.18/188.02 fof(fact_set__drop__subset__set__drop,axiom,
% 187.18/188.02 ! [V_xs_2,T_a,V_m_2,V_n_2] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2))
% 187.18/188.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_m_2),V_xs_2))),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n_2),V_xs_2)))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_drop__eq__Nil,axiom,
% 187.18/188.02 ! [V_xs_2,V_n_2,T_a] :
% 187.18/188.02 ( hAPP(hAPP(c_List_Odrop(T_a),V_n_2),V_xs_2) = c_List_Olist_ONil(T_a)
% 187.18/188.02 <=> 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_2)),V_n_2)) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_drop__all,axiom,
% 187.18/188.02 ! [V_n,V_xs,T_a] :
% 187.18/188.02 ( 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))
% 187.18/188.02 => hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = c_List_Olist_ONil(T_a) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_drop__append,axiom,
% 187.18/188.02 ! [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)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_append__eq__conv__conj,axiom,
% 187.18/188.02 ! [V_zs_2,V_ys_2,V_xs_2,T_a] :
% 187.18/188.02 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = V_zs_2
% 187.18/188.02 <=> ( V_xs_2 = hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),V_zs_2)
% 187.18/188.02 & V_ys_2 = hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),V_zs_2) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_drop__Cons,axiom,
% 187.18/188.02 ! [V_xs_2,V_x_2,V_n_2,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = c_Nat_Onat_Onat__case(tc_List_Olist(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Odrop(T_a)),V_xs_2),V_n_2) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_drop__Cons_H,axiom,
% 187.18/188.02 ! [V_xs,V_x,T_a,V_n] :
% 187.18/188.02 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.18/188.02 => 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) )
% 187.18/188.02 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.18/188.02 => 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) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_nth__drop,axiom,
% 187.18/188.02 ! [V_xs,T_a,V_i,V_n] :
% 187.18/188.02 ( 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)))
% 187.18/188.02 => 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)) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_append__eq__append__conv__if,axiom,
% 187.18/188.02 ! [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_a] :
% 187.18/188.02 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_092_060_094isub_0621_2),V_xs_092_060_094isub_0622_2) = hAPP(hAPP(c_List_Oappend(T_a),V_ys_092_060_094isub_0621_2),V_ys_092_060_094isub_0622_2)
% 187.18/188.02 <=> ( ( 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_092_060_094isub_0621_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_092_060_094isub_0621_2)))
% 187.18/188.02 => ( V_xs_092_060_094isub_0621_2 = hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_092_060_094isub_0621_2)),V_ys_092_060_094isub_0621_2)
% 187.18/188.02 & V_xs_092_060_094isub_0622_2 = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_092_060_094isub_0621_2)),V_ys_092_060_094isub_0621_2)),V_ys_092_060_094isub_0622_2) ) )
% 187.18/188.02 & ( ~ 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_092_060_094isub_0621_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_092_060_094isub_0621_2)))
% 187.18/188.02 => ( hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_092_060_094isub_0621_2)),V_xs_092_060_094isub_0621_2) = V_ys_092_060_094isub_0621_2
% 187.18/188.02 & hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),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 ) ) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_nth__drop_H,axiom,
% 187.18/188.02 ! [V_xs,T_a,V_i] :
% 187.18/188.02 ( 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)))
% 187.18/188.02 => 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) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_drop__Cons__number__of,axiom,
% 187.18/188.02 ! [V_xs,V_x,T_a,V_v] :
% 187.18/188.02 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.18/188.02 => 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) )
% 187.18/188.02 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.18/188.02 => 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) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_take__add,axiom,
% 187.18/188.02 ! [V_xs,T_a,V_j,V_i] :
% 187.18/188.02 ( 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)))
% 187.18/188.02 => 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))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_zip__append2,axiom,
% 187.18/188.02 ! [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)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_zip__append1,axiom,
% 187.18/188.02 ! [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))) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_take__hd__drop,axiom,
% 187.18/188.02 ! [V_xs,T_a,V_n] :
% 187.18/188.02 ( 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)))
% 187.18/188.02 => 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) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_hd__drop__conv__nth,axiom,
% 187.18/188.02 ! [V_n,T_a,V_xs] :
% 187.18/188.02 ( V_xs != c_List_Olist_ONil(T_a)
% 187.18/188.02 => ( 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)))
% 187.18/188.02 => 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) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_hd_Osimps,axiom,
% 187.18/188.02 ! [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 ).
% 187.18/188.02
% 187.18/188.02 fof(fact_hd__append2,axiom,
% 187.18/188.02 ! [V_ys,T_a,V_xs] :
% 187.18/188.02 ( V_xs != c_List_Olist_ONil(T_a)
% 187.18/188.02 => 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) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_hd__append,axiom,
% 187.18/188.02 ! [V_ys,T_a,V_xs] :
% 187.18/188.02 ( ( V_xs = c_List_Olist_ONil(T_a)
% 187.18/188.02 => 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) )
% 187.18/188.02 & ( V_xs != c_List_Olist_ONil(T_a)
% 187.18/188.02 => 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) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_hd__in__set,axiom,
% 187.18/188.02 ! [T_a,V_xs_2] :
% 187.18/188.02 ( V_xs_2 != c_List_Olist_ONil(T_a)
% 187.18/188.02 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_List_Ohd(T_a),V_xs_2)),hAPP(c_List_Oset(T_a),V_xs_2))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_hd__conv__nth,axiom,
% 187.18/188.02 ! [T_a,V_xs] :
% 187.18/188.02 ( V_xs != c_List_Olist_ONil(T_a)
% 187.18/188.02 => 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)) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_rotate1__hd__tl,axiom,
% 187.18/188.02 ! [T_a,V_xs] :
% 187.18/188.02 ( V_xs != c_List_Olist_ONil(T_a)
% 187.18/188.02 => 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))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_option_Osize_I4_J,axiom,
% 187.18/188.02 ! [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) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_drop__tl,axiom,
% 187.18/188.02 ! [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)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_tl__drop,axiom,
% 187.18/188.02 ! [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)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_tl_Osimps_I1_J,axiom,
% 187.18/188.02 ! [T_a] : hAPP(c_List_Otl(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_distinct__tl,axiom,
% 187.18/188.02 ! [V_xs,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 187.18/188.02 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Otl(T_a),V_xs))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_tl_Osimps_I2_J,axiom,
% 187.18/188.02 ! [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 ).
% 187.18/188.02
% 187.18/188.02 fof(fact_tl__append2,axiom,
% 187.18/188.02 ! [V_ys,T_a,V_xs] :
% 187.18/188.02 ( V_xs != c_List_Olist_ONil(T_a)
% 187.18/188.02 => 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) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_take__tl,axiom,
% 187.18/188.02 ! [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)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_drop__Suc,axiom,
% 187.18/188.02 ! [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)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_tl__append,axiom,
% 187.18/188.02 ! [V_ys_2,V_xs_2,T_a] : hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(T_a),T_a,hAPP(c_List_Otl(T_a),V_ys_2),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),T_a),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Oappend(T_a)),V_ys_2))),V_xs_2) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_length__tl,axiom,
% 187.18/188.02 ! [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)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_tl__take,axiom,
% 187.18/188.02 ! [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)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_take__Suc,axiom,
% 187.18/188.02 ! [V_n,T_a,V_xs] :
% 187.18/188.02 ( V_xs != c_List_Olist_ONil(T_a)
% 187.18/188.02 => 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))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_fold1__set,axiom,
% 187.18/188.02 ! [V_xs_2,T_a] :
% 187.18/188.02 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 187.18/188.02 => ( V_xs_2 != c_List_Olist_ONil(T_a)
% 187.18/188.02 => hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),hAPP(c_List_Oset(T_a),V_xs_2)) = hAPP(c_List_Ofoldl(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a),hAPP(c_List_Ohd(T_a),V_xs_2)),hAPP(c_List_Otl(T_a),V_xs_2)) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_hd__rotate__conv__nth,axiom,
% 187.18/188.02 ! [V_n,T_a,V_xs] :
% 187.18/188.02 ( V_xs != c_List_Olist_ONil(T_a)
% 187.18/188.02 => 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))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_length__rotate,axiom,
% 187.18/188.02 ! [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) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_foldl__append,axiom,
% 187.18/188.02 ! [V_ys_2,V_xs_2,V_a_2,V_f_2,T_b,T_a] : hAPP(c_List_Ofoldl(T_a,T_b,V_f_2,V_a_2),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(c_List_Ofoldl(T_a,T_b,V_f_2,hAPP(c_List_Ofoldl(T_a,T_b,V_f_2,V_a_2),V_xs_2)),V_ys_2) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_foldl__Cons,axiom,
% 187.18/188.02 ! [V_xs_2,V_x_2,V_a_2,V_f_2,T_b,T_a] : hAPP(c_List_Ofoldl(T_a,T_b,V_f_2,V_a_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(c_List_Ofoldl(T_a,T_b,V_f_2,hAPP(hAPP(V_f_2,V_a_2),V_x_2)),V_xs_2) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_set__rotate,axiom,
% 187.18/188.02 ! [V_xs_2,V_n_2,T_a] : hAPP(c_List_Oset(T_a),hAPP(c_List_Orotate(T_a,V_n_2),V_xs_2)) = hAPP(c_List_Oset(T_a),V_xs_2) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_start__le__sum,axiom,
% 187.18/188.02 ! [V_ns_2,V_n_2,V_m_2] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 187.18/188.02 => 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))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_foldl__absorb0,axiom,
% 187.18/188.02 ! [V_zs_2,V_x_2,T_a] :
% 187.18/188.02 ( class_Groups_Omonoid__add(T_a)
% 187.18/188.02 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x_2),hAPP(c_List_Ofoldl(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_zs_2)) = hAPP(c_List_Ofoldl(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),V_x_2),V_zs_2) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_foldl__assoc,axiom,
% 187.18/188.02 ! [V_zs_2,V_y_2,V_x_2,T_a] :
% 187.18/188.02 ( class_Groups_Osemigroup__add(T_a)
% 187.18/188.02 => hAPP(c_List_Ofoldl(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x_2),V_y_2)),V_zs_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x_2),hAPP(c_List_Ofoldl(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),V_y_2),V_zs_2)) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_rotate__rotate,axiom,
% 187.18/188.02 ! [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) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_rotate0,axiom,
% 187.18/188.02 ! [T_a] : c_List_Orotate(T_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(T_a)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_rotate__add,axiom,
% 187.18/188.02 ! [V_n_2,V_m_2,T_a] : c_List_Orotate(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)) = hAPP(c_Fun_Ocomp(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_List_Olist(T_a),c_List_Orotate(T_a,V_m_2)),c_List_Orotate(T_a,V_n_2)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_distinct__rotate,axiom,
% 187.18/188.02 ! [V_xs_2,V_n_2,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Orotate(T_a,V_n_2),V_xs_2)))
% 187.18/188.02 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_foldl__Nil,axiom,
% 187.18/188.02 ! [V_a_2,V_f_2,T_b,T_a] : hAPP(c_List_Ofoldl(T_a,T_b,V_f_2,V_a_2),c_List_Olist_ONil(T_b)) = V_a_2 ).
% 187.18/188.02
% 187.18/188.02 fof(fact_rotate__is__Nil__conv,axiom,
% 187.18/188.02 ! [V_xs_2,V_n_2,T_a] :
% 187.18/188.02 ( hAPP(c_List_Orotate(T_a,V_n_2),V_xs_2) = c_List_Olist_ONil(T_a)
% 187.18/188.02 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_rotate1__rotate__swap,axiom,
% 187.18/188.02 ! [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)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_rotate__def,axiom,
% 187.18/188.02 ! [V_n_2,T_a] : c_List_Orotate(T_a,V_n_2) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_n_2),c_List_Orotate1(T_a)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_rotate__conv__mod,axiom,
% 187.18/188.02 ! [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) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_rotate__Suc,axiom,
% 187.18/188.02 ! [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)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_listsum__foldl,axiom,
% 187.18/188.02 ! [T_a] :
% 187.18/188.02 ( class_Groups_Omonoid__add(T_a)
% 187.18/188.02 => c_List_Omonoid__add__class_Olistsum(T_a) = c_List_Ofoldl(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_sum__eq__0__conv,axiom,
% 187.18/188.02 ! [V_ns_2,V_m_2] :
% 187.18/188.02 ( 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)
% 187.18/188.02 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.18/188.02 & ! [B_x] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
% 187.18/188.02 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_rotate__id,axiom,
% 187.18/188.02 ! [V_xs,T_a,V_n] :
% 187.18/188.02 ( 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)
% 187.18/188.02 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_rotate__length01,axiom,
% 187.18/188.02 ! [V_n,V_xs,T_a] :
% 187.18/188.02 ( 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)))
% 187.18/188.02 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_fun__left__comm__idem_Ofold__set,axiom,
% 187.18/188.02 ! [V_xs_2,V_y_2,V_f_2,T_b,T_a] :
% 187.18/188.02 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2)
% 187.18/188.02 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_y_2),hAPP(c_List_Oset(T_a),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_a,hAPP(c_COMBC(T_a,T_b,T_b),V_f_2),V_y_2),V_xs_2) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_Sup__set__fold,axiom,
% 187.18/188.02 ! [V_xs_2,T_a] :
% 187.18/188.02 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 187.18/188.02 => c_Complete__Lattice_OSup__class_OSup(T_a,hAPP(c_List_Oset(T_a),V_xs_2)) = hAPP(c_List_Ofoldl(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Orderings_Obot__class_Obot(T_a)),V_xs_2) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_Inf__set__fold,axiom,
% 187.18/188.02 ! [V_xs_2,T_a] :
% 187.18/188.02 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 187.18/188.02 => c_Complete__Lattice_OInf__class_OInf(T_a,hAPP(c_List_Oset(T_a),V_xs_2)) = hAPP(c_List_Ofoldl(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Orderings_Otop__class_Otop(T_a)),V_xs_2) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_Sup__fin__set__fold,axiom,
% 187.18/188.02 ! [V_xs_2,V_x_2,T_a] :
% 187.18/188.02 ( class_Lattices_Olattice(T_a)
% 187.18/188.02 => c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),V_xs_2) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_Inf__fin__set__fold,axiom,
% 187.18/188.02 ! [V_xs_2,V_x_2,T_a] :
% 187.18/188.02 ( class_Lattices_Olattice(T_a)
% 187.18/188.02 => c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),V_xs_2) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_Min__fin__set__fold,axiom,
% 187.18/188.02 ! [V_xs_2,V_x_2,T_a] :
% 187.18/188.02 ( class_Orderings_Olinorder(T_a)
% 187.18/188.02 => c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_a,T_a,c_Orderings_Oord__class_Omin(T_a),V_x_2),V_xs_2) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_Max__fin__set__fold,axiom,
% 187.18/188.02 ! [V_xs_2,V_x_2,T_a] :
% 187.18/188.02 ( class_Orderings_Olinorder(T_a)
% 187.18/188.02 => c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_a,T_a,c_Orderings_Oord__class_Omax(T_a),V_x_2),V_xs_2) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_min__max_OInf__fin__set__fold,axiom,
% 187.18/188.02 ! [V_xs_2,V_x_2,T_a] :
% 187.18/188.02 ( class_Orderings_Olinorder(T_a)
% 187.18/188.02 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_a,T_a,c_Orderings_Oord__class_Omin(T_a),V_x_2),V_xs_2) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_min__max_OSup__fin__set__fold,axiom,
% 187.18/188.02 ! [V_xs_2,V_x_2,T_a] :
% 187.18/188.02 ( class_Orderings_Olinorder(T_a)
% 187.18/188.02 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_a,T_a,c_Orderings_Oord__class_Omax(T_a),V_x_2),V_xs_2) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_SUPR__set__fold,axiom,
% 187.18/188.02 ! [V_f_2,V_xs_2,T_b,T_a] :
% 187.18/188.02 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 187.18/188.02 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_a),hAPP(c_List_Oset(T_b),V_xs_2)),V_f_2) = hAPP(c_List_Ofoldl(T_a,T_b,hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Lattices_Osemilattice__sup__class_Osup(T_a)),V_f_2)),c_Orderings_Obot__class_Obot(T_a)),V_xs_2) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_INFI__set__fold,axiom,
% 187.18/188.02 ! [V_f_2,V_xs_2,T_b,T_a] :
% 187.18/188.02 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 187.18/188.02 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_a),hAPP(c_List_Oset(T_b),V_xs_2)),V_f_2) = hAPP(c_List_Ofoldl(T_a,T_b,hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_f_2)),c_Orderings_Otop__class_Otop(T_a)),V_xs_2) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_map__upds__fold__map__upd,axiom,
% 187.18/188.02 ! [V_vs_2,V_ks_2,V_m_2,T_b,T_a] : c_Map_Omap__upds(T_a,T_b,V_m_2,V_ks_2,V_vs_2) = hAPP(c_List_Ofoldl(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_prod(T_a,T_b),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_b,tc_fun(T_a,tc_Option_Ooption(T_b)))),tc_fun(tc_prod(T_a,T_b),tc_fun(T_a,tc_Option_Ooption(T_b))),tc_fun(T_a,tc_Option_Ooption(T_b))),c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_fun(T_a,tc_Option_Ooption(T_b)))),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_a,tc_fun(T_b,tc_fun(T_a,tc_Option_Ooption(T_b))))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_b,tc_fun(T_a,tc_Option_Ooption(T_b))))),tc_fun(tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_a,tc_fun(T_b,tc_fun(T_a,tc_Option_Ooption(T_b))))),tc_fun(T_a,tc_Option_Ooption(T_b))),c_COMBC(T_a,tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_b,tc_fun(T_a,tc_Option_Ooption(T_b))))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Option_Ooption(T_b),tc_fun(T_a,tc_Option_Ooption(T_b)))),tc_fun(T_a,tc_fun(tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_b,tc_fun(T_a,tc_Option_Ooption(T_b))))),tc_fun(T_a,tc_Option_Ooption(T_b))),hAPP(c_COMBB(tc_fun(tc_Option_Ooption(T_b),tc_fun(T_a,tc_Option_Ooption(T_b))),tc_fun(tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_b,tc_fun(T_a,tc_Option_Ooption(T_b)))),T_a),c_COMBB(tc_Option_Ooption(T_b),tc_fun(T_a,tc_Option_Ooption(T_b)),T_b))),c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b))))),c_Option_Ooption_OSome(T_b))),V_m_2),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_ks_2),V_vs_2)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_elem__le__sum,axiom,
% 187.18/188.02 ! [V_ns_2,V_n_2] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_n_2),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
% 187.18/188.02 => 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))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_rotate__drop__take,axiom,
% 187.18/188.02 ! [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)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_ran__def,axiom,
% 187.18/188.02 ! [V_m_2,T_a,T_b] : c_Map_Oran(T_b,T_a,V_m_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_a),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBC(T_b,tc_Option_Ooption(T_a),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_a),tc_fun(tc_Option_Ooption(T_a),tc_HOL_Obool),T_b),c_fequal),V_m_2))),c_Option_Ooption_OSome(T_a)))) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_lexord__append__rightI,axiom,
% 187.18/188.02 ! [V_r_2,V_x_2,T_a,V_y_2] :
% 187.18/188.02 ( ? [B_b,B_z] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_b),B_z)
% 187.18/188.02 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),hAPP(hAPP(c_List_Oappend(T_a),V_x_2),V_y_2))),c_List_Olexord(T_a,V_r_2))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_ranI,axiom,
% 187.18/188.02 ! [T_b,V_b_2,T_a,V_a_2,V_m_2] :
% 187.18/188.02 ( hAPP(V_m_2,V_a_2) = hAPP(c_Option_Ooption_OSome(T_a),V_b_2)
% 187.18/188.02 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Map_Oran(T_b,T_a,V_m_2))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_sorted__list__of__set__insert,axiom,
% 187.18/188.02 ! [V_x_2,V_A_2,T_a] :
% 187.18/188.02 ( class_Orderings_Olinorder(T_a)
% 187.18/188.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.02 => c_List_Olinorder__class_Osorted__list__of__set(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_x_2),c_List_Olinorder__class_Osorted__list__of__set(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_lexord__Nil__left,axiom,
% 187.18/188.02 ! [V_r_2,V_y_2,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),V_y_2)),c_List_Olexord(T_a,V_r_2)))
% 187.18/188.02 <=> ? [B_a,B_x] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_a),B_x) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_length__insort,axiom,
% 187.18/188.02 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] :
% 187.18/188.02 ( class_Orderings_Olinorder(T_b)
% 187.18/188.02 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_x_2),V_xs_2)) = hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_insort__key_Osimps_I1_J,axiom,
% 187.18/188.02 ! [V_x_2,V_f_2,T_a,T_b] :
% 187.18/188.02 ( class_Orderings_Olinorder(T_b)
% 187.18/188.02 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_x_2),c_List_Olist_ONil(T_a)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_insort__key_Osimps_I2_J,axiom,
% 187.18/188.02 ! [V_ys_2,T_b,V_y_2,V_x_2,V_f_2,T_a] :
% 187.18/188.02 ( class_Orderings_Olinorder(T_a)
% 187.18/188.02 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
% 187.18/188.02 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)) )
% 187.18/188.02 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
% 187.18/188.02 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),V_ys_2)) ) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_set__insort,axiom,
% 187.18/188.02 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] :
% 187.18/188.02 ( class_Orderings_Olinorder(T_b)
% 187.18/188.02 => hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_insort__left__comm,axiom,
% 187.18/188.02 ! [V_xs_2,V_y_2,V_x_2,T_a] :
% 187.18/188.02 ( class_Orderings_Olinorder(T_a)
% 187.18/188.02 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_x_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_y_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_x_2),V_xs_2)) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_insort__key__left__comm,axiom,
% 187.18/188.02 ! [V_xs_2,T_b,V_y_2,V_x_2,V_f_2,T_a] :
% 187.18/188.02 ( class_Orderings_Olinorder(T_a)
% 187.18/188.02 => ( hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2)
% 187.18/188.02 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_y_2),V_xs_2)) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_fun__left__comm__insort,axiom,
% 187.18/188.02 ! [T_a] :
% 187.18/188.02 ( class_Orderings_Olinorder(T_a)
% 187.18/188.02 => c_Finite__Set_Ofun__left__comm(T_a,tc_List_Olist(T_a),c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_remove1__insort,axiom,
% 187.18/188.02 ! [V_xs_2,V_x_2,T_a] :
% 187.18/188.02 ( class_Orderings_Olinorder(T_a)
% 187.18/188.02 => c_List_Oremove1(T_a,V_x_2,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_x_2),V_xs_2)) = V_xs_2 ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_insort__not__Nil,axiom,
% 187.18/188.02 ! [V_xs_2,V_a_2,V_f_2,T_a,T_b] :
% 187.18/188.02 ( class_Orderings_Olinorder(T_b)
% 187.18/188.02 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_a_2),V_xs_2) != c_List_Olist_ONil(T_a) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_distinct__insort,axiom,
% 187.18/188.02 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] :
% 187.18/188.02 ( class_Orderings_Olinorder(T_b)
% 187.18/188.02 => ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_x_2),V_xs_2)))
% 187.18/188.02 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 187.18/188.02 & hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_insort__insert__insort__key,axiom,
% 187.18/188.02 ! [V_xs_2,T_b,V_x_2,V_f_2,T_a] :
% 187.18/188.02 ( class_Orderings_Olinorder(T_a)
% 187.18/188.02 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(c_List_Oset(T_b),V_xs_2))))
% 187.18/188.02 => c_List_Olinorder__class_Oinsort__insert__key(T_b,T_a,V_f_2,V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),V_xs_2) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_insort__insert__insort,axiom,
% 187.18/188.02 ! [V_xs_2,V_x_2,T_a] :
% 187.18/188.02 ( class_Orderings_Olinorder(T_a)
% 187.18/188.02 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 187.18/188.02 => c_List_Olinorder__class_Oinsort__insert__key(T_a,T_a,c_COMBI(T_a),V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_x_2),V_xs_2) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_distinct__insort__insert,axiom,
% 187.18/188.02 ! [V_x_2,V_f_2,V_xs_2,T_a,T_b] :
% 187.18/188.02 ( class_Orderings_Olinorder(T_b)
% 187.18/188.02 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 187.18/188.02 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olinorder__class_Oinsort__insert__key(T_a,T_b,V_f_2,V_x_2,V_xs_2))) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_insort__insert__triv,axiom,
% 187.18/188.02 ! [V_xs_2,V_x_2,T_a] :
% 187.18/188.02 ( class_Orderings_Olinorder(T_a)
% 187.18/188.02 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 187.18/188.02 => c_List_Olinorder__class_Oinsort__insert__key(T_a,T_a,c_COMBI(T_a),V_x_2,V_xs_2) = V_xs_2 ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_set__insort__insert,axiom,
% 187.18/188.02 ! [V_xs_2,V_x_2,T_a] :
% 187.18/188.02 ( class_Orderings_Olinorder(T_a)
% 187.18/188.02 => hAPP(c_List_Oset(T_a),c_List_Olinorder__class_Oinsort__insert__key(T_a,T_a,c_COMBI(T_a),V_x_2,V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_insort__insert__key__triv,axiom,
% 187.18/188.02 ! [V_xs_2,T_b,V_x_2,V_f_2,T_a] :
% 187.18/188.02 ( class_Orderings_Olinorder(T_a)
% 187.18/188.02 => ( hBOOL(hAPP(hAPP(c_member(T_a),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(c_List_Oset(T_b),V_xs_2))))
% 187.18/188.02 => c_List_Olinorder__class_Oinsort__insert__key(T_b,T_a,V_f_2,V_x_2,V_xs_2) = V_xs_2 ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_last__list__update,axiom,
% 187.18/188.02 ! [V_x,V_k,T_a,V_xs] :
% 187.18/188.02 ( V_xs != c_List_Olist_ONil(T_a)
% 187.18/188.02 => ( ( 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))
% 187.18/188.02 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = V_x )
% 187.18/188.02 & ( 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))
% 187.18/188.02 => 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) ) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_last__conv__nth,axiom,
% 187.18/188.02 ! [T_a,V_xs] :
% 187.18/188.02 ( V_xs != c_List_Olist_ONil(T_a)
% 187.18/188.02 => 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))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_last__append,axiom,
% 187.18/188.02 ! [V_xs,T_a,V_ys] :
% 187.18/188.02 ( ( V_ys = c_List_Olist_ONil(T_a)
% 187.18/188.02 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) )
% 187.18/188.02 & ( V_ys != c_List_Olist_ONil(T_a)
% 187.18/188.02 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_last__appendR,axiom,
% 187.18/188.02 ! [V_xs,T_a,V_ys] :
% 187.18/188.02 ( V_ys != c_List_Olist_ONil(T_a)
% 187.18/188.02 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_last__appendL,axiom,
% 187.18/188.02 ! [V_xs,T_a,V_ys] :
% 187.18/188.02 ( V_ys = c_List_Olist_ONil(T_a)
% 187.18/188.02 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_last_Osimps,axiom,
% 187.18/188.02 ! [V_x,T_a,V_xs] :
% 187.18/188.02 ( ( V_xs = c_List_Olist_ONil(T_a)
% 187.18/188.02 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x )
% 187.18/188.02 & ( V_xs != c_List_Olist_ONil(T_a)
% 187.18/188.02 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_last__ConsR,axiom,
% 187.18/188.02 ! [V_x,T_a,V_xs] :
% 187.18/188.02 ( V_xs != c_List_Olist_ONil(T_a)
% 187.18/188.02 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_last__ConsL,axiom,
% 187.18/188.02 ! [V_x,T_a,V_xs] :
% 187.18/188.02 ( V_xs = c_List_Olist_ONil(T_a)
% 187.18/188.02 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_last__in__set,axiom,
% 187.18/188.02 ! [T_a,V_as_2] :
% 187.18/188.02 ( V_as_2 != c_List_Olist_ONil(T_a)
% 187.18/188.02 => hBOOL(hAPP(hAPP(c_member(T_a),c_List_Olast(T_a,V_as_2)),hAPP(c_List_Oset(T_a),V_as_2))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_last__snoc,axiom,
% 187.18/188.02 ! [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 ).
% 187.18/188.02
% 187.18/188.02 fof(fact_last__drop,axiom,
% 187.18/188.02 ! [V_xs,T_a,V_n] :
% 187.18/188.02 ( 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)))
% 187.18/188.02 => c_List_Olast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = c_List_Olast(T_a,V_xs) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_snoc__eq__iff__butlast,axiom,
% 187.18/188.02 ! [V_ys_2,V_x_2,V_xs_2,T_a] :
% 187.18/188.02 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a))) = V_ys_2
% 187.18/188.02 <=> ( V_ys_2 != c_List_Olist_ONil(T_a)
% 187.18/188.02 & c_List_Obutlast(T_a,V_ys_2) = V_xs_2
% 187.18/188.02 & c_List_Olast(T_a,V_ys_2) = V_x_2 ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_append__butlast__last__id,axiom,
% 187.18/188.02 ! [T_a,V_xs] :
% 187.18/188.02 ( V_xs != c_List_Olist_ONil(T_a)
% 187.18/188.02 => 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 ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_lists_Osimps,axiom,
% 187.18/188.02 ! [V_A_2,V_a_2,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_a_2),c_List_Olists(T_a,V_A_2)))
% 187.18/188.02 <=> ( V_a_2 = c_List_Olist_ONil(T_a)
% 187.18/188.02 | ? [B_a,B_l] :
% 187.18/188.02 ( V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_a),B_l)
% 187.18/188.02 & hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2))
% 187.18/188.02 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_l),c_List_Olists(T_a,V_A_2))) ) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_map__of__zip__upd,axiom,
% 187.18/188.02 ! [V_z_2,V_y_2,V_x_2,V_zs_2,V_xs_2,T_b,V_ys_2,T_a] :
% 187.18/188.02 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)
% 187.18/188.02 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_zs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)
% 187.18/188.02 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 187.18/188.02 => ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),hAPP(c_Map_Omap__of(T_b,T_a),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs_2),V_ys_2))),V_x_2),hAPP(c_Option_Ooption_OSome(T_a),V_y_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),hAPP(c_Map_Omap__of(T_b,T_a),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs_2),V_zs_2))),V_x_2),hAPP(c_Option_Ooption_OSome(T_a),V_z_2))
% 187.18/188.02 => hAPP(c_Map_Omap__of(T_b,T_a),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs_2),V_ys_2)) = hAPP(c_Map_Omap__of(T_b,T_a),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs_2),V_zs_2)) ) ) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_finite__dom__map__of,axiom,
% 187.18/188.02 ! [V_l_2,T_b,T_a] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Map_Odom(T_a,T_b,hAPP(c_Map_Omap__of(T_a,T_b),V_l_2)))) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_map__of__zip__inject,axiom,
% 187.18/188.02 ! [V_zs_2,V_xs_2,T_b,V_ys_2,T_a] :
% 187.18/188.02 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)
% 187.18/188.02 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_zs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)
% 187.18/188.02 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 187.18/188.02 => ( hAPP(c_Map_Omap__of(T_b,T_a),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs_2),V_ys_2)) = hAPP(c_Map_Omap__of(T_b,T_a),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs_2),V_zs_2))
% 187.18/188.02 => V_ys_2 = V_zs_2 ) ) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_body__def,axiom,
% 187.18/188.02 c_Com_Obody = hAPP(c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom),c_Com_Obodies) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_map__of__Cons__code_I2_J,axiom,
% 187.18/188.02 ! [V_ps,V_v,T_c,T_b,V_k,V_l] :
% 187.18/188.02 ( ( V_l = V_k
% 187.18/188.02 => 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) )
% 187.18/188.02 & ( V_l != V_k
% 187.18/188.02 => 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) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_map__of__eq__dom,axiom,
% 187.18/188.02 ! [V_ys_2,V_xs_2,T_b,T_a] :
% 187.18/188.02 ( hAPP(c_Map_Omap__of(T_a,T_b),V_xs_2) = hAPP(c_Map_Omap__of(T_a,T_b),V_ys_2)
% 187.18/188.02 => hAPP(c_Set_Oimage(tc_prod(T_a,T_b),T_a,c_Product__Type_Ofst(T_a,T_b)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_xs_2)) = hAPP(c_Set_Oimage(tc_prod(T_a,T_b),T_a,c_Product__Type_Ofst(T_a,T_b)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_ys_2)) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_finite__range__map__of,axiom,
% 187.18/188.02 ! [V_xys_2,T_b,T_a] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_a)),hAPP(c_Set_Oimage(T_b,tc_Option_Ooption(T_a),hAPP(c_Map_Omap__of(T_b,T_a),V_xys_2)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_map__of__SomeD,axiom,
% 187.18/188.02 ! [V_y_2,V_k_2,V_xs_2,T_a,T_b] :
% 187.18/188.02 ( hAPP(hAPP(c_Map_Omap__of(T_b,T_a),V_xs_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2)
% 187.18/188.02 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_k_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_b,T_a)),V_xs_2))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_map__of__is__SomeD,axiom,
% 187.18/188.02 ! [V_y_2,V_x_2,V_xys_2,T_a,T_b] :
% 187.18/188.02 ( hAPP(hAPP(c_Map_Omap__of(T_b,T_a),V_xys_2),V_x_2) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2)
% 187.18/188.02 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_b,T_a)),V_xys_2))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_dom__map__of__conv__image__fst,axiom,
% 187.18/188.02 ! [V_xys_2,T_b,T_a] : c_Map_Odom(T_a,T_b,hAPP(c_Map_Omap__of(T_a,T_b),V_xys_2)) = hAPP(c_Set_Oimage(tc_prod(T_a,T_b),T_a,c_Product__Type_Ofst(T_a,T_b)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_xys_2)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_map__of__zip__is__Some,axiom,
% 187.18/188.02 ! [V_x_2,V_ys_2,T_b,V_xs_2,T_a] :
% 187.18/188.02 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)
% 187.18/188.02 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 187.18/188.02 <=> ? [B_y] : hAPP(hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)),V_x_2) = hAPP(c_Option_Ooption_OSome(T_b),B_y) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_dom__map__of__zip,axiom,
% 187.18/188.02 ! [V_ys_2,T_b,V_xs_2,T_a] :
% 187.18/188.02 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)
% 187.18/188.02 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 187.18/188.02 => c_Map_Odom(T_a,T_b,hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2))) = hAPP(c_List_Oset(T_a),V_xs_2) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_map__of_Osimps_I2_J,axiom,
% 187.18/188.02 ! [V_ps_2,V_p_2,T_b,T_a] : hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Olist_OCons(tc_prod(T_a,T_b)),V_p_2),V_ps_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),hAPP(c_Map_Omap__of(T_a,T_b),V_ps_2)),hAPP(c_Product__Type_Ofst(T_a,T_b),V_p_2)),hAPP(c_Option_Ooption_OSome(T_b),hAPP(c_Product__Type_Osnd(T_a,T_b),V_p_2))) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_ran__distinct,axiom,
% 187.18/188.02 ! [V_al_2,T_b,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_al_2)))
% 187.18/188.02 => c_Map_Oran(T_a,T_b,hAPP(c_Map_Omap__of(T_a,T_b),V_al_2)) = hAPP(c_Set_Oimage(tc_prod(T_a,T_b),T_b,c_Product__Type_Osnd(T_a,T_b)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_al_2)) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_set__map__of__compr,axiom,
% 187.18/188.02 ! [V_xs_2,T_b,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_xs_2)))
% 187.18/188.02 => hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_xs_2) = hAPP(c_Set_OCollect(tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBB(tc_Option_Ooption(T_b),tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_b),tc_fun(tc_Option_Ooption(T_b),tc_HOL_Obool),T_a),c_fequal),hAPP(c_Map_Omap__of(T_a,T_b),V_xs_2)))),c_Option_Ooption_OSome(T_b)))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_inj__mapI,axiom,
% 187.18/188.02 ! [V_f_2,T_b,T_a] :
% 187.18/188.02 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 187.18/188.02 => c_Fun_Oinj__on(tc_List_Olist(T_a),tc_List_Olist(T_b),hAPP(c_List_Omap(T_a,T_b),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_listsum__abs,axiom,
% 187.18/188.02 ! [V_xs_2,T_a] :
% 187.18/188.02 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 187.18/188.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_a,T_a),c_Groups_Oabs__class_Oabs(T_a)),V_xs_2)))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_foldl__map,axiom,
% 187.18/188.02 ! [V_xs_2,V_f_2,T_c,V_a_2,V_g_2,T_b,T_a] : hAPP(c_List_Ofoldl(T_a,T_b,V_g_2,V_a_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(c_List_Ofoldl(T_a,T_c,hAPP(hAPP(c_COMBC(T_a,tc_fun(T_c,T_b),tc_fun(T_c,T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_a),tc_fun(tc_fun(T_c,T_b),tc_fun(T_c,T_a)),T_a),c_COMBB(T_b,T_a,T_c)),V_g_2)),V_f_2),V_a_2),V_xs_2) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_zip__map__map,axiom,
% 187.18/188.02 ! [V_ys_2,V_g_2,T_d,V_xs_2,V_f_2,T_c,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Omap(T_c,T_a),V_f_2),V_xs_2)),hAPP(hAPP(c_List_Omap(T_d,T_b),V_g_2),V_ys_2)) = hAPP(hAPP(c_List_Omap(tc_prod(T_c,T_d),tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,T_b),tc_fun(T_d,tc_prod(T_a,T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(tc_fun(T_d,T_b),tc_fun(T_d,tc_prod(T_a,T_b))),T_c),c_COMBB(T_b,tc_prod(T_a,T_b),T_d)),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_b,tc_prod(T_a,T_b)),T_c),c_Product__Type_OPair(T_a,T_b)),V_f_2))),V_g_2))),hAPP(hAPP(c_List_Ozip(T_c,T_d),V_xs_2),V_ys_2)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_zip__map1,axiom,
% 187.18/188.02 ! [V_ys_2,V_xs_2,V_f_2,T_c,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Omap(T_c,T_a),V_f_2),V_xs_2)),V_ys_2) = hAPP(hAPP(c_List_Omap(tc_prod(T_c,T_b),tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_b,tc_prod(T_a,T_b)),T_c),c_Product__Type_OPair(T_a,T_b)),V_f_2))),hAPP(hAPP(c_List_Ozip(T_c,T_b),V_xs_2),V_ys_2)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_map__zip__map,axiom,
% 187.18/188.02 ! [V_ys_2,V_xs_2,V_g_2,T_d,V_f_2,T_a,T_c,T_b] : hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_a),V_f_2),hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Omap(T_d,T_b),V_g_2),V_xs_2)),V_ys_2)) = hAPP(hAPP(c_List_Omap(tc_prod(T_d,T_c),T_a),hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_c,T_a),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,T_a),T_d),hAPP(c_COMBB(tc_prod(T_b,T_c),T_a,T_c),V_f_2)),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_g_2)))),hAPP(hAPP(c_List_Ozip(T_d,T_c),V_xs_2),V_ys_2)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_map__zip__map2,axiom,
% 187.18/188.02 ! [V_ys_2,V_g_2,T_d,V_xs_2,V_f_2,T_a,T_c,T_b] : hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_a),V_f_2),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_g_2),V_ys_2))) = hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_d),T_a),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_d,T_a),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_b,T_c)),tc_fun(T_d,T_a),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),T_a,T_d),V_f_2)),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_g_2)))),hAPP(hAPP(c_List_Ozip(T_b,T_d),V_xs_2),V_ys_2)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_zip__map2,axiom,
% 187.18/188.02 ! [V_ys_2,V_f_2,T_c,V_xs_2,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_ys_2)) = hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_c),tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_c,tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_c,T_b),tc_fun(T_c,tc_prod(T_a,T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(tc_fun(T_c,T_b),tc_fun(T_c,tc_prod(T_a,T_b))),T_a),c_COMBB(T_b,tc_prod(T_a,T_b),T_c)),c_Product__Type_OPair(T_a,T_b))),V_f_2))),hAPP(hAPP(c_List_Ozip(T_a,T_c),V_xs_2),V_ys_2)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_List_Omap_Ocomp,axiom,
% 187.18/188.02 ! [V_g_2,V_f_2,T_a,T_b,T_c] : hAPP(c_Fun_Ocomp(tc_List_Olist(T_c),tc_List_Olist(T_b),tc_List_Olist(T_a),hAPP(c_List_Omap(T_c,T_b),V_f_2)),hAPP(c_List_Omap(T_a,T_c),V_g_2)) = hAPP(c_List_Omap(T_a,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_f_2),V_g_2)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_map__comp__map,axiom,
% 187.18/188.02 ! [V_g_2,V_f_2,T_a,T_b,T_c] : hAPP(c_Fun_Ocomp(tc_List_Olist(T_c),tc_List_Olist(T_b),tc_List_Olist(T_a),hAPP(c_List_Omap(T_c,T_b),V_f_2)),hAPP(c_List_Omap(T_a,T_c),V_g_2)) = hAPP(c_List_Omap(T_a,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_f_2),V_g_2)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_List_Omap_Ocompositionality,axiom,
% 187.18/188.02 ! [V_list_2,V_g_2,T_c,V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_list_2)) = hAPP(hAPP(c_List_Omap(T_c,T_a),hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_f_2),V_g_2)),V_list_2) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_map__map,axiom,
% 187.18/188.02 ! [V_xs_2,V_g_2,T_c,V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_a),hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_f_2),V_g_2)),V_xs_2) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_List_Omap_Oid,axiom,
% 187.18/188.02 ! [T_a] : hAPP(c_List_Omap(T_a,T_a),c_Fun_Oid(T_a)) = c_Fun_Oid(tc_List_Olist(T_a)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_List_Omap_Oidentity,axiom,
% 187.18/188.02 ! [T_a] : hAPP(c_List_Omap(T_a,T_a),c_COMBI(T_a)) = c_Fun_Oid(tc_List_Olist(T_a)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_list__size__map,axiom,
% 187.18/188.02 ! [V_xs_2,V_g_2,T_b,V_f_2,T_a] : c_List_Olist_Olist__size(T_a,V_f_2,hAPP(hAPP(c_List_Omap(T_b,T_a),V_g_2),V_xs_2)) = c_List_Olist_Olist__size(T_b,hAPP(c_Fun_Ocomp(T_a,tc_Nat_Onat,T_b,V_f_2),V_g_2),V_xs_2) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_nth__map,axiom,
% 187.18/188.02 ! [V_f_2,T_b,V_xs_2,T_a,V_n_2] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))
% 187.18/188.02 => hAPP(hAPP(c_List_Onth(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)),V_n_2) = hAPP(V_f_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_n_2)) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_map__fun__upd,axiom,
% 187.18/188.02 ! [V_v_2,V_f_2,T_b,V_xs_2,V_y_2,T_a] :
% 187.18/188.02 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 187.18/188.02 => hAPP(hAPP(c_List_Omap(T_a,T_b),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_y_2),V_v_2)),V_xs_2) = hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_map__tl,axiom,
% 187.18/188.02 ! [V_xs_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(c_List_Otl(T_b),V_xs_2)) = hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_length__map,axiom,
% 187.18/188.02 ! [V_xs_2,V_f_2,T_b,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_map__eq__imp__length__eq,axiom,
% 187.18/188.02 ! [V_ys_2,V_g_2,T_c,V_xs_2,V_f_2,T_a,T_b] :
% 187.18/188.02 ( hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_c,T_a),V_g_2),V_ys_2)
% 187.18/188.02 => 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) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_set__map,axiom,
% 187.18/188.02 ! [V_xs_2,V_f_2,T_b,T_a] : hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) = hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(c_List_Oset(T_b),V_xs_2)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_map__append,axiom,
% 187.18/188.02 ! [V_ys_2,V_xs_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_ys_2)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_map_Osimps_I2_J,axiom,
% 187.18/188.02 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(V_f_2,V_x_2)),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_map__update,axiom,
% 187.18/188.02 ! [V_y_2,V_k_2,V_xs_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_k_2),V_y_2)) = hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)),V_k_2),hAPP(V_f_2,V_y_2)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_map__eq__conv,axiom,
% 187.18/188.02 ! [V_g_2,V_xs_2,V_f_2,T_a,T_b] :
% 187.18/188.02 ( hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_g_2),V_xs_2)
% 187.18/188.02 <=> ! [B_x] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 187.18/188.02 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_listsum__addf,axiom,
% 187.18/188.02 ! [V_xs_2,V_g_2,V_f_2,T_b,T_a] :
% 187.18/188.02 ( class_Groups_Ocomm__monoid__add(T_a)
% 187.18/188.02 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),hAPP(hAPP(c_COMBS(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Groups_Oplus__class_Oplus(T_a)),V_f_2)),V_g_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_g_2),V_xs_2))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_listsum__subtractf,axiom,
% 187.18/188.02 ! [V_xs_2,V_g_2,V_f_2,T_b,T_a] :
% 187.18/188.02 ( class_Groups_Oab__group__add(T_a)
% 187.18/188.02 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),hAPP(hAPP(c_COMBS(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Groups_Ominus__class_Ominus(T_a)),V_f_2)),V_g_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_g_2),V_xs_2))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_listsum__0,axiom,
% 187.18/188.02 ! [V_xs_2,T_b,T_a] :
% 187.18/188.02 ( class_Groups_Omonoid__add(T_a)
% 187.18/188.02 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),hAPP(c_COMBK(T_a,T_b),c_Groups_Ozero__class_Ozero(T_a))),V_xs_2)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_listsum__const__mult,axiom,
% 187.18/188.02 ! [V_xs_2,V_f_2,V_c_2,T_b,T_a] :
% 187.18/188.02 ( class_Rings_Osemiring__0(T_a)
% 187.18/188.02 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,T_b),hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2)),V_f_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_listsum__mult__const,axiom,
% 187.18/188.02 ! [V_xs_2,V_c_2,V_f_2,T_b,T_a] :
% 187.18/188.02 ( class_Rings_Osemiring__0(T_a)
% 187.18/188.02 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),hAPP(hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Groups_Otimes__class_Otimes(T_a)),V_f_2)),V_c_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))),V_c_2) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_map__ident,axiom,
% 187.18/188.02 ! [V_xs_2,T_a] : hAPP(hAPP(c_List_Omap(T_a,T_a),c_COMBI(T_a)),V_xs_2) = V_xs_2 ).
% 187.18/188.02
% 187.18/188.02 fof(fact_take__map,axiom,
% 187.18/188.02 ! [V_xs_2,V_f_2,T_b,V_n_2,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_n_2),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_map__butlast,axiom,
% 187.18/188.02 ! [V_xs_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_Obutlast(T_b,V_xs_2)) = c_List_Obutlast(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_map__is__Nil__conv,axiom,
% 187.18/188.02 ! [V_xs_2,V_f_2,T_a,T_b] :
% 187.18/188.02 ( hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2) = c_List_Olist_ONil(T_a)
% 187.18/188.02 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_map_Osimps_I1_J,axiom,
% 187.18/188.02 ! [V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_a) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_Nil__is__map__conv,axiom,
% 187.18/188.02 ! [V_xs_2,V_f_2,T_b,T_a] :
% 187.18/188.02 ( c_List_Olist_ONil(T_a) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)
% 187.18/188.02 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_map__injective,axiom,
% 187.18/188.02 ! [V_ys_2,V_xs_2,V_f_2,T_a,T_b] :
% 187.18/188.02 ( hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_ys_2)
% 187.18/188.02 => ( c_Fun_Oinj__on(T_b,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 187.18/188.02 => V_xs_2 = V_ys_2 ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_inj__map__eq__map,axiom,
% 187.18/188.02 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_a] :
% 187.18/188.02 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 187.18/188.02 => ( hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_ys_2)
% 187.18/188.02 <=> V_xs_2 = V_ys_2 ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_hd__map,axiom,
% 187.18/188.02 ! [V_f_2,T_b,T_a,V_xs_2] :
% 187.18/188.02 ( V_xs_2 != c_List_Olist_ONil(T_a)
% 187.18/188.02 => hAPP(c_List_Ohd(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)) = hAPP(V_f_2,hAPP(c_List_Ohd(T_a),V_xs_2)) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_drop__map,axiom,
% 187.18/188.02 ! [V_xs_2,V_f_2,T_b,V_n_2,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n_2),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_inj__on__map__eq__map,axiom,
% 187.18/188.02 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_a] :
% 187.18/188.02 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(c_List_Oset(T_a),V_ys_2)))
% 187.18/188.02 => ( hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_ys_2)
% 187.18/188.02 <=> V_xs_2 = V_ys_2 ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_map__inj__on,axiom,
% 187.18/188.02 ! [V_ys_2,V_xs_2,V_f_2,T_a,T_b] :
% 187.18/188.02 ( hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_ys_2)
% 187.18/188.02 => ( c_Fun_Oinj__on(T_b,T_a,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)))
% 187.18/188.02 => V_xs_2 = V_ys_2 ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_rotate__map,axiom,
% 187.18/188.02 ! [V_xs_2,V_f_2,T_b,V_n_2,T_a] : hAPP(c_List_Orotate(T_a,V_n_2),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_distinct__map,axiom,
% 187.18/188.02 ! [V_xs_2,V_f_2,T_b,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)))
% 187.18/188.02 <=> ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 187.18/188.02 & c_Fun_Oinj__on(T_b,T_a,V_f_2,hAPP(c_List_Oset(T_b),V_xs_2)) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_last__map,axiom,
% 187.18/188.02 ! [V_f_2,T_b,T_a,V_xs_2] :
% 187.18/188.02 ( V_xs_2 != c_List_Olist_ONil(T_a)
% 187.18/188.02 => c_List_Olast(T_b,hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)) = hAPP(V_f_2,c_List_Olast(T_a,V_xs_2)) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_uminus__listsum__map,axiom,
% 187.18/188.02 ! [V_xs_2,V_f_2,T_b,T_a] :
% 187.18/188.02 ( class_Groups_Oab__group__add(T_a)
% 187.18/188.02 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),hAPP(c_Fun_Ocomp(T_a,T_a,T_b,c_Groups_Ouminus__class_Ouminus(T_a)),V_f_2)),V_xs_2)) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_inj__on__mapI,axiom,
% 187.18/188.02 ! [V_A_2,V_f_2,T_b,T_a] :
% 187.18/188.02 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool),c_List_Oset(T_a)),V_A_2)))
% 187.18/188.02 => c_Fun_Oinj__on(tc_List_Olist(T_a),tc_List_Olist(T_b),hAPP(c_List_Omap(T_a,T_b),V_f_2),V_A_2) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_map__fst__zip,axiom,
% 187.18/188.02 ! [V_ys_2,T_b,V_xs_2,T_a] :
% 187.18/188.02 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)
% 187.18/188.02 => hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)) = V_xs_2 ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_map__snd__zip,axiom,
% 187.18/188.02 ! [V_ys_2,T_b,V_xs_2,T_a] :
% 187.18/188.02 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)
% 187.18/188.02 => hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_b),c_Product__Type_Osnd(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)) = V_ys_2 ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_zip__map__fst__snd,axiom,
% 187.18/188.02 ! [V_zs_2,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_zs_2)),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_b),c_Product__Type_Osnd(T_a,T_b)),V_zs_2)) = V_zs_2 ).
% 187.18/188.02
% 187.18/188.02 fof(fact_inj__mapD,axiom,
% 187.18/188.02 ! [V_f_2,T_b,T_a] :
% 187.18/188.02 ( c_Fun_Oinj__on(tc_List_Olist(T_a),tc_List_Olist(T_b),hAPP(c_List_Omap(T_a,T_b),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)))
% 187.18/188.02 => c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_inj__map,axiom,
% 187.18/188.02 ! [V_f_2,T_b,T_a] :
% 187.18/188.02 ( c_Fun_Oinj__on(tc_List_Olist(T_a),tc_List_Olist(T_b),hAPP(c_List_Omap(T_a,T_b),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)))
% 187.18/188.02 <=> c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_pick__member,axiom,
% 187.18/188.02 ! [V_xs_2,T_a,V_i_2] :
% 187.18/188.02 ( 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_a),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_a)),V_xs_2))))
% 187.18/188.02 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Random_Opick(T_a,V_xs_2),V_i_2)),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a),T_a),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,T_a)),V_xs_2)))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_listsum__distinct__conv__setsum__set,axiom,
% 187.18/188.02 ! [V_f_2,V_xs_2,T_a,T_b] :
% 187.18/188.02 ( class_Groups_Ocomm__monoid__add(T_b)
% 187.18/188.02 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 187.18/188.02 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(c_List_Oset(T_a),V_xs_2)) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_zip__eq__conv,axiom,
% 187.18/188.02 ! [V_zs_2,V_ys_2,T_b,V_xs_2,T_a] :
% 187.18/188.02 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)
% 187.18/188.02 => ( hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2) = V_zs_2
% 187.18/188.02 <=> ( hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_zs_2) = V_xs_2
% 187.18/188.02 & hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_b),c_Product__Type_Osnd(T_a,T_b)),V_zs_2) = V_ys_2 ) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_listsum__triv,axiom,
% 187.18/188.02 ! [V_xs_2,V_r_2,T_b,T_a] :
% 187.18/188.02 ( class_Rings_Osemiring__1(T_a)
% 187.18/188.02 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),hAPP(c_COMBK(T_a,T_b),V_r_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))),V_r_2) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_map__of__inject__set,axiom,
% 187.18/188.02 ! [V_ys_2,V_xs_2,T_b,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_xs_2)))
% 187.18/188.02 => ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_ys_2)))
% 187.18/188.02 => ( hAPP(c_Map_Omap__of(T_a,T_b),V_xs_2) = hAPP(c_Map_Omap__of(T_a,T_b),V_ys_2)
% 187.18/188.02 <=> hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_xs_2) = hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_ys_2) ) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_listsum__map__remove1,axiom,
% 187.18/188.02 ! [V_f_2,V_xs_2,V_x_2,T_a,T_b] :
% 187.18/188.02 ( class_Groups_Ocomm__monoid__add(T_b)
% 187.18/188.02 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 187.18/188.02 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_f_2,V_x_2)),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),c_List_Oremove1(T_a,V_x_2,V_xs_2)))) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_select__weight__member,axiom,
% 187.18/188.02 ! [V_s_2,V_xs_2,T_a] :
% 187.18/188.02 ( 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_a),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_a)),V_xs_2))))
% 187.18/188.02 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Product__Type_Ofst(T_a,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect__weight(T_a,V_xs_2),V_s_2))),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a),T_a),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,T_a)),V_xs_2)))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_select__weight__def,axiom,
% 187.18/188.02 ! [V_xs_2,T_a] : c_Random_Oselect__weight(T_a,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_a,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_a),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_a)),V_xs_2)))),hAPP(hAPP(c_COMBB(T_a,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_a,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(T_a,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Opick(T_a,V_xs_2))) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_map__of__mapk__SomeI,axiom,
% 187.18/188.02 ! [V_x_2,V_k_2,V_t_2,T_c,V_f_2,T_b,T_a] :
% 187.18/188.02 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 187.18/188.02 => ( hAPP(hAPP(c_Map_Omap__of(T_a,T_c),V_t_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_c),V_x_2)
% 187.18/188.02 => hAPP(hAPP(c_Map_Omap__of(T_b,T_c),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_c),tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,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_a),c_Product__Type_OPair(T_b,T_c)),V_f_2))),V_t_2)),hAPP(V_f_2,V_k_2)) = hAPP(c_Option_Ooption_OSome(T_c),V_x_2) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_map__of__is__SomeI,axiom,
% 187.18/188.02 ! [V_y_2,V_x_2,V_xys_2,T_b,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_xys_2)))
% 187.18/188.02 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_xys_2)))
% 187.18/188.02 => hAPP(hAPP(c_Map_Omap__of(T_a,T_b),V_xys_2),V_x_2) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_map__of__eq__Some__iff,axiom,
% 187.18/188.02 ! [V_y_2,V_x_2,V_xys_2,T_b,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_xys_2)))
% 187.18/188.02 => ( hAPP(hAPP(c_Map_Omap__of(T_a,T_b),V_xys_2),V_x_2) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2)
% 187.18/188.02 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_xys_2))) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_Some__eq__map__of__iff,axiom,
% 187.18/188.02 ! [V_x_2,V_y_2,V_xys_2,T_b,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_xys_2)))
% 187.18/188.02 => ( hAPP(c_Option_Ooption_OSome(T_b),V_y_2) = hAPP(hAPP(c_Map_Omap__of(T_a,T_b),V_xys_2),V_x_2)
% 187.18/188.02 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_xys_2))) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_Nitpick_Osetsum_H__def,axiom,
% 187.18/188.02 ! [V_f_2,V_A_2,T_a,T_b] :
% 187.18/188.02 ( class_Groups_Ocomm__monoid__add(T_b)
% 187.18/188.02 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.02 => c_Nitpick_Osetsum_H(T_a,T_b,V_f_2,V_A_2) = hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),c_Hilbert__Choice_OEps(tc_List_Olist(T_a),hAPP(hAPP(c_COMBS(tc_List_Olist(T_a),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_a)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_a)),c_fequal),c_List_Oset(T_a))),V_A_2))),c_List_Odistinct(T_a))))) )
% 187.18/188.02 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.02 => c_Nitpick_Osetsum_H(T_a,T_b,V_f_2,V_A_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_listsum__mono,axiom,
% 187.18/188.02 ! [V_g_2,V_f_2,V_xs_2,T_a,T_b] :
% 187.18/188.02 ( ( class_Groups_Omonoid__add(T_b)
% 187.18/188.02 & class_Groups_Oordered__ab__semigroup__add(T_b) )
% 187.18/188.02 => ( ! [B_x] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 187.18/188.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 187.18/188.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_g_2),V_xs_2)))) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_zip__same__conv__map,axiom,
% 187.18/188.02 ! [V_xs_2,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_a),V_xs_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_a,tc_prod(T_a,T_a)),hAPP(hAPP(c_COMBS(T_a,T_a,tc_prod(T_a,T_a)),c_Product__Type_OPair(T_a,T_a)),c_COMBI(T_a))),V_xs_2) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_list__size__conv__listsum,axiom,
% 187.18/188.02 ! [V_xs_2,V_f_2,T_a] : c_List_Olist_Olist__size(T_a,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_a,tc_Nat_Onat),V_f_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_setsum__set__upto__conv__listsum__int,axiom,
% 187.18/188.02 ! [V_j_2,V_i_2,V_f_2,T_a] :
% 187.18/188.02 ( class_Groups_Ocomm__monoid__add(T_a)
% 187.18/188.02 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_a),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_a),hAPP(hAPP(c_List_Omap(tc_Int_Oint,T_a),V_f_2),c_List_Oupto(V_i_2,V_j_2))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_interv__listsum__conv__setsum__set__int,axiom,
% 187.18/188.02 ! [V_l_2,V_k_2,V_f_2,T_a] :
% 187.18/188.02 ( class_Groups_Ocomm__monoid__add(T_a)
% 187.18/188.02 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(tc_Int_Oint,T_a),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_a),V_f_2),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_k_2,V_l_2))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_map__of__map__restrict,axiom,
% 187.18/188.02 ! [V_ks_2,V_f_2,T_b,T_a] : hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Omap(T_a,tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBS(T_a,T_b,tc_prod(T_a,T_b)),c_Product__Type_OPair(T_a,T_b)),V_f_2)),V_ks_2)) = c_Map_Orestrict__map(T_a,T_b,hAPP(c_Fun_Ocomp(T_b,tc_Option_Ooption(T_b),T_a,c_Option_Ooption_OSome(T_b)),V_f_2),hAPP(c_List_Oset(T_a),V_ks_2)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_map__of__map__keys,axiom,
% 187.18/188.02 ! [V_m_2,T_b,V_xs_2,T_a] :
% 187.18/188.02 ( hAPP(c_List_Oset(T_a),V_xs_2) = c_Map_Odom(T_a,T_b,V_m_2)
% 187.18/188.02 => hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Omap(T_a,tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBS(T_a,T_b,tc_prod(T_a,T_b)),c_Product__Type_OPair(T_a,T_b)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_b),T_b,T_a),c_Option_Othe(T_b)),V_m_2))),V_xs_2)) = V_m_2 ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_select__weigth__select,axiom,
% 187.18/188.02 ! [T_a,V_xs_2] :
% 187.18/188.02 ( V_xs_2 != c_List_Olist_ONil(T_a)
% 187.18/188.02 => c_Random_Oselect__weight(T_a,hAPP(hAPP(c_List_Omap(T_a,tc_prod(tc_Code__Numeral_Ocode__numeral,T_a)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_a),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),V_xs_2)) = c_Random_Oselect(T_a,V_xs_2) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_pick__same,axiom,
% 187.18/188.02 ! [V_xs_2,T_a,V_l_2] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_l_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))
% 187.18/188.02 => hAPP(c_Random_Opick(T_a,hAPP(hAPP(c_List_Omap(T_a,tc_prod(tc_Code__Numeral_Ocode__numeral,T_a)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_a),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_a),V_xs_2),V_l_2) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_map__of__map,axiom,
% 187.18/188.02 ! [V_xs_2,V_f_2,T_c,T_b,T_a] : hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_c),tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_c,tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_c,T_b),tc_fun(T_c,tc_prod(T_a,T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(tc_fun(T_c,T_b),tc_fun(T_c,tc_prod(T_a,T_b))),T_a),c_COMBB(T_b,tc_prod(T_a,T_b),T_c)),c_Product__Type_OPair(T_a,T_b))),V_f_2))),V_xs_2)) = hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_c),tc_Option_Ooption(T_b),T_a,hAPP(c_Option_Omap(T_c,T_b),V_f_2)),hAPP(c_Map_Omap__of(T_a,T_c),V_xs_2)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_option__map__comp,axiom,
% 187.18/188.02 ! [V_opt_2,V_g_2,T_c,V_f_2,T_a,T_b] : hAPP(hAPP(c_Option_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_Option_Omap(T_c,T_b),V_g_2),V_opt_2)) = hAPP(hAPP(c_Option_Omap(T_c,T_a),hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_f_2),V_g_2)),V_opt_2) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_Option_Omap_Ocompositionality,axiom,
% 187.18/188.02 ! [V_option_2,V_g_2,T_c,V_f_2,T_a,T_b] : hAPP(hAPP(c_Option_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_Option_Omap(T_c,T_b),V_g_2),V_option_2)) = hAPP(hAPP(c_Option_Omap(T_c,T_a),hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_f_2),V_g_2)),V_option_2) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_Option_Omap_Ocomp,axiom,
% 187.18/188.02 ! [V_g_2,V_f_2,T_a,T_b,T_c] : hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_c),tc_Option_Ooption(T_b),tc_Option_Ooption(T_a),hAPP(c_Option_Omap(T_c,T_b),V_f_2)),hAPP(c_Option_Omap(T_a,T_c),V_g_2)) = hAPP(c_Option_Omap(T_a,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_f_2),V_g_2)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_option__map__o__map__upd,axiom,
% 187.18/188.02 ! [V_b_2,V_a_2,V_m_2,V_f_2,T_a,T_b,T_c] : hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_c),tc_Option_Ooption(T_b),T_a,hAPP(c_Option_Omap(T_c,T_b),V_f_2)),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_c)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_c),V_b_2))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_c),tc_Option_Ooption(T_b),T_a,hAPP(c_Option_Omap(T_c,T_b),V_f_2)),V_m_2)),V_a_2),hAPP(c_Option_Ooption_OSome(T_b),hAPP(V_f_2,V_b_2))) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_number__of__code__numeral__def,axiom,
% 187.18/188.02 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) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_Option_Omap_Oid,axiom,
% 187.18/188.02 ! [T_a] : hAPP(c_Option_Omap(T_a,T_a),c_Fun_Oid(T_a)) = c_Fun_Oid(tc_Option_Ooption(T_a)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_Option_Omap_Oidentity,axiom,
% 187.18/188.02 ! [T_a] : hAPP(c_Option_Omap(T_a,T_a),c_COMBI(T_a)) = c_Fun_Oid(tc_Option_Ooption(T_a)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_code__numeral_Oof__nat__inject,axiom,
% 187.18/188.02 ! [V_y_2,V_x_2] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 187.18/188.02 => ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 187.18/188.02 => ( hAPP(c_Code__Numeral_Oof__nat,V_x_2) = hAPP(c_Code__Numeral_Oof__nat,V_y_2)
% 187.18/188.02 <=> V_x_2 = V_y_2 ) ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_less__code__numeral__code,axiom,
% 187.18/188.02 ! [V_m_2,V_n_2] :
% 187.18/188.02 ( 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)))
% 187.18/188.02 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_option__map__eq__Some,axiom,
% 187.18/188.02 ! [V_y_2,V_xo_2,V_f_2,T_a,T_b] :
% 187.18/188.02 ( hAPP(hAPP(c_Option_Omap(T_b,T_a),V_f_2),V_xo_2) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2)
% 187.18/188.02 <=> ? [B_z] :
% 187.18/188.02 ( V_xo_2 = hAPP(c_Option_Ooption_OSome(T_b),B_z)
% 187.18/188.02 & hAPP(V_f_2,B_z) = V_y_2 ) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_option__map__Some,axiom,
% 187.18/188.02 ! [V_x_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_Option_Omap(T_b,T_a),V_f_2),hAPP(c_Option_Ooption_OSome(T_b),V_x_2)) = hAPP(c_Option_Ooption_OSome(T_a),hAPP(V_f_2,V_x_2)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_dom__option__map,axiom,
% 187.18/188.02 ! [V_m_2,V_f_2,T_c,T_b,T_a] : c_Map_Odom(T_a,T_b,hAPP(hAPP(c_COMBS(T_a,tc_Option_Ooption(T_c),tc_Option_Ooption(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_b),tc_fun(tc_Option_Ooption(T_c),tc_Option_Ooption(T_b)),T_a),c_Option_Omap(T_c,T_b)),V_f_2)),V_m_2)) = c_Map_Odom(T_a,T_c,V_m_2) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_Code__Numeral_Oof__nat__inject,axiom,
% 187.18/188.02 ! [V_m_2,V_n_2] :
% 187.18/188.02 ( hAPP(c_Code__Numeral_Oof__nat,V_n_2) = hAPP(c_Code__Numeral_Oof__nat,V_m_2)
% 187.18/188.02 <=> V_n_2 = V_m_2 ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_times__code__numeral__code,axiom,
% 187.18/188.02 ! [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)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_Code__Numeral_Oof__nat__code,axiom,
% 187.18/188.02 c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_zero__code__numeral__def,axiom,
% 187.18/188.02 c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_one__code__numeral__def,axiom,
% 187.18/188.02 c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_plus__code__numeral__code,axiom,
% 187.18/188.02 ! [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)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_less__eq__code__numeral__code,axiom,
% 187.18/188.02 ! [V_m_2,V_n_2] :
% 187.18/188.02 ( 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)))
% 187.18/188.02 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_code__numeral__not__eq__zero,axiom,
% 187.18/188.02 ! [V_i_2] :
% 187.18/188.02 ( V_i_2 != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 187.18/188.02 <=> 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)) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_select__def,axiom,
% 187.18/188.02 ! [V_xs_2,T_a] : c_Random_Oselect(T_a,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_a,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_a)),V_xs_2)))),hAPP(hAPP(c_COMBB(T_a,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_a,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(T_a,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,tc_Code__Numeral_Ocode__numeral),hAPP(c_List_Onth(T_a),V_xs_2)),c_Code__Numeral_Onat__of))) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_subtract__code__numeral__code,axiom,
% 187.18/188.02 ! [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)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_type__definition__code__numeral,axiom,
% 187.18/188.02 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))) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_nat__of__of__nat,axiom,
% 187.18/188.02 ! [V_n] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_n)) = V_n ).
% 187.18/188.02
% 187.18/188.02 fof(fact_of__nat__nat__of,axiom,
% 187.18/188.02 ! [V_k] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_k)) = V_k ).
% 187.18/188.02
% 187.18/188.02 fof(fact_nat__of__inverse,axiom,
% 187.18/188.02 ! [V_x] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_x)) = V_x ).
% 187.18/188.02
% 187.18/188.02 fof(fact_times__code__numeral__def,axiom,
% 187.18/188.02 ! [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))) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_code__numeral_Onat__of__inject,axiom,
% 187.18/188.02 ! [V_y_2,V_x_2] :
% 187.18/188.02 ( hAPP(c_Code__Numeral_Onat__of,V_x_2) = hAPP(c_Code__Numeral_Onat__of,V_y_2)
% 187.18/188.02 <=> V_x_2 = V_y_2 ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_Code__Numeral_Onat__of__inject,axiom,
% 187.18/188.02 ! [V_l_2,V_k_2] :
% 187.18/188.02 ( hAPP(c_Code__Numeral_Onat__of,V_k_2) = hAPP(c_Code__Numeral_Onat__of,V_l_2)
% 187.18/188.02 <=> V_k_2 = V_l_2 ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_less__code__numeral__def,axiom,
% 187.18/188.02 ! [V_m_2,V_n_2] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2))
% 187.18/188.02 <=> 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))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_nat__of,axiom,
% 187.18/188.02 ! [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)))) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_nat__of__number,axiom,
% 187.18/188.02 ! [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) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_int__of__def,axiom,
% 187.18/188.02 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) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_less__eq__code__numeral__def,axiom,
% 187.18/188.02 ! [V_m_2,V_n_2] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2))
% 187.18/188.02 <=> 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))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_nat__of__code,axiom,
% 187.18/188.02 ! [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)) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_nat__of__aux__def,axiom,
% 187.18/188.02 ! [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) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_Suc__code__numeral__def,axiom,
% 187.18/188.02 ! [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))) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_minus__code__numeral__def,axiom,
% 187.18/188.02 ! [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))) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_of__nat__inverse,axiom,
% 187.18/188.02 ! [V_y_2] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 187.18/188.02 => hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_y_2)) = V_y_2 ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_plus__code__numeral__def,axiom,
% 187.18/188.02 ! [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))) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_div__code__numeral__def,axiom,
% 187.18/188.02 ! [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))) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_subtract__code__numeral__def,axiom,
% 187.18/188.02 c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_minus__code__numeral__code,axiom,
% 187.18/188.02 ! [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) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_mod__code__numeral__def,axiom,
% 187.18/188.02 ! [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))) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_code__numeral__decr,axiom,
% 187.18/188.02 ! [V_k] :
% 187.18/188.02 ( V_k != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 187.18/188.02 => 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))) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_New__DSequence_Opos__not__seq__def,axiom,
% 187.18/188.02 ! [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))) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_weak__map__of__SomeI,axiom,
% 187.18/188.02 ! [V_l_2,V_x_2,V_k_2,T_b,T_a] :
% 187.18/188.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_k_2),V_x_2)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_l_2)))
% 187.18/188.02 => ? [B_x] : hAPP(hAPP(c_Map_Omap__of(T_a,T_b),V_l_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),B_x) ) ).
% 187.18/188.02
% 187.18/188.02 fof(fact_map__of__zip__map,axiom,
% 187.18/188.02 ! [V_f_2,T_b,V_xs_2,V_x_2,T_a] :
% 187.18/188.02 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 187.18/188.02 => hAPP(hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2))),V_x_2) = hAPP(c_Option_Ooption_OSome(T_b),hAPP(V_f_2,V_x_2)) )
% 187.18/188.02 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 187.18/188.02 => hAPP(hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2))),V_x_2) = c_Option_Ooption_ONone(T_b) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_partition__set,axiom,
% 187.18/188.03 ! [V_no_2,V_yes_2,V_xs_2,V_P_2,T_a] :
% 187.18/188.03 ( c_List_Opartition(T_a,V_P_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_yes_2),V_no_2)
% 187.18/188.03 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_yes_2)),hAPP(c_List_Oset(T_a),V_no_2)) = hAPP(c_List_Oset(T_a),V_xs_2) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_option__map__o__empty,axiom,
% 187.18/188.03 ! [V_x_2,V_f_2,T_c,T_a,T_b] : hAPP(hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_b),tc_Option_Ooption(T_a),T_c,hAPP(c_Option_Omap(T_b,T_a),V_f_2)),hAPP(c_COMBK(tc_Option_Ooption(T_b),T_c),c_Option_Ooption_ONone(T_b))),V_x_2) = c_Option_Ooption_ONone(T_a) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_option__map__None,axiom,
% 187.18/188.03 ! [V_f_2,T_a,T_b] : hAPP(hAPP(c_Option_Omap(T_b,T_a),V_f_2),c_Option_Ooption_ONone(T_b)) = c_Option_Ooption_ONone(T_a) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_option__map__is__None,axiom,
% 187.18/188.03 ! [V_opt_2,V_f_2,T_a,T_b] :
% 187.18/188.03 ( hAPP(hAPP(c_Option_Omap(T_b,T_a),V_f_2),V_opt_2) = c_Option_Ooption_ONone(T_a)
% 187.18/188.03 <=> V_opt_2 = c_Option_Ooption_ONone(T_b) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_map__of__Cons__code_I1_J,axiom,
% 187.18/188.03 ! [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) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_set__empty__eq,axiom,
% 187.18/188.03 ! [V_xo_2,T_a] :
% 187.18/188.03 ( c_Option_Oset(T_a,V_xo_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/188.03 <=> V_xo_2 = c_Option_Ooption_ONone(T_a) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_Option_Oset_Osimps_I1_J,axiom,
% 187.18/188.03 ! [T_a] : c_Option_Oset(T_a,c_Option_Ooption_ONone(T_a)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_empty__upd__none,axiom,
% 187.18/188.03 ! [V_xa_2,V_x_2,T_a,T_b] : hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),hAPP(c_COMBK(tc_Option_Ooption(T_a),T_b),c_Option_Ooption_ONone(T_a))),V_x_2),c_Option_Ooption_ONone(T_a)),V_xa_2) = c_Option_Ooption_ONone(T_a) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_dom__def,axiom,
% 187.18/188.03 ! [V_m_2,T_b,T_a] : c_Map_Odom(T_a,T_b,V_m_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,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_a),c_fequal),V_m_2)),c_Option_Ooption_ONone(T_b)))) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_domIff,axiom,
% 187.18/188.03 ! [V_m_2,T_b,V_a_2,T_a] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Map_Odom(T_a,T_b,V_m_2)))
% 187.18/188.03 <=> hAPP(V_m_2,V_a_2) != c_Option_Ooption_ONone(T_b) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_dom__empty,axiom,
% 187.18/188.03 ! [T_b,T_a] : c_Map_Odom(T_a,T_b,hAPP(c_COMBK(tc_Option_Ooption(T_b),T_a),c_Option_Ooption_ONone(T_b))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_dom__eq__empty__conv,axiom,
% 187.18/188.03 ! [V_f_2,T_b,T_a] :
% 187.18/188.03 ( c_Map_Odom(T_a,T_b,V_f_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/188.03 <=> V_f_2 = hAPP(c_COMBK(tc_Option_Ooption(T_b),T_a),c_Option_Ooption_ONone(T_b)) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_restrict__map__def,axiom,
% 187.18/188.03 ! [V_m_2,T_b,V_A_2,V_x_2,T_a] :
% 187.18/188.03 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 187.18/188.03 => hAPP(c_Map_Orestrict__map(T_a,T_b,V_m_2,V_A_2),V_x_2) = hAPP(V_m_2,V_x_2) )
% 187.18/188.03 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 187.18/188.03 => hAPP(c_Map_Orestrict__map(T_a,T_b,V_m_2,V_A_2),V_x_2) = c_Option_Ooption_ONone(T_b) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_restrict__out,axiom,
% 187.18/188.03 ! [V_m_2,T_b,V_A_2,V_x_2,T_a] :
% 187.18/188.03 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 187.18/188.03 => hAPP(c_Map_Orestrict__map(T_a,T_b,V_m_2,V_A_2),V_x_2) = c_Option_Ooption_ONone(T_b) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_restrict__map__empty,axiom,
% 187.18/188.03 ! [V_x_2,V_D_2,T_a,T_b] : hAPP(c_Map_Orestrict__map(T_b,T_a,hAPP(c_COMBK(tc_Option_Ooption(T_a),T_b),c_Option_Ooption_ONone(T_a)),V_D_2),V_x_2) = c_Option_Ooption_ONone(T_a) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_restrict__map__to__empty,axiom,
% 187.18/188.03 ! [V_x_2,V_m_2,T_a,T_b] : hAPP(c_Map_Orestrict__map(T_b,T_a,V_m_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_x_2) = c_Option_Ooption_ONone(T_a) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_option_Osimps_I4_J,axiom,
% 187.18/188.03 ! [V_f2_2,V_f1_2,T_b,T_a] : hAPP(c_Option_Ooption_Ooption__case(T_a,T_b,V_f1_2,V_f2_2),c_Option_Ooption_ONone(T_b)) = V_f1_2 ).
% 187.18/188.03
% 187.18/188.03 fof(fact_map__upd__nonempty,axiom,
% 187.18/188.03 ! [V_x_2,V_k_2,V_t_2,T_b,T_a] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_t_2),V_k_2),hAPP(c_Option_Ooption_OSome(T_b),V_x_2)) != hAPP(c_COMBK(tc_Option_Ooption(T_b),T_a),c_Option_Ooption_ONone(T_b)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_option_Osimps_I2_J,axiom,
% 187.18/188.03 ! [V_a_H,T_a] : c_Option_Ooption_ONone(T_a) != hAPP(c_Option_Ooption_OSome(T_a),V_a_H) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_option_Osimps_I3_J,axiom,
% 187.18/188.03 ! [V_a_H,T_a] : hAPP(c_Option_Ooption_OSome(T_a),V_a_H) != c_Option_Ooption_ONone(T_a) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_not__Some__eq,axiom,
% 187.18/188.03 ! [T_a,V_x_2] :
% 187.18/188.03 ( ! [B_y] : V_x_2 != hAPP(c_Option_Ooption_OSome(T_a),B_y)
% 187.18/188.03 <=> V_x_2 = c_Option_Ooption_ONone(T_a) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_not__None__eq,axiom,
% 187.18/188.03 ! [T_a,V_x_2] :
% 187.18/188.03 ( V_x_2 != c_Option_Ooption_ONone(T_a)
% 187.18/188.03 <=> ? [B_y] : V_x_2 = hAPP(c_Option_Ooption_OSome(T_a),B_y) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_ran__empty,axiom,
% 187.18/188.03 ! [T_a,T_b] : c_Map_Oran(T_b,T_a,hAPP(c_COMBK(tc_Option_Ooption(T_a),T_b),c_Option_Ooption_ONone(T_a))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_map__of_Osimps_I1_J,axiom,
% 187.18/188.03 ! [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) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_Option_Omap__def,axiom,
% 187.18/188.03 ! [V_f_2,T_b,T_a] : hAPP(c_Option_Omap(T_a,T_b),V_f_2) = c_Option_Ooption_Ooption__case(tc_Option_Ooption(T_b),T_a,c_Option_Ooption_ONone(T_b),hAPP(hAPP(c_COMBB(T_b,tc_Option_Ooption(T_b),T_a),c_Option_Ooption_OSome(T_b)),V_f_2)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_option_Osize_I3_J,axiom,
% 187.18/188.03 ! [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) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_option_Osize_I1_J,axiom,
% 187.18/188.03 ! [V_fa_2,T_a] : c_Option_Ooption_Ooption__size(T_a,V_fa_2,c_Option_Ooption_ONone(T_a)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_dom__minus,axiom,
% 187.18/188.03 ! [V_A_2,T_b,T_a,V_x_2,V_f_2] :
% 187.18/188.03 ( hAPP(V_f_2,V_x_2) = c_Option_Ooption_ONone(T_a)
% 187.18/188.03 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),c_Map_Odom(T_b,T_a,V_f_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),c_Map_Odom(T_b,T_a,V_f_2)),V_A_2) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_WT_OBody,axiom,
% 187.18/188.03 ! [V_pn] :
% 187.18/188.03 ( hAPP(c_Com_Obody,V_pn) != c_Option_Ooption_ONone(tc_Com_Ocom)
% 187.18/188.03 => hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_pn))) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_partition__P,axiom,
% 187.18/188.03 ! [V_no_2,V_yes_2,V_xs_2,V_P_2,T_a] :
% 187.18/188.03 ( c_List_Opartition(T_a,V_P_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_yes_2),V_no_2)
% 187.18/188.03 => ( ! [B_x] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_yes_2)))
% 187.18/188.03 => hBOOL(hAPP(V_P_2,B_x)) )
% 187.18/188.03 & ! [B_x] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_no_2)))
% 187.18/188.03 => ~ hBOOL(hAPP(V_P_2,B_x)) ) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_partition_Osimps_I1_J,axiom,
% 187.18/188.03 ! [V_P_2,T_a] : c_List_Opartition(T_a,V_P_2,c_List_Olist_ONil(T_a)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_List_Olist_ONil(T_a)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_ran__map__upd,axiom,
% 187.18/188.03 ! [V_b_2,T_b,T_a,V_a_2,V_m_2] :
% 187.18/188.03 ( hAPP(V_m_2,V_a_2) = c_Option_Ooption_ONone(T_a)
% 187.18/188.03 => c_Map_Oran(T_b,T_a,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_a),V_b_2))) = hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Map_Oran(T_b,T_a,V_m_2)) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_map__of__zip__is__None,axiom,
% 187.18/188.03 ! [V_x_2,V_ys_2,T_b,V_xs_2,T_a] :
% 187.18/188.03 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)
% 187.18/188.03 => ( hAPP(hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)),V_x_2) = c_Option_Ooption_ONone(T_b)
% 187.18/188.03 <=> ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_partition_Osimps_I2_J,axiom,
% 187.18/188.03 ! [V_xs_2,V_x_2,V_P_2,T_a] : c_List_Opartition(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)))),tc_fun(tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)))),tc_List_Olist(T_a)),c_COMBS(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_fun(tc_List_Olist(T_a),tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)))),tc_List_Olist(T_a)),hAPP(c_COMBB(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_List_Olist(T_a)),hAPP(c_If(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(V_P_2,V_x_2)))),hAPP(hAPP(c_COMBB(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_List_Olist(T_a)),c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(c_List_Olist_OCons(T_a),V_x_2))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_fun(tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)))),tc_List_Olist(T_a)),c_COMBB(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_List_Olist(T_a))),c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)))),hAPP(c_List_Olist_OCons(T_a),V_x_2)))),c_List_Opartition(T_a,V_P_2,V_xs_2)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_dom__fun__upd,axiom,
% 187.18/188.03 ! [V_x_2,V_f_2,T_b,T_a,V_y_2] :
% 187.18/188.03 ( ( V_y_2 = c_Option_Ooption_ONone(T_a)
% 187.18/188.03 => c_Map_Odom(T_b,T_a,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),V_f_2),V_x_2),V_y_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),c_Map_Odom(T_b,T_a,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)))) )
% 187.18/188.03 & ( V_y_2 != c_Option_Ooption_ONone(T_a)
% 187.18/188.03 => c_Map_Odom(T_b,T_a,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),V_f_2),V_x_2),V_y_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Map_Odom(T_b,T_a,V_f_2)) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_restrict__complement__singleton__eq,axiom,
% 187.18/188.03 ! [V_x_2,V_f_2,T_b,T_a] : c_Map_Orestrict__map(T_a,T_b,V_f_2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_f_2),V_x_2),c_Option_Ooption_ONone(T_b)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_map__of__eq__None__iff,axiom,
% 187.18/188.03 ! [V_x_2,V_xys_2,T_a,T_b] :
% 187.18/188.03 ( hAPP(hAPP(c_Map_Omap__of(T_b,T_a),V_xys_2),V_x_2) = c_Option_Ooption_ONone(T_a)
% 187.18/188.03 <=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Set_Oimage(tc_prod(T_b,T_a),T_b,c_Product__Type_Ofst(T_b,T_a)),hAPP(c_List_Oset(tc_prod(T_b,T_a)),V_xys_2)))) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_UNIV__option__conv,axiom,
% 187.18/188.03 ! [T_a] : c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(T_a),tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(tc_Option_Ooption(T_a)),c_Option_Ooption_ONone(T_a)),hAPP(c_Set_Oimage(T_a,tc_Option_Ooption(T_a),c_Option_Ooption_OSome(T_a)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_dom__eq__singleton__conv,axiom,
% 187.18/188.03 ! [V_x_2,V_f_2,T_b,T_a] :
% 187.18/188.03 ( c_Map_Odom(T_a,T_b,V_f_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))
% 187.18/188.03 <=> ? [B_v] : V_f_2 = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),hAPP(c_COMBK(tc_Option_Ooption(T_b),T_a),c_Option_Ooption_ONone(T_b))),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),B_v)) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_fun__upd__None__restrict,axiom,
% 187.18/188.03 ! [V_m_2,T_b,V_D_2,V_x_2,T_a] :
% 187.18/188.03 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2))
% 187.18/188.03 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_m_2,V_D_2)),V_x_2),c_Option_Ooption_ONone(T_b)) = c_Map_Orestrict__map(T_a,T_b,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_D_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) )
% 187.18/188.03 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2))
% 187.18/188.03 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_m_2,V_D_2)),V_x_2),c_Option_Ooption_ONone(T_b)) = c_Map_Orestrict__map(T_a,T_b,V_m_2,V_D_2) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_lists__Int__eq,axiom,
% 187.18/188.03 ! [V_B_2,V_A_2,T_a] : c_List_Olistsp(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(T_a))),c_List_Olists(T_a,V_A_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(T_a))),c_List_Olists(T_a,V_B_2))) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_lists__IntI,axiom,
% 187.18/188.03 ! [V_B_2,V_A_2,V_l_2,T_a] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_l_2),c_List_Olists(T_a,V_A_2)))
% 187.18/188.03 => ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_l_2),c_List_Olists(T_a,V_B_2)))
% 187.18/188.03 => hBOOL(hAPP(c_List_Olistsp(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))),V_l_2)) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_listsp_ONil,axiom,
% 187.18/188.03 ! [V_A_2,T_a] : hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),c_List_Olist_ONil(T_a))) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_append__in__listsp__conv,axiom,
% 187.18/188.03 ! [V_ys_2,V_xs_2,V_A_2,T_a] :
% 187.18/188.03 ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)))
% 187.18/188.03 <=> ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_xs_2))
% 187.18/188.03 & hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_ys_2)) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_listsp_Oequations_I2_J,axiom,
% 187.18/188.03 ! [V_a2_2,V_a1_2,V_A_2,T_a] :
% 187.18/188.03 ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a1_2),V_a2_2)))
% 187.18/188.03 <=> ( hBOOL(hAPP(V_A_2,V_a1_2))
% 187.18/188.03 & hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_a2_2)) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_in__listsp__conv__set,axiom,
% 187.18/188.03 ! [V_xs_2,V_A_2,T_a] :
% 187.18/188.03 ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_xs_2))
% 187.18/188.03 <=> ! [B_x] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 187.18/188.03 => hBOOL(hAPP(V_A_2,B_x)) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_listsp__conj__eq,axiom,
% 187.18/188.03 ! [V_x_2,V_B_2,V_A_2,T_a] :
% 187.18/188.03 ( hBOOL(hAPP(c_List_Olistsp(T_a,hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),V_A_2)),V_B_2)),V_x_2))
% 187.18/188.03 <=> ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_x_2))
% 187.18/188.03 & hBOOL(hAPP(c_List_Olistsp(T_a,V_B_2),V_x_2)) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_listsp__inf__eq,axiom,
% 187.18/188.03 ! [V_B_2,V_A_2,T_a] : c_List_Olistsp(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),c_List_Olistsp(T_a,V_A_2)),c_List_Olistsp(T_a,V_B_2)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_listsp__infI,axiom,
% 187.18/188.03 ! [V_B_2,V_l_2,V_A_2,T_a] :
% 187.18/188.03 ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_l_2))
% 187.18/188.03 => ( hBOOL(hAPP(c_List_Olistsp(T_a,V_B_2),V_l_2))
% 187.18/188.03 => hBOOL(hAPP(c_List_Olistsp(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_l_2)) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_listsp_Oequations_I1_J,axiom,
% 187.18/188.03 ! [V_A_2,T_a] : hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),c_List_Olist_ONil(T_a))) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_listsp__mono,axiom,
% 187.18/188.03 ! [V_B_2,V_A_2,T_a] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 187.18/188.03 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),c_List_Olistsp(T_a,V_A_2)),c_List_Olistsp(T_a,V_B_2))) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_listsp__lists__eq,axiom,
% 187.18/188.03 ! [V_x_2,V_A_2,T_a] :
% 187.18/188.03 ( hBOOL(hAPP(c_List_Olistsp(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)),V_x_2))
% 187.18/188.03 <=> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_x_2),c_List_Olists(T_a,V_A_2))) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_,axiom,
% 187.18/188.03 ! [V_y_2,V_x_2,T_a] : c_Smallcheck_Oorelse(T_a,V_x_2,V_y_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(T_a),T_a,V_y_2,c_Option_Ooption_OSome(T_a)),V_x_2) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_product_Osimps_I2_J,axiom,
% 187.18/188.03 ! [V_ys_2,V_xs_2,V_x_2,T_b,T_a] : c_Enum_Oproduct(T_a,T_b,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Omap(T_b,tc_prod(T_a,T_b)),hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2)),V_ys_2)),c_Enum_Oproduct(T_a,T_b,V_xs_2,V_ys_2)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_product_Osimps_I1_J,axiom,
% 187.18/188.03 ! [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)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_distinct__product,axiom,
% 187.18/188.03 ! [V_ys,T_b,V_xs,T_a] :
% 187.18/188.03 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 187.18/188.03 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_ys))
% 187.18/188.03 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),c_Enum_Oproduct(T_a,T_b,V_xs,V_ys))) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_product__list__set,axiom,
% 187.18/188.03 ! [V_ys_2,V_xs_2,T_b,T_a] : hAPP(c_List_Oset(tc_prod(T_a,T_b)),c_Enum_Oproduct(T_a,T_b,V_xs_2,V_ys_2)) = hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_List_Oset(T_b),V_ys_2))) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_sublists__powset,axiom,
% 187.18/188.03 ! [V_xs_2,T_a] : hAPP(c_Set_Oimage(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool),c_List_Oset(T_a)),hAPP(c_List_Oset(tc_List_Olist(T_a)),c_Enum_Osublists(T_a,V_xs_2))) = hAPP(c_Set_OPow(T_a),hAPP(c_List_Oset(T_a),V_xs_2)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_length__sublists,axiom,
% 187.18/188.03 ! [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)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_sublists_Osimps_I1_J,axiom,
% 187.18/188.03 ! [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))) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_sublists_Osimps_I2_J,axiom,
% 187.18/188.03 ! [V_xs_2,V_x_2,T_a] : c_Enum_Osublists(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = hAPP(hAPP(c_HOL_OLet(tc_List_Olist(tc_List_Olist(T_a)),tc_List_Olist(tc_List_Olist(T_a))),c_Enum_Osublists(T_a,V_xs_2)),hAPP(hAPP(c_COMBS(tc_List_Olist(tc_List_Olist(T_a)),tc_List_Olist(tc_List_Olist(T_a)),tc_List_Olist(tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_List_Olist(T_a)),tc_fun(tc_List_Olist(tc_List_Olist(T_a)),tc_List_Olist(tc_List_Olist(T_a))),tc_List_Olist(tc_List_Olist(T_a))),c_List_Oappend(tc_List_Olist(T_a))),hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(c_List_Olist_OCons(T_a),V_x_2)))),c_COMBI(tc_List_Olist(tc_List_Olist(T_a))))) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_distinct__set__sublists,axiom,
% 187.18/188.03 ! [V_xs_2,T_a] :
% 187.18/188.03 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 187.18/188.03 => hBOOL(hAPP(c_List_Odistinct(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool)),c_List_Oset(T_a)),c_Enum_Osublists(T_a,V_xs_2)))) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_set__n__lists,axiom,
% 187.18/188.03 ! [V_xs_2,V_n_2,T_a] : hAPP(c_List_Oset(tc_List_Olist(T_a)),c_Enum_On__lists(T_a,V_n_2,V_xs_2)) = hAPP(c_Set_OCollect(tc_List_Olist(T_a)),hAPP(hAPP(c_COMBS(tc_List_Olist(T_a),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_a)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),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_a)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),V_n_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_a)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool))),c_List_Oset(T_a))),hAPP(c_List_Oset(T_a),V_xs_2)))) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_enum__the__def,axiom,
% 187.18/188.03 ! [V_P_2,T_a] : c_Enum_Oenum__the(T_a,V_P_2) = c_HOL_OThe(T_a,V_P_2) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_distinct__n__lists,axiom,
% 187.18/188.03 ! [V_n,V_xs,T_a] :
% 187.18/188.03 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 187.18/188.03 => hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_a)),c_Enum_On__lists(T_a,V_n,V_xs))) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_n__lists__Nil,axiom,
% 187.18/188.03 ! [T_a,V_n] :
% 187.18/188.03 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.18/188.03 => 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))) )
% 187.18/188.03 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.18/188.03 => c_Enum_On__lists(T_a,V_n,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(tc_List_Olist(T_a)) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_n__lists_Osimps_I1_J,axiom,
% 187.18/188.03 ! [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))) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_length__n__lists,axiom,
% 187.18/188.03 ! [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) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_length__n__lists__elem,axiom,
% 187.18/188.03 ! [V_xs_2,V_n_2,V_ys_2,T_a] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_ys_2),hAPP(c_List_Oset(tc_List_Olist(T_a)),c_Enum_On__lists(T_a,V_n_2,V_xs_2))))
% 187.18/188.03 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) = V_n_2 ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_full__small__int__def,axiom,
% 187.18/188.03 ! [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))) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_small_H_Osimps,axiom,
% 187.18/188.03 ! [V_f_2,V_i_2,V_d_2] :
% 187.18/188.03 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 187.18/188.03 => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) )
% 187.18/188.03 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 187.18/188.03 => 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)) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_small_H_Opsimps,axiom,
% 187.18/188.03 ! [V_i_2,V_d_2,V_f_2] :
% 187.18/188.03 ( 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))))
% 187.18/188.03 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 187.18/188.03 => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) )
% 187.18/188.03 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 187.18/188.03 => 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)) ) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_small__int__def,axiom,
% 187.18/188.03 ! [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))) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_small__prod__def,axiom,
% 187.18/188.03 ! [V_d_2,V_f_2,T_a,T_b] :
% 187.18/188.03 ( ( class_Smallcheck_Osmall(T_b)
% 187.18/188.03 & class_Smallcheck_Osmall(T_a) )
% 187.18/188.03 => hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_prod(T_a,T_b)),V_f_2),V_d_2) = hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(T_a),hAPP(hAPP(c_COMBC(T_a,tc_Code__Numeral_Ocode__numeral,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(hAPP(c_COMBB(tc_fun(T_b,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_a),c_Smallcheck_Osmall__class_Osmall(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),T_b),V_f_2)),c_Product__Type_OPair(T_a,T_b)))),V_d_2)),V_d_2) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_small_H_Opinduct,axiom,
% 187.18/188.03 ! [V_P_2,V_a2_2,V_a1_2,V_a0_2] :
% 187.18/188.03 ( 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))))
% 187.18/188.03 => ( ! [B_f,B_d,B_i] :
% 187.18/188.03 ( 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))))
% 187.18/188.03 => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_d),B_i))
% 187.18/188.03 => ( hAPP(B_f,B_i) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
% 187.18/188.03 => 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)))) ) )
% 187.18/188.03 => hBOOL(hAPP(hAPP(hAPP(V_P_2,B_f),B_d),B_i)) ) )
% 187.18/188.03 => hBOOL(hAPP(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2),V_a2_2)) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_map__of__zip__enum__inject,axiom,
% 187.18/188.03 ! [V_ys_2,V_xs_2,T_a,T_b] :
% 187.18/188.03 ( ( class_Enum_Oenum(T_b)
% 187.18/188.03 & class_Enum_Oenum(T_a) )
% 187.18/188.03 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_Enum_Oenum__class_Oenum(T_b))
% 187.18/188.03 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_Enum_Oenum__class_Oenum(T_b))
% 187.18/188.03 => ( hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_a),T_a,T_b,c_Option_Othe(T_a)),hAPP(c_Map_Omap__of(T_b,T_a),hAPP(hAPP(c_List_Ozip(T_b,T_a),c_Enum_Oenum__class_Oenum(T_b)),V_xs_2))) = hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_a),T_a,T_b,c_Option_Othe(T_a)),hAPP(c_Map_Omap__of(T_b,T_a),hAPP(hAPP(c_List_Ozip(T_b,T_a),c_Enum_Oenum__class_Oenum(T_b)),V_ys_2)))
% 187.18/188.03 => V_xs_2 = V_ys_2 ) ) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_enum__prod__def,axiom,
% 187.18/188.03 ! [T_b,T_a] :
% 187.18/188.03 ( ( class_Enum_Oenum(T_a)
% 187.18/188.03 & class_Enum_Oenum(T_b) )
% 187.18/188.03 => 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)) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_enum__UNIV,axiom,
% 187.18/188.03 ! [T_a] :
% 187.18/188.03 ( class_Enum_Oenum(T_a)
% 187.18/188.03 => hAPP(c_List_Oset(T_a),c_Enum_Oenum__class_Oenum(T_a)) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_UNIV__enum,axiom,
% 187.18/188.03 ! [T_a] :
% 187.18/188.03 ( class_Enum_Oenum(T_a)
% 187.18/188.03 => c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) = hAPP(c_List_Oset(T_a),c_Enum_Oenum__class_Oenum(T_a)) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_in__enum,axiom,
% 187.18/188.03 ! [V_x_2,T_a] :
% 187.18/188.03 ( class_Enum_Oenum(T_a)
% 187.18/188.03 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_Enum_Oenum__class_Oenum(T_a)))) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_enum__option__def,axiom,
% 187.18/188.03 ! [T_a] :
% 187.18/188.03 ( class_Enum_Oenum(T_a)
% 187.18/188.03 => c_Enum_Oenum__class_Oenum(tc_Option_Ooption(T_a)) = hAPP(hAPP(c_List_Olist_OCons(tc_Option_Ooption(T_a)),c_Option_Ooption_ONone(T_a)),hAPP(hAPP(c_List_Omap(T_a,tc_Option_Ooption(T_a)),c_Option_Ooption_OSome(T_a)),c_Enum_Oenum__class_Oenum(T_a))) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_enum__distinct,axiom,
% 187.18/188.03 ! [T_a] :
% 187.18/188.03 ( class_Enum_Oenum(T_a)
% 187.18/188.03 => hBOOL(hAPP(c_List_Odistinct(T_a),c_Enum_Oenum__class_Oenum(T_a))) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_enum__fun__def,axiom,
% 187.18/188.03 ! [T_b,T_a] :
% 187.18/188.03 ( ( class_Enum_Oenum(T_a)
% 187.18/188.03 & class_Enum_Oenum(T_b) )
% 187.18/188.03 => c_Enum_Oenum__class_Oenum(tc_fun(T_a,T_b)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_fun(T_a,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,T_b),tc_List_Olist(T_b)),c_Fun_Ocomp(tc_Option_Ooption(T_b),T_b,T_a,c_Option_Othe(T_b))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(T_a,T_b)),tc_fun(T_a,tc_Option_Ooption(T_b)),tc_List_Olist(T_b)),c_Map_Omap__of(T_a,T_b)),hAPP(c_List_Ozip(T_a,T_b),c_Enum_Oenum__class_Oenum(T_a))))),c_Enum_On__lists(T_b,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_Enum_Oenum__class_Oenum(T_a)),c_Enum_Oenum__class_Oenum(T_b))) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_enum__fun__code,axiom,
% 187.18/188.03 ! [T_b,T_a] :
% 187.18/188.03 ( ( class_Enum_Oenum(T_a)
% 187.18/188.03 & class_HOL_Oequal(T_a)
% 187.18/188.03 & class_Enum_Oenum(T_b) )
% 187.18/188.03 => c_Enum_Oenum__class_Oenum(tc_fun(T_a,T_b)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_fun(T_a,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,T_b),tc_List_Olist(T_b)),c_Fun_Ocomp(tc_Option_Ooption(T_b),T_b,T_a,c_Option_Othe(T_b))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(T_a,T_b)),tc_fun(T_a,tc_Option_Ooption(T_b)),tc_List_Olist(T_b)),c_Map_Omap__of(T_a,T_b)),hAPP(c_List_Ozip(T_a,T_b),c_Enum_Oenum__class_Oenum(T_a))))),c_Enum_On__lists(T_b,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_Enum_Oenum__class_Oenum(T_a)),c_Enum_Oenum__class_Oenum(T_b))) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_ex__n__lists__def,axiom,
% 187.18/188.03 ! [V_n_2,V_P_2,T_a] :
% 187.18/188.03 ( class_Enum_Oenum(T_a)
% 187.18/188.03 => ( c_Enum_Oex__n__lists(T_a,V_P_2,V_n_2)
% 187.18/188.03 <=> ? [B_x] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_a)),c_Enum_On__lists(T_a,V_n_2,c_Enum_Oenum__class_Oenum(T_a)))))
% 187.18/188.03 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_all__n__lists__def,axiom,
% 187.18/188.03 ! [V_n_2,V_P_2,T_a] :
% 187.18/188.03 ( class_Enum_Oenum(T_a)
% 187.18/188.03 => ( c_Enum_Oall__n__lists(T_a,V_P_2,V_n_2)
% 187.18/188.03 <=> ! [B_x] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_a)),c_Enum_On__lists(T_a,V_n_2,c_Enum_Oenum__class_Oenum(T_a)))))
% 187.18/188.03 => hBOOL(hAPP(V_P_2,B_x)) ) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_enum__ex__fun__code,axiom,
% 187.18/188.03 ! [V_P_2,T_a,T_b] :
% 187.18/188.03 ( ( class_Enum_Oenum(T_b)
% 187.18/188.03 & class_Enum_Oenum(T_a)
% 187.18/188.03 & class_HOL_Oequal(T_a) )
% 187.18/188.03 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(T_a,T_b)),V_P_2))
% 187.18/188.03 <=> c_Enum_Oex__n__lists(T_b,hAPP(hAPP(c_COMBB(tc_fun(T_a,T_b),tc_HOL_Obool,tc_List_Olist(T_b)),V_P_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,T_b),tc_List_Olist(T_b)),c_Fun_Ocomp(tc_Option_Ooption(T_b),T_b,T_a,c_Option_Othe(T_b))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(T_a,T_b)),tc_fun(T_a,tc_Option_Ooption(T_b)),tc_List_Olist(T_b)),c_Map_Omap__of(T_a,T_b)),hAPP(c_List_Ozip(T_a,T_b),c_Enum_Oenum__class_Oenum(T_a))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_Enum_Oenum__class_Oenum(T_a))) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_enum__all__fun__code,axiom,
% 187.18/188.03 ! [V_P_2,T_a,T_b] :
% 187.18/188.03 ( ( class_Enum_Oenum(T_b)
% 187.18/188.03 & class_Enum_Oenum(T_a)
% 187.18/188.03 & class_HOL_Oequal(T_a) )
% 187.18/188.03 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(T_a,T_b)),V_P_2))
% 187.18/188.03 <=> c_Enum_Oall__n__lists(T_b,hAPP(hAPP(c_COMBB(tc_fun(T_a,T_b),tc_HOL_Obool,tc_List_Olist(T_b)),V_P_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,T_b),tc_List_Olist(T_b)),c_Fun_Ocomp(tc_Option_Ooption(T_b),T_b,T_a,c_Option_Othe(T_b))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(T_a,T_b)),tc_fun(T_a,tc_Option_Ooption(T_b)),tc_List_Olist(T_b)),c_Map_Omap__of(T_a,T_b)),hAPP(c_List_Ozip(T_a,T_b),c_Enum_Oenum__class_Oenum(T_a))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_Enum_Oenum__class_Oenum(T_a))) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_enum__ex__prod__def,axiom,
% 187.18/188.03 ! [V_P_2,T_a,T_b] :
% 187.18/188.03 ( ( class_Enum_Oenum(T_b)
% 187.18/188.03 & class_Enum_Oenum(T_a) )
% 187.18/188.03 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(T_a,T_b)),V_P_2))
% 187.18/188.03 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_a),c_Enum_Oenum__class_Oenum__ex(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_HOL_Obool,T_b),V_P_2)),c_Product__Type_OPair(T_a,T_b))))) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_enum__all__prod__def,axiom,
% 187.18/188.03 ! [V_P_2,T_a,T_b] :
% 187.18/188.03 ( ( class_Enum_Oenum(T_b)
% 187.18/188.03 & class_Enum_Oenum(T_a) )
% 187.18/188.03 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(T_a,T_b)),V_P_2))
% 187.18/188.03 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_a),c_Enum_Oenum__class_Oenum__all(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_HOL_Obool,T_b),V_P_2)),c_Product__Type_OPair(T_a,T_b))))) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_enum__ex,axiom,
% 187.18/188.03 ! [V_P_2,T_a] :
% 187.18/188.03 ( class_Enum_Oenum(T_a)
% 187.18/188.03 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_a),V_P_2))
% 187.18/188.03 <=> ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_enum__all,axiom,
% 187.18/188.03 ! [V_P_2,T_a] :
% 187.18/188.03 ( class_Enum_Oenum(T_a)
% 187.18/188.03 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_a),V_P_2))
% 187.18/188.03 <=> ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_exists__code,axiom,
% 187.18/188.03 ! [V_P_2,T_a] :
% 187.18/188.03 ( class_Enum_Oenum(T_a)
% 187.18/188.03 => ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 187.18/188.03 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_a),V_P_2)) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_all__code,axiom,
% 187.18/188.03 ! [V_P_2,T_a] :
% 187.18/188.03 ( class_Enum_Oenum(T_a)
% 187.18/188.03 => ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 187.18/188.03 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_a),V_P_2)) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_enum__ex__option__def,axiom,
% 187.18/188.03 ! [V_P_2,T_a] :
% 187.18/188.03 ( class_Enum_Oenum(T_a)
% 187.18/188.03 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_Option_Ooption(T_a)),V_P_2))
% 187.18/188.03 <=> ( hBOOL(hAPP(V_P_2,c_Option_Ooption_ONone(T_a)))
% 187.18/188.03 | hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_a),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_a),tc_HOL_Obool,T_a),V_P_2),c_Option_Ooption_OSome(T_a)))) ) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_enum__all__option__def,axiom,
% 187.18/188.03 ! [V_P_2,T_a] :
% 187.18/188.03 ( class_Enum_Oenum(T_a)
% 187.18/188.03 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_Option_Ooption(T_a)),V_P_2))
% 187.18/188.03 <=> ( hBOOL(hAPP(V_P_2,c_Option_Ooption_ONone(T_a)))
% 187.18/188.03 & hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_a),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_a),tc_HOL_Obool,T_a),V_P_2),c_Option_Ooption_OSome(T_a)))) ) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_order__fun_I1_J,axiom,
% 187.18/188.03 ! [V_g_2,V_f_2,T_a,T_b] :
% 187.18/188.03 ( ( class_Orderings_Oorder(T_b)
% 187.18/188.03 & class_Enum_Oenum(T_a) )
% 187.18/188.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2))
% 187.18/188.03 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_a),hAPP(hAPP(c_COMBS(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),c_Orderings_Oord__class_Oless__eq(T_b)),V_f_2)),V_g_2))) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_order__fun_I2_J,axiom,
% 187.18/188.03 ! [V_g_2,V_f_2,T_a,T_b] :
% 187.18/188.03 ( ( class_Orderings_Oorder(T_b)
% 187.18/188.03 & class_Enum_Oenum(T_a) )
% 187.18/188.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b)),V_f_2),V_g_2))
% 187.18/188.03 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2))
% 187.18/188.03 & hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBS(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),c_fequal),V_f_2)),V_g_2)))) ) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_enum__all__fun__def,axiom,
% 187.18/188.03 ! [V_P_2,T_a,T_b] :
% 187.18/188.03 ( ( class_Enum_Oenum(T_b)
% 187.18/188.03 & class_Enum_Oenum(T_a) )
% 187.18/188.03 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(T_a,T_b)),V_P_2))
% 187.18/188.03 <=> c_Enum_Oall__n__lists(T_b,hAPP(hAPP(c_COMBB(tc_fun(T_a,T_b),tc_HOL_Obool,tc_List_Olist(T_b)),V_P_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,T_b),tc_List_Olist(T_b)),c_Fun_Ocomp(tc_Option_Ooption(T_b),T_b,T_a,c_Option_Othe(T_b))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(T_a,T_b)),tc_fun(T_a,tc_Option_Ooption(T_b)),tc_List_Olist(T_b)),c_Map_Omap__of(T_a,T_b)),hAPP(c_List_Ozip(T_a,T_b),c_Enum_Oenum__class_Oenum(T_a))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_Enum_Oenum__class_Oenum(T_a))) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_enum__ex__fun__def,axiom,
% 187.18/188.03 ! [V_P_2,T_a,T_b] :
% 187.18/188.03 ( ( class_Enum_Oenum(T_b)
% 187.18/188.03 & class_Enum_Oenum(T_a) )
% 187.18/188.03 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(T_a,T_b)),V_P_2))
% 187.18/188.03 <=> c_Enum_Oex__n__lists(T_b,hAPP(hAPP(c_COMBB(tc_fun(T_a,T_b),tc_HOL_Obool,tc_List_Olist(T_b)),V_P_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,T_b),tc_List_Olist(T_b)),c_Fun_Ocomp(tc_Option_Ooption(T_b),T_b,T_a,c_Option_Othe(T_b))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(T_a,T_b)),tc_fun(T_a,tc_Option_Ooption(T_b)),tc_List_Olist(T_b)),c_Map_Omap__of(T_a,T_b)),hAPP(c_List_Ozip(T_a,T_b),c_Enum_Oenum__class_Oenum(T_a))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_Enum_Oenum__class_Oenum(T_a))) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_map__of__zip__enum__is__Some,axiom,
% 187.18/188.03 ! [V_x,V_ys,T_b,T_a] :
% 187.18/188.03 ( class_Enum_Oenum(T_a)
% 187.18/188.03 => ( 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))
% 187.18/188.03 => ? [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) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_list__all2__def,axiom,
% 187.18/188.03 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] :
% 187.18/188.03 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2)
% 187.18/188.03 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)
% 187.18/188.03 & ! [B_x] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),B_x),hAPP(c_List_Oset(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2))))
% 187.18/188.03 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_P_2),B_x)) ) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_list__all2__lengthD,axiom,
% 187.18/188.03 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] :
% 187.18/188.03 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2)
% 187.18/188.03 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_list__all2__dropI,axiom,
% 187.18/188.03 ! [V_n_2,V_bs_2,V_as_2,V_P_2,T_b,T_a] :
% 187.18/188.03 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_as_2,V_bs_2)
% 187.18/188.03 => c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(hAPP(c_List_Odrop(T_a),V_n_2),V_as_2),hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_bs_2)) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_list__all2__takeI,axiom,
% 187.18/188.03 ! [V_n_2,V_ys_2,V_xs_2,V_P_2,T_b,T_a] :
% 187.18/188.03 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2)
% 187.18/188.03 => c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_xs_2),hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_ys_2)) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_list__all2__eq,axiom,
% 187.18/188.03 ! [T_a,V_ys_2,V_xs_2] :
% 187.18/188.03 ( V_xs_2 = V_ys_2
% 187.18/188.03 <=> c_List_Olist__all2(T_a,T_a,c_fequal,V_xs_2,V_ys_2) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_list__all2__appendI,axiom,
% 187.18/188.03 ! [V_d_2,V_c_2,V_b_2,V_a_2,V_P_2,T_b,T_a] :
% 187.18/188.03 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_a_2,V_b_2)
% 187.18/188.03 => ( c_List_Olist__all2(T_a,T_b,V_P_2,V_c_2,V_d_2)
% 187.18/188.03 => c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_a_2),V_c_2),hAPP(hAPP(c_List_Oappend(T_b),V_b_2),V_d_2)) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_list__all2__Nil2,axiom,
% 187.18/188.03 ! [V_xs_2,V_P_2,T_b,T_a] :
% 187.18/188.03 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,c_List_Olist_ONil(T_b))
% 187.18/188.03 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_list__all2__Nil,axiom,
% 187.18/188.03 ! [V_ys_2,V_P_2,T_b,T_a] :
% 187.18/188.03 ( c_List_Olist__all2(T_a,T_b,V_P_2,c_List_Olist_ONil(T_a),V_ys_2)
% 187.18/188.03 <=> V_ys_2 = c_List_Olist_ONil(T_b) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_list__all2__append,axiom,
% 187.18/188.03 ! [V_vs_2,V_us_2,V_P_2,V_ys_2,T_b,V_xs_2,T_a] :
% 187.18/188.03 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)
% 187.18/188.03 => ( c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_us_2),hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_vs_2))
% 187.18/188.03 <=> ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2)
% 187.18/188.03 & c_List_Olist__all2(T_a,T_b,V_P_2,V_us_2,V_vs_2) ) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_list__all2__map1,axiom,
% 187.18/188.03 ! [V_bs_2,V_as_2,V_f_2,T_c,V_P_2,T_b,T_a] :
% 187.18/188.03 ( c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(hAPP(c_List_Omap(T_c,T_a),V_f_2),V_as_2),V_bs_2)
% 187.18/188.03 <=> c_List_Olist__all2(T_c,T_b,hAPP(hAPP(c_COMBB(T_a,tc_fun(T_b,tc_HOL_Obool),T_c),V_P_2),V_f_2),V_as_2,V_bs_2) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_list__all2__map2,axiom,
% 187.18/188.03 ! [V_bs_2,V_f_2,T_c,V_as_2,V_P_2,T_b,T_a] :
% 187.18/188.03 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_as_2,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_bs_2))
% 187.18/188.03 <=> c_List_Olist__all2(T_a,T_c,hAPP(hAPP(c_COMBC(T_a,tc_fun(T_c,T_b),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_fun(T_c,tc_HOL_Obool)),T_a),c_COMBB(T_b,tc_HOL_Obool,T_c)),V_P_2)),V_f_2),V_as_2,V_bs_2) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_list__all2__Cons,axiom,
% 187.18/188.03 ! [V_ys_2,V_y_2,V_xs_2,V_x_2,V_P_2,T_b,T_a] :
% 187.18/188.03 ( c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))
% 187.18/188.03 <=> ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
% 187.18/188.03 & c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_list__all2__conv__all__nth,axiom,
% 187.18/188.03 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] :
% 187.18/188.03 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2)
% 187.18/188.03 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)
% 187.18/188.03 & ! [B_i] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))
% 187.18/188.03 => hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i)),hAPP(hAPP(c_List_Onth(T_b),V_ys_2),B_i))) ) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_list__all2__nthD,axiom,
% 187.18/188.03 ! [V_p_2,V_ys_2,V_xs_2,V_P_2,T_b,T_a] :
% 187.18/188.03 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2)
% 187.18/188.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_p_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))
% 187.18/188.03 => hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_p_2)),hAPP(hAPP(c_List_Onth(T_b),V_ys_2),V_p_2))) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_list__all2__nthD2,axiom,
% 187.18/188.03 ! [V_p_2,V_ys_2,V_xs_2,V_P_2,T_b,T_a] :
% 187.18/188.03 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2)
% 187.18/188.03 => ( 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_ys_2)))
% 187.18/188.03 => hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_p_2)),hAPP(hAPP(c_List_Onth(T_b),V_ys_2),V_p_2))) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_list__all2__update__cong,axiom,
% 187.18/188.03 ! [V_y_2,V_x_2,V_ys_2,V_P_2,T_b,V_xs_2,T_a,V_i_2] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))
% 187.18/188.03 => ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2)
% 187.18/188.03 => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
% 187.18/188.03 => c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_i_2),V_x_2),hAPP(hAPP(c_List_Olist__update(T_b,V_ys_2),V_i_2),V_y_2)) ) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_list__all2__update__cong2,axiom,
% 187.18/188.03 ! [V_i_2,V_y_2,V_x_2,V_ys_2,V_xs_2,V_P_2,T_b,T_a] :
% 187.18/188.03 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2)
% 187.18/188.03 => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
% 187.18/188.03 => ( 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_ys_2)))
% 187.18/188.03 => c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_i_2),V_x_2),hAPP(hAPP(c_List_Olist__update(T_b,V_ys_2),V_i_2),V_y_2)) ) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_list__all2I,axiom,
% 187.18/188.03 ! [V_P_2,V_b_2,V_a_2,T_b,T_a] :
% 187.18/188.03 ( ! [B_x] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),B_x),hAPP(c_List_Oset(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_a_2),V_b_2))))
% 187.18/188.03 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_P_2),B_x)) )
% 187.18/188.03 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_a_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_b_2)
% 187.18/188.03 => c_List_Olist__all2(T_a,T_b,V_P_2,V_a_2,V_b_2) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_all__nth__imp__all__set,axiom,
% 187.18/188.03 ! [V_x_2,V_P_2,V_xs_2,T_a] :
% 187.18/188.03 ( ! [B_i] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))
% 187.18/188.03 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i))) )
% 187.18/188.03 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 187.18/188.03 => hBOOL(hAPP(V_P_2,V_x_2)) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_fun__left__comm_Ofold__set__remdups,axiom,
% 187.18/188.03 ! [V_xs_2,V_y_2,V_f_2,T_b,T_a] :
% 187.18/188.03 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2)
% 187.18/188.03 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_y_2),hAPP(c_List_Oset(T_a),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_a,hAPP(c_COMBC(T_a,T_b,T_b),V_f_2),V_y_2),c_List_Oremdups(T_a,V_xs_2)) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_map__removeAll__inj__on,axiom,
% 187.18/188.03 ! [V_xs_2,V_x_2,V_f_2,T_b,T_a] :
% 187.18/188.03 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 187.18/188.03 => hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),hAPP(c_List_OremoveAll(T_a,V_x_2),V_xs_2)) = hAPP(c_List_OremoveAll(T_b,hAPP(V_f_2,V_x_2)),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_distinct__remdups,axiom,
% 187.18/188.03 ! [V_xs,T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremdups(T_a,V_xs))) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_length__remdups__leq,axiom,
% 187.18/188.03 ! [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))) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_removeAll__id,axiom,
% 187.18/188.03 ! [V_xs_2,V_x_2,T_a] :
% 187.18/188.03 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 187.18/188.03 => hAPP(c_List_OremoveAll(T_a,V_x_2),V_xs_2) = V_xs_2 ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_distinct__remdups__id,axiom,
% 187.18/188.03 ! [V_xs,T_a] :
% 187.18/188.03 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 187.18/188.03 => c_List_Oremdups(T_a,V_xs) = V_xs ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_distinct__removeAll,axiom,
% 187.18/188.03 ! [V_x,V_xs,T_a] :
% 187.18/188.03 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 187.18/188.03 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_OremoveAll(T_a,V_x),V_xs))) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_remdups__id__iff__distinct,axiom,
% 187.18/188.03 ! [V_xs_2,T_a] :
% 187.18/188.03 ( c_List_Oremdups(T_a,V_xs_2) = V_xs_2
% 187.18/188.03 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_remove1__remdups,axiom,
% 187.18/188.03 ! [V_x,V_xs,T_a] :
% 187.18/188.03 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 187.18/188.03 => 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)) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_length__remdups__eq,axiom,
% 187.18/188.03 ! [V_xs_2,T_a] :
% 187.18/188.03 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oremdups(T_a,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)
% 187.18/188.03 <=> c_List_Oremdups(T_a,V_xs_2) = V_xs_2 ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_set__remdups,axiom,
% 187.18/188.03 ! [V_xs_2,T_a] : hAPP(c_List_Oset(T_a),c_List_Oremdups(T_a,V_xs_2)) = hAPP(c_List_Oset(T_a),V_xs_2) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_remdups__remdups,axiom,
% 187.18/188.03 ! [V_xs,T_a] : c_List_Oremdups(T_a,c_List_Oremdups(T_a,V_xs)) = c_List_Oremdups(T_a,V_xs) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_removeAll__append,axiom,
% 187.18/188.03 ! [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)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_remdups__eq__nil__iff,axiom,
% 187.18/188.03 ! [V_x_2,T_a] :
% 187.18/188.03 ( c_List_Oremdups(T_a,V_x_2) = c_List_Olist_ONil(T_a)
% 187.18/188.03 <=> V_x_2 = c_List_Olist_ONil(T_a) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_removeAll_Osimps_I1_J,axiom,
% 187.18/188.03 ! [V_x,T_a] : hAPP(c_List_OremoveAll(T_a,V_x),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_remdups__eq__nil__right__iff,axiom,
% 187.18/188.03 ! [V_x_2,T_a] :
% 187.18/188.03 ( c_List_Olist_ONil(T_a) = c_List_Oremdups(T_a,V_x_2)
% 187.18/188.03 <=> V_x_2 = c_List_Olist_ONil(T_a) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_remdups_Osimps_I1_J,axiom,
% 187.18/188.03 ! [T_a] : c_List_Oremdups(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_remdups__map__remdups,axiom,
% 187.18/188.03 ! [V_xs_2,V_f_2,T_b,T_a] : c_List_Oremdups(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_Oremdups(T_b,V_xs_2))) = c_List_Oremdups(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_removeAll_Osimps_I2_J,axiom,
% 187.18/188.03 ! [V_xs,T_a,V_y,V_x] :
% 187.18/188.03 ( ( V_x = V_y
% 187.18/188.03 => 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) )
% 187.18/188.03 & ( V_x != V_y
% 187.18/188.03 => 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)) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_distinct__remove1__removeAll,axiom,
% 187.18/188.03 ! [V_x,V_xs,T_a] :
% 187.18/188.03 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 187.18/188.03 => c_List_Oremove1(T_a,V_x,V_xs) = hAPP(c_List_OremoveAll(T_a,V_x),V_xs) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_remdups_Osimps_I2_J,axiom,
% 187.18/188.03 ! [V_xs_2,V_x_2,T_a] :
% 187.18/188.03 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 187.18/188.03 => c_List_Oremdups(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = c_List_Oremdups(T_a,V_xs_2) )
% 187.18/188.03 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 187.18/188.03 => c_List_Oremdups(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Oremdups(T_a,V_xs_2)) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_length__remdups__card__conv,axiom,
% 187.18/188.03 ! [V_xs_2,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oremdups(T_a,V_xs_2)) = hAPP(c_Finite__Set_Ocard(T_a),hAPP(c_List_Oset(T_a),V_xs_2)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_map__removeAll__inj,axiom,
% 187.18/188.03 ! [V_xs_2,V_x_2,V_f_2,T_b,T_a] :
% 187.18/188.03 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 187.18/188.03 => hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),hAPP(c_List_OremoveAll(T_a,V_x_2),V_xs_2)) = hAPP(c_List_OremoveAll(T_b,hAPP(V_f_2,V_x_2)),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_set__removeAll,axiom,
% 187.18/188.03 ! [V_xs_2,V_x_2,T_a] : hAPP(c_List_Oset(T_a),hAPP(c_List_OremoveAll(T_a,V_x_2),V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_length__remdups__concat,axiom,
% 187.18/188.03 ! [V_xss_2,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oremdups(T_a,c_List_Oconcat(T_a,V_xss_2))) = hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xss_2)),c_List_Oset(T_a))) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_sorted__list__of__set__sort__remdups,axiom,
% 187.18/188.03 ! [V_xs_2,T_a] :
% 187.18/188.03 ( class_Orderings_Olinorder(T_a)
% 187.18/188.03 => c_List_Olinorder__class_Osorted__list__of__set(T_a,hAPP(c_List_Oset(T_a),V_xs_2)) = c_List_Olinorder__class_Osort__key(T_a,T_a,c_COMBI(T_a),c_List_Oremdups(T_a,V_xs_2)) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_concat_Osimps_I2_J,axiom,
% 187.18/188.03 ! [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)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_map__concat,axiom,
% 187.18/188.03 ! [V_xs_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_Oconcat(T_b,V_xs_2)) = c_List_Oconcat(T_a,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_a)),hAPP(c_List_Omap(T_b,T_a),V_f_2)),V_xs_2)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_concat__eq__Nil__conv,axiom,
% 187.18/188.03 ! [V_xss_2,T_a] :
% 187.18/188.03 ( c_List_Oconcat(T_a,V_xss_2) = c_List_Olist_ONil(T_a)
% 187.18/188.03 <=> ! [B_x] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xss_2)))
% 187.18/188.03 => B_x = c_List_Olist_ONil(T_a) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_Nil__eq__concat__conv,axiom,
% 187.18/188.03 ! [V_xss_2,T_a] :
% 187.18/188.03 ( c_List_Olist_ONil(T_a) = c_List_Oconcat(T_a,V_xss_2)
% 187.18/188.03 <=> ! [B_x] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xss_2)))
% 187.18/188.03 => B_x = c_List_Olist_ONil(T_a) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_concat_Osimps_I1_J,axiom,
% 187.18/188.03 ! [T_a] : c_List_Oconcat(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(T_a) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_sort__key__simps_I1_J,axiom,
% 187.18/188.03 ! [V_f_2,T_a,T_b] :
% 187.18/188.03 ( class_Orderings_Olinorder(T_b)
% 187.18/188.03 => c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_concat__conv__foldl,axiom,
% 187.18/188.03 ! [V_xss_2,T_a] : c_List_Oconcat(T_a,V_xss_2) = hAPP(c_List_Ofoldl(tc_List_Olist(T_a),tc_List_Olist(T_a),c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_xss_2) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_foldl__conv__concat,axiom,
% 187.18/188.03 ! [V_xss_2,V_xs_2,T_a] : hAPP(c_List_Ofoldl(tc_List_Olist(T_a),tc_List_Olist(T_a),c_List_Oappend(T_a),V_xs_2),V_xss_2) = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),c_List_Oconcat(T_a,V_xss_2)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_set__sort,axiom,
% 187.18/188.03 ! [V_xs_2,V_f_2,T_a,T_b] :
% 187.18/188.03 ( class_Orderings_Olinorder(T_b)
% 187.18/188.03 => hAPP(c_List_Oset(T_a),c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,V_xs_2)) = hAPP(c_List_Oset(T_a),V_xs_2) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_length__sort,axiom,
% 187.18/188.03 ! [V_xs_2,V_f_2,T_a,T_b] :
% 187.18/188.03 ( class_Orderings_Olinorder(T_b)
% 187.18/188.03 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_distinct__sort,axiom,
% 187.18/188.03 ! [V_xs_2,V_f_2,T_a,T_b] :
% 187.18/188.03 ( class_Orderings_Olinorder(T_b)
% 187.18/188.03 => ( hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,V_xs_2)))
% 187.18/188.03 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_length__concat,axiom,
% 187.18/188.03 ! [V_xss_2,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oconcat(T_a,V_xss_2)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),V_xss_2)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_set__concat,axiom,
% 187.18/188.03 ! [V_xs_2,T_a] : hAPP(c_List_Oset(T_a),c_List_Oconcat(T_a,V_xs_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2)),c_List_Oset(T_a)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_sort__key__simps_I2_J,axiom,
% 187.18/188.03 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] :
% 187.18/188.03 ( class_Orderings_Olinorder(T_b)
% 187.18/188.03 => c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_x_2),c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,V_xs_2)) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_concat__append,axiom,
% 187.18/188.03 ! [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)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_sort__foldl__insort,axiom,
% 187.18/188.03 ! [V_xs_2,T_a] :
% 187.18/188.03 ( class_Orderings_Olinorder(T_a)
% 187.18/188.03 => c_List_Olinorder__class_Osort__key(T_a,T_a,c_COMBI(T_a),V_xs_2) = hAPP(c_List_Ofoldl(tc_List_Olist(T_a),T_a,hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a))),c_List_Olist_ONil(T_a)),V_xs_2) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_concat__injective,axiom,
% 187.18/188.03 ! [V_ys_2,V_xs_2,T_a] :
% 187.18/188.03 ( c_List_Oconcat(T_a,V_xs_2) = c_List_Oconcat(T_a,V_ys_2)
% 187.18/188.03 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),V_ys_2)
% 187.18/188.03 => ( ! [B_x] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),B_x),hAPP(c_List_Oset(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2))))
% 187.18/188.03 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_Nat_Onat),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_a),tc_Nat_Onat),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_List_Olist(T_a)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_a)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),B_x)) )
% 187.18/188.03 => V_xs_2 = V_ys_2 ) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_concat__eq__concat__iff,axiom,
% 187.18/188.03 ! [V_ys_2,V_xs_2,T_a] :
% 187.18/188.03 ( ! [B_x] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),B_x),hAPP(c_List_Oset(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2))))
% 187.18/188.03 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_Nat_Onat),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_a),tc_Nat_Onat),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_List_Olist(T_a)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_a)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),B_x)) )
% 187.18/188.03 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),V_ys_2)
% 187.18/188.03 => ( c_List_Oconcat(T_a,V_xs_2) = c_List_Oconcat(T_a,V_ys_2)
% 187.18/188.03 <=> V_xs_2 = V_ys_2 ) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_concat__map__singleton,axiom,
% 187.18/188.03 ! [V_xs_2,V_f_2,T_b,T_a] : c_List_Oconcat(T_a,hAPP(hAPP(c_List_Omap(T_b,tc_List_Olist(T_a)),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_COMBB(T_a,tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),T_b),c_List_Olist_OCons(T_a)),V_f_2)),c_List_Olist_ONil(T_a))),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_n__lists_Osimps_I2_J,axiom,
% 187.18/188.03 ! [V_xs_2,V_n_2,T_a] : c_Enum_On__lists(T_a,hAPP(c_Nat_OSuc,V_n_2),V_xs_2) = c_List_Oconcat(tc_List_Olist(T_a),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_List_Olist(T_a)),tc_fun(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a))),tc_List_Olist(T_a)),c_List_Omap(T_a,tc_List_Olist(T_a))),hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)))),V_xs_2)),c_Enum_On__lists(T_a,V_n_2,V_xs_2))) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_transpose_Osimps_I3_J,axiom,
% 187.18/188.03 ! [V_xss_2,V_xs_2,V_x_2,T_a] : c_List_Otranspose(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),V_xss_2)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Oconcat(T_a,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_Olist__case(tc_List_Olist(T_a),T_a,c_List_Olist_ONil(T_a),hAPP(hAPP(c_COMBB(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),T_a),c_COMBK(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)),c_List_Olist_ONil(T_a))))),V_xss_2)))),c_List_Otranspose(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),V_xs_2),c_List_Oconcat(tc_List_Olist(T_a),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_a)),T_a,c_List_Olist_ONil(tc_List_Olist(T_a)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a))),T_a),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a)),tc_List_Olist(tc_List_Olist(T_a))),c_List_Olist_OCons(tc_List_Olist(T_a))),c_List_Olist_ONil(tc_List_Olist(T_a)))))),V_xss_2))))) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_transpose__aux__filter__head,axiom,
% 187.18/188.03 ! [V_xss_2,T_a] : c_List_Oconcat(T_a,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_Olist__case(tc_List_Olist(T_a),T_a,c_List_Olist_ONil(T_a),hAPP(hAPP(c_COMBB(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),T_a),c_COMBK(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)),c_List_Olist_ONil(T_a))))),V_xss_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),T_a),c_List_Ohd(T_a)),hAPP(c_List_Ofilter(tc_List_Olist(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_a)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_a)))),V_xss_2)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_filter__concat,axiom,
% 187.18/188.03 ! [V_xs_2,V_p_2,T_a] : hAPP(c_List_Ofilter(T_a,V_p_2),c_List_Oconcat(T_a,V_xs_2)) = c_List_Oconcat(T_a,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Ofilter(T_a,V_p_2)),V_xs_2)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_filter__sort,axiom,
% 187.18/188.03 ! [V_xs_2,V_f_2,V_P_2,T_a,T_b] :
% 187.18/188.03 ( class_Orderings_Olinorder(T_b)
% 187.18/188.03 => hAPP(c_List_Ofilter(T_a,V_P_2),c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,V_xs_2)) = c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2)) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_transpose_Osimps_I2_J,axiom,
% 187.18/188.03 ! [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) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_partition__filter2,axiom,
% 187.18/188.03 ! [V_xs_2,V_P_2,T_a] : hAPP(c_Product__Type_Osnd(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Opartition(T_a,V_P_2,V_xs_2)) = hAPP(c_List_Ofilter(T_a,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,T_a,c_fNot),V_P_2)),V_xs_2) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_distinct__filter,axiom,
% 187.18/188.03 ! [V_P_2,V_xs_2,T_a] :
% 187.18/188.03 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 187.18/188.03 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2))) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_sum__length__filter__compl,axiom,
% 187.18/188.03 ! [V_xs_2,V_P_2,T_a] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Ofilter(T_a,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),V_P_2)),V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_length__filter__le,axiom,
% 187.18/188.03 ! [V_xs_2,V_P_2,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)),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_filter__is__subset,axiom,
% 187.18/188.03 ! [V_xs_2,V_P_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2))),hAPP(c_List_Oset(T_a),V_xs_2))) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_filter__id__conv,axiom,
% 187.18/188.03 ! [V_xs_2,V_P_2,T_a] :
% 187.18/188.03 ( hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) = V_xs_2
% 187.18/188.03 <=> ! [B_x] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 187.18/188.03 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_filter__insort__triv,axiom,
% 187.18/188.03 ! [V_xs_2,V_f_2,T_a,V_x_2,V_P_2,T_b] :
% 187.18/188.03 ( class_Orderings_Olinorder(T_b)
% 187.18/188.03 => ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 187.18/188.03 => hAPP(c_List_Ofilter(T_a,V_P_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_x_2),V_xs_2)) = hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_filter__remove1,axiom,
% 187.18/188.03 ! [V_xs_2,V_x_2,V_Q_2,T_a] : hAPP(c_List_Ofilter(T_a,V_Q_2),c_List_Oremove1(T_a,V_x_2,V_xs_2)) = c_List_Oremove1(T_a,V_x_2,hAPP(c_List_Ofilter(T_a,V_Q_2),V_xs_2)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_remove1__filter__not,axiom,
% 187.18/188.03 ! [V_xs_2,T_a,V_x_2,V_P_2] :
% 187.18/188.03 ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 187.18/188.03 => c_List_Oremove1(T_a,V_x_2,hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2)) = hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_filter__filter,axiom,
% 187.18/188.03 ! [V_xs_2,V_Q_2,V_P_2,T_a] : hAPP(c_List_Ofilter(T_a,V_P_2),hAPP(c_List_Ofilter(T_a,V_Q_2),V_xs_2)) = hAPP(c_List_Ofilter(T_a,hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),V_Q_2)),V_P_2)),V_xs_2) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_partition__filter1,axiom,
% 187.18/188.03 ! [V_xs_2,V_P_2,T_a] : hAPP(c_Product__Type_Ofst(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Opartition(T_a,V_P_2,V_xs_2)) = hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_filter__append,axiom,
% 187.18/188.03 ! [V_ys_2,V_xs_2,V_P_2,T_a] : hAPP(c_List_Ofilter(T_a,V_P_2),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2)),hAPP(c_List_Ofilter(T_a,V_P_2),V_ys_2)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_filter_Osimps_I1_J,axiom,
% 187.18/188.03 ! [V_P_2,T_a] : hAPP(c_List_Ofilter(T_a,V_P_2),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_transpose_Osimps_I1_J,axiom,
% 187.18/188.03 ! [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)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_filter__empty__conv,axiom,
% 187.18/188.03 ! [V_xs_2,V_P_2,T_a] :
% 187.18/188.03 ( hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) = c_List_Olist_ONil(T_a)
% 187.18/188.03 <=> ! [B_x] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 187.18/188.03 => ~ hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_filter_Osimps_I2_J,axiom,
% 187.18/188.03 ! [V_xs_2,T_a,V_x_2,V_P_2] :
% 187.18/188.03 ( ( hBOOL(hAPP(V_P_2,V_x_2))
% 187.18/188.03 => hAPP(c_List_Ofilter(T_a,V_P_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2)) )
% 187.18/188.03 & ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 187.18/188.03 => hAPP(c_List_Ofilter(T_a,V_P_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_filter__map,axiom,
% 187.18/188.03 ! [V_xs_2,V_f_2,T_b,V_P_2,T_a] : hAPP(c_List_Ofilter(T_a,V_P_2),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(c_List_Ofilter(T_b,hAPP(c_Fun_Ocomp(T_a,tc_HOL_Obool,T_b,V_P_2),V_f_2)),V_xs_2)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_removeAll__filter__not__eq,axiom,
% 187.18/188.03 ! [V_x_2,T_a] : c_List_OremoveAll(T_a,V_x_2) = c_List_Ofilter(T_a,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(c_fequal,V_x_2))) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_remdups__filter,axiom,
% 187.18/188.03 ! [V_xs_2,V_P_2,T_a] : c_List_Oremdups(T_a,hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2)) = hAPP(c_List_Ofilter(T_a,V_P_2),c_List_Oremdups(T_a,V_xs_2)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_removeAll__filter__not,axiom,
% 187.18/188.03 ! [V_xs_2,T_a,V_x_2,V_P_2] :
% 187.18/188.03 ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 187.18/188.03 => hAPP(c_List_OremoveAll(T_a,V_x_2),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2)) = hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_nth__transpose,axiom,
% 187.18/188.03 ! [V_xs_2,T_a,V_i_2] :
% 187.18/188.03 ( 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_a))),c_List_Otranspose(T_a,V_xs_2))))
% 187.18/188.03 => hAPP(hAPP(c_List_Onth(tc_List_Olist(T_a)),c_List_Otranspose(T_a,V_xs_2)),V_i_2) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),T_a),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_Nat_Onat,T_a),c_List_Onth(T_a)),V_i_2)),hAPP(c_List_Ofilter(tc_List_Olist(T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_a)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),V_xs_2)) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_transpose__map__map,axiom,
% 187.18/188.03 ! [V_xs_2,V_f_2,T_b,T_a] : c_List_Otranspose(T_a,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_a)),hAPP(c_List_Omap(T_b,T_a),V_f_2)),V_xs_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_a)),hAPP(c_List_Omap(T_b,T_a),V_f_2)),c_List_Otranspose(T_b,V_xs_2)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_set__filter,axiom,
% 187.18/188.03 ! [V_xs_2,V_P_2,T_a] : hAPP(c_List_Oset(T_a),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2)) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),hAPP(c_List_Oset(T_a),V_xs_2)))),V_P_2)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_length__filter__map,axiom,
% 187.18/188.03 ! [V_xs_2,V_f_2,T_b,V_P_2,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Ofilter(T_a,V_P_2),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,hAPP(c_Fun_Ocomp(T_a,tc_HOL_Obool,T_b,V_P_2),V_f_2)),V_xs_2)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_length__filter__less,axiom,
% 187.18/188.03 ! [V_P_2,V_xs_2,V_x_2,T_a] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 187.18/188.03 => ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 187.18/188.03 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_partition__filter__conv,axiom,
% 187.18/188.03 ! [V_xs_2,V_f_2,T_a] : c_List_Opartition(T_a,V_f_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(c_List_Ofilter(T_a,V_f_2),V_xs_2)),hAPP(c_List_Ofilter(T_a,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,T_a,c_fNot),V_f_2)),V_xs_2)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_set__minus__filter__out,axiom,
% 187.18/188.03 ! [V_y_2,V_xs_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = hAPP(c_List_Oset(T_a),hAPP(c_List_Ofilter(T_a,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_y_2))),V_xs_2)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_filter__in__sublist,axiom,
% 187.18/188.03 ! [V_s_2,V_xs_2,T_a] :
% 187.18/188.03 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 187.18/188.03 => hAPP(c_List_Ofilter(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),hAPP(c_List_Oset(T_a),c_List_Osublist(T_a,V_xs_2,V_s_2)))),V_xs_2) = c_List_Osublist(T_a,V_xs_2,V_s_2) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_transpose__empty,axiom,
% 187.18/188.03 ! [V_xs_2,T_a] :
% 187.18/188.03 ( c_List_Otranspose(T_a,V_xs_2) = c_List_Olist_ONil(tc_List_Olist(T_a))
% 187.18/188.03 <=> ! [B_x] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2)))
% 187.18/188.03 => B_x = c_List_Olist_ONil(T_a) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_length__filter__conv__card,axiom,
% 187.18/188.03 ! [V_xs_2,V_p_2,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Ofilter(T_a,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_a)),V_xs_2)))),hAPP(hAPP(c_COMBB(T_a,tc_HOL_Obool,tc_Nat_Onat),V_p_2),hAPP(c_List_Onth(T_a),V_xs_2))))) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_transpose__aux__filter__tail,axiom,
% 187.18/188.03 ! [V_xss_2,T_a] : c_List_Oconcat(tc_List_Olist(T_a),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_a)),T_a,c_List_Olist_ONil(tc_List_Olist(T_a)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a))),T_a),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a)),tc_List_Olist(tc_List_Olist(T_a))),c_List_Olist_OCons(tc_List_Olist(T_a))),c_List_Olist_ONil(tc_List_Olist(T_a)))))),V_xss_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Otl(T_a)),hAPP(c_List_Ofilter(tc_List_Olist(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_a)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_a)))),V_xss_2)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_transpose_Opsimps_I3_J,axiom,
% 187.18/188.03 ! [V_xss_2,V_xs_2,V_x_2,T_a] :
% 187.18/188.03 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_a)),c_List_Otranspose__rel(T_a)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),V_xss_2)))
% 187.18/188.03 => c_List_Otranspose(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),V_xss_2)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Oconcat(T_a,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_Olist__case(tc_List_Olist(T_a),T_a,c_List_Olist_ONil(T_a),hAPP(hAPP(c_COMBB(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),T_a),c_COMBK(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)),c_List_Olist_ONil(T_a))))),V_xss_2)))),c_List_Otranspose(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),V_xs_2),c_List_Oconcat(tc_List_Olist(T_a),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_a)),T_a,c_List_Olist_ONil(tc_List_Olist(T_a)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a))),T_a),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a)),tc_List_Olist(tc_List_Olist(T_a))),c_List_Olist_OCons(tc_List_Olist(T_a))),c_List_Olist_ONil(tc_List_Olist(T_a)))))),V_xss_2))))) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_map__filter__def,axiom,
% 187.18/188.03 ! [V_xs_2,V_f_2,T_a,T_b] : c_List_Omap__filter(T_b,T_a,V_f_2,V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,T_a),hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_a),T_a,T_b,c_Option_Othe(T_a)),V_f_2)),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,tc_Option_Ooption(T_a),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_a),tc_fun(tc_Option_Ooption(T_a),tc_HOL_Obool),T_b),c_fequal),V_f_2)),c_Option_Ooption_ONone(T_a)))),V_xs_2)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_map__filter__simps_I2_J,axiom,
% 187.18/188.03 ! [V_f_2,T_a,T_b] : c_List_Omap__filter(T_b,T_a,V_f_2,c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_a) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_map__of__filter__in,axiom,
% 187.18/188.03 ! [V_P_2,V_z_2,V_k_2,V_xs_2,T_a,T_b] :
% 187.18/188.03 ( hAPP(hAPP(c_Map_Omap__of(T_b,T_a),V_xs_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_z_2)
% 187.18/188.03 => ( hBOOL(hAPP(hAPP(V_P_2,V_k_2),V_z_2))
% 187.18/188.03 => hAPP(hAPP(c_Map_Omap__of(T_b,T_a),hAPP(c_List_Ofilter(tc_prod(T_b,T_a),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_a,tc_HOL_Obool),V_P_2)),V_xs_2)),V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_z_2) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_map__filter__simps_I1_J,axiom,
% 187.18/188.03 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] : c_List_Omap__filter(T_b,T_a,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(c_Option_Ooption_Ooption__case(tc_List_Olist(T_a),T_a,c_List_Omap__filter(T_b,T_a,V_f_2,V_xs_2),hAPP(hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)),c_List_Omap__filter(T_b,T_a,V_f_2,V_xs_2))),hAPP(V_f_2,V_x_2)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_sublist__shift__lemma__Suc,axiom,
% 187.18/188.03 ! [V_is_2,V_xs_2,V_P_2,T_a] : hAPP(hAPP(c_List_Omap(tc_prod(T_a,tc_Nat_Onat),T_a),c_Product__Type_Ofst(T_a,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_a,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(T_a,tc_Nat_Onat)),V_P_2),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_prod(T_a,tc_Nat_Onat)),c_Nat_OSuc),c_Product__Type_Osnd(T_a,tc_Nat_Onat)))),hAPP(hAPP(c_List_Ozip(T_a,tc_Nat_Onat),V_xs_2),V_is_2))) = hAPP(hAPP(c_List_Omap(tc_prod(T_a,tc_Nat_Onat),T_a),c_Product__Type_Ofst(T_a,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_a,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(T_a,tc_Nat_Onat)),V_P_2),c_Product__Type_Osnd(T_a,tc_Nat_Onat))),hAPP(hAPP(c_List_Ozip(T_a,tc_Nat_Onat),V_xs_2),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),V_is_2)))) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_select__weigth__drop__zero,axiom,
% 187.18/188.03 ! [V_xs_2,T_a] : c_Random_Oselect__weight(T_a,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,T_a)),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_a,V_xs_2) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_pick__drop__zero,axiom,
% 187.18/188.03 ! [V_xs_2,T_a] : c_Random_Opick(T_a,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,T_a)),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_a,V_xs_2) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_transpose_Opsimps_I1_J,axiom,
% 187.18/188.03 ! [T_a] :
% 187.18/188.03 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_a)),c_List_Otranspose__rel(T_a)),c_List_Olist_ONil(tc_List_Olist(T_a))))
% 187.18/188.03 => c_List_Otranspose(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(tc_List_Olist(T_a)) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_map__filter__map__filter,axiom,
% 187.18/188.03 ! [V_xs_2,V_P_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)) = c_List_Omap__filter(T_b,T_a,hAPP(hAPP(c_COMBC(T_b,tc_Option_Ooption(T_a),tc_Option_Ooption(T_a)),hAPP(hAPP(c_COMBS(T_b,tc_Option_Ooption(T_a),tc_fun(tc_Option_Ooption(T_a),tc_Option_Ooption(T_a))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(T_a),tc_fun(tc_Option_Ooption(T_a),tc_Option_Ooption(T_a))),T_b),c_If(tc_Option_Ooption(T_a))),V_P_2)),hAPP(hAPP(c_COMBB(T_a,tc_Option_Ooption(T_a),T_b),c_Option_Ooption_OSome(T_a)),V_f_2))),c_Option_Ooption_ONone(T_a)),V_xs_2) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_transpose_Opsimps_I2_J,axiom,
% 187.18/188.03 ! [V_xss_2,T_a] :
% 187.18/188.03 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_a)),c_List_Otranspose__rel(T_a)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),V_xss_2)))
% 187.18/188.03 => c_List_Otranspose(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),V_xss_2)) = c_List_Otranspose(T_a,V_xss_2) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_transpose__max__length,axiom,
% 187.18/188.03 ! [V_xs_2,T_a] : c_List_Ofoldr(tc_List_Olist(T_a),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_a)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),c_List_Otranspose(T_a,V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),hAPP(c_List_Ofilter(tc_List_Olist(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_a)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_a)))),V_xs_2)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_transpose__aux__max,axiom,
% 187.18/188.03 ! [V_xss_2,T_b,V_xs_2,T_a] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),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_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_a)),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)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),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_b)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),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),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_foldr__append,axiom,
% 187.18/188.03 ! [V_a_2,V_ys_2,V_xs_2,V_f_2,T_a,T_b] : c_List_Ofoldr(T_b,T_a,V_f_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2),V_a_2) = c_List_Ofoldr(T_b,T_a,V_f_2,V_xs_2,c_List_Ofoldr(T_b,T_a,V_f_2,V_ys_2,V_a_2)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_foldr_Osimps_I1_J,axiom,
% 187.18/188.03 ! [V_a_2,V_f_2,T_a,T_b] : c_List_Ofoldr(T_b,T_a,V_f_2,c_List_Olist_ONil(T_b),V_a_2) = V_a_2 ).
% 187.18/188.03
% 187.18/188.03 fof(fact_foldr_Osimps_I2_J,axiom,
% 187.18/188.03 ! [V_a_2,V_xs_2,V_x_2,V_f_2,T_a,T_b] : c_List_Ofoldr(T_b,T_a,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2),V_a_2) = hAPP(hAPP(V_f_2,V_x_2),c_List_Ofoldr(T_b,T_a,V_f_2,V_xs_2,V_a_2)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_foldr__conv__foldl,axiom,
% 187.18/188.03 ! [V_a_2,V_xs_2,T_a] :
% 187.18/188.03 ( class_Groups_Oab__semigroup__add(T_a)
% 187.18/188.03 => c_List_Ofoldr(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),V_xs_2,V_a_2) = hAPP(c_List_Ofoldl(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_xs_2) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_foldr__map,axiom,
% 187.18/188.03 ! [V_a_2,V_xs_2,V_f_2,T_c,V_g_2,T_a,T_b] : c_List_Ofoldr(T_b,T_a,V_g_2,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2),V_a_2) = c_List_Ofoldr(T_c,T_a,hAPP(c_Fun_Ocomp(T_b,tc_fun(T_a,T_a),T_c,V_g_2),V_f_2),V_xs_2,V_a_2) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_foldl__foldr1,axiom,
% 187.18/188.03 ! [V_xs_2,T_a] :
% 187.18/188.03 ( class_Groups_Omonoid__add(T_a)
% 187.18/188.03 => hAPP(c_List_Ofoldl(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_xs_2) = c_List_Ofoldr(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),V_xs_2,c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_foldl__foldr1__lemma,axiom,
% 187.18/188.03 ! [V_xs_2,V_a_2,T_a] :
% 187.18/188.03 ( class_Groups_Omonoid__add(T_a)
% 187.18/188.03 => hAPP(c_List_Ofoldl(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_xs_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),c_List_Ofoldr(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),V_xs_2,c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_length__transpose,axiom,
% 187.18/188.03 ! [V_xs_2,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),c_List_Otranspose(T_a,V_xs_2)) = c_List_Ofoldr(tc_List_Olist(T_a),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_a)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),V_xs_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_sublist__def,axiom,
% 187.18/188.03 ! [V_A_2,V_xs_2,T_a] : c_List_Osublist(T_a,V_xs_2,V_A_2) = hAPP(hAPP(c_List_Omap(tc_prod(T_a,tc_Nat_Onat),T_a),c_Product__Type_Ofst(T_a,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_a,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_a,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_a,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(T_a,tc_Nat_Onat))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_a,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_a)),V_xs_2))))) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_sublist__shift__lemma,axiom,
% 187.18/188.03 ! [V_i_2,V_xs_2,V_A_2,T_a] : hAPP(hAPP(c_List_Omap(tc_prod(T_a,tc_Nat_Onat),T_a),c_Product__Type_Ofst(T_a,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_a,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_a,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_a,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(T_a,tc_Nat_Onat))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_a,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_a)),V_xs_2)))))) = hAPP(hAPP(c_List_Omap(tc_prod(T_a,tc_Nat_Onat),T_a),c_Product__Type_Ofst(T_a,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_a,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_a,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_a,tc_Nat_Onat)),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(T_a,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_a,tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Product__Type_Osnd(T_a,tc_Nat_Onat))),V_i_2))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_a,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_a)),V_xs_2))))) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_set__upt,axiom,
% 187.18/188.03 ! [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) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_atLeastLessThan__upt,axiom,
% 187.18/188.03 ! [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)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_length__upt,axiom,
% 187.18/188.03 ! [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) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_upt__Suc,axiom,
% 187.18/188.03 ! [V_j,V_i] :
% 187.18/188.03 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 187.18/188.03 => 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))) )
% 187.18/188.03 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 187.18/188.03 => c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_upt__Suc__append,axiom,
% 187.18/188.03 ! [V_j,V_i] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 187.18/188.03 => 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))) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_upt__rec,axiom,
% 187.18/188.03 ! [V_j,V_i] :
% 187.18/188.03 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 187.18/188.03 => 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)) )
% 187.18/188.03 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 187.18/188.03 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_upt__conv__Cons,axiom,
% 187.18/188.03 ! [V_j,V_i] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 187.18/188.03 => 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)) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_upt__conv__Nil,axiom,
% 187.18/188.03 ! [V_i,V_j] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i))
% 187.18/188.03 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_upt__eq__Nil__conv,axiom,
% 187.18/188.03 ! [V_j_2,V_i_2] :
% 187.18/188.03 ( c_List_Oupt(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Nat_Onat)
% 187.18/188.03 <=> ( V_j_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.18/188.03 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_upt__0,axiom,
% 187.18/188.03 ! [V_i] : c_List_Oupt(V_i,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_upt__add__eq__append,axiom,
% 187.18/188.03 ! [V_k,V_j,V_i] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 187.18/188.03 => 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))) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_sorted__list__of__set__range,axiom,
% 187.18/188.03 ! [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) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_take__upt,axiom,
% 187.18/188.03 ! [V_n,V_m,V_i] :
% 187.18/188.03 ( 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))
% 187.18/188.03 => 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)) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_hd__upt,axiom,
% 187.18/188.03 ! [V_j,V_i] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 187.18/188.03 => hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(V_i,V_j)) = V_i ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_drop__upt,axiom,
% 187.18/188.03 ! [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) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_distinct__upt,axiom,
% 187.18/188.03 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(V_i,V_j))) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_upt__rec__number__of,axiom,
% 187.18/188.03 ! [V_n,V_m] :
% 187.18/188.03 ( ( 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)))
% 187.18/188.03 => 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))) )
% 187.18/188.03 & ( ~ 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)))
% 187.18/188.03 => 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) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_upt__eq__Cons__conv,axiom,
% 187.18/188.03 ! [V_xs_2,V_x_2,V_j_2,V_i_2] :
% 187.18/188.03 ( c_List_Oupt(V_i_2,V_j_2) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_x_2),V_xs_2)
% 187.18/188.03 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_j_2))
% 187.18/188.03 & V_i_2 = V_x_2
% 187.18/188.03 & 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 ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_last__upt,axiom,
% 187.18/188.03 ! [V_j,V_i] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 187.18/188.03 => 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)) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_map__Suc__upt,axiom,
% 187.18/188.03 ! [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)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_atLeastAtMost__upt,axiom,
% 187.18/188.03 ! [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))) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_atLeast__upt,axiom,
% 187.18/188.03 ! [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)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_nth__upt,axiom,
% 187.18/188.03 ! [V_j,V_k,V_i] :
% 187.18/188.03 ( 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))
% 187.18/188.03 => 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) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_greaterThanAtMost__upt,axiom,
% 187.18/188.03 ! [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))) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_greaterThanLessThan__upt,axiom,
% 187.18/188.03 ! [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)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_atMost__upto,axiom,
% 187.18/188.03 ! [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))) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_map__nth,axiom,
% 187.18/188.03 ! [V_xs_2,T_a] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_a),hAPP(c_List_Onth(T_a),V_xs_2)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) = V_xs_2 ).
% 187.18/188.03
% 187.18/188.03 fof(fact_setsum__set__upt__conv__listsum__nat,axiom,
% 187.18/188.03 ! [V_n_2,V_m_2,V_f_2,T_a] :
% 187.18/188.03 ( class_Groups_Ocomm__monoid__add(T_a)
% 187.18/188.03 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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_a),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_a),V_f_2),c_List_Oupt(V_m_2,V_n_2))) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_interv__listsum__conv__setsum__set__nat,axiom,
% 187.18/188.03 ! [V_n_2,V_m_2,V_f_2,T_a] :
% 187.18/188.03 ( class_Groups_Ocomm__monoid__add(T_a)
% 187.18/188.03 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_a),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_a),V_f_2),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_m_2,V_n_2))) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_nth__map__upt,axiom,
% 187.18/188.03 ! [V_f_2,T_a,V_m_2,V_n_2,V_i_2] :
% 187.18/188.03 ( 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)))
% 187.18/188.03 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_a),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)) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_transpose__rectangle,axiom,
% 187.18/188.03 ! [V_n_2,T_a,V_xs_2] :
% 187.18/188.03 ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_a))
% 187.18/188.03 => V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 187.18/188.03 => ( ! [B_i] :
% 187.18/188.03 ( 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_a))),V_xs_2)))
% 187.18/188.03 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_a)),V_xs_2),B_i)) = V_n_2 )
% 187.18/188.03 => c_List_Otranspose(T_a,V_xs_2) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(T_a)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(T_a)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,T_a),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(T_a)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,T_a)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,T_a),hAPP(hAPP(c_COMBB(tc_List_Olist(T_a),tc_fun(tc_Nat_Onat,T_a),tc_Nat_Onat),c_List_Onth(T_a)),hAPP(c_List_Onth(tc_List_Olist(T_a)),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_a))),V_xs_2)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_insort__key__remove1,axiom,
% 187.18/188.03 ! [V_f_2,V_xs_2,V_a_2,T_a,T_b] :
% 187.18/188.03 ( class_Orderings_Olinorder(T_b)
% 187.18/188.03 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 187.18/188.03 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2))
% 187.18/188.03 => ( hAPP(c_List_Ohd(T_a),hAPP(c_List_Ofilter(T_a,hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,T_a),hAPP(c_fequal,hAPP(V_f_2,V_a_2))),V_f_2)),V_xs_2)) = V_a_2
% 187.18/188.03 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_a_2),c_List_Oremove1(T_a,V_a_2,V_xs_2)) = V_xs_2 ) ) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_sorted_ONil,axiom,
% 187.18/188.03 ! [T_a] :
% 187.18/188.03 ( class_Orderings_Olinorder(T_a)
% 187.18/188.03 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_sorted__single,axiom,
% 187.18/188.03 ! [V_x,T_a] :
% 187.18/188.03 ( class_Orderings_Olinorder(T_a)
% 187.18/188.03 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_sorted__upt,axiom,
% 187.18/188.03 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(V_i,V_j)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_sorted__Cons,axiom,
% 187.18/188.03 ! [V_xs_2,V_x_2,T_a] :
% 187.18/188.03 ( class_Orderings_Olinorder(T_a)
% 187.18/188.03 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))
% 187.18/188.03 <=> ( c_List_Olinorder__class_Osorted(T_a,V_xs_2)
% 187.18/188.03 & ! [B_x] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 187.18/188.03 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_x)) ) ) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_sorted__sort,axiom,
% 187.18/188.03 ! [V_xs_2,T_a] :
% 187.18/188.03 ( class_Orderings_Olinorder(T_a)
% 187.18/188.03 => c_List_Olinorder__class_Osorted(T_a,c_List_Olinorder__class_Osort__key(T_a,T_a,c_COMBI(T_a),V_xs_2)) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_sorted__insort,axiom,
% 187.18/188.03 ! [V_xs_2,V_x_2,T_a] :
% 187.18/188.03 ( class_Orderings_Olinorder(T_a)
% 187.18/188.03 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_x_2),V_xs_2))
% 187.18/188.03 <=> c_List_Olinorder__class_Osorted(T_a,V_xs_2) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_sorted__drop,axiom,
% 187.18/188.03 ! [V_n,V_xs,T_a] :
% 187.18/188.03 ( class_Orderings_Olinorder(T_a)
% 187.18/188.03 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 187.18/188.03 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_sorted__remove1,axiom,
% 187.18/188.03 ! [V_a,V_xs,T_a] :
% 187.18/188.03 ( class_Orderings_Olinorder(T_a)
% 187.18/188.03 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 187.18/188.03 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremove1(T_a,V_a,V_xs)) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_sorted__upto,axiom,
% 187.18/188.03 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(V_i,V_j)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_sorted__take,axiom,
% 187.18/188.03 ! [V_n,V_xs,T_a] :
% 187.18/188.03 ( class_Orderings_Olinorder(T_a)
% 187.18/188.03 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 187.18/188.03 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_sorted__tl,axiom,
% 187.18/188.03 ! [V_xs,T_a] :
% 187.18/188.03 ( class_Orderings_Olinorder(T_a)
% 187.18/188.03 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 187.18/188.03 => c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Otl(T_a),V_xs)) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_sorted__insort__insert,axiom,
% 187.18/188.03 ! [V_x_2,V_xs_2,T_a] :
% 187.18/188.03 ( class_Orderings_Olinorder(T_a)
% 187.18/188.03 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2)
% 187.18/188.03 => c_List_Olinorder__class_Osorted(T_a,c_List_Olinorder__class_Oinsort__insert__key(T_a,T_a,c_COMBI(T_a),V_x_2,V_xs_2)) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_sorted__butlast,axiom,
% 187.18/188.03 ! [V_xs,T_a] :
% 187.18/188.03 ( class_Orderings_Olinorder(T_a)
% 187.18/188.03 => ( V_xs != c_List_Olist_ONil(T_a)
% 187.18/188.03 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 187.18/188.03 => c_List_Olinorder__class_Osorted(T_a,c_List_Obutlast(T_a,V_xs)) ) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_sorted_Oequations_I1_J,axiom,
% 187.18/188.03 ! [T_a] :
% 187.18/188.03 ( class_Orderings_Olinorder(T_a)
% 187.18/188.03 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_sorted__many__eq,axiom,
% 187.18/188.03 ! [V_zs_2,V_y_2,V_x_2,T_a] :
% 187.18/188.03 ( class_Orderings_Olinorder(T_a)
% 187.18/188.03 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_zs_2)))
% 187.18/188.03 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 187.18/188.03 & c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_zs_2)) ) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_sorted__many,axiom,
% 187.18/188.03 ! [V_zs,V_y,V_x,T_a] :
% 187.18/188.03 ( class_Orderings_Olinorder(T_a)
% 187.18/188.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 187.18/188.03 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_zs))
% 187.18/188.03 => 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))) ) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_sorted__remdups,axiom,
% 187.18/188.03 ! [V_l,T_a] :
% 187.18/188.03 ( class_Orderings_Olinorder(T_a)
% 187.18/188.03 => ( c_List_Olinorder__class_Osorted(T_a,V_l)
% 187.18/188.03 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremdups(T_a,V_l)) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_sorted__distinct__set__unique,axiom,
% 187.18/188.03 ! [V_ys_2,V_xs_2,T_a] :
% 187.18/188.03 ( class_Orderings_Olinorder(T_a)
% 187.18/188.03 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2)
% 187.18/188.03 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 187.18/188.03 => ( c_List_Olinorder__class_Osorted(T_a,V_ys_2)
% 187.18/188.03 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_ys_2))
% 187.18/188.03 => ( hAPP(c_List_Oset(T_a),V_xs_2) = hAPP(c_List_Oset(T_a),V_ys_2)
% 187.18/188.03 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_sorted__sort__key,axiom,
% 187.18/188.03 ! [V_xs_2,V_f_2,T_b,T_a] :
% 187.18/188.03 ( class_Orderings_Olinorder(T_a)
% 187.18/188.03 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_Olinorder__class_Osort__key(T_b,T_a,V_f_2,V_xs_2))) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_sorted__insort__insert__key,axiom,
% 187.18/188.03 ! [V_x_2,V_xs_2,V_f_2,T_b,T_a] :
% 187.18/188.03 ( class_Orderings_Olinorder(T_a)
% 187.18/188.03 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))
% 187.18/188.03 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_Olinorder__class_Oinsort__insert__key(T_b,T_a,V_f_2,V_x_2,V_xs_2))) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_sorted__map__remove1,axiom,
% 187.18/188.03 ! [V_x_2,V_xs_2,V_f_2,T_b,T_a] :
% 187.18/188.03 ( class_Orderings_Olinorder(T_a)
% 187.18/188.03 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))
% 187.18/188.03 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_Oremove1(T_b,V_x_2,V_xs_2))) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_sorted__insort__key,axiom,
% 187.18/188.03 ! [V_xs_2,V_x_2,V_f_2,T_b,T_a] :
% 187.18/188.03 ( class_Orderings_Olinorder(T_a)
% 187.18/188.03 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),V_xs_2)))
% 187.18/188.03 <=> c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_sorted__filter,axiom,
% 187.18/188.03 ! [V_P_2,V_xs_2,V_f_2,T_b,T_a] :
% 187.18/188.03 ( class_Orderings_Olinorder(T_a)
% 187.18/188.03 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))
% 187.18/188.03 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2))) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_sorted__map__same,axiom,
% 187.18/188.03 ! [V_xs_2,V_g_2,V_f_2,T_b,T_a] :
% 187.18/188.03 ( class_Orderings_Olinorder(T_a)
% 187.18/188.03 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBC(T_b,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,tc_HOL_Obool),T_b),c_fequal),V_f_2)),hAPP(V_g_2,V_xs_2))),V_xs_2))) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_sorted__same,axiom,
% 187.18/188.03 ! [V_xs_2,V_g_2,T_a] :
% 187.18/188.03 ( class_Orderings_Olinorder(T_a)
% 187.18/188.03 => c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Ofilter(T_a,hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),hAPP(V_g_2,V_xs_2))),V_xs_2)) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_sorted__append,axiom,
% 187.18/188.03 ! [V_ys_2,V_xs_2,T_a] :
% 187.18/188.03 ( class_Orderings_Olinorder(T_a)
% 187.18/188.03 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2))
% 187.18/188.03 <=> ( c_List_Olinorder__class_Osorted(T_a,V_xs_2)
% 187.18/188.03 & c_List_Olinorder__class_Osorted(T_a,V_ys_2)
% 187.18/188.03 & ! [B_x] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 187.18/188.03 => ! [B_xa] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),hAPP(c_List_Oset(T_a),V_ys_2)))
% 187.18/188.03 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),B_xa)) ) ) ) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_filter__insort,axiom,
% 187.18/188.03 ! [V_x_2,V_P_2,V_xs_2,V_f_2,T_b,T_a] :
% 187.18/188.03 ( class_Orderings_Olinorder(T_a)
% 187.18/188.03 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))
% 187.18/188.03 => ( hBOOL(hAPP(V_P_2,V_x_2))
% 187.18/188.03 => hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)) ) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_sorted_Oequations_I2_J,axiom,
% 187.18/188.03 ! [V_a1_2,V_a2_2,T_a] :
% 187.18/188.03 ( class_Orderings_Olinorder(T_a)
% 187.18/188.03 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_a2_2),V_a1_2))
% 187.18/188.03 <=> ( ! [B_x] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_a1_2)))
% 187.18/188.03 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a2_2),B_x)) )
% 187.18/188.03 & c_List_Olinorder__class_Osorted(T_a,V_a1_2) ) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_sorted__list__of__set,axiom,
% 187.18/188.03 ! [V_A_2,T_a] :
% 187.18/188.03 ( class_Orderings_Olinorder(T_a)
% 187.18/188.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.03 => ( hAPP(c_List_Oset(T_a),c_List_Olinorder__class_Osorted__list__of__set(T_a,V_A_2)) = V_A_2
% 187.18/188.03 & c_List_Olinorder__class_Osorted(T_a,c_List_Olinorder__class_Osorted__list__of__set(T_a,V_A_2))
% 187.18/188.03 & hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olinorder__class_Osorted__list__of__set(T_a,V_A_2))) ) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_insort__remove1,axiom,
% 187.18/188.03 ! [V_xs_2,V_a_2,T_a] :
% 187.18/188.03 ( class_Orderings_Olinorder(T_a)
% 187.18/188.03 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 187.18/188.03 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2)
% 187.18/188.03 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_a_2),c_List_Oremove1(T_a,V_a_2,V_xs_2)) = V_xs_2 ) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_sorted__nth__mono,axiom,
% 187.18/188.03 ! [V_j,V_i,V_xs,T_a] :
% 187.18/188.03 ( class_Orderings_Olinorder(T_a)
% 187.18/188.03 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 187.18/188.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 187.18/188.03 => ( 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)))
% 187.18/188.03 => 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))) ) ) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_sorted__equals__nth__mono,axiom,
% 187.18/188.03 ! [V_xs_2,T_a] :
% 187.18/188.03 ( class_Orderings_Olinorder(T_a)
% 187.18/188.03 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2)
% 187.18/188.03 <=> ! [B_j] :
% 187.18/188.03 ( 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_2)))
% 187.18/188.03 => ! [B_i] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j))
% 187.18/188.03 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i)),hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_j))) ) ) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_map__sorted__distinct__set__unique,axiom,
% 187.18/188.03 ! [V_ys_2,V_xs_2,V_f_2,T_a,T_b] :
% 187.18/188.03 ( class_Orderings_Olinorder(T_b)
% 187.18/188.03 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(c_List_Oset(T_a),V_ys_2)))
% 187.18/188.03 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2))
% 187.18/188.03 => ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)))
% 187.18/188.03 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_ys_2))
% 187.18/188.03 => ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_ys_2)))
% 187.18/188.03 => ( hAPP(c_List_Oset(T_a),V_xs_2) = hAPP(c_List_Oset(T_a),V_ys_2)
% 187.18/188.03 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_transpose__column,axiom,
% 187.18/188.03 ! [V_i_2,V_xs_2,T_a] :
% 187.18/188.03 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),V_xs_2)))
% 187.18/188.03 => ( 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_a))),V_xs_2)))
% 187.18/188.03 => hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),T_a),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_Nat_Onat,T_a),c_List_Onth(T_a)),V_i_2)),hAPP(c_List_Ofilter(tc_List_Olist(T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_a)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),c_List_Otranspose(T_a,V_xs_2))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(T_a)),V_xs_2),V_i_2) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_nth__nth__transpose__sorted,axiom,
% 187.18/188.03 ! [V_j_2,V_i_2,V_xs_2,T_a] :
% 187.18/188.03 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),V_xs_2)))
% 187.18/188.03 => ( 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_a))),c_List_Otranspose(T_a,V_xs_2))))
% 187.18/188.03 => ( 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_a))),hAPP(c_List_Ofilter(tc_List_Olist(T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_a)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),V_xs_2))))
% 187.18/188.03 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_a)),c_List_Otranspose(T_a,V_xs_2)),V_i_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_a)),V_xs_2),V_j_2)),V_i_2) ) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_inj__on__rev,axiom,
% 187.18/188.03 ! [V_A_2,T_a] : c_Fun_Oinj__on(tc_List_Olist(T_a),tc_List_Olist(T_a),c_List_Orev(T_a),V_A_2) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_distinct__rev,axiom,
% 187.18/188.03 ! [V_xs_2,T_a] :
% 187.18/188.03 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Orev(T_a),V_xs_2)))
% 187.18/188.03 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_rev__append,axiom,
% 187.18/188.03 ! [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)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_rev__is__Nil__conv,axiom,
% 187.18/188.03 ! [V_xs_2,T_a] :
% 187.18/188.03 ( hAPP(c_List_Orev(T_a),V_xs_2) = c_List_Olist_ONil(T_a)
% 187.18/188.03 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_Nil__is__rev__conv,axiom,
% 187.18/188.03 ! [V_xs_2,T_a] :
% 187.18/188.03 ( c_List_Olist_ONil(T_a) = hAPP(c_List_Orev(T_a),V_xs_2)
% 187.18/188.03 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_rev_Osimps_I1_J,axiom,
% 187.18/188.03 ! [T_a] : hAPP(c_List_Orev(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_rev__singleton__conv,axiom,
% 187.18/188.03 ! [V_x_2,V_xs_2,T_a] :
% 187.18/188.03 ( hAPP(c_List_Orev(T_a),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a))
% 187.18/188.03 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_singleton__rev__conv,axiom,
% 187.18/188.03 ! [V_xs_2,V_x_2,T_a] :
% 187.18/188.03 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)) = hAPP(c_List_Orev(T_a),V_xs_2)
% 187.18/188.03 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_rev__eq__Cons__iff,axiom,
% 187.18/188.03 ! [V_ys_2,V_y_2,V_xs_2,T_a] :
% 187.18/188.03 ( hAPP(c_List_Orev(T_a),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2)
% 187.18/188.03 <=> V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_Orev(T_a),V_ys_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),c_List_Olist_ONil(T_a))) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_rev_Osimps_I2_J,axiom,
% 187.18/188.03 ! [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))) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_rev__concat,axiom,
% 187.18/188.03 ! [V_xs_2,T_a] : hAPP(c_List_Orev(T_a),c_List_Oconcat(T_a,V_xs_2)) = c_List_Oconcat(T_a,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Orev(T_a)),hAPP(c_List_Orev(tc_List_Olist(T_a)),V_xs_2))) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_rev__map,axiom,
% 187.18/188.03 ! [V_xs_2,V_f_2,T_b,T_a] : hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(c_List_Orev(T_b),V_xs_2)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_rev__filter,axiom,
% 187.18/188.03 ! [V_xs_2,V_P_2,T_a] : hAPP(c_List_Orev(T_a),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2)) = hAPP(c_List_Ofilter(T_a,V_P_2),hAPP(c_List_Orev(T_a),V_xs_2)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_zip__rev,axiom,
% 187.18/188.03 ! [V_ys,T_b,V_xs,T_a] :
% 187.18/188.03 ( 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)
% 187.18/188.03 => 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)) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_set__rev,axiom,
% 187.18/188.03 ! [V_xs_2,T_a] : hAPP(c_List_Oset(T_a),hAPP(c_List_Orev(T_a),V_xs_2)) = hAPP(c_List_Oset(T_a),V_xs_2) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_list__all2__rev,axiom,
% 187.18/188.03 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] :
% 187.18/188.03 ( c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(c_List_Orev(T_a),V_xs_2),hAPP(c_List_Orev(T_b),V_ys_2))
% 187.18/188.03 <=> c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_list__all2__rev1,axiom,
% 187.18/188.03 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] :
% 187.18/188.03 ( c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(c_List_Orev(T_a),V_xs_2),V_ys_2)
% 187.18/188.03 <=> c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,hAPP(c_List_Orev(T_b),V_ys_2)) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_listsum__rev,axiom,
% 187.18/188.03 ! [V_xs,T_a] :
% 187.18/188.03 ( class_Groups_Ocomm__monoid__add(T_a)
% 187.18/188.03 => 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) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_rev__rev__ident,axiom,
% 187.18/188.03 ! [V_xs,T_a] : hAPP(c_List_Orev(T_a),hAPP(c_List_Orev(T_a),V_xs)) = V_xs ).
% 187.18/188.03
% 187.18/188.03 fof(fact_rev__swap,axiom,
% 187.18/188.03 ! [V_ys_2,V_xs_2,T_a] :
% 187.18/188.03 ( hAPP(c_List_Orev(T_a),V_xs_2) = V_ys_2
% 187.18/188.03 <=> V_xs_2 = hAPP(c_List_Orev(T_a),V_ys_2) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_rev__is__rev__conv,axiom,
% 187.18/188.03 ! [V_ys_2,V_xs_2,T_a] :
% 187.18/188.03 ( hAPP(c_List_Orev(T_a),V_xs_2) = hAPP(c_List_Orev(T_a),V_ys_2)
% 187.18/188.03 <=> V_xs_2 = V_ys_2 ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_length__rev,axiom,
% 187.18/188.03 ! [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) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_foldr__foldl,axiom,
% 187.18/188.03 ! [V_a_2,V_xs_2,V_f_2,T_a,T_b] : c_List_Ofoldr(T_b,T_a,V_f_2,V_xs_2,V_a_2) = hAPP(c_List_Ofoldl(T_a,T_b,hAPP(c_COMBC(T_b,T_a,T_a),V_f_2),V_a_2),hAPP(c_List_Orev(T_b),V_xs_2)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_foldl__foldr,axiom,
% 187.18/188.03 ! [V_xs_2,V_a_2,V_f_2,T_b,T_a] : hAPP(c_List_Ofoldl(T_a,T_b,V_f_2,V_a_2),V_xs_2) = c_List_Ofoldr(T_b,T_a,hAPP(c_COMBC(T_a,T_b,T_a),V_f_2),hAPP(c_List_Orev(T_b),V_xs_2),V_a_2) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_hd__rev,axiom,
% 187.18/188.03 ! [T_a,V_xs] :
% 187.18/188.03 ( V_xs != c_List_Olist_ONil(T_a)
% 187.18/188.03 => hAPP(c_List_Ohd(T_a),hAPP(c_List_Orev(T_a),V_xs)) = c_List_Olast(T_a,V_xs) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_last__rev,axiom,
% 187.18/188.03 ! [T_a,V_xs] :
% 187.18/188.03 ( V_xs != c_List_Olist_ONil(T_a)
% 187.18/188.03 => c_List_Olast(T_a,hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Ohd(T_a),V_xs) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_sorted__transpose,axiom,
% 187.18/188.03 ! [V_xs_2,T_a] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),c_List_Otranspose(T_a,V_xs_2)))) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_rev__foldl__cons,axiom,
% 187.18/188.03 ! [V_xs_2,T_a] : hAPP(c_List_Orev(T_a),V_xs_2) = hAPP(c_List_Ofoldl(tc_List_Olist(T_a),T_a,hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)),c_List_Olist_ONil(T_a)),V_xs_2) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_rev__drop,axiom,
% 187.18/188.03 ! [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)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_rev__take,axiom,
% 187.18/188.03 ! [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)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_rotate__rev,axiom,
% 187.18/188.03 ! [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)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_rev__nth,axiom,
% 187.18/188.03 ! [V_xs,T_a,V_n] :
% 187.18/188.03 ( 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)))
% 187.18/188.03 => 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))) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_rev__update,axiom,
% 187.18/188.03 ! [V_y,V_xs,T_a,V_k] :
% 187.18/188.03 ( 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)))
% 187.18/188.03 => 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) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_sorted__rev__nth__mono,axiom,
% 187.18/188.03 ! [V_j,V_i,V_xs,T_a] :
% 187.18/188.03 ( class_Orderings_Olinorder(T_a)
% 187.18/188.03 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Orev(T_a),V_xs))
% 187.18/188.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 187.18/188.03 => ( 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)))
% 187.18/188.03 => 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))) ) ) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_foldr__max__sorted,axiom,
% 187.18/188.03 ! [V_y_2,V_xs_2,T_a] :
% 187.18/188.03 ( class_Orderings_Olinorder(T_a)
% 187.18/188.03 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Orev(T_a),V_xs_2))
% 187.18/188.03 => ( ( V_xs_2 = c_List_Olist_ONil(T_a)
% 187.18/188.03 => c_List_Ofoldr(T_a,T_a,c_Orderings_Oord__class_Omax(T_a),V_xs_2,V_y_2) = V_y_2 )
% 187.18/188.03 & ( V_xs_2 != c_List_Olist_ONil(T_a)
% 187.18/188.03 => c_List_Ofoldr(T_a,T_a,c_Orderings_Oord__class_Omax(T_a),V_xs_2,V_y_2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_y_2) ) ) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_length__transpose__sorted,axiom,
% 187.18/188.03 ! [V_xs_2,T_a] :
% 187.18/188.03 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),V_xs_2)))
% 187.18/188.03 => ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_a))
% 187.18/188.03 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),c_List_Otranspose(T_a,V_xs_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 187.18/188.03 & ( V_xs_2 != c_List_Olist_ONil(tc_List_Olist(T_a))
% 187.18/188.03 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),c_List_Otranspose(T_a,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_a)),V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_transpose__column__length,axiom,
% 187.18/188.03 ! [V_i_2,V_xs_2,T_a] :
% 187.18/188.03 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),V_xs_2)))
% 187.18/188.03 => ( 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_a))),V_xs_2)))
% 187.18/188.03 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),hAPP(c_List_Ofilter(tc_List_Olist(T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_a)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),c_List_Otranspose(T_a,V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_a)),V_xs_2),V_i_2)) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_transpose__transpose,axiom,
% 187.18/188.03 ! [V_xs_2,T_a] :
% 187.18/188.03 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),V_xs_2)))
% 187.18/188.03 => c_List_Otranspose(T_a,c_List_Otranspose(T_a,V_xs_2)) = c_List_OtakeWhile(tc_List_Olist(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_a)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_a))),V_xs_2) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_transfer__nat__int__list__functions_I2_J,axiom,
% 187.18/188.03 c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_sorted__takeWhile,axiom,
% 187.18/188.03 ! [V_P_2,V_xs_2,T_a] :
% 187.18/188.03 ( class_Orderings_Olinorder(T_a)
% 187.18/188.03 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2)
% 187.18/188.03 => c_List_Olinorder__class_Osorted(T_a,c_List_OtakeWhile(T_a,V_P_2,V_xs_2)) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_length__takeWhile__le,axiom,
% 187.18/188.03 ! [V_xs_2,V_P_2,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_OtakeWhile(T_a,V_P_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_takeWhile__eq__all__conv,axiom,
% 187.18/188.03 ! [V_xs_2,V_P_2,T_a] :
% 187.18/188.03 ( c_List_OtakeWhile(T_a,V_P_2,V_xs_2) = V_xs_2
% 187.18/188.03 <=> ! [B_x] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 187.18/188.03 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_set__takeWhileD,axiom,
% 187.18/188.03 ! [V_xs_2,V_P_2,V_x_2,T_a] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_OtakeWhile(T_a,V_P_2,V_xs_2))))
% 187.18/188.03 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 187.18/188.03 & hBOOL(hAPP(V_P_2,V_x_2)) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_zip__takeWhile__fst,axiom,
% 187.18/188.03 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)),V_ys_2) = c_List_OtakeWhile(tc_prod(T_a,T_b),hAPP(c_Fun_Ocomp(T_a,tc_HOL_Obool,tc_prod(T_a,T_b),V_P_2),c_Product__Type_Ofst(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_zip__takeWhile__snd,axiom,
% 187.18/188.03 ! [V_ys_2,V_P_2,V_xs_2,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),c_List_OtakeWhile(T_b,V_P_2,V_ys_2)) = c_List_OtakeWhile(tc_prod(T_a,T_b),hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,tc_prod(T_a,T_b),V_P_2),c_Product__Type_Osnd(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_takeWhile__map,axiom,
% 187.18/188.03 ! [V_xs_2,V_f_2,T_b,V_P_2,T_a] : c_List_OtakeWhile(T_a,V_P_2,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_OtakeWhile(T_b,hAPP(c_Fun_Ocomp(T_a,tc_HOL_Obool,T_b,V_P_2),V_f_2),V_xs_2)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_takeWhile__tail,axiom,
% 187.18/188.03 ! [V_l_2,V_xs_2,T_a,V_x_2,V_P_2] :
% 187.18/188.03 ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 187.18/188.03 => c_List_OtakeWhile(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_l_2))) = c_List_OtakeWhile(T_a,V_P_2,V_xs_2) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_takeWhile_Osimps_I2_J,axiom,
% 187.18/188.03 ! [V_xs_2,T_a,V_x_2,V_P_2] :
% 187.18/188.03 ( ( hBOOL(hAPP(V_P_2,V_x_2))
% 187.18/188.03 => c_List_OtakeWhile(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)) )
% 187.18/188.03 & ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 187.18/188.03 => c_List_OtakeWhile(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = c_List_Olist_ONil(T_a) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_takeWhile_Osimps_I1_J,axiom,
% 187.18/188.03 ! [V_P_2,T_a] : c_List_OtakeWhile(T_a,V_P_2,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_takeWhile__eq__take,axiom,
% 187.18/188.03 ! [V_xs_2,V_P_2,T_a] : c_List_OtakeWhile(T_a,V_P_2,V_xs_2) = hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OtakeWhile(T_a,V_P_2,V_xs_2))),V_xs_2) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_distinct__takeWhile,axiom,
% 187.18/188.03 ! [V_P_2,V_xs_2,T_a] :
% 187.18/188.03 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 187.18/188.03 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_OtakeWhile(T_a,V_P_2,V_xs_2))) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_return__list__def,axiom,
% 187.18/188.03 ! [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) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_takeWhile__append1,axiom,
% 187.18/188.03 ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_a] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 187.18/188.03 => ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 187.18/188.03 => c_List_OtakeWhile(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) = c_List_OtakeWhile(T_a,V_P_2,V_xs_2) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_takeWhile__nth,axiom,
% 187.18/188.03 ! [V_xs_2,V_P_2,T_a,V_j_2] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OtakeWhile(T_a,V_P_2,V_xs_2))))
% 187.18/188.03 => hAPP(hAPP(c_List_Onth(T_a),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_j_2) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_nth__length__takeWhile,axiom,
% 187.18/188.03 ! [V_xs_2,V_P_2,T_a] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OtakeWhile(T_a,V_P_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))
% 187.18/188.03 => ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OtakeWhile(T_a,V_P_2,V_xs_2))))) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_takeWhile__not__last,axiom,
% 187.18/188.03 ! [T_a,V_xs_2] :
% 187.18/188.03 ( V_xs_2 != c_List_Olist_ONil(T_a)
% 187.18/188.03 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 187.18/188.03 => c_List_OtakeWhile(T_a,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),c_List_Olast(T_a,V_xs_2))),V_xs_2) = c_List_Obutlast(T_a,V_xs_2) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_filter__equals__takeWhile__sorted__rev,axiom,
% 187.18/188.03 ! [V_t_2,V_xs_2,V_f_2,T_b,T_a] :
% 187.18/188.03 ( class_Orderings_Olinorder(T_a)
% 187.18/188.03 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)))
% 187.18/188.03 => hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBB(T_a,tc_HOL_Obool,T_b),hAPP(c_Orderings_Oord__class_Oless(T_a),V_t_2)),V_f_2)),V_xs_2) = c_List_OtakeWhile(T_b,hAPP(hAPP(c_COMBB(T_a,tc_HOL_Obool,T_b),hAPP(c_Orderings_Oord__class_Oless(T_a),V_t_2)),V_f_2),V_xs_2) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_transfer__nat__int__list__return__embed,axiom,
% 187.18/188.03 ! [V_l] :
% 187.18/188.03 ( c_List_Onat__list(V_l)
% 187.18/188.03 => c_List_Oembed__list(c_List_Oreturn__list(V_l)) = V_l ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_transfer__nat__int__list__functions_I1_J,axiom,
% 187.18/188.03 ! [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))) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_embed__list__def,axiom,
% 187.18/188.03 ! [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) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_takeWhile__neq__rev,axiom,
% 187.18/188.03 ! [V_x_2,V_xs_2,T_a] :
% 187.18/188.03 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 187.18/188.03 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 187.18/188.03 => c_List_OtakeWhile(T_a,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_x_2)),hAPP(c_List_Orev(T_a),V_xs_2)) = hAPP(c_List_Orev(T_a),hAPP(c_List_Otl(T_a),c_List_OdropWhile(T_a,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_x_2)),V_xs_2))) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_dropWhile__neq__rev,axiom,
% 187.18/188.03 ! [V_x_2,V_xs_2,T_a] :
% 187.18/188.03 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 187.18/188.03 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 187.18/188.03 => c_List_OdropWhile(T_a,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_x_2)),hAPP(c_List_Orev(T_a),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),hAPP(c_List_Orev(T_a),c_List_OtakeWhile(T_a,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_x_2)),V_xs_2))) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_takeWhile__dropWhile__id,axiom,
% 187.18/188.03 ! [V_xs_2,V_P_2,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)),c_List_OdropWhile(T_a,V_P_2,V_xs_2)) = V_xs_2 ).
% 187.18/188.03
% 187.18/188.03 fof(fact_dropWhile__map,axiom,
% 187.18/188.03 ! [V_xs_2,V_f_2,T_b,V_P_2,T_a] : c_List_OdropWhile(T_a,V_P_2,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_OdropWhile(T_b,hAPP(c_Fun_Ocomp(T_a,tc_HOL_Obool,T_b,V_P_2),V_f_2),V_xs_2)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_sorted__dropWhile,axiom,
% 187.18/188.03 ! [V_P_2,V_xs_2,T_a] :
% 187.18/188.03 ( class_Orderings_Olinorder(T_a)
% 187.18/188.03 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2)
% 187.18/188.03 => c_List_Olinorder__class_Osorted(T_a,c_List_OdropWhile(T_a,V_P_2,V_xs_2)) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_length__dropWhile__le,axiom,
% 187.18/188.03 ! [V_xs_2,V_P_2,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_OdropWhile(T_a,V_P_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_dropWhile__eq__Nil__conv,axiom,
% 187.18/188.03 ! [V_xs_2,V_P_2,T_a] :
% 187.18/188.03 ( c_List_OdropWhile(T_a,V_P_2,V_xs_2) = c_List_Olist_ONil(T_a)
% 187.18/188.03 <=> ! [B_x] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 187.18/188.03 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_dropWhile_Osimps_I2_J,axiom,
% 187.18/188.03 ! [V_xs_2,T_a,V_x_2,V_P_2] :
% 187.18/188.03 ( ( hBOOL(hAPP(V_P_2,V_x_2))
% 187.18/188.03 => c_List_OdropWhile(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = c_List_OdropWhile(T_a,V_P_2,V_xs_2) )
% 187.18/188.03 & ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 187.18/188.03 => c_List_OdropWhile(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_dropWhile_Osimps_I1_J,axiom,
% 187.18/188.03 ! [V_P_2,T_a] : c_List_OdropWhile(T_a,V_P_2,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_distinct__dropWhile,axiom,
% 187.18/188.03 ! [V_P_2,V_xs_2,T_a] :
% 187.18/188.03 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 187.18/188.03 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_OdropWhile(T_a,V_P_2,V_xs_2))) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_hd__dropWhile,axiom,
% 187.18/188.03 ! [V_xs_2,V_P_2,T_a] :
% 187.18/188.03 ( c_List_OdropWhile(T_a,V_P_2,V_xs_2) != c_List_Olist_ONil(T_a)
% 187.18/188.03 => ~ hBOOL(hAPP(V_P_2,hAPP(c_List_Ohd(T_a),c_List_OdropWhile(T_a,V_P_2,V_xs_2)))) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_dropWhile__append1,axiom,
% 187.18/188.03 ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_a] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 187.18/188.03 => ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 187.18/188.03 => c_List_OdropWhile(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_a),c_List_OdropWhile(T_a,V_P_2,V_xs_2)),V_ys_2) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_dropWhile__eq__Cons__conv,axiom,
% 187.18/188.03 ! [V_ys_2,V_y_2,V_xs_2,V_P_2,T_a] :
% 187.18/188.03 ( c_List_OdropWhile(T_a,V_P_2,V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2)
% 187.18/188.03 <=> ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2))
% 187.18/188.03 & ~ hBOOL(hAPP(V_P_2,V_y_2)) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_dropWhile__eq__drop,axiom,
% 187.18/188.03 ! [V_xs_2,V_P_2,T_a] : c_List_OdropWhile(T_a,V_P_2,V_xs_2) = hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OtakeWhile(T_a,V_P_2,V_xs_2))),V_xs_2) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_dropWhile__nth,axiom,
% 187.18/188.03 ! [V_xs_2,V_P_2,T_a,V_j_2] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OdropWhile(T_a,V_P_2,V_xs_2))))
% 187.18/188.03 => hAPP(hAPP(c_List_Onth(T_a),c_List_OdropWhile(T_a,V_P_2,V_xs_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_a),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_a)),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)))) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_listsum__map__filter,axiom,
% 187.18/188.03 ! [V_f_2,V_P_2,V_xs_2,T_a,T_b] :
% 187.18/188.03 ( class_Groups_Omonoid__add(T_b)
% 187.18/188.03 => ( ! [B_x] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 187.18/188.03 => ( ~ hBOOL(hAPP(V_P_2,B_x))
% 187.18/188.03 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) )
% 187.18/188.03 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_sorted__nth__monoI,axiom,
% 187.18/188.03 ! [V_xs,T_a] :
% 187.18/188.03 ( class_Orderings_Olinorder(T_a)
% 187.18/188.03 => ( ! [B_i,B_j] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j))
% 187.18/188.03 => ( 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)))
% 187.18/188.03 => 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))) ) )
% 187.18/188.03 => c_List_Olinorder__class_Osorted(T_a,V_xs) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_takeWhile__eq__filter,axiom,
% 187.18/188.03 ! [V_xs_2,V_P_2,T_a] :
% 187.18/188.03 ( ! [B_x] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),c_List_OdropWhile(T_a,V_P_2,V_xs_2))))
% 187.18/188.03 => ~ hBOOL(hAPP(V_P_2,B_x)) )
% 187.18/188.03 => c_List_OtakeWhile(T_a,V_P_2,V_xs_2) = hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_takeWhile__eq__take__P__nth,axiom,
% 187.18/188.03 ! [V_P_2,V_xs_2,T_a,V_n_2] :
% 187.18/188.03 ( ! [B_i] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
% 187.18/188.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))
% 187.18/188.03 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i))) ) )
% 187.18/188.03 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))
% 187.18/188.03 => ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_n_2))) )
% 187.18/188.03 => c_List_OtakeWhile(T_a,V_P_2,V_xs_2) = hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_xs_2) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_length__takeWhile__less__P__nth,axiom,
% 187.18/188.03 ! [V_xs_2,T_a,V_P_2,V_j_2] :
% 187.18/188.03 ( ! [B_i] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_j_2))
% 187.18/188.03 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i))) )
% 187.18/188.03 => ( 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_a)),V_xs_2)))
% 187.18/188.03 => 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_a)),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)))) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_sorted_Osimps,axiom,
% 187.18/188.03 ! [V_a_2,T_a] :
% 187.18/188.03 ( class_Orderings_Olinorder(T_a)
% 187.18/188.03 => ( c_List_Olinorder__class_Osorted(T_a,V_a_2)
% 187.18/188.03 <=> ( V_a_2 = c_List_Olist_ONil(T_a)
% 187.18/188.03 | ? [B_xs,B_x] :
% 187.18/188.03 ( V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_x),B_xs)
% 187.18/188.03 & ! [B_xa] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),hAPP(c_List_Oset(T_a),B_xs)))
% 187.18/188.03 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),B_xa)) )
% 187.18/188.03 & c_List_Olinorder__class_Osorted(T_a,B_xs) ) ) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_map__upds__def,axiom,
% 187.18/188.03 ! [V_ys_2,V_xs_2,V_m_2,T_b,T_a] : c_Map_Omap__upds(T_a,T_b,V_m_2,V_xs_2,V_ys_2) = c_Map_Omap__add(T_a,T_b,V_m_2,hAPP(c_Map_Omap__of(T_a,T_b),hAPP(c_List_Orev(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)))) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_map__comp__def,axiom,
% 187.18/188.03 ! [V_k_2,V_g_2,V_f_2,T_c,T_a,T_b] : c_Map_Omap__comp(T_b,T_a,T_c,V_f_2,V_g_2,V_k_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(T_a),T_b,c_Option_Ooption_ONone(T_a),V_f_2),hAPP(V_g_2,V_k_2)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_map__of__append,axiom,
% 187.18/188.03 ! [V_ys_2,V_xs_2,T_b,T_a] : hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Oappend(tc_prod(T_a,T_b)),V_xs_2),V_ys_2)) = c_Map_Omap__add(T_a,T_b,hAPP(c_Map_Omap__of(T_a,T_b),V_ys_2),hAPP(c_Map_Omap__of(T_a,T_b),V_xs_2)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_map__comp__empty_I2_J,axiom,
% 187.18/188.03 ! [V_x_2,V_m_2,T_c,T_a,T_b] : c_Map_Omap__comp(T_b,T_a,T_c,hAPP(c_COMBK(tc_Option_Ooption(T_a),T_b),c_Option_Ooption_ONone(T_a)),V_m_2,V_x_2) = c_Option_Ooption_ONone(T_a) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_map__comp__empty_I1_J,axiom,
% 187.18/188.03 ! [V_x_2,V_m_2,T_c,T_a,T_b] : c_Map_Omap__comp(T_b,T_a,T_c,V_m_2,hAPP(c_COMBK(tc_Option_Ooption(T_b),T_c),c_Option_Ooption_ONone(T_b)),V_x_2) = c_Option_Ooption_ONone(T_a) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_map__comp__Some__iff,axiom,
% 187.18/188.03 ! [V_v_2,V_k_2,V_m2_2,V_m1_2,T_c,T_a,T_b] :
% 187.18/188.03 ( c_Map_Omap__comp(T_b,T_a,T_c,V_m1_2,V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_v_2)
% 187.18/188.03 <=> ? [B_k_H] :
% 187.18/188.03 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),B_k_H)
% 187.18/188.03 & hAPP(V_m1_2,B_k_H) = hAPP(c_Option_Ooption_OSome(T_a),V_v_2) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_map__add__find__right,axiom,
% 187.18/188.03 ! [V_m_2,T_b,V_xx_2,T_a,V_k_2,V_n_2] :
% 187.18/188.03 ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_xx_2)
% 187.18/188.03 => hAPP(c_Map_Omap__add(T_b,T_a,V_m_2,V_n_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_xx_2) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_map__comp__simps_I2_J,axiom,
% 187.18/188.03 ! [V_m1_2,T_b,T_c,V_k_H_2,T_a,V_k_2,V_m2_2] :
% 187.18/188.03 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_k_H_2)
% 187.18/188.03 => c_Map_Omap__comp(T_a,T_c,T_b,V_m1_2,V_m2_2,V_k_2) = hAPP(V_m1_2,V_k_H_2) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_map__add__upd,axiom,
% 187.18/188.03 ! [V_y_2,V_x_2,V_g_2,V_f_2,T_b,T_a] : c_Map_Omap__add(T_a,T_b,V_f_2,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_g_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Omap__add(T_a,T_b,V_f_2,V_g_2)),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_map__add__Some__iff,axiom,
% 187.18/188.03 ! [V_x_2,V_k_2,V_n_2,V_m_2,T_a,T_b] :
% 187.18/188.03 ( hAPP(c_Map_Omap__add(T_b,T_a,V_m_2,V_n_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2)
% 187.18/188.03 <=> ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2)
% 187.18/188.03 | ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_a)
% 187.18/188.03 & hAPP(V_m_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) ) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_map__add__SomeD,axiom,
% 187.18/188.03 ! [V_x_2,V_k_2,V_n_2,V_m_2,T_a,T_b] :
% 187.18/188.03 ( hAPP(c_Map_Omap__add(T_b,T_a,V_m_2,V_n_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2)
% 187.18/188.03 => ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2)
% 187.18/188.03 | ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_a)
% 187.18/188.03 & hAPP(V_m_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) ) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_empty__map__add,axiom,
% 187.18/188.03 ! [V_m_2,T_b,T_a] : c_Map_Omap__add(T_a,T_b,hAPP(c_COMBK(tc_Option_Ooption(T_b),T_a),c_Option_Ooption_ONone(T_b)),V_m_2) = V_m_2 ).
% 187.18/188.03
% 187.18/188.03 fof(fact_map__add__empty,axiom,
% 187.18/188.03 ! [V_m_2,T_b,T_a] : c_Map_Omap__add(T_a,T_b,V_m_2,hAPP(c_COMBK(tc_Option_Ooption(T_b),T_a),c_Option_Ooption_ONone(T_b))) = V_m_2 ).
% 187.18/188.03
% 187.18/188.03 fof(fact_map__add__None,axiom,
% 187.18/188.03 ! [V_k_2,V_n_2,V_m_2,T_a,T_b] :
% 187.18/188.03 ( hAPP(c_Map_Omap__add(T_b,T_a,V_m_2,V_n_2),V_k_2) = c_Option_Ooption_ONone(T_a)
% 187.18/188.03 <=> ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_a)
% 187.18/188.03 & hAPP(V_m_2,V_k_2) = c_Option_Ooption_ONone(T_a) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_map__comp__simps_I1_J,axiom,
% 187.18/188.03 ! [V_m1_2,T_b,T_c,T_a,V_k_2,V_m2_2] :
% 187.18/188.03 ( hAPP(V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_a)
% 187.18/188.03 => c_Map_Omap__comp(T_a,T_c,T_b,V_m1_2,V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_c) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_map__add__upds,axiom,
% 187.18/188.03 ! [V_ys_2,V_xs_2,V_m2_2,V_m1_2,T_b,T_a] : c_Map_Omap__add(T_a,T_b,V_m1_2,c_Map_Omap__upds(T_a,T_b,V_m2_2,V_xs_2,V_ys_2)) = c_Map_Omap__upds(T_a,T_b,c_Map_Omap__add(T_a,T_b,V_m1_2,V_m2_2),V_xs_2,V_ys_2) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_dom__map__add,axiom,
% 187.18/188.03 ! [V_n_2,V_m_2,T_b,T_a] : c_Map_Odom(T_a,T_b,c_Map_Omap__add(T_a,T_b,V_m_2,V_n_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_Map_Odom(T_a,T_b,V_n_2)),c_Map_Odom(T_a,T_b,V_m_2)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_map__add__assoc,axiom,
% 187.18/188.03 ! [V_m3_2,V_m2_2,V_m1_2,T_b,T_a] : c_Map_Omap__add(T_a,T_b,V_m1_2,c_Map_Omap__add(T_a,T_b,V_m2_2,V_m3_2)) = c_Map_Omap__add(T_a,T_b,c_Map_Omap__add(T_a,T_b,V_m1_2,V_m2_2),V_m3_2) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_map__add__dom__app__simps_I1_J,axiom,
% 187.18/188.03 ! [V_l1_2,V_l2_2,T_b,V_m_2,T_a] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_member(T_a),V_m_2),c_Map_Odom(T_a,T_b,V_l2_2)))
% 187.18/188.03 => hAPP(c_Map_Omap__add(T_a,T_b,V_l1_2,V_l2_2),V_m_2) = hAPP(V_l2_2,V_m_2) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_map__add__dom__app__simps_I3_J,axiom,
% 187.18/188.03 ! [V_l1_2,V_l2_2,T_b,V_m_2,T_a] :
% 187.18/188.03 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_m_2),c_Map_Odom(T_a,T_b,V_l2_2)))
% 187.18/188.03 => hAPP(c_Map_Omap__add(T_a,T_b,V_l1_2,V_l2_2),V_m_2) = hAPP(V_l1_2,V_m_2) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_map__add__dom__app__simps_I2_J,axiom,
% 187.18/188.03 ! [V_l2_2,V_l1_2,T_b,V_m_2,T_a] :
% 187.18/188.03 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_m_2),c_Map_Odom(T_a,T_b,V_l1_2)))
% 187.18/188.03 => hAPP(c_Map_Omap__add(T_a,T_b,V_l1_2,V_l2_2),V_m_2) = hAPP(V_l2_2,V_m_2) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_inj__on__map__add__dom,axiom,
% 187.18/188.03 ! [V_m_H_2,V_m_2,T_b,T_a] :
% 187.18/188.03 ( c_Fun_Oinj__on(T_a,tc_Option_Ooption(T_b),c_Map_Omap__add(T_a,T_b,V_m_2,V_m_H_2),c_Map_Odom(T_a,T_b,V_m_H_2))
% 187.18/188.03 <=> c_Fun_Oinj__on(T_a,tc_Option_Ooption(T_b),V_m_H_2,c_Map_Odom(T_a,T_b,V_m_H_2)) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_map__add__def,axiom,
% 187.18/188.03 ! [V_x_2,V_m2_2,V_m1_2,T_a,T_b] : hAPP(c_Map_Omap__add(T_b,T_a,V_m1_2,V_m2_2),V_x_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(T_a),T_a,hAPP(V_m1_2,V_x_2),c_Option_Ooption_OSome(T_a)),hAPP(V_m2_2,V_x_2)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_map__add__comm,axiom,
% 187.18/188.03 ! [V_m2_2,V_m1_2,T_b,T_a] :
% 187.18/188.03 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Map_Odom(T_a,T_b,V_m1_2)),c_Map_Odom(T_a,T_b,V_m2_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 187.18/188.03 => c_Map_Omap__add(T_a,T_b,V_m1_2,V_m2_2) = c_Map_Omap__add(T_a,T_b,V_m2_2,V_m1_2) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_map__comp__None__iff,axiom,
% 187.18/188.03 ! [V_k_2,V_m2_2,V_m1_2,T_c,T_a,T_b] :
% 187.18/188.03 ( c_Map_Omap__comp(T_b,T_a,T_c,V_m1_2,V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_a)
% 187.18/188.03 <=> ( hAPP(V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_b)
% 187.18/188.03 | ? [B_k_H] :
% 187.18/188.03 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),B_k_H)
% 187.18/188.03 & hAPP(V_m1_2,B_k_H) = c_Option_Ooption_ONone(T_a) ) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_map__add__map__of__foldr,axiom,
% 187.18/188.03 ! [V_ps_2,V_m_2,T_b,T_a] : c_Map_Omap__add(T_a,T_b,V_m_2,hAPP(c_Map_Omap__of(T_a,T_b),V_ps_2)) = c_List_Ofoldr(tc_prod(T_a,T_b),tc_fun(T_a,tc_Option_Ooption(T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_fun(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,tc_Option_Ooption(T_b)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_b,tc_fun(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,tc_Option_Ooption(T_b))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(T_b),tc_fun(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,tc_Option_Ooption(T_b)))),tc_fun(tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_b,tc_fun(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,tc_Option_Ooption(T_b))))),T_a),c_COMBB(tc_Option_Ooption(T_b),tc_fun(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,tc_Option_Ooption(T_b))),T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(tc_Option_Ooption(T_b),tc_fun(T_a,tc_Option_Ooption(T_b)))),tc_fun(tc_Option_Ooption(T_b),tc_fun(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,tc_Option_Ooption(T_b)))),T_a),c_COMBC(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_Option_Ooption(T_b),tc_fun(T_a,tc_Option_Ooption(T_b)))),hAPP(c_COMBC(tc_fun(T_a,tc_Option_Ooption(T_b)),T_a,tc_fun(tc_Option_Ooption(T_b),tc_fun(T_a,tc_Option_Ooption(T_b)))),c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)))))),c_Option_Ooption_OSome(T_b))),V_ps_2,V_m_2) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_map__add__upd__left,axiom,
% 187.18/188.03 ! [V_u1_2,V_e1_2,V_e2_2,T_b,V_m_2,T_a] :
% 187.18/188.03 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_m_2),c_Map_Odom(T_a,T_b,V_e2_2)))
% 187.18/188.03 => c_Map_Omap__add(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_e1_2),V_m_2),hAPP(c_Option_Ooption_OSome(T_b),V_u1_2)),V_e2_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Omap__add(T_a,T_b,V_e1_2,V_e2_2)),V_m_2),hAPP(c_Option_Ooption_OSome(T_b),V_u1_2)) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_finite__range__map__of__map__add,axiom,
% 187.18/188.03 ! [V_l_2,V_f_2,T_b,T_a] :
% 187.18/188.03 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_a)),hAPP(c_Set_Oimage(T_b,tc_Option_Ooption(T_a),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))))
% 187.18/188.03 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_a)),hAPP(c_Set_Oimage(T_b,tc_Option_Ooption(T_a),c_Map_Omap__add(T_b,T_a,V_f_2,hAPP(c_Map_Omap__of(T_b,T_a),V_l_2))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_List_Oinsert__def,axiom,
% 187.18/188.03 ! [V_xs_2,V_x_2,T_a] :
% 187.18/188.03 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 187.18/188.03 => c_List_Oinsert(T_a,V_x_2,V_xs_2) = V_xs_2 )
% 187.18/188.03 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 187.18/188.03 => c_List_Oinsert(T_a,V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_not__in__set__insert,axiom,
% 187.18/188.03 ! [V_xs_2,V_x_2,T_a] :
% 187.18/188.03 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 187.18/188.03 => c_List_Oinsert(T_a,V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_distinct__insert,axiom,
% 187.18/188.03 ! [V_x,V_xs,T_a] :
% 187.18/188.03 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 187.18/188.03 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oinsert(T_a,V_x,V_xs))) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_insert__remdups,axiom,
% 187.18/188.03 ! [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)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_in__set__insert,axiom,
% 187.18/188.03 ! [V_xs_2,V_x_2,T_a] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 187.18/188.03 => c_List_Oinsert(T_a,V_x_2,V_xs_2) = V_xs_2 ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_List_Oset__insert,axiom,
% 187.18/188.03 ! [V_xs_2,V_x_2,T_a] : hAPP(c_List_Oset(T_a),c_List_Oinsert(T_a,V_x_2,V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_insert__Nil,axiom,
% 187.18/188.03 ! [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)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_maps__def,axiom,
% 187.18/188.03 ! [V_xs_2,V_f_2,T_a,T_b] : c_List_Omaps(T_b,T_a,V_f_2,V_xs_2) = c_List_Oconcat(T_a,hAPP(hAPP(c_List_Omap(T_b,tc_List_Olist(T_a)),V_f_2),V_xs_2)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_concat__map__maps,axiom,
% 187.18/188.03 ! [V_xs_2,V_f_2,T_b,T_a] : c_List_Oconcat(T_a,hAPP(hAPP(c_List_Omap(T_b,tc_List_Olist(T_a)),V_f_2),V_xs_2)) = c_List_Omaps(T_b,T_a,V_f_2,V_xs_2) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_maps__simps_I2_J,axiom,
% 187.18/188.03 ! [V_f_2,T_a,T_b] : c_List_Omaps(T_b,T_a,V_f_2,c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_a) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_maps__simps_I1_J,axiom,
% 187.18/188.03 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] : c_List_Omaps(T_b,T_a,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(V_f_2,V_x_2)),c_List_Omaps(T_b,T_a,V_f_2,V_xs_2)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_distinct__concat,axiom,
% 187.18/188.03 ! [V_xs_2,T_a] :
% 187.18/188.03 ( hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_a)),V_xs_2))
% 187.18/188.03 => ( ! [B_ys] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2)))
% 187.18/188.03 => hBOOL(hAPP(c_List_Odistinct(T_a),B_ys)) )
% 187.18/188.03 => ( ! [B_ys] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2)))
% 187.18/188.03 => ! [B_zs] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_zs),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2)))
% 187.18/188.03 => ( B_ys != B_zs
% 187.18/188.03 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),B_ys)),hAPP(c_List_Oset(T_a),B_zs)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) )
% 187.18/188.03 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oconcat(T_a,V_xs_2))) ) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_ran__restrictD,axiom,
% 187.18/188.03 ! [V_A_2,V_m_2,T_b,V_y_2,T_a] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),c_Map_Oran(T_b,T_a,c_Map_Orestrict__map(T_b,T_a,V_m_2,V_A_2))))
% 187.18/188.03 => ? [B_x] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 187.18/188.03 & hAPP(V_m_2,B_x) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_measures__lesseq,axiom,
% 187.18/188.03 ! [V_fs_2,T_a,V_y_2,V_x_2,V_f_2] :
% 187.18/188.03 ( 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)))
% 187.18/188.03 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_List_Omeasures(T_a,V_fs_2)))
% 187.18/188.03 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_List_Omeasures(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_a,tc_Nat_Onat)),V_f_2),V_fs_2)))) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_measures__less,axiom,
% 187.18/188.03 ! [V_fs_2,T_a,V_y_2,V_x_2,V_f_2] :
% 187.18/188.03 ( 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)))
% 187.18/188.03 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_List_Omeasures(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_a,tc_Nat_Onat)),V_f_2),V_fs_2)))) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_wf__measures,axiom,
% 187.18/188.03 ! [V_fs_2,T_a] : c_Wellfounded_Owf(T_a,c_List_Omeasures(T_a,V_fs_2)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_in__measures_I1_J,axiom,
% 187.18/188.03 ! [V_y_2,V_x_2,T_a] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_List_Omeasures(T_a,c_List_Olist_ONil(tc_fun(T_a,tc_Nat_Onat))))) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_measures__def,axiom,
% 187.18/188.03 ! [V_fs_2,T_a] : c_List_Omeasures(T_a,V_fs_2) = hAPP(hAPP(c_Relation_Oinv__image(tc_List_Olist(tc_Nat_Onat),T_a),c_List_Olex(tc_Nat_Onat,c_Wellfounded_Oless__than)),hAPP(hAPP(c_COMBC(T_a,tc_List_Olist(tc_fun(T_a,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_Nat_Onat),tc_Nat_Onat),tc_fun(tc_List_Olist(tc_fun(T_a,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),T_a),c_List_Omap(tc_fun(T_a,tc_Nat_Onat),tc_Nat_Onat)),hAPP(c_COMBC(tc_fun(T_a,tc_Nat_Onat),T_a,tc_Nat_Onat),c_COMBI(tc_fun(T_a,tc_Nat_Onat))))),V_fs_2)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_in__measures_I2_J,axiom,
% 187.18/188.03 ! [V_fs_2,V_f_2,V_y_2,V_x_2,T_a] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_List_Omeasures(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_a,tc_Nat_Onat)),V_f_2),V_fs_2))))
% 187.18/188.03 <=> ( 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)))
% 187.18/188.03 | ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 187.18/188.03 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_List_Omeasures(T_a,V_fs_2))) ) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_foldl__apply,axiom,
% 187.18/188.03 ! [V_s_2,V_g_2,V_h_2,V_f_2,T_b,T_c,V_xs_2,T_a] :
% 187.18/188.03 ( ! [B_x] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 187.18/188.03 => hAPP(c_Fun_Ocomp(T_c,T_c,T_b,hAPP(V_f_2,B_x)),V_h_2) = hAPP(c_Fun_Ocomp(T_b,T_c,T_b,V_h_2),hAPP(V_g_2,B_x)) )
% 187.18/188.03 => hAPP(c_List_Ofoldl(T_c,T_a,hAPP(c_COMBC(T_a,T_c,T_c),V_f_2),hAPP(V_h_2,V_s_2)),V_xs_2) = hAPP(V_h_2,hAPP(c_List_Ofoldl(T_b,T_a,hAPP(c_COMBC(T_a,T_b,T_b),V_g_2),V_s_2),V_xs_2)) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_zip__obtain__same__length,axiom,
% 187.18/188.03 ! [V_P_2,V_ys_2,T_b,V_xs_2,T_a] :
% 187.18/188.03 ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2))),V_xs_2)) = 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_a)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2))),V_ys_2))
% 187.18/188.03 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2))),V_xs_2)),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_a)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2))),V_ys_2)))) )
% 187.18/188.03 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2))) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_map__of__eqI,axiom,
% 187.18/188.03 ! [V_ys_2,V_xs_2,T_b,T_a] :
% 187.18/188.03 ( hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_xs_2)) = hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_ys_2))
% 187.18/188.03 => ( ! [B_x] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_xs_2))))
% 187.18/188.03 => hAPP(hAPP(c_Map_Omap__of(T_a,T_b),V_xs_2),B_x) = hAPP(hAPP(c_Map_Omap__of(T_a,T_b),V_ys_2),B_x) )
% 187.18/188.03 => hAPP(c_Map_Omap__of(T_a,T_b),V_xs_2) = hAPP(c_Map_Omap__of(T_a,T_b),V_ys_2) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_pos__not__random__dseq__def,axiom,
% 187.18/188.03 ! [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)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_dropWhile__append2,axiom,
% 187.18/188.03 ! [V_ys_2,V_P_2,V_xs_2,T_a] :
% 187.18/188.03 ( ! [B_x] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 187.18/188.03 => hBOOL(hAPP(V_P_2,B_x)) )
% 187.18/188.03 => c_List_OdropWhile(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) = c_List_OdropWhile(T_a,V_P_2,V_ys_2) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_list__all2__all__nthI,axiom,
% 187.18/188.03 ! [V_P_2,V_b_2,T_b,V_a_2,T_a] :
% 187.18/188.03 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_a_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_b_2)
% 187.18/188.03 => ( ! [B_n] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_a_2)))
% 187.18/188.03 => hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_a_2),B_n)),hAPP(hAPP(c_List_Onth(T_b),V_b_2),B_n))) )
% 187.18/188.03 => c_List_Olist__all2(T_a,T_b,V_P_2,V_a_2,V_b_2) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_finite__map__freshness,axiom,
% 187.18/188.03 ! [V_f_2,T_b,T_a] :
% 187.18/188.03 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Map_Odom(T_a,T_b,V_f_2)))
% 187.18/188.03 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))
% 187.18/188.03 => ? [B_x] : hAPP(V_f_2,B_x) = c_Option_Ooption_ONone(T_b) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_finite__sorted__distinct__unique,axiom,
% 187.18/188.03 ! [V_A_2,T_a] :
% 187.18/188.03 ( class_Orderings_Olinorder(T_a)
% 187.18/188.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 187.18/188.03 => ? [B_x] :
% 187.18/188.03 ( hAPP(c_List_Oset(T_a),B_x) = V_A_2
% 187.18/188.03 & c_List_Olinorder__class_Osorted(T_a,B_x)
% 187.18/188.03 & hBOOL(hAPP(c_List_Odistinct(T_a),B_x))
% 187.18/188.03 & ! [B_y] :
% 187.18/188.03 ( ( hAPP(c_List_Oset(T_a),B_y) = V_A_2
% 187.18/188.03 & c_List_Olinorder__class_Osorted(T_a,B_y)
% 187.18/188.03 & hBOOL(hAPP(c_List_Odistinct(T_a),B_y)) )
% 187.18/188.03 => B_y = B_x ) ) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_takeWhile__append2,axiom,
% 187.18/188.03 ! [V_ys_2,V_P_2,V_xs_2,T_a] :
% 187.18/188.03 ( ! [B_x] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 187.18/188.03 => hBOOL(hAPP(V_P_2,B_x)) )
% 187.18/188.03 => c_List_OtakeWhile(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),c_List_OtakeWhile(T_a,V_P_2,V_ys_2)) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_insort__is__Cons,axiom,
% 187.18/188.03 ! [V_a_2,V_f_2,V_xs_2,T_a,T_b] :
% 187.18/188.03 ( class_Orderings_Olinorder(T_b)
% 187.18/188.03 => ( ! [B_x] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 187.18/188.03 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_a_2)),hAPP(V_f_2,B_x))) )
% 187.18/188.03 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_a_2),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_2),V_xs_2) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_Cons__eq__filter__iff,axiom,
% 187.18/188.03 ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_a] :
% 187.18/188.03 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) = hAPP(c_List_Ofilter(T_a,V_P_2),V_ys_2)
% 187.18/188.03 <=> ? [B_us,B_vs] :
% 187.18/188.03 ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_a),B_us),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_vs))
% 187.18/188.03 & ! [B_x] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),B_us)))
% 187.18/188.03 => ~ hBOOL(hAPP(V_P_2,B_x)) )
% 187.18/188.03 & hBOOL(hAPP(V_P_2,V_x_2))
% 187.18/188.03 & V_xs_2 = hAPP(c_List_Ofilter(T_a,V_P_2),B_vs) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_filter__eq__Cons__iff,axiom,
% 187.18/188.03 ! [V_xs_2,V_x_2,V_ys_2,V_P_2,T_a] :
% 187.18/188.03 ( hAPP(c_List_Ofilter(T_a,V_P_2),V_ys_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)
% 187.18/188.03 <=> ? [B_us,B_vs] :
% 187.18/188.03 ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_a),B_us),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_vs))
% 187.18/188.03 & ! [B_x] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),B_us)))
% 187.18/188.03 => ~ hBOOL(hAPP(V_P_2,B_x)) )
% 187.18/188.03 & hBOOL(hAPP(V_P_2,V_x_2))
% 187.18/188.03 & V_xs_2 = hAPP(c_List_Ofilter(T_a,V_P_2),B_vs) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_list__ball__nth,axiom,
% 187.18/188.03 ! [V_P_2,V_xs_2,T_a,V_n_2] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))
% 187.18/188.03 => ( ! [B_x] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 187.18/188.03 => hBOOL(hAPP(V_P_2,B_x)) )
% 187.18/188.03 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_n_2))) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_sorted_OCons,axiom,
% 187.18/188.03 ! [V_x_2,V_xs_2,T_a] :
% 187.18/188.03 ( class_Orderings_Olinorder(T_a)
% 187.18/188.03 => ( ! [B_x] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 187.18/188.03 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_x)) )
% 187.18/188.03 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2)
% 187.18/188.03 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) ) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_list__ex__length,axiom,
% 187.18/188.03 ! [V_xs_2,V_P_2,T_a] :
% 187.18/188.03 ( c_List_Olist__ex(T_a,V_P_2,V_xs_2)
% 187.18/188.03 <=> ? [B_n] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))
% 187.18/188.03 & hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_n))) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_in__set__conv__decomp__first,axiom,
% 187.18/188.03 ! [V_xs_2,V_x_2,T_a] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 187.18/188.03 <=> ? [B_ys] :
% 187.18/188.03 ( ? [B_zs] : V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),B_ys),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_zs))
% 187.18/188.03 & ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),B_ys))) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_list__ex__simps_I2_J,axiom,
% 187.18/188.03 ! [V_P_2,T_a] : ~ c_List_Olist__ex(T_a,V_P_2,c_List_Olist_ONil(T_a)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_list__ex__append,axiom,
% 187.18/188.03 ! [V_ys_2,V_xs_2,V_P_2,T_a] :
% 187.18/188.03 ( c_List_Olist__ex(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2))
% 187.18/188.03 <=> ( c_List_Olist__ex(T_a,V_P_2,V_xs_2)
% 187.18/188.03 | c_List_Olist__ex(T_a,V_P_2,V_ys_2) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_list__ex__iff,axiom,
% 187.18/188.03 ! [V_xs_2,V_P_2,T_a] :
% 187.18/188.03 ( c_List_Olist__ex(T_a,V_P_2,V_xs_2)
% 187.18/188.03 <=> ? [B_x] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 187.18/188.03 & hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_list__ex__rev,axiom,
% 187.18/188.03 ! [V_xs_2,V_P_2,T_a] :
% 187.18/188.03 ( c_List_Olist__ex(T_a,V_P_2,hAPP(c_List_Orev(T_a),V_xs_2))
% 187.18/188.03 <=> c_List_Olist__ex(T_a,V_P_2,V_xs_2) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_list__ex__simps_I1_J,axiom,
% 187.18/188.03 ! [V_xs_2,V_x_2,V_P_2,T_a] :
% 187.18/188.03 ( c_List_Olist__ex(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))
% 187.18/188.03 <=> ( hBOOL(hAPP(V_P_2,V_x_2))
% 187.18/188.03 | c_List_Olist__ex(T_a,V_P_2,V_xs_2) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_in__set__conv__decomp,axiom,
% 187.18/188.03 ! [V_xs_2,V_x_2,T_a] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 187.18/188.03 <=> ? [B_ys,B_zs] : V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),B_ys),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_zs)) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_in__set__conv__decomp__last,axiom,
% 187.18/188.03 ! [V_xs_2,V_x_2,T_a] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 187.18/188.03 <=> ? [B_ys,B_zs] :
% 187.18/188.03 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),B_ys),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_zs))
% 187.18/188.03 & ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),B_zs))) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_option_Orecs_I2_J,axiom,
% 187.18/188.03 ! [V_a_2,V_f2_2,V_f1_2,T_b,T_a] : c_Option_Ooption_Ooption__rec(T_a,T_b,V_f1_2,V_f2_2,hAPP(c_Option_Ooption_OSome(T_b),V_a_2)) = hAPP(V_f2_2,V_a_2) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_option_Orecs_I1_J,axiom,
% 187.18/188.03 ! [V_f2_2,V_f1_2,T_b,T_a] : c_Option_Ooption_Ooption__rec(T_a,T_b,V_f1_2,V_f2_2,c_Option_Ooption_ONone(T_b)) = V_f1_2 ).
% 187.18/188.03
% 187.18/188.03 fof(fact_list__all__length,axiom,
% 187.18/188.03 ! [V_xs_2,V_P_2,T_a] :
% 187.18/188.03 ( c_List_Olist__all(T_a,V_P_2,V_xs_2)
% 187.18/188.03 <=> ! [B_n] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))
% 187.18/188.03 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_n))) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_measure__function__int,axiom,
% 187.18/188.03 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))) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_list__all__simps_I1_J,axiom,
% 187.18/188.03 ! [V_xs_2,V_x_2,V_P_2,T_a] :
% 187.18/188.03 ( c_List_Olist__all(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))
% 187.18/188.03 <=> ( hBOOL(hAPP(V_P_2,V_x_2))
% 187.18/188.03 & c_List_Olist__all(T_a,V_P_2,V_xs_2) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_list__all__rev,axiom,
% 187.18/188.03 ! [V_xs_2,V_P_2,T_a] :
% 187.18/188.03 ( c_List_Olist__all(T_a,V_P_2,hAPP(c_List_Orev(T_a),V_xs_2))
% 187.18/188.03 <=> c_List_Olist__all(T_a,V_P_2,V_xs_2) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_Ball__set__list__all,axiom,
% 187.18/188.03 ! [V_P_2,V_xs_2,T_a] :
% 187.18/188.03 ( ! [B_x] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 187.18/188.03 => hBOOL(hAPP(V_P_2,B_x)) )
% 187.18/188.03 <=> c_List_Olist__all(T_a,V_P_2,V_xs_2) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_measure__fst,axiom,
% 187.18/188.03 ! [T_b,V_f_2,T_a] :
% 187.18/188.03 ( c_FunDef_Ois__measure(T_a,V_f_2)
% 187.18/188.03 => c_FunDef_Ois__measure(tc_prod(T_a,T_b),hAPP(hAPP(c_COMBB(T_a,tc_Nat_Onat,tc_prod(T_a,T_b)),V_f_2),c_Product__Type_Ofst(T_a,T_b))) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_measure__snd,axiom,
% 187.18/188.03 ! [T_b,V_f_2,T_a] :
% 187.18/188.03 ( c_FunDef_Ois__measure(T_a,V_f_2)
% 187.18/188.03 => c_FunDef_Ois__measure(tc_prod(T_b,T_a),hAPP(hAPP(c_COMBB(T_a,tc_Nat_Onat,tc_prod(T_b,T_a)),V_f_2),c_Product__Type_Osnd(T_b,T_a))) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_list__all__iff,axiom,
% 187.18/188.03 ! [V_xs_2,V_P_2,T_a] :
% 187.18/188.03 ( c_List_Olist__all(T_a,V_P_2,V_xs_2)
% 187.18/188.03 <=> ! [B_x] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 187.18/188.03 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_is__measure_Ointros,axiom,
% 187.18/188.03 ! [V_f_2,T_a] : c_FunDef_Ois__measure(T_a,V_f_2) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_is__measure_Oequations,axiom,
% 187.18/188.03 ! [V_a_2,T_a] : c_FunDef_Ois__measure(T_a,V_a_2) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_is__measure_Osimps,axiom,
% 187.18/188.03 ! [V_a_2,T_a] : c_FunDef_Ois__measure(T_a,V_a_2) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_measure__size,axiom,
% 187.18/188.03 ! [T_a] :
% 187.18/188.03 ( class_Nat_Osize(T_a)
% 187.18/188.03 => c_FunDef_Ois__measure(T_a,c_Nat_Osize__class_Osize(T_a)) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_list__all__append,axiom,
% 187.18/188.03 ! [V_ys_2,V_xs_2,V_P_2,T_a] :
% 187.18/188.03 ( c_List_Olist__all(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2))
% 187.18/188.03 <=> ( c_List_Olist__all(T_a,V_P_2,V_xs_2)
% 187.18/188.03 & c_List_Olist__all(T_a,V_P_2,V_ys_2) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_list__all__simps_I2_J,axiom,
% 187.18/188.03 ! [V_P_2,T_a] : c_List_Olist__all(T_a,V_P_2,c_List_Olist_ONil(T_a)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_list__all__iff__raw,axiom,
% 187.18/188.03 ! [V_xs_2,V_P_2,T_a] :
% 187.18/188.03 ( c_List_Olist__all(T_a,V_P_2,V_xs_2)
% 187.18/188.03 <=> ! [B_x] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 187.18/188.03 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_list__ex1__simps_I2_J,axiom,
% 187.18/188.03 ! [V_xs_2,V_x_2,V_P_2,T_a] :
% 187.18/188.03 ( c_List_Olist__ex1(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))
% 187.18/188.03 <=> ( ( hBOOL(hAPP(V_P_2,V_x_2))
% 187.18/188.03 => c_List_Olist__all(T_a,hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),V_P_2))),hAPP(c_fequal,V_x_2)),V_xs_2) )
% 187.18/188.03 & ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 187.18/188.03 => c_List_Olist__ex1(T_a,V_P_2,V_xs_2) ) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_equal__fun__def,axiom,
% 187.18/188.03 ! [V_g_2,V_f_2,T_a,T_b] :
% 187.18/188.03 ( ( class_HOL_Oequal(T_b)
% 187.18/188.03 & class_Enum_Oenum(T_a) )
% 187.18/188.03 => ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_fun(T_a,T_b)),V_f_2),V_g_2))
% 187.18/188.03 <=> ! [B_x] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),c_Enum_Oenum__class_Oenum(T_a))))
% 187.18/188.03 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_list__ex1__simps_I1_J,axiom,
% 187.18/188.03 ! [V_P_2,T_a] : ~ c_List_Olist__ex1(T_a,V_P_2,c_List_Olist_ONil(T_a)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_eq__equal,axiom,
% 187.18/188.03 ! [T_a] :
% 187.18/188.03 ( class_HOL_Oequal(T_a)
% 187.18/188.03 => c_fequal = c_HOL_Oequal__class_Oequal(T_a) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_equal__eq,axiom,
% 187.18/188.03 ! [V_y_2,V_x_2,T_a] :
% 187.18/188.03 ( class_HOL_Oequal(T_a)
% 187.18/188.03 => ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(T_a),V_x_2),V_y_2))
% 187.18/188.03 <=> V_x_2 = V_y_2 ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_equal__refl,axiom,
% 187.18/188.03 ! [V_x,T_a] :
% 187.18/188.03 ( class_HOL_Oequal(T_a)
% 187.18/188.03 => hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(T_a),V_x),V_x)) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_equal,axiom,
% 187.18/188.03 ! [T_a] :
% 187.18/188.03 ( class_HOL_Oequal(T_a)
% 187.18/188.03 => c_HOL_Oequal__class_Oequal(T_a) = c_fequal ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_exists1__code,axiom,
% 187.18/188.03 ! [V_P_2,T_a] :
% 187.18/188.03 ( class_Enum_Oenum(T_a)
% 187.18/188.03 => ( ? [B_x] :
% 187.18/188.03 ( hBOOL(hAPP(V_P_2,B_x))
% 187.18/188.03 & ! [B_y] :
% 187.18/188.03 ( hBOOL(hAPP(V_P_2,B_y))
% 187.18/188.03 => B_y = B_x ) )
% 187.18/188.03 <=> c_List_Olist__ex1(T_a,V_P_2,c_Enum_Oenum__class_Oenum(T_a)) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_bool_Osize_I3_J,axiom,
% 187.18/188.03 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_bool_Osize_I4_J,axiom,
% 187.18/188.03 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_list__ex1__iff,axiom,
% 187.18/188.03 ! [V_xs_2,V_P_2,T_a] :
% 187.18/188.03 ( c_List_Olist__ex1(T_a,V_P_2,V_xs_2)
% 187.18/188.03 <=> ? [B_x] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 187.18/188.03 & hBOOL(hAPP(V_P_2,B_x))
% 187.18/188.03 & ! [B_y] :
% 187.18/188.03 ( ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),hAPP(c_List_Oset(T_a),V_xs_2)))
% 187.18/188.03 & hBOOL(hAPP(V_P_2,B_y)) )
% 187.18/188.03 => B_y = B_x ) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_size__code,axiom,
% 187.18/188.03 ! [V_xq_2,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_a)),V_xq_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(T_a,tc_Lazy__Sequence_Olazy__sequence(T_a)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat),hAPP(c_COMBK(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat),T_a),hAPP(hAPP(c_COMBC(tc_Lazy__Sequence_Olazy__sequence(T_a),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_a)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_a)))),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),hAPP(c_Lazy__Sequence_Oyield(T_a),V_xq_2)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_transfer__morphism__int__nat,axiom,
% 187.18/188.03 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)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_eq__int__code_I11_J,axiom,
% 187.18/188.03 ! [V_k1] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(V_k1)),c_Int_OMin)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_eq__int__code_I7_J,axiom,
% 187.18/188.03 ! [V_k2] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k2))) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_eq__int__code_I13_J,axiom,
% 187.18/188.03 ! [V_k2_2,V_k1_2] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 187.18/188.03 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_eq__int__code_I16_J,axiom,
% 187.18/188.03 ! [V_k2_2,V_k1_2] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 187.18/188.03 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_eq__int__code_I1_J,axiom,
% 187.18/188.03 hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_eq__number__of__int__code,axiom,
% 187.18/188.03 ! [V_l_2,V_k_2] :
% 187.18/188.03 ( 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)))
% 187.18/188.03 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_eq__int__code_I6_J,axiom,
% 187.18/188.03 hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_eq__int__code_I10_J,axiom,
% 187.18/188.03 ! [V_k1] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1)),c_Int_OPls)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_eq__int__code_I4_J,axiom,
% 187.18/188.03 ! [V_k2] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k2))) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_equal__int__def,axiom,
% 187.18/188.03 ! [V_l_2,V_k_2] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k_2),V_l_2))
% 187.18/188.03 <=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k_2),V_l_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_eq__int__code_I15_J,axiom,
% 187.18/188.03 ! [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))) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_eq__int__code_I14_J,axiom,
% 187.18/188.03 ! [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))) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_eq__int__code_I9_J,axiom,
% 187.18/188.03 ! [V_k1_2] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OPls))
% 187.18/188.03 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),c_Int_OPls)) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_eq__int__code_I3_J,axiom,
% 187.18/188.03 ! [V_k2_2] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k2_2)))
% 187.18/188.03 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),V_k2_2)) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_eq__int__code_I12_J,axiom,
% 187.18/188.03 ! [V_k1_2] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OMin))
% 187.18/188.03 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),c_Int_OMin)) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_eq__int__code_I8_J,axiom,
% 187.18/188.03 ! [V_k2_2] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k2_2)))
% 187.18/188.03 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),V_k2_2)) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_eq__int__code_I2_J,axiom,
% 187.18/188.03 ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_eq__int__code_I5_J,axiom,
% 187.18/188.03 ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_lazy__sequence__size__code,axiom,
% 187.18/188.03 ! [V_xq_2,V_s_2,T_a] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_a,V_s_2),V_xq_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(T_a,tc_Lazy__Sequence_Olazy__sequence(T_a)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat),hAPP(hAPP(c_COMBC(T_a,tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat)),T_a),c_COMBC(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),T_a),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(T_a)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat))),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_a),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_a),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat)),T_a),c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Lazy__Sequence_Olazy__sequence(T_a))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),T_a),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_s_2))),c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_a,V_s_2))))),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(c_Lazy__Sequence_Oyield(T_a),V_xq_2)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_seq__case,axiom,
% 187.18/188.03 ! [V_xq_2,V_g_2,V_f_2,T_b,T_a] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(T_a,T_b,V_f_2,V_g_2,V_xq_2) = hAPP(c_Option_Ooption_Ooption__case(T_a,tc_prod(T_b,tc_Lazy__Sequence_Olazy__sequence(T_b)),V_f_2,hAPP(c_Product__Type_Oprod_Oprod__case(T_b,tc_Lazy__Sequence_Olazy__sequence(T_b),T_a),V_g_2)),hAPP(c_Lazy__Sequence_Oyield(T_b),V_xq_2)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_eq__int__refl,axiom,
% 187.18/188.03 ! [V_k] : hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k),V_k)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_yieldn__def,axiom,
% 187.18/188.03 ! [T_a] : c_Lazy__Sequence_Oyieldn(T_a) = c_Lazy__Sequence_Oanamorph(tc_Lazy__Sequence_Olazy__sequence(T_a),T_a,c_Lazy__Sequence_Oyield(T_a)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_lazy__sequence_Osize_I2_J,axiom,
% 187.18/188.03 ! [V_lazy__sequence_2,V_a_2,V_fa_2,T_a] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_a,V_fa_2),c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,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_a,V_fa_2),V_lazy__sequence_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_lazy__sequence_Osimps_I5_J,axiom,
% 187.18/188.03 ! [V_lazy__sequence_2,V_a_2,V_f2_2,V_f1_2,T_b,T_a] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(T_a,T_b,V_f1_2,V_f2_2,c_Lazy__Sequence_Olazy__sequence_OInsert(T_b,V_a_2,V_lazy__sequence_2)) = hAPP(hAPP(V_f2_2,V_a_2),V_lazy__sequence_2) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_lazy__sequence_Oinject,axiom,
% 187.18/188.03 ! [V_lazy__sequence_H_2,V_a_H_2,V_lazy__sequence_2,V_a_2,T_a] :
% 187.18/188.03 ( c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_a_2,V_lazy__sequence_2) = c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_a_H_2,V_lazy__sequence_H_2)
% 187.18/188.03 <=> ( V_a_2 = V_a_H_2
% 187.18/188.03 & V_lazy__sequence_2 = V_lazy__sequence_H_2 ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact__01,axiom,
% 187.18/188.03 ! [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)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_lazy__sequence_Osize_I4_J,axiom,
% 187.18/188.03 ! [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))) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_New__DSequence_Oneg__decr__bind__def,axiom,
% 187.18/188.03 ! [V_f_2,V_x_2,T_a,T_b,V_i_2] :
% 187.18/188.03 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 187.18/188.03 => hAPP(c_New__DSequence_Oneg__decr__bind(T_b,T_a,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Ohit__bound(T_a) )
% 187.18/188.03 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 187.18/188.03 => hAPP(c_New__DSequence_Oneg__decr__bind(T_b,T_a,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Ohb__bind(T_b,T_a,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_b,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_a))),V_f_2),V_i_2)) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_New__DSequence_Opos__decr__bind__def,axiom,
% 187.18/188.03 ! [V_f_2,V_x_2,T_a,T_b,V_i_2] :
% 187.18/188.03 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 187.18/188.03 => hAPP(c_New__DSequence_Opos__decr__bind(T_b,T_a,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Oempty(T_a) )
% 187.18/188.03 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 187.18/188.03 => hAPP(c_New__DSequence_Opos__decr__bind(T_b,T_a,V_x_2,V_f_2),V_i_2) = hAPP(c_Lazy__Sequence_Obind(T_b,T_a,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_b,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_a)),V_f_2),V_i_2)) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_New__Random__Sequence_Oneg__decr__bind__def,axiom,
% 187.18/188.03 ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_a,T_b] : c_New__Random__Sequence_Oneg__decr__bind(T_b,T_a,V_R_2,V_f_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Oneg__decr__bind(T_b,T_a,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_b,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_a)))),hAPP(hAPP(c_COMBC(T_b,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_a))))),hAPP(hAPP(c_COMBC(T_b,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_a)))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_New__Random__Sequence_Opos__decr__bind__def,axiom,
% 187.18/188.03 ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_a,T_b] : c_New__Random__Sequence_Opos__decr__bind(T_b,T_a,V_R_2,V_f_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__decr__bind(T_b,T_a,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_b,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_a))),hAPP(hAPP(c_COMBC(T_b,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_a)))),hAPP(hAPP(c_COMBC(T_b,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_a))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_New__DSequence_Oneg__bind__def,axiom,
% 187.18/188.03 ! [V_i_2,V_f_2,V_x_2,T_a,T_b] : hAPP(c_New__DSequence_Oneg__bind(T_b,T_a,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Ohb__bind(T_b,T_a,hAPP(V_x_2,V_i_2),hAPP(hAPP(c_COMBC(T_b,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_a))),V_f_2),V_i_2)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_New__DSequence_Opos__empty__def,axiom,
% 187.18/188.03 ! [V_i_1,T_a] : hAPP(c_New__DSequence_Opos__empty(T_a),V_i_1) = c_Lazy__Sequence_Oempty(T_a) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_pos__empty__def,axiom,
% 187.18/188.03 ! [V_seed_2,V_size_2,V_nrandom_2,T_a] : c_New__Random__Sequence_Opos__empty(T_a,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__empty(T_a) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_neg__bind__def,axiom,
% 187.18/188.03 ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_a,T_b] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(T_b,T_a,V_R_2,V_f_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Oneg__bind(T_b,T_a,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_b,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_a)))),hAPP(hAPP(c_COMBC(T_b,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_a))))),hAPP(hAPP(c_COMBC(T_b,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_a)))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_New__DSequence_Opos__bind__def,axiom,
% 187.18/188.03 ! [V_i_2,V_f_2,V_x_2,T_a,T_b] : hAPP(c_New__DSequence_Opos__bind(T_b,T_a,V_x_2,V_f_2),V_i_2) = hAPP(c_Lazy__Sequence_Obind(T_b,T_a,hAPP(V_x_2,V_i_2)),hAPP(hAPP(c_COMBC(T_b,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_a)),V_f_2),V_i_2)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_neg__map__def,axiom,
% 187.18/188.03 ! [V_P_2,V_f_2,T_a,T_b] : c_New__Random__Sequence_Oneg__map(T_b,T_a,V_f_2,V_P_2) = c_New__Random__Sequence_Oneg__bind(T_b,T_a,V_P_2,hAPP(c_Fun_Ocomp(T_a,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_a)))))),T_b,c_New__Random__Sequence_Oneg__single(T_a)),V_f_2)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_neg__single__def,axiom,
% 187.18/188.03 ! [V_seed_2,V_size_2,V_nrandom_2,V_x_2,T_a] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(T_a),V_x_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Oneg__single(T_a,V_x_2) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_pos__bind__def,axiom,
% 187.18/188.03 ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_a,T_b] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(T_b,T_a,V_R_2,V_f_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Opos__bind(T_b,T_a,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_b,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_a))),hAPP(hAPP(c_COMBC(T_b,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_a)))),hAPP(hAPP(c_COMBC(T_b,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_a))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_New__DSequence_Oneg__single__def,axiom,
% 187.18/188.03 ! [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) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_pos__map__def,axiom,
% 187.18/188.03 ! [V_P_2,V_f_2,T_a,T_b] : c_New__Random__Sequence_Opos__map(T_b,T_a,V_f_2,V_P_2) = c_New__Random__Sequence_Opos__bind(T_b,T_a,V_P_2,hAPP(c_Fun_Ocomp(T_a,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_a))))),T_b,c_New__Random__Sequence_Opos__single(T_a)),V_f_2)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_pos__single__def,axiom,
% 187.18/188.03 ! [V_seed_2,V_size_2,V_nrandom_2,V_x_2,T_a] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(T_a),V_x_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Opos__single(T_a,V_x_2) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_length__splice,axiom,
% 187.18/188.03 ! [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)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_splice_Osimps_I3_J,axiom,
% 187.18/188.03 ! [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))) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_splice_Osimps_I1_J,axiom,
% 187.18/188.03 ! [V_ys,T_a] : c_List_Osplice(T_a,c_List_Olist_ONil(T_a),V_ys) = V_ys ).
% 187.18/188.03
% 187.18/188.03 fof(fact_splice__Nil2,axiom,
% 187.18/188.03 ! [V_xs,T_a] : c_List_Osplice(T_a,V_xs,c_List_Olist_ONil(T_a)) = V_xs ).
% 187.18/188.03
% 187.18/188.03 fof(fact_splice_Osimps_I2_J,axiom,
% 187.18/188.03 ! [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) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_New__DSequence_Opos__single__def,axiom,
% 187.18/188.03 ! [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) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_acyclicP__converse,axiom,
% 187.18/188.03 ! [V_r_2,T_a] :
% 187.18/188.03 ( c_Wellfounded_Oacyclic(T_a,hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),c_Predicate_Oconversep(T_a,T_a,V_r_2))))
% 187.18/188.03 <=> c_Wellfounded_Oacyclic(T_a,hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),V_r_2))) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_converse__meet,axiom,
% 187.18/188.03 ! [V_s_2,V_r_2,T_a,T_b] : c_Predicate_Oconversep(T_b,T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool))),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),c_Predicate_Oconversep(T_b,T_a,V_r_2)),c_Predicate_Oconversep(T_b,T_a,V_s_2)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_conversep__noteq,axiom,
% 187.18/188.03 ! [V_y_2,V_x_2,T_a] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_a,T_a,hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot)),c_fequal)),V_x_2),V_y_2))
% 187.18/188.03 <=> V_x_2 != V_y_2 ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_conversepD,axiom,
% 187.18/188.03 ! [V_b_2,V_a_2,V_r_2,T_b,T_a] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_a,T_b,V_r_2),V_a_2),V_b_2))
% 187.18/188.03 => hBOOL(hAPP(hAPP(V_r_2,V_b_2),V_a_2)) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_conversep_Ointros,axiom,
% 187.18/188.03 ! [T_b,T_a,V_b_2,V_a_2,V_r_2] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 187.18/188.03 => hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_a,T_b,V_r_2),V_b_2),V_a_2)) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_conversep_Oequations,axiom,
% 187.18/188.03 ! [V_a1_2,V_a2_2,V_r_2,T_b,T_a] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_a,T_b,V_r_2),V_a2_2),V_a1_2))
% 187.18/188.03 <=> hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2)) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_conversep__iff,axiom,
% 187.18/188.03 ! [V_b_2,V_a_2,V_r_2,T_b,T_a] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_a,T_b,V_r_2),V_a_2),V_b_2))
% 187.18/188.03 <=> hBOOL(hAPP(hAPP(V_r_2,V_b_2),V_a_2)) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_conversep__conversep,axiom,
% 187.18/188.03 ! [V_r_2,T_a,T_b] : c_Predicate_Oconversep(T_b,T_a,c_Predicate_Oconversep(T_a,T_b,V_r_2)) = V_r_2 ).
% 187.18/188.03
% 187.18/188.03 fof(fact_conversep__eq,axiom,
% 187.18/188.03 ! [T_a] : c_Predicate_Oconversep(T_a,T_a,c_fequal) = c_fequal ).
% 187.18/188.03
% 187.18/188.03 fof(fact_converse__pred__comp,axiom,
% 187.18/188.03 ! [V_s_2,V_r_2,T_c,T_a,T_b] : c_Predicate_Oconversep(T_b,T_a,c_Predicate_Opred__comp(T_b,T_c,T_a,V_r_2,V_s_2)) = c_Predicate_Opred__comp(T_a,T_c,T_b,c_Predicate_Oconversep(T_c,T_a,V_s_2),c_Predicate_Oconversep(T_b,T_c,V_r_2)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_converse__join,axiom,
% 187.18/188.03 ! [V_s_2,V_r_2,T_a,T_b] : c_Predicate_Oconversep(T_b,T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool))),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),c_Predicate_Oconversep(T_b,T_a,V_r_2)),c_Predicate_Oconversep(T_b,T_a,V_s_2)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_conversep__converse__eq,axiom,
% 187.18/188.03 ! [V_y_2,V_x_2,V_r_2,T_b,T_a] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_a,T_b,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,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_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_r_2)),V_x_2),V_y_2))
% 187.18/188.03 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_a,T_b),V_r_2))) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact__02,axiom,
% 187.18/188.03 ! [V_s2_2,V_s1_2,T_b,T_a] : c_Lazy__Sequence_Oproduct(T_a,T_b,V_s1_2,V_s2_2) = hAPP(c_Lazy__Sequence_Obind(T_a,tc_prod(T_a,T_b),V_s1_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_a,T_b))),tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_a,T_b)),T_a),c_Lazy__Sequence_Obind(T_b,tc_prod(T_a,T_b),V_s2_2)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_a,T_b))),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_a,T_b)),T_b),c_Lazy__Sequence_Osingle(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_tl__replicate,axiom,
% 187.18/188.03 ! [V_x,T_a,V_n] :
% 187.18/188.03 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.18/188.03 => 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) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_zip__replicate,axiom,
% 187.18/188.03 ! [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)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_replicate__app__Cons__same,axiom,
% 187.18/188.03 ! [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)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_replicate__Suc,axiom,
% 187.18/188.03 ! [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)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_rev__replicate,axiom,
% 187.18/188.03 ! [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) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_last__replicate,axiom,
% 187.18/188.03 ! [V_x,T_a,V_n] :
% 187.18/188.03 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.18/188.03 => c_List_Olast(T_a,c_List_Oreplicate(T_a,V_n,V_x)) = V_x ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_drop__replicate,axiom,
% 187.18/188.03 ! [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) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_hd__replicate,axiom,
% 187.18/188.03 ! [V_x,T_a,V_n] :
% 187.18/188.03 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.18/188.03 => hAPP(c_List_Ohd(T_a),c_List_Oreplicate(T_a,V_n,V_x)) = V_x ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_take__replicate,axiom,
% 187.18/188.03 ! [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) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_Bex__set__replicate,axiom,
% 187.18/188.03 ! [V_P_2,V_a_2,V_n_2,T_a] :
% 187.18/188.03 ( ? [B_x] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),c_List_Oreplicate(T_a,V_n_2,V_a_2))))
% 187.18/188.03 & hBOOL(hAPP(V_P_2,B_x)) )
% 187.18/188.03 <=> ( hBOOL(hAPP(V_P_2,V_a_2))
% 187.18/188.03 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_Ball__set__replicate,axiom,
% 187.18/188.03 ! [V_P_2,V_a_2,V_n_2,T_a] :
% 187.18/188.03 ( ! [B_x] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),c_List_Oreplicate(T_a,V_n_2,V_a_2))))
% 187.18/188.03 => hBOOL(hAPP(V_P_2,B_x)) )
% 187.18/188.03 <=> ( hBOOL(hAPP(V_P_2,V_a_2))
% 187.18/188.03 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_replicate__eq__replicate,axiom,
% 187.18/188.03 ! [V_y_2,V_n_2,V_x_2,V_m_2,T_a] :
% 187.18/188.03 ( c_List_Oreplicate(T_a,V_m_2,V_x_2) = c_List_Oreplicate(T_a,V_n_2,V_y_2)
% 187.18/188.03 <=> ( V_m_2 = V_n_2
% 187.18/188.03 & ( V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 187.18/188.03 => V_x_2 = V_y_2 ) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_nth__replicate,axiom,
% 187.18/188.03 ! [V_x,T_a,V_n,V_i] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n))
% 187.18/188.03 => hAPP(hAPP(c_List_Onth(T_a),c_List_Oreplicate(T_a,V_n,V_x)),V_i) = V_x ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_in__set__replicate,axiom,
% 187.18/188.03 ! [V_y_2,V_n_2,V_x_2,T_a] :
% 187.18/188.03 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Oreplicate(T_a,V_n_2,V_y_2))))
% 187.18/188.03 <=> ( V_x_2 = V_y_2
% 187.18/188.03 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_append__replicate__commute,axiom,
% 187.18/188.03 ! [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)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_replicate__add,axiom,
% 187.18/188.03 ! [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)) ).
% 187.18/188.03
% 187.18/188.03 fof(fact_filter__replicate,axiom,
% 187.18/188.03 ! [V_n_2,T_a,V_x_2,V_P_2] :
% 187.18/188.03 ( ( hBOOL(hAPP(V_P_2,V_x_2))
% 187.18/188.03 => hAPP(c_List_Ofilter(T_a,V_P_2),c_List_Oreplicate(T_a,V_n_2,V_x_2)) = c_List_Oreplicate(T_a,V_n_2,V_x_2) )
% 187.18/188.03 & ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 187.18/188.03 => hAPP(c_List_Ofilter(T_a,V_P_2),c_List_Oreplicate(T_a,V_n_2,V_x_2)) = c_List_Olist_ONil(T_a) ) ) ).
% 187.18/188.03
% 187.18/188.03 %----Arity declarations (231)
% 187.18/188.03 fof(arity_HOL__Obool__Lattices_Obounded__lattice,axiom,
% 187.18/188.03 class_Lattices_Obounded__lattice(tc_HOL_Obool) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_fun__Lattices_Obounded__lattice,axiom,
% 187.18/188.03 ! [T_2,T_1] :
% 187.18/188.03 ( class_Lattices_Obounded__lattice(T_1)
% 187.18/188.03 => class_Lattices_Obounded__lattice(tc_fun(T_2,T_1)) ) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_fun__Complete__Lattice_Ocomplete__lattice,axiom,
% 187.18/188.03 ! [T_2,T_1] :
% 187.18/188.03 ( class_Complete__Lattice_Ocomplete__lattice(T_1)
% 187.18/188.03 => class_Complete__Lattice_Ocomplete__lattice(tc_fun(T_2,T_1)) ) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_fun__Lattices_Obounded__lattice__top,axiom,
% 187.18/188.03 ! [T_2,T_1] :
% 187.18/188.03 ( class_Lattices_Obounded__lattice(T_1)
% 187.18/188.03 => class_Lattices_Obounded__lattice__top(tc_fun(T_2,T_1)) ) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_fun__Lattices_Obounded__lattice__bot,axiom,
% 187.18/188.03 ! [T_2,T_1] :
% 187.18/188.03 ( class_Lattices_Obounded__lattice(T_1)
% 187.18/188.03 => class_Lattices_Obounded__lattice__bot(tc_fun(T_2,T_1)) ) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_fun__Lattices_Osemilattice__sup,axiom,
% 187.18/188.03 ! [T_2,T_1] :
% 187.18/188.03 ( class_Lattices_Olattice(T_1)
% 187.18/188.03 => class_Lattices_Osemilattice__sup(tc_fun(T_2,T_1)) ) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_fun__Lattices_Osemilattice__inf,axiom,
% 187.18/188.03 ! [T_2,T_1] :
% 187.18/188.03 ( class_Lattices_Olattice(T_1)
% 187.18/188.03 => class_Lattices_Osemilattice__inf(tc_fun(T_2,T_1)) ) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_fun__Lattices_Odistrib__lattice,axiom,
% 187.18/188.03 ! [T_2,T_1] :
% 187.18/188.03 ( class_Lattices_Odistrib__lattice(T_1)
% 187.18/188.03 => class_Lattices_Odistrib__lattice(tc_fun(T_2,T_1)) ) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_fun__Lattices_Oboolean__algebra,axiom,
% 187.18/188.03 ! [T_2,T_1] :
% 187.18/188.03 ( class_Lattices_Oboolean__algebra(T_1)
% 187.18/188.03 => class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1)) ) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_fun__Orderings_Opreorder,axiom,
% 187.18/188.03 ! [T_2,T_1] :
% 187.18/188.03 ( class_Orderings_Opreorder(T_1)
% 187.18/188.03 => class_Orderings_Opreorder(tc_fun(T_2,T_1)) ) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_fun__Finite__Set_Ofinite,axiom,
% 187.18/188.03 ! [T_1,T_2] :
% 187.18/188.03 ( ( class_Finite__Set_Ofinite(T_2)
% 187.18/188.03 & class_Finite__Set_Ofinite(T_1) )
% 187.18/188.03 => class_Finite__Set_Ofinite(tc_fun(T_2,T_1)) ) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_fun__Lattices_Olattice,axiom,
% 187.18/188.03 ! [T_2,T_1] :
% 187.18/188.03 ( class_Lattices_Olattice(T_1)
% 187.18/188.03 => class_Lattices_Olattice(tc_fun(T_2,T_1)) ) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_fun__Orderings_Oorder,axiom,
% 187.18/188.03 ! [T_2,T_1] :
% 187.18/188.03 ( class_Orderings_Oorder(T_1)
% 187.18/188.03 => class_Orderings_Oorder(tc_fun(T_2,T_1)) ) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_fun__Orderings_Otop,axiom,
% 187.18/188.03 ! [T_2,T_1] :
% 187.18/188.03 ( class_Orderings_Otop(T_1)
% 187.18/188.03 => class_Orderings_Otop(tc_fun(T_2,T_1)) ) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_fun__Orderings_Oord,axiom,
% 187.18/188.03 ! [T_2,T_1] :
% 187.18/188.03 ( class_Orderings_Oord(T_1)
% 187.18/188.03 => class_Orderings_Oord(tc_fun(T_2,T_1)) ) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_fun__Orderings_Obot,axiom,
% 187.18/188.03 ! [T_2,T_1] :
% 187.18/188.03 ( class_Orderings_Obot(T_1)
% 187.18/188.03 => class_Orderings_Obot(tc_fun(T_2,T_1)) ) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_fun__Groups_Ouminus,axiom,
% 187.18/188.03 ! [T_2,T_1] :
% 187.18/188.03 ( class_Groups_Ouminus(T_1)
% 187.18/188.03 => class_Groups_Ouminus(tc_fun(T_2,T_1)) ) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_fun__Groups_Ominus,axiom,
% 187.18/188.03 ! [T_2,T_1] :
% 187.18/188.03 ( class_Groups_Ominus(T_1)
% 187.18/188.03 => class_Groups_Ominus(tc_fun(T_2,T_1)) ) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_fun__HOL_Oequal,axiom,
% 187.18/188.03 ! [T_1,T_2] :
% 187.18/188.03 ( ( class_Enum_Oenum(T_2)
% 187.18/188.03 & class_HOL_Oequal(T_1) )
% 187.18/188.03 => class_HOL_Oequal(tc_fun(T_2,T_1)) ) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_fun__Enum_Oenum,axiom,
% 187.18/188.03 ! [T_1,T_2] :
% 187.18/188.03 ( ( class_Enum_Oenum(T_2)
% 187.18/188.03 & class_Enum_Oenum(T_1) )
% 187.18/188.03 => class_Enum_Oenum(tc_fun(T_2,T_1)) ) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_Com__Ocom__HOL_Oequal,axiom,
% 187.18/188.03 class_HOL_Oequal(tc_Com_Ocom) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_Com__Ocom__Nat_Osize,axiom,
% 187.18/188.03 class_Nat_Osize(tc_Com_Ocom) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 187.18/188.03 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 187.18/188.03 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 187.18/188.03 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,axiom,
% 187.18/188.03 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_Int__Oint__Rings_Olinordered__semiring__1__strict,axiom,
% 187.18/188.03 class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_Int__Oint__Groups_Olinordered__ab__semigroup__add,axiom,
% 187.18/188.03 class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_Int__Oint__Rings_Olinordered__semiring__strict,axiom,
% 187.18/188.03 class_Rings_Olinordered__semiring__strict(tc_Int_Oint) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add,axiom,
% 187.18/188.03 class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_Int__Oint__Groups_Oordered__ab__group__add__abs,axiom,
% 187.18/188.03 class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_Int__Oint__Groups_Oordered__comm__monoid__add,axiom,
% 187.18/188.03 class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_Int__Oint__Groups_Olinordered__ab__group__add,axiom,
% 187.18/188.03 class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,axiom,
% 187.18/188.03 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_Int__Oint__Rings_Oring__1__no__zero__divisors,axiom,
% 187.18/188.03 class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_Int__Oint__Rings_Oordered__cancel__semiring,axiom,
% 187.18/188.03 class_Rings_Oordered__cancel__semiring(tc_Int_Oint) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_Int__Oint__Rings_Olinordered__ring__strict,axiom,
% 187.18/188.03 class_Rings_Olinordered__ring__strict(tc_Int_Oint) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_Int__Oint__Rings_Oring__no__zero__divisors,axiom,
% 187.18/188.03 class_Rings_Oring__no__zero__divisors(tc_Int_Oint) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_Int__Oint__Rings_Oordered__comm__semiring,axiom,
% 187.18/188.03 class_Rings_Oordered__comm__semiring(tc_Int_Oint) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_Int__Oint__Rings_Olinordered__semiring__1,axiom,
% 187.18/188.03 class_Rings_Olinordered__semiring__1(tc_Int_Oint) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_Int__Oint__Groups_Oordered__ab__group__add,axiom,
% 187.18/188.03 class_Groups_Oordered__ab__group__add(tc_Int_Oint) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_Int__Oint__Groups_Ocancel__semigroup__add,axiom,
% 187.18/188.03 class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_Int__Oint__Rings_Olinordered__semiring,axiom,
% 187.18/188.03 class_Rings_Olinordered__semiring(tc_Int_Oint) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_Int__Oint__Rings_Olinordered__semidom,axiom,
% 187.18/188.03 class_Rings_Olinordered__semidom(tc_Int_Oint) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_Int__Oint__Lattices_Osemilattice__sup,axiom,
% 187.18/188.03 class_Lattices_Osemilattice__sup(tc_Int_Oint) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_Int__Oint__Lattices_Osemilattice__inf,axiom,
% 187.18/188.03 class_Lattices_Osemilattice__inf(tc_Int_Oint) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_Int__Oint__Lattices_Odistrib__lattice,axiom,
% 187.18/188.03 class_Lattices_Odistrib__lattice(tc_Int_Oint) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_Int__Oint__Groups_Oab__semigroup__mult,axiom,
% 187.18/188.03 class_Groups_Oab__semigroup__mult(tc_Int_Oint) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_Int__Oint__Groups_Ocomm__monoid__mult,axiom,
% 187.18/188.03 class_Groups_Ocomm__monoid__mult(tc_Int_Oint) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_Int__Oint__Groups_Oab__semigroup__add,axiom,
% 187.18/188.03 class_Groups_Oab__semigroup__add(tc_Int_Oint) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_Int__Oint__Rings_Oordered__semiring,axiom,
% 187.18/188.03 class_Rings_Oordered__semiring(tc_Int_Oint) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_Int__Oint__Rings_Oordered__ring__abs,axiom,
% 187.18/188.03 class_Rings_Oordered__ring__abs(tc_Int_Oint) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_Int__Oint__Rings_Ono__zero__divisors,axiom,
% 187.18/188.03 class_Rings_Ono__zero__divisors(tc_Int_Oint) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_Int__Oint__Groups_Ocomm__monoid__add,axiom,
% 187.18/188.03 class_Groups_Ocomm__monoid__add(tc_Int_Oint) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_Int__Oint__Rings_Olinordered__ring,axiom,
% 187.18/188.03 class_Rings_Olinordered__ring(tc_Int_Oint) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_Int__Oint__Rings_Olinordered__idom,axiom,
% 187.18/188.03 class_Rings_Olinordered__idom(tc_Int_Oint) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_Int__Oint__Rings_Ocomm__semiring__1,axiom,
% 187.18/188.03 class_Rings_Ocomm__semiring__1(tc_Int_Oint) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_Int__Oint__Groups_Osemigroup__add,axiom,
% 187.18/188.03 class_Groups_Osemigroup__add(tc_Int_Oint) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_Int__Oint__Divides_Osemiring__div,axiom,
% 187.18/188.03 class_Divides_Osemiring__div(tc_Int_Oint) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_Int__Oint__Rings_Ocomm__semiring,axiom,
% 187.18/188.03 class_Rings_Ocomm__semiring(tc_Int_Oint) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_Int__Oint__Nat_Osemiring__char__0,axiom,
% 187.18/188.03 class_Nat_Osemiring__char__0(tc_Int_Oint) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_Int__Oint__Groups_Oab__group__add,axiom,
% 187.18/188.03 class_Groups_Oab__group__add(tc_Int_Oint) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_Int__Oint__Rings_Ozero__neq__one,axiom,
% 187.18/188.03 class_Rings_Ozero__neq__one(tc_Int_Oint) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_Int__Oint__Rings_Oordered__ring,axiom,
% 187.18/188.03 class_Rings_Oordered__ring(tc_Int_Oint) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_Int__Oint__Orderings_Opreorder,axiom,
% 187.18/188.03 class_Orderings_Opreorder(tc_Int_Oint) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_Int__Oint__Orderings_Olinorder,axiom,
% 187.18/188.03 class_Orderings_Olinorder(tc_Int_Oint) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_Int__Oint__Groups_Omonoid__mult,axiom,
% 187.18/188.03 class_Groups_Omonoid__mult(tc_Int_Oint) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_Int__Oint__Rings_Ocomm__ring__1,axiom,
% 187.18/188.03 class_Rings_Ocomm__ring__1(tc_Int_Oint) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_Int__Oint__Groups_Omonoid__add,axiom,
% 187.18/188.03 class_Groups_Omonoid__add(tc_Int_Oint) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_Int__Oint__Smallcheck_Osmall,axiom,
% 187.18/188.03 class_Smallcheck_Osmall(tc_Int_Oint) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_Int__Oint__Rings_Osemiring__1,axiom,
% 187.18/188.03 class_Rings_Osemiring__1(tc_Int_Oint) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_Int__Oint__Rings_Osemiring__0,axiom,
% 187.18/188.03 class_Rings_Osemiring__0(tc_Int_Oint) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_Int__Oint__Lattices_Olattice,axiom,
% 187.18/188.03 class_Lattices_Olattice(tc_Int_Oint) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_Int__Oint__Groups_Ogroup__add,axiom,
% 187.18/188.03 class_Groups_Ogroup__add(tc_Int_Oint) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_Int__Oint__Divides_Oring__div,axiom,
% 187.18/188.03 class_Divides_Oring__div(tc_Int_Oint) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_Int__Oint__Rings_Omult__zero,axiom,
% 187.18/188.03 class_Rings_Omult__zero(tc_Int_Oint) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_Int__Oint__Orderings_Oorder,axiom,
% 187.18/188.03 class_Orderings_Oorder(tc_Int_Oint) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_Int__Oint__Int_Oring__char__0,axiom,
% 187.18/188.03 class_Int_Oring__char__0(tc_Int_Oint) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_Int__Oint__Int_Onumber__ring,axiom,
% 187.18/188.03 class_Int_Onumber__ring(tc_Int_Oint) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_Int__Oint__Rings_Osemiring,axiom,
% 187.18/188.03 class_Rings_Osemiring(tc_Int_Oint) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_Int__Oint__Orderings_Oord,axiom,
% 187.18/188.03 class_Orderings_Oord(tc_Int_Oint) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_Int__Oint__Groups_Ouminus,axiom,
% 187.18/188.03 class_Groups_Ouminus(tc_Int_Oint) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_Int__Oint__Groups_Osgn__if,axiom,
% 187.18/188.03 class_Groups_Osgn__if(tc_Int_Oint) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_Int__Oint__Groups_Oabs__if,axiom,
% 187.18/188.03 class_Groups_Oabs__if(tc_Int_Oint) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_Int__Oint__Rings_Oring__1,axiom,
% 187.18/188.03 class_Rings_Oring__1(tc_Int_Oint) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_Int__Oint__Groups_Ominus,axiom,
% 187.18/188.03 class_Groups_Ominus(tc_Int_Oint) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_Int__Oint__Power_Opower,axiom,
% 187.18/188.03 class_Power_Opower(tc_Int_Oint) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_Int__Oint__Groups_Ozero,axiom,
% 187.18/188.03 class_Groups_Ozero(tc_Int_Oint) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_Int__Oint__Rings_Oring,axiom,
% 187.18/188.03 class_Rings_Oring(tc_Int_Oint) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_Int__Oint__Rings_Oidom,axiom,
% 187.18/188.03 class_Rings_Oidom(tc_Int_Oint) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_Int__Oint__Int_Onumber,axiom,
% 187.18/188.03 class_Int_Onumber(tc_Int_Oint) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_Int__Oint__Groups_Oone,axiom,
% 187.18/188.03 class_Groups_Oone(tc_Int_Oint) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_Int__Oint__HOL_Oequal,axiom,
% 187.18/188.03 class_HOL_Oequal(tc_Int_Oint) ).
% 187.18/188.03
% 187.18/188.03 fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 187.18/188.04 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 187.18/188.04 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 187.18/188.04 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,axiom,
% 187.18/188.04 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Nat__Onat__Groups_Olinordered__ab__semigroup__add,axiom,
% 187.18/188.04 class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Nat__Onat__Rings_Olinordered__semiring__strict,axiom,
% 187.18/188.04 class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom,
% 187.18/188.04 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom,
% 187.18/188.04 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom,
% 187.18/188.04 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Nat__Onat__Rings_Oordered__cancel__semiring,axiom,
% 187.18/188.04 class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Nat__Onat__Rings_Oordered__comm__semiring,axiom,
% 187.18/188.04 class_Rings_Oordered__comm__semiring(tc_Nat_Onat) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom,
% 187.18/188.04 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Nat__Onat__Rings_Olinordered__semiring,axiom,
% 187.18/188.04 class_Rings_Olinordered__semiring(tc_Nat_Onat) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom,
% 187.18/188.04 class_Rings_Olinordered__semidom(tc_Nat_Onat) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Nat__Onat__Lattices_Osemilattice__sup,axiom,
% 187.18/188.04 class_Lattices_Osemilattice__sup(tc_Nat_Onat) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Nat__Onat__Lattices_Osemilattice__inf,axiom,
% 187.18/188.04 class_Lattices_Osemilattice__inf(tc_Nat_Onat) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Nat__Onat__Lattices_Odistrib__lattice,axiom,
% 187.18/188.04 class_Lattices_Odistrib__lattice(tc_Nat_Onat) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Nat__Onat__Groups_Oab__semigroup__mult,axiom,
% 187.18/188.04 class_Groups_Oab__semigroup__mult(tc_Nat_Onat) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Nat__Onat__Groups_Ocomm__monoid__mult,axiom,
% 187.18/188.04 class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom,
% 187.18/188.04 class_Groups_Oab__semigroup__add(tc_Nat_Onat) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Nat__Onat__Rings_Oordered__semiring,axiom,
% 187.18/188.04 class_Rings_Oordered__semiring(tc_Nat_Onat) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Nat__Onat__Rings_Ono__zero__divisors,axiom,
% 187.18/188.04 class_Rings_Ono__zero__divisors(tc_Nat_Onat) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom,
% 187.18/188.04 class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom,
% 187.18/188.04 class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Nat__Onat__Groups_Osemigroup__add,axiom,
% 187.18/188.04 class_Groups_Osemigroup__add(tc_Nat_Onat) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Nat__Onat__Divides_Osemiring__div,axiom,
% 187.18/188.04 class_Divides_Osemiring__div(tc_Nat_Onat) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Nat__Onat__Rings_Ocomm__semiring,axiom,
% 187.18/188.04 class_Rings_Ocomm__semiring(tc_Nat_Onat) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Nat__Onat__Orderings_Owellorder,axiom,
% 187.18/188.04 class_Orderings_Owellorder(tc_Nat_Onat) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Nat__Onat__Nat_Osemiring__char__0,axiom,
% 187.18/188.04 class_Nat_Osemiring__char__0(tc_Nat_Onat) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom,
% 187.18/188.04 class_Rings_Ozero__neq__one(tc_Nat_Onat) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Nat__Onat__Orderings_Opreorder,axiom,
% 187.18/188.04 class_Orderings_Opreorder(tc_Nat_Onat) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Nat__Onat__Orderings_Olinorder,axiom,
% 187.18/188.04 class_Orderings_Olinorder(tc_Nat_Onat) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Nat__Onat__Groups_Omonoid__mult,axiom,
% 187.18/188.04 class_Groups_Omonoid__mult(tc_Nat_Onat) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Nat__Onat__Groups_Omonoid__add,axiom,
% 187.18/188.04 class_Groups_Omonoid__add(tc_Nat_Onat) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Nat__Onat__Rings_Osemiring__1,axiom,
% 187.18/188.04 class_Rings_Osemiring__1(tc_Nat_Onat) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Nat__Onat__Rings_Osemiring__0,axiom,
% 187.18/188.04 class_Rings_Osemiring__0(tc_Nat_Onat) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Nat__Onat__Lattices_Olattice,axiom,
% 187.18/188.04 class_Lattices_Olattice(tc_Nat_Onat) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Nat__Onat__Rings_Omult__zero,axiom,
% 187.18/188.04 class_Rings_Omult__zero(tc_Nat_Onat) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Nat__Onat__Orderings_Oorder,axiom,
% 187.18/188.04 class_Orderings_Oorder(tc_Nat_Onat) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Nat__Onat__Rings_Osemiring,axiom,
% 187.18/188.04 class_Rings_Osemiring(tc_Nat_Onat) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Nat__Onat__Orderings_Oord,axiom,
% 187.18/188.04 class_Orderings_Oord(tc_Nat_Onat) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Nat__Onat__Orderings_Obot,axiom,
% 187.18/188.04 class_Orderings_Obot(tc_Nat_Onat) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Nat__Onat__Groups_Ominus,axiom,
% 187.18/188.04 class_Groups_Ominus(tc_Nat_Onat) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Nat__Onat__Power_Opower,axiom,
% 187.18/188.04 class_Power_Opower(tc_Nat_Onat) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Nat__Onat__Groups_Ozero,axiom,
% 187.18/188.04 class_Groups_Ozero(tc_Nat_Onat) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Nat__Onat__Int_Onumber,axiom,
% 187.18/188.04 class_Int_Onumber(tc_Nat_Onat) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Nat__Onat__Groups_Oone,axiom,
% 187.18/188.04 class_Groups_Oone(tc_Nat_Onat) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Nat__Onat__HOL_Oequal,axiom,
% 187.18/188.04 class_HOL_Oequal(tc_Nat_Onat) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Nat__Onat__Nat_Osize,axiom,
% 187.18/188.04 class_Nat_Osize(tc_Nat_Onat) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice,axiom,
% 187.18/188.04 class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_HOL__Obool__Lattices_Obounded__lattice__top,axiom,
% 187.18/188.04 class_Lattices_Obounded__lattice__top(tc_HOL_Obool) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_HOL__Obool__Lattices_Obounded__lattice__bot,axiom,
% 187.18/188.04 class_Lattices_Obounded__lattice__bot(tc_HOL_Obool) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_HOL__Obool__Lattices_Osemilattice__sup,axiom,
% 187.18/188.04 class_Lattices_Osemilattice__sup(tc_HOL_Obool) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_HOL__Obool__Lattices_Osemilattice__inf,axiom,
% 187.18/188.04 class_Lattices_Osemilattice__inf(tc_HOL_Obool) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_HOL__Obool__Lattices_Odistrib__lattice,axiom,
% 187.18/188.04 class_Lattices_Odistrib__lattice(tc_HOL_Obool) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_HOL__Obool__Lattices_Oboolean__algebra,axiom,
% 187.18/188.04 class_Lattices_Oboolean__algebra(tc_HOL_Obool) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_HOL__Obool__Orderings_Opreorder,axiom,
% 187.18/188.04 class_Orderings_Opreorder(tc_HOL_Obool) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_HOL__Obool__Finite__Set_Ofinite,axiom,
% 187.18/188.04 class_Finite__Set_Ofinite(tc_HOL_Obool) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_HOL__Obool__Lattices_Olattice,axiom,
% 187.18/188.04 class_Lattices_Olattice(tc_HOL_Obool) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_HOL__Obool__Orderings_Oorder,axiom,
% 187.18/188.04 class_Orderings_Oorder(tc_HOL_Obool) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_HOL__Obool__Orderings_Otop,axiom,
% 187.18/188.04 class_Orderings_Otop(tc_HOL_Obool) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_HOL__Obool__Orderings_Oord,axiom,
% 187.18/188.04 class_Orderings_Oord(tc_HOL_Obool) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_HOL__Obool__Orderings_Obot,axiom,
% 187.18/188.04 class_Orderings_Obot(tc_HOL_Obool) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_HOL__Obool__Groups_Ouminus,axiom,
% 187.18/188.04 class_Groups_Ouminus(tc_HOL_Obool) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_HOL__Obool__Groups_Ominus,axiom,
% 187.18/188.04 class_Groups_Ominus(tc_HOL_Obool) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_HOL__Obool__HOL_Oequal,axiom,
% 187.18/188.04 class_HOL_Oequal(tc_HOL_Obool) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_HOL__Obool__Enum_Oenum,axiom,
% 187.18/188.04 class_Enum_Oenum(tc_HOL_Obool) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_HOL__Obool__Nat_Osize,axiom,
% 187.18/188.04 class_Nat_Osize(tc_HOL_Obool) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Com__Ostate__HOL_Oequal,axiom,
% 187.18/188.04 class_HOL_Oequal(tc_Com_Ostate) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Com__Ostate__Nat_Osize,axiom,
% 187.18/188.04 class_Nat_Osize(tc_Com_Ostate) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_List__Olist__HOL_Oequal,axiom,
% 187.18/188.04 ! [T_1] : class_HOL_Oequal(tc_List_Olist(T_1)) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_List__Olist__Nat_Osize,axiom,
% 187.18/188.04 ! [T_1] : class_Nat_Osize(tc_List_Olist(T_1)) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_sum__Finite__Set_Ofinite,axiom,
% 187.18/188.04 ! [T_1,T_2] :
% 187.18/188.04 ( ( class_Finite__Set_Ofinite(T_2)
% 187.18/188.04 & class_Finite__Set_Ofinite(T_1) )
% 187.18/188.04 => class_Finite__Set_Ofinite(tc_sum(T_2,T_1)) ) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_sum__HOL_Oequal,axiom,
% 187.18/188.04 ! [T_1,T_2] : class_HOL_Oequal(tc_sum(T_2,T_1)) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_sum__Enum_Oenum,axiom,
% 187.18/188.04 ! [T_1,T_2] :
% 187.18/188.04 ( ( class_Enum_Oenum(T_2)
% 187.18/188.04 & class_Enum_Oenum(T_1) )
% 187.18/188.04 => class_Enum_Oenum(tc_sum(T_2,T_1)) ) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_sum__Nat_Osize,axiom,
% 187.18/188.04 ! [T_1,T_2] : class_Nat_Osize(tc_sum(T_2,T_1)) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Option__Ooption__Finite__Set_Ofinite,axiom,
% 187.18/188.04 ! [T_1] :
% 187.18/188.04 ( class_Finite__Set_Ofinite(T_1)
% 187.18/188.04 => class_Finite__Set_Ofinite(tc_Option_Ooption(T_1)) ) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Option__Ooption__HOL_Oequal,axiom,
% 187.18/188.04 ! [T_1] : class_HOL_Oequal(tc_Option_Ooption(T_1)) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Option__Ooption__Enum_Oenum,axiom,
% 187.18/188.04 ! [T_1] :
% 187.18/188.04 ( class_Enum_Oenum(T_1)
% 187.18/188.04 => class_Enum_Oenum(tc_Option_Ooption(T_1)) ) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Option__Ooption__Nat_Osize,axiom,
% 187.18/188.04 ! [T_1] : class_Nat_Osize(tc_Option_Ooption(T_1)) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_prod__Finite__Set_Ofinite,axiom,
% 187.18/188.04 ! [T_1,T_2] :
% 187.18/188.04 ( ( class_Finite__Set_Ofinite(T_2)
% 187.18/188.04 & class_Finite__Set_Ofinite(T_1) )
% 187.18/188.04 => class_Finite__Set_Ofinite(tc_prod(T_2,T_1)) ) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_prod__Smallcheck_Osmall,axiom,
% 187.18/188.04 ! [T_1,T_2] :
% 187.18/188.04 ( ( class_Smallcheck_Osmall(T_2)
% 187.18/188.04 & class_Smallcheck_Osmall(T_1) )
% 187.18/188.04 => class_Smallcheck_Osmall(tc_prod(T_2,T_1)) ) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_prod__HOL_Oequal,axiom,
% 187.18/188.04 ! [T_1,T_2] : class_HOL_Oequal(tc_prod(T_2,T_1)) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_prod__Enum_Oenum,axiom,
% 187.18/188.04 ! [T_1,T_2] :
% 187.18/188.04 ( ( class_Enum_Oenum(T_2)
% 187.18/188.04 & class_Enum_Oenum(T_1) )
% 187.18/188.04 => class_Enum_Oenum(tc_prod(T_2,T_1)) ) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_prod__Nat_Osize,axiom,
% 187.18/188.04 ! [T_1,T_2] : class_Nat_Osize(tc_prod(T_2,T_1)) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Product____Type__Ounit__Finite__Set_Ofinite,axiom,
% 187.18/188.04 class_Finite__Set_Ofinite(tc_Product__Type_Ounit) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Product____Type__Ounit__Smallcheck_Osmall,axiom,
% 187.18/188.04 class_Smallcheck_Osmall(tc_Product__Type_Ounit) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Product____Type__Ounit__HOL_Oequal,axiom,
% 187.18/188.04 class_HOL_Oequal(tc_Product__Type_Ounit) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Product____Type__Ounit__Enum_Oenum,axiom,
% 187.18/188.04 class_Enum_Oenum(tc_Product__Type_Ounit) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Product____Type__Ounit__Nat_Osize,axiom,
% 187.18/188.04 class_Nat_Osize(tc_Product__Type_Ounit) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Code____Evaluation__Oterm__HOL_Oequal,axiom,
% 187.18/188.04 class_HOL_Oequal(tc_Code__Evaluation_Oterm) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Code____Evaluation__Oterm__Nat_Osize,axiom,
% 187.18/188.04 class_Nat_Osize(tc_Code__Evaluation_Oterm) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Hoare____Mirabelle__Otriple__HOL_Oequal,axiom,
% 187.18/188.04 ! [T_1] : class_HOL_Oequal(tc_Hoare__Mirabelle_Otriple(T_1)) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Hoare____Mirabelle__Otriple__Nat_Osize,axiom,
% 187.18/188.04 ! [T_1] : class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(T_1)) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 187.18/188.04 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 187.18/188.04 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__comm__semiring__strict,axiom,
% 187.18/188.04 class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Code____Numeral__Ocode____numeral__Groups_Olinordered__ab__semigroup__add,axiom,
% 187.18/188.04 class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring__strict,axiom,
% 187.18/188.04 class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add,axiom,
% 187.18/188.04 class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__comm__monoid__add,axiom,
% 187.18/188.04 class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__ab__semigroup__add,axiom,
% 187.18/188.04 class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__cancel__semiring,axiom,
% 187.18/188.04 class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring,axiom,
% 187.18/188.04 class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add,axiom,
% 187.18/188.04 class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring,axiom,
% 187.18/188.04 class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semidom,axiom,
% 187.18/188.04 class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__mult,axiom,
% 187.18/188.04 class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__mult,axiom,
% 187.18/188.04 class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__add,axiom,
% 187.18/188.04 class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring,axiom,
% 187.18/188.04 class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ono__zero__divisors,axiom,
% 187.18/188.04 class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__add,axiom,
% 187.18/188.04 class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1,axiom,
% 187.18/188.04 class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Code____Numeral__Ocode____numeral__Groups_Osemigroup__add,axiom,
% 187.18/188.04 class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Code____Numeral__Ocode____numeral__Divides_Osemiring__div,axiom,
% 187.18/188.04 class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring,axiom,
% 187.18/188.04 class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osemiring__char__0,axiom,
% 187.18/188.04 class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ozero__neq__one,axiom,
% 187.18/188.04 class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Opreorder,axiom,
% 187.18/188.04 class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder,axiom,
% 187.18/188.04 class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__mult,axiom,
% 187.18/188.04 class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__add,axiom,
% 187.18/188.04 class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1,axiom,
% 187.18/188.04 class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0,axiom,
% 187.18/188.04 class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Code____Numeral__Ocode____numeral__Rings_Omult__zero,axiom,
% 187.18/188.04 class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oorder,axiom,
% 187.18/188.04 class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring,axiom,
% 187.18/188.04 class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oord,axiom,
% 187.18/188.04 class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ominus,axiom,
% 187.18/188.04 class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Code____Numeral__Ocode____numeral__Power_Opower,axiom,
% 187.18/188.04 class_Power_Opower(tc_Code__Numeral_Ocode__numeral) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ozero,axiom,
% 187.18/188.04 class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Code____Numeral__Ocode____numeral__Int_Onumber,axiom,
% 187.18/188.04 class_Int_Onumber(tc_Code__Numeral_Ocode__numeral) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oone,axiom,
% 187.18/188.04 class_Groups_Oone(tc_Code__Numeral_Ocode__numeral) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Code____Numeral__Ocode____numeral__HOL_Oequal,axiom,
% 187.18/188.04 class_HOL_Oequal(tc_Code__Numeral_Ocode__numeral) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osize,axiom,
% 187.18/188.04 class_Nat_Osize(tc_Code__Numeral_Ocode__numeral) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Lazy____Sequence__Olazy____sequence__HOL_Oequal,axiom,
% 187.18/188.04 ! [T_1] : class_HOL_Oequal(tc_Lazy__Sequence_Olazy__sequence(T_1)) ).
% 187.18/188.04
% 187.18/188.04 fof(arity_Lazy____Sequence__Olazy____sequence__Nat_Osize,axiom,
% 187.18/188.04 ! [T_1] : class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(T_1)) ).
% 187.18/188.04
% 187.18/188.04 %----Helper facts (20)
% 187.18/188.04 fof(help_c__COMBI__1,axiom,
% 187.18/188.04 ! [V_P,T_a] : hAPP(c_COMBI(T_a),V_P) = V_P ).
% 187.18/188.04
% 187.18/188.04 fof(help_c__COMBK__1,axiom,
% 187.18/188.04 ! [V_Q,V_P,T_b,T_a] : hAPP(hAPP(c_COMBK(T_a,T_b),V_P),V_Q) = V_P ).
% 187.18/188.04
% 187.18/188.04 fof(help_c__COMBB__1,axiom,
% 187.18/188.04 ! [V_R_2,V_Q_2,V_P_2,T_c,T_a,T_b] : hAPP(hAPP(hAPP(c_COMBB(T_b,T_a,T_c),V_P_2),V_Q_2),V_R_2) = hAPP(V_P_2,hAPP(V_Q_2,V_R_2)) ).
% 187.18/188.04
% 187.18/188.04 fof(help_c__COMBC__1,axiom,
% 187.18/188.04 ! [V_R_2,V_Q_2,V_P_2,T_a,T_c,T_b] : hAPP(hAPP(hAPP(c_COMBC(T_b,T_c,T_a),V_P_2),V_Q_2),V_R_2) = hAPP(hAPP(V_P_2,V_R_2),V_Q_2) ).
% 187.18/188.04
% 187.18/188.04 fof(help_c__COMBS__1,axiom,
% 187.18/188.04 ! [V_R_2,V_Q_2,V_P_2,T_a,T_c,T_b] : hAPP(hAPP(hAPP(c_COMBS(T_b,T_c,T_a),V_P_2),V_Q_2),V_R_2) = hAPP(hAPP(V_P_2,V_R_2),hAPP(V_Q_2,V_R_2)) ).
% 187.18/188.04
% 187.18/188.04 fof(help_c__fequal__1,axiom,
% 187.18/188.04 ! [V_y_2,V_x_2] :
% 187.18/188.04 ( ~ hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2))
% 187.18/188.04 | V_x_2 = V_y_2 ) ).
% 187.18/188.04
% 187.18/188.04 fof(help_c__fequal__2,axiom,
% 187.18/188.04 ! [V_y_2,V_x_2] :
% 187.18/188.04 ( V_x_2 != V_y_2
% 187.18/188.04 | hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) ) ).
% 187.18/188.04
% 187.18/188.04 fof(help_c__fFalse__1,axiom,
% 187.18/188.04 ~ hBOOL(c_fFalse) ).
% 187.18/188.04
% 187.18/188.04 fof(help_c__fTrue__1,axiom,
% 187.18/188.04 hBOOL(c_fTrue) ).
% 187.18/188.04
% 187.18/188.04 fof(help_c__fNot__1,axiom,
% 187.18/188.04 ! [V_P_2] :
% 187.18/188.04 ( ~ hBOOL(hAPP(c_fNot,V_P_2))
% 187.18/188.04 | ~ hBOOL(V_P_2) ) ).
% 187.18/188.04
% 187.18/188.04 fof(help_c__fNot__2,axiom,
% 187.18/188.04 ! [V_P_2] :
% 187.18/188.04 ( ~ ~ hBOOL(V_P_2)
% 187.18/188.04 | hBOOL(hAPP(c_fNot,V_P_2)) ) ).
% 187.18/188.04
% 187.18/188.04 fof(help_c__fconj__1,axiom,
% 187.18/188.04 ! [V_Q_2,V_P_2] :
% 187.18/188.04 ( ~ hBOOL(V_P_2)
% 187.18/188.04 | ~ hBOOL(V_Q_2)
% 187.18/188.04 | hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2)) ) ).
% 187.18/188.04
% 187.18/188.04 fof(help_c__fconj__2,axiom,
% 187.18/188.04 ! [V_Q_2,V_P_2] :
% 187.18/188.04 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2))
% 187.18/188.04 | hBOOL(V_P_2) ) ).
% 187.18/188.04
% 187.18/188.04 fof(help_c__fconj__3,axiom,
% 187.18/188.04 ! [V_Q_2,V_P_2] :
% 187.18/188.04 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2))
% 187.18/188.04 | hBOOL(V_Q_2) ) ).
% 187.18/188.04
% 187.18/188.04 fof(help_c__fdisj__1,axiom,
% 187.18/188.04 ! [V_Q_2,V_P_2] :
% 187.18/188.04 ( ~ hBOOL(V_P_2)
% 187.18/188.04 | hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2)) ) ).
% 187.18/188.04
% 187.18/188.04 fof(help_c__fdisj__2,axiom,
% 187.18/188.04 ! [V_P_2,V_Q_2] :
% 187.18/188.04 ( ~ hBOOL(V_Q_2)
% 187.18/188.04 | hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2)) ) ).
% 187.18/188.04
% 187.18/188.04 fof(help_c__fdisj__3,axiom,
% 187.18/188.04 ! [V_Q_2,V_P_2] :
% 187.18/188.04 ( ~ hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2))
% 187.18/188.04 | hBOOL(V_P_2)
% 187.18/188.04 | hBOOL(V_Q_2) ) ).
% 187.18/188.04
% 187.18/188.04 fof(help_c__fimplies__1,axiom,
% 187.18/188.04 ! [V_Q_2,V_P_2] :
% 187.18/188.04 ( hBOOL(V_P_2)
% 187.18/188.04 | hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2)) ) ).
% 187.18/188.04
% 187.18/188.04 fof(help_c__fimplies__2,axiom,
% 187.18/188.04 ! [V_P_2,V_Q_2] :
% 187.18/188.04 ( ~ hBOOL(V_Q_2)
% 187.18/188.04 | hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2)) ) ).
% 187.18/188.04
% 187.18/188.04 fof(help_c__fimplies__3,axiom,
% 187.18/188.04 ! [V_Q_2,V_P_2] :
% 187.18/188.04 ( ~ hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2))
% 187.18/188.04 | ~ hBOOL(V_P_2)
% 187.18/188.04 | hBOOL(V_Q_2) ) ).
% 187.18/188.04
% 187.18/188.04 %----Conjectures (4)
% 187.18/188.04 fof(conj_0,hypothesis,
% 187.18/188.04 hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),v_F)) ).
% 187.18/188.04
% 187.18/188.04 fof(conj_1,hypothesis,
% 187.18/188.04 c_Hoare__Mirabelle_Ostate__not__singleton ).
% 187.18/188.04
% 187.18/188.04 fof(conj_2,hypothesis,
% 187.18/188.04 c_Com_OWT__bodies ).
% 187.18/188.04
% 187.18/188.04 fof(conj_3,conjecture,
% 187.18/188.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),v_F),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Hoare__Mirabelle_OMGT),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody))))
% 187.18/188.04 => c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Hoare__Mirabelle_OMGT),c_Com_Ocom_OBODY)),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody)),v_F) ) ).
% 187.18/188.04
% 187.18/188.04 %------------------------------------------------------------------------------
% 187.18/188.04 %-------------------------------------------
% 187.18/188.04 % Proof found
% 187.18/188.04 % SZS status Theorem for theBenchmark
% 187.18/188.04 % SZS output start Proof
% 187.18/188.04 %ClaNum:10204(EqnAxiom:2865)
% 187.18/188.04 %VarNum:70227(SingletonVarNum:20476)
% 187.18/188.04 %MaxLitNum:8
% 187.18/188.04 %MaxfuncDepth:15
% 187.18/188.04 %SharedTerms:1088
% 187.18/188.04 %goalClause: 4323 4560
% 187.18/188.04 %singleGoalClaCount:2
% 187.18/188.04 [2866]P1(a5000)
% 187.18/188.04 [2867]P2(a5000)
% 187.18/188.04 [2871]P24(a192)
% 187.18/188.04 [2872]P25(a869)
% 187.18/188.04 [2873]P25(a874)
% 187.18/188.04 [2874]P25(a1)
% 187.18/188.04 [2875]P25(a104)
% 187.18/188.04 [2876]P26(a869)
% 187.18/188.04 [2877]P26(a874)
% 187.18/188.04 [2878]P26(a1)
% 187.18/188.04 [2879]P26(a104)
% 187.18/188.04 [2880]P27(a874)
% 187.18/188.04 [2881]P27(a1)
% 187.18/188.04 [2882]P27(a104)
% 187.18/188.04 [2883]P106(a869)
% 187.18/188.04 [2884]P106(a874)
% 187.18/188.04 [2885]P106(a1)
% 187.18/188.04 [2886]P106(a104)
% 187.18/188.04 [2887]P28(a869)
% 187.18/188.04 [2888]P28(a877)
% 187.18/188.04 [2889]P65(a869)
% 187.18/188.04 [2890]P65(a874)
% 187.18/188.04 [2891]P66(a869)
% 187.18/188.04 [2892]P66(a874)
% 187.18/188.04 [2893]P66(a1)
% 187.18/188.04 [2894]P102(a869)
% 187.18/188.04 [2895]P102(a874)
% 187.18/188.04 [2896]P102(a1)
% 187.18/188.04 [2897]P67(a869)
% 187.18/188.04 [2898]P68(a869)
% 187.18/188.04 [2899]P68(a874)
% 187.18/188.04 [2900]P68(a1)
% 187.18/188.04 [2901]P68(a104)
% 187.18/188.04 [2902]P103(a869)
% 187.18/188.04 [2903]P103(a874)
% 187.18/188.04 [2904]P103(a1)
% 187.18/188.04 [2905]P100(a869)
% 187.18/188.04 [2906]P100(a874)
% 187.18/188.04 [2907]P100(a1)
% 187.18/188.04 [2908]P80(a1)
% 187.18/188.04 [2909]P69(a1)
% 187.18/188.04 [2910]P107(a1)
% 187.18/188.04 [2911]P70(a874)
% 187.18/188.04 [2912]P70(a1)
% 187.18/188.04 [2913]P70(a104)
% 187.18/188.04 [2914]P134(a874)
% 187.18/188.04 [2915]P134(a1)
% 187.18/188.04 [2916]P134(a104)
% 187.18/188.04 [2917]P72(a874)
% 187.18/188.04 [2918]P72(a1)
% 187.18/188.04 [2919]P72(a104)
% 187.18/188.04 [2920]P76(a874)
% 187.18/188.04 [2921]P76(a1)
% 187.18/188.04 [2922]P76(a104)
% 187.18/188.04 [2923]P84(a874)
% 187.18/188.04 [2924]P84(a1)
% 187.18/188.04 [2925]P84(a104)
% 187.18/188.04 [2926]P81(a874)
% 187.18/188.04 [2927]P81(a1)
% 187.18/188.04 [2928]P81(a104)
% 187.18/188.04 [2929]P71(a874)
% 187.18/188.04 [2930]P71(a1)
% 187.18/188.04 [2931]P71(a104)
% 187.18/188.04 [2932]P73(a874)
% 187.18/188.04 [2933]P73(a1)
% 187.18/188.04 [2934]P73(a104)
% 187.18/188.04 [2935]P74(a874)
% 187.18/188.04 [2936]P74(a1)
% 187.18/188.04 [2937]P74(a104)
% 187.18/188.04 [2938]P85(a874)
% 187.18/188.04 [2939]P85(a1)
% 187.18/188.04 [2940]P85(a104)
% 187.18/188.04 [2941]P86(a874)
% 187.18/188.04 [2942]P86(a1)
% 187.18/188.04 [2943]P86(a104)
% 187.18/188.04 [2944]P77(a1)
% 187.18/188.04 [2945]P82(a874)
% 187.18/188.04 [2946]P82(a1)
% 187.18/188.04 [2947]P82(a104)
% 187.18/188.04 [2948]P108(a1)
% 187.18/188.04 [2949]P109(a874)
% 187.18/188.04 [2950]P109(a1)
% 187.18/188.04 [2951]P109(a104)
% 187.18/188.04 [2952]P115(a1)
% 187.18/188.04 [2953]P139(a874)
% 187.18/188.04 [2954]P139(a1)
% 187.18/188.04 [2955]P110(a874)
% 187.18/188.04 [2956]P110(a1)
% 187.18/188.04 [2957]P110(a104)
% 187.18/188.04 [2958]P135(a874)
% 187.18/188.04 [2959]P135(a1)
% 187.18/188.04 [2960]P135(a104)
% 187.18/188.04 [2961]P121(a874)
% 187.18/188.04 [2962]P121(a1)
% 187.18/188.04 [2963]P121(a104)
% 187.18/188.04 [2964]P124(a1)
% 187.18/188.04 [2965]P127(a874)
% 187.18/188.04 [2966]P127(a1)
% 187.18/188.04 [2967]P127(a104)
% 187.18/188.04 [2968]P88(a874)
% 187.18/188.04 [2969]P88(a1)
% 187.18/188.04 [2970]P88(a104)
% 187.18/188.04 [2971]P83(a874)
% 187.18/188.04 [2972]P83(a1)
% 187.18/188.04 [2973]P83(a104)
% 187.18/188.04 [2974]P78(a1)
% 187.18/188.04 [2975]P136(a1)
% 187.18/188.04 [2976]P128(a874)
% 187.18/188.04 [2977]P128(a1)
% 187.18/188.04 [2978]P128(a104)
% 187.18/188.04 [2979]P140(a874)
% 187.18/188.04 [2980]P140(a1)
% 187.18/188.04 [2981]P140(a104)
% 187.18/188.04 [2982]P89(a874)
% 187.18/188.04 [2983]P89(a1)
% 187.18/188.04 [2984]P89(a104)
% 187.18/188.04 [2985]P122(a1)
% 187.18/188.04 [2986]P123(a1)
% 187.18/188.04 [2987]P130(a874)
% 187.18/188.04 [2988]P130(a1)
% 187.18/188.04 [2989]P130(a104)
% 187.18/188.04 [2990]P132(a874)
% 187.18/188.04 [2991]P132(a1)
% 187.18/188.04 [2992]P132(a104)
% 187.18/188.04 [2993]P131(a874)
% 187.18/188.04 [2994]P131(a1)
% 187.18/188.04 [2995]P131(a104)
% 187.18/188.04 [2996]P129(a874)
% 187.18/188.04 [2997]P129(a1)
% 187.18/188.04 [2998]P129(a104)
% 187.18/188.04 [2999]P116(a874)
% 187.18/188.04 [3000]P116(a1)
% 187.18/188.04 [3001]P116(a104)
% 187.18/188.04 [3002]P125(a874)
% 187.18/188.04 [3003]P125(a1)
% 187.18/188.04 [3004]P125(a104)
% 187.18/188.04 [3005]P126(a1)
% 187.18/188.04 [3006]P137(a1)
% 187.18/188.04 [3007]P111(a874)
% 187.18/188.04 [3008]P111(a1)
% 187.18/188.04 [3009]P111(a104)
% 187.18/188.04 [3010]P138(a1)
% 187.18/188.04 [3011]P93(a1)
% 187.18/188.04 [3012]P29(a874)
% 187.18/188.04 [3013]P29(a1)
% 187.18/188.04 [3014]P29(a104)
% 187.18/188.04 [3015]P30(a1)
% 187.18/188.04 [3016]P104(a874)
% 187.18/188.04 [3017]P104(a1)
% 187.18/188.04 [3018]P104(a104)
% 187.18/188.04 [3019]P141(a874)
% 187.18/188.04 [3020]P141(a1)
% 187.18/188.04 [3021]P141(a104)
% 187.18/188.04 [3022]P87(a1)
% 187.18/188.04 [3023]P133(a1)
% 187.18/188.04 [3024]P79(a874)
% 187.18/188.04 [3025]P79(a1)
% 187.18/188.04 [3026]P79(a104)
% 187.18/188.04 [3027]P112(a869)
% 187.18/188.04 [3028]P101(a869)
% 187.18/188.04 [3029]P31(a869)
% 187.18/188.04 [3030]P97(a869)
% 187.18/188.04 [3031]P90(a869)
% 187.18/188.04 [3032]P90(a1)
% 187.18/188.04 [3033]P117(a1)
% 187.18/188.04 [3034]P114(a1)
% 187.18/188.04 [3035]P75(a1)
% 187.18/188.04 [3036]P91(a1)
% 187.18/188.04 [3037]P94(a1)
% 187.18/188.04 [3038]P95(a874)
% 187.18/188.04 [3039]P95(a1)
% 187.18/188.04 [3040]P95(a104)
% 187.18/188.04 [3041]P113(a874)
% 187.18/188.04 [3042]P92(a874)
% 187.18/188.04 [3043]P92(a1)
% 187.18/188.04 [3044]P92(a104)
% 187.18/188.04 [3045]P142(a1)
% 187.18/188.04 [3046]P142(a877)
% 187.18/188.04 [3047]P60(a869)
% 187.18/188.04 [3048]P60(a877)
% 187.18/188.04 [3049]P96(a869)
% 187.18/188.04 [3050]P96(a870)
% 187.18/188.04 [3051]P96(a871)
% 187.18/188.04 [3052]P96(a874)
% 187.18/188.04 [3053]P96(a1)
% 187.18/188.04 [3054]P96(a877)
% 187.18/188.04 [3055]P96(a104)
% 187.18/188.04 [3056]P96(a325)
% 187.18/188.04 [3057]P105(a869)
% 187.18/188.04 [3058]P105(a870)
% 187.18/188.04 [3059]P105(a871)
% 187.18/188.04 [3060]P105(a874)
% 187.18/188.04 [3061]P105(a877)
% 187.18/188.04 [3062]P105(a104)
% 187.18/188.04 [3063]P105(a325)
% 187.18/188.04 [3064]P99(a869)
% 187.18/188.04 [3084]P42(a874,a248)
% 187.18/188.04 [3085]P42(a874,a319)
% 187.18/188.04 [4453]~E(a102,a83)
% 187.18/188.04 [4454]~P24(a247)
% 187.18/188.04 [2868]E(f2(a1),a83)
% 187.18/188.04 [2869]E(f105(a104),a3)
% 187.18/188.04 [2870]E(f22(a104),a23)
% 187.18/188.04 [3065]E(f193(a874),f2(a874))
% 187.18/188.04 [3066]E(f31(a24),f2(a874))
% 187.18/188.04 [3067]E(f106(a874),f241(a874))
% 187.18/188.04 [3068]E(f115(a874),f242(a874))
% 187.18/188.04 [3069]E(f107(a1),f34(a1))
% 187.18/188.04 [3070]E(f84(a247),f2(a874))
% 187.18/188.04 [3071]E(f84(a192),f2(a874))
% 187.18/188.04 [3072]P32(f78(a1))
% 187.18/188.04 [3073]P32(f2(a1))
% 187.18/188.04 [3122]P24(f329(a25,a24))
% 187.18/188.04 [3135]P42(f880(a874,a874),a35)
% 187.18/188.04 [3489]E(f322(a874,a874,a248,a248),a35)
% 187.18/188.04 [4455]~E(f78(a1),f2(a1))
% 187.18/188.04 [3074]E(f4(f2(a104)),f2(a874))
% 187.18/188.04 [3075]E(f116(f2(a874)),f2(a874))
% 187.18/188.04 [3087]E(f329(f79(a1),a83),a83)
% 187.18/188.04 [3090]E(f329(a117,f2(a874)),f78(a874))
% 187.18/188.04 [3091]E(f329(a109,f78(a1)),f78(a874))
% 187.18/188.04 [3092]E(f329(a3,f78(a874)),f78(a104))
% 187.18/188.04 [3094]E(f329(a3,f2(a874)),f2(a104))
% 187.18/188.04 [3096]E(f329(f108(a1),a83),f2(a1))
% 187.18/188.04 [3097]E(f329(f108(a104),a83),f2(a104))
% 187.18/188.04 [3098]E(f329(a109,f2(a1)),f2(a874))
% 187.18/188.04 [3099]E(f329(f194(a869),a247),f2(a874))
% 187.18/188.04 [3100]E(f329(f194(a869),a192),f2(a874))
% 187.18/188.04 [3101]E(f329(f194(a870),a24),f2(a874))
% 187.18/188.04 [3102]E(f329(f108(a874),a83),f2(a874))
% 187.18/188.04 [3106]E(f329(f79(a1),f78(a1)),a102)
% 187.18/188.04 [3114]E(f329(f194(a104),f2(a104)),f2(a874))
% 187.18/188.04 [3115]E(f329(f105(a1),f78(a874)),f78(a1))
% 187.18/188.04 [3116]E(f329(f105(a1),f2(a874)),f2(a1))
% 187.18/188.04 [3117]E(f329(f79(a1),f2(a1)),f2(a1))
% 187.18/188.04 [3131]E(f329(a109,f78(a1)),f329(a117,f2(a874)))
% 187.18/188.04 [3132]E(f329(f177(a872,a870),a27),a28)
% 187.18/188.04 [3133]E(f320(f880(a874,a874),a35),a36)
% 187.18/188.04 [3134]E(f321(f880(a874,a874),a35),a37)
% 187.18/188.04 [3156]E(f329(f250(a874),f2(a874)),f193(f881(a874,a869)))
% 187.18/188.04 [3157]E(f329(f251(a874),f2(a874)),f252(f881(a874,a869)))
% 187.18/188.04 [3165]P43(f193(f881(a1,a869)))
% 187.18/188.04 [3202]E(f329(f329(f22(a104),f2(a104)),f78(a104)),f2(a104))
% 187.18/188.04 [3281]P24(f329(f329(f244(a1),a102),f2(a1)))
% 187.18/188.04 [3306]P24(f329(f329(f243(a1),f2(a1)),f78(a1)))
% 187.18/188.04 [3308]P24(f329(f329(f244(a1),f2(a1)),f78(a1)))
% 187.18/188.04 [3481]P24(f329(f62(a872),f183(a872,a870,a28)))
% 187.18/188.04 [3519]E(f329(f329(f286(a874,a874,a874),a319),f305(a874,a319)),a248)
% 187.18/188.04 [3557]P45(a1,a874,a109,f329(f243(a1),f2(a1)))
% 187.18/188.04 [3561]E(f329(f329(f42(a874,f881(a874,a869)),f252(f881(a874,a869))),f250(a874)),f252(f881(a874,a869)))
% 187.18/188.04 [3562]E(f329(f329(f42(a874,f881(a874,a869)),f252(f881(a874,a869))),f298(a874)),f252(f881(a874,a869)))
% 187.18/188.04 [3563]E(f329(f329(f42(a874,f881(a874,a869)),f252(f881(a874,a869))),f251(a874)),f252(f881(a874,a869)))
% 187.18/188.04 [3564]E(f329(f329(f43(a874,f881(a874,a869)),f252(f881(a874,a869))),f301(a874)),f193(f881(a874,a869)))
% 187.18/188.04 [3580]P21(a874,a1,f105(a1),f252(f881(a874,a869)))
% 187.18/188.04 [3593]P45(a874,a1,f105(a1),f329(f16(a869,a874),a192))
% 187.18/188.04 [3728]E(f329(f73(a874,a104,a1,a3),a109),f108(a104))
% 187.18/188.04 [3953]P56(a104,a874,a19,a3,f252(f881(a874,a869)))
% 187.18/188.04 [3962]P56(a1,f881(f880(a874,a874),a869),a111,a89,a103)
% 187.18/188.04 [4227]E(f269(a1,a1,a1,a1,f34(a1),f79(a1)),a51)
% 187.18/188.04 [4478]~E(f329(f108(a1),a102),f329(f108(a1),a83))
% 187.18/188.04 [4479]~P24(f329(a198,f78(a1)))
% 187.18/188.04 [4480]~P24(f329(a198,f2(a1)))
% 187.18/188.04 [4521]~P24(f329(f329(f244(a1),a83),f2(a1)))
% 187.18/188.04 [4560]~P20(a871,f329(f308(a872,f873(a871),f329(f329(f8(a870,f873(a871),a872),a93),a26)),f183(a872,a870,a28)),a882)
% 187.18/188.04 [3148]E(f329(f329(f22(a1),a102),a102),a83)
% 187.18/188.04 [3163]E(f329(f105(a1),f329(a117,f2(a874))),f78(a1))
% 187.18/188.04 [3174]P24(f329(f62(f873(a871)),a882))
% 187.18/188.04 [3230]E(f329(f38(a877),f252(f881(a877,a869))),f78(a874))
% 187.18/188.04 [3251]P24(f329(a198,f329(f108(a1),a102)))
% 187.18/188.04 [3253]P24(f329(f329(f243(a1),a102),a83))
% 187.18/188.04 [3255]P24(f329(f329(f244(a1),a102),a83))
% 187.18/188.04 [3318]E(f329(f329(f307(a874),f2(a874)),f193(f881(a874,a869))),f329(f298(a874),f2(a874)))
% 187.18/188.04 [3373]P24(f329(f329(f243(a1),f2(a1)),f329(f108(a1),a83)))
% 187.18/188.04 [3385]E(f329(f308(a874,a874,a117),f252(f881(a874,a869))),f329(f301(a874),f2(a874)))
% 187.18/188.04 [3425]P6(f880(a874,a874),f252(f881(f880(a874,a874),a869)),a113)
% 187.18/188.04 [3736]E(f329(f73(a874,a1,a104,f105(a1)),a19),a20)
% 187.18/188.04 [3796]P42(a874,f329(f249(f880(a874,a874)),f329(f268(a874,a874,a869),f244(a874))))
% 187.18/188.04 [4323]P24(f329(f329(f243(f881(f873(a871),a869)),a882),f329(f308(a872,f873(a871),f329(f329(f8(a870,f873(a871),a872),a93),f329(f329(f8(f878(a870),a870,a872),f240(a870)),a28))),f183(a872,a870,a28))))
% 187.18/188.04 [4510]~P24(f329(a198,f329(f108(a1),a83)))
% 187.18/188.04 [4511]~P24(f329(f329(f243(a1),a83),a102))
% 187.18/188.04 [4512]~P24(f329(f329(f244(a1),a83),a83))
% 187.18/188.04 [4513]~P24(f329(f329(f244(a1),a83),a102))
% 187.18/188.04 [4514]~P24(f329(f329(f244(a1),a102),a102))
% 187.18/188.04 [4515]~P24(f329(f329(f91(a1),a83),a102))
% 187.18/188.04 [4516]~P24(f329(f329(f91(a1),a102),a83))
% 187.18/188.04 [4527]~P24(f329(f62(a874),f252(f881(a874,a869))))
% 187.18/188.04 [4528]~P24(f329(f62(a1),f252(f881(a1,a869))))
% 187.18/188.04 [4399]E(f329(f268(a1,a1,a869),f329(f329(f8(f881(a1,a869),f881(a1,a869),a1),f329(f18(a1,a869,a869),f329(f329(f8(a869,f881(a869,a869),a1),a327),f329(f244(a1),f2(a1))))),f329(f329(f7(a1,a1,f881(a1,a869)),f329(f329(f8(f881(a1,f881(a1,a869)),f881(a1,f881(a1,a869)),a1),f7(a1,a1,a869)),f329(f329(f8(f881(a1,a1),f881(a1,f881(a1,a869)),a1),f329(f8(a1,f881(a1,a869),a1),a326)),a225))),f78(a1)))),a221)
% 187.18/188.04 [3463]E(f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102),f329(f79(a1),a102))
% 187.18/188.04 [3502]E(f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102),f329(f329(f22(a1),a83),a102))
% 187.18/188.04 [3662]E(f329(f329(f61(f880(a874,a874)),f252(f881(f880(a874,a874),a869))),a113),a103)
% 187.18/188.04 [3691]E(f329(f108(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f78(a1))
% 187.18/188.04 [3692]E(f329(f108(a104),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f78(a104))
% 187.18/188.04 [3693]E(f329(f108(a874),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f78(a874))
% 187.18/188.04 [3697]E(f329(f108(a874),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(a117,f2(a874)))
% 187.18/188.04 [4087]E(f329(f329(f115(f881(f880(f880(a874,a874),f880(a874,a874)),a869)),a35),f305(f880(a874,a874),f193(f881(f880(f880(a874,a874),f880(a874,a874)),a869)))),a70)
% 187.18/188.04 [4158]E(f329(a89,f329(f283(f880(a874,a874),f880(a874,a874),a113),f329(f329(f307(f880(a874,a874)),f329(f329(f264(a874,a874),f78(a874)),f2(a874))),f193(f881(f880(a874,a874),a869))))),f78(a1))
% 187.18/188.04 [4159]E(f329(a89,f329(f283(f880(a874,a874),f880(a874,a874),a113),f329(f329(f307(f880(a874,a874)),f329(f329(f264(a874,a874),f2(a874)),f2(a874))),f193(f881(f880(a874,a874),a869))))),f2(a1))
% 187.18/188.04 [4174]E(f329(f249(f880(a874,a874)),f329(f268(a874,a874,a869),f329(f329(f8(a874,f881(a874,a869),a874),f329(f7(a874,a874,a869),a326)),a117))),a319)
% 187.18/188.04 [4144]E(f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102))),f329(a117,f329(a117,f2(a874))))
% 187.18/188.04 [4147]E(f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102))),f329(f329(f80(a874),f78(a874)),f78(a874)))
% 187.18/188.04 [4148]E(f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102))),f329(f38(a869),f252(f881(a869,a869))))
% 187.18/188.04 [4213]P32(f329(f108(a1),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102))))
% 187.18/188.04 [4285]P22(f881(f880(a874,a874),a869),f329(f329(f264(f881(f880(f881(f880(a874,a874),a869),f881(f880(a874,a874),a869)),a869),f881(f880(f881(f880(a874,a874),a869),f881(f880(a874,a874),a869)),a869)),a36),a71))
% 187.18/188.04 [4286]P22(f881(f880(a874,a874),a869),f329(f329(f264(f881(f880(f881(f880(a874,a874),a869),f881(f880(a874,a874),a869)),a869),f881(f880(f881(f880(a874,a874),a869),f881(f880(a874,a874),a869)),a869)),a37),a69))
% 187.18/188.04 [4327]E(f329(f329(f115(f881(f880(f881(f880(a874,a874),a869),f881(f880(a874,a874),a869)),a869)),f321(f880(a874,a874),a70)),f329(f329(f307(f880(f881(f880(a874,a874),a869),f881(f880(a874,a874),a869))),f329(f329(f264(f881(f880(a874,a874),a869),f881(f880(a874,a874),a869)),f193(f881(f880(a874,a874),a869))),f193(f881(f880(a874,a874),a869)))),f193(f881(f880(f881(f880(a874,a874),a869),f881(f880(a874,a874),a869)),a869)))),a69)
% 187.18/188.04 [4328]E(f329(f329(f115(f881(f880(f881(f880(a874,a874),a869),f881(f880(a874,a874),a869)),a869)),f320(f880(a874,a874),a70)),f329(f329(f307(f880(f881(f880(a874,a874),a869),f881(f880(a874,a874),a869))),f329(f329(f264(f881(f880(a874,a874),a869),f881(f880(a874,a874),a869)),f193(f881(f880(a874,a874),a869))),f193(f881(f880(a874,a874),a869)))),f193(f881(f880(f881(f880(a874,a874),a869),f881(f880(a874,a874),a869)),a869)))),a71)
% 187.18/188.04 [4215]E(f329(a109,f329(f108(a1),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))),f329(a117,f329(a117,f2(a874))))
% 187.18/188.04 [4262]E(f329(f105(a1),f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))),f329(f108(a1),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102))))
% 187.18/188.04 [4297]P24(f329(f329(f243(a1),f2(a1)),f329(f108(a1),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))))
% 187.18/188.04 [4298]E(f329(f108(a874),f329(f329(f22(a1),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102))),a102)),f329(a117,f329(a117,f329(a117,f2(a874)))))
% 187.18/188.04 [4341]P32(f329(f108(a1),f329(f329(f22(a1),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102))),a102)))
% 187.18/188.04 [4369]E(f329(f105(a1),f329(f108(a874),f329(f329(f22(a1),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102))),a102))),f329(f108(a1),f329(f329(f22(a1),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102))),a102)))
% 187.18/188.04 [4384]P24(f329(f329(f243(a1),f2(a1)),f329(f108(a1),f329(f329(f22(a1),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102))),a102))))
% 187.18/188.04 [3086]P5(x30861,a326)
% 187.18/188.04 [3490]P21(a874,a874,a117,x34901)
% 187.18/188.04 [3076]P96(f873(x30761))
% 187.18/188.04 [3077]P96(f878(x30771))
% 187.18/188.04 [3078]P96(f875(x30781))
% 187.18/188.04 [3079]P96(f876(x30791))
% 187.18/188.04 [3080]P105(f873(x30801))
% 187.18/188.04 [3081]P105(f878(x30811))
% 187.18/188.04 [3082]P105(f875(x30821))
% 187.18/188.04 [3083]P105(f876(x30831))
% 187.18/188.04 [3103]P42(a1,f110(x31031))
% 187.18/188.04 [3104]P42(a1,f112(x31041))
% 187.18/188.04 [3153]P42(f881(x31531,a869),f304(x31531))
% 187.18/188.04 [3178]E(f253(x31781,x31781,a326),a326)
% 187.18/188.04 [3193]E(f45(a1,x31931,x31931),f2(a1))
% 187.18/188.04 [3248]P11(x32481,f881(x32481,a869),f307(x32481))
% 187.18/188.04 [4457]~E(f329(a26,x44571),a24)
% 187.18/188.04 [4459]~E(f329(a117,x44591),x44591)
% 187.18/188.04 [4469]~E(f329(a117,x44691),f2(a874))
% 187.18/188.04 [3088]E(f329(f194(a874),x30881),x30881)
% 187.18/188.04 [3089]E(f329(f108(a1),x30891),x30891)
% 187.18/188.04 [3105]E(f329(a89,f330(x31051)),x31051)
% 187.18/188.04 [3118]E(f119(x31181,f118(x31181)),f118(x31181))
% 187.18/188.04 [3119]E(f150(x31191,f118(x31191)),f118(x31191))
% 187.18/188.04 [3123]E(f31(f329(a26,x31231)),f2(a874))
% 187.18/188.04 [3128]E(f329(f166(x31281),f118(x31281)),f118(x31281))
% 187.18/188.04 [3129]E(f329(f170(x31291),f118(x31291)),f118(x31291))
% 187.18/188.04 [3130]E(f329(f167(x31301),f118(x31301)),f118(x31301))
% 187.18/188.04 [3136]E(f329(f108(a1),x31361),f329(f107(a1),x31361))
% 187.18/188.04 [3137]E(f329(a89,f329(a111,x31371)),x31371)
% 187.18/188.04 [3139]E(f329(a3,f329(a19,x31391)),x31391)
% 187.18/188.04 [3140]E(f329(a19,f329(a3,x31401)),x31401)
% 187.18/188.04 [3141]P32(f329(f105(a1),x31411))
% 187.18/188.04 [3146]E(f329(f194(f878(x31461)),f206(x31461)),f2(a874))
% 187.18/188.04 [3147]E(f329(f194(f875(x31471)),f118(x31471)),f2(a874))
% 187.18/188.04 [3152]E(f329(f194(a870),f329(a26,x31521)),f2(a874))
% 187.18/188.04 [3161]E(f235(x31611,f206(x31611)),f193(f881(x31611,a869)))
% 187.18/188.04 [3168]E(f329(f329(f22(a874),x31681),f2(a874)),x31681)
% 187.18/188.04 [3169]E(f329(f329(f81(a874),x31691),f78(a874)),x31691)
% 187.18/188.04 [3170]E(f329(f329(f81(a1),x31701),f78(a1)),x31701)
% 187.18/188.04 [3171]E(f329(f329(f80(a874),x31711),f2(a874)),x31711)
% 187.18/188.04 [3172]E(f329(f329(f80(a1),x31721),f2(a1)),x31721)
% 187.18/188.04 [3173]E(f329(f329(f242(a874),x31731),f2(a874)),x31731)
% 187.18/188.04 [3175]E(f329(f329(f81(a874),x31751),f2(a874)),f2(a874))
% 187.18/188.04 [3176]E(f329(f329(f39(a1),x31761),f2(a1)),f2(a1))
% 187.18/188.04 [3177]E(f329(f329(f241(a874),x31771),f2(a874)),f2(a874))
% 187.18/188.04 [3184]E(f329(f171(x31841),f118(x31841)),f193(f881(x31841,a869)))
% 187.18/188.04 [3188]P24(f329(f135(x31881),f118(x31881)))
% 187.18/188.04 [3194]E(f329(f152(x31941,x31941),f5(x31941)),f34(f875(x31941)))
% 187.18/188.04 [3195]E(f329(f152(x31951,x31951),f34(x31951)),f34(f875(x31951)))
% 187.18/188.04 [3196]E(f329(f207(x31961,x31961),f5(x31961)),f34(f878(x31961)))
% 187.18/188.04 [3197]E(f329(f207(x31971,x31971),f34(x31971)),f34(f878(x31971)))
% 187.18/188.04 [3198]E(f45(a1,x31981,f2(a1)),x31981)
% 187.18/188.04 [3199]E(f329(f243(a874),f329(a117,x31991)),f329(f244(a874),x31991))
% 187.18/188.04 [3200]E(f329(f250(a874),f329(a117,x32001)),f329(f298(a874),x32001))
% 187.18/188.04 [3201]E(f329(f251(a874),f329(a117,x32011)),f329(f301(a874),x32011))
% 187.18/188.04 [3203]E(f45(a1,f2(a1),x32031),f2(a1))
% 187.18/188.04 [3214]E(f329(f329(f80(a874),x32141),f78(a874)),f329(a117,x32141))
% 187.18/188.04 [3224]E(f329(f299(a874,x32241),f2(a874)),f193(f881(a874,a869)))
% 187.18/188.04 [3236]E(f300(a874,f2(a874),x32361),f329(f298(a874),x32361))
% 187.18/188.04 [3284]E(f329(f329(f22(a874),f329(a117,x32841)),f78(a874)),x32841)
% 187.18/188.04 [3297]E(f47(f2(a1),x32971),f329(f329(f264(a1,a1),f2(a1)),f2(a1)))
% 187.18/188.04 [3313]E(f329(f329(f329(f92(a871),a326),x33131),f199(x33131)),f329(a93,x33131))
% 187.18/188.04 [3347]P24(f329(f329(f244(a874),x33471),f329(a117,x33471)))
% 187.18/188.04 [3359]P24(f329(f329(f244(a874),f2(a874)),f329(a117,x33591)))
% 187.18/188.04 [3648]E(f329(f329(f22(a104),f329(a3,f329(a117,f329(a19,x36481)))),f78(a104)),x36481)
% 187.18/188.04 [3720]P24(f329(f329(f243(a1),f329(f79(a1),f329(f105(a1),x37201))),f2(a1)))
% 187.18/188.04 [3869]P24(f329(f329(f244(a1),f329(f79(a1),f329(f105(a1),f329(a117,x38691)))),f2(a1)))
% 187.18/188.04 [4485]~E(f252(f881(x44851,a869)),f193(f881(x44851,a869)))
% 187.18/188.04 [4524]~P24(f329(f329(f244(a874),x45241),f2(a874)))
% 187.18/188.04 [4536]~P24(f329(f329(f244(a1),f329(f105(a1),x45361)),f2(a1)))
% 187.18/188.04 [3151]E(f179(x31511,f118(f875(x31511))),f118(f875(x31511)))
% 187.18/188.04 [3154]E(f329(f329(f81(a1),a83),x31541),a83)
% 187.18/188.04 [3155]E(f329(f329(f80(a1),a83),x31551),x31551)
% 187.18/188.04 [3158]E(f329(a109,f329(f105(a1),x31581)),x31581)
% 187.18/188.04 [3159]E(f329(f329(f22(a1),x31591),a83),x31591)
% 187.18/188.04 [3160]E(f329(f329(f80(a1),x31601),a83),x31601)
% 187.18/188.04 [3162]E(f329(f329(f22(a874),x31621),x31621),f2(a874))
% 187.18/188.04 [3166]E(f329(f38(a874),f329(f250(a874),x31661)),x31661)
% 187.18/188.04 [3167]E(f329(f79(a1),f329(f79(a1),x31671)),x31671)
% 187.18/188.04 [3179]E(f329(f329(f81(a874),f78(a874)),x31791),x31791)
% 187.18/188.04 [3180]E(f329(f329(f81(a1),f78(a1)),x31801),x31801)
% 187.18/188.04 [3181]E(f329(f329(f80(a874),f2(a874)),x31811),x31811)
% 187.18/188.04 [3182]E(f329(f329(f80(a1),f2(a1)),x31821),x31821)
% 187.18/188.04 [3183]E(f329(f329(f242(a874),f2(a874)),x31831),x31831)
% 187.18/188.04 [3189]E(f329(f329(f22(a874),f2(a874)),x31891),f2(a874))
% 187.18/188.04 [3190]E(f329(f329(f81(a874),f2(a874)),x31901),f2(a874))
% 187.18/188.04 [3191]E(f329(f329(f39(a1),f2(a1)),x31911),f2(a1))
% 187.18/188.04 [3192]E(f329(f329(f241(a874),f2(a874)),x31921),f2(a874))
% 187.18/188.04 [3209]E(f329(f299(a874,f2(a874)),x32091),f329(f250(a874),x32091))
% 187.18/188.04 [3210]E(f329(f329(f81(a1),a102),x32101),f329(f79(a1),x32101))
% 187.18/188.04 [3216]E(f329(a109,f329(f108(a1),x32161)),f329(f108(a874),x32161))
% 187.18/188.04 [3217]E(f329(a19,f329(f108(a104),x32171)),f329(f108(a874),x32171))
% 187.18/188.04 [3218]E(f329(f38(a874),f329(f298(a874),x32181)),f329(a117,x32181))
% 187.18/188.04 [3228]E(f329(f329(f80(a874),f78(a874)),x32281),f329(a117,x32281))
% 187.18/188.04 [3232]E(f329(f75(a1),f329(f105(a1),x32321)),f329(f105(a1),x32321))
% 187.18/188.04 [3233]E(f329(f107(a1),f329(f105(a1),x32331)),f329(f105(a1),x32331))
% 187.18/188.04 [3238]E(f329(f38(x32381),f193(f881(x32381,a869))),f2(a874))
% 187.18/188.04 [3240]E(f329(f329(f39(a874),x32401),f329(a117,f2(a874))),x32401)
% 187.18/188.04 [3249]E(f45(a874,x32491,f329(a117,f2(a874))),f2(a874))
% 187.18/188.04 [3250]E(f45(a1,x32501,f329(f108(a1),a102)),f2(a1))
% 187.18/188.04 [3266]E(f329(f329(f39(a1),x32661),f329(f108(a1),a102)),f329(f79(a1),x32661))
% 187.18/188.04 [3270]E(f137(a874,f329(f299(a874,x32701),f2(a874))),f118(a874))
% 187.18/188.04 [3271]E(f329(f329(f80(a1),x32711),f78(a1)),f329(f329(f22(a1),x32711),a102))
% 187.18/188.04 [3272]E(f329(f329(f22(a1),x32721),f78(a1)),f329(f329(f80(a1),x32721),a102))
% 187.18/188.04 [3276]P24(f329(f329(f243(a874),x32761),x32761))
% 187.18/188.04 [3277]P24(f329(f329(f243(a1),x32771),x32771))
% 187.18/188.04 [3279]P24(f329(f329(f199(a24),x32791),x32791))
% 187.18/188.04 [3280]P24(f329(f329(f91(a1),x32801),x32801))
% 187.18/188.04 [3285]E(f329(f79(a1),f329(f108(a1),x32851)),f329(f108(a1),f329(f79(a1),x32851)))
% 187.18/188.04 [3286]P24(f329(f62(a874),f329(f250(a874),x32861)))
% 187.18/188.04 [3287]P24(f329(f62(a874),f329(f298(a874),x32871)))
% 187.18/188.04 [3295]E(f159(x32951,f252(f881(x32951,a869))),f252(f881(f875(x32951),a869)))
% 187.18/188.04 [3300]P24(f329(f329(f243(a874),f2(a874)),x33001))
% 187.18/188.04 [3310]E(f329(f329(f80(a874),f116(x33101)),f329(a117,f2(a874))),f116(f329(a117,x33101)))
% 187.18/188.04 [3311]E(f329(f249(x33111),f329(f16(a869,x33111),a247)),f193(f881(x33111,a869)))
% 187.18/188.04 [3312]E(f329(f249(x33121),f329(f16(a869,x33121),a192)),f252(f881(x33121,a869)))
% 187.18/188.04 [3317]E(f329(f329(f307(a874),x33171),f329(f250(a874),x33171)),f329(f250(a874),f329(a117,x33171)))
% 187.18/188.04 [3329]E(f329(f329(f80(a1),f78(a1)),f329(f105(a1),x33291)),f329(f105(a1),f329(a117,x33291)))
% 187.18/188.04 [3331]E(f329(f329(f149(f875(x33311)),f118(x33311)),f118(f875(x33311))),f54(x33311,f118(x33311)))
% 187.18/188.04 [3350]E(f193(f881(f880(x33501,x33501),a869)),f261(x33501,f193(f881(x33501,a869))))
% 187.18/188.04 [3351]E(f329(f306(x33511),f252(f881(x33511,a869))),f252(f881(f881(x33511,a869),a869)))
% 187.18/188.04 [3352]E(f329(f79(f881(x33521,a869)),f193(f881(x33521,a869))),f252(f881(x33521,a869)))
% 187.18/188.04 [3353]E(f329(f79(f881(x33531,a869)),f252(f881(x33531,a869))),f193(f881(x33531,a869)))
% 187.18/188.04 [3355]P24(f329(f62(x33551),f193(f881(x33551,a869))))
% 187.18/188.04 [3357]E(f329(f299(a874,x33571),f329(a117,x33571)),f329(f329(f307(a874),x33571),f193(f881(a874,a869))))
% 187.18/188.04 [3358]E(f85(f880(a874,a874),f48(x33581,f2(a874))),f329(f329(f264(a874,a874),f2(a874)),x33581))
% 187.18/188.04 [3372]E(f329(f329(f307(a874),f329(a117,x33721)),f329(f298(a874),x33721)),f329(f298(a874),f329(a117,x33721)))
% 187.18/188.04 [3376]P42(x33761,f193(f881(f880(x33761,x33761),a869)))
% 187.18/188.04 [3379]P24(f329(f329(f243(a1),f2(a1)),f329(f105(a1),x33791)))
% 187.18/188.04 [3387]E(f329(f329(f80(a874),f329(f194(a874),x33871)),f329(a117,f2(a874))),f329(f194(a874),f329(a117,x33871)))
% 187.18/188.04 [3497]P43(f329(f308(a874,a1,f105(a1)),x34971))
% 187.18/188.04 [3535]P44(x35351,f193(f881(x35351,a869)),f193(f881(f880(x35351,x35351),a869)))
% 187.18/188.04 [3554]E(f329(f329(f264(a1,a1),f329(f108(a1),a102)),f329(f329(f22(a1),x35541),f78(a1))),f50(f329(f108(a1),a102),x35541))
% 187.18/188.04 [3605]P59(x36051,f329(f16(f881(x36051,a869),x36051),f329(f16(a869,x36051),a247)))
% 187.18/188.04 [3808]P24(f329(f329(f331(f881(f880(a874,a874),a869)),f330(x38081)),a103))
% 187.18/188.04 [3833]P24(f329(f329(f331(f881(f880(a874,a874),a869)),f329(a111,x38331)),a103))
% 187.18/188.04 [3971]P21(x39711,f881(x39711,a869),f329(f329(f7(x39711,f881(x39711,a869),f881(x39711,a869)),f307(x39711)),f193(f881(x39711,a869))),f252(f881(x39711,a869)))
% 187.18/188.04 [4482]~E(f329(f329(f80(a1),x44821),x44821),a102)
% 187.18/188.04 [4509]~E(f329(a3,f329(a117,f329(a19,x45091))),f2(a104))
% 187.18/188.04 [4517]~P24(f329(a198,f329(f105(a1),x45171)))
% 187.18/188.04 [4520]~P24(f329(f329(f244(a874),x45201),x45201))
% 187.18/188.04 [4529]~P24(f329(f329(f243(a874),f329(a117,x45291)),x45291))
% 187.18/188.04 [3302]E(f329(a109,f329(f79(a1),f329(f105(a1),x33021))),f2(a874))
% 187.18/188.04 [3305]E(f329(f329(f80(a1),f329(f79(a1),x33051)),x33051),f2(a1))
% 187.18/188.04 [3309]E(f329(f38(a1),f329(f299(a1,f2(a1)),x33091)),f329(a109,x33091))
% 187.18/188.04 [3322]E(f329(f329(f254(a874),f329(a117,f2(a874))),x33221),f329(a117,f2(a874)))
% 187.18/188.04 [3422]E(f329(f282(x34221),f193(f881(f880(x34221,x34221),a869))),f193(f881(x34221,a869)))
% 187.18/188.04 [3430]E(f41(f881(x34301,a869),f193(f881(f881(x34301,a869),a869))),f252(f881(x34301,a869)))
% 187.18/188.04 [3431]E(f41(f881(x34311,a869),f252(f881(f881(x34311,a869),a869))),f193(f881(x34311,a869)))
% 187.18/188.04 [3432]E(f40(f881(x34321,a869),f193(f881(f881(x34321,a869),a869))),f193(f881(x34321,a869)))
% 187.18/188.04 [3433]E(f40(f881(x34331,a869),f252(f881(f881(x34331,a869),a869))),f252(f881(x34331,a869)))
% 187.18/188.04 [3479]E(f329(f329(f307(f875(x34791)),f118(x34791)),f193(f881(f875(x34791),a869))),f159(x34791,f193(f881(x34791,a869))))
% 187.18/188.04 [3480]E(f329(f329(f307(f875(x34801)),f118(x34801)),f193(f881(f875(x34801),a869))),f160(x34801,f118(f881(x34801,a869))))
% 187.18/188.04 [3518]E(f329(f329(f80(a874),f4(x35181)),f329(a117,f2(a874))),f4(f329(a3,f329(a117,f329(a19,x35181)))))
% 187.18/188.04 [3546]E(f329(f38(a1),f329(f308(a874,a1,f105(a1)),x35461)),f329(f38(a874),x35461))
% 187.18/188.04 [3547]P24(f329(f329(f243(a874),x35471),f329(f329(f81(a874),x35471),x35471)))
% 187.18/188.04 [3584]E(f329(f308(a1,a874,a109),f300(a1,f2(a1),f329(f105(a1),x35841))),f329(f298(a874),x35841))
% 187.18/188.04 [3600]E(f329(f329(f39(a874),f329(a117,f2(a874))),f329(f108(a874),x36001)),f329(a109,f329(f329(f39(a1),f78(a1)),f329(f108(a1),x36001))))
% 187.18/188.04 [3602]E(f329(f171(a874),f137(a874,f329(f299(a874,f2(a874)),f329(a117,x36021)))),f329(f298(a874),x36021))
% 187.18/188.04 [3603]E(f329(f329(f80(a874),f329(f194(a104),x36031)),f329(a117,f2(a874))),f329(f194(a104),f329(a3,f329(a117,f329(a19,x36031)))))
% 187.18/188.04 [3622]E(f329(f308(a1,a874,a109),f329(f308(a874,a1,f105(a1)),x36221)),x36221)
% 187.18/188.04 [3654]E(f329(f329(f307(a874),f2(a874)),f329(f308(a874,a874,a117),f329(f250(a874),x36541))),f329(f250(a874),f329(a117,x36541)))
% 187.18/188.04 [3661]P54(x36611,x36611,f305(x36611,f193(f881(f880(x36611,x36611),a869))))
% 187.18/188.04 [3667]P24(f329(a198,f329(f79(a1),f329(f105(a1),f329(a117,x36671)))))
% 187.18/188.04 [3678]E(f329(f329(f22(f881(a874,a869)),f329(f251(a874),x36781)),f329(f329(f307(a874),x36781),f193(f881(a874,a869)))),f329(f251(a874),f329(a117,x36781)))
% 187.18/188.04 [3694]E(f329(f329(f80(a1),f329(f329(f22(a1),a83),x36941)),f329(f329(f22(a1),a83),x36941)),f329(f329(f22(a1),a83),f329(f329(f80(a1),x36941),x36941)))
% 187.18/188.04 [3710]E(f329(f329(f307(f881(x37101,a869)),f193(f881(x37101,a869))),f193(f881(f881(x37101,a869),a869))),f329(f306(x37101),f193(f881(x37101,a869))))
% 187.18/188.04 [3737]E(f329(f329(f22(f881(a874,a869)),f329(f301(a874),x37371)),f329(f329(f307(a874),f329(a117,x37371)),f193(f881(a874,a869)))),f329(f301(a874),f329(a117,x37371)))
% 187.18/188.04 [3746]E(f329(f329(f307(f878(x37461)),f206(x37461)),f329(f308(x37461,f878(x37461),f236(x37461)),f252(f881(x37461,a869)))),f252(f881(f878(x37461),a869)))
% 187.18/188.04 [3845]E(f329(f108(a874),f329(f329(f80(a1),x38451),x38451)),f329(f329(f86(a874,a874),f329(f108(a874),x38451)),f329(f329(f18(a874,a874,a874),f80(a874)),f5(a874))))
% 187.18/188.04 [4236]P11(x42361,f881(x42361,a869),f329(f329(f8(f881(x42361,a869),f881(f881(x42361,a869),f881(x42361,a869)),x42361),f329(f7(f881(x42361,a869),f881(x42361,a869),f881(x42361,a869)),f22(f881(x42361,a869)))),f329(f329(f7(x42361,f881(x42361,a869),f881(x42361,a869)),f307(x42361)),f193(f881(x42361,a869)))))
% 187.18/188.04 [4326]E(f329(f249(f880(a1,a1)),f329(f268(a1,a1,a869),f329(f329(f8(f881(a1,a869),f881(a1,a869),a1),f329(f18(a1,a869,a869),f329(f329(f8(a869,f881(a869,a869),a1),a327),f329(f243(a1),x43261)))),f244(a1)))),f112(x43261))
% 187.18/188.04 [4359]E(f329(f249(f880(a1,a1)),f329(f268(a1,a1,a869),f329(f329(f18(a1,f881(a1,a869),f881(a1,a869)),f329(f329(f8(f881(a869,a869),f881(f881(a1,a869),f881(a1,a869)),a1),f8(a869,a869,a1)),f329(f329(f8(a869,f881(a869,a869),a1),a327),f329(f243(a1),x43591)))),f244(a1)))),f110(x43591))
% 187.18/188.04 [4414]E(f329(f249(f880(f881(x44141,a869),f881(x44141,a869))),f329(f268(f881(x44141,a869),f881(x44141,a869),a869),f329(f329(f7(f881(x44141,a869),f881(f881(x44141,a869),a869),f881(f881(x44141,a869),a869)),f329(f329(f8(f881(f881(x44141,a869),f881(a869,a869)),f881(f881(f881(x44141,a869),a869),f881(f881(x44141,a869),a869)),f881(x44141,a869)),f18(f881(x44141,a869),a869,a869)),f329(f329(f8(f881(f881(x44141,a869),a869),f881(f881(x44141,a869),f881(a869,a869)),f881(x44141,a869)),f329(f8(a869,f881(a869,a869),f881(x44141,a869)),a327)),f244(f881(x44141,a869))))),f62(x44141)))),f304(x44141))
% 187.18/188.04 [4533]~P24(f329(f62(f875(x45331)),f252(f881(f875(x45331),a869))))
% 187.18/188.04 [4538]~P24(f329(f329(f91(a1),a102),f329(f329(f80(a1),x45381),x45381)))
% 187.18/188.04 [4548]~P24(f329(f329(f243(a1),f2(a1)),f329(f79(a1),f329(f105(a1),f329(a117,x45481)))))
% 187.18/188.04 [3457]E(f329(f329(f22(a1),f329(f329(f80(a1),x34571),a102)),a102),x34571)
% 187.18/188.04 [3473]E(f329(f171(a874),f137(a874,f329(f299(a874,f2(a874)),x34731))),f329(f250(a874),x34731))
% 187.18/188.04 [3716]E(f329(f329(f80(a1),f329(f329(f80(a1),f78(a1)),x37161)),x37161),f329(f329(f22(a1),f329(f329(f80(a1),x37161),x37161)),a102))
% 187.18/188.04 [3763]E(f329(f284(x37631,x37631),f305(x37631,f193(f881(f880(x37631,x37631),a869)))),f305(x37631,f193(f881(f880(x37631,x37631),a869))))
% 187.18/188.04 [3811]P24(f329(f329(f243(a874),x38111),f329(f329(f81(a874),x38111),f329(f329(f81(a874),x38111),x38111))))
% 187.18/188.04 [4091]P24(f329(f62(a874),f329(f249(a874),f329(f329(f7(a874,a874,a869),f243(a874)),x40911))))
% 187.18/188.04 [4092]P24(f329(f62(a874),f329(f249(a874),f329(f329(f7(a874,a874,a869),f244(a874)),x40921))))
% 187.18/188.04 [4379]E(f329(f249(f880(x43791,x43791)),f329(f329(f8(f881(x43791,a869),a869,f880(x43791,x43791)),f87(x43791)),f329(f329(f7(f880(x43791,x43791),f881(x43791,f880(x43791,x43791)),f881(x43791,a869)),f329(f329(f8(f881(f880(x43791,x43791),a869),f881(f881(x43791,f880(x43791,x43791)),f881(x43791,a869)),f880(x43791,x43791)),f8(f880(x43791,x43791),a869,x43791)),a326)),f329(f329(f18(x43791,x43791,f880(x43791,x43791)),f264(x43791,x43791)),f5(x43791))))),f305(x43791,f193(f881(f880(x43791,x43791),a869))))
% 187.18/188.04 [4535]~E(f329(f329(f22(a1),f329(f329(f80(a1),x45351),x45351)),a102),a83)
% 187.18/188.04 [4537]~E(f329(f329(f80(a1),f329(f329(f80(a1),f78(a1)),x45371)),x45371),f2(a1))
% 187.18/188.04 [4545]~P24(f329(f329(f91(a1),f329(f329(f80(a1),x45451),x45451)),a102))
% 187.18/188.04 [3858]E(f329(f329(f80(a1),f329(f329(f22(a1),a102),x38581)),f329(f329(f22(a1),a102),x38581)),f329(f329(f22(a1),a102),f329(f329(f22(a1),f329(f329(f80(a1),x38581),x38581)),a102)))
% 187.18/188.04 [3980]E(f329(f329(f22(a1),f329(f329(f80(a1),f329(f329(f22(a1),a102),x39801)),f329(f329(f22(a1),a102),x39801))),a102),f329(f329(f22(a1),a102),f329(f329(f80(a1),x39801),x39801)))
% 187.18/188.04 [4015]E(f329(f329(f22(a1),f329(f329(f80(a1),f329(f329(f80(a1),x40151),a102)),f329(f329(f80(a1),x40151),a102))),a102),f329(f329(f80(a1),f329(f329(f80(a1),x40151),x40151)),a102))
% 187.18/188.04 [4053]E(f329(f329(f22(a1),f329(f329(f80(a1),f329(f329(f22(a1),a102),x40531)),f329(f329(f22(a1),a102),x40531))),a102),f329(f329(f22(a1),a83),f329(f329(f22(a1),f329(f329(f80(a1),x40531),x40531)),a102)))
% 187.18/188.04 [4154]E(f329(a89,f329(f283(f880(a874,a874),f880(a874,a874),a113),f329(f329(f307(f880(a874,a874)),f329(f329(f264(a874,a874),x41541),f2(a874))),f193(f881(f880(a874,a874),a869))))),f329(f105(a1),x41541))
% 187.18/188.04 [4164]E(f329(a89,f329(f283(f880(a874,a874),f880(a874,a874),a113),f329(f329(f307(f880(a874,a874)),f329(f329(f264(a874,a874),f334(x41641)),f495(x41641))),f193(f881(f880(a874,a874),a869))))),x41641)
% 187.18/188.04 [4198]E(f329(f249(a1),f329(f329(f18(a1,a869,a869),f329(f329(f8(a869,f881(a869,a869),a1),a327),f329(f243(a1),f2(a1)))),x41981)),f329(f308(a874,a1,f105(a1)),f329(f249(a874),f329(f329(f8(a1,a869,a874),x41981),f105(a1)))))
% 187.18/188.04 [4244]P43(f329(f249(a1),f329(f329(f18(a1,a869,a869),f329(f329(f8(a869,f881(a869,a869),a1),a327),f329(f243(a1),f2(a1)))),x42441)))
% 187.18/188.04 [4265]P24(f329(f329(f331(f880(f881(f880(a874,a874),a869),f881(f880(a874,a874),a869))),f329(f329(f264(f881(f880(a874,a874),a869),f881(f880(a874,a874),a869)),x42651),f193(f881(f880(a874,a874),a869)))),a71))
% 187.18/188.04 [4271]E(f329(f308(a1,a874,a109),f329(f249(a1),f329(f329(f18(a1,a869,a869),f329(f329(f8(a869,f881(a869,a869),a1),a327),f329(f243(a1),f2(a1)))),f329(f329(f8(a874,a869,a1),x42711),a109)))),f329(f249(a874),x42711))
% 187.18/188.04 [4428]E(f310(a874,f329(f329(f42(f880(a874,a874),f881(a874,a869)),f329(a111,x44281)),f329(f268(a874,a874,f881(a874,a869)),f329(f329(f7(a874,f881(a874,a869),f881(a874,f881(a874,a869))),f329(f329(f8(f881(a874,f881(f881(a874,a869),f881(a874,a869))),f881(f881(a874,a869),f881(a874,f881(a874,a869))),a874),f7(a874,f881(a874,a869),f881(a874,a869))),f329(f329(f8(f881(a874,a874),f881(a874,f881(f881(a874,a869),f881(a874,a869))),a874),f329(f8(a874,f881(f881(a874,a869),f881(a874,a869)),a874),f307(a874))),f22(a874)))),f193(f881(a874,a869)))))),f329(a109,x44281))
% 187.18/188.04 [4550]~P24(f329(f329(f91(a1),a83),f329(f329(f22(a1),f329(f329(f80(a1),x45501),x45501)),a102)))
% 187.18/188.04 [3903]E(f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),x39031),x39031)),a102)),a102),f329(f329(f80(a1),x39031),x39031))
% 187.18/188.04 [3954]E(f329(f329(f22(a1),f329(f329(f22(a1),f329(f329(f80(a1),x39541),x39541)),a102)),a102),f329(f329(f80(a1),f329(f329(f22(a1),x39541),a102)),f329(f329(f22(a1),x39541),a102)))
% 187.18/188.04 [4172]E(f329(f329(f22(a1),f329(f329(f80(a1),f329(f329(f80(a1),f329(f79(a1),x41721)),a102)),f329(f329(f80(a1),f329(f79(a1),x41721)),a102))),a102),f329(f79(a1),f329(f329(f22(a1),f329(f329(f80(a1),x41721),x41721)),a102)))
% 187.18/188.04 [4558]~P24(f329(f329(f91(a1),f329(f329(f22(a1),f329(f329(f80(a1),x45581),x45581)),a102)),a83))
% 187.18/188.04 [4216]E(f329(f329(f80(a874),x42161),f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))),f329(a117,f329(a117,x42161)))
% 187.18/188.04 [4217]E(f329(f329(f81(a874),x42171),f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))),f329(f329(f80(a874),x42171),x42171))
% 187.18/188.04 [4218]E(f329(f329(f39(a874),f329(f329(f80(a874),x42181),x42181)),f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))),x42181)
% 187.18/188.04 [4300]E(f45(a874,f329(a117,f329(a117,x43001)),f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))),f45(a874,x43001,f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))))
% 187.18/188.04 [4443]E(f329(a89,f329(f329(f42(f880(a874,a874),f881(f880(a874,a874),a869)),f329(a111,x44431)),f329(f268(a874,a874,f881(f880(a874,a874),a869)),f329(f329(f8(f881(a874,f881(f880(a874,a874),a869)),f881(a874,f881(f880(a874,a874),a869)),a874),f329(f8(f881(f880(a874,a874),a869),f881(f880(a874,a874),a869),a874),f283(f880(a874,a874),f880(a874,a874),a113))),f329(f329(f7(a874,f881(f880(a874,a874),a869),f881(a874,f881(f880(a874,a874),a869))),f329(f329(f8(f881(a874,f881(f881(f880(a874,a874),a869),f881(f880(a874,a874),a869))),f881(f881(f880(a874,a874),a869),f881(a874,f881(f880(a874,a874),a869))),a874),f7(a874,f881(f880(a874,a874),a869),f881(f880(a874,a874),a869))),f329(f329(f8(f881(a874,f880(a874,a874)),f881(a874,f881(f881(f880(a874,a874),a869),f881(f880(a874,a874),a869))),a874),f329(f8(f880(a874,a874),f881(f881(f880(a874,a874),a869),f881(f880(a874,a874),a869)),a874),f307(f880(a874,a874)))),f329(f7(a874,a874,f880(a874,a874)),f264(a874,a874))))),f193(f881(f880(a874,a874),a869))))))),f329(f79(a1),x44431))
% 187.18/188.04 [4295]E(f329(f329(f80(a874),f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))),x42951),f329(a117,f329(a117,x42951)))
% 187.18/188.04 [4296]E(f329(f329(f81(a874),f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))),x42961),f329(f329(f80(a874),x42961),x42961))
% 187.18/188.04 [4331]E(f329(f329(f39(a874),f329(a117,f329(a117,x43311))),f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))),f329(a117,f329(f329(f39(a874),x43311),f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102))))))
% 187.18/188.04 [4385]E(f329(f329(f80(a874),f329(f108(a874),f329(f329(f22(a1),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102))),a102))),x43851),f329(a117,f329(a117,f329(a117,x43851))))
% 187.18/188.04 [4451]E(f329(f268(a1,a1,f880(a1,a1)),f329(f329(f18(a1,f881(a1,f880(a1,a1)),f881(a1,f880(a1,a1))),f329(f329(f8(f881(a1,f881(f880(a1,a1),f880(a1,a1))),f881(f881(a1,f880(a1,a1)),f881(a1,f880(a1,a1))),a1),f18(a1,f880(a1,a1),f880(a1,a1))),f329(f329(f8(f881(a1,f880(a1,a1)),f881(a1,f881(f880(a1,a1),f880(a1,a1))),a1),f329(f18(a1,f880(a1,a1),f881(f880(a1,a1),f880(a1,a1))),f329(f329(f8(a869,f881(f880(a1,a1),f881(f880(a1,a1),f880(a1,a1))),a1),f101(f880(a1,a1))),f329(f329(f8(a1,a869,a1),f329(f243(a1),f2(a1))),f329(f329(f7(a1,a1,a1),f22(a1)),x44511))))),f329(f329(f7(a1,f881(a1,a1),f881(a1,f880(a1,a1))),f329(f329(f8(f881(a1,f880(a1,a1)),f881(f881(a1,a1),f881(a1,f880(a1,a1))),a1),f8(a1,f880(a1,a1),a1)),f329(f329(f8(a1,f881(a1,f880(a1,a1)),a1),f264(a1,a1)),f329(f329(f7(a1,a1,a1),f329(f329(f8(a1,f881(a1,a1),a1),f80(a1)),f329(f81(a1),f329(f108(a1),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))))),f78(a1))))),f329(f329(f7(a1,a1,a1),f22(a1)),x44511))))),f329(f329(f8(a1,f881(a1,f880(a1,a1)),a1),f264(a1,a1)),f329(f81(a1),f329(f108(a1),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102))))))),f44(x44511))
% 187.18/188.04 [3124]P96(f879(x31241,x31242))
% 187.18/188.04 [3125]P96(f880(x31251,x31252))
% 187.18/188.04 [3126]P105(f879(x31261,x31262))
% 187.18/188.04 [3127]P105(f880(x31271,x31272))
% 187.18/188.04 [3144]P33(a1,f178(x31441,x31442))
% 187.18/188.04 [3145]P42(x31451,f151(x31451,x31452))
% 187.18/188.04 [3211]P36(x32111,x32112,f118(x32111))
% 187.18/188.04 [3244]P44(x32441,x32442,f261(x32441,x32442))
% 187.18/188.04 [3245]P54(x32451,x32451,f261(x32451,x32452))
% 187.18/188.04 [3521]P21(x35211,x35211,f5(x35211),x35212)
% 187.18/188.04 [3522]P21(x35221,x35221,f34(x35221),x35222)
% 187.18/188.04 [3530]P37(x35301,x35302,f118(x35301),f118(x35301))
% 187.18/188.04 [3531]P21(x35311,f878(x35311),f236(x35311),x35312)
% 187.18/188.04 [3540]P21(f875(x35401),f875(x35401),f167(x35401),x35402)
% 187.18/188.04 [4462]~E(f33(x44621,x44622),a24)
% 187.18/188.04 [4463]~E(f32(x44631,x44632),a24)
% 187.18/188.04 [4492]~P38(x44921,x44922,f118(x44921))
% 187.18/188.04 [4493]~P40(x44931,x44932,f118(x44931))
% 187.18/188.04 [3107]E(f329(f5(x31071),x31072),x31072)
% 187.18/188.04 [3108]E(f329(f249(x31081),x31082),x31082)
% 187.18/188.04 [3110]E(f329(f34(x31101),x31102),x31102)
% 187.18/188.04 [3120]E(f329(f196(x31201),x31202),f120(x31201))
% 187.18/188.04 [3142]E(f85(x31421,f329(a326,x31422)),x31422)
% 187.18/188.04 [3143]E(f90(x31431,f329(a326,x31432)),x31432)
% 187.18/188.04 [3164]E(f329(f134(x31641,x31642),f118(x31641)),f118(x31641))
% 187.18/188.04 [3185]E(f305(x31851,f305(x31851,x31852)),f305(x31851,x31852))
% 187.18/188.04 [3186]E(f150(x31861,f150(x31861,x31862)),f150(x31861,x31862))
% 187.18/188.04 [3206]E(f329(f329(f126(x32061),x32062),f118(x32061)),x32062)
% 187.18/188.04 [3212]E(f172(x32121,x32122,f118(x32121)),x32122)
% 187.18/188.04 [3213]E(f172(x32131,f118(x32131),x32132),x32132)
% 187.18/188.04 [3219]E(f329(f329(f174(x32191),x32192),f118(x32191)),f118(x32191))
% 187.18/188.04 [3220]E(f329(f329(f136(x32201),x32202),f118(x32201)),f118(x32201))
% 187.18/188.04 [3222]E(f153(x32221,x32222,f118(x32221)),f2(a874))
% 187.18/188.04 [3223]E(f237(x32231,x32232,f206(x32231)),f2(a874))
% 187.18/188.04 [3225]E(f168(x32251,x32252,f118(x32251)),f118(x32251))
% 187.18/188.04 [3226]E(f176(x32261,x32262,f118(x32261)),f118(x32261))
% 187.18/188.04 [3227]E(f175(x32271,f118(x32271),x32272),f118(x32271))
% 187.18/188.04 [3231]E(f329(f171(x32311),f150(x32311,x32312)),f329(f171(x32311),x32312))
% 187.18/188.04 [3234]E(f329(f260(x32341,x32341),f261(x32341,x32342)),x32342)
% 187.18/188.04 [3235]E(f329(f262(x32351,x32351),f261(x32351,x32352)),x32352)
% 187.18/188.04 [3243]E(f329(f284(x32431,x32431),f261(x32431,x32432)),f261(x32431,x32432))
% 187.18/188.04 [3258]E(f305(f875(x32581),f155(x32581,x32582)),f156(x32581,f305(x32581,x32582)))
% 187.18/188.04 [3260]P24(f329(f135(a1),f178(x32601,x32602)))
% 187.18/188.04 [3268]E(f329(f260(x32681,x32681),f305(x32681,x32682)),f252(f881(x32681,a869)))
% 187.18/188.04 [3269]E(f329(f262(x32691,x32691),f305(x32691,x32692)),f252(f881(x32691,a869)))
% 187.18/188.04 [3273]P24(f329(f135(x32731),f150(x32731,x32732)))
% 187.18/188.04 [3275]P24(f329(f158(x32751,x32752),f118(x32751)))
% 187.18/188.04 [3283]E(f329(f171(a1),f178(x32831,x32832)),f300(a1,x32831,x32832))
% 187.18/188.04 [3298]P55(x32981,f193(f881(x32981,a869)),x32982)
% 187.18/188.04 [3303]E(f329(f267(a1,a1),f46(x33031,x33032)),f45(a1,x33031,x33032))
% 187.18/188.04 [3304]E(f329(f299(a874,x33041),f329(a117,x33042)),f300(a874,x33041,x33042))
% 187.18/188.04 [3321]E(f329(f329(f149(x33211),x33212),f118(x33211)),f138(x33211,x33212,f118(x33211)))
% 187.18/188.04 [3333]E(f300(a874,f329(a117,x33331),x33332),f302(a874,x33331,x33332))
% 187.18/188.04 [3336]P44(x33361,f252(f881(x33361,a869)),f305(x33361,x33362))
% 187.18/188.04 [3399]E(f329(f329(f22(a874),x33991),f329(a117,x33992)),f329(f38(a874),f303(a874,x33992,x33991)))
% 187.18/188.04 [3458]E(f165(x34581,x34582,f118(x34581)),f329(f329(f264(f875(x34581),f875(x34581)),f118(x34581)),f118(x34581)))
% 187.18/188.04 [3477]E(f329(f268(x34771,x34772,f880(x34771,x34772)),f264(x34771,x34772)),f34(f880(x34771,x34772)))
% 187.18/188.04 [3482]P24(f329(f329(f331(f875(x34821)),f118(x34821)),f159(x34821,x34822)))
% 187.18/188.04 [3483]E(f329(f194(f875(x34831)),f119(x34831,x34832)),f329(f329(f22(a874),f329(f194(f875(x34831)),x34832)),f78(a874)))
% 187.18/188.04 [3491]P24(f329(f62(a874),f300(a874,x34911,x34912)))
% 187.18/188.04 [3492]P24(f329(f62(a874),f303(a874,x34921,x34922)))
% 187.18/188.04 [3493]P24(f329(f62(a874),f302(a874,x34931,x34932)))
% 187.18/188.04 [3494]P24(f329(f62(a1),f300(a1,x34941,x34942)))
% 187.18/188.04 [3495]P24(f329(f62(a1),f303(a1,x34951,x34952)))
% 187.18/188.04 [3496]P24(f329(f62(a1),f302(a1,x34961,x34962)))
% 187.18/188.04 [3599]E(f329(f308(a874,a874,a117),f300(a874,x35991,x35992)),f300(a874,f329(a117,x35991),f329(a117,x35992)))
% 187.18/188.04 [3619]E(f329(f329(f286(x36191,x36191,x36191),f305(x36191,x36192)),f305(x36191,x36192)),f305(x36191,x36192))
% 187.18/188.04 [3652]E(f329(f329(f264(a1,a1),f329(f329(f39(a1),x36521),x36522)),f45(a1,x36521,x36522)),f46(x36521,x36522))
% 187.18/188.04 [3653]E(f329(f329(f264(a104,a104),f329(f329(f39(a104),x36531),x36532)),f45(a104,x36531,x36532)),f21(x36531,x36532))
% 187.18/188.04 [3682]E(f329(f329(f264(a874,a874),f329(f329(f39(a874),x36821),x36822)),f45(a874,x36821,x36822)),f85(f880(a874,a874),f48(x36821,x36822)))
% 187.18/188.04 [3733]P24(f329(f329(f244(a874),f329(f329(f22(a874),x37331),x37332)),f329(a117,x37331)))
% 187.18/188.04 [3832]E(f329(f329(f80(a1),f329(f329(f81(a1),x38321),f329(f329(f39(a1),x38322),x38321))),f45(a1,x38322,x38321)),x38322)
% 187.18/188.04 [3836]E(f329(f329(f42(a874,f881(f880(f875(x38361),f875(x38361)),a869)),f252(f881(a874,a869))),f141(x38361,x38362)),f143(x38361,x38362))
% 187.18/188.04 [4066]P24(f329(f329(f331(f880(f875(x40661),f875(x40661))),f329(f329(f264(f875(x40661),f875(x40661)),f118(x40661)),f118(x40661))),f156(x40661,x40662)))
% 187.18/188.04 [4229]E(f269(x42291,x42291,x42292,x42292,f5(x42291),f5(x42292)),f34(f880(x42291,x42292)))
% 187.18/188.04 [4231]E(f269(x42311,x42311,x42312,x42312,f34(x42311),f34(x42312)),f34(f880(x42311,x42312)))
% 187.18/188.04 [4471]~E(f329(f236(x44711),x44712),f206(x44711))
% 187.18/188.04 [3204]E(f329(f240(x32041),f329(f236(x32041),x32042)),x32042)
% 187.18/188.04 [3205]E(f329(f167(x32051),f329(f167(x32051),x32052)),x32052)
% 187.18/188.04 [3207]E(f329(f329(f136(x32071),f2(a874)),x32072),x32072)
% 187.18/188.04 [3221]E(f329(f329(f174(x32211),f2(a874)),x32212),f118(x32211))
% 187.18/188.04 [3229]E(f329(f329(f126(x32291),f118(x32291)),x32292),x32292)
% 187.18/188.04 [3237]E(f329(f194(f878(x32371)),f329(f236(x32371),x32372)),f2(a874))
% 187.18/188.04 [3239]E(f40(f881(x32391,a869),f329(f306(x32391),x32392)),x32392)
% 187.18/188.04 [3241]E(f329(f171(x32411),f329(f166(x32411),x32412)),f329(f171(x32411),x32412))
% 187.18/188.04 [3242]E(f329(f171(x32421),f329(f167(x32421),x32422)),f329(f171(x32421),x32422))
% 187.18/188.04 [3247]E(f329(f329(f22(a104),x32471),x32472),f329(f329(a23,x32471),x32472))
% 187.18/188.04 [3262]E(f329(f329(f81(a874),x32621),x32622),f329(f329(f81(a874),x32622),x32621))
% 187.18/188.04 [3263]E(f329(f329(f81(a1),x32631),x32632),f329(f329(f81(a1),x32632),x32631))
% 187.18/188.04 [3264]E(f329(f329(f80(a874),x32641),x32642),f329(f329(f80(a874),x32642),x32641))
% 187.18/188.04 [3265]E(f329(f329(f80(a1),x32651),x32652),f329(f329(f80(a1),x32652),x32651))
% 187.18/188.04 [3290]E(f329(f329(f188(x32901,x32901),f2(a874)),x32902),f34(x32901))
% 187.18/188.04 [3291]E(f329(f194(f875(x32911)),f329(f166(x32911),x32912)),f329(f194(f875(x32911)),x32912))
% 187.18/188.04 [3292]E(f329(f194(f875(x32921)),f329(f167(x32921),x32922)),f329(f194(f875(x32921)),x32922))
% 187.18/188.04 [3293]E(f175(x32931,x32932,f193(f881(a874,a869))),f118(x32931))
% 187.18/188.04 [3294]E(f329(f329(f152(x32941,x32941),f5(x32941)),x32942),x32942)
% 187.18/188.04 [3296]E(f329(f263(a1,a1),f46(x32961,x32962)),f329(f329(f39(a1),x32961),x32962))
% 187.18/188.04 [3314]E(f329(f194(f875(x33141)),f150(x33141,x33142)),f329(f38(x33141),f329(f171(x33141),x33142)))
% 187.18/188.04 [3315]E(f31(f32(x33151,x33152)),f329(f329(f80(a874),f31(x33152)),f329(a117,f2(a874))))
% 187.18/188.04 [3316]E(f329(f282(x33161),f329(f284(x33161,x33161),x33162)),f329(f282(x33161),x33162))
% 187.18/188.04 [3320]P24(f329(f62(x33201),f329(f171(x33201),x33202)))
% 187.18/188.04 [3328]E(f329(f329(f80(a1),x33281),f329(f79(a1),x33282)),f329(f329(f22(a1),x33281),x33282))
% 187.18/188.04 [3335]P20(x33351,x33352,f193(f881(f873(x33351),a869)))
% 187.18/188.04 [3337]E(f329(f308(x33371,x33371,f5(x33371)),x33372),x33372)
% 187.18/188.04 [3338]E(f329(f308(x33381,x33381,f34(x33381)),x33382),x33382)
% 187.18/188.04 [3339]E(f329(f309(x33391,x33391,f5(x33391)),x33392),x33392)
% 187.18/188.04 [3340]E(f329(f309(x33401,x33401,f34(x33401)),x33402),x33402)
% 187.18/188.04 [3341]P24(f329(f252(f881(x33411,a869)),x33412))
% 187.18/188.04 [3343]E(f329(f38(a874),f329(f299(a874,x33431),x33432)),f329(f329(f22(a874),x33432),x33431))
% 187.18/188.04 [3344]E(f329(f299(a874,f329(a117,x33441)),x33442),f303(a874,x33441,x33442))
% 187.18/188.04 [3356]E(f329(f329(f307(x33561),x33562),f193(f881(x33561,a869))),f329(f249(x33561),f329(a326,x33562)))
% 187.18/188.04 [3360]E(f329(f329(f307(x33601),x33602),f193(f881(x33601,a869))),f235(x33601,f329(f236(x33601),x33602)))
% 187.18/188.04 [3362]E(f305(x33621,f329(f284(x33621,x33621),x33622)),f329(f284(x33621,x33621),f305(x33621,x33622)))
% 187.18/188.04 [3367]E(f329(f329(f80(a874),f329(a117,x33671)),x33672),f329(f329(f80(a874),x33671),f329(a117,x33672)))
% 187.18/188.04 [3368]E(f329(f329(f22(a874),f329(a117,x33681)),f329(a117,x33682)),f329(f329(f22(a874),x33681),x33682))
% 187.18/188.04 [3374]E(f55(x33741,f2(a874),x33742),f329(f329(f149(f875(x33741)),f118(x33741)),f118(f875(x33741))))
% 187.18/188.04 [3375]E(f329(f38(a874),f302(a874,x33751,x33752)),f329(f329(f22(a874),x33752),x33751))
% 187.18/188.04 [3384]P42(x33841,f329(f329(f285(a874,x33841),a248),x33842))
% 187.18/188.04 [3386]P33(a874,f137(a874,f329(f299(a874,x33861),x33862)))
% 187.18/188.04 [3388]P24(f329(f62(a874),f329(f299(a874,x33881),x33882)))
% 187.18/188.04 [3389]P24(f329(f62(a1),f329(f299(a1,x33891),x33892)))
% 187.18/188.04 [3392]E(f329(f284(f875(x33921),f875(x33921)),f155(x33921,x33922)),f155(x33921,f329(f284(x33921,x33921),x33922)))
% 187.18/188.04 [3393]E(f329(f194(a870),f32(x33931,x33932)),f329(f329(f80(a874),f329(f194(a870),x33932)),f329(a117,f2(a874))))
% 187.18/188.04 [3395]E(f329(f299(a1,x33951),f329(f329(f80(a1),x33952),f78(a1))),f300(a1,x33951,x33952))
% 187.18/188.04 [3398]E(f329(f329(f39(a1),f329(f79(a1),x33981)),f329(f79(a1),x33982)),f329(f329(f39(a1),x33981),x33982))
% 187.18/188.04 [3406]E(f183(x34061,x34062,f329(f16(f878(x34062),x34061),f206(x34062))),f193(f881(x34061,a869)))
% 187.18/188.04 [3407]E(f185(x34071,x34072,f329(f16(f878(x34072),x34071),f206(x34072))),f193(f881(x34072,a869)))
% 187.18/188.04 [3408]E(f329(f329(f188(f880(x34081,x34081),a869),f78(a874)),x34082),x34082)
% 187.18/188.04 [3410]E(f329(f329(f115(f881(x34101,a869)),x34102),f193(f881(x34101,a869))),x34102)
% 187.18/188.04 [3411]E(f329(f329(f22(f881(x34111,a869)),x34112),f193(f881(x34111,a869))),x34112)
% 187.18/188.04 [3412]E(f329(f329(f106(f881(x34121,a869)),x34122),f252(f881(x34121,a869))),x34122)
% 187.18/188.04 [3413]E(f329(f263(a874,a874),f85(f880(a874,a874),f48(x34131,x34132))),f329(f329(f39(a874),x34131),x34132))
% 187.18/188.04 [3420]E(f311(x34201,f329(a20,x34202),f329(f79(a1),f329(a20,x34202))),f329(f329(f314(a1),x34201),x34202))
% 187.18/188.04 [3421]E(f300(a1,f329(f329(f80(a1),x34211),f78(a1)),x34212),f302(a1,x34211,x34212))
% 187.18/188.04 [3426]E(f329(f267(a874,a874),f85(f880(a874,a874),f48(x34261,x34262))),f45(a874,x34261,x34262))
% 187.18/188.04 [3434]E(f312(x34341,f329(a20,x34342),f329(f79(a1),f329(a20,x34342))),f313(a1,x34341,x34342))
% 187.18/188.04 [3437]P24(f329(f329(f331(x34371),x34372),f252(f881(x34371,a869))))
% 187.18/188.04 [3442]E(f329(f329(f22(a874),f329(a117,x34421)),x34422),f329(f38(a874),f300(a874,x34422,x34421)))
% 187.18/188.04 [3469]E(f329(f329(f115(f881(x34691,a869)),x34692),f252(f881(x34691,a869))),f252(f881(x34691,a869)))
% 187.18/188.04 [3470]E(f329(f329(f22(f881(x34701,a869)),x34702),f252(f881(x34701,a869))),f193(f881(x34701,a869)))
% 187.18/188.04 [3471]E(f329(f329(f106(f881(x34711,a869)),x34712),f193(f881(x34711,a869))),f193(f881(x34711,a869)))
% 187.18/188.04 [3486]E(f45(a1,f329(f105(a1),x34861),f329(f105(a1),x34862)),f329(f105(a1),f45(a874,x34861,x34862)))
% 187.18/188.04 [3487]E(f45(a1,f329(f79(a1),x34871),f329(f79(a1),x34872)),f329(f79(a1),f45(a1,x34871,x34872)))
% 187.18/188.04 [3498]E(f329(f194(f875(x34981)),f329(f170(x34981),x34982)),f329(f329(f22(a874),f329(f194(f875(x34981)),x34982)),f78(a874)))
% 187.18/188.04 [3523]E(f329(f329(f39(a1),f45(a1,x35231,x35232)),x35232),f2(a1))
% 187.18/188.04 [3533]E(f329(a3,f45(a874,f329(a19,x35331),f329(a19,x35332))),f45(a104,x35331,x35332))
% 187.18/188.04 [3566]E(f329(a3,f329(f329(f22(a874),f329(a19,x35661)),f329(a19,x35662))),f329(f329(f22(a104),x35661),x35662))
% 187.18/188.04 [3567]E(f329(a3,f329(f329(f81(a874),f329(a19,x35671)),f329(a19,x35672))),f329(f329(f81(a104),x35671),x35672))
% 187.18/188.04 [3568]E(f329(a3,f329(f329(f80(a874),f329(a19,x35681)),f329(a19,x35682))),f329(f329(f80(a104),x35681),x35682))
% 187.18/188.04 [3569]E(f329(a3,f329(f329(f39(a874),f329(a19,x35691)),f329(a19,x35692))),f329(f329(f39(a104),x35691),x35692))
% 187.18/188.04 [3578]E(f329(f308(a874,a874,a117),f329(f299(a874,x35781),x35782)),f329(f299(a874,f329(a117,x35781)),f329(a117,x35782)))
% 187.18/188.04 [3604]P24(f329(f48(x36041,x36042),f85(f880(a874,a874),f48(x36041,x36042))))
% 187.18/188.04 [3625]E(f329(f329(f80(a874),f329(f329(f80(a874),f31(x36251)),f31(x36252))),f329(a117,f2(a874))),f31(f33(x36251,x36252)))
% 187.18/188.04 [3626]E(f45(a874,f329(a117,f45(a874,x36261,x36262)),x36262),f45(a874,f329(a117,x36261),x36262))
% 187.18/188.04 [3640]E(f329(f329(f43(f881(x36401,a869),f881(x36401,a869)),x36402),f5(f881(x36401,a869))),f41(f881(x36401,a869),x36402))
% 187.18/188.04 [3641]E(f329(f329(f42(f881(x36411,a869),f881(x36411,a869)),x36412),f5(f881(x36411,a869))),f40(f881(x36411,a869),x36412))
% 187.18/188.04 [3642]E(f329(f308(f875(x36421),f881(x36421,a869),f171(x36421)),f329(f171(f875(x36421)),f54(x36421,x36422))),f329(f306(x36421),f329(f171(x36421),x36422)))
% 187.18/188.04 [3645]P24(f329(f329(f331(f881(x36451,a869)),x36452),f329(f306(x36451),x36452)))
% 187.18/188.04 [3651]E(f45(a1,f329(f79(a1),f45(a1,x36511,x36512)),x36512),f45(a1,f329(f79(a1),x36511),x36512))
% 187.18/188.04 [3663]P24(f329(f329(f243(f881(x36631,a869)),x36632),f252(f881(x36631,a869))))
% 187.18/188.04 [3665]E(f329(f329(f286(x36651,x36651,x36651),f305(x36651,x36652)),f305(x36651,f305(x36651,x36652))),f305(x36651,x36652))
% 187.18/188.04 [3666]E(f329(f329(f115(f881(x36661,a869)),f329(f262(x36661,x36661),x36662)),f329(f260(x36661,x36661),x36662)),f329(f282(x36661),x36662))
% 187.18/188.04 [3687]E(f316(x36871,x36872,f252(f881(x36871,a869)),f252(f881(x36872,a869))),f252(f881(f879(x36871,x36872),a869)))
% 187.18/188.04 [3738]P24(f329(f329(f243(a874),f45(a874,x37381,x37382)),x37381))
% 187.18/188.04 [3761]P24(f329(f329(f243(a1),f329(f79(a1),f329(f105(a1),x37611))),f329(f105(a1),x37612)))
% 187.18/188.04 [3787]P24(f329(f329(f331(f881(x37871,a869)),f193(f881(x37871,a869))),f329(f306(x37871),x37872)))
% 187.18/188.04 [3792]E(f305(x37921,f329(f329(f286(x37921,x37921,x37921),x37922),f305(x37921,x37922))),f305(x37921,x37922))
% 187.18/188.04 [3795]E(f329(f329(f286(x37951,x37951,x37951),f305(x37951,x37952)),x37952),f329(f329(f286(x37951,x37951,x37951),x37952),f305(x37951,x37952)))
% 187.18/188.04 [3797]E(f329(a109,f329(f329(f80(a1),f329(f329(f22(a1),x37971),x37972)),f78(a1))),f329(f38(a1),f300(a1,x37972,x37971)))
% 187.18/188.04 [3812]E(f329(f260(x38121,x38121),f329(f329(f286(x38121,x38121,x38121),x38122),f305(x38121,x38122))),f329(f260(x38121,x38121),x38122))
% 187.18/188.04 [3813]E(f329(f262(x38131,x38131),f329(f329(f286(x38131,x38131,x38131),x38132),f305(x38131,x38132))),f329(f262(x38131,x38131),x38132))
% 187.18/188.04 [3829]E(f329(f329(f80(a874),f329(f329(f80(a874),f329(f194(a870),x38291)),f329(f194(a870),x38292))),f329(a117,f2(a874))),f329(f194(a870),f33(x38291,x38292)))
% 187.18/188.04 [3840]P21(a874,a874,f329(f329(f7(a874,a874,a874),f80(a874)),x38401),x38402)
% 187.18/188.04 [3842]P33(a874,f329(f167(a874),f329(f329(f152(f875(x38421),a874),f194(f875(x38421))),f179(x38421,x38422))))
% 187.18/188.04 [3889]P24(f329(f329(f244(a1),f329(f79(a1),f329(f105(a1),f329(a117,x38891)))),f329(f105(a1),x38892)))
% 187.18/188.04 [3935]E(f329(f140(f875(x39351),x39351,f329(f7(x39351,f875(x39351),f875(x39351)),f149(x39351)),f118(x39351)),x39352),f329(f167(x39351),x39352))
% 187.18/188.04 [3987]P24(f329(f329(f243(f881(f880(f875(x39871),f875(x39871)),a869)),f156(x39871,x39872)),f305(f875(x39871),f155(x39871,x39872))))
% 187.18/188.04 [4019]P24(f329(f48(x40191,x40192),f329(f329(f264(a874,a874),f329(f329(f39(a874),x40191),x40192)),f45(a874,x40191,x40192))))
% 187.18/188.04 [4030]P24(f329(f329(f243(f881(f880(f875(x40301),f875(x40301)),a869)),f155(x40301,f305(x40301,x40302))),f305(f875(x40301),f155(x40301,x40302))))
% 187.18/188.04 [4255]E(f329(f329(f270(f880(a104,a104),a104,f880(a104,a104),f880(x42551,f880(a104,a104))),f274(f329(f164(a104),f329(f329(f152(f880(a104,x42551),a104),f263(a104,x42551)),x42552)))),f329(f329(f8(x42551,f881(f880(a104,a104),f880(x42551,f880(a104,a104))),a104),f264(x42551,f880(a104,a104))),f275(x42551,x42552))),f273(x42551,x42552))
% 187.18/188.04 [4367]E(f329(f238(a874,f880(x43671,f876(x43671)),f2(a874),f329(f268(x43671,f876(x43671),a874),f329(f16(f881(f876(x43671),a874),x43671),f329(f329(f7(f876(x43671),a874,a874),f329(f329(f8(a874,f881(a874,a874),f876(x43671)),f80(a874)),f194(f876(x43671)))),f78(a874))))),f329(f133(x43671),x43672)),f329(f194(f876(x43671)),x43672))
% 187.18/188.04 [4442]E(f329(f268(f881(f880(x44421,x44421),a869),f881(f880(x44421,x44421),a869),f881(f881(x44422,x44421),f880(f881(f880(x44422,x44422),a869),f881(f880(x44422,x44422),a869)))),f329(f329(f7(f881(f880(x44421,x44421),a869),f881(f881(f880(x44421,x44421),a869),f881(f881(x44422,x44421),f881(f880(x44422,x44422),a869))),f881(f881(f880(x44421,x44421),a869),f881(f881(x44422,x44421),f880(f881(f880(x44422,x44422),a869),f881(f880(x44422,x44422),a869))))),f329(f329(f8(f881(f881(f881(x44422,x44421),f881(f880(x44422,x44422),a869)),f881(f881(x44422,x44421),f880(f881(f880(x44422,x44422),a869),f881(f880(x44422,x44422),a869)))),f881(f881(f881(f880(x44421,x44421),a869),f881(f881(x44422,x44421),f881(f880(x44422,x44422),a869))),f881(f881(f880(x44421,x44421),a869),f881(f881(x44422,x44421),f880(f881(f880(x44422,x44422),a869),f881(f880(x44422,x44422),a869))))),f881(f880(x44421,x44421),a869)),f8(f881(f881(x44422,x44421),f881(f880(x44422,x44422),a869)),f881(f881(x44422,x44421),f880(f881(f880(x44422,x44422),a869),f881(f880(x44422,x44422),a869))),f881(f880(x44421,x44421),a869))),f329(f329(f8(f881(f881(x44422,x44421),f881(f881(f880(x44422,x44422),a869),f880(f881(f880(x44422,x44422),a869),f881(f880(x44422,x44422),a869)))),f881(f881(f881(x44422,x44421),f881(f880(x44422,x44422),a869)),f881(f881(x44422,x44421),f880(f881(f880(x44422,x44422),a869),f881(f880(x44422,x44422),a869)))),f881(f880(x44421,x44421),a869)),f18(f881(x44422,x44421),f881(f880(x44422,x44422),a869),f880(f881(f880(x44422,x44422),a869),f881(f880(x44422,x44422),a869)))),f329(f329(f8(f881(f881(x44422,x44421),f881(f880(x44422,x44422),a869)),f881(f881(x44422,x44421),f881(f881(f880(x44422,x44422),a869),f880(f881(f880(x44422,x44422),a869),f881(f880(x44422,x44422),a869)))),f881(f880(x44421,x44421),a869)),f329(f8(f881(f880(x44422,x44422),a869),f881(f881(f880(x44422,x44422),a869),f880(f881(f880(x44422,x44422),a869),f881(f880(x44422,x44422),a869))),f881(x44422,x44421)),f264(f881(f880(x44422,x44422),a869),f881(f880(x44422,x44422),a869)))),f285(x44421,x44422))))),f285(x44421,x44422))),f74(x44421,x44422))
% 187.18/188.04 [4518]~E(f329(f306(x45181),x45182),f193(f881(f881(x45181,a869),a869)))
% 187.18/188.04 [4532]~P24(f329(f329(f331(x45321),x45322),f193(f881(x45321,a869))))
% 187.18/188.04 [4542]~P24(f329(f329(f244(f881(x45421,a869)),x45422),f193(f881(x45421,a869))))
% 187.18/188.04 [3346]E(f329(f329(f22(a874),x33461),f329(f329(f80(a874),x33461),x33462)),f2(a874))
% 187.18/188.04 [3348]E(f329(f329(f115(f881(x33481,a869)),x33482),x33482),x33482)
% 187.18/188.04 [3349]E(f329(f329(f106(f881(x33491,a869)),x33492),x33492),x33492)
% 187.18/188.04 [3377]E(f329(f329(f22(f881(x33771,a869)),x33772),x33772),f193(f881(x33771,a869)))
% 187.18/188.04 [3380]E(f329(f141(x33801,x33802),f2(a874)),f193(f881(f880(f875(x33801),f875(x33801)),a869)))
% 187.18/188.04 [3381]E(f329(f329(f80(a874),x33811),f329(a117,x33812)),f329(a117,f329(f329(f80(a874),x33811),x33812)))
% 187.18/188.04 [3394]E(f200(f329(f105(a1),x33941),f329(f105(a1),x33942)),f329(f105(a1),f329(f329(f22(a874),x33941),x33942)))
% 187.18/188.04 [3397]E(f329(f329(f39(a1),f329(f79(a1),x33971)),x33972),f329(f329(f39(a1),x33971),f329(f79(a1),x33972)))
% 187.18/188.04 [3401]E(f329(f38(a1),f329(f299(a1,x34011),x34012)),f329(a109,f329(f329(f22(a1),x34012),x34011)))
% 187.18/188.04 [3404]E(f329(f329(f80(a874),f329(a117,x34041)),x34042),f329(a117,f329(f329(f80(a874),x34041),x34042)))
% 187.18/188.04 [3409]E(f329(f79(f881(x34091,a869)),f329(f79(f881(x34091,a869)),x34092)),x34092)
% 187.18/188.04 [3423]E(f179(x34231,f329(f329(f149(f875(x34231)),f118(x34231)),x34232)),f179(x34231,x34232))
% 187.18/188.04 [3427]E(f329(f329(f80(a874),x34271),f329(f329(f81(a874),x34271),x34272)),f329(f329(f81(a874),x34271),f329(a117,x34272)))
% 187.18/188.04 [3435]E(f329(f329(a23,f329(a3,x34351)),f329(a3,x34352)),f329(a3,f329(f329(f22(a874),x34351),x34352)))
% 187.18/188.04 [3449]E(f329(f329(f81(a1),f329(f79(a1),x34491)),x34492),f329(f79(a1),f329(f329(f81(a1),x34491),x34492)))
% 187.18/188.04 [3451]E(f329(f329(f254(a1),f329(f105(a1),x34511)),x34512),f329(f105(a1),f329(f329(f254(a874),x34511),x34512)))
% 187.18/188.04 [3452]E(f329(f329(f81(a104),f329(a3,x34521)),f329(a3,x34522)),f329(a3,f329(f329(f81(a874),x34521),x34522)))
% 187.18/188.04 [3453]E(f329(f329(f80(a104),f329(a3,x34531)),f329(a3,x34532)),f329(a3,f329(f329(f80(a874),x34531),x34532)))
% 187.18/188.04 [3454]E(f329(f329(f241(a874),f329(a117,x34541)),f329(a117,x34542)),f329(a117,f329(f329(f241(a874),x34541),x34542)))
% 187.18/188.04 [3455]E(f329(f329(f242(a874),f329(a117,x34551)),f329(a117,x34552)),f329(a117,f329(f329(f242(a874),x34551),x34552)))
% 187.18/188.04 [3461]E(f329(f171(a874),f137(a874,f329(f299(a874,x34611),x34612))),f329(f299(a874,x34611),x34612))
% 187.18/188.04 [3462]E(f310(x34621,f329(f329(f307(x34621),x34622),f193(f881(x34621,a869)))),x34622)
% 187.18/188.04 [3467]E(f329(f260(x34671,x34672),f193(f881(f880(x34671,x34672),a869))),f193(f881(x34672,a869)))
% 187.18/188.04 [3468]E(f329(f262(x34681,x34682),f193(f881(f880(x34681,x34682),a869))),f193(f881(x34681,a869)))
% 187.18/188.04 [3472]E(f329(a109,f329(f329(f22(a1),x34721),x34722)),f329(f38(a1),f302(a1,x34722,x34721)))
% 187.18/188.04 [3476]E(f329(f329(f80(a874),x34761),f329(f329(f81(a874),x34762),x34761)),f329(f329(f81(a874),f329(a117,x34762)),x34761))
% 187.18/188.04 [3478]E(f329(f329(f61(x34781),f193(f881(x34781,a869))),x34782),f193(f881(f881(x34781,a869),a869)))
% 187.18/188.04 [3488]E(f329(f194(f875(a874)),f137(a874,f329(f299(a874,x34881),x34882))),f329(f329(f22(a874),x34882),x34881))
% 187.18/188.04 [3503]E(f329(f329(f115(f881(x35031,a869)),f193(f881(x35031,a869))),x35032),x35032)
% 187.18/188.04 [3504]E(f329(f329(f106(f881(x35041,a869)),f252(f881(x35041,a869))),x35042),x35042)
% 187.18/188.04 [3507]E(f329(f329(f80(a1),f329(f79(a1),x35071)),f329(f79(a1),x35072)),f329(f79(a1),f329(f329(f80(a1),x35071),x35072)))
% 187.18/188.04 [3510]E(f329(f329(f81(a1),f329(f105(a1),x35101)),f329(f105(a1),x35102)),f329(f105(a1),f329(f329(f81(a874),x35101),x35102)))
% 187.18/188.04 [3511]E(f329(f329(f81(a1),f329(f108(a1),x35111)),f329(f108(a1),x35112)),f329(f108(a1),f329(f329(f81(a1),x35111),x35112)))
% 187.18/188.04 [3513]E(f329(f329(f80(a1),f329(f105(a1),x35131)),f329(f105(a1),x35132)),f329(f105(a1),f329(f329(f80(a874),x35131),x35132)))
% 187.18/188.04 [3514]E(f329(f329(f80(a1),f329(f108(a1),x35141)),f329(f108(a1),x35142)),f329(f108(a1),f329(f329(f80(a1),x35141),x35142)))
% 187.18/188.04 [3515]E(f329(f329(f39(a1),f329(f105(a1),x35151)),f329(f105(a1),x35152)),f329(f105(a1),f329(f329(f39(a874),x35151),x35152)))
% 187.18/188.04 [3534]E(f329(f329(f6(x35341,a874),f329(f16(a874,x35341),f78(a874))),x35342),f329(f38(x35341),x35342))
% 187.18/188.04 [3541]E(f329(f79(a1),f45(a1,f329(f79(a1),x35411),x35412)),f45(a1,x35411,f329(f79(a1),x35412)))
% 187.18/188.04 [3543]E(f329(f171(a1),f178(x35431,f329(f329(f22(a1),x35432),f78(a1)))),f329(f299(a1,x35431),x35432))
% 187.18/188.04 [3548]P24(f329(f329(f243(a874),x35481),f329(f329(f80(a874),x35482),x35481)))
% 187.18/188.04 [3549]P24(f329(f329(f243(a874),x35491),f329(f329(f80(a874),x35491),x35492)))
% 187.18/188.04 [3551]E(f329(f329(f115(f881(x35511,a869)),f252(f881(x35511,a869))),x35512),f252(f881(x35511,a869)))
% 187.18/188.04 [3552]E(f329(f329(f22(f881(x35521,a869)),f193(f881(x35521,a869))),x35522),f193(f881(x35521,a869)))
% 187.18/188.04 [3553]E(f329(f329(f106(f881(x35531,a869)),f193(f881(x35531,a869))),x35532),f193(f881(x35531,a869)))
% 187.18/188.04 [3558]E(f329(f329(f264(a1,a1),x35581),f329(f79(a1),x35582)),f329(a51,f329(f329(f264(a1,a1),x35581),x35582)))
% 187.18/188.04 [3559]E(f329(f299(a1,f329(f329(f80(a1),x35591),f78(a1))),x35592),f303(a1,x35591,x35592))
% 187.18/188.04 [3570]E(f329(f329(f81(a874),x35701),f329(f329(f39(a874),x35702),x35701)),f329(f329(f22(a874),x35702),f45(a874,x35702,x35701)))
% 187.18/188.04 [3571]E(f329(f329(f81(a1),x35711),f329(f329(f39(a1),x35712),x35711)),f329(f329(f22(a1),x35712),f45(a1,x35712,x35711)))
% 187.18/188.04 [3575]E(f329(f171(a1),f178(f329(f329(f80(a1),x35751),f78(a1)),x35752)),f302(a1,x35751,x35752))
% 187.18/188.04 [3579]P24(f329(f329(f243(f881(x35791,a869)),x35792),x35792))
% 187.18/188.04 [3582]E(f329(f329(f115(f881(x35821,a869)),x35822),f329(f79(f881(x35821,a869)),x35822)),f252(f881(x35821,a869)))
% 187.18/188.04 [3583]E(f329(f329(f106(f881(x35831,a869)),x35832),f329(f79(f881(x35831,a869)),x35832)),f193(f881(x35831,a869)))
% 187.18/188.04 [3591]E(f329(f329(f22(a874),f329(f329(f22(a874),x35911),f78(a874))),x35912),f329(f329(f22(a874),x35911),f329(a117,x35912)))
% 187.18/188.04 [3596]E(f329(f329(f22(f881(x35961,a869)),f252(f881(x35961,a869))),x35962),f329(f79(f881(x35961,a869)),x35962))
% 187.18/188.04 [3597]E(f329(f329(f22(a1),f329(f108(a1),x35971)),f329(f108(a1),x35972)),f329(f108(a1),f329(f329(f80(a1),x35971),f329(f79(a1),x35972))))
% 187.18/188.04 [3609]E(f329(f171(a874),f137(a874,f329(f299(a874,x36091),f329(a117,x36092)))),f300(a874,x36091,x36092))
% 187.18/188.04 [3617]P24(f329(f329(f329(f329(a201,a24),x36171),x36172),x36171))
% 187.18/188.04 [3623]E(f329(f194(f875(f875(x36231))),f54(x36231,x36232)),f329(f329(f254(a874),f329(a117,f329(a117,f2(a874)))),f329(f194(f875(x36231)),x36232)))
% 187.18/188.04 [3643]E(f329(f329(f188(f880(x36431,x36431),a869),f2(a874)),x36432),f305(x36431,f193(f881(f880(x36431,x36431),a869))))
% 187.18/188.04 [3647]P24(f329(f135(a874),f137(a874,f329(f299(a874,x36471),x36472))))
% 187.18/188.04 [3664]E(f329(f308(a1,a874,a109),f300(a1,f329(f105(a1),x36641),f329(f105(a1),x36642))),f300(a874,x36641,x36642))
% 187.18/188.04 [3674]E(f190(a874,f2(a874),f5(a874),f329(f329(f22(a874),x36741),x36742)),f329(f329(f22(a874),x36741),f329(a117,x36742)))
% 187.18/188.04 [3675]E(f329(a109,f329(f329(f22(a1),x36751),f329(f329(f80(a1),x36752),f78(a1)))),f329(f38(a1),f303(a1,x36752,x36751)))
% 187.18/188.04 [3711]E(f329(f329(f152(a874,a874),a117),f137(a874,f329(f299(a874,x37111),x37112))),f137(a874,f329(f299(a874,f329(a117,x37111)),f329(a117,x37112))))
% 187.18/188.04 [3718]E(f329(f171(a1),f178(f329(f329(f80(a1),x37181),f78(a1)),f329(f329(f22(a1),x37182),f78(a1)))),f303(a1,x37181,x37182))
% 187.18/188.04 [3729]P24(f329(f329(f243(f881(x37291,a869)),f193(f881(x37291,a869))),x37292))
% 187.18/188.04 [3734]E(f85(x37341,f329(f329(f7(x37341,x37341,a869),a326),x37342)),x37342)
% 187.18/188.04 [3735]E(f90(x37351,f329(f329(f7(x37351,x37351,a869),a326),x37352)),x37352)
% 187.18/188.04 [3739]E(f329(f171(a874),f137(a874,f329(f299(a874,f329(a117,x37391)),f329(a117,x37392)))),f302(a874,x37391,x37392))
% 187.18/188.04 [3764]E(f329(f329(f266(x37641,x37642),f252(f881(x37641,a869))),f329(f16(f881(x37642,a869),x37641),f252(f881(x37642,a869)))),f252(f881(f880(x37641,x37642),a869)))
% 187.18/188.04 [3799]E(f329(f249(x37991),f329(f329(f8(a869,a869,x37991),a324),x37992)),f329(f79(f881(x37991,a869)),f329(f249(x37991),x37992)))
% 187.18/188.04 [3802]E(f329(f249(x38021),f329(f329(f7(x38021,x38021,a869),a326),x38022)),f329(f329(f307(x38021),x38022),f193(f881(x38021,a869))))
% 187.18/188.04 [3809]E(f329(f329(f80(a1),f329(f329(f22(a1),x38091),x38092)),f329(f329(f22(a1),x38091),x38092)),f329(f329(f22(a1),f329(f329(f80(a1),x38091),x38091)),f329(f329(f80(a1),x38092),x38092)))
% 187.18/188.04 [3810]E(f329(f329(f80(a1),f329(f329(f80(a1),x38101),x38101)),f329(f329(f80(a1),x38102),x38102)),f329(f329(f80(a1),f329(f329(f80(a1),x38101),x38102)),f329(f329(f80(a1),x38101),x38102)))
% 187.18/188.04 [3826]P24(f329(f329(f243(a874),f329(f38(x38261),f329(f171(x38261),x38262))),f329(f194(f875(x38261)),x38262)))
% 187.18/188.04 [3827]P24(f329(f329(f243(a874),f329(f194(f875(x38271)),f150(x38271,x38272))),f329(f194(f875(x38271)),x38272)))
% 187.18/188.04 [3837]E(f329(f249(x38371),f329(f329(f7(x38371,f881(x38371,a869),a869),f331(x38371)),x38372)),x38372)
% 187.18/188.04 [3853]E(f329(f329(f174(x38531),f329(f329(f22(a874),f329(f194(f875(x38531)),x38532)),f78(a874))),x38532),f119(x38531,x38532))
% 187.18/188.04 [3876]E(f190(a874,f2(a874),f329(f329(f8(a874,a874,a874),a117),f329(f241(a874),x38761)),x38762),f329(f329(f241(a874),f329(a117,x38761)),x38762))
% 187.18/188.04 [3880]E(f40(f881(x38801,a869),f329(f308(f881(f880(x38801,x38801),a869),f881(x38801,a869),f282(x38801)),x38802)),f329(f282(x38801),f40(f881(f880(x38801,x38801),a869),x38802)))
% 187.18/188.04 [3881]E(f190(a874,f329(a117,x38811),f329(f329(f8(a874,a874,a874),a117),f329(f242(a874),x38811)),x38812),f329(f329(f242(a874),f329(a117,x38811)),x38812))
% 187.18/188.04 [3883]E(f329(f329(f264(a1,a1),f329(f329(f39(a1),f329(f75(a1),x38831)),f329(f75(a1),x38832))),f45(a1,f329(f75(a1),x38831),f329(f75(a1),x38832))),f53(x38831,x38832))
% 187.18/188.04 [3906]P24(f329(f329(f243(f881(f881(x39061,a869),a869)),x39062),f329(f306(x39061),f40(f881(x39061,a869),x39062))))
% 187.18/188.04 [3940]E(f329(f329(f42(x39401,f881(x39401,a869)),x39402),f329(f329(f7(x39401,f881(x39401,a869),f881(x39401,a869)),f307(x39401)),f193(f881(x39401,a869)))),x39402)
% 187.18/188.04 [3941]E(f329(f329(f286(x39411,x39411,x39411),f329(f284(x39411,x39411),x39412)),f305(x39411,f329(f284(x39411,x39411),x39412))),f329(f284(x39411,x39411),f329(f329(f286(x39411,x39411,x39411),x39412),f305(x39411,x39412))))
% 187.18/188.04 [4010]E(f329(f171(x40101),f329(f140(f875(x40101),f875(x40101),f126(x40101),f118(x40101)),x40102)),f329(f329(f42(f875(x40101),f881(x40101,a869)),f329(f171(f875(x40101)),x40102)),f171(x40101)))
% 187.18/188.04 [4042]E(f329(f329(f115(f881(f880(x40421,x40421),a869)),f305(x40421,f193(f881(f880(x40421,x40421),a869)))),f329(f329(f286(x40421,x40421,x40421),f305(x40421,x40422)),x40422)),f305(x40421,x40422))
% 187.18/188.04 [4076]E(f329(f329(f181(x40761,x40761),x40762),x40762),f329(f329(f152(x40761,f880(x40761,x40761)),f329(f329(f18(x40761,x40761,f880(x40761,x40761)),f264(x40761,x40761)),f5(x40761))),x40762))
% 187.18/188.04 [4192]E(f329(f140(a874,f875(x41921),f329(f7(f875(x41921),a874,a874),f329(f329(f8(a874,f881(a874,a874),f875(x41921)),f242(a874)),f194(f875(x41921)))),f2(a874)),f329(f167(f875(x41921)),x41922)),f329(f194(f875(f875(x41921))),f179(x41921,x41922)))
% 187.18/188.04 [4270]E(f329(f329(f285(f880(a874,f875(x42701)),f875(x42701)),f322(a874,f875(x42701),a248,f143(x42701,x42702))),f329(f329(f18(f875(x42701),f875(x42701),f880(a874,f875(x42701))),f329(f329(f8(a874,f881(f875(x42701),f880(a874,f875(x42701))),f875(x42701)),f264(a874,f875(x42701))),f194(f875(x42701)))),f5(f875(x42701)))),f144(x42701,x42702))
% 187.18/188.04 [4401]E(f329(f249(x44011),f329(f329(f8(f881(f881(x44011,a869),a869),a869,x44011),f88(f881(x44011,a869))),f329(f329(f8(f881(f881(x44011,a869),a869),f881(f881(x44011,a869),a869),x44011),f329(f18(f881(x44011,a869),a869,a869),f329(f329(f8(a869,f881(a869,a869),f881(x44011,a869)),a332),f329(f329(f7(f881(x44011,a869),f881(f881(x44011,a869),a869),a869),f331(f881(x44011,a869))),x44012)))),f331(x44011)))),f41(f881(x44011,a869),x44012))
% 187.18/188.04 [4543]~P24(f329(f329(f244(a1),f329(f105(a1),x45431)),f329(f79(a1),f329(f105(a1),x45432))))
% 187.18/188.04 [4559]~P24(f329(f329(f91(a1),f329(f329(f22(a1),f329(f329(f80(a1),x45591),x45591)),a102)),f329(f329(f80(a1),x45592),x45592)))
% 187.18/188.04 [3474]E(f329(f329(f22(a874),f329(f329(f80(a874),x34741),x34742)),x34742),x34741)
% 187.18/188.04 [3475]E(f329(f329(f22(a874),f329(f329(f80(a874),x34751),x34752)),x34751),x34752)
% 187.18/188.04 [3542]E(f329(f329(f80(a874),f329(f329(f22(a874),x35421),x35422)),x35422),f329(f329(f242(a874),x35421),x35422))
% 187.18/188.04 [3650]E(f329(f329(f81(a874),f329(f329(f39(a874),x36501),x36502)),x36502),f329(f329(f22(a874),x36501),f45(a874,x36501,x36502)))
% 187.18/188.04 [3679]E(f329(f171(a874),f137(a874,f329(f299(a874,f329(a117,x36791)),x36792))),f303(a874,x36791,x36792))
% 187.18/188.04 [3686]E(f329(f105(a1),f224(f329(a109,f329(f75(a1),x36861)),f329(a109,f329(f75(a1),x36862)))),f329(f329(a225,x36861),x36862))
% 187.18/188.04 [3688]E(f329(f329(f115(f881(x36881,a869)),f329(f79(f881(x36881,a869)),x36882)),x36882),f252(f881(x36881,a869)))
% 187.18/188.04 [3689]E(f329(f329(f106(f881(x36891,a869)),f329(f79(f881(x36891,a869)),x36892)),x36892),f193(f881(x36891,a869)))
% 187.18/188.04 [3707]P24(f329(f329(f243(a874),f329(f329(f22(a874),x37071),x37072)),x37071))
% 187.18/188.04 [3708]P24(f329(f329(f243(a874),f329(f329(f39(a874),x37081),x37082)),x37081))
% 187.18/188.04 [3731]P24(f329(f329(f244(a874),x37311),f329(a117,f329(f329(f80(a874),x37312),x37311))))
% 187.18/188.04 [3732]P24(f329(f329(f244(a874),x37321),f329(a117,f329(f329(f80(a874),x37321),x37322))))
% 187.18/188.04 [3750]E(f329(f329(f81(a874),f329(a109,f329(f75(a1),x37501))),f329(a109,f329(f75(a1),x37502))),f329(a109,f329(f75(a1),f329(f329(f81(a1),x37501),x37502))))
% 187.18/188.04 [3760]P24(f329(f329(f243(a1),f2(a1)),f329(f329(f254(a1),f329(f75(a1),x37601)),x37602)))
% 187.18/188.04 [3831]E(f329(f283(f875(x38311),f875(x38311),f156(x38311,x38312)),f329(f329(f307(f875(x38311)),f118(x38311)),f193(f881(f875(x38311),a869)))),f329(f329(f307(f875(x38311)),f118(x38311)),f193(f881(f875(x38311),a869))))
% 187.18/188.04 [3851]E(f329(f329(f115(f881(f880(x38511,x38511),a869)),f305(x38511,x38512)),f305(x38511,f193(f881(f880(x38511,x38511),a869)))),f305(x38511,x38512))
% 187.18/188.04 [3866]E(f329(f329(f39(a1),f329(f108(a1),f329(f329(f80(a1),x38661),x38661))),f329(f108(a1),f329(f329(f80(a1),x38662),x38662))),f329(f329(f39(a1),f329(f108(a1),x38661)),f329(f108(a1),x38662)))
% 187.18/188.04 [3930]E(f329(f329(f254(a1),x39301),f329(f108(a874),f329(f329(f80(a1),x39302),x39302))),f329(f329(f86(a1,a1),f329(f329(f254(a1),x39301),f329(f108(a874),x39302))),f329(f329(f18(a1,a1,a1),f81(a1)),f5(a1))))
% 187.18/188.04 [3936]E(f329(f249(f881(x39361,a869)),f329(f329(f7(f881(x39361,a869),f881(x39361,a869),a869),f243(f881(x39361,a869))),x39362)),f329(f306(x39361),x39362))
% 187.18/188.04 [3951]E(f329(f329(f152(a1,a874),a109),f329(f329(f126(a1),f329(f329(f152(a874,a1),f105(a1)),x39511)),f329(f329(f152(a874,a1),f105(a1)),x39512))),f329(f329(f126(a874),x39511),x39512))
% 187.18/188.04 [3986]E(f329(f308(a1,a1,f329(f329(f7(a1,a1,a1),f80(a1)),x39861)),f329(f299(a1,f2(a1)),f329(f329(f22(a1),x39862),x39861))),f329(f299(a1,x39861),x39862))
% 187.18/188.04 [3988]P46(x39881,f329(f329(f22(f881(f880(x39881,x39881),a869)),x39882),f305(x39881,f193(f881(f880(x39881,x39881),a869)))))
% 187.18/188.04 [4008]E(f329(f194(f875(x40081)),f329(f140(f875(x40081),f875(x40081),f126(x40081),f118(x40081)),x40082)),f329(f164(a874),f329(f329(f152(f875(x40081),a874),f194(f875(x40081))),x40082)))
% 187.18/188.04 [4013]P44(x40131,f252(f881(x40131,a869)),f329(f329(f115(f881(f880(x40131,x40131),a869)),x40132),f305(x40131,f193(f881(f880(x40131,x40131),a869)))))
% 187.18/188.04 [4056]E(f190(a874,f2(a874),f329(f329(f8(a874,a874,a874),a117),f329(f329(f7(a874,a874,a874),f241(a874)),x40561)),x40562),f329(f329(f241(a874),x40562),f329(a117,x40561)))
% 187.18/188.04 [4059]E(f190(a874,f329(a117,x40591),f329(f329(f8(a874,a874,a874),a117),f329(f329(f7(a874,a874,a874),f242(a874)),x40591)),x40592),f329(f329(f242(a874),x40592),f329(a117,x40591)))
% 187.18/188.04 [4062]E(f329(f308(x40621,f875(x40621),f329(f329(f7(x40621,f875(x40621),f875(x40621)),f149(x40621)),f118(x40621))),x40622),f173(x40621,x40622,f329(f329(f307(f875(x40621)),f118(x40621)),f193(f881(f875(x40621),a869)))))
% 187.18/188.04 [4063]E(f329(f329(f115(f881(f880(x40631,x40631),a869)),f329(f329(f286(x40631,x40631,x40631),x40632),f305(x40631,x40632))),f305(x40631,f193(f881(f880(x40631,x40631),a869)))),f305(x40631,x40632))
% 187.18/188.04 [4071]P24(f329(f329(f243(f881(f880(x40711,x40711),a869)),f261(x40711,x40712)),f329(f329(f266(x40711,x40711),x40712),f329(f16(f881(x40711,a869),x40711),x40712))))
% 187.18/188.04 [4074]E(f329(f308(a1,a874,a109),f329(f329(f115(f881(a1,a869)),f329(f308(a874,a1,f105(a1)),x40741)),f329(f308(a874,a1,f105(a1)),x40742))),f329(f329(f115(f881(a874,a869)),x40741),x40742))
% 187.18/188.04 [4075]E(f329(f308(a1,a874,a109),f329(f329(f106(f881(a1,a869)),f329(f308(a874,a1,f105(a1)),x40751)),f329(f308(a874,a1,f105(a1)),x40752))),f329(f329(f106(f881(a874,a869)),x40751),x40752))
% 187.18/188.04 [4079]E(f329(f249(x40791),f329(f329(f8(a869,a869,x40791),a324),f329(f329(f7(x40791,f881(x40791,a869),a869),f331(x40791)),x40792))),f329(f79(f881(x40791,a869)),x40792))
% 187.18/188.04 [4106]E(f329(f140(f875(x41061),f875(x41061),f126(x41061),f118(x41061)),f329(f329(f152(f875(x41061),f875(x41061)),f167(x41061)),f329(f167(f875(x41061)),x41062))),f329(f167(x41061),f329(f140(f875(x41061),f875(x41061),f126(x41061),f118(x41061)),x41062)))
% 187.18/188.04 [4135]E(f329(f329(f42(a874,f881(f880(x41351,x41351),a869)),f252(f881(a874,a869))),f329(f329(f7(a874,f881(f880(x41351,x41351),a869),f881(f880(x41351,x41351),a869)),f188(f880(x41351,x41351),a869)),x41352)),f305(x41351,x41352))
% 187.18/188.04 [4155]E(f85(x41551,f329(f329(f8(f881(x41551,a869),a869,x41551),f329(a326,x41552)),f329(f329(f7(x41551,f881(x41551,a869),f881(x41551,a869)),f307(x41551)),f193(f881(x41551,a869))))),f310(x41551,x41552))
% 187.18/188.04 [4163]E(f329(f194(f875(x41631)),f150(x41631,f329(f140(f875(x41631),f875(x41631),f126(x41631),f118(x41631)),x41632))),f329(f38(x41631),f329(f329(f42(f875(x41631),f881(x41631,a869)),f329(f171(f875(x41631)),x41632)),f171(x41631))))
% 187.18/188.04 [4179]E(f329(f329(f115(f881(f880(x41791,x41791),a869)),x41792),f329(f329(f286(x41791,x41791,x41791),f329(f329(f286(x41791,x41791,x41791),x41792),f305(x41791,x41792))),x41792)),f329(f329(f286(x41791,x41791,x41791),x41792),f305(x41791,x41792)))
% 187.18/188.04 [4202]P24(f329(f329(f243(f881(f880(x42021,x42021),a869)),f329(f329(f286(x42021,x42021,x42021),x42022),f305(x42021,x42022))),f329(f329(f266(x42021,x42021),f329(f282(x42021),x42022)),f329(f16(f881(x42021,a869),x42021),f329(f282(x42021),x42022)))))
% 187.18/188.04 [4245]E(f329(f249(f875(x42451)),f329(f329(f7(f875(x42451),f881(x42451,a869),a869),f329(f329(f8(f881(x42451,a869),f881(f881(x42451,a869),a869),f875(x42451)),f243(f881(x42451,a869))),f171(x42451))),x42452)),f159(x42451,x42452))
% 187.18/188.04 [4257]E(f329(f154(f875(x42571),x42571,f118(x42571),f329(f329(f8(f875(x42571),f881(f875(x42571),f875(x42571)),x42571),f329(f7(f875(x42571),f875(x42571),f875(x42571)),f126(x42571))),f329(f329(f7(x42571,f875(x42571),f875(x42571)),f149(x42571)),f118(x42571)))),x42572),f329(f166(x42571),x42572))
% 187.18/188.04 [4299]P21(f881(x42991,x42992),f881(f880(x42991,x42992),a869),f329(f329(f8(f881(f880(x42991,x42992),a869),f881(f880(x42991,x42992),a869),f881(x42991,x42992)),f249(f880(x42991,x42992))),f329(f329(f8(f881(x42991,f881(x42992,a869)),f881(f880(x42991,x42992),a869),f881(x42991,x42992)),f268(x42991,x42992,a869)),f329(f8(x42992,f881(x42992,a869),x42991),f329(f7(x42992,x42992,a869),a326)))),f252(f881(f881(x42991,x42992),a869)))
% 187.18/188.04 [4304]E(f45(a1,f329(f108(a1),f329(f329(f80(a1),x43041),x43041)),f329(f108(a1),f329(f329(f80(a1),x43042),x43042))),f329(f329(f81(a1),f329(f108(a1),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))),f45(a1,f329(f108(a1),x43041),f329(f108(a1),x43042))))
% 187.18/188.04 [4348]E(f329(f329(f42(x43481,f881(f880(x43481,x43481),a869)),x43482),f329(f329(f7(x43481,f881(f880(x43481,x43481),a869),f881(f880(x43481,x43481),a869)),f329(f329(f8(f880(x43481,x43481),f881(f881(f880(x43481,x43481),a869),f881(f880(x43481,x43481),a869)),x43481),f307(f880(x43481,x43481))),f329(f329(f18(x43481,x43481,f880(x43481,x43481)),f264(x43481,x43481)),f5(x43481)))),f193(f881(f880(x43481,x43481),a869)))),f261(x43481,x43482))
% 187.18/188.04 [4356]E(f211(x43561,f329(f329(f264(a1,a1),f329(f79(a1),f329(f329(f73(f880(a1,a1),a1,x43561,f263(a1,a1)),f220(x43561)),x43562))),f329(f329(f73(f880(a1,a1),a1,x43561,f267(a1,a1)),f220(x43561)),x43562))),f228(x43561,x43562))
% 187.18/188.04 [4437]E(f329(f249(f881(x44371,a869)),f329(f329(f8(f881(f881(x44371,a869),a869),a869,f881(x44371,a869)),f87(f881(x44371,a869))),f329(f329(f7(f881(x44371,a869),f881(f881(x44371,a869),a869),f881(f881(x44371,a869),a869)),f329(f329(f8(f881(f881(x44371,a869),f881(a869,a869)),f881(f881(f881(x44371,a869),a869),f881(f881(x44371,a869),a869)),f881(x44371,a869)),f18(f881(x44371,a869),a869,a869)),f329(f329(f8(f881(f881(x44371,a869),a869),f881(f881(x44371,a869),f881(a869,a869)),f881(x44371,a869)),f329(f8(a869,f881(a869,a869),f881(x44371,a869)),a327)),f329(f329(f7(f881(x44371,a869),f881(f881(x44371,a869),f881(x44371,a869)),f881(f881(x44371,a869),a869)),f329(f329(f8(f881(f881(x44371,a869),a869),f881(f881(f881(x44371,a869),f881(x44371,a869)),f881(f881(x44371,a869),a869)),f881(x44371,a869)),f8(f881(x44371,a869),a869,f881(x44371,a869))),a326)),f79(f881(x44371,a869)))))),f329(f329(f8(f881(f881(x44371,a869),a869),a869,f881(x44371,a869)),f329(f331(f881(x44371,a869)),x44372)),f306(x44371))))),f329(f306(x44371),f329(f79(f881(x44371,a869)),x44372)))
% 187.18/188.04 [4540]~E(f329(f329(f80(a1),x45401),x45401),f329(f329(f22(a1),f329(f329(f80(a1),x45402),x45402)),a102))
% 187.18/188.04 [4546]~P24(f329(f329(f244(a874),f329(f329(f80(a874),x45461),x45462)),x45462))
% 187.18/188.04 [4547]~P24(f329(f329(f244(a874),f329(f329(f80(a874),x45471),x45472)),x45471))
% 187.18/188.04 [3765]E(f329(f329(f22(a874),x37651),f329(f329(f81(a874),f329(f329(f39(a874),x37651),x37652)),x37652)),f45(a874,x37651,x37652))
% 187.18/188.04 [3766]E(f329(f329(f22(a1),x37661),f329(f329(f81(a1),f329(f329(f39(a1),x37661),x37662)),x37662)),f45(a1,x37661,x37662))
% 187.18/188.04 [3800]E(f329(f329(f152(a874,x38001),f329(f163(x38001),x38002)),f137(a874,f329(f299(a874,f2(a874)),f329(f194(f875(x38001)),x38002)))),x38002)
% 187.18/188.04 [3862]E(f329(f283(x38621,x38621,f305(x38621,f193(f881(f880(x38621,x38621),a869)))),x38622),x38622)
% 187.18/188.04 [3991]E(f305(x39911,f329(f329(f115(f881(f880(x39911,x39911),a869)),x39912),f305(x39911,f193(f881(f880(x39911,x39911),a869))))),f305(x39911,x39912))
% 187.18/188.04 [3992]E(f305(x39921,f329(f329(f22(f881(f880(x39921,x39921),a869)),x39922),f305(x39921,f193(f881(f880(x39921,x39921),a869))))),f305(x39921,x39922))
% 187.18/188.04 [4045]E(f329(f329(f22(a1),f329(f329(f22(a1),f329(f329(f80(a1),x40451),x40451)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),x40452),x40452)),a102)),f329(f329(f80(a1),f329(f329(f22(a1),x40451),x40452)),f329(f329(f22(a1),x40451),x40452)))
% 187.18/188.04 [4084]E(f329(f329(f22(a1),f329(f329(f80(a1),f329(f329(f80(a1),x40841),x40842)),f329(f329(f80(a1),x40841),x40842))),a102),f329(f329(f80(a1),f329(f329(f80(a1),x40841),x40841)),f329(f329(f22(a1),f329(f329(f80(a1),x40842),x40842)),a102)))
% 187.18/188.04 [4110]E(f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),x41101),x41101)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),x41102),x41102)),a102)),f329(f329(f80(a1),f329(f329(f80(a1),x41101),f329(f329(f22(a1),x41102),a102))),f329(f329(f80(a1),x41101),f329(f329(f22(a1),x41102),a102))))
% 187.18/188.04 [4120]E(f329(f329(f22(a1),f329(f329(f80(a1),f329(f329(f22(a1),x41201),x41202)),f329(f329(f22(a1),x41201),x41202))),a102),f329(f329(f22(a1),f329(f329(f22(a1),f329(f329(f80(a1),x41201),x41201)),a102)),f329(f329(f80(a1),x41202),x41202)))
% 187.18/188.04 [4121]E(f329(f329(f22(a1),f329(f329(f80(a1),f329(f329(f80(a1),x41211),x41212)),f329(f329(f80(a1),x41211),x41212))),a102),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),x41211),x41211)),a102)),f329(f329(f80(a1),x41212),x41212)))
% 187.18/188.04 [4176]E(f329(f105(a1),f329(f329(f39(a874),f329(f329(f81(a874),f329(a109,f329(f75(a1),x41761))),f329(a109,f329(f75(a1),x41762)))),f224(f329(a109,f329(f75(a1),x41761)),f329(a109,f329(f75(a1),x41762))))),f226(x41761,x41762))
% 187.18/188.04 [4222]E(f329(f329(f270(f880(a104,a104),a104,f880(a104,a104),f880(x42221,f880(a104,a104))),f274(f329(a3,f329(f194(f875(x42221)),x42222)))),f329(f329(f8(x42221,f881(f880(a104,a104),f880(x42221,f880(a104,a104))),a104),f264(x42221,f880(a104,a104))),f329(f329(f8(a874,x42221,a104),f329(f163(x42221),x42222)),a19))),f280(x42221,x42222))
% 187.18/188.04 [4305]E(f329(f140(a874,f875(x43051),f329(f7(f875(x43051),a874,a874),f329(f329(f8(a874,f881(a874,a874),f875(x43051)),f242(a874)),f194(f875(x43051)))),f2(a874)),f329(f167(f875(x43051)),f179(x43051,x43052))),f329(f194(f875(f875(x43051))),f329(f134(f875(x43051),f329(f329(f8(a869,a869,f875(x43051)),a324),f329(f329(f7(f875(x43051),f875(x43051),a869),a326),f118(x43051)))),x43052)))
% 187.18/188.04 [4311]E(f329(f329(f42(a874,f881(x43111,a869)),f252(f881(a874,a869))),f329(f329(f7(a874,f881(a874,f881(x43111,a869)),f881(x43111,a869)),f329(f329(f8(f881(a874,a869),f881(f881(a874,f881(x43111,a869)),f881(x43111,a869)),a874),f42(a874,f881(x43111,a869))),f299(a874,f2(a874)))),x43112)),f329(f329(f42(a874,f881(x43111,a869)),f252(f881(a874,a869))),x43112))
% 187.18/188.04 [4332]P24(f329(f62(a874),f329(f249(a874),f329(f329(f18(a874,a869,a869),f329(f329(f8(a869,f881(a869,a869),a874),a327),x43321)),f329(f329(f7(a874,a874,a869),f244(a874)),x43322)))))
% 187.18/188.04 [4448]E(f329(f249(f880(f875(x44481),f875(x44481))),f329(f268(f875(x44481),f875(x44481),a869),f329(f329(f18(f875(x44481),f881(f875(x44481),a869),f881(f875(x44481),a869)),f329(f329(f8(f881(f875(x44481),f881(a869,a869)),f881(f881(f875(x44481),a869),f881(f875(x44481),a869)),f875(x44481)),f18(f875(x44481),a869,a869)),f329(f329(f8(f881(f875(x44481),a869),f881(f875(x44481),f881(a869,a869)),f875(x44481)),f329(f8(a869,f881(a869,a869),f875(x44481)),a328)),f329(f329(f7(f875(x44481),f881(f875(x44481),a874),f881(f875(x44481),a869)),f329(f329(f8(f881(a874,a869),f881(f881(f875(x44481),a874),f881(f875(x44481),a869)),f875(x44481)),f8(a874,a869,f875(x44481))),f329(f329(f8(a874,f881(a874,a869),f875(x44481)),f244(a874)),f194(f875(x44481))))),f194(f875(x44481)))))),f329(f329(f18(f875(x44481),f881(f875(x44481),a869),f881(f875(x44481),a869)),f329(f329(f8(f881(f875(x44481),f881(a869,a869)),f881(f881(f875(x44481),a869),f881(f875(x44481),a869)),f875(x44481)),f18(f875(x44481),a869,a869)),f329(f329(f8(f881(f875(x44481),a869),f881(f875(x44481),f881(a869,a869)),f875(x44481)),f329(f8(a869,f881(a869,a869),f875(x44481)),a327)),f329(f329(f7(f875(x44481),f881(f875(x44481),a874),f881(f875(x44481),a869)),f329(f329(f8(f881(a874,a869),f881(f881(f875(x44481),a874),f881(f875(x44481),a869)),f875(x44481)),f8(a874,a869,f875(x44481))),f329(f329(f8(a874,f881(a874,a869),f875(x44481)),a326),f194(f875(x44481))))),f194(f875(x44481)))))),f329(f329(f7(f875(x44481),f881(f880(f875(x44481),f875(x44481)),a869),f881(f875(x44481),a869)),f329(f329(f8(f881(f875(x44481),f881(f881(f880(f875(x44481),f875(x44481)),a869),a869)),f881(f881(f880(f875(x44481),f875(x44481)),a869),f881(f875(x44481),a869)),f875(x44481)),f7(f875(x44481),f881(f880(f875(x44481),f875(x44481)),a869),a869)),f329(f329(f8(f881(f875(x44481),f880(f875(x44481),f875(x44481))),f881(f875(x44481),f881(f881(f880(f875(x44481),f875(x44481)),a869),a869)),f875(x44481)),f329(f8(f880(f875(x44481),f875(x44481)),f881(f881(f880(f875(x44481),f875(x44481)),a869),a869),f875(x44481)),f331(f880(f875(x44481),f875(x44481))))),f264(f875(x44481),f875(x44481))))),f143(x44481,x44482)))))),f144(x44481,x44482))
% 187.18/188.04 [4552]~P24(f329(f329(f91(a1),f329(f329(f80(a1),x45521),x45521)),f329(f329(f22(a1),f329(f329(f80(a1),x45522),x45522)),a102)))
% 187.18/188.04 [4113]E(f329(f329(f80(a1),f329(f329(f80(a1),f329(f329(f81(a1),x41131),x41132)),f329(f329(f81(a1),x41131),x41132))),x41132),f329(f329(f81(a1),f329(f329(f22(a1),f329(f329(f80(a1),x41131),x41131)),a102)),x41132))
% 187.18/188.04 [4220]E(f329(a109,f329(a89,f329(f283(f880(a874,a874),f880(a874,a874),a113),f329(f329(f307(f880(a874,a874)),f329(f329(f264(a874,a874),x42201),x42202)),f193(f881(f880(a874,a874),a869)))))),f329(f329(f22(a874),x42201),x42202))
% 187.18/188.04 [4225]E(f329(f329(f286(x42251,x42251,x42251),f329(f329(f115(f881(f880(x42251,x42251),a869)),x42252),f305(x42251,f193(f881(f880(x42251,x42251),a869))))),f305(x42251,f329(f329(f115(f881(f880(x42251,x42251),a869)),x42252),f305(x42251,f193(f881(f880(x42251,x42251),a869)))))),f305(x42251,x42252))
% 187.18/188.04 [4263]E(f275(x42631,f329(f134(f880(a104,x42631),f329(f268(a104,x42631,a869),f329(f329(f8(a869,f881(x42631,a869),a104),f16(a869,x42631)),f329(f244(a104),f2(a104))))),x42632)),f275(x42631,x42632))
% 187.18/188.04 [4264]E(f273(x42641,f329(f134(f880(a104,x42641),f329(f268(a104,x42641,a869),f329(f329(f8(a869,f881(x42641,a869),a104),f16(a869,x42641)),f329(f244(a104),f2(a104))))),x42642)),f273(x42641,x42642))
% 187.18/188.04 [4266]E(f329(f79(a1),f329(a89,f329(f283(f880(a874,a874),f880(a874,a874),a113),f329(f329(f307(f880(a874,a874)),f329(f329(f264(a874,a874),x42661),x42662)),f193(f881(f880(a874,a874),a869)))))),f329(a89,f329(f283(f880(a874,a874),f880(a874,a874),a113),f329(f329(f307(f880(a874,a874)),f329(f329(f264(a874,a874),x42662),x42661)),f193(f881(f880(a874,a874),a869))))))
% 187.18/188.04 [4324]E(f329(f329(f285(f875(a874),x43241),f143(a874,a248)),f329(f329(f7(x43241,f875(f881(x43241,a874)),f875(a874)),f329(f329(f8(f881(f881(x43241,a874),a874),f881(f875(f881(x43241,a874)),f875(a874)),x43241),f152(f881(x43241,a874),a874)),f329(f7(f881(x43241,a874),x43241,a874),f5(f881(x43241,a874))))),x43242)),f151(x43241,x43242))
% 187.18/188.04 [4345]E(f329(f329(f86(a1,a874),f329(f108(a1),f329(f329(f80(a1),x43451),a102))),f329(f329(f18(a1,a874,a874),f329(f329(f7(a1,a874,f881(a874,a874)),f329(f329(f8(a869,f881(a874,f881(a874,a874)),a1),f101(a874)),a198)),f2(a874))),f329(f329(f8(a874,a874,a1),a117),f329(f329(f8(a874,a874,a1),f329(f241(a874),x43452)),a109)))),f329(f329(f241(a874),f329(a117,x43452)),f329(f108(a874),x43451)))
% 187.18/188.04 [4346]E(f329(f329(f86(a1,a874),f329(f108(a1),f329(f329(f80(a1),x43461),a102))),f329(f329(f18(a1,a874,a874),f329(f329(f7(a1,a874,f881(a874,a874)),f329(f329(f8(a869,f881(a874,f881(a874,a874)),a1),f101(a874)),a198)),f329(a117,x43462))),f329(f329(f8(a874,a874,a1),a117),f329(f329(f8(a874,a874,a1),f329(f242(a874),x43462)),a109)))),f329(f329(f242(a874),f329(a117,x43462)),f329(f108(a874),x43461)))
% 187.18/188.04 [4366]E(f329(f140(f875(x43661),f875(x43661),f126(x43661),f118(x43661)),f329(f329(f152(f875(x43661),f875(x43661)),f154(f875(x43661),x43661,f118(x43661),f329(f329(f8(f875(x43661),f881(f875(x43661),f875(x43661)),x43661),f16(f875(x43661),f875(x43661))),f329(f329(f7(x43661,f875(x43661),f875(x43661)),f149(x43661)),f118(x43661))))),x43662)),f329(f329(f152(f875(x43661),x43661),f139(x43661)),f329(f134(f875(x43661),f329(f329(f8(a869,a869,f875(x43661)),a324),f329(f329(f7(f875(x43661),f875(x43661),a869),a326),f118(x43661)))),x43662)))
% 187.18/188.04 [4429]E(f329(f268(a1,a1,a869),f329(f329(f7(a1,f881(a1,a869),f881(a1,a869)),f329(f329(f8(f881(a1,f881(a869,a869)),f881(f881(a1,a869),f881(a1,a869)),a1),f18(a1,a869,a869)),f329(f329(f8(f881(a1,a869),f881(a1,f881(a869,a869)),a1),f329(f8(a869,f881(a869,a869),a1),a327)),f329(f329(f8(f881(a1,a1),f881(a1,a869),a1),f329(f8(a1,a869,a1),f329(a326,x44291))),f329(f329(f8(a1,f881(a1,a1),a1),f80(a1)),f329(f81(a1),x44292)))))),f329(f329(f18(a1,a869,a869),f329(f329(f8(a869,f881(a869,a869),a1),a327),f329(f329(f8(a869,a869,a1),f329(a332,f329(f329(f244(a1),f2(a1)),x44292))),f329(f329(f18(a1,a869,a869),f329(f329(f8(a869,f881(a869,a869),a1),a327),f329(f243(a1),f2(a1)))),f329(f329(f7(a1,a1,a869),f244(a1)),x44292))))),f329(f329(f8(a869,a869,a1),f329(a332,f329(a324,f329(f329(f244(a1),f2(a1)),x44292)))),f329(f329(f18(a1,a869,a869),f329(f329(f8(a869,f881(a869,a869),a1),a327),f329(f244(a1),x44292))),f329(f329(f7(a1,a1,a869),f243(a1)),f2(a1))))))),f49(x44291,x44292))
% 187.18/188.04 [4431]E(f329(f249(x44311),f329(f329(f8(f881(a874,a869),a869,x44311),f87(a874)),f329(f329(f7(x44311,f881(a874,a869),f881(a874,a869)),f329(f329(f8(f881(a874,f881(a869,a869)),f881(f881(a874,a869),f881(a874,a869)),x44311),f18(a874,a869,a869)),f329(f329(f8(f881(a874,a869),f881(a874,f881(a869,a869)),x44311),f329(f8(a869,f881(a869,a869),a874),a327)),f329(f329(f7(x44311,f881(a874,x44311),f881(a874,a869)),f329(f329(f8(f881(x44311,a869),f881(f881(a874,x44311),f881(a874,a869)),x44311),f8(x44311,a869,a874)),a326)),f329(f163(x44311),x44312))))),f329(f329(f7(a874,a874,a869),f244(a874)),f329(f194(f875(x44311)),x44312))))),f329(f171(x44311),x44312))
% 187.18/188.04 [4235]E(f329(f329(f22(a1),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),x42351),a102)),x42352)),f329(f329(f22(a1),f329(f329(f80(a1),x42351),a102)),x42352))),a102),f329(f329(f22(a1),f329(f329(f80(a1),x42351),x42351)),f329(f329(f22(a1),f329(f329(f80(a1),x42352),x42352)),a102)))
% 187.18/188.04 [4361]E(f329(f140(f875(f875(x43611)),f875(f875(x43611)),f126(f875(x43611)),f118(f875(x43611))),f329(f329(f152(f875(x43611),f875(f875(x43611))),f154(f875(f875(x43611)),x43611,f118(f875(x43611)),f329(f16(f881(f875(x43611),f875(f875(x43611))),x43611),f329(f329(f7(f875(x43611),f875(f875(x43611)),f875(f875(x43611))),f149(f875(x43611))),f118(f875(x43611)))))),x43612)),f329(f329(f152(f875(x43611),f875(x43611)),f170(x43611)),f329(f134(f875(x43611),f329(f329(f8(a869,a869,f875(x43611)),a324),f329(f329(f7(f875(x43611),f875(x43611),a869),a326),f118(x43611)))),x43612)))
% 187.18/188.04 [4372]E(f329(f329(f86(a1,a874),f329(f108(a1),f329(f329(f80(a1),x43721),a102))),f329(f329(f18(a1,a874,a874),f329(f329(f7(a1,a874,f881(a874,a874)),f329(f329(f8(a869,f881(a874,f881(a874,a874)),a1),f101(a874)),a198)),f2(a874))),f329(f329(f8(a874,a874,a1),a117),f329(f329(f7(a1,a874,a874),f329(f329(f8(a874,f881(a874,a874),a1),f241(a874)),a109)),x43722)))),f329(f329(f241(a874),f329(f108(a874),x43721)),f329(a117,x43722)))
% 187.18/188.04 [4373]E(f329(f329(f86(a1,a874),f329(f108(a1),f329(f329(f80(a1),x43731),a102))),f329(f329(f18(a1,a874,a874),f329(f329(f7(a1,a874,f881(a874,a874)),f329(f329(f8(a869,f881(a874,f881(a874,a874)),a1),f101(a874)),a198)),f329(a117,x43732))),f329(f329(f8(a874,a874,a1),a117),f329(f329(f7(a1,a874,a874),f329(f329(f8(a874,f881(a874,a874),a1),f242(a874)),a109)),x43732)))),f329(f329(f242(a874),f329(f108(a874),x43731)),f329(a117,x43732)))
% 187.18/188.04 [4360]E(f329(f268(x43601,x43601,a869),f329(f329(f18(x43601,a869,f881(x43601,a869)),f329(f329(f8(f881(x43601,f881(a869,a869)),f881(a869,f881(x43601,a869)),x43601),f7(x43601,a869,a869)),f329(f329(f8(f881(x43601,a869),f881(x43601,f881(a869,a869)),x43601),f329(f8(a869,f881(a869,a869),x43601),a327)),a326))),x43602)),f261(x43601,x43602))
% 187.18/188.04 [4407]E(f329(f329(f39(a874),x44071),f329(f329(f80(a874),f329(f108(a874),f329(f329(f22(a1),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102))),a102))),x44072)),f329(f329(f39(a874),x44071),f329(a117,f329(a117,f329(a117,x44072)))))
% 187.18/188.04 [4408]E(f45(a874,x44081,f329(f329(f80(a874),f329(f108(a874),f329(f329(f22(a1),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102))),a102))),x44082)),f45(a874,x44081,f329(a117,f329(a117,f329(a117,x44082)))))
% 187.18/188.04 [4409]E(f45(a874,f329(f329(f80(a874),f329(f108(a874),f329(f329(f22(a1),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102))),a102))),x44091),x44092),f45(a874,f329(a117,f329(a117,f329(a117,x44091))),x44092))
% 187.18/188.04 [4422]E(f125(f329(x44221,f329(f329(f81(a104),f329(f108(a104),f329(f329(f22(a1),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102))),a102))),x44222))),f329(f209(x44221),x44222))
% 187.18/188.04 [4423]E(f329(f329(f39(a874),f329(f329(f80(a874),f329(f108(a874),f329(f329(f22(a1),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102))),a102))),x44231)),x44232),f329(f329(f39(a874),f329(a117,f329(a117,f329(a117,x44231)))),x44232))
% 187.18/188.04 [4472]~E(f33(x44721,x44722),f329(a26,x44723))
% 187.18/188.04 [4473]~E(f32(x44731,x44732),f329(a26,x44733))
% 187.18/188.04 [4474]~E(f329(a26,x44741),f33(x44742,x44743))
% 187.18/188.04 [4475]~E(f329(a26,x44751),f32(x44752,x44753))
% 187.18/188.04 [4488]~E(f30(x44881,x44882,x44883),a24)
% 187.18/188.04 [4489]~E(f29(x44891,x44892,x44893),a24)
% 187.18/188.04 [3187]E(f329(f197(x31871,x31872),x31873),f123(x31871,x31872))
% 187.18/188.04 [3208]E(f329(f208(x32081,x32082),x32083),f329(f127(x32081),x32082))
% 187.18/188.04 [3288]E(f329(f329(f152(x32881,x32882),x32883),f118(x32881)),f118(x32882))
% 187.18/188.04 [3289]E(f329(f329(f207(x32891,x32892),x32893),f206(x32891)),f206(x32892))
% 187.18/188.04 [3330]E(f329(f189(x33301,x33302,x33303),f2(a874)),x33302)
% 187.18/188.04 [3332]E(f329(f329(f181(x33321,x33322),x33323),f118(x33322)),f118(f880(x33321,x33322)))
% 187.18/188.04 [3366]E(f85(x33661,f63(x33661,x33662,x33663)),f329(f64(x33661,x33662),x33663))
% 187.18/188.04 [3370]E(f253(x33701,x33702,f253(x33702,x33701,x33703)),x33703)
% 187.18/188.04 [3390]E(f329(f167(x33901),f169(x33901,x33902,x33903)),f169(x33901,x33902,x33903))
% 187.18/188.04 [3419]E(f138(x34191,x34192,f150(x34191,x34193)),f150(x34191,f138(x34191,x34192,x34193)))
% 187.18/188.04 [3438]E(f329(f263(f875(x34381),f875(x34381)),f165(x34381,x34382,x34383)),f329(f134(x34381,x34382),x34383))
% 187.18/188.04 [3484]E(f329(f329(f149(x34841),x34842),f169(x34841,x34843,x34842)),f169(x34841,f329(a117,x34843),x34842))
% 187.18/188.04 [3516]E(f190(x35161,x35162,x35163,f2(a874)),x35162)
% 187.18/188.04 [3517]E(f17(x35171,x35172,x35173,f2(a104)),x35172)
% 187.18/188.04 [3524]E(f161(x35241,x35242,x35243,f118(x35241)),f118(x35242))
% 187.18/188.04 [3525]E(f162(x35251,x35252,x35253,f118(x35251)),f118(x35252))
% 187.18/188.04 [3532]E(f329(f329(f163(x35321),f329(f329(f149(x35321),x35322),x35323)),f2(a874)),x35322)
% 187.18/188.04 [3560]E(f60(x35601,x35602,f118(x35601),x35603),f118(f880(x35601,x35602)))
% 187.18/188.04 [3581]P21(x35811,x35812,x35813,f193(f881(x35811,a869)))
% 187.18/188.04 [3740]E(f329(f73(x37401,x37402,x37401,x37403),f34(x37401)),x37403)
% 187.18/188.04 [3921]P24(f329(f329(f331(f880(x39211,x39211)),f329(f329(f264(x39211,x39211),x39212),x39212)),f305(x39211,x39213)))
% 187.18/188.04 [4553]~P24(f329(f329(f331(f880(f875(x45531),f875(x45531))),f329(f329(f264(f875(x45531),f875(x45531)),x45532),f118(x45531))),f143(x45531,x45533)))
% 187.18/188.04 [4554]~P24(f329(f329(f331(f880(f875(x45541),f875(x45541))),f329(f329(f264(f875(x45541),f875(x45541)),x45542),f118(x45541))),f145(x45541,x45543)))
% 187.18/188.04 [4555]~P24(f329(f329(f331(f880(f875(x45551),f875(x45551))),f329(f329(f264(f875(x45551),f875(x45551)),x45552),f118(x45551))),f155(x45551,x45553)))
% 187.18/188.04 [4556]~P24(f329(f329(f331(f880(f875(x45561),f875(x45561))),f329(f329(f264(f875(x45561),f875(x45561)),f118(x45561)),x45562)),f143(x45561,x45563)))
% 187.18/188.04 [4557]~P24(f329(f329(f331(f880(f875(x45571),f875(x45571))),f329(f329(f264(f875(x45571),f875(x45571)),f118(x45571)),x45572)),f155(x45571,x45573)))
% 187.18/188.04 [3261]E(f329(f329(f210(x32611),x32612),x32613),f211(x32611,f223(x32612,x32613)))
% 187.18/188.04 [3319]E(f329(f284(x33191,x33192),f329(f284(x33192,x33191),x33193)),x33193)
% 187.18/188.04 [3342]E(f329(f329(f181(x33421,x33422),f118(x33421)),x33423),f118(f880(x33421,x33422)))
% 187.18/188.04 [3345]E(f175(x33451,x33452,f329(f250(a874),x33453)),f329(f329(f174(x33451),x33453),x33452))
% 187.18/188.04 [3363]E(f150(x33631,f329(f134(x33631,x33632),x33633)),f329(f134(x33631,x33632),f150(x33631,x33633)))
% 187.18/188.04 [3364]E(f329(f260(x33641,x33642),f329(f284(x33642,x33641),x33643)),f329(f262(x33642,x33641),x33643))
% 187.18/188.04 [3365]E(f329(f262(x33651,x33652),f329(f284(x33652,x33651),x33653)),f329(f260(x33652,x33651),x33653))
% 187.18/188.04 [3382]E(f329(f134(x33821,x33822),f329(f167(x33821),x33823)),f329(f167(x33821),f329(f134(x33821,x33822),x33823)))
% 187.18/188.04 [3396]E(f329(f329(f136(x33961),x33962),f329(f170(x33961),x33963)),f329(f329(f136(x33961),f329(a117,x33962)),x33963))
% 187.18/188.04 [3414]E(f31(f29(x34141,x34142,x34143)),f329(f329(f80(a874),f31(x34143)),f329(a117,f2(a874))))
% 187.18/188.04 [3415]E(f329(f308(x34151,x34152,x34153),f193(f881(x34151,a869))),f193(f881(x34152,a869)))
% 187.18/188.04 [3416]E(f329(f283(x34161,x34162,x34163),f193(f881(x34161,a869))),f193(f881(x34162,a869)))
% 187.18/188.04 [3417]E(f329(f309(x34171,x34172,x34173),f193(f881(x34172,a869))),f193(f881(x34171,a869)))
% 187.18/188.04 [3418]E(f329(f309(x34181,x34182,x34183),f252(f881(x34182,a869))),f252(f881(x34181,a869)))
% 187.18/188.04 [3447]E(f329(f329(f307(x34471),x34472),f329(f171(x34471),x34473)),f329(f171(x34471),f138(x34471,x34472,x34473)))
% 187.18/188.04 [3459]E(f237(x34591,x34592,f329(f236(x34591),x34593)),f329(f329(f80(a874),f329(x34592,x34593)),f329(a117,f2(a874))))
% 187.18/188.04 [3536]E(f329(f194(a870),f29(x35361,x35362,x35363)),f329(f329(f80(a874),f329(f194(a870),x35363)),f329(a117,f2(a874))))
% 187.18/188.04 [3537]E(f329(f308(f880(x35371,x35372),x35372,f267(x35371,x35372)),x35373),f329(f260(x35371,x35372),x35373))
% 187.18/188.04 [3538]E(f329(f308(f880(x35381,x35382),x35381,f263(x35381,x35382)),x35383),f329(f262(x35381,x35382),x35383))
% 187.18/188.04 [3608]E(f329(f329(f264(x36081,x36082),f329(f263(x36081,x36082),x36083)),f329(f267(x36081,x36082),x36083)),x36083)
% 187.18/188.04 [3615]E(f329(f194(f876(x36151)),f128(x36151,x36152,x36153)),f329(f329(f80(a874),f329(f194(f876(x36151)),x36153)),f329(a117,f2(a874))))
% 187.18/188.04 [3618]E(f329(f329(f268(x36181,x36182,x36181),f16(x36181,x36182)),x36183),f329(f263(x36181,x36182),x36183))
% 187.18/188.04 [3638]E(f184(x36381,x36382,x36383,f329(f16(f878(x36382),x36381),f206(x36382))),x36383)
% 187.18/188.04 [3639]E(f184(x36391,x36392,f329(f16(f878(x36392),x36391),f206(x36392)),x36393),x36393)
% 187.18/188.04 [3695]E(f31(f30(x36951,x36952,x36953)),f329(f329(f80(a874),f329(f329(f80(a874),f31(x36952)),f31(x36953))),f329(a117,f2(a874))))
% 187.18/188.04 [3745]E(f329(f73(x37451,x37451,x37452,f34(x37451)),x37453),x37453)
% 187.18/188.04 [3854]E(f329(f194(a870),f30(x38541,x38542,x38543)),f329(f329(f80(a874),f329(f329(f80(a874),f329(f194(a870),x38542)),f329(f194(a870),x38543))),f329(a117,f2(a874))))
% 187.18/188.04 [3931]P24(f329(f329(f243(f881(x39311,a869)),f329(f171(x39311),f329(f134(x39311,x39312),x39313))),f329(f171(x39311),x39313)))
% 187.18/188.04 [3976]P24(f329(f329(f243(f881(x39761,a869)),f329(f171(x39761),f329(f329(f174(x39761),x39762),x39763))),f329(f171(x39761),x39763)))
% 187.18/188.04 [3977]P24(f329(f329(f243(f881(x39771,a869)),f329(f171(x39771),f329(f329(f136(x39771),x39772),x39773))),f329(f171(x39771),x39773)))
% 187.18/188.04 [3982]P24(f329(f329(f243(f881(x39821,a869)),f329(f171(x39821),f175(x39821,x39822,x39823))),f329(f171(x39821),x39822)))
% 187.18/188.04 [3983]P24(f329(f329(f243(f881(x39831,a869)),f329(f171(x39831),f168(x39831,x39832,x39833))),f329(f171(x39831),x39833)))
% 187.18/188.04 [4006]P21(f880(x40061,x40062),f880(x40062,x40061),f329(f268(x40061,x40062,f880(x40062,x40061)),f329(f7(x40062,x40061,f880(x40062,x40061)),f264(x40062,x40061))),x40063)
% 187.18/188.04 [4018]E(f329(f329(f329(f188(f875(x40181),f875(x40181)),f45(a874,x40182,f329(f194(f875(x40181)),x40183))),f166(x40181)),x40183),f329(f329(f329(f188(f875(x40181),f875(x40181)),x40182),f166(x40181)),x40183))
% 187.18/188.04 [4060]P24(f329(f329(f331(f880(f875(x40601),f875(x40601))),f329(f329(f264(f875(x40601),f875(x40601)),x40602),x40602)),f156(x40601,f305(x40601,x40603))))
% 187.18/188.04 [4205]E(f85(f880(x42051,x42052),f329(f329(f18(f880(x42051,x42052),x42052,a869),f329(f329(f8(x42051,f881(x42052,a869),f880(x42051,x42052)),x42053),f263(x42051,x42052))),f267(x42051,x42052))),f85(f880(x42051,x42052),f329(f268(x42051,x42052,a869),x42053)))
% 187.18/188.04 [4206]E(f90(f880(x42061,x42062),f329(f329(f18(f880(x42061,x42062),x42062,a869),f329(f329(f8(x42061,f881(x42062,a869),f880(x42061,x42062)),x42063),f263(x42061,x42062))),f267(x42061,x42062))),f90(f880(x42061,x42062),f329(f268(x42061,x42062,a869),x42063)))
% 187.18/188.04 [4242]E(f329(f329(f285(f880(a874,x42421),x42421),f322(a874,x42421,a248,x42422)),f329(f329(f18(x42421,x42421,f880(a874,x42421)),f329(f329(f8(a874,f881(x42421,f880(a874,x42421)),x42421),f264(a874,x42421)),x42423)),f5(x42421))),f323(x42421,x42423,x42422))
% 187.18/188.04 [4307]E(f329(f269(x43071,x43071,x43072,x43072,f5(x43071),f5(x43072)),x43073),x43073)
% 187.18/188.04 [4383]E(f329(f140(f875(f875(x43831)),f875(f875(x43831)),f126(f875(x43831)),f118(f875(x43831))),f329(f329(f152(f875(x43831),f875(f875(x43831))),f329(f329(f7(f875(x43831),f875(x43831),f875(f875(x43831))),f329(f329(f8(f881(x43831,f875(x43831)),f881(f875(x43831),f875(f875(x43831))),f875(x43831)),f152(x43831,f875(x43831))),f329(f7(x43831,f875(x43831),f875(x43831)),f149(x43831)))),x43832)),f55(x43831,x43833,x43832))),f55(x43831,f329(a117,x43833),x43832))
% 187.18/188.04 [4444]E(f329(f238(a874,f880(x44441,f876(x44441)),f2(a874),f329(f268(x44441,f876(x44441),a874),f329(f329(f7(x44441,a874,f881(f876(x44441),a874)),f329(f329(f8(f881(f876(x44441),f881(a874,a874)),f881(a874,f881(f876(x44441),a874)),x44441),f7(f876(x44441),a874,a874)),f329(f329(f8(f881(f876(x44441),a874),f881(f876(x44441),f881(a874,a874)),x44441),f329(f8(a874,f881(a874,a874),f876(x44441)),f80(a874))),f329(f329(f7(x44441,f881(f876(x44441),a874),f881(f876(x44441),a874)),f329(f329(f8(f881(a874,a874),f881(f881(f876(x44441),a874),f881(f876(x44441),a874)),x44441),f8(a874,a874,f876(x44441))),f329(f329(f8(a874,f881(a874,a874),x44441),f80(a874)),x44442))),f130(x44441,x44442))))),f78(a874)))),f329(f133(x44441),x44443)),f329(f130(x44441,x44442),x44443))
% 187.18/188.04 [4447]E(f329(f329(f86(a1,x44471),f226(f329(f329(f73(f880(a1,a1),a1,x44471,f267(a1,a1)),f220(x44471)),x44472),f329(f329(f73(f880(a1,a1),a1,x44471,f267(a1,a1)),f220(x44471)),x44473))),f329(f329(f18(a1,a1,x44471),f329(f329(f8(a1,f881(a1,x44471),a1),f210(x44471)),f329(f329(f18(a1,a1,a1),f329(f329(f8(a1,f881(a1,a1),a1),f80(a1)),f329(f329(f8(a1,a1,a1),f329(f81(a1),f329(f329(f73(f880(a1,a1),a1,x44471,f263(a1,a1)),f220(x44471)),x44472))),f329(f329(f7(a1,a1,a1),f39(a1)),f329(f329(f73(f880(a1,a1),a1,x44471,f267(a1,a1)),f220(x44471)),x44472))))),f329(f329(f8(a1,a1,a1),f329(f81(a1),f329(f329(f73(f880(a1,a1),a1,x44471,f263(a1,a1)),f220(x44471)),x44473))),f329(f329(f7(a1,a1,a1),f39(a1)),f329(f329(f73(f880(a1,a1),a1,x44471,f267(a1,a1)),f220(x44471)),x44473)))))),f5(a1))),f231(x44471,x44472,x44473))
% 187.18/188.04 [4484]~E(f329(f329(f149(x44841),x44842),x44843),x44843)
% 187.18/188.04 [4491]~E(f329(f329(f149(x44911),x44912),x44913),f118(x44911))
% 187.18/188.04 [4507]~E(f329(f329(f307(x45071),x45072),x45073),f193(f881(x45071,a869)))
% 187.18/188.04 [4530]~E(f329(f308(x45301,f881(x45301,a869),x45302),x45303),f329(f306(x45301),x45303))
% 187.18/188.04 [3324]E(f329(f329(f157(x33241,f118(x33241)),x33242),x33243),f118(x33241))
% 187.18/188.04 [3325]E(f329(f139(x33251),f329(f329(f149(x33251),x33252),x33253)),x33252)
% 187.18/188.04 [3326]E(f329(f170(x33261),f329(f329(f149(x33261),x33262),x33263)),x33263)
% 187.18/188.04 [3369]E(f329(f329(f136(x33691),f78(a874)),f329(f329(f149(x33691),x33692),x33693)),x33693)
% 187.18/188.04 [3403]E(f119(x34031,f329(f329(f136(x34031),x34032),x34033)),f329(f329(f136(x34031),x34032),f119(x34031,x34033)))
% 187.18/188.04 [3405]E(f329(f329(f157(x34051,x34052),x34053),f329(f329(f163(x34051),x34052),x34053)),x34052)
% 187.18/188.04 [3429]E(f329(f329(f307(x34291),x34292),f329(f329(f307(x34291),x34292),x34293)),f329(f329(f307(x34291),x34292),x34293))
% 187.18/188.04 [3440]E(f329(f329(f177(x34401,x34402),f118(f880(x34401,x34402))),x34403),f206(x34402))
% 187.18/188.04 [3443]E(f329(f329(f307(x34431),x34432),f329(f171(x34431),x34433)),f329(f171(x34431),f329(f329(f149(x34431),x34432),x34433)))
% 187.18/188.04 [3445]E(f329(f329(f136(x34451),x34452),f329(f170(x34451),x34453)),f329(f170(x34451),f329(f329(f136(x34451),x34452),x34453)))
% 187.18/188.04 [3456]E(f329(f329(f174(x34561),f78(a874)),f329(f329(f149(x34561),x34562),x34563)),f329(f329(f149(x34561),x34562),f118(x34561)))
% 187.18/188.04 [3501]E(f329(f64(x35011,x35012),f329(f329(f307(x35011),x35013),f193(f881(x35011,a869)))),x35013)
% 187.18/188.04 [3544]E(f329(f329(f80(a874),x35441),f329(f329(f80(a874),x35442),x35443)),f329(f329(f80(a874),x35442),f329(f329(f80(a874),x35441),x35443)))
% 187.18/188.04 [3545]E(f329(f329(f80(a1),x35451),f329(f329(f80(a1),x35452),x35453)),f329(f329(f80(a1),x35452),f329(f329(f80(a1),x35451),x35453)))
% 187.18/188.04 [3550]E(f329(f329(f266(x35501,x35502),f193(f881(x35501,a869))),x35503),f193(f881(f880(x35501,x35502),a869)))
% 187.18/188.04 [3573]E(f329(f329(f115(f881(x35731,a869)),x35732),x35733),f329(f329(f115(f881(x35731,a869)),x35733),x35732))
% 187.18/188.04 [3574]E(f329(f329(f106(f881(x35741,a869)),x35742),x35743),f329(f329(f106(f881(x35741,a869)),x35743),x35742))
% 187.18/188.04 [3576]E(f329(f329(f126(x35761),x35762),f329(f329(f149(x35761),x35763),f118(x35761))),f329(f166(x35761),f329(f329(f149(x35761),x35763),x35762)))
% 187.18/188.04 [3577]E(f329(f329(f126(x35771),f329(f167(x35771),x35772)),f329(f167(x35771),x35773)),f329(f167(x35771),f329(f329(f126(x35771),x35773),x35772)))
% 187.18/188.04 [3587]E(f329(f170(x35871),f329(f329(f174(x35871),f329(a117,x35872)),x35873)),f329(f329(f174(x35871),x35872),f329(f170(x35871),x35873)))
% 187.18/188.04 [3594]P24(f329(f329(f331(x35941),x35942),f329(f329(f307(x35941),x35942),x35943)))
% 187.18/188.04 [3598]E(f329(f329(f43(x35981,f881(x35982,a869)),f193(f881(x35981,a869))),x35983),f252(f881(x35982,a869)))
% 187.18/188.04 [3601]E(f329(f283(x36011,x36011,f261(x36011,x36012)),x36013),f329(f329(f106(f881(x36011,a869)),x36012),x36013))
% 187.18/188.04 [3614]E(f329(f194(f875(x36141)),f329(f329(f149(x36141),x36142),x36143)),f329(f329(f80(a874),f329(f194(f875(x36141)),x36143)),f329(a117,f2(a874))))
% 187.18/188.04 [3620]E(f119(x36201,f329(f329(f126(x36201),x36202),f329(f329(f149(x36201),x36203),f118(x36201)))),x36202)
% 187.18/188.04 [3621]E(f142(x36211,f329(f329(f126(x36211),x36212),f329(f329(f149(x36211),x36213),f118(x36211)))),x36213)
% 187.18/188.04 [3627]E(f329(f329(f126(x36271),f329(f329(f174(x36271),x36272),x36273)),f329(f329(f136(x36271),x36272),x36273)),x36273)
% 187.18/188.04 [3636]E(f329(f329(f22(a874),f329(f329(f80(a874),x36361),x36362)),f329(f329(f80(a874),x36363),x36362)),f329(f329(f22(a874),x36361),x36363))
% 187.18/188.04 [3637]E(f329(f329(f22(a874),f329(f329(f80(a874),x36371),x36372)),f329(f329(f80(a874),x36371),x36373)),f329(f329(f22(a874),x36372),x36373))
% 187.18/188.04 [3644]E(f329(f329(f126(x36441),f329(f167(x36441),x36442)),f329(f329(f149(x36441),x36443),f118(x36441))),f329(f167(x36441),f329(f329(f149(x36441),x36443),x36442)))
% 187.18/188.04 [3646]E(f329(f329(f80(a874),f329(f194(f875(x36461)),x36462)),f329(f194(f875(x36461)),x36463)),f329(f194(f875(x36461)),f329(f329(f126(x36461),x36462),x36463)))
% 187.18/188.04 [3649]E(f329(f329(f80(a874),f329(f194(f875(x36491)),x36492)),f329(f194(f875(x36491)),x36493)),f329(f194(f875(x36491)),f172(x36491,x36492,x36493)))
% 187.18/188.04 [3657]E(f329(f329(f115(f881(x36571,a869)),f329(f171(x36571),x36572)),f329(f171(x36571),x36573)),f329(f171(x36571),f329(f329(f126(x36571),x36572),x36573)))
% 187.18/188.04 [3658]E(f45(a874,f329(f329(f81(a874),x36581),x36582),f329(f329(f81(a874),x36581),x36583)),f329(f329(f81(a874),x36581),f45(a874,x36582,x36583)))
% 187.18/188.04 [3671]E(f329(f329(f174(x36711),f329(f329(f22(a874),x36712),f78(a874))),f329(f170(x36711),x36713)),f329(f170(x36711),f329(f329(f174(x36711),x36712),x36713)))
% 187.18/188.04 [3676]E(f329(f329(f106(f881(x36761,a869)),x36762),f329(f79(f881(x36761,a869)),x36763)),f329(f329(f22(f881(x36761,a869)),x36762),x36763))
% 187.18/188.04 [3677]E(f329(f329(f22(f881(x36771,a869)),x36772),f329(f79(f881(x36771,a869)),x36773)),f329(f329(f106(f881(x36771,a869)),x36772),x36773))
% 187.18/188.04 [3699]E(f329(f329(f266(x36991,x36992),x36993),f329(f16(f881(x36992,a869),x36991),f193(f881(x36992,a869)))),f193(f881(f880(x36991,x36992),a869)))
% 187.18/188.04 [3701]E(f329(f329(f22(a874),f329(f329(f81(a874),x37011),x37012)),f329(f329(f81(a874),x37011),x37013)),f329(f329(f81(a874),x37011),f329(f329(f22(a874),x37012),x37013)))
% 187.18/188.04 [3702]E(f329(f329(f80(a874),f329(f329(f81(a874),x37021),x37022)),f329(f329(f81(a874),x37021),x37023)),f329(f329(f81(a874),x37021),f329(f329(f80(a874),x37022),x37023)))
% 187.18/188.04 [3703]E(f329(f329(f22(a1),f329(f329(f81(a1),x37031),x37032)),f329(f329(f81(a1),x37031),x37033)),f329(f329(f81(a1),x37031),f329(f329(f22(a1),x37032),x37033)))
% 187.18/188.04 [3704]E(f329(f329(f80(a1),f329(f329(f81(a1),x37041),x37042)),f329(f329(f81(a1),x37041),x37043)),f329(f329(f81(a1),x37041),f329(f329(f80(a1),x37042),x37043)))
% 187.18/188.04 [3705]E(f329(f329(f81(a1),f329(f329(f254(a1),x37051),x37052)),f329(f329(f254(a1),x37051),x37053)),f329(f329(f254(a1),x37051),f329(f329(f80(a874),x37052),x37053)))
% 187.18/188.04 [3719]E(f329(f329(f42(x37191,f881(x37192,a869)),x37193),f329(f16(f881(x37192,a869),x37191),f193(f881(x37192,a869)))),f193(f881(x37192,a869)))
% 187.18/188.04 [3721]E(f45(a874,f329(f329(f81(a874),x37211),x37212),f329(f329(f81(a874),x37213),x37212)),f329(f329(f81(a874),f45(a874,x37211,x37213)),x37212))
% 187.18/188.04 [3725]E(f45(a1,f329(f329(f22(a1),x37251),f45(a1,x37252,x37253)),x37253),f45(a1,f329(f329(f22(a1),x37251),x37252),x37253))
% 187.18/188.04 [3726]E(f45(a1,f329(f329(f81(a1),x37261),f45(a1,x37262,x37263)),x37263),f45(a1,f329(f329(f81(a1),x37261),x37262),x37263))
% 187.18/188.04 [3727]P24(f329(f329(f243(f881(x37271,a869)),x37272),f329(f329(f307(x37271),x37273),x37272)))
% 187.18/188.04 [3730]E(f329(f308(f880(x37301,x37302),x37301,f263(x37301,x37302)),f329(f171(f880(x37301,x37302)),x37303)),f183(x37301,x37302,f329(f177(x37301,x37302),x37303)))
% 187.18/188.04 [3779]P24(f329(f62(x37791),f183(x37791,x37792,f329(f177(x37791,x37792),x37793))))
% 187.18/188.04 [3804]E(f329(f329(f43(f881(x38041,a869),f881(x38041,a869)),x38042),f329(f115(f881(x38041,a869)),x38043)),f329(f329(f115(f881(x38041,a869)),x38043),f41(f881(x38041,a869),x38042)))
% 187.18/188.04 [3805]E(f329(f329(f42(f881(x38051,a869),f881(x38051,a869)),x38052),f329(f106(f881(x38051,a869)),x38053)),f329(f329(f106(f881(x38051,a869)),x38053),f40(f881(x38051,a869),x38052)))
% 187.18/188.04 [3816]E(f329(f171(x38161),f329(f329(f329(f188(f875(x38161),f875(x38161)),x38162),f166(x38161)),x38163)),f329(f171(x38161),x38163))
% 187.18/188.04 [3820]E(f329(f329(f174(x38201),f329(f194(f875(x38201)),f176(x38201,x38202,x38203))),x38203),f176(x38201,x38202,x38203))
% 187.18/188.04 [3821]E(f183(x38211,x38212,f329(f329(f8(x38212,f878(x38212),x38211),f236(x38212)),x38213)),f252(f881(x38211,a869)))
% 187.18/188.04 [3825]E(f329(f194(f875(x38251)),f329(f329(f329(f188(f875(x38251),f875(x38251)),x38252),f166(x38251)),x38253)),f329(f194(f875(x38251)),x38253))
% 187.18/188.04 [3828]E(f329(f329(f268(x38281,x38282,x38282),f329(f16(f881(x38282,x38282),x38281),f5(x38282))),x38283),f329(f267(x38281,x38282),x38283))
% 187.18/188.04 [3834]E(f45(a1,f329(f329(f22(a1),f45(a1,x38341,x38342)),x38343),x38342),f45(a1,f329(f329(f22(a1),x38341),x38343),x38342))
% 187.18/188.04 [3835]E(f45(a1,f329(f329(f254(a1),f45(a1,x38351,x38352)),x38353),x38352),f45(a1,f329(f329(f254(a1),x38351),x38353),x38352))
% 187.18/188.04 [3838]E(f329(f329(f42(f881(f880(x38381,x38382),a869),f881(x38382,a869)),x38383),f260(x38381,x38382)),f329(f260(x38381,x38382),f40(f881(f880(x38381,x38382),a869),x38383)))
% 187.18/188.04 [3839]E(f329(f329(f42(f881(f880(x38391,x38392),a869),f881(x38391,a869)),x38393),f262(x38391,x38392)),f329(f262(x38391,x38392),f40(f881(f880(x38391,x38392),a869),x38393)))
% 187.18/188.04 [3867]E(f329(f73(x38671,x38671,x38671,x38672),f329(f329(f188(x38671,x38671),x38673),x38672)),f329(f329(f188(x38671,x38671),f329(a117,x38673)),x38672))
% 187.18/188.04 [3877]E(f238(f878(x38771),x38772,f206(x38771),f329(f329(f8(x38771,f878(x38771),x38772),f236(x38771)),x38773)),f329(f207(x38772,x38771),x38773))
% 187.18/188.04 [3884]E(f329(f329(f136(x38841),f329(f329(f22(a874),f329(f194(f875(x38841)),x38842)),x38843)),f329(f167(x38841),x38842)),f329(f167(x38841),f329(f329(f174(x38841),x38843),x38842)))
% 187.18/188.04 [3885]E(f329(f329(f174(x38851),f329(f329(f22(a874),f329(f194(f875(x38851)),x38852)),x38853)),f329(f167(x38851),x38852)),f329(f167(x38851),f329(f329(f136(x38851),x38853),x38852)))
% 187.18/188.04 [3888]E(f329(f329(f80(a874),f329(f164(a874),f329(f329(f152(x38881,a874),x38882),x38883))),f329(f194(f875(x38881)),x38883)),f153(x38881,x38882,x38883))
% 187.18/188.04 [3907]E(f329(f166(x39071),f329(f329(f329(f188(f875(x39071),f875(x39071)),x39072),f166(x39071)),x39073)),f329(f329(f329(f188(f875(x39071),f875(x39071)),f329(a117,x39072)),f166(x39071)),x39073))
% 187.18/188.04 [3922]P24(f329(f329(f243(a874),f329(f194(f875(x39221)),f329(f134(x39221,x39222),x39223))),f329(f194(f875(x39221)),x39223)))
% 187.18/188.04 [3939]E(f329(f329(f115(f881(f881(x39391,a869),a869)),f329(f306(x39391),x39392)),f329(f308(f881(x39391,a869),f881(x39391,a869),f329(f307(x39391),x39393)),f329(f306(x39391),x39392))),f329(f306(x39391),f329(f329(f307(x39391),x39393),x39392)))
% 187.18/188.04 [3958]P20(x39581,x39582,f329(f329(f307(f873(x39581)),f329(f329(f329(f92(x39581),x39583),a24),x39583)),f193(f881(f873(x39581),a869))))
% 187.18/188.04 [3973]P24(f329(f329(f243(a874),f329(f194(f875(x39731)),f176(x39731,x39732,x39733))),f329(f194(f875(x39731)),x39733)))
% 187.18/188.04 [3981]E(f329(f262(x39811,x39812),f329(f249(f880(x39811,x39812)),f329(f268(x39811,x39812,a869),x39813))),f329(f249(x39811),f329(f329(f8(f881(x39812,a869),a869,x39811),f87(x39812)),x39813)))
% 187.18/188.04 [3993]E(f329(f308(a874,a874,f329(f329(f7(a874,a874,a874),f80(a874)),x39931)),f300(a874,x39932,x39933)),f300(a874,f329(f329(f80(a874),x39932),x39931),f329(f329(f80(a874),x39933),x39931)))
% 187.18/188.04 [3996]P24(f329(f62(f878(x39961)),f329(f308(x39962,f878(x39961),f329(f177(x39962,x39961),x39963)),f252(f881(x39962,a869)))))
% 187.18/188.04 [4009]E(f329(f308(a874,a874,f329(f329(f7(a874,a874,a874),f80(a874)),x40091)),f329(f299(a874,x40092),x40093)),f329(f299(a874,f329(f329(f80(a874),x40092),x40091)),f329(f329(f80(a874),x40093),x40091)))
% 187.18/188.04 [4027]E(f329(f329(f181(x40271,x40272),f329(f329(f152(f880(x40271,x40272),x40271),f263(x40271,x40272)),x40273)),f329(f329(f152(f880(x40271,x40272),x40272),f267(x40271,x40272)),x40273)),x40273)
% 187.18/188.04 [4032]E(f329(f329(f80(a874),f329(f329(f81(a874),x40321),f45(a874,f329(f329(f39(a874),x40322),x40321),x40323))),f45(a874,x40322,x40321)),f45(a874,x40322,f329(f329(f81(a874),x40321),x40323)))
% 187.18/188.04 [4046]E(f329(f329(f126(x40461),x40462),f329(f140(f875(x40461),f875(x40461),f126(x40461),f118(x40461)),x40463)),f329(f140(f875(x40461),f875(x40461),f126(x40461),x40462),x40463))
% 187.18/188.04 [4064]P24(f329(f329(f331(f880(x40641,x40641)),f329(f329(f264(x40641,x40641),x40642),x40642)),f329(f329(f188(f880(x40641,x40641),a869),f2(a874)),x40643)))
% 187.18/188.04 [4070]E(f329(f249(x40701),f329(f329(f8(f881(x40702,a869),a869,x40701),f87(x40702)),f329(f7(x40702,x40701,a869),x40703))),f329(f260(x40702,x40701),f329(f249(f880(x40702,x40701)),f329(f268(x40702,x40701,a869),x40703))))
% 187.18/188.04 [4088]E(f329(f329(f115(f881(x40881,a869)),f329(f329(f42(a874,f881(x40881,a869)),f300(a874,f78(a874),x40882)),x40883)),f329(x40883,f2(a874))),f329(f329(f42(a874,f881(x40881,a869)),f329(f298(a874),x40882)),x40883))
% 187.18/188.04 [4103]E(f329(f140(f875(x41031),f875(x41031),f126(x41031),f118(x41031)),f329(f329(f152(f875(x41031),f875(x41031)),f134(x41031,x41032)),x41033)),f329(f134(x41031,x41032),f329(f140(f875(x41031),f875(x41031),f126(x41031),f118(x41031)),x41033)))
% 187.18/188.04 [4108]E(f329(f267(f875(x41081),f875(x41081)),f165(x41081,x41082,x41083)),f329(f134(x41081,f329(f73(a869,a869,x41081,a324),x41082)),x41083))
% 187.18/188.04 [4126]E(f329(f329(f43(x41261,f881(x41262,a869)),f252(f881(x41261,a869))),f329(f329(f8(f881(x41262,a869),f881(x41262,a869),x41261),f249(x41262)),f329(f7(x41262,x41261,a869),x41263))),f329(f249(x41262),f329(f329(f8(f881(x41261,a869),a869,x41262),f88(x41261)),x41263)))
% 187.18/188.04 [4157]E(f329(f329(f80(a1),f329(f329(f80(a1),f329(f329(f81(a1),x41571),f329(f329(f39(a1),x41572),x41571))),f45(a1,x41572,x41571))),x41573),f329(f329(f80(a1),x41572),x41573))
% 187.18/188.04 [4194]E(f329(f329(f80(a1),f329(f329(f80(a1),f329(f329(f81(a1),f329(f329(f39(a1),x41941),x41942)),x41942)),f45(a1,x41941,x41942))),x41943),f329(f329(f80(a1),x41941),x41943))
% 187.18/188.04 [4223]E(f85(f880(x42231,x42232),f329(f268(x42231,x42232,a869),f329(f329(f8(f881(x42232,f880(x42231,x42232)),f881(x42232,a869),x42231),f329(f8(f880(x42231,x42232),a869,x42232),x42233)),f264(x42231,x42232)))),f85(f880(x42231,x42232),x42233))
% 187.18/188.04 [4224]E(f90(f880(x42241,x42242),f329(f268(x42241,x42242,a869),f329(f329(f8(f881(x42242,f880(x42241,x42242)),f881(x42242,a869),x42241),f329(f8(f880(x42241,x42242),a869,x42242),x42243)),f264(x42241,x42242)))),f90(f880(x42241,x42242),x42243))
% 187.18/188.04 [4252]P24(f329(f329(f243(f881(x42521,a869)),f40(f881(x42521,a869),f329(f329(f106(f881(f881(x42521,a869),a869)),x42522),x42523))),f329(f329(f106(f881(x42521,a869)),f40(f881(x42521,a869),x42522)),f40(f881(x42521,a869),x42523))))
% 187.18/188.04 [4253]E(f329(f167(x42531),f329(f329(f329(f188(f875(x42531),f875(x42531)),f329(f329(f22(a874),f329(f194(f875(x42531)),x42532)),f45(a874,x42533,f329(f194(f875(x42531)),x42532)))),f166(x42531)),x42532)),f329(f329(f329(f188(f875(x42531),f875(x42531)),x42533),f166(x42531)),f329(f167(x42531),x42532)))
% 187.18/188.04 [4267]E(f329(f249(x42671),f329(f329(f8(a869,a869,x42671),a324),f329(f329(f7(x42671,f878(x42672),a869),f329(f329(f8(f878(x42672),f881(f878(x42672),a869),x42671),a326),x42673)),f206(x42672)))),f183(x42671,x42672,x42673))
% 187.18/188.04 [4292]P24(f329(f329(f243(a874),f329(f194(f875(x42921)),f329(f329(f136(x42921),f329(f194(f875(x42921)),f176(x42921,x42922,x42923))),x42923))),f329(f194(f875(x42921)),x42923)))
% 187.18/188.04 [4334]E(f329(f249(x43341),f329(f329(f8(f881(x43342,a869),a869,x43341),f87(x43342)),f329(f329(f8(f878(x43341),f881(x43342,a869),x43341),f329(f7(x43342,f878(x43341),a869),f329(f329(f8(f878(x43341),f881(f878(x43341),a869),x43342),a326),x43343))),f236(x43341)))),f185(x43342,x43341,x43343))
% 187.18/188.04 [4544]~P24(f329(f63(x45441,x45442,f193(f881(x45441,a869))),x45443))
% 187.18/188.04 [4551]~P24(f329(f329(f331(f880(x45511,x45511)),f329(f329(f264(x45511,x45511),x45512),x45513)),f151(x45511,f118(f881(x45511,a874)))))
% 187.18/188.04 [3588]E(f329(f194(f875(x35881)),f329(f329(f174(x35881),x35882),x35883)),f329(f329(f241(a874),f329(f194(f875(x35881)),x35883)),x35882))
% 187.18/188.04 [3589]E(f329(f194(f875(x35891)),f329(f329(f136(x35891),x35892),x35893)),f329(f329(f22(a874),f329(f194(f875(x35891)),x35893)),x35892))
% 187.18/188.04 [3613]E(f329(f194(f875(f875(x36131))),f55(x36131,x36132,x36133)),f329(f329(f254(a874),f329(f194(f875(x36131)),x36133)),x36132))
% 187.18/188.04 [3629]E(f329(f329(f39(a874),f329(f329(f39(a874),x36291),x36292)),x36293),f329(f329(f39(a874),x36291),f329(f329(f81(a874),x36292),x36293)))
% 187.18/188.04 [3630]E(f329(f329(f22(a874),f329(f329(f22(a874),x36301),x36302)),x36303),f329(f329(f22(a874),x36301),f329(f329(f80(a874),x36302),x36303)))
% 187.18/188.04 [3631]E(f329(f329(f81(a874),f329(f329(f81(a874),x36311),x36312)),x36313),f329(f329(f81(a874),x36311),f329(f329(f81(a874),x36312),x36313)))
% 187.18/188.04 [3632]E(f329(f329(f81(a1),f329(f329(f81(a1),x36321),x36322)),x36323),f329(f329(f81(a1),x36321),f329(f329(f81(a1),x36322),x36323)))
% 187.18/188.04 [3633]E(f329(f329(f80(a874),f329(f329(f80(a874),x36331),x36332)),x36333),f329(f329(f80(a874),x36331),f329(f329(f80(a874),x36332),x36333)))
% 187.18/188.04 [3634]E(f329(f329(f80(a1),f329(f329(f80(a1),x36341),x36342)),x36343),f329(f329(f80(a1),x36341),f329(f329(f80(a1),x36342),x36343)))
% 187.18/188.04 [3635]E(f329(f329(f254(a1),f329(f329(f254(a1),x36351),x36352)),x36353),f329(f329(f254(a1),x36351),f329(f329(f81(a874),x36352),x36353)))
% 187.18/188.04 [3655]E(f160(x36551,f329(f329(f149(f881(x36551,a869)),x36552),x36553)),f173(x36551,x36552,f160(x36551,x36553)))
% 187.18/188.04 [3700]E(f329(f329(f22(a874),f329(f329(f22(a874),x37001),x37002)),x37003),f329(f329(f22(a874),f329(f329(f22(a874),x37001),x37003)),x37002))
% 187.18/188.04 [3706]E(f329(f236(f880(x37061,f876(x37061))),f329(f329(f264(x37061,f876(x37061)),x37062),x37063)),f329(f133(x37061),f128(x37061,x37062,x37063)))
% 187.18/188.04 [3709]E(f329(f329(f106(f881(x37091,a869)),x37092),f329(f329(f22(f881(x37091,a869)),x37093),x37092)),f193(f881(x37091,a869)))
% 187.18/188.04 [3751]E(f41(f881(x37511,a869),f329(f329(f307(f881(x37511,a869)),x37512),x37513)),f329(f329(f106(f881(x37511,a869)),x37512),f41(f881(x37511,a869),x37513)))
% 187.18/188.04 [3752]E(f40(f881(x37521,a869),f329(f329(f307(f881(x37521,a869)),x37522),x37523)),f329(f329(f115(f881(x37521,a869)),x37522),f40(f881(x37521,a869),x37523)))
% 187.18/188.04 [3754]E(f329(f329(f22(a874),f329(f329(f81(a874),x37541),x37542)),f329(f329(f81(a874),x37543),x37542)),f329(f329(f81(a874),f329(f329(f22(a874),x37541),x37543)),x37542))
% 187.18/188.04 [3755]E(f329(f329(f80(a874),f329(f329(f81(a874),x37551),x37552)),f329(f329(f81(a874),x37553),x37552)),f329(f329(f81(a874),f329(f329(f80(a874),x37551),x37553)),x37552))
% 187.18/188.04 [3756]E(f329(f329(f22(a1),f329(f329(f81(a1),x37561),x37562)),f329(f329(f81(a1),x37563),x37562)),f329(f329(f81(a1),f329(f329(f22(a1),x37561),x37563)),x37562))
% 187.18/188.04 [3757]E(f329(f329(f80(a1),f329(f329(f81(a1),x37571),x37572)),f329(f329(f81(a1),x37573),x37572)),f329(f329(f81(a1),f329(f329(f80(a1),x37571),x37573)),x37572))
% 187.18/188.04 [3759]E(f329(f329(f241(a874),f329(f329(f22(a874),x37591),x37592)),f329(f329(f22(a874),x37593),x37592)),f329(f329(f22(a874),f329(f329(f241(a874),x37591),x37593)),x37592))
% 187.18/188.04 [3782]E(f329(f329(f106(f881(f875(x37821),a869)),f158(x37821,x37822)),f158(x37821,x37823)),f158(x37821,f329(f329(f106(f881(x37821,a869)),x37822),x37823)))
% 187.18/188.04 [3784]E(f329(f329(f115(f881(x37841,a869)),x37842),f329(f329(f115(f881(x37841,a869)),x37842),x37843)),f329(f329(f115(f881(x37841,a869)),x37842),x37843))
% 187.18/188.04 [3785]E(f329(f329(f115(f881(x37851,a869)),x37852),f329(f329(f22(f881(x37851,a869)),x37853),x37852)),f329(f329(f115(f881(x37851,a869)),x37852),x37853))
% 187.18/188.04 [3786]E(f329(f329(f106(f881(x37861,a869)),x37862),f329(f329(f106(f881(x37861,a869)),x37862),x37863)),f329(f329(f106(f881(x37861,a869)),x37862),x37863))
% 187.18/188.04 [3798]E(f329(f329(f286(x37981,x37982,x37982),x37983),f305(x37982,f193(f881(f880(x37982,x37982),a869)))),x37983)
% 187.18/188.04 [3801]E(f329(f329(f115(f881(x38011,a869)),f329(f329(f307(x38011),x38012),f193(f881(x38011,a869)))),x38013),f329(f329(f307(x38011),x38012),x38013))
% 187.18/188.04 [3819]E(f329(f329(f22(a874),f329(f329(f22(a874),f329(a117,x38191)),x38192)),f329(a117,x38193)),f329(f329(f22(a874),f329(f329(f22(a874),x38191),x38192)),x38193))
% 187.18/188.04 [3848]E(f329(f329(f106(f881(f881(x38481,a869),a869)),f329(f306(x38481),x38482)),f329(f306(x38481),x38483)),f329(f306(x38481),f329(f329(f106(f881(x38481,a869)),x38482),x38483)))
% 187.18/188.04 [3852]E(f329(f329(f115(f881(x38521,a869)),f329(f79(f881(x38521,a869)),x38522)),x38523),f329(f79(f881(x38521,a869)),f329(f329(f22(f881(x38521,a869)),x38522),x38523)))
% 187.18/188.04 [3864]E(f329(f329(f307(x38641),x38642),f329(f329(f22(f881(x38641,a869)),x38643),f329(f329(f307(x38641),x38642),f193(f881(x38641,a869))))),f329(f329(f307(x38641),x38642),x38643))
% 187.18/188.04 [3874]P24(f329(f329(f243(f881(x38741,a869)),x38742),f329(f329(f115(f881(x38741,a869)),x38743),x38742)))
% 187.18/188.04 [3875]P24(f329(f329(f243(f881(x38751,a869)),x38752),f329(f329(f115(f881(x38751,a869)),x38752),x38753)))
% 187.18/188.04 [3878]E(f329(f329(f106(f881(x38781,a869)),f329(f79(f881(x38781,a869)),x38782)),f329(f79(f881(x38781,a869)),x38783)),f329(f79(f881(x38781,a869)),f329(f329(f115(f881(x38781,a869)),x38782),x38783)))
% 187.18/188.04 [3879]E(f329(f329(f115(f881(x38791,a869)),f329(f79(f881(x38791,a869)),x38792)),f329(f79(f881(x38791,a869)),x38793)),f329(f79(f881(x38791,a869)),f329(f329(f106(f881(x38791,a869)),x38792),x38793)))
% 187.18/188.04 [3893]P24(f329(f329(f243(f881(x38931,a869)),f329(f171(x38931),x38932)),f329(f171(x38931),f329(f329(f149(x38931),x38933),x38932))))
% 187.18/188.04 [3904]E(f329(f329(f115(f881(x39041,a869)),f329(f329(f22(f881(x39041,a869)),x39042),x39043)),f329(f329(f106(f881(x39041,a869)),x39042),x39043)),x39042)
% 187.18/188.04 [3960]E(f329(f329(f6(x39601,a1),f329(f329(f8(a874,a1,x39601),f105(a1)),x39602)),x39603),f329(f105(a1),f329(f329(f6(x39601,a874),x39602),x39603)))
% 187.18/188.04 [3961]E(f329(f329(f9(x39611,a1),f329(f329(f8(a874,a1,x39611),f105(a1)),x39612)),x39613),f329(f105(a1),f329(f329(f9(x39611,a874),x39612),x39613)))
% 187.18/188.04 [4011]E(f329(f329(f126(x40111),f176(x40111,x40112,x40113)),f329(f329(f136(x40111),f329(f194(f875(x40111)),f176(x40111,x40112,x40113))),x40113)),x40113)
% 187.18/188.04 [4016]E(f329(f79(f881(f880(x40161,x40162),a869)),f329(f329(f266(x40161,x40162),x40163),f329(f16(f881(x40162,a869),x40161),f252(f881(x40162,a869))))),f329(f329(f266(x40161,x40162),f329(f79(f881(x40161,a869)),x40163)),f329(f16(f881(x40162,a869),x40161),f252(f881(x40162,a869)))))
% 187.18/188.04 [4017]E(f329(f79(f881(f880(x40171,x40172),a869)),f329(f329(f266(x40171,x40172),f252(f881(x40171,a869))),f329(f16(f881(x40172,a869),x40171),x40173))),f329(f329(f266(x40171,x40172),f252(f881(x40171,a869))),f329(f16(f881(x40172,a869),x40171),f329(f79(f881(x40172,a869)),x40173))))
% 187.18/188.04 [4065]E(f329(f329(f42(f881(x40651,a869),f881(x40651,a869)),x40652),f329(f329(f7(f881(x40651,a869),f881(x40651,a869),f881(x40651,a869)),f106(f881(x40651,a869))),x40653)),f329(f329(f106(f881(x40651,a869)),f40(f881(x40651,a869),x40652)),x40653))
% 187.18/188.04 [4072]E(f329(f140(f875(x40721),f875(x40721),f126(x40721),f118(x40721)),f329(f329(f149(f875(x40721)),x40722),x40723)),f329(f329(f126(x40721),x40722),f329(f140(f875(x40721),f875(x40721),f126(x40721),f118(x40721)),x40723)))
% 187.18/188.04 [4094]E(f329(f329(f307(f881(x40941,a869)),f329(f283(x40941,x40941,x40942),f329(f329(f307(x40941),x40943),f193(f881(x40941,a869))))),f193(f881(f881(x40941,a869),a869))),f329(f329(f61(x40941),f329(f329(f307(x40941),x40943),f193(f881(x40941,a869)))),x40942))
% 187.18/188.04 [4104]E(f329(f329(f80(a874),f329(f329(f81(a874),x41041),f329(f329(f39(a874),x41042),x41043))),f329(f329(f39(a874),f329(f329(f81(a874),x41041),f45(a874,x41042,x41043))),x41043)),f329(f329(f39(a874),f329(f329(f81(a874),x41041),x41042)),x41043))
% 187.18/188.04 [4105]E(f329(f329(f80(a1),f329(f329(f81(a1),x41051),f329(f329(f39(a1),x41052),x41053))),f329(f329(f39(a1),f329(f329(f81(a1),x41051),f45(a1,x41052,x41053))),x41053)),f329(f329(f39(a1),f329(f329(f81(a1),x41051),x41052)),x41053))
% 187.18/188.04 [4142]E(f329(f329(f22(f881(x41421,a869)),f329(f171(x41421),x41422)),f329(f329(f307(x41421),x41423),f193(f881(x41421,a869)))),f329(f171(x41421),f329(f134(x41421,f329(f329(f8(a869,a869,x41421),a324),f329(a326,x41423))),x41422)))
% 187.18/188.04 [4191]E(f329(f329(f126(x41911),f329(f140(f875(x41911),f875(x41911),f126(x41911),f118(x41911)),x41912)),f329(f140(f875(x41911),f875(x41911),f126(x41911),f118(x41911)),x41913)),f329(f140(f875(x41911),f875(x41911),f126(x41911),f118(x41911)),f329(f329(f126(f875(x41911)),x41912),x41913)))
% 187.18/188.04 [4196]E(f329(f329(f264(f875(x41961),f875(x41961)),f329(f134(x41961,x41962),x41963)),f329(f134(x41961,f329(f73(a869,a869,x41961,a324),x41962)),x41963)),f165(x41961,x41962,x41963))
% 187.18/188.04 [4199]E(f329(f329(f80(a874),f329(f329(f80(a874),f329(f329(f39(a874),x41991),x41992)),f329(f329(f39(a874),x41993),x41992))),f329(f329(f39(a874),f329(f329(f80(a874),f45(a874,x41991,x41992)),f45(a874,x41993,x41992))),x41992)),f329(f329(f39(a874),f329(f329(f80(a874),x41991),x41993)),x41992))
% 187.18/188.04 [4200]E(f329(f329(f80(a1),f329(f329(f80(a1),f329(f329(f39(a1),x42001),x42002)),f329(f329(f39(a1),x42003),x42002))),f329(f329(f39(a1),f329(f329(f80(a1),f45(a1,x42001,x42002)),f45(a1,x42003,x42002))),x42002)),f329(f329(f39(a1),f329(f329(f80(a1),x42001),x42003)),x42002))
% 187.18/188.04 [4256]E(f329(f329(f106(f881(f875(x42561),a869)),f329(f329(f7(f875(x42561),f881(f875(x42561),a869),a869),f331(f875(x42561))),f159(x42561,x42562))),f329(f329(f7(f875(x42561),f881(f875(x42561),a869),a869),f331(f875(x42561))),f159(x42561,x42563))),f158(x42561,f329(f329(f106(f881(x42561,a869)),f329(f329(f7(x42561,f881(x42561,a869),a869),f331(x42561)),x42562)),f329(f329(f7(x42561,f881(x42561,a869),a869),f331(x42561)),x42563))))
% 187.18/188.04 [4269]E(f329(f249(x42691),f329(f329(f18(x42691,a869,a869),f329(f329(f8(a869,f881(a869,a869),x42691),a328),f329(f329(f7(x42691,x42691,a869),a326),x42692))),f329(f329(f7(x42691,f881(x42691,a869),a869),f331(x42691)),x42693))),f329(f329(f307(x42691),x42692),x42693))
% 187.18/188.04 [4289]E(f329(f329(f86(f875(f875(x42891)),f875(f875(x42891))),f54(x42891,x42892)),f329(f329(f18(f875(f875(x42891)),f875(f875(x42891)),f875(f875(x42891))),f329(f329(f8(f875(f875(x42891)),f881(f875(f875(x42891)),f875(f875(x42891))),f875(f875(x42891))),f126(f875(x42891))),f329(f152(f875(x42891),f875(x42891)),f329(f149(x42891),x42893)))),f5(f875(f875(x42891))))),f54(x42891,f329(f329(f149(x42891),x42893),x42892)))
% 187.18/188.04 [4293]E(f329(f249(x42931),f329(f329(f18(x42931,a869,a869),f329(f329(f8(a869,f881(a869,a869),x42931),a328),f329(f329(f7(x42931,f881(x42931,a869),a869),f331(x42931)),x42932))),f329(f329(f7(x42931,f881(x42931,a869),a869),f331(x42931)),x42933))),f329(f329(f115(f881(x42931,a869)),x42932),x42933))
% 187.18/188.04 [4294]E(f329(f249(x42941),f329(f329(f18(x42941,a869,a869),f329(f329(f8(a869,f881(a869,a869),x42941),a327),f329(f329(f7(x42941,f881(x42941,a869),a869),f331(x42941)),x42942))),f329(f329(f7(x42941,f881(x42941,a869),a869),f331(x42941)),x42943))),f329(f329(f106(f881(x42941,a869)),x42942),x42943))
% 187.18/188.04 [4386]E(f329(f329(f42(x43861,f881(f881(x43861,a869),a869)),x43862),f329(f329(f7(x43861,f881(f881(x43861,a869),a869),f881(f881(x43861,a869),a869)),f329(f329(f8(f881(x43861,a869),f881(f881(f881(x43861,a869),a869),f881(f881(x43861,a869),a869)),x43861),f307(f881(x43861,a869))),f329(f329(f8(f881(x43861,a869),f881(x43861,a869),x43861),f283(x43861,x43861,x43863)),f329(f329(f7(x43861,f881(x43861,a869),f881(x43861,a869)),f307(x43861)),f193(f881(x43861,a869)))))),f193(f881(f881(x43861,a869),a869)))),f329(f329(f61(x43861),x43862),x43863))
% 187.18/188.04 [4388]E(f329(f329(f210(x43881),f329(f329(f81(a1),f329(f329(f73(f880(a1,a1),a1,x43881,f263(a1,a1)),f220(x43881)),x43882)),f329(f329(f73(f880(a1,a1),a1,x43881,f263(a1,a1)),f220(x43881)),x43883))),f329(f329(f81(a1),f329(f329(f73(f880(a1,a1),a1,x43881,f267(a1,a1)),f220(x43881)),x43882)),f329(f329(f73(f880(a1,a1),a1,x43881,f267(a1,a1)),f220(x43881)),x43883))),f229(x43881,x43882,x43883))
% 187.18/188.04 [4391]E(f329(f249(f875(x43911)),f329(f329(f18(f875(x43911),a869,a869),f329(f329(f8(a869,f881(a869,a869),f875(x43911)),a327),f329(f329(f7(f875(x43911),a874,a869),f329(f329(f8(a874,f881(a874,a869),f875(x43911)),a326),f194(f875(x43911)))),x43912))),f329(f329(f7(f875(x43911),f881(x43911,a869),a869),f329(f329(f8(f881(x43911,a869),f881(f881(x43911,a869),a869),f875(x43911)),f243(f881(x43911,a869))),f171(x43911))),f329(f171(x43911),x43913)))),f329(f171(f875(x43911)),f55(x43911,x43912,x43913)))
% 187.18/188.04 [3772]E(f45(a874,f329(f329(f80(a874),f329(f329(f81(a874),x37721),x37722)),x37723),x37722),f45(a874,x37723,x37722))
% 187.18/188.04 [3818]E(f137(a874,f329(f299(a874,f329(f329(f80(a874),x38181),x38182)),x38183)),f329(f329(f136(a874),x38182),f137(a874,f329(f299(a874,x38181),x38183))))
% 187.18/188.04 [3863]E(f329(f329(f80(a1),f329(f105(a1),x38631)),f329(f329(f80(a1),f329(f105(a1),x38632)),x38633)),f329(f329(f80(a1),f329(f105(a1),f329(f329(f80(a874),x38631),x38632))),x38633))
% 187.18/188.04 [3870]E(f329(f329(f115(f881(x38701,a869)),f329(f329(f22(f881(x38701,a869)),x38702),x38703)),x38703),f329(f329(f115(f881(x38701,a869)),x38702),x38703))
% 187.18/188.04 [3871]E(f329(f329(f22(f881(x38711,a869)),f329(f329(f22(f881(x38711,a869)),x38712),x38713)),x38713),f329(f329(f22(f881(x38711,a869)),x38712),x38713))
% 187.18/188.04 [3894]E(f329(f329(f286(x38941,x38941,x38942),f305(x38941,f193(f881(f880(x38941,x38941),a869)))),x38943),x38943)
% 187.18/188.04 [3901]E(f329(f329(f115(f881(x39011,a869)),f329(f282(x39011),x39012)),f329(f282(x39011),x39013)),f329(f282(x39011),f329(f329(f115(f881(f880(x39011,x39011),a869)),x39012),x39013)))
% 187.18/188.04 [3912]E(f273(x39121,f329(f329(f149(f880(a104,x39121)),f329(f329(f264(a104,x39121),f2(a104)),x39122)),x39123)),f273(x39121,x39123))
% 187.18/188.04 [3915]E(f329(f329(f106(f881(x39151,a869)),f41(f881(x39151,a869),x39152)),f41(f881(x39151,a869),x39153)),f41(f881(x39151,a869),f329(f329(f115(f881(f881(x39151,a869),a869)),x39152),x39153)))
% 187.18/188.04 [3916]E(f329(f329(f115(f881(x39161,a869)),f40(f881(x39161,a869),x39162)),f40(f881(x39161,a869),x39163)),f40(f881(x39161,a869),f329(f329(f115(f881(f881(x39161,a869),a869)),x39162),x39163)))
% 187.18/188.04 [3952]E(f329(f329(f286(x39521,x39521,x39521),f329(f329(f188(f880(x39521,x39521),a869),x39522),x39523)),x39523),f329(f329(f188(f880(x39521,x39521),a869),f329(a117,x39522)),x39523))
% 187.18/188.04 [4002]P24(f329(f329(f243(f881(x40021,a869)),f329(f329(f22(f881(x40021,a869)),x40022),x40023)),x40022))
% 187.18/188.04 [4003]P24(f329(f329(f243(f881(x40031,a869)),f329(f329(f106(f881(x40031,a869)),x40032),x40033)),x40033))
% 187.18/188.04 [4004]P24(f329(f329(f243(f881(x40041,a869)),f329(f329(f106(f881(x40041,a869)),x40042),x40043)),x40042))
% 187.18/188.04 [4029]E(f305(x40291,f329(f329(f115(f881(f880(x40291,x40291),a869)),f305(x40291,x40292)),f305(x40291,x40293))),f305(x40291,f329(f329(f115(f881(f880(x40291,x40291),a869)),x40292),x40293)))
% 187.18/188.04 [4033]E(f40(f881(x40331,a869),f329(f329(f307(f881(x40331,a869)),x40332),f329(f329(f307(f881(x40331,a869)),x40333),f193(f881(f881(x40331,a869),a869))))),f329(f329(f115(f881(x40331,a869)),x40332),x40333))
% 187.18/188.04 [4034]E(f41(f881(x40341,a869),f329(f329(f307(f881(x40341,a869)),x40342),f329(f329(f307(f881(x40341,a869)),x40343),f193(f881(f881(x40341,a869),a869))))),f329(f329(f106(f881(x40341,a869)),x40342),x40343))
% 187.18/188.04 [4040]E(f329(f329(f286(x40401,x40401,x40401),f329(f329(f188(f880(x40401,x40401),a869),x40402),x40403)),x40403),f329(f329(f286(x40401,x40401,x40401),x40403),f329(f329(f188(f880(x40401,x40401),a869),x40402),x40403)))
% 187.18/188.04 [4109]E(f329(f329(f115(f881(x41091,a869)),f329(f249(x41091),f329(f329(f7(x41091,x41091,a869),a326),x41092))),x41093),f329(f329(f307(x41091),x41092),x41093))
% 187.18/188.04 [4111]E(f329(a109,f329(f329(f6(x41111,a1),f329(f329(f8(a874,a1,x41111),f105(a1)),x41112)),x41113)),f329(f329(f6(x41111,a874),x41112),x41113))
% 187.18/188.04 [4112]E(f329(a109,f329(f329(f9(x41121,a1),f329(f329(f8(a874,a1,x41121),f105(a1)),x41122)),x41123)),f329(f329(f9(x41121,a874),x41122),x41123))
% 187.18/188.04 [4188]E(f329(f154(f875(x41881),x41881,f329(f170(x41881),x41882),f329(f16(f881(f875(x41881),f875(x41881)),x41881),f329(f329(f7(f875(x41881),f875(x41881),f875(x41881)),f126(x41881)),x41882))),x41883),f329(f170(x41881),f329(f329(f126(x41881),x41883),x41882)))
% 187.18/188.04 [4219]P24(f329(f329(f243(f881(f881(x42191,a869),a869)),f329(f329(f115(f881(f881(x42191,a869),a869)),f329(f306(x42191),x42192)),f329(f306(x42191),x42193))),f329(f306(x42191),f329(f329(f115(f881(x42191,a869)),x42192),x42193))))
% 187.18/188.04 [4312]E(f329(f249(x43121),f329(f329(f18(x43121,a869,a869),f329(f329(f8(a869,f881(a869,a869),x43121),a327),f329(f329(f7(x43121,f881(x43121,a869),a869),f331(x43121)),x43122))),f329(f329(f8(a869,a869,x43121),a324),f329(f329(f7(x43121,f881(x43121,a869),a869),f331(x43121)),x43123)))),f329(f329(f22(f881(x43121,a869)),x43122),x43123))
% 187.18/188.04 [4335]E(f329(f38(a874),f329(f249(a874),f329(f329(f18(a874,a869,a869),f329(f329(f8(a869,f881(a869,a869),a874),a327),f329(f329(f7(a874,a874,a869),f244(a874)),f329(f194(f875(x43351)),x43352)))),f329(f329(f8(x43351,a869,a874),x43353),f329(f163(x43351),x43352))))),f329(f194(f875(x43351)),f329(f134(x43351,x43353),x43352)))
% 187.18/188.04 [4337]E(f329(f194(f875(x43371)),f175(x43371,x43372,x43373)),f329(f38(a874),f329(f249(a874),f329(f329(f18(a874,a869,a869),f329(f329(f8(a869,f881(a869,a869),a874),a327),f329(f329(f7(a874,a874,a869),f244(a874)),f329(f194(f875(x43371)),x43372)))),f329(f329(f7(a874,f881(a874,a869),a869),f331(a874)),x43373)))))
% 187.18/188.04 [4434]E(f329(f329(f106(f881(f880(f875(x44341),f875(x44341)),a869)),f329(f308(f880(f880(x44341,f875(x44341)),f880(x44341,f875(x44341))),f880(f875(x44341),f875(x44341)),f269(f880(x44341,f875(x44341)),f875(x44341),f880(x44341,f875(x44341)),f875(x44341),f329(f268(x44341,f875(x44341),f875(x44341)),f149(x44341)),f329(f268(x44341,f875(x44341),f875(x44341)),f149(x44341)))),f322(x44341,f875(x44341),x44342,f329(f141(x44341,x44342),x44343)))),f329(f249(f880(f875(x44341),f875(x44341))),f329(f268(f875(x44341),f875(x44341),a869),f329(f329(f7(f875(x44341),f881(f875(x44341),a869),f881(f875(x44341),a869)),f329(f329(f8(f881(a869,a869),f881(f881(f875(x44341),a869),f881(f875(x44341),a869)),f875(x44341)),f8(a869,a869,f875(x44341))),f329(f329(f8(a869,f881(a869,a869),f875(x44341)),a327),f329(f329(f7(f875(x44341),a874,a869),f329(f329(f8(a874,f881(a874,a869),f875(x44341)),a326),f194(f875(x44341)))),f329(a117,x44343))))),f329(f329(f7(f875(x44341),a874,a869),f329(f329(f8(a874,f881(a874,a869),f875(x44341)),a326),f194(f875(x44341)))),f329(a117,x44343)))))),f329(f141(x44341,x44342),f329(a117,x44343)))
% 187.18/188.04 [3917]E(f45(a874,f329(a117,f329(f329(f80(a874),f329(f329(f81(a874),x39171),x39172)),x39173)),x39172),f45(a874,f329(a117,x39173),x39172))
% 187.18/188.04 [4177]E(f329(f249(x41771),f329(f329(f18(x41771,a869,a869),f329(f329(f8(a869,f881(a869,a869),x41771),a327),x41772)),x41773)),f329(f329(f106(f881(x41771,a869)),f329(f249(x41771),x41772)),f329(f249(x41771),x41773)))
% 187.18/188.04 [4178]E(f329(f249(x41781),f329(f329(f18(x41781,a869,a869),f329(f329(f8(a869,f881(a869,a869),x41781),a328),x41782)),x41783)),f329(f329(f115(f881(x41781,a869)),f329(f249(x41781),x41782)),f329(f249(x41781),x41783)))
% 187.18/188.04 [4180]E(f329(f329(f126(x41801),f329(f329(f136(x41801),f45(a874,x41802,f329(f194(f875(x41801)),x41803))),x41803)),f329(f329(f174(x41801),f45(a874,x41802,f329(f194(f875(x41801)),x41803))),x41803)),f329(f329(f329(f188(f875(x41801),f875(x41801)),x41802),f166(x41801)),x41803))
% 187.18/188.04 [4185]E(f329(f249(x41851),f329(f329(f18(x41851,a869,a869),f329(f329(f8(a869,f881(a869,a869),x41851),a332),x41852)),x41853)),f329(f329(f115(f881(x41851,a869)),f329(f79(f881(x41851,a869)),f329(f249(x41851),x41852))),f329(f249(x41851),x41853)))
% 187.18/188.04 [4201]E(f329(f329(f80(a874),f329(f194(f875(x42011)),f329(f134(x42011,x42012),x42013))),f329(f194(f875(x42011)),f329(f134(x42011,f329(f329(f8(a869,a869,x42011),a324),x42012)),x42013))),f329(f194(f875(x42011)),x42013))
% 187.18/188.04 [4226]P24(f329(f329(f243(f881(x42261,a869)),f329(f329(f115(f881(x42261,a869)),f41(f881(x42261,a869),x42262)),f41(f881(x42261,a869),x42263))),f41(f881(x42261,a869),f329(f329(f106(f881(f881(x42261,a869),a869)),x42262),x42263))))
% 187.18/188.04 [4240]E(f329(f171(x42401),f329(f134(x42401,f329(f329(f8(a869,a869,x42401),a324),f329(f329(f7(x42401,x42401,a869),a326),x42402))),x42403)),f329(f329(f22(f881(x42401,a869)),f329(f171(x42401),x42403)),f329(f329(f307(x42401),x42402),f193(f881(x42401,a869)))))
% 187.18/188.04 [4249]P24(f329(f329(f243(f881(f880(x42491,x42491),a869)),f329(f329(f115(f881(f880(x42491,x42491),a869)),f305(x42491,x42492)),f305(x42491,x42493))),f305(x42491,f329(f329(f115(f881(f880(x42491,x42491),a869)),x42492),x42493))))
% 187.18/188.04 [4274]E(f329(f329(f81(a874),f329(a117,f329(a117,f2(a874)))),f329(f329(f6(a874,a874),f329(f329(f8(a874,a874,a874),f329(f80(a874),x42741)),f329(f329(f7(a874,a874,a874),f81(a874)),x42742))),f329(f250(a874),x42743))),f329(f329(f81(a874),x42743),f329(f329(f80(a874),x42741),f329(f329(f80(a874),x42741),f329(f329(f81(a874),f329(f329(f22(a874),x42743),f78(a874))),x42742)))))
% 187.18/188.04 [4284]E(f329(f249(x42841),f329(f329(f18(x42841,a869,a869),f329(f329(f8(a869,f881(a869,a869),x42841),a327),f329(f329(f7(x42841,f881(x42841,a869),a869),f331(x42841)),f329(f171(x42841),x42842)))),x42843)),f329(f171(x42841),f329(f134(x42841,x42843),x42842)))
% 187.18/188.04 [4433]E(f329(f249(x44331),f329(f329(f8(f881(a874,a869),a869,x44331),f87(a874)),f329(f329(f7(x44331,f881(a874,a869),f881(a874,a869)),f329(f329(f8(f881(a874,f881(a869,a869)),f881(f881(a874,a869),f881(a874,a869)),x44331),f18(a874,a869,a869)),f329(f329(f8(f881(a874,a869),f881(a874,f881(a869,a869)),x44331),f329(f8(a869,f881(a869,a869),a874),a327)),f329(f329(f7(x44331,f881(a874,x44331),f881(a874,a869)),f329(f329(f8(f881(x44331,a869),f881(f881(a874,x44331),f881(a874,a869)),x44331),f8(x44331,a869,a874)),a326)),f329(f163(x44331),x44332))))),f329(f329(f18(a874,a869,a869),f329(f329(f8(a869,f881(a869,a869),a874),a327),f329(f329(f7(a874,a874,a869),f244(a874)),f329(f194(f875(x44331)),x44332)))),f329(f329(f7(a874,f881(a874,a869),a869),f331(a874)),x44333))))),f329(f171(x44331),f175(x44331,x44332,x44333)))
% 187.18/188.04 [4325]E(f329(f249(x43251),f329(f329(f18(x43251,a869,a869),f329(f329(f8(a869,f881(a869,a869),x43251),a332),f329(f329(f8(a869,a869,x43251),a324),f329(f329(f7(x43251,x43251,a869),a326),x43252)))),x43253)),f329(f329(f307(x43251),x43252),f329(f249(x43251),x43253)))
% 187.18/188.04 [4357]E(f329(f329(f152(f880(x43571,a874),x43571),f263(x43571,a874)),f329(f134(f880(x43571,a874),f329(f329(f7(f880(x43571,a874),f881(a874,a869),a869),f329(f329(f8(a874,f881(f881(a874,a869),a869),f880(x43571,a874)),f331(a874)),f267(x43571,a874))),x43572)),f329(f329(f181(x43571,a874),x43573),f137(a874,f329(f299(a874,f2(a874)),f329(f194(f875(x43571)),x43573)))))),f175(x43571,x43573,x43572))
% 187.18/188.04 [4387]E(f329(f329(f81(a1),f329(f108(a1),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))),f329(f329(f6(a874,a1),f329(f329(f8(a1,a1,a874),f329(f80(a1),x43871)),f329(f329(f7(a874,a1,a1),f329(f329(f8(a1,f881(a1,a1),a874),f81(a1)),f105(a1))),x43872))),f329(f250(a874),x43873))),f329(f329(f81(a1),f329(f105(a1),x43873)),f329(f329(f80(a1),x43871),f329(f329(f80(a1),x43871),f329(f329(f81(a1),f329(f105(a1),f329(f329(f22(a874),x43873),f78(a874)))),x43872)))))
% 187.18/188.04 [4427]E(f329(f249(f880(x44271,x44272)),f329(f268(x44271,x44272,a869),f329(f329(f7(x44271,f881(f880(x44272,x44271),a869),f881(x44272,a869)),f329(f329(f8(f881(x44272,f881(f881(f880(x44272,x44271),a869),a869)),f881(f881(f880(x44272,x44271),a869),f881(x44272,a869)),x44271),f7(x44272,f881(f880(x44272,x44271),a869),a869)),f329(f329(f8(f881(x44272,f880(x44272,x44271)),f881(x44272,f881(f881(f880(x44272,x44271),a869),a869)),x44271),f329(f8(f880(x44272,x44271),f881(f881(f880(x44272,x44271),a869),a869),x44272),f331(f880(x44272,x44271)))),f329(f7(x44272,x44271,f880(x44272,x44271)),f264(x44272,x44271))))),x44273))),f329(f284(x44272,x44271),x44273))
% 187.18/188.04 [4449]E(f329(f249(f875(x44491)),f329(f329(f8(f881(x44491,a869),a869,f875(x44491)),f87(x44491)),f329(f329(f8(f881(x44491,f881(f875(x44491),a869)),f881(x44491,a869),f875(x44491)),f329(f8(f881(f875(x44491),a869),a869,x44491),f87(f875(x44491)))),f329(f329(f7(f875(x44491),f881(x44491,f881(f875(x44491),a869)),f881(x44491,f881(f875(x44491),a869))),f329(f329(f8(f881(x44491,f881(f881(f875(x44491),a869),f881(f875(x44491),a869))),f881(f881(x44491,f881(f875(x44491),a869)),f881(x44491,f881(f875(x44491),a869))),f875(x44491)),f18(x44491,f881(f875(x44491),a869),f881(f875(x44491),a869))),f329(f329(f8(f881(x44491,f881(f875(x44491),f881(a869,a869))),f881(x44491,f881(f881(f875(x44491),a869),f881(f875(x44491),a869))),f875(x44491)),f329(f8(f881(f875(x44491),f881(a869,a869)),f881(f881(f875(x44491),a869),f881(f875(x44491),a869)),x44491),f18(f875(x44491),a869,a869))),f329(f329(f8(f881(x44491,f881(f875(x44491),a869)),f881(x44491,f881(f875(x44491),f881(a869,a869))),f875(x44491)),f329(f8(f881(f875(x44491),a869),f881(f875(x44491),f881(a869,a869)),x44491),f329(f8(a869,f881(a869,a869),f875(x44491)),a327))),f329(f329(f7(f875(x44491),f881(x44491,f881(f875(x44491),f875(x44491))),f881(x44491,f881(f875(x44491),a869))),f329(f329(f8(f881(f881(f875(x44491),f875(x44491)),f881(f875(x44491),a869)),f881(f881(x44491,f881(f875(x44491),f875(x44491))),f881(x44491,f881(f875(x44491),a869))),f875(x44491)),f8(f881(f875(x44491),f875(x44491)),f881(f875(x44491),a869),x44491)),f329(f329(f8(f881(f875(x44491),a869),f881(f881(f875(x44491),f875(x44491)),f881(f875(x44491),a869)),f875(x44491)),f8(f875(x44491),a869,f875(x44491))),a326))),f149(x44491)))))),f329(f329(f7(x44491,f881(f875(x44491),a869),f881(f875(x44491),a869)),f329(f329(f8(f881(a869,a869),f881(f881(f875(x44491),a869),f881(f875(x44491),a869)),x44491),f8(a869,a869,f875(x44491))),f329(f329(f8(a869,f881(a869,a869),x44491),a327),f329(f329(f7(x44491,f881(x44491,a869),a869),f331(x44491)),x44492)))),f329(f329(f7(f875(x44491),f881(f875(x44491),a869),a869),f331(f875(x44491))),x44493)))))),f173(x44491,x44492,x44493))
% 187.18/188.04 [4446]E(f329(f329(f86(a1,f880(a1,a1)),f329(f329(f22(a1),x44461),x44462)),f329(f329(f7(a1,f880(a1,a1),f880(a1,a1)),f329(f329(f18(a1,f880(a1,a1),f881(f880(a1,a1),f880(a1,a1))),f329(f329(f8(a869,f881(f880(a1,a1),f881(f880(a1,a1),f880(a1,a1))),a1),f101(f880(a1,a1))),f329(f243(a1),f2(a1)))),f329(f264(a1,a1),f329(f329(f80(a1),f329(f329(f81(a1),f329(f108(a1),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))),x44463)),f78(a1))))),f329(f329(f264(a1,a1),f329(f329(f81(a1),f329(f108(a1),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))),x44463)),x44461))),f329(f44(x44462),f329(f329(f264(a1,a1),x44463),x44461)))
% 187.18/188.04 [4477]~E(f32(x44771,x44772),f33(x44773,x44774))
% 187.18/188.04 [4494]~E(f329(a26,x44941),f30(x44942,x44943,x44944))
% 187.18/188.04 [4495]~E(f329(a26,x44951),f29(x44952,x44953,x44954))
% 187.18/188.04 [4496]~E(f30(x44961,x44962,x44963),f329(a26,x44964))
% 187.18/188.04 [4497]~E(f29(x44971,x44972,x44973),f329(a26,x44974))
% 187.18/188.04 [3466]E(f329(f329(f329(f72(x34661,x34662),x34663),x34664),f329(x34663,x34664)),x34663)
% 187.18/188.04 [3526]E(f329(f329(f255(x35261,x35262,x35263),x35264),f2(a874)),x35262)
% 187.18/188.04 [3565]E(f190(x35651,x35652,x35653,f329(a117,x35654)),f329(x35653,x35654))
% 187.18/188.04 [3606]E(f168(x36061,x36062,f168(x36061,x36063,x36064)),f168(x36061,x36063,f168(x36061,x36062,x36064)))
% 187.18/188.04 [3741]E(f329(f154(x37411,x37412,x37413,x37414),f118(x37412)),x37413)
% 187.18/188.04 [3742]E(f329(f238(x37421,x37422,x37423,x37424),f206(x37422)),x37423)
% 187.18/188.04 [3743]E(f329(f140(x37431,x37432,x37433,x37434),f118(x37432)),x37434)
% 187.18/188.04 [3847]E(f329(f329(f126(x38471),f169(x38471,x38472,x38473)),f169(x38471,x38474,x38473)),f329(f329(f126(x38471),f169(x38471,x38474,x38473)),f169(x38471,x38472,x38473)))
% 187.18/188.04 [3860]E(f329(f238(f878(x38601),x38602,f206(x38601),f329(f16(f878(x38601),x38602),f206(x38601))),f329(x38603,x38604)),f206(x38601))
% 187.18/188.04 [3905]E(f329(f329(f115(f881(x39051,a869)),f183(x39051,x39052,x39053)),f183(x39051,x39052,x39054)),f183(x39051,x39052,f184(x39051,x39052,x39054,x39053)))
% 187.18/188.04 [3937]E(f329(f329(f270(x39371,x39372,x39373,f880(x39372,x39373)),x39374),f264(x39372,x39373)),x39374)
% 187.18/188.04 [3946]E(f186(x39461,x39462,x39463,x39464,f118(x39462)),x39463)
% 187.18/188.04 [3947]E(f239(x39471,x39472,x39473,x39474,f206(x39472)),x39473)
% 187.18/188.04 [3948]E(f186(x39481,x39482,x39483,f118(x39481),x39484),x39483)
% 187.18/188.04 [4233]P47(x42331,x42332,x42333,x42334,f193(f881(x42331,a869)),x42334)
% 187.18/188.04 [3267]E(f329(f329(f16(x32671,x32672),x32673),x32674),x32673)
% 187.18/188.04 [3383]E(f329(f329(f207(x33831,x33832),x33833),f329(f236(x33831),x33834)),f329(f236(x33832),f329(x33833,x33834)))
% 187.18/188.04 [3556]E(f168(x35561,x35562,f329(f134(x35561,x35563),x35564)),f329(f134(x35561,x35563),f168(x35561,x35562,x35564)))
% 187.18/188.04 [3590]E(f329(f329(f65(x35901,x35902,x35903),x35904),f193(f881(x35901,a869))),x35904)
% 187.18/188.04 [3612]E(f329(f329(f163(x36121),f329(f329(f149(x36121),x36122),x36123)),f329(a117,x36124)),f329(f329(f163(x36121),x36123),x36124))
% 187.18/188.04 [3656]P34(x36561,f2(a874),f329(f329(f329(f92(x36561),x36562),f329(a26,x36563)),x36564))
% 187.18/188.04 [3681]E(f329(f329(x36811,x36812),f329(f189(x36813,x36814,x36811),x36812)),f329(f189(x36813,x36814,x36811),f329(a117,x36812)))
% 187.18/188.04 [3777]E(f329(f329(f157(x37771,f329(f329(f149(x37771),x37772),x37773)),f2(a874)),x37774),f329(f329(f149(x37771),x37774),x37773))
% 187.18/188.04 [3788]E(f329(f329(f42(f881(x37881,a869),f881(x37882,a869)),x37883),f308(x37881,x37882,x37884)),f329(f308(x37881,x37882,x37884),f40(f881(x37881,a869),x37883)))
% 187.18/188.04 [3789]E(f329(f329(f42(f881(x37891,a869),f881(x37892,a869)),x37893),f309(x37892,x37891,x37894)),f329(f309(x37892,x37891,x37894),f40(f881(x37891,a869),x37893)))
% 187.18/188.04 [3887]E(f183(x38871,x38872,f187(x38871,x38872,x38873,x38874)),f329(f329(f106(f881(x38871,a869)),f183(x38871,x38872,x38873)),x38874))
% 187.18/188.04 [3891]E(f329(f130(x38911,x38912),f128(x38911,x38913,x38914)),f329(f329(f80(a874),f329(f329(f80(a874),f329(x38912,x38913)),f329(f130(x38911,x38912),x38914))),f329(a117,f2(a874))))
% 187.18/188.04 [3911]E(f329(f140(x39111,x39112,f329(f7(x39112,x39111,x39111),x39113),x39114),f329(f167(x39112),f118(x39112))),x39114)
% 187.18/188.04 [3959]E(f76(x39591,x39592,x39593,x39594,f193(f881(x39591,a869))),x39593)
% 187.18/188.04 [4005]E(f329(f329(f329(f329(f72(x40051,f878(x40052)),f329(f16(f878(x40052),x40051),f206(x40052))),x40053),f206(x40052)),x40054),f206(x40052))
% 187.18/188.04 [4160]E(f329(f268(x41601,x41602,x41603),f329(f329(f8(f881(x41602,f880(x41601,x41602)),f881(x41602,x41603),x41601),f329(f8(f880(x41601,x41602),x41603,x41602),x41604)),f264(x41601,x41602))),x41604)
% 187.18/188.04 [3464]E(f329(f267(x34641,x34642),f329(f329(f264(x34641,x34642),x34643),x34644)),x34644)
% 187.18/188.04 [3465]E(f329(f263(x34651,x34652),f329(f329(f264(x34651,x34652),x34653),x34654)),x34653)
% 187.18/188.04 [3499]E(f329(f194(f875(x34991)),f329(f329(f157(x34991,x34992),x34993),x34994)),f329(f194(f875(x34991)),x34992))
% 187.18/188.04 [3500]E(f329(f194(f875(x35001)),f329(f329(f152(x35002,x35001),x35003),x35004)),f329(f194(f875(x35002)),x35004))
% 187.18/188.04 [3520]E(f329(f329(f136(x35201),f329(a117,x35202)),f329(f329(f149(x35201),x35203),x35204)),f329(f329(f136(x35201),x35202),x35204))
% 187.18/188.04 [3585]E(f329(f329(f174(x35851),x35852),f169(x35851,x35853,x35854)),f169(x35851,f329(f329(f241(a874),x35852),x35853),x35854))
% 187.18/188.04 [3586]E(f329(f329(f136(x35861),x35862),f169(x35861,x35863,x35864)),f169(x35861,f329(f329(f22(a874),x35863),x35862),x35864))
% 187.18/188.04 [3592]E(f329(f329(f307(x35921),x35922),f329(f329(f307(x35921),x35923),x35924)),f329(f329(f307(x35921),x35923),f329(f329(f307(x35921),x35922),x35924)))
% 187.18/188.04 [3595]E(f329(f329(f152(x35951,x35952),x35953),f119(x35951,x35954)),f119(x35952,f329(f329(f152(x35951,x35952),x35953),x35954)))
% 187.18/188.04 [3610]E(f329(f167(x36101),f329(f329(f152(x36102,x36101),x36103),x36104)),f329(f329(f152(x36102,x36101),x36103),f329(f167(x36102),x36104)))
% 187.18/188.04 [3611]E(f329(f329(f152(x36111,x36112),x36113),f329(f170(x36111),x36114)),f329(f170(x36112),f329(f329(f152(x36111,x36112),x36113),x36114)))
% 187.18/188.04 [3624]E(f329(f329(f174(x36241),f329(a117,x36242)),f329(f329(f149(x36241),x36243),x36244)),f329(f329(f149(x36241),x36243),f329(f329(f174(x36241),x36242),x36244)))
% 187.18/188.04 [3628]E(f329(f171(x36281),f329(f329(f152(x36282,x36281),x36283),x36284)),f329(f308(x36282,x36281,x36283),f329(f171(x36282),x36284)))
% 187.18/188.04 [3680]E(f17(x36801,x36802,x36803,f329(a3,f329(a117,f329(a19,x36804)))),f329(x36803,x36804))
% 187.18/188.04 [3683]E(f329(f329(f126(x36831),f329(f134(x36831,x36832),x36833)),f329(f134(x36831,x36832),x36834)),f329(f134(x36831,x36832),f329(f329(f126(x36831),x36833),x36834)))
% 187.18/188.04 [3696]E(f150(x36961,f329(f329(f152(x36962,x36961),x36963),f150(x36962,x36964))),f150(x36961,f329(f329(f152(x36962,x36961),x36963),x36964)))
% 187.18/188.04 [3712]E(f329(f284(x37121,x37121),f329(f329(f285(x37122,x37121),x37123),x37124)),f329(f329(f285(x37122,x37121),f329(f284(x37122,x37122),x37123)),x37124))
% 187.18/188.04 [3722]E(f329(f329(f286(x37221,x37222,x37223),x37224),f193(f881(f880(x37222,x37223),a869))),f193(f881(f880(x37221,x37223),a869)))
% 187.18/188.04 [3723]E(f329(f329(f174(x37231),f329(f329(f22(a874),x37232),x37233)),f329(f329(f136(x37231),x37233),x37234)),f329(f329(f136(x37231),x37233),f329(f329(f174(x37231),x37232),x37234)))
% 187.18/188.04 [3744]E(f329(f329(f126(x37441),f169(x37441,x37442,x37443)),f169(x37441,x37444,x37443)),f169(x37441,f329(f329(f80(a874),x37442),x37444),x37443))
% 187.18/188.04 [3769]E(f41(f881(x37691,a869),f329(f308(x37692,f881(x37691,a869),x37693),x37694)),f329(f329(f43(x37692,f881(x37691,a869)),x37694),x37693))
% 187.18/188.04 [3770]E(f40(f881(x37701,a869),f329(f308(x37702,f881(x37701,a869),x37703),x37704)),f329(f329(f42(x37702,f881(x37701,a869)),x37704),x37703))
% 187.18/188.04 [3771]E(f329(f194(f875(f880(x37711,x37712))),f329(f329(f181(x37711,x37712),x37713),x37714)),f329(f329(f241(a874),f329(f194(f875(x37711)),x37713)),f329(f194(f875(x37712)),x37714)))
% 187.18/188.04 [3773]E(f329(f309(x37731,x37732,x37733),f329(f79(f881(x37732,a869)),x37734)),f329(f79(f881(x37731,a869)),f329(f309(x37731,x37732,x37733),x37734)))
% 187.18/188.04 [3803]E(f329(f187(x38031,x38032,x38033,f193(f881(x38031,a869))),x38034),f206(x38032))
% 187.18/188.04 [3824]E(f329(f309(x38241,x38242,x38243),f329(f249(x38242),x38244)),f329(f249(x38241),f329(f329(f8(x38242,a869,x38241),x38244),x38243)))
% 187.18/188.04 [3841]E(f329(f329(f163(x38411),f329(f329(f126(x38411),x38412),f329(f329(f149(x38411),x38413),x38414))),f329(f194(f875(x38411)),x38412)),x38413)
% 187.18/188.04 [3846]E(f329(f187(x38461,x38462,f329(f16(f878(x38462),x38461),f206(x38462)),x38463),x38464),f206(x38462))
% 187.18/188.04 [3868]E(f329(f308(x38681,x38682,x38683),f329(f309(x38681,x38682,x38683),x38684)),f329(f329(f106(f881(x38682,a869)),x38684),f329(f308(x38681,x38682,x38683),f252(f881(x38681,a869)))))
% 187.18/188.04 [3886]P24(f329(f329(f331(x38861),f329(x38862,x38863)),f329(f308(x38864,x38861,x38862),f252(f881(x38864,a869)))))
% 187.18/188.04 [3898]E(f329(f329(f126(x38981),f169(x38981,x38982,x38983)),f329(f329(f149(x38981),x38983),x38984)),f329(f329(f149(x38981),x38983),f329(f329(f126(x38981),f169(x38981,x38982,x38983)),x38984)))
% 187.18/188.04 [3900]E(f329(f329(f266(x39001,x39002),f329(f171(x39001),x39003)),f329(f16(f881(x39002,a869),x39001),f329(f171(x39002),x39004))),f329(f171(f880(x39001,x39002)),f60(x39001,x39002,x39003,x39004)))
% 187.18/188.04 [3914]E(f153(x39141,x39142,f329(f329(f149(x39141),x39143),x39144)),f329(f329(f80(a874),f329(f329(f80(a874),f329(x39142,x39143)),f153(x39141,x39142,x39144))),f329(a117,f2(a874))))
% 187.18/188.04 [3928]E(f190(f875(x39281),f329(f329(f149(x39281),x39282),x39283),f329(f329(f7(a874,f875(x39281),f875(x39281)),f136(x39281)),x39283),x39284),f329(f329(f136(x39281),x39284),f329(f329(f149(x39281),x39282),x39283)))
% 187.18/188.04 [3929]P21(x39291,f880(x39292,x39291),f333(x39293,x39294,x39292,x39291),f329(f329(f42(x39292,f881(x39291,a869)),x39294),x39293))
% 187.18/188.04 [3938]E(f329(f329(f22(f881(x39381,a869)),f329(f329(f22(f881(x39381,a869)),x39382),x39383)),f329(f329(f307(x39381),x39384),f193(f881(x39381,a869)))),f329(f329(f22(f881(x39381,a869)),x39382),f329(f329(f307(x39381),x39384),x39383)))
% 187.18/188.04 [3950]E(f329(f329(f188(f881(x39501,x39502),f881(x39501,x39502)),x39503),f73(x39502,x39502,x39501,x39504)),f73(x39502,x39502,x39501,f329(f329(f188(x39502,x39502),x39503),x39504)))
% 187.18/188.04 [4028]E(f329(f329(f329(f188(f875(x40281),f875(x40281)),x40282),f166(x40281)),f329(f329(f329(f188(f875(x40281),f875(x40281)),x40283),f166(x40281)),x40284)),f329(f329(f329(f188(f875(x40281),f875(x40281)),f329(f329(f80(a874),x40282),x40283)),f166(x40281)),x40284))
% 187.18/188.04 [4114]P24(f329(f329(f243(f881(x41141,a869)),f329(f171(x41141),f329(f329(f157(x41141,x41142),x41143),x41144))),f329(f329(f307(x41141),x41144),f329(f171(x41141),x41142))))
% 187.18/188.04 [4150]E(f329(f329(f42(f881(x41501,a869),f881(f880(x41501,x41502),a869)),x41503),f329(f329(f7(f881(x41501,a869),f881(x41501,f881(x41502,a869)),f881(f880(x41501,x41502),a869)),f266(x41501,x41502)),x41504)),f329(f329(f266(x41501,x41502),f40(f881(x41501,a869),x41503)),x41504))
% 187.18/188.04 [4187]E(f217(x41871,x41872,x41873,f329(f73(x41872,f881(a104,f881(a104,f881(f880(a104,a104),f881(a104,f876(x41872))))),x41871,f216(x41872)),x41874)),f218(x41871,x41872,x41874,x41873))
% 187.18/188.04 [4204]E(f213(x42041,x42042,x42043,f329(f73(x42042,f881(a104,f881(a104,f881(f880(a104,a104),f881(a104,f876(f878(x42042)))))),x42041,f212(x42042)),x42044)),f214(x42041,x42042,x42044,x42043))
% 187.18/188.04 [4209]P24(f329(f67(x42091,x42092,x42093,x42094,f193(f881(x42091,a869))),x42094))
% 187.18/188.04 [4251]E(f329(f329(f42(x42511,f881(x42512,a869)),x42513),f329(f329(f7(x42511,f881(x42512,a869),f881(x42512,a869)),f329(f329(f8(x42512,f881(f881(x42512,a869),f881(x42512,a869)),x42511),f307(x42512)),x42514)),f193(f881(x42512,a869)))),f329(f308(x42511,x42512,x42514),x42513))
% 187.18/188.04 [4258]P24(f329(f329(f243(f881(x42581,a869)),f329(f260(x42582,x42581),f329(f329(f106(f881(f880(x42582,x42581),a869)),x42583),x42584))),f329(f329(f106(f881(x42581,a869)),f329(f260(x42582,x42581),x42583)),f329(f260(x42582,x42581),x42584))))
% 187.18/188.04 [4259]P24(f329(f329(f243(f881(x42591,a869)),f329(f262(x42591,x42592),f329(f329(f106(f881(f880(x42591,x42592),a869)),x42593),x42594))),f329(f329(f106(f881(x42591,a869)),f329(f262(x42591,x42592),x42593)),f329(f262(x42591,x42592),x42594))))
% 187.18/188.04 [4321]P24(f329(f329(f243(f881(f880(x43211,x43212),a869)),f329(f308(x43212,f880(x43211,x43212),f333(x43213,x43214,x43211,x43212)),f329(f329(f42(x43211,f881(x43212,a869)),x43214),x43213))),f329(f329(f266(x43211,x43212),x43214),x43213)))
% 187.18/188.04 [4322]E(f329(f121(x43221,f880(x43221,x43222),x43223),f329(f329(f8(f881(x43222,f876(f880(x43221,x43222))),f876(f880(x43221,x43222)),x43221),f121(x43222,f880(x43221,x43222),x43224)),f329(f329(f8(f881(x43222,f880(x43221,x43222)),f881(x43222,f876(f880(x43221,x43222))),x43221),f329(f8(f880(x43221,x43222),f876(f880(x43221,x43222)),x43222),f127(f880(x43221,x43222)))),f264(x43221,x43222)))),f132(x43221,x43222,x43223,x43224))
% 187.18/188.04 [4363]E(f85(f880(x43631,x43632),f329(f268(x43631,x43632,a869),f329(f329(f7(x43631,f881(x43632,a869),f881(x43632,a869)),f329(f329(f8(f881(a869,a869),f881(f881(x43632,a869),f881(x43632,a869)),x43631),f8(a869,a869,x43632)),f329(f329(f8(a869,f881(a869,a869),x43631),a327),f329(a326,x43633)))),f329(a326,x43634)))),f329(f329(f264(x43631,x43632),x43633),x43634))
% 187.18/188.04 [4364]E(f90(f880(x43641,x43642),f329(f268(x43641,x43642,a869),f329(f329(f7(x43641,f881(x43642,a869),f881(x43642,a869)),f329(f329(f8(f881(a869,a869),f881(f881(x43642,a869),f881(x43642,a869)),x43641),f8(a869,a869,x43642)),f329(f329(f8(a869,f881(a869,a869),x43641),a327),f329(a326,x43643)))),f329(a326,x43644)))),f329(f329(f264(x43641,x43642),x43643),x43644))
% 187.18/188.04 [4435]E(f329(f329(f268(f875(x44351),f875(x44351),f880(f875(x44351),f875(x44351))),f329(f329(f18(f875(x44351),f881(f875(x44351),f880(f875(x44351),f875(x44351))),f881(f875(x44351),f880(f875(x44351),f875(x44351)))),f329(f329(f8(f881(f875(x44351),f881(f880(f875(x44351),f875(x44351)),f880(f875(x44351),f875(x44351)))),f881(f881(f875(x44351),f880(f875(x44351),f875(x44351))),f881(f875(x44351),f880(f875(x44351),f875(x44351)))),f875(x44351)),f18(f875(x44351),f880(f875(x44351),f875(x44351)),f880(f875(x44351),f875(x44351)))),f329(f329(f8(f881(f875(x44351),f880(f875(x44351),f875(x44351))),f881(f875(x44351),f881(f880(f875(x44351),f875(x44351)),f880(f875(x44351),f875(x44351)))),f875(x44351)),f329(f8(f880(f875(x44351),f875(x44351)),f881(f880(f875(x44351),f875(x44351)),f880(f875(x44351),f875(x44351))),f875(x44351)),f329(f101(f880(f875(x44351),f875(x44351))),f329(x44352,x44353)))),f329(f329(f8(f875(x44351),f881(f875(x44351),f880(f875(x44351),f875(x44351))),f875(x44351)),f264(f875(x44351),f875(x44351))),f329(f149(x44351),x44353))))),f329(f329(f7(f875(x44351),f881(f875(x44351),f875(x44351)),f881(f875(x44351),f880(f875(x44351),f875(x44351)))),f329(f329(f8(f881(f875(x44351),f880(f875(x44351),f875(x44351))),f881(f881(f875(x44351),f875(x44351)),f881(f875(x44351),f880(f875(x44351),f875(x44351)))),f875(x44351)),f8(f875(x44351),f880(f875(x44351),f875(x44351)),f875(x44351))),f264(f875(x44351),f875(x44351)))),f329(f149(x44351),x44353)))),f165(x44351,x44352,x44354)),f165(x44351,x44352,f329(f329(f149(x44351),x44353),x44354)))
% 187.18/188.04 [4441]E(f329(f140(f881(x44411,f878(x44412)),f880(x44411,x44412),f329(f7(f880(x44411,x44412),f881(x44411,f878(x44412)),f881(x44411,f878(x44412))),f329(f268(x44411,x44412,f881(f881(x44411,f878(x44412)),f881(x44411,f878(x44412)))),f329(f329(f7(x44411,f881(x44412,f878(x44412)),f881(x44412,f881(f881(x44411,f878(x44412)),f881(x44411,f878(x44412))))),f329(f329(f8(f881(f878(x44412),f881(f881(x44411,f878(x44412)),f881(x44411,f878(x44412)))),f881(f881(x44412,f878(x44412)),f881(x44412,f881(f881(x44411,f878(x44412)),f881(x44411,f878(x44412))))),x44411),f8(f878(x44412),f881(f881(x44411,f878(x44412)),f881(x44411,f878(x44412))),x44412)),f329(f329(f8(f881(f881(x44411,f878(x44412)),f881(f878(x44412),f881(x44411,f878(x44412)))),f881(f878(x44412),f881(f881(x44411,f878(x44412)),f881(x44411,f878(x44412)))),x44411),f7(f881(x44411,f878(x44412)),f878(x44412),f881(x44411,f878(x44412)))),f329(f7(f881(x44411,f878(x44412)),x44411,f881(f878(x44412),f881(x44411,f878(x44412)))),f72(x44411,f878(x44412)))))),f236(x44412)))),x44413),f329(f167(f880(x44411,x44412)),x44414)),f184(x44411,x44412,x44413,f329(f177(x44411,x44412),x44414)))
% 187.18/188.04 [3539]E(f329(f194(f873(x35391)),f329(f329(f329(f92(x35391),x35392),x35393),x35394)),f2(a874))
% 187.18/188.04 [3659]E(f329(f329(f174(x36591),x36592),f329(f329(f174(x36591),x36593),x36594)),f329(f329(f174(x36591),f329(f329(f241(a874),x36592),x36593)),x36594))
% 187.18/188.04 [3660]E(f329(f329(f136(x36601),x36602),f329(f329(f136(x36601),x36603),x36604)),f329(f329(f136(x36601),f329(f329(f80(a874),x36602),x36603)),x36604))
% 187.18/188.04 [3672]E(f329(f329(f126(x36721),f329(f329(f149(x36721),x36722),x36723)),x36724),f329(f329(f149(x36721),x36722),f329(f329(f126(x36721),x36723),x36724)))
% 187.18/188.04 [3673]E(f329(f329(f126(x36731),f329(f329(f126(x36731),x36732),x36733)),x36734),f329(f329(f126(x36731),x36732),f329(f329(f126(x36731),x36733),x36734)))
% 187.18/188.04 [3753]E(f329(f329(f163(x37531),f329(f329(f149(x37531),x37532),x37533)),x37534),f190(x37531,x37532,f329(f163(x37531),x37533),x37534))
% 187.18/188.04 [3762]E(f329(f329(f188(x37621,x37621),x37622),f329(f329(f188(x37621,x37621),x37623),x37624)),f329(f329(f188(x37621,x37621),f329(f329(f81(a874),x37623),x37622)),x37624))
% 187.18/188.04 [3791]E(f329(f329(f115(f881(x37911,a869)),x37912),f329(f329(f307(x37911),x37913),x37914)),f329(f329(f307(x37911),x37913),f329(f329(f115(f881(x37911,a869)),x37912),x37914)))
% 187.18/188.04 [3806]E(f329(f329(f329(f188(x38061,x38061),x38062),x38063),f329(x38063,x38064)),f329(x38063,f329(f329(f329(f188(x38061,x38061),x38062),x38063),x38064)))
% 187.18/188.04 [3814]E(f329(f329(f286(x38141,x38142,x38143),f193(f881(f880(x38141,x38142),a869))),x38144),f193(f881(f880(x38141,x38143),a869)))
% 187.18/188.04 [3830]E(f329(f329(f115(f881(x38301,a869)),f329(f329(f307(x38301),x38302),x38303)),x38304),f329(f329(f307(x38301),x38302),f329(f329(f115(f881(x38301,a869)),x38303),x38304)))
% 187.18/188.04 [3849]E(f184(x38491,x38492,f329(f177(x38491,x38492),x38493),f329(f177(x38491,x38492),x38494)),f329(f177(x38491,x38492),f329(f329(f126(f880(x38491,x38492)),x38494),x38493)))
% 187.18/188.04 [3850]E(f329(f38(f880(x38501,x38502)),f329(f329(f266(x38501,x38502),x38503),f329(f16(f881(x38502,a869),x38501),x38504))),f329(f329(f81(a874),f329(f38(x38501),x38503)),f329(f38(x38502),x38504)))
% 187.18/188.04 [3857]E(f329(f329(f106(f881(x38571,a869)),f329(f329(f307(x38571),x38572),x38573)),f329(f329(f307(x38571),x38572),x38574)),f329(f329(f307(x38571),x38572),f329(f329(f106(f881(x38571,a869)),x38573),x38574)))
% 187.18/188.04 [3872]E(f329(f329(f115(f881(x38721,a869)),x38722),f329(f329(f115(f881(x38721,a869)),x38723),x38724)),f329(f329(f115(f881(x38721,a869)),x38723),f329(f329(f115(f881(x38721,a869)),x38722),x38724)))
% 187.18/188.04 [3873]E(f329(f329(f106(f881(x38731,a869)),x38732),f329(f329(f106(f881(x38731,a869)),x38733),x38734)),f329(f329(f106(f881(x38731,a869)),x38733),f329(f329(f106(f881(x38731,a869)),x38732),x38734)))
% 187.18/188.04 [3882]E(f65(x38821,x38822,f329(f329(f8(x38822,f881(x38822,x38822),x38821),x38823),x38824)),f329(f66(x38822,x38821,x38823),x38824))
% 187.18/188.04 [3892]E(f179(x38921,f329(f329(f152(f875(x38922),f875(x38921)),f329(f152(x38922,x38921),x38923)),x38924)),f329(f329(f152(f875(x38922),f875(x38921)),f329(f152(x38922,x38921),x38923)),f179(x38922,x38924)))
% 187.18/188.04 [3910]E(f329(f140(f875(x39101),f875(x39101),f126(x39101),f118(x39101)),f329(f329(f152(x39102,f875(x39101)),x39103),x39104)),f162(x39102,x39101,x39103,x39104))
% 187.18/188.04 [3913]E(f187(x39131,x39132,x39133,f329(f79(f881(x39131,a869)),f329(f329(f307(x39131),x39134),f193(f881(x39131,a869))))),f329(f329(f329(f72(x39131,f878(x39132)),x39133),x39134),f206(x39132)))
% 187.18/188.04 [3955]E(f329(f329(f329(f72(x39551,f878(x39552)),f329(f177(x39551,x39552),x39553)),f329(f263(x39551,x39552),x39554)),f329(f236(x39552),f329(f267(x39551,x39552),x39554))),f329(f177(x39551,x39552),f329(f329(f149(f880(x39551,x39552)),x39554),x39553)))
% 187.18/188.04 [3972]E(f329(f73(x39721,x39721,x39721,f329(f329(f188(x39721,x39721),x39722),x39723)),f329(f329(f188(x39721,x39721),x39724),x39723)),f329(f329(f188(x39721,x39721),f329(f329(f80(a874),x39722),x39724)),x39723))
% 187.18/188.04 [3997]E(f329(f329(f106(f881(x39971,a869)),f329(f329(f115(f881(x39971,a869)),x39972),x39973)),f329(f329(f115(f881(x39971,a869)),x39972),x39974)),f329(f329(f115(f881(x39971,a869)),x39972),f329(f329(f106(f881(x39971,a869)),x39973),x39974)))
% 187.18/188.04 [3998]E(f329(f329(f106(f881(x39981,a869)),f329(f329(f22(f881(x39981,a869)),x39982),x39983)),f329(f329(f22(f881(x39981,a869)),x39982),x39984)),f329(f329(f22(f881(x39981,a869)),x39982),f329(f329(f115(f881(x39981,a869)),x39983),x39984)))
% 187.18/188.04 [3999]E(f329(f329(f115(f881(x39991,a869)),f329(f329(f22(f881(x39991,a869)),x39992),x39993)),f329(f329(f22(f881(x39991,a869)),x39992),x39994)),f329(f329(f22(f881(x39991,a869)),x39992),f329(f329(f106(f881(x39991,a869)),x39993),x39994)))
% 187.18/188.04 [4000]E(f329(f329(f115(f881(x40001,a869)),f329(f329(f106(f881(x40001,a869)),x40002),x40003)),f329(f329(f106(f881(x40001,a869)),x40002),x40004)),f329(f329(f106(f881(x40001,a869)),x40002),f329(f329(f115(f881(x40001,a869)),x40003),x40004)))
% 187.18/188.04 [4001]E(f329(f329(f22(f881(x40011,a869)),f329(f329(f106(f881(x40011,a869)),x40012),x40013)),f329(f329(f106(f881(x40011,a869)),x40012),x40014)),f329(f329(f106(f881(x40011,a869)),x40012),f329(f329(f22(f881(x40011,a869)),x40013),x40014)))
% 187.18/188.04 [4007]E(f329(f38(f880(x40071,x40072)),f329(f329(f266(x40071,x40072),f329(f329(f307(x40071),x40073),f193(f881(x40071,a869)))),f329(f16(f881(x40072,a869),x40071),x40074))),f329(f38(x40072),x40074))
% 187.18/188.04 [4043]E(f329(f329(f43(x40431,f881(x40432,a869)),x40433),f329(f329(f8(f881(x40432,a869),f881(x40432,a869),x40431),f79(f881(x40432,a869))),x40434)),f329(f79(f881(x40432,a869)),f329(f329(f42(x40431,f881(x40432,a869)),x40433),x40434)))
% 187.18/188.04 [4044]E(f329(f329(f42(x40441,f881(x40442,a869)),x40443),f329(f329(f8(f881(x40442,a869),f881(x40442,a869),x40441),f79(f881(x40442,a869))),x40444)),f329(f79(f881(x40442,a869)),f329(f329(f43(x40441,f881(x40442,a869)),x40443),x40444)))
% 187.18/188.04 [4058]E(f329(f329(f286(x40581,x40581,x40581),f329(f329(f188(f880(x40581,x40581),a869),x40582),x40583)),f329(f329(f188(f880(x40581,x40581),a869),x40584),x40583)),f329(f329(f188(f880(x40581,x40581),a869),f329(f329(f80(a874),x40582),x40584)),x40583))
% 187.18/188.04 [4089]E(f329(f329(f43(x40891,f881(f881(x40892,a869),a869)),x40893),f329(f329(f8(f881(x40892,a869),f881(f881(x40892,a869),a869),x40891),f306(x40892)),x40894)),f329(f306(x40892),f329(f329(f43(x40891,f881(x40892,a869)),x40893),x40894)))
% 187.18/188.04 [4118]E(f329(f329(f42(f881(x41181,a869),f881(x41182,a869)),x41183),f329(f329(f7(f881(x41181,a869),f881(x41181,f881(x41182,a869)),f881(x41182,a869)),f42(x41181,f881(x41182,a869))),x41184)),f329(f329(f42(x41181,f881(x41182,a869)),f40(f881(x41181,a869),x41183)),x41184))
% 187.18/188.04 [4119]E(f329(f329(f43(f881(x41191,a869),f881(x41192,a869)),x41193),f329(f329(f7(f881(x41191,a869),f881(x41191,f881(x41192,a869)),f881(x41192,a869)),f43(x41191,f881(x41192,a869))),x41194)),f329(f329(f43(x41191,f881(x41192,a869)),f40(f881(x41191,a869),x41193)),x41194))
% 187.18/188.04 [4124]E(f329(f329(f152(x41241,x41242),x41243),f329(f140(f875(x41241),f875(x41241),f126(x41241),f118(x41241)),x41244)),f329(f140(f875(x41242),f875(x41242),f126(x41242),f118(x41242)),f329(f329(f152(f875(x41241),f875(x41242)),f329(f152(x41241,x41242),x41243)),x41244)))
% 187.18/188.04 [4128]E(f190(f875(x41281),f118(x41281),f329(f329(f8(f875(x41281),f875(x41281),a874),f329(f149(x41281),x41282)),f329(f329(f7(a874,f875(x41281),f875(x41281)),f174(x41281)),x41283)),x41284),f329(f329(f174(x41281),x41284),f329(f329(f149(x41281),x41282),x41283)))
% 187.18/188.04 [4170]P24(f329(f329(f243(f881(x41701,a869)),f329(f308(x41702,x41701,x41703),f329(f309(x41702,x41701,x41703),x41704))),x41704))
% 187.18/188.04 [4173]E(f329(f308(f880(x41731,x41732),f880(x41732,x41731),f329(f268(x41731,x41732,f880(x41732,x41731)),f329(f7(x41732,x41731,f880(x41732,x41731)),f264(x41732,x41731)))),f329(f329(f266(x41731,x41732),x41733),f329(f16(f881(x41732,a869),x41731),x41734))),f329(f329(f266(x41732,x41731),x41734),f329(f16(f881(x41731,a869),x41732),x41733)))
% 187.18/188.04 [4182]E(f329(f329(f42(x41821,f881(x41822,a869)),x41823),f329(f329(f8(f881(x41821,a869),f881(x41822,a869),x41821),f283(x41821,x41822,x41824)),f329(f329(f7(x41821,f881(x41821,a869),f881(x41821,a869)),f307(x41821)),f193(f881(x41821,a869))))),f329(f283(x41821,x41822,x41824),x41823))
% 187.18/188.04 [4183]E(f329(f329(f42(x41831,f881(x41832,a869)),x41833),f329(f329(f8(f881(x41831,a869),f881(x41832,a869),x41831),f309(x41832,x41831,x41834)),f329(f329(f7(x41831,f881(x41831,a869),f881(x41831,a869)),f307(x41831)),f193(f881(x41831,a869))))),f329(f309(x41832,x41831,x41834),x41833))
% 187.18/188.04 [4273]E(f329(f329(f115(f881(x42731,a869)),f329(f329(f115(f881(x42731,a869)),f329(f329(f106(f881(x42731,a869)),x42732),x42733)),f329(f329(f106(f881(x42731,a869)),x42733),x42734))),f329(f329(f106(f881(x42731,a869)),x42734),x42732)),f329(f329(f106(f881(x42731,a869)),f329(f329(f106(f881(x42731,a869)),f329(f329(f115(f881(x42731,a869)),x42732),x42733)),f329(f329(f115(f881(x42731,a869)),x42733),x42734))),f329(f329(f115(f881(x42731,a869)),x42734),x42732)))
% 187.18/188.04 [4336]E(f329(f140(f875(x43361),f875(x43361),f126(x43361),f118(x43361)),f329(f329(f152(x43362,f875(x43361)),f329(f329(f7(x43362,f875(x43361),f875(x43361)),f329(f329(f8(x43361,f881(f875(x43361),f875(x43361)),x43362),f149(x43361)),x43363)),f118(x43361))),x43364)),f329(f329(f152(x43362,x43361),x43363),x43364))
% 187.18/188.04 [4347]E(f329(f329(f86(a1,x43471),f329(f108(a1),f329(f329(f80(a1),x43472),a102))),f329(f329(f18(a1,x43471,x43471),f329(f329(f7(a1,x43471,f881(x43471,x43471)),f329(f329(f8(a869,f881(x43471,f881(x43471,x43471)),a1),f101(x43471)),a198)),x43473)),f329(f329(f8(a874,x43471,a1),x43474),a109))),f190(x43471,x43473,x43474,f329(f108(a874),x43472)))
% 187.18/188.04 [4549]~P24(f329(f329(f193(f881(x45491,f881(x45492,a869))),x45493),x45494))
% 187.18/188.04 [3817]E(f329(f329(f163(x38171),f329(f329(f126(x38171),x38172),x38173)),f329(f329(f80(a874),f329(f194(f875(x38171)),x38172)),x38174)),f329(f329(f163(x38171),x38173),x38174))
% 187.18/188.04 [3823]E(f329(f329(f136(x38231),x38232),f329(f329(f174(x38231),f329(f329(f80(a874),x38233),x38232)),x38234)),f329(f329(f174(x38231),x38233),f329(f329(f136(x38231),x38232),x38234)))
% 187.18/188.04 [3926]E(f329(f329(f115(f881(x39261,a869)),f329(f260(x39262,x39261),x39263)),f329(f260(x39262,x39261),x39264)),f329(f260(x39262,x39261),f329(f329(f115(f881(f880(x39262,x39261),a869)),x39263),x39264)))
% 187.18/188.04 [3927]E(f329(f329(f115(f881(x39271,a869)),f329(f262(x39271,x39272),x39273)),f329(f262(x39271,x39272),x39274)),f329(f262(x39271,x39272),f329(f329(f115(f881(f880(x39271,x39272),a869)),x39273),x39274)))
% 187.18/188.04 [3932]E(f329(f329(f115(f881(x39321,a869)),f329(f329(f115(f881(x39321,a869)),x39322),x39323)),x39324),f329(f329(f115(f881(x39321,a869)),x39322),f329(f329(f115(f881(x39321,a869)),x39323),x39324)))
% 187.18/188.04 [3933]E(f329(f329(f22(f881(x39331,a869)),f329(f329(f106(f881(x39331,a869)),x39332),x39333)),x39334),f329(f329(f106(f881(x39331,a869)),x39332),f329(f329(f22(f881(x39331,a869)),x39333),x39334)))
% 187.18/188.04 [3934]E(f329(f329(f106(f881(x39341,a869)),f329(f329(f106(f881(x39341,a869)),x39342),x39343)),x39344),f329(f329(f106(f881(x39341,a869)),x39342),f329(f329(f106(f881(x39341,a869)),x39343),x39344)))
% 187.18/188.04 [3974]E(f329(f329(f115(f881(f880(x39741,x39742),a869)),f329(f284(x39742,x39741),x39743)),f329(f284(x39742,x39741),x39744)),f329(f284(x39742,x39741),f329(f329(f115(f881(f880(x39742,x39741),a869)),x39743),x39744)))
% 187.18/188.04 [3975]E(f329(f329(f106(f881(f880(x39751,x39752),a869)),f329(f284(x39752,x39751),x39753)),f329(f284(x39752,x39751),x39754)),f329(f284(x39752,x39751),f329(f329(f106(f881(f880(x39752,x39751),a869)),x39753),x39754)))
% 187.18/188.04 [3989]E(f329(f329(f115(f881(x39891,f881(x39892,a869))),f253(x39892,x39891,x39893)),f253(x39892,x39891,x39894)),f253(x39892,x39891,f329(f329(f115(f881(x39892,f881(x39891,a869))),x39893),x39894)))
% 187.18/188.04 [3990]E(f329(f329(f106(f881(x39901,f881(x39902,a869))),f253(x39902,x39901,x39903)),f253(x39902,x39901,x39904)),f253(x39902,x39901,f329(f329(f106(f881(x39902,f881(x39901,a869))),x39903),x39904)))
% 187.18/188.04 [4047]E(f329(f329(f106(f881(x40471,a869)),f329(f329(f115(f881(x40471,a869)),x40472),x40473)),f329(f329(f115(f881(x40471,a869)),x40474),x40473)),f329(f329(f115(f881(x40471,a869)),f329(f329(f106(f881(x40471,a869)),x40472),x40474)),x40473))
% 187.18/188.04 [4048]E(f329(f329(f115(f881(x40481,a869)),f329(f329(f22(f881(x40481,a869)),x40482),x40483)),f329(f329(f22(f881(x40481,a869)),x40484),x40483)),f329(f329(f22(f881(x40481,a869)),f329(f329(f115(f881(x40481,a869)),x40482),x40484)),x40483))
% 187.18/188.04 [4049]E(f329(f329(f115(f881(x40491,a869)),f329(f329(f106(f881(x40491,a869)),x40492),x40493)),f329(f329(f106(f881(x40491,a869)),x40494),x40493)),f329(f329(f106(f881(x40491,a869)),f329(f329(f115(f881(x40491,a869)),x40492),x40494)),x40493))
% 187.18/188.04 [4050]E(f329(f329(f22(f881(x40501,a869)),f329(f329(f106(f881(x40501,a869)),x40502),x40503)),f329(f329(f106(f881(x40501,a869)),x40504),x40503)),f329(f329(f106(f881(x40501,a869)),f329(f329(f22(f881(x40501,a869)),x40502),x40504)),x40503))
% 187.18/188.04 [4051]E(f329(f329(f22(f881(x40511,a869)),f329(f329(f106(f881(x40511,a869)),x40512),x40513)),f329(f329(f106(f881(x40511,a869)),x40514),x40513)),f329(f329(f22(f881(x40511,a869)),f329(f329(f106(f881(x40511,a869)),x40512),x40513)),x40514))
% 187.18/188.04 [4061]E(f329(f329(f22(f881(x40611,a869)),f329(f329(f22(f881(x40611,a869)),x40612),f329(f329(f307(x40611),x40613),f193(f881(x40611,a869))))),x40614),f329(f329(f22(f881(x40611,a869)),x40612),f329(f329(f307(x40611),x40613),x40614)))
% 187.18/188.04 [4115]E(f329(f329(f115(f881(x41151,a869)),f329(f329(f307(x41151),x41152),f329(f329(f307(x41151),x41153),f193(f881(x41151,a869))))),f329(f282(x41151),x41154)),f329(f282(x41151),f329(f329(f307(f880(x41151,x41151)),f329(f329(f264(x41151,x41151),x41152),x41153)),x41154)))
% 187.18/188.04 [4145]E(f329(f329(f42(a874,f881(x41451,a869)),f329(f298(a874),x41452)),f329(f329(f8(a874,f881(x41451,a869),a874),x41453),f329(f329(f7(a874,a874,a874),f80(a874)),x41454))),f329(f329(f42(a874,f881(x41451,a869)),f300(a874,x41454,f329(f329(f80(a874),x41452),x41454))),x41453))
% 187.18/188.04 [4146]E(f173(x41461,f329(f283(x41461,x41461,x41462),f329(f329(f307(x41461),x41463),f193(f881(x41461,a869)))),f329(f283(f875(x41461),f875(x41461),f156(x41461,x41462)),f329(f329(f307(f875(x41461)),x41464),f193(f881(f875(x41461),a869))))),f329(f283(f875(x41461),f875(x41461),f156(x41461,x41462)),f329(f329(f307(f875(x41461)),f329(f329(f149(x41461),x41463),x41464)),f193(f881(f875(x41461),a869)))))
% 187.18/188.04 [4207]E(f329(f177(x42071,x42072),f329(f329(f152(x42071,f880(x42071,x42072)),f329(f329(f18(x42071,x42072,f880(x42071,x42072)),f264(x42071,x42072)),x42073)),x42074)),f187(x42071,x42072,f329(f73(x42072,f878(x42072),x42071,f236(x42072)),x42073),f329(f171(x42071),x42074)))
% 187.18/188.04 [4212]E(f329(f249(x42121),f329(f329(f7(x42121,f881(x42122,a869),a869),f329(f329(f8(x42122,f881(f881(x42122,a869),a869),x42121),f331(x42122)),x42123)),x42124)),f329(f309(x42121,x42122,x42123),x42124))
% 187.18/188.04 [4306]E(f329(f249(x43061),f329(f329(f7(x43061,f881(f880(x43062,x43061),a869),a869),f329(f329(f8(f880(x43062,x43061),f881(f881(f880(x43062,x43061),a869),a869),x43061),f331(f880(x43062,x43061))),f329(f264(x43062,x43061),x43063))),x43064)),f329(f283(x43062,x43061,x43064),f329(f329(f307(x43062),x43063),f193(f881(x43062,a869)))))
% 187.18/188.04 [4320]E(f329(f329(f152(f880(x43201,a874),x43201),f263(x43201,a874)),f329(f134(f880(x43201,a874),f329(f329(f8(a874,a869,f880(x43201,a874)),x43202),f329(f329(f8(a874,a874,f880(x43201,a874)),a117),f267(x43201,a874)))),f329(f329(f181(x43201,a874),x43203),x43204))),f329(f329(f152(f880(x43201,a874),x43201),f263(x43201,a874)),f329(f134(f880(x43201,a874),f329(f329(f8(a874,a869,f880(x43201,a874)),x43202),f267(x43201,a874))),f329(f329(f181(x43201,a874),x43203),f329(f329(f152(a874,a874),a117),x43204)))))
% 187.18/188.04 [4329]P24(f329(f329(f243(f881(f881(x43291,a869),a869)),f329(f329(f42(x43292,f881(f881(x43291,a869),a869)),x43293),f329(f329(f8(f881(x43291,a869),f881(f881(x43291,a869),a869),x43292),f306(x43291)),x43294))),f329(f306(x43291),f329(f329(f42(x43292,f881(x43291,a869)),x43293),x43294))))
% 187.18/188.04 [4371]E(f329(f329(f86(a1,x43711),f329(f108(a1),f329(f329(f80(a1),x43712),a102))),f329(f329(f18(a1,x43711,x43711),f329(f329(f7(a1,x43711,f881(x43711,x43711)),f329(f329(f8(a869,f881(x43711,f881(x43711,x43711)),a1),f101(x43711)),a198)),x43713)),f329(f329(f18(a1,x43711,x43711),f329(f329(f8(a874,f881(x43711,x43711),a1),x43714),a109)),f329(f329(f8(a874,x43711,a1),f189(x43711,x43713,x43714)),a109)))),f329(f189(x43711,x43713,x43714),f329(f108(a874),x43712)))
% 187.18/188.04 [4374]E(f329(f329(f152(x43741,x43742),f329(f73(f878(x43742),x43742,x43741,f240(x43742)),x43743)),f329(f134(x43741,f329(f329(f8(a869,a869,x43741),a324),f329(f329(f7(x43741,f878(x43742),a869),f329(f329(f8(f878(x43742),f881(f878(x43742),a869),x43741),a326),x43743)),f206(x43742)))),x43744)),f161(x43741,x43742,x43743,x43744))
% 187.18/188.04 [4397]E(f329(f249(f880(x43971,x43972)),f329(f268(x43971,x43972,a869),f329(f329(f7(x43971,f881(x43972,a869),f881(x43972,a869)),f329(f329(f8(f881(a869,a869),f881(f881(x43972,a869),f881(x43972,a869)),x43971),f8(a869,a869,x43972)),f329(f329(f8(a869,f881(a869,a869),x43971),a327),f329(f329(f7(x43971,f881(x43971,a869),a869),f331(x43971)),x43973)))),f329(f329(f7(x43972,f881(x43972,a869),a869),f331(x43972)),x43974)))),f230(x43971,x43972,x43973,x43974))
% 187.18/188.04 [4430]E(f329(f329(f42(x44301,f881(f880(x44301,x44302),a869)),x44303),f329(f329(f18(x44301,f881(x44302,f881(f880(x44301,x44302),a869)),f881(f880(x44301,x44302),a869)),f329(f329(f8(f881(x44302,a869),f881(f881(x44302,f881(f880(x44301,x44302),a869)),f881(f880(x44301,x44302),a869)),x44301),f42(x44302,f881(f880(x44301,x44302),a869))),x44304)),f329(f329(f7(x44301,f881(f880(x44301,x44302),a869),f881(x44302,f881(f880(x44301,x44302),a869))),f329(f329(f8(f881(x44302,f881(f881(f880(x44301,x44302),a869),f881(f880(x44301,x44302),a869))),f881(f881(f880(x44301,x44302),a869),f881(x44302,f881(f880(x44301,x44302),a869))),x44301),f7(x44302,f881(f880(x44301,x44302),a869),f881(f880(x44301,x44302),a869))),f329(f329(f8(f881(x44302,f880(x44301,x44302)),f881(x44302,f881(f881(f880(x44301,x44302),a869),f881(f880(x44301,x44302),a869))),x44301),f329(f8(f880(x44301,x44302),f881(f881(f880(x44301,x44302),a869),f881(f880(x44301,x44302),a869)),x44302),f307(f880(x44301,x44302)))),f264(x44301,x44302)))),f193(f881(f880(x44301,x44302),a869))))),f329(f329(f266(x44301,x44302),x44303),x44304))
% 187.18/188.04 [3984]E(f329(f329(f126(x39841),f329(f329(f174(x39841),x39842),x39843)),f329(f329(f174(x39841),f329(f329(f22(a874),x39842),f329(f194(f875(x39841)),x39843))),x39844)),f329(f329(f174(x39841),x39842),f329(f329(f126(x39841),x39843),x39844)))
% 187.18/188.04 [3985]E(f329(f329(f126(x39851),f329(f329(f136(x39851),x39852),x39853)),f329(f329(f136(x39851),f329(f329(f22(a874),x39852),f329(f194(f875(x39851)),x39853))),x39854)),f329(f329(f136(x39851),x39852),f329(f329(f126(x39851),x39853),x39854)))
% 187.18/188.04 [4037]E(f329(f329(f80(a874),f329(f329(f81(a874),x40371),x40372)),f329(f329(f80(a874),f329(f329(f81(a874),x40373),x40372)),x40374)),f329(f329(f80(a874),f329(f329(f81(a874),f329(f329(f80(a874),x40371),x40373)),x40372)),x40374))
% 187.18/188.04 [4237]P24(f329(f329(f243(f881(x42371,a869)),f329(f329(f22(f881(x42371,a869)),f329(f260(x42372,x42371),x42373)),f329(f260(x42372,x42371),x42374))),f329(f260(x42372,x42371),f329(f329(f22(f881(f880(x42372,x42371),a869)),x42373),x42374))))
% 187.18/188.04 [4238]P24(f329(f329(f243(f881(x42381,a869)),f329(f329(f22(f881(x42381,a869)),f329(f262(x42381,x42382),x42383)),f329(f262(x42381,x42382),x42384))),f329(f262(x42381,x42382),f329(f329(f22(f881(f880(x42381,x42382),a869)),x42383),x42384))))
% 187.18/188.04 [4349]E(f329(f329(f80(a1),f329(a89,f329(f283(f880(a874,a874),f880(a874,a874),a113),f329(f329(f307(f880(a874,a874)),f329(f329(f264(a874,a874),x43491),x43492)),f193(f881(f880(a874,a874),a869)))))),f329(a89,f329(f283(f880(a874,a874),f880(a874,a874),a113),f329(f329(f307(f880(a874,a874)),f329(f329(f264(a874,a874),x43493),x43494)),f193(f881(f880(a874,a874),a869)))))),f329(a89,f329(f283(f880(a874,a874),f880(a874,a874),a113),f329(f329(f307(f880(a874,a874)),f329(f329(f264(a874,a874),f329(f329(f80(a874),x43491),x43493)),f329(f329(f80(a874),x43492),x43494))),f193(f881(f880(a874,a874),a869))))))
% 187.18/188.04 [4392]E(f329(f329(f81(a1),f329(a89,f329(f283(f880(a874,a874),f880(a874,a874),a113),f329(f329(f307(f880(a874,a874)),f329(f329(f264(a874,a874),x43921),x43922)),f193(f881(f880(a874,a874),a869)))))),f329(a89,f329(f283(f880(a874,a874),f880(a874,a874),a113),f329(f329(f307(f880(a874,a874)),f329(f329(f264(a874,a874),x43923),x43924)),f193(f881(f880(a874,a874),a869)))))),f329(a89,f329(f283(f880(a874,a874),f880(a874,a874),a113),f329(f329(f307(f880(a874,a874)),f329(f329(f264(a874,a874),f329(f329(f80(a874),f329(f329(f81(a874),x43921),x43923)),f329(f329(f81(a874),x43922),x43924))),f329(f329(f80(a874),f329(f329(f81(a874),x43921),x43924)),f329(f329(f81(a874),x43922),x43923)))),f193(f881(f880(a874,a874),a869))))))
% 187.18/188.04 [4412]E(f329(f249(x44121),f329(f329(f8(f881(x44122,a869),a869,x44121),f88(x44122)),f329(f329(f8(f881(x44122,a869),f881(x44122,a869),x44121),f329(f18(x44122,a869,a869),f329(f329(f8(a869,f881(a869,a869),x44122),a332),f329(f329(f7(x44122,f881(x44122,a869),a869),f331(x44122)),x44123)))),f329(f329(f7(x44121,f881(x44122,f881(x44121,a869)),f881(x44122,a869)),f329(f329(f8(f881(f881(x44121,a869),a869),f881(f881(x44122,f881(x44121,a869)),f881(x44122,a869)),x44121),f8(f881(x44121,a869),a869,x44122)),f331(x44121))),x44124)))),f329(f329(f43(x44122,f881(x44121,a869)),x44123),x44124))
% 187.18/188.04 [4445]E(f329(f329(f286(x44451,x44451,x44451),f329(f329(f307(f880(x44451,x44451)),f329(f329(f264(x44451,x44451),x44452),x44453)),x44454)),f305(x44451,f329(f329(f307(f880(x44451,x44451)),f329(f329(f264(x44451,x44451),x44452),x44453)),x44454))),f329(f329(f115(f881(f880(x44451,x44451),a869)),f329(f329(f286(x44451,x44451,x44451),x44454),f305(x44451,x44454))),f329(f249(f880(x44451,x44451)),f329(f268(x44451,x44451,a869),f329(f329(f7(x44451,f881(x44451,a869),f881(x44451,a869)),f329(f329(f8(f881(a869,a869),f881(f881(x44451,a869),f881(x44451,a869)),x44451),f8(a869,a869,x44451)),f329(f329(f8(a869,f881(a869,a869),x44451),a327),f329(f329(f7(x44451,f881(f880(x44451,x44451),a869),a869),f329(f329(f8(f880(x44451,x44451),f881(f881(f880(x44451,x44451),a869),a869),x44451),f331(f880(x44451,x44451))),f329(f329(f7(x44451,x44451,f880(x44451,x44451)),f264(x44451,x44451)),x44452))),f305(x44451,x44454))))),f329(f329(f7(x44451,f881(f880(x44451,x44451),a869),a869),f329(f329(f8(f880(x44451,x44451),f881(f881(f880(x44451,x44451),a869),a869),x44451),f331(f880(x44451,x44451))),f329(f264(x44451,x44451),x44453))),f305(x44451,x44454)))))))
% 187.18/188.04 [4239]E(f329(f134(x42391,f329(f329(f18(x42391,a869,a869),f329(f329(f8(a869,f881(a869,a869),x42391),a327),x42392)),x42393)),x42394),f329(f134(x42391,x42393),f329(f134(x42391,x42392),x42394)))
% 187.18/188.04 [4343]E(f329(f329(f126(x43431),f329(f329(f329(f101(f875(x43431)),f329(f329(f331(a874),f2(a874)),x43432)),f329(f329(f149(x43431),x43433),f118(x43431))),f118(x43431))),f175(x43431,x43434,f329(f249(a874),f329(f329(f7(a874,f881(a874,a869),a869),f329(f329(f8(a874,f881(f881(a874,a869),a869),a874),f331(a874)),a117)),x43432)))),f175(x43431,f329(f329(f149(x43431),x43433),x43434),x43432))
% 187.18/188.04 [4439]E(f329(f249(f880(x44391,x44392)),f329(f329(f8(f881(a874,a869),a869,f880(x44391,x44392)),f87(a874)),f329(f329(f7(f880(x44391,x44392),f881(a874,a869),f881(a874,a869)),f329(f329(f8(f881(a874,f881(a869,a869)),f881(f881(a874,a869),f881(a874,a869)),f880(x44391,x44392)),f18(a874,a869,a869)),f329(f329(f8(f881(a874,a869),f881(a874,f881(a869,a869)),f880(x44391,x44392)),f329(f8(a869,f881(a869,a869),a874),a327)),f329(f329(f7(f880(x44391,x44392),f881(a874,f880(x44391,x44392)),f881(a874,a869)),f329(f329(f8(f881(f880(x44391,x44392),a869),f881(f881(a874,f880(x44391,x44392)),f881(a874,a869)),f880(x44391,x44392)),f8(f880(x44391,x44392),a869,a874)),a326)),f329(f329(f18(a874,x44392,f880(x44391,x44392)),f329(f329(f8(x44391,f881(x44392,f880(x44391,x44392)),a874),f264(x44391,x44392)),f329(f163(x44391),x44393))),f329(f163(x44392),x44394)))))),f329(f329(f7(a874,a874,a869),f244(a874)),f329(f329(f241(a874),f329(f194(f875(x44391)),x44393)),f329(f194(f875(x44392)),x44394)))))),f329(f171(f880(x44391,x44392)),f329(f329(f181(x44391,x44392),x44393),x44394)))
% 187.18/188.04 [4362]E(f329(f249(f880(x43621,x43622)),f329(f268(x43621,x43622,a869),f329(f329(f7(x43621,f881(x43622,a869),f881(x43622,a869)),f329(f329(f8(f881(a869,a869),f881(f881(x43622,a869),f881(x43622,a869)),x43621),f8(a869,a869,x43622)),f329(f329(f8(a869,f881(a869,a869),x43621),a327),x43623))),x43624))),f329(f329(f266(x43621,x43622),f329(f249(x43621),x43623)),f329(f16(f881(x43622,a869),x43621),f329(f249(x43622),x43624))))
% 187.18/188.04 [4365]E(f329(f249(f880(x43651,x43652)),f329(f268(x43651,x43652,a869),f329(f329(f18(x43651,f881(x43652,a869),f881(x43652,a869)),f329(f329(f8(f881(a869,a869),f881(f881(x43652,a869),f881(x43652,a869)),x43651),f8(a869,a869,x43652)),f329(f329(f8(a869,f881(a869,a869),x43651),a327),x43653))),x43654))),f329(f329(f266(x43651,x43652),f329(f249(x43651),x43653)),f329(f329(f8(f881(x43652,a869),f881(x43652,a869),x43651),f249(x43652)),x43654)))
% 187.18/188.04 [4381]E(f329(f249(x43811),f329(f329(f8(f881(x43812,a869),a869,x43811),f88(x43812)),f329(f329(f8(f881(x43812,a869),f881(x43812,a869),x43811),f329(f18(x43812,a869,a869),f329(f329(f8(a869,f881(a869,a869),x43812),a332),f329(f329(f7(x43812,f881(x43812,a869),a869),f331(x43812)),x43813)))),x43814))),f329(f329(f43(x43812,f881(x43811,a869)),x43813),f329(f329(f8(f881(x43811,a869),f881(x43811,a869),x43812),f249(x43811)),f329(f7(x43811,x43812,a869),x43814))))
% 187.18/188.04 [4425]E(f329(f329(f152(f880(x44251,a874),x44251),f263(x44251,a874)),f329(f134(f880(x44251,a874),f329(f329(f7(f880(x44251,a874),f881(a874,a869),a869),f329(f329(f8(a874,f881(f881(a874,a869),a869),f880(x44251,a874)),f331(a874)),f267(x44251,a874))),x44252)),f329(f329(f181(x44251,a874),x44253),f137(a874,f329(f299(a874,x44254),f329(f329(f80(a874),x44254),f329(f194(f875(x44251)),x44253))))))),f329(f329(f152(f880(x44251,a874),x44251),f263(x44251,a874)),f329(f134(f880(x44251,a874),f329(f329(f7(f880(x44251,a874),f881(a874,a869),a869),f329(f329(f8(a874,f881(f881(a874,a869),a869),f880(x44251,a874)),f331(a874)),f329(f329(f7(f880(x44251,a874),a874,a874),f329(f329(f8(a874,f881(a874,a874),f880(x44251,a874)),f80(a874)),f267(x44251,a874))),x44254))),x44252)),f329(f329(f181(x44251,a874),x44253),f137(a874,f329(f299(a874,f2(a874)),f329(f194(f875(x44251)),x44253)))))))
% 187.18/188.04 [4426]E(f329(a117,f329(f329(f242(a874),f329(f194(f875(x44261)),x44262)),f329(f140(a874,f875(x44263),f329(f7(f875(x44263),a874,a874),f329(f329(f8(a874,f881(a874,a874),f875(x44263)),f242(a874)),f329(f329(f7(f875(x44263),a874,a874),f329(f329(f8(a874,f881(a874,a874),f875(x44263)),f22(a874)),f194(f875(x44263)))),f329(a117,f2(a874))))),f2(a874)),f329(f167(f875(x44263)),f329(f134(f875(x44263),f329(f329(f8(a869,a869,f875(x44263)),a324),f329(f329(f7(f875(x44263),f875(x44263),a869),a326),f118(x44263)))),x44264))))),f329(f329(f242(a874),f329(a117,f329(f194(f875(x44261)),x44262))),f329(f140(a874,f875(x44263),f329(f7(f875(x44263),a874,a874),f329(f329(f8(a874,f881(a874,a874),f875(x44263)),f242(a874)),f194(f875(x44263)))),f2(a874)),f329(f167(f875(x44263)),x44264))))
% 187.18/188.04 [4380]E(f329(f329(f126(x43801),f175(x43801,x43802,x43803)),f175(x43801,x43804,f329(f249(a874),f329(f329(f7(a874,f881(a874,a869),a869),f329(f329(f8(a874,f881(f881(a874,a869),a869),a874),f331(a874)),f329(f329(f7(a874,a874,a874),f80(a874)),f329(f194(f875(x43801)),x43802)))),x43803)))),f175(x43801,f329(f329(f126(x43801),x43802),x43804),x43803))
% 187.18/188.04 [4432]E(f329(f329(f149(f875(x44321)),f329(f329(f149(x44321),x44322),f329(f140(f875(x44321),f875(x44321),f126(x44321),f118(x44321)),f329(f329(f152(f875(x44321),f875(x44321)),f154(f875(x44321),x44321,f118(x44321),f329(f329(f8(f875(x44321),f881(f875(x44321),f875(x44321)),x44321),f16(f875(x44321),f875(x44321))),f329(f329(f7(x44321,f875(x44321),f875(x44321)),f149(x44321)),f118(x44321))))),x44323)))),f179(x44321,f329(f329(f149(f875(x44321)),x44324),f329(f140(f875(f875(x44321)),f875(f875(x44321)),f126(f875(x44321)),f118(f875(x44321))),f329(f329(f152(f875(x44321),f875(f875(x44321))),f154(f875(f875(x44321)),x44321,f118(f875(x44321)),f329(f16(f881(f875(x44321),f875(f875(x44321))),x44321),f329(f329(f7(f875(x44321),f875(f875(x44321)),f875(f875(x44321))),f149(f875(x44321))),f118(f875(x44321)))))),x44323))))),f179(x44321,f329(f329(f149(f875(x44321)),f329(f329(f149(x44321),x44322),x44324)),x44323)))
% 187.18/188.04 [4440]E(f329(f249(f880(x44401,x44401)),f329(f268(x44401,x44401,a869),f329(f329(f7(x44401,f881(f880(x44402,x44402),a869),f881(x44401,a869)),f329(f329(f8(f881(x44401,f881(f881(f880(x44402,x44402),a869),a869)),f881(f881(f880(x44402,x44402),a869),f881(x44401,a869)),x44401),f7(x44401,f881(f880(x44402,x44402),a869),a869)),f329(f329(f8(f881(x44401,f880(x44402,x44402)),f881(x44401,f881(f881(f880(x44402,x44402),a869),a869)),x44401),f329(f8(f880(x44402,x44402),f881(f881(f880(x44402,x44402),a869),a869),x44401),f331(f880(x44402,x44402)))),f329(f329(f7(x44401,f881(x44401,x44402),f881(x44401,f880(x44402,x44402))),f329(f329(f8(f881(x44402,f880(x44402,x44402)),f881(f881(x44401,x44402),f881(x44401,f880(x44402,x44402))),x44401),f8(x44402,f880(x44402,x44402),x44401)),f329(f329(f8(x44402,f881(x44402,f880(x44402,x44402)),x44401),f264(x44402,x44402)),x44403))),x44403)))),x44404))),f329(f329(f285(x44402,x44401),x44404),x44403))
% 187.18/188.04 [4498]~E(f33(x44981,x44982),f30(x44983,x44984,x44985))
% 187.18/188.04 [4499]~E(f33(x44991,x44992),f29(x44993,x44994,x44995))
% 187.18/188.04 [4500]~E(f32(x45001,x45002),f30(x45003,x45004,x45005))
% 187.18/188.04 [4501]~E(f32(x45011,x45012),f29(x45013,x45014,x45015))
% 187.18/188.04 [4502]~E(f30(x45021,x45022,x45023),f33(x45024,x45025))
% 187.18/188.04 [4503]~E(f30(x45031,x45032,x45033),f32(x45034,x45035))
% 187.18/188.04 [4504]~E(f29(x45041,x45042,x45043),f33(x45044,x45045))
% 187.18/188.04 [4505]~E(f29(x45051,x45052,x45053),f32(x45054,x45055))
% 187.18/188.04 [3924]E(f329(f184(x39241,x39242,x39243,x39244),x39245),f329(f238(f878(x39242),x39242,f329(x39243,x39245),f236(x39242)),f329(x39244,x39245)))
% 187.18/188.04 [4012]E(f184(x40121,x40122,f184(x40121,x40122,x40123,x40124),x40125),f184(x40121,x40122,x40123,f184(x40121,x40122,x40124,x40125)))
% 187.18/188.04 [4186]E(f265(x41861,x41862,x41863,f253(x41862,x41861,x41864),f253(x41863,x41862,x41865)),f253(x41863,x41861,f265(x41863,x41862,x41861,x41865,x41864)))
% 187.18/188.04 [4193]E(f329(f329(f115(f881(x41931,a869)),f329(f171(x41931),f329(f329(f174(x41931),f329(f194(f875(x41932)),x41933)),x41934))),f183(x41931,x41932,x41935)),f183(x41931,x41932,f186(x41931,x41932,x41935,x41934,x41933)))
% 187.18/188.04 [3749]E(f329(f329(f268(x37491,x37492,x37493),x37494),x37495),f329(f329(x37494,f329(f263(x37491,x37492),x37495)),f329(f267(x37491,x37492),x37495)))
% 187.18/188.04 [3774]E(f329(f238(x37741,x37742,x37743,x37744),f329(f236(x37742),x37745)),f329(x37744,x37745))
% 187.18/188.04 [3783]E(f329(f329(f329(f66(x37831,x37832,x37833),x37834),x37835),f193(f881(x37832,a869))),x37835)
% 187.18/188.04 [3956]E(f239(x39561,x39562,x39563,x39564,f329(f236(x39562),x39565)),f329(x39564,x39565))
% 187.18/188.04 [4067]E(f329(f73(f878(x40671),f878(x40672),f878(x40673),f329(f207(x40671,x40672),x40674)),f329(f207(x40673,x40671),x40675)),f329(f207(x40673,x40672),f329(f73(x40671,x40672,x40673,x40674),x40675)))
% 187.18/188.04 [4069]E(f329(f73(f875(x40691),f875(x40692),f875(x40693),f329(f152(x40691,x40692),x40694)),f329(f152(x40693,x40691),x40695)),f329(f152(x40693,x40692),f329(f73(x40691,x40692,x40693,x40694),x40695)))
% 187.18/188.04 [4125]E(f329(f238(x41251,f880(x41252,f876(x41252)),x41253,f329(f268(x41252,f876(x41252),x41251),x41254)),f329(f133(x41252),x41255)),f131(x41251,x41252,x41253,x41254,x41255))
% 187.18/188.04 [4149]E(f85(x41491,f67(x41492,x41491,x41493,x41494,x41495)),f329(f329(f65(x41492,x41491,x41493),x41494),x41495))
% 187.18/188.04 [4184]E(f329(f329(f80(a874),f329(f329(f80(a874),f329(x41841,f329(f263(x41842,x41843),x41844))),f329(x41845,f329(f267(x41842,x41843),x41844)))),f329(a117,f2(a874))),f272(x41842,x41843,x41841,x41845,x41844))
% 187.18/188.04 [4376]E(f161(x43761,x43762,f329(f329(f7(x43761,f878(x43762),f878(x43762)),f329(f329(f18(x43761,f878(x43762),f881(f878(x43762),f878(x43762))),f329(f329(f8(a869,f881(f878(x43762),f881(f878(x43762),f878(x43762))),x43761),f101(f878(x43762))),x43763)),f329(f329(f8(x43762,f878(x43762),x43761),f236(x43762)),x43764))),f206(x43762)),x43765),f329(f329(f152(x43761,x43762),x43764),f329(f134(x43761,x43763),x43765)))
% 187.18/188.04 [4541]~E(f329(f329(f329(f72(x45411,f878(x45412)),x45413),x45414),f329(f236(x45412),x45415)),f329(f16(f878(x45412),x45411),f206(x45412)))
% 187.18/188.04 [3684]E(f329(f329(f174(x36841),x36842),f329(f329(f152(x36843,x36841),x36844),x36845)),f329(f329(f152(x36843,x36841),x36844),f329(f329(f174(x36843),x36842),x36845)))
% 187.18/188.04 [3685]E(f329(f329(f136(x36851),x36852),f329(f329(f152(x36853,x36851),x36854),x36855)),f329(f329(f152(x36853,x36851),x36854),f329(f329(f136(x36853),x36852),x36855)))
% 187.18/188.04 [3717]E(f329(f329(f152(x37171,x37172),x37173),f329(f329(f149(x37171),x37174),x37175)),f329(f329(f149(x37172),f329(x37173,x37174)),f329(f329(f152(x37171,x37172),x37173),x37175)))
% 187.18/188.04 [3778]E(f329(f308(x37781,x37782,x37783),f329(f329(f307(x37781),x37784),x37785)),f329(f329(f307(x37782),f329(x37783,x37784)),f329(f308(x37781,x37782,x37783),x37785)))
% 187.18/188.04 [3807]E(f172(x38071,f329(f329(f149(x38071),x38072),x38073),f329(f329(f149(x38071),x38074),x38075)),f329(f329(f149(x38071),x38072),f329(f329(f149(x38071),x38074),f172(x38071,x38073,x38075))))
% 187.18/188.04 [3843]E(f329(f329(f181(x38431,x38432),f329(f329(f174(x38431),x38433),x38434)),f329(f329(f174(x38432),x38433),x38435)),f329(f329(f174(f880(x38431,x38432)),x38433),f329(f329(f181(x38431,x38432),x38434),x38435)))
% 187.18/188.04 [3844]E(f329(f329(f181(x38441,x38442),f329(f329(f136(x38441),x38443),x38444)),f329(f329(f136(x38442),x38443),x38445)),f329(f329(f136(f880(x38441,x38442)),x38443),f329(f329(f181(x38441,x38442),x38444),x38445)))
% 187.18/188.04 [3856]E(f329(f329(f157(x38561,f329(f329(f149(x38561),x38562),x38563)),f329(a117,x38564)),x38565),f329(f329(f149(x38561),x38562),f329(f329(f157(x38561,x38563),x38564),x38565)))
% 187.18/188.04 [3859]E(f329(f238(f878(x38591),x38592,f206(x38591),x38593),f329(f329(f16(f878(x38592),x38594),f206(x38592)),x38595)),f206(x38591))
% 187.18/188.04 [3861]E(f329(f329(f126(x38611),f329(f329(f152(x38612,x38611),x38613),x38614)),f329(f329(f152(x38612,x38611),x38613),x38615)),f329(f329(f152(x38612,x38611),x38613),f329(f329(f126(x38612),x38614),x38615)))
% 187.18/188.04 [3865]E(f329(f329(x38651,x38652),f329(f329(f255(x38653,x38654,x38651),x38652),x38655)),f329(f329(f255(x38653,x38654,x38651),x38652),f329(a117,x38655)))
% 187.18/188.04 [3895]E(f162(x38951,x38952,x38953,f329(f329(f149(x38951),x38954),x38955)),f329(f329(f126(x38952),f329(x38953,x38954)),f162(x38951,x38952,x38953,x38955)))
% 187.18/188.04 [3908]E(f329(f329(f286(x39081,x39082,x39083),f329(f284(x39082,x39081),x39084)),f329(f284(x39083,x39082),x39085)),f329(f284(x39083,x39081),f329(f329(f286(x39083,x39082,x39081),x39085),x39084)))
% 187.18/188.04 [3942]E(f329(f329(f329(f188(f875(x39421),f875(x39421)),x39422),f166(x39421)),f329(f329(f152(x39423,x39421),x39424),x39425)),f329(f329(f152(x39423,x39421),x39424),f329(f329(f329(f188(f875(x39423),f875(x39423)),x39422),f166(x39423)),x39425)))
% 187.18/188.04 [3943]E(f329(f329(f270(x39431,x39432,x39431,x39433),f329(f264(x39432,x39431),x39434)),x39435),f329(x39435,x39434))
% 187.18/188.04 [3970]E(f153(x39701,x39702,f329(f329(f152(x39703,x39701),x39704),x39705)),f153(x39703,f329(f73(x39701,a874,x39703,x39702),x39704),x39705))
% 187.18/188.04 [4035]E(f329(f329(f73(f878(x40351),f878(x40352),x40353,f329(f207(x40351,x40352),x40354)),f329(f16(f878(x40351),x40353),f206(x40351))),x40355),f206(x40352))
% 187.18/188.04 [4036]E(f176(f880(x40361,x40362),f329(f73(x40362,a869,f880(x40361,x40362),x40363),f267(x40361,x40362)),f329(f329(f181(x40361,x40362),x40364),x40365)),f329(f329(f181(x40361,x40362),x40364),f176(x40362,x40363,x40365)))
% 187.18/188.04 [4041]E(f329(f308(x40411,x40412,f329(f329(f8(x40413,x40412,x40411),x40414),x40415)),f252(f881(x40411,a869))),f329(f308(x40413,x40412,x40414),f329(f308(x40411,x40413,x40415),f252(f881(x40411,a869)))))
% 187.18/188.04 [4054]E(f176(f880(x40541,x40542),f329(f73(x40541,a869,f880(x40541,x40542),x40543),f263(x40541,x40542)),f329(f329(f181(x40541,x40542),x40544),x40545)),f329(f329(f181(x40541,x40542),f176(x40541,x40543,x40544)),x40545))
% 187.18/188.04 [4073]E(f329(f329(f115(f881(x40731,a869)),f329(f309(x40731,x40732,x40733),f329(f329(f307(x40732),x40734),f193(f881(x40732,a869))))),f329(f309(x40731,x40732,x40733),x40735)),f329(f309(x40731,x40732,x40733),f329(f329(f307(x40732),x40734),x40735)))
% 187.18/188.04 [4133]E(f329(f329(f126(f880(x41331,x41332)),f329(f329(f152(x41332,f880(x41331,x41332)),f329(f264(x41331,x41332),x41333)),x41334)),f60(x41331,x41332,x41335,x41334)),f60(x41331,x41332,f329(f329(f149(x41331),x41333),x41335),x41334))
% 187.18/188.04 [4134]E(f329(f329(f152(x41341,x41342),x41343),f176(x41341,f329(f73(x41342,a869,x41341,x41344),x41343),x41345)),f176(x41342,x41344,f329(f329(f152(x41341,x41342),x41343),x41345)))
% 187.18/188.04 [4140]E(f329(f140(x41401,x41402,f329(f7(x41402,x41401,x41401),f329(f7(x41401,x41402,x41401),x41403)),x41404),f329(f167(x41402),f329(f167(x41402),x41405))),f329(f140(x41401,x41402,x41403,x41404),x41405))
% 187.18/188.04 [4141]E(f329(f329(f329(f72(x41411,f878(x41412)),f187(x41411,x41412,x41413,x41414)),x41415),f329(x41413,x41415)),f187(x41411,x41412,x41413,f329(f329(f307(x41411),x41415),x41414)))
% 187.18/188.04 [4210]E(f329(f238(f875(x42101),x42101,f161(x42102,x42101,x42103,x42104),f329(f329(f7(x42101,f875(x42101),f875(x42101)),f149(x42101)),f161(x42102,x42101,x42103,x42104))),f329(x42103,x42105)),f161(x42102,x42101,x42103,f329(f329(f149(x42102),x42105),x42104)))
% 187.18/188.04 [4247]P24(f329(f329(f243(f881(x42471,a869)),f329(f308(x42472,x42471,x42473),f329(f329(f106(f881(x42472,a869)),x42474),x42475))),f329(f329(f106(f881(x42471,a869)),f329(f308(x42472,x42471,x42473),x42474)),f329(f308(x42472,x42471,x42473),x42475))))
% 187.18/188.04 [4248]P24(f329(f329(f243(f881(x42481,a869)),f329(f283(x42482,x42481,x42483),f329(f329(f106(f881(x42482,a869)),x42484),x42485))),f329(f329(f106(f881(x42481,a869)),f329(f283(x42482,x42481,x42483),x42484)),f329(f283(x42482,x42481,x42483),x42485))))
% 187.18/188.04 [4350]E(f329(f267(x43501,x43502),f329(f269(x43503,x43501,x43502,x43502,x43504,f34(x43502)),x43505)),f329(f267(x43503,x43502),x43505))
% 187.18/188.04 [4351]E(f329(f263(x43511,x43512),f329(f269(x43511,x43511,x43513,x43512,f34(x43511),x43514),x43515)),f329(f263(x43511,x43513),x43515))
% 187.18/188.04 [4436]E(f329(f140(f881(x44361,f878(x44362)),f880(x44361,x44362),f329(f329(f8(f881(x44361,f881(x44362,f881(x44361,f878(x44362)))),f881(f880(x44361,x44362),f881(x44361,f878(x44362))),f881(x44361,f878(x44362))),f268(x44361,x44362,f881(x44361,f878(x44362)))),f329(f329(f7(f881(x44361,f878(x44362)),f881(x44362,f878(x44362)),f881(x44361,f881(x44362,f881(x44361,f878(x44362))))),f329(f329(f8(f881(x44361,f881(f881(x44362,f878(x44362)),f881(x44362,f881(x44361,f878(x44362))))),f881(f881(x44362,f878(x44362)),f881(x44361,f881(x44362,f881(x44361,f878(x44362))))),f881(x44361,f878(x44362))),f7(x44361,f881(x44362,f878(x44362)),f881(x44362,f881(x44361,f878(x44362))))),f329(f329(f8(f881(x44361,f881(f878(x44362),f881(x44361,f878(x44362)))),f881(x44361,f881(f881(x44362,f878(x44362)),f881(x44362,f881(x44361,f878(x44362))))),f881(x44361,f878(x44362))),f329(f8(f881(f878(x44362),f881(x44361,f878(x44362))),f881(f881(x44362,f878(x44362)),f881(x44362,f881(x44361,f878(x44362)))),x44361),f8(f878(x44362),f881(x44361,f878(x44362)),x44362))),f72(x44361,f878(x44362))))),f236(x44362))),x44363),f329(f329(f181(x44361,x44362),x44364),x44365)),f186(x44361,x44362,x44363,x44364,x44365))
% 187.18/188.04 [4438]P20(x44381,x44382,f329(f329(f307(f873(x44381)),f329(f329(f329(f92(x44381),f329(f329(f7(x44381,f881(a871,a869),f881(a871,a869)),f329(f329(f8(f881(a871,f881(a869,a869)),f881(f881(a871,a869),f881(a871,a869)),x44381),f18(a871,a869,a869)),f329(f329(f8(f881(a871,a869),f881(a871,f881(a869,a869)),x44381),f329(f8(a869,f881(a869,a869),a871),a327)),x44383))),f329(f329(f8(a869,a869,a871),a324),x44384))),f32(x44384,x44385)),x44383)),f193(f881(f873(x44381),a869))))
% 187.18/188.04 [3527]E(f329(f329(f329(f329(f212(x35271),x35272),x35273),x35274),x35275),f197(x35271,x35272))
% 187.18/188.04 [3528]E(f329(f329(f329(f329(f216(x35281),x35282),x35283),x35284),x35285),f208(x35281,x35282))
% 187.18/188.04 [3572]E(f98(x35721,x35722,f329(f329(f329(f92(x35721),x35723),x35724),x35725)),f2(a874))
% 187.18/188.04 [3668]E(f329(f329(f329(f329(f72(x36681,x36682),x36683),x36684),x36685),x36684),x36685)
% 187.18/188.04 [3896]E(f329(f329(f42(x38961,f881(x38962,a869)),f329(f329(f307(x38961),x38963),x38964)),x38965),f329(f329(f115(f881(x38962,a869)),f329(x38965,x38963)),f329(f329(f42(x38961,f881(x38962,a869)),x38964),x38965)))
% 187.18/188.04 [3897]E(f329(f329(f43(x38971,f881(x38972,a869)),f329(f329(f307(x38971),x38973),x38974)),x38975),f329(f329(f106(f881(x38972,a869)),f329(x38975,x38973)),f329(f329(f43(x38971,f881(x38972,a869)),x38974),x38975)))
% 187.18/188.04 [3949]E(f329(f121(x39491,x39492,f329(x39493,x39494)),f329(f329(f7(x39491,a104,f876(x39492)),x39495),x39494)),f329(f204(x39491,x39492,x39493,x39495),x39494))
% 187.18/188.04 [3963]E(f329(f329(f115(f881(x39631,a869)),f329(f308(x39632,x39631,x39633),x39634)),f329(f308(x39632,x39631,x39633),x39635)),f329(f308(x39632,x39631,x39633),f329(f329(f115(f881(x39632,a869)),x39634),x39635)))
% 187.18/188.04 [3964]E(f329(f329(f115(f881(x39641,a869)),f329(f283(x39642,x39641,x39643),x39644)),f329(f283(x39642,x39641,x39643),x39645)),f329(f283(x39642,x39641,x39643),f329(f329(f115(f881(x39642,a869)),x39644),x39645)))
% 187.18/188.04 [3965]E(f329(f329(f115(f881(x39651,a869)),f329(f309(x39651,x39652,x39653),x39654)),f329(f309(x39651,x39652,x39653),x39655)),f329(f309(x39651,x39652,x39653),f329(f329(f115(f881(x39652,a869)),x39654),x39655)))
% 187.18/188.04 [3966]E(f329(f329(f22(f881(x39661,a869)),f329(f309(x39661,x39662,x39663),x39664)),f329(f309(x39661,x39662,x39663),x39665)),f329(f309(x39661,x39662,x39663),f329(f329(f22(f881(x39662,a869)),x39664),x39665)))
% 187.18/188.04 [3967]E(f329(f329(f106(f881(x39671,a869)),f329(f309(x39671,x39672,x39673),x39674)),f329(f309(x39671,x39672,x39673),x39675)),f329(f309(x39671,x39672,x39673),f329(f329(f106(f881(x39672,a869)),x39674),x39675)))
% 187.18/188.04 [3969]E(f187(x39691,x39692,f187(x39691,x39692,x39693,x39694),x39695),f187(x39691,x39692,x39693,f329(f329(f106(f881(x39691,a869)),x39694),x39695)))
% 187.18/188.04 [4031]E(f329(f329(f157(x40311,f329(f329(f126(x40311),x40312),f329(f329(f149(x40311),x40313),x40314))),f329(f194(f875(x40311)),x40312)),x40315),f329(f329(f126(x40311),x40312),f329(f329(f149(x40311),x40315),x40314)))
% 187.18/188.04 [4039]E(f329(f329(f43(x40391,f881(x40392,a869)),x40393),f329(f329(f8(f881(x40392,a869),f881(x40392,a869),x40391),f329(f307(x40392),x40394)),x40395)),f329(f329(f307(x40392),x40394),f329(f329(f43(x40391,f881(x40392,a869)),x40393),x40395)))
% 187.18/188.04 [4107]E(f187(x41071,x41072,f329(f329(f329(f72(x41071,f878(x41072)),x41073),x41074),f329(f236(x41072),x41075)),f329(f79(f881(x41071,a869)),f329(f329(f307(x41071),x41074),f193(f881(x41071,a869))))),f187(x41071,x41072,x41073,f329(f79(f881(x41071,a869)),f329(f329(f307(x41071),x41074),f193(f881(x41071,a869))))))
% 187.18/188.04 [4197]E(f329(f329(f152(x41971,x41972),x41973),f329(f134(x41971,f329(f73(x41972,a869,x41971,x41974),x41973)),x41975)),f329(f134(x41972,x41974),f329(f329(f152(x41971,x41972),x41973),x41975)))
% 187.18/188.04 [4203]E(f329(f194(f875(x42031)),f329(f134(x42031,x42032),f329(f329(f152(x42033,x42031),x42034),x42035))),f329(f194(f875(x42033)),f329(f134(x42033,f329(f73(x42031,a869,x42033,x42032),x42034)),x42035)))
% 187.18/188.04 [4342]E(f329(f329(f115(f881(x43421,a869)),f329(f329(f22(f881(x43421,a869)),f183(x43421,x43422,x43423)),f329(f249(x43421),f329(f329(f7(x43421,f881(x43421,a869),a869),f331(x43421)),f329(f329(f22(f881(x43421,a869)),x43424),f183(x43421,x43422,x43425)))))),f329(f249(x43421),f329(f329(f7(x43421,f881(x43421,a869),a869),f331(x43421)),f329(f329(f106(f881(x43421,a869)),x43424),f183(x43421,x43422,x43425))))),f183(x43421,x43422,f76(x43421,f878(x43422),x43423,x43425,x43424)))
% 187.18/188.04 [4417]E(f329(f154(f875(f880(x44171,x44172)),x44172,f118(f880(x44171,x44172)),f329(f329(f7(x44172,f881(f875(x44172),f875(f880(x44171,x44172))),f881(f875(x44172),f875(f880(x44171,x44172)))),f329(f329(f8(f881(f875(f880(x44171,x44172)),f875(f880(x44171,x44172))),f881(f881(f875(x44172),f875(f880(x44171,x44172))),f881(f875(x44172),f875(f880(x44171,x44172)))),x44172),f8(f875(f880(x44171,x44172)),f875(f880(x44171,x44172)),f875(x44172))),f329(f329(f8(f880(x44171,x44172),f881(f875(f880(x44171,x44172)),f875(f880(x44171,x44172))),x44172),f149(f880(x44171,x44172))),f329(f264(x44171,x44172),x44173)))),f329(f181(x44171,x44172),x44174))),x44175),f329(f329(f181(x44171,x44172),f329(f329(f149(x44171),x44173),x44174)),x44175))
% 187.18/188.04 [3890]E(f329(f329(f157(x38901,f329(f329(f157(x38901,x38902),x38903),x38904)),x38903),x38905),f329(f329(f157(x38901,x38902),x38903),x38905))
% 187.18/188.04 [3944]E(f329(f260(x39441,x39442),f329(f329(f307(f880(x39441,x39442)),f329(f329(f264(x39441,x39442),x39443),x39444)),x39445)),f329(f329(f307(x39442),x39444),f329(f260(x39441,x39442),x39445)))
% 187.18/188.04 [3945]E(f329(f262(x39451,x39452),f329(f329(f307(f880(x39451,x39452)),f329(f329(f264(x39451,x39452),x39453),x39454)),x39455)),f329(f329(f307(x39451),x39453),f329(f262(x39451,x39452),x39455)))
% 187.18/188.04 [3994]E(f124(x39941,x39942,f329(x39943,x39944),f329(f329(f7(x39941,a104,f876(f878(x39942))),x39945),x39944)),f329(f202(x39941,x39942,x39943,x39945),x39944))
% 187.18/188.04 [4024]E(f329(f329(f115(f881(f880(x40241,x40242),a869)),f329(f329(f266(x40241,x40242),x40243),x40244)),f329(f329(f266(x40241,x40242),x40245),x40244)),f329(f329(f266(x40241,x40242),f329(f329(f115(f881(x40241,a869)),x40243),x40245)),x40244))
% 187.18/188.04 [4025]E(f329(f329(f22(f881(f880(x40251,x40252),a869)),f329(f329(f266(x40251,x40252),x40253),x40254)),f329(f329(f266(x40251,x40252),x40255),x40254)),f329(f329(f266(x40251,x40252),f329(f329(f22(f881(x40251,a869)),x40253),x40255)),x40254))
% 187.18/188.04 [4026]E(f329(f329(f106(f881(f880(x40261,x40262),a869)),f329(f329(f266(x40261,x40262),x40263),x40264)),f329(f329(f266(x40261,x40262),x40265),x40264)),f329(f329(f266(x40261,x40262),f329(f329(f106(f881(x40261,a869)),x40263),x40265)),x40264))
% 187.18/188.04 [4085]E(f329(f329(f115(f881(x40851,a869)),f329(f329(f42(x40852,f881(x40851,a869)),x40853),x40854)),f329(f329(f42(x40852,f881(x40851,a869)),x40855),x40854)),f329(f329(f42(x40852,f881(x40851,a869)),f329(f329(f115(f881(x40852,a869)),x40853),x40855)),x40854))
% 187.18/188.04 [4086]E(f329(f329(f106(f881(x40861,a869)),f329(f329(f43(x40862,f881(x40861,a869)),x40863),x40864)),f329(f329(f43(x40862,f881(x40861,a869)),x40865),x40864)),f329(f329(f43(x40862,f881(x40861,a869)),f329(f329(f115(f881(x40862,a869)),x40863),x40865)),x40864))
% 187.18/188.04 [4100]E(f329(f329(f42(x41001,f881(x41002,a869)),x41003),f329(f329(f8(f881(x41002,a869),f881(x41002,a869),x41001),f329(f22(f881(x41002,a869)),x41004)),x41005)),f329(f329(f22(f881(x41002,a869)),x41004),f329(f329(f43(x41001,f881(x41002,a869)),x41003),x41005)))
% 187.18/188.04 [4101]E(f329(f329(f42(x41011,f881(x41012,a869)),x41013),f329(f329(f8(f881(x41012,a869),f881(x41012,a869),x41011),f329(f106(f881(x41012,a869)),x41014)),x41015)),f329(f329(f106(f881(x41012,a869)),x41014),f329(f329(f42(x41011,f881(x41012,a869)),x41013),x41015)))
% 187.18/188.04 [4102]E(f329(f329(f43(x41021,f881(x41022,a869)),x41023),f329(f329(f8(f881(x41022,a869),f881(x41022,a869),x41021),f329(f115(f881(x41022,a869)),x41024)),x41025)),f329(f329(f115(f881(x41022,a869)),x41024),f329(f329(f43(x41021,f881(x41022,a869)),x41023),x41025)))
% 187.18/188.04 [4139]E(f184(x41391,x41392,x41393,f329(f177(x41391,x41392),f329(f167(f880(x41391,x41392)),f329(f329(f181(x41391,x41392),x41394),x41395)))),f186(x41391,x41392,x41393,x41394,x41395))
% 187.18/188.04 [4161]E(f190(f875(x41611),f329(f329(f149(x41611),x41612),x41613),f329(f329(f8(f875(x41611),f875(x41611),a874),f329(f149(x41611),x41614)),f329(f329(f7(a874,x41611,f875(x41611)),f157(x41611,x41613)),x41612)),x41615),f329(f329(f157(x41611,f329(f329(f149(x41611),x41614),x41613)),x41615),x41612))
% 187.18/188.04 [4165]E(f329(f329(f42(x41651,f881(f880(x41652,x41653),a869)),x41654),f329(f329(f8(f881(f880(x41653,x41652),a869),f881(f880(x41652,x41653),a869),x41651),f284(x41653,x41652)),x41655)),f329(f284(x41653,x41652),f329(f329(f42(x41651,f881(f880(x41653,x41652),a869)),x41654),x41655)))
% 187.18/188.04 [4166]E(f329(f329(f43(x41661,f881(f880(x41662,x41663),a869)),x41664),f329(f329(f8(f881(f880(x41663,x41662),a869),f881(f880(x41662,x41663),a869),x41661),f284(x41663,x41662)),x41665)),f329(f284(x41663,x41662),f329(f329(f43(x41661,f881(f880(x41663,x41662),a869)),x41664),x41665)))
% 187.18/188.04 [4221]E(f183(x42211,x42212,f329(f329(f18(x42211,f878(x42213),f878(x42212)),f329(f329(f8(f881(x42213,x42212),f881(f878(x42213),f878(x42212)),x42211),f207(x42213,x42212)),x42214)),x42215)),f183(x42211,x42213,x42215))
% 187.18/188.04 [4272]P24(f329(f329(f243(f881(x42721,a869)),f329(f329(f22(f881(x42721,a869)),f329(f308(x42722,x42721,x42723),x42724)),f329(f308(x42722,x42721,x42723),x42725))),f329(f308(x42722,x42721,x42723),f329(f329(f22(f881(x42722,a869)),x42724),x42725))))
% 187.18/188.04 [4421]E(f329(f154(f875(f880(x44211,x44212)),x44211,f118(f880(x44211,x44212)),f329(f329(f7(x44211,f881(f875(x44211),f875(f880(x44211,x44212))),f881(f875(x44211),f875(f880(x44211,x44212)))),f329(f329(f8(f881(f875(f880(x44211,x44212)),f875(f880(x44211,x44212))),f881(f881(f875(x44211),f875(f880(x44211,x44212))),f881(f875(x44211),f875(f880(x44211,x44212)))),x44211),f8(f875(f880(x44211,x44212)),f875(f880(x44211,x44212)),f875(x44211))),f329(f329(f8(f880(x44211,x44212),f881(f875(f880(x44211,x44212)),f875(f880(x44211,x44212))),x44211),f149(f880(x44211,x44212))),f329(f329(f7(x44211,x44212,f880(x44211,x44212)),f264(x44211,x44212)),x44213)))),f329(f329(f7(f875(x44211),f875(x44212),f875(f880(x44211,x44212))),f181(x44211,x44212)),x44214))),x44215),f329(f329(f181(x44211,x44212),x44215),f329(f329(f149(x44212),x44213),x44214)))
% 187.18/188.04 [4127]E(f329(f329(f115(f881(x41271,a869)),f329(f283(x41272,x41271,x41273),x41274)),f329(f283(x41272,x41271,x41275),x41274)),f329(f283(x41272,x41271,f329(f329(f115(f881(f880(x41272,x41271),a869)),x41273),x41275)),x41274))
% 187.18/188.04 [4168]E(f329(f329(f126(f880(x41681,x41682)),f329(f329(f181(x41681,x41682),x41683),f329(f329(f174(x41682),f329(f194(f875(x41681)),x41683)),x41684))),f329(f329(f181(x41681,x41682),x41685),f329(f329(f136(x41682),f329(f194(f875(x41681)),x41683)),x41684))),f329(f329(f181(x41681,x41682),f329(f329(f126(x41681),x41683),x41685)),x41684))
% 187.18/188.04 [4275]E(f329(f329(f266(x42751,x42752),x42753),f329(f329(f18(x42751,f881(x42752,a869),f881(x42752,a869)),f329(f329(f8(f881(x42752,a869),f881(f881(x42752,a869),f881(x42752,a869)),x42751),f115(f881(x42752,a869))),x42754)),x42755)),f329(f329(f115(f881(f880(x42751,x42752),a869)),f329(f329(f266(x42751,x42752),x42753),x42754)),f329(f329(f266(x42751,x42752),x42753),x42755)))
% 187.18/188.04 [4276]E(f329(f329(f266(x42761,x42762),x42763),f329(f329(f18(x42761,f881(x42762,a869),f881(x42762,a869)),f329(f329(f8(f881(x42762,a869),f881(f881(x42762,a869),f881(x42762,a869)),x42761),f22(f881(x42762,a869))),x42764)),x42765)),f329(f329(f22(f881(f880(x42761,x42762),a869)),f329(f329(f266(x42761,x42762),x42763),x42764)),f329(f329(f266(x42761,x42762),x42763),x42765)))
% 187.18/188.04 [4277]E(f329(f329(f266(x42771,x42772),x42773),f329(f329(f18(x42771,f881(x42772,a869),f881(x42772,a869)),f329(f329(f8(f881(x42772,a869),f881(f881(x42772,a869),f881(x42772,a869)),x42771),f106(f881(x42772,a869))),x42774)),x42775)),f329(f329(f106(f881(f880(x42771,x42772),a869)),f329(f329(f266(x42771,x42772),x42773),x42774)),f329(f329(f266(x42771,x42772),x42773),x42775)))
% 187.18/188.04 [4281]E(f329(f329(f42(x42811,f881(x42812,a869)),x42813),f329(f329(f7(x42811,f881(x42812,a869),f881(x42812,a869)),f329(f329(f8(f881(x42812,a869),f881(f881(x42812,a869),f881(x42812,a869)),x42811),f22(f881(x42812,a869))),x42814)),x42815)),f329(f329(f22(f881(x42812,a869)),f329(f329(f42(x42811,f881(x42812,a869)),x42813),x42814)),x42815))
% 187.18/188.04 [4282]E(f329(f329(f42(x42821,f881(x42822,a869)),x42823),f329(f329(f7(x42821,f881(x42822,a869),f881(x42822,a869)),f329(f329(f8(f881(x42822,a869),f881(f881(x42822,a869),f881(x42822,a869)),x42821),f106(f881(x42822,a869))),x42824)),x42825)),f329(f329(f106(f881(x42822,a869)),f329(f329(f42(x42821,f881(x42822,a869)),x42823),x42824)),x42825))
% 187.18/188.04 [4283]E(f329(f329(f43(x42831,f881(x42832,a869)),x42833),f329(f329(f7(x42831,f881(x42832,a869),f881(x42832,a869)),f329(f329(f8(f881(x42832,a869),f881(f881(x42832,a869),f881(x42832,a869)),x42831),f115(f881(x42832,a869))),x42834)),x42835)),f329(f329(f115(f881(x42832,a869)),f329(f329(f43(x42831,f881(x42832,a869)),x42833),x42834)),x42835))
% 187.18/188.04 [4287]E(f329(f329(f42(x42871,f881(x42872,a869)),x42873),f329(f329(f18(x42871,f881(x42872,a869),f881(x42872,a869)),f329(f329(f8(f881(x42872,a869),f881(f881(x42872,a869),f881(x42872,a869)),x42871),f115(f881(x42872,a869))),x42874)),x42875)),f329(f329(f115(f881(x42872,a869)),f329(f329(f42(x42871,f881(x42872,a869)),x42873),x42874)),f329(f329(f42(x42871,f881(x42872,a869)),x42873),x42875)))
% 187.18/188.04 [4288]E(f329(f329(f43(x42881,f881(x42882,a869)),x42883),f329(f329(f18(x42881,f881(x42882,a869),f881(x42882,a869)),f329(f329(f8(f881(x42882,a869),f881(f881(x42882,a869),f881(x42882,a869)),x42881),f106(f881(x42882,a869))),x42884)),x42885)),f329(f329(f106(f881(x42882,a869)),f329(f329(f43(x42881,f881(x42882,a869)),x42883),x42884)),f329(f329(f43(x42881,f881(x42882,a869)),x42883),x42885)))
% 187.18/188.04 [4302]E(f329(f329(f42(x43021,f881(x43022,a869)),x43023),f329(f329(f18(x43021,f881(x43022,a869),f881(x43022,a869)),f329(f329(f8(f881(x43022,a869),f881(f881(x43022,a869),f881(x43022,a869)),x43021),f115(f881(x43022,a869))),x43024)),x43025)),f329(f329(f115(f881(x43022,a869)),f40(f881(x43022,a869),f329(f308(x43021,f881(x43022,a869),x43024),x43023))),f40(f881(x43022,a869),f329(f308(x43021,f881(x43022,a869),x43025),x43023))))
% 187.18/188.04 [4303]E(f329(f329(f43(x43031,f881(x43032,a869)),x43033),f329(f329(f18(x43031,f881(x43032,a869),f881(x43032,a869)),f329(f329(f8(f881(x43032,a869),f881(f881(x43032,a869),f881(x43032,a869)),x43031),f106(f881(x43032,a869))),x43034)),x43035)),f329(f329(f106(f881(x43032,a869)),f41(f881(x43032,a869),f329(f308(x43031,f881(x43032,a869),x43034),x43033))),f41(f881(x43032,a869),f329(f308(x43031,f881(x43032,a869),x43035),x43033))))
% 187.18/188.04 [4338]E(f329(f329(f136(x43381),f329(f194(f875(x43381)),f176(x43381,x43382,f329(f329(f152(x43383,x43381),x43384),x43385)))),f329(f329(f152(x43383,x43381),x43384),x43385)),f329(f329(f152(x43383,x43381),x43384),f329(f329(f136(x43383),f329(f194(f875(x43383)),f176(x43383,f329(f73(x43381,a869,x43383,x43382),x43384),x43385))),x43385)))
% 187.18/188.04 [4211]E(f329(f329(f126(f880(x42111,x42112)),f329(f329(f181(x42111,x42112),f329(f329(f174(x42111),f329(f194(f875(x42112)),x42113)),x42114)),x42113)),f329(f329(f181(x42111,x42112),f329(f329(f136(x42111),f329(f194(f875(x42112)),x42113)),x42114)),x42115)),f329(f329(f181(x42111,x42112),x42114),f329(f329(f126(x42112),x42113),x42115)))
% 187.18/188.04 [4330]E(f85(x43301,f329(f329(f18(x43301,a869,a869),f329(f329(f8(a869,f881(a869,a869),x43301),a327),f329(f329(f7(x43301,f881(x43301,a869),a869),f331(x43301)),x43302))),f329(f329(f7(x43301,x43303,a869),f329(f329(f8(x43303,f881(x43303,a869),x43301),a326),x43304)),x43305))),f329(f77(x43301,x43303,x43302,x43304),x43305))
% 187.18/188.04 [4382]E(f329(f329(f86(a1,x43821),f329(f108(a1),f329(f329(f80(a1),x43822),a102))),f329(f329(f18(a1,x43821,x43821),f329(f329(f7(a1,x43821,f881(x43821,x43821)),f329(f329(f8(a869,f881(x43821,f881(x43821,x43821)),a1),f101(x43821)),a198)),f190(x43821,x43823,x43824,x43825))),f329(f329(f8(a874,x43821,a1),x43824),f329(f329(f7(a1,a874,a874),f329(f329(f8(a874,f881(a874,a874),a1),f80(a874)),a109)),x43825)))),f190(x43821,x43823,x43824,f329(f329(f80(a874),f329(f108(a874),x43822)),x43825)))
% 187.18/188.04 [4418]E(f329(f177(x44181,x44182),f329(f329(f152(f880(x44181,x44183),f880(x44181,x44182)),f329(f268(x44181,x44183,f880(x44181,x44182)),f329(f329(f7(x44181,f881(x44183,x44182),f881(x44183,f880(x44181,x44182))),f329(f329(f8(f881(x44182,f880(x44181,x44182)),f881(f881(x44183,x44182),f881(x44183,f880(x44181,x44182))),x44181),f8(x44182,f880(x44181,x44182),x44183)),f264(x44181,x44182))),x44184))),x44185)),f329(f73(f878(x44183),f878(x44182),x44181,f329(f207(x44183,x44182),x44184)),f329(f177(x44181,x44183),x44185)))
% 187.18/188.04 [4375]E(f183(x43751,x43752,f329(f329(f18(x43751,f878(x43752),f878(x43752)),f329(f329(f18(x43751,f878(x43752),f881(f878(x43752),f878(x43752))),f329(f329(f8(a869,f881(f878(x43752),f881(f878(x43752),f878(x43752))),x43751),f101(f878(x43752))),x43753)),x43754)),x43755)),f329(f329(f115(f881(x43751,a869)),f329(f329(f106(f881(x43751,a869)),f183(x43751,x43752,x43754)),f329(f249(x43751),x43753))),f329(f329(f106(f881(x43751,a869)),f183(x43751,x43752,x43755)),f329(f249(x43751),f329(f329(f8(a869,a869,x43751),a324),x43753)))))
% 187.18/188.04 [4416]E(f329(f329(f86(a1,x44161),f329(f108(a1),f329(f329(f80(a1),x44162),a102))),f329(f329(f18(a1,x44161,x44161),f329(f329(f7(a1,x44161,f881(x44161,x44161)),f329(f329(f8(a869,f881(x44161,f881(x44161,x44161)),a1),f101(x44161)),a198)),f329(f189(x44161,x44163,x44164),x44165))),f329(f329(f18(a1,x44161,x44161),f329(f329(f8(a874,f881(x44161,x44161),a1),x44164),f329(f329(f7(a1,a874,a874),f329(f329(f8(a874,f881(a874,a874),a1),f80(a874)),a109)),x44165))),f329(f329(f8(a874,x44161,a1),f189(x44161,x44163,x44164)),f329(f329(f7(a1,a874,a874),f329(f329(f8(a874,f881(a874,a874),a1),f80(a874)),a109)),x44165))))),f329(f189(x44161,x44163,x44164),f329(f329(f80(a874),f329(f108(a874),x44162)),x44165)))
% 187.18/188.04 [4450]E(f329(f249(f880(x44501,x44502)),f329(f268(x44501,x44502,a869),f329(f329(f8(f881(x44502,f881(x44503,a869)),f881(x44502,a869),x44501),f329(f8(f881(x44503,a869),a869,x44502),f87(x44503))),f329(f329(f7(x44501,f881(x44502,f881(x44503,a869)),f881(x44502,f881(x44503,a869))),f329(f329(f8(f881(f881(x44503,a869),f881(x44503,a869)),f881(f881(x44502,f881(x44503,a869)),f881(x44502,f881(x44503,a869))),x44501),f8(f881(x44503,a869),f881(x44503,a869),x44502)),f329(f329(f8(f881(x44503,f881(a869,a869)),f881(f881(x44503,a869),f881(x44503,a869)),x44501),f18(x44503,a869,a869)),f329(f329(f8(f881(x44503,a869),f881(x44503,f881(a869,a869)),x44501),f329(f8(a869,f881(a869,a869),x44503),a327)),f329(f329(f7(x44501,f881(f880(x44501,x44503),a869),f881(x44503,a869)),f329(f329(f8(f881(x44503,f881(f881(f880(x44501,x44503),a869),a869)),f881(f881(f880(x44501,x44503),a869),f881(x44503,a869)),x44501),f7(x44503,f881(f880(x44501,x44503),a869),a869)),f329(f329(f8(f881(x44503,f880(x44501,x44503)),f881(x44503,f881(f881(f880(x44501,x44503),a869),a869)),x44501),f329(f8(f880(x44501,x44503),f881(f881(f880(x44501,x44503),a869),a869),x44503),f331(f880(x44501,x44503)))),f264(x44501,x44503)))),x44504))))),f329(f329(f7(x44502,f881(f880(x44503,x44502),a869),f881(x44503,a869)),f329(f329(f8(f881(x44503,f881(f881(f880(x44503,x44502),a869),a869)),f881(f881(f880(x44503,x44502),a869),f881(x44503,a869)),x44502),f7(x44503,f881(f880(x44503,x44502),a869),a869)),f329(f329(f8(f881(x44503,f880(x44503,x44502)),f881(x44503,f881(f881(f880(x44503,x44502),a869),a869)),x44502),f329(f8(f880(x44503,x44502),f881(f881(f880(x44503,x44502),a869),a869),x44503),f331(f880(x44503,x44502)))),f329(f7(x44503,x44502,f880(x44503,x44502)),f264(x44503,x44502))))),x44505))))),f329(f329(f286(x44501,x44503,x44502),x44504),x44505))
% 187.18/188.04 [4526]~E(f29(x45261,x45262,x45263),f30(x45264,x45265,x45266))
% 187.18/188.04 [3979]E(f131(x39791,x39792,x39793,x39794,f128(x39792,x39795,x39796)),f329(f329(x39794,x39795),x39796))
% 187.18/188.04 [4195]E(f186(x41951,x41952,f184(x41951,x41952,x41953,x41954),x41955,x41956),f184(x41951,x41952,x41953,f186(x41951,x41952,x41954,x41955,x41956)))
% 187.18/188.04 [4318]E(f329(f73(f880(x43181,x43182),x43182,f880(x43183,x43184),f267(x43181,x43182)),f269(x43183,x43181,x43184,x43182,x43185,x43186)),f329(f73(x43184,x43182,f880(x43183,x43184),x43186),f267(x43183,x43184)))
% 187.18/188.04 [4319]E(f329(f73(f880(x43191,x43192),x43191,f880(x43193,x43194),f263(x43191,x43192)),f269(x43193,x43191,x43194,x43192,x43195,x43196)),f329(f73(x43193,x43191,f880(x43193,x43194),x43195),f263(x43193,x43194)))
% 187.18/188.04 [3919]E(f329(f329(f73(x39191,x39192,x39193,x39194),x39195),x39196),f329(x39194,f329(x39195,x39196)))
% 187.18/188.04 [3715]E(f329(f329(f268(x37151,x37152,x37153),x37154),f329(f329(f264(x37151,x37152),x37155),x37156)),f329(f329(x37154,x37155),x37156))
% 187.18/188.04 [3775]E(f329(f329(f329(f8(x37751,x37752,x37753),x37754),x37755),x37756),f329(x37754,f329(x37755,x37756)))
% 187.18/188.04 [3776]E(f329(f329(f329(f7(x37761,x37762,x37763),x37764),x37765),x37766),f329(f329(x37764,x37766),x37765))
% 187.18/188.04 [3793]E(f329(f329(f329(f18(x37931,x37932,x37933),x37934),x37935),x37936),f329(f329(x37934,x37936),f329(x37935,x37936)))
% 187.18/188.04 [3815]E(f329(f154(x38151,x38152,x38153,x38154),f329(f329(f149(x38152),x38155),x38156)),f329(f329(x38154,x38155),x38156))
% 187.18/188.04 [3855]E(f169(f880(x38551,x38552),f329(f329(f241(a874),x38553),x38554),f329(f329(f264(x38551,x38552),x38555),x38556)),f329(f329(f181(x38551,x38552),f169(x38551,x38553,x38555)),f169(x38552,x38554,x38556)))
% 187.18/188.04 [3923]E(f329(f329(f149(f880(x39231,x39232)),f329(f329(f264(x39231,x39232),x39233),x39234)),f329(f329(f181(x39231,x39232),x39235),x39236)),f329(f329(f181(x39231,x39232),f329(f329(f149(x39231),x39233),x39235)),f329(f329(f149(x39232),x39234),x39236)))
% 187.18/188.04 [3925]E(f329(f329(f152(x39251,x39252),x39253),f329(f329(f157(x39251,x39254),x39255),x39256)),f329(f329(f157(x39252,f329(f329(f152(x39251,x39252),x39253),x39254)),x39255),f329(x39253,x39256)))
% 187.18/188.04 [3968]E(f329(f140(x39681,x39682,x39683,x39684),f329(f329(f149(x39682),x39685),x39686)),f329(f140(x39681,x39682,x39683,f329(f329(x39683,x39684),x39685)),x39686))
% 187.18/188.04 [3995]E(f271(x39951,x39952,x39953,x39954,f329(f329(f264(x39951,x39952),x39955),x39956)),f329(f329(x39954,x39955),x39956))
% 187.18/188.04 [4078]E(f329(f329(f42(x40781,f881(x40782,a869)),x40783),f329(f73(x40784,f881(x40782,a869),x40781,x40785),x40786)),f329(f329(f42(x40784,f881(x40782,a869)),f329(f308(x40781,x40784,x40786),x40783)),x40785))
% 187.18/188.04 [4130]E(f329(f329(f152(x41301,x41302),x41303),f329(f329(f152(x41304,x41301),x41305),x41306)),f329(f329(f152(x41304,x41302),f329(f73(x41301,x41302,x41304,x41303),x41305)),x41306))
% 187.18/188.04 [4132]E(f329(f329(f207(x41321,x41322),x41323),f329(f329(f207(x41324,x41321),x41325),x41326)),f329(f329(f207(x41324,x41322),f329(f73(x41321,x41322,x41324,x41323),x41325)),x41326))
% 187.18/188.04 [4137]E(f329(f308(x41371,x41372,f329(f73(x41373,x41372,x41371,x41374),x41375)),x41376),f329(f308(x41373,x41372,x41374),f329(f308(x41371,x41373,x41375),x41376)))
% 187.18/188.04 [4138]E(f329(f309(x41381,x41382,f329(f73(x41383,x41382,x41381,x41384),x41385)),x41386),f329(f309(x41381,x41383,x41385),f329(f309(x41383,x41382,x41384),x41386)))
% 187.18/188.04 [4167]E(f184(x41671,x41672,x41673,f329(f329(f329(f72(x41671,f878(x41672)),x41674),x41675),f329(f236(x41672),x41676))),f329(f329(f329(f72(x41671,f878(x41672)),f184(x41671,x41672,x41673,x41674)),x41675),f329(f236(x41672),x41676)))
% 187.18/188.04 [4169]E(f329(f140(x41691,x41692,x41693,f329(f140(x41691,x41692,x41693,x41694),x41695)),x41696),f329(f140(x41691,x41692,x41693,x41694),f329(f329(f126(x41692),x41695),x41696)))
% 187.18/188.04 [4308]E(f329(f269(x43081,x43081,x43082,x43083,f34(x43081),x43084),f329(f329(f264(x43081,x43082),x43085),x43086)),f329(f329(f264(x43081,x43083),x43085),f329(x43084,x43086)))
% 187.18/188.04 [4309]E(f329(f269(x43091,x43092,x43093,x43093,x43094,f34(x43093)),f329(f329(f264(x43091,x43093),x43095),x43096)),f329(f329(f264(x43092,x43093),f329(x43094,x43095)),x43096))
% 187.18/188.04 [4400]E(f329(f329(f152(f880(x44001,x44002),f880(x44001,x44003)),f329(f268(x44001,x44002,f880(x44001,x44003)),f329(f329(f7(x44001,f881(x44002,x44003),f881(x44002,f880(x44001,x44003))),f329(f329(f8(f881(x44003,f880(x44001,x44003)),f881(f881(x44002,x44003),f881(x44002,f880(x44001,x44003))),x44001),f8(x44003,f880(x44001,x44003),x44002)),f264(x44001,x44003))),x44004))),f329(f329(f181(x44001,x44002),x44005),x44006)),f329(f329(f181(x44001,x44003),x44005),f329(f329(f152(x44002,x44003),x44004),x44006)))
% 187.18/188.04 [3780]E(f99(x37801,x37802,x37803,f329(f329(f329(f92(x37801),x37804),x37805),x37806)),f329(f329(f329(x37803,x37804),x37805),x37806))
% 187.18/188.04 [3781]E(f100(x37811,x37812,x37813,f329(f329(f329(f92(x37811),x37814),x37815),x37816)),f329(f329(f329(x37813,x37814),x37815),x37816))
% 187.18/188.04 [3978]E(f329(f329(f73(x39781,x39782,x39783,f329(f16(x39782,x39781),x39784)),x39785),x39786),x39784)
% 187.18/188.04 [4014]E(f329(f308(x40141,x40142,x40143),f329(f308(x40144,x40141,x40145),x40146)),f329(f308(x40144,x40142,f329(f329(f8(x40141,x40142,x40144),x40143),x40145)),x40146))
% 187.18/188.04 [4020]E(f329(f329(f42(x40201,f881(x40202,a869)),f329(f308(x40203,x40201,x40204),x40205)),x40206),f329(f329(f42(x40203,f881(x40202,a869)),x40205),f329(f329(f8(x40201,f881(x40202,a869),x40203),x40206),x40204)))
% 187.18/188.04 [4021]E(f329(f329(f43(x40211,f881(x40212,a869)),f329(f308(x40213,x40211,x40214),x40215)),x40216),f329(f329(f43(x40213,f881(x40212,a869)),x40215),f329(f329(f8(x40211,f881(x40212,a869),x40213),x40216),x40214)))
% 187.18/188.04 [4022]E(f329(f329(f42(x40221,f881(x40222,a869)),x40223),f329(f329(f8(x40224,f881(x40222,a869),x40221),x40225),x40226)),f329(f329(f42(x40224,f881(x40222,a869)),f329(f308(x40221,x40224,x40226),x40223)),x40225))
% 187.18/188.04 [4023]E(f329(f329(f43(x40231,f881(x40232,a869)),x40233),f329(f329(f8(x40234,f881(x40232,a869),x40231),x40235),x40236)),f329(f329(f43(x40234,f881(x40232,a869)),f329(f308(x40231,x40234,x40236),x40233)),x40235))
% 187.18/188.04 [4080]E(f329(f329(f42(x40801,f881(x40802,a869)),x40803),f329(f329(f8(f881(x40804,a869),f881(x40802,a869),x40801),f308(x40804,x40802,x40805)),x40806)),f329(f308(x40804,x40802,x40805),f329(f329(f42(x40801,f881(x40804,a869)),x40803),x40806)))
% 187.18/188.04 [4081]E(f329(f329(f42(x40811,f881(x40812,a869)),x40813),f329(f329(f8(f881(x40814,a869),f881(x40812,a869),x40811),f283(x40814,x40812,x40815)),x40816)),f329(f283(x40814,x40812,x40815),f329(f329(f42(x40811,f881(x40814,a869)),x40813),x40816)))
% 187.18/188.04 [4082]E(f329(f329(f42(x40821,f881(x40822,a869)),x40823),f329(f329(f8(f881(x40824,a869),f881(x40822,a869),x40821),f309(x40822,x40824,x40825)),x40826)),f329(f309(x40822,x40824,x40825),f329(f329(f42(x40821,f881(x40824,a869)),x40823),x40826)))
% 187.18/188.04 [4083]E(f329(f329(f43(x40831,f881(x40832,a869)),x40833),f329(f329(f8(f881(x40834,a869),f881(x40832,a869),x40831),f309(x40832,x40834,x40835)),x40836)),f329(f309(x40832,x40834,x40835),f329(f329(f43(x40831,f881(x40834,a869)),x40833),x40836)))
% 187.18/188.04 [4175]E(f329(f140(x41751,x41752,f329(f7(x41752,x41751,x41751),x41753),x41754),f329(f167(x41752),f329(f329(f149(x41752),x41755),x41756))),f329(f329(x41753,x41755),f329(f140(x41751,x41752,f329(f7(x41752,x41751,x41751),x41753),x41754),f329(f167(x41752),x41756))))
% 187.18/188.04 [4234]E(f329(f329(f18(f880(x42341,x42342),x42342,x42343),f329(f329(f8(x42344,f881(x42342,x42343),f880(x42341,x42342)),x42345),f329(f329(f8(x42341,x42344,f880(x42341,x42342)),x42346),f263(x42341,x42342)))),f267(x42341,x42342)),f329(f268(x42341,x42342,x42343),f329(f329(f8(x42344,f881(x42342,x42343),x42341),x42345),x42346)))
% 187.18/188.04 [4241]E(f329(f140(x42411,x42412,f329(f7(x42412,x42411,x42411),x42413),f329(f140(x42411,x42412,f329(f7(x42412,x42411,x42411),x42413),x42414),f329(f167(x42412),x42415))),f329(f167(x42412),x42416)),f329(f140(x42411,x42412,f329(f7(x42412,x42411,x42411),x42413),x42414),f329(f167(x42412),f329(f329(f126(x42412),x42416),x42415))))
% 187.18/188.04 [4243]E(f329(f329(f152(f880(x42431,x42432),f880(x42433,x42432)),f329(f268(x42431,x42432,f880(x42433,x42432)),f329(f329(f8(x42433,f881(x42432,f880(x42433,x42432)),x42431),f264(x42433,x42432)),x42434))),f329(f329(f181(x42431,x42432),x42435),x42436)),f329(f329(f181(x42433,x42432),f329(f329(f152(x42431,x42433),x42434),x42435)),x42436))
% 187.18/188.04 [4291]P24(f329(f329(f243(f881(x42911,a869)),f329(f283(x42912,x42911,x42913),f329(f329(f43(x42914,f881(x42912,a869)),x42915),x42916))),f329(f329(f43(x42914,f881(x42911,a869)),x42915),f329(f329(f8(f881(x42912,a869),f881(x42911,a869),x42914),f283(x42912,x42911,x42913)),x42916))))
% 187.18/188.04 [4093]E(f329(f329(f181(x40931,x40932),f329(f329(f157(x40931,x40933),x40934),f329(f263(x40931,x40932),x40935))),f329(f329(f157(x40932,x40936),x40934),f329(f267(x40931,x40932),x40935))),f329(f329(f157(f880(x40931,x40932),f329(f329(f181(x40931,x40932),x40933),x40936)),x40934),x40935))
% 187.18/188.04 [4156]E(f329(f329(f115(f881(f880(x41561,x41562),a869)),f329(f329(f286(x41561,x41563,x41562),x41564),x41565)),f329(f329(f286(x41561,x41563,x41562),x41564),x41566)),f329(f329(f286(x41561,x41563,x41562),x41564),f329(f329(f115(f881(f880(x41563,x41562),a869)),x41565),x41566)))
% 187.18/188.04 [4254]E(f329(f329(f307(f880(x42541,x42542)),f329(f329(f264(x42541,x42542),x42543),x42544)),f329(f329(f115(f881(f880(x42541,x42542),a869)),f329(f329(f266(x42541,x42542),x42545),f329(f16(f881(x42542,a869),x42541),f329(f329(f307(x42542),x42544),x42546)))),f329(f329(f266(x42541,x42542),f329(f329(f307(x42541),x42543),x42545)),f329(f16(f881(x42542,a869),x42541),x42546)))),f329(f329(f266(x42541,x42542),f329(f329(f307(x42541),x42543),x42545)),f329(f16(f881(x42542,a869),x42541),f329(f329(f307(x42542),x42544),x42546))))
% 187.18/188.04 [4333]E(f329(f329(f106(f881(x43331,a869)),f329(f309(x43331,x43332,f329(f73(f880(x43332,x43333),x43332,x43331,f263(x43332,x43333)),x43334)),x43335)),f329(f309(x43331,x43333,f329(f73(f880(x43332,x43333),x43333,x43331,f267(x43332,x43333)),x43334)),x43336)),f329(f309(x43331,f880(x43332,x43333),x43334),f329(f329(f266(x43332,x43333),x43335),f329(f16(f881(x43333,a869),x43332),x43336))))
% 187.18/188.04 [4077]E(f329(f329(f329(f72(x40771,x40772),f329(f329(f329(f72(x40771,x40772),x40773),x40774),x40775)),x40774),x40776),f329(f329(f329(f72(x40771,x40772),x40773),x40774),x40776))
% 187.18/188.04 [4181]E(f329(f329(f115(f881(f880(x41811,x41812),a869)),f329(f329(f286(x41811,x41813,x41812),x41814),x41815)),f329(f329(f286(x41811,x41813,x41812),x41816),x41815)),f329(f329(f286(x41811,x41813,x41812),f329(f329(f115(f881(f880(x41811,x41813),a869)),x41814),x41816)),x41815))
% 187.18/188.04 [4316]E(f329(f329(f42(x43161,f881(x43162,a869)),x43163),f329(f329(f7(x43161,f881(x43164,f881(x43162,a869)),f881(x43162,a869)),f329(f329(f8(f881(x43164,a869),f881(f881(x43164,f881(x43162,a869)),f881(x43162,a869)),x43161),f42(x43164,f881(x43162,a869))),x43165)),x43166)),f329(f329(f42(x43164,f881(x43162,a869)),f329(f329(f42(x43161,f881(x43164,a869)),x43163),x43165)),x43166))
% 187.18/188.04 [4317]E(f329(f329(f43(x43171,f881(x43172,a869)),x43173),f329(f329(f7(x43171,f881(x43174,f881(x43172,a869)),f881(x43172,a869)),f329(f329(f8(f881(x43174,a869),f881(f881(x43174,f881(x43172,a869)),f881(x43172,a869)),x43171),f43(x43174,f881(x43172,a869))),x43175)),x43176)),f329(f329(f43(x43174,f881(x43172,a869)),f329(f329(f42(x43171,f881(x43174,a869)),x43173),x43175)),x43176))
% 187.18/188.04 [4370]E(f329(f268(x43701,x43702,f880(x43703,x43704)),f329(f329(f7(x43701,f881(x43702,x43704),f881(x43702,f880(x43703,x43704))),f329(f329(f8(f881(x43704,f880(x43703,x43704)),f881(f881(x43702,x43704),f881(x43702,f880(x43703,x43704))),x43701),f8(x43704,f880(x43703,x43704),x43702)),f329(f329(f8(x43703,f881(x43704,f880(x43703,x43704)),x43701),f264(x43703,x43704)),x43705))),x43706)),f269(x43701,x43703,x43702,x43704,x43705,x43706))
% 187.18/188.04 [4290]E(f329(f329(f329(f72(x42901,f878(x42902)),f187(x42901,x42902,x42903,f329(f329(f22(f881(x42901,a869)),x42904),f329(f329(f307(x42901),x42905),f193(f881(x42901,a869)))))),x42905),x42906),f329(f329(f329(f72(x42901,f878(x42902)),f187(x42901,x42902,x42903,x42904)),x42905),x42906))
% 187.18/188.04 [4395]E(f329(f308(x43951,x43952,f329(f329(f18(x43951,x43952,x43952),f329(f329(f18(x43951,x43952,f881(x43952,x43952)),f329(f329(f8(a869,f881(x43952,f881(x43952,x43952)),x43951),f101(x43952)),x43953)),x43954)),x43955)),x43956),f329(f329(f115(f881(x43952,a869)),f329(f308(x43951,x43952,x43954),f329(f329(f106(f881(x43951,a869)),x43956),f329(f249(x43951),x43953)))),f329(f308(x43951,x43952,x43955),f329(f329(f106(f881(x43951,a869)),x43956),f329(f249(x43951),f329(f329(f8(a869,a869,x43951),a324),x43953))))))
% 187.18/188.04 [4406]E(f329(f308(x44061,f880(x44062,x44063),f329(f329(f18(x44061,x44063,f880(x44062,x44063)),f329(f329(f8(x44062,f881(x44063,f880(x44062,x44063)),x44061),f264(x44062,x44063)),x44064)),x44065)),x44066),f329(f329(f266(x44062,x44063),f329(f308(x44061,x44062,x44064),x44066)),f329(f329(f8(f881(x44061,a869),f881(x44063,a869),x44062),f308(x44061,x44063,x44065)),f329(f329(f7(x44062,f881(x44061,a869),f881(x44061,a869)),f329(f329(f8(f881(x44061,a869),f881(f881(x44061,a869),f881(x44061,a869)),x44062),f106(f881(x44061,a869))),f329(f329(f8(f881(x44062,a869),f881(x44061,a869),x44062),f309(x44061,x44062,x44064)),f329(f329(f7(x44062,f881(x44062,a869),f881(x44062,a869)),f307(x44062)),f193(f881(x44062,a869)))))),x44066))))
% 187.18/188.04 [4352]E(f329(f267(x43521,x43522),f329(f269(x43523,x43521,x43524,x43522,x43525,x43526),x43527)),f329(x43526,f329(f267(x43523,x43524),x43527)))
% 187.18/188.04 [4353]E(f329(f263(x43531,x43532),f329(f269(x43533,x43531,x43534,x43532,x43535,x43536),x43537)),f329(x43535,f329(f263(x43533,x43534),x43537)))
% 187.18/188.04 [4055]E(f329(f329(f181(x40551,x40552),f329(f329(f157(x40551,x40553),x40554),x40555)),f329(f329(f157(x40552,x40556),x40554),x40557)),f329(f329(f157(f880(x40551,x40552),f329(f329(f181(x40551,x40552),x40553),x40556)),x40554),f329(f329(f264(x40551,x40552),x40555),x40557)))
% 187.18/188.04 [4123]E(f329(f329(f329(f270(x41231,x41232,x41233,x41234),x41235),x41236),x41237),f329(f329(f268(x41232,x41233,x41234),x41236),f329(x41235,x41237)))
% 187.18/188.04 [4136]E(f329(f329(f329(f270(x41361,x41362,x41363,x41364),x41365),x41366),x41367),f329(f329(x41366,f329(f263(x41362,x41363),f329(x41365,x41367))),f329(f267(x41362,x41363),f329(x41365,x41367))))
% 187.18/188.04 [4171]E(f186(x41711,x41712,f329(f329(f329(f72(x41711,f878(x41712)),x41713),x41714),f329(f236(x41712),x41715)),x41716,x41717),f186(x41711,x41712,x41713,f329(f329(f149(x41711),x41714),x41716),f329(f329(f149(x41712),x41715),x41717)))
% 187.18/188.04 [4189]E(f329(f73(x41891,x41892,x41893,x41894),f329(f73(x41895,x41891,x41893,x41896),x41897)),f329(f73(x41895,x41892,x41893,f329(f73(x41891,x41892,x41895,x41894),x41896)),x41897))
% 187.18/188.04 [4250]E(f329(f73(f878(x42501),f878(x42502),x42503,f329(f207(x42501,x42502),x42504)),f329(f329(f329(f72(x42503,f878(x42501)),x42505),x42506),f329(f236(x42501),x42507))),f329(f329(f329(f72(x42503,f878(x42502)),f329(f73(f878(x42501),f878(x42502),x42503,f329(f207(x42501,x42502),x42504)),x42505)),x42506),f329(f236(x42502),f329(x42504,x42507))))
% 187.18/188.04 [4377]E(f329(f269(x43771,x43772,x43773,x43773,x43774,f34(x43773)),f329(f269(x43771,x43771,x43775,x43773,f34(x43771),x43776),x43777)),f329(f329(f264(x43772,x43773),f329(x43774,f329(f263(x43771,x43775),x43777))),f329(x43776,f329(f267(x43771,x43775),x43777))))
% 187.18/188.04 [4378]E(f329(f269(x43781,x43781,x43782,x43783,f34(x43781),x43784),f329(f269(x43785,x43781,x43782,x43782,x43786,f34(x43782)),x43787)),f329(f329(f264(x43781,x43783),f329(x43786,f329(f263(x43785,x43782),x43787))),f329(x43784,f329(f267(x43785,x43782),x43787))))
% 187.18/188.04 [4393]E(f329(f269(x43931,x43932,x43933,x43933,x43934,f34(x43933)),f329(f269(x43935,x43931,x43933,x43933,x43936,f34(x43933)),x43937)),f329(f269(x43935,x43932,x43933,x43933,f329(f73(x43931,x43932,x43935,x43934),x43936),f34(x43933)),x43937))
% 187.18/188.04 [4394]E(f329(f269(x43941,x43941,x43942,x43943,f34(x43941),x43944),f329(f269(x43941,x43941,x43945,x43942,f34(x43941),x43946),x43947)),f329(f269(x43941,x43941,x43945,x43943,f34(x43941),f329(f73(x43942,x43943,x43945,x43944),x43946)),x43947))
% 187.18/188.04 [4403]E(f329(f269(x44031,x44032,x44033,x44033,x44034,f34(x44033)),f329(f269(x44031,x44031,x44035,x44033,f34(x44031),x44036),x44037)),f329(f269(x44032,x44032,x44035,x44033,f34(x44032),x44036),f329(f269(x44031,x44032,x44035,x44035,x44034,f34(x44035)),x44037)))
% 187.18/188.04 [4090]E(f329(f329(f286(x40901,x40902,x40903),f329(f329(f286(x40901,x40904,x40902),x40905),x40906)),x40907),f329(f329(f286(x40901,x40904,x40903),x40905),f329(f329(f286(x40904,x40902,x40903),x40906),x40907)))
% 187.18/188.04 [4162]E(f329(f329(f268(x41621,x41622,x41623),f329(f73(x41624,f881(x41622,x41623),x41621,x41625),x41626)),x41627),f329(f329(x41625,f329(x41626,f329(f263(x41621,x41622),x41627))),f329(f267(x41621,x41622),x41627)))
% 187.18/188.04 [4214]E(f329(f73(x42141,x42142,x42143,x42144),f329(f329(f329(f72(x42143,x42141),x42145),x42146),x42147)),f329(f329(f329(f72(x42143,x42142),f329(f73(x42141,x42142,x42143,x42144),x42145)),x42146),f329(x42144,x42147)))
% 187.18/188.04 [4246]E(f329(f140(x42461,x42462,f329(f7(x42462,x42461,x42461),x42463),x42464),f329(f167(x42462),f329(f329(f152(x42465,x42462),x42466),x42467))),f329(f140(x42461,x42465,f329(f7(x42465,x42461,x42461),f329(f73(x42462,f881(x42461,x42461),x42465,x42463),x42466)),x42464),f329(f167(x42465),x42467)))
% 187.18/188.04 [4190]E(f329(f329(f42(x41901,f881(f880(x41902,x41903),a869)),x41904),f329(f329(f8(f881(f880(x41905,x41903),a869),f881(f880(x41902,x41903),a869),x41901),f329(f286(x41902,x41905,x41903),x41906)),x41907)),f329(f329(f286(x41902,x41905,x41903),x41906),f329(f329(f42(x41901,f881(f880(x41905,x41903),a869)),x41904),x41907)))
% 187.18/188.04 [4339]E(f329(f329(f42(x43391,f881(f880(x43392,x43393),a869)),x43394),f329(f329(f7(x43391,f881(f880(x43395,x43393),a869),f881(f880(x43392,x43393),a869)),f329(f329(f8(f881(f880(x43392,x43395),a869),f881(f881(f880(x43395,x43393),a869),f881(f880(x43392,x43393),a869)),x43391),f286(x43392,x43395,x43393)),x43396)),x43397)),f329(f329(f286(x43392,x43395,x43393),f329(f329(f42(x43391,f881(f880(x43392,x43395),a869)),x43394),x43396)),x43397))
% 187.18/188.04 [4340]E(f329(f140(x43401,x43402,f329(f329(f7(x43401,f881(x43402,x43403),f881(x43402,x43401)),f329(f329(f8(f881(x43403,x43401),f881(f881(x43402,x43403),f881(x43402,x43401)),x43401),f8(x43403,x43401,x43402)),x43404)),x43405),x43406),x43407),f329(f140(x43401,x43403,x43404,x43406),f329(f329(f152(x43402,x43403),x43405),x43407)))
% 187.18/188.04 [4404]E(f329(f329(f43(x44041,f881(x44042,a869)),x44043),f329(f329(f8(f881(x44044,f881(x44042,a869)),f881(x44042,a869),x44041),f329(f43(x44044,f881(x44042,a869)),x44045)),f329(f329(f7(x44041,f881(x44044,f881(x44042,a869)),f881(x44044,f881(x44042,a869))),f329(f329(f8(f881(f881(x44042,a869),f881(x44042,a869)),f881(f881(x44044,f881(x44042,a869)),f881(x44044,f881(x44042,a869))),x44041),f8(f881(x44042,a869),f881(x44042,a869),x44044)),f329(f329(f8(f881(x44042,a869),f881(f881(x44042,a869),f881(x44042,a869)),x44041),f115(f881(x44042,a869))),x44046))),x44047))),f329(f329(f115(f881(x44042,a869)),f329(f329(f43(x44041,f881(x44042,a869)),x44043),x44046)),f329(f329(f43(x44044,f881(x44042,a869)),x44045),x44047)))
% 187.18/188.04 [4405]E(f329(f329(f42(x44051,f881(x44052,a869)),x44053),f329(f329(f8(f881(x44054,f881(x44052,a869)),f881(x44052,a869),x44051),f329(f42(x44054,f881(x44052,a869)),x44055)),f329(f329(f7(x44051,f881(x44054,f881(x44052,a869)),f881(x44054,f881(x44052,a869))),f329(f329(f8(f881(f881(x44052,a869),f881(x44052,a869)),f881(f881(x44054,f881(x44052,a869)),f881(x44054,f881(x44052,a869))),x44051),f8(f881(x44052,a869),f881(x44052,a869),x44054)),f329(f329(f8(f881(x44052,a869),f881(f881(x44052,a869),f881(x44052,a869)),x44051),f106(f881(x44052,a869))),x44056))),x44057))),f329(f329(f106(f881(x44052,a869)),f329(f329(f42(x44051,f881(x44052,a869)),x44053),x44056)),f329(f329(f42(x44054,f881(x44052,a869)),x44055),x44057)))
% 187.18/188.04 [4398]E(f204(x43981,x43982,f329(f329(f329(x43983,x43984),x43985),x43986),f329(f329(f7(x43981,f880(a104,a104),f881(a104,f876(x43982))),f329(f329(f7(x43981,a104,f881(f880(a104,a104),f881(a104,f876(x43982)))),f329(f329(f7(x43981,a104,f881(a104,f881(f880(a104,a104),f881(a104,f876(x43982))))),x43987),x43984)),x43985)),x43986)),f329(f329(f329(f217(x43981,x43982,x43983,x43987),x43984),x43985),x43986))
% 187.18/188.04 [4411]E(f205(x44111,x44112,f329(f329(f329(x44113,x44114),x44115),x44116),f329(f329(f7(x44111,f880(a104,a104),f881(a104,f876(x44112))),f329(f329(f7(x44111,a104,f881(f880(a104,a104),f881(a104,f876(x44112)))),f329(f329(f7(x44111,a104,f881(a104,f881(f880(a104,a104),f881(a104,f876(x44112))))),x44117),x44114)),x44115)),x44116)),f219(x44111,x44112,x44113,x44117,x44114,x44115,x44116))
% 187.18/188.04 [4402]E(f202(x44021,x44022,f329(f329(f329(x44023,x44024),x44025),x44026),f329(f329(f7(x44021,f880(a104,a104),f881(a104,f876(f878(x44022)))),f329(f329(f7(x44021,a104,f881(f880(a104,a104),f881(a104,f876(f878(x44022))))),f329(f329(f7(x44021,a104,f881(a104,f881(f880(a104,a104),f881(a104,f876(f878(x44022)))))),x44027),x44024)),x44025)),x44026)),f329(f329(f329(f213(x44021,x44022,x44023,x44027),x44024),x44025),x44026))
% 187.18/188.04 [4413]E(f203(x44131,x44132,f329(f329(f329(x44133,x44134),x44135),x44136),f329(f329(f7(x44131,f880(a104,a104),f881(a104,f876(f878(x44132)))),f329(f329(f7(x44131,a104,f881(f880(a104,a104),f881(a104,f876(f878(x44132))))),f329(f329(f7(x44131,a104,f881(a104,f881(f880(a104,a104),f881(a104,f876(f878(x44132)))))),x44137),x44134)),x44135)),x44136)),f215(x44131,x44132,x44133,x44137,x44134,x44135,x44136))
% 187.18/188.04 [4310]E(f329(f269(x43101,x43102,x43103,x43104,x43105,x43106),f329(f329(f264(x43101,x43103),x43107),x43108)),f329(f329(f264(x43102,x43104),f329(x43105,x43107)),f329(x43106,x43108)))
% 187.18/188.04 [4415]E(f329(f329(f152(f880(x44151,x44152),f880(x44153,x44154)),f329(f268(x44151,x44152,f880(x44153,x44154)),f329(f329(f7(x44151,f881(x44152,x44154),f881(x44152,f880(x44153,x44154))),f329(f329(f8(f881(x44154,f880(x44153,x44154)),f881(f881(x44152,x44154),f881(x44152,f880(x44153,x44154))),x44151),f8(x44154,f880(x44153,x44154),x44152)),f329(f329(f8(x44153,f881(x44154,f880(x44153,x44154)),x44151),f264(x44153,x44154)),x44155))),x44156))),f329(f329(f181(x44151,x44152),x44157),x44158)),f329(f329(f181(x44153,x44154),f329(f329(f152(x44151,x44153),x44155),x44157)),f329(f329(f152(x44152,x44154),x44156),x44158)))
% 187.18/188.04 [4419]E(f329(f329(f152(f880(x44191,x44192),x44193),f329(f268(x44191,x44192,x44193),f329(f329(f8(f881(x44192,f880(x44191,x44194)),f881(x44192,x44193),x44191),f329(f8(f880(x44191,x44194),x44193,x44192),x44195)),f329(f329(f7(x44191,f881(x44192,x44194),f881(x44192,f880(x44191,x44194))),f329(f329(f8(f881(x44194,f880(x44191,x44194)),f881(f881(x44192,x44194),f881(x44192,f880(x44191,x44194))),x44191),f8(x44194,f880(x44191,x44194),x44192)),f264(x44191,x44194))),x44196)))),f329(f329(f181(x44191,x44192),x44197),x44198)),f329(f329(f152(f880(x44191,x44194),x44193),x44195),f329(f329(f181(x44191,x44194),x44197),f329(f329(f152(x44192,x44194),x44196),x44198))))
% 187.18/188.04 [4344]E(f329(f329(f152(f880(x43441,x43442),x43443),f329(f268(x43441,x43442,x43443),f329(f329(f8(f881(x43442,f880(x43444,x43442)),f881(x43442,x43443),x43441),f329(f8(f880(x43444,x43442),x43443,x43442),x43445)),f329(f329(f8(x43444,f881(x43442,f880(x43444,x43442)),x43441),f264(x43444,x43442)),x43446)))),f329(f329(f181(x43441,x43442),x43447),x43448)),f329(f329(f152(f880(x43444,x43442),x43443),x43445),f329(f329(f181(x43444,x43442),f329(f329(f152(x43441,x43444),x43446),x43447)),x43448)))
% 187.18/188.04 [4301]E(f329(f329(f268(x43011,x43012,x43013),f329(f329(f8(f881(x43012,f880(x43014,x43015)),f881(x43012,x43013),x43011),f329(f8(f880(x43014,x43015),x43013,x43012),f329(f268(x43014,x43015,x43013),x43016))),x43017)),x43018),f329(f329(f268(x43014,x43015,x43013),x43016),f329(f329(f268(x43011,x43012,f880(x43014,x43015)),x43017),x43018)))
% 187.18/188.04 [4420]E(f329(f329(f42(f880(x44201,x44202),f881(f880(x44203,x44204),a869)),f329(f329(f266(x44201,x44202),x44205),f329(f16(f881(x44202,a869),x44201),x44206))),f329(f268(x44201,x44202,f881(f880(x44203,x44204),a869)),f329(f329(f7(x44201,f881(x44202,f881(x44203,f881(x44204,a869))),f881(x44202,f881(f880(x44203,x44204),a869))),f329(f329(f8(f881(f881(x44203,f881(x44204,a869)),f881(f880(x44203,x44204),a869)),f881(f881(x44202,f881(x44203,f881(x44204,a869))),f881(x44202,f881(f880(x44203,x44204),a869))),x44201),f8(f881(x44203,f881(x44204,a869)),f881(f880(x44203,x44204),a869),x44202)),f329(f329(f8(f881(x44203,a869),f881(f881(x44203,f881(x44204,a869)),f881(f880(x44203,x44204),a869)),x44201),f266(x44203,x44204)),x44207))),f329(f329(f8(f881(x44204,a869),f881(x44203,f881(x44204,a869)),x44202),f16(f881(x44204,a869),x44203)),x44208)))),f329(f329(f266(x44203,x44204),f329(f329(f42(x44201,f881(x44203,a869)),x44205),x44207)),f329(f16(f881(x44204,a869),x44203),f329(f329(f42(x44202,f881(x44204,a869)),x44206),x44208))))
% 187.18/188.04 [4358]E(f329(f329(f270(x43581,x43582,x43583,x43584),f329(f329(f270(x43581,x43585,x43586,f880(x43582,x43583)),x43587),x43588)),x43589),f329(f329(f270(x43581,x43585,x43586,x43584),x43587),f329(f329(f7(x43585,f881(x43582,f881(x43583,x43584)),f881(x43586,x43584)),f329(f329(f8(f881(x43586,f880(x43582,x43583)),f881(f881(x43582,f881(x43583,x43584)),f881(x43586,x43584)),x43585),f270(x43586,x43582,x43583,x43584)),x43588)),x43589)))
% 187.18/188.04 [4390]E(f329(f73(f880(x43901,x43902),f880(x43903,x43904),f880(x43905,x43906),f269(x43901,x43903,x43902,x43904,x43907,x43908)),f269(x43905,x43901,x43906,x43902,x43909,x439010)),f269(x43905,x43903,x43906,x43904,f329(f73(x43901,x43903,x43905,x43907),x43909),f329(f73(x43902,x43904,x43906,x43908),x439010)))
% 187.18/188.04 [4396]E(f329(f269(x43961,x43962,x43963,x43964,x43965,x43966),f329(f269(x43967,x43961,x43968,x43963,x43969,x439610),x439611)),f329(f269(x43967,x43962,x43968,x43964,f329(f73(x43961,x43962,x43967,x43965),x43969),f329(f73(x43963,x43964,x43968,x43966),x439610)),x439611))
% 187.18/188.04 [4562]~P96(x45621)+E(f91(x45621),a326)
% 187.18/188.04 [4563]~P28(x45631)+P28(f878(x45631))
% 187.18/188.04 [4564]~P60(x45641)+P60(f878(x45641))
% 187.18/188.04 [4567]~P140(x45671)+~E(f78(x45671),f2(x45671))
% 187.18/188.04 [4569]~E(x45691,f2(a104))+E(f329(a20,x45691),f2(a1))
% 187.18/188.04 [4570]~E(x45701,f2(a1))+E(f82(a1,x45701),f2(a1))
% 187.18/188.04 [4576]~P141(x45761)+P35(x45761,f2(x45761))
% 187.18/188.04 [4578]~P27(x45781)+P33(x45781,f118(x45781))
% 187.18/188.04 [4587]P24(x45871)+P24(f329(a324,x45871))
% 187.18/188.04 [4630]~P141(x46301)+~P35(x46301,f78(x46301))
% 187.18/188.04 [4676]~P24(x46761)+~P24(f329(a324,x46761))
% 187.18/188.04 [4699]E(f329(a109,x46991),f2(a874))+~P24(f329(a198,x46991))
% 187.18/188.04 [4763]~P102(x47631)+P11(x47631,x47631,f115(x47631))
% 187.18/188.04 [4764]~P103(x47641)+P11(x47641,x47641,f106(x47641))
% 187.18/188.04 [4765]~P98(x47651)+P11(x47651,x47651,f81(x47651))
% 187.18/188.04 [4766]~P27(x47661)+P11(x47661,x47661,f241(x47661))
% 187.18/188.04 [4767]~P27(x47671)+P11(x47671,x47671,f242(x47671))
% 187.18/188.04 [4768]~P70(x47681)+P12(x47681,x47681,f81(x47681))
% 187.18/188.04 [4573]~E(x45731,f2(a874))+E(f329(f105(a1),x45731),f2(a1))
% 187.18/188.04 [4580]~P94(x45801)+E(f329(f108(x45801),a83),f2(x45801))
% 187.18/188.04 [4583]~E(f550(x45831),f2(a874))+E(f329(f164(a874),x45831),f2(a874))
% 187.18/188.04 [4584]~P26(x45841)+E(f245(x45841,f243(x45841)),f241(x45841))
% 187.18/188.04 [4585]~P26(x45851)+E(f246(x45851,f243(x45851)),f242(x45851))
% 187.18/188.04 [4586]~P91(x45861)+E(f82(x45861,f2(x45861)),f2(x45861))
% 187.18/188.04 [4595]~P141(x45951)+E(f329(f105(x45951),f78(a874)),f78(x45951))
% 187.18/188.04 [4596]~P141(x45961)+E(f329(f105(x45961),f2(a874)),f2(x45961))
% 187.18/188.04 [4597]~P138(x45971)+E(f329(f107(x45971),f78(a1)),f78(x45971))
% 187.18/188.04 [4598]~P138(x45981)+E(f329(f107(x45981),f2(a1)),f2(x45981))
% 187.18/188.04 [4599]E(x45991,f2(a874))+~E(f329(f105(a1),x45991),f2(a1))
% 187.18/188.04 [4624]~P115(x46241)+E(f329(f75(x46241),f78(x46241)),f78(x46241))
% 187.18/188.04 [4625]~P87(x46251)+E(f329(f75(x46251),f2(x46251)),f2(x46251))
% 187.18/188.04 [4626]~P97(x46261)+E(f329(f79(x46261),f193(x46261)),f252(x46261))
% 187.18/188.04 [4627]~P77(x46271)+E(f329(f79(x46271),f2(x46271)),f2(x46271))
% 187.18/188.04 [4628]~P97(x46281)+E(f329(f79(x46281),f252(x46281)),f193(x46281))
% 187.18/188.04 [4629]~P83(x46291)+E(f329(f164(x46291),f118(x46291)),f2(x46291))
% 187.18/188.04 [4650]~P41(x46501)+P43(f329(f171(a1),x46501))
% 187.18/188.04 [4681]~P94(x46811)+E(f329(f79(x46811),f78(x46811)),f329(f108(x46811),a102))
% 187.18/188.04 [4698]~P94(x46981)+P35(x46981,f329(f108(x46981),a83))
% 187.18/188.04 [4715]~P60(x47151)+E(f329(f171(x47151),f56(x47151)),f252(f881(x47151,a869)))
% 187.18/188.04 [4725]P41(x47251)+~P43(f329(f171(a1),x47251))
% 187.18/188.04 [4726]~P60(x47261)+P24(f329(f135(x47261),f56(x47261)))
% 187.18/188.04 [4769]E(f329(f105(a1),f329(a109,x47691)),x47691)+P24(f329(a198,x47691))
% 187.18/188.04 [4786]~P26(x47861)+E(f94(x47861,x47861,f5(x47861)),f95(x47861))
% 187.18/188.04 [4839]~P111(x48391)+E(f255(x48391,f78(x48391),f81(x48391)),f254(x48391))
% 187.18/188.04 [4869]~P94(x48691)+~P35(x48691,f329(f108(x48691),a102))
% 187.18/188.04 [4879]E(f329(a28,x48791),f206(a870))+P24(f329(a25,f329(a26,x48791)))
% 187.18/188.04 [5010]E(f329(f75(a1),x50101),x50101)+P24(f329(f329(f244(a1),x50101),f2(a1)))
% 187.18/188.04 [5031]~E(f329(a109,x50311),f2(a874))+P24(f329(f329(f243(a1),x50311),f2(a1)))
% 187.18/188.04 [5093]~P24(f329(a198,x50931))+P24(f329(f329(f244(a1),x50931),f2(a1)))
% 187.18/188.04 [5133]~P121(x51331)+P24(f329(f329(f243(x51331),f2(x51331)),f78(x51331)))
% 187.18/188.04 [5134]~P138(x51341)+P24(f329(f329(f331(x51341),f78(x51341)),f114(x51341)))
% 187.18/188.04 [5135]~P141(x51351)+P24(f329(f329(f331(x51351),f78(x51351)),f191(x51351)))
% 187.18/188.04 [5136]~P138(x51361)+P24(f329(f329(f331(x51361),f2(x51361)),f114(x51361)))
% 187.18/188.04 [5137]~P141(x51371)+P24(f329(f329(f331(x51371),f2(x51371)),f191(x51371)))
% 187.18/188.04 [5138]~P121(x51381)+P24(f329(f329(f244(x51381),f2(x51381)),f78(x51381)))
% 187.18/188.04 [5141]E(f329(f236(a870),f690(x51411)),f329(a28,x51411))+~P24(f329(a25,f329(a26,x51411)))
% 187.18/188.04 [5142]E(f329(f236(a870),f704(x51421)),f329(a28,x51421))+~P24(f329(a25,f329(a26,x51421)))
% 187.18/188.04 [5197]E(x51971,f2(a874))+~P24(f329(f329(f243(a874),x51971),f2(a874)))
% 187.18/188.04 [5241]E(f329(a109,x52411),f2(a874))+~P24(f329(f329(f243(a1),x52411),f2(a1)))
% 187.18/188.04 [5304]P24(f329(a198,x53041))+~P24(f329(f329(f244(a1),x53041),f2(a1)))
% 187.18/188.04 [5309]~P27(x53091)+P12(x53091,f875(x53091),f146(x53091,x53091,f5(x53091)))
% 187.18/188.04 [5326]P43(x53261)+~P24(f329(f329(f243(a1),f2(a1)),f336(x53261)))
% 187.18/188.04 [5332]E(f329(f75(a1),x53321),f329(f79(a1),x53321))+~P24(f329(f329(f244(a1),x53321),f2(a1)))
% 187.18/188.04 [5504]~P121(x55041)+~P24(f329(f329(f243(x55041),f78(x55041)),f2(x55041)))
% 187.18/188.04 [5505]~P121(x55051)+~P24(f329(f329(f244(x55051),f78(x55051)),f2(x55051)))
% 187.18/188.04 [5515]~E(x55151,f2(a874))+P24(f329(f329(f243(a1),f329(f105(a1),x55151)),f2(a1)))
% 187.18/188.04 [5516]~E(x55161,f2(a1))+P24(f329(f329(f244(a1),f329(f75(a1),x55161)),f78(a1)))
% 187.18/188.04 [5635]~P83(x56351)+E(f140(x56351,x56351,f80(x56351),f2(x56351)),f164(x56351))
% 187.18/188.04 [5807]~P104(x58071)+P21(a874,x58071,f105(x58071),f252(f881(a874,a869)))
% 187.18/188.04 [6003]E(x60031,f2(a874))+~P24(f329(f329(f243(a1),f329(f105(a1),x60031)),f2(a1)))
% 187.18/188.04 [6004]E(x60041,f2(a1))+~P24(f329(f329(f244(a1),f329(f75(a1),x60041)),f78(a1)))
% 187.18/188.04 [6801]~P24(f329(f329(f244(a1),x68011),f2(a1)))+P24(f329(f329(f244(a1),f329(f329(f80(a1),x68011),x68011)),f2(a1)))
% 187.18/188.04 [7350]P24(f329(f329(f244(a1),x73501),f2(a1)))+~P24(f329(f329(f244(a1),f329(f329(f80(a1),x73501),x73501)),f2(a1)))
% 187.18/188.04 [7912]E(x79121,f329(a3,f2(a874)))+P24(f329(f329(f244(a874),f329(f329(f22(a874),f329(a19,x79121)),f329(a117,f2(a874)))),f329(a19,x79121)))
% 187.18/188.04 [8682]~P24(f329(f329(f244(a1),x86821),f2(a1)))+P24(f329(f329(f244(a1),f329(f329(f22(a1),f329(f329(f80(a1),x86821),x86821)),a102)),f2(a1)))
% 187.18/188.04 [8768]~P24(f329(f329(f244(a1),x87681),f2(a1)))+P24(f329(f329(f244(a1),f329(f329(f80(a1),f329(f329(f80(a1),f78(a1)),x87681)),x87681)),f2(a1)))
% 187.18/188.04 [9093]P24(f329(f329(f244(a1),x90931),f2(a1)))+~P24(f329(f329(f244(a1),f329(f329(f22(a1),f329(f329(f80(a1),x90931),x90931)),a102)),f2(a1)))
% 187.18/188.04 [9156]P24(f329(f329(f244(a1),x91561),f2(a1)))+~P24(f329(f329(f244(a1),f329(f329(f80(a1),f329(f329(f80(a1),f78(a1)),x91561)),x91561)),f2(a1)))
% 187.18/188.04 [4669]~E(a83,x46691)+E(f329(f329(f80(a1),x46691),x46691),a83)
% 187.18/188.04 [4670]~E(x46701,a83)+E(f329(f329(f80(a1),x46701),x46701),a83)
% 187.18/188.04 [4684]E(x46841,f2(a1))+E(f329(f329(f39(a1),x46841),x46841),f78(a1))
% 187.18/188.04 [4815]E(x48151,a83)+~E(f329(f329(f80(a1),x48151),x48151),a83)
% 187.18/188.04 [4816]E(a83,x48161)+~E(f329(f329(f80(a1),x48161),x48161),a83)
% 187.18/188.04 [4829]~P31(x48291)+E(f41(x48291,f193(f881(x48291,a869))),f252(x48291))
% 187.18/188.04 [4830]~P31(x48301)+E(f41(x48301,f252(f881(x48301,a869))),f193(x48301))
% 187.18/188.04 [4831]~P31(x48311)+E(f40(x48311,f193(f881(x48311,a869))),f193(x48311))
% 187.18/188.04 [4832]~P31(x48321)+E(f40(x48321,f252(f881(x48321,a869))),f252(x48321))
% 187.18/188.04 [4833]~P27(x48331)+E(f137(x48331,f193(f881(x48331,a869))),f118(x48331))
% 187.18/188.04 [4968]E(x49681,f2(a874))+P24(f329(f329(f244(a874),f2(a874)),x49681))
% 187.18/188.04 [4987]~P32(x49871)+P24(f329(f329(f243(a1),f2(a1)),x49871))
% 187.18/188.04 [5022]~E(f329(f108(a874),x50221),f2(a874))+P24(f329(f329(f243(a1),x50221),a83))
% 187.18/188.04 [5027]P43(x50271)+P24(f329(f329(f331(a1),f336(x50271)),x50271))
% 187.18/188.04 [5028]E(x50281,f329(a3,f2(a874)))+P24(f329(f329(f243(a104),f78(a104)),x50281))
% 187.18/188.04 [5067]P24(f329(a198,x50671))+P24(f329(f329(f243(a1),f2(a1)),x50671))
% 187.18/188.04 [5115]E(f329(f105(a1),f329(a109,x51151)),f2(a1))+P24(f329(f329(f243(a1),f2(a1)),x51151))
% 187.18/188.04 [5183]E(f329(f105(a1),f329(f108(a874),x51831)),f329(f108(a1),x51831))+P24(f329(a198,f329(f108(a1),x51831)))
% 187.18/188.04 [5203]E(f329(f108(a874),x52031),f2(a874))+~P24(f329(a198,f329(f108(a1),x52031)))
% 187.18/188.04 [5204]E(f329(f108(a874),x52041),f2(a874))+~P24(f329(f329(f243(a1),x52041),a83))
% 187.18/188.04 [5238]P32(x52381)+~P24(f329(f329(f243(a1),f2(a1)),x52381))
% 187.18/188.04 [5312]E(f329(a117,f805(x53121)),x53121)+~P24(f329(f329(f244(a874),f2(a874)),x53121))
% 187.18/188.04 [5320]E(f329(a117,f329(f108(a874),x53201)),f78(a874))+~P24(f329(a198,f329(f108(a1),x53201)))
% 187.18/188.04 [5328]E(f329(f105(a1),f356(x53281)),x53281)+~P24(f329(f329(f244(a1),f2(a1)),x53281))
% 187.18/188.04 [5335]~E(x53351,f329(a3,f2(a874)))+~P24(f329(f329(f243(a104),f78(a104)),x53351))
% 187.18/188.04 [5342]E(f329(f105(a1),f329(f108(a874),x53421)),f2(a1))+~P24(f329(a198,f329(f108(a1),x53421)))
% 187.18/188.04 [5368]E(f329(f164(a874),x53681),f2(a874))+P24(f329(f329(f331(a874),f550(x53681)),f329(f171(a874),x53681)))
% 187.18/188.04 [5389]E(f329(f105(a1),f329(a109,x53891)),x53891)+~P24(f329(f329(f243(a1),f2(a1)),x53891))
% 187.18/188.04 [5398]~P24(f329(a198,x53981))+~P24(f329(f329(f243(a1),f2(a1)),x53981))
% 187.18/188.04 [5497]E(f329(f329(f80(a874),f78(a874)),f329(f108(a874),x54971)),f78(a874))+~P24(f329(f329(f244(a1),x54971),a83))
% 187.18/188.04 [5555]E(x55551,f2(a874))+~P24(f329(f329(f244(a874),x55551),f329(a117,f2(a874))))
% 187.18/188.04 [5594]E(f329(f329(f22(a874),f329(f108(a874),x55941)),f78(a874)),f2(a874))+~P24(f329(f329(f243(a1),x55941),a83))
% 187.18/188.04 [5595]E(f329(f329(f80(a874),f329(f108(a874),x55951)),f78(a874)),f78(a874))+~P24(f329(f329(f244(a1),x55951),a83))
% 187.18/188.04 [5605]~P43(x56051)+E(f329(f38(a874),f329(f308(a1,a874,a109),x56051)),f329(f38(a1),x56051))
% 187.18/188.04 [5636]~P27(x56361)+E(f246(x56361,f329(f7(x56361,x56361,a869),f243(x56361))),f241(x56361))
% 187.18/188.04 [5637]~P27(x56371)+E(f245(x56371,f329(f7(x56371,x56371,a869),f243(x56371))),f242(x56371))
% 187.18/188.04 [5647]E(f45(a874,f329(a117,f2(a874)),f329(f108(a874),x56471)),f329(a117,f2(a874)))+~P24(f329(a198,f329(f108(a1),x56471)))
% 187.18/188.04 [5656]~P24(f329(f329(f244(a1),f2(a1)),x56561))+P24(f329(f329(f243(a1),f78(a1)),x56561))
% 187.18/188.04 [5657]P24(f329(f329(f244(a1),f2(a1)),x56571))+~P24(f329(f329(f243(a1),f78(a1)),x56571))
% 187.18/188.04 [5668]E(f329(a117,f329(f329(f22(a874),x56681),f78(a874))),x56681)+~P24(f329(f329(f244(a874),f2(a874)),x56681))
% 187.18/188.04 [5726]P24(f329(f329(f244(a874),f2(a874)),f356(x57261)))+~P24(f329(f329(f244(a1),f2(a1)),x57261))
% 187.18/188.04 [5785]E(f45(a1,f329(f108(a1),a102),x57851),f329(f329(f22(a1),x57851),f78(a1)))+~P24(f329(f329(f244(a1),f2(a1)),x57851))
% 187.18/188.04 [5819]~P24(f329(f329(f244(a1),a83),x58191))+P24(f329(f329(f244(a874),f2(a874)),f329(f108(a874),x58191)))
% 187.18/188.04 [5869]P24(f329(f329(f244(a874),f2(a874)),f329(a109,x58691)))+~P24(f329(f329(f244(a1),f2(a1)),x58691))
% 187.18/188.04 [5921]~P24(f329(f329(f244(a874),f2(a874)),x59211))+P24(f329(f329(f244(a1),f2(a1)),f329(f105(a1),x59211)))
% 187.18/188.04 [5959]~P24(f329(f329(f244(a874),f2(a874)),f329(a109,x59591)))+P24(f329(f329(f244(a1),f2(a1)),x59591))
% 187.18/188.04 [5974]~P43(x59741)+E(f329(f308(a874,a1,f105(a1)),f329(f308(a1,a874,a109),x59741)),x59741)
% 187.18/188.04 [5984]P24(f329(f329(f244(a1),a83),x59841))+~P24(f329(f329(f244(a874),f2(a874)),f329(f108(a874),x59841)))
% 187.18/188.04 [6032]~P60(x60321)+E(f329(f329(f149(f878(x60321)),f206(x60321)),f329(f329(f152(x60321,f878(x60321)),f236(x60321)),f56(x60321))),f56(f878(x60321)))
% 187.18/188.04 [6043]P24(f329(f329(f244(a874),f2(a874)),x60431))+~P24(f329(f329(f244(a1),f2(a1)),f329(f105(a1),x60431)))
% 187.18/188.04 [6158]E(f329(f308(a874,a1,f105(a1)),f329(f250(a874),f329(a109,x61581))),f329(f299(a1,f2(a1)),x61581))+~P24(f329(f329(f243(a1),f2(a1)),x61581))
% 187.18/188.04 [6173]~P121(x61731)+P24(f329(f329(f244(x61731),f2(x61731)),f329(f329(f80(x61731),f78(x61731)),f78(x61731))))
% 187.18/188.04 [6224]P24(f329(f329(f244(a874),f329(a117,f2(a874))),f329(a109,x62241)))+~P24(f329(f329(f244(a1),f78(a1)),x62241))
% 187.18/188.04 [6319]E(x63191,f2(a1))+P24(f329(f49(f2(a1),x63191),f329(f329(f264(a1,a1),f2(a1)),f2(a1))))
% 187.18/188.04 [6484]~P24(f329(f329(f244(a874),f329(a117,f2(a874))),f329(a109,x64841)))+P24(f329(f329(f244(a1),f78(a1)),x64841))
% 187.18/188.04 [6913]~P113(x69131)+P42(x69131,f329(f249(f880(x69131,x69131)),f329(f268(x69131,x69131,a869),f244(x69131))))
% 187.18/188.04 [5542]E(f329(f108(a874),f329(f329(f22(a1),x55421),a102)),f329(a117,f329(f108(a874),x55421)))+P24(f329(a198,f329(f108(a1),x55421)))
% 187.18/188.04 [5558]~P41(x55581)+E(f329(f329(f152(a874,a1),f105(a1)),f329(f329(f152(a1,a874),a109),x55581)),x55581)
% 187.18/188.04 [5674]E(f329(f79(a1),f329(f105(a1),f329(a117,f446(x56741)))),x56741)+~P24(f329(f329(f244(a1),x56741),f2(a1)))
% 187.18/188.04 [5684]E(f329(f329(f80(a874),f78(a874)),f329(f108(a874),x56841)),f329(f108(a874),f329(f329(f22(a1),x56841),a102)))+P24(f329(f329(f244(a1),x56841),a83))
% 187.18/188.04 [5728]E(f329(f329(f39(a1),f329(f108(a1),a102)),x57281),f329(f108(a1),a102))+~P24(f329(f329(f244(a1),f2(a1)),x57281))
% 187.18/188.04 [5815]E(f329(f329(f22(a874),f329(f108(a874),x58151)),f78(a874)),f329(f108(a874),f329(f329(f80(a1),x58151),a102)))+P24(f329(f329(f243(a1),x58151),a83))
% 187.18/188.04 [5816]E(f329(f329(f80(a874),f329(f108(a874),x58161)),f78(a874)),f329(f108(a874),f329(f329(f22(a1),x58161),a102)))+P24(f329(f329(f244(a1),x58161),a83))
% 187.18/188.04 [5857]E(f329(a109,f329(f329(f80(a1),f78(a1)),x58571)),f329(a117,f329(a109,x58571)))+~P24(f329(f329(f243(a1),f2(a1)),x58571))
% 187.18/188.04 [5893]E(f329(a117,f329(f329(f22(a874),x58931),f329(a117,f2(a874)))),x58931)+~P24(f329(f329(f244(a874),f2(a874)),x58931))
% 187.18/188.04 [6103]E(f45(a874,f329(a117,f2(a874)),f329(f108(a874),x61031)),f329(a109,f45(a1,f78(a1),f329(f108(a1),x61031))))+P24(f329(a198,f329(f108(a1),x61031)))
% 187.18/188.04 [6148]~P24(f329(f329(f243(a1),a83),x61481))+P24(f329(f329(f243(a1),a83),f329(f329(f80(a1),x61481),x61481)))
% 187.18/188.04 [6149]~P24(f329(f329(f244(a1),a102),x61491))+P24(f329(f329(f243(a1),a102),f329(f329(f80(a1),x61491),x61491)))
% 187.18/188.04 [6150]~P24(f329(f329(f244(a1),a83),x61501))+P24(f329(f329(f244(a1),a83),f329(f329(f80(a1),x61501),x61501)))
% 187.18/188.04 [6151]~P24(f329(f329(f244(a1),a102),x61511))+P24(f329(f329(f244(a1),a102),f329(f329(f80(a1),x61511),x61511)))
% 187.18/188.04 [6152]~P24(f329(f329(f91(a1),a83),x61521))+P24(f329(f329(f91(a1),a83),f329(f329(f80(a1),x61521),x61521)))
% 187.18/188.04 [6332]~P24(f329(f62(x63321),f252(f881(x63321,a869))))+P24(f329(f62(f878(x63321)),f252(f881(f878(x63321),a869))))
% 187.18/188.04 [6416]~P24(f329(f329(f243(a1),f2(a1)),x64161))+P24(f329(f329(f244(a1),f2(a1)),f329(f329(f80(a1),f78(a1)),x64161)))
% 187.18/188.04 [6423]E(f329(f263(a1,a1),f47(f78(a1),f329(f108(a1),x64231))),f329(f329(f39(a1),f78(a1)),f329(f108(a1),x64231)))+~P24(f329(f329(f243(a1),f2(a1)),f329(f108(a1),x64231)))
% 187.18/188.04 [6443]E(f329(f267(a1,a1),f47(f78(a1),f329(f108(a1),x64431))),f45(a1,f78(a1),f329(f108(a1),x64431)))+~P24(f329(f329(f243(a1),f2(a1)),f329(f108(a1),x64431)))
% 187.18/188.04 [6455]P24(f329(f62(x64551),f252(f881(x64551,a869))))+~P24(f329(f62(f878(x64551)),f252(f881(f878(x64551),a869))))
% 187.18/188.04 [6485]P24(f329(f329(f243(a1),a83),x64851))+~P24(f329(f329(f243(a1),a83),f329(f329(f80(a1),x64851),x64851)))
% 187.18/188.04 [6486]P24(f329(f329(f244(a1),a83),x64861))+~P24(f329(f329(f244(a1),a83),f329(f329(f80(a1),x64861),x64861)))
% 187.18/188.04 [6487]P24(f329(f329(f244(a1),a102),x64871))+~P24(f329(f329(f243(a1),a102),f329(f329(f80(a1),x64871),x64871)))
% 187.18/188.04 [6488]P24(f329(f329(f244(a1),a102),x64881))+~P24(f329(f329(f244(a1),a102),f329(f329(f80(a1),x64881),x64881)))
% 187.18/188.04 [6489]P24(f329(f329(f91(a1),a83),x64891))+~P24(f329(f329(f91(a1),a83),f329(f329(f80(a1),x64891),x64891)))
% 187.18/188.04 [6805]~P24(f329(f62(x68051),f252(f881(x68051,a869))))+P24(f329(f329(f244(a874),f2(a874)),f329(f38(x68051),f252(f881(x68051,a869)))))
% 187.18/188.04 [7393]P24(f329(f62(a874),x73931))+~P24(f329(f62(a1),f329(f308(a874,a1,f105(a1)),x73931)))
% 187.18/188.04 [5472]~E(a102,x54721)+E(f329(f329(f22(a1),f329(f329(f80(a1),x54721),x54721)),a102),a102)
% 187.18/188.04 [5473]~E(x54731,a102)+E(f329(f329(f22(a1),f329(f329(f80(a1),x54731),x54731)),a102),a102)
% 187.18/188.04 [5979]E(x59791,a102)+~E(f329(f329(f22(a1),f329(f329(f80(a1),x59791),x59791)),a102),a102)
% 187.18/188.04 [5980]E(a102,x59801)+~E(f329(f329(f22(a1),f329(f329(f80(a1),x59801),x59801)),a102),a102)
% 187.18/188.04 [6385]~E(f329(f108(a874),x63851),f2(a874))+P24(f329(a198,f329(f108(a1),f329(f329(f80(a1),x63851),a102))))
% 187.18/188.04 [6731]~P24(f329(a198,f329(f108(a1),x67311)))+P24(f329(a198,f329(f108(a1),f329(f329(f80(a1),x67311),x67311))))
% 187.18/188.04 [6732]~P24(f329(f329(f243(a1),x67321),a83))+P24(f329(f329(f243(a1),f329(f329(f80(a1),x67321),x67321)),a83))
% 187.18/188.04 [6733]~P24(f329(f329(f243(a1),x67331),a102))+P24(f329(f329(f243(a1),f329(f329(f80(a1),x67331),x67331)),a102))
% 187.18/188.04 [6734]~P24(f329(f329(f244(a1),x67341),a83))+P24(f329(f329(f244(a1),f329(f329(f80(a1),x67341),x67341)),a83))
% 187.18/188.04 [6735]~P24(f329(f329(f243(a1),x67351),a102))+P24(f329(f329(f244(a1),f329(f329(f80(a1),x67351),x67351)),a102))
% 187.18/188.04 [6736]~P24(f329(f329(f91(a1),x67361),a83))+P24(f329(f329(f91(a1),f329(f329(f80(a1),x67361),x67361)),a83))
% 187.18/188.04 [7060]E(f329(f108(a874),x70601),f2(a874))+~P24(f329(a198,f329(f108(a1),f329(f329(f80(a1),x70601),a102))))
% 187.18/188.04 [7299]~P24(f329(f329(f243(a1),f2(a1)),f329(f108(a1),x72991)))+P24(f329(f329(f243(a1),f2(a1)),f329(f108(a1),f329(f329(f80(a1),x72991),x72991))))
% 187.18/188.04 [7300]P24(f329(a198,f329(f108(a1),x73001)))+~P24(f329(a198,f329(f108(a1),f329(f329(f80(a1),x73001),x73001))))
% 187.18/188.04 [7301]P24(f329(f329(f243(a1),x73011),a83))+~P24(f329(f329(f243(a1),f329(f329(f80(a1),x73011),x73011)),a83))
% 187.18/188.04 [7302]P24(f329(f329(f243(a1),x73021),a102))+~P24(f329(f329(f243(a1),f329(f329(f80(a1),x73021),x73021)),a102))
% 187.18/188.04 [7303]P24(f329(f329(f243(a1),x73031),a102))+~P24(f329(f329(f244(a1),f329(f329(f80(a1),x73031),x73031)),a102))
% 187.18/188.04 [7304]P24(f329(f329(f244(a1),x73041),a83))+~P24(f329(f329(f244(a1),f329(f329(f80(a1),x73041),x73041)),a83))
% 187.18/188.04 [7305]P24(f329(f329(f91(a1),x73051),a83))+~P24(f329(f329(f91(a1),f329(f329(f80(a1),x73051),x73051)),a83))
% 187.18/188.04 [7676]E(f329(a111,f545(x76761)),x76761)+~P24(f329(f329(f331(f881(f880(a874,a874),a869)),x76761),a103))
% 187.18/188.04 [6305]~P94(x63051)+E(f329(f108(x63051),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f78(x63051))
% 187.18/188.04 [6783]~P24(f329(a198,f329(f108(a1),x67831)))+E(f329(f108(a874),f329(f329(f22(a1),f329(f329(f80(a1),x67831),x67831)),a102)),f2(a874))
% 187.18/188.04 [7857]~P24(f329(f329(f244(a1),f329(f108(a1),x78571)),f2(a1)))+E(f329(f263(a1,a1),f329(a51,f50(f329(f79(a1),f78(a1)),f329(f79(a1),f329(f108(a1),x78571))))),f329(f329(f39(a1),f78(a1)),f329(f108(a1),x78571)))
% 187.18/188.04 [7870]~P24(f329(f329(f244(a1),f329(f108(a1),x78701)),f2(a1)))+E(f329(f267(a1,a1),f329(a51,f50(f329(f79(a1),f78(a1)),f329(f79(a1),f329(f108(a1),x78701))))),f45(a1,f78(a1),f329(f108(a1),x78701)))
% 187.18/188.04 [7918]~P24(f329(f329(f243(a1),a83),x79181))+P24(f329(f329(f243(a1),a83),f329(f329(f22(a1),f329(f329(f80(a1),x79181),x79181)),a102)))
% 187.18/188.04 [7919]~P24(f329(f329(f243(a1),a102),x79191))+P24(f329(f329(f243(a1),a102),f329(f329(f22(a1),f329(f329(f80(a1),x79191),x79191)),a102)))
% 187.18/188.04 [7920]~P24(f329(f329(f243(a1),a83),x79201))+P24(f329(f329(f244(a1),a83),f329(f329(f22(a1),f329(f329(f80(a1),x79201),x79201)),a102)))
% 187.18/188.04 [7921]~P24(f329(f329(f244(a1),a102),x79211))+P24(f329(f329(f244(a1),a102),f329(f329(f22(a1),f329(f329(f80(a1),x79211),x79211)),a102)))
% 187.18/188.04 [7922]~P24(f329(f329(f91(a1),a102),x79221))+P24(f329(f329(f91(a1),a102),f329(f329(f22(a1),f329(f329(f80(a1),x79221),x79221)),a102)))
% 187.18/188.04 [8230]~P94(x82301)+~P35(x82301,f329(f108(x82301),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))
% 187.18/188.04 [8410]P24(f329(f329(f243(a1),a83),x84101))+~P24(f329(f329(f243(a1),a83),f329(f329(f22(a1),f329(f329(f80(a1),x84101),x84101)),a102)))
% 187.18/188.04 [8411]P24(f329(f329(f243(a1),a83),x84111))+~P24(f329(f329(f244(a1),a83),f329(f329(f22(a1),f329(f329(f80(a1),x84111),x84111)),a102)))
% 187.18/188.04 [8412]P24(f329(f329(f243(a1),a102),x84121))+~P24(f329(f329(f243(a1),a102),f329(f329(f22(a1),f329(f329(f80(a1),x84121),x84121)),a102)))
% 187.18/188.04 [8413]P24(f329(f329(f244(a1),a102),x84131))+~P24(f329(f329(f244(a1),a102),f329(f329(f22(a1),f329(f329(f80(a1),x84131),x84131)),a102)))
% 187.18/188.04 [8414]P24(f329(f329(f91(a1),a102),x84141))+~P24(f329(f329(f91(a1),a102),f329(f329(f22(a1),f329(f329(f80(a1),x84141),x84141)),a102)))
% 187.18/188.04 [8726]E(f329(f108(a874),f329(f329(f22(a1),f329(f329(f80(a1),x87261),x87261)),a102)),f329(f329(f86(a874,a874),f329(f108(a874),x87261)),f329(f329(f8(a874,a874,a874),a117),f329(f329(f18(a874,a874,a874),f80(a874)),f5(a874)))))+P24(f329(a198,f329(f108(a1),x87261)))
% 187.18/188.04 [9573]E(x95731,f193(f881(f880(a874,a874),a869)))+P24(f329(f329(f331(f880(f881(f880(a874,a874),a869),f881(f880(a874,a874),a869))),f329(f329(f264(f881(f880(a874,a874),a869),f881(f880(a874,a874),a869)),x95731),f193(f881(f880(a874,a874),a869)))),a36))
% 187.18/188.04 [8657]~P24(f329(a198,f329(f108(a1),x86571)))+P24(f329(a198,f329(f108(a1),f329(f329(f22(a1),f329(f329(f80(a1),x86571),x86571)),a102))))
% 187.18/188.04 [8658]~P24(f329(f329(f244(a1),x86581),a83))+P24(f329(f329(f243(a1),f329(f329(f22(a1),f329(f329(f80(a1),x86581),x86581)),a102)),a83))
% 187.18/188.04 [8659]~P24(f329(f329(f243(a1),x86591),a102))+P24(f329(f329(f243(a1),f329(f329(f22(a1),f329(f329(f80(a1),x86591),x86591)),a102)),a102))
% 187.18/188.04 [8660]~P24(f329(f329(f244(a1),x86601),a83))+P24(f329(f329(f244(a1),f329(f329(f22(a1),f329(f329(f80(a1),x86601),x86601)),a102)),a83))
% 187.18/188.04 [8661]~P24(f329(f329(f244(a1),x86611),a102))+P24(f329(f329(f244(a1),f329(f329(f22(a1),f329(f329(f80(a1),x86611),x86611)),a102)),a102))
% 187.18/188.04 [8662]~P24(f329(f329(f91(a1),x86621),a102))+P24(f329(f329(f91(a1),f329(f329(f22(a1),f329(f329(f80(a1),x86621),x86621)),a102)),a102))
% 187.18/188.04 [8761]~P24(f329(f329(f243(a1),f2(a1)),f329(f108(a1),x87611)))+P24(f329(f329(f243(a1),f2(a1)),f329(f108(a1),f329(f329(f22(a1),f329(f329(f80(a1),x87611),x87611)),a102))))
% 187.18/188.04 [8921]~P94(x89211)+E(f329(f329(f80(x89211),f78(x89211)),f78(x89211)),f329(f108(x89211),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102))))
% 187.18/188.04 [9077]P24(f329(a198,f329(f108(a1),x90771)))+~P24(f329(a198,f329(f108(a1),f329(f329(f22(a1),f329(f329(f80(a1),x90771),x90771)),a102))))
% 187.18/188.04 [9078]P24(f329(f329(f243(a1),x90781),a102))+~P24(f329(f329(f243(a1),f329(f329(f22(a1),f329(f329(f80(a1),x90781),x90781)),a102)),a102))
% 187.18/188.04 [9079]P24(f329(f329(f244(a1),x90791),a83))+~P24(f329(f329(f243(a1),f329(f329(f22(a1),f329(f329(f80(a1),x90791),x90791)),a102)),a83))
% 187.18/188.04 [9080]P24(f329(f329(f244(a1),x90801),a83))+~P24(f329(f329(f244(a1),f329(f329(f22(a1),f329(f329(f80(a1),x90801),x90801)),a102)),a83))
% 187.18/188.04 [9081]P24(f329(f329(f244(a1),x90811),a102))+~P24(f329(f329(f244(a1),f329(f329(f22(a1),f329(f329(f80(a1),x90811),x90811)),a102)),a102))
% 187.18/188.04 [9082]P24(f329(f329(f91(a1),x90821),a102))+~P24(f329(f329(f91(a1),f329(f329(f22(a1),f329(f329(f80(a1),x90821),x90821)),a102)),a102))
% 187.18/188.04 [9619]~P24(f329(f62(f880(a874,a874)),x96191))+P24(f329(f329(f331(f880(f881(f880(a874,a874),a869),f881(f880(a874,a874),a869))),f329(f329(f264(f881(f880(a874,a874),a869),f881(f880(a874,a874),a869)),f193(f881(f880(a874,a874),a869))),x96191)),a69))
% 187.18/188.04 [9405]~P141(x94051)+E(f329(f329(f254(x94051),f78(x94051)),f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))),f78(x94051))
% 187.18/188.04 [9406]~P141(x94061)+E(f329(f329(f254(x94061),f2(x94061)),f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))),f2(x94061))
% 187.18/188.04 [9848]~P24(f329(f329(f244(a874),f78(a874)),x98481))+P24(f329(f329(f244(a874),f2(a874)),f329(f329(f39(a874),x98481),f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102))))))
% 187.18/188.04 [9860]~P24(f329(f329(f244(a874),f2(a874)),x98601))+P24(f329(f329(f244(a874),f2(a874)),f329(f329(f39(a874),f329(f329(f80(a874),x98601),f78(a874))),f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102))))))
% 187.18/188.04 [9902]~E(f45(a874,x99021,f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))),f78(a874))+P24(f329(f329(f244(a874),f2(a874)),f45(a874,x99021,f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102))))))
% 187.18/188.04 [9921]E(f45(a874,x99211,f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))),f78(a874))+~P24(f329(f329(f244(a874),f2(a874)),f45(a874,x99211,f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102))))))
% 187.18/188.04 [4603]~P42(x46031,x46032)+P57(x46031,x46032)
% 187.18/188.04 [4604]~P48(x46041,x46042)+P57(x46041,x46042)
% 187.18/188.04 [4565]~E(x45651,x45652)+E(f276(x45651,x45652),f78(a104))
% 187.18/188.04 [4568]E(f224(x45681,x45682),x45681)+~E(x45682,f2(a874))
% 187.18/188.04 [4575]~E(x45752,f118(x45751))+E(f150(x45751,x45752),f118(x45751))
% 187.18/188.04 [4594]~E(f150(x45942,x45941),f118(x45942))+E(x45941,f118(x45942))
% 187.18/188.04 [4608]~P25(x46082)+P25(f881(x46081,x46082))
% 187.18/188.04 [4609]~P26(x46092)+P26(f881(x46091,x46092))
% 187.18/188.04 [4610]~P106(x46102)+P106(f881(x46101,x46102))
% 187.18/188.04 [4611]~P65(x46112)+P65(f881(x46111,x46112))
% 187.18/188.04 [4612]~P66(x46122)+P66(f881(x46121,x46122))
% 187.18/188.04 [4613]~P66(x46132)+P102(f881(x46131,x46132))
% 187.18/188.04 [4614]~P99(x46142)+P67(f881(x46141,x46142))
% 187.18/188.04 [4615]~P68(x46152)+P68(f881(x46151,x46152))
% 187.18/188.04 [4616]~P66(x46162)+P103(f881(x46161,x46162))
% 187.18/188.04 [4617]~P100(x46172)+P100(f881(x46171,x46172))
% 187.18/188.04 [4618]~P112(x46182)+P112(f881(x46181,x46182))
% 187.18/188.04 [4619]~P99(x46192)+P101(f881(x46191,x46192))
% 187.18/188.04 [4620]~P31(x46202)+P31(f881(x46201,x46202))
% 187.18/188.04 [4621]~P97(x46212)+P97(f881(x46211,x46212))
% 187.18/188.04 [4622]~P90(x46222)+P90(f881(x46221,x46222))
% 187.18/188.04 [4623]~P99(x46232)+P99(f881(x46231,x46232))
% 187.18/188.04 [4635]E(x46351,x46352)+~E(f329(a26,x46351),f329(a26,x46352))
% 187.18/188.04 [4637]E(x46371,x46372)+~E(f329(a117,x46371),f329(a117,x46372))
% 187.18/188.04 [4638]E(x46381,x46382)+~E(f329(a111,x46381),f329(a111,x46382))
% 187.18/188.04 [4639]E(x46391,x46392)+~E(f329(a3,x46391),f329(a3,x46392))
% 187.18/188.04 [4641]E(x46411,x46412)+~E(f329(a19,x46411),f329(a19,x46412))
% 187.18/188.04 [4742]~P29(x47421)+E(f45(x47421,x47422,x47422),f2(x47421))
% 187.18/188.04 [4776]~P42(x47761,x47762)+P42(f875(x47761),f144(x47761,x47762))
% 187.18/188.04 [4777]~P42(x47771,x47772)+P42(f875(x47771),f143(x47771,x47772))
% 187.18/188.04 [4874]~P42(x48741,x48742)+P42(f881(x48741,a869),f321(x48741,x48742))
% 187.18/188.04 [4875]~P42(x48751,x48752)+P42(f881(x48751,a869),f320(x48751,x48752))
% 187.18/188.04 [4993]~P32(x49931)+P43(f300(a1,x49931,x49932))
% 187.18/188.04 [5096]~P42(x50961,x50962)+P59(x50961,f68(x50961,x50961,x50962))
% 187.18/188.04 [5599]~P80(x55991)+P21(x55991,x55991,f79(x55991),x55992)
% 187.18/188.04 [4589]~E(x45892,f118(x45891))+E(f329(f166(x45891),x45892),f118(x45891))
% 187.18/188.04 [4590]~E(x45902,f118(x45901))+E(f329(f167(x45901),x45902),f118(x45901))
% 187.18/188.04 [4645]E(x46451,f329(a109,x46452))+~E(f329(f105(a1),x46451),x46452)
% 187.18/188.04 [4648]E(x46481,f118(x46482))+~E(f329(f166(x46482),x46481),f118(x46482))
% 187.18/188.04 [4649]E(x46491,f118(x46492))+~E(f329(f167(x46492),x46491),f118(x46492))
% 187.18/188.04 [4666]~P94(x46661)+E(f329(f108(x46661),x46662),f329(f107(x46661),x46662))
% 187.18/188.04 [4673]~E(x46732,f206(x46731))+E(f235(x46731,x46732),f193(f881(x46731,a869)))
% 187.18/188.04 [4675]~P28(x46751)+P24(f329(f62(x46751),x46752))
% 187.18/188.04 [4682]E(x46821,f206(x46822))+E(f329(f236(x46822),f683(x46822,x46821)),x46821)
% 187.18/188.04 [4683]E(x46831,f206(x46832))+E(f329(f236(x46832),f716(x46832,x46831)),x46831)
% 187.18/188.04 [4685]~E(f717(x46852,x46851),f118(x46851))+E(f179(x46851,x46852),f118(f875(x46851)))
% 187.18/188.04 [4694]~E(x46942,f118(x46941))+E(f329(f171(x46941),x46942),f193(f881(x46941,a869)))
% 187.18/188.04 [4695]~E(x46952,f118(x46951))+E(f193(f881(x46951,a869)),f329(f171(x46951),x46952))
% 187.18/188.04 [4697]E(x46971,x46972)+~E(f329(f105(a1),x46971),f329(f105(a1),x46972))
% 187.18/188.04 [4700]E(f222(x47001,x47002),f2(a874))+P24(f329(f62(x47001),x47002))
% 187.18/188.04 [4720]~P115(x47201)+E(f82(x47201,f82(x47201,x47202)),f82(x47201,x47202))
% 187.18/188.04 [4733]~P82(x47331)+E(f329(f329(f254(x47331),x47332),f78(a874)),x47332)
% 187.18/188.04 [4734]~P109(x47341)+E(f329(f329(f254(x47341),x47342),f78(a874)),x47342)
% 187.18/188.04 [4736]E(x47361,x47362)+E(f276(x47361,x47362),f329(f329(f80(a104),x47362),f78(a104)))
% 187.18/188.04 [4739]E(f329(f38(x47391),x47392),f2(a874))+P24(f329(f62(x47391),x47392))
% 187.18/188.04 [4743]~E(f150(x47431,x47432),x47432)+P24(f329(f135(x47431),x47432))
% 187.18/188.04 [4746]~P67(x47461)+E(f329(f329(f115(x47461),x47462),f193(x47461)),x47462)
% 187.18/188.04 [4747]~P77(x47471)+E(f329(f329(f22(x47471),x47472),f2(x47471)),x47472)
% 187.18/188.04 [4748]~P101(x47481)+E(f329(f329(f106(x47481),x47482),f252(x47481)),x47482)
% 187.18/188.04 [4749]~P76(x47491)+E(f329(f329(f81(x47491),x47492),f78(x47491)),x47492)
% 187.18/188.04 [4750]~P82(x47501)+E(f329(f329(f81(x47501),x47502),f78(x47501)),x47502)
% 187.18/188.04 [4751]~P109(x47511)+E(f329(f329(f81(x47511),x47512),f78(x47511)),x47512)
% 187.18/188.04 [4752]~P72(x47521)+E(f329(f329(f80(x47521),x47522),f2(x47521)),x47522)
% 187.18/188.04 [4753]~P109(x47531)+E(f329(f329(f80(x47531),x47532),f2(x47531)),x47532)
% 187.18/188.04 [4754]~P83(x47541)+E(f329(f329(f80(x47541),x47542),f2(x47541)),x47542)
% 187.18/188.04 [4755]~P118(x47551)+E(f329(f329(f287(x47551),x47552),f78(x47551)),x47552)
% 187.18/188.04 [4756]~P29(x47561)+E(f329(f329(f39(x47561),x47562),f78(x47561)),x47562)
% 187.18/188.04 [4757]~P109(x47571)+E(f329(f329(f254(x47571),x47572),f2(a874)),f78(x47571))
% 187.18/188.04 [4758]~P111(x47581)+E(f329(f329(f254(x47581),x47582),f2(a874)),f78(x47581))
% 187.18/188.04 [4759]~E(x47592,f193(f881(x47591,a869)))+E(f329(f38(x47591),x47592),f2(a874))
% 187.18/188.04 [4770]~P29(x47701)+E(f45(x47701,x47702,f2(x47701)),x47702)
% 187.18/188.04 [4778]~P101(x47781)+E(f329(f329(f115(x47781),x47782),f252(x47781)),f252(x47781))
% 187.18/188.04 [4779]~P67(x47791)+E(f329(f329(f106(x47791),x47792),f193(x47791)),f193(x47791))
% 187.18/188.04 [4780]~P109(x47801)+E(f329(f329(f81(x47801),x47802),f2(x47801)),f2(x47801))
% 187.18/188.04 [4781]~P128(x47811)+E(f329(f329(f81(x47811),x47812),f2(x47811)),f2(x47811))
% 187.18/188.04 [4782]~P119(x47821)+E(f329(f329(f287(x47821),x47822),f2(x47821)),f2(x47821))
% 187.18/188.04 [4783]~P29(x47831)+E(f329(f329(f39(x47831),x47832),f2(x47831)),f2(x47831))
% 187.18/188.04 [4784]E(x47841,f206(x47842))+~E(f235(x47842,x47841),f193(f881(x47842,a869)))
% 187.18/188.04 [4787]~P29(x47871)+E(f45(x47871,x47872,f78(x47871)),f2(x47871))
% 187.18/188.04 [4788]~P29(x47881)+E(f45(x47881,f2(x47881),x47882),f2(x47881))
% 187.18/188.04 [4817]E(x48171,f2(a874))+E(f55(x48172,x48171,f118(x48172)),f118(f875(x48172)))
% 187.18/188.04 [4841]P42(x48411,x48412)+~E(f551(x48412,x48411),f193(f881(x48411,a869)))
% 187.18/188.04 [4842]E(x48421,f118(x48422))+~E(f329(f171(x48422),x48421),f193(f881(x48422,a869)))
% 187.18/188.04 [4843]E(x48431,f118(x48432))+~E(f193(f881(x48432,a869)),f329(f171(x48432),x48431))
% 187.18/188.04 [4846]~E(x48461,x48462)+P24(f329(f329(a326,x48461),x48462))
% 187.18/188.04 [4856]P24(x48561)+P24(f329(f329(a332,x48561),x48562))
% 187.18/188.04 [4857]E(x48571,f118(x48572))+E(f329(f329(f163(x48572),x48571),f2(a874)),f329(f139(x48572),x48571))
% 187.18/188.04 [4860]E(f150(x48601,x48602),x48602)+~P24(f329(f135(x48601),x48602))
% 187.18/188.04 [4865]~P24(x48652)+P24(f329(f329(a332,x48651),x48652))
% 187.18/188.04 [4866]~P24(x48662)+P24(f329(f329(a328,x48661),x48662))
% 187.18/188.04 [4867]~P24(x48671)+P24(f329(f329(a328,x48671),x48672))
% 187.18/188.04 [4877]~E(f684(x48772,x48771),f689(x48772,x48771))+P24(f329(f135(x48771),x48772))
% 187.18/188.04 [4885]E(f329(f249(x48851),x48852),f193(f881(x48851,a869)))+P24(f329(x48852,f335(x48852)))
% 187.18/188.04 [4886]E(f193(f881(x48861,a869)),f329(f249(x48861),x48862))+P24(f329(x48862,f420(x48862)))
% 187.18/188.04 [4950]~P115(x49501)+E(f329(f329(f81(x49501),x49502),f82(x49501,x49502)),f329(f75(x49501),x49502))
% 187.18/188.04 [4961]~E(x49611,f2(a1))+E(f46(x49611,x49612),f329(f329(f264(a1,a1),f2(a1)),f2(a1)))
% 187.18/188.04 [4992]~P57(x49921,x49922)+P57(x49921,f329(f284(x49921,x49921),x49922))
% 187.18/188.04 [5011]~E(f329(a28,x50111),f329(f236(a870),x50112))+P24(f329(a25,f329(a26,x50111)))
% 187.18/188.04 [5016]E(x50161,x50162)+~P24(f329(f329(a326,x50161),x50162))
% 187.18/188.04 [5020]~P24(f329(a25,x50202))+P24(f329(a25,f32(x50201,x50202)))
% 187.18/188.04 [5029]P24(x50291)+~P24(f329(f329(a327,x50292),x50291))
% 187.18/188.04 [5030]P24(x50301)+~P24(f329(f329(a327,x50301),x50302))
% 187.18/188.04 [5035]~P112(x50351)+P24(f329(f329(f243(x50351),x50352),f252(x50351)))
% 187.18/188.04 [5039]E(x50391,x50392)+~E(f329(x50391,f421(x50392,x50391)),f329(x50392,f421(x50392,x50391)))
% 187.18/188.04 [5069]E(x50691,f2(a874))+E(f224(x50691,f45(a874,x50692,x50691)),f224(x50692,x50691))
% 187.18/188.04 [5074]~P27(x50741)+P33(x50741,f329(f329(f149(x50741),x50742),f118(x50741)))
% 187.18/188.04 [5076]E(x50761,f2(a1))+P24(f329(f49(x50762,x50761),f46(x50762,x50761)))
% 187.18/188.04 [5094]~E(x50941,x50942)+P24(f329(f329(f244(a874),x50941),f329(a117,x50942)))
% 187.18/188.04 [5104]~E(x51041,f2(a874))+P24(f329(f329(f244(a874),x51041),f329(a117,x51042)))
% 187.18/188.04 [5114]P24(f329(x51141,x51142))+P24(f329(f329(f243(a1),f2(a1)),f407(x51141)))
% 187.18/188.04 [5151]P24(f329(a25,x51511))+~P24(f329(a25,f32(x51512,x51511)))
% 187.18/188.04 [5153]P24(f329(a25,x51531))+~P24(f329(a25,f33(x51532,x51531)))
% 187.18/188.04 [5155]P24(f329(a25,x51551))+~P24(f329(a25,f33(x51551,x51552)))
% 187.18/188.04 [5187]P57(x51871,x51872)+~P57(x51871,f329(f284(x51871,x51871),x51872))
% 187.18/188.04 [5190]~E(f45(a874,x51902,x51901),f2(a874))+E(f329(f329(f81(a874),x51901),f338(x51901,x51902)),x51902)
% 187.18/188.04 [5191]~E(f45(a1,x51912,x51911),f2(a1))+E(f329(f329(f81(a1),x51911),f339(x51911,x51912)),x51912)
% 187.18/188.04 [5217]~P24(f329(x52171,x52172))+P24(f329(f329(f243(a1),f2(a1)),f337(x52171)))
% 187.18/188.04 [5229]E(f329(f329(f22(a874),f329(a109,x52291)),f329(a109,x52292)),f329(a109,x52291))+~P24(f329(a198,x52292))
% 187.18/188.04 [5259]E(f277(x52591,x52592),f78(a104))+~P24(f329(f329(f243(a104),x52591),f78(a104)))
% 187.18/188.04 [5354]E(f329(f329(f163(x53541),x53542),f684(x53542,x53541)),f329(f329(f163(x53541),x53542),f689(x53542,x53541)))+P24(f329(f135(x53541),x53542))
% 187.18/188.04 [5399]~P24(f329(x53991,f90(x53992,x53991)))+P24(f329(x53991,f554(x53992,x53991)))
% 187.18/188.04 [5462]P59(x54621,x54622)+~P24(f329(f317(x54621,x54622),f533(x54622,x54621)))
% 187.18/188.04 [5606]~E(f329(a117,f45(a874,x56061,x56062)),x56062)+E(f45(a874,f329(a117,x56061),x56062),f2(a874))
% 187.18/188.04 [5663]P42(x56631,x56632)+P24(f329(f329(f331(x56631),f597(x56632,x56631)),f598(x56632,x56631)))
% 187.18/188.04 [5670]~P138(x56701)+P24(f329(f329(f331(x56701),f329(f105(x56701),x56702)),f114(x56701)))
% 187.18/188.04 [5671]~P141(x56711)+P24(f329(f329(f331(x56711),f329(f105(x56711),x56712)),f191(x56711)))
% 187.18/188.04 [5672]~P138(x56721)+P24(f329(f329(f331(x56721),f329(f107(x56721),x56722)),f114(x56721)))
% 187.18/188.04 [5673]~P94(x56731)+P24(f329(f329(f331(x56731),f329(f108(x56731),x56732)),f114(x56731)))
% 187.18/188.04 [5818]E(f329(a117,f45(a874,x58181,x58182)),x58182)+E(f45(a874,f329(a117,x58181),x58182),f329(a117,f45(a874,x58181,x58182)))
% 187.18/188.04 [6236]P42(x62361,x62362)+~P24(f329(f329(f331(x62361),f501(x62362,x62361)),f318(x62361,x62362)))
% 187.18/188.04 [6271]~P121(x62711)+~P24(f329(f329(f244(x62711),f329(f105(x62711),x62712)),f2(x62711)))
% 187.18/188.04 [6272]~P87(x62721)+~P24(f329(f329(f244(x62721),f329(f75(x62721),x62722)),f2(x62721)))
% 187.18/188.04 [6358]P24(f329(f329(f244(a1),x63581),f45(a1,x63582,x63581)))+~P24(f329(f329(f244(a1),x63581),f2(a1)))
% 187.18/188.04 [6457]E(f329(f329(f307(a874),f329(a117,x64571)),f300(a874,x64572,x64571)),f300(a874,x64572,f329(a117,x64571)))+~P24(f329(f329(f243(a874),x64572),f329(a117,x64571)))
% 187.18/188.04 [6545]~P27(x65451)+P33(x65451,f148(x65451,x65451,f5(x65451),x65452))
% 187.18/188.04 [6675]E(f329(f166(x66751),x66752),x66752)+~P24(f329(f329(f243(a874),f329(f194(f875(x66751)),x66752)),f78(a874)))
% 187.18/188.04 [6695]~P87(x66951)+P24(f329(f329(f243(x66951),f329(f79(x66951),f329(f75(x66951),x66952))),f2(x66951)))
% 187.18/188.04 [6728]~P42(x67281,x67282)+P42(x67281,f329(f329(f286(x67281,x67281,x67281),x67282),f305(x67281,x67282)))
% 187.18/188.04 [6951]~P24(f329(f329(f244(a1),x69512),f2(a1)))+P24(f329(f329(f243(a1),f45(a1,x69511,x69512)),f2(a1)))
% 187.18/188.04 [7347]~P141(x73471)+E(f195(x73471,f329(f329(f7(x73471,x73471,x73471),f80(x73471)),f78(x73471)),x73472,f2(x73471)),f329(f105(x73471),x73472))
% 187.18/188.04 [7375]~P122(x73751)+~P24(f329(f329(f244(x73751),f329(f329(f81(x73751),x73752),x73752)),f2(x73751)))
% 187.18/188.04 [10011]~P115(x100111)+~P24(f329(f329(f244(x100111),f329(f329(f254(x100111),x100112),f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102))))),f2(x100111)))
% 187.18/188.04 [4646]~E(x46462,f118(x46461))+E(f329(f194(f875(x46461)),x46462),f2(a874))
% 187.18/188.04 [4686]~E(x46861,f2(a874))+E(f329(f329(f80(a874),x46861),x46862),x46862)
% 187.18/188.04 [4687]~E(x46872,f2(a874))+E(f329(f329(f81(a874),x46871),x46872),f2(a874))
% 187.18/188.04 [4689]~E(x46891,f2(a874))+E(f329(f329(f81(a874),x46891),x46892),f2(a874))
% 187.18/188.04 [4690]~E(x46902,f2(a874))+E(f329(f329(f254(a874),x46901),x46902),f78(a874))
% 187.18/188.04 [4691]~E(x46912,f2(a1))+E(f329(f329(f39(a1),x46911),x46912),f2(a1))
% 187.18/188.04 [4701]E(x47011,f118(x47012))+~E(f329(f194(f875(x47012)),x47011),f2(a874))
% 187.18/188.04 [4702]~P66(x47021)+E(f329(f329(f115(x47021),x47022),x47022),x47022)
% 187.18/188.04 [4704]~P102(x47041)+E(f329(f329(f115(x47041),x47042),x47042),x47042)
% 187.18/188.04 [4705]~P66(x47051)+E(f329(f329(f106(x47051),x47052),x47052),x47052)
% 187.18/188.04 [4707]~P103(x47071)+E(f329(f329(f106(x47071),x47072),x47072),x47072)
% 187.18/188.04 [4709]~P98(x47091)+E(f329(f329(f81(x47091),x47092),x47092),x47092)
% 187.18/188.04 [4711]~P27(x47111)+E(f329(f329(f241(x47111),x47112),x47112),x47112)
% 187.18/188.04 [4713]~P27(x47131)+E(f329(f329(f242(x47131),x47132),x47132),x47132)
% 187.18/188.04 [4732]~P77(x47321)+E(f329(f329(f22(x47321),x47322),x47322),f2(x47321))
% 187.18/188.04 [4744]~P77(x47441)+E(f329(f79(x47441),f329(f79(x47441),x47442)),x47442)
% 187.18/188.04 [4745]~P97(x47451)+E(f329(f79(x47451),f329(f79(x47451),x47452)),x47452)
% 187.18/188.04 [4762]~E(x47622,f2(a874))+E(f329(f329(f254(a874),x47621),x47622),f329(a117,f2(a874)))
% 187.18/188.04 [4796]~P67(x47961)+E(f329(f329(f115(x47961),f193(x47961)),x47962),x47962)
% 187.18/188.04 [4797]~P101(x47971)+E(f329(f329(f106(x47971),f252(x47971)),x47972),x47972)
% 187.18/188.04 [4798]~P76(x47981)+E(f329(f329(f81(x47981),f78(x47981)),x47982),x47982)
% 187.18/188.04 [4799]~P82(x47991)+E(f329(f329(f81(x47991),f78(x47991)),x47992),x47992)
% 187.18/188.04 [4800]~P109(x48001)+E(f329(f329(f81(x48001),f78(x48001)),x48002),x48002)
% 187.18/188.04 [4801]~P72(x48011)+E(f329(f329(f80(x48011),f2(x48011)),x48012),x48012)
% 187.18/188.04 [4802]~P109(x48021)+E(f329(f329(f80(x48021),f2(x48021)),x48022),x48022)
% 187.18/188.04 [4803]~P83(x48031)+E(f329(f329(f80(x48031),f2(x48031)),x48032),x48032)
% 187.18/188.04 [4822]~P101(x48221)+E(f329(f329(f115(x48221),f252(x48221)),x48222),f252(x48221))
% 187.18/188.04 [4823]~P67(x48231)+E(f329(f329(f106(x48231),f193(x48231)),x48232),f193(x48231))
% 187.18/188.04 [4824]~P109(x48241)+E(f329(f329(f81(x48241),f2(x48241)),x48242),f2(x48241))
% 187.18/188.04 [4825]~P128(x48251)+E(f329(f329(f81(x48251),f2(x48251)),x48252),f2(x48251))
% 187.18/188.04 [4826]~P82(x48261)+E(f329(f329(f254(x48261),f78(x48261)),x48262),f78(x48261))
% 187.18/188.04 [4827]~P118(x48271)+E(f329(f329(f287(x48271),f2(x48271)),x48272),f2(x48271))
% 187.18/188.04 [4828]~P29(x48281)+E(f329(f329(f39(x48281),f2(x48281)),x48282),f2(x48281))
% 187.18/188.04 [4836]E(x48361,f118(x48362))+E(f142(x48362,f329(f167(x48362),x48361)),f329(f139(x48362),x48361))
% 187.18/188.04 [4837]E(x48371,f118(x48372))+E(f329(f139(x48372),f329(f167(x48372),x48371)),f142(x48372,x48371))
% 187.18/188.04 [4838]E(x48381,f2(a874))+~E(f329(f329(f80(a874),x48382),x48381),x48382)
% 187.18/188.04 [4844]~P138(x48441)+E(f329(f107(x48441),f329(f105(a1),x48442)),f329(f105(x48441),x48442))
% 187.18/188.04 [4845]~P94(x48451)+E(f329(f107(x48451),f329(f108(a1),x48452)),f329(f108(x48451),x48452))
% 187.18/188.04 [4852]E(x48521,f78(a874))+~E(f329(f329(f81(a874),x48522),x48521),f78(a874))
% 187.18/188.04 [4853]E(x48531,f78(a874))+~E(f329(f329(f81(a874),x48531),x48532),f78(a874))
% 187.18/188.04 [4854]E(x48541,f2(a874))+~E(f329(f329(f80(a874),x48542),x48541),f2(a874))
% 187.18/188.04 [4855]E(x48551,f2(a874))+~E(f329(f329(f80(a874),x48551),x48552),f2(a874))
% 187.18/188.04 [4870]~P115(x48701)+E(f329(f75(x48701),f329(f105(x48701),x48702)),f329(f105(x48701),x48702))
% 187.18/188.04 [4871]~P87(x48711)+E(f329(f75(x48711),f329(f75(x48711),x48712)),f329(f75(x48711),x48712))
% 187.18/188.04 [4872]~P87(x48721)+E(f329(f75(x48721),f329(f79(x48721),x48722)),f329(f75(x48721),x48722))
% 187.18/188.04 [4873]~P72(x48731)+E(f329(f164(x48731),f329(f167(x48731),x48732)),f329(f164(x48731),x48732))
% 187.18/188.04 [4878]~E(x48781,f329(a117,f2(a874)))+E(f329(f329(f254(a874),x48781),x48782),f329(a117,f2(a874)))
% 187.18/188.04 [4888]~P77(x48881)+E(f329(f329(f22(x48881),f2(x48881)),x48882),f329(f79(x48881),x48882))
% 187.18/188.04 [4889]~E(x48892,f2(a874))+E(f137(a874,f329(f299(a874,x48891),x48892)),f118(a874))
% 187.18/188.04 [4898]~P94(x48981)+E(f329(f329(f80(x48981),x48982),f329(f108(x48981),a83)),x48982)
% 187.18/188.04 [4899]E(x48991,f2(a1))+E(f47(f329(f75(a1),x48992),f329(f75(a1),x48991)),f53(x48992,x48991))
% 187.18/188.04 [4913]~E(x49131,x49132)+P24(f329(f329(f243(a874),x49131),x49132))
% 187.18/188.04 [4920]~E(x49201,f2(a104))+E(f329(f329(f80(a874),f329(a19,x49201)),x49202),x49202)
% 187.18/188.04 [4921]~E(f329(f108(a1),x49212),f329(f105(a1),x49211))+E(x49211,f329(a109,f329(f108(a1),x49212)))
% 187.18/188.04 [4930]~P32(x49301)+P32(f329(f329(f254(a1),x49301),x49302))
% 187.18/188.04 [4931]~P97(x49311)+E(f329(f329(f115(x49311),x49312),f329(f79(x49311),x49312)),f252(x49311))
% 187.18/188.04 [4932]~P97(x49321)+E(f329(f329(f106(x49321),x49322),f329(f79(x49321),x49322)),f193(x49321))
% 187.18/188.04 [4933]~P77(x49331)+E(f329(f329(f80(x49331),x49332),f329(f79(x49331),x49332)),f2(x49331))
% 187.18/188.04 [4958]E(x49581,f2(a874))+~E(f329(f79(a1),f329(f105(a1),x49582)),f329(f105(a1),x49581))
% 187.18/188.04 [4959]E(x49591,f2(a874))+~E(f329(f79(a1),f329(f105(a1),x49591)),f329(f105(a1),x49592))
% 187.18/188.04 [4969]E(f200(x49691,x49692),f2(a1))+P24(f329(f329(f243(a1),x49692),x49691))
% 187.18/188.04 [4970]E(f178(x49701,x49702),f118(a1))+P24(f329(f329(f243(a1),x49701),x49702))
% 187.18/188.04 [4983]E(x49831,f329(a117,f2(a874)))+~E(f329(f329(f81(a874),x49832),x49831),f329(a117,f2(a874)))
% 187.18/188.04 [4984]E(x49841,f329(a117,f2(a874)))+~E(f329(f329(f81(a874),x49841),x49842),f329(a117,f2(a874)))
% 187.18/188.04 [4985]~P25(x49851)+P24(f329(f329(f243(x49851),x49852),x49852))
% 187.18/188.04 [4986]~P96(x49861)+P24(f329(f329(f91(x49861),x49862),x49862))
% 187.18/188.04 [4989]~P94(x49891)+E(f329(f329(f81(x49891),x49892),f329(f108(x49891),a102)),f329(f79(x49891),x49892))
% 187.18/188.04 [5007]~P138(x50071)+E(f329(f79(x50071),f329(f107(x50071),x50072)),f329(f107(x50071),f329(f79(a1),x50072)))
% 187.18/188.04 [5008]~P94(x50081)+E(f329(f79(x50081),f329(f108(x50081),x50082)),f329(f108(x50081),f329(f79(a1),x50082)))
% 187.18/188.04 [5040]~E(x50401,f329(a117,x50402))+P24(f329(f329(f244(a874),f2(a874)),x50401))
% 187.18/188.04 [5057]~P27(x50571)+E(f329(f79(f881(x50571,a869)),f329(f250(x50571),x50572)),f329(f251(x50571),x50572))
% 187.18/188.04 [5058]~P27(x50581)+E(f329(f79(f881(x50581,a869)),f329(f298(x50581),x50582)),f329(f301(x50581),x50582))
% 187.18/188.04 [5059]~P27(x50591)+E(f329(f79(f881(x50591,a869)),f329(f251(x50591),x50592)),f329(f250(x50591),x50592))
% 187.18/188.04 [5060]~P27(x50601)+E(f329(f79(f881(x50601,a869)),f329(f301(x50601),x50602)),f329(f298(x50601),x50602))
% 187.18/188.04 [5068]~E(f329(f105(a1),x50682),x50681)+P24(f329(f329(f243(a1),f2(a1)),x50681))
% 187.18/188.04 [5075]~E(x50752,f2(a1))+E(f53(x50751,x50752),f329(f329(f264(a1,a1),f2(a1)),f329(f75(a1),x50751)))
% 187.18/188.04 [5077]~P65(x50771)+P24(f329(f329(f243(x50771),f193(x50771)),x50772))
% 187.18/188.04 [5109]E(x51091,x51092)+~E(f329(f329(f80(a1),x51091),x51091),f329(f329(f80(a1),x51092),x51092))
% 187.18/188.04 [5113]~P24(f329(x51131,x51132))+P24(f329(x51131,f329(a109,f337(x51131))))
% 187.18/188.04 [5139]~P115(x51391)+E(f329(f329(f81(x51391),f82(x51391,x51392)),f329(f75(x51391),x51392)),x51392)
% 187.18/188.04 [5140]E(x51401,x51402)+~P24(f329(f329(f199(a24),x51401),x51402))
% 187.18/188.04 [5149]~E(x51492,f2(a874))+E(f85(f880(a874,a874),f48(x51491,x51492)),f329(f329(f264(a874,a874),f2(a874)),x51491))
% 187.18/188.04 [5160]~E(x51601,x51602)+~P24(f329(f329(f244(a874),x51601),x51602))
% 187.18/188.04 [5161]~E(x51611,x51612)+~P24(f329(f329(f244(a1),x51611),x51612))
% 187.18/188.04 [5164]~P141(x51641)+E(f329(f329(f80(x51641),f78(x51641)),f329(f105(x51641),x51642)),f329(f105(x51641),f329(a117,x51642)))
% 187.18/188.04 [5168]~E(x51681,f2(a874))+~P24(f329(f329(f244(a874),x51682),x51681))
% 187.18/188.04 [5184]E(f150(x51841,x51842),x51842)+~E(f329(f194(f875(x51841)),f150(x51841,x51842)),f329(f194(f875(x51841)),x51842))
% 187.18/188.04 [5185]E(f329(f38(x51851),f329(f171(x51851),x51852)),f329(f194(f875(x51851)),x51852))+~P24(f329(f135(x51851),x51852))
% 187.18/188.04 [5195]~P24(f329(x51951,f353(x51951)))+P24(f329(x51951,f329(f105(a1),x51952)))
% 187.18/188.04 [5206]E(f277(x52061,x52062),f78(a104))+~P24(f329(f329(f244(a104),x52062),x52061))
% 187.18/188.04 [5207]E(f178(x52071,x52072),f118(a1))+~P24(f329(f329(f244(a1),x52072),x52071))
% 187.18/188.04 [5210]~P106(x52101)+E(f300(x52101,x52102,x52102),f329(f329(f307(x52101),x52102),f193(f881(x52101,a869))))
% 187.18/188.04 [5232]~E(f329(f329(f22(a874),x52321),x52322),f2(a874))+P24(f329(f329(f243(a874),x52321),x52322))
% 187.18/188.04 [5233]~E(f329(f329(f22(a1),x52331),x52332),f2(a1))+P24(f329(f329(f91(a1),x52331),x52332))
% 187.18/188.04 [5256]~E(x52562,f2(a874))+E(f55(x52561,x52562,f118(x52561)),f329(f329(f149(f875(x52561)),f118(x52561)),f118(f875(x52561))))
% 187.18/188.04 [5260]~P25(x52601)+~P24(f329(f329(f244(x52601),x52602),x52602))
% 187.18/188.04 [5263]~E(f45(a1,x52631,x52632),f2(a1))+E(f45(a1,x52631,f329(f79(a1),x52632)),f2(a1))
% 187.18/188.04 [5265]~E(f45(a1,x52651,x52652),f2(a1))+E(f45(a1,f329(f79(a1),x52651),x52652),f2(a1))
% 187.18/188.04 [5274]E(f329(f299(a874,x52741),f329(a117,x52742)),f193(f881(a874,a869)))+P24(f329(f329(f243(a874),x52741),x52742))
% 187.18/188.04 [5295]E(f137(a874,f329(f299(a874,x52951),x52952)),f118(a874))+P24(f329(f329(f244(a874),x52951),x52952))
% 187.18/188.04 [5300]~E(f329(f38(x53001),f329(f171(x53001),x53002)),f329(f194(f875(x53001)),x53002))+P24(f329(f135(x53001),x53002))
% 187.18/188.04 [5305]~P24(f329(f135(x53051),x53052))+P24(f329(f135(x53051),f329(f166(x53051),x53052)))
% 187.18/188.04 [5306]~P24(f329(f135(x53061),x53062))+P24(f329(f135(x53061),f329(f170(x53061),x53062)))
% 187.18/188.04 [5307]~P24(f329(f135(x53071),x53072))+P24(f329(f135(x53071),f329(f167(x53071),x53072)))
% 187.18/188.04 [5314]P24(f329(x53141,x53142))+~P24(f329(x53141,f329(a109,f407(x53141))))
% 187.18/188.04 [5315]P24(f329(f329(f243(a874),x53152),x53151))+P24(f329(f329(f243(a874),x53151),x53152))
% 187.18/188.04 [5316]P24(f329(f329(f243(a1),x53162),x53161))+P24(f329(f329(f243(a1),x53161),x53162))
% 187.18/188.04 [5318]~P87(x53181)+P24(f329(f329(f243(x53181),x53182),f329(f75(x53181),x53182)))
% 187.18/188.04 [5321]P24(f329(x53211,f354(x53211)))+~P24(f329(x53211,f329(f105(a1),x53212)))
% 187.18/188.04 [5346]E(f329(f329(f22(a874),x53461),x53462),f2(a874))+~P24(f329(f329(f243(a874),x53461),x53462))
% 187.18/188.04 [5347]E(f329(f329(f22(a1),x53471),x53472),f2(a1))+~P24(f329(f329(f91(a1),x53471),x53472))
% 187.18/188.04 [5348]E(f329(f329(f39(a874),x53481),x53482),f2(a874))+~P24(f329(f329(f244(a874),x53481),x53482))
% 187.18/188.04 [5366]E(f45(a874,x53661,x53662),x53661)+~P24(f329(f329(f244(a874),x53661),x53662))
% 187.18/188.04 [5375]E(f45(a1,x53751,f329(f79(a1),x53752)),f288(x53751,x53752))+P24(f329(f329(f243(a1),f2(a1)),x53752))
% 187.18/188.04 [5387]E(f329(f329(f22(a1),x53871),x53872),f200(x53871,x53872))+~P24(f329(f329(f243(a1),x53872),x53871))
% 187.18/188.04 [5406]P24(f329(f329(f243(a1),f2(a1)),f353(x54061)))+P24(f329(x54061,f329(f105(a1),x54062)))
% 187.18/188.04 [5418]~P60(x54181)+P24(f329(f329(f331(x54181),x54182),f329(f171(x54181),f56(x54181))))
% 187.18/188.04 [5420]~P121(x54201)+P24(f329(f329(f243(x54201),f2(x54201)),f329(f105(x54201),x54202)))
% 187.18/188.04 [5421]~P87(x54211)+P24(f329(f329(f243(x54211),f2(x54211)),f329(f75(x54211),x54212)))
% 187.18/188.04 [5448]E(f329(f329(f80(a874),x54481),f806(x54482,x54481)),x54482)+~P24(f329(f329(f243(a874),x54481),x54482))
% 187.18/188.04 [5460]~E(f329(f108(a1),x54601),f329(f105(a1),x54602))+P24(f329(f329(f243(a1),f2(a1)),f329(f108(a1),x54601)))
% 187.18/188.04 [5463]E(f300(a1,x54631,x54632),f193(f881(a1,a869)))+~P24(f329(f329(f244(a1),x54632),x54631))
% 187.18/188.04 [5465]~P115(x54651)+E(f329(f329(f81(x54651),f329(f75(x54651),x54652)),f329(f75(x54651),x54652)),f329(f329(f81(x54651),x54652),x54652))
% 187.18/188.04 [5471]E(f137(a874,f329(f299(a874,x54711),f329(a117,x54712))),f118(a874))+P24(f329(f329(f243(a874),x54711),x54712))
% 187.18/188.04 [5475]E(f329(f329(f39(a1),x54751),x54752),f289(x54751,x54752))+~P24(f329(f329(f243(a1),f2(a1)),x54752))
% 187.18/188.04 [5495]P24(f329(f135(x54951),x54952))+~P24(f329(f135(x54951),f329(f166(x54951),x54952)))
% 187.18/188.04 [5496]P24(f329(f135(x54961),x54962))+~P24(f329(f135(x54961),f329(f167(x54961),x54962)))
% 187.18/188.04 [5517]P24(f329(f62(a874),x55171))+P24(f329(f329(f331(a874),f341(x55171,x55172)),x55171))
% 187.18/188.04 [5518]P24(f329(f62(a874),x55181))+P24(f329(f329(f331(a874),f346(x55181,x55182)),x55181))
% 187.18/188.04 [5519]P24(f329(f329(f244(a874),x55192),f329(a117,x55191)))+P24(f329(f329(f244(a874),x55191),x55192))
% 187.18/188.04 [5520]E(f45(a1,x55201,x55202),f288(x55201,x55202))+~P24(f329(f329(f243(a1),f2(a1)),x55202))
% 187.18/188.04 [5523]E(f137(a874,f329(f299(a874,x55231),x55232)),f118(a874))+~P24(f329(f329(f243(a874),x55232),x55231))
% 187.18/188.04 [5524]~P80(x55241)+E(f329(f308(x55241,x55241,f79(x55241)),f329(f250(x55241),x55242)),f329(f301(x55241),f329(f79(x55241),x55242)))
% 187.18/188.04 [5525]~P80(x55251)+E(f329(f308(x55251,x55251,f79(x55251)),f329(f298(x55251),x55252)),f329(f251(x55251),f329(f79(x55251),x55252)))
% 187.18/188.04 [5526]~P80(x55261)+E(f329(f308(x55261,x55261,f79(x55261)),f329(f251(x55261),x55262)),f329(f298(x55261),f329(f79(x55261),x55262)))
% 187.18/188.04 [5527]~P80(x55271)+E(f329(f308(x55271,x55271,f79(x55271)),f329(f301(x55271),x55272)),f329(f250(x55271),f329(f79(x55271),x55272)))
% 187.18/188.04 [5538]E(x55381,f193(f881(x55382,a869)))+P24(f329(f329(f331(x55382),f357(x55381,x55382)),x55381))
% 187.18/188.04 [5539]E(x55391,f193(f881(x55392,a869)))+P24(f329(f329(f331(x55392),f358(x55391,x55392)),x55391))
% 187.18/188.04 [5550]~P24(f329(f329(f244(a874),x55501),x55502))+P24(f329(f329(f243(a874),x55501),x55502))
% 187.18/188.04 [5551]~P24(f329(f329(f244(a1),x55511),x55512))+P24(f329(f329(f243(a1),x55511),x55512))
% 187.18/188.04 [5567]E(f47(x55671,x55672),f329(f329(f264(a1,a1),f2(a1)),x55671))+~P24(f329(f329(f244(a1),x55671),x55672))
% 187.18/188.04 [5569]E(f223(f329(f79(a1),x55691),f329(f79(a1),x55692)),f223(x55691,x55692))+~P24(f329(f329(f244(a1),x55692),f2(a1)))
% 187.18/188.04 [5580]E(x55801,x55802)+~E(f329(a3,f329(a117,f329(a19,x55801))),f329(a3,f329(a117,f329(a19,x55802))))
% 187.18/188.04 [5585]E(f47(x55851,x55852),f329(f329(f264(a1,a1),f2(a1)),x55851))+~P24(f329(f329(f243(a1),x55852),f2(a1)))
% 187.18/188.04 [5612]E(f45(a874,f329(f108(a874),x56121),f329(f108(a874),x56122)),f2(a874))+~P24(f329(a198,f329(f108(a1),x56121)))
% 187.18/188.04 [5627]P24(f329(f329(f243(a1),f2(a1)),f354(x56271)))+~P24(f329(x56271,f329(f105(a1),x56272)))
% 187.18/188.04 [5661]P43(f300(a1,x56611,x56612))+~P24(f329(f329(f243(a1),f2(a1)),x56611))
% 187.18/188.04 [5666]~P24(f329(f62(x56661),x56662))+P24(f329(f62(f881(x56661,a869)),f329(f306(x56661),x56662)))
% 187.18/188.04 [5679]E(f329(f329(f80(a1),x56791),f329(f105(a1),f360(x56792,x56791))),x56792)+~P24(f329(f329(f243(a1),x56791),x56792))
% 187.18/188.04 [5687]P24(f329(f329(f243(a874),x56871),x56872))+P24(f329(f329(f243(a874),f329(a117,x56872)),x56871))
% 187.18/188.04 [5732]E(f329(f329(f39(a874),f329(f108(a874),x57321)),f329(f108(a874),x57322)),f2(a874))+~P24(f329(a198,f329(f108(a1),x57321)))
% 187.18/188.04 [5733]E(f329(f329(f81(a874),f329(f108(a874),x57331)),f329(f108(a874),x57332)),f2(a874))+~P24(f329(f329(f244(a1),x57331),a83))
% 187.18/188.04 [5735]P24(f329(f329(f243(a874),x57351),f329(a117,x57352)))+~P24(f329(f329(f243(a874),x57351),x57352))
% 187.18/188.04 [5737]P24(f329(f329(f244(a874),x57371),f329(a117,x57372)))+~P24(f329(f329(f243(a874),x57371),x57372))
% 187.18/188.04 [5739]P24(f329(f329(f244(a874),x57391),f329(a117,x57392)))+~P24(f329(f329(f244(a874),x57391),x57392))
% 187.18/188.04 [5742]~E(x57421,x57422)+P24(f329(f329(f244(a1),x57421),f329(f329(f80(a1),x57422),f78(a1))))
% 187.18/188.04 [5745]E(f45(a1,x57451,x57452),f2(a1))+E(f329(f329(f22(a1),x57452),f45(a1,x57451,x57452)),f45(a1,f329(f79(a1),x57451),x57452))
% 187.18/188.04 [5754]E(x57541,f118(x57542))+P24(f329(f329(f331(x57542),f142(x57542,x57541)),f329(f171(x57542),x57541)))
% 187.18/188.04 [5766]E(f85(f880(a874,a874),f48(x57661,x57662)),f329(f329(f264(a874,a874),f2(a874)),x57661))+~P24(f329(f329(f244(a874),x57661),x57662))
% 187.18/188.04 [5799]E(f329(f329(f22(a874),f329(f108(a874),x57991)),f329(f108(a874),x57992)),f329(f108(a874),x57991))+~P24(f329(f329(f244(a1),x57992),a83))
% 187.18/188.04 [5800]E(f329(f329(f80(a874),f329(f108(a874),x58001)),f329(f108(a874),x58002)),f329(f108(a874),x58002))+~P24(f329(f329(f244(a1),x58001),a83))
% 187.18/188.04 [5805]E(f329(a117,f329(f329(f80(a874),x58051),f855(x58052,x58051))),x58052)+~P24(f329(f329(f244(a874),x58051),x58052))
% 187.18/188.04 [5828]P24(f329(x58281,x58282))+~P24(f329(x58281,f329(a89,f553(x58282,x58281))))
% 187.18/188.04 [5836]~P24(f329(f329(f244(a874),x58361),f329(a117,x58362)))+P24(f329(f329(f243(a874),x58361),x58362))
% 187.18/188.04 [5882]E(f329(f329(f307(a874),x58821),f329(f299(a874,x58822),x58821)),f329(f299(a874,x58822),f329(a117,x58821)))+~P24(f329(f329(f243(a874),x58822),x58821))
% 187.18/188.04 [5886]E(x58861,f118(x58862))+E(f329(f329(f126(x58862),f119(x58862,x58861)),f329(f329(f149(x58862),f142(x58862,x58861)),f118(x58862))),x58861)
% 187.18/188.04 [5900]P24(f329(f62(x59001),x59002))+~P24(f329(f329(f244(a874),f2(a874)),f329(f38(x59001),x59002)))
% 187.18/188.04 [5902]~E(x59021,f193(f881(x59022,a869)))+~P24(f329(f329(f244(a874),f2(a874)),f329(f38(x59022),x59021)))
% 187.18/188.04 [5914]~P24(f329(f329(f244(a874),x59141),x59142))+P24(f329(f329(f243(a874),f329(a117,x59141)),x59142))
% 187.18/188.04 [5922]~P27(x59221)+E(f148(x59221,x59221,f5(x59221),f150(x59221,x59222)),f137(x59221,f329(f171(x59221),x59222)))
% 187.18/188.04 [5925]E(x59251,f118(x59252))+P24(f329(f329(f331(x59252),f329(f139(x59252),x59251)),f329(f171(x59252),x59251)))
% 187.18/188.04 [5931]~P121(x59311)+P24(f329(f329(f244(x59311),x59312),f329(f329(f80(x59311),x59312),f78(x59311))))
% 187.18/188.04 [5933]~P87(x59331)+P24(f329(f329(f243(x59331),f329(f79(x59331),x59332)),f329(f75(x59331),x59332)))
% 187.18/188.04 [5966]P24(f329(f62(a874),x59661))+~P24(f329(f329(f243(a874),f346(x59661,x59662)),x59662))
% 187.18/188.04 [5967]P24(f329(f62(a874),x59671))+~P24(f329(f329(f244(a874),f341(x59671,x59672)),x59672))
% 187.18/188.04 [5971]~P24(f329(f62(f880(x59711,x59711)),x59712))+P24(f329(f62(x59711),f329(f282(x59711),x59712)))
% 187.18/188.04 [6024]~P24(f329(f329(f244(a874),x60242),f329(a117,x60241)))+~P24(f329(f329(f244(a874),x60241),x60242))
% 187.18/188.04 [6025]~P106(x60251)+E(f329(f329(f106(f881(x60251,a869)),f329(f298(x60251),x60252)),f329(f251(x60251),x60252)),f329(f329(f307(x60251),x60252),f193(f881(x60251,a869))))
% 187.18/188.04 [6038]P24(f329(f62(x60381),x60382))+~P24(f329(f62(f881(x60381,a869)),f329(f306(x60381),x60382)))
% 187.18/188.04 [6062]P24(f329(f329(f243(a874),f329(a117,x60621)),f329(a117,x60622)))+~P24(f329(f329(f243(a874),x60621),x60622))
% 187.18/188.04 [6063]P24(f329(f329(f243(a874),f329(a19,x60631)),f329(a19,x60632)))+~P24(f329(f329(f243(a104),x60631),x60632))
% 187.18/188.04 [6064]P24(f329(f329(f243(a104),f329(a3,x60641)),f329(a3,x60642)))+~P24(f329(f329(f243(a874),x60641),x60642))
% 187.18/188.04 [6066]P24(f329(f329(f244(a874),f329(a117,x60661)),f329(a117,x60662)))+~P24(f329(f329(f244(a874),x60661),x60662))
% 187.18/188.04 [6067]P24(f329(f329(f244(a874),f329(a19,x60671)),f329(a19,x60672)))+~P24(f329(f329(f244(a104),x60671),x60672))
% 187.18/188.04 [6068]P24(f329(f329(f244(a104),f329(a3,x60681)),f329(a3,x60682)))+~P24(f329(f329(f244(a874),x60681),x60682))
% 187.18/188.04 [6071]E(x60711,x60712)+~E(f329(f308(a874,a1,f105(a1)),x60711),f329(f308(a874,a1,f105(a1)),x60712))
% 187.18/188.04 [6087]P24(f329(f329(f243(a874),x60871),x60872))+~P24(f329(f329(f243(a874),f329(a117,x60871)),x60872))
% 187.18/188.04 [6090]P24(f329(f329(f244(a874),x60901),x60902))+~P24(f329(f329(f243(a874),f329(a117,x60901)),x60902))
% 187.18/188.04 [6091]P24(f329(f329(f244(a874),x60911),x60912))+~P24(f329(f329(f244(a874),f329(a117,x60911)),x60912))
% 187.18/188.04 [6106]E(f45(a1,x61061,x61062),f2(a1))+E(f329(f329(f22(a1),f45(a1,x61061,x61062)),x61062),f45(a1,x61061,f329(f79(a1),x61062)))
% 187.18/188.04 [6176]E(f329(f38(f881(x61761,a869)),f329(f306(x61761),x61762)),f329(f329(f254(a874),f329(a117,f329(a117,f2(a874)))),f329(f38(x61761),x61762)))+~P24(f329(f62(x61761),x61762))
% 187.18/188.04 [6179]E(x61791,f118(x61792))+E(f329(f329(f163(x61792),x61791),f329(f329(f22(a874),f329(f194(f875(x61792)),x61791)),f78(a874))),f142(x61792,x61791))
% 187.18/188.04 [6204]E(x62041,f118(x62042))+E(f329(f329(f126(x62042),f329(f170(x62042),x62041)),f329(f329(f149(x62042),f329(f139(x62042),x62041)),f118(x62042))),f329(f166(x62042),x62041))
% 187.18/188.04 [6233]~P24(f329(f62(x62331),f40(f881(x62331,a869),x62332)))+P24(f329(f62(f881(x62331,a869)),x62332))
% 187.18/188.04 [6256]P24(f329(f329(f243(a874),f329(f108(a874),x62561)),f329(f108(a874),x62562)))+~P24(f329(f329(f243(a1),x62561),a83))
% 187.18/188.04 [6273]~P24(f329(f329(f244(a1),x62731),x62732))+P24(f329(f329(f243(a1),x62731),f329(f329(f22(a1),x62732),f78(a1))))
% 187.18/188.04 [6274]~P24(f329(f329(f243(a1),x62741),x62742))+P24(f329(f329(f244(a1),x62741),f329(f329(f80(a1),x62742),f78(a1))))
% 187.18/188.04 [6275]~P24(f329(f329(f244(a1),x62751),x62752))+P24(f329(f329(f244(a1),x62751),f329(f329(f80(a1),x62752),f78(a1))))
% 187.18/188.04 [6277]~P24(f329(f329(f243(a1),x62771),x62772))+P24(f329(f329(f243(a874),f329(f108(a874),x62771)),f329(f108(a874),x62772)))
% 187.18/188.04 [6279]~P24(f329(f329(f243(a874),x62791),x62792))+P24(f329(f329(f243(a1),f329(f105(a1),x62791)),f329(f105(a1),x62792)))
% 187.18/188.04 [6280]~P24(f329(f329(f243(a1),x62801),x62802))+P24(f329(f329(f243(a1),f329(f108(a1),x62801)),f329(f108(a1),x62802)))
% 187.18/188.04 [6282]~P24(f329(f329(f244(a874),x62821),x62822))+P24(f329(f329(f244(a1),f329(f105(a1),x62821)),f329(f105(a1),x62822)))
% 187.18/188.04 [6283]~P24(f329(f329(f244(a1),x62831),x62832))+P24(f329(f329(f244(a1),f329(f108(a1),x62831)),f329(f108(a1),x62832)))
% 187.18/188.04 [6284]~P24(f329(f329(f91(a1),x62841),x62842))+P24(f329(f329(f91(a1),f329(f108(a1),x62841)),f329(f108(a1),x62842)))
% 187.18/188.04 [6302]~P24(f329(f329(f243(a874),x63021),x63022))+~P24(f329(f329(f243(a874),f329(a117,x63022)),x63021))
% 187.18/188.04 [6344]~P24(f329(f329(f243(a874),f329(a117,x63441)),f329(a117,x63442)))+P24(f329(f329(f243(a874),x63441),x63442))
% 187.18/188.04 [6345]~P24(f329(f329(f243(a104),f329(a3,x63451)),f329(a3,x63452)))+P24(f329(f329(f243(a874),x63451),x63452))
% 187.18/188.04 [6346]~P24(f329(f329(f243(a874),f329(a19,x63461)),f329(a19,x63462)))+P24(f329(f329(f243(a104),x63461),x63462))
% 187.18/188.04 [6348]~P24(f329(f329(f244(a874),f329(a117,x63481)),f329(a117,x63482)))+P24(f329(f329(f244(a874),x63481),x63482))
% 187.18/188.04 [6349]~P24(f329(f329(f244(a104),f329(a3,x63491)),f329(a3,x63492)))+P24(f329(f329(f244(a874),x63491),x63492))
% 187.18/188.04 [6350]~P24(f329(f329(f244(a874),f329(a109,x63501)),f329(a109,x63502)))+P24(f329(f329(f244(a1),x63501),x63502))
% 187.18/188.04 [6351]~P24(f329(f329(f244(a874),f329(a19,x63511)),f329(a19,x63512)))+P24(f329(f329(f244(a104),x63511),x63512))
% 187.18/188.04 [6391]~P24(f329(f329(f244(a874),f329(a109,x63912)),f329(a109,x63911)))+P24(f329(f329(f244(a1),f2(a1)),x63911))
% 187.18/188.04 [6422]P24(f329(f329(f243(a1),f2(a1)),f45(a1,x64221,x64222)))+~P24(f329(f329(f244(a1),f2(a1)),x64222))
% 187.18/188.04 [6581]P42(x65811,x65812)+~E(f329(f329(f286(x65811,x65811,x65811),x65812),x65812),f193(f881(f880(x65811,x65811),a869)))
% 187.18/188.04 [6593]~P42(x65931,x65932)+P42(x65931,f329(f329(f286(x65931,x65931,x65931),x65932),x65932))
% 187.18/188.04 [6605]P24(f329(f329(f243(a1),x66051),x66052))+~P24(f329(f329(f244(a1),x66051),f329(f329(f80(a1),x66052),f78(a1))))
% 187.18/188.04 [6606]P24(f329(f329(f244(a1),x66061),x66062))+~P24(f329(f329(f243(a1),x66061),f329(f329(f22(a1),x66062),f78(a1))))
% 187.18/188.04 [6609]P24(f329(f329(f243(a874),x66091),x66092))+~P24(f329(f329(f243(a1),f329(f105(a1),x66091)),f329(f105(a1),x66092)))
% 187.18/188.04 [6610]P24(f329(f329(f243(a1),x66101),x66102))+~P24(f329(f329(f243(a1),f329(f108(a1),x66101)),f329(f108(a1),x66102)))
% 187.18/188.04 [6612]P24(f329(f329(f244(a874),x66121),x66122))+~P24(f329(f329(f244(a1),f329(f105(a1),x66121)),f329(f105(a1),x66122)))
% 187.18/188.04 [6613]P24(f329(f329(f244(a1),x66131),x66132))+~P24(f329(f329(f244(a874),f329(f108(a874),x66131)),f329(f108(a874),x66132)))
% 187.18/188.04 [6614]P24(f329(f329(f244(a1),x66141),x66142))+~P24(f329(f329(f244(a1),f329(f108(a1),x66141)),f329(f108(a1),x66142)))
% 187.18/188.04 [6615]P24(f329(f329(f91(a1),x66151),x66152))+~P24(f329(f329(f91(a1),f329(f108(a1),x66151)),f329(f108(a1),x66152)))
% 187.18/188.04 [6708]~E(f732(x67082,x67081),f118(x67081))+E(f329(f140(f875(x67081),f875(x67081),f126(x67081),f118(x67081)),x67082),f118(x67081))
% 187.18/188.04 [6709]~E(f733(x67092,x67091),f118(x67091))+E(f329(f140(f875(x67091),f875(x67091),f126(x67091),f118(x67091)),x67092),f118(x67091))
% 187.18/188.04 [6716]~P31(x67161)+E(f329(f140(x67161,x67161,f106(x67161),f252(x67161)),x67162),f41(x67161,f329(f171(x67161),x67162)))
% 187.18/188.04 [6717]~P31(x67171)+E(f329(f140(x67171,x67171,f115(x67171),f193(x67171)),x67172),f40(x67171,f329(f171(x67171),x67172)))
% 187.18/188.04 [6729]E(x67291,f2(a104))+E(f329(f329(f80(a874),f329(a19,f329(f329(f22(a104),x67291),f78(a104)))),f329(a117,x67292)),f329(f329(f80(a874),f329(a19,x67291)),x67292))
% 187.18/188.04 [6779]P24(f329(f329(f244(a1),f329(f329(f22(a1),x67791),x67792)),f2(a1)))+~P24(f329(f329(f244(a1),x67791),x67792))
% 187.18/188.04 [6807]~P27(x68071)+E(f329(f329(f115(f881(x68071,a869)),f329(f329(f307(x68071),x68072),f193(f881(x68071,a869)))),f329(f301(x68071),x68072)),f329(f251(x68071),x68072))
% 187.18/188.04 [6882]~P59(x68821,x68822)+P42(x68821,f329(f249(f880(x68821,x68821)),f329(f268(x68821,x68821,a869),x68822)))
% 187.18/188.04 [6883]~P59(x68831,x68832)+P57(x68831,f329(f249(f880(x68831,x68831)),f329(f268(x68831,x68831,a869),x68832)))
% 187.18/188.04 [6884]E(x68841,f193(f881(x68842,a869)))+~P24(f329(f329(f243(f881(x68842,a869)),x68841),f193(f881(x68842,a869))))
% 187.18/188.04 [6967]~P24(f329(f329(f244(a874),f2(a874)),x69672))+P24(f329(f329(f243(a874),f45(a874,x69671,x69672)),x69672))
% 187.18/188.04 [6968]~P24(f329(f329(f243(a1),f2(a1)),x69681))+P24(f329(f329(f243(a1),f45(a1,x69681,x69682)),x69681))
% 187.18/188.04 [6969]~P24(f329(f329(f244(a874),f2(a874)),x69692))+P24(f329(f329(f244(a874),f45(a874,x69691,x69692)),x69692))
% 187.18/188.04 [6971]~P24(f329(f329(f244(a1),f2(a1)),x69712))+P24(f329(f329(f244(a1),f45(a1,x69711,x69712)),x69712))
% 187.18/188.04 [7049]~P106(x70491)+E(f329(f329(f22(f881(x70491,a869)),f329(f329(f307(x70491),x70492),f193(f881(x70491,a869)))),f329(f250(x70491),x70492)),f329(f329(f307(x70491),x70492),f193(f881(x70491,a869))))
% 187.18/188.04 [7122]~P53(x71221,x71222)+P44(x71221,f252(f881(x71221,a869)),f329(f249(f880(x71221,x71221)),f329(f268(x71221,x71221,a869),x71222)))
% 187.18/188.04 [7123]P24(f329(x71231,x71232))+P24(f329(f329(f331(f881(f880(a874,a874),a869)),f553(x71232,x71231)),a103))
% 187.18/188.04 [7168]E(f329(f329(f126(a874),f137(a874,f329(f299(a874,x71681),x71682))),f329(f329(f149(a874),x71682),f118(a874))),f137(a874,f329(f299(a874,x71681),f329(a117,x71682))))+~P24(f329(f329(f243(a874),x71681),x71682))
% 187.18/188.04 [7309]E(x73091,f2(a874))+~E(f329(f140(a874,a874,f80(a874),x73091),x73092),f2(a874))
% 187.18/188.04 [7337]~P24(f329(f329(f244(a1),f329(f329(f22(a1),x73371),x73372)),f2(a1)))+P24(f329(f329(f244(a1),x73371),x73372))
% 187.18/188.04 [7366]P42(x73661,x73662)+~P42(x73661,f329(f329(f286(x73661,x73661,x73661),x73662),x73662))
% 187.18/188.04 [7396]~P24(f329(f329(f243(a874),f329(a117,x73961)),x73962))+P24(f190(a869,a247,f329(f243(a874),x73961),x73962))
% 187.18/188.04 [7554]P21(a874,a874,f329(f329(f7(a874,a874,a874),f22(a874)),x75541),x75542)+P24(f329(f329(f331(a874),f561(x75541,x75542)),x75542))
% 187.18/188.04 [7610]E(f329(f329(f329(f66(a874,x76101,f80(a874)),f329(f16(a874,x76101),f78(a874))),f2(a874)),x76102),f329(f38(x76101),x76102))+~P24(f329(f62(x76101),x76102))
% 187.18/188.04 [7652]P21(a874,a874,f329(f329(f7(a874,a874,a874),f22(a874)),x76521),x76522)+~P24(f329(f329(f243(a874),x76521),f561(x76521,x76522)))
% 187.18/188.04 [7712]P42(x77121,x77122)+P24(f329(f329(f243(f881(x77121,a869)),f551(x77122,x77121)),f329(f283(x77121,x77121,x77122),f551(x77122,x77121))))
% 187.18/188.04 [7717]P59(x77171,x77172)+~P42(x77171,f329(f249(f880(x77171,x77171)),f329(f268(x77171,x77171,a869),x77172)))
% 187.18/188.04 [7790]P24(f329(f329(f243(a874),f329(a117,x77901)),x77902))+~P24(f190(a869,a247,f329(f243(a874),x77901),x77902))
% 187.18/188.04 [7845]P24(f329(f329(f331(f880(a874,a874)),f329(f329(f264(a874,a874),x78451),x78452)),f305(a874,a319)))+~P24(f329(f329(f243(a874),x78451),x78452))
% 187.18/188.04 [7942]P53(x79421,x79422)+~P44(x79421,f252(f881(x79421,a869)),f329(f249(f880(x79421,x79421)),f329(f268(x79421,x79421,a869),x79422)))
% 187.18/188.04 [8002]~P24(f329(f135(x80021),x80022))+P24(f329(f135(f881(x80021,a869)),f329(f329(f152(f875(x80021),f881(x80021,a869)),f171(x80021)),f54(x80021,x80022))))
% 187.18/188.04 [8207]~P42(x82071,f329(f284(x82071,x82071),x82072))+P42(x82071,f329(f284(x82071,x82071),f329(f329(f286(x82071,x82071,x82071),x82072),f305(x82071,x82072))))
% 187.18/188.04 [8328]P24(f329(f62(f880(x83281,x83281)),f329(f329(f286(x83281,x83281,x83281),x83282),f305(x83281,x83282))))+~P24(f329(f62(f880(x83281,x83281)),x83282))
% 187.18/188.04 [8359]E(x83591,f2(a1))+P24(f329(f49(x83592,x83591),f329(f329(f264(a1,a1),f329(f329(f39(a1),x83592),x83591)),f45(a1,x83592,x83591))))
% 187.18/188.04 [8370]~P24(f329(f329(f331(f880(a874,a874)),f329(f329(f264(a874,a874),x83701),x83702)),f305(a874,a319)))+P24(f329(f329(f243(a874),x83701),x83702))
% 187.18/188.04 [8387]~P83(x83871)+E(f329(f140(x83871,x83871,f329(f7(x83871,x83871,x83871),f80(x83871)),f2(x83871)),f329(f167(x83871),x83872)),f329(f140(x83871,x83871,f80(x83871),f2(x83871)),x83872))
% 187.18/188.04 [8565]~P27(x85651)+E(f329(f140(f875(x85651),x85651,f329(f7(x85651,f875(x85651),f875(x85651)),f146(x85651,x85651,f5(x85651))),f118(x85651)),x85652),f148(x85651,x85651,f5(x85651),x85652))
% 187.18/188.04 [8667]~P57(x86671,f329(f249(f880(x86671,x86671)),f329(f268(x86671,x86671,a869),x86672)))+P57(x86671,f329(f249(f880(x86671,x86671)),f329(f268(x86671,x86671,a869),f253(x86671,x86671,x86672))))
% 187.18/188.04 [8681]P24(f329(f329(f331(f880(a874,a874)),f329(f329(f264(a874,a874),x86811),x86812)),f329(f329(f286(a874,a874,a874),a319),f305(a874,a319))))+~P24(f329(f329(f244(a874),x86811),x86812))
% 187.18/188.04 [8724]~P24(f329(f62(f880(x87241,x87241)),f329(f329(f286(x87241,x87241,x87241),x87242),f305(x87241,x87242))))+P24(f329(f62(f880(x87241,x87241)),x87242))
% 187.18/188.04 [8775]~P57(x87751,f329(f249(f880(x87751,x87751)),f329(f268(x87751,x87751,a869),f253(x87751,x87751,x87752))))+P57(x87751,f329(f249(f880(x87751,x87751)),f329(f268(x87751,x87751,a869),x87752)))
% 187.18/188.04 [8978]P57(x89781,x89782)+P24(f329(f329(f331(f880(x89781,x89781)),f329(f329(f264(x89781,x89781),f590(x89782,x89781)),f590(x89782,x89781))),f329(f329(f286(x89781,x89781,x89781),x89782),f305(x89781,x89782))))
% 187.18/188.04 [8979]P57(x89791,x89792)+P24(f329(f329(f331(f880(x89791,x89791)),f329(f329(f264(x89791,x89791),f595(x89792,x89791)),f595(x89792,x89791))),f329(f329(f286(x89791,x89791,x89791),x89792),f305(x89791,x89792))))
% 187.18/188.04 [9096]~P24(f329(f329(f331(f880(a874,a874)),f329(f329(f264(a874,a874),x90961),x90962)),f329(f329(f286(a874,a874,a874),a319),f305(a874,a319))))+P24(f329(f329(f244(a874),x90961),x90962))
% 187.18/188.04 [5053]~P94(x50531)+E(f329(f329(f80(x50531),f329(f108(x50531),a83)),x50532),x50532)
% 187.18/188.04 [5082]~P97(x50821)+E(f329(f329(f115(x50821),f329(f79(x50821),x50822)),x50822),f252(x50821))
% 187.18/188.04 [5083]~P97(x50831)+E(f329(f329(f106(x50831),f329(f79(x50831),x50832)),x50832),f193(x50831))
% 187.18/188.04 [5084]~P69(x50841)+E(f329(f329(f80(x50841),f329(f79(x50841),x50842)),x50842),f2(x50841))
% 187.18/188.04 [5085]~P77(x50851)+E(f329(f329(f80(x50851),f329(f79(x50851),x50852)),x50852),f2(x50851))
% 187.18/188.04 [5117]~P94(x51171)+E(f329(f329(f81(x51171),f329(f108(x51171),a102)),x51172),f329(f79(x51171),x51172))
% 187.18/188.04 [5288]~P114(x52881)+E(f329(f329(f81(x52881),f329(f79(x52881),f78(x52881))),x52882),f329(f79(x52881),x52882))
% 187.18/188.04 [5331]E(f329(f75(a1),x53311),f78(a1))+~E(f329(f75(a1),f329(f329(f81(a1),x53311),x53312)),f78(a1))
% 187.18/188.04 [5423]~P94(x54231)+E(f329(f329(f80(x54231),f78(x54231)),f329(f108(x54231),x54232)),f329(f108(x54231),f329(f329(f22(a1),x54232),a102)))
% 187.18/188.04 [5476]~P66(x54761)+E(f10(x54761,f329(f329(f307(x54761),x54762),f193(f881(x54761,a869)))),x54762)
% 187.18/188.04 [5477]~P66(x54771)+E(f13(x54771,f329(f329(f307(x54771),x54772),f193(f881(x54771,a869)))),x54772)
% 187.18/188.04 [5478]~P27(x54781)+E(f14(x54781,f329(f329(f307(x54781),x54782),f193(f881(x54781,a869)))),x54782)
% 187.18/188.04 [5479]~P27(x54791)+E(f15(x54791,f329(f329(f307(x54791),x54792),f193(f881(x54791,a869)))),x54792)
% 187.18/188.04 [5480]~P31(x54801)+E(f41(x54801,f329(f329(f307(x54801),x54802),f193(f881(x54801,a869)))),x54802)
% 187.18/188.04 [5481]~P31(x54811)+E(f40(x54811,f329(f329(f307(x54811),x54812),f193(f881(x54811,a869)))),x54812)
% 187.18/188.04 [5503]E(f329(f329(f80(a874),x55031),f329(f329(f22(a874),x55032),x55031)),x55032)+P24(f329(f329(f244(a874),x55032),x55031))
% 187.18/188.04 [5533]E(x55331,f118(x55332))+P24(f329(f329(f244(a874),f2(a874)),f329(f194(f875(x55332)),x55331)))
% 187.18/188.04 [5658]~P27(x56581)+E(f11(x56581,f241(x56581),f329(f329(f307(x56581),x56582),f193(f881(x56581,a869)))),x56582)
% 187.18/188.04 [5659]~P27(x56591)+E(f12(x56591,f242(x56591),f329(f329(f307(x56591),x56592),f193(f881(x56591,a869)))),x56592)
% 187.18/188.04 [5722]E(f329(f329(f22(a874),x57221),f329(f329(f22(a874),x57221),x57222)),x57222)+~P24(f329(f329(f243(a874),x57222),x57221))
% 187.18/188.04 [5723]E(f329(f329(f80(a874),x57231),f329(f329(f22(a874),x57232),x57231)),x57232)+~P24(f329(f329(f243(a874),x57231),x57232))
% 187.18/188.04 [5744]E(f45(a874,f329(f329(f22(a874),x57441),x57442),x57442),f45(a874,x57441,x57442))+P24(f329(f329(f244(a874),x57441),x57442))
% 187.18/188.04 [5755]E(f329(f79(a1),f329(f329(f39(a1),x57551),f329(f79(a1),x57552))),f289(x57551,x57552))+P24(f329(f329(f243(a1),f2(a1)),x57552))
% 187.18/188.04 [5757]~E(x57572,f2(a874))+P24(f329(f329(f244(a874),f2(a874)),f329(f329(f254(a874),x57571),x57572)))
% 187.18/188.04 [5808]~P94(x58081)+E(f329(f329(f80(x58081),f329(f79(x58081),f78(x58081))),f329(f108(x58081),x58082)),f329(f108(x58081),f329(f329(f80(a1),x58082),a102)))
% 187.18/188.04 [5809]E(f329(f329(f254(a874),f329(f108(a874),x58091)),x58092),f329(f329(f254(a874),f2(a874)),x58092))+~P24(f329(a198,f329(f108(a1),x58091)))
% 187.18/188.04 [5906]E(f329(f139(a874),f137(a874,f329(f299(a874,x59061),x59062))),x59061)+~P24(f329(f329(f244(a874),x59061),x59062))
% 187.18/188.04 [5926]E(f329(f329(f81(a874),f329(f108(a874),x59261)),f329(f108(a874),x59262)),f329(f108(a874),f329(f329(f81(a1),x59261),x59262)))+P24(f329(f329(f244(a1),x59261),a83))
% 187.18/188.04 [5932]~P122(x59321)+P24(f329(f329(f243(x59321),f2(x59321)),f329(f329(f81(x59321),x59322),x59322)))
% 187.18/188.04 [5944]E(f329(f329(f22(a874),f329(a117,x59441)),x59442),f329(a117,f329(f329(f22(a874),x59441),x59442)))+~P24(f329(f329(f243(a874),x59442),x59441))
% 187.18/188.04 [5947]E(f45(a874,f329(f329(f22(a874),x59471),x59472),x59472),f45(a874,x59471,x59472))+~P24(f329(f329(f243(a874),x59472),x59471))
% 187.18/188.04 [5999]E(f329(f329(f254(a874),f329(a109,x59991)),x59992),f329(a109,f329(f329(f254(a1),x59991),x59992)))+~P24(f329(f329(f243(a1),f2(a1)),x59991))
% 187.18/188.04 [6015]P24(f329(f135(x60151),x60152))+P24(f329(f329(f244(a874),f684(x60152,x60151)),f329(f194(f875(x60151)),x60152)))
% 187.18/188.04 [6016]P24(f329(f135(x60161),x60162))+P24(f329(f329(f244(a874),f689(x60162,x60161)),f329(f194(f875(x60161)),x60162)))
% 187.18/188.04 [6031]~E(x60311,f118(x60312))+~P24(f329(f329(f244(a874),f2(a874)),f329(f194(f875(x60312)),x60311)))
% 187.18/188.04 [6045]E(f142(a874,f137(a874,f329(f299(a874,x60451),x60452))),f329(f329(f22(a874),x60452),f78(a874)))+~P24(f329(f329(f244(a874),x60451),x60452))
% 187.18/188.04 [6048]E(f329(f329(f80(a1),x60481),f329(f105(a1),f329(a117,f362(x60482,x60481)))),x60482)+~P24(f329(f329(f244(a1),x60481),x60482))
% 187.18/188.04 [6055]E(x60551,f2(a874))+E(f329(f329(f81(a874),x60552),f329(f329(f254(a874),x60552),f329(f329(f22(a874),x60551),f78(a874)))),f329(f329(f254(a874),x60552),x60551))
% 187.18/188.04 [6081]E(f329(f329(f81(a874),f329(a109,x60811)),f329(a109,x60812)),f329(a109,f329(f329(f81(a1),x60811),x60812)))+~P24(f329(f329(f243(a1),f2(a1)),x60811))
% 187.18/188.04 [6082]E(f329(f329(f39(a874),f329(a109,x60821)),f329(a109,x60822)),f329(a109,f329(f329(f39(a1),x60821),x60822)))+~P24(f329(f329(f243(a1),f2(a1)),x60821))
% 187.18/188.04 [6096]~P109(x60961)+E(f329(f329(f80(x60961),x60962),x60962),f329(f329(f81(x60961),f329(f329(f80(x60961),f78(x60961)),f78(x60961))),x60962))
% 187.18/188.04 [6113]E(f329(f329(f22(a1),f329(f105(a1),x61131)),f329(f105(a1),x61132)),f329(f105(a1),f329(f329(f22(a874),x61131),x61132)))+~P24(f329(f329(f243(a874),x61132),x61131))
% 187.18/188.04 [6115]E(f329(f329(f264(a1,a1),f329(f108(a1),a102)),f329(f329(f80(a1),x61151),x61152)),f50(x61151,x61152))+~P24(f329(f329(f243(a1),x61152),f2(a1)))
% 187.18/188.04 [6155]E(f179(x61551,x61552),f118(f875(x61551)))+P24(f329(f329(f331(f875(x61551)),f717(x61552,x61551)),f329(f171(f875(x61551)),x61552)))
% 187.18/188.04 [6239]E(f329(f329(f149(a1),x62391),f178(f329(f329(f80(a1),x62391),f78(a1)),x62392)),f178(x62391,x62392))+~P24(f329(f329(f243(a1),x62391),x62392))
% 187.18/188.04 [6276]~P24(f329(f329(f244(a874),x62762),x62761))+P24(f329(f329(f244(a874),f2(a874)),f329(f329(f22(a874),x62761),x62762)))
% 187.18/188.04 [6307]~P24(f329(f329(f244(a874),x63071),f329(a109,x63072)))+P24(f329(f329(f244(a1),f329(f105(a1),x63071)),x63072))
% 187.18/188.04 [6336]~P27(x63361)+E(f329(f329(f115(f881(x63361,a869)),f329(f250(x63361),x63362)),f329(f329(f307(x63361),x63362),f193(f881(x63361,a869)))),f329(f298(x63361),x63362))
% 187.18/188.04 [6337]~P24(f329(f329(f243(a1),f2(a1)),x63371))+P24(f329(f329(f243(a1),f2(a1)),f329(f329(f254(a1),x63371),x63372)))
% 187.18/188.04 [6340]~P24(f329(f329(f244(a874),f2(a874)),x63401))+P24(f329(f329(f244(a874),f2(a874)),f329(f329(f254(a874),x63401),x63402)))
% 187.18/188.04 [6367]~E(f329(x63671,f2(a874)),f2(a874))+E(f329(f329(f6(a874,a874),x63671),f300(a874,f329(a117,f2(a874)),x63672)),f329(f329(f6(a874,a874),x63671),f300(a874,f2(a874),x63672)))
% 187.18/188.04 [6430]~P94(x64301)+E(f329(f329(f81(x64301),f329(f329(f80(x64301),f78(x64301)),f78(x64301))),f329(f108(x64301),x64302)),f329(f108(x64301),f329(f329(f80(a1),x64302),x64302)))
% 187.18/188.04 [6446]E(f329(f329(f307(a1),x64461),f300(a1,f329(f329(f80(a1),x64461),f78(a1)),x64462)),f300(a1,x64461,x64462))+P24(f329(f329(f244(a1),x64462),x64461))
% 187.18/188.04 [6447]P24(f329(f329(f244(a874),x64471),f329(a109,x64472)))+~P24(f329(f329(f244(a1),f329(f105(a1),x64471)),x64472))
% 187.18/188.04 [6549]E(f329(a109,f329(f329(f39(a1),f329(f108(a1),x65491)),f329(f108(a1),x65492))),f329(f329(f39(a874),f329(f108(a874),x65491)),f329(f108(a874),x65492)))+P24(f329(a198,f329(f108(a1),x65491)))
% 187.18/188.04 [6607]P24(f329(f329(f244(a874),x66071),x66072))+~P24(f329(f329(f244(a874),f2(a874)),f329(f329(f22(a874),x66072),x66071)))
% 187.18/188.04 [6651]P24(f329(f329(f244(a874),f2(a874)),x66511))+~P24(f329(f329(f244(a874),f2(a874)),f329(f329(f81(a874),x66512),x66511)))
% 187.18/188.04 [6652]P24(f329(f329(f244(a874),f2(a874)),x66521))+~P24(f329(f329(f244(a874),f2(a874)),f329(f329(f81(a874),x66521),x66522)))
% 187.18/188.04 [6669]~P24(f329(f329(f243(a1),x66691),f2(a1)))+E(f329(f329(f81(a874),f329(a109,f329(f79(a1),x66691))),f329(a109,f329(f79(a1),x66692))),f329(a109,f329(f329(f81(a1),x66691),x66692)))
% 187.18/188.04 [6727]~E(x67272,f193(f881(x67271,a869)))+P24(f329(f329(f243(f881(x67271,a869)),x67272),f329(f79(f881(x67271,a869)),x67272)))
% 187.18/188.04 [6790]~P94(x67901)+E(f329(f329(f80(x67901),f329(f329(f80(x67901),f2(x67901)),f329(f108(x67901),x67902))),f329(f108(x67901),x67902)),f329(f108(x67901),f329(f329(f80(a1),x67902),x67902)))
% 187.18/188.04 [6847]~P24(f329(f329(f244(a1),x68471),x68472))+P24(f329(f329(f243(a1),f329(f329(f80(a1),x68471),f78(a1))),x68472))
% 187.18/188.04 [6914]E(x69141,f2(a874))+~P24(f329(f329(f243(a1),f329(f105(a1),x69142)),f329(f79(a1),f329(f105(a1),x69141))))
% 187.18/188.04 [6915]E(x69151,f2(a874))+~P24(f329(f329(f243(a1),f329(f105(a1),x69151)),f329(f79(a1),f329(f105(a1),x69152))))
% 187.18/188.04 [7020]E(f329(f329(f264(a1,a1),f329(f108(a1),a102)),f329(f329(f80(a1),x70201),x70202)),f50(x70201,x70202))+~P24(f329(f329(f243(a1),f2(a1)),f329(f329(f80(a1),x70201),x70202)))
% 187.18/188.04 [7062]~P22(x70621,x70622)+P42(x70621,f329(f263(f881(f880(x70621,x70621),a869),f881(f880(x70621,x70621),a869)),x70622))
% 187.18/188.04 [7080]~P24(f329(f329(f243(a874),f329(a117,f2(a874))),x70801))+P24(f329(f329(f243(a874),f329(a117,f2(a874))),f329(f329(f254(a874),x70801),x70802)))
% 187.18/188.04 [7250]~P24(f329(f329(f243(a1),x72501),x72502))+P24(f329(f329(f243(a1),f329(f329(f80(a1),x72501),x72501)),f329(f329(f80(a1),x72502),x72502)))
% 187.18/188.04 [7255]~P24(f329(f329(f244(a1),x72551),x72552))+P24(f329(f329(f244(a1),f329(f329(f80(a1),x72551),x72551)),f329(f329(f80(a1),x72552),x72552)))
% 187.18/188.04 [7256]~P24(f329(f329(f91(a1),x72561),x72562))+P24(f329(f329(f91(a1),f329(f329(f80(a1),x72561),x72561)),f329(f329(f80(a1),x72562),x72562)))
% 187.18/188.04 [7311]~P24(f329(f329(f244(a874),f2(a874)),x73111))+P24(f329(f329(f244(a874),f329(f329(f22(a874),x73111),f329(a117,x73112))),x73111))
% 187.18/188.04 [7348]P24(f329(f329(f243(a874),f329(a117,f2(a874))),x73481))+~P24(f329(f329(f243(a874),f329(a117,f2(a874))),f329(f329(f81(a874),x73482),x73481)))
% 187.18/188.04 [7349]P24(f329(f329(f243(a874),f329(a117,f2(a874))),x73491))+~P24(f329(f329(f243(a874),f329(a117,f2(a874))),f329(f329(f81(a874),x73491),x73492)))
% 187.18/188.04 [7353]P24(f329(f329(f243(a874),f329(f329(f163(a874),x73531),x73532)),f329(f164(a874),x73531)))+~P24(f329(f329(f244(a874),x73532),f329(f194(f875(a874)),x73531)))
% 187.18/188.04 [7395]P24(f329(f329(f244(a1),x73951),x73952))+~P24(f329(f329(f243(a1),f329(f329(f80(a1),x73951),f78(a1))),x73952))
% 187.18/188.04 [7440]P24(f329(f62(x74401),f252(f881(x74401,a869))))+~P24(f329(f62(f881(x74402,x74401)),f252(f881(f881(x74402,x74401),a869))))
% 187.18/188.04 [7441]P24(f329(f62(x74411),f252(f881(x74411,a869))))+~P24(f329(f62(f879(x74412,x74411)),f252(f881(f879(x74412,x74411),a869))))
% 187.18/188.04 [7442]P24(f329(f62(x74421),f252(f881(x74421,a869))))+~P24(f329(f62(f879(x74421,x74422)),f252(f881(f879(x74421,x74422),a869))))
% 187.18/188.04 [7484]E(x74841,f193(f881(x74842,a869)))+~P24(f329(f329(f243(f881(x74842,a869)),x74841),f329(f79(f881(x74842,a869)),x74841)))
% 187.18/188.04 [7620]E(f329(f140(f875(x76201),f875(x76201),f126(x76201),f118(x76201)),x76202),f118(x76201))+P24(f329(f329(f331(f875(x76201)),f732(x76202,x76201)),f329(f171(f875(x76201)),x76202)))
% 187.18/188.04 [7621]E(f329(f140(f875(x76211),f875(x76211),f126(x76211),f118(x76211)),x76212),f118(x76211))+P24(f329(f329(f331(f875(x76211)),f733(x76212,x76211)),f329(f171(f875(x76211)),x76212)))
% 187.18/188.04 [7862]P24(f329(f329(f243(a1),x78621),x78622))+~P24(f329(f329(f243(a1),f329(f329(f80(a1),x78621),x78621)),f329(f329(f80(a1),x78622),x78622)))
% 187.18/188.04 [7867]P24(f329(f329(f244(a1),x78671),x78672))+~P24(f329(f329(f244(a1),f329(f329(f80(a1),x78671),x78671)),f329(f329(f80(a1),x78672),x78672)))
% 187.18/188.04 [7868]P24(f329(f329(f91(a1),x78681),x78682))+~P24(f329(f329(f91(a1),f329(f329(f80(a1),x78681),x78681)),f329(f329(f80(a1),x78682),x78682)))
% 187.18/188.04 [7962]~P109(x79621)+E(f329(f329(f81(x79621),f329(f329(f80(x79621),f78(x79621)),f78(x79621))),f329(f329(f6(a874,x79621),f105(x79621)),f300(a874,f78(a874),x79622))),f329(f329(f81(x79621),f329(f105(x79621),x79622)),f329(f329(f80(x79621),f329(f105(x79621),x79622)),f78(x79621))))
% 187.18/188.04 [8018]P24(f329(f329(f331(a874),x80181),x80182))+~P24(f329(f329(f331(a1),f329(f105(a1),x80181)),f329(f308(a874,a1,f105(a1)),x80182)))
% 187.18/188.04 [8178]~P24(f329(f62(x81781),x81782))+E(f329(f308(a874,x81781,f424(x81782,x81781)),f329(f249(a874),f329(f329(f7(a874,a874,a869),f244(a874)),f425(x81782,x81781)))),x81782)
% 187.18/188.04 [8467]P46(x84671,x84672)+P24(f329(f329(f331(f880(x84671,x84671)),f329(f329(f264(x84671,x84671),f491(x84672,x84671)),f491(x84672,x84671))),x84672))
% 187.18/188.04 [8606]~P94(x86061)+E(f329(f329(f22(x86061),f78(x86061)),f329(f108(x86061),x86062)),f329(f108(x86061),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f79(a1),x86062))))
% 187.18/188.04 [8721]~P24(f329(f329(f244(f881(a874,a869)),x87211),x87212))+P24(f329(f329(f244(f881(a1,a869)),f329(f308(a874,a1,f105(a1)),x87211)),f329(f308(a874,a1,f105(a1)),x87212)))
% 187.18/188.04 [8749]~P24(f329(f329(f244(a1),x87491),x87492))+P24(f329(f329(f243(a1),f329(f329(f22(a1),f329(f329(f80(a1),x87491),x87491)),a102)),f329(f329(f80(a1),x87492),x87492)))
% 187.18/188.04 [8751]~P24(f329(f329(f244(a1),x87511),x87512))+P24(f329(f329(f244(a1),f329(f329(f22(a1),f329(f329(f80(a1),x87511),x87511)),a102)),f329(f329(f80(a1),x87512),x87512)))
% 187.18/188.04 [8821]~P24(f329(f329(f331(a874),x88211),f329(f171(a874),x88212)))+P24(f329(f329(f243(a874),x88211),f329(f140(a874,a874,f80(a874),f2(a874)),x88212)))
% 187.18/188.04 [8914]P50(x89141,x89142)+~P24(f329(f329(f331(f880(x89141,x89141)),f329(f329(f264(x89141,x89141),f480(x89142,x89141)),f480(x89142,x89141))),x89142))
% 187.18/188.04 [8994]P20(a871,x89941,f329(f329(f307(f873(a871)),f329(a93,f329(a26,x89942))),f193(f881(f873(a871),a869))))+~P20(a871,f329(f329(f307(f873(a871)),f329(a93,f329(a26,x89942))),x89941),f329(f329(f307(f873(a871)),f329(a93,f329(f240(a870),f329(a28,x89942)))),f193(f881(f873(a871),a869))))
% 187.18/188.04 [9062]~P24(f329(f329(f243(f881(a1,a869)),f329(f308(a874,a1,f105(a1)),x90621)),f329(f308(a874,a1,f105(a1)),x90622)))+P24(f329(f329(f243(f881(a874,a869)),x90621),x90622))
% 187.18/188.04 [9063]~P24(f329(f329(f244(f881(a1,a869)),f329(f308(a874,a1,f105(a1)),x90631)),f329(f308(a874,a1,f105(a1)),x90632)))+P24(f329(f329(f244(f881(a874,a869)),x90631),x90632))
% 187.18/188.04 [9143]P24(f329(f329(f244(a1),x91431),x91432))+~P24(f329(f329(f243(a1),f329(f329(f22(a1),f329(f329(f80(a1),x91431),x91431)),a102)),f329(f329(f80(a1),x91432),x91432)))
% 187.18/188.04 [9145]P24(f329(f329(f244(a1),x91451),x91452))+~P24(f329(f329(f244(a1),f329(f329(f22(a1),f329(f329(f80(a1),x91451),x91451)),a102)),f329(f329(f80(a1),x91452),x91452)))
% 187.18/188.04 [10052]~P24(f329(f62(x100521),x100522))+E(f329(f194(f875(x100521)),f90(f875(x100521),f329(f329(f18(f875(x100521),a869,a869),f329(f329(f8(a869,f881(a869,a869),f875(x100521)),a327),f329(f329(f7(f875(x100521),f881(x100521,a869),a869),f329(f329(f8(f881(x100521,a869),f881(f881(x100521,a869),a869),f875(x100521)),a326),f171(x100521))),x100522))),f135(x100521)))),f222(x100521,x100522))
% 187.18/188.04 [10188]~P20(a871,x101881,f329(f329(f307(f873(a871)),f329(a93,x101882)),f193(f881(f873(a871),a869))))+P20(a871,x101881,f329(f329(f307(f873(a871)),f329(f329(f329(f92(a871),f329(f329(f8(f881(a871,f881(a871,a869)),f881(a871,a869),a871),f329(f8(f881(a871,a869),a869,a871),f88(a871))),f329(f329(f8(f881(a871,a869),f881(a871,f881(a871,a869)),a871),f329(f7(a871,f881(a871,a869),f881(a871,a869)),f329(f329(f8(f881(a871,f881(a869,a869)),f881(f881(a871,a869),f881(a871,a869)),a871),f18(a871,a869,a869)),f329(f329(f8(f881(a871,a869),f881(a871,f881(a869,a869)),a871),f329(f8(a869,f881(a869,a869),a871),a332)),f199(x101882))))),a326))),x101882),a326)),f193(f881(f873(a871),a869))))
% 187.18/188.04 [6044]E(f329(f329(f80(a874),f329(f329(f22(a874),x60441),x60442)),x60442),x60441)+~P24(f329(f329(f243(a874),x60442),x60441))
% 187.18/188.04 [6109]E(f329(f329(f39(a874),f329(f329(f81(a874),x61091),x61092)),x61092),x61091)+~P24(f329(f329(f244(a874),f2(a874)),x61092))
% 187.18/188.04 [6110]E(f329(f329(f39(a874),f329(f329(f81(a874),x61101),x61102)),x61101),x61102)+~P24(f329(f329(f244(a874),f2(a874)),x61101))
% 187.18/188.04 [6114]~P72(x61141)+E(f329(f329(f6(a874,x61141),f329(f163(x61141),x61142)),f329(f299(a874,f2(a874)),f329(f194(f875(x61141)),x61142))),f329(f164(x61141),x61142))
% 187.18/188.04 [6231]E(f45(a874,f329(a117,f329(f329(f81(a874),x62311),x62312)),x62311),f78(a874))+~P24(f329(f329(f244(a874),f78(a874)),x62311))
% 187.18/188.04 [6237]E(f329(a117,f329(f329(f80(a874),f329(f108(a874),x62371)),x62372)),f329(f329(f80(a874),f78(a874)),x62372))+~P24(f329(a198,f329(f108(a1),x62371)))
% 187.18/188.04 [6265]E(f329(a109,f329(f329(f254(a1),f329(f108(a1),x62651)),x62652)),f329(f329(f254(a874),f329(f108(a874),x62651)),x62652))+P24(f329(a198,f329(f108(a1),x62651)))
% 187.18/188.04 [6501]E(f329(f329(f22(a874),x65011),f329(f108(a874),f329(f329(f80(a1),x65012),a102))),f329(f329(f22(a874),f329(a117,x65011)),f329(f108(a874),x65012)))+~P24(f329(f329(f244(a1),a83),x65012))
% 187.18/188.04 [6580]E(x65801,f2(a874))+E(f329(a117,f329(f329(f80(a874),f329(f329(f22(a874),x65801),f78(a874))),x65802)),f329(f329(f80(a874),x65801),x65802))
% 187.18/188.04 [6621]E(x66211,f2(a1))+P24(f329(f329(f244(a1),f2(a1)),f329(f329(f254(a1),f329(f75(a1),x66211)),x66212)))
% 187.18/188.04 [6636]~E(x66362,f2(a874))+P24(f329(f329(f244(a1),f2(a1)),f329(f329(f254(a1),f329(f75(a1),x66361)),x66362)))
% 187.18/188.04 [6673]E(x66731,f2(a874))+E(f329(f329(f80(a874),x66732),f329(f329(f81(a874),f329(f329(f22(a874),x66731),f78(a874))),x66732)),f329(f329(f81(a874),x66731),x66732))
% 187.18/188.04 [6721]~P24(f329(f329(f243(a1),x67211),x67212))+P24(f329(f329(f244(a1),f329(f329(f80(a1),x67211),a102)),x67212))
% 187.18/188.04 [6850]E(f329(f329(f149(a874),x68501),f137(a874,f329(f299(a874,f329(a117,x68501)),x68502))),f137(a874,f329(f299(a874,x68501),x68502)))+~P24(f329(f329(f244(a874),x68501),x68502))
% 187.18/188.04 [7053]E(x70531,x70532)+~E(f329(f329(f22(a1),f329(f329(f80(a1),x70531),x70531)),a102),f329(f329(f22(a1),f329(f329(f80(a1),x70532),x70532)),a102))
% 187.18/188.04 [7056]E(x70561,f118(x70562))+E(f273(x70562,f329(f329(f152(x70562,f880(a104,x70562)),f329(f264(a104,x70562),f78(a104))),x70561)),f280(x70562,x70561))
% 187.18/188.04 [7280]P24(f329(f329(f243(a1),x72801),x72802))+~P24(f329(f329(f244(a1),f329(f329(f80(a1),x72801),a102)),x72802))
% 187.18/188.04 [7767]~P24(f329(f329(f244(a874),x77671),x77672))+P24(f329(f329(f331(f880(a874,a874)),f329(f329(f264(a874,a874),x77671),x77672)),a248))
% 187.18/188.04 [7990]~P24(f329(f329(f244(a104),f2(a104)),x79901))+P24(f329(f329(f244(a104),f329(f263(a104,f880(a104,a104)),f329(f274(x79901),x79902))),x79901))
% 187.18/188.04 [8306]~P87(x83061)+P24(f329(f329(f243(x83061),f329(f75(x83061),f329(f164(x83061),x83062))),f329(f164(x83061),f329(f329(f152(x83061,x83061),f75(x83061)),x83062))))
% 187.18/188.04 [8330]P24(f329(f329(f244(a874),x83301),x83302))+~P24(f329(f329(f331(f880(a874,a874)),f329(f329(f264(a874,a874),x83301),x83302)),a248))
% 187.18/188.04 [8490]E(f329(f329(f264(x84901,x84901),f618(x84902,x84901)),f618(x84902,x84901)),x84902)+~P24(f329(f329(f331(f880(x84901,x84901)),x84902),f305(x84901,f193(f881(f880(x84901,x84901),a869)))))
% 187.18/188.04 [8531]E(f329(f299(a874,x85311),f329(f329(f80(a874),x85311),f329(f38(a874),x85312))),x85312)+~P24(f329(f329(f243(f881(a874,a869)),x85312),f329(f299(a874,x85311),f329(f329(f80(a874),x85311),f329(f38(a874),x85312)))))
% 187.18/188.04 [8860]E(f329(f329(f39(a1),f329(f108(a1),f329(f329(f22(a1),f329(f329(f80(a1),x88601),x88601)),a102))),f329(f108(a1),f329(f329(f80(a1),x88602),x88602))),f329(f329(f39(a1),f329(f108(a1),x88601)),f329(f108(a1),x88602)))+~P24(f329(f329(f243(a1),f2(a1)),f329(f108(a1),x88602)))
% 187.18/188.04 [8989]E(f176(f875(x89891),f329(f329(f8(a869,a869,f875(x89891)),a324),f329(f329(f7(f875(x89891),f875(x89891),a869),a326),f118(x89891))),x89892),f179(x89891,f179(x89891,x89892)))+~P33(a874,f329(f167(a874),f329(f329(f152(f875(x89891),a874),f194(f875(x89891))),x89892)))
% 187.18/188.04 [8992]E(f329(f329(f39(a1),f329(f108(a1),f329(f329(f22(a1),f329(f329(f80(a1),x89921),x89921)),a102))),f329(f108(a1),f329(f329(f80(a1),x89922),x89922))),f329(f329(f39(a1),f329(f329(f80(a1),f329(f108(a1),x89921)),f78(a1))),f329(f108(a1),x89922)))+P24(f329(f329(f243(a1),f2(a1)),f329(f108(a1),x89922)))
% 187.18/188.04 [9827]P24(f329(a198,x98272))+E(f329(f329(f86(a1,a874),f329(f329(f22(a1),x98271),x98272)),f329(f329(f18(a1,a874,a874),f329(f329(f7(a1,a874,f881(a874,a874)),f329(f329(f8(a869,f881(a874,f881(a874,a874)),a1),f101(a874)),a198)),f2(a874))),a109)),f329(f329(f22(a874),f329(a109,x98271)),f329(a109,x98272)))
% 187.18/188.04 [9835]E(f329(f329(f86(a1,a874),f329(f108(a1),f329(f329(f80(a1),x98351),f329(f79(a1),x98352)))),f329(f329(f18(a1,a874,a874),f329(f329(f7(a1,a874,f881(a874,a874)),f329(f329(f8(a869,f881(a874,f881(a874,a874)),a1),f101(a874)),a198)),f2(a874))),a109)),f329(f329(f22(a874),f329(f108(a874),x98351)),f329(f108(a874),x98352)))+P24(f329(f329(f244(a1),x98352),a83))
% 187.18/188.04 [9837]~P22(x98371,x98372)+P24(f329(f329(f243(f881(f880(x98371,x98371),a869)),f329(f329(f286(x98371,x98371,x98371),f329(f263(f881(f880(x98371,x98371),a869),f881(f880(x98371,x98371),a869)),x98372)),f329(f267(f881(f880(x98371,x98371),a869),f881(f880(x98371,x98371),a869)),x98372))),f329(f263(f881(f880(x98371,x98371),a869),f881(f880(x98371,x98371),a869)),x98372)))
% 187.18/188.04 [9903]~E(f329(f38(a874),f329(f249(a874),f329(f329(f18(a874,a869,a869),f329(f329(f8(a869,f881(a869,a869),a874),a327),f329(f329(f7(a874,f881(a874,a869),a869),f331(a874)),x99031))),f329(f329(f7(a874,a874,a869),f244(a874)),f329(a117,x99032))))),f2(a874))+~P24(f329(f329(f331(a874),f2(a874)),x99031))
% 187.18/188.04 [9959]E(f45(a1,f329(f108(a1),f329(f329(f22(a1),f329(f329(f80(a1),x99591),x99591)),a102)),f329(f108(a1),f329(f329(f80(a1),x99592),x99592))),f329(f329(f80(a1),f329(f329(f81(a1),f329(f108(a1),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))),f45(a1,f329(f108(a1),x99591),f329(f108(a1),x99592)))),f78(a1)))+~P24(f329(f329(f243(a1),f2(a1)),f329(f108(a1),x99592)))
% 187.18/188.04 [9968]E(f45(a1,f329(f108(a1),f329(f329(f22(a1),f329(f329(f80(a1),x99681),x99681)),a102)),f329(f108(a1),f329(f329(f80(a1),x99682),x99682))),f329(f329(f22(a1),f329(f329(f81(a1),f329(f108(a1),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))),f45(a1,f329(f329(f80(a1),f329(f108(a1),x99681)),f78(a1)),f329(f108(a1),x99682)))),f78(a1)))+P24(f329(f329(f243(a1),f2(a1)),f329(f108(a1),x99682)))
% 187.18/188.04 [10020]~P31(x100201)+E(f40(x100201,f329(f249(x100201),f329(f329(f8(f881(x100201,a869),a869,x100201),f88(x100201)),f329(f329(f8(f881(x100201,a869),f881(x100201,a869),x100201),f329(f18(x100201,a869,a869),f329(f329(f8(a869,f881(a869,a869),x100201),a332),f329(f329(f7(x100201,f881(x100201,a869),a869),f331(x100201)),x100202)))),f243(x100201))))),f41(x100201,x100202))
% 187.18/188.04 [10045]~P42(x100451,x100452)+P59(x100451,f329(f329(f7(x100451,f881(f880(x100451,x100451),a869),f881(x100451,a869)),f329(f329(f8(f881(x100451,f881(f881(f880(x100451,x100451),a869),a869)),f881(f881(f880(x100451,x100451),a869),f881(x100451,a869)),x100451),f7(x100451,f881(f880(x100451,x100451),a869),a869)),f329(f329(f8(f881(x100451,f880(x100451,x100451)),f881(x100451,f881(f881(f880(x100451,x100451),a869),a869)),x100451),f329(f8(f880(x100451,x100451),f881(f881(f880(x100451,x100451),a869),a869),x100451),f331(f880(x100451,x100451)))),f264(x100451,x100451)))),x100452))
% 187.18/188.04 [10046]~P6(x100461,f252(f881(x100461,a869)),x100462)+P5(x100461,f329(f329(f7(x100461,f881(f880(x100461,x100461),a869),f881(x100461,a869)),f329(f329(f8(f881(x100461,f881(f881(f880(x100461,x100461),a869),a869)),f881(f881(f880(x100461,x100461),a869),f881(x100461,a869)),x100461),f7(x100461,f881(f880(x100461,x100461),a869),a869)),f329(f329(f8(f881(x100461,f880(x100461,x100461)),f881(x100461,f881(f881(f880(x100461,x100461),a869),a869)),x100461),f329(f8(f880(x100461,x100461),f881(f881(f880(x100461,x100461),a869),a869),x100461),f331(f880(x100461,x100461)))),f264(x100461,x100461)))),x100462))
% 187.18/188.04 [10083]P42(x100831,x100832)+~P59(x100831,f329(f329(f7(x100831,f881(f880(x100831,x100831),a869),f881(x100831,a869)),f329(f329(f8(f881(x100831,f881(f881(f880(x100831,x100831),a869),a869)),f881(f881(f880(x100831,x100831),a869),f881(x100831,a869)),x100831),f7(x100831,f881(f880(x100831,x100831),a869),a869)),f329(f329(f8(f881(x100831,f880(x100831,x100831)),f881(x100831,f881(f881(f880(x100831,x100831),a869),a869)),x100831),f329(f8(f880(x100831,x100831),f881(f881(f880(x100831,x100831),a869),a869),x100831),f331(f880(x100831,x100831)))),f264(x100831,x100831)))),x100832))
% 187.18/188.04 [10084]P6(x100841,f252(f881(x100841,a869)),x100842)+~P5(x100841,f329(f329(f7(x100841,f881(f880(x100841,x100841),a869),f881(x100841,a869)),f329(f329(f8(f881(x100841,f881(f881(f880(x100841,x100841),a869),a869)),f881(f881(f880(x100841,x100841),a869),f881(x100841,a869)),x100841),f7(x100841,f881(f880(x100841,x100841),a869),a869)),f329(f329(f8(f881(x100841,f880(x100841,x100841)),f881(x100841,f881(f881(f880(x100841,x100841),a869),a869)),x100841),f329(f8(f880(x100841,x100841),f881(f881(f880(x100841,x100841),a869),a869),x100841),f331(f880(x100841,x100841)))),f264(x100841,x100841)))),x100842))
% 187.18/188.04 [7231]E(f329(f329(f80(a874),f329(f108(a874),f329(f329(f22(a1),x72311),a102))),x72312),f329(a117,f329(f329(f80(a874),f329(f108(a874),x72311)),x72312)))+P24(f329(a198,f329(f108(a1),x72311)))
% 187.18/188.04 [7680]~P94(x76801)+E(f329(f329(f80(x76801),f329(f329(f80(x76801),f78(x76801)),f329(f108(x76801),x76802))),f329(f108(x76801),x76802)),f329(f108(x76801),f329(f329(f22(a1),f329(f329(f80(a1),x76802),x76802)),a102)))
% 187.18/188.04 [8332]~P24(f329(f329(f243(a1),x83321),x83322))+P24(f329(f329(f243(a1),f329(f329(f80(a1),x83321),x83321)),f329(f329(f22(a1),f329(f329(f80(a1),x83322),x83322)),a102)))
% 187.18/188.04 [8334]~P24(f329(f329(f243(a1),x83341),x83342))+P24(f329(f329(f244(a1),f329(f329(f80(a1),x83341),x83341)),f329(f329(f22(a1),f329(f329(f80(a1),x83342),x83342)),a102)))
% 187.18/188.04 [8753]P24(f329(f329(f243(a1),x87531),x87532))+~P24(f329(f329(f243(a1),f329(f329(f80(a1),x87531),x87531)),f329(f329(f22(a1),f329(f329(f80(a1),x87532),x87532)),a102)))
% 187.18/188.04 [8755]P24(f329(f329(f243(a1),x87551),x87552))+~P24(f329(f329(f244(a1),f329(f329(f80(a1),x87551),x87551)),f329(f329(f22(a1),f329(f329(f80(a1),x87552),x87552)),a102)))
% 187.18/188.04 [9050]~P24(f329(f329(f243(a1),x90501),x90502))+P24(f329(f329(f243(a1),f329(f329(f22(a1),f329(f329(f80(a1),x90501),x90501)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),x90502),x90502)),a102)))
% 187.18/188.04 [9052]~P24(f329(f329(f244(a1),x90521),x90522))+P24(f329(f329(f244(a1),f329(f329(f22(a1),f329(f329(f80(a1),x90521),x90521)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),x90522),x90522)),a102)))
% 187.18/188.04 [9053]~P24(f329(f329(f91(a1),x90531),x90532))+P24(f329(f329(f91(a1),f329(f329(f22(a1),f329(f329(f80(a1),x90531),x90531)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),x90532),x90532)),a102)))
% 187.18/188.04 [9318]P24(f329(f329(f243(a1),x93181),x93182))+~P24(f329(f329(f243(a1),f329(f329(f22(a1),f329(f329(f80(a1),x93181),x93181)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),x93182),x93182)),a102)))
% 187.18/188.04 [9320]P24(f329(f329(f244(a1),x93201),x93202))+~P24(f329(f329(f244(a1),f329(f329(f22(a1),f329(f329(f80(a1),x93201),x93201)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),x93202),x93202)),a102)))
% 187.18/188.04 [9321]P24(f329(f329(f91(a1),x93211),x93212))+~P24(f329(f329(f91(a1),f329(f329(f22(a1),f329(f329(f80(a1),x93211),x93211)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),x93212),x93212)),a102)))
% 187.18/188.04 [9353]~P24(f329(f62(x93531),x93532))+P24(f329(f62(f881(x93531,a869)),f329(f249(f881(x93531,a869)),f329(f329(f7(f881(x93531,a869),f881(x93531,a869),a869),f243(f881(x93531,a869))),x93532))))
% 187.18/188.04 [9400]~E(f329(f283(f880(a874,a874),f880(a874,a874),a113),f329(f329(f307(f880(a874,a874)),x94001),f193(f881(f880(a874,a874),a869)))),f329(f283(f880(a874,a874),f880(a874,a874),a113),f329(f329(f307(f880(a874,a874)),x94002),f193(f881(f880(a874,a874),a869)))))+P24(f329(f329(f331(f880(f880(a874,a874),f880(a874,a874))),f329(f329(f264(f880(a874,a874),f880(a874,a874)),x94001),x94002)),a113))
% 187.18/188.04 [9484]E(f329(f283(f880(a874,a874),f880(a874,a874),a113),f329(f329(f307(f880(a874,a874)),x94841),f193(f881(f880(a874,a874),a869)))),f329(f283(f880(a874,a874),f880(a874,a874),a113),f329(f329(f307(f880(a874,a874)),x94842),f193(f881(f880(a874,a874),a869)))))+~P24(f329(f329(f331(f880(f880(a874,a874),f880(a874,a874))),f329(f329(f264(f880(a874,a874),f880(a874,a874)),x94841),x94842)),a113))
% 187.18/188.04 [9521]P24(f329(f329(f243(a1),f2(a1)),f655(x95211,x95212)))+E(f329(f249(a1),f329(f329(f18(a1,a869,a869),f329(f329(f8(a869,f881(a869,a869),a1),a327),f329(f243(a1),f2(a1)))),x95211)),f329(f249(a1),f329(f329(f18(a1,a869,a869),f329(f329(f8(a869,f881(a869,a869),a1),a327),f329(f243(a1),f2(a1)))),x95212)))
% 187.18/188.04 [10030]~P31(x100301)+E(f41(x100301,f329(f249(x100301),f329(f329(f8(f881(x100301,a869),a869,x100301),f88(x100301)),f329(f329(f8(f881(x100301,a869),f881(x100301,a869),x100301),f329(f18(x100301,a869,a869),f329(f329(f8(a869,f881(a869,a869),x100301),a332),f329(f329(f7(x100301,f881(x100301,a869),a869),f331(x100301)),x100302)))),f329(f7(x100301,x100301,a869),f243(x100301)))))),f40(x100301,x100302))
% 187.18/188.04 [10051]P24(f329(f329(f331(a874),f2(a874)),x100511))+E(f329(f38(a874),f329(f249(a874),f329(f329(f18(a874,a869,a869),f329(f329(f8(a869,f881(a869,a869),a874),a327),f329(f329(f7(a874,f881(a874,a869),a869),f329(f329(f8(a874,f881(f881(a874,a869),a869),a874),f331(a874)),a117)),x100511))),f329(f329(f7(a874,a874,a869),f244(a874)),x100512)))),f329(f38(a874),f329(f249(a874),f329(f329(f18(a874,a869,a869),f329(f329(f8(a869,f881(a869,a869),a874),a327),f329(f329(f7(a874,f881(a874,a869),a869),f331(a874)),x100511))),f329(f329(f7(a874,a874,a869),f244(a874)),f329(a117,x100512))))))
% 187.18/188.04 [7548]~P94(x75481)+E(f329(f329(f81(x75481),x75482),f329(f108(x75481),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102))),x75482)
% 187.18/188.04 [7815]~P94(x78151)+E(f329(f329(f80(x78151),f329(f108(x78151),x78152)),f78(x78151)),f329(f108(x78151),f329(f329(f80(a1),x78152),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102))))
% 187.18/188.04 [7960]P24(f329(f329(f243(a1),f2(a1)),f329(f108(a1),x79602)))+E(f329(f329(f254(a1),x79601),f329(f108(a874),f329(f329(f22(a1),f329(f329(f80(a1),x79602),x79602)),a102))),f78(a1))
% 187.18/188.04 [9378]~P24(f329(f329(f243(a1),f2(a1)),f329(f108(a1),x93782)))+E(f329(f329(f254(a1),x93781),f329(f108(a874),f329(f329(f22(a1),f329(f329(f80(a1),x93782),x93782)),a102))),f329(f329(f86(a1,a1),f329(f329(f254(a1),x93781),f329(f108(a874),x93782))),f329(f329(f18(a1,a1,a1),f329(f329(f8(a1,f881(a1,a1),a1),f81(a1)),f329(f81(a1),x93781))),f5(a1))))
% 187.18/188.04 [9742]~P24(f329(f329(f243(a874),f666(x97422,x97421)),f329(x97421,f666(x97422,x97421))))+P24(f329(f62(a874),f329(f249(a874),f329(f329(f7(a874,a874,a869),f329(f329(f8(a874,f881(a874,a869),a874),f243(a874)),x97421)),x97422))))
% 187.18/188.04 [9893]~P24(f329(f329(f243(a874),f329(f108(a874),x98931)),f329(a117,x98932)))+P24(f329(f329(f86(a1,a869),f329(f108(a1),f329(f329(f80(a1),x98931),a102))),f329(f329(f18(a1,a869,a869),f329(f329(f8(a869,f881(a869,a869),a1),a332),f329(f329(f8(a869,a869,a1),a324),a198))),f329(f329(f7(a1,a874,a869),f329(f329(f8(a874,f881(a874,a869),a1),f243(a874)),a109)),x98932))))
% 187.18/188.04 [9894]~P24(f329(f329(f244(a874),f329(f108(a874),x98941)),f329(a117,x98942)))+P24(f329(f329(f86(a1,a869),f329(f108(a1),f329(f329(f80(a1),x98941),a102))),f329(f329(f18(a1,a869,a869),f329(f329(f8(a869,f881(a869,a869),a1),a332),f329(f329(f8(a869,a869,a1),a324),a198))),f329(f329(f7(a1,a874,a869),f329(f329(f8(a874,f881(a874,a869),a1),f244(a874)),a109)),x98942))))
% 187.18/188.04 [9943]P24(f329(f329(f243(a874),f329(f108(a874),x99431)),f329(a117,x99432)))+~P24(f329(f329(f86(a1,a869),f329(f108(a1),f329(f329(f80(a1),x99431),a102))),f329(f329(f18(a1,a869,a869),f329(f329(f8(a869,f881(a869,a869),a1),a332),f329(f329(f8(a869,a869,a1),a324),a198))),f329(f329(f7(a1,a874,a869),f329(f329(f8(a874,f881(a874,a869),a1),f243(a874)),a109)),x99432))))
% 187.18/188.04 [9944]P24(f329(f329(f244(a874),f329(f108(a874),x99441)),f329(a117,x99442)))+~P24(f329(f329(f86(a1,a869),f329(f108(a1),f329(f329(f80(a1),x99441),a102))),f329(f329(f18(a1,a869,a869),f329(f329(f8(a869,f881(a869,a869),a1),a332),f329(f329(f8(a869,a869,a1),a324),a198))),f329(f329(f7(a1,a874,a869),f329(f329(f8(a874,f881(a874,a869),a1),f244(a874)),a109)),x99442))))
% 187.18/188.04 [9974]~P24(f329(f329(f243(a874),f329(a117,x99742)),f329(f108(a874),x99741)))+P24(f329(f329(f86(a1,a869),f329(f108(a1),f329(f329(f80(a1),x99741),a102))),f329(f329(f18(a1,a869,a869),f329(f329(f8(a869,f881(a869,a869),a1),a327),f329(f329(f8(a869,a869,a1),a324),a198))),f329(f329(f18(a1,a869,a869),f329(f329(f8(a869,f881(a869,a869),a1),a332),f329(f329(f8(a869,a869,a1),a324),a198))),f329(f329(f8(a874,a869,a1),f329(f243(a874),x99742)),a109)))))
% 187.18/188.04 [9975]~P24(f329(f329(f244(a874),f329(a117,x99752)),f329(f108(a874),x99751)))+P24(f329(f329(f86(a1,a869),f329(f108(a1),f329(f329(f80(a1),x99751),a102))),f329(f329(f18(a1,a869,a869),f329(f329(f8(a869,f881(a869,a869),a1),a327),f329(f329(f8(a869,a869,a1),a324),a198))),f329(f329(f18(a1,a869,a869),f329(f329(f8(a869,f881(a869,a869),a1),a332),f329(f329(f8(a869,a869,a1),a324),a198))),f329(f329(f8(a874,a869,a1),f329(f244(a874),x99752)),a109)))))
% 187.18/188.04 [10018]P24(f329(f329(f243(a874),f329(a117,x100181)),f329(f108(a874),x100182)))+~P24(f329(f329(f86(a1,a869),f329(f108(a1),f329(f329(f80(a1),x100182),a102))),f329(f329(f18(a1,a869,a869),f329(f329(f8(a869,f881(a869,a869),a1),a327),f329(f329(f8(a869,a869,a1),a324),a198))),f329(f329(f18(a1,a869,a869),f329(f329(f8(a869,f881(a869,a869),a1),a332),f329(f329(f8(a869,a869,a1),a324),a198))),f329(f329(f8(a874,a869,a1),f329(f243(a874),x100181)),a109)))))
% 187.18/188.04 [10019]P24(f329(f329(f244(a874),f329(a117,x100191)),f329(f108(a874),x100192)))+~P24(f329(f329(f86(a1,a869),f329(f108(a1),f329(f329(f80(a1),x100192),a102))),f329(f329(f18(a1,a869,a869),f329(f329(f8(a869,f881(a869,a869),a1),a327),f329(f329(f8(a869,a869,a1),a324),a198))),f329(f329(f18(a1,a869,a869),f329(f329(f8(a869,f881(a869,a869),a1),a332),f329(f329(f8(a869,a869,a1),a324),a198))),f329(f329(f8(a874,a869,a1),f329(f244(a874),x100191)),a109)))))
% 187.18/188.04 [10091]~P24(f329(f329(f331(a874),f2(a874)),x100911))+E(f329(a117,f329(f38(a874),f329(f249(a874),f329(f329(f18(a874,a869,a869),f329(f329(f8(a869,f881(a869,a869),a874),a327),f329(f329(f7(a874,f881(a874,a869),a869),f329(f329(f8(a874,f881(f881(a874,a869),a869),a874),f331(a874)),a117)),x100911))),f329(f329(f7(a874,a874,a869),f244(a874)),x100912))))),f329(f38(a874),f329(f249(a874),f329(f329(f18(a874,a869,a869),f329(f329(f8(a869,f881(a869,a869),a874),a327),f329(f329(f7(a874,f881(a874,a869),a869),f331(a874)),x100911))),f329(f329(f7(a874,a874,a869),f244(a874)),f329(a117,x100912))))))
% 187.18/188.04 [8515]~P94(x85151)+E(f329(f329(f81(x85151),f329(f108(x85151),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102))),x85152),x85152)
% 187.18/188.04 [8574]~P94(x85741)+E(f329(f329(f80(x85741),f78(x85741)),f329(f108(x85741),x85742)),f329(f108(x85741),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),x85742)))
% 187.18/188.04 [8632]~P94(x86321)+E(f329(f329(f22(x86321),f329(f108(x86321),x86322)),f78(x86321)),f329(f108(x86321),f329(f329(f80(a1),x86322),f329(f79(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))))
% 187.18/188.04 [8771]~P24(f329(f329(f244(a874),f329(f108(a874),a83)),x87712))+E(f329(f329(f22(a874),x87711),f329(f329(f22(a874),x87712),f329(f108(a874),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))),f329(f329(f22(a874),f329(a117,x87711)),x87712))
% 187.18/188.04 [9416]~P109(x94161)+E(f329(f329(f81(x94161),x94162),x94162),f329(f329(f254(x94161),x94162),f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))))
% 187.18/188.04 [9417]~P82(x94171)+E(f329(f329(f254(x94171),x94172),f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))),f329(f329(f81(x94171),x94172),x94172))
% 187.18/188.04 [9419]~P94(x94191)+E(f329(f329(f81(x94191),x94192),f329(f108(x94191),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))),f329(f329(f80(x94191),x94192),x94192))
% 187.18/188.04 [9660]~P115(x96601)+E(f329(f329(f254(x96601),f329(f75(x96601),x96602)),f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))),f329(f329(f254(x96601),x96602),f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))))
% 187.18/188.04 [9661]~P138(x96611)+E(f329(f329(f254(x96611),f329(f79(x96611),x96612)),f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))),f329(f329(f254(x96611),x96612),f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))))
% 187.18/188.04 [9657]~P94(x96571)+E(f329(f329(f81(x96571),f329(f108(x96571),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))),x96572),f329(f329(f80(x96571),x96572),x96572))
% 187.18/188.04 [9782]~P115(x97821)+E(f329(f75(x97821),f329(f329(f254(x97821),x97822),f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102))))),f329(f329(f254(x97821),x97822),f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))))
% 187.18/188.04 [9845]~P115(x98451)+P24(f329(f329(f243(x98451),f2(x98451)),f329(f329(f254(x98451),x98452),f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102))))))
% 187.18/188.04 [10009]~E(f329(a117,x100092),f329(f108(a874),x100091))+P24(f329(f329(f86(a1,a869),f329(f108(a1),f329(f329(f80(a1),x100091),a102))),f329(f329(f18(a1,a869,a869),f329(f329(f8(a869,f881(a869,a869),a1),a327),f329(f329(f8(a869,a869,a1),a324),a198))),f329(f329(f18(a1,a869,a869),f329(f329(f8(a869,f881(a869,a869),a1),a332),f329(f329(f8(a869,a869,a1),a324),a198))),f329(f329(f7(a1,a874,a869),f329(f329(f8(a874,f881(a874,a869),a1),a326),a109)),x100092)))))
% 187.18/188.04 [10010]~E(f329(f108(a874),x100101),f329(a117,x100102))+P24(f329(f329(f86(a1,a869),f329(f108(a1),f329(f329(f80(a1),x100101),a102))),f329(f329(f18(a1,a869,a869),f329(f329(f8(a869,f881(a869,a869),a1),a327),f329(f329(f8(a869,a869,a1),a324),a198))),f329(f329(f18(a1,a869,a869),f329(f329(f8(a869,f881(a869,a869),a1),a332),f329(f329(f8(a869,a869,a1),a324),a198))),f329(f329(f7(a1,a874,a869),f329(f329(f8(a874,f881(a874,a869),a1),a326),a109)),x100102)))))
% 187.18/188.04 [10054]E(f329(a117,x100541),f329(f108(a874),x100542))+~P24(f329(f329(f86(a1,a869),f329(f108(a1),f329(f329(f80(a1),x100542),a102))),f329(f329(f18(a1,a869,a869),f329(f329(f8(a869,f881(a869,a869),a1),a327),f329(f329(f8(a869,a869,a1),a324),a198))),f329(f329(f18(a1,a869,a869),f329(f329(f8(a869,f881(a869,a869),a1),a332),f329(f329(f8(a869,a869,a1),a324),a198))),f329(f329(f7(a1,a874,a869),f329(f329(f8(a874,f881(a874,a869),a1),a326),a109)),x100541)))))
% 187.18/188.04 [10055]E(f329(f108(a874),x100551),f329(a117,x100552))+~P24(f329(f329(f86(a1,a869),f329(f108(a1),f329(f329(f80(a1),x100551),a102))),f329(f329(f18(a1,a869,a869),f329(f329(f8(a869,f881(a869,a869),a1),a327),f329(f329(f8(a869,a869,a1),a324),a198))),f329(f329(f18(a1,a869,a869),f329(f329(f8(a869,f881(a869,a869),a1),a332),f329(f329(f8(a869,a869,a1),a324),a198))),f329(f329(f7(a1,a874,a869),f329(f329(f8(a874,f881(a874,a869),a1),a326),a109)),x100552)))))
% 187.18/188.04 [9842]~P94(x98421)+E(f329(f329(f254(x98421),f329(f108(x98421),a102)),f329(f329(f81(a874),f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))),x98422)),f78(x98421))
% 187.18/188.04 [9843]~P138(x98431)+E(f329(f329(f254(x98431),f329(f79(x98431),f78(x98431))),f329(f329(f81(a874),f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))),x98432)),f78(x98431))
% 187.18/188.04 [9847]~P82(x98471)+E(f329(f329(f254(x98471),x98472),f329(f108(a874),f329(f329(f22(a1),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102))),a102))),f329(f329(f81(x98471),f329(f329(f81(x98471),x98472),x98472)),x98472))
% 187.18/188.04 [10033]~P24(f329(f329(f243(a1),f2(a1)),x100332))+E(f45(a1,f329(f329(f80(a1),f78(a1)),f329(f329(f81(a1),f329(f108(a1),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))),x100331)),f329(f329(f81(a1),f329(f108(a1),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))),x100332)),f329(f329(f80(a1),f78(a1)),f329(f329(f81(a1),f329(f108(a1),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))),f45(a1,x100331,x100332))))
% 187.18/188.04 [10057]~P24(f329(f329(f243(a1),f2(a1)),x100572))+E(f329(f329(f39(a1),f329(f329(f80(a1),f78(a1)),f329(f329(f81(a1),f329(f108(a1),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))),x100571))),f329(f329(f81(a1),f329(f108(a1),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))),x100572)),f329(f329(f39(a1),x100571),x100572))
% 187.18/188.04 [10059]~P24(f329(f329(f243(a1),x100592),f2(a1)))+E(f329(f329(f39(a1),f329(f329(f80(a1),f78(a1)),f329(f329(f81(a1),f329(f108(a1),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))),x100591))),f329(f329(f81(a1),f329(f108(a1),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))),x100592)),f329(f329(f39(a1),f329(f329(f80(a1),x100591),f78(a1))),x100592))
% 187.18/188.04 [10060]~P24(f329(f329(f243(a1),x100602),f2(a1)))+E(f45(a1,f329(f329(f80(a1),f78(a1)),f329(f329(f81(a1),f329(f108(a1),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))),x100601)),f329(f329(f81(a1),f329(f108(a1),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))),x100602)),f329(f329(f22(a1),f329(f329(f81(a1),f329(f108(a1),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))),f45(a1,f329(f329(f80(a1),x100601),f78(a1)),x100602))),f78(a1)))
% 187.18/188.04 [9934]~P94(x99341)+E(f329(f329(f254(x99341),f329(f108(x99341),a102)),f329(a117,f329(f329(f81(a874),f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))),x99342))),f329(f108(x99341),a102))
% 187.18/188.04 [9936]~P138(x99361)+E(f329(f329(f254(x99361),f329(f79(x99361),f78(x99361))),f329(a117,f329(f329(f81(a874),f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))),x99362))),f329(f79(x99361),f78(x99361)))
% 187.18/188.04 [5090]~P20(x50901,x50902,x50903)+P23(x50901,x50902,x50903)
% 187.18/188.04 [8033]~E(x80332,x80333)+P39(x80331,x80331,a326,x80332,x80333)
% 187.18/188.04 [8587]E(x85871,x85872)+~P39(x85873,x85873,a326,x85871,x85872)
% 187.18/188.04 [5095]~P42(x50951,x50953)+P42(x50951,f323(x50951,x50952,x50953))
% 187.18/188.04 [5268]P34(x52681,x52682,x52683)+~P34(x52681,f329(a117,x52682),x52683)
% 187.18/188.04 [5355]~P6(x53551,x53552,x53553)+P6(f875(x53551),f159(x53551,x53552),f156(x53551,x53553))
% 187.18/188.04 [5356]~P44(x53561,x53562,x53563)+P44(f875(x53561),f159(x53561,x53562),f156(x53561,x53563))
% 187.18/188.04 [5468]P55(x54681,x54682,x54683)+~E(f576(x54683,x54682,x54681),f577(x54683,x54682,x54681))
% 187.18/188.04 [5469]P54(x54691,x54692,x54693)+~E(f592(x54693,x54692,x54691),f593(x54693,x54692,x54691))
% 187.18/188.04 [6405]P23(x64051,x64052,x64053)+~P34(x64051,f568(x64053,x64052,x64051),f570(x64053,x64052,x64051))
% 187.18/188.04 [4643]~E(x46431,f206(x46432))+~E(x46431,f329(f236(x46432),x46433))
% 187.18/188.04 [4692]~E(f329(f167(x46922),x46921),x46923)+E(x46921,f329(f167(x46922),x46923))
% 187.18/188.04 [4693]~E(x46932,f329(f167(x46931),x46933))+E(f329(f167(x46931),x46932),x46933)
% 187.18/188.04 [4740]E(x47401,x47402)+~E(f329(f236(x47403),x47401),f329(f236(x47403),x47402))
% 187.18/188.04 [4741]E(x47411,x47412)+~E(f329(f167(x47413),x47411),f329(f167(x47413),x47412))
% 187.18/188.04 [4946]~P5(x49463,x49461)+P24(f329(f329(x49461,x49462),x49462))
% 187.18/188.04 [4947]~P53(x49473,x49471)+P24(f329(f329(x49471,x49472),x49472))
% 187.18/188.04 [4949]~P59(x49491,x49492)+P24(f329(f317(x49491,x49492),x49493))
% 187.18/188.04 [5012]~P42(x50121,x50122)+P42(f875(x50121),f329(f141(x50121,x50122),x50123))
% 187.18/188.04 [5017]~P24(f329(x50172,x50173))+~E(f329(f249(x50171),x50172),f193(f881(x50171,a869)))
% 187.18/188.04 [5018]~P24(f329(x50182,x50183))+~E(f193(f881(x50181,a869)),f329(f249(x50181),x50182))
% 187.18/188.04 [5032]E(x50321,f2(a874))+E(f142(x50322,f169(x50322,x50321,x50323)),x50323)
% 187.18/188.04 [5050]~P24(f329(x50501,x50503))+P24(f329(x50501,f90(x50502,x50501)))
% 187.18/188.04 [5062]E(x50621,f2(a874))+E(f329(f139(x50622),f169(x50622,x50621,x50623)),x50623)
% 187.18/188.04 [5176]~E(x51762,x51763)+P24(f329(f329(f331(x51761),x51762),f329(a326,x51763)))
% 187.18/188.04 [5188]P24(f329(x51881,x51882))+~P24(f329(x51881,f552(x51881,x51883)))
% 187.18/188.04 [5234]E(f329(f167(x52341),x52342),f329(f329(f149(x52341),x52343),f118(x52341)))+~E(x52342,f329(f329(f149(x52341),x52343),f118(x52341)))
% 187.18/188.04 [5235]~E(x52353,f329(f329(f149(x52351),x52352),f118(x52351)))+E(f329(f329(f149(x52351),x52352),f118(x52351)),f329(f167(x52351),x52353))
% 187.18/188.04 [5261]~E(x52613,f329(f16(f878(x52612),x52611),f206(x52612)))+E(f183(x52611,x52612,x52613),f193(f881(x52611,a869)))
% 187.18/188.04 [5283]~P38(x52831,x52832,x52833)+P38(x52831,x52832,f329(f167(x52831),x52833))
% 187.18/188.04 [5284]~P36(x52841,x52842,x52843)+P36(x52841,x52842,f329(f167(x52841),x52843))
% 187.18/188.04 [5287]E(f329(f38(x52871),f777(x52872,x52873,x52871)),x52872)+~E(f329(f38(x52871),x52873),f329(a117,x52872))
% 187.18/188.04 [5293]~P42(x52931,x52933)+P24(f329(f329(f331(x52931),x52932),f318(x52931,x52933)))
% 187.18/188.04 [5297]~E(f329(f167(x52972),x52971),f329(f329(f149(x52972),x52973),f118(x52972)))+E(x52971,f329(f329(f149(x52972),x52973),f118(x52972)))
% 187.18/188.04 [5298]~E(f329(f329(f149(x52982),x52983),f118(x52982)),f329(f167(x52982),x52981))+E(x52981,f329(f329(f149(x52982),x52983),f118(x52982)))
% 187.18/188.04 [5313]E(x53131,f329(f16(f878(x53132),x53133),f206(x53132)))+~E(f183(x53133,x53132,x53131),f193(f881(x53133,a869)))
% 187.18/188.04 [5319]E(f85(f880(a874,a874),f48(x53191,x53192)),x53193)+~P24(f329(f48(x53191,x53192),x53193))
% 187.18/188.04 [5327]~E(x53273,f329(f236(x53271),x53272))+P24(f329(f329(f331(x53271),x53272),f235(x53271,x53273)))
% 187.18/188.04 [5359]P38(x53591,x53592,x53593)+~P38(x53591,x53592,f329(f167(x53591),x53593))
% 187.18/188.04 [5360]P36(x53601,x53602,x53603)+~P36(x53601,x53602,f329(f167(x53601),x53603))
% 187.18/188.04 [5422]~E(x54222,f118(x54221))+P24(f329(f329(f331(f875(x54221)),x54222),f159(x54221,x54223)))
% 187.18/188.04 [5429]~P44(x54291,x54292,x54293)+P44(x54291,x54292,f329(f284(x54291,x54291),x54293))
% 187.18/188.04 [5430]~P55(x54301,x54302,x54303)+P55(x54301,x54302,f329(f284(x54301,x54301),x54303))
% 187.18/188.04 [5449]~P29(x54491)+E(f45(x54491,f45(x54491,x54492,x54493),x54493),f45(x54491,x54492,x54493))
% 187.18/188.04 [5544]E(x55441,x55442)+~P24(f329(f329(f331(x55443),x55441),f329(a326,x55442)))
% 187.18/188.04 [5590]~P141(x55901)+E(f195(x55901,x55902,f2(a874),x55903),x55903)
% 187.18/188.04 [5610]P44(x56101,x56102,x56103)+~P44(x56101,x56102,f329(f284(x56101,x56101),x56103))
% 187.18/188.04 [5611]P55(x56111,x56112,x56113)+~P55(x56111,x56112,f329(f284(x56111,x56111),x56113))
% 187.18/188.04 [5615]~P27(x56152)+E(f148(x56151,x56152,x56153,f118(x56151)),f118(x56151))
% 187.18/188.04 [5628]E(f168(x56281,x56282,f150(x56281,x56283)),f150(x56281,f168(x56281,x56282,x56283)))+~P24(f329(f135(x56281),x56283))
% 187.18/188.04 [5634]E(x56341,f329(f236(x56342),x56343))+~P24(f329(f329(f331(x56342),x56343),f235(x56342,x56341)))
% 187.18/188.04 [5720]~P24(f329(a25,x57203))+P24(f329(a25,f29(x57201,x57202,x57203)))
% 187.18/188.04 [5731]E(f329(f134(x57311,x57312),x57313),f118(x57311))+P24(f329(x57312,f730(x57313,x57312,x57311)))
% 187.18/188.04 [5874]~P24(f329(f135(x58741),x58742))+P24(f329(f135(x58741),f175(x58741,x58742,x58743)))
% 187.18/188.04 [5875]~P24(f329(f135(x58751),x58753))+P24(f329(f135(x58751),f168(x58751,x58752,x58753)))
% 187.18/188.04 [5876]~P24(f329(f135(x58761),x58763))+P24(f329(f135(x58761),f176(x58761,x58762,x58763)))
% 187.18/188.04 [5877]~P24(f329(f135(x58771),x58773))+P24(f329(f135(x58771),f138(x58771,x58772,x58773)))
% 187.18/188.04 [5878]~P143(x58781,x58782,x58783)+P24(f329(x58781,f45(a1,x58782,x58783)))
% 187.18/188.04 [5897]~P38(x58973,x58971,x58972)+P24(f329(x58971,f780(x58972,x58971,x58973)))
% 187.18/188.04 [5898]~P40(x58983,x58981,x58982)+P24(f329(x58981,f807(x58982,x58981,x58983)))
% 187.18/188.04 [5920]E(f329(f134(x59201,x59202),x59203),f176(x59201,x59202,x59203))+P24(f329(x59202,f757(x59203,x59202,x59201)))
% 187.18/188.04 [5962]~P24(f329(f135(x59621),x59623))+P24(f329(f135(f875(x59621)),f55(x59621,x59622,x59623)))
% 187.18/188.04 [5994]~P106(x59941)+E(f329(f329(f106(f881(x59941,a869)),f329(f250(x59941),x59942)),f300(x59941,x59942,x59943)),f193(f881(x59941,a869)))
% 187.18/188.04 [5995]~P106(x59951)+E(f329(f329(f106(f881(x59951,a869)),f329(f298(x59951),x59952)),f303(x59951,x59952,x59953)),f193(f881(x59951,a869)))
% 187.18/188.04 [5996]~P106(x59961)+E(f329(f329(f106(f881(x59961,a869)),f329(f298(x59961),x59962)),f302(x59961,x59962,x59963)),f193(f881(x59961,a869)))
% 187.18/188.04 [6143]P24(f329(a25,x61431))+~P24(f329(a25,f29(x61432,x61433,x61431)))
% 187.18/188.04 [6145]P24(f329(a25,x61451))+~P24(f329(a25,f30(x61452,x61453,x61451)))
% 187.18/188.04 [6147]P24(f329(a25,x61471))+~P24(f329(a25,f30(x61472,x61471,x61473)))
% 187.18/188.04 [6227]E(f329(f134(x62271,x62272),x62273),x62273)+~P24(f329(x62272,f731(x62273,x62272,x62271)))
% 187.18/188.04 [6229]E(f329(f329(f307(x62291),f857(x62292,x62293,x62291)),f777(x62292,x62293,x62291)),x62293)+~E(f329(f38(x62291),x62293),f329(a117,x62292))
% 187.18/188.04 [6245]P143(x62451,x62452,x62453)+~P24(f329(x62451,f45(a1,x62452,x62453)))
% 187.18/188.04 [6292]P36(x62921,x62922,x62923)+~P24(f329(x62922,f795(x62922,x62923,x62921)))
% 187.18/188.04 [6293]P36(x62931,x62932,x62933)+~P24(f329(x62932,f802(x62933,x62932,x62931)))
% 187.18/188.04 [6294]P36(x62941,x62942,x62943)+~P24(f329(x62942,f803(x62943,x62942,x62941)))
% 187.18/188.04 [6296]E(f176(x62961,x62962,x62963),x62963)+~P24(f329(x62962,f752(x62963,x62962,x62961)))
% 187.18/188.04 [6374]~P24(f329(x63742,f559(x63743,x63742,x63741)))+P24(f329(f257(x63741,x63742),x63743))
% 187.18/188.04 [6375]~P24(f329(x63752,f720(x63753,x63752,x63751)))+P24(f329(f158(x63751,x63752),x63753))
% 187.18/188.04 [6622]~P24(f329(f317(x66221,x66222),f474(x66223,x66222,x66221)))+P24(f329(f317(x66221,x66222),x66223))
% 187.18/188.04 [6623]~P24(f329(f317(x66231,x66232),f489(x66233,x66232,x66231)))+P24(f329(f317(x66231,x66232),x66233))
% 187.18/188.04 [7232]~P29(x72321)+E(f329(f329(f80(x72321),f329(f329(f81(x72321),x72322),f329(f329(f39(x72321),x72323),x72322))),f45(x72321,x72323,x72322)),x72323)
% 187.18/188.04 [7704]E(f329(f329(f264(x77041,x77041),f503(x77042,x77043,x77041)),f503(x77042,x77043,x77041)),x77043)+~P24(f329(f329(f331(f880(x77041,x77041)),x77043),f261(x77041,x77042)))
% 187.18/188.04 [7823]~P24(f329(f329(f331(x78231),f515(x78233,x78232,x78231)),f318(x78231,x78233)))+P24(f329(f329(f331(x78231),x78232),f318(x78231,x78233)))
% 187.18/188.04 [7824]~P24(f329(f329(f331(x78241),f580(x78243,x78242,x78241)),f318(x78241,x78243)))+P24(f329(f329(f331(x78241),x78242),f318(x78241,x78243)))
% 187.18/188.04 [7825]~P24(f329(f329(f331(x78251),f582(x78253,x78252,x78251)),f318(x78251,x78253)))+P24(f329(f329(f331(x78251),x78252),f318(x78251,x78253)))
% 187.18/188.04 [8014]~P29(x80141)+E(f329(f329(f80(x80141),f329(f329(f81(x80141),f329(f329(f39(x80141),x80142),x80143)),x80143)),f45(x80141,x80142,x80143)),x80142)
% 187.18/188.04 [8059]~E(f329(f38(x80591),x80592),f329(a117,x80593))+~P24(f329(f329(f331(x80591),f857(x80593,x80592,x80591)),f777(x80593,x80592,x80591)))
% 187.18/188.04 [8683]P24(f329(f329(f243(f881(f880(x86831,x86831),a869)),f305(x86831,x86832)),f305(x86831,x86833)))+~P24(f329(f329(f243(f881(f880(x86831,x86831),a869)),x86832),f305(x86831,x86833)))
% 187.18/188.04 [8958]E(x89581,f118(x89582))+~P24(f329(f329(f331(f880(f875(x89582),f875(x89582))),f329(f329(f264(f875(x89582),f875(x89582)),x89581),f118(x89582))),f156(x89582,x89583)))
% 187.18/188.04 [8983]E(x89831,f118(x89832))+~P24(f329(f329(f331(f880(f875(x89832),f875(x89832))),f329(f329(f264(f875(x89832),f875(x89832)),f118(x89832)),x89831)),f156(x89832,x89833)))
% 187.18/188.04 [9107]E(f329(f329(f149(x91071),f707(x91072,x91073,x91071)),f708(x91072,x91073,x91071)),x91073)+~P24(f329(f329(f331(f880(f875(x91071),f875(x91071))),f329(f329(f264(f875(x91071),f875(x91071)),f118(x91071)),x91073)),f145(x91071,x91072)))
% 187.18/188.04 [9346]~P122(x93461)+~P24(f329(f329(f244(x93461),f329(f329(f80(x93461),f329(f329(f81(x93461),x93462),x93462)),f329(f329(f81(x93461),x93463),x93463))),f2(x93461)))
% 187.18/188.04 [9395]P24(f329(f62(x93951),x93952))+~P24(f329(f329(f331(f880(f881(x93951,a869),f881(x93951,a869))),f329(f329(f264(f881(x93951,a869),f881(x93951,a869)),x93953),x93952)),f304(x93951)))
% 187.18/188.04 [9682]~P51(x96821,x96822,x96823)+P24(f329(f329(f243(a1),f329(f329(f73(f880(a1,a1),a1,x96821,f263(a1,a1)),f220(x96821)),f231(x96821,x96822,f228(x96821,x96823)))),f2(a1)))
% 187.18/188.04 [9683]~P52(x96831,x96832,x96833)+P24(f329(f329(f244(a1),f329(f329(f73(f880(a1,a1),a1,x96831,f263(a1,a1)),f220(x96831)),f231(x96831,x96832,f228(x96831,x96833)))),f2(a1)))
% 187.18/188.04 [9811]P52(x98111,x98112,x98113)+~P24(f329(f329(f244(a1),f329(f329(f73(f880(a1,a1),a1,x98111,f263(a1,a1)),f220(x98111)),f231(x98111,x98112,f228(x98111,x98113)))),f2(a1)))
% 187.18/188.04 [9812]P51(x98121,x98122,x98123)+~P24(f329(f329(f243(a1),f329(f329(f73(f880(a1,a1),a1,x98121,f263(a1,a1)),f220(x98121)),f231(x98121,x98122,f228(x98121,x98123)))),f2(a1)))
% 187.18/188.04 [10134]~P115(x101341)+~P24(f329(f329(f244(x101341),f329(f329(f80(x101341),f329(f329(f254(x101341),x101342),f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102))))),f329(f329(f254(x101341),x101343),f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))))),f2(x101341)))
% 187.18/188.04 [4723]~E(x47233,f118(x47231))+E(f329(f329(f126(x47231),x47232),x47233),x47232)
% 187.18/188.04 [4724]~E(x47242,f118(x47241))+E(f329(f329(f126(x47241),x47242),x47243),x47243)
% 187.18/188.04 [4731]~E(x47312,f2(a874))+E(f329(f329(f174(x47311),x47312),x47313),f118(x47311))
% 187.18/188.04 [4735]~E(x47353,f118(x47351))+E(f329(f329(f174(x47351),x47352),x47353),f118(x47351))
% 187.18/188.04 [4775]~E(x47751,x47753)+E(x47751,f329(f329(f126(x47752),f118(x47752)),x47753))
% 187.18/188.04 [4863]~P65(x48632)+E(f329(f193(f881(x48631,x48632)),x48633),f193(x48632))
% 187.18/188.04 [4864]~P112(x48642)+E(f329(f252(f881(x48641,x48642)),x48643),f252(x48642))
% 187.18/188.04 [4883]E(x48831,f118(x48832))+~E(f329(f329(f126(x48832),x48833),x48831),x48833)
% 187.18/188.04 [4884]E(x48841,f118(x48842))+~E(f329(f329(f126(x48842),x48841),x48843),x48843)
% 187.18/188.04 [4892]E(x48921,f118(x48922))+~E(f329(f329(f126(x48922),x48923),x48921),f118(x48922))
% 187.18/188.04 [4893]E(x48931,f118(x48932))+~E(f329(f329(f126(x48932),x48931),x48933),f118(x48932))
% 187.18/188.04 [4916]~E(x49162,f2(a874))+E(f329(f329(f81(a874),x49161),x49162),f329(f329(f81(a874),x49163),x49162))
% 187.18/188.04 [4918]~E(x49181,f2(a874))+E(f329(f329(f81(a874),x49181),x49182),f329(f329(f81(a874),x49181),x49183))
% 187.18/188.04 [4971]~P66(x49711)+E(f329(f329(f115(x49711),x49712),x49713),f329(f329(f115(x49711),x49713),x49712))
% 187.18/188.04 [4973]~P102(x49731)+E(f329(f329(f115(x49731),x49732),x49733),f329(f329(f115(x49731),x49733),x49732))
% 187.18/188.04 [4974]~P66(x49741)+E(f329(f329(f106(x49741),x49742),x49743),f329(f329(f106(x49741),x49743),x49742))
% 187.18/188.04 [4976]~P103(x49761)+E(f329(f329(f106(x49761),x49762),x49763),f329(f329(f106(x49761),x49763),x49762))
% 187.18/188.04 [4977]~P109(x49771)+E(f329(f329(f81(x49771),x49772),x49773),f329(f329(f81(x49771),x49773),x49772))
% 187.18/188.04 [4978]~P109(x49781)+E(f329(f329(f80(x49781),x49782),x49783),f329(f329(f80(x49781),x49783),x49782))
% 187.18/188.04 [4980]~P27(x49801)+E(f329(f329(f241(x49801),x49802),x49803),f329(f329(f241(x49801),x49803),x49802))
% 187.18/188.04 [4982]~P27(x49821)+E(f329(f329(f242(x49821),x49822),x49823),f329(f329(f242(x49821),x49823),x49822))
% 187.18/188.04 [5045]E(f45(a874,x50451,x50452),f2(a874))+~E(x50451,f329(f329(f81(a874),x50452),x50453))
% 187.18/188.04 [5046]E(f45(a1,x50461,x50462),f2(a1))+~E(x50461,f329(f329(f81(a1),x50462),x50463))
% 187.18/188.04 [5107]E(x51071,x51072)+~E(f329(f329(f80(a874),x51073),x51071),f329(f329(f80(a874),x51073),x51072))
% 187.18/188.04 [5108]E(x51081,x51082)+~E(f329(f329(f80(a874),x51081),x51083),f329(f329(f80(a874),x51082),x51083))
% 187.18/188.04 [5118]~P97(x51181)+E(f329(f329(f106(x51181),x51182),f329(f79(x51181),x51183)),f329(f329(f22(x51181),x51182),x51183))
% 187.18/188.04 [5119]~P69(x51191)+E(f329(f329(f80(x51191),x51192),f329(f79(x51191),x51193)),f329(f329(f22(x51191),x51192),x51193))
% 187.18/188.04 [5120]~P77(x51201)+E(f329(f329(f80(x51201),x51202),f329(f79(x51201),x51203)),f329(f329(f22(x51201),x51202),x51203))
% 187.18/188.04 [5121]~P114(x51211)+E(f329(f329(f80(x51211),x51212),f329(f79(x51211),x51213)),f329(f329(f22(x51211),x51212),x51213))
% 187.18/188.04 [5122]~P77(x51221)+E(f329(f329(f22(x51221),x51222),f329(f79(x51221),x51223)),f329(f329(f80(x51221),x51222),x51223))
% 187.18/188.04 [5169]~P24(f329(x51693,x51692))+P24(f329(f329(f331(x51691),x51692),x51693))
% 187.18/188.04 [5171]~P72(x51712)+E(f329(f329(f6(x51711,x51712),x51713),f193(f881(x51711,a869))),f2(x51712))
% 187.18/188.04 [5173]~P76(x51732)+E(f329(f329(f9(x51731,x51732),x51733),f193(f881(x51731,a869))),f78(x51732))
% 187.18/188.04 [5222]~E(x52222,f329(f329(f80(a874),x52221),x52223))+P24(f329(f329(f243(a874),x52221),x52222))
% 187.18/188.04 [5225]~E(x52252,f193(f881(x52251,a869)))+E(f329(f329(f61(x52251),x52252),x52253),f193(f881(f881(x52251,a869),a869)))
% 187.18/188.04 [5226]~E(x52262,f193(f881(x52261,a869)))+E(f193(f881(f881(x52261,a869),a869)),f329(f329(f61(x52261),x52262),x52263))
% 187.18/188.04 [5302]~E(f329(f260(x53022,x53023),x53021),f193(f881(x53023,a869)))+E(x53021,f193(f881(f880(x53022,x53023),a869)))
% 187.18/188.04 [5303]~E(f329(f262(x53032,x53033),x53031),f193(f881(x53032,a869)))+E(x53031,f193(f881(f880(x53032,x53033),a869)))
% 187.18/188.04 [5333]E(f329(f260(x53331,x53332),x53333),f193(f881(x53332,a869)))+~E(x53333,f193(f881(f880(x53331,x53332),a869)))
% 187.18/188.04 [5334]E(f329(f262(x53341,x53342),x53343),f193(f881(x53341,a869)))+~E(x53343,f193(f881(f880(x53341,x53342),a869)))
% 187.18/188.04 [5337]E(f279(x53371,x53372,x53373),f329(f329(f22(a104),x53372),x53373))+P24(f329(f329(f244(a104),x53372),x53373))
% 187.18/188.04 [5353]P24(f329(x53531,x53532))+~P24(f329(f329(f331(x53533),x53532),x53531))
% 187.18/188.04 [5392]E(x53921,x53922)+~E(f329(f79(f881(x53923,a869)),x53921),f329(f79(f881(x53923,a869)),x53922))
% 187.18/188.04 [5397]E(f311(x53971,x53972,x53973),f206(f875(a325)))+~P24(f329(f329(f244(a1),x53972),x53973))
% 187.18/188.04 [5402]~E(x54021,f193(f881(x54022,a869)))+~P24(f329(f329(f331(x54022),x54023),x54021))
% 187.18/188.04 [5431]~E(x54312,f329(f329(f80(a1),x54311),f329(f105(a1),x54313)))+P24(f329(f329(f243(a1),x54311),x54312))
% 187.18/188.04 [5447]E(f329(f329(f307(x54471),x54472),x54473),x54473)+~P24(f329(f329(f331(x54471),x54472),x54473))
% 187.18/188.04 [5458]E(x54581,f193(f881(x54582,a869)))+~E(f329(f329(f61(x54582),x54581),x54583),f193(f881(f881(x54582,a869),a869)))
% 187.18/188.04 [5459]E(x54591,f193(f881(x54592,a869)))+~E(f193(f881(f881(x54592,a869),a869)),f329(f329(f61(x54592),x54591),x54593))
% 187.18/188.04 [5466]~P107(x54661)+E(f329(f329(f81(x54661),f329(f79(x54661),x54662)),f329(f79(x54661),x54663)),f329(f329(f81(x54661),x54662),x54663))
% 187.18/188.04 [5467]~P61(x54671)+E(f329(f329(f287(x54671),f329(f79(x54671),x54672)),f329(f79(x54671),x54673)),f329(f329(f287(x54671),x54672),x54673))
% 187.18/188.04 [5499]~P24(f329(x54993,x54992))+P24(f329(f329(f331(x54991),x54992),f329(f249(x54991),x54993)))
% 187.18/188.04 [5537]E(f168(x55371,x55372,x55373),x55373)+P24(f329(f329(f331(x55371),x55372),f329(f171(x55371),x55373)))
% 187.18/188.04 [5619]~P24(f329(f135(x56191),x56193))+P24(f329(f135(x56191),f329(f134(x56191,x56192),x56193)))
% 187.18/188.04 [5664]~P29(x56641)+E(f329(f329(f39(x56641),f45(x56641,x56642,x56643)),x56643),f2(x56641))
% 187.18/188.04 [5683]E(f175(x56831,f329(f329(f149(x56831),x56832),f118(x56831)),x56833),f118(x56831))+P24(f329(f329(f331(a874),f2(a874)),x56833))
% 187.18/188.04 [5689]E(x56891,f2(a874))+E(f329(f170(x56892),f169(x56892,x56891,x56893)),f169(x56892,f329(f329(f22(a874),x56891),f78(a874)),x56893))
% 187.18/188.04 [5741]E(f329(f329(f149(x57411),x57412),x57413),f138(x57411,x57412,x57413))+P24(f329(f329(f331(x57411),x57412),f329(f171(x57411),x57413)))
% 187.18/188.04 [5750]E(x57501,x57502)+~E(f329(f329(f81(a874),f329(a117,x57503)),x57501),f329(f329(f81(a874),f329(a117,x57503)),x57502))
% 187.18/188.04 [5751]~E(x57512,f329(f329(f80(a1),x57511),f329(f105(a1),f329(a117,x57513))))+P24(f329(f329(f244(a1),x57511),x57512))
% 187.18/188.04 [5856]~E(x58563,f118(x58561))+E(f329(f329(f329(f188(f875(x58561),f875(x58561)),x58562),f166(x58561)),x58563),f118(x58561))
% 187.18/188.04 [5860]P24(f329(x58601,x58602))+~P24(f329(f329(f331(x58603),x58602),f329(f249(x58603),x58601)))
% 187.18/188.04 [5892]E(x58921,x58922)+~E(f329(f329(f307(x58923),x58921),f193(f881(x58923,a869))),f329(f329(f307(x58923),x58922),f193(f881(x58923,a869))))
% 187.18/188.04 [5903]~P106(x59031)+E(f329(f329(f106(f881(x59031,a869)),f329(f250(x59031),x59032)),f329(f299(x59031,x59032),x59033)),f193(f881(x59031,a869)))
% 187.18/188.04 [5946]E(f138(x59461,x59462,x59463),x59463)+~P24(f329(f329(f331(x59461),x59462),f329(f171(x59461),x59463)))
% 187.18/188.04 [5970]~P80(x59701)+E(f329(f308(x59701,x59701,f79(x59701)),f329(f299(x59701,x59702),x59703)),f302(x59701,f329(f79(x59701),x59703),f329(f79(x59701),x59702)))
% 187.18/188.04 [5978]E(f329(f194(f875(x59781)),f168(x59781,x59782,x59783)),f329(f194(f875(x59781)),x59783))+P24(f329(f329(f331(x59781),x59782),f329(f171(x59781),x59783)))
% 187.18/188.04 [6030]~P106(x60301)+E(f329(f329(f106(f881(x60301,a869)),f329(f299(x60301,x60302),x60303)),f329(f251(x60301),x60303)),f193(f881(x60301,a869)))
% 187.18/188.04 [6053]~P80(x60531)+E(f329(f308(x60531,x60531,f79(x60531)),f300(x60531,x60532,x60533)),f300(x60531,f329(f79(x60531),x60533),f329(f79(x60531),x60532)))
% 187.18/188.04 [6054]~P80(x60541)+E(f329(f308(x60541,x60541,f79(x60541)),f303(x60541,x60542,x60543)),f303(x60541,f329(f79(x60541),x60543),f329(f79(x60541),x60542)))
% 187.18/188.04 [6111]E(f175(x61111,f329(f329(f149(x61111),x61112),f118(x61111)),x61113),f329(f329(f149(x61111),x61112),f118(x61111)))+~P24(f329(f329(f331(a874),f2(a874)),x61113))
% 187.18/188.04 [6118]~P80(x61181)+E(f329(f308(x61181,x61181,f79(x61181)),f302(x61181,x61182,x61183)),f329(f299(x61181,f329(f79(x61181),x61183)),f329(f79(x61181),x61182)))
% 187.18/188.04 [6138]~P30(x61381)+E(f45(x61381,f329(f79(x61381),f45(x61381,x61382,x61383)),x61383),f45(x61381,f329(f79(x61381),x61382),x61383))
% 187.18/188.04 [6242]~P24(f329(f62(f880(x62422,x62421)),x62423))+P24(f329(f62(x62421),f329(f260(x62422,x62421),x62423)))
% 187.18/188.04 [6243]~P24(f329(f62(f880(x62431,x62432)),x62433))+P24(f329(f62(x62431),f329(f262(x62431,x62432),x62433)))
% 187.18/188.04 [6249]~P106(x62491)+E(f329(f329(f106(f881(x62491,a869)),f300(x62491,x62492,x62493)),f329(f301(x62491),x62493)),f193(f881(x62491,a869)))
% 187.18/188.04 [6250]~P106(x62501)+E(f329(f329(f106(f881(x62501,a869)),f303(x62501,x62502,x62503)),f329(f251(x62501),x62503)),f193(f881(x62501,a869)))
% 187.18/188.04 [6251]~P106(x62511)+E(f329(f329(f106(f881(x62511,a869)),f302(x62511,x62512,x62513)),f329(f301(x62511),x62513)),f193(f881(x62511,a869)))
% 187.18/188.04 [6317]E(f329(f329(f163(x63171),x63172),f650(x63172,x63173,x63171)),x63173)+~P24(f329(f329(f331(x63171),x63173),f329(f171(x63171),x63172)))
% 187.18/188.04 [6456]E(x64561,f118(x64562))+~E(f329(f329(f329(f188(f875(x64562),f875(x64562)),x64563),f166(x64562)),x64561),f118(x64562))
% 187.18/188.04 [6559]~P24(f329(f62(f880(x65592,x65591)),x65593))+P24(f329(f62(f880(x65591,x65592)),f329(f284(x65592,x65591),x65593)))
% 187.18/188.04 [6710]P55(x67101,x67102,x67103)+P24(f329(f329(f331(x67101),f577(x67103,x67102,x67101)),x67102))
% 187.18/188.04 [6711]P55(x67111,x67112,x67113)+P24(f329(f329(f331(x67111),f576(x67113,x67112,x67111)),x67112))
% 187.18/188.04 [6723]P24(f329(f317(x67231,x67232),x67233))+P24(f329(f329(x67232,f474(x67233,x67232,x67231)),x67233))
% 187.18/188.04 [6724]P24(f329(f317(x67241,x67242),x67243))+P24(f329(f329(x67242,f489(x67243,x67242,x67241)),x67243))
% 187.18/188.04 [6755]E(f329(f194(f875(x67551)),f168(x67551,x67552,x67553)),f329(f329(f22(a874),f329(f194(f875(x67551)),x67553)),f78(a874)))+~P24(f329(f329(f331(x67551),x67552),f329(f171(x67551),x67553)))
% 187.18/188.04 [6795]P24(f329(f257(x67951,x67952),x67953))+P24(f329(f329(f331(x67951),f559(x67953,x67952,x67951)),x67953))
% 187.18/188.04 [6806]~P24(f329(f62(f880(x68062,x68061)),f329(f284(x68061,x68062),x68063)))+P24(f329(f62(f880(x68061,x68062)),x68063))
% 187.18/188.04 [6862]~P24(f329(f329(f331(x68621),x68622),f329(f171(x68621),f119(x68621,x68623))))+P24(f329(f329(f331(x68621),x68622),f329(f171(x68621),x68623)))
% 187.18/188.04 [6867]P23(x68671,x68672,x68673)+P24(f329(f329(f331(f873(x68671)),f570(x68673,x68672,x68671)),x68673))
% 187.18/188.04 [6897]E(f329(f134(x68971,x68972),x68973),x68973)+P24(f329(f329(f331(x68971),f731(x68973,x68972,x68971)),f329(f171(x68971),x68973)))
% 187.18/188.04 [6912]E(f329(f134(x69121,x69122),x69123),f118(x69121))+P24(f329(f329(f331(x69121),f730(x69123,x69122,x69121)),f329(f171(x69121),x69123)))
% 187.18/188.04 [6935]P36(x69351,x69352,x69353)+P24(f329(f329(f331(x69351),f802(x69353,x69352,x69351)),f329(f171(x69351),x69353)))
% 187.18/188.04 [6936]P36(x69361,x69362,x69363)+P24(f329(f329(f331(x69361),f803(x69363,x69362,x69361)),f329(f171(x69361),x69363)))
% 187.18/188.04 [6937]P36(x69371,x69372,x69373)+P24(f329(f329(f331(x69371),f795(x69372,x69373,x69371)),f329(f171(x69371),x69373)))
% 187.18/188.04 [6940]E(f176(x69401,x69402,x69403),x69403)+P24(f329(f329(f331(x69401),f752(x69403,x69402,x69401)),f329(f171(x69401),x69403)))
% 187.18/188.04 [7021]P24(f329(f158(x70211,x70212),x70213))+P24(f329(f329(f331(x70211),f720(x70213,x70212,x70211)),f329(f171(x70211),x70213)))
% 187.18/188.04 [7030]~P38(x70301,x70303,x70302)+P24(f329(f329(f331(x70301),f780(x70302,x70303,x70301)),f329(f171(x70301),x70302)))
% 187.18/188.04 [7031]~P40(x70311,x70313,x70312)+P24(f329(f329(f331(x70311),f807(x70312,x70313,x70311)),f329(f171(x70311),x70312)))
% 187.18/188.04 [7066]P24(f329(f329(f331(x70661),x70662),f652(x70663,x70662,x70661)))+~P24(f329(f329(f331(x70661),x70662),f40(f881(x70661,a869),x70663)))
% 187.18/188.04 [7067]~P72(x70671)+E(f329(f329(f80(x70671),f329(f329(f6(a874,x70671),x70672),f329(f250(a874),x70673))),f329(x70672,x70673)),f329(f329(f6(a874,x70671),x70672),f329(f250(a874),f329(a117,x70673))))
% 187.18/188.04 [7156]~P38(x71562,x71561,x71563)+P24(f329(x71561,f329(f329(f163(x71562),x71563),f792(x71563,x71561,x71562))))
% 187.18/188.04 [7169]~P24(f329(f329(f331(x71691),x71692),f640(x71692,x71693,x71691)))+P24(f329(f329(f331(x71691),x71692),f41(f881(x71691,a869),x71693)))
% 187.18/188.04 [7199]~P72(x71991)+E(f329(f329(f80(x71991),f329(f329(f6(a874,x71991),x71992),f329(f298(a874),x71993))),f329(x71992,f329(a117,x71993))),f329(f329(f6(a874,x71991),x71992),f329(f298(a874),f329(a117,x71993))))
% 187.18/188.04 [7334]P24(f329(f329(f331(f875(x73341)),x73342),f159(x73341,x73343)))+P24(f329(f329(f331(x73341),f675(x73343,x73342,x73341)),f329(f171(x73341),x73342)))
% 187.18/188.04 [7351]~P24(f329(f329(f331(f875(x73511)),x73512),f159(x73511,f318(x73511,x73513))))+P24(f329(f329(f331(f875(x73511)),x73512),f318(f875(x73511),f155(x73511,x73513))))
% 187.18/188.04 [7377]~P24(f329(f329(f331(f875(x73771)),x73772),f318(f875(x73771),f155(x73771,x73773))))+P24(f329(f329(f331(f875(x73771)),x73772),f159(x73771,f318(x73771,x73773))))
% 187.18/188.04 [7413]E(f329(f329(f329(f188(f875(x74131),f875(x74131)),x74132),f166(x74131)),x74133),x74133)+~P24(f329(f329(f243(a874),f329(f194(f875(x74131)),x74133)),f78(a874)))
% 187.18/188.04 [7449]E(f329(f329(f126(x74491),f797(x74492,x74493,x74491)),f329(f329(f149(x74491),x74493),f798(x74492,x74493,x74491))),x74492)+~P24(f329(f329(f331(x74491),x74493),f329(f171(x74491),x74492)))
% 187.18/188.04 [7450]E(f329(f329(f126(x74501),f793(x74502,x74503,x74501)),f329(f329(f149(x74501),x74503),f794(x74502,x74503,x74501))),x74502)+~P24(f329(f329(f331(x74501),x74503),f329(f171(x74501),x74502)))
% 187.18/188.04 [7451]E(f329(f329(f126(x74511),f799(x74512,x74513,x74511)),f329(f329(f149(x74511),x74513),f800(x74512,x74513,x74511))),x74512)+~P24(f329(f329(f331(x74511),x74513),f329(f171(x74511),x74512)))
% 187.18/188.04 [7475]~P21(x74751,x74752,x74753,f252(f881(x74751,a869)))+P21(f875(x74751),f875(x74752),f329(f152(x74751,x74752),x74753),f252(f881(f875(x74751),a869)))
% 187.18/188.04 [7623]E(x76231,f329(f329(f80(a874),f329(f329(f81(a874),f329(f263(a874,a874),x76232)),x76233)),f329(f267(a874,a874),x76232)))+~P24(f329(f48(x76231,x76233),x76232))
% 187.18/188.04 [7631]P21(x76311,x76312,x76313,f252(f881(x76311,a869)))+~P21(f875(x76311),f875(x76312),f329(f152(x76311,x76312),x76313),f252(f881(f875(x76311),a869)))
% 187.18/188.04 [7670]~P24(f329(f329(f199(x76701),x76702),x76703))+P24(f329(f329(f329(f329(a201,x76701),x76702),f860(x76703,x76702,x76701)),x76703))
% 187.18/188.04 [7675]P24(f329(f329(f331(f881(x76751,a869)),f640(x76752,x76753,x76751)),x76753))+P24(f329(f329(f331(x76751),x76752),f41(f881(x76751,a869),x76753)))
% 187.18/188.04 [7771]P24(f329(f329(f331(f875(x77711)),x77712),f159(x77711,x77713)))+~P24(f329(f329(f331(x77711),f675(x77713,x77712,x77711)),x77713))
% 187.18/188.04 [7872]P36(x78721,x78722,x78723)+~P24(f329(x78722,f329(f329(f163(x78721),x78723),f796(x78723,x78722,x78721))))
% 187.18/188.04 [7897]E(x78971,x78972)+~E(f329(f329(f7(x78973,f881(x78973,a869),a869),f331(x78973)),x78971),f329(f329(f7(x78973,f881(x78973,a869),a869),f331(x78973)),x78972))
% 187.18/188.04 [7903]~P24(f329(f329(f331(f880(x79031,x79031)),x79033),f261(x79031,x79032)))+P24(f329(f329(f331(x79031),f503(x79032,x79033,x79031)),x79032))
% 187.18/188.04 [7905]~P24(f329(f329(f331(x79051),x79053),f40(f881(x79051,a869),x79052)))+P24(f329(f329(f331(f881(x79051,a869)),f652(x79052,x79053,x79051)),x79052))
% 187.18/188.04 [8087]~P24(f329(f329(f331(x80871),x80872),f329(f171(x80871),f793(x80873,x80872,x80871))))+~P24(f329(f329(f331(x80871),x80872),f329(f171(x80871),x80873)))
% 187.18/188.04 [8088]~P24(f329(f329(f331(x80881),x80882),f329(f171(x80881),f800(x80883,x80882,x80881))))+~P24(f329(f329(f331(x80881),x80882),f329(f171(x80881),x80883)))
% 187.18/188.04 [8177]E(f329(f238(f878(f875(a325)),f875(a325),f311(x81771,x81772,f329(f329(f80(a1),x81773),f78(a1))),f236(f875(a325))),f329(x81771,x81773)),f311(x81771,x81772,x81773))+P24(f329(f329(f244(a1),x81772),x81773))
% 187.18/188.04 [8279]E(x82791,f118(x82792))+P24(f329(f329(f331(x82792),f329(f263(x82792,f880(a104,a104)),f329(f280(x82792,x82791),x82793))),f329(f171(x82792),x82791)))
% 187.18/188.04 [8375]~P71(x83751)+E(f329(f140(x83751,x83751,f329(f7(x83751,x83751,x83751),f80(x83751)),x83752),f329(f167(x83751),x83753)),f329(f140(x83751,x83751,f80(x83751),x83752),x83753))
% 187.18/188.04 [8866]~P27(x88661)+E(f329(f171(x88661),f147(x88661,x88661,f5(x88661),x88662,x88663)),f329(f329(f307(x88661),x88662),f329(f171(x88661),x88663)))
% 187.18/188.04 [8877]P24(f329(f329(f244(a874),f2(a874)),f607(x88771,x88772,x88773)))+~P24(f329(f329(f331(f880(x88773,x88773)),x88772),f329(f329(f286(x88773,x88773,x88773),x88771),f305(x88773,x88771))))
% 187.18/188.04 [9167]~P57(x91671,x91672)+~P24(f329(f329(f331(f880(x91671,x91671)),f329(f329(f264(x91671,x91671),x91673),x91673)),f329(f329(f286(x91671,x91671,x91671),x91672),f305(x91671,x91672))))
% 187.18/188.04 [9301]~E(f329(f329(f106(f881(f880(x93011,x93011),a869)),f329(f284(x93011,x93011),x93012)),f305(x93011,x93012)),f193(f881(f880(x93011,x93011),a869)))+~P24(f329(f329(f331(f880(x93011,x93011)),f329(f329(f264(x93011,x93011),x93013),x93013)),f329(f329(f286(x93011,x93011,x93011),x93012),f305(x93011,x93012))))
% 187.18/188.04 [9479]~P24(f329(f62(x94791),x94792))+P24(f329(f329(f243(a874),f329(f38(x94791),f329(f329(f22(f881(x94791,a869)),x94792),f329(f329(f307(x94791),x94793),f193(f881(x94791,a869)))))),f329(f38(x94791),x94792)))
% 187.18/188.04 [5034]~E(x50343,f118(x50341))+E(f142(x50341,f329(f329(f149(x50341),x50342),x50343)),x50342)
% 187.18/188.04 [5042]~E(x50423,f118(x50421))+E(f119(x50421,f329(f329(f149(x50421),x50422),x50423)),f118(x50421))
% 187.18/188.04 [5071]E(x50711,f118(x50712))+E(f142(x50712,f329(f329(f149(x50712),x50713),x50711)),f142(x50712,x50711))
% 187.18/188.04 [5073]E(x50731,f118(x50732))+E(f142(x50732,f329(f329(f126(x50732),x50733),x50731)),f142(x50732,x50731))
% 187.18/188.04 [5078]~E(x50783,f118(x50781))+E(f119(x50781,f329(f329(f126(x50781),x50782),x50783)),f119(x50781,x50782))
% 187.18/188.04 [5080]~E(x50803,f118(x50801))+E(f142(x50801,f329(f329(f126(x50801),x50802),x50803)),f142(x50801,x50802))
% 187.18/188.04 [5112]E(x51121,f118(x51122))+E(f329(f139(x51122),f329(f329(f126(x51122),x51121),x51123)),f329(f139(x51122),x51121))
% 187.18/188.04 [5143]~E(x51432,f118(x51431))+E(f329(f139(x51431),f329(f329(f126(x51431),x51432),x51433)),f329(f139(x51431),x51433))
% 187.18/188.04 [5198]~P66(x51981)+E(f329(f329(f115(x51981),x51982),f329(f329(f106(x51981),x51982),x51983)),x51982)
% 187.18/188.04 [5199]~P66(x51991)+E(f329(f329(f106(x51991),x51992),f329(f329(f115(x51991),x51992),x51993)),x51992)
% 187.18/188.04 [5200]~P27(x52001)+E(f329(f329(f241(x52001),x52002),f329(f329(f242(x52001),x52002),x52003)),x52002)
% 187.18/188.04 [5201]~P27(x52011)+E(f329(f329(f242(x52011),x52012),f329(f329(f241(x52011),x52012),x52013)),x52012)
% 187.18/188.04 [5220]~P29(x52201)+E(f45(x52201,f329(f329(f81(x52201),x52202),x52203),x52203),f2(x52201))
% 187.18/188.04 [5221]~P29(x52211)+E(f45(x52211,f329(f329(f81(x52211),x52212),x52213),x52212),f2(x52211))
% 187.18/188.04 [5296]~P69(x52961)+E(f329(f79(x52961),f329(f329(f22(x52961),x52962),x52963)),f329(f329(f22(x52961),x52963),x52962))
% 187.18/188.04 [5357]E(x53571,f118(x53572))+E(f119(x53572,f329(f329(f149(x53572),x53573),x53571)),f329(f329(f149(x53572),x53573),f119(x53572,x53571)))
% 187.18/188.04 [5358]E(x53581,f118(x53582))+E(f119(x53582,f329(f329(f126(x53582),x53583),x53581)),f329(f329(f126(x53582),x53583),f119(x53582,x53581)))
% 187.18/188.04 [5361]~P31(x53611)+E(f41(x53611,f329(f329(f307(x53611),x53612),x53613)),f329(f329(f106(x53611),x53612),f41(x53611,x53613)))
% 187.18/188.04 [5362]~P31(x53621)+E(f40(x53621,f329(f329(f307(x53621),x53622),x53623)),f329(f329(f115(x53621),x53622),f40(x53621,x53623)))
% 187.18/188.04 [5407]~P66(x54071)+E(f329(f329(f115(x54071),x54072),f329(f329(f115(x54071),x54072),x54073)),f329(f329(f115(x54071),x54072),x54073))
% 187.18/188.04 [5409]~P102(x54091)+E(f329(f329(f115(x54091),x54092),f329(f329(f115(x54091),x54092),x54093)),f329(f329(f115(x54091),x54092),x54093))
% 187.18/188.04 [5410]~P66(x54101)+E(f329(f329(f106(x54101),x54102),f329(f329(f106(x54101),x54102),x54103)),f329(f329(f106(x54101),x54102),x54103))
% 187.18/188.04 [5412]~P103(x54121)+E(f329(f329(f106(x54121),x54122),f329(f329(f106(x54121),x54122),x54123)),f329(f329(f106(x54121),x54122),x54123))
% 187.18/188.04 [5413]~P98(x54131)+E(f329(f329(f81(x54131),x54132),f329(f329(f81(x54131),x54132),x54133)),f329(f329(f81(x54131),x54132),x54133))
% 187.18/188.04 [5415]~P27(x54151)+E(f329(f329(f241(x54151),x54152),f329(f329(f241(x54151),x54152),x54153)),f329(f329(f241(x54151),x54152),x54153))
% 187.18/188.04 [5417]~P27(x54171)+E(f329(f329(f242(x54171),x54172),f329(f329(f242(x54171),x54172),x54173)),f329(f329(f242(x54171),x54172),x54173))
% 187.18/188.04 [5425]~P29(x54251)+E(f45(x54251,f329(f329(f80(x54251),x54252),x54253),x54253),f45(x54251,x54252,x54253))
% 187.18/188.04 [5426]~P29(x54261)+E(f45(x54261,f329(f329(f80(x54261),x54262),x54263),x54262),f45(x54261,x54263,x54262))
% 187.18/188.04 [5432]~P107(x54321)+E(f329(f329(f81(x54321),x54322),f329(f79(x54321),x54323)),f329(f79(x54321),f329(f329(f81(x54321),x54322),x54323)))
% 187.18/188.04 [5433]~P61(x54331)+E(f329(f329(f287(x54331),x54332),f329(f79(x54331),x54333)),f329(f79(x54331),f329(f329(f287(x54331),x54332),x54333)))
% 187.18/188.04 [5434]~P83(x54341)+E(f329(f329(f80(x54341),x54342),f329(f164(x54341),x54343)),f329(f164(x54341),f329(f329(f149(x54341),x54342),x54343)))
% 187.18/188.04 [5464]~P107(x54641)+E(f329(f329(f81(x54641),f329(f79(x54641),x54642)),x54643),f329(f329(f81(x54641),x54642),f329(f79(x54641),x54643)))
% 187.18/188.04 [5470]~P6(x54701,x54702,x54703)+E(f40(f881(x54701,a869),f329(f329(f61(x54701),x54702),x54703)),x54702)
% 187.18/188.04 [5529]~P111(x55291)+E(f329(f329(f81(x55291),x55292),f329(f329(f254(x55291),x55292),x55293)),f329(f329(f254(x55291),x55292),f329(a117,x55293)))
% 187.18/188.04 [5530]~P109(x55301)+E(f329(f329(f81(x55301),x55302),f329(f329(f254(x55301),x55302),x55303)),f329(f329(f254(x55301),x55302),f329(a117,x55303)))
% 187.18/188.04 [5540]~P77(x55401)+E(f329(f329(f80(x55401),f329(f79(x55401),x55402)),f329(f329(f80(x55401),x55402),x55403)),x55403)
% 187.18/188.04 [5563]~P141(x55631)+E(f329(f329(f254(x55631),f329(f105(x55631),x55632)),x55633),f329(f105(x55631),f329(f329(f254(a874),x55632),x55633)))
% 187.18/188.04 [5564]~P138(x55641)+E(f329(f329(f254(x55641),f329(f107(x55641),x55642)),x55643),f329(f107(x55641),f329(f329(f254(a1),x55642),x55643)))
% 187.18/188.04 [5570]~P87(x55701)+E(f329(f75(x55701),f329(f329(f22(x55701),x55702),x55703)),f329(f75(x55701),f329(f329(f22(x55701),x55703),x55702)))
% 187.18/188.04 [5572]~P115(x55721)+E(f329(f329(f81(x55721),f82(x55721,x55722)),f82(x55721,x55723)),f82(x55721,f329(f329(f81(x55721),x55722),x55723)))
% 187.18/188.04 [5576]E(x55761,f118(x55762))+E(f329(f329(f126(x55762),f329(f170(x55762),x55761)),x55763),f329(f170(x55762),f329(f329(f126(x55762),x55761),x55763)))
% 187.18/188.04 [5581]~E(x55812,f329(a117,f329(f329(f80(a874),x55811),x55813)))+P24(f329(f329(f244(a874),x55811),x55812))
% 187.18/188.04 [5582]~P115(x55821)+E(f329(f329(f254(x55821),f329(f75(x55821),x55822)),x55823),f329(f75(x55821),f329(f329(f254(x55821),x55822),x55823)))
% 187.18/188.04 [5583]~P107(x55831)+E(f329(f329(f81(x55831),f329(f79(x55831),x55832)),x55833),f329(f79(x55831),f329(f329(f81(x55831),x55832),x55833)))
% 187.18/188.04 [5584]~P118(x55841)+E(f329(f329(f287(x55841),f329(f79(x55841),x55842)),x55843),f329(f79(x55841),f329(f329(f287(x55841),x55842),x55843)))
% 187.18/188.04 [5682]E(f555(x56821,x56822,x56823),f578(x56821,x56822,x56823))+E(f329(f329(f106(f881(x56823,a869)),x56822),x56821),f193(f881(x56823,a869)))
% 187.18/188.04 [5697]~P72(x56972)+E(f329(f329(f6(x56971,x56972),f329(f16(x56972,x56971),f2(x56972))),x56973),f2(x56972))
% 187.18/188.04 [5698]~P76(x56982)+E(f329(f329(f9(x56981,x56982),f329(f16(x56982,x56981),f78(x56982))),x56983),f78(x56982))
% 187.18/188.04 [5700]~P141(x57001)+E(f329(f329(f81(x57001),f329(f105(x57001),x57002)),f329(f105(x57001),x57003)),f329(f105(x57001),f329(f329(f81(a874),x57002),x57003)))
% 187.18/188.04 [5701]~P141(x57011)+E(f329(f329(f80(x57011),f329(f105(x57011),x57012)),f329(f105(x57011),x57013)),f329(f105(x57011),f329(f329(f80(a874),x57012),x57013)))
% 187.18/188.04 [5702]~P138(x57021)+E(f329(f329(f22(x57021),f329(f107(x57021),x57022)),f329(f107(x57021),x57023)),f329(f107(x57021),f329(f329(f22(a1),x57022),x57023)))
% 187.18/188.04 [5703]~P138(x57031)+E(f329(f329(f81(x57031),f329(f107(x57031),x57032)),f329(f107(x57031),x57033)),f329(f107(x57031),f329(f329(f81(a1),x57032),x57033)))
% 187.18/188.04 [5704]~P138(x57041)+E(f329(f329(f80(x57041),f329(f107(x57041),x57042)),f329(f107(x57041),x57043)),f329(f107(x57041),f329(f329(f80(a1),x57042),x57043)))
% 187.18/188.04 [5705]~P94(x57051)+E(f329(f329(f22(x57051),f329(f108(x57051),x57052)),f329(f108(x57051),x57053)),f329(f108(x57051),f329(f329(f22(a1),x57052),x57053)))
% 187.18/188.04 [5708]~P94(x57081)+E(f329(f329(f81(x57081),f329(f108(x57081),x57082)),f329(f108(x57081),x57083)),f329(f108(x57081),f329(f329(f81(a1),x57082),x57083)))
% 187.18/188.04 [5709]~P94(x57091)+E(f329(f329(f80(x57091),f329(f108(x57091),x57092)),f329(f108(x57091),x57093)),f329(f108(x57091),f329(f329(f80(a1),x57092),x57093)))
% 187.18/188.04 [5758]~E(x57583,x57582)+P24(f329(f329(f243(f881(x57581,a869)),x57582),x57583))
% 187.18/188.04 [5764]~E(x57642,x57643)+P24(f329(f329(f243(f881(x57641,a869)),x57642),x57643))
% 187.18/188.04 [5769]~P115(x57691)+E(f329(f329(f81(x57691),f329(f75(x57691),x57692)),f329(f75(x57691),x57693)),f329(f75(x57691),f329(f329(f81(x57691),x57692),x57693)))
% 187.18/188.04 [5770]~P63(x57701)+E(f329(f329(f287(x57701),f329(f75(x57701),x57702)),f329(f75(x57701),x57703)),f329(f75(x57701),f329(f329(f287(x57701),x57702),x57703)))
% 187.18/188.04 [5771]~P97(x57711)+E(f329(f329(f106(x57711),f329(f79(x57711),x57712)),f329(f79(x57711),x57713)),f329(f79(x57711),f329(f329(f115(x57711),x57712),x57713)))
% 187.18/188.04 [5772]~P97(x57721)+E(f329(f329(f115(x57721),f329(f79(x57721),x57722)),f329(f79(x57721),x57723)),f329(f79(x57721),f329(f329(f106(x57721),x57722),x57723)))
% 187.18/188.04 [5773]~P77(x57731)+E(f329(f329(f80(x57731),f329(f79(x57731),x57732)),f329(f79(x57731),x57733)),f329(f79(x57731),f329(f329(f80(x57731),x57733),x57732)))
% 187.18/188.04 [5774]~P69(x57741)+E(f329(f329(f80(x57741),f329(f79(x57741),x57742)),f329(f79(x57741),x57743)),f329(f79(x57741),f329(f329(f80(x57741),x57742),x57743)))
% 187.18/188.04 [5775]~P78(x57751)+E(f329(f329(f242(x57751),f329(f79(x57751),x57752)),f329(f79(x57751),x57753)),f329(f79(x57751),f329(f329(f241(x57751),x57752),x57753)))
% 187.18/188.04 [5776]~P78(x57761)+E(f329(f329(f241(x57761),f329(f79(x57761),x57762)),f329(f79(x57761),x57763)),f329(f79(x57761),f329(f329(f242(x57761),x57762),x57763)))
% 187.18/188.04 [5777]~P83(x57771)+E(f329(f329(f80(x57771),f329(f164(x57771),x57772)),f329(f164(x57771),x57773)),f329(f164(x57771),f329(f329(f126(x57771),x57772),x57773)))
% 187.18/188.04 [5778]E(x57781,f193(f881(x57782,a869)))+~E(f329(f329(f115(f881(x57782,a869)),x57783),x57781),f193(f881(x57782,a869)))
% 187.18/188.04 [5779]E(x57791,f193(f881(x57792,a869)))+~E(f329(f329(f115(f881(x57792,a869)),x57791),x57793),f193(f881(x57792,a869)))
% 187.18/188.04 [5780]~P144(x57801,x57802,x57803)+P24(f329(x57801,f329(f329(f39(a1),x57802),x57803)))
% 187.18/188.04 [5830]~P24(f329(f62(x58301),x58303))+P24(f329(f62(x58301),f329(f329(f307(x58301),x58302),x58303)))
% 187.18/188.04 [5831]~P24(f329(f135(x58311),x58313))+P24(f329(f135(x58311),f329(f329(f174(x58311),x58312),x58313)))
% 187.18/188.04 [5832]~P24(f329(f135(x58321),x58323))+P24(f329(f135(x58321),f329(f329(f136(x58321),x58322),x58323)))
% 187.18/188.04 [5861]~P66(x58611)+P24(f329(f329(f243(x58611),x58612),f329(f329(f115(x58611),x58613),x58612)))
% 187.18/188.04 [5862]~P102(x58621)+P24(f329(f329(f243(x58621),x58622),f329(f329(f115(x58621),x58623),x58622)))
% 187.18/188.04 [5863]~P66(x58631)+P24(f329(f329(f243(x58631),x58632),f329(f329(f115(x58631),x58632),x58633)))
% 187.18/188.04 [5864]~P102(x58641)+P24(f329(f329(f243(x58641),x58642),f329(f329(f115(x58641),x58642),x58643)))
% 187.18/188.04 [5865]~P27(x58651)+P24(f329(f329(f243(x58651),x58652),f329(f329(f242(x58651),x58653),x58652)))
% 187.18/188.04 [5866]~P27(x58661)+P24(f329(f329(f243(x58661),x58662),f329(f329(f242(x58661),x58662),x58663)))
% 187.18/188.04 [5880]~E(x58801,f2(a874))+E(f329(f329(f39(a874),f329(f329(f81(a874),x58801),x58802)),f329(f329(f81(a874),x58801),x58803)),f2(a874))
% 187.18/188.04 [5949]P24(f329(x59491,x59492))+P24(f329(f329(f199(f32(x59491,x59493)),x59492),x59492))
% 187.18/188.04 [5964]~P94(x59641)+E(f329(f329(f22(x59641),f329(f108(x59641),x59642)),f329(f108(x59641),x59643)),f329(f108(x59641),f329(f329(f80(a1),x59642),f329(f79(a1),x59643))))
% 187.18/188.04 [6017]E(x60171,f2(a874))+E(f329(f329(f39(a874),f329(f329(f81(a874),x60171),x60172)),f329(f329(f81(a874),x60171),x60173)),f329(f329(f39(a874),x60172),x60173))
% 187.18/188.04 [6051]E(f150(x60511,f329(f329(f149(x60511),x60512),x60513)),f329(f329(f149(x60511),x60512),f150(x60511,x60513)))+P24(f329(f329(f331(x60511),x60512),f329(f171(x60511),x60513)))
% 187.18/188.04 [6085]P144(x60851,x60852,x60853)+~P24(f329(x60851,f329(f329(f39(a1),x60852),x60853)))
% 187.18/188.04 [6160]E(x61601,f118(x61602))+E(f329(f329(f149(x61602),f329(f139(x61602),x61601)),f329(f329(f174(x61602),x61603),f329(f170(x61602),x61601))),f329(f329(f174(x61602),f329(a117,x61603)),x61601))
% 187.18/188.04 [6166]E(f329(f329(f22(f881(x61661,a869)),x61662),x61663),x61662)+~E(f329(f329(f106(f881(x61661,a869)),x61662),x61663),f193(f881(x61661,a869)))
% 187.18/188.04 [6180]E(f150(x61801,f329(f329(f149(x61801),x61802),x61803)),f150(x61801,x61803))+~P24(f329(f329(f331(x61801),x61802),f329(f171(x61801),x61803)))
% 187.18/188.04 [6212]~P24(f329(f329(f243(a874),x62121),x62123))+P24(f329(f329(f243(a874),x62121),f329(f329(f80(a874),x62122),x62123)))
% 187.18/188.04 [6214]~P24(f329(f329(f243(a874),x62141),x62142))+P24(f329(f329(f243(a874),x62141),f329(f329(f80(a874),x62142),x62143)))
% 187.18/188.04 [6216]~P24(f329(f329(f244(a874),x62161),x62163))+P24(f329(f329(f244(a874),x62161),f329(f329(f80(a874),x62162),x62163)))
% 187.18/188.04 [6218]~P24(f329(f329(f244(a874),x62181),x62182))+P24(f329(f329(f244(a874),x62181),f329(f329(f80(a874),x62182),x62183)))
% 187.18/188.04 [6257]P24(f329(f62(x62571),x62572))+~P24(f329(f62(x62571),f329(f329(f307(x62571),x62573),x62572)))
% 187.18/188.04 [6258]P24(f329(f135(x62581),x62582))+~P24(f329(f135(x62581),f329(f329(f149(x62581),x62583),x62582)))
% 187.18/188.04 [6259]P24(f329(f135(x62591),x62592))+~P24(f329(f135(x62591),f329(f329(f126(x62591),x62593),x62592)))
% 187.18/188.04 [6260]P24(f329(f135(x62601),x62602))+~P24(f329(f135(x62601),f329(f329(f126(x62601),x62602),x62603)))
% 187.18/188.04 [6306]~P109(x63061)+E(f329(f329(f80(x63061),x63062),f329(f329(f81(x63061),x63063),x63062)),f329(f329(f81(x63061),f329(f329(f80(x63061),x63063),f78(x63061))),x63062))
% 187.18/188.04 [6352]~E(x63521,x63522)+~P24(f329(f329(f244(f881(x63523,a869)),x63521),x63522))
% 187.18/188.04 [6396]P24(f329(f329(f331(x63961),x63962),x63963))+P24(f329(f329(f331(x63961),x63962),f329(f79(f881(x63961,a869)),x63963)))
% 187.18/188.04 [6402]E(f142(x64021,f329(f329(f136(x64021),x64022),x64023)),f142(x64021,x64023))+~P24(f329(f329(f244(a874),x64022),f329(f194(f875(x64021)),x64023)))
% 187.18/188.04 [6403]E(f329(f329(f174(x64031),x64032),f119(x64031,x64033)),f329(f329(f174(x64031),x64032),x64033))+~P24(f329(f329(f244(a874),x64032),f329(f194(f875(x64031)),x64033)))
% 187.18/188.04 [6458]E(f329(f329(f329(f188(f875(x64581),f875(x64581)),x64582),f166(x64581)),x64583),x64583)+~E(f45(a874,x64582,f329(f194(f875(x64581)),x64583)),f2(a874))
% 187.18/188.04 [6465]~P6(x64651,x64653,x64652)+E(f329(f329(f286(x64651,x64651,x64651),f329(f284(x64651,x64651),x64652)),x64652),x64652)
% 187.18/188.04 [6508]~E(f329(f329(f115(f881(x65081,a869)),x65082),x65083),x65083)+P24(f329(f329(f243(f881(x65081,a869)),x65082),x65083))
% 187.18/188.04 [6513]~P54(x65131,x65131,x65133)+P54(x65131,x65131,f329(f329(f188(f880(x65131,x65131),a869),x65132),x65133))
% 187.18/188.04 [6515]~P24(f329(f329(f331(x65151),x65153),f329(f171(x65151),x65152)))+P24(f329(f329(f244(a874),f2(a874)),f329(f194(f875(x65151)),x65152)))
% 187.18/188.04 [6541]~P87(x65411)+E(f329(f75(x65411),f329(f329(f80(x65411),f329(f75(x65411),x65412)),f329(f75(x65411),x65413))),f329(f329(f80(x65411),f329(f75(x65411),x65412)),f329(f75(x65411),x65413)))
% 187.18/188.04 [6552]E(f329(f329(f39(a874),f329(f329(f81(a874),x65521),x65522)),f329(f329(f81(a874),x65521),x65523)),f329(f329(f39(a874),x65522),x65523))+~P24(f329(f329(f244(a874),f2(a874)),x65521))
% 187.18/188.04 [6600]E(x66001,x66002)+~P24(f329(f329(f329(f329(a201,a24),x66001),x66003),x66002))
% 187.18/188.04 [6689]~P24(f329(f62(x66891),x66893))+E(f329(f329(f65(x66891,f881(x66891,a869),f307(x66891)),x66892),x66893),f329(f329(f115(f881(x66891,a869)),x66893),x66892))
% 187.18/188.04 [6748]E(f329(f329(f115(f881(x67481,a869)),x67482),x67483),x67482)+~P24(f329(f329(f243(f881(x67481,a869)),x67483),x67482))
% 187.18/188.04 [6750]E(f329(f329(f115(f881(x67501,a869)),x67502),x67503),x67503)+~P24(f329(f329(f243(f881(x67501,a869)),x67502),x67503))
% 187.18/188.04 [6751]E(f329(f329(f106(f881(x67511,a869)),x67512),x67513),x67513)+~P24(f329(f329(f243(f881(x67511,a869)),x67513),x67512))
% 187.18/188.04 [6752]E(f329(f329(f106(f881(x67521,a869)),x67522),x67523),x67522)+~P24(f329(f329(f243(f881(x67521,a869)),x67522),x67523))
% 187.18/188.04 [6804]~P24(f329(f135(x68041),x68042))+E(f329(f329(f22(f881(x68041,a869)),f329(f171(x68041),x68042)),f329(f329(f307(x68041),x68043),f193(f881(x68041,a869)))),f329(f171(x68041),f168(x68041,x68043,x68042)))
% 187.18/188.04 [6857]P42(x68571,x68572)+~P42(x68571,f329(f329(f188(f880(x68571,x68571),a869),x68573),x68572))
% 187.18/188.04 [6923]P24(f329(f49(x69231,x69232),f329(a51,x69233)))+~P24(f329(f49(f329(f79(a1),x69231),f329(f79(a1),x69232)),x69233))
% 187.18/188.04 [6928]E(f329(f329(f22(f881(x69281,a869)),f329(f329(f307(x69281),x69282),x69283)),f329(f329(f307(x69281),x69282),f193(f881(x69281,a869)))),x69283)+P24(f329(f329(f331(x69281),x69282),x69283))
% 187.18/188.04 [6949]E(f329(f329(f106(f881(x69491,a869)),f329(f171(x69491),x69492)),f329(f171(x69491),x69493)),f193(f881(x69491,a869)))+~P24(f329(f135(x69491),f329(f329(f126(x69491),x69492),x69493)))
% 187.18/188.04 [6965]~P24(f329(f329(f331(x69651),x69652),f329(f171(x69651),x69653)))+~P24(f329(f135(x69651),f329(f329(f149(x69651),x69652),x69653)))
% 187.18/188.04 [7037]P36(x70371,x70372,x70373)+P24(f329(f329(f244(a874),f796(x70373,x70372,x70371)),f329(f194(f875(x70371)),x70373)))
% 187.18/188.04 [7047]E(f329(f329(f106(f881(x70471,a869)),x70472),x70473),f193(f881(x70471,a869)))+P24(f329(f329(f331(x70471),f555(x70473,x70472,x70471)),x70472))
% 187.18/188.04 [7048]E(f329(f329(f106(f881(x70481,a869)),x70482),x70483),f193(f881(x70481,a869)))+P24(f329(f329(f331(x70481),f578(x70483,x70482,x70481)),x70483))
% 187.18/188.04 [7052]E(f119(x70521,f329(f329(f174(x70521),x70522),x70523)),f329(f329(f174(x70521),f329(f329(f22(a874),x70522),f78(a874))),x70523))+~P24(f329(f329(f243(a874),x70522),f329(f194(f875(x70521)),x70523)))
% 187.18/188.04 [7111]~P38(x71113,x71112,x71111)+P24(f329(f329(f244(a874),f792(x71111,x71112,x71113)),f329(f194(f875(x71113)),x71111)))
% 187.18/188.04 [7129]P24(f329(f329(f244(a874),f2(a874)),x71291))+P24(f329(f329(f243(a874),f329(f329(f81(a874),x71292),x71291)),f329(f329(f81(a874),x71293),x71291)))
% 187.18/188.04 [7130]P24(f329(f329(f244(a874),f2(a874)),x71301))+P24(f329(f329(f243(a874),f329(f329(f81(a874),x71301),x71302)),f329(f329(f81(a874),x71301),x71303)))
% 187.18/188.04 [7133]~P24(f329(f329(f331(x71331),x71332),x71333))+~P24(f329(f329(f331(x71331),x71332),f329(f79(f881(x71331,a869)),x71333)))
% 187.18/188.04 [7140]~P24(f329(f329(f244(f881(x71401,a869)),x71402),x71403))+P24(f329(f329(f243(f881(x71401,a869)),x71402),x71403))
% 187.18/188.04 [7239]~P24(f329(f329(f243(a874),x72393),x72392))+P24(f329(f329(f243(a874),f329(f329(f22(a874),x72391),x72392)),f329(f329(f22(a874),x72391),x72393)))
% 187.18/188.04 [7240]~P24(f329(f329(f243(a874),x72401),x72403))+P24(f329(f329(f243(a874),f329(f329(f22(a874),x72401),x72402)),f329(f329(f22(a874),x72403),x72402)))
% 187.18/188.04 [7242]~P24(f329(f329(f243(a874),x72422),x72423))+P24(f329(f329(f243(a874),f329(f329(f81(a874),x72421),x72422)),f329(f329(f81(a874),x72421),x72423)))
% 187.18/188.04 [7244]~P24(f329(f329(f243(a874),x72441),x72443))+P24(f329(f329(f243(a874),f329(f329(f81(a874),x72441),x72442)),f329(f329(f81(a874),x72443),x72442)))
% 187.18/188.04 [7245]~P24(f329(f329(f243(a874),x72452),x72453))+P24(f329(f329(f243(a874),f329(f329(f80(a874),x72451),x72452)),f329(f329(f80(a874),x72451),x72453)))
% 187.18/188.04 [7246]~P24(f329(f329(f243(a874),x72461),x72463))+P24(f329(f329(f243(a874),f329(f329(f80(a874),x72461),x72462)),f329(f329(f80(a874),x72463),x72462)))
% 187.18/188.04 [7247]~P24(f329(f329(f243(a874),x72471),x72473))+P24(f329(f329(f243(a874),f329(f329(f39(a874),x72471),x72472)),f329(f329(f39(a874),x72473),x72472)))
% 187.18/188.04 [7248]~P24(f329(f329(f243(a1),x72482),x72483))+P24(f329(f329(f243(a1),f329(f329(f80(a1),x72481),x72482)),f329(f329(f80(a1),x72481),x72483)))
% 187.18/188.04 [7251]~P24(f329(f329(f244(a874),x72512),x72513))+P24(f329(f329(f244(a874),f329(f329(f80(a874),x72511),x72512)),f329(f329(f80(a874),x72511),x72513)))
% 187.18/188.04 [7252]~P24(f329(f329(f244(a874),x72521),x72523))+P24(f329(f329(f244(a874),f329(f329(f80(a874),x72521),x72522)),f329(f329(f80(a874),x72523),x72522)))
% 187.18/188.04 [7253]~P24(f329(f329(f244(a1),x72531),x72533))+P24(f329(f329(f244(a1),f329(f329(f80(a1),x72531),x72532)),f329(f329(f80(a1),x72533),x72532)))
% 187.18/188.04 [7333]E(x73331,x73332)+~P24(f329(f329(f331(x73333),x73331),f329(f329(f307(x73333),x73332),f193(f881(x73333,a869)))))
% 187.18/188.04 [7335]~E(f329(f329(f106(f881(x73351,a869)),x73352),x73353),f193(f881(x73351,a869)))+P24(f329(f329(f243(f881(x73351,a869)),x73352),f329(f79(f881(x73351,a869)),x73353)))
% 187.18/188.04 [7343]P24(f329(f329(f331(f881(x73431,a869)),x73432),f329(f306(x73431),x73433)))+~P24(f329(f329(f243(f881(x73431,a869)),x73432),x73433))
% 187.18/188.04 [7397]E(f329(f329(f149(x73971),f329(f329(f163(x73971),x73972),x73973)),f329(f329(f136(x73971),f329(a117,x73973)),x73972)),f329(f329(f136(x73971),x73973),x73972))+~P24(f329(f329(f244(a874),x73973),f329(f194(f875(x73971)),x73972)))
% 187.18/188.04 [7424]P24(f329(f329(f331(f880(x74241,x74241)),x74242),f305(x74241,x74243)))+~P24(f329(f329(f331(f880(x74241,x74241)),x74242),x74243))
% 187.18/188.04 [7435]~P24(f329(f329(f331(f881(x74351,a869)),x74352),f329(f306(x74351),x74353)))+P24(f329(f329(f243(f881(x74351,a869)),x74352),x74353))
% 187.18/188.04 [7481]P24(f329(f329(f243(f881(x74811,a869)),x74812),f40(f881(x74811,a869),x74813)))+~P24(f329(f329(f331(f881(x74811,a869)),x74812),x74813))
% 187.18/188.04 [7506]~P138(x75061)+E(f329(f329(f81(x75061),f329(f329(f254(x75061),f329(f79(x75061),f78(x75061))),x75062)),f329(f329(f254(x75061),x75063),x75062)),f329(f329(f254(x75061),f329(f79(x75061),x75063)),x75062))
% 187.18/188.04 [7527]E(f329(f329(f163(x75271),x75272),f329(f329(f22(a874),f329(f194(f875(x75271)),x75272)),f329(a117,x75273))),f329(f329(f163(x75271),f329(f167(x75271),x75272)),x75273))+~P24(f329(f329(f244(a874),x75273),f329(f194(f875(x75271)),x75272)))
% 187.18/188.04 [7544]~E(f329(f329(f106(f881(x75441,a869)),f631(x75443,x75442,x75441)),x75443),f193(f881(x75441,a869)))+E(f329(f329(f106(f881(x75441,a869)),f40(f881(x75441,a869),x75442)),x75443),f193(f881(x75441,a869)))
% 187.18/188.04 [7605]~P24(f329(f329(f331(x76053),x76052),f329(f171(x76053),x76051)))+P24(f329(f329(f244(a874),f650(x76051,x76052,x76053)),f329(f194(f875(x76053)),x76051)))
% 187.18/188.04 [7613]P24(f329(f329(f331(x76131),f329(f329(f163(x76131),x76132),x76133)),f329(f171(x76131),x76132)))+~P24(f329(f329(f244(a874),x76133),f329(f194(f875(x76131)),x76132)))
% 187.18/188.04 [7715]~P24(f329(x77152,f753(x77153,x77152,x77151)))+E(f329(f329(f136(x77151),f329(f194(f875(x77151)),f176(x77151,x77152,x77153))),x77153),f118(x77151))
% 187.18/188.04 [7726]P24(f329(f329(f243(f881(f875(x77261),a869)),f159(x77261,x77262)),f159(x77261,x77263)))+~P24(f329(f329(f243(f881(x77261,a869)),x77262),x77263))
% 187.18/188.04 [7727]P24(f329(f329(f243(f881(f875(x77271),a869)),f158(x77271,x77272)),f158(x77271,x77273)))+~P24(f329(f329(f243(f881(x77271,a869)),x77272),x77273))
% 187.18/188.04 [7756]E(f329(f329(f106(f881(x77561,a869)),f40(f881(x77561,a869),x77562)),x77563),f193(f881(x77561,a869)))+P24(f329(f329(f331(f881(x77561,a869)),f631(x77563,x77562,x77561)),x77562))
% 187.18/188.04 [7759]~P24(f329(f329(f331(f881(x77591,a869)),x77593),x77592))+P24(f329(f329(f243(f881(x77591,a869)),f41(f881(x77591,a869),x77592)),x77593))
% 187.18/188.04 [7761]E(f329(f329(f106(f881(x77611,a869)),x77612),x77613),f193(f881(x77611,a869)))+~P24(f329(f329(f243(f881(x77611,a869)),x77612),f329(f79(f881(x77611,a869)),x77613)))
% 187.18/188.04 [7810]E(f329(f329(f22(a874),f329(f329(f80(a874),f329(f164(a874),x78101)),x78102)),f329(f329(f163(a874),x78101),x78103)),f329(f164(a874),f329(f329(f157(a874,x78101),x78103),x78102)))+~P24(f329(f329(f244(a874),x78103),f329(f194(f875(a874)),x78101)))
% 187.18/188.04 [7860]P24(f329(f329(f243(a874),x78601),x78602))+~P24(f329(f329(f243(a874),f329(f329(f80(a874),x78603),x78601)),f329(f329(f80(a874),x78603),x78602)))
% 187.18/188.04 [7863]P24(f329(f329(f244(a874),x78631),x78632))+~P24(f329(f329(f244(a874),f329(f329(f80(a874),x78633),x78631)),f329(f329(f80(a874),x78633),x78632)))
% 187.18/188.04 [7864]P24(f329(f329(f244(a874),x78641),x78642))+~P24(f329(f329(f244(a874),f329(f329(f81(a874),x78643),x78641)),f329(f329(f81(a874),x78643),x78642)))
% 187.18/188.04 [7865]P24(f329(f329(f244(a874),x78651),x78652))+~P24(f329(f329(f244(a874),f329(f329(f81(a874),x78651),x78653)),f329(f329(f81(a874),x78652),x78653)))
% 187.18/188.04 [7895]P24(f329(f329(f244(a874),f2(a874)),x78951))+~P24(f329(f329(f244(a874),f329(f329(f81(a874),x78952),x78951)),f329(f329(f81(a874),x78953),x78951)))
% 187.18/188.04 [7896]P24(f329(f329(f244(a874),f2(a874)),x78961))+~P24(f329(f329(f244(a874),f329(f329(f81(a874),x78961),x78962)),f329(f329(f81(a874),x78961),x78963)))
% 187.18/188.04 [7969]E(f256(x79691,x79692,x79693),x79692)+~P24(f329(f329(f243(f881(x79691,a869)),x79693),f329(f329(f307(x79691),x79692),f193(f881(x79691,a869)))))
% 187.18/188.04 [8027]~P24(f329(f135(x80271),x80273))+E(f329(f134(x80271,f329(f329(f8(a869,a869,x80271),a324),f329(a326,x80272))),x80273),f168(x80271,x80272,x80273))
% 187.18/188.04 [8050]E(f329(f329(f136(x80501),f329(f194(f875(x80501)),f176(x80501,x80502,x80503))),x80503),f118(x80501))+P24(f329(f329(f331(x80501),f753(x80503,x80502,x80501)),f329(f171(x80501),x80503)))
% 187.18/188.04 [8054]E(f329(f329(f126(x80541),f329(f329(f174(x80541),x80542),x80543)),f329(f329(f149(x80541),f329(f329(f163(x80541),x80543),x80542)),f118(x80541))),f329(f329(f174(x80541),f329(a117,x80542)),x80543))+~P24(f329(f329(f244(a874),x80542),f329(f194(f875(x80541)),x80543)))
% 187.18/188.04 [8116]E(f329(f134(x81161,f329(f329(f8(a869,a869,x81161),a324),f329(a326,x81162))),x81163),x81163)+P24(f329(f329(f331(x81161),x81162),f329(f171(x81161),x81163)))
% 187.18/188.04 [8124]P24(f329(f329(f243(f881(f881(x81241,a869),a869)),f257(x81241,x81242)),f257(x81241,x81243)))+~P24(f329(f329(f243(f881(x81241,a869)),x81242),x81243))
% 187.18/188.04 [8168]~P24(f329(f135(x81681),x81683))+P24(f329(f135(x81681),f329(f329(f329(f188(f875(x81681),f875(x81681)),x81682),f166(x81681)),x81683)))
% 187.18/188.04 [8174]~P24(f329(f329(f244(a874),x81742),x81743))+P24(f329(f329(f244(a874),f329(f329(f81(a874),f329(a117,x81741)),x81742)),f329(f329(f81(a874),f329(a117,x81741)),x81743)))
% 187.18/188.04 [8196]P24(f329(f329(f243(f881(f881(x81961,a869),a869)),f329(f306(x81961),x81962)),f329(f306(x81961),x81963)))+~P24(f329(f329(f243(f881(x81961,a869)),x81962),x81963))
% 187.18/188.04 [8358]~P24(f329(f329(f243(f881(x83581,a869)),x83583),x83582))+P24(f329(f329(f243(f881(x83581,a869)),f329(f79(f881(x83581,a869)),x83582)),f329(f79(f881(x83581,a869)),x83583)))
% 187.18/188.04 [8390]E(f329(f308(a874,a874,f329(f329(f7(a874,a874,a874),f22(a874)),x83901)),f329(f299(a874,x83902),x83903)),f329(f299(a874,f329(f329(f22(a874),x83902),x83901)),f329(f329(f22(a874),x83903),x83901)))+~P24(f329(f329(f244(a874),x83901),x83903))
% 187.18/188.04 [8419]~P83(x84191)+E(f329(f329(f80(x84191),x84192),f329(f140(x84191,x84191,f80(x84191),f2(x84191)),x84193)),f329(f140(x84191,x84191,f80(x84191),x84192),x84193))
% 187.18/188.04 [8502]~P87(x85021)+P24(f329(f329(f243(x85021),f329(f75(x85021),f329(f329(f22(x85021),x85022),x85023))),f329(f329(f80(x85021),f329(f75(x85021),x85022)),f329(f75(x85021),x85023))))
% 187.18/188.04 [8503]~P87(x85031)+P24(f329(f329(f243(x85031),f329(f75(x85031),f329(f329(f80(x85031),x85032),x85033))),f329(f329(f80(x85031),f329(f75(x85031),x85032)),f329(f75(x85031),x85033))))
% 187.18/188.04 [8513]E(f329(f329(f80(a1),f329(f329(f81(a1),x85131),f45(a1,f329(f329(f39(a1),x85132),x85131),x85133))),f45(a1,x85132,x85131)),f45(a1,x85132,f329(f329(f81(a1),x85131),x85133)))+~P24(f329(f329(f244(a1),f2(a1)),x85133))
% 187.18/188.04 [8519]E(f329(f329(f126(x85191),f329(f329(f174(x85191),x85192),x85193)),f329(f329(f149(x85191),f329(f139(x85191),f329(f329(f136(x85191),x85192),x85193))),f118(x85191))),f329(f329(f174(x85191),f329(a117,x85192)),x85193))+~P24(f329(f329(f244(a874),x85192),f329(f194(f875(x85191)),x85193)))
% 187.18/188.04 [8538]E(f329(f275(x85381,f329(f329(f152(x85381,f880(a104,x85381)),f329(f264(a104,x85381),f78(a104))),x85382)),f329(a3,x85383)),f329(f329(f163(x85381),x85382),x85383))+~P24(f329(f329(f244(a874),x85383),f329(f194(f875(x85381)),x85382)))
% 187.18/188.04 [8603]P24(f329(f329(f331(f880(x86031,x86031)),x86032),f329(f329(f286(x86031,x86031,x86031),x86033),f305(x86031,x86033))))+~P24(f329(f329(f331(f880(x86031,x86031)),x86032),x86033))
% 187.18/188.04 [8622]P24(f329(f329(f243(a874),x86221),x86222))+~P24(f329(f329(f243(a874),f329(f329(f81(a874),f329(a117,x86223)),x86221)),f329(f329(f81(a874),f329(a117,x86223)),x86222)))
% 187.18/188.04 [8637]P24(f329(f329(f243(f881(x86371,a869)),x86372),x86373))+~P24(f329(f329(f243(f881(x86371,a869)),f329(f79(f881(x86371,a869)),x86373)),f329(f79(f881(x86371,a869)),x86372)))
% 187.18/188.04 [8656]P24(f329(f135(x86561),x86562))+~P24(f329(f135(x86561),f329(f329(f329(f188(f875(x86561),f875(x86561)),x86563),f166(x86561)),x86562)))
% 187.18/188.04 [8716]E(f329(f308(f880(x87161,x87162),x87162,f267(x87161,x87162)),f329(f171(f880(x87161,x87162)),x87163)),f185(x87161,x87162,f329(f177(x87161,x87162),x87163)))+~P24(f329(f135(x87161),f329(f329(f152(f880(x87161,x87162),x87161),f263(x87161,x87162)),x87163)))
% 187.18/188.04 [8725]E(f329(f283(x87251,x87251,f305(x87251,x87252)),x87253),x87253)+~P24(f329(f329(f243(f881(x87251,a869)),f329(f283(x87251,x87251,x87252),x87253)),x87253))
% 187.18/188.04 [8767]~P27(x87671)+P33(x87671,f329(f134(x87671,f329(f329(f7(x87671,x87671,a869),a326),f329(x87672,x87673))),x87673))
% 187.18/188.04 [8773]~P24(f329(f329(f243(a874),x87731),x87732))+P24(f329(f329(f243(a874),x87731),f329(f140(a874,a874,f80(a874),x87732),x87733)))
% 187.18/188.04 [8850]~P24(f329(f329(f331(f880(x88501,x88501)),x88502),f305(x88501,x88503)))+P24(f329(f329(f331(f880(x88501,x88501)),x88502),f329(f329(f188(f880(x88501,x88501),a869),f594(x88503,x88502,x88501)),x88503)))
% 187.18/188.04 [8944]~P83(x89441)+E(f329(f329(f80(x89441),x89442),f329(f140(x89441,x89441,f329(f7(x89441,x89441,x89441),f80(x89441)),f2(x89441)),f329(f167(x89441),x89443))),f329(f140(x89441,x89441,f80(x89441),x89442),x89443))
% 187.18/188.04 [9213]P54(x92131,x92132,x92133)+P24(f329(f329(f331(f880(x92131,x92132)),f329(f329(f264(x92131,x92132),f596(x92133,x92132,x92131)),f593(x92133,x92132,x92131))),x92133))
% 187.18/188.04 [9214]P54(x92141,x92142,x92143)+P24(f329(f329(f331(f880(x92141,x92142)),f329(f329(f264(x92141,x92142),f596(x92143,x92142,x92141)),f592(x92143,x92142,x92141))),x92143))
% 187.18/188.04 [9286]~P24(f329(f329(f331(f880(x92861,x92861)),x92862),f329(f329(f286(x92861,x92861,x92861),x92863),f305(x92861,x92863))))+P24(f329(f329(f331(f880(x92861,x92861)),x92862),f329(f329(f188(f880(x92861,x92861),a869),f607(x92863,x92862,x92861)),x92863)))
% 187.18/188.04 [9287]~P24(f329(x92871,f329(f329(f163(x92872),x92873),f329(f194(f875(x92872)),f176(x92872,x92871,x92873)))))+~P24(f329(f329(f244(a874),f329(f194(f875(x92872)),f176(x92872,x92871,x92873))),f329(f194(f875(x92872)),x92873)))
% 187.18/188.04 [9376]~P24(f329(f329(f243(f881(x93761,a869)),x93762),x93763))+P24(f329(f329(f243(f881(x93761,a869)),f329(f329(f7(x93761,f881(x93761,a869),a869),f331(x93761)),x93762)),f329(f329(f7(x93761,f881(x93761,a869),a869),f331(x93761)),x93763)))
% 187.18/188.04 [9428]~P24(f329(f329(f331(f880(f881(x94281,a869),f881(x94281,a869))),f329(f329(f264(f881(x94281,a869),f881(x94281,a869)),x94282),x94283)),f304(x94281)))+P24(f329(f329(f244(f881(x94281,a869)),x94282),x94283))
% 187.18/188.04 [9453]P55(x94531,x94532,x94533)+~P24(f329(f329(f331(f880(x94531,x94531)),f329(f329(f264(x94531,x94531),f577(x94533,x94532,x94531)),f576(x94533,x94532,x94531))),x94533))
% 187.18/188.04 [9454]P55(x94541,x94542,x94543)+~P24(f329(f329(f331(f880(x94541,x94541)),f329(f329(f264(x94541,x94541),f576(x94543,x94542,x94541)),f577(x94543,x94542,x94541))),x94543))
% 187.18/188.04 [9491]~P24(f329(f329(f331(f880(f875(x94911),f875(x94911))),f329(f329(f264(f875(x94911),f875(x94911)),x94912),x94912)),f145(x94911,x94913)))+P24(f329(f329(f331(f880(x94911,x94911)),f329(f329(f264(x94911,x94911),f674(x94912,x94913,x94911)),f674(x94912,x94913,x94911))),x94913))
% 187.18/188.04 [9542]P24(f329(f329(f243(f881(x95421,a869)),x95422),x95423))+~P24(f329(f329(f243(f881(x95421,a869)),f329(f329(f7(x95421,f881(x95421,a869),a869),f331(x95421)),x95422)),f329(f329(f7(x95421,f881(x95421,a869),a869),f331(x95421)),x95423)))
% 187.18/188.04 [9623]E(f329(f329(f22(a874),f329(f329(f6(a874,a874),x96231),f329(f250(a874),x96232))),f329(f329(f6(a874,a874),x96233),f329(f250(a874),x96232))),f329(f329(f6(a874,a874),f329(f329(f18(a874,a874,a874),f329(f329(f8(a874,f881(a874,a874),a874),f22(a874)),x96231)),x96233)),f329(f250(a874),x96232)))+~P24(f329(f329(f243(a874),f329(x96233,f367(x96232,x96231,x96233))),f329(x96231,f367(x96232,x96231,x96233))))
% 187.18/188.04 [9928]E(f329(f249(f880(x99281,x99282)),f329(f268(x99281,x99282,a869),f329(f329(f7(x99281,f881(x99282,f878(x99282)),f881(x99282,a869)),f329(f329(f8(f881(f878(x99282),a869),f881(f881(x99282,f878(x99282)),f881(x99282,a869)),x99281),f8(f878(x99282),a869,x99282)),f329(f329(f8(f878(x99282),f881(f878(x99282),a869),x99281),a326),f329(f177(x99281,x99282),x99283)))),f236(x99282)))),f329(f171(f880(x99281,x99282)),x99283))+~P24(f329(f135(x99281),f329(f329(f152(f880(x99281,x99282),x99281),f263(x99281,x99282)),x99283)))
% 187.18/188.04 [5616]~P77(x56161)+E(f329(f329(f22(x56161),f329(f329(f80(x56161),x56162),x56163)),x56163),x56162)
% 187.18/188.04 [5617]~P77(x56171)+E(f329(f329(f80(x56171),f329(f329(f22(x56171),x56172),x56173)),x56173),x56172)
% 187.18/188.04 [5838]~P77(x58381)+E(f329(f329(f80(x58381),x58382),f329(f329(f80(x58381),f329(f79(x58381),x58382)),x58383)),x58383)
% 187.18/188.04 [5923]~P82(x59231)+E(f329(f329(f81(x59231),f329(f329(f254(x59231),x59232),x59233)),x59232),f329(f329(f254(x59231),x59232),f329(a117,x59233)))
% 187.18/188.04 [5924]~P109(x59241)+E(f329(f329(f81(x59241),f329(f329(f254(x59241),x59242),x59243)),x59242),f329(f329(f254(x59241),x59242),f329(a117,x59243)))
% 187.18/188.04 [6135]~P115(x61351)+E(f329(f75(x61351),f329(f329(f254(x61351),f329(f79(x61351),x61352)),x61353)),f329(f75(x61351),f329(f329(f254(x61351),x61352),x61353)))
% 187.18/188.04 [6192]~P82(x61921)+E(f329(f329(f81(x61921),f329(f329(f254(x61921),x61922),x61923)),x61922),f329(f329(f81(x61921),x61922),f329(f329(f254(x61921),x61922),x61923)))
% 187.18/188.04 [6248]E(f329(f329(f22(a104),f329(f329(f80(a104),x62481),x62482)),x62483),f279(x62481,x62482,x62483))+~P24(f329(f329(f244(a104),x62482),x62483))
% 187.18/188.04 [6269]~E(f329(f329(f136(x62691),x62693),x62692),f118(x62691))+P24(f329(f329(f243(a874),f329(f194(f875(x62691)),x62692)),x62693))
% 187.18/188.04 [6401]E(f329(f329(f81(a874),f329(f108(a874),x64011)),f329(f329(f81(a874),f329(f108(a874),x64012)),x64013)),f2(a874))+~P24(f329(f329(f244(a1),x64011),a83))
% 187.18/188.04 [6417]~P61(x64171)+E(f329(f329(f254(x64171),f329(f329(f287(x64171),f78(x64171)),x64172)),x64173),f329(f329(f287(x64171),f78(x64171)),f329(f329(f254(x64171),x64172),x64173)))
% 187.18/188.04 [6495]E(f329(f329(f22(a874),f329(f329(f80(a874),x64951),x64952)),x64953),f329(f329(f22(a874),x64951),f329(f329(f22(a874),x64953),x64952)))+~P24(f329(f329(f243(a874),x64952),x64953))
% 187.18/188.04 [6497]E(f329(f329(f22(a874),f329(f329(f80(a874),x64971),x64972)),x64973),f329(f329(f80(a874),x64971),f329(f329(f22(a874),x64972),x64973)))+~P24(f329(f329(f243(a874),x64973),x64972))
% 187.18/188.04 [6532]~P66(x65321)+P24(f329(f329(f243(x65321),f329(f329(f106(x65321),x65322),x65323)),x65323))
% 187.18/188.04 [6533]~P103(x65331)+P24(f329(f329(f243(x65331),f329(f329(f106(x65331),x65332),x65333)),x65333))
% 187.18/188.04 [6534]~P66(x65341)+P24(f329(f329(f243(x65341),f329(f329(f106(x65341),x65342),x65343)),x65342))
% 187.18/188.04 [6535]~P103(x65351)+P24(f329(f329(f243(x65351),f329(f329(f106(x65351),x65352),x65353)),x65352))
% 187.18/188.04 [6536]~P27(x65361)+P24(f329(f329(f243(x65361),f329(f329(f241(x65361),x65362),x65363)),x65363))
% 187.18/188.04 [6537]~P27(x65371)+P24(f329(f329(f243(x65371),f329(f329(f241(x65371),x65372),x65373)),x65372))
% 187.18/188.04 [6551]E(f329(f329(f39(a1),f329(f329(f39(a1),x65511),x65512)),x65513),f329(f329(f39(a1),x65511),f329(f329(f81(a1),x65512),x65513)))+~P24(f329(f329(f244(a1),f2(a1)),x65513))
% 187.18/188.04 [6603]~P109(x66031)+E(f329(f329(f80(x66031),f329(f329(f81(x66031),x66032),x66033)),x66033),f329(f329(f81(x66031),f329(f329(f80(x66031),x66032),f78(x66031))),x66033))
% 187.18/188.04 [6604]~P94(x66041)+E(f329(f329(f81(x66041),f329(f79(x66041),f329(f108(x66041),x66042))),x66043),f329(f329(f81(x66041),f329(f108(x66041),f329(f79(a1),x66042))),x66043))
% 187.18/188.04 [6676]~P83(x66761)+E(f329(f164(x66761),f329(f329(f152(x66762,x66761),f329(f16(x66761,x66762),f2(x66761))),x66763)),f2(x66761))
% 187.18/188.04 [6692]E(f329(f329(f80(a874),f329(f108(a874),x66921)),f329(f329(f80(a874),f329(f108(a874),x66922)),x66923)),f329(f329(f80(a874),f329(f108(a874),x66922)),x66923))+~P24(f329(a198,f329(f108(a1),x66921)))
% 187.18/188.04 [6706]~P31(x67061)+E(f41(x67061,f329(f329(f307(x67061),x67062),f329(f329(f307(x67061),x67063),f193(f881(x67061,a869))))),f329(f329(f106(x67061),x67062),x67063))
% 187.18/188.04 [6707]~P31(x67071)+E(f40(x67071,f329(f329(f307(x67071),x67072),f329(f329(f307(x67071),x67073),f193(f881(x67071,a869))))),f329(f329(f115(x67071),x67072),x67073))
% 187.18/188.04 [6730]E(f329(f329(f174(x67301),x67302),x67303),x67303)+~P24(f329(f329(f243(a874),f329(f194(f875(x67301)),x67303)),x67302))
% 187.18/188.04 [6743]E(f329(f329(f136(x67431),x67432),x67433),f118(x67431))+~P24(f329(f329(f243(a874),f329(f194(f875(x67431)),x67433)),x67432))
% 187.18/188.04 [6754]E(f329(f329(f80(a874),f329(f329(f22(a874),x67541),x67542)),x67543),f329(f329(f22(a874),f329(f329(f80(a874),x67541),x67543)),x67542))+~P24(f329(f329(f243(a874),x67542),x67541))
% 187.18/188.04 [6768]~P24(f329(f329(f244(a874),x67681),x67683))+P24(f329(f329(f244(a874),f329(f329(f22(a874),x67681),x67682)),x67683))
% 187.18/188.04 [6796]~P27(x67961)+E(f168(x67961,x67962,f329(f329(f146(x67961,x67961,f5(x67961)),x67962),x67963)),x67963)
% 187.18/188.04 [6885]E(f329(f329(f22(a874),f329(f329(f80(a874),x68851),x68852)),f329(a117,x68853)),f329(f329(f22(a874),x68851),f329(a117,f329(f329(f22(a874),x68853),x68852))))+~P24(f329(f329(f243(a874),x68852),x68853))
% 187.18/188.04 [6886]~P115(x68861)+P24(f329(f329(f243(x68861),f2(x68861)),f329(f329(f254(x68861),f329(f75(x68861),x68862)),x68863)))
% 187.18/188.04 [6933]P20(x69331,x69332,x69333)+~P24(f329(f329(f243(f881(f873(x69331),a869)),x69333),x69332))
% 187.18/188.04 [6976]~P24(f329(f62(x69761),x69762))+P24(f329(f62(x69761),f329(f329(f22(f881(x69761,a869)),x69762),x69763)))
% 187.18/188.04 [6977]~P24(f329(f62(x69771),x69773))+P24(f329(f62(x69771),f329(f329(f106(f881(x69771,a869)),x69772),x69773)))
% 187.18/188.04 [6978]~P24(f329(f62(x69781),x69782))+P24(f329(f62(x69781),f329(f329(f106(f881(x69781,a869)),x69782),x69783)))
% 187.18/188.04 [7119]~P42(x71191,x71193)+P42(x71191,f329(f329(f106(f881(f880(x71191,x71191),a869)),x71192),x71193))
% 187.18/188.04 [7120]~P42(x71201,x71202)+P42(x71201,f329(f329(f106(f881(f880(x71201,x71201),a869)),x71202),x71203))
% 187.18/188.04 [7235]~P66(x72351)+E(f10(x72351,f329(f171(x72351),f329(f329(f149(x72351),x72352),x72353))),f329(f140(x72351,x72351,f106(x72351),x72352),x72353))
% 187.18/188.04 [7236]~P66(x72361)+E(f13(x72361,f329(f171(x72361),f329(f329(f149(x72361),x72362),x72363))),f329(f140(x72361,x72361,f115(x72361),x72362),x72363))
% 187.18/188.04 [7237]~P27(x72371)+E(f14(x72371,f329(f171(x72371),f329(f329(f149(x72371),x72372),x72373))),f329(f140(x72371,x72371,f241(x72371),x72372),x72373))
% 187.18/188.04 [7238]~P27(x72381)+E(f15(x72381,f329(f171(x72381),f329(f329(f149(x72381),x72382),x72383))),f329(f140(x72381,x72381,f242(x72381),x72382),x72383))
% 187.18/188.04 [7298]~P24(f329(f62(x72981),x72982))+P24(f329(f329(f243(a874),f329(f38(x72981),x72982)),f329(f38(x72981),f329(f329(f307(x72981),x72983),x72982))))
% 187.18/188.04 [7306]E(f329(f329(f115(f881(a874,a869)),f329(f299(a874,x73061),x73062)),f329(f299(a874,x73062),f329(f329(f80(a874),x73062),x73063))),f329(f299(a874,x73061),f329(f329(f80(a874),x73062),x73063)))+~P24(f329(f329(f243(a874),x73061),x73062))
% 187.18/188.04 [7316]P24(f329(f329(f243(a874),x73161),x73162))+~P24(f329(f329(f243(a874),f329(f329(f80(a874),x73163),x73161)),x73162))
% 187.18/188.04 [7317]P24(f329(f329(f243(a874),x73171),x73172))+~P24(f329(f329(f243(a874),f329(f329(f80(a874),x73171),x73173)),x73172))
% 187.18/188.04 [7318]P24(f329(f329(f244(a874),x73181),x73182))+~P24(f329(f329(f244(a874),f329(f329(f80(a874),x73181),x73183)),x73182))
% 187.18/188.04 [7360]~P27(x73601)+E(f11(x73601,f241(x73601),f329(f171(x73601),f329(f329(f149(x73601),x73602),x73603))),f329(f140(x73601,x73601,f241(x73601),x73602),x73603))
% 187.18/188.04 [7361]~P27(x73611)+E(f12(x73611,f242(x73611),f329(f171(x73611),f329(f329(f149(x73611),x73612),x73613))),f329(f140(x73611,x73611,f242(x73611),x73612),x73613))
% 187.18/188.04 [7365]~E(x73652,f193(f881(f880(x73651,x73651),a869)))+P24(f329(f329(f243(f881(f880(x73651,x73651),a869)),x73652),x73653))
% 187.18/188.04 [7476]E(f329(f329(f115(f881(x74761,a869)),x74762),f329(f329(f22(f881(x74761,a869)),x74763),x74762)),x74763)+~P24(f329(f329(f243(f881(x74761,a869)),x74762),x74763))
% 187.18/188.04 [7477]~P24(f329(f329(f243(a874),x74771),f329(f329(f80(a874),x74773),x74772)))+P24(f329(f329(f243(a874),f329(f329(f22(a874),x74771),x74772)),x74773))
% 187.18/188.04 [7478]~P24(f329(f329(f244(a874),x74781),f329(f329(f22(a874),x74783),x74782)))+P24(f329(f329(f244(a874),f329(f329(f80(a874),x74781),x74782)),x74783))
% 187.18/188.04 [7534]E(x75341,f118(x75342))+E(f329(f139(x75342),f329(f329(f329(f188(f875(x75342),f875(x75342)),x75343),f166(x75342)),x75341)),f329(f329(f163(x75342),x75341),f45(a874,x75343,f329(f194(f875(x75342)),x75341))))
% 187.18/188.04 [7543]E(f329(f329(f307(x75431),x75432),f329(f329(f22(f881(x75431,a869)),x75433),f329(f329(f307(x75431),x75432),f193(f881(x75431,a869))))),x75433)+~P24(f329(f329(f331(x75431),x75432),x75433))
% 187.18/188.04 [7706]P24(f329(f329(f243(a874),x77061),f329(f329(f80(a874),x77062),x77063)))+~P24(f329(f329(f243(a874),f329(f329(f22(a874),x77061),x77063)),x77062))
% 187.18/188.04 [7707]P24(f329(f329(f244(a874),x77071),f329(f329(f22(a874),x77072),x77073)))+~P24(f329(f329(f244(a874),f329(f329(f80(a874),x77071),x77073)),x77072))
% 187.18/188.04 [7730]P24(f329(f62(x77301),x77302))+~P24(f329(f62(x77301),f329(f329(f115(f881(x77301,a869)),x77303),x77302)))
% 187.18/188.04 [7731]P24(f329(f62(x77311),x77312))+~P24(f329(f62(x77311),f329(f329(f115(f881(x77311,a869)),x77312),x77313)))
% 187.18/188.04 [7809]~P50(x78091,x78093)+P24(f329(f329(f331(f880(x78091,x78091)),f329(f329(f264(x78091,x78091),x78092),x78092)),x78093))
% 187.18/188.04 [7943]E(f329(f329(f163(a874),f137(a874,f329(f299(a874,x79431),x79432))),x79433),f329(f329(f80(a874),x79431),x79433))+~P24(f329(f329(f244(a874),f329(f329(f80(a874),x79431),x79433)),x79432))
% 187.18/188.04 [8011]~P24(f329(f329(f199(f329(a26,x80111)),x80112),x80113))+P24(f329(f329(f199(f329(f240(a870),f329(a28,x80111))),x80112),x80113))
% 187.18/188.04 [8016]E(f329(f329(f174(a874),x80161),f137(a874,f329(f299(a874,x80162),x80163))),f137(a874,f329(f299(a874,x80162),f329(f329(f80(a874),x80162),x80161))))+~P24(f329(f329(f243(a874),f329(f329(f80(a874),x80162),x80161)),x80163))
% 187.18/188.04 [8069]~P94(x80691)+E(f329(f329(f254(x80691),x80692),f329(f108(a874),f329(f329(f80(a1),x80693),x80693))),f329(f329(f86(x80691,x80691),f329(f329(f254(x80691),x80692),f329(f108(a874),x80693))),f329(f329(f18(x80691,x80691,x80691),f81(x80691)),f5(x80691))))
% 187.18/188.04 [8278]P24(f329(f329(f199(f329(a26,x82781)),x82782),x82783))+~P24(f329(f329(f199(f329(f240(a870),f329(a28,x82781))),x82782),x82783))
% 187.18/188.04 [8338]E(f329(f329(f126(x83381),f329(f329(f174(x83381),x83382),x83383)),f329(f329(f149(x83381),f329(f329(f163(x83381),x83383),x83382)),f329(f329(f136(x83381),f329(a117,x83382)),x83383))),x83383)+~P24(f329(f329(f244(a874),x83382),f329(f194(f875(x83381)),x83383)))
% 187.18/188.04 [8345]P24(f329(f329(f243(f881(x83451,a869)),f317(x83451,x83452)),f317(x83451,x83453)))+~P24(f329(f329(f243(f881(x83451,f881(x83451,a869))),x83453),x83452))
% 187.18/188.04 [8347]~P55(x83471,x83472,x83473)+P55(x83471,x83472,f329(f329(f22(f881(f880(x83471,x83471),a869)),x83473),f305(x83471,f193(f881(f880(x83471,x83471),a869)))))
% 187.18/188.04 [8364]P24(f329(f329(f243(f881(x83641,a869)),f318(x83641,x83642)),f318(x83641,x83643)))+~P24(f329(f329(f243(f881(f880(x83641,x83641),a869)),x83643),x83642))
% 187.18/188.04 [8371]~P122(x83711)+P24(f329(f329(f243(x83711),f2(x83711)),f329(f329(f80(x83711),f329(f329(f81(x83711),x83712),x83712)),f329(f329(f81(x83711),x83713),x83713))))
% 187.18/188.04 [8406]P24(f329(f329(f243(f881(x84061,a869)),f329(f282(x84061),x84062)),f329(f282(x84061),x84063)))+~P24(f329(f329(f243(f881(f880(x84061,x84061),a869)),x84062),x84063))
% 187.18/188.04 [8440]~P46(x84401,x84402)+~P24(f329(f329(f331(f880(x84401,x84401)),f329(f329(f264(x84401,x84401),x84403),x84403)),x84402))
% 187.18/188.04 [8442]~P42(x84421,x84422)+~P24(f329(f329(f331(f880(x84421,x84421)),f329(f329(f264(x84421,x84421),x84423),x84423)),x84422))
% 187.18/188.04 [8504]P24(f329(f329(f243(f881(x85041,a869)),f41(f881(x85041,a869),x85042)),f41(f881(x85041,a869),x85043)))+~P24(f329(f329(f243(f881(f881(x85041,a869),a869)),x85043),x85042))
% 187.18/188.04 [8505]P24(f329(f329(f243(f881(x85051,a869)),f40(f881(x85051,a869),x85052)),f40(f881(x85051,a869),x85053)))+~P24(f329(f329(f243(f881(f881(x85051,a869),a869)),x85052),x85053))
% 187.18/188.04 [8557]~P6(x85571,x85573,x85572)+P24(f329(f329(f243(f881(f880(x85571,x85571),a869)),x85572),f329(f329(f266(x85571,x85571),x85573),f329(f16(f881(x85571,a869),x85571),x85573))))
% 187.18/188.04 [8558]~P44(x85581,x85583,x85582)+P24(f329(f329(f243(f881(f880(x85581,x85581),a869)),x85582),f329(f329(f266(x85581,x85581),x85583),f329(f16(f881(x85581,a869),x85581),x85583))))
% 187.18/188.04 [8604]~P87(x86041)+P24(f329(f329(f243(x86041),f329(f329(f22(x86041),f329(f75(x86041),x86042)),f329(f75(x86041),x86043))),f329(f75(x86041),f329(f329(f22(x86041),x86043),x86042))))
% 187.18/188.04 [8605]~P87(x86051)+P24(f329(f329(f243(x86051),f329(f329(f22(x86051),f329(f75(x86051),x86052)),f329(f75(x86051),x86053))),f329(f75(x86051),f329(f329(f22(x86051),x86052),x86053))))
% 187.18/188.04 [8635]P24(f329(f329(f243(f881(f880(x86351,x86351),a869)),f305(x86351,x86352)),f305(x86351,x86353)))+~P24(f329(f329(f243(f881(f880(x86351,x86351),a869)),x86352),x86353))
% 187.18/188.04 [8791]P55(x87911,x87912,x87913)+~P55(x87911,x87912,f329(f329(f22(f881(f880(x87911,x87911),a869)),x87913),f305(x87911,f193(f881(f880(x87911,x87911),a869)))))
% 187.18/188.04 [8809]P24(f329(f329(f243(f881(f880(f875(x88091),f875(x88091)),a869)),f155(x88091,x88092)),f155(x88091,x88093)))+~P24(f329(f329(f243(f881(f880(x88091,x88091),a869)),x88092),x88093))
% 187.18/188.04 [8810]P24(f329(f329(f243(f881(f880(f875(x88101),f875(x88101)),a869)),f156(x88101,x88102)),f156(x88101,x88103)))+~P24(f329(f329(f243(f881(f880(x88101,x88101),a869)),x88102),x88103))
% 187.18/188.04 [8829]~P44(x88291,x88293,x88292)+P24(f329(f329(f243(f881(f880(x88291,x88291),a869)),x88292),f329(f329(f286(x88291,x88291,x88291),f329(f284(x88291,x88291),x88292)),x88292)))
% 187.18/188.04 [8878]~P24(f329(f135(x88781),x88782))+E(f329(f134(x88781,f329(f329(f7(x88781,f881(x88781,a869),a869),f331(x88781)),f329(f171(x88781),f175(x88781,x88782,x88783)))),x88782),f175(x88781,x88782,x88783))
% 187.18/188.04 [8942]E(x89421,x89422)+~P24(f329(f329(f331(f880(x89423,x89423)),f329(f329(f264(x89423,x89423),x89421),x89422)),f305(x89423,f193(f881(f880(x89423,x89423),a869)))))
% 187.18/188.04 [9028]P24(f329(f329(f331(x90281),x90282),f318(x90281,x90283)))+P24(f329(f329(f331(f880(x90281,x90281)),f329(f329(f264(x90281,x90281),f515(x90283,x90282,x90281)),x90282)),x90283))
% 187.18/188.04 [9029]P24(f329(f329(f331(x90291),x90292),f318(x90291,x90293)))+P24(f329(f329(f331(f880(x90291,x90291)),f329(f329(f264(x90291,x90291),f580(x90293,x90292,x90291)),x90292)),x90293))
% 187.18/188.04 [9030]P24(f329(f329(f331(x90301),x90302),f318(x90301,x90303)))+P24(f329(f329(f331(f880(x90301,x90301)),f329(f329(f264(x90301,x90301),f582(x90303,x90302,x90301)),x90302)),x90303))
% 187.18/188.04 [9116]~P24(f329(f329(f331(f875(x91161)),x91163),f159(x91161,x91162)))+P24(f329(f158(x91161,f329(f329(f7(x91161,f881(x91161,a869),a869),f331(x91161)),x91162)),x91163))
% 187.18/188.04 [9137]P24(f329(x91373,x91372))+E(f329(f249(x91371),f329(f329(f18(x91371,a869,a869),f329(f329(f8(a869,f881(a869,a869),x91371),a327),f329(a326,x91372))),x91373)),f193(f881(x91371,a869)))
% 187.18/188.04 [9158]~P87(x91581)+P24(f329(f329(f243(x91581),f329(f75(x91581),f329(f329(f22(x91581),f329(f75(x91581),x91582)),f329(f75(x91581),x91583)))),f329(f75(x91581),f329(f329(f22(x91581),x91582),x91583))))
% 187.18/188.04 [9172]~P24(f329(x91723,x91722))+E(f329(f249(x91721),f329(f329(f18(x91721,a869,a869),f329(f329(f8(a869,f881(a869,a869),x91721),a327),f329(a326,x91722))),x91723)),f329(f329(f307(x91721),x91722),f193(f881(x91721,a869))))
% 187.18/188.04 [9179]~P24(f329(f329(f331(f881(x91791,a869)),x91793),f329(f306(x91791),x91792)))+P24(f329(f257(x91791,f329(f329(f7(x91791,f881(x91791,a869),a869),f331(x91791)),x91792)),x91793))
% 187.18/188.04 [9212]P42(x92121,x92122)+P24(f329(f329(f331(f880(x92121,x92121)),f329(f329(f264(x92121,x92121),f329(f523(x92122,x92121),f329(a117,x92123))),f329(f523(x92122,x92121),x92123))),x92122))
% 187.18/188.04 [9355]P24(f329(f329(f331(f875(x93551)),x93552),f159(x93551,x93553)))+~P24(f329(f158(x93551,f329(f329(f7(x93551,f881(x93551,a869),a869),f331(x93551)),x93553)),x93552))
% 187.18/188.04 [9368]P24(f329(f329(f331(f881(x93681,a869)),x93682),f329(f306(x93681),x93683)))+~P24(f329(f257(x93681,f329(f329(f7(x93681,f881(x93681,a869),a869),f331(x93681)),x93683)),x93682))
% 187.18/188.04 [9424]P24(f329(f329(f331(x94241),f329(f275(x94241,x94242),x94243)),f329(f171(x94241),f329(f329(f152(f880(a104,x94241),x94241),f267(a104,x94241)),x94242))))+~P24(f329(f329(f244(a104),x94243),f329(f164(a104),f329(f329(f152(f880(a104,x94241),a104),f263(a104,x94241)),x94242))))
% 187.18/188.04 [9472]P24(f329(f329(f243(f881(f880(f875(x94721),f875(x94721)),a869)),f156(x94721,x94722)),f329(f329(f266(f875(x94721),f875(x94721)),f159(x94721,x94723)),f329(f16(f881(f875(x94721),a869),f875(x94721)),f159(x94721,x94723)))))+~P24(f329(f329(f243(f881(f880(x94721,x94721),a869)),x94722),f329(f329(f266(x94721,x94721),x94723),f329(f16(f881(x94721,a869),x94721),x94723))))
% 187.18/188.04 [9494]P24(f329(f329(f331(x94941),f329(f263(x94941,f880(a104,a104)),f329(f273(x94941,x94942),x94943))),f329(f171(x94941),f329(f329(f152(f880(a104,x94941),x94941),f267(a104,x94941)),x94942))))+~P24(f329(f329(f244(a104),f2(a104)),f329(f164(a104),f329(f329(f152(f880(a104,x94941),a104),f263(a104,x94941)),x94942))))
% 187.18/188.04 [9511]~P24(f329(f329(f243(f881(f880(x95111,x95111),a869)),x95112),f329(f329(f266(x95111,x95111),x95113),f329(f16(f881(x95111,a869),x95111),x95113))))+P24(f329(f329(f243(f881(f880(x95111,x95111),a869)),f329(f329(f286(x95111,x95111,x95111),x95112),f305(x95111,x95112))),f329(f329(f266(x95111,x95111),x95113),f329(f16(f881(x95111,a869),x95111),x95113))))
% 187.18/188.04 [9814]~P42(x98141,x98142)+~P24(f329(f329(f331(f880(x98141,x98141)),f329(f329(f264(x98141,x98141),f329(x98143,f329(a117,f524(x98142,x98141,x98143)))),f329(x98143,f524(x98142,x98141,x98143)))),x98142))
% 187.18/188.04 [9815]~P42(x98151,x98152)+~P24(f329(f329(f331(f880(x98151,x98151)),f329(f329(f264(x98151,x98151),f329(x98153,f329(a117,f587(x98153,x98152,x98151)))),f329(x98153,f587(x98153,x98152,x98151)))),x98152))
% 187.18/188.04 [10068]P24(f329(f329(f243(f881(f880(f881(x100681,a869),f881(x100681,a869)),a869)),f329(f329(f286(f881(x100681,a869),f881(x100681,a869),f881(x100681,a869)),f321(x100681,x100682)),f329(f329(f115(f881(f880(f881(x100681,a869),f881(x100681,a869)),a869)),f321(x100681,x100683)),f329(f329(f307(f880(f881(x100681,a869),f881(x100681,a869))),f329(f329(f264(f881(x100681,a869),f881(x100681,a869)),f193(f881(x100681,a869))),f193(f881(x100681,a869)))),f193(f881(f880(f881(x100681,a869),f881(x100681,a869)),a869)))))),f321(x100681,x100682)))+~P24(f329(f329(f243(f881(f880(x100681,x100681),a869)),f329(f329(f286(x100681,x100681,x100681),x100682),x100683)),x100682))
% 187.18/188.04 [10069]P24(f329(f329(f243(f881(f880(f881(x100691,a869),f881(x100691,a869)),a869)),f329(f329(f286(f881(x100691,a869),f881(x100691,a869),f881(x100691,a869)),f320(x100691,x100692)),f329(f329(f115(f881(f880(f881(x100691,a869),f881(x100691,a869)),a869)),f320(x100691,x100693)),f329(f329(f307(f880(f881(x100691,a869),f881(x100691,a869))),f329(f329(f264(f881(x100691,a869),f881(x100691,a869)),f193(f881(x100691,a869))),f193(f881(x100691,a869)))),f193(f881(f880(f881(x100691,a869),f881(x100691,a869)),a869)))))),f320(x100691,x100692)))+~P24(f329(f329(f243(f881(f880(x100691,x100691),a869)),f329(f329(f286(x100691,x100691,x100691),x100692),x100693)),x100692))
% 187.18/188.04 [7234]~P24(f329(f329(f243(a874),x72342),x72341))+E(f329(f329(f22(a874),f329(a117,f329(f329(f22(a874),x72341),x72342))),x72343),f329(f329(f22(a874),f329(a117,x72341)),f329(f329(f80(a874),x72342),x72343)))
% 187.18/188.04 [7273]~P29(x72731)+E(f329(f329(f80(x72731),f45(x72731,x72732,x72733)),f329(f329(f81(x72731),f329(f329(f39(x72731),x72732),x72733)),x72733)),x72732)
% 187.18/188.04 [7482]E(f329(f329(f81(a874),f329(f108(a874),x74821)),f329(f329(f81(a874),f329(f108(a874),x74822)),x74823)),f329(f329(f81(a874),f329(f108(a874),f329(f329(f81(a1),x74821),x74822))),x74823))+P24(f329(f329(f244(a1),x74821),a83))
% 187.18/188.04 [7952]~P24(f329(f329(f243(a874),x79523),x79522))+P24(f329(f329(f243(a874),x79521),f329(f329(f22(a874),f329(f329(f80(a874),x79522),x79521)),x79523)))
% 187.18/188.04 [8158]~P24(f329(f329(f243(a874),x81581),x81582))+E(f329(f329(f126(a874),f137(a874,f329(f299(a874,x81581),x81582))),f137(a874,f329(f299(a874,x81582),f329(f329(f80(a874),x81582),x81583)))),f137(a874,f329(f299(a874,x81581),f329(f329(f80(a874),x81582),x81583))))
% 187.18/188.04 [8416]~P24(f329(f62(x84161),x84162))+E(f329(a117,f329(f38(x84161),f329(f329(f22(f881(x84161,a869)),x84162),f329(f329(f307(x84161),x84163),f193(f881(x84161,a869)))))),f329(f38(x84161),f329(f329(f307(x84161),x84163),x84162)))
% 187.18/188.04 [8464]~P24(f329(f62(x84641),x84642))+E(f329(f329(f80(a874),f78(a874)),f329(f38(x84641),f329(f329(f22(f881(x84641,a869)),x84642),f329(f329(f307(x84641),x84643),f193(f881(x84641,a869)))))),f329(f38(x84641),f329(f329(f307(x84641),x84643),x84642)))
% 187.18/188.04 [8644]E(f329(f329(f22(a874),f329(f38(x86441),x86442)),f329(f38(x86441),f329(f329(f106(f881(x86441,a869)),x86442),x86443))),f329(f38(x86441),f329(f329(f22(f881(x86441,a869)),x86442),x86443)))+~P24(f329(f62(x86441),f329(f329(f106(f881(x86441,a869)),x86442),x86443)))
% 187.18/188.04 [8874]~P32(f329(x88742,f413(x88742,x88743,x88741)))+E(f329(f105(a1),f329(f329(f6(x88741,a874),f329(f329(f8(a1,a874,x88741),a109),x88742)),x88743)),f329(f329(f6(x88741,a1),x88742),x88743))
% 187.18/188.04 [8875]~P32(f329(x88752,f414(x88752,x88753,x88751)))+E(f329(f105(a1),f329(f329(f9(x88751,a874),f329(f329(f8(a1,a874,x88751),a109),x88752)),x88753)),f329(f329(f9(x88751,a1),x88752),x88753))
% 187.18/188.04 [8924]~P24(f329(f62(x89241),x89243))+P24(f329(f329(f243(a874),f329(f329(f22(a874),f329(f38(x89241),x89242)),f329(f38(x89241),x89243))),f329(f38(x89241),f329(f329(f22(f881(x89241,a869)),x89242),x89243))))
% 187.18/188.04 [8950]P24(f329(f329(f331(x89501),f413(x89502,x89503,x89501)),x89503))+E(f329(f105(a1),f329(f329(f6(x89501,a874),f329(f329(f8(a1,a874,x89501),a109),x89502)),x89503)),f329(f329(f6(x89501,a1),x89502),x89503))
% 187.18/188.04 [8951]P24(f329(f329(f331(x89511),f414(x89512,x89513,x89511)),x89513))+E(f329(f105(a1),f329(f329(f9(x89511,a874),f329(f329(f8(a1,a874,x89511),a109),x89512)),x89513)),f329(f329(f9(x89511,a1),x89512),x89513))
% 187.18/188.04 [9020]E(f85(x90201,f329(f329(f7(x90201,f881(x90201,a869),a869),f331(x90201)),f329(f329(f22(f881(x90201,a869)),x90202),f329(f329(f307(x90201),x90203),f193(f881(x90201,a869)))))),f256(x90201,x90203,x90202))+P24(f329(f329(f243(f881(x90201,a869)),x90202),f329(f329(f307(x90201),x90203),f193(f881(x90201,a869)))))
% 187.18/188.04 [9369]E(f329(f329(f152(f875(x93691),x93691),f329(f329(f7(f875(x93691),a874,x93691),f163(x93691)),x93692)),f329(f134(f875(x93691),f329(f329(f8(a874,a869,f875(x93691)),f329(f244(a874),x93692)),f194(f875(x93691)))),x93693)),f329(f329(f163(f875(x93691)),f179(x93691,x93693)),x93692))+~P24(f329(f329(f244(a874),x93692),f329(f194(f875(f875(x93691))),f179(x93691,x93693))))
% 187.18/188.04 [9441]E(f329(f134(x94411,x94412),x94413),f176(x94411,x94412,x94413))+P24(f329(f329(f331(x94411),f757(x94413,x94412,x94411)),f329(f171(x94411),f329(f329(f136(x94411),f329(f194(f875(x94411)),f176(x94411,x94412,x94413))),x94413))))
% 187.18/188.04 [9582]E(f329(f329(f136(x95821),f329(f194(f875(x95821)),f176(x95821,x95822,x95823))),x95823),f118(x95821))+~P24(f329(x95822,f329(f139(x95821),f329(f329(f136(x95821),f329(f194(f875(x95821)),f176(x95821,x95822,x95823))),x95823))))
% 187.18/188.04 [9675]~P24(f329(f329(f331(f880(x96751,x96751)),x96752),f305(x96751,x96753)))+P24(f329(f329(f331(f880(x96751,x96751)),x96752),f329(f329(f42(a874,f881(f880(x96751,x96751),a869)),f252(f881(a874,a869))),f329(f329(f7(a874,f881(f880(x96751,x96751),a869),f881(f880(x96751,x96751),a869)),f188(f880(x96751,x96751),a869)),x96753))))
% 187.18/188.04 [9732]~P24(f329(f329(f243(f881(x97321,a869)),f329(f329(f42(a874,f881(x97321,a869)),f329(f299(a874,f2(a874)),f442(x97323,x97322,x97321))),x97322)),x97323))+P24(f329(f329(f243(f881(x97321,a869)),f329(f329(f42(a874,f881(x97321,a869)),f252(f881(a874,a869))),x97322)),x97323))
% 187.18/188.04 [9790]~P24(f329(f329(f244(a1),f2(a1)),x97903))+P24(f329(f329(f244(a1),x97901),f329(f329(f80(a1),x97902),f329(f329(f81(a1),f329(f329(f80(a1),f329(f75(a1),f329(f329(f22(a1),x97902),x97901))),f78(a1))),x97903))))
% 187.18/188.04 [9801]~P42(x98011,f329(f329(f115(f881(f880(x98011,x98011),a869)),x98012),x98013))+P42(x98011,f329(f329(f115(f881(f880(x98011,x98011),a869)),f329(f329(f115(f881(f880(x98011,x98011),a869)),f329(f329(f286(x98011,x98011,x98011),x98012),x98012)),f329(f329(f286(x98011,x98011,x98011),x98013),x98012))),x98013))
% 187.18/188.04 [9884]P42(x98841,f329(f329(f115(f881(f880(x98841,x98841),a869)),x98842),x98843))+~P42(x98841,f329(f329(f115(f881(f880(x98841,x98841),a869)),f329(f329(f115(f881(f880(x98841,x98841),a869)),f329(f329(f286(x98841,x98841,x98841),x98842),x98842)),f329(f329(f286(x98841,x98841,x98841),x98843),x98842))),x98843))
% 187.18/188.04 [9445]~P138(x94451)+E(f329(f107(x94451),f329(a89,f329(f283(f880(a874,a874),f880(a874,a874),a113),f329(f329(f307(f880(a874,a874)),f329(f329(f264(a874,a874),x94452),x94453)),f193(f881(f880(a874,a874),a869)))))),f329(f329(f22(x94451),f329(f105(x94451),x94452)),f329(f105(x94451),x94453)))
% 187.18/188.04 [9529]P24(f329(x95293,x95292))+E(f329(f249(x95291),f329(f329(f18(x95291,a869,a869),f329(f329(f8(a869,f881(a869,a869),x95291),a327),f329(f329(f7(x95291,x95291,a869),a326),x95292))),x95293)),f193(f881(x95291,a869)))
% 187.18/188.04 [9531]~P24(f329(x95313,x95312))+E(f329(f249(x95311),f329(f329(f18(x95311,a869,a869),f329(f329(f8(a869,f881(a869,a869),x95311),a327),f329(f329(f7(x95311,x95311,a869),a326),x95312))),x95313)),f329(f329(f307(x95311),x95312),f193(f881(x95311,a869))))
% 187.18/188.04 [9768]E(x97681,x97682)+P24(f329(f329(f253(x97683,x97683,f329(f329(f8(f881(x97683,a869),f881(x97683,a869),x97683),f329(f8(a869,a869,x97683),a324)),a326)),x97681),x97682))
% 187.18/188.04 [9862]~E(x98621,x98622)+~P24(f329(f329(f253(x98623,x98623,f329(f329(f8(f881(x98623,a869),f881(x98623,a869),x98623),f329(f8(a869,a869,x98623),a324)),a326)),x98621),x98622))
% 187.18/188.04 [9876]~P24(f329(f62(x98761),x98763))+E(f329(f329(f65(x98761,f881(x98761,a869),f329(f329(f8(f881(x98761,a869),f881(f881(x98761,a869),f881(x98761,a869)),x98761),f329(f7(f881(x98761,a869),f881(x98761,a869),f881(x98761,a869)),f22(f881(x98761,a869)))),f329(f329(f7(x98761,f881(x98761,a869),f881(x98761,a869)),f307(x98761)),f193(f881(x98761,a869))))),x98762),x98763),f329(f329(f22(f881(x98761,a869)),x98762),x98763))
% 187.18/188.04 [9908]~P24(f329(f329(f244(a1),f2(a1)),x99083))+P24(f329(f329(f244(a1),f329(f329(f22(a1),x99081),f329(f329(f81(a1),f329(f329(f80(a1),f329(f75(a1),f329(f329(f22(a1),x99081),x99082))),f78(a1))),x99083))),x99082))
% 187.18/188.04 [10130]~P24(f329(f329(f331(x101301),x101303),f318(x101301,x101302)))+P24(f329(f317(x101301,f329(f329(f7(x101301,f881(f880(x101301,x101301),a869),f881(x101301,a869)),f329(f329(f8(f881(x101301,f881(f881(f880(x101301,x101301),a869),a869)),f881(f881(f880(x101301,x101301),a869),f881(x101301,a869)),x101301),f7(x101301,f881(f880(x101301,x101301),a869),a869)),f329(f329(f8(f881(x101301,f880(x101301,x101301)),f881(x101301,f881(f881(f880(x101301,x101301),a869),a869)),x101301),f329(f8(f880(x101301,x101301),f881(f881(f880(x101301,x101301),a869),a869),x101301),f331(f880(x101301,x101301)))),f264(x101301,x101301)))),x101302)),x101303))
% 187.18/188.04 [10142]P24(f329(f329(f331(x101421),x101422),f318(x101421,x101423)))+~P24(f329(f317(x101421,f329(f329(f7(x101421,f881(f880(x101421,x101421),a869),f881(x101421,a869)),f329(f329(f8(f881(x101421,f881(f881(f880(x101421,x101421),a869),a869)),f881(f881(f880(x101421,x101421),a869),f881(x101421,a869)),x101421),f7(x101421,f881(f880(x101421,x101421),a869),a869)),f329(f329(f8(f881(x101421,f880(x101421,x101421)),f881(x101421,f881(f881(f880(x101421,x101421),a869),a869)),x101421),f329(f8(f880(x101421,x101421),f881(f881(f880(x101421,x101421),a869),a869),x101421),f331(f880(x101421,x101421)))),f264(x101421,x101421)))),x101423)),x101422))
% 187.18/188.04 [9730]~P24(f329(f62(x97301),f329(f249(x97301),x97303)))+P24(f329(f62(x97301),f329(f249(x97301),f329(f329(f18(x97301,a869,a869),f329(f329(f8(a869,f881(a869,a869),x97301),a327),x97302)),x97303))))
% 187.18/188.04 [9731]~P24(f329(f62(x97311),f329(f249(x97311),x97312)))+P24(f329(f62(x97311),f329(f249(x97311),f329(f329(f18(x97311,a869,a869),f329(f329(f8(a869,f881(a869,a869),x97311),a327),x97312)),x97313))))
% 187.18/188.04 [9833]P24(f329(f62(x98331),f329(f249(x98331),x98332)))+~P24(f329(f62(x98331),f329(f249(x98331),f329(f329(f18(x98331,a869,a869),f329(f329(f8(a869,f881(a869,a869),x98331),a328),x98333)),x98332))))
% 187.18/188.04 [9834]P24(f329(f62(x98341),f329(f249(x98341),x98342)))+~P24(f329(f62(x98341),f329(f249(x98341),f329(f329(f18(x98341,a869,a869),f329(f329(f8(a869,f881(a869,a869),x98341),a328),x98342)),x98343))))
% 187.18/188.04 [10117]~P24(f329(f62(x101171),x101172))+P24(f329(f62(f875(x101171)),f329(f249(f875(x101171)),f329(f329(f18(f875(x101171),a869,a869),f329(f329(f8(a869,f881(a869,a869),f875(x101171)),a327),f329(f329(f7(f875(x101171),f881(x101171,a869),a869),f329(f329(f8(f881(x101171,a869),f881(f881(x101171,a869),a869),f875(x101171)),f243(f881(x101171,a869))),f171(x101171))),x101172))),f329(f329(f7(f875(x101171),a874,a869),f329(f329(f8(a874,f881(a874,a869),f875(x101171)),a326),f194(f875(x101171)))),x101173)))))
% 187.18/188.04 [10118]~P24(f329(f62(x101181),x101182))+P24(f329(f62(f875(x101181)),f329(f249(f875(x101181)),f329(f329(f18(f875(x101181),a869,a869),f329(f329(f8(a869,f881(a869,a869),f875(x101181)),a327),f329(f329(f7(f875(x101181),f881(x101181,a869),a869),f329(f329(f8(f881(x101181,a869),f881(f881(x101181,a869),a869),f875(x101181)),f243(f881(x101181,a869))),f171(x101181))),x101182))),f329(f329(f7(f875(x101181),a874,a869),f329(f329(f8(a874,f881(a874,a869),f875(x101181)),f243(a874)),f194(f875(x101181)))),x101183)))))
% 187.18/188.04 [9849]~P109(x98491)+E(f329(f329(f254(x98491),x98492),f329(f329(f81(a874),f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))),x98493)),f329(f329(f81(x98491),f329(f329(f254(x98491),x98492),x98493)),f329(f329(f254(x98491),x98492),x98493)))
% 187.18/188.04 [9889]~P82(x98891)+E(f329(f329(f254(x98891),f329(f329(f254(x98891),x98892),x98893)),f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))),f329(f329(f254(x98891),x98892),f329(f329(f81(a874),f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))),x98893)))
% 187.18/188.04 [9935]~P138(x99351)+E(f329(f329(f254(x99351),f329(f79(x99351),x99352)),f329(f329(f81(a874),f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))),x99353)),f329(f329(f254(x99351),x99352),f329(f329(f81(a874),f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))),x99353)))
% 187.18/188.04 [10075]~P115(x100751)+P24(f329(f329(f243(x100751),f2(x100751)),f329(f329(f80(x100751),f329(f329(f254(x100751),x100752),f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102))))),f329(f329(f254(x100751),x100753),f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))))))
% 187.18/188.04 [9945]~P109(x99451)+E(f329(f329(f254(x99451),x99452),f329(a117,f329(f329(f81(a874),f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))),x99453))),f329(f329(f81(x99451),x99452),f329(f329(f81(x99451),f329(f329(f254(x99451),x99452),x99453)),f329(f329(f254(x99451),x99452),x99453))))
% 187.18/188.04 [9994]~P82(x99941)+E(f329(f329(f81(x99941),x99942),f329(f329(f254(x99941),f329(f329(f254(x99941),x99942),x99943)),f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102))))),f329(f329(f254(x99941),x99942),f329(a117,f329(f329(f81(a874),f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))),x99943))))
% 187.18/188.04 [10032]~P115(x100321)+P24(f329(f329(f243(x100321),f2(x100321)),f329(f329(f254(x100321),x100322),f329(f329(f81(a874),f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))),x100323))))
% 187.18/188.05 [10098]~P94(x100981)+E(f329(f329(f22(x100981),f329(f329(f80(x100981),f329(f329(f254(x100981),x100982),f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102))))),f329(f329(f254(x100981),x100983),f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))))),f329(f329(f81(x100981),f329(f329(f81(x100981),f329(f108(x100981),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))),x100982)),x100983)),f329(f329(f254(x100981),f329(f329(f22(x100981),x100982),x100983)),f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))))
% 187.18/188.05 [10099]~P94(x100991)+E(f329(f329(f80(x100991),f329(f329(f80(x100991),f329(f329(f254(x100991),x100992),f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102))))),f329(f329(f254(x100991),x100993),f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))))),f329(f329(f81(x100991),f329(f329(f81(x100991),f329(f108(x100991),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))),x100992)),x100993)),f329(f329(f254(x100991),f329(f329(f80(x100991),x100992),x100993)),f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))))
% 187.18/188.05 [10197]~P34(x101971,x101972,x101973)+P24(f99(x101971,a869,f329(f329(f8(f881(a870,f881(f881(x101971,f881(a871,a869)),f881(x101971,a869))),f881(a870,f881(f881(x101971,f881(a871,a869)),a869)),f881(x101971,f881(a871,a869))),f329(f8(f881(f881(x101971,f881(a871,a869)),f881(x101971,a869)),f881(f881(x101971,f881(a871,a869)),a869),a870),f329(f8(f881(x101971,a869),a869,f881(x101971,f881(a871,a869))),f88(x101971)))),f329(f329(f8(f881(a870,f881(f881(x101971,f881(a871,a869)),f881(x101971,f881(a871,a869)))),f881(a870,f881(f881(x101971,f881(a871,a869)),f881(x101971,a869))),f881(x101971,f881(a871,a869))),f329(f8(f881(f881(x101971,f881(a871,a869)),f881(x101971,f881(a871,a869))),f881(f881(x101971,f881(a871,a869)),f881(x101971,a869)),a870),f329(f8(f881(x101971,f881(a871,a869)),f881(x101971,a869),f881(x101971,f881(a871,a869))),f329(f8(f881(a871,a869),a869,x101971),f88(a871))))),f329(f329(f7(f881(x101971,f881(a871,a869)),f881(a870,f881(f881(x101971,f881(a871,a869)),f881(x101971,f881(a871,a869)))),f881(a870,f881(f881(x101971,f881(a871,a869)),f881(x101971,f881(a871,a869))))),f329(f329(f8(f881(f881(f881(x101971,f881(a871,a869)),f881(x101971,f881(a871,a869))),f881(f881(x101971,f881(a871,a869)),f881(x101971,f881(a871,a869)))),f881(f881(a870,f881(f881(x101971,f881(a871,a869)),f881(x101971,f881(a871,a869)))),f881(a870,f881(f881(x101971,f881(a871,a869)),f881(x101971,f881(a871,a869))))),f881(x101971,f881(a871,a869))),f8(f881(f881(x101971,f881(a871,a869)),f881(x101971,f881(a871,a869))),f881(f881(x101971,f881(a871,a869)),f881(x101971,f881(a871,a869))),a870)),f329(f329(f8(f881(f881(x101971,f881(a871,a869)),f881(x101971,f881(a871,a869))),f881(f881(f881(x101971,f881(a871,a869)),f881(x101971,f881(a871,a869))),f881(f881(x101971,f881(a871,a869)),f881(x101971,f881(a871,a869)))),f881(x101971,f881(a871,a869))),f8(f881(x101971,f881(a871,a869)),f881(x101971,f881(a871,a869)),f881(x101971,f881(a871,a869)))),f329(f329(f8(f881(x101971,f881(f881(a871,a869),f881(a871,a869))),f881(f881(x101971,f881(a871,a869)),f881(x101971,f881(a871,a869))),f881(x101971,f881(a871,a869))),f18(x101971,f881(a871,a869),f881(a871,a869))),f329(f329(f8(f881(x101971,f881(a871,f881(a869,a869))),f881(x101971,f881(f881(a871,a869),f881(a871,a869))),f881(x101971,f881(a871,a869))),f329(f8(f881(a871,f881(a869,a869)),f881(f881(a871,a869),f881(a871,a869)),x101971),f18(a871,a869,a869))),f329(f8(f881(a871,a869),f881(a871,f881(a869,a869)),x101971),f329(f8(a869,f881(a869,a869),a871),a332))))))),f329(f329(f8(f881(f881(x101971,f881(a871,a869)),f881(x101971,f881(a871,f881(a871,a869)))),f881(f881(x101971,f881(a871,a869)),f881(x101971,f881(a871,a869))),a870),f329(f8(f881(x101971,f881(a871,f881(a871,a869))),f881(x101971,f881(a871,a869)),f881(x101971,f881(a871,a869))),f329(f8(f881(a871,f881(a871,a869)),f881(a871,a869),x101971),f329(f8(f881(a871,a869),a869,a871),f88(a871))))),f329(f329(f8(f881(f881(a871,a869),f881(a871,f881(a871,a869))),f881(f881(x101971,f881(a871,a869)),f881(x101971,f881(a871,f881(a871,a869)))),a870),f8(f881(a871,a869),f881(a871,f881(a871,a869)),x101971)),f329(f329(f8(f881(a871,f881(f881(a871,a869),f881(a871,a869))),f881(f881(a871,a869),f881(a871,f881(a871,a869))),a870),f7(a871,f881(a871,a869),f881(a871,a869))),f329(f329(f8(f881(a871,f881(a871,f881(a869,a869))),f881(a871,f881(f881(a871,a869),f881(a871,a869))),a870),f329(f8(f881(a871,f881(a869,a869)),f881(f881(a871,a869),f881(a871,a869)),a871),f18(a871,a869,a869))),f329(f329(f8(f881(a871,f881(a871,a869)),f881(a871,f881(a871,f881(a869,a869))),a870),f329(f8(f881(a871,a869),f881(a871,f881(a869,a869)),a871),f329(f8(a869,f881(a869,a869),a871),a332))),f329(f329(f7(a870,a874,f881(a871,f881(a871,a869))),f329(f329(f8(f881(a871,f881(a874,f881(a871,a869))),f881(a874,f881(a871,f881(a871,a869))),a870),f7(a871,a874,f881(a871,a869))),a201)),x101972))))))))),x101973))
% 187.18/188.05 [10199]P34(x101991,x101992,x101993)+~P24(f99(x101991,a869,f329(f329(f8(f881(a870,f881(f881(x101991,f881(a871,a869)),f881(x101991,a869))),f881(a870,f881(f881(x101991,f881(a871,a869)),a869)),f881(x101991,f881(a871,a869))),f329(f8(f881(f881(x101991,f881(a871,a869)),f881(x101991,a869)),f881(f881(x101991,f881(a871,a869)),a869),a870),f329(f8(f881(x101991,a869),a869,f881(x101991,f881(a871,a869))),f88(x101991)))),f329(f329(f8(f881(a870,f881(f881(x101991,f881(a871,a869)),f881(x101991,f881(a871,a869)))),f881(a870,f881(f881(x101991,f881(a871,a869)),f881(x101991,a869))),f881(x101991,f881(a871,a869))),f329(f8(f881(f881(x101991,f881(a871,a869)),f881(x101991,f881(a871,a869))),f881(f881(x101991,f881(a871,a869)),f881(x101991,a869)),a870),f329(f8(f881(x101991,f881(a871,a869)),f881(x101991,a869),f881(x101991,f881(a871,a869))),f329(f8(f881(a871,a869),a869,x101991),f88(a871))))),f329(f329(f7(f881(x101991,f881(a871,a869)),f881(a870,f881(f881(x101991,f881(a871,a869)),f881(x101991,f881(a871,a869)))),f881(a870,f881(f881(x101991,f881(a871,a869)),f881(x101991,f881(a871,a869))))),f329(f329(f8(f881(f881(f881(x101991,f881(a871,a869)),f881(x101991,f881(a871,a869))),f881(f881(x101991,f881(a871,a869)),f881(x101991,f881(a871,a869)))),f881(f881(a870,f881(f881(x101991,f881(a871,a869)),f881(x101991,f881(a871,a869)))),f881(a870,f881(f881(x101991,f881(a871,a869)),f881(x101991,f881(a871,a869))))),f881(x101991,f881(a871,a869))),f8(f881(f881(x101991,f881(a871,a869)),f881(x101991,f881(a871,a869))),f881(f881(x101991,f881(a871,a869)),f881(x101991,f881(a871,a869))),a870)),f329(f329(f8(f881(f881(x101991,f881(a871,a869)),f881(x101991,f881(a871,a869))),f881(f881(f881(x101991,f881(a871,a869)),f881(x101991,f881(a871,a869))),f881(f881(x101991,f881(a871,a869)),f881(x101991,f881(a871,a869)))),f881(x101991,f881(a871,a869))),f8(f881(x101991,f881(a871,a869)),f881(x101991,f881(a871,a869)),f881(x101991,f881(a871,a869)))),f329(f329(f8(f881(x101991,f881(f881(a871,a869),f881(a871,a869))),f881(f881(x101991,f881(a871,a869)),f881(x101991,f881(a871,a869))),f881(x101991,f881(a871,a869))),f18(x101991,f881(a871,a869),f881(a871,a869))),f329(f329(f8(f881(x101991,f881(a871,f881(a869,a869))),f881(x101991,f881(f881(a871,a869),f881(a871,a869))),f881(x101991,f881(a871,a869))),f329(f8(f881(a871,f881(a869,a869)),f881(f881(a871,a869),f881(a871,a869)),x101991),f18(a871,a869,a869))),f329(f8(f881(a871,a869),f881(a871,f881(a869,a869)),x101991),f329(f8(a869,f881(a869,a869),a871),a332))))))),f329(f329(f8(f881(f881(x101991,f881(a871,a869)),f881(x101991,f881(a871,f881(a871,a869)))),f881(f881(x101991,f881(a871,a869)),f881(x101991,f881(a871,a869))),a870),f329(f8(f881(x101991,f881(a871,f881(a871,a869))),f881(x101991,f881(a871,a869)),f881(x101991,f881(a871,a869))),f329(f8(f881(a871,f881(a871,a869)),f881(a871,a869),x101991),f329(f8(f881(a871,a869),a869,a871),f88(a871))))),f329(f329(f8(f881(f881(a871,a869),f881(a871,f881(a871,a869))),f881(f881(x101991,f881(a871,a869)),f881(x101991,f881(a871,f881(a871,a869)))),a870),f8(f881(a871,a869),f881(a871,f881(a871,a869)),x101991)),f329(f329(f8(f881(a871,f881(f881(a871,a869),f881(a871,a869))),f881(f881(a871,a869),f881(a871,f881(a871,a869))),a870),f7(a871,f881(a871,a869),f881(a871,a869))),f329(f329(f8(f881(a871,f881(a871,f881(a869,a869))),f881(a871,f881(f881(a871,a869),f881(a871,a869))),a870),f329(f8(f881(a871,f881(a869,a869)),f881(f881(a871,a869),f881(a871,a869)),a871),f18(a871,a869,a869))),f329(f329(f8(f881(a871,f881(a871,a869)),f881(a871,f881(a871,f881(a869,a869))),a870),f329(f8(f881(a871,a869),f881(a871,f881(a869,a869)),a871),f329(f8(a869,f881(a869,a869),a871),a332))),f329(f329(f7(a870,a874,f881(a871,f881(a871,a869))),f329(f329(f8(f881(a871,f881(a874,f881(a871,a869))),f881(a874,f881(a871,f881(a871,a869))),a870),f7(a871,a874,f881(a871,a869))),a201)),x101992))))))))),x101993))
% 187.18/188.05 [4662]E(x46621,x46622)+~E(f33(x46623,x46621),f33(x46624,x46622))
% 187.18/188.05 [4663]E(x46631,x46632)+~E(f33(x46631,x46633),f33(x46632,x46634))
% 187.18/188.05 [4664]E(x46641,x46642)+~E(f32(x46643,x46641),f32(x46644,x46642))
% 187.18/188.05 [4665]E(x46651,x46652)+~E(f32(x46651,x46653),f32(x46652,x46654))
% 187.18/188.05 [7750]P21(x77501,x77502,x77503,x77504)+~E(f509(x77504,x77503,x77502,x77501),f510(x77504,x77503,x77502,x77501))
% 187.18/188.05 [8048]P39(x80481,x80482,x80483,x80484,f118(x80482))+~E(x80484,f118(x80481))
% 187.18/188.05 [8049]P39(x80491,x80492,x80493,f118(x80491),x80494)+~E(x80494,f118(x80492))
% 187.18/188.05 [8263]~P21(x82631,f878(x82632),x82634,f183(x82631,x82632,x82634))+P21(x82631,f878(x82632),f184(x82631,x82632,x82633,x82634),f183(x82631,x82632,x82634))
% 187.18/188.05 [8478]~P21(x84781,f878(x84782),f184(x84781,x84782,x84784,x84783),f183(x84781,x84782,x84783))+P21(x84781,f878(x84782),x84783,f183(x84781,x84782,x84783))
% 187.18/188.05 [8594]~P39(x85942,x85943,x85944,x85941,f118(x85943))+E(x85941,f118(x85942))
% 187.18/188.05 [8595]~P39(x85953,x85952,x85954,f118(x85953),x85951)+E(x85951,f118(x85952))
% 187.18/188.05 [5038]~P13(x50383,x50381,x50384)+E(f329(f329(x50381,x50382),x50382),x50382)
% 187.18/188.05 [5294]P24(f329(x52942,x52944))+E(f329(f134(x52941,x52942),f169(x52941,x52943,x52944)),f118(x52941))
% 187.18/188.05 [5330]~E(x53304,f193(f881(x53301,a869)))+E(f329(f308(x53301,x53302,x53303),x53304),f193(f881(x53302,a869)))
% 187.18/188.05 [5568]~P24(f329(x55682,x55684))+E(f329(f134(x55681,x55682),f169(x55681,x55683,x55684)),f169(x55681,x55683,x55684))
% 187.18/188.05 [5597]~E(f329(f308(x55972,x55973,x55974),x55971),f193(f881(x55973,a869)))+E(x55971,f193(f881(x55972,a869)))
% 187.18/188.05 [5881]~P27(x58812)+E(f329(f329(f146(x58811,x58812,x58813),x58814),f118(x58811)),f329(f329(f149(x58811),x58814),f118(x58811)))
% 187.18/188.05 [5919]E(f329(x59191,x59192),f206(x59193))+P24(f329(f329(f331(x59194),x59192),f183(x59194,x59193,x59191)))
% 187.18/188.05 [6241]~E(x62411,f193(f881(x62412,a869)))+~P24(f329(f63(x62412,x62413,x62411),x62414))
% 187.18/188.05 [6263]~P58(x62631,x62633,x62634,x62632)+P24(f329(f62(x62631),x62632))
% 187.18/188.05 [6264]~P58(x62641,x62643,x62642,x62644)+P24(f329(f62(x62641),x62642))
% 187.18/188.05 [6270]~P58(x62702,x62703,x62704,x62701)+~E(x62701,f193(f881(x62702,a869)))
% 187.18/188.05 [6301]~P106(x63011)+E(f329(f329(f106(f881(x63011,a869)),f329(f299(x63011,x63012),x63013)),f300(x63011,x63013,x63014)),f193(f881(x63011,a869)))
% 187.18/188.05 [6328]~P24(f329(f329(x63283,x63284),x63282))+P24(f329(f329(f331(x63281),x63282),f290(x63281,x63283,x63284)))
% 187.18/188.05 [6329]~P24(f329(f329(x63293,x63294),x63292))+P24(f329(f329(f331(x63291),x63292),f291(x63291,x63293,x63294)))
% 187.18/188.05 [6330]~P24(f329(f329(x63303,x63302),x63304))+P24(f329(f329(f331(x63301),x63302),f292(x63301,x63303,x63304)))
% 187.18/188.05 [6331]~P24(f329(f329(x63313,x63312),x63314))+P24(f329(f329(f331(x63311),x63312),f295(x63311,x63313,x63314)))
% 187.18/188.05 [6469]~P106(x64691)+E(f329(f329(f106(f881(x64691,a869)),f300(x64691,x64692,x64693)),f303(x64691,x64693,x64694)),f193(f881(x64691,a869)))
% 187.18/188.05 [6470]~P106(x64701)+E(f329(f329(f106(f881(x64701,a869)),f300(x64701,x64702,x64703)),f302(x64701,x64703,x64704)),f193(f881(x64701,a869)))
% 187.18/188.05 [6471]~P106(x64711)+E(f329(f329(f106(f881(x64711,a869)),f303(x64711,x64712,x64713)),f300(x64711,x64713,x64714)),f193(f881(x64711,a869)))
% 187.18/188.05 [6472]~P106(x64721)+E(f329(f329(f106(f881(x64721,a869)),f302(x64721,x64722,x64723)),f303(x64721,x64723,x64724)),f193(f881(x64721,a869)))
% 187.18/188.05 [6473]~P106(x64731)+E(f329(f329(f106(f881(x64731,a869)),f302(x64731,x64732,x64733)),f302(x64731,x64733,x64734)),f193(f881(x64731,a869)))
% 187.18/188.05 [6511]P24(f329(f329(x65111,x65112),f520(x65112,x65111)))+~P24(f329(f258(x65113,x65114,x65111),x65112))
% 187.18/188.05 [6560]~E(f329(x65601,x65602),f206(x65603))+~P24(f329(f329(f331(x65604),x65602),f183(x65604,x65603,x65601)))
% 187.18/188.05 [6589]~P27(x65892)+E(f329(f171(x65891),f148(x65891,x65892,x65893,x65894)),f329(f171(x65891),x65894))
% 187.18/188.05 [6641]~P141(x66411)+E(f195(x66411,x66412,f329(a117,x66413),x66414),f195(x66411,x66412,x66413,f329(x66412,x66414)))
% 187.18/188.05 [6701]~P24(f329(f329(f331(x67014),x67013),f290(x67014,x67011,x67012)))+P24(f329(f329(x67011,x67012),x67013))
% 187.18/188.05 [6702]~P24(f329(f329(f331(x67024),x67023),f291(x67024,x67021,x67022)))+P24(f329(f329(x67021,x67022),x67023))
% 187.18/188.05 [6703]~P24(f329(f329(f331(x67034),x67032),f292(x67034,x67031,x67033)))+P24(f329(f329(x67031,x67032),x67033))
% 187.18/188.05 [6704]~P24(f329(f329(f331(x67044),x67042),f295(x67044,x67041,x67043)))+P24(f329(f329(x67041,x67042),x67043))
% 187.18/188.05 [6781]E(f329(f38(f879(x67811,x67812)),f316(x67811,x67812,x67813,x67814)),f2(a874))+P24(f329(f62(x67812),x67814))
% 187.18/188.05 [6782]E(f329(f38(f879(x67821,x67822)),f316(x67821,x67822,x67823,x67824)),f2(a874))+P24(f329(f62(x67821),x67823))
% 187.18/188.05 [6985]~P11(x69854,x69851,x69852)+E(f329(f73(x69851,x69851,x69851,f329(x69852,x69853)),f329(x69852,x69853)),f329(x69852,x69853))
% 187.18/188.05 [7789]~P24(f329(x77891,x77894))+P24(f329(x77891,f96(x77892,a874,x77893,x77891)))
% 187.18/188.05 [7873]~E(x78732,x78733)+P24(f329(f329(f331(f880(x78731,x78731)),f329(f329(f264(x78731,x78731),x78732),x78733)),f305(x78731,x78734)))
% 187.18/188.05 [7902]~P21(x79021,x79022,x79023,f252(f881(x79021,a869)))+E(f329(f77(x79021,x79022,f252(f881(x79021,a869)),x79023),f329(x79023,x79024)),x79024)
% 187.18/188.05 [7994]~P24(f329(f329(f331(f875(x79941)),f329(f329(f149(x79941),x79944),x79942)),f159(x79941,x79943)))+P24(f329(f329(f331(f875(x79941)),x79942),f159(x79941,x79943)))
% 187.18/188.05 [7995]~P24(f329(f329(f331(f875(x79951)),f329(f329(f126(x79951),x79954),x79952)),f159(x79951,x79953)))+P24(f329(f329(f331(f875(x79951)),x79952),f159(x79951,x79953)))
% 187.18/188.05 [7996]~P24(f329(f329(f331(f875(x79961)),f329(f329(f126(x79961),x79962),x79964)),f159(x79961,x79963)))+P24(f329(f329(f331(f875(x79961)),x79962),f159(x79961,x79963)))
% 187.18/188.05 [8012]~P27(x80121)+P33(x80121,f329(f329(f152(x80122,x80121),x80123),f148(x80122,x80121,x80123,x80124)))
% 187.18/188.05 [8110]P21(x81104,x81103,x81101,x81102)+E(f329(x81101,f509(x81102,x81101,x81103,x81104)),f329(x81101,f510(x81102,x81101,x81103,x81104)))
% 187.18/188.05 [8123]E(f184(x81231,x81232,x81233,x81234),f184(x81231,x81232,x81234,x81233))+~E(f329(f329(f106(f881(x81231,a869)),f183(x81231,x81232,x81233)),f183(x81231,x81232,x81234)),f193(f881(x81231,a869)))
% 187.18/188.05 [8226]~P21(x82262,x82261,x82264,x82263)+P21(x82261,x82262,f77(x82262,x82261,x82263,x82264),f329(f308(x82262,x82261,x82264),x82263))
% 187.18/188.05 [8362]P42(f880(x83622,x83624),f281(x83622,x83624,x83621,x83623))+P24(f329(x83621,f522(x83622,x83623,x83624,x83621)))
% 187.18/188.05 [8485]E(x84851,x84852)+~P24(f329(f329(f331(f880(x84853,x84853)),f329(f329(f264(x84853,x84853),x84851),x84852)),f261(x84853,x84854)))
% 187.18/188.05 [8549]~P24(f329(f62(f879(x85493,x85491)),f316(x85493,x85491,x85494,x85492)))+P24(f329(f62(x85491),x85492))
% 187.18/188.05 [8550]~P24(f329(f62(f879(x85501,x85503)),f316(x85501,x85503,x85502,x85504)))+P24(f329(f62(x85501),x85502))
% 187.18/188.05 [8728]P42(f880(x87281,x87282),f281(x87281,x87282,x87283,x87284))+~P42(x87282,f329(x87284,f522(x87281,x87284,x87282,x87283)))
% 187.18/188.05 [9291]E(f329(f329(f157(x92911,x92912),f686(x92913,x92914,x92912,x92911)),f687(x92913,x92914,x92912,x92911)),x92914)+~P24(f329(f329(f331(f880(f875(x92911),f875(x92911))),f329(f329(f264(f875(x92911),f875(x92911)),x92912),x92914)),f155(x92911,x92913)))
% 187.18/188.05 [9292]~P24(f329(x92923,x92924))+P24(f329(f329(f243(a874),f329(x92921,f96(x92922,a874,x92921,x92923))),f329(x92921,x92924)))
% 187.18/188.05 [9298]~P24(f329(f329(f331(f880(f875(x92981),f875(x92981))),f329(f329(f264(f875(x92981),f875(x92981)),x92982),x92983)),f143(x92981,x92984)))+P24(f329(f329(f331(f880(f875(x92981),f875(x92981))),f329(f329(f264(f875(x92981),f875(x92981)),x92982),x92983)),f145(x92981,x92984)))
% 187.18/188.05 [9403]P24(f329(f62(x94031),x94032))+~P24(f329(f329(f331(f880(f881(x94031,a869),f881(x94031,a869))),f329(f329(f264(f881(x94031,a869),f881(x94031,a869)),x94033),x94032)),f321(x94031,x94034)))
% 187.18/188.05 [9404]P24(f329(f62(x94041),x94042))+~P24(f329(f329(f331(f880(f881(x94041,a869),f881(x94041,a869))),f329(f329(f264(f881(x94041,a869),f881(x94041,a869)),x94042),x94043)),f321(x94041,x94044)))
% 187.18/188.05 [9407]~E(x94071,f193(f881(x94072,a869)))+~P24(f329(f329(f331(f880(f881(x94072,a869),f881(x94072,a869))),f329(f329(f264(f881(x94072,a869),f881(x94072,a869)),x94073),x94071)),f321(x94072,x94074)))
% 187.18/188.05 [10044]P9(x100441,x100442,x100443,x100444)+~P24(f329(f329(f268(x100441,x100441,a869),f329(f329(f7(x100441,f881(x100441,x100442),f881(x100441,a869)),f329(f329(f8(f881(x100442,a869),f881(f881(x100441,x100442),f881(x100441,a869)),x100441),f8(x100442,a869,x100441)),f329(f329(f8(x100442,f881(x100442,a869),x100441),a326),x100444))),x100444)),f562(x100444,x100443,x100442,x100441)))
% 187.18/188.05 [4937]~E(x49372,f118(x49371))+E(f329(f329(f157(x49371,x49372),x49373),x49374),f118(x49371))
% 187.18/188.05 [4938]~E(x49384,f118(x49381))+E(f329(f329(f152(x49381,x49382),x49383),x49384),f118(x49382))
% 187.18/188.05 [4939]~E(x49394,f206(x49391))+E(f329(f329(f207(x49391,x49392),x49393),x49394),f206(x49392))
% 187.18/188.05 [5178]E(x51781,f118(x51782))+~E(f329(f329(f152(x51782,x51783),x51784),x51781),f118(x51783))
% 187.18/188.05 [5179]E(x51791,f206(x51792))+~E(f329(f329(f207(x51792,x51793),x51794),x51791),f206(x51793))
% 187.18/188.05 [5180]E(x51801,f118(x51802))+~E(f329(f329(f157(x51802,x51801),x51803),x51804),f118(x51802))
% 187.18/188.05 [5212]E(x52121,x52122)+~E(f329(f329(f126(x52123),x52124),x52121),f329(f329(f126(x52123),x52124),x52122))
% 187.18/188.05 [5213]E(x52131,x52132)+~E(f329(f329(f126(x52133),x52131),x52134),f329(f329(f126(x52133),x52132),x52134))
% 187.18/188.05 [5367]P24(f329(x53673,x53672))+E(f168(x53671,x53672,f329(f134(x53671,x53673),x53674)),f329(f134(x53671,x53673),x53674))
% 187.18/188.05 [5370]~P24(f329(x53702,x53703))+P38(x53701,x53702,f329(f329(f149(x53701),x53703),x53704))
% 187.18/188.05 [5379]E(x53791,x53792)+~E(f137(a874,f329(f299(a874,x53791),x53793)),f329(f329(f149(a874),x53792),x53794))
% 187.18/188.05 [5427]~P22(x54272,x54273)+P22(x54271,f329(f329(f74(x54272,x54271),x54273),x54274))
% 187.18/188.05 [5428]~P42(x54282,x54283)+P42(x54281,f329(f329(f285(x54282,x54281),x54283),x54284))
% 187.18/188.05 [5552]~P38(x55521,x55522,x55524)+P38(x55521,x55522,f329(f329(f149(x55521),x55523),x55524))
% 187.18/188.05 [5553]~P38(x55531,x55532,x55534)+P38(x55531,x55532,f329(f329(f126(x55531),x55533),x55534))
% 187.18/188.05 [5554]~P38(x55541,x55542,x55543)+P38(x55541,x55542,f329(f329(f126(x55541),x55543),x55544))
% 187.18/188.05 [5640]~E(x56401,f118(x56402))+~E(f329(f329(f126(x56402),x56403),f329(f329(f149(x56402),x56404),f118(x56402))),x56401)
% 187.18/188.05 [5665]~P36(x56653,x56651,f329(f329(f149(x56653),x56652),x56654))+P24(f329(x56651,x56652))
% 187.18/188.05 [5675]E(f119(x56751,x56752),x56753)+~E(f329(f329(f126(x56751),x56753),f329(f329(f149(x56751),x56754),f118(x56751))),x56752)
% 187.18/188.05 [5676]E(f142(x56761,x56762),x56763)+~E(f329(f329(f126(x56761),x56764),f329(f329(f149(x56761),x56763),f118(x56761))),x56762)
% 187.18/188.05 [5786]~E(f137(a874,f329(f299(a874,x57861),x57862)),f329(f329(f149(a874),x57863),x57864))+P24(f329(f329(f244(a874),x57861),x57862))
% 187.18/188.05 [5794]P36(x57941,x57942,x57943)+~P36(x57941,x57942,f329(f329(f149(x57941),x57944),x57943))
% 187.18/188.05 [5795]P36(x57951,x57952,x57953)+~P36(x57951,x57952,f329(f329(f126(x57951),x57954),x57953))
% 187.18/188.05 [5796]P36(x57961,x57962,x57963)+~P36(x57961,x57962,f329(f329(f126(x57961),x57963),x57964))
% 187.18/188.05 [5985]E(x59851,f329(f329(f126(x59852),f329(f167(x59852),x59853)),f329(f329(f149(x59852),x59854),f118(x59852))))+~E(f329(f167(x59852),x59851),f329(f329(f149(x59852),x59854),x59853))
% 187.18/188.05 [6162]~P106(x61621)+E(f329(f329(f106(f881(x61621,a869)),f329(f299(x61621,x61622),x61623)),f329(f299(x61621,x61623),x61624)),f193(f881(x61621,a869)))
% 187.18/188.05 [6172]E(f329(f329(f163(x61721),f169(x61721,x61722,x61723)),x61724),x61723)+~P24(f329(f329(f244(a874),x61724),x61722))
% 187.18/188.05 [6199]~P72(x61991)+E(f329(f164(x61991),f329(f329(f152(a1,x61991),x61992),f178(x61993,x61994))),f329(f329(f6(a1,x61991),x61992),f329(f171(a1),f178(x61993,x61994))))
% 187.18/188.05 [6200]~P72(x62001)+E(f329(f329(f6(a1,x62001),x62002),f329(f171(a1),f178(x62003,x62004))),f329(f164(x62001),f329(f329(f152(a1,x62001),x62002),f178(x62003,x62004))))
% 187.18/188.05 [6341]~E(x63412,f329(f329(f126(x63411),f329(f167(x63411),x63414)),f329(f329(f149(x63411),x63413),f118(x63411))))+E(f329(f167(x63411),x63412),f329(f329(f149(x63411),x63413),x63414))
% 187.18/188.05 [6356]~P15(x63562,x63563,x63564,x63561)+E(f329(x63561,f193(f881(x63562,a869))),f34(x63563))
% 187.18/188.05 [6382]~P106(x63821)+E(f329(f329(f106(f881(x63821,a869)),f303(x63821,x63822,x63823)),f329(f299(x63821,x63823),x63824)),f193(f881(x63821,a869)))
% 187.18/188.05 [6590]E(x65901,f193(f881(x65902,a869)))+~E(f316(x65903,x65902,x65904,x65901),f193(f881(f879(x65903,x65902),a869)))
% 187.18/188.05 [6591]E(x65911,f193(f881(x65912,a869)))+~E(f316(x65912,x65913,x65911,x65914),f193(f881(f879(x65912,x65913),a869)))
% 187.18/188.05 [6660]~P27(x66602)+E(f329(f194(f875(x66601)),f148(x66601,x66602,x66603,x66604)),f329(f194(f875(x66601)),x66604))
% 187.18/188.05 [6672]~P24(f329(f259(x66723,x66724,x66721),x66722))+P24(f329(f329(x66721,f521(x66722,x66721)),x66722))
% 187.18/188.05 [6712]~P24(f329(f62(x67122),x67124))+P24(f329(f62(x67121),f329(f308(x67122,x67121,x67123),x67124)))
% 187.18/188.05 [6945]~P21(x69452,x69451,x69453,x69454)+E(f329(f38(x69451),f329(f308(x69452,x69451,x69453),x69454)),f329(f38(x69452),x69454))
% 187.18/188.05 [6964]E(f329(f308(x69641,x69642,x69643),f329(f309(x69641,x69642,x69643),x69644)),x69644)+~E(f329(f308(x69641,x69642,x69643),f252(f881(x69641,a869))),f252(f881(x69642,a869)))
% 187.18/188.05 [7374]~P21(x73741,x73742,x73743,f252(f881(x73741,a869)))+E(f329(f309(x73741,x73742,x73743),f329(f308(x73741,x73742,x73743),x73744)),x73744)
% 187.18/188.05 [7662]E(x76621,x76622)+~P24(f329(f329(f331(x76623),x76621),f329(f171(x76623),f169(x76623,x76624,x76622))))
% 187.18/188.05 [7672]~E(x76721,f2(a874))+~P24(f329(f329(f331(x76722),x76723),f329(f171(x76722),f169(x76722,x76721,x76724))))
% 187.18/188.05 [7709]P24(f329(x77091,x77092))+~P24(f329(f329(f331(x77093),x77092),f329(f171(x77093),f176(x77093,x77091,x77094))))
% 187.18/188.05 [7820]~P24(f329(f329(f331(f875(x78201)),f329(f329(f149(x78201),x78202),x78204)),f159(x78201,x78203)))+P24(f329(f329(f331(x78201),x78202),x78203))
% 187.18/188.05 [7949]~P24(f329(f329(f331(x79491),x79492),f329(f171(x79491),f175(x79491,x79493,x79494))))+P24(f329(f329(f331(x79491),x79492),f329(f171(x79491),x79493)))
% 187.18/188.05 [7950]~P24(f329(f329(f331(x79501),x79502),f329(f171(x79501),f168(x79501,x79504,x79503))))+P24(f329(f329(f331(x79501),x79502),f329(f171(x79501),x79503)))
% 187.18/188.05 [7951]~P24(f329(f329(f331(x79511),x79512),f329(f171(x79511),f176(x79511,x79514,x79513))))+P24(f329(f329(f331(x79511),x79512),f329(f171(x79511),x79513)))
% 187.18/188.05 [7961]E(f329(f194(f875(x79611)),x79612),x79613)+~P24(f329(f329(f331(f875(x79611)),x79612),f329(f171(f875(x79611)),f55(x79611,x79613,x79614))))
% 187.18/188.05 [8060]P24(f329(x80603,x80602))+E(f329(f134(x80601,f329(f329(f8(a869,a869,x80601),a324),f329(a326,x80602))),f329(f134(x80601,x80603),x80604)),f329(f134(x80601,x80603),x80604))
% 187.18/188.05 [8175]E(f329(f329(f163(x81751),f176(x81751,x81752,x81753)),x81754),f329(f329(f163(x81751),x81753),x81754))+~P24(f329(f329(f244(a874),x81754),f329(f194(f875(x81751)),f176(x81751,x81752,x81753))))
% 187.18/188.05 [8261]~P72(x82611)+E(f329(f329(f6(a874,x82611),f329(f329(f8(a874,x82611,a874),x82612),a117)),f329(f299(a874,x82613),x82614)),f329(f329(f6(a874,x82611),x82612),f329(f299(a874,f329(a117,x82613)),f329(a117,x82614))))
% 187.18/188.05 [8270]~P72(x82701)+E(f329(f329(f6(a874,x82701),f329(f329(f8(a874,x82701,a874),x82702),a117)),f300(a874,x82703,x82704)),f329(f329(f6(a874,x82701),x82702),f300(a874,f329(a117,x82703),f329(a117,x82704))))
% 187.18/188.05 [8399]~P21(x83991,x83993,x83994,f252(f881(x83991,a869)))+P21(x83991,f881(x83992,x83993),f329(f329(f8(x83993,f881(x83992,x83993),x83991),f16(x83993,x83992)),x83994),f252(f881(x83991,a869)))
% 187.18/188.05 [8493]~P21(x84932,x84931,x84934,x84933)+E(f329(f308(x84931,x84932,f77(x84932,x84931,x84933,x84934)),f329(f308(x84932,x84931,x84934),x84933)),x84933)
% 187.18/188.05 [8551]~P24(f329(f329(f331(f880(x85511,x85511)),f329(f329(f264(x85511,x85511),x85512),x85514)),f261(x85511,x85513)))+P24(f329(f329(f331(x85511),x85512),x85513))
% 187.18/188.05 [8640]E(f329(f329(f329(f72(x86401,f878(x86402)),f329(f16(f878(x86402),x86401),f206(x86402))),x86403),f329(f236(x86402),f721(x86403,x86404,x86402,x86401))),x86404)+~E(f183(x86401,x86402,x86404),f329(f329(f307(x86401),x86403),f193(f881(x86401,a869))))
% 187.18/188.05 [8763]~E(f329(f329(f6(x87631,a874),x87634),x87633),f329(a117,x87632))+P24(f329(f329(f331(x87631),f451(x87632,x87633,x87634,x87631)),x87633))
% 187.18/188.05 [8783]~E(f329(f329(f6(x87834,a874),x87831),x87833),f329(a117,x87832))+P24(f329(f329(f244(a874),f2(a874)),f329(x87831,f451(x87832,x87833,x87831,x87834))))
% 187.18/188.05 [8794]~P24(f329(f62(x87942),x87944))+P24(f329(f329(f243(a874),f329(f38(x87941),f329(f308(x87942,x87941,x87943),x87944))),f329(f38(x87942),x87944)))
% 187.18/188.05 [8795]E(f329(f329(f264(x87951,x87952),f657(x87953,x87954,x87952,x87951)),f658(x87953,x87954,x87952,x87951)),x87954)+~P24(f329(f329(f331(f880(x87951,x87952)),x87954),f329(f284(x87952,x87951),x87953)))
% 187.18/188.05 [8803]P21(x88031,x88032,x88033,x88034)+P24(f329(f329(f331(x88031),f509(x88034,x88033,x88032,x88031)),x88034))
% 187.18/188.05 [8804]P21(x88041,x88042,x88043,x88044)+P24(f329(f329(f331(x88041),f510(x88044,x88043,x88042,x88041)),x88044))
% 187.18/188.05 [8865]P9(x88651,x88652,x88653,x88654)+P24(f329(f329(f331(f880(x88651,x88651)),f562(x88654,x88653,x88652,x88651)),x88653))
% 187.18/188.05 [8928]P24(f329(x89281,x89282))+~P24(f329(x89281,f329(f329(f264(x89283,x89284),f481(x89284,x89283,x89281)),f483(x89284,x89283,x89281))))
% 187.18/188.05 [8945]E(f329(f194(f875(x89451)),x89452),f329(f194(f875(x89451)),x89453))+~P24(f329(f329(f331(f880(f875(x89451),f875(x89451))),f329(f329(f264(f875(x89451),f875(x89451)),x89452),x89453)),f143(x89451,x89454)))
% 187.18/188.05 [8946]E(f329(f194(f875(x89461)),x89462),f329(f194(f875(x89461)),x89463))+~P24(f329(f329(f331(f880(f875(x89461),f875(x89461))),f329(f329(f264(f875(x89461),f875(x89461)),x89462),x89463)),f155(x89461,x89464)))
% 187.18/188.05 [8949]E(f329(f194(f875(x89491)),x89492),f329(f194(f875(x89491)),x89493))+~P24(f329(f329(f331(f880(f875(x89491),f875(x89491))),f329(f329(f264(f875(x89491),f875(x89491)),x89492),x89493)),f156(x89491,x89494)))
% 187.18/188.05 [9024]P24(f329(f329(f243(a874),f153(x90241,x90242,x90243)),f153(x90241,x90244,x90243)))+P24(f329(f329(f331(x90241),f685(x90244,x90242,x90243,x90241)),f329(f171(x90241),x90243)))
% 187.18/188.05 [9027]E(f329(f194(f875(x90271)),x90272),f329(f194(f875(x90271)),x90273))+~P24(f329(f329(f331(f880(f875(x90271),f875(x90271))),f329(f329(f264(f875(x90271),f875(x90271)),x90272),x90273)),f305(f875(x90271),f155(x90271,x90274))))
% 187.18/188.05 [9263]~P21(x92631,x92632,x92633,x92634)+~P24(f329(f329(f244(a874),f329(f38(x92632),f329(f308(x92631,x92632,x92633),x92634))),f329(f38(x92631),x92634)))
% 187.18/188.05 [9309]~P24(f329(f329(f331(f880(f875(x93091),f875(x93091))),f329(f329(f264(f875(x93091),f875(x93091)),x93092),x93093)),f155(x93091,x93094)))+P24(f329(f329(f331(f880(f875(x93091),f875(x93091))),f329(f329(f264(f875(x93091),f875(x93091)),x93092),x93093)),f156(x93091,f305(x93091,x93094))))
% 187.18/188.05 [9313]~P24(f329(f329(f331(f880(f875(x93131),f875(x93131))),f329(f329(f264(f875(x93131),f875(x93131)),x93132),x93133)),f156(x93131,x93134)))+P24(f329(f329(f331(f880(f875(x93131),f875(x93131))),f329(f329(f264(f875(x93131),f875(x93131)),x93132),x93133)),f305(f875(x93131),f155(x93131,x93134))))
% 187.18/188.05 [9330]P24(f329(f329(f331(f880(x93301,x93301)),f329(f329(f264(x93301,x93301),x93302),x93303)),f305(x93301,x93304)))+~P24(f329(f329(f331(f880(x93301,x93301)),f329(f329(f264(x93301,x93301),x93302),x93303)),f329(f329(f286(x93301,x93301,x93301),x93304),f305(x93301,x93304))))
% 187.18/188.05 [9512]E(f329(f329(f126(x95121),f698(x95122,x95123,x95124,x95121)),f329(f329(f149(x95121),f699(x95122,x95123,x95124,x95121)),f702(x95122,x95123,x95124,x95121))),x95124)+~P24(f329(f329(f331(f880(f875(x95121),f875(x95121))),f329(f329(f264(f875(x95121),f875(x95121)),x95124),x95123)),f155(x95121,x95122)))
% 187.18/188.05 [9513]E(f329(f329(f126(x95131),f698(x95132,x95133,x95134,x95131)),f329(f329(f149(x95131),f700(x95132,x95133,x95134,x95131)),f702(x95132,x95133,x95134,x95131))),x95133)+~P24(f329(f329(f331(f880(f875(x95131),f875(x95131))),f329(f329(f264(f875(x95131),f875(x95131)),x95134),x95133)),f155(x95131,x95132)))
% 187.18/188.05 [9589]P24(f329(f329(f331(f880(x95891,x95891)),f329(f329(f264(x95891,x95891),x95892),f620(x95893,x95894,x95892,x95891))),f305(x95891,x95893)))+~P24(f329(f329(f331(f880(x95891,x95891)),f329(f329(f264(x95891,x95891),x95892),x95894)),f329(f329(f286(x95891,x95891,x95891),x95893),f305(x95891,x95893))))
% 187.18/188.05 [9658]P24(f329(f329(f243(a874),f153(x96581,x96582,x96583)),f153(x96581,x96584,x96583)))+~P24(f329(f329(f244(a874),f329(x96582,f685(x96584,x96582,x96583,x96581))),f329(x96584,f685(x96584,x96582,x96583,x96581))))
% 187.18/188.05 [9726]P24(f329(f329(f331(f880(x97261,x97261)),f329(f329(f264(x97261,x97261),f619(x97262,x97263,x97264,x97261)),x97263)),f305(x97261,x97262)))+~P24(f329(f329(f331(f880(x97261,x97261)),f329(f329(f264(x97261,x97261),x97264),x97263)),f329(f329(f286(x97261,x97261,x97261),x97262),f305(x97261,x97262))))
% 187.18/188.05 [5194]~E(x51942,x51943)+E(f168(x51941,x51942,f329(f329(f149(x51941),x51943),x51944)),x51944)
% 187.18/188.05 [5322]P24(f329(x53222,x53223))+E(f176(x53221,x53222,f329(f329(f149(x53221),x53223),x53224)),f118(x53221))
% 187.18/188.05 [5391]~P90(x53912)+E(f329(f329(f79(f881(x53911,x53912)),x53913),x53914),f329(f79(x53912),f329(x53913,x53914)))
% 187.18/188.05 [5403]~E(x54032,f2(a874))+E(f329(f329(f136(x54031),x54032),f329(f329(f149(x54031),x54033),x54034)),f329(f329(f149(x54031),x54033),x54034))
% 187.18/188.05 [5404]P24(f329(x54042,x54043))+E(f329(f134(x54041,x54042),f329(f329(f149(x54041),x54043),x54044)),f329(f134(x54041,x54042),x54044))
% 187.18/188.05 [5535]~E(x55352,x55354)+P24(f329(f329(f329(f307(x55351),x55352),x55353),x55354))
% 187.18/188.05 [5543]E(x55431,f118(x55432))+E(f142(x55433,f329(f329(f152(x55432,x55433),x55434),x55431)),f329(x55434,f142(x55432,x55431)))
% 187.18/188.05 [5557]~E(x55571,f64(x55572,x55574))+E(f329(x55571,f329(f329(f307(x55572),x55573),f193(f881(x55572,a869)))),x55573)
% 187.18/188.05 [5592]E(x55921,f118(x55922))+E(f329(f139(x55923),f329(f329(f152(x55922,x55923),x55924),x55921)),f329(x55924,f329(f139(x55922),x55921)))
% 187.18/188.05 [5695]~P24(f329(x56953,x56954))+P24(f329(f329(f329(f307(x56951),x56952),x56953),x56954))
% 187.18/188.05 [5811]~P14(x58112,x58114,x58111)+E(f329(x58111,f329(f329(f307(x58112),x58113),f193(f881(x58112,a869)))),x58113)
% 187.18/188.05 [5835]~E(x58352,x58353)+P24(f329(f329(f331(x58351),x58352),f329(f329(f307(x58351),x58353),x58354)))
% 187.18/188.05 [5839]~P66(x58391)+E(f329(f329(f115(x58391),x58392),f329(f329(f115(x58391),x58393),x58394)),f329(f329(f115(x58391),x58393),f329(f329(f115(x58391),x58392),x58394)))
% 187.18/188.05 [5841]~P102(x58411)+E(f329(f329(f115(x58411),x58412),f329(f329(f115(x58411),x58413),x58414)),f329(f329(f115(x58411),x58413),f329(f329(f115(x58411),x58412),x58414)))
% 187.18/188.05 [5842]~P66(x58421)+E(f329(f329(f106(x58421),x58422),f329(f329(f106(x58421),x58423),x58424)),f329(f329(f106(x58421),x58423),f329(f329(f106(x58421),x58422),x58424)))
% 187.18/188.05 [5844]~P103(x58441)+E(f329(f329(f106(x58441),x58442),f329(f329(f106(x58441),x58443),x58444)),f329(f329(f106(x58441),x58443),f329(f329(f106(x58441),x58442),x58444)))
% 187.18/188.05 [5845]~P109(x58451)+E(f329(f329(f81(x58451),x58452),f329(f329(f81(x58451),x58453),x58454)),f329(f329(f81(x58451),x58453),f329(f329(f81(x58451),x58452),x58454)))
% 187.18/188.05 [5846]~P109(x58461)+E(f329(f329(f80(x58461),x58462),f329(f329(f80(x58461),x58463),x58464)),f329(f329(f80(x58461),x58463),f329(f329(f80(x58461),x58462),x58464)))
% 187.18/188.05 [5848]~P27(x58481)+E(f329(f329(f241(x58481),x58482),f329(f329(f241(x58481),x58483),x58484)),f329(f329(f241(x58481),x58483),f329(f329(f241(x58481),x58482),x58484)))
% 187.18/188.05 [5850]~P27(x58501)+E(f329(f329(f242(x58501),x58502),f329(f329(f242(x58501),x58503),x58504)),f329(f329(f242(x58501),x58503),f329(f329(f242(x58501),x58502),x58504)))
% 187.18/188.05 [5855]E(x58551,x58552)+E(f168(x58553,x58551,f329(f329(f149(x58553),x58552),x58554)),f329(f329(f149(x58553),x58552),f168(x58553,x58551,x58554)))
% 187.18/188.05 [5868]~P24(f329(x58682,x58683))+E(f329(f134(x58681,x58682),f329(f329(f149(x58681),x58683),x58684)),f329(f329(f149(x58681),x58683),f329(f134(x58681,x58682),x58684)))
% 187.18/188.05 [6005]~P24(f329(x60052,x60053))+E(f176(x60051,x60052,f329(f329(f149(x60051),x60053),x60054)),f329(f329(f149(x60051),x60053),f176(x60051,x60052,x60054)))
% 187.18/188.05 [6056]P20(x60561,x60562,x60563)+~P20(x60561,x60562,f329(f329(f307(f873(x60561)),x60564),x60563))
% 187.18/188.05 [6069]E(x60691,f193(f881(x60692,a869)))+E(f329(f329(f42(x60692,f881(x60693,a869)),x60691),f329(f16(f881(x60693,a869),x60692),x60694)),x60694)
% 187.18/188.05 [6070]E(x60701,f193(f881(x60702,a869)))+E(f329(f329(f43(x60702,f881(x60703,a869)),x60701),f329(f16(f881(x60703,a869),x60702),x60704)),x60704)
% 187.18/188.05 [6079]~E(x60794,f193(f881(x60792,a869)))+E(f329(f329(f266(x60791,x60792),x60793),f329(f16(f881(x60792,a869),x60791),x60794)),f193(f881(f880(x60791,x60792),a869)))
% 187.18/188.05 [6080]~E(x60803,f193(f881(x60801,a869)))+E(f329(f329(f266(x60801,x60802),x60803),f329(f16(f881(x60802,a869),x60801),x60804)),f193(f881(f880(x60801,x60802),a869)))
% 187.18/188.05 [6126]E(x61261,f2(a874))+E(f329(f329(f136(x61262),x61261),f329(f329(f149(x61262),x61263),x61264)),f329(f329(f136(x61262),f329(f329(f22(a874),x61261),f78(a874))),x61264))
% 187.18/188.05 [6156]E(x61561,f193(f881(x61562,a869)))+E(f329(f308(x61562,x61563,f329(f16(x61563,x61562),x61564)),x61561),f329(f329(f307(x61563),x61564),f193(f881(x61563,a869))))
% 187.18/188.05 [6159]E(f329(f309(x61591,x61592,f329(f16(x61592,x61591),x61593)),x61594),f193(f881(x61591,a869)))+P24(f329(f329(f331(x61592),x61593),x61594))
% 187.18/188.05 [6225]~E(x62253,f193(f881(x62251,a869)))+E(f329(f329(f42(x62251,f881(x62252,a869)),x62253),f329(f16(f881(x62252,a869),x62251),x62254)),f193(f881(x62252,a869)))
% 187.18/188.05 [6226]~E(x62263,f193(f881(x62261,a869)))+E(f329(f329(f43(x62261,f881(x62262,a869)),x62263),f329(f16(f881(x62262,a869),x62261),x62264)),f252(f881(x62262,a869)))
% 187.18/188.05 [6228]~P29(x62281)+E(f45(x62281,f329(f329(f81(x62281),x62282),x62283),f329(f329(f81(x62281),x62282),x62284)),f329(f329(f81(x62281),x62282),f45(x62281,x62283,x62284)))
% 187.18/188.05 [6392]E(f329(f309(x63921,x63922,f329(f16(x63922,x63921),x63923)),x63924),f252(f881(x63921,a869)))+~P24(f329(f329(f331(x63922),x63923),x63924))
% 187.18/188.05 [6415]~P24(f329(f329(f331(x64151),x64152),x64154))+P24(f329(f329(f331(x64151),x64152),f329(f329(f307(x64151),x64153),x64154)))
% 187.18/188.05 [6420]P24(f329(x64201,x64202))+~P24(f329(f158(x64203,x64201),f329(f329(f149(x64203),x64202),x64204)))
% 187.18/188.05 [6429]~E(x64293,f329(f329(f22(a874),f329(f194(f875(x64291)),x64292)),f78(a874)))+E(f119(x64291,f329(f329(f157(x64291,x64292),x64293),x64294)),f119(x64291,x64292))
% 187.18/188.05 [6448]~P27(x64481)+E(f329(f329(f106(f881(x64481,a869)),f329(f298(x64481),x64482)),f300(x64481,x64483,x64484)),f300(x64481,x64483,f329(f329(f241(x64481),x64482),x64484)))
% 187.18/188.05 [6449]~P27(x64491)+E(f329(f329(f106(f881(x64491,a869)),f329(f251(x64491),x64492)),f300(x64491,x64493,x64494)),f300(x64491,f329(f329(f242(x64491),x64492),x64493),x64494))
% 187.18/188.05 [6464]E(f329(f329(f106(f881(x64641,a869)),x64642),f329(f329(f307(x64641),x64643),x64644)),f329(f329(f106(f881(x64641,a869)),x64642),x64644))+P24(f329(f329(f331(x64641),x64643),x64642))
% 187.18/188.05 [6476]E(f168(x64761,x64762,f329(f329(f126(x64761),x64763),x64764)),f329(f329(f126(x64761),x64763),f168(x64761,x64762,x64764)))+P24(f329(f329(f331(x64761),x64762),f329(f171(x64761),x64763)))
% 187.18/188.05 [6480]~P82(x64801)+E(f329(f329(f81(x64801),f329(f329(f254(x64801),x64802),x64803)),f329(f329(f254(x64801),x64802),x64804)),f329(f329(f254(x64801),x64802),f329(f329(f80(a874),x64803),x64804)))
% 187.18/188.05 [6481]~P109(x64811)+E(f329(f329(f81(x64811),f329(f329(f254(x64811),x64812),x64813)),f329(f329(f254(x64811),x64812),x64814)),f329(f329(f254(x64811),x64812),f329(f329(f80(a874),x64813),x64814)))
% 187.18/188.05 [6518]~P100(x65181)+E(f329(f329(f106(x65181),f329(f329(f115(x65181),x65182),x65183)),f329(f329(f115(x65181),x65182),x65184)),f329(f329(f115(x65181),x65182),f329(f329(f106(x65181),x65183),x65184)))
% 187.18/188.05 [6519]~P100(x65191)+E(f329(f329(f115(x65191),f329(f329(f106(x65191),x65192),x65193)),f329(f329(f106(x65191),x65192),x65194)),f329(f329(f106(x65191),x65192),f329(f329(f115(x65191),x65193),x65194)))
% 187.18/188.05 [6520]~P109(x65201)+E(f329(f329(f80(x65201),f329(f329(f81(x65201),x65202),x65203)),f329(f329(f81(x65201),x65202),x65204)),f329(f329(f81(x65201),x65202),f329(f329(f80(x65201),x65203),x65204)))
% 187.18/188.05 [6521]~P27(x65211)+E(f329(f329(f242(x65211),f329(f329(f241(x65211),x65212),x65213)),f329(f329(f241(x65211),x65212),x65214)),f329(f329(f241(x65211),x65212),f329(f329(f242(x65211),x65213),x65214)))
% 187.18/188.05 [6522]~P27(x65221)+E(f329(f329(f241(x65221),f329(f329(f242(x65221),x65222),x65223)),f329(f329(f242(x65221),x65222),x65224)),f329(f329(f242(x65221),x65222),f329(f329(f241(x65221),x65223),x65224)))
% 187.18/188.05 [6554]~P29(x65541)+E(f45(x65541,f329(f329(f81(x65541),x65542),x65543),f329(f329(f81(x65541),x65544),x65543)),f329(f329(f81(x65541),f45(x65541,x65542,x65544)),x65543))
% 187.18/188.05 [6557]~E(f329(f194(f875(x65571)),x65573),f329(f194(f875(x65572)),x65574))+E(f329(f329(f152(f880(x65571,x65572),x65572),f267(x65571,x65572)),f329(f329(f181(x65571,x65572),x65573),x65574)),x65574)
% 187.18/188.05 [6558]~E(f329(f194(f875(x65581)),x65583),f329(f194(f875(x65582)),x65584))+E(f329(f329(f152(f880(x65581,x65582),x65581),f263(x65581,x65582)),f329(f329(f181(x65581,x65582),x65583),x65584)),x65583)
% 187.18/188.05 [6564]P24(f329(f158(x65641,x65642),x65643))+~P24(f329(f158(x65641,x65642),f329(f329(f149(x65641),x65644),x65643)))
% 187.18/188.05 [6565]P24(f329(f158(x65651,x65652),x65653))+~P24(f329(f158(x65651,x65652),f329(f329(f126(x65651),x65654),x65653)))
% 187.18/188.05 [6566]P24(f329(f158(x65661,x65662),x65663))+~P24(f329(f158(x65661,x65662),f329(f329(f126(x65661),x65663),x65664)))
% 187.18/188.05 [6571]~P30(x65711)+E(f45(x65711,f329(f329(f22(x65711),x65712),f45(x65711,x65713,x65714)),x65714),f45(x65711,f329(f329(f22(x65711),x65712),x65713),x65714))
% 187.18/188.05 [6572]~P29(x65721)+E(f45(x65721,f329(f329(f81(x65721),x65722),f45(x65721,x65723,x65724)),x65724),f45(x65721,f329(f329(f81(x65721),x65722),x65723),x65724))
% 187.18/188.05 [6574]~P29(x65741)+E(f45(x65741,f329(f329(f80(x65741),x65742),f45(x65741,x65743,x65744)),x65744),f45(x65741,f329(f329(f80(x65741),x65742),x65743),x65744))
% 187.18/188.05 [6654]~P27(x66541)+E(f329(f329(f106(f881(x66541,a869)),f300(x66541,x66542,x66543)),f329(f298(x66541),x66544)),f300(x66541,x66542,f329(f329(f241(x66541),x66543),x66544)))
% 187.18/188.05 [6655]~P27(x66551)+E(f329(f329(f106(f881(x66551,a869)),f300(x66551,x66552,x66553)),f329(f251(x66551),x66554)),f300(x66551,f329(f329(f242(x66551),x66552),x66554),x66553))
% 187.18/188.05 [6658]~E(f329(f194(f875(x66581)),x66583),f329(f194(f875(x66582)),x66584))+E(f329(f329(f181(x66581,x66582),f329(f167(x66581),x66583)),f329(f167(x66582),x66584)),f329(f167(f880(x66581,x66582)),f329(f329(f181(x66581,x66582),x66583),x66584)))
% 187.18/188.05 [6668]E(x66681,f329(f329(f22(a874),f329(f194(f875(x66682)),x66683)),f78(a874)))+E(f119(x66682,f329(f329(f157(x66682,x66683),x66681),x66684)),f329(f329(f157(x66682,f119(x66682,x66683)),x66681),x66684))
% 187.18/188.05 [6683]~P24(f329(f135(x66832),x66834))+P24(f329(f135(f880(x66831,x66832)),f329(f329(f181(x66831,x66832),x66833),x66834)))
% 187.18/188.05 [6684]~P24(f329(f135(x66841),x66843))+P24(f329(f135(f880(x66841,x66842)),f329(f329(f181(x66841,x66842),x66843),x66844)))
% 187.18/188.05 [6948]E(f329(f329(f39(a874),x69481),x69482),x69483)+~P24(f329(f48(x69481,x69482),f329(f329(f264(a874,a874),x69483),x69484)))
% 187.18/188.05 [6972]E(f45(a874,x69721,x69722),x69723)+~P24(f329(f48(x69721,x69722),f329(f329(f264(a874,a874),x69724),x69723)))
% 187.18/188.05 [6975]P24(f329(f135(x69751),x69752))+~P24(f329(f135(x69753),f329(f329(f152(x69751,x69753),x69754),x69752)))
% 187.18/188.05 [6983]~P20(x69831,x69832,f329(f329(f307(f873(x69831)),x69833),x69834))+P20(x69831,x69832,f329(f329(f307(f873(x69831)),x69833),f193(f881(f873(x69831),a869))))
% 187.18/188.05 [6989]P24(f329(f329(f199(x69891),x69892),x69893))+~P24(f329(f329(f329(f329(a201,x69891),x69892),x69894),x69893))
% 187.18/188.05 [7061]E(f168(x70611,x70612,f329(f329(f126(x70611),x70613),x70614)),f329(f329(f126(x70611),f168(x70611,x70612,x70613)),x70614))+~P24(f329(f329(f331(x70611),x70612),f329(f171(x70611),x70613)))
% 187.18/188.05 [7151]~P30(x71511)+E(f45(x71511,f329(f329(f22(x71511),f45(x71511,x71512,x71513)),x71514),x71513),f45(x71511,f329(f329(f22(x71511),x71512),x71514),x71513))
% 187.18/188.05 [7154]~P29(x71541)+E(f45(x71541,f329(f329(f81(x71541),f45(x71541,x71542,x71543)),x71544),x71543),f45(x71541,f329(f329(f81(x71541),x71542),x71544),x71543))
% 187.18/188.05 [7155]~P29(x71551)+E(f45(x71551,f329(f329(f80(x71551),f45(x71551,x71552,x71553)),x71554),x71553),f45(x71551,f329(f329(f80(x71551),x71552),x71554),x71553))
% 187.18/188.05 [7345]~E(x73451,f329(f329(f149(x73452),x73453),x73454))+~P24(f329(f329(f243(a874),f329(f194(f875(x73452)),x73451)),f329(f194(f875(x73452)),x73454)))
% 187.18/188.05 [7421]~E(f329(f177(x74211,x74212),x74213),f329(f177(x74211,x74212),x74214))+E(f329(f308(f880(x74211,x74212),x74211,f263(x74211,x74212)),f329(f171(f880(x74211,x74212)),x74213)),f329(f308(f880(x74211,x74212),x74211,f263(x74211,x74212)),f329(f171(f880(x74211,x74212)),x74214)))
% 187.18/188.05 [7555]P21(x75551,x75552,x75553,f329(f171(x75551),x75554))+~P24(f329(f135(x75552),f329(f329(f152(x75551,x75552),x75553),x75554)))
% 187.18/188.05 [7629]~P24(f329(f329(f243(f881(x76291,a869)),x76292),x76294))+P24(f329(f329(f243(f881(x76291,a869)),x76292),f329(f329(f307(x76291),x76293),x76294)))
% 187.18/188.05 [7663]~P30(x76631)+E(f45(x76631,f329(f329(f22(x76631),f45(x76631,x76632,x76633)),f45(x76631,x76634,x76633)),x76633),f45(x76631,f329(f329(f22(x76631),x76632),x76634),x76633))
% 187.18/188.05 [7664]~P29(x76641)+E(f45(x76641,f329(f329(f81(x76641),f45(x76641,x76642,x76643)),f45(x76641,x76644,x76643)),x76643),f45(x76641,f329(f329(f81(x76641),x76642),x76644),x76643))
% 187.18/188.05 [7665]~P29(x76651)+E(f45(x76651,f329(f329(f80(x76651),f45(x76651,x76652,x76653)),f45(x76651,x76654,x76653)),x76653),f45(x76651,f329(f329(f80(x76651),x76652),x76654),x76653))
% 187.18/188.05 [7768]P24(f329(f329(f329(f329(a201,x77681),x77682),f329(a117,x77683)),x77684))+~P24(f329(f329(f329(f329(a201,x77681),x77682),x77683),x77684))
% 187.18/188.05 [7775]~E(f329(x77754,f422(x77754,x77753,x77751,x77752)),f193(f881(x77752,a869)))+E(f329(f329(f42(x77751,f881(x77752,a869)),x77753),x77754),f193(f881(x77752,a869)))
% 187.18/188.05 [7776]~E(f329(x77764,f603(x77764,x77763,x77761,x77762)),f252(f881(x77762,a869)))+E(f329(f329(f43(x77761,f881(x77762,a869)),x77763),x77764),f252(f881(x77762,a869)))
% 187.18/188.05 [7777]~E(f329(x77774,f423(x77774,x77773,x77772,x77771)),f193(f881(x77772,a869)))+E(f329(f329(f42(x77771,f881(x77772,a869)),x77773),x77774),f193(f881(x77772,a869)))
% 187.18/188.05 [7778]~E(f329(x77784,f604(x77784,x77783,x77782,x77781)),f252(f881(x77782,a869)))+E(f329(f329(f43(x77781,f881(x77782,a869)),x77783),x77784),f252(f881(x77782,a869)))
% 187.18/188.05 [8176]P24(f329(x81761,x81762))+~P24(f329(f329(f331(x81763),x81762),f329(f329(f106(f881(x81763,a869)),x81764),f329(f249(x81763),x81761))))
% 187.18/188.05 [8215]~P24(f329(f329(f243(f881(x82151,a869)),x82153),x82154))+P24(f329(f329(f243(f881(x82151,a869)),f329(f329(f307(x82151),x82152),x82153)),f329(f329(f307(x82151),x82152),x82154)))
% 187.18/188.05 [8382]P24(f329(f329(f199(x83821),x83822),f605(x83823,x83822,x83824,x83821)))+~P24(f329(f329(f199(f33(x83821,x83824)),x83822),x83823))
% 187.18/188.05 [8391]P24(f329(x83912,x83913))+E(f329(f329(f136(x83911),f329(f194(f875(x83911)),f176(x83911,x83912,f329(f329(f149(x83911),x83913),x83914)))),f329(f329(f149(x83911),x83913),x83914)),f329(f329(f149(x83911),x83913),x83914))
% 187.18/188.05 [8507]~P24(f329(f329(f244(a874),f329(x85074,x85072)),f329(x85074,x85073)))+P24(f329(f329(f331(f880(x85071,x85071)),f329(f329(f264(x85071,x85071),x85072),x85073)),f329(f329(f285(a874,x85071),a248),x85074)))
% 187.18/188.05 [8597]~P24(f329(x85972,f782(x85974,x85972,x85973,x85971)))+E(f176(x85971,x85972,f329(f329(f126(x85971),x85973),x85974)),f329(f329(f126(x85971),x85973),f176(x85971,x85972,x85974)))
% 187.18/188.05 [8668]P21(f875(x86681),f875(x86682),f329(f152(x86681,x86682),x86683),x86684)+~P21(x86681,x86682,x86683,f40(f881(x86681,a869),f329(f308(f875(x86681),f881(x86681,a869),f171(x86681)),x86684)))
% 187.18/188.05 [8735]~P24(f329(x87352,x87353))+E(f329(f329(f136(x87351),f329(f194(f875(x87351)),f176(x87351,x87352,f329(f329(f149(x87351),x87353),x87354)))),f329(f329(f149(x87351),x87353),x87354)),f329(f329(f136(x87351),f329(f194(f875(x87351)),f176(x87351,x87352,x87354))),x87354))
% 187.18/188.05 [8774]~E(x87742,x87743)+E(f329(f134(x87741,f329(f329(f8(a869,a869,x87741),a324),f329(a326,x87742))),f329(f329(f149(x87741),x87743),x87744)),f329(f134(x87741,f329(f329(f8(a869,a869,x87741),a324),f329(a326,x87742))),x87744))
% 187.18/188.05 [8784]E(f329(f329(f42(x87841,f881(x87842,a869)),x87843),x87844),f193(f881(x87842,a869)))+P24(f329(f329(f331(x87841),f422(x87844,x87843,x87841,x87842)),x87843))
% 187.18/188.05 [8785]E(f329(f329(f43(x87851,f881(x87852,a869)),x87853),x87854),f252(f881(x87852,a869)))+P24(f329(f329(f331(x87851),f603(x87854,x87853,x87851,x87852)),x87853))
% 187.18/188.05 [8786]E(f329(f329(f42(x87861,f881(x87862,a869)),x87863),x87864),f193(f881(x87862,a869)))+P24(f329(f329(f331(x87861),f423(x87864,x87863,x87862,x87861)),x87863))
% 187.18/188.05 [8787]E(f329(f329(f43(x87871,f881(x87872,a869)),x87873),x87874),f252(f881(x87872,a869)))+P24(f329(f329(f331(x87871),f604(x87874,x87873,x87872,x87871)),x87873))
% 187.18/188.05 [8823]P24(f329(f329(f244(a874),f329(x88231,x88232)),f329(x88231,x88233)))+~P24(f329(f329(f331(f880(x88234,x88234)),f329(f329(f264(x88234,x88234),x88232),x88233)),f329(f329(f285(a874,x88234),a248),x88231)))
% 187.18/188.05 [8844]E(f176(x88441,x88442,f329(f329(f126(x88441),x88443),x88444)),f329(f329(f126(x88441),x88443),f176(x88441,x88442,x88444)))+P24(f329(f329(f331(x88441),f782(x88444,x88442,x88443,x88441)),f329(f171(x88441),x88443)))
% 187.18/188.05 [8881]P24(f329(f329(f199(x88811),f605(x88812,x88813,x88811,x88814)),x88812))+~P24(f329(f329(f199(f33(x88814,x88811)),x88813),x88812))
% 187.18/188.05 [9013]P24(f329(f329(f331(x90131),f497(x90132,x90133,x90134,x90131)),x90133))+~P24(f329(f329(f331(f881(x90131,a869)),x90134),f329(f329(f61(x90131),x90133),x90132)))
% 187.18/188.05 [9016]E(x90161,x90162)+~P24(f329(f329(f331(f880(x90163,x90163)),f329(f329(f264(x90163,x90163),x90161),x90162)),f329(f329(f188(f880(x90163,x90163),a869),f2(a874)),x90164)))
% 187.18/188.05 [9095]E(f329(f283(x90951,x90951,x90952),f329(f329(f307(x90951),f497(x90952,x90953,x90954,x90951)),f193(f881(x90951,a869)))),x90954)+~P24(f329(f329(f331(f881(x90951,a869)),x90954),f329(f329(f61(x90951),x90953),x90952)))
% 187.18/188.05 [9100]~P24(f329(f329(f331(f880(x91001,x91001)),f329(f329(f264(x91001,x91001),x91003),x91002)),f305(x91001,x91004)))+P24(f329(f329(f331(f880(x91001,x91001)),f329(f329(f264(x91001,x91001),x91002),x91003)),f305(x91001,f329(f284(x91001,x91001),x91004))))
% 187.18/188.05 [9112]~P29(x91121)+E(f329(f329(f80(x91121),f329(f329(f80(x91121),f329(f329(f81(x91121),x91122),f329(f329(f39(x91121),x91123),x91122))),f45(x91121,x91123,x91122))),x91124),f329(f329(f80(x91121),x91123),x91124))
% 187.18/188.05 [9122]~P24(f329(f329(f331(x91221),x91223),x91224))+P24(f329(f329(f331(f881(x91221,a869)),f329(f283(x91221,x91221,x91222),f329(f329(f307(x91221),x91223),f193(f881(x91221,a869))))),f329(f329(f61(x91221),x91224),x91222)))
% 187.18/188.05 [9133]P24(f329(f329(f331(f880(x91331,x91331)),f329(f329(f264(x91331,x91331),x91332),x91333)),f305(x91331,x91334)))+~P24(f329(f329(f331(f880(x91331,x91331)),f329(f329(f264(x91331,x91331),x91333),x91332)),f305(x91331,f329(f284(x91331,x91331),x91334))))
% 187.18/188.05 [9225]E(f329(f329(f157(x92251,f329(f167(x92251),x92252)),f329(f329(f22(a874),f329(f329(f22(a874),f329(f194(f875(x92251)),x92252)),x92253)),f78(a874))),x92254),f329(f167(x92251),f329(f329(f157(x92251,x92252),x92253),x92254)))+~P24(f329(f329(f244(a874),x92253),f329(f194(f875(x92251)),x92252)))
% 187.18/188.05 [9228]~P24(f329(x92282,f773(x92284,x92282,x92283,x92281)))+E(f329(f329(f136(x92281),f329(f194(f875(x92281)),f176(x92281,x92282,f329(f329(f126(x92281),x92283),x92284)))),f329(f329(f126(x92281),x92283),x92284)),f329(f329(f136(x92281),f329(f194(f875(x92281)),f176(x92281,x92282,x92284))),x92284))
% 187.18/188.05 [9269]~P21(x92692,x92691,x92693,f252(f881(x92692,a869)))+P24(f329(f329(f243(f881(x92691,a869)),f329(f308(x92692,x92691,x92693),f329(f79(f881(x92692,a869)),x92694))),f329(f79(f881(x92691,a869)),f329(f308(x92692,x92691,x92693),x92694))))
% 187.18/188.05 [9282]~P31(x92821)+E(f329(f140(x92821,x92822,f329(f7(x92822,x92821,x92821),f329(f329(f8(x92821,f881(x92821,x92821),x92822),f115(x92821)),x92823)),f193(x92821)),x92824),f329(f329(f42(x92822,x92821),f329(f171(x92822),x92824)),x92823))
% 187.18/188.05 [9283]~P31(x92831)+E(f329(f140(x92831,x92832,f329(f7(x92832,x92831,x92831),f329(f329(f8(x92831,f881(x92831,x92831),x92832),f106(x92831)),x92833)),f252(x92831)),x92834),f329(f329(f43(x92832,x92831),f329(f171(x92832),x92834)),x92833))
% 187.18/188.05 [9295]E(f329(f329(f136(x92951),f329(f194(f875(x92951)),f176(x92951,x92952,f329(f329(f126(x92951),x92953),x92954)))),f329(f329(f126(x92951),x92953),x92954)),f329(f329(f136(x92951),f329(f194(f875(x92951)),f176(x92951,x92952,x92954))),x92954))+P24(f329(f329(f331(x92951),f773(x92954,x92952,x92953,x92951)),f329(f171(x92951),x92953)))
% 187.18/188.05 [9363]~P24(f329(f329(f331(f880(f875(x93634),f875(x93634))),f329(f329(f264(f875(x93634),f875(x93634)),x93633),x93632)),f155(x93634,x93631)))+P24(f329(f329(f244(a874),f686(x93631,x93632,x93633,x93634)),f329(f194(f875(x93634)),x93633)))
% 187.18/188.05 [9364]~P29(x93641)+E(f329(f329(f80(x93641),f329(f329(f80(x93641),f329(f329(f81(x93641),f329(f329(f39(x93641),x93642),x93643)),x93643)),f45(x93641,x93642,x93643))),x93644),f329(f329(f80(x93641),x93642),x93644))
% 187.18/188.05 [9391]~P24(f329(f329(f331(f880(f875(x93911),f875(x93911))),f329(f329(f264(f875(x93911),f875(x93911)),x93912),x93913)),f329(f284(f875(x93911),f875(x93911)),f155(x93911,x93914))))+P24(f329(f329(f331(f880(f875(x93911),f875(x93911))),f329(f329(f264(f875(x93911),f875(x93911)),x93912),x93913)),f155(x93911,f329(f284(x93911,x93911),x93914))))
% 187.18/188.05 [9392]P24(f329(f329(f331(f880(f875(x93921),f875(x93921))),f329(f329(f264(f875(x93921),f875(x93921)),x93922),x93923)),f329(f284(f875(x93921),f875(x93921)),f155(x93921,x93924))))+~P24(f329(f329(f331(f880(f875(x93921),f875(x93921))),f329(f329(f264(f875(x93921),f875(x93921)),x93922),x93923)),f155(x93921,f329(f284(x93921,x93921),x93924))))
% 187.18/188.05 [9426]~P24(f329(f329(f331(x94261),x94263),f329(f262(x94261,x94262),x94264)))+P24(f329(f329(f331(f880(x94261,x94262)),f329(f329(f264(x94261,x94262),x94263),f529(x94264,x94262,x94263,x94261))),x94264))
% 187.18/188.05 [9427]~P24(f329(f329(f331(x94271),x94273),f329(f262(x94271,x94272),x94274)))+P24(f329(f329(f331(f880(x94271,x94272)),f329(f329(f264(x94271,x94272),x94273),f531(x94274,x94272,x94273,x94271))),x94274))
% 187.18/188.05 [9537]~P24(f329(f62(f878(x95371)),f329(f308(x95372,f878(x95371),x95373),f252(f881(x95372,a869)))))+P24(f329(f62(f878(x95371)),f329(f308(x95372,f878(x95371),f184(x95372,x95371,x95373,f329(f177(x95372,x95371),x95374))),f252(f881(x95372,a869)))))
% 187.18/188.05 [9584]~P24(f329(f329(f331(f880(x95841,x95841)),f329(f329(f264(x95841,x95841),x95842),x95844)),f329(f329(f286(x95841,x95841,x95841),x95843),f305(x95841,x95843))))+P24(f329(f329(f331(f880(x95841,x95841)),f329(f329(f264(x95841,x95841),x95842),f619(x95843,x95844,x95842,x95841))),x95843))
% 187.18/188.05 [9753]~P24(f329(f329(f331(f880(x97532,x97531)),x97534),f329(f284(x97531,x97532),x97533)))+P24(f329(f329(f331(f880(x97531,x97532)),f329(f329(f264(x97531,x97532),f658(x97533,x97534,x97531,x97532)),f657(x97533,x97534,x97531,x97532))),x97533))
% 187.18/188.05 [9781]~P24(f329(f329(f331(f880(f875(x97811),f875(x97811))),f329(f329(f264(f875(x97811),f875(x97811)),x97814),x97813)),f155(x97811,x97812)))+P24(f329(f329(f331(f880(x97811,x97811)),f329(f329(f264(x97811,x97811),f699(x97812,x97813,x97814,x97811)),f700(x97812,x97813,x97814,x97811))),x97812))
% 187.18/188.05 [9878]~P24(f329(f329(f331(f880(f875(x98781),f875(x98781))),f329(f329(f264(f875(x98781),f875(x98781)),x98782),x98784)),f155(x98781,x98783)))+P24(f329(f329(f331(f880(x98781,x98781)),f329(f329(f264(x98781,x98781),f329(f329(f163(x98781),x98782),f686(x98783,x98784,x98782,x98781))),f687(x98783,x98784,x98782,x98781))),x98783))
% 187.18/188.05 [9900]~P24(f329(f62(x99002),x99004))+E(f329(f329(f329(f66(f881(x99001,a869),x99002,f115(f881(x99001,a869))),f329(f329(f7(x99002,f881(x99001,a869),f881(x99001,a869)),f329(f329(f8(x99001,f881(f881(x99001,a869),f881(x99001,a869)),x99002),f307(x99001)),x99003)),f193(f881(x99001,a869)))),f193(f881(x99001,a869))),x99004),f329(f308(x99002,x99001,x99003),x99004))
% 187.18/188.05 [9995]~P21(x99951,x99952,x99953,f252(f881(x99951,a869)))+P24(f329(f329(f243(f881(x99951,a869)),f329(f309(x99951,x99952,x99953),f329(f329(f307(x99952),x99954),f193(f881(x99952,a869))))),f329(f329(f307(x99951),f85(x99951,f329(f329(f7(x99951,x99952,a869),f329(f329(f8(x99952,f881(x99952,a869),x99951),a326),x99953)),x99954))),f193(f881(x99951,a869)))))
% 187.18/188.05 [5601]~E(f329(f329(f126(x56011),x56012),x56014),x56013)+E(f329(f329(f174(x56011),f329(f194(f875(x56011)),x56012)),x56013),x56012)
% 187.18/188.05 [5602]~E(f329(f329(f126(x56022),x56023),x56021),x56024)+E(x56021,f329(f329(f136(x56022),f329(f194(f875(x56022)),x56023)),x56024))
% 187.18/188.05 [5613]~E(x56134,f2(a874))+E(f329(f329(f163(x56131),f329(f329(f149(x56131),x56132),x56133)),x56134),x56132)
% 187.18/188.05 [6139]~P109(x61391)+E(f329(f329(f254(x61391),f329(f329(f254(x61391),x61392),x61393)),x61394),f329(f329(f254(x61391),x61392),f329(f329(f81(a874),x61393),x61394)))
% 187.18/188.05 [6140]~P82(x61401)+E(f329(f329(f254(x61401),f329(f329(f254(x61401),x61402),x61403)),x61404),f329(f329(f254(x61401),x61402),f329(f329(f81(a874),x61403),x61404)))
% 187.18/188.05 [6157]E(x61571,f2(a874))+E(f329(f329(f163(x61572),f329(f329(f149(x61572),x61573),x61574)),x61571),f329(f329(f163(x61572),x61574),f329(f329(f22(a874),x61571),f78(a874))))
% 187.18/188.05 [6182]~P118(x61821)+E(f329(f329(f287(x61821),f329(f329(f81(x61821),x61822),x61823)),x61824),f329(f329(f81(x61821),x61822),f329(f329(f287(x61821),x61823),x61824)))
% 187.18/188.05 [6184]~P66(x61841)+E(f329(f329(f115(x61841),f329(f329(f115(x61841),x61842),x61843)),x61844),f329(f329(f115(x61841),x61842),f329(f329(f115(x61841),x61843),x61844)))
% 187.18/188.05 [6186]~P102(x61861)+E(f329(f329(f115(x61861),f329(f329(f115(x61861),x61862),x61863)),x61864),f329(f329(f115(x61861),x61862),f329(f329(f115(x61861),x61863),x61864)))
% 187.18/188.05 [6187]~P66(x61871)+E(f329(f329(f106(x61871),f329(f329(f106(x61871),x61872),x61873)),x61874),f329(f329(f106(x61871),x61872),f329(f329(f106(x61871),x61873),x61874)))
% 187.18/188.05 [6189]~P103(x61891)+E(f329(f329(f106(x61891),f329(f329(f106(x61891),x61892),x61893)),x61894),f329(f329(f106(x61891),x61892),f329(f329(f106(x61891),x61893),x61894)))
% 187.18/188.05 [6190]~P70(x61901)+E(f329(f329(f81(x61901),f329(f329(f81(x61901),x61902),x61903)),x61904),f329(f329(f81(x61901),x61902),f329(f329(f81(x61901),x61903),x61904)))
% 187.18/188.05 [6191]~P109(x61911)+E(f329(f329(f81(x61911),f329(f329(f81(x61911),x61912),x61913)),x61914),f329(f329(f81(x61911),x61912),f329(f329(f81(x61911),x61913),x61914)))
% 187.18/188.05 [6193]~P71(x61931)+E(f329(f329(f80(x61931),f329(f329(f80(x61931),x61932),x61933)),x61934),f329(f329(f80(x61931),x61932),f329(f329(f80(x61931),x61933),x61934)))
% 187.18/188.05 [6194]~P109(x61941)+E(f329(f329(f80(x61941),f329(f329(f80(x61941),x61942),x61943)),x61944),f329(f329(f80(x61941),x61942),f329(f329(f80(x61941),x61943),x61944)))
% 187.18/188.05 [6196]~P27(x61961)+E(f329(f329(f241(x61961),f329(f329(f241(x61961),x61962),x61963)),x61964),f329(f329(f241(x61961),x61962),f329(f329(f241(x61961),x61963),x61964)))
% 187.18/188.05 [6198]~P27(x61981)+E(f329(f329(f242(x61981),f329(f329(f242(x61981),x61982),x61983)),x61984),f329(f329(f242(x61981),x61982),f329(f329(f242(x61981),x61983),x61984)))
% 187.18/188.05 [6209]~P29(x62091)+E(f45(x62091,f329(f329(f80(x62091),x62092),f329(f329(f81(x62091),x62093),x62094)),x62094),f45(x62091,x62092,x62094))
% 187.18/188.05 [6210]~P29(x62101)+E(f45(x62101,f329(f329(f80(x62101),x62102),f329(f329(f81(x62101),x62103),x62104)),x62103),f45(x62101,x62102,x62103))
% 187.18/188.05 [6342]E(f329(f329(f163(x63421),f329(f329(f174(x63421),x63422),x63423)),x63424),f329(f329(f163(x63421),x63423),x63424))+~P24(f329(f329(f244(a874),x63424),x63422))
% 187.18/188.05 [6516]~P109(x65161)+E(f329(f329(f81(x65161),f329(f329(f81(x65161),x65162),x65163)),x65164),f329(f329(f81(x65161),f329(f329(f81(x65161),x65162),x65164)),x65163))
% 187.18/188.05 [6517]~P109(x65171)+E(f329(f329(f80(x65171),f329(f329(f80(x65171),x65172),x65173)),x65174),f329(f329(f80(x65171),f329(f329(f80(x65171),x65172),x65174)),x65173))
% 187.18/188.05 [6577]~P141(x65772)+E(f329(f329(f6(x65771,x65772),f329(f16(x65772,x65771),x65773)),x65774),f329(f329(f81(x65772),f329(f105(x65772),f329(f38(x65771),x65774))),x65773))
% 187.18/188.05 [6746]E(f329(f329(f106(f881(x67461,a869)),f329(f329(f307(x67461),x67462),x67463)),x67464),f329(f329(f106(f881(x67461,a869)),x67463),x67464))+P24(f329(f329(f331(x67461),x67462),x67464))
% 187.18/188.05 [6816]~P100(x68161)+E(f329(f329(f106(x68161),f329(f329(f115(x68161),x68162),x68163)),f329(f329(f115(x68161),x68164),x68163)),f329(f329(f115(x68161),f329(f329(f106(x68161),x68162),x68164)),x68163))
% 187.18/188.05 [6817]~P80(x68171)+E(f329(f329(f241(x68171),f329(f329(f22(x68171),x68172),x68173)),f329(f329(f22(x68171),x68174),x68173)),f329(f329(f22(x68171),f329(f329(f241(x68171),x68172),x68174)),x68173))
% 187.18/188.05 [6818]~P80(x68181)+E(f329(f329(f242(x68181),f329(f329(f22(x68181),x68182),x68183)),f329(f329(f22(x68181),x68184),x68183)),f329(f329(f22(x68181),f329(f329(f242(x68181),x68182),x68184)),x68183))
% 187.18/188.05 [6819]~P100(x68191)+E(f329(f329(f115(x68191),f329(f329(f106(x68191),x68192),x68193)),f329(f329(f106(x68191),x68194),x68193)),f329(f329(f106(x68191),f329(f329(f115(x68191),x68192),x68194)),x68193))
% 187.18/188.05 [6821]~P110(x68211)+E(f329(f329(f80(x68211),f329(f329(f81(x68211),x68212),x68213)),f329(f329(f81(x68211),x68214),x68213)),f329(f329(f81(x68211),f329(f329(f80(x68211),x68212),x68214)),x68213))
% 187.18/188.05 [6822]~P85(x68221)+E(f329(f329(f241(x68221),f329(f329(f80(x68221),x68222),x68223)),f329(f329(f80(x68221),x68224),x68223)),f329(f329(f80(x68221),f329(f329(f241(x68221),x68222),x68224)),x68223))
% 187.18/188.05 [6823]~P85(x68231)+E(f329(f329(f242(x68231),f329(f329(f80(x68231),x68232),x68233)),f329(f329(f80(x68231),x68234),x68233)),f329(f329(f80(x68231),f329(f329(f242(x68231),x68232),x68234)),x68233))
% 187.18/188.05 [6824]~P76(x68241)+E(f329(f329(f81(x68241),f329(f329(f254(x68241),x68242),x68243)),f329(f329(f254(x68241),x68244),x68243)),f329(f329(f254(x68241),f329(f329(f81(x68241),x68242),x68244)),x68243))
% 187.18/188.05 [6825]~P109(x68251)+E(f329(f329(f81(x68251),f329(f329(f254(x68251),x68252),x68253)),f329(f329(f254(x68251),x68254),x68253)),f329(f329(f254(x68251),f329(f329(f81(x68251),x68252),x68254)),x68253))
% 187.18/188.05 [6826]~P61(x68261)+E(f329(f329(f287(x68261),f329(f329(f254(x68261),x68262),x68263)),f329(f329(f254(x68261),x68264),x68263)),f329(f329(f254(x68261),f329(f329(f287(x68261),x68262),x68264)),x68263))
% 187.18/188.05 [6827]~P118(x68271)+E(f329(f329(f22(x68271),f329(f329(f287(x68271),x68272),x68273)),f329(f329(f287(x68271),x68274),x68273)),f329(f329(f287(x68271),f329(f329(f22(x68271),x68272),x68274)),x68273))
% 187.18/188.05 [6828]~P118(x68281)+E(f329(f329(f80(x68281),f329(f329(f287(x68281),x68282),x68283)),f329(f329(f287(x68281),x68284),x68283)),f329(f329(f287(x68281),f329(f329(f80(x68281),x68282),x68284)),x68283))
% 187.18/188.05 [6829]~P27(x68291)+E(f329(f329(f242(x68291),f329(f329(f241(x68291),x68292),x68293)),f329(f329(f241(x68291),x68294),x68293)),f329(f329(f241(x68291),f329(f329(f242(x68291),x68292),x68294)),x68293))
% 187.18/188.05 [6830]~P27(x68301)+E(f329(f329(f241(x68301),f329(f329(f242(x68301),x68302),x68303)),f329(f329(f242(x68301),x68304),x68303)),f329(f329(f242(x68301),f329(f329(f241(x68301),x68302),x68304)),x68303))
% 187.18/188.05 [6831]~P109(x68311)+E(f329(f329(f80(x68311),f329(f329(f81(x68311),x68312),x68313)),f329(f329(f81(x68311),x68314),x68313)),f329(f329(f81(x68311),f329(f329(f80(x68311),x68312),x68314)),x68313))
% 187.18/188.05 [6863]E(f329(f329(f157(x68631,x68632),x68633),x68634),x68632)+~P24(f329(f329(f243(a874),f329(f194(f875(x68631)),x68632)),x68633))
% 187.18/188.05 [6888]~P24(f329(x68883,x68884))+P24(f329(f329(f329(f115(f881(x68881,a869)),x68882),x68883),x68884))
% 187.18/188.05 [6890]~P24(f329(x68902,x68904))+P24(f329(f329(f329(f115(f881(x68901,a869)),x68902),x68903),x68904))
% 187.18/188.05 [6911]E(f329(f329(f163(x69111),f329(f329(f126(x69111),x69112),x69113)),x69114),f329(f329(f163(x69111),x69112),x69114))+~P24(f329(f329(f244(a874),x69114),f329(f194(f875(x69111)),x69112)))
% 187.18/188.05 [6921]E(f329(f329(f22(f881(x69211,a869)),f329(f329(f307(x69211),x69212),x69213)),x69214),f329(f329(f22(f881(x69211,a869)),x69213),x69214))+~P24(f329(f329(f331(x69211),x69212),x69214))
% 187.18/188.05 [6962]~E(f137(a874,f329(f299(a874,x69621),x69622)),f329(f329(f149(a874),x69624),x69623))+E(f137(a874,f329(f299(a874,f329(f329(f80(a874),x69621),f78(a874))),x69622)),x69623)
% 187.18/188.05 [7035]E(x70351,f2(a874))+E(f329(f329(f149(x70352),x70353),f329(f329(f174(x70352),f329(f329(f22(a874),x70351),f78(a874))),x70354)),f329(f329(f174(x70352),x70351),f329(f329(f149(x70352),x70353),x70354)))
% 187.18/188.05 [7135]E(f329(f329(f163(x71351),x71352),f329(f329(f22(a874),x71353),f329(f194(f875(x71351)),x71354))),f329(f329(f163(x71351),f329(f329(f126(x71351),x71354),x71352)),x71353))+P24(f329(f329(f244(a874),x71353),f329(f194(f875(x71351)),x71354)))
% 187.18/188.05 [7165]E(f329(f329(f106(f881(x71651,a869)),x71652),f329(f329(f307(x71651),x71653),x71654)),f329(f329(f307(x71651),x71653),f329(f329(f106(f881(x71651,a869)),x71652),x71654)))+~P24(f329(f329(f331(x71651),x71653),x71652))
% 187.18/188.05 [7200]E(f329(f329(f163(x72001),f329(f329(f157(x72001,x72002),x72003),x72004)),x72003),x72004)+~P24(f329(f329(f244(a874),x72003),f329(f194(f875(x72001)),x72002)))
% 187.18/188.05 [7221]E(x72211,f193(f881(x72212,a869)))+E(f329(f308(f880(x72213,x72212),x72213,f263(x72213,x72212)),f329(f329(f266(x72213,x72212),x72214),f329(f16(f881(x72212,a869),x72213),x72211))),x72214)
% 187.18/188.05 [7222]E(x72221,f193(f881(x72222,a869)))+E(f329(f308(f880(x72222,x72223),x72223,f267(x72222,x72223)),f329(f329(f266(x72222,x72223),x72221),f329(f16(f881(x72223,a869),x72222),x72224))),x72224)
% 187.18/188.05 [7289]E(f329(f329(f22(f881(x72891,a869)),f329(f329(f307(x72891),x72892),x72893)),x72894),f329(f329(f307(x72891),x72892),f329(f329(f22(f881(x72891,a869)),x72893),x72894)))+P24(f329(f329(f331(x72891),x72892),x72894))
% 187.18/188.05 [7321]P24(f329(x73211,x73212))+P24(f329(f329(f329(f329(a201,f32(x73211,x73213)),x73212),x73214),x73212))
% 187.18/188.05 [7328]~E(x73284,f193(f881(x73282,a869)))+E(f329(f308(f880(x73281,x73282),x73281,f263(x73281,x73282)),f329(f329(f266(x73281,x73282),x73283),f329(f16(f881(x73282,a869),x73281),x73284))),f193(f881(x73281,a869)))
% 187.18/188.05 [7329]~E(x73293,f193(f881(x73291,a869)))+E(f329(f308(f880(x73291,x73292),x73292,f267(x73291,x73292)),f329(f329(f266(x73291,x73292),x73293),f329(f16(f881(x73292,a869),x73291),x73294))),f193(f881(x73292,a869)))
% 187.18/188.05 [7386]~P24(f329(f329(f331(x73861),x73862),x73864))+P24(f329(f329(f331(x73861),x73862),f329(f329(f115(f881(x73861,a869)),x73863),x73864)))
% 187.18/188.05 [7389]~P24(f329(f329(f331(x73891),x73892),x73893))+P24(f329(f329(f331(x73891),x73892),f329(f329(f115(f881(x73891,a869)),x73893),x73894)))
% 187.18/188.05 [7408]E(f329(f329(f106(f881(x74081,a869)),f329(f329(f307(x74081),x74082),x74083)),x74084),f329(f329(f307(x74081),x74082),f329(f329(f106(f881(x74081,a869)),x74083),x74084)))+~P24(f329(f329(f331(x74081),x74082),x74084))
% 187.18/188.05 [7687]P24(f329(x76871,x76872))+~P24(f329(f329(f329(f106(f881(x76873,a869)),x76874),x76871),x76872))
% 187.18/188.05 [7688]P24(f329(x76881,x76882))+~P24(f329(f329(f329(f106(f881(x76883,a869)),x76881),x76884),x76882))
% 187.18/188.05 [7691]E(f329(f329(f6(x76911,a874),x76912),f329(f329(f22(f881(x76911,a869)),x76913),f329(f329(f307(x76911),x76914),f193(f881(x76911,a869))))),f329(f329(f6(x76911,a874),x76912),x76913))+P24(f329(f329(f331(x76911),x76914),x76913))
% 187.18/188.05 [7697]~P72(x76971)+E(f329(f164(x76971),f329(f329(f152(a874,x76971),x76972),f137(a874,f329(f299(a874,x76973),x76974)))),f329(f329(f6(a874,x76971),x76972),f329(f171(a874),f137(a874,f329(f299(a874,x76973),x76974)))))
% 187.18/188.05 [7698]~P72(x76981)+E(f329(f329(f6(a874,x76981),x76982),f329(f171(a874),f137(a874,f329(f299(a874,x76983),x76984)))),f329(f164(x76981),f329(f329(f152(a874,x76981),x76982),f137(a874,f329(f299(a874,x76983),x76984)))))
% 187.18/188.05 [7813]~E(x78133,x78134)+P24(f329(f63(x78131,x78132,f329(f329(f307(x78131),x78133),f193(f881(x78131,a869)))),x78134))
% 187.18/188.05 [7910]P24(f329(f329(f331(x79101),x79102),f329(f171(x79101),x79103)))+~P24(f329(f329(f331(x79101),x79102),f329(f171(x79101),f329(f329(f174(x79101),x79104),x79103))))
% 187.18/188.05 [7911]P24(f329(f329(f331(x79111),x79112),f329(f171(x79111),x79113)))+~P24(f329(f329(f331(x79111),x79112),f329(f171(x79111),f329(f329(f136(x79111),x79114),x79113))))
% 187.18/188.05 [7984]P24(f329(f329(f331(x79841),x79842),x79843))+~P24(f329(f329(f331(x79841),x79842),f329(f329(f22(f881(x79841,a869)),x79843),x79844)))
% 187.18/188.05 [7986]P24(f329(f329(f331(x79861),x79862),x79863))+~P24(f329(f329(f331(x79861),x79862),f329(f329(f106(f881(x79861,a869)),x79864),x79863)))
% 187.18/188.05 [7989]P24(f329(f329(f331(x79891),x79892),x79893))+~P24(f329(f329(f331(x79891),x79892),f329(f329(f106(f881(x79891,a869)),x79893),x79894)))
% 187.18/188.05 [8007]E(f329(f329(f126(x80071),f329(f329(f174(x80071),x80072),x80073)),f329(f329(f149(x80071),x80074),f329(f329(f136(x80071),f329(a117,x80072)),x80073))),f329(f329(f157(x80071,x80073),x80072),x80074))+~P24(f329(f329(f244(a874),x80072),f329(f194(f875(x80071)),x80073)))
% 187.18/188.05 [8032]P24(f329(f329(f331(x80321),x80322),x80323))+~P24(f329(f329(f243(f881(x80321,a869)),f329(f329(f307(x80321),x80322),x80324)),x80323))
% 187.18/188.05 [8065]~P24(f329(f329(f331(x80651),x80652),x80653))+~P24(f329(f329(f331(x80651),x80652),f329(f329(f22(f881(x80651,a869)),x80654),x80653)))
% 187.18/188.05 [8098]~P24(f329(f329(f244(a874),x80984),f329(f194(f875(x80981)),x80983)))+P24(f329(f329(f331(x80981),x80982),f329(f171(x80981),f329(f329(f157(x80981,x80983),x80984),x80982))))
% 187.18/188.05 [8153]E(f329(f329(f163(x81531),f329(f329(f136(x81531),x81532),x81533)),x81534),f329(f329(f163(x81531),x81533),f329(f329(f80(a874),x81532),x81534)))+~P24(f329(f329(f243(a874),f329(f329(f80(a874),x81532),x81534)),f329(f194(f875(x81531)),x81533)))
% 187.18/188.05 [8163]~P141(x81632)+E(f329(f329(f6(x81631,x81632),f329(f329(f8(a874,x81632,x81631),f105(x81632)),x81633)),x81634),f329(f105(x81632),f329(f329(f6(x81631,a874),x81633),x81634)))
% 187.18/188.05 [8164]~P138(x81642)+E(f329(f329(f6(x81641,x81642),f329(f329(f8(a1,x81642,x81641),f107(x81642)),x81643)),x81644),f329(f107(x81642),f329(f329(f6(x81641,a1),x81643),x81644)))
% 187.18/188.05 [8217]~P64(x82172)+E(f329(f329(f9(x82171,x82172),f329(f329(f8(x82172,x82172,x82171),f75(x82172)),x82173)),x82174),f329(f75(x82172),f329(f329(f9(x82171,x82172),x82173),x82174)))
% 187.18/188.05 [8218]~P69(x82182)+E(f329(f329(f6(x82181,x82182),f329(f329(f8(x82182,x82182,x82181),f79(x82182)),x82183)),x82184),f329(f79(x82182),f329(f329(f6(x82181,x82182),x82183),x82184)))
% 187.18/188.05 [8220]E(f329(f329(f6(x82201,a874),x82202),f329(f329(f22(f881(x82201,a869)),x82203),f329(f329(f307(x82201),x82204),f193(f881(x82201,a869))))),f329(f329(f22(a874),f329(f329(f6(x82201,a874),x82202),x82203)),f329(x82202,x82204)))+~P24(f329(f329(f331(x82201),x82204),x82203))
% 187.18/188.05 [8240]P24(f329(f329(f243(f881(x82401,a869)),x82402),x82403))+~P24(f329(f329(f243(f881(x82401,a869)),f329(f329(f307(x82401),x82404),x82402)),x82403))
% 187.18/188.05 [8448]E(f329(a117,f352(x84481,x84482,x84483,x84484)),x84482)+~P24(f329(f329(f329(f329(a201,f329(a26,x84484)),x84483),x84482),x84481))
% 187.18/188.05 [8450]E(f329(f329(f177(x84501,x84502),x84503),x84504),f206(x84502))+P24(f329(f329(f331(x84501),x84504),f329(f308(f880(x84501,x84502),x84501,f263(x84501,x84502)),f329(f171(f880(x84501,x84502)),x84503))))
% 187.18/188.05 [8451]P42(x84511,x84512)+~P42(x84511,f329(f329(f307(f880(x84511,x84511)),f329(f329(f264(x84511,x84511),x84513),x84514)),x84512))
% 187.18/188.05 [8452]P57(x84521,x84522)+~P57(x84521,f329(f329(f307(f880(x84521,x84521)),f329(f329(f264(x84521,x84521),x84523),x84524)),x84522))
% 187.18/188.05 [8461]~P27(x84611)+E(f329(f329(f146(x84611,x84611,f5(x84611)),x84612),f329(f329(f146(x84611,x84611,f5(x84611)),x84613),x84614)),f329(f329(f146(x84611,x84611,f5(x84611)),x84613),f329(f329(f146(x84611,x84611,f5(x84611)),x84612),x84614)))
% 187.18/188.05 [8471]E(x84711,x84712)+~P24(f329(f63(x84713,x84714,f329(f329(f307(x84713),x84711),f193(f881(x84713,a869)))),x84712))
% 187.18/188.05 [8481]E(f329(f329(f126(x84811),f329(f329(f174(x84811),x84812),x84813)),f329(f329(f174(x84811),x84814),f329(f329(f136(x84811),x84812),x84813))),f329(f329(f174(x84811),f329(f329(f80(a874),x84812),x84814)),x84813))+~P24(f329(f329(f243(a874),f329(f329(f80(a874),x84812),x84814)),f329(f194(f875(x84811)),x84813)))
% 187.18/188.05 [8521]P24(f329(f62(x85211),x85212))+~E(x85212,f329(f308(a874,x85211,x85213),f329(f249(a874),f329(f329(f7(a874,a874,a869),f244(a874)),x85214))))
% 187.18/188.05 [8541]~P92(x85411)+E(f329(f140(x85411,x85411,f80(x85411),f329(f329(f80(x85411),x85412),x85413)),x85414),f329(f329(f80(x85411),x85412),f329(f140(x85411,x85411,f80(x85411),x85413),x85414)))
% 187.18/188.05 [8575]P24(f329(f329(f243(f881(x85751,a869)),f329(f262(x85751,x85752),x85753)),f329(f262(x85751,x85752),x85754)))+~P24(f329(f329(f243(f881(f880(x85751,x85752),a869)),x85753),x85754))
% 187.18/188.05 [8588]~P24(f329(f329(f243(a874),x85882),x85884))+P24(f329(f329(f243(f881(x85881,a869)),f329(f171(x85881),f329(f329(f174(x85881),x85882),x85883))),f329(f171(x85881),f329(f329(f174(x85881),x85884),x85883))))
% 187.18/188.05 [8589]~P24(f329(f329(f243(a874),x85894),x85892))+P24(f329(f329(f243(f881(x85891,a869)),f329(f171(x85891),f329(f329(f136(x85891),x85892),x85893))),f329(f171(x85891),f329(f329(f136(x85891),x85894),x85893))))
% 187.18/188.05 [8642]~P24(f329(f62(x86421),f329(f329(f22(f881(x86421,a869)),x86422),x86424)))+P24(f329(f62(x86421),f329(f329(f22(f881(x86421,a869)),x86422),f329(f329(f307(x86421),x86423),x86424))))
% 187.18/188.05 [8679]P24(f329(f329(f331(f880(x86791,x86791)),x86792),f305(x86791,x86793)))+~P24(f329(f329(f331(f880(x86791,x86791)),x86792),f329(f329(f188(f880(x86791,x86791),a869),x86794),x86793)))
% 187.18/188.05 [8756]~P24(f329(f62(x87561),f329(f329(f22(f881(x87561,a869)),x87562),f329(f329(f307(x87561),x87564),x87563))))+P24(f329(f62(x87561),f329(f329(f22(f881(x87561,a869)),x87562),x87563)))
% 187.18/188.05 [8903]~E(f329(f329(f177(x89031,x89032),x89033),x89034),f206(x89032))+~P24(f329(f329(f331(x89031),x89034),f329(f308(f880(x89031,x89032),x89031,f263(x89031,x89032)),f329(f171(f880(x89031,x89032)),x89033))))
% 187.18/188.05 [8971]~P66(x89711)+P24(f329(f329(f243(x89711),f329(f329(f115(x89711),x89712),f329(f329(f106(x89711),x89713),x89714))),f329(f329(f106(x89711),f329(f329(f115(x89711),x89712),x89713)),f329(f329(f115(x89711),x89712),x89714))))
% 187.18/188.05 [8972]~P27(x89721)+P24(f329(f329(f243(x89721),f329(f329(f242(x89721),x89722),f329(f329(f241(x89721),x89723),x89724))),f329(f329(f241(x89721),f329(f329(f242(x89721),x89722),x89723)),f329(f329(f242(x89721),x89722),x89724))))
% 187.18/188.05 [9118]E(x91181,x91182)+~P24(f329(f329(f331(f880(x91183,x91183)),f329(f329(f264(x91183,x91183),x91181),x91182)),f329(f171(f880(x91183,x91183)),f329(f329(f181(x91183,x91183),x91184),x91184))))
% 187.18/188.05 [9151]~P24(f329(f329(f331(f880(x91511,x91511)),f329(f329(f264(x91511,x91511),x91513),x91512)),f305(x91511,x91514)))+~P42(x91511,f329(f329(f307(f880(x91511,x91511)),f329(f329(f264(x91511,x91511),x91512),x91513)),x91514))
% 187.18/188.05 [9152]~P24(f329(f329(f331(f880(x91521,x91521)),f329(f329(f264(x91521,x91521),x91523),x91522)),f305(x91521,x91524)))+~P57(x91521,f329(f329(f307(f880(x91521,x91521)),f329(f329(f264(x91521,x91521),x91522),x91523)),x91524))
% 187.18/188.05 [9157]E(x91571,x91572)+E(f329(f134(x91573,f329(f329(f8(a869,a869,x91573),a324),f329(a326,x91571))),f329(f329(f149(x91573),x91572),x91574)),f329(f329(f149(x91573),x91572),f329(f134(x91573,f329(f329(f8(a869,a869,x91573),a324),f329(a326,x91571))),x91574)))
% 187.18/188.05 [9201]~P66(x92011)+P24(f329(f329(f243(x92011),f329(f329(f115(x92011),f329(f329(f106(x92011),x92012),x92013)),f329(f329(f106(x92011),x92012),x92014))),f329(f329(f106(x92011),x92012),f329(f329(f115(x92011),x92013),x92014))))
% 187.18/188.05 [9202]~P27(x92021)+P24(f329(f329(f243(x92021),f329(f329(f242(x92021),f329(f329(f241(x92021),x92022),x92023)),f329(f329(f241(x92021),x92022),x92024))),f329(f329(f241(x92021),x92022),f329(f329(f242(x92021),x92023),x92024))))
% 187.18/188.05 [9278]~E(f329(f308(x92782,x92781,x92783),f252(f881(x92782,a869))),f252(f881(x92781,a869)))+P24(f329(f329(f243(f881(x92781,a869)),f329(f79(f881(x92781,a869)),f329(f308(x92782,x92781,x92783),x92784))),f329(f308(x92782,x92781,x92783),f329(f79(f881(x92782,a869)),x92784))))
% 187.18/188.05 [9356]P24(f329(f329(f329(f329(a201,f329(f240(a870),f329(a28,x93561))),x93562),f352(x93563,x93564,x93562,x93561)),x93563))+~P24(f329(f329(f329(f329(a201,f329(a26,x93561)),x93562),x93564),x93563))
% 187.18/188.05 [9598]P24(f329(f329(f331(f880(x95981,x95981)),f329(f329(f264(x95981,x95981),x95982),x95983)),f329(f284(x95981,x95981),f329(f329(f286(x95981,x95981,x95981),x95984),f305(x95981,x95984)))))+~P24(f329(f329(f331(f880(x95981,x95981)),f329(f329(f264(x95981,x95981),x95982),x95983)),f329(f329(f286(x95981,x95981,x95981),f329(f284(x95981,x95981),x95984)),f305(x95981,f329(f284(x95981,x95981),x95984)))))
% 187.18/188.05 [9599]~P24(f329(f329(f331(f880(x95991,x95991)),f329(f329(f264(x95991,x95991),x95992),x95993)),f329(f284(x95991,x95991),f329(f329(f286(x95991,x95991,x95991),x95994),f305(x95991,x95994)))))+P24(f329(f329(f331(f880(x95991,x95991)),f329(f329(f264(x95991,x95991),x95992),x95993)),f329(f329(f286(x95991,x95991,x95991),f329(f284(x95991,x95991),x95994)),f305(x95991,f329(f284(x95991,x95991),x95994)))))
% 187.18/188.05 [9620]~P24(f329(f329(f331(x96202),x96204),f329(f260(x96201,x96202),x96203)))+P24(f329(f329(f331(f880(x96201,x96202)),f329(f329(f264(x96201,x96202),f528(x96203,x96201,x96204,x96202)),x96204)),x96203))
% 187.18/188.05 [9621]~P24(f329(f329(f331(x96212),x96214),f329(f260(x96211,x96212),x96213)))+P24(f329(f329(f331(f880(x96211,x96212)),f329(f329(f264(x96211,x96212),f530(x96213,x96211,x96214,x96212)),x96214)),x96213))
% 187.18/188.05 [9646]~P24(f329(f329(f331(x96461),x96464),f329(f329(f115(f881(x96461,a869)),x96462),x96463)))+P24(f329(f329(f329(f115(f881(x96461,a869)),f329(f329(f7(x96461,f881(x96461,a869),a869),f331(x96461)),x96462)),f329(f329(f7(x96461,f881(x96461,a869),a869),f331(x96461)),x96463)),x96464))
% 187.18/188.05 [9647]~P24(f329(f329(f331(x96471),x96474),f329(f329(f106(f881(x96471,a869)),x96472),x96473)))+P24(f329(f329(f329(f106(f881(x96471,a869)),f329(f329(f7(x96471,f881(x96471,a869),a869),f331(x96471)),x96472)),f329(f329(f7(x96471,f881(x96471,a869),a869),f331(x96471)),x96473)),x96474))
% 187.18/188.05 [9724]~P24(f329(f329(f331(f880(x97241,x97241)),f329(f329(f264(x97241,x97241),x97244),x97243)),f329(f329(f286(x97241,x97241,x97241),x97242),f305(x97241,x97242))))+P24(f329(f329(f331(f880(x97241,x97241)),f329(f329(f264(x97241,x97241),f620(x97242,x97243,x97244,x97241)),x97243)),x97242))
% 187.18/188.05 [9769]P24(f329(f329(f331(x97691),x97692),f329(f329(f115(f881(x97691,a869)),x97693),x97694)))+~P24(f329(f329(f329(f115(f881(x97691,a869)),f329(f329(f7(x97691,f881(x97691,a869),a869),f331(x97691)),x97693)),f329(f329(f7(x97691,f881(x97691,a869),a869),f331(x97691)),x97694)),x97692))
% 187.18/188.05 [9770]P24(f329(f329(f331(x97701),x97702),f329(f329(f106(f881(x97701,a869)),x97703),x97704)))+~P24(f329(f329(f329(f106(f881(x97701,a869)),f329(f329(f7(x97701,f881(x97701,a869),a869),f331(x97701)),x97703)),f329(f329(f7(x97701,f881(x97701,a869),a869),f331(x97701)),x97704)),x97702))
% 187.18/188.05 [10049]P37(x100491,f329(f329(f7(x100491,f881(f880(x100491,x100491),a869),f881(x100491,a869)),f329(f329(f8(f881(x100491,f881(f881(f880(x100491,x100491),a869),a869)),f881(f881(f880(x100491,x100491),a869),f881(x100491,a869)),x100491),f7(x100491,f881(f880(x100491,x100491),a869),a869)),f329(f329(f8(f881(x100491,f880(x100491,x100491)),f881(x100491,f881(f881(f880(x100491,x100491),a869),a869)),x100491),f329(f8(f880(x100491,x100491),f881(f881(f880(x100491,x100491),a869),a869),x100491),f331(f880(x100491,x100491)))),f264(x100491,x100491)))),x100492),x100493,x100494)+~P24(f329(f329(f331(f880(f875(x100491),f875(x100491))),f329(f329(f264(f875(x100491),f875(x100491)),x100493),x100494)),f156(x100491,x100492)))
% 187.18/188.05 [10053]P58(x100531,f329(f329(f7(x100531,f881(f880(x100531,x100531),a869),f881(x100531,a869)),f329(f329(f8(f881(x100531,f881(f881(f880(x100531,x100531),a869),a869)),f881(f881(f880(x100531,x100531),a869),f881(x100531,a869)),x100531),f7(x100531,f881(f880(x100531,x100531),a869),a869)),f329(f329(f8(f881(x100531,f880(x100531,x100531)),f881(x100531,f881(f881(f880(x100531,x100531),a869),a869)),x100531),f329(f8(f880(x100531,x100531),f881(f881(f880(x100531,x100531),a869),a869),x100531),f331(f880(x100531,x100531)))),f264(x100531,x100531)))),x100532),x100533,x100534)+~P24(f329(f329(f331(f880(f881(x100531,a869),f881(x100531,a869))),f329(f329(f264(f881(x100531,a869),f881(x100531,a869)),x100533),x100534)),f321(x100531,x100532)))
% 187.18/188.05 [10082]E(x100821,x100822)+~E(f329(f329(f7(x100823,f881(f880(x100823,x100824),a869),f881(x100824,a869)),f329(f329(f8(f881(x100824,f881(f881(f880(x100823,x100824),a869),a869)),f881(f881(f880(x100823,x100824),a869),f881(x100824,a869)),x100823),f7(x100824,f881(f880(x100823,x100824),a869),a869)),f329(f329(f8(f881(x100824,f880(x100823,x100824)),f881(x100824,f881(f881(f880(x100823,x100824),a869),a869)),x100823),f329(f8(f880(x100823,x100824),f881(f881(f880(x100823,x100824),a869),a869),x100824),f331(f880(x100823,x100824)))),f264(x100823,x100824)))),x100821),f329(f329(f7(x100823,f881(f880(x100823,x100824),a869),f881(x100824,a869)),f329(f329(f8(f881(x100824,f881(f881(f880(x100823,x100824),a869),a869)),f881(f881(f880(x100823,x100824),a869),f881(x100824,a869)),x100823),f7(x100824,f881(f880(x100823,x100824),a869),a869)),f329(f329(f8(f881(x100824,f880(x100823,x100824)),f881(x100824,f881(f881(f880(x100823,x100824),a869),a869)),x100823),f329(f8(f880(x100823,x100824),f881(f881(f880(x100823,x100824),a869),a869),x100824),f331(f880(x100823,x100824)))),f264(x100823,x100824)))),x100822))
% 187.18/188.05 [10086]~P37(x100861,f329(f329(f7(x100861,f881(f880(x100861,x100861),a869),f881(x100861,a869)),f329(f329(f8(f881(x100861,f881(f881(f880(x100861,x100861),a869),a869)),f881(f881(f880(x100861,x100861),a869),f881(x100861,a869)),x100861),f7(x100861,f881(f880(x100861,x100861),a869),a869)),f329(f329(f8(f881(x100861,f880(x100861,x100861)),f881(x100861,f881(f881(f880(x100861,x100861),a869),a869)),x100861),f329(f8(f880(x100861,x100861),f881(f881(f880(x100861,x100861),a869),a869),x100861),f331(f880(x100861,x100861)))),f264(x100861,x100861)))),x100864),x100862,x100863)+P24(f329(f329(f331(f880(f875(x100861),f875(x100861))),f329(f329(f264(f875(x100861),f875(x100861)),x100862),x100863)),f156(x100861,x100864)))
% 187.18/188.05 [10087]~P58(x100871,f329(f329(f7(x100871,f881(f880(x100871,x100871),a869),f881(x100871,a869)),f329(f329(f8(f881(x100871,f881(f881(f880(x100871,x100871),a869),a869)),f881(f881(f880(x100871,x100871),a869),f881(x100871,a869)),x100871),f7(x100871,f881(f880(x100871,x100871),a869),a869)),f329(f329(f8(f881(x100871,f880(x100871,x100871)),f881(x100871,f881(f881(f880(x100871,x100871),a869),a869)),x100871),f329(f8(f880(x100871,x100871),f881(f881(f880(x100871,x100871),a869),a869),x100871),f331(f880(x100871,x100871)))),f264(x100871,x100871)))),x100874),x100872,x100873)+P24(f329(f329(f331(f880(f881(x100871,a869),f881(x100871,a869))),f329(f329(f264(f881(x100871,a869),f881(x100871,a869)),x100872),x100873)),f321(x100871,x100874)))
% 187.18/188.05 [7460]~P94(x74601)+E(f329(f329(f81(x74601),f329(f108(x74601),x74602)),f329(f329(f81(x74601),f329(f108(x74601),x74603)),x74604)),f329(f329(f81(x74601),f329(f108(x74601),f329(f329(f81(a1),x74602),x74603))),x74604))
% 187.18/188.05 [7461]~P94(x74611)+E(f329(f329(f80(x74611),f329(f108(x74611),x74612)),f329(f329(f22(x74611),f329(f108(x74611),x74613)),x74614)),f329(f329(f22(x74611),f329(f108(x74611),f329(f329(f80(a1),x74612),x74613))),x74614))
% 187.18/188.05 [7462]~P94(x74621)+E(f329(f329(f80(x74621),f329(f108(x74621),x74622)),f329(f329(f80(x74621),f329(f108(x74621),x74623)),x74624)),f329(f329(f80(x74621),f329(f108(x74621),f329(f329(f80(a1),x74622),x74623))),x74624))
% 187.18/188.05 [7507]~P141(x75071)+E(f329(f164(x75071),f329(f329(f152(x75072,x75071),f329(f16(x75071,x75072),x75073)),x75074)),f329(f329(f81(x75071),f329(f105(x75071),f329(f194(f875(x75072)),x75074))),x75073))
% 187.18/188.05 [7744]E(f329(f275(x77441,f329(f329(f149(f880(a104,x77441)),x77442),x77443)),x77444),f329(f267(a104,x77441),x77442))+~P24(f329(f329(f244(a104),x77444),f329(f263(a104,x77441),x77442)))
% 187.18/188.05 [7791]~P94(x77911)+E(f329(f329(f80(x77911),f329(f108(x77911),x77912)),f329(f329(f22(x77911),x77913),f329(f108(x77911),x77914))),f329(f329(f80(x77911),f329(f108(x77911),f329(f329(f80(a1),x77912),f329(f79(a1),x77914)))),x77913))
% 187.18/188.05 [7923]E(f329(f275(x79231,x79232),f329(f329(f22(a104),x79233),f329(f263(a104,x79231),x79234))),f329(f275(x79231,f329(f329(f149(f880(a104,x79231)),x79234),x79232)),x79233))+P24(f329(f329(f244(a104),x79233),f329(f263(a104,x79231),x79234)))
% 187.18/188.05 [8366]~P24(f329(f329(f331(x83661),x83662),f329(f171(x83661),f119(x83661,x83664))))+P24(f329(f329(f331(x83661),x83662),f329(f171(x83661),f119(x83661,f329(f329(f126(x83661),x83663),x83664)))))
% 187.18/188.05 [8367]~P24(f329(f329(f331(x83671),x83672),f329(f171(x83671),f119(x83671,x83673))))+P24(f329(f329(f331(x83671),x83672),f329(f171(x83671),f119(x83671,f329(f329(f126(x83671),x83673),x83674)))))
% 187.18/188.05 [8386]E(f329(f329(f115(f881(x83861,a869)),f329(f329(f106(f881(x83861,a869)),x83862),x83863)),x83864),f329(f329(f106(f881(x83861,a869)),x83862),f329(f329(f115(f881(x83861,a869)),x83863),x83864)))+~P24(f329(f329(f243(f881(x83861,a869)),x83864),x83862))
% 187.18/188.05 [8692]~E(f329(f329(f115(f881(x86921,a869)),f329(f329(f106(f881(x86921,a869)),x86923),x86924)),x86922),f329(f329(f106(f881(x86921,a869)),x86923),f329(f329(f115(f881(x86921,a869)),x86924),x86922)))+P24(f329(f329(f243(f881(x86921,a869)),x86922),x86923))
% 187.18/188.05 [8977]~P24(f329(f329(f243(f881(x89771,a869)),x89772),f329(f329(f115(f881(x89771,a869)),x89773),x89774)))+P24(f329(f329(f243(f881(x89771,a869)),f329(f329(f22(f881(x89771,a869)),x89772),x89773)),x89774))
% 187.18/188.05 [9037]~P24(f329(f329(f329(f329(a201,f329(a26,x90371)),x90372),f329(a117,x90373)),x90374))+P24(f329(f329(f329(f329(a201,f329(f240(a870),f329(a28,x90371))),x90372),x90373),x90374))
% 187.18/188.05 [9097]P24(f329(f329(f243(f881(x90971,a869)),x90972),f329(f329(f115(f881(x90971,a869)),x90973),x90974)))+~P24(f329(f329(f243(f881(x90971,a869)),f329(f329(f22(f881(x90971,a869)),x90972),x90973)),x90974))
% 187.18/188.05 [9150]P24(f329(f329(f329(f329(a201,f329(a26,x91501)),x91502),f329(a117,x91503)),x91504))+~P24(f329(f329(f329(f329(a201,f329(f240(a870),f329(a28,x91501))),x91502),x91503),x91504))
% 187.18/188.05 [9182]~P87(x91821)+E(f329(f75(x91821),f329(f329(f6(x91822,x91821),f329(f329(f8(x91821,x91821,x91822),f75(x91821)),x91823)),x91824)),f329(f329(f6(x91822,x91821),f329(f329(f8(x91821,x91821,x91822),f75(x91821)),x91823)),x91824))
% 187.18/188.05 [9354]~P87(x93541)+P24(f329(f329(f243(x93541),f2(x93541)),f329(f329(f6(x93542,x93541),f329(f329(f8(x93541,x93541,x93542),f75(x93541)),x93543)),x93544)))
% 187.18/188.05 [9359]~P69(x93591)+E(f329(f164(x93591),f329(f329(f152(x93592,x93591),f329(f73(x93591,x93591,x93592,f79(x93591)),x93593)),x93594)),f329(f79(x93591),f329(f164(x93591),f329(f329(f152(x93592,x93591),x93593),x93594))))
% 187.18/188.05 [9493]~P87(x94931)+P24(f329(f329(f243(x94931),f329(f75(x94931),f329(f329(f6(x94932,x94931),x94933),x94934))),f329(f329(f6(x94932,x94931),f329(f329(f8(x94931,x94931,x94932),f75(x94931)),x94933)),x94934)))
% 187.18/188.05 [9523]~E(f329(f329(f80(a874),x95231),x95234),f329(f329(f80(a874),x95233),x95232))+P24(f329(f329(f331(f880(f880(a874,a874),f880(a874,a874))),f329(f329(f264(f880(a874,a874),f880(a874,a874)),f329(f329(f264(a874,a874),x95231),x95232)),f329(f329(f264(a874,a874),x95233),x95234))),a113))
% 187.18/188.05 [9524]~P24(f329(f329(f244(a874),x95241),x95243))+P24(f329(f329(f331(f880(f880(a874,a874),f880(a874,a874))),f329(f329(f264(f880(a874,a874),f880(a874,a874)),f329(f329(f264(a874,a874),x95241),x95242)),f329(f329(f264(a874,a874),x95243),x95244))),a35))
% 187.18/188.05 [9525]~P24(f329(f329(f244(a874),x95251),x95253))+P24(f329(f329(f331(f880(f880(a874,a874),f880(a874,a874))),f329(f329(f264(f880(a874,a874),f880(a874,a874)),f329(f329(f264(a874,a874),x95251),x95252)),f329(f329(f264(a874,a874),x95253),x95254))),a70))
% 187.18/188.05 [9671]E(f329(f329(f80(a874),x96711),x96712),f329(f329(f80(a874),x96713),x96714))+~P24(f329(f329(f331(f880(f880(a874,a874),f880(a874,a874))),f329(f329(f264(f880(a874,a874),f880(a874,a874)),f329(f329(f264(a874,a874),x96711),x96714)),f329(f329(f264(a874,a874),x96713),x96712))),a113))
% 187.18/188.05 [9697]E(f329(f329(f163(x96971),f329(f329(f136(x96971),f329(f194(f875(x96971)),f176(x96971,x96972,x96973))),x96973)),x96974),f329(f329(f163(x96971),x96973),f329(f329(f80(a874),x96974),f329(f194(f875(x96971)),f176(x96971,x96972,x96973)))))+~P24(f329(f329(f244(a874),x96974),f329(f194(f875(x96971)),f329(f329(f136(x96971),f329(f194(f875(x96971)),f176(x96971,x96972,x96973))),x96973))))
% 187.18/188.05 [9715]~P24(f329(f329(f331(x97152),x97154),f329(f329(f42(x97151,f881(x97152,a869)),f252(f881(x97151,a869))),x97153)))+P24(f329(f329(f329(f42(x97151,f881(x97152,a869)),f252(f881(x97151,a869))),f329(f329(f8(f881(x97152,a869),f881(x97152,a869),x97151),f329(f7(x97152,f881(x97152,a869),a869),f331(x97152))),x97153)),x97154))
% 187.18/188.05 [9716]~P24(f329(f329(f331(x97162),x97164),f329(f329(f43(x97161,f881(x97162,a869)),f252(f881(x97161,a869))),x97163)))+P24(f329(f329(f329(f43(x97161,f881(x97162,a869)),f252(f881(x97161,a869))),f329(f329(f8(f881(x97162,a869),f881(x97162,a869),x97161),f329(f7(x97162,f881(x97162,a869),a869),f331(x97162))),x97163)),x97164))
% 187.18/188.05 [9797]~P24(f329(f49(x97971,x97972),f329(f329(f264(a1,a1),x97974),x97973)))+P24(f329(f49(f329(f79(a1),x97971),x97972),f329(f329(f264(a1,a1),f329(f329(f329(f101(a1),f329(f329(a326,x97973),f2(a1))),f329(f79(a1),x97974)),f329(f329(f22(a1),f329(f79(a1),x97974)),f78(a1)))),f329(f329(f329(f101(a1),f329(f329(a326,x97973),f2(a1))),f2(a1)),f329(f329(f22(a1),x97972),x97973)))))
% 187.18/188.05 [9806]P24(f329(f329(f331(x98061),x98062),f329(f329(f42(x98063,f881(x98061,a869)),f252(f881(x98063,a869))),x98064)))+~P24(f329(f329(f329(f42(x98063,f881(x98061,a869)),f252(f881(x98063,a869))),f329(f329(f8(f881(x98061,a869),f881(x98061,a869),x98063),f329(f7(x98061,f881(x98061,a869),a869),f331(x98061))),x98064)),x98062))
% 187.18/188.05 [9807]P24(f329(f329(f331(x98071),x98072),f329(f329(f43(x98073,f881(x98071,a869)),f252(f881(x98073,a869))),x98074)))+~P24(f329(f329(f329(f43(x98073,f881(x98071,a869)),f252(f881(x98073,a869))),f329(f329(f8(f881(x98071,a869),f881(x98071,a869),x98073),f329(f7(x98071,f881(x98071,a869),a869),f331(x98071))),x98074)),x98072))
% 187.18/188.05 [9819]E(f329(f329(f42(a874,f881(x98191,a869)),f252(f881(a874,a869))),x98192),f329(f329(f42(a874,f881(x98191,a869)),f252(f881(a874,a869))),x98193))+~E(f329(f329(f42(a874,f881(x98191,a869)),f329(f299(a874,f2(a874)),f443(x98192,x98194,x98193,x98191))),x98193),f329(f329(f42(a874,f881(x98191,a869)),f329(f299(a874,f2(a874)),f329(f329(f80(a874),f443(x98192,x98194,x98193,x98191)),x98194))),x98192))
% 187.18/188.05 [10140]~P24(f329(f329(f243(f881(f880(x101401,x101402),a869)),x101403),x101404))+P24(f329(f329(f243(f881(x101401,f881(x101402,a869))),f329(f329(f7(x101401,f881(f880(x101401,x101402),a869),f881(x101402,a869)),f329(f329(f8(f881(x101402,f881(f881(f880(x101401,x101402),a869),a869)),f881(f881(f880(x101401,x101402),a869),f881(x101402,a869)),x101401),f7(x101402,f881(f880(x101401,x101402),a869),a869)),f329(f329(f8(f881(x101402,f880(x101401,x101402)),f881(x101402,f881(f881(f880(x101401,x101402),a869),a869)),x101401),f329(f8(f880(x101401,x101402),f881(f881(f880(x101401,x101402),a869),a869),x101402),f331(f880(x101401,x101402)))),f264(x101401,x101402)))),x101403)),f329(f329(f7(x101401,f881(f880(x101401,x101402),a869),f881(x101402,a869)),f329(f329(f8(f881(x101402,f881(f881(f880(x101401,x101402),a869),a869)),f881(f881(f880(x101401,x101402),a869),f881(x101402,a869)),x101401),f7(x101402,f881(f880(x101401,x101402),a869),a869)),f329(f329(f8(f881(x101402,f880(x101401,x101402)),f881(x101402,f881(f881(f880(x101401,x101402),a869),a869)),x101401),f329(f8(f880(x101401,x101402),f881(f881(f880(x101401,x101402),a869),a869),x101402),f331(f880(x101401,x101402)))),f264(x101401,x101402)))),x101404)))
% 187.18/188.05 [10157]P24(f329(f329(f243(f881(f880(x101571,x101572),a869)),x101573),x101574))+~P24(f329(f329(f243(f881(x101571,f881(x101572,a869))),f329(f329(f7(x101571,f881(f880(x101571,x101572),a869),f881(x101572,a869)),f329(f329(f8(f881(x101572,f881(f881(f880(x101571,x101572),a869),a869)),f881(f881(f880(x101571,x101572),a869),f881(x101572,a869)),x101571),f7(x101572,f881(f880(x101571,x101572),a869),a869)),f329(f329(f8(f881(x101572,f880(x101571,x101572)),f881(x101572,f881(f881(f880(x101571,x101572),a869),a869)),x101571),f329(f8(f880(x101571,x101572),f881(f881(f880(x101571,x101572),a869),a869),x101572),f331(f880(x101571,x101572)))),f264(x101571,x101572)))),x101573)),f329(f329(f7(x101571,f881(f880(x101571,x101572),a869),f881(x101572,a869)),f329(f329(f8(f881(x101572,f881(f881(f880(x101571,x101572),a869),a869)),f881(f881(f880(x101571,x101572),a869),f881(x101572,a869)),x101571),f7(x101572,f881(f880(x101571,x101572),a869),a869)),f329(f329(f8(f881(x101572,f880(x101571,x101572)),f881(x101572,f881(f881(f880(x101571,x101572),a869),a869)),x101571),f329(f8(f880(x101571,x101572),f881(f881(f880(x101571,x101572),a869),a869),x101572),f331(f880(x101571,x101572)))),f264(x101571,x101572)))),x101574)))
% 187.18/188.05 [9231]~P24(f329(f329(f331(f880(x92311,x92311)),x92312),f305(x92311,x92314)))+P24(f329(f329(f331(f880(x92311,x92311)),x92312),f305(x92311,f329(f329(f115(f881(f880(x92311,x92311),a869)),x92313),x92314))))
% 187.18/188.05 [9232]~P24(f329(f329(f331(f880(x92321,x92321)),x92322),f305(x92321,x92323)))+P24(f329(f329(f331(f880(x92321,x92321)),x92322),f305(x92321,f329(f329(f115(f881(f880(x92321,x92321),a869)),x92323),x92324))))
% 187.18/188.05 [9590]~E(f329(f171(x95901),x95904),f183(x95901,x95902,x95903))+E(f329(f177(x95901,x95902),f329(f329(f152(x95901,f880(x95901,x95902)),f329(f329(f18(x95901,x95902,f880(x95901,x95902)),f264(x95901,x95902)),f329(f329(f8(f878(x95902),x95902,x95901),f240(x95902)),x95903))),x95904)),x95903)
% 187.18/188.05 [9914]~P24(f329(f329(f243(a874),f329(f329(f80(a874),x99141),x99144)),f329(f329(f80(a874),x99143),x99142)))+P24(f329(f329(f243(a1),f329(a89,f329(f283(f880(a874,a874),f880(a874,a874),a113),f329(f329(f307(f880(a874,a874)),f329(f329(f264(a874,a874),x99141),x99142)),f193(f881(f880(a874,a874),a869)))))),f329(a89,f329(f283(f880(a874,a874),f880(a874,a874),a113),f329(f329(f307(f880(a874,a874)),f329(f329(f264(a874,a874),x99143),x99144)),f193(f881(f880(a874,a874),a869)))))))
% 187.18/188.05 [9915]~P24(f329(f329(f244(a874),f329(f329(f80(a874),x99151),x99154)),f329(f329(f80(a874),x99153),x99152)))+P24(f329(f329(f244(a1),f329(a89,f329(f283(f880(a874,a874),f880(a874,a874),a113),f329(f329(f307(f880(a874,a874)),f329(f329(f264(a874,a874),x99151),x99152)),f193(f881(f880(a874,a874),a869)))))),f329(a89,f329(f283(f880(a874,a874),f880(a874,a874),a113),f329(f329(f307(f880(a874,a874)),f329(f329(f264(a874,a874),x99153),x99154)),f193(f881(f880(a874,a874),a869)))))))
% 187.18/188.05 [9992]P24(f329(f329(f243(a874),f329(f329(f80(a874),x99921),x99922)),f329(f329(f80(a874),x99923),x99924)))+~P24(f329(f329(f243(a1),f329(a89,f329(f283(f880(a874,a874),f880(a874,a874),a113),f329(f329(f307(f880(a874,a874)),f329(f329(f264(a874,a874),x99921),x99924)),f193(f881(f880(a874,a874),a869)))))),f329(a89,f329(f283(f880(a874,a874),f880(a874,a874),a113),f329(f329(f307(f880(a874,a874)),f329(f329(f264(a874,a874),x99923),x99922)),f193(f881(f880(a874,a874),a869)))))))
% 187.18/188.05 [9993]P24(f329(f329(f244(a874),f329(f329(f80(a874),x99931),x99932)),f329(f329(f80(a874),x99933),x99934)))+~P24(f329(f329(f244(a1),f329(a89,f329(f283(f880(a874,a874),f880(a874,a874),a113),f329(f329(f307(f880(a874,a874)),f329(f329(f264(a874,a874),x99931),x99934)),f193(f881(f880(a874,a874),a869)))))),f329(a89,f329(f283(f880(a874,a874),f880(a874,a874),a113),f329(f329(f307(f880(a874,a874)),f329(f329(f264(a874,a874),x99933),x99932)),f193(f881(f880(a874,a874),a869)))))))
% 187.18/188.05 [10034]P24(f329(f329(f243(f881(x100341,a869)),f329(f329(f42(a874,f881(x100341,a869)),f252(f881(a874,a869))),x100342)),f329(f329(f42(a874,f881(x100341,a869)),f252(f881(a874,a869))),x100343)))+~P24(f329(f329(f243(f881(x100341,a869)),f329(f329(f42(a874,f881(x100341,a869)),f329(f299(a874,f2(a874)),f444(x100343,x100344,x100342,x100341))),x100342)),f329(f329(f42(a874,f881(x100341,a869)),f329(f299(a874,f2(a874)),f329(f329(f80(a874),f444(x100343,x100344,x100342,x100341)),x100344))),x100343)))
% 187.18/188.05 [10131]~P24(f329(f329(f331(x101312),x101314),f329(f260(x101311,x101312),x101313)))+P24(f329(f259(x101311,x101312,f329(f329(f7(x101311,f881(f880(x101311,x101312),a869),f881(x101312,a869)),f329(f329(f8(f881(x101312,f881(f881(f880(x101311,x101312),a869),a869)),f881(f881(f880(x101311,x101312),a869),f881(x101312,a869)),x101311),f7(x101312,f881(f880(x101311,x101312),a869),a869)),f329(f329(f8(f881(x101312,f880(x101311,x101312)),f881(x101312,f881(f881(f880(x101311,x101312),a869),a869)),x101311),f329(f8(f880(x101311,x101312),f881(f881(f880(x101311,x101312),a869),a869),x101312),f331(f880(x101311,x101312)))),f264(x101311,x101312)))),x101313)),x101314))
% 187.18/188.05 [10132]~P24(f329(f329(f331(x101321),x101324),f329(f262(x101321,x101322),x101323)))+P24(f329(f258(x101321,x101322,f329(f329(f7(x101321,f881(f880(x101321,x101322),a869),f881(x101322,a869)),f329(f329(f8(f881(x101322,f881(f881(f880(x101321,x101322),a869),a869)),f881(f881(f880(x101321,x101322),a869),f881(x101322,a869)),x101321),f7(x101322,f881(f880(x101321,x101322),a869),a869)),f329(f329(f8(f881(x101322,f880(x101321,x101322)),f881(x101322,f881(f881(f880(x101321,x101322),a869),a869)),x101321),f329(f8(f880(x101321,x101322),f881(f881(f880(x101321,x101322),a869),a869),x101322),f331(f880(x101321,x101322)))),f264(x101321,x101322)))),x101323)),x101324))
% 187.18/188.05 [10143]P24(f329(f329(f331(x101431),x101432),f329(f260(x101433,x101431),x101434)))+~P24(f329(f259(x101433,x101431,f329(f329(f7(x101433,f881(f880(x101433,x101431),a869),f881(x101431,a869)),f329(f329(f8(f881(x101431,f881(f881(f880(x101433,x101431),a869),a869)),f881(f881(f880(x101433,x101431),a869),f881(x101431,a869)),x101433),f7(x101431,f881(f880(x101433,x101431),a869),a869)),f329(f329(f8(f881(x101431,f880(x101433,x101431)),f881(x101431,f881(f881(f880(x101433,x101431),a869),a869)),x101433),f329(f8(f880(x101433,x101431),f881(f881(f880(x101433,x101431),a869),a869),x101431),f331(f880(x101433,x101431)))),f264(x101433,x101431)))),x101434)),x101432))
% 187.18/188.05 [10144]P24(f329(f329(f331(x101441),x101442),f329(f262(x101441,x101443),x101444)))+~P24(f329(f258(x101441,x101443,f329(f329(f7(x101441,f881(f880(x101441,x101443),a869),f881(x101443,a869)),f329(f329(f8(f881(x101443,f881(f881(f880(x101441,x101443),a869),a869)),f881(f881(f880(x101441,x101443),a869),f881(x101443,a869)),x101441),f7(x101443,f881(f880(x101441,x101443),a869),a869)),f329(f329(f8(f881(x101443,f880(x101441,x101443)),f881(x101443,f881(f881(f880(x101441,x101443),a869),a869)),x101441),f329(f8(f880(x101441,x101443),f881(f881(f880(x101441,x101443),a869),a869),x101443),f331(f880(x101441,x101443)))),f264(x101441,x101443)))),x101444)),x101442))
% 187.18/188.05 [9829]P24(f329(f158(x98291,x98292),x98293))+~P24(f329(f158(x98291,f329(f329(f18(x98291,a869,a869),f329(f329(f8(a869,f881(a869,a869),x98291),a327),x98294)),x98292)),x98293))
% 187.18/188.05 [9830]P24(f329(f158(x98301,x98302),x98303))+~P24(f329(f158(x98301,f329(f329(f18(x98301,a869,a869),f329(f329(f8(a869,f881(a869,a869),x98301),a327),x98302)),x98304)),x98303))
% 187.18/188.05 [9916]~P109(x99161)+E(f329(f329(f81(x99161),f329(f329(f80(x99161),f78(x99161)),f78(x99161))),f329(f329(f6(a874,x99161),f329(f329(f8(x99161,x99161,a874),f329(f80(x99161),x99162)),f329(f329(f7(a874,x99161,x99161),f329(f329(f8(x99161,f881(x99161,x99161),a874),f81(x99161)),f105(x99161))),x99163))),f329(f250(a874),x99164))),f329(f329(f81(x99161),f329(f105(x99161),x99164)),f329(f329(f80(x99161),x99162),f329(f329(f80(x99161),x99162),f329(f329(f81(x99161),f329(f105(x99161),f329(f329(f22(a874),x99164),f78(a874)))),x99163)))))
% 187.18/188.05 [10056]P24(f329(x100561,f527(x100562,x100563,x100564,x100561)))+P42(x100562,f329(f249(f880(x100562,x100562)),f329(f268(x100562,x100562,a869),f329(f329(f8(f881(x100562,a869),f881(x100562,a869),x100562),f329(f18(x100562,a869,a869),f329(f329(f8(a869,f881(a869,a869),x100562),a327),x100561))),f329(f329(f7(x100562,f881(x100562,x100562),f881(x100562,a869)),f329(f329(f8(f881(x100562,a869),f881(f881(x100562,x100562),f881(x100562,a869)),x100562),f8(x100562,a869,x100562)),a326)),x100563)))))
% 187.18/188.05 [10070]~P24(f329(f329(f244(a874),f329(x100704,f329(x100703,f527(x100701,x100703,x100704,x100702)))),f329(x100704,f527(x100701,x100703,x100704,x100702))))+P42(x100701,f329(f249(f880(x100701,x100701)),f329(f268(x100701,x100701,a869),f329(f329(f8(f881(x100701,a869),f881(x100701,a869),x100701),f329(f18(x100701,a869,a869),f329(f329(f8(a869,f881(a869,a869),x100701),a327),x100702))),f329(f329(f7(x100701,f881(x100701,x100701),f881(x100701,a869)),f329(f329(f8(f881(x100701,a869),f881(f881(x100701,x100701),f881(x100701,a869)),x100701),f8(x100701,a869,x100701)),a326)),x100703)))))
% 187.18/188.05 [10170]~P24(f329(f329(f331(f880(x101701,x101701)),f329(f329(f264(x101701,x101701),x101703),x101704)),f329(f329(f115(f881(f880(x101701,x101701),a869)),x101702),f305(x101701,f193(f881(f880(x101701,x101701),a869))))))+P24(f329(f329(f329(f329(f115(f881(x101701,f881(x101701,a869))),f329(f329(f7(x101701,f881(f880(x101701,x101701),a869),f881(x101701,a869)),f329(f329(f8(f881(x101701,f881(f881(f880(x101701,x101701),a869),a869)),f881(f881(f880(x101701,x101701),a869),f881(x101701,a869)),x101701),f7(x101701,f881(f880(x101701,x101701),a869),a869)),f329(f329(f8(f881(x101701,f880(x101701,x101701)),f881(x101701,f881(f881(f880(x101701,x101701),a869),a869)),x101701),f329(f8(f880(x101701,x101701),f881(f881(f880(x101701,x101701),a869),a869),x101701),f331(f880(x101701,x101701)))),f264(x101701,x101701)))),x101702)),a326),x101703),x101704))
% 187.18/188.05 [10180]P24(f329(f329(f331(f880(x101801,x101801)),f329(f329(f264(x101801,x101801),x101802),x101803)),f329(f329(f115(f881(f880(x101801,x101801),a869)),x101804),f305(x101801,f193(f881(f880(x101801,x101801),a869))))))+~P24(f329(f329(f329(f329(f115(f881(x101801,f881(x101801,a869))),f329(f329(f7(x101801,f881(f880(x101801,x101801),a869),f881(x101801,a869)),f329(f329(f8(f881(x101801,f881(f881(f880(x101801,x101801),a869),a869)),f881(f881(f880(x101801,x101801),a869),f881(x101801,a869)),x101801),f7(x101801,f881(f880(x101801,x101801),a869),a869)),f329(f329(f8(f881(x101801,f880(x101801,x101801)),f881(x101801,f881(f881(f880(x101801,x101801),a869),a869)),x101801),f329(f8(f880(x101801,x101801),f881(f881(f880(x101801,x101801),a869),a869),x101801),f331(f880(x101801,x101801)))),f264(x101801,x101801)))),x101804)),a326),x101802),x101803))
% 187.18/188.05 [10042]~P26(x100423)+E(f90(x100421,f329(f329(f18(x100421,a869,a869),f329(f329(f8(a869,f881(a869,a869),x100421),a327),x100422)),f329(f329(f8(f881(x100421,a869),a869,x100421),f88(x100421)),f329(f329(f8(f881(x100421,a869),f881(x100421,a869),x100421),f329(f18(x100421,a869,a869),f329(f329(f8(a869,f881(a869,a869),x100421),a332),x100422))),f329(f329(f8(x100423,f881(x100421,a869),x100421),f329(f7(x100421,x100423,a869),f329(f329(f8(x100423,f881(x100423,a869),x100421),f243(x100423)),x100424))),x100424))))),f329(f94(x100421,x100423,x100424),x100422))
% 187.18/188.05 [10085]~P26(x100853)+E(f90(x100851,f329(f329(f18(x100851,a869,a869),f329(f329(f8(a869,f881(a869,a869),x100851),a327),x100852)),f329(f329(f8(f881(x100851,a869),a869,x100851),f88(x100851)),f329(f329(f8(f881(x100851,a869),f881(x100851,a869),x100851),f329(f18(x100851,a869,a869),f329(f329(f8(a869,f881(a869,a869),x100851),a332),x100852))),f329(f329(f7(x100851,f881(x100851,x100853),f881(x100851,a869)),f329(f329(f8(f881(x100853,a869),f881(f881(x100851,x100853),f881(x100851,a869)),x100851),f8(x100853,a869,x100851)),f329(f329(f8(x100853,f881(x100853,a869),x100851),f243(x100853)),x100854))),x100854))))),f96(x100851,x100853,x100854,x100852))
% 187.18/188.05 [10129]E(f329(f329(f149(f875(x101291)),f329(f329(f149(x101291),x101292),f329(f140(f875(x101291),f875(x101291),f126(x101291),f118(x101291)),f329(f329(f152(f875(x101291),f875(x101291)),f154(f875(x101291),x101291,f118(x101291),f329(f329(f8(f875(x101291),f881(f875(x101291),f875(x101291)),x101291),f16(f875(x101291),f875(x101291))),f329(f329(f7(x101291,f875(x101291),f875(x101291)),f149(x101291)),f118(x101291))))),x101293)))),f179(x101291,f329(f329(f149(f875(x101291)),x101294),f329(f140(f875(f875(x101291)),f875(f875(x101291)),f126(f875(x101291)),f118(f875(x101291))),f329(f329(f152(f875(x101291),f875(f875(x101291))),f154(f875(f875(x101291)),x101291,f118(f875(x101291)),f329(f16(f881(f875(x101291),f875(f875(x101291))),x101291),f329(f329(f7(f875(x101291),f875(f875(x101291)),f875(f875(x101291))),f149(f875(x101291))),f118(f875(x101291)))))),x101293))))),f179(x101291,f329(f329(f149(f875(x101291)),f329(f329(f149(x101291),x101292),x101294)),x101293)))+~P24(f329(f317(f875(f875(x101291)),f180(x101291)),f329(f329(f149(f875(x101291)),f329(f329(f149(x101291),x101292),x101294)),x101293)))
% 187.18/188.05 [10169]~P24(f329(f62(x101692),f329(f249(x101692),x101694)))+P24(f329(f62(x101691),f329(f249(x101691),f329(f329(f8(f881(x101692,a869),a869,x101691),f87(x101692)),f329(f329(f7(x101691,f881(x101692,a869),f881(x101692,a869)),f329(f329(f8(f881(x101692,f881(a869,a869)),f881(f881(x101692,a869),f881(x101692,a869)),x101691),f18(x101692,a869,a869)),f329(f329(f8(f881(x101692,a869),f881(x101692,f881(a869,a869)),x101691),f329(f8(a869,f881(a869,a869),x101692),a327)),f329(f329(f7(x101691,f881(x101692,x101691),f881(x101692,a869)),f329(f329(f8(f881(x101691,a869),f881(f881(x101692,x101691),f881(x101692,a869)),x101691),f8(x101691,a869,x101692)),a326)),x101693)))),x101694)))))
% 187.18/188.05 [5248]E(x52481,x52482)+~E(f128(x52483,x52484,x52481),f128(x52483,x52485,x52482))
% 187.18/188.05 [5249]E(x52491,x52492)+~E(f128(x52493,x52491,x52494),f128(x52493,x52492,x52495))
% 187.18/188.05 [5250]E(x52501,x52502)+~E(f169(x52503,x52501,x52504),f169(x52503,x52502,x52505))
% 187.18/188.05 [5626]E(f329(f329(f307(x56261),x56262),f183(x56261,x56263,x56264)),f183(x56261,x56263,x56264))+~E(f329(x56264,x56262),f329(f236(x56263),x56265))
% 187.18/188.05 [6035]P24(f329(f259(x60351,x60352,x60353),x60354))+~P24(f329(f329(x60353,x60355),x60354))
% 187.18/188.05 [6037]P24(f329(f258(x60371,x60372,x60373),x60374))+~P24(f329(f329(x60373,x60374),x60375))
% 187.18/188.05 [6040]~E(f329(x60404,x60402),f329(f236(x60403),x60405))+P24(f329(f329(f331(x60401),x60402),f183(x60401,x60403,x60404)))
% 187.18/188.05 [6041]~E(f329(x60414,x60415),f329(f236(x60411),x60412))+P24(f329(f329(f331(x60411),x60412),f185(x60413,x60411,x60414)))
% 187.18/188.05 [6506]~E(x65065,f2(a104))+E(f329(f203(x65061,x65062,x65063,x65064),x65065),f129(x65062))
% 187.18/188.05 [6507]~E(x65075,f2(a104))+E(f329(f205(x65071,x65072,x65073,x65074),x65075),f120(x65072))
% 187.18/188.05 [6643]~E(x66433,f2(a104))+E(f329(f278(x66431,x66432,x66433,x66434),x66435),f329(f264(x66431,x66432),x66435))
% 187.18/188.05 [6715]~E(f329(x67154,x67155),f206(x67152))+E(f329(f238(f878(x67151),x67152,f206(x67151),x67153),f329(x67154,x67155)),f206(x67151))
% 187.18/188.05 [7340]E(f329(x73401,x73402),f206(x73403))+~E(f329(f184(x73404,x73403,x73405,x73401),x73402),f206(x73403))
% 187.18/188.05 [7341]E(f329(x73411,x73412),f206(x73413))+~E(f329(f184(x73414,x73413,x73411,x73415),x73412),f206(x73413))
% 187.18/188.05 [7378]E(f329(f184(x73781,x73782,x73783,x73784),x73785),f329(x73783,x73785))+P24(f329(f329(f331(x73781),x73785),f183(x73781,x73782,x73784)))
% 187.18/188.05 [7379]E(f329(f184(x73791,x73792,x73793,x73794),x73795),f329(x73794,x73795))+P24(f329(f329(f331(x73791),x73795),f183(x73791,x73792,x73793)))
% 187.18/188.05 [7702]~P16(x77024,x77021,x77022,x77025)+E(f329(f73(x77021,x77021,x77021,f329(x77022,x77023)),f329(x77022,x77023)),f329(x77022,x77023))
% 187.18/188.05 [7748]E(f329(f184(x77481,x77482,x77483,x77484),x77485),f329(x77484,x77485))+~P24(f329(f329(f331(x77481),x77485),f183(x77481,x77482,x77484)))
% 187.18/188.05 [8099]~P12(x80995,x80991,x80992)+E(f329(f73(x80991,x80991,x80991,f329(x80992,x80993)),f329(x80992,x80994)),f329(f73(x80991,x80991,x80991,f329(x80992,x80994)),f329(x80992,x80993)))
% 187.18/188.05 [8429]P24(f329(f329(f331(f880(x84291,x84291)),f329(f329(f264(x84291,x84291),x84292),x84293)),f323(x84291,x84294,x84295)))+~P24(f329(f329(f244(a874),f329(x84294,x84292)),f329(x84294,x84293)))
% 187.18/188.05 [8527]~P24(f329(f329(f331(x85274),x85273),f293(x85274,x85271,x85272,x85275)))+P24(f329(f329(x85271,x85272),x85273))
% 187.18/188.05 [8528]~P24(f329(f329(f331(x85284),x85283),f296(x85284,x85281,x85282,x85285)))+P24(f329(f329(x85281,x85282),x85283))
% 187.18/188.05 [8529]~P24(f329(f329(f331(x85294),x85292),f293(x85294,x85291,x85295,x85293)))+P24(f329(f329(x85291,x85292),x85293))
% 187.18/188.05 [8530]~P24(f329(f329(f331(x85304),x85302),f296(x85304,x85301,x85305,x85303)))+P24(f329(f329(x85301,x85302),x85303))
% 187.18/188.05 [8669]~P56(x86692,x86691,x86695,x86693,x86694)+E(f329(f308(x86691,x86692,x86693),x86694),f252(f881(x86692,a869)))
% 187.18/188.05 [9108]~P39(x91081,x91082,x91083,x91084,x91085)+P39(x91081,x91082,x91083,f329(f167(x91081),x91084),f329(f167(x91082),x91085))
% 187.18/188.05 [9110]~P39(x91101,x91102,x91103,f329(f167(x91101),x91104),x91105)+P39(x91101,x91102,x91103,x91104,f329(f167(x91102),x91105))
% 187.18/188.05 [9111]~P39(x91111,x91112,x91113,x91114,f329(f167(x91112),x91115))+P39(x91111,x91112,x91113,f329(f167(x91111),x91114),x91115)
% 187.18/188.05 [9117]P39(x91171,x91172,x91173,x91174,x91175)+~P39(x91171,x91172,x91173,f329(f167(x91171),x91174),f329(f167(x91172),x91175))
% 187.18/188.05 [9514]P24(f329(f329(f331(f880(f875(x95141),f875(x95141))),f329(f329(f264(f875(x95141),f875(x95141)),f329(f329(f149(x95141),x95142),x95143)),f329(f329(f149(x95141),x95142),x95144))),f155(x95141,x95145)))+~P24(f329(f329(f331(f880(f875(x95141),f875(x95141))),f329(f329(f264(f875(x95141),f875(x95141)),x95143),x95144)),f155(x95141,x95145)))
% 187.18/188.05 [9515]P24(f329(f329(f331(f880(f875(x95151),f875(x95151))),f329(f329(f264(f875(x95151),f875(x95151)),f329(f329(f126(x95151),x95152),x95153)),f329(f329(f126(x95151),x95152),x95154))),f145(x95151,x95155)))+~P24(f329(f329(f331(f880(f875(x95151),f875(x95151))),f329(f329(f264(f875(x95151),f875(x95151)),x95153),x95154)),f145(x95151,x95155)))
% 187.18/188.05 [9705]E(f329(f329(f149(x97051),f670(x97052,x97053,x97054,x97055,x97051)),f673(x97052,x97053,x97054,x97055,x97051)),x97055)+~P24(f329(f329(f331(f880(f875(x97051),f875(x97051))),f329(f329(f264(f875(x97051),f875(x97051)),x97055),f329(f329(f149(x97051),x97054),x97053))),f156(x97051,x97052)))
% 187.18/188.05 [9727]E(f329(f329(f149(x97271),f671(x97272,x97273,x97274,x97275,x97271)),f672(x97272,x97273,x97274,x97275,x97271)),x97273)+~P24(f329(f329(f331(f880(f875(x97271),f875(x97271))),f329(f329(f264(f875(x97271),f875(x97271)),f329(f329(f149(x97271),x97275),x97274)),x97273)),f156(x97271,x97272)))
% 187.18/188.05 [9890]~P24(f329(f329(f331(f880(f875(x98901),f875(x98901))),f329(f329(f264(f875(x98901),f875(x98901)),f329(f329(f149(x98901),x98905),x98902)),x98904)),f156(x98901,x98903)))+P24(f329(f329(f331(f880(f875(x98901),f875(x98901))),f329(f329(f264(f875(x98901),f875(x98901)),x98902),f672(x98903,x98904,x98902,x98905,x98901))),f156(x98901,x98903)))
% 187.18/188.05 [9960]~P24(f329(f329(f331(f880(f875(x99601),f875(x99601))),f329(f329(f264(f875(x99601),f875(x99601)),x99605),f329(f329(f149(x99601),x99604),x99603))),f156(x99601,x99602)))+P24(f329(f329(f331(f880(f875(x99601),f875(x99601))),f329(f329(f264(f875(x99601),f875(x99601)),f673(x99602,x99603,x99604,x99605,x99601)),x99603)),f156(x99601,x99602)))
% 187.18/188.05 [10124]P24(f329(f329(f331(f880(x101241,x101241)),f329(f329(f264(x101241,x101241),f329(x101242,f329(f329(f80(a874),x101243),x101244))),f329(x101242,x101243))),f305(x101241,x101245)))+~P24(f329(f329(f331(f880(x101241,x101241)),f329(f329(f264(x101241,x101241),f329(x101242,f329(a117,f591(x101244,x101243,x101245,x101242,x101241)))),f329(x101242,f591(x101244,x101243,x101245,x101242,x101241)))),f305(x101241,x101245)))
% 187.18/188.05 [5214]E(x52141,x52142)+~E(f329(f329(f149(x52143),x52144),x52141),f329(f329(f149(x52143),x52145),x52142))
% 187.18/188.05 [5215]E(x52151,x52152)+~E(f329(f329(f149(x52153),x52151),x52154),f329(f329(f149(x52153),x52152),x52155))
% 187.18/188.05 [5266]P24(f329(x52661,x52662))+~E(f329(f134(x52663,x52661),x52664),f329(f329(f149(x52663),x52662),x52665))
% 187.18/188.05 [5267]P24(f329(x52671,x52672))+~E(f329(f329(f149(x52673),x52672),x52674),f329(f134(x52673,x52671),x52675))
% 187.18/188.05 [5424]~E(f329(f329(f136(x54241),x54243),x54242),f329(f329(f149(x54241),x54244),x54245))+E(f329(f329(f163(x54241),x54242),x54243),x54244)
% 187.18/188.05 [5556]~P11(x55564,x55565,x55561)+E(f329(f329(x55561,x55562),f329(f329(x55561,x55562),x55563)),f329(f329(x55561,x55562),x55563))
% 187.18/188.05 [6093]~E(x60934,f2(a104))+E(f329(f329(f122(x60931,x60932,x60933),x60934),x60935),f329(f329(f264(f875(x60932),x60931),f118(x60932)),x60935))
% 187.18/188.05 [6165]~P27(x61652)+~E(f329(f329(f146(x61651,x61652,x61653),x61654),x61655),f118(x61651))
% 187.18/188.05 [6543]E(x65431,x65432)+~E(f329(f329(f126(x65433),x65434),f329(f329(f149(x65433),x65431),f118(x65433))),f329(f329(f126(x65433),x65435),f329(f329(f149(x65433),x65432),f118(x65433))))
% 187.18/188.05 [6544]E(x65441,x65442)+~E(f329(f329(f126(x65443),x65441),f329(f329(f149(x65443),x65444),f118(x65443))),f329(f329(f126(x65443),x65442),f329(f329(f149(x65443),x65445),f118(x65443))))
% 187.18/188.05 [6799]E(f329(f187(x67991,x67992,x67993,x67994),x67995),f206(x67992))+P24(f329(f329(f331(x67991),x67995),x67994))
% 187.18/188.05 [6861]E(f329(f329(f307(x68611),f329(x68612,x68613)),f329(f308(x68614,x68611,x68612),x68615)),f329(f308(x68614,x68611,x68612),x68615))+~P24(f329(f329(f331(x68614),x68613),x68615))
% 187.18/188.05 [6868]~P24(f329(x68684,f329(x68683,x68685)))+P24(f329(f329(f309(x68681,x68682,x68683),x68684),x68685))
% 187.18/188.05 [6871]~P24(f329(f329(x68713,x68715),x68714))+P24(f329(f329(f253(x68711,x68712,x68713),x68714),x68715))
% 187.18/188.05 [6966]~E(f329(f308(x69661,x69662,x69663),x69664),x69665)+E(f329(f308(f881(x69661,a869),f881(x69662,a869),f308(x69661,x69662,x69663)),f329(f306(x69661),x69664)),f329(f306(x69662),x69665))
% 187.18/188.05 [6998]E(f329(f187(x69981,x69982,x69983,x69984),x69985),f329(x69983,x69985))+~P24(f329(f329(f331(x69981),x69985),x69984))
% 187.18/188.05 [7297]P21(x72971,x72972,x72973,x72974)+~P21(x72971,x72972,x72973,f329(f329(f307(x72971),x72975),x72974))
% 187.18/188.05 [7367]P24(f329(x73671,x73672))+~P24(f329(f329(f97(x73673,x73674,x73671),x73675),x73672))
% 187.18/188.05 [7412]~P24(f329(f329(f331(x74124),x74123),x74125))+P24(f329(f329(f331(x74121),f329(x74122,x74123)),f329(f308(x74124,x74121,x74122),x74125)))
% 187.18/188.05 [7436]~P27(x74362)+E(f148(x74361,x74362,x74363,f329(f134(x74361,x74364),x74365)),f329(f134(x74361,x74364),f148(x74361,x74362,x74363,x74365)))
% 187.18/188.05 [7469]P24(f329(x74691,f329(x74692,x74693)))+~P24(f329(f329(f309(x74694,x74695,x74692),x74691),x74693))
% 187.18/188.05 [7472]P24(f329(f329(x74721,x74722),x74723))+~P24(f329(f329(f253(x74724,x74725,x74721),x74723),x74722))
% 187.18/188.05 [7473]P24(f329(f329(x74731,x74732),x74733))+~P24(f329(f329(f97(x74734,x74731,x74735),x74732),x74733))
% 187.18/188.05 [7536]~P24(f329(f329(f331(x75363),f329(x75364,x75362)),x75365))+P24(f329(f329(f331(x75361),x75362),f329(f309(x75361,x75363,x75364),x75365)))
% 187.18/188.05 [7937]~P24(f329(f329(f331(x79375),x79373),f329(f309(x79375,x79371,x79372),x79374)))+P24(f329(f329(f331(x79371),f329(x79372,x79373)),x79374))
% 187.18/188.05 [8165]~E(x81653,f329(f329(f329(f72(x81651,f878(x81652)),f329(f16(f878(x81652),x81651),f206(x81652))),x81654),f329(f236(x81652),x81655)))+E(f183(x81651,x81652,x81653),f329(f329(f307(x81651),x81654),f193(f881(x81651,a869))))
% 187.18/188.05 [8245]~P12(x82452,x82451,x82453)+E(f329(f140(x82451,x82452,f329(f7(x82452,x82451,x82451),x82453),x82454),f150(x82452,x82455)),f329(f329(f65(x82452,x82451,x82453),x82454),f329(f171(x82452),x82455)))
% 187.18/188.05 [8264]E(f329(x82641,f394(x82642,x82641,x82643,x82644)),x82644)+~P24(f329(f329(f331(x82645),x82644),f329(f308(x82643,x82645,x82641),x82642)))
% 187.18/188.05 [8573]~E(x85732,f329(f329(f149(x85731),x85734),x85735))+P24(f329(f329(f331(f880(f875(x85731),f875(x85731))),f329(f329(f264(f875(x85731),f875(x85731)),f118(x85731)),x85732)),f145(x85731,x85733)))
% 187.18/188.05 [8626]~P39(x86261,x86263,x86265,x86262,x86264)+E(f329(f194(f875(x86261)),x86262),f329(f194(f875(x86263)),x86264))
% 187.18/188.05 [8636]P24(f329(f329(f243(f881(x86361,a869)),f329(f329(f43(x86362,f881(x86361,a869)),x86363),x86364)),f329(x86364,x86365)))+~P24(f329(f329(f331(x86362),x86365),x86363))
% 187.18/188.05 [8685]~P56(x86851,x86852,x86853,x86855,x86854)+E(f329(f308(x86851,x86852,x86853),f252(f881(x86851,a869))),x86854)
% 187.18/188.05 [8889]E(f329(f329(f329(f72(x88891,f878(x88892)),f187(x88891,x88892,x88893,x88894)),x88895),f206(x88892)),f187(x88891,x88892,x88893,x88894))+P24(f329(f329(f331(x88891),x88895),x88894))
% 187.18/188.05 [8894]E(f329(f134(x88941,x88942),f784(x88943,x88944,x88945,x88942,x88941)),x88943)+~E(f329(f134(x88941,x88942),x88945),f329(f329(f149(x88941),x88944),x88943))
% 187.18/188.05 [8895]E(f329(f134(x88951,x88952),f785(x88953,x88952,x88954,x88955,x88951)),x88954)+~E(f329(f329(f149(x88951),x88955),x88954),f329(f134(x88951,x88952),x88953))
% 187.18/188.05 [8896]E(f329(x88961,f711(x88962,x88963,x88961,x88964,x88965)),x88962)+~E(f329(f329(f207(x88965,x88964),x88961),x88963),f329(f236(x88964),x88962))
% 187.18/188.05 [8900]E(f329(f236(x89001),f711(x89002,x89003,x89004,x89005,x89001)),x89003)+~E(f329(f329(f207(x89001,x89005),x89004),x89003),f329(f236(x89005),x89002))
% 187.18/188.05 [9000]E(f329(f194(f875(x90001)),x90002),x90003)+~P24(f329(f329(f331(f880(f875(x90001),f875(x90001))),f329(f329(f264(f875(x90001),f875(x90001)),x90004),x90002)),f329(f141(x90001,x90005),x90003)))
% 187.18/188.05 [9001]E(f329(f194(f875(x90011)),x90012),x90013)+~P24(f329(f329(f331(f880(f875(x90011),f875(x90011))),f329(f329(f264(f875(x90011),f875(x90011)),x90012),x90014)),f329(f141(x90011,x90015),x90013)))
% 187.18/188.05 [9068]P24(f329(f329(f331(x90681),f394(x90682,x90683,x90681,x90684)),x90682))+~P24(f329(f329(f331(x90685),x90684),f329(f308(x90681,x90685,x90683),x90682)))
% 187.18/188.05 [9229]E(f329(f308(x92291,x92292,x92293),f558(x92294,x92293,x92291,x92295,x92292)),x92295)+~P24(f329(f329(f243(f881(x92292,a869)),x92295),f329(f308(x92291,x92292,x92293),x92294)))
% 187.18/188.05 [9483]E(f329(x94831,f771(x94832,x94831,x94833,x94834,x94835)),f329(f236(x94835),x94834))+~P24(f329(f329(f331(x94835),x94834),f185(x94833,x94835,f187(x94833,x94835,x94831,x94832))))
% 187.18/188.05 [9530]P24(f329(f329(f331(f880(f875(x95301),f875(x95301))),f329(f329(f264(f875(x95301),f875(x95301)),f329(f329(f149(x95301),x95302),x95303)),f329(f329(f149(x95301),x95302),x95304))),f305(f875(x95301),f155(x95301,x95305))))+~P24(f329(f329(f331(f880(f875(x95301),f875(x95301))),f329(f329(f264(f875(x95301),f875(x95301)),x95303),x95304)),f305(f875(x95301),f155(x95301,x95305))))
% 187.18/188.05 [9561]~E(f329(x95613,f713(x95615,x95614,x95613,x95612,x95611)),f329(x95615,f713(x95615,x95614,x95613,x95612,x95611)))+E(f329(f329(f152(x95611,x95612),x95613),x95614),f329(f329(f152(x95611,x95612),x95615),x95614))
% 187.18/188.05 [9637]~E(f329(f134(x96371,x96375),x96374),f329(f329(f149(x96371),x96373),x96372))+E(f329(f329(f126(x96371),f788(x96372,x96373,x96374,x96375,x96371)),f329(f329(f149(x96371),x96373),f784(x96372,x96373,x96374,x96375,x96371))),x96374)
% 187.18/188.05 [9638]~E(f329(f329(f149(x96381),x96385),x96384),f329(f134(x96381,x96383),x96382))+E(f329(f329(f126(x96381),f786(x96382,x96383,x96384,x96385,x96381)),f329(f329(f149(x96381),x96385),f785(x96382,x96383,x96384,x96385,x96381))),x96382)
% 187.18/188.05 [9642]E(f329(f329(f152(x96421,x96422),x96423),x96424),f329(f329(f152(x96421,x96422),x96425),x96424))+P24(f329(f329(f331(x96421),f713(x96423,x96424,x96425,x96422,x96421)),f329(f171(x96421),x96424)))
% 187.18/188.05 [9672]~P24(f329(f329(f331(x96725),x96724),f329(f283(x96721,x96725,x96723),x96722)))+P24(f329(f329(f331(x96721),f494(x96722,x96723,x96721,x96724,x96725)),x96722))
% 187.18/188.05 [9673]~P24(f329(f329(f331(x96735),x96734),f329(f283(x96731,x96735,x96733),x96732)))+P24(f329(f329(f331(x96731),f498(x96732,x96733,x96731,x96734,x96735)),x96732))
% 187.18/188.05 [9698]~P24(f329(f329(f243(f881(x96985,a869)),x96984),f329(f308(x96981,x96985,x96983),x96982)))+P24(f329(f329(f243(f881(x96981,a869)),f558(x96982,x96983,x96981,x96984,x96985)),x96982))
% 187.18/188.05 [9750]~P24(f329(f329(f331(x97505),x97504),f185(x97501,x97505,f187(x97501,x97505,x97503,x97502))))+P24(f329(f329(f331(x97501),f771(x97502,x97503,x97501,x97504,x97505)),x97502))
% 187.18/188.05 [10146]E(x101461,f2(a104))+E(f329(f238(f880(f875(x101462),x101463),f880(x101462,x101463),f329(f329(f264(f875(x101462),x101463),f118(x101462)),x101464),f329(f268(x101462,x101463,f880(f875(x101462),x101463)),f329(f329(f7(x101462,f881(x101463,f880(f875(x101462),x101463)),f881(x101463,f880(f875(x101462),x101463))),f329(f329(f8(f881(f880(f875(x101462),x101463),f880(f875(x101462),x101463)),f881(f881(x101463,f880(f875(x101462),x101463)),f881(x101463,f880(f875(x101462),x101463))),x101462),f8(f880(f875(x101462),x101463),f880(f875(x101462),x101463),x101463)),f329(f329(f8(f881(f875(x101462),f881(x101463,f880(f875(x101462),x101463))),f881(f880(f875(x101462),x101463),f880(f875(x101462),x101463)),x101462),f268(f875(x101462),x101463,f880(f875(x101462),x101463))),f329(f329(f8(f881(f875(x101462),f875(x101462)),f881(f875(x101462),f881(x101463,f880(f875(x101462),x101463))),x101462),f329(f8(f875(x101462),f881(x101463,f880(f875(x101462),x101463)),f875(x101462)),f264(f875(x101462),x101463))),f149(x101462))))),f329(f122(x101463,x101462,x101465),f329(f329(f22(a104),x101461),f78(a104)))))),f329(x101465,x101464)),f329(f329(f122(x101463,x101462,x101465),x101461),x101464))
% 187.18/188.05 [5437]~E(f329(x54373,x54374),x54375)+E(f329(f329(f329(f72(x54371,x54372),x54373),x54374),x54375),x54373)
% 187.18/188.05 [5879]E(f329(x58791,x58792),x58793)+~E(f329(f329(f329(f72(x58794,x58795),x58791),x58792),x58793),x58791)
% 187.18/188.05 [5975]E(x59751,x59752)+~E(f329(f267(x59753,x59754),f329(f329(f264(x59753,x59754),x59755),x59751)),x59752)
% 187.18/188.05 [5976]E(x59761,x59762)+~E(f329(f263(x59763,x59764),f329(f329(f264(x59763,x59764),x59761),x59765)),x59762)
% 187.18/188.05 [6240]~E(x62403,f329(f329(f126(x62401),x62404),f329(f329(f149(x62401),x62402),x62405)))+P24(f329(f329(f331(x62401),x62402),f329(f171(x62401),x62403)))
% 187.18/188.05 [6630]E(f329(f308(x66301,x66302,f329(f16(x66302,x66301),x66303)),x66304),f329(f329(f307(x66302),x66303),f193(f881(x66302,a869))))+~P24(f329(f329(f331(x66301),x66305),x66304))
% 187.18/188.05 [6700]E(f329(f329(f115(f881(x67001,a869)),f329(f171(x67001),x67002)),f329(f171(x67001),x67003)),f329(f171(x67001),x67004))+~E(f165(x67001,x67005,x67004),f329(f329(f264(f875(x67001),f875(x67001)),x67002),x67003))
% 187.18/188.05 [6803]~P27(x68032)+E(f329(f194(f875(x68031)),f329(f329(f146(x68031,x68032,x68033),x68034),x68035)),f329(a117,f329(f194(f875(x68031)),x68035)))
% 187.18/188.05 [6815]~P27(x68152)+E(f329(f171(x68151),f329(f329(f146(x68151,x68152,x68153),x68154),x68155)),f329(f329(f307(x68151),x68154),f329(f171(x68151),x68155)))
% 187.18/188.05 [7089]~P109(x70891)+E(f329(f329(f81(x70891),f329(f329(f81(x70891),x70892),x70893)),f329(f329(f81(x70891),x70894),x70895)),f329(f329(f81(x70891),f329(f329(f81(x70891),x70892),x70894)),f329(f329(f81(x70891),x70893),x70895)))
% 187.18/188.05 [7090]~P109(x70901)+E(f329(f329(f80(x70901),f329(f329(f80(x70901),x70902),x70903)),f329(f329(f80(x70901),x70904),x70905)),f329(f329(f80(x70901),f329(f329(f80(x70901),x70902),x70904)),f329(f329(f80(x70901),x70903),x70905)))
% 187.18/188.05 [7091]~P61(x70911)+E(f329(f329(f287(x70911),f329(f329(f81(x70911),x70912),x70913)),f329(f329(f81(x70911),x70914),x70915)),f329(f329(f81(x70911),f329(f329(f287(x70911),x70912),x70914)),f329(f329(f287(x70911),x70913),x70915)))
% 187.18/188.05 [7105]~P27(x71051)+E(f300(x71051,f329(f329(f242(x71051),x71052),x71053),f329(f329(f241(x71051),x71054),x71055)),f329(f329(f106(f881(x71051,a869)),f300(x71051,x71052,x71054)),f300(x71051,x71053,x71055)))
% 187.18/188.05 [7106]~P27(x71061)+E(f303(x71061,f329(f329(f242(x71061),x71062),x71063),f329(f329(f241(x71061),x71064),x71065)),f329(f329(f106(f881(x71061,a869)),f303(x71061,x71062,x71064)),f303(x71061,x71063,x71065)))
% 187.18/188.05 [7107]~P27(x71071)+E(f302(x71071,f329(f329(f242(x71071),x71072),x71073),f329(f329(f241(x71071),x71074),x71075)),f329(f329(f106(f881(x71071,a869)),f302(x71071,x71072,x71074)),f302(x71071,x71073,x71075)))
% 187.18/188.05 [7108]~P27(x71081)+E(f329(f329(f106(f881(x71081,a869)),f329(f299(x71081,x71082),x71083)),f329(f299(x71081,x71084),x71085)),f329(f299(x71081,f329(f329(f242(x71081),x71082),x71084)),f329(f329(f241(x71081),x71083),x71085)))
% 187.18/188.05 [7223]~P24(f329(x72231,f478(x72233,x72232,x72231)))+P24(f329(x72231,f329(f329(f264(x72232,x72233),x72234),x72235)))
% 187.18/188.05 [7310]~E(f329(x73103,x73104),f206(x73102))+E(f185(x73101,x73102,f329(f329(f329(f72(x73101,f878(x73102)),x73103),x73104),f329(f236(x73102),x73105))),f329(f329(f307(x73102),x73105),f185(x73101,x73102,x73103)))
% 187.18/188.05 [7331]~E(x73312,f329(x73314,x73315))+P24(f329(f329(f331(x73311),x73312),f329(f308(x73313,x73311,x73314),f252(f881(x73313,a869)))))
% 187.18/188.05 [7390]~E(f329(x73903,x73904),f206(x73902))+E(f329(f329(f22(f881(x73901,a869)),f183(x73901,x73902,x73903)),f329(f329(f307(x73901),x73904),x73905)),f329(f329(f22(f881(x73901,a869)),f183(x73901,x73902,x73903)),x73905))
% 187.18/188.05 [7409]~P11(x74093,x74092,x74094)+P11(x74091,x74092,f329(f329(f8(x74093,f881(x74092,x74092),x74091),x74094),x74095))
% 187.18/188.05 [7410]~P12(x74103,x74102,x74104)+P12(x74101,x74102,f329(f329(f8(x74103,f881(x74102,x74102),x74101),x74104),x74105))
% 187.18/188.05 [7552]~P21(x75521,x75522,x75523,x75524)+P21(x75521,x75522,x75523,f329(f329(f22(f881(x75521,a869)),x75524),x75525))
% 187.18/188.05 [7711]~P24(f329(f329(x77113,x77114),x77115))+P24(f329(f329(f268(x77111,x77112,a869),x77113),f329(f329(f264(x77111,x77112),x77114),x77115)))
% 187.18/188.05 [7826]~P24(f329(x78262,x78264))+~E(f329(f329(f136(x78261),f329(f194(f875(x78261)),f176(x78261,x78262,x78263))),x78263),f329(f329(f149(x78261),x78264),x78265))
% 187.18/188.05 [7846]P21(x78461,x78462,x78463,x78464)+~P21(x78461,x78462,x78463,f329(f329(f115(f881(x78461,a869)),x78465),x78464))
% 187.18/188.05 [7847]P21(x78471,x78472,x78473,x78474)+~P21(x78471,x78472,x78473,f329(f329(f115(f881(x78471,a869)),x78474),x78475))
% 187.18/188.05 [7894]~P27(x78942)+E(f329(f329(f146(x78941,x78942,x78943),x78944),f148(x78941,x78942,x78943,x78945)),f148(x78941,x78942,x78943,f329(f329(f149(x78941),x78944),x78945)))
% 187.18/188.05 [8058]~P34(x80581,f329(a117,x80582),f329(f329(f329(f92(x80581),x80583),f329(a26,x80584)),x80585))+P34(x80581,x80582,f329(f329(f329(f92(x80581),x80583),f329(f240(a870),f329(a28,x80584))),x80585))
% 187.18/188.05 [8192]P34(x81921,f329(a117,x81922),f329(f329(f329(f92(x81921),x81923),f329(a26,x81924)),x81925))+~P34(x81921,x81922,f329(f329(f329(f92(x81921),x81923),f329(f240(a870),f329(a28,x81924))),x81925))
% 187.18/188.05 [8221]~P11(x82212,x82211,x82213)+E(f329(f140(x82211,x82212,f329(f7(x82212,x82211,x82211),x82213),x82214),x82215),f329(f329(f65(x82212,x82211,x82213),x82214),f329(f171(x82212),x82215)))
% 187.18/188.05 [8250]~E(f329(f329(f136(x82501),f329(f194(f875(x82501)),f176(x82501,x82502,x82503))),x82503),f329(f329(f149(x82501),x82504),x82505))+E(f329(f329(f126(x82501),f176(x82501,x82502,x82503)),f329(f329(f149(x82501),x82504),x82505)),x82503)
% 187.18/188.05 [8274]P24(f329(f329(x82741,x82742),x82743))+~P24(f329(f329(f268(x82744,x82745,a869),x82741),f329(f329(f264(x82744,x82745),x82742),x82743)))
% 187.18/188.05 [8337]~E(f329(f329(f177(x83371,x83372),x83375),x83373),f329(f236(x83372),x83374))+P24(f329(f329(f331(f880(x83371,x83372)),f329(f329(f264(x83371,x83372),x83373),x83374)),f329(f171(f880(x83371,x83372)),x83375)))
% 187.18/188.05 [8740]P24(f329(f329(f243(f881(x87401,a869)),f329(f308(x87402,x87401,x87403),x87404)),f329(f308(x87402,x87401,x87403),x87405)))+~P24(f329(f329(f243(f881(x87402,a869)),x87404),x87405))
% 187.18/188.05 [8741]P24(f329(f329(f243(f881(x87411,a869)),f329(f309(x87411,x87412,x87413),x87414)),f329(f309(x87411,x87412,x87413),x87415)))+~P24(f329(f329(f243(f881(x87412,a869)),x87414),x87415))
% 187.18/188.05 [8816]E(x88161,f2(a104))+E(f329(f329(f270(x88162,x88163,x88162,f880(x88163,x88162)),f329(x88164,x88165)),f278(x88163,x88162,f329(f329(f22(a104),x88161),f78(a104)),x88164)),f329(f278(x88163,x88162,x88161,x88164),x88165))
% 187.18/188.05 [9138]P34(x91381,x91382,f329(f329(f329(f92(x91381),x91383),x91384),x91385))+P24(f329(f329(x91383,f343(x91385,x91384,x91383,x91382)),f344(x91385,x91384,x91383,x91382)))
% 187.18/188.05 [9340]E(f329(f236(x93401),f715(x93402,x93403,x93404,x93401,x93405)),f329(f329(f177(x93405,x93401),x93402),x93404))+~P24(f329(f329(f331(f880(x93405,x93401)),f329(f329(f264(x93405,x93401),x93404),x93403)),f329(f171(f880(x93405,x93401)),x93402)))
% 187.18/188.05 [9384]P34(x93841,x93842,f329(f329(f329(f92(x93841),x93843),x93844),x93845))+~P24(f329(f329(x93845,f343(x93845,x93844,x93843,x93842)),f345(x93845,x93844,x93843,x93842)))
% 187.18/188.05 [9443]P34(x94431,x94432,f329(f329(f329(f92(x94431),x94433),x94434),x94435))+P24(f329(f329(f329(f329(a201,x94434),f344(x94435,x94434,x94433,x94432)),x94432),f345(x94435,x94434,x94433,x94432)))
% 187.18/188.05 [9446]~P20(x94461,x94462,f329(f329(f307(f873(x94461)),f329(f329(f329(f92(x94461),x94463),f329(f240(a870),f329(a28,x94464))),x94465)),f193(f881(f873(x94461),a869))))+P20(x94461,x94462,f329(f329(f307(f873(x94461)),f329(f329(f329(f92(x94461),x94463),f329(a26,x94464)),x94465)),f193(f881(f873(x94461),a869))))
% 187.18/188.05 [9474]~P24(f329(f62(x94743),f329(f308(x94742,x94743,x94745),f252(f881(x94742,a869)))))+P24(f329(f62(x94741),f329(f308(x94742,x94741,f329(f329(f8(x94743,x94741,x94742),x94744),x94745)),f252(f881(x94742,a869)))))
% 187.18/188.05 [9497]P24(f329(f329(f243(f881(f881(x94971,a869),a869)),f329(f308(f881(x94972,a869),f881(x94971,a869),f308(x94972,x94971,x94973)),f329(f306(x94972),x94974))),f329(f306(x94971),x94975)))+~P24(f329(f329(f243(f881(x94971,a869)),f329(f308(x94972,x94971,x94973),x94974)),x94975))
% 187.18/188.05 [9510]~P24(f329(f62(f878(x95101)),f329(f308(x95102,f878(x95101),x95103),f252(f881(x95102,a869)))))+P24(f329(f62(f878(x95101)),f329(f308(x95102,f878(x95101),f329(f329(f329(f72(x95102,f878(x95101)),x95103),x95104),f329(f236(x95101),x95105))),f252(f881(x95102,a869)))))
% 187.18/188.05 [9570]E(x95701,x95702)+~P24(f329(f67(x95703,x95704,x95705,x95701,f193(f881(x95703,a869))),x95702))
% 187.18/188.05 [9585]E(f329(f329(f264(x95851,x95852),f540(x95853,x95854,x95855,x95852,x95851)),f541(x95853,x95854,x95855,x95852,x95851)),x95855)+~P24(f329(f329(f331(f880(x95851,x95852)),x95855),f329(f329(f266(x95851,x95852),x95854),x95853)))
% 187.18/188.05 [9677]P24(f329(f329(f331(x96771),f540(x96772,x96773,x96774,x96775,x96771)),x96773))+~P24(f329(f329(f331(f880(x96771,x96775)),x96774),f329(f329(f266(x96771,x96775),x96773),x96772)))
% 187.18/188.05 [9786]P20(x97865,x97864,f329(f329(f307(f873(x97865)),f329(f329(f329(f92(x97865),x97861),x97863),x97862)),f193(f881(f873(x97865),a869))))+P24(f329(f329(x97861,f438(x97862,x97863,x97864,x97865,x97861)),f445(x97862,x97863,x97864,x97865,x97861)))
% 187.18/188.05 [9838]P24(f329(f329(f331(x98381),f541(x98382,x98383,x98384,x98381,x98385)),f329(x98382,f540(x98382,x98383,x98384,x98381,x98385))))+~P24(f329(f329(f331(f880(x98385,x98381)),x98384),f329(f329(f266(x98385,x98381),x98383),x98382)))
% 187.18/188.05 [9866]P24(f329(f329(f331(f880(x98661,x98661)),f329(f329(f264(x98661,x98661),x98662),f616(x98663,x98664,x98665,x98662,x98661))),x98663))+~P24(f329(f329(f331(f880(x98661,x98661)),f329(f329(f264(x98661,x98661),x98662),x98665)),f329(f329(f188(f880(x98661,x98661),a869),f329(a117,x98664)),x98663)))
% 187.18/188.05 [9867]P24(f329(f329(f331(f880(x98671,x98671)),f329(f329(f264(x98671,x98671),x98672),f621(x98673,x98674,x98675,x98672,x98671))),x98673))+~P24(f329(f329(f331(f880(x98671,x98671)),f329(f329(f264(x98671,x98671),x98672),x98675)),f329(f329(f188(f880(x98671,x98671),a869),f329(a117,x98674)),x98673)))
% 187.18/188.05 [9885]~P24(f329(f329(f331(f880(f875(x98851),f875(x98851))),f329(f329(f264(f875(x98851),f875(x98851)),f329(f329(f149(x98851),x98852),x98855)),x98854)),f156(x98851,x98853)))+P24(f329(f329(f331(f880(x98851,x98851)),f329(f329(f264(x98851,x98851),x98852),f671(x98853,x98854,x98855,x98852,x98851))),x98853))
% 187.18/188.05 [9887]~P20(x98871,x98872,f329(f329(f307(f873(x98871)),f329(f329(f329(f92(x98871),f97(x98871,x98873,x98874)),x98875),x98873)),f193(f881(f873(x98871),a869))))+P20(x98871,x98872,f329(f329(f307(f873(x98871)),f329(f329(f329(f92(x98871),x98873),f32(x98874,x98875)),f97(x98871,x98873,f329(f73(a869,a869,a871,a324),x98874)))),f193(f881(f873(x98871),a869))))
% 187.18/188.05 [9888]~P23(x98881,x98882,f329(f329(f307(f873(x98881)),f329(f329(f329(f92(x98881),f97(x98881,x98883,x98884)),x98885),x98883)),f193(f881(f873(x98881),a869))))+P23(x98881,x98882,f329(f329(f307(f873(x98881)),f329(f329(f329(f92(x98881),x98883),f32(x98884,x98885)),f97(x98881,x98883,f329(f73(a869,a869,a871,a324),x98884)))),f193(f881(f873(x98881),a869))))
% 187.18/188.05 [10147]P20(x101471,x101472,f329(f329(f307(f873(x101471)),f329(f329(f329(f92(x101471),x101473),x101474),x101475)),f193(f881(f873(x101471),a869))))+~P20(x101471,x101472,f329(f329(f307(f873(x101471)),f329(f329(f329(f92(x101471),f329(f16(f881(a871,a869),x101471),f329(f329(f7(a871,a871,a869),a326),f445(x101475,x101474,x101472,x101471,x101473)))),x101474),f329(f16(f881(a871,a869),x101471),f329(x101475,f438(x101475,x101474,x101472,x101471,x101473))))),f193(f881(f873(x101471),a869))))
% 187.18/188.05 [6314]P24(f329(x63142,x63144))+E(f176(x63141,x63142,f329(f329(f126(x63141),x63143),f329(f329(f149(x63141),x63144),x63145))),f176(x63141,x63142,x63143))
% 187.18/188.05 [6361]~P66(x63612)+E(f329(f329(f329(f115(f881(x63611,x63612)),x63613),x63614),x63615),f329(f329(f115(x63612),f329(x63613,x63615)),f329(x63614,x63615)))
% 187.18/188.05 [6363]~P68(x63632)+E(f329(f329(f329(f22(f881(x63631,x63632)),x63633),x63634),x63635),f329(f329(f22(x63632),f329(x63633,x63635)),f329(x63634,x63635)))
% 187.18/188.05 [6365]~P66(x63652)+E(f329(f329(f329(f106(f881(x63651,x63652)),x63653),x63654),x63655),f329(f329(f106(x63652),f329(x63653,x63655)),f329(x63654,x63655)))
% 187.18/188.05 [6383]E(x63831,x63832)+E(f329(f329(f163(x63833),f329(f329(f157(x63833,x63834),x63831),x63835)),x63832),f329(f329(f163(x63833),x63834),x63832))
% 187.18/188.05 [6648]~E(x66484,f193(f881(x66483,a869)))+E(f329(f329(f115(f881(x66481,a869)),x66482),f329(f329(f42(x66483,f881(x66481,a869)),x66484),x66485)),x66482)
% 187.18/188.05 [6649]~E(x66494,f193(f881(x66493,a869)))+E(f329(f329(f22(f881(x66491,a869)),x66492),f329(f329(f42(x66493,f881(x66491,a869)),x66494),x66495)),x66492)
% 187.18/188.05 [6650]~E(x66504,f193(f881(x66503,a869)))+E(f329(f329(f106(f881(x66501,a869)),x66502),f329(f329(f43(x66503,f881(x66501,a869)),x66504),x66505)),x66502)
% 187.18/188.05 [6664]~E(x66644,f193(f881(x66643,a869)))+E(f329(f329(f307(x66641),x66642),f329(f329(f42(x66643,f881(x66641,a869)),x66644),x66645)),f329(f329(f307(x66641),x66642),f193(f881(x66641,a869))))
% 187.18/188.05 [7458]E(f329(f329(f163(x74581),f329(f329(f152(x74582,x74581),x74583),x74584)),x74585),f329(x74583,f329(f329(f163(x74582),x74584),x74585)))+~P24(f329(f329(f244(a874),x74585),f329(f194(f875(x74582)),x74584)))
% 187.18/188.05 [7524]E(f329(f329(f115(f881(x75241,a869)),f329(x75242,x75243)),f329(f329(f42(x75244,f881(x75241,a869)),x75245),x75242)),f329(f329(f42(x75244,f881(x75241,a869)),x75245),x75242))+~P24(f329(f329(f331(x75244),x75243),x75245))
% 187.18/188.05 [7525]E(f329(f329(f106(f881(x75251,a869)),f329(x75252,x75253)),f329(f329(f43(x75254,f881(x75251,a869)),x75255),x75252)),f329(f329(f43(x75254,f881(x75251,a869)),x75255),x75252))+~P24(f329(f329(f331(x75254),x75253),x75255))
% 187.18/188.05 [8137]~E(x81373,f193(f881(x81371,a869)))+E(f329(f329(f42(x81371,f881(x81372,a869)),x81373),f329(f329(f8(f881(x81372,a869),f881(x81372,a869),x81371),f329(f307(x81372),x81374)),x81375)),f193(f881(x81372,a869)))
% 187.18/188.05 [8143]~P24(f329(f329(f331(x81434),x81433),x81435))+P24(f329(f329(f243(f881(x81431,a869)),f329(x81432,x81433)),f329(f329(f42(x81434,f881(x81431,a869)),x81435),x81432)))
% 187.18/188.05 [8273]~E(f329(x82734,x82732),x82735)+P24(f329(f329(f331(x82731),x82732),f329(f309(x82731,x82733,x82734),f329(f329(f307(x82733),x82735),f193(f881(x82733,a869))))))
% 187.18/188.05 [8319]~P54(x83191,x83192,f329(f284(x83192,x83191),x83193))+E(f329(f329(f106(f881(x83191,a869)),f329(f283(x83192,x83191,x83193),x83194)),f329(f283(x83192,x83191,x83193),x83195)),f329(f283(x83192,x83191,x83193),f329(f329(f106(f881(x83192,a869)),x83194),x83195)))
% 187.18/188.05 [8395]E(x83951,f2(a104))+E(f329(f121(x83952,x83953,f329(x83954,f329(f329(f22(a104),x83951),f78(a104)))),f329(f329(f7(x83952,a104,f876(x83953)),x83955),x83951)),f329(f205(x83952,x83953,x83954,x83955),x83951))
% 187.18/188.05 [8439]E(x84391,f193(f881(x84392,a869)))+E(f329(f329(f42(x84392,f881(x84393,a869)),x84391),f329(f329(f8(f881(x84393,a869),f881(x84393,a869),x84392),f329(f307(x84393),x84394)),x84395)),f329(f329(f307(x84393),x84394),f329(f329(f42(x84392,f881(x84393,a869)),x84391),x84395)))
% 187.18/188.05 [8494]~P21(x84942,x84941,x84943,f252(f881(x84942,a869)))+E(f329(f329(f22(f881(x84941,a869)),f329(f308(x84942,x84941,x84943),x84944)),f329(f308(x84942,x84941,x84943),x84945)),f329(f308(x84942,x84941,x84943),f329(f329(f22(f881(x84942,a869)),x84944),x84945)))
% 187.18/188.05 [8495]~P21(x84952,x84951,x84953,f252(f881(x84952,a869)))+E(f329(f329(f106(f881(x84951,a869)),f329(f308(x84952,x84951,x84953),x84954)),f329(f308(x84952,x84951,x84953),x84955)),f329(f308(x84952,x84951,x84953),f329(f329(f106(f881(x84952,a869)),x84954),x84955)))
% 187.18/188.05 [8559]~P24(f329(f329(f68(x85591,x85592,x85595),x85593),x85594))+P24(f329(f329(f331(f880(x85591,x85592)),f329(f329(f264(x85591,x85592),x85593),x85594)),x85595))
% 187.18/188.05 [8591]P24(f329(f329(f331(x85911),x85912),f329(f260(x85913,x85911),x85914)))+~P24(f329(f329(f331(f880(x85913,x85911)),f329(f329(f264(x85913,x85911),x85915),x85912)),x85914))
% 187.18/188.05 [8593]P24(f329(f329(f331(x85931),x85932),f329(f262(x85931,x85933),x85934)))+~P24(f329(f329(f331(f880(x85931,x85933)),f329(f329(f264(x85931,x85933),x85932),x85935)),x85934))
% 187.18/188.05 [8727]P24(f329(f329(f68(x87271,x87272,x87273),x87274),x87275))+~P24(f329(f329(f331(f880(x87271,x87272)),f329(f329(f264(x87271,x87272),x87274),x87275)),x87273))
% 187.18/188.05 [8762]E(f329(x87621,x87622),x87623)+~P24(f329(f329(f331(x87624),x87622),f329(f309(x87624,x87625,x87621),f329(f329(f307(x87625),x87623),f193(f881(x87625,a869))))))
% 187.18/188.05 [8997]P24(f329(f329(f331(f880(x89971,x89972)),f329(f329(f264(x89971,x89972),x89973),x89974)),f329(f284(x89972,x89971),x89975)))+~P24(f329(f329(f331(f880(x89972,x89971)),f329(f329(f264(x89972,x89971),x89974),x89973)),x89975))
% 187.18/188.05 [9015]~P24(f329(f329(x90151,x90155),x90154))+P24(f329(f329(x90151,f329(f267(x90152,x90153),f329(f329(f264(x90152,x90153),x90154),x90155))),f329(f263(x90152,x90153),f329(f329(f264(x90152,x90153),x90154),x90155))))
% 187.18/188.05 [9045]~P24(f329(f329(f331(f880(x90452,x90451)),f329(f329(f264(x90452,x90451),x90454),x90453)),f329(f284(x90451,x90452),x90455)))+P24(f329(f329(f331(f880(x90451,x90452)),f329(f329(f264(x90451,x90452),x90453),x90454)),x90455))
% 187.18/188.05 [9075]~P24(f329(f329(f331(f880(x90753,x90751)),f329(f329(f264(x90753,x90751),x90755),x90752)),x90754))+P24(f329(f329(f331(x90751),x90752),f329(f283(x90753,x90751,x90754),f329(f329(f307(x90753),x90755),f193(f881(x90753,a869))))))
% 187.18/188.05 [9120]P24(f329(f329(f331(f880(x91201,x91202)),f329(f329(f264(x91201,x91202),x91203),x91204)),x91205))+~P24(f329(f329(f331(x91202),x91204),f329(f283(x91201,x91202,x91205),f329(f329(f307(x91201),x91203),f193(f881(x91201,a869))))))
% 187.18/188.05 [9141]E(f329(f329(f329(f72(x91411,f878(x91412)),f187(x91411,x91412,x91413,x91414)),x91415),f206(x91412)),f187(x91411,x91412,x91413,f329(f329(f22(f881(x91411,a869)),x91414),f329(f329(f307(x91411),x91415),f193(f881(x91411,a869))))))+~P24(f329(f329(f331(x91411),x91415),x91414))
% 187.18/188.05 [9209]~P72(x92091)+E(f329(f329(f6(a874,x92091),x92092),f300(a874,f329(f329(f80(a874),x92093),x92094),f329(f329(f80(a874),x92095),x92094))),f329(f329(f6(a874,x92091),f329(f329(f8(a874,x92091,a874),x92092),f329(f329(f7(a874,a874,a874),f80(a874)),x92094))),f300(a874,x92093,x92095)))
% 187.18/188.05 [9233]~P72(x92331)+E(f329(f329(f6(a874,x92331),x92332),f329(f299(a874,f329(f329(f80(a874),x92333),x92334)),f329(f329(f80(a874),x92335),x92334))),f329(f329(f6(a874,x92331),f329(f329(f8(a874,x92331,a874),x92332),f329(f329(f7(a874,a874,a874),f80(a874)),x92334))),f329(f299(a874,x92333),x92335)))
% 187.18/188.05 [9288]~P21(x92881,x92882,x92883,f252(f881(x92881,a869)))+E(f329(f329(f152(x92881,x92882),x92883),f329(f134(x92881,f329(f329(f8(a869,a869,x92881),a324),f329(a326,x92884))),x92885)),f329(f134(x92882,f329(f329(f8(a869,a869,x92882),a324),f329(a326,f329(x92883,x92884)))),f329(f329(f152(x92881,x92882),x92883),x92885)))
% 187.18/188.05 [9306]~P21(x93061,x93062,x93063,f329(f329(f307(x93061),x93064),f329(f171(x93061),x93065)))+E(f329(f329(f152(x93061,x93062),x93063),f329(f134(x93061,f329(f329(f8(a869,a869,x93061),a324),f329(a326,x93064))),x93065)),f329(f134(x93062,f329(f329(f8(a869,a869,x93062),a324),f329(a326,f329(x93063,x93064)))),f329(f329(f152(x93061,x93062),x93063),x93065)))
% 187.18/188.05 [9461]P24(f329(f329(f331(f880(f875(x94611),f875(x94611))),f329(f329(f264(f875(x94611),f875(x94611)),f329(f329(f149(x94611),x94612),x94613)),f329(f329(f149(x94611),x94614),x94613))),f155(x94611,x94615)))+~P24(f329(f329(f331(f880(x94611,x94611)),f329(f329(f264(x94611,x94611),x94612),x94614)),x94615))
% 187.18/188.05 [9498]P24(f329(f329(f329(f329(a201,x94981),x94982),x94983),f340(x94984,x94983,x94982,x94985,x94981)))+~P24(f329(f329(f329(f329(a201,f33(x94981,x94985)),x94982),x94983),x94984))
% 187.18/188.05 [9568]P20(x95681,x95682,f329(f329(f307(f873(x95681)),f329(f329(f329(f92(x95681),x95683),f329(a26,x95684)),x95685)),f193(f881(f873(x95681),a869))))+~P20(x95681,f329(f329(f307(f873(x95681)),f329(f329(f329(f92(x95681),x95683),f329(a26,x95684)),x95685)),x95682),f329(f329(f307(f873(x95681)),f329(f329(f329(f92(x95681),x95683),f329(f240(a870),f329(a28,x95684))),x95685)),f193(f881(f873(x95681),a869))))
% 187.18/188.05 [9580]E(f329(f329(f307(x95801),f776(x95802,x95803,x95804,x95805,x95801)),f791(x95802,x95803,x95804,x95805,x95801)),f329(f329(f307(x95801),x95804),x95803))+~P24(f329(f63(x95801,x95805,f329(f329(f307(x95801),x95804),x95803)),x95802))
% 187.18/188.05 [9581]E(f329(f329(f307(x95811),f801(x95812,x95813,x95814,x95815,x95811)),f814(x95812,x95813,x95814,x95815,x95811)),f329(f329(f307(x95811),x95814),x95813))+~P24(f329(f63(x95811,x95815,f329(f329(f307(x95811),x95814),x95813)),x95812))
% 187.18/188.05 [9663]P24(f329(f329(f331(x96631),f627(x96632,x96633,x96634,x96635,x96631)),x96634))+P24(f329(f329(f329(f43(x96631,f881(x96635,a869)),x96634),x96633),x96632))
% 187.18/188.05 [9668]P24(f329(f329(f331(x96681),f622(x96682,x96683,x96681,x96684,x96685)),x96683))+P24(f329(f329(f331(x96685),x96684),f329(f329(f43(x96681,f881(x96685,a869)),x96683),x96682)))
% 187.18/188.05 [9676]P24(f329(f329(f331(x96761),f624(x96762,x96763,x96761,x96764,x96765)),x96763))+P24(f329(f329(f243(f881(x96765,a869)),x96764),f329(f329(f43(x96761,f881(x96765,a869)),x96763),x96762)))
% 187.18/188.05 [9678]P24(f329(f329(x96781,f433(x96782,x96781,x96783,x96784,x96785)),x96782))+~P24(f329(f329(f329(f42(x96785,f881(x96784,a869)),x96783),x96781),x96782))
% 187.18/188.05 [9681]P24(f329(f329(f331(x96811),f433(x96812,x96813,x96814,x96815,x96811)),x96814))+~P24(f329(f329(f329(f42(x96811,f881(x96815,a869)),x96814),x96813),x96812))
% 187.18/188.05 [9691]P24(f329(f329(f331(x96911),f439(x96912,x96913,x96911,x96914,x96915)),x96913))+~P24(f329(f329(f331(x96915),x96914),f329(f329(f42(x96911,f881(x96915,a869)),x96913),x96912)))
% 187.18/188.05 [9696]P24(f329(f329(f331(x96961),x96962),f329(x96963,f439(x96963,x96964,x96965,x96962,x96961))))+~P24(f329(f329(f331(x96961),x96962),f329(f329(f42(x96965,f881(x96961,a869)),x96964),x96963)))
% 187.18/188.05 [9791]~P24(f329(f329(x97914,f627(x97915,x97914,x97913,x97912,x97911)),x97915))+P24(f329(f329(f329(f43(x97911,f881(x97912,a869)),x97913),x97914),x97915))
% 187.18/188.05 [9794]~P24(f329(f329(f331(x97941),x97942),f329(x97945,f622(x97945,x97944,x97943,x97942,x97941))))+P24(f329(f329(f331(x97941),x97942),f329(f329(f43(x97943,f881(x97941,a869)),x97944),x97945)))
% 187.18/188.05 [9798]~P24(f329(f329(f243(f881(x97981,a869)),x97982),f329(x97985,f624(x97985,x97984,x97983,x97982,x97981))))+P24(f329(f329(f243(f881(x97981,a869)),x97982),f329(f329(f43(x97983,f881(x97981,a869)),x97984),x97985)))
% 187.18/188.05 [9844]P24(f329(f329(f329(f329(a201,x98441),f340(x98442,x98443,x98444,x98441,x98445)),x98443),x98442))+~P24(f329(f329(f329(f329(a201,f33(x98445,x98441)),x98444),x98443),x98442))
% 187.18/188.05 [9870]~P24(f329(f329(f331(x98701),f776(x98705,x98704,x98703,x98702,x98701)),f791(x98705,x98704,x98703,x98702,x98701)))+~P24(f329(f63(x98701,x98702,f329(f329(f307(x98701),x98703),x98704)),x98705))
% 187.18/188.05 [9871]~P24(f329(f329(f331(x98711),f801(x98715,x98714,x98713,x98712,x98711)),f814(x98715,x98714,x98713,x98712,x98711)))+~P24(f329(f63(x98711,x98712,f329(f329(f307(x98711),x98713),x98714)),x98715))
% 187.18/188.05 [9872]~P24(f329(f329(f331(f880(x98721,x98721)),f329(f329(f264(x98721,x98721),x98722),x98725)),f329(f329(f188(f880(x98721,x98721),a869),f329(a117,x98724)),x98723)))+P24(f329(f329(f331(f880(x98721,x98721)),f329(f329(f264(x98721,x98721),x98722),f617(x98723,x98724,x98725,x98722,x98721))),f329(f329(f188(f880(x98721,x98721),a869),x98724),x98723)))
% 187.18/188.05 [9879]P24(f329(f67(x98791,x98791,x98792,f776(x98793,x98794,x98795,x98792,x98791),f791(x98793,x98794,x98795,x98792,x98791)),x98793))+~P24(f329(f63(x98791,x98792,f329(f329(f307(x98791),x98795),x98794)),x98793))
% 187.18/188.05 [9880]P24(f329(f67(x98801,x98801,x98802,f801(x98803,x98804,x98805,x98802,x98801),f814(x98803,x98804,x98805,x98802,x98801)),x98803))+~P24(f329(f63(x98801,x98802,f329(f329(f307(x98801),x98805),x98804)),x98803))
% 187.18/188.05 [9892]~P27(x98921)+P33(x98921,f329(f329(f152(x98922,x98921),x98923),f329(f134(x98922,f329(f329(f7(x98922,x98921,a869),f329(f329(f8(x98921,f881(x98921,a869),x98922),a326),x98923)),f329(x98924,x98925))),x98925)))
% 187.18/188.05 [9932]~P24(f329(f329(f331(x99322),x99325),f329(f283(x99321,x99322,x99324),x99323)))+P24(f329(f329(f331(f880(x99321,x99322)),f329(f329(f264(x99321,x99322),f494(x99323,x99324,x99321,x99325,x99322)),x99325)),x99324))
% 187.18/188.05 [9933]~P24(f329(f329(f331(x99332),x99335),f329(f283(x99331,x99332,x99334),x99333)))+P24(f329(f329(f331(f880(x99331,x99332)),f329(f329(f264(x99331,x99332),f498(x99333,x99334,x99331,x99335,x99332)),x99335)),x99334))
% 187.18/188.05 [9953]~P24(f329(f329(f331(f880(x99531,x99531)),f329(f329(f264(x99531,x99531),x99535),x99534)),f329(f329(f188(f880(x99531,x99531),a869),f329(a117,x99533)),x99532)))+P24(f329(f329(f331(f880(x99531,x99531)),f329(f329(f264(x99531,x99531),f617(x99532,x99533,x99534,x99535,x99531)),x99534)),x99532))
% 187.18/188.05 [9956]~P24(f329(f329(f331(f880(x99561,x99561)),f329(f329(f264(x99561,x99561),x99565),x99564)),f329(f329(f188(f880(x99561,x99561),a869),f329(a117,x99563)),x99562)))+P24(f329(f329(f331(f880(x99561,x99561)),f329(f329(f264(x99561,x99561),f616(x99562,x99563,x99564,x99565,x99561)),x99564)),f329(f329(f188(f880(x99561,x99561),a869),x99563),x99562)))
% 187.18/188.05 [9957]~P24(f329(f329(f331(f880(x99571,x99571)),f329(f329(f264(x99571,x99571),x99575),x99574)),f329(f329(f188(f880(x99571,x99571),a869),f329(a117,x99573)),x99572)))+P24(f329(f329(f331(f880(x99571,x99571)),f329(f329(f264(x99571,x99571),f621(x99572,x99573,x99574,x99575,x99571)),x99574)),f329(f329(f188(f880(x99571,x99571),a869),x99573),x99572)))
% 187.18/188.05 [9958]~P24(f329(f329(f331(f880(f875(x99581),f875(x99581))),f329(f329(f264(f875(x99581),f875(x99581)),x99585),f329(f329(f149(x99581),x99584),x99583))),f156(x99581,x99582)))+P24(f329(f329(f331(f880(x99581,x99581)),f329(f329(f264(x99581,x99581),f670(x99582,x99583,x99584,x99585,x99581)),x99584)),x99582))
% 187.18/188.05 [7051]E(x70511,f206(x70512))+E(f183(x70513,x70512,f329(f329(f329(f72(x70513,f878(x70512)),x70514),x70515),x70511)),f329(f329(f307(x70513),x70515),f183(x70513,x70512,x70514)))
% 187.18/188.05 [7545]~E(x75453,f193(f881(x75452,a869)))+E(f329(f329(f115(f881(x75451,a869)),f329(f329(f42(x75452,f881(x75451,a869)),x75453),x75454)),x75455),x75455)
% 187.18/188.05 [7546]~E(x75463,f193(f881(x75462,a869)))+E(f329(f329(f106(f881(x75461,a869)),f329(f329(f43(x75462,f881(x75461,a869)),x75463),x75464)),x75465),x75465)
% 187.18/188.05 [7909]~E(x79095,f206(x79092))+E(f183(x79091,x79092,f329(f329(f329(f72(x79091,f878(x79092)),x79093),x79094),x79095)),f329(f329(f22(f881(x79091,a869)),f183(x79091,x79092,x79093)),f329(f329(f307(x79091),x79094),f193(f881(x79091,a869)))))
% 187.18/188.05 [7978]~E(x79783,f193(f881(x79782,a869)))+E(f329(f329(f22(f881(x79781,a869)),f329(f329(f43(x79782,f881(x79781,a869)),x79783),x79784)),x79785),f329(f329(f22(f881(x79781,a869)),f252(f881(x79781,a869))),x79785))
% 187.18/188.05 [8109]E(f329(f329(f157(x81091,f329(f329(f126(x81091),x81092),x81093)),x81094),x81095),f329(f329(f126(x81091),f329(f329(f157(x81091,x81092),x81094),x81095)),x81093))+~P24(f329(f329(f244(a874),x81094),f329(f194(f875(x81091)),x81092)))
% 187.18/188.05 [8225]P24(f329(f329(f331(x82251),x82255),f329(f171(x82251),x82253)))+E(f329(f329(f177(x82251,x82252),f329(f329(f181(x82251,x82252),x82253),f329(f329(f152(x82251,x82252),x82254),x82253))),x82255),f206(x82252))
% 187.18/188.05 [8346]~P24(f329(f329(f331(x83461),x83465),f329(f171(x83461),x83463)))+E(f329(f329(f177(x83461,x83462),f329(f329(f181(x83461,x83462),x83463),f329(f329(f152(x83461,x83462),x83464),x83463))),x83465),f329(f236(x83462),f329(x83464,x83465)))
% 187.18/188.05 [8385]E(f329(f329(f163(x83851),f329(f329(f152(a874,x83851),x83852),f137(a874,f329(f299(a874,x83853),x83854)))),x83855),f329(x83852,f329(f329(f80(a874),x83853),x83855)))+~P24(f329(f329(f244(a874),x83855),f329(f329(f22(a874),x83854),x83853)))
% 187.18/188.05 [8400]E(x84001,f2(a104))+E(f124(x84002,x84003,f329(x84004,f329(f329(f22(a104),x84001),f78(a104))),f329(f329(f7(x84002,a104,f876(f878(x84003))),x84005),x84001)),f329(f203(x84002,x84003,x84004,x84005),x84001))
% 187.18/188.05 [8426]~E(x84263,f193(f881(x84261,a869)))+E(f329(f329(f42(x84261,f881(x84262,a869)),x84263),f329(f329(f8(f881(x84262,a869),f881(x84262,a869),x84261),f329(f115(f881(x84262,a869)),x84264)),x84265)),f193(f881(x84262,a869)))
% 187.18/188.05 [8427]~E(x84273,f193(f881(x84271,a869)))+E(f329(f329(f43(x84271,f881(x84272,a869)),x84273),f329(f329(f8(f881(x84272,a869),f881(x84272,a869),x84271),f329(f22(f881(x84272,a869)),x84274)),x84275)),f252(f881(x84272,a869)))
% 187.18/188.05 [8428]~E(x84283,f193(f881(x84281,a869)))+E(f329(f329(f43(x84281,f881(x84282,a869)),x84283),f329(f329(f8(f881(x84282,a869),f881(x84282,a869),x84281),f329(f106(f881(x84282,a869)),x84284)),x84285)),f252(f881(x84282,a869)))
% 187.18/188.05 [8433]~P134(x84332)+E(f329(f329(f6(x84331,x84332),f329(f329(f8(x84332,x84332,x84331),f329(f81(x84332),x84333)),x84334)),x84335),f329(f329(f81(x84332),x84333),f329(f329(f6(x84331,x84332),x84334),x84335)))
% 187.18/188.05 [8712]E(x87121,f193(f881(x87122,a869)))+E(f329(f329(f42(x87122,f881(x87123,a869)),x87121),f329(f329(f8(f881(x87123,a869),f881(x87123,a869),x87122),f329(f115(f881(x87123,a869)),x87124)),x87125)),f329(f329(f115(f881(x87123,a869)),x87124),f329(f329(f42(x87122,f881(x87123,a869)),x87121),x87125)))
% 187.18/188.05 [8713]E(x87131,f193(f881(x87132,a869)))+E(f329(f329(f43(x87132,f881(x87133,a869)),x87131),f329(f329(f8(f881(x87133,a869),f881(x87133,a869),x87132),f329(f22(f881(x87133,a869)),x87134)),x87135)),f329(f329(f22(f881(x87133,a869)),x87134),f329(f329(f42(x87132,f881(x87133,a869)),x87131),x87135)))
% 187.18/188.05 [8714]E(x87141,f193(f881(x87142,a869)))+E(f329(f329(f43(x87142,f881(x87143,a869)),x87141),f329(f329(f8(f881(x87143,a869),f881(x87143,a869),x87142),f329(f106(f881(x87143,a869)),x87144)),x87145)),f329(f329(f106(f881(x87143,a869)),x87144),f329(f329(f43(x87142,f881(x87143,a869)),x87141),x87145)))
% 187.18/188.05 [8909]~P24(f329(f329(f244(a874),f329(x89094,x89092)),f329(x89094,x89093)))+P24(f329(f329(f331(f880(x89091,x89091)),f329(f329(f264(x89091,x89091),x89092),x89093)),f151(x89091,f329(f329(f149(f881(x89091,a874)),x89094),x89095))))
% 187.18/188.05 [9176]~P21(x91762,x91761,x91763,f329(f329(f115(f881(x91762,a869)),x91764),x91765))+E(f329(f329(f106(f881(x91761,a869)),f329(f308(x91762,x91761,x91763),f329(f329(f22(f881(x91762,a869)),x91764),x91765))),f329(f308(x91762,x91761,x91763),f329(f329(f22(f881(x91762,a869)),x91765),x91764))),f193(f881(x91761,a869)))
% 187.18/188.05 [9457]~P24(f329(f329(f243(f881(x94573,a869)),f329(f283(x94571,x94573,x94574),x94572)),x94575))+P24(f329(f329(f243(f881(x94571,a869)),x94572),f329(f79(f881(x94571,a869)),f329(f283(x94573,x94571,f329(f284(x94571,x94573),x94574)),f329(f79(f881(x94573,a869)),x94575)))))
% 187.18/188.05 [9482]~P21(x94821,x94822,x94823,f329(f329(f307(x94821),x94824),x94825))+~P24(f329(f329(f331(x94822),f329(x94823,x94824)),f329(f308(x94821,x94822,x94823),f329(f329(f22(f881(x94821,a869)),x94825),f329(f329(f307(x94821),x94824),f193(f881(x94821,a869)))))))
% 187.18/188.05 [9534]P24(f329(f329(f243(f881(x95341,a869)),f329(f283(x95342,x95341,x95343),x95344)),x95345))+~P24(f329(f329(f243(f881(x95342,a869)),x95344),f329(f79(f881(x95342,a869)),f329(f283(x95341,x95342,f329(f284(x95342,x95341),x95343)),f329(f79(f881(x95341,a869)),x95345)))))
% 187.18/188.05 [9608]~P87(x96081)+P24(f329(f329(f243(x96081),f329(f75(x96081),f329(f329(f22(x96081),f329(f329(f80(x96081),x96082),x96083)),f329(f329(f80(x96081),x96084),x96085)))),f329(f329(f80(x96081),f329(f75(x96081),f329(f329(f22(x96081),x96082),x96084))),f329(f75(x96081),f329(f329(f22(x96081),x96083),x96085)))))
% 187.18/188.05 [9712]P24(f329(f329(f331(x97121),f441(x97122,x97123,x97124,x97121,x97125)),x97124))+P24(f329(f329(f243(f881(x97125,a869)),f329(f329(f42(x97121,f881(x97125,a869)),x97124),x97123)),x97122))
% 187.18/188.05 [9910]~P24(f329(f329(f243(f881(x99101,a869)),f329(x99104,f441(x99105,x99104,x99103,x99102,x99101))),x99105))+P24(f329(f329(f243(f881(x99101,a869)),f329(f329(f42(x99102,f881(x99101,a869)),x99103),x99104)),x99105))
% 187.18/188.05 [8540]E(f329(f329(f126(x85401),x85402),f329(f329(f157(x85401,x85403),f329(f329(f22(a874),x85404),f329(f194(f875(x85401)),x85402))),x85405)),f329(f329(f157(x85401,f329(f329(f126(x85401),x85402),x85403)),x85404),x85405))+P24(f329(f329(f244(a874),x85404),f329(f194(f875(x85401)),x85402)))
% 187.18/188.05 [8567]~P135(x85671)+E(f329(f329(f80(x85671),f329(f329(f81(x85671),x85672),x85673)),f329(f329(f80(x85671),f329(f329(f81(x85671),x85674),x85673)),x85675)),f329(f329(f80(x85671),f329(f329(f81(x85671),f329(f329(f80(x85671),x85672),x85674)),x85673)),x85675))
% 187.18/188.05 [9130]~P134(x91301)+E(f329(f164(x91301),f329(f329(f152(x91302,x91301),f329(f329(f8(x91301,x91301,x91302),f329(f81(x91301),x91303)),x91304)),x91305)),f329(f329(f81(x91301),x91303),f329(f164(x91301),f329(f329(f152(x91302,x91301),x91304),x91305))))
% 187.18/188.05 [9305]E(f329(f194(f875(x93051)),f329(f329(f174(x93051),f329(f329(f241(a874),f329(f194(f875(x93051)),x93052)),f329(f194(f875(x93053)),x93054))),x93052)),f329(f194(f875(x93053)),f329(f329(f174(x93053),f329(f329(f241(a874),f329(f194(f875(x93051)),x93052)),f329(f194(f875(x93053)),x93054))),x93054)))+P24(f329(x93055,f329(f329(f181(x93051,x93053),x93052),x93054)))
% 187.18/188.05 [9545]~P134(x95452)+E(f329(f329(f6(x95451,x95452),f329(f329(f7(x95451,x95452,x95452),f329(f329(f8(x95452,f881(x95452,x95452),x95451),f81(x95452)),x95453)),x95454)),x95455),f329(f329(f81(x95452),f329(f329(f6(x95451,x95452),x95453),x95455)),x95454))
% 187.18/188.05 [9546]~P62(x95462)+E(f329(f329(f6(x95461,x95462),f329(f329(f7(x95461,x95462,x95462),f329(f329(f8(x95462,f881(x95462,x95462),x95461),f287(x95462)),x95463)),x95464)),x95465),f329(f329(f287(x95462),f329(f329(f6(x95461,x95462),x95463),x95465)),x95464))
% 187.18/188.05 [9553]~P69(x95532)+E(f329(f329(f6(x95531,x95532),f329(f329(f18(x95531,x95532,x95532),f329(f329(f8(x95532,f881(x95532,x95532),x95531),f22(x95532)),x95533)),x95534)),x95535),f329(f329(f22(x95532),f329(f329(f6(x95531,x95532),x95533),x95535)),f329(f329(f6(x95531,x95532),x95534),x95535)))
% 187.18/188.05 [9554]~P72(x95542)+E(f329(f329(f6(x95541,x95542),f329(f329(f18(x95541,x95542,x95542),f329(f329(f8(x95542,f881(x95542,x95542),x95541),f80(x95542)),x95543)),x95544)),x95545),f329(f329(f80(x95542),f329(f329(f6(x95541,x95542),x95543),x95545)),f329(f329(f6(x95541,x95542),x95544),x95545)))
% 187.18/188.05 [9555]~P76(x95552)+E(f329(f329(f9(x95551,x95552),f329(f329(f18(x95551,x95552,x95552),f329(f329(f8(x95552,f881(x95552,x95552),x95551),f81(x95552)),x95553)),x95554)),x95555),f329(f329(f81(x95552),f329(f329(f9(x95551,x95552),x95553),x95555)),f329(f329(f9(x95551,x95552),x95554),x95555)))
% 187.18/188.05 [9593]~E(x95933,f193(f881(x95931,a869)))+E(f329(f329(f42(x95931,f881(x95932,a869)),x95933),f329(f329(f7(x95931,f881(x95932,a869),f881(x95932,a869)),f329(f329(f8(f881(x95932,a869),f881(f881(x95932,a869),f881(x95932,a869)),x95931),f115(f881(x95932,a869))),x95934)),x95935)),f193(f881(x95932,a869)))
% 187.18/188.05 [9594]~E(x95943,f193(f881(x95941,a869)))+E(f329(f329(f43(x95941,f881(x95942,a869)),x95943),f329(f329(f7(x95941,f881(x95942,a869),f881(x95942,a869)),f329(f329(f8(f881(x95942,a869),f881(f881(x95942,a869),f881(x95942,a869)),x95941),f22(f881(x95942,a869))),x95944)),x95945)),f252(f881(x95942,a869)))
% 187.18/188.05 [9595]~E(x95953,f193(f881(x95951,a869)))+E(f329(f329(f43(x95951,f881(x95952,a869)),x95953),f329(f329(f7(x95951,f881(x95952,a869),f881(x95952,a869)),f329(f329(f8(f881(x95952,a869),f881(f881(x95952,a869),f881(x95952,a869)),x95951),f106(f881(x95952,a869))),x95954)),x95955)),f252(f881(x95952,a869)))
% 187.18/188.05 [9616]E(x96161,f193(f881(x96162,a869)))+E(f329(f329(f42(x96162,f881(x96163,a869)),x96161),f329(f329(f7(x96162,f881(x96163,a869),f881(x96163,a869)),f329(f329(f8(f881(x96163,a869),f881(f881(x96163,a869),f881(x96163,a869)),x96162),f115(f881(x96163,a869))),x96164)),x96165)),f329(f329(f115(f881(x96163,a869)),f329(f329(f42(x96162,f881(x96163,a869)),x96161),x96164)),x96165))
% 187.18/188.05 [9617]E(x96171,f193(f881(x96172,a869)))+E(f329(f329(f43(x96172,f881(x96173,a869)),x96171),f329(f329(f7(x96172,f881(x96173,a869),f881(x96173,a869)),f329(f329(f8(f881(x96173,a869),f881(f881(x96173,a869),f881(x96173,a869)),x96172),f22(f881(x96173,a869))),x96174)),x96175)),f329(f329(f22(f881(x96173,a869)),f329(f329(f43(x96172,f881(x96173,a869)),x96171),x96174)),x96175))
% 187.18/188.05 [9618]E(x96181,f193(f881(x96182,a869)))+E(f329(f329(f43(x96182,f881(x96183,a869)),x96181),f329(f329(f7(x96182,f881(x96183,a869),f881(x96183,a869)),f329(f329(f8(f881(x96183,a869),f881(f881(x96183,a869),f881(x96183,a869)),x96182),f106(f881(x96183,a869))),x96184)),x96185)),f329(f329(f106(f881(x96183,a869)),f329(f329(f43(x96182,f881(x96183,a869)),x96181),x96184)),x96185))
% 187.18/188.05 [9183]~P24(f329(f329(f243(a874),x91831),x91834))+E(f329(f329(f22(a874),f329(f329(f80(a874),f329(f329(f81(a874),x91831),x91832)),x91833)),f329(f329(f80(a874),f329(f329(f81(a874),x91834),x91832)),x91835)),f329(f329(f22(a874),x91833),f329(f329(f80(a874),f329(f329(f81(a874),f329(f329(f22(a874),x91834),x91831)),x91832)),x91835)))
% 187.18/188.05 [9772]~P134(x97721)+E(f329(f164(x97721),f329(f329(f152(x97722,x97721),f329(f329(f7(x97722,x97721,x97721),f329(f329(f8(x97721,f881(x97721,x97721),x97722),f81(x97721)),x97723)),x97724)),x97725)),f329(f329(f81(x97721),f329(f164(x97721),f329(f329(f152(x97722,x97721),x97723),x97725))),x97724))
% 187.18/188.05 [9778]~P69(x97781)+E(f329(f164(x97781),f329(f329(f152(x97782,x97781),f329(f329(f18(x97782,x97781,x97781),f329(f329(f8(x97781,f881(x97781,x97781),x97782),f22(x97781)),x97783)),x97784)),x97785)),f329(f329(f22(x97781),f329(f164(x97781),f329(f329(f152(x97782,x97781),x97783),x97785))),f329(f164(x97781),f329(f329(f152(x97782,x97781),x97784),x97785))))
% 187.18/188.05 [9779]~P72(x97791)+E(f329(f164(x97791),f329(f329(f152(x97792,x97791),f329(f329(f18(x97792,x97791,x97791),f329(f329(f8(x97791,f881(x97791,x97791),x97792),f80(x97791)),x97793)),x97794)),x97795)),f329(f329(f80(x97791),f329(f164(x97791),f329(f329(f152(x97792,x97791),x97793),x97795))),f329(f164(x97791),f329(f329(f152(x97792,x97791),x97794),x97795))))
% 187.18/188.05 [9923]P24(f329(x99231,f329(f329(f181(x99232,x99233),x99234),x99235)))+~P24(f329(x99231,f329(f329(f181(x99232,x99233),f329(f329(f174(x99232),f329(f329(f241(a874),f329(f194(f875(x99232)),x99234)),f329(f194(f875(x99233)),x99235))),x99234)),f329(f329(f174(x99233),f329(f329(f241(a874),f329(f194(f875(x99232)),x99234)),f329(f194(f875(x99233)),x99235))),x99235))))
% 187.18/188.05 [10156]~P24(f329(f329(f331(f880(x101562,x101561)),f329(f329(f264(x101562,x101561),x101564),x101565)),f329(f284(x101561,x101562),x101563)))+P24(f329(f329(f253(x101561,x101562,f329(f329(f7(x101561,f881(f880(x101561,x101562),a869),f881(x101562,a869)),f329(f329(f8(f881(x101562,f881(f881(f880(x101561,x101562),a869),a869)),f881(f881(f880(x101561,x101562),a869),f881(x101562,a869)),x101561),f7(x101562,f881(f880(x101561,x101562),a869),a869)),f329(f329(f8(f881(x101562,f880(x101561,x101562)),f881(x101562,f881(f881(f880(x101561,x101562),a869),a869)),x101561),f329(f8(f880(x101561,x101562),f881(f881(f880(x101561,x101562),a869),a869),x101562),f331(f880(x101561,x101562)))),f264(x101561,x101562)))),x101563)),x101564),x101565))
% 187.18/188.05 [10165]P24(f329(f329(f331(f880(x101651,x101652)),f329(f329(f264(x101651,x101652),x101653),x101654)),f329(f284(x101652,x101651),x101655)))+~P24(f329(f329(f253(x101652,x101651,f329(f329(f7(x101652,f881(f880(x101652,x101651),a869),f881(x101651,a869)),f329(f329(f8(f881(x101651,f881(f881(f880(x101652,x101651),a869),a869)),f881(f881(f880(x101652,x101651),a869),f881(x101651,a869)),x101652),f7(x101651,f881(f880(x101652,x101651),a869),a869)),f329(f329(f8(f881(x101651,f880(x101652,x101651)),f881(x101651,f881(f881(f880(x101652,x101651),a869),a869)),x101652),f329(f8(f880(x101652,x101651),f881(f881(f880(x101652,x101651),a869),a869),x101651),f331(f880(x101652,x101651)))),f264(x101652,x101651)))),x101655)),x101653),x101654))
% 187.18/188.05 [9425]~P24(f329(f329(f243(a874),x94254),x94251))+E(f329(f329(f22(a874),f329(f329(f80(a874),f329(f329(f81(a874),x94251),x94252)),x94253)),f329(f329(f80(a874),f329(f329(f81(a874),x94254),x94252)),x94255)),f329(f329(f22(a874),f329(f329(f80(a874),f329(f329(f81(a874),f329(f329(f22(a874),x94251),x94254)),x94252)),x94253)),x94255))
% 187.18/188.05 [10174]P20(x101741,x101742,f329(f308(a872,f873(x101741),f329(f329(f18(a872,f881(x101741,f881(a871,a869)),f873(x101741)),f329(f329(f18(a872,a870,f881(f881(x101741,f881(a871,a869)),f873(x101741))),f329(f329(f8(f881(x101741,f881(a871,a869)),f881(a870,f881(f881(x101741,f881(a871,a869)),f873(x101741))),a872),f92(x101741)),x101743)),a26)),x101744)),x101745))+~P20(x101741,f329(f329(f115(f881(f873(x101741),a869)),x101742),f329(f308(a872,f873(x101741),f329(f329(f18(a872,f881(x101741,f881(a871,a869)),f873(x101741)),f329(f329(f18(a872,a870,f881(f881(x101741,f881(a871,a869)),f873(x101741))),f329(f329(f8(f881(x101741,f881(a871,a869)),f881(a870,f881(f881(x101741,f881(a871,a869)),f873(x101741))),a872),f92(x101741)),x101743)),a26)),x101744)),x101745)),f329(f308(a872,f873(x101741),f329(f329(f18(a872,f881(x101741,f881(a871,a869)),f873(x101741)),f329(f329(f18(a872,a870,f881(f881(x101741,f881(a871,a869)),f873(x101741))),f329(f329(f8(f881(x101741,f881(a871,a869)),f881(a870,f881(f881(x101741,f881(a871,a869)),f873(x101741))),a872),f92(x101741)),x101743)),f329(f329(f8(f878(a870),a870,a872),f240(a870)),a28))),x101744)),x101745))
% 187.18/188.05 [10175]P23(x101751,x101752,f329(f308(a872,f873(x101751),f329(f329(f18(a872,f881(x101751,f881(a871,a869)),f873(x101751)),f329(f329(f18(a872,a870,f881(f881(x101751,f881(a871,a869)),f873(x101751))),f329(f329(f8(f881(x101751,f881(a871,a869)),f881(a870,f881(f881(x101751,f881(a871,a869)),f873(x101751))),a872),f92(x101751)),x101753)),a26)),x101754)),x101755))+~P23(x101751,f329(f329(f115(f881(f873(x101751),a869)),x101752),f329(f308(a872,f873(x101751),f329(f329(f18(a872,f881(x101751,f881(a871,a869)),f873(x101751)),f329(f329(f18(a872,a870,f881(f881(x101751,f881(a871,a869)),f873(x101751))),f329(f329(f8(f881(x101751,f881(a871,a869)),f881(a870,f881(f881(x101751,f881(a871,a869)),f873(x101751))),a872),f92(x101751)),x101753)),a26)),x101754)),x101755)),f329(f308(a872,f873(x101751),f329(f329(f18(a872,f881(x101751,f881(a871,a869)),f873(x101751)),f329(f329(f18(a872,a870,f881(f881(x101751,f881(a871,a869)),f873(x101751))),f329(f329(f8(f881(x101751,f881(a871,a869)),f881(a870,f881(f881(x101751,f881(a871,a869)),f873(x101751))),a872),f92(x101751)),x101753)),f329(f329(f8(f878(a870),a870,a872),f240(a870)),a28))),x101754)),x101755))
% 187.18/188.05 [5242]E(x52421,x52422)+~E(f30(x52423,x52424,x52421),f30(x52425,x52426,x52422))
% 187.18/188.05 [5243]E(x52431,x52432)+~E(f30(x52433,x52431,x52434),f30(x52435,x52432,x52436))
% 187.18/188.05 [5244]E(x52441,x52442)+~E(f30(x52441,x52443,x52444),f30(x52442,x52445,x52446))
% 187.18/188.05 [5245]E(x52451,x52452)+~E(f29(x52453,x52454,x52451),f29(x52455,x52456,x52452))
% 187.18/188.05 [5246]E(x52461,x52462)+~E(f29(x52463,x52461,x52464),f29(x52465,x52462,x52466))
% 187.18/188.05 [5247]E(x52471,x52472)+~E(f29(x52471,x52473,x52474),f29(x52472,x52475,x52476))
% 187.18/188.05 [6691]E(f329(f184(x66911,x66912,x66913,x66914),x66915),f329(f236(x66912),x66916))+~E(f329(x66914,x66915),f329(f236(x66912),x66916))
% 187.18/188.05 [6835]E(f329(f238(f878(x68351),x68352,f206(x68351),x68353),f329(x68354,x68355)),f329(x68353,x68356))+~E(f329(x68354,x68355),f329(f236(x68352),x68356))
% 187.18/188.05 [8369]~P15(x83695,x83691,x83692,x83696)+E(f329(f73(x83691,x83691,x83691,f329(x83692,x83693)),f329(x83692,x83694)),f329(f73(x83691,x83691,x83691,f329(x83692,x83694)),f329(x83692,x83693)))
% 187.18/188.05 [8608]~P56(x86084,x86085,x86082,x86081,x86086)+E(f329(x86081,f329(x86082,x86083)),x86083)
% 187.18/188.05 [8760]P21(x87601,x87602,x87603,x87604)+~P21(x87601,x87605,f329(f73(x87602,x87605,x87601,x87606),x87603),x87604)
% 187.18/188.05 [8843]~P21(x88434,x88432,f329(f73(x88431,x88432,x88434,x88433),x88435),x88436)+P21(x88431,x88432,x88433,f329(f308(x88434,x88431,x88435),x88436))
% 187.18/188.05 [9556]P24(f329(f62(x95561),x95562))+~P24(f329(f67(x95561,x95563,x95564,x95565,x95562),x95566))
% 187.18/188.05 [9564]~P24(f329(f329(f331(x95644),x95643),f297(x95644,x95645,x95641,x95642,x95646)))+P24(f329(f329(x95641,x95642),x95643))
% 187.18/188.05 [9565]~P24(f329(f329(f331(x95654),x95653),f294(x95654,x95651,x95655,x95652,x95656)))+P24(f329(f329(x95651,x95652),x95653))
% 187.18/188.05 [9566]~P24(f329(f329(f331(x95664),x95662),f297(x95664,x95661,x95665,x95666,x95663)))+P24(f329(f329(x95661,x95662),x95663))
% 187.18/188.05 [9567]~P24(f329(f329(f331(x95674),x95672),f294(x95674,x95675,x95671,x95676,x95673)))+P24(f329(f329(x95671,x95672),x95673))
% 187.18/188.05 [5747]E(x57471,x57472)+~E(f329(f329(f264(x57473,x57474),x57475),x57471),f329(f329(f264(x57473,x57474),x57476),x57472))
% 187.18/188.05 [5749]E(x57491,x57492)+~E(f329(f329(f264(x57493,x57494),x57491),x57495),f329(f329(f264(x57493,x57494),x57492),x57496))
% 187.18/188.05 [5873]~P12(x58735,x58736,x58731)+E(f329(f329(x58731,x58732),f329(f329(x58731,x58733),x58734)),f329(f329(x58731,x58733),f329(f329(x58731,x58732),x58734)))
% 187.18/188.05 [7291]~P37(x72914,x72911,f329(f329(f149(x72914),x72912),x72915),f329(f329(f149(x72914),x72913),x72916))+P24(f329(f329(x72911,x72912),x72913))
% 187.18/188.05 [7659]P37(x76591,x76592,x76593,x76594)+~P37(x76591,x76592,f329(f329(f149(x76591),x76595),x76593),f329(f329(f149(x76591),x76596),x76594))
% 187.18/188.05 [8703]~P56(x87035,x87031,x87032,x87036,x87034)+P24(f329(f329(f331(x87031),f329(x87032,x87033)),x87034))
% 187.18/188.05 [8871]E(f329(f76(x88711,x88712,x88713,x88714,x88715),x88716),f329(x88713,x88716))+P24(f329(f329(f331(x88711),x88716),x88715))
% 187.18/188.05 [8892]~E(x88923,f329(f329(f149(x88921),x88925),x88926))+P24(f329(f329(f331(f880(f875(x88921),f875(x88921))),f329(f329(f264(f875(x88921),f875(x88921)),x88922),f329(f329(f126(x88921),x88922),x88923))),f145(x88921,x88924)))
% 187.18/188.05 [8899]E(f329(f76(x88991,x88992,x88993,x88994,x88995),x88996),f329(x88994,x88996))+~P24(f329(f329(f331(x88991),x88996),x88995))
% 187.18/188.05 [8904]E(f329(f186(x89041,x89042,x89043,x89044,x89045),x89046),f329(x89043,x89046))+P24(f329(f329(f331(x89041),x89046),f329(f171(x89041),x89044)))
% 187.18/188.05 [9134]~P39(x91341,x91342,x91343,x91345,x91346)+P39(x91341,x91342,x91343,f329(f329(f174(x91341),x91344),x91345),f329(f329(f174(x91342),x91344),x91346))
% 187.18/188.05 [9135]~P39(x91351,x91352,x91353,x91355,x91356)+P39(x91351,x91352,x91353,f329(f329(f136(x91351),x91354),x91355),f329(f329(f136(x91352),x91354),x91356))
% 187.18/188.05 [9628]~P19(x96284,x96282,x96285,x96283,x96286,x96281)+E(f329(x96281,f193(f881(x96282,a869))),x96283)
% 187.18/188.05 [9873]~E(f329(x98734,f329(f263(x98731,x98733),x98735)),f329(x98736,f329(f263(x98731,x98733),x98735)))+E(f329(f269(x98731,x98732,x98733,x98733,x98734,f34(x98733)),x98735),f329(f269(x98731,x98732,x98733,x98733,x98736,f34(x98733)),x98735))
% 187.18/188.05 [9874]~E(f329(x98744,f329(f267(x98741,x98742),x98745)),f329(x98746,f329(f267(x98741,x98742),x98745)))+E(f329(f269(x98741,x98741,x98742,x98743,f34(x98741),x98744),x98745),f329(f269(x98741,x98741,x98742,x98743,f34(x98741),x98746),x98745))
% 187.18/188.05 [9919]~E(f329(f269(x99192,x99196,x99193,x99193,x99191,f34(x99193)),x99194),f329(f269(x99192,x99196,x99193,x99193,x99195,f34(x99193)),x99194))+E(f329(x99191,f329(f263(x99192,x99193),x99194)),f329(x99195,f329(f263(x99192,x99193),x99194)))
% 187.18/188.05 [9920]~E(f329(f269(x99202,x99202,x99203,x99206,f34(x99202),x99201),x99204),f329(f269(x99202,x99202,x99203,x99206,f34(x99202),x99205),x99204))+E(f329(x99201,f329(f267(x99202,x99203),x99204)),f329(x99205,f329(f267(x99202,x99203),x99204)))
% 187.18/188.05 [8799]P24(f329(f329(f331(x87991),x87992),x87993))+~P24(f329(f329(f331(f880(x87991,x87994)),f329(f329(f264(x87991,x87994),x87992),x87995)),f329(f329(f266(x87991,x87994),x87993),x87996)))
% 187.18/188.05 [8813]P24(f329(f329(f331(x88131),x88132),f329(x88133,x88134)))+~P24(f329(f329(f331(f880(x88135,x88131)),f329(f329(f264(x88135,x88131),x88134),x88132)),f329(f329(f266(x88135,x88131),x88136),x88133)))
% 187.18/188.05 [8901]~E(f329(f194(f875(x89011)),x89014),f329(f194(f875(x89012)),x89015))+E(f186(x89011,x89012,x89013,x89014,f329(f329(f126(x89012),x89015),x89016)),f186(x89011,x89012,x89013,x89014,x89015))
% 187.18/188.05 [8902]~E(f329(f194(f875(x89021)),x89024),f329(f194(f875(x89022)),x89026))+E(f186(x89021,x89022,x89023,f329(f329(f126(x89021),x89024),x89025),x89026),f186(x89021,x89022,x89023,x89024,x89026))
% 187.18/188.05 [9155]P24(f329(f329(f331(x91551),x91554),f183(x91551,x91552,x91556)))+E(f184(x91551,x91552,f329(f329(f329(f72(x91551,f878(x91552)),x91553),x91554),f329(f236(x91552),x91555)),x91556),f329(f329(f329(f72(x91551,f878(x91552)),f184(x91551,x91552,x91553,x91556)),x91554),f329(f236(x91552),x91555)))
% 187.18/188.05 [9256]P24(f329(f329(f331(f880(x92561,x92561)),f329(f329(f264(x92561,x92561),f329(x92562,x92563)),f329(x92562,x92564))),x92565))+~P24(f329(f329(f331(f880(x92566,x92566)),f329(f329(f264(x92566,x92566),x92563),x92564)),f329(f329(f285(x92561,x92566),x92565),x92562)))
% 187.18/188.05 [9276]~P24(f329(f329(f331(f880(x92764,x92764)),f329(f329(f264(x92764,x92764),f329(x92766,x92762)),f329(x92766,x92763))),x92765))+P24(f329(f329(f331(f880(x92761,x92761)),f329(f329(f264(x92761,x92761),x92762),x92763)),f329(f329(f285(x92764,x92761),x92765),x92766)))
% 187.18/188.05 [9922]E(f329(f329(f264(x99221,x99222),f659(x99223,x99224,x99225,x99226,x99222,x99221)),f660(x99223,x99224,x99225,x99226,x99222,x99221)),x99226)+~P24(f329(f329(f331(f880(x99221,x99222)),x99226),f329(f329(f286(x99221,x99225,x99222),x99224),x99223)))
% 187.18/188.05 [10122]~P24(f329(f329(f331(f880(x101221,x101226)),x101225),f329(f329(f286(x101221,x101222,x101226),x101224),x101223)))+P24(f329(f329(f331(f880(x101221,x101222)),f329(f329(f264(x101221,x101222),f659(x101223,x101224,x101222,x101225,x101226,x101221)),f661(x101223,x101224,x101222,x101225,x101226,x101221))),x101224))
% 187.18/188.05 [10123]~P24(f329(f329(f331(f880(x101236,x101232)),x101235),f329(f329(f286(x101236,x101231,x101232),x101234),x101233)))+P24(f329(f329(f331(f880(x101231,x101232)),f329(f329(f264(x101231,x101232),f661(x101233,x101234,x101231,x101235,x101232,x101236)),f660(x101233,x101234,x101231,x101235,x101232,x101236))),x101233))
% 187.18/188.05 [6154]~E(x61546,x61544)+E(f329(f329(f329(f329(f72(x61541,x61542),x61543),x61544),x61545),x61546),x61545)
% 187.18/188.05 [6203]E(x62031,x62032)+E(f329(f329(f329(f329(f72(x62033,x62034),x62035),x62032),x62036),x62031),f329(x62035,x62031))
% 187.18/188.05 [7732]~P31(x77322)+E(f329(f329(f42(x77321,x77322),x77323),f329(f329(f7(x77321,x77324,x77322),x77325),x77326)),f329(f329(f329(f42(x77321,f881(x77324,x77322)),x77323),x77325),x77326))
% 187.18/188.05 [7733]~P31(x77332)+E(f329(f329(f43(x77331,x77332),x77333),f329(f329(f7(x77331,x77334,x77332),x77335),x77336)),f329(f329(f329(f43(x77331,f881(x77334,x77332)),x77333),x77335),x77336))
% 187.18/188.05 [8522]E(f329(f329(f42(x85221,f881(x85222,a869)),x85223),f329(f329(f8(f881(x85222,a869),f881(x85222,a869),x85221),f329(f307(x85222),x85224)),x85225)),f329(f329(f307(x85222),x85224),f329(f329(f42(x85221,f881(x85222,a869)),x85223),x85225)))+~P24(f329(f329(f331(x85221),x85226),x85223))
% 187.18/188.05 [8956]~P31(x89562)+E(f329(f329(f42(x89561,x89562),x89563),f329(f329(f8(f881(x89564,x89562),x89562,x89561),f329(f42(x89564,x89562),x89565)),f329(f7(x89564,x89561,x89562),x89566))),f329(f329(f42(x89564,x89562),x89565),f329(f329(f8(f881(x89561,x89562),x89562,x89564),f329(f42(x89561,x89562),x89563)),x89566)))
% 187.18/188.05 [8957]~P31(x89572)+E(f329(f329(f43(x89571,x89572),x89573),f329(f329(f8(f881(x89574,x89572),x89572,x89571),f329(f43(x89574,x89572),x89575)),f329(f7(x89574,x89571,x89572),x89576))),f329(f329(f43(x89574,x89572),x89575),f329(f329(f8(f881(x89571,x89572),x89572,x89574),f329(f43(x89571,x89572),x89573)),x89576)))
% 187.18/188.05 [9164]P24(f329(f329(f331(x91641),x91642),f329(f171(x91641),x91643)))+~P24(f329(f329(f331(f880(x91644,x91641)),f329(f329(f264(x91644,x91641),x91645),x91642)),f329(f171(f880(x91644,x91641)),f329(f329(f181(x91644,x91641),x91646),x91643))))
% 187.18/188.05 [9165]P24(f329(f329(f331(x91651),x91652),f329(f171(x91651),x91653)))+~P24(f329(f329(f331(f880(x91651,x91654)),f329(f329(f264(x91651,x91654),x91652),x91655)),f329(f171(f880(x91651,x91654)),f329(f329(f181(x91651,x91654),x91653),x91656))))
% 187.18/188.05 [9270]P24(f329(f329(f243(f881(x92701,a869)),f329(f283(x92702,x92701,x92703),x92704)),x92705))+~P24(f329(f329(f243(f881(f880(x92702,x92701),a869)),x92703),f329(f329(f266(x92702,x92701),x92706),f329(f16(f881(x92701,a869),x92702),x92705))))
% 187.18/188.05 [9460]P24(f329(f329(f331(f880(f875(x94601),f875(x94601))),f329(f329(f264(f875(x94601),f875(x94601)),f329(f329(f149(x94601),x94602),x94603)),f329(f329(f149(x94601),x94604),x94605))),f145(x94601,x94606)))+~P24(f329(f329(f331(f880(x94601,x94601)),f329(f329(f264(x94601,x94601),x94602),x94604)),x94606))
% 187.18/188.05 [9918]E(f329(f329(f264(x99181,x99182),f571(x99183,x99184,x99185,x99182,x99181,x99186)),f572(x99183,x99184,x99185,x99182,x99181,x99186)),x99186)+P24(f329(f329(f331(x99185),x99184),f329(f329(f268(x99181,x99182,f881(x99185,a869)),x99183),x99186)))
% 187.18/188.05 [9924]E(f329(f329(f264(x99241,x99242),f566(x99243,x99244,x99242,x99241,x99245,x99246)),f567(x99243,x99244,x99242,x99241,x99245,x99246)),x99243)+~P24(f329(f329(f331(x99246),x99245),f329(f329(f268(x99241,x99242,f881(x99246,a869)),x99244),x99243)))
% 187.18/188.05 [10081]P24(f329(f329(f331(x100811),x100812),f329(f329(x100813,f566(x100814,x100813,x100815,x100816,x100812,x100811)),f567(x100814,x100813,x100815,x100816,x100812,x100811))))+~P24(f329(f329(f331(x100811),x100812),f329(f329(f268(x100816,x100815,f881(x100811,a869)),x100813),x100814)))
% 187.18/188.05 [10100]~P24(f329(f329(f331(x101001),x101002),f329(f329(x101005,f571(x101005,x101002,x101001,x101004,x101003,x101006)),f572(x101005,x101002,x101001,x101004,x101003,x101006))))+P24(f329(f329(f331(x101001),x101002),f329(f329(f268(x101003,x101004,f881(x101001,a869)),x101005),x101006)))
% 187.18/188.05 [7855]P24(f329(f329(f331(x78551),x78554),x78556))+E(f187(x78551,x78552,f329(f329(f329(f72(x78551,f878(x78552)),x78553),x78554),x78555),x78556),f187(x78551,x78552,x78553,x78556))
% 187.18/188.05 [7932]P24(f329(f329(f331(x79321),x79324),x79326))+E(f329(f308(x79321,x79322,f329(f329(f329(f72(x79321,x79322),x79323),x79324),x79325)),x79326),f329(f308(x79321,x79322,x79323),x79326))
% 187.18/188.05 [7959]P24(f329(f329(f331(x79591),x79594),f329(f171(x79591),x79596)))+E(f329(f329(f152(x79591,x79592),f329(f329(f329(f72(x79591,x79592),x79593),x79594),x79595)),x79596),f329(f329(f152(x79591,x79592),x79593),x79596))
% 187.18/188.05 [8418]E(x84181,x84182)+E(f329(f329(f157(x84183,f329(f329(f157(x84183,x84184),x84181),x84185)),x84182),x84186),f329(f329(f157(x84183,f329(f329(f157(x84183,x84184),x84182),x84186)),x84181),x84185))
% 187.18/188.05 [8962]~P24(f329(f329(f331(x89623),x89626),x89625))+E(f329(f329(f307(x89621),x89622),f329(f308(x89623,x89621,x89624),f329(f329(f22(f881(x89623,a869)),x89625),f329(f329(f307(x89623),x89626),f193(f881(x89623,a869)))))),f329(f308(x89623,x89621,f329(f329(f329(f72(x89623,x89621),x89624),x89626),x89622)),x89625))
% 187.18/188.05 [9734]E(f186(x97341,x97342,x97343,f329(f329(f126(x97341),x97344),f329(f329(f149(x97341),x97345),f118(x97341))),x97346),f329(f329(f329(f72(x97341,f878(x97342)),f186(x97341,x97342,x97343,x97344,x97346)),x97345),f329(f236(x97342),f329(f329(f163(x97342),x97346),f329(f194(f875(x97341)),x97344)))))+~P24(f329(f329(f244(a874),f329(f194(f875(x97341)),x97344)),f329(f194(f875(x97342)),x97346)))
% 187.18/188.05 [8742]~E(x87423,x87426)+E(f329(f329(f177(x87421,x87422),f329(f329(f149(f880(x87421,x87422)),f329(f329(f264(x87421,x87422),x87423),x87424)),x87425)),x87426),f329(f236(x87422),x87424))
% 187.18/188.05 [8769]E(x87691,x87692)+E(f329(f329(f177(x87693,x87694),f329(f329(f149(f880(x87693,x87694)),f329(f329(f264(x87693,x87694),x87691),x87695)),x87696)),x87692),f329(f329(f177(x87693,x87694),x87696),x87692))
% 187.18/188.05 [9039]~P24(f329(f329(x90394,x90395),x90396))+P24(f329(f329(f329(f329(f115(f881(x90391,f881(x90392,a869))),x90393),x90394),x90395),x90396))
% 187.18/188.05 [9041]~P24(f329(f329(x90413,x90415),x90416))+P24(f329(f329(f329(f329(f115(f881(x90411,f881(x90412,a869))),x90413),x90414),x90415),x90416))
% 187.18/188.05 [9327]P24(f329(f329(x93271,x93272),x93273))+~P24(f329(f329(f329(f329(f106(f881(x93274,f881(x93275,a869))),x93276),x93271),x93272),x93273))
% 187.18/188.05 [9328]P24(f329(f329(x93281,x93282),x93283))+~P24(f329(f329(f329(f329(f106(f881(x93284,f881(x93285,a869))),x93281),x93286),x93282),x93283))
% 187.18/188.05 [9756]~P72(x97562)+E(f329(f329(f6(x97561,x97562),f329(f329(f7(x97561,f881(x97563,a869),x97562),f329(f329(f8(f881(x97563,x97562),f881(f881(x97563,a869),x97562),x97561),f6(x97563,x97562)),x97564)),x97565)),x97566),f329(f329(f6(f880(x97561,x97563),x97562),f329(f268(x97561,x97563,x97562),x97564)),f329(f329(f266(x97561,x97563),x97566),f329(f16(f881(x97563,a869),x97561),x97565))))
% 187.18/188.05 [9757]~P76(x97572)+E(f329(f329(f9(x97571,x97572),f329(f329(f7(x97571,f881(x97573,a869),x97572),f329(f329(f8(f881(x97573,x97572),f881(f881(x97573,a869),x97572),x97571),f9(x97573,x97572)),x97574)),x97575)),x97576),f329(f329(f9(f880(x97571,x97573),x97572),f329(f268(x97571,x97573,x97572),x97574)),f329(f329(f266(x97571,x97573),x97576),f329(f16(f881(x97573,a869),x97571),x97575))))
% 187.18/188.05 [9901]~P72(x99012)+E(f329(f329(f6(x99011,x99012),f329(f329(f7(x99011,f881(x99013,a869),x99012),f329(f329(f8(f881(x99013,x99012),f881(f881(x99013,a869),x99012),x99011),f6(x99013,x99012)),f329(f7(x99013,x99011,x99012),x99014))),x99015)),x99016),f329(f329(f6(x99013,x99012),f329(f329(f7(x99013,f881(x99011,a869),x99012),f329(f329(f8(f881(x99011,x99012),f881(f881(x99011,a869),x99012),x99013),f6(x99011,x99012)),x99014)),x99016)),x99015))
% 187.18/188.05 [9597]~P24(f329(f329(f331(x95971),x95975),x95974))+E(f329(f329(f329(f72(x95971,f878(x95972)),f187(x95971,x95972,x95973,f329(f329(f22(f881(x95971,a869)),x95974),f329(f329(f307(x95971),x95975),f193(f881(x95971,a869)))))),x95975),x95976),f187(x95971,x95972,f329(f329(f329(f72(x95971,f878(x95972)),x95973),x95975),x95976),x95974))
% 187.18/188.05 [10178]~P24(f329(f329(f331(f880(x101781,x101782)),f329(f329(f264(x101781,x101782),x101785),x101786)),f329(f329(f115(f881(f880(x101781,x101782),a869)),x101783),x101784)))+P24(f329(f329(f329(f329(f115(f881(x101781,f881(x101782,a869))),f329(f329(f7(x101781,f881(f880(x101781,x101782),a869),f881(x101782,a869)),f329(f329(f8(f881(x101782,f881(f881(f880(x101781,x101782),a869),a869)),f881(f881(f880(x101781,x101782),a869),f881(x101782,a869)),x101781),f7(x101782,f881(f880(x101781,x101782),a869),a869)),f329(f329(f8(f881(x101782,f880(x101781,x101782)),f881(x101782,f881(f881(f880(x101781,x101782),a869),a869)),x101781),f329(f8(f880(x101781,x101782),f881(f881(f880(x101781,x101782),a869),a869),x101782),f331(f880(x101781,x101782)))),f264(x101781,x101782)))),x101783)),f329(f329(f7(x101781,f881(f880(x101781,x101782),a869),f881(x101782,a869)),f329(f329(f8(f881(x101782,f881(f881(f880(x101781,x101782),a869),a869)),f881(f881(f880(x101781,x101782),a869),f881(x101782,a869)),x101781),f7(x101782,f881(f880(x101781,x101782),a869),a869)),f329(f329(f8(f881(x101782,f880(x101781,x101782)),f881(x101782,f881(f881(f880(x101781,x101782),a869),a869)),x101781),f329(f8(f880(x101781,x101782),f881(f881(f880(x101781,x101782),a869),a869),x101782),f331(f880(x101781,x101782)))),f264(x101781,x101782)))),x101784)),x101785),x101786))
% 187.18/188.05 [10179]~P24(f329(f329(f331(f880(x101791,x101792)),f329(f329(f264(x101791,x101792),x101795),x101796)),f329(f329(f106(f881(f880(x101791,x101792),a869)),x101793),x101794)))+P24(f329(f329(f329(f329(f106(f881(x101791,f881(x101792,a869))),f329(f329(f7(x101791,f881(f880(x101791,x101792),a869),f881(x101792,a869)),f329(f329(f8(f881(x101792,f881(f881(f880(x101791,x101792),a869),a869)),f881(f881(f880(x101791,x101792),a869),f881(x101792,a869)),x101791),f7(x101792,f881(f880(x101791,x101792),a869),a869)),f329(f329(f8(f881(x101792,f880(x101791,x101792)),f881(x101792,f881(f881(f880(x101791,x101792),a869),a869)),x101791),f329(f8(f880(x101791,x101792),f881(f881(f880(x101791,x101792),a869),a869),x101792),f331(f880(x101791,x101792)))),f264(x101791,x101792)))),x101793)),f329(f329(f7(x101791,f881(f880(x101791,x101792),a869),f881(x101792,a869)),f329(f329(f8(f881(x101792,f881(f881(f880(x101791,x101792),a869),a869)),f881(f881(f880(x101791,x101792),a869),f881(x101792,a869)),x101791),f7(x101792,f881(f880(x101791,x101792),a869),a869)),f329(f329(f8(f881(x101792,f880(x101791,x101792)),f881(x101792,f881(f881(f880(x101791,x101792),a869),a869)),x101791),f329(f8(f880(x101791,x101792),f881(f881(f880(x101791,x101792),a869),a869),x101792),f331(f880(x101791,x101792)))),f264(x101791,x101792)))),x101794)),x101795),x101796))
% 187.18/188.05 [10185]P24(f329(f329(f331(f880(x101851,x101852)),f329(f329(f264(x101851,x101852),x101853),x101854)),f329(f329(f115(f881(f880(x101851,x101852),a869)),x101855),x101856)))+~P24(f329(f329(f329(f329(f115(f881(x101851,f881(x101852,a869))),f329(f329(f7(x101851,f881(f880(x101851,x101852),a869),f881(x101852,a869)),f329(f329(f8(f881(x101852,f881(f881(f880(x101851,x101852),a869),a869)),f881(f881(f880(x101851,x101852),a869),f881(x101852,a869)),x101851),f7(x101852,f881(f880(x101851,x101852),a869),a869)),f329(f329(f8(f881(x101852,f880(x101851,x101852)),f881(x101852,f881(f881(f880(x101851,x101852),a869),a869)),x101851),f329(f8(f880(x101851,x101852),f881(f881(f880(x101851,x101852),a869),a869),x101852),f331(f880(x101851,x101852)))),f264(x101851,x101852)))),x101855)),f329(f329(f7(x101851,f881(f880(x101851,x101852),a869),f881(x101852,a869)),f329(f329(f8(f881(x101852,f881(f881(f880(x101851,x101852),a869),a869)),f881(f881(f880(x101851,x101852),a869),f881(x101852,a869)),x101851),f7(x101852,f881(f880(x101851,x101852),a869),a869)),f329(f329(f8(f881(x101852,f880(x101851,x101852)),f881(x101852,f881(f881(f880(x101851,x101852),a869),a869)),x101851),f329(f8(f880(x101851,x101852),f881(f881(f880(x101851,x101852),a869),a869),x101852),f331(f880(x101851,x101852)))),f264(x101851,x101852)))),x101856)),x101853),x101854))
% 187.18/188.05 [10186]P24(f329(f329(f331(f880(x101861,x101862)),f329(f329(f264(x101861,x101862),x101863),x101864)),f329(f329(f106(f881(f880(x101861,x101862),a869)),x101865),x101866)))+~P24(f329(f329(f329(f329(f106(f881(x101861,f881(x101862,a869))),f329(f329(f7(x101861,f881(f880(x101861,x101862),a869),f881(x101862,a869)),f329(f329(f8(f881(x101862,f881(f881(f880(x101861,x101862),a869),a869)),f881(f881(f880(x101861,x101862),a869),f881(x101862,a869)),x101861),f7(x101862,f881(f880(x101861,x101862),a869),a869)),f329(f329(f8(f881(x101862,f880(x101861,x101862)),f881(x101862,f881(f881(f880(x101861,x101862),a869),a869)),x101861),f329(f8(f880(x101861,x101862),f881(f881(f880(x101861,x101862),a869),a869),x101862),f331(f880(x101861,x101862)))),f264(x101861,x101862)))),x101865)),f329(f329(f7(x101861,f881(f880(x101861,x101862),a869),f881(x101862,a869)),f329(f329(f8(f881(x101862,f881(f881(f880(x101861,x101862),a869),a869)),f881(f881(f880(x101861,x101862),a869),f881(x101862,a869)),x101861),f7(x101862,f881(f880(x101861,x101862),a869),a869)),f329(f329(f8(f881(x101862,f880(x101861,x101862)),f881(x101862,f881(f881(f880(x101861,x101862),a869),a869)),x101861),f329(f8(f880(x101861,x101862),f881(f881(f880(x101861,x101862),a869),a869),x101862),f331(f880(x101861,x101862)))),f264(x101861,x101862)))),x101866)),x101863),x101864))
% 187.18/188.05 [10172]~P24(f329(f329(f331(f880(x101722,x101723)),f329(f329(f264(x101722,x101723),x101725),x101726)),f329(f329(f42(x101721,f881(f880(x101722,x101723),a869)),f252(f881(x101721,a869))),x101724)))+P24(f329(f329(f329(f329(f42(x101721,f881(x101722,f881(x101723,a869))),f252(f881(x101721,a869))),f329(f329(f8(f881(f880(x101722,x101723),a869),f881(x101722,f881(x101723,a869)),x101721),f329(f7(x101722,f881(f880(x101722,x101723),a869),f881(x101723,a869)),f329(f329(f8(f881(x101723,f881(f881(f880(x101722,x101723),a869),a869)),f881(f881(f880(x101722,x101723),a869),f881(x101723,a869)),x101722),f7(x101723,f881(f880(x101722,x101723),a869),a869)),f329(f329(f8(f881(x101723,f880(x101722,x101723)),f881(x101723,f881(f881(f880(x101722,x101723),a869),a869)),x101722),f329(f8(f880(x101722,x101723),f881(f881(f880(x101722,x101723),a869),a869),x101723),f331(f880(x101722,x101723)))),f264(x101722,x101723))))),x101724)),x101725),x101726))
% 187.18/188.05 [10173]~P24(f329(f329(f331(f880(x101732,x101733)),f329(f329(f264(x101732,x101733),x101735),x101736)),f329(f329(f43(x101731,f881(f880(x101732,x101733),a869)),f252(f881(x101731,a869))),x101734)))+P24(f329(f329(f329(f329(f43(x101731,f881(x101732,f881(x101733,a869))),f252(f881(x101731,a869))),f329(f329(f8(f881(f880(x101732,x101733),a869),f881(x101732,f881(x101733,a869)),x101731),f329(f7(x101732,f881(f880(x101732,x101733),a869),f881(x101733,a869)),f329(f329(f8(f881(x101733,f881(f881(f880(x101732,x101733),a869),a869)),f881(f881(f880(x101732,x101733),a869),f881(x101733,a869)),x101732),f7(x101733,f881(f880(x101732,x101733),a869),a869)),f329(f329(f8(f881(x101733,f880(x101732,x101733)),f881(x101733,f881(f881(f880(x101732,x101733),a869),a869)),x101732),f329(f8(f880(x101732,x101733),f881(f881(f880(x101732,x101733),a869),a869),x101733),f331(f880(x101732,x101733)))),f264(x101732,x101733))))),x101734)),x101735),x101736))
% 187.18/188.05 [10182]P24(f329(f329(f331(f880(x101821,x101822)),f329(f329(f264(x101821,x101822),x101823),x101824)),f329(f329(f42(x101825,f881(f880(x101821,x101822),a869)),f252(f881(x101825,a869))),x101826)))+~P24(f329(f329(f329(f329(f42(x101825,f881(x101821,f881(x101822,a869))),f252(f881(x101825,a869))),f329(f329(f8(f881(f880(x101821,x101822),a869),f881(x101821,f881(x101822,a869)),x101825),f329(f7(x101821,f881(f880(x101821,x101822),a869),f881(x101822,a869)),f329(f329(f8(f881(x101822,f881(f881(f880(x101821,x101822),a869),a869)),f881(f881(f880(x101821,x101822),a869),f881(x101822,a869)),x101821),f7(x101822,f881(f880(x101821,x101822),a869),a869)),f329(f329(f8(f881(x101822,f880(x101821,x101822)),f881(x101822,f881(f881(f880(x101821,x101822),a869),a869)),x101821),f329(f8(f880(x101821,x101822),f881(f881(f880(x101821,x101822),a869),a869),x101822),f331(f880(x101821,x101822)))),f264(x101821,x101822))))),x101826)),x101823),x101824))
% 187.18/188.05 [10183]P24(f329(f329(f331(f880(x101831,x101832)),f329(f329(f264(x101831,x101832),x101833),x101834)),f329(f329(f43(x101835,f881(f880(x101831,x101832),a869)),f252(f881(x101835,a869))),x101836)))+~P24(f329(f329(f329(f329(f43(x101835,f881(x101831,f881(x101832,a869))),f252(f881(x101835,a869))),f329(f329(f8(f881(f880(x101831,x101832),a869),f881(x101831,f881(x101832,a869)),x101835),f329(f7(x101831,f881(f880(x101831,x101832),a869),f881(x101832,a869)),f329(f329(f8(f881(x101832,f881(f881(f880(x101831,x101832),a869),a869)),f881(f881(f880(x101831,x101832),a869),f881(x101832,a869)),x101831),f7(x101832,f881(f880(x101831,x101832),a869),a869)),f329(f329(f8(f881(x101832,f880(x101831,x101832)),f881(x101832,f881(f881(f880(x101831,x101832),a869),a869)),x101831),f329(f8(f880(x101831,x101832),f881(f881(f880(x101831,x101832),a869),a869),x101832),f331(f880(x101831,x101832)))),f264(x101831,x101832))))),x101836)),x101833),x101834))
% 187.18/188.05 [7405]E(f329(x74051,f329(x74052,x74053)),f329(x74054,x74053))+~E(f329(f73(x74055,x74056,x74057,x74051),x74052),x74054)
% 187.18/188.05 [9627]~P18(x96273,x96274,x96271,x96275,x96276,x96277)+E(f329(f329(x96271,x96272),x96272),x96272)
% 187.18/188.05 [9998]~E(f329(f238(f878(x99987),x99981,f206(x99987),x99985),f329(x99984,x99983)),f329(f236(x99987),x99982))+E(f329(f236(x99981),f768(x99982,x99983,x99984,x99985,x99986,x99987,x99981)),f329(x99984,x99983))
% 187.18/188.05 [9999]~E(f329(f238(f878(x99996),x99997,f206(x99996),x99991),f329(x99994,x99993)),f329(f236(x99996),x99992))+E(f329(x99991,f768(x99992,x99993,x99994,x99991,x99995,x99996,x99997)),f329(f236(x99996),x99992))
% 187.18/188.05 [5977]~E(f329(f329(f152(x59771,x59775),x59776),x59772),f329(f329(f152(x59773,x59775),x59777),x59774))+E(f329(f194(f875(x59771)),x59772),f329(f194(f875(x59773)),x59774))
% 187.18/188.05 [7483]E(x74831,x74832)+~E(f329(f329(f329(f72(x74833,f878(x74834)),x74835),x74836),f329(f236(x74834),x74831)),f329(f329(f329(f72(x74833,f878(x74834)),x74837),x74836),f329(f236(x74834),x74832)))
% 187.18/188.05 [8457]E(f329(x84571,f329(x84572,x84573)),f329(x84574,x84573))+~E(f329(f73(x84575,x84576,x84577,x84571),x84572),f329(f73(x84576,x84576,x84577,f34(x84576)),x84574))
% 187.18/188.05 [8788]~P39(x87884,x87885,x87881,f329(f329(f149(x87884),x87882),x87886),f329(f329(f149(x87885),x87883),x87887))+P24(f329(f329(x87881,x87882),x87883))
% 187.18/188.05 [9171]P39(x91711,x91712,x91713,x91714,x91715)+~P39(x91711,x91712,x91713,f329(f329(f149(x91711),x91716),x91714),f329(f329(f149(x91712),x91717),x91715))
% 187.18/188.05 [9795]P24(f329(f329(x97951,x97952),f519(x97953,x97952,x97954,x97951)))+~P24(f329(f329(f265(x97955,x97956,x97957,x97951,x97954),x97952),x97953))
% 187.18/188.05 [9816]P24(f329(f329(x98161,f519(x98162,x98163,x98161,x98164)),x98162))+~P24(f329(f329(f265(x98165,x98166,x98167,x98164,x98161),x98163),x98162))
% 187.18/188.05 [6020]E(x60201,x60202)+~E(f329(f329(f329(f92(x60203),x60204),x60205),x60201),f329(f329(f329(f92(x60203),x60206),x60207),x60202))
% 187.18/188.05 [6021]E(x60211,x60212)+~E(f329(f329(f329(f92(x60213),x60214),x60211),x60215),f329(f329(f329(f92(x60213),x60216),x60212),x60217))
% 187.18/188.05 [6022]E(x60221,x60222)+~E(f329(f329(f329(f92(x60223),x60221),x60224),x60225),f329(f329(f329(f92(x60223),x60222),x60226),x60227))
% 187.18/188.05 [8907]~P16(x89076,x89071,x89073,x89077)+E(f329(f73(x89071,x89071,x89072,f329(x89073,x89074)),f329(f73(x89071,x89071,x89072,f329(x89073,x89074)),x89075)),f329(f73(x89071,x89071,x89072,f329(x89073,x89074)),x89075))
% 187.18/188.05 [9279]~P39(x92793,x92792,x92794,f329(f329(f152(x92791,x92793),x92795),x92796),x92797)+P39(x92791,x92792,f329(f329(f8(x92793,f881(x92792,a869),x92791),x92794),x92795),x92796,x92797)
% 187.18/188.05 [9302]P39(x93021,x93022,x93023,f329(f329(f152(x93024,x93021),x93025),x93026),x93027)+~P39(x93024,x93022,f329(f329(f8(x93021,f881(x93022,a869),x93024),x93023),x93025),x93026,x93027)
% 187.18/188.05 [9714]E(f186(x97141,x97142,f329(f329(f329(f72(x97141,f878(x97142)),x97143),x97144),f329(f236(x97142),x97145)),x97146,x97147),f329(f329(f329(f72(x97141,f878(x97142)),f186(x97141,x97142,x97143,x97146,x97147)),x97144),f329(f236(x97142),x97145)))+P24(f329(f329(f331(x97141),x97144),f329(f171(x97141),x97146)))
% 187.18/188.05 [8906]~P24(f329(f329(f331(x89061),x89062),f329(f329(x89065,x89066),x89067)))+P24(f329(f329(f331(x89061),x89062),f329(f329(f268(x89063,x89064,f881(x89061,a869)),x89065),f329(f329(f264(x89063,x89064),x89066),x89067))))
% 187.18/188.05 [9197]P24(f329(f329(f329(x91971,x91972),x91973),x91974))+~P24(f329(f329(f329(f268(x91975,x91976,f881(x91977,a869)),x91971),f329(f329(f264(x91975,x91976),x91972),x91973)),x91974))
% 187.18/188.05 [9341]P24(f329(f329(f331(x93411),f329(f329(x93412,x93413),x93414)),f329(f308(f880(x93415,x93416),x93411,f329(f268(x93415,x93416,x93411),x93412)),x93417)))+~P24(f329(f329(f331(f880(x93415,x93416)),f329(f329(f264(x93415,x93416),x93413),x93414)),x93417))
% 187.18/188.05 [9674]P24(f329(f329(f331(f880(f875(x96741),f875(x96741))),f329(f329(f264(f875(x96741),f875(x96741)),f329(f329(f126(x96741),x96742),f329(f329(f149(x96741),x96743),x96744))),f329(f329(f126(x96741),x96742),f329(f329(f149(x96741),x96745),x96746)))),f145(x96741,x96747)))+~P24(f329(f329(f331(f880(x96741,x96741)),f329(f329(f264(x96741,x96741),x96743),x96745)),x96747))
% 187.18/188.05 [9736]~P39(x97361,x97363,x97364,x97366,f329(f329(f152(x97362,x97363),x97365),x97367))+P39(x97361,x97362,f329(f329(f7(x97361,f881(x97362,x97363),f881(x97362,a869)),f329(f329(f8(f881(x97363,a869),f881(f881(x97362,x97363),f881(x97362,a869)),x97361),f8(x97363,a869,x97362)),x97364)),x97365),x97366,x97367)
% 187.18/188.05 [9820]P39(x98201,x98202,x98203,x98204,f329(f329(f152(x98205,x98202),x98206),x98207))+~P39(x98201,x98205,f329(f329(f7(x98201,f881(x98205,x98202),f881(x98205,a869)),f329(f329(f8(f881(x98202,a869),f881(f881(x98205,x98202),f881(x98205,a869)),x98201),f8(x98202,a869,x98205)),x98203)),x98206),x98204,x98207)
% 187.18/188.05 [9189]E(x91891,x91892)+E(f329(f329(f329(f72(x91893,x91894),f329(f329(f329(f72(x91893,x91894),x91895),x91891),x91896)),x91892),x91897),f329(f329(f329(f72(x91893,x91894),f329(f329(f329(f72(x91893,x91894),x91895),x91892),x91897)),x91891),x91896))
% 187.18/188.05 [9434]E(f186(x94341,x94342,f329(f329(f329(f72(x94341,f878(x94342)),x94343),x94344),f329(f236(x94342),x94345)),x94346,x94347),f186(x94341,x94342,x94343,x94346,x94347))+~P24(f329(f329(f331(x94341),x94344),f329(f171(x94341),f329(f329(f174(x94341),f329(f194(f875(x94342)),x94347)),x94346))))
% 187.18/188.05 [9747]E(f186(x97471,x97472,f329(f329(f329(f72(x97471,f878(x97472)),x97473),x97474),f329(f236(x97472),x97475)),x97476,x97477),f329(f329(f329(f72(x97471,f878(x97472)),f186(x97471,x97472,x97473,x97476,x97477)),x97474),f329(f236(x97472),x97475)))+P24(f329(f329(f331(x97471),x97474),f329(f171(x97471),f329(f329(f174(x97471),f329(f194(f875(x97472)),x97477)),x97476))))
% 187.18/188.05 [10111]P24(f329(f329(f331(x101111),f628(x101112,x101113,x101114,x101115,x101116,x101117,x101111)),x101115))+P24(f329(f329(f329(f329(f43(x101111,f881(x101117,f881(x101116,a869))),x101115),x101114),x101113),x101112))
% 187.18/188.05 [10112]P24(f329(f329(f331(x101121),f459(x101122,x101123,x101124,x101125,x101126,x101127,x101121)),x101125))+~P24(f329(f329(f329(f329(f42(x101121,f881(x101127,f881(x101126,a869))),x101125),x101124),x101123),x101122))
% 187.18/188.05 [10137]P24(f329(f329(f329(x101371,f459(x101372,x101373,x101371,x101374,x101375,x101376,x101377)),x101373),x101372))+~P24(f329(f329(f329(f329(f42(x101377,f881(x101376,f881(x101375,a869))),x101374),x101371),x101373),x101372))
% 187.18/188.05 [10154]~P24(f329(f329(f329(x101545,f628(x101547,x101546,x101545,x101544,x101543,x101542,x101541)),x101546),x101547))+P24(f329(f329(f329(f329(f43(x101541,f881(x101542,f881(x101543,a869))),x101544),x101545),x101546),x101547))
% 187.18/188.05 [10171]~P24(f329(f329(f331(f880(x101711,x101713)),f329(f329(f264(x101711,x101713),x101716),x101717)),f329(f329(f286(x101711,x101712,x101713),x101714),x101715)))+P24(f329(f329(f265(x101711,x101712,x101713,f329(f329(f7(x101711,f881(f880(x101711,x101712),a869),f881(x101712,a869)),f329(f329(f8(f881(x101712,f881(f881(f880(x101711,x101712),a869),a869)),f881(f881(f880(x101711,x101712),a869),f881(x101712,a869)),x101711),f7(x101712,f881(f880(x101711,x101712),a869),a869)),f329(f329(f8(f881(x101712,f880(x101711,x101712)),f881(x101712,f881(f881(f880(x101711,x101712),a869),a869)),x101711),f329(f8(f880(x101711,x101712),f881(f881(f880(x101711,x101712),a869),a869),x101712),f331(f880(x101711,x101712)))),f264(x101711,x101712)))),x101714),f329(f329(f7(x101712,f881(f880(x101712,x101713),a869),f881(x101713,a869)),f329(f329(f8(f881(x101713,f881(f881(f880(x101712,x101713),a869),a869)),f881(f881(f880(x101712,x101713),a869),f881(x101713,a869)),x101712),f7(x101713,f881(f880(x101712,x101713),a869),a869)),f329(f329(f8(f881(x101713,f880(x101712,x101713)),f881(x101713,f881(f881(f880(x101712,x101713),a869),a869)),x101712),f329(f8(f880(x101712,x101713),f881(f881(f880(x101712,x101713),a869),a869),x101713),f331(f880(x101712,x101713)))),f264(x101712,x101713)))),x101715)),x101716),x101717))
% 187.18/188.05 [10181]P24(f329(f329(f331(f880(x101811,x101812)),f329(f329(f264(x101811,x101812),x101813),x101814)),f329(f329(f286(x101811,x101815,x101812),x101816),x101817)))+~P24(f329(f329(f265(x101811,x101815,x101812,f329(f329(f7(x101811,f881(f880(x101811,x101815),a869),f881(x101815,a869)),f329(f329(f8(f881(x101815,f881(f881(f880(x101811,x101815),a869),a869)),f881(f881(f880(x101811,x101815),a869),f881(x101815,a869)),x101811),f7(x101815,f881(f880(x101811,x101815),a869),a869)),f329(f329(f8(f881(x101815,f880(x101811,x101815)),f881(x101815,f881(f881(f880(x101811,x101815),a869),a869)),x101811),f329(f8(f880(x101811,x101815),f881(f881(f880(x101811,x101815),a869),a869),x101815),f331(f880(x101811,x101815)))),f264(x101811,x101815)))),x101816),f329(f329(f7(x101815,f881(f880(x101815,x101812),a869),f881(x101812,a869)),f329(f329(f8(f881(x101812,f881(f881(f880(x101815,x101812),a869),a869)),f881(f881(f880(x101815,x101812),a869),f881(x101812,a869)),x101815),f7(x101812,f881(f880(x101815,x101812),a869),a869)),f329(f329(f8(f881(x101812,f880(x101815,x101812)),f881(x101812,f881(f881(f880(x101815,x101812),a869),a869)),x101815),f329(f8(f880(x101815,x101812),f881(f881(f880(x101815,x101812),a869),a869),x101812),f331(f880(x101815,x101812)))),f264(x101815,x101812)))),x101817)),x101813),x101814))
% 187.18/188.05 [10121]~P134(x101212)+E(f329(f329(f6(x101211,x101212),f329(f329(f7(x101211,f881(x101213,a869),x101212),f329(f329(f8(f881(x101213,x101212),f881(f881(x101213,a869),x101212),x101211),f6(x101213,x101212)),f329(f329(f7(x101211,f881(x101213,x101212),f881(x101213,x101212)),f329(f329(f8(f881(x101212,x101212),f881(f881(x101213,x101212),f881(x101213,x101212)),x101211),f8(x101212,x101212,x101213)),f329(f329(f8(x101212,f881(x101212,x101212),x101211),f81(x101212)),x101214))),x101215))),x101216)),x101217),f329(f329(f81(x101212),f329(f329(f6(x101211,x101212),x101214),x101217)),f329(f329(f6(x101213,x101212),x101215),x101216)))
% 187.18/188.05 [9230]~P15(x92307,x92301,x92303,x92308)+E(f329(f73(x92301,x92301,x92302,f329(x92303,x92304)),f329(f73(x92301,x92301,x92302,f329(x92303,x92305)),x92306)),f329(f73(x92301,x92301,x92302,f329(x92303,x92305)),f329(f73(x92301,x92301,x92302,f329(x92303,x92304)),x92306)))
% 187.18/188.05 [10176]E(f329(f329(f264(x101761,x101762),f329(x101763,f542(x101764,x101765,x101763,x101766,x101767,x101768,x101762,x101761))),f329(x101765,f543(x101764,x101765,x101763,x101766,x101767,x101768,x101762,x101761))),x101768)+~P24(f329(f329(f331(f880(x101761,x101762)),x101768),f329(f308(f880(x101767,x101766),f880(x101761,x101762),f269(x101767,x101761,x101766,x101762,x101763,x101765)),x101764)))
% 187.18/188.05 [10192]~P24(f329(f329(f331(f880(x101928,x101927)),x101926),f329(f308(f880(x101921,x101922),f880(x101928,x101927),f269(x101921,x101928,x101922,x101927,x101925,x101924)),x101923)))+P24(f329(f329(f331(f880(x101921,x101922)),f329(f329(f264(x101921,x101922),f542(x101923,x101924,x101925,x101922,x101921,x101926,x101927,x101928)),f543(x101923,x101924,x101925,x101922,x101921,x101926,x101927,x101928))),x101923))
% 187.18/188.05 [9664]P24(f329(f329(f331(f880(f880(x96641,x96642),f880(x96641,x96642))),f329(f329(f264(f880(x96641,x96642),f880(x96641,x96642)),f329(f329(f264(x96641,x96642),x96643),x96644)),f329(f329(f264(x96641,x96642),x96645),x96646))),f322(x96641,x96642,x96647,x96648)))+~P24(f329(f329(f331(f880(x96641,x96641)),f329(f329(f264(x96641,x96641),x96643),x96645)),x96647))
% 187.18/188.05 [10164]E(f329(f140(x101641,x101642,f329(f7(x101642,x101641,x101641),x101643),f329(x101644,x101645)),x101646),f329(x101644,f329(f140(x101647,x101642,f329(f7(x101642,x101647,x101647),x101648),x101645),x101646)))+P24(f329(f329(f331(x101642),f772(x101645,x101648,x101644,x101643,x101647,x101641,x101646,x101642)),f329(f171(x101642),x101646)))
% 187.18/188.05 [10184]~E(f329(f73(x101841,x101841,x101847,f329(x101843,f772(x101845,x101848,x101844,x101843,x101847,x101841,x101846,x101842))),x101844),f329(f73(x101847,x101841,x101847,x101844),f329(x101848,f772(x101845,x101848,x101844,x101843,x101847,x101841,x101846,x101842))))+E(f329(f140(x101841,x101842,f329(f7(x101842,x101841,x101841),x101843),f329(x101844,x101845)),x101846),f329(x101844,f329(f140(x101847,x101842,f329(f7(x101842,x101847,x101847),x101848),x101845),x101846)))
% 187.18/188.05 [8463]E(f329(x84631,f329(x84632,x84633)),f329(x84634,f329(x84635,x84633)))+~E(f329(f73(x84636,x84637,x84638,x84631),x84632),f329(f73(x84639,x84637,x84638,x84634),x84635))
% 187.18/188.05 [10050]P24(f329(f329(f331(f880(x100501,x100502)),f329(f329(f264(x100501,x100502),f329(x100503,x100504)),f329(x100505,x100506))),f329(f308(f880(x100507,x100508),f880(x100501,x100502),f269(x100507,x100501,x100508,x100502,x100503,x100505)),x100509)))+~P24(f329(f329(f331(f880(x100507,x100508)),f329(f329(f264(x100507,x100508),x100504),x100506)),x100509))
% 187.18/188.05 [8736]~E(f329(x87364,f329(x87365,x87366)),f329(x87369,f329(x873610,x873611)))+E(f329(f329(f73(x87361,x87362,x87363,x87364),x87365),x87366),f329(f329(f73(x87367,x87362,x87368,x87369),x873610),x873611))
% 187.18/188.05 [4571]~P27(x45711)+~P103(x45711)+E(f106(x45711),f241(x45711))
% 187.18/188.05 [4572]~P27(x45721)+~P102(x45721)+E(f115(x45721),f242(x45721))
% 187.18/188.05 [4814]~P115(x48141)+~P94(x48141)+E(f329(f75(x48141),f329(f108(x48141),a102)),f78(x48141))
% 187.18/188.05 [5092]E(x50921,f2(a1))+E(f82(a1,x50921),f329(f79(a1),f78(a1)))+P24(f329(f329(f244(a1),f2(a1)),x50921))
% 187.18/188.05 [5308]E(x53081,f2(a1))+E(f82(a1,x53081),f78(a1))+~P24(f329(f329(f244(a1),f2(a1)),x53081))
% 187.18/188.05 [7295]~P43(x72951)+P24(f329(f62(a1),x72951))+~P24(f329(f62(a874),f329(f308(a1,a874,a109),x72951)))
% 187.18/188.05 [8564]~P2(a5000)+~P24(f329(f329(f331(f880(a872,a870)),x85641),f329(f171(f880(a872,a870)),a27)))+P24(f329(f329(f268(a872,a870,a869),f329(f16(f881(a870,a869),a872),a25)),x85641))
% 187.18/188.05 [9626]E(x96261,f193(f881(f880(a874,a874),a869)))+~P24(f329(f62(f880(a874,a874)),x96261))+P24(f329(f329(f331(f880(f881(f880(a874,a874),a869),f881(f880(a874,a874),a869))),f329(f329(f264(f881(f880(a874,a874),a869),f881(f880(a874,a874),a869)),f193(f881(f880(a874,a874),a869))),x96261)),a37))
% 187.18/188.05 [9796]E(x97961,f2(a874))+E(x97961,f329(a117,f2(a874)))+~P24(f329(f329(f244(a874),x97961),f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))))
% 187.18/188.05 [10078]E(x100781,f2(a104))+E(f329(f329(f80(a1),f329(f329(f81(a1),f329(f108(a1),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))),f329(a20,f329(f329(f39(a104),x100781),f329(f108(a104),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102))))))),f78(a1)),f329(a20,x100781))+E(f45(a104,x100781,f329(f108(a104),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))),f2(a104))
% 187.18/188.05 [9929]E(x99291,f2(a104))+~E(f45(a104,x99291,f329(f108(a104),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))),f2(a104))+E(f329(f329(f81(a1),f329(f108(a1),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))),f329(a20,f329(f329(f39(a104),x99291),f329(f108(a104),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))))),f329(a20,x99291))
% 187.18/188.05 [4644]~P57(x46441,x46442)+P48(x46441,x46442)+~P49(a869)
% 187.18/188.05 [4581]~P141(x45811)+P35(x45811,x45812)+~E(x45812,f2(x45811))
% 187.18/188.05 [4582]~P27(x45821)+P33(x45821,x45822)+~E(x45822,f118(x45821))
% 187.18/188.05 [4591]~P115(x45911)+~E(x45912,f2(x45911))+E(f82(x45911,x45912),f2(x45911))
% 187.18/188.05 [4592]~P91(x45921)+~E(x45922,f2(x45921))+E(f82(x45921,x45922),f2(x45921))
% 187.18/188.05 [4600]~P141(x46002)+~P35(x46002,x46001)+E(x46001,f2(x46002))
% 187.18/188.05 [4634]~P115(x46342)+~E(f82(x46342,x46341),f2(x46342))+E(x46341,f2(x46342))
% 187.18/188.05 [4651]~P28(x46512)+~P28(x46511)+P28(f881(x46511,x46512))
% 187.18/188.05 [4652]~P28(x46522)+~P28(x46521)+P28(f879(x46521,x46522))
% 187.18/188.05 [4653]~P28(x46532)+~P28(x46531)+P28(f880(x46531,x46532))
% 187.18/188.05 [4654]~P32(x46542)+~P32(x46541)+P32(f200(x46541,x46542))
% 187.18/188.05 [4655]~P142(x46552)+~P142(x46551)+P142(f880(x46551,x46552))
% 187.18/188.05 [4656]~P60(x46562)+~P60(x46561)+P60(f881(x46561,x46562))
% 187.18/188.05 [4657]~P60(x46572)+~P60(x46571)+P60(f879(x46571,x46572))
% 187.18/188.05 [4658]~P60(x46582)+~P60(x46581)+P60(f880(x46581,x46582))
% 187.18/188.05 [4659]~P60(x46591)+~P96(x46592)+P96(f881(x46591,x46592))
% 187.18/188.05 [4785]~P27(x47851)+~P33(x47851,x47852)+P33(x47851,f150(x47851,x47852))
% 187.18/188.05 [5023]~P32(x50232)+~P32(x50231)+P32(f45(a1,x50231,x50232))
% 187.18/188.05 [4602]~P78(x46021)+~E(x46022,f2(x46021))+E(f329(f79(x46021),x46022),x46022)
% 187.18/188.05 [4606]~P138(x46061)+~E(x46062,f2(a1))+E(f329(f107(x46061),x46062),f2(x46061))
% 187.18/188.05 [4607]~P93(x46071)+~E(x46072,f2(a1))+E(f329(f107(x46071),x46072),f2(x46071))
% 187.18/188.05 [4631]~P77(x46311)+~E(f2(x46311),x46312)+E(f329(f79(x46311),x46312),f2(x46311))
% 187.18/188.05 [4632]~P87(x46321)+~E(x46322,f2(x46321))+E(f329(f75(x46321),x46322),f2(x46321))
% 187.18/188.05 [4633]~P77(x46331)+~E(x46332,f2(x46331))+E(f329(f79(x46331),x46332),f2(x46331))
% 187.18/188.05 [4661]~P78(x46612)+E(x46611,f2(x46612))+~E(f329(f79(x46612),x46611),x46611)
% 187.18/188.05 [4667]E(x46671,f329(a109,x46672))+~E(x46671,f2(a874))+~E(x46672,f329(f105(a1),x46671))
% 187.18/188.05 [4668]E(f329(a109,x46681),x46682)+~E(x46682,f2(a874))+~E(x46681,f329(f105(a1),x46682))
% 187.18/188.05 [4672]~P93(x46722)+E(x46721,f2(a1))+~E(f329(f107(x46722),x46721),f2(x46722))
% 187.18/188.05 [4677]~P87(x46772)+E(x46771,f2(x46772))+~E(f329(f75(x46772),x46771),f2(x46772))
% 187.18/188.05 [4678]~P77(x46782)+E(x46781,f2(x46782))+~E(f329(f79(x46782),x46781),f2(x46782))
% 187.18/188.05 [4679]~P77(x46791)+E(f2(x46791),x46792)+~E(f329(f79(x46791),x46792),f2(x46791))
% 187.18/188.05 [4819]~P2(a5000)+~E(f329(a28,x48192),f329(f236(a870),x48191))+P24(f329(a25,x48191))
% 187.18/188.05 [4861]~P27(x48611)+~P33(x48611,x48612)+P33(x48611,f329(f170(x48611),x48612))
% 187.18/188.05 [4887]~P24(x48872)+~P24(x48871)+P24(f329(f329(a327,x48871),x48872))
% 187.18/188.05 [4919]~E(f78(a874),f2(a874))+E(f329(f38(x49191),x49192),f2(a874))+~P24(f329(f62(x49191),x49192))
% 187.18/188.05 [4952]~P134(x49521)+~P111(x49521)+E(f329(f329(f254(x49521),f2(x49521)),f329(a117,x49522)),f2(x49521))
% 187.18/188.05 [4990]~P27(x49901)+P33(x49901,f137(x49901,x49902))+~P24(f329(f62(x49901),x49902))
% 187.18/188.05 [4991]~P27(x49911)+P33(x49911,f760(x49912,x49911))+~P24(f329(f62(x49911),x49912))
% 187.18/188.05 [5013]~P27(x50131)+E(f329(f171(x50131),f137(x50131,x50132)),x50132)+~P24(f329(f62(x50131),x50132))
% 187.18/188.05 [5014]~P27(x50141)+E(f329(f171(x50141),f760(x50142,x50141)),x50142)+~P24(f329(f62(x50141),x50142))
% 187.18/188.05 [5044]P24(x50441)+P24(x50442)+~P24(f329(f329(a328,x50442),x50441))
% 187.18/188.05 [5056]E(x50561,f193(f881(x50562,a869)))+~E(f329(f38(x50562),x50561),f2(a874))+~P24(f329(f62(x50562),x50561))
% 187.18/188.05 [5061]P24(x50611)+~P24(x50612)+~P24(f329(f329(a332,x50612),x50611))
% 187.18/188.05 [5110]~P75(x51101)+E(f329(f75(x51101),x51102),x51102)+P24(f329(f329(f244(x51101),x51102),f2(x51101)))
% 187.18/188.05 [5181]~P60(x51812)+~P24(f329(f58(x51812),x51811))+P24(f329(x51811,f718(x51811,x51812)))
% 187.18/188.05 [5182]~P60(x51822)+~P24(f329(f58(x51822),x51821))+P24(f329(x51821,f727(x51821,x51822)))
% 187.18/188.05 [5209]~P24(f329(a25,x52092))+~P24(f329(a25,x52091))+P24(f329(a25,f33(x52091,x52092)))
% 187.18/188.05 [5218]E(x52181,f118(x52182))+P24(f329(f135(x52182),f119(x52182,x52181)))+~P24(f329(f135(x52182),x52181))
% 187.18/188.05 [5223]~P27(x52231)+~P24(f329(f62(x52231),x52232))+P24(f329(f135(x52231),f137(x52231,x52232)))
% 187.18/188.05 [5224]~P27(x52241)+~P24(f329(f62(x52241),x52242))+P24(f329(f135(x52241),f760(x52242,x52241)))
% 187.18/188.05 [5230]~P138(x52301)+E(f329(f105(x52301),f329(a109,x52302)),f329(f107(x52301),x52302))+P24(f329(f329(f244(a1),x52302),f2(a1)))
% 187.18/188.05 [5258]P5(x52582,x52581)+E(f329(x52581,f496(x52581)),f329(x52581,f499(x52581)))+P24(f329(f329(x52581,f496(x52581)),f499(x52581)))
% 187.18/188.05 [5273]E(f329(f105(a1),f410(x52731,x52732)),x52731)+P24(f329(x52732,f329(a109,x52731)))+~P24(f329(x52732,f2(a874)))
% 187.18/188.05 [5285]~P60(x52851)+~P24(f329(x52852,f728(x52852,x52851)))+P24(f329(f59(x52851),x52852))
% 187.18/188.05 [5286]~P60(x52861)+~P24(f329(x52862,f729(x52862,x52861)))+P24(f329(f59(x52861),x52862))
% 187.18/188.05 [5301]~P60(x53012)+~P40(x53012,x53011,f56(x53012))+P24(f329(x53011,f778(x53011,x53012)))
% 187.18/188.05 [5317]~P115(x53171)+~E(f82(x53171,x53172),f329(f79(x53171),f78(x53171)))+P24(f329(f329(f244(x53171),x53172),f2(x53171)))
% 187.18/188.05 [5393]~E(x53932,f2(a1))+E(f223(x53931,x53932),f329(f329(f264(a1,a1),f2(a1)),f78(a1)))+P24(f329(f329(f244(a1),x53932),f2(a1)))
% 187.18/188.05 [5394]~E(x53941,f2(a1))+E(f223(x53941,x53942),f329(f329(f264(a1,a1),f2(a1)),f78(a1)))+P24(f329(f329(f244(a1),x53942),f2(a1)))
% 187.18/188.05 [5446]E(f329(f105(a1),f410(x54461,x54462)),x54461)+P24(f329(x54462,f329(a109,x54461)))+P24(f329(f329(f244(a1),x54461),f2(a1)))
% 187.18/188.05 [5509]~P115(x55091)+E(f82(x55091,x55092),f329(f79(x55091),f78(x55091)))+~P24(f329(f329(f244(x55091),x55092),f2(x55091)))
% 187.18/188.05 [5510]~P87(x55101)+E(f329(f75(x55101),x55102),f329(f79(x55101),x55102))+~P24(f329(f329(f243(x55101),x55102),f2(x55101)))
% 187.18/188.05 [5511]~P87(x55111)+E(f329(f75(x55111),x55112),f329(f79(x55111),x55112))+~P24(f329(f329(f244(x55111),x55112),f2(x55111)))
% 187.18/188.05 [5512]~P75(x55121)+E(f329(f75(x55121),x55122),f329(f79(x55121),x55122))+~P24(f329(f329(f244(x55121),x55122),f2(x55121)))
% 187.18/188.05 [5607]~P24(f329(x56071,f410(x56072,x56071)))+P24(f329(x56071,f329(a109,x56072)))+~P24(f329(x56071,f2(a874)))
% 187.18/188.05 [5614]E(x56141,f2(a874))+E(f329(a117,f854(x56142,x56141)),x56141)+~P24(f329(f329(f244(a874),x56141),f329(a117,x56142)))
% 187.18/188.05 [5618]P5(x56181,x56182)+~E(f329(x56182,f496(x56182)),f329(x56182,f499(x56182)))+~P24(f329(f329(x56182,f496(x56182)),f499(x56182)))
% 187.18/188.05 [5638]~P27(x56381)+P33(x56381,x56382)+P24(f329(f329(f243(a874),f744(x56382,x56381)),f745(x56382,x56381)))
% 187.18/188.05 [5639]~P27(x56391)+P33(x56391,x56392)+P24(f329(f329(f243(a874),f751(x56392,x56391)),f756(x56392,x56391)))
% 187.18/188.05 [5727]~P87(x57271)+~E(x57272,f2(x57271))+P24(f329(f329(f243(x57271),f329(f75(x57271),x57272)),f2(x57271)))
% 187.18/188.05 [5806]~P60(x58062)+~P60(x58061)+E(f60(x58061,x58062,f56(x58061),f56(x58062)),f56(f880(x58061,x58062)))
% 187.18/188.05 [5810]~P24(f329(x58101,f410(x58102,x58101)))+P24(f329(x58101,f329(a109,x58102)))+P24(f329(f329(f244(a1),x58102),f2(a1)))
% 187.18/188.05 [5833]~P24(f329(x58331,f329(a109,x58332)))+P24(f329(x58331,f2(a874)))+~P24(f329(f329(f244(a1),x58332),f2(a1)))
% 187.18/188.05 [6175]~P115(x61751)+~P24(f329(f329(f244(x61751),x61752),f2(x61751)))+P24(f329(f329(f244(x61751),f82(x61751,x61752)),f2(x61751)))
% 187.18/188.05 [6289]~P115(x62891)+P24(f329(f329(f243(x62891),f329(f107(x62891),x62892)),f2(x62891)))+~P24(f329(f329(f243(a1),x62892),f2(a1)))
% 187.18/188.05 [6290]~P115(x62901)+P24(f329(f329(f244(x62901),f329(f107(x62901),x62902)),f2(x62901)))+~P24(f329(f329(f244(a1),x62902),f2(a1)))
% 187.18/188.05 [6297]~P87(x62972)+E(x62971,f2(x62972))+~P24(f329(f329(f243(x62972),f329(f75(x62972),x62971)),f2(x62972)))
% 187.18/188.05 [6372]~P138(x63721)+~P24(f329(f329(f331(x63721),x63722),f114(x63721)))+P24(f329(f329(f331(x63721),f329(f79(x63721),x63722)),f114(x63721)))
% 187.18/188.05 [6404]~P115(x64041)+~P24(f329(f329(f244(x64041),f82(x64041,x64042)),f2(x64041)))+P24(f329(f329(f244(x64041),x64042),f2(x64041)))
% 187.18/188.05 [6575]~P115(x65752)+~P24(f329(f329(f243(x65752),f329(f107(x65752),x65751)),f2(x65752)))+P24(f329(f329(f243(a1),x65751),f2(a1)))
% 187.18/188.05 [6576]~P115(x65762)+~P24(f329(f329(f244(x65762),f329(f107(x65762),x65761)),f2(x65762)))+P24(f329(f329(f244(a1),x65761),f2(a1)))
% 187.18/188.05 [7081]~P78(x70811)+~P24(f329(f329(f243(x70811),x70812),f2(x70811)))+P24(f329(f329(f243(x70811),f329(f329(f80(x70811),x70812),x70812)),f2(x70811)))
% 187.18/188.05 [7083]~P115(x70831)+~P24(f329(f329(f244(x70831),x70832),f2(x70831)))+P24(f329(f329(f244(x70831),f329(f329(f80(x70831),x70832),x70832)),f2(x70831)))
% 187.18/188.05 [7084]~P78(x70841)+~P24(f329(f329(f244(x70841),x70842),f2(x70841)))+P24(f329(f329(f244(x70841),f329(f329(f80(x70841),x70842),x70842)),f2(x70841)))
% 187.18/188.05 [7653]~P78(x76531)+~P24(f329(f329(f243(x76531),f329(f329(f80(x76531),x76532),x76532)),f2(x76531)))+P24(f329(f329(f243(x76531),x76532),f2(x76531)))
% 187.18/188.05 [7654]~P115(x76541)+~P24(f329(f329(f244(x76541),f329(f329(f80(x76541),x76542),x76542)),f2(x76541)))+P24(f329(f329(f244(x76541),x76542),f2(x76541)))
% 187.18/188.05 [7655]~P78(x76551)+~P24(f329(f329(f244(x76551),f329(f329(f80(x76551),x76552),x76552)),f2(x76551)))+P24(f329(f329(f244(x76551),x76552),f2(x76551)))
% 187.18/188.05 [4717]~E(x47172,f78(a874))+~E(x47171,f78(a874))+E(f329(f329(f81(a874),x47171),x47172),f78(a874))
% 187.18/188.05 [4718]~E(x47182,f78(a1))+~E(x47181,f78(a1))+E(f329(f329(f81(a1),x47181),x47182),f78(a1))
% 187.18/188.05 [4719]~E(x47192,f2(a874))+~E(x47191,f2(a874))+E(f329(f329(f80(a874),x47191),x47192),f2(a874))
% 187.18/188.05 [4771]~P118(x47712)+E(x47711,f2(x47712))+E(f329(f329(f287(x47712),x47711),x47711),f78(x47712))
% 187.18/188.05 [4772]~P29(x47722)+E(x47721,f2(x47722))+E(f329(f329(f39(x47722),x47721),x47721),f78(x47722))
% 187.18/188.05 [4773]~P119(x47732)+E(x47731,f2(x47732))+E(f329(f329(f287(x47732),x47731),x47731),f78(x47732))
% 187.18/188.05 [4792]~P137(x47921)+~E(x47922,f78(x47921))+E(f329(f329(f81(x47921),x47922),x47922),f78(x47921))
% 187.18/188.05 [4793]~P78(x47931)+~E(x47932,f2(x47931))+E(f329(f329(f80(x47931),x47932),x47932),f2(x47931))
% 187.18/188.05 [4794]~P119(x47941)+~E(x47942,f2(x47941))+E(f329(f329(f287(x47941),x47942),x47942),f2(x47941))
% 187.18/188.05 [4840]~E(x48402,f2(a874))+~E(x48401,f2(a874))+E(f329(f79(a1),f329(f105(a1),x48401)),f329(f105(a1),x48402))
% 187.18/188.05 [4858]E(x48581,f78(a874))+E(x48582,f2(a874))+~E(f329(f329(f81(a874),x48582),x48581),x48582)
% 187.18/188.05 [4868]E(x48681,f2(a874))+E(x48682,f2(a874))+~E(f329(f329(f81(a874),x48682),x48681),f2(a874))
% 187.18/188.05 [4896]~E(x48962,f2(a874))+~E(x48961,f329(a117,f2(a874)))+E(f329(f329(f80(a874),x48961),x48962),f329(a117,f2(a874)))
% 187.18/188.05 [4897]~E(x48971,f2(a874))+~E(x48972,f329(a117,f2(a874)))+E(f329(f329(f80(a874),x48971),x48972),f329(a117,f2(a874)))
% 187.18/188.05 [4902]E(x49021,f78(a1))+E(x49022,f329(f108(a1),a102))+~E(f329(f329(f81(a1),x49021),x49022),f78(a1))
% 187.18/188.05 [4903]E(x49031,f78(a1))+E(x49032,f329(f108(a1),a102))+~E(f329(f329(f81(a1),x49032),x49031),f78(a1))
% 187.18/188.05 [4904]E(x49041,f78(a1))+E(x49041,f329(f108(a1),a102))+~E(f329(f329(f81(a1),x49042),x49041),f78(a1))
% 187.18/188.05 [4906]E(x49061,f78(a1))+E(x49061,f329(f108(a1),a102))+~E(f329(f329(f81(a1),x49061),x49062),f78(a1))
% 187.18/188.05 [4923]~P78(x49232)+E(x49231,f2(x49232))+~E(f329(f329(f80(x49232),x49231),x49231),f2(x49232))
% 187.18/188.05 [4929]~E(x49291,f329(f108(a1),a102))+~E(x49292,f329(f108(a1),a102))+E(f329(f329(f81(a1),x49291),x49292),f78(a1))
% 187.18/188.05 [4941]E(x49411,f2(a874))+E(x49412,f2(a874))+~E(f329(f329(f80(a874),x49412),x49411),f329(a117,f2(a874)))
% 187.18/188.05 [4951]~P61(x49511)+~P94(x49511)+E(f329(f329(f287(x49511),x49512),f329(f108(x49511),a83)),f2(x49511))
% 187.18/188.05 [4957]~P137(x49571)+~E(x49572,f329(f79(x49571),f78(x49571)))+E(f329(f329(f81(x49571),x49572),x49572),f78(x49571))
% 187.18/188.05 [4962]~P32(x49622)+~P32(x49621)+P32(f329(f329(f81(a1),x49621),x49622))
% 187.18/188.05 [4963]~P32(x49632)+~P32(x49631)+P32(f329(f329(f80(a1),x49631),x49632))
% 187.18/188.05 [4964]~P32(x49642)+~P32(x49641)+P32(f329(f329(f39(a1),x49641),x49642))
% 187.18/188.05 [4966]~E(x49662,f2(a1))+E(x49661,f2(a1))+E(f46(x49661,x49662),f329(f329(f264(a1,a1),f2(a1)),x49661))
% 187.18/188.05 [4988]~E(x49882,f329(a117,f2(a874)))+~E(x49881,f329(a117,f2(a874)))+E(f329(f329(f81(a874),x49881),x49882),f329(a117,f2(a874)))
% 187.18/188.05 [5003]E(x50031,f2(a874))+E(x50032,f329(a117,f2(a874)))+~E(f329(f329(f254(a874),x50032),x50031),f329(a117,f2(a874)))
% 187.18/188.05 [5004]E(x50041,f2(a874))+E(x50041,f329(a117,f2(a874)))+~E(f329(f329(f80(a874),x50042),x50041),f329(a117,f2(a874)))
% 187.18/188.05 [5005]E(x50051,f2(a874))+E(x50051,f329(a117,f2(a874)))+~E(f329(f329(f80(a874),x50051),x50052),f329(a117,f2(a874)))
% 187.18/188.05 [5015]~P61(x50151)+~P94(x50151)+E(f329(f329(f287(x50151),x50152),f329(f108(x50151),a102)),f329(f79(x50151),x50152))
% 187.18/188.05 [5036]E(x50361,f329(a109,x50362))+~E(x50361,f2(a874))+P24(f329(f329(f243(a1),f2(a1)),x50362))
% 187.18/188.05 [5037]E(f329(a109,x50371),x50372)+~E(x50372,f2(a874))+P24(f329(f329(f243(a1),f2(a1)),x50371))
% 187.18/188.05 [5052]E(x50521,f329(a117,f2(a874)))+E(x50522,f329(a117,f2(a874)))+~E(f329(f329(f80(a874),x50521),x50522),f329(a117,f2(a874)))
% 187.18/188.05 [5063]~E(x50631,f329(a109,x50632))+E(x50631,f2(a874))+P24(f329(f329(f243(a1),f2(a1)),x50632))
% 187.18/188.05 [5064]~E(f329(a109,x50642),x50641)+E(x50641,f2(a874))+P24(f329(f329(f243(a1),f2(a1)),x50642))
% 187.18/188.05 [5086]~P66(x50861)+E(f329(f64(x50861,f106(x50861)),x50862),f10(x50861,x50862))+~P24(f329(f62(x50861),x50862))
% 187.18/188.05 [5087]~P66(x50871)+E(f329(f64(x50871,f115(x50871)),x50872),f13(x50871,x50872))+~P24(f329(f62(x50871),x50872))
% 187.18/188.05 [5088]~P27(x50881)+E(f329(f64(x50881,f241(x50881)),x50882),f14(x50881,x50882))+~P24(f329(f62(x50881),x50882))
% 187.18/188.05 [5089]~P27(x50891)+E(f329(f64(x50891,f242(x50891)),x50892),f15(x50891,x50892))+~P24(f329(f62(x50891),x50892))
% 187.18/188.05 [5091]~P60(x50911)+~P24(f329(x50912,f206(x50911)))+P24(f329(f58(f878(x50911)),x50912))
% 187.18/188.05 [5174]~P60(x51742)+P24(f329(x51741,f206(x51742)))+~P24(f329(f59(f878(x51742)),x51741))
% 187.18/188.05 [5175]E(x51751,x51752)+~E(f329(f329(f22(a874),x51752),x51751),f2(a874))+~E(f329(f329(f22(a874),x51751),x51752),f2(a874))
% 187.18/188.05 [5189]P32(x51891)+~P43(x51892)+~P24(f329(f329(f331(a1),x51891),x51892))
% 187.18/188.05 [5219]~P115(x52191)+~E(f82(x52191,x52192),f78(x52191))+P24(f329(f329(f244(x52191),f2(x52191)),x52192))
% 187.18/188.05 [5231]~P94(x52311)+E(f329(f105(x52311),f329(f108(a874),x52312)),f329(f108(x52311),x52312))+P24(f329(a198,f329(f108(a1),x52312)))
% 187.18/188.05 [5237]~P48(x52371,x52372)+P49(a869)+P24(f329(f62(f880(x52371,x52371)),x52372))
% 187.18/188.05 [5310]~P27(x53101)+E(f329(f64(x53101,f241(x53101)),x53102),f11(x53101,f241(x53101),x53102))+~P24(f329(f62(x53101),x53102))
% 187.18/188.05 [5311]~P27(x53111)+E(f329(f64(x53111,f242(x53111)),x53112),f12(x53111,f242(x53111),x53112))+~P24(f329(f62(x53111),x53112))
% 187.18/188.05 [5324]E(x53241,x53242)+P24(f329(f329(f244(a874),x53242),x53241))+P24(f329(f329(f244(a874),x53241),x53242))
% 187.18/188.05 [5325]E(x53251,x53252)+P24(f329(f329(f244(a1),x53252),x53251))+P24(f329(f329(f244(a1),x53251),x53252))
% 187.18/188.05 [5380]~P94(x53801)+E(f329(f105(x53801),f329(f108(a874),x53802)),f2(x53801))+~P24(f329(a198,f329(f108(a1),x53802)))
% 187.18/188.05 [5383]~E(x53832,f329(a109,x53831))+E(x53831,f329(f105(a1),x53832))+~P24(f329(f329(f243(a1),f2(a1)),x53831))
% 187.18/188.05 [5384]~E(f329(a109,x53841),x53842)+E(x53841,f329(f105(a1),x53842))+~P24(f329(f329(f243(a1),f2(a1)),x53841))
% 187.18/188.05 [5385]~E(x53851,f329(a109,x53852))+E(f329(f105(a1),x53851),x53852)+~P24(f329(f329(f243(a1),f2(a1)),x53852))
% 187.18/188.05 [5395]E(x53951,f329(a109,x53952))+~E(x53952,f329(f105(a1),x53951))+~P24(f329(f329(f243(a1),f2(a1)),x53952))
% 187.18/188.05 [5396]E(f329(a109,x53961),x53962)+~E(x53961,f329(f105(a1),x53962))+~P24(f329(f329(f243(a1),f2(a1)),x53961))
% 187.18/188.05 [5435]~P87(x54352)+E(x54351,f2(x54352))+P24(f329(f329(f244(x54352),f2(x54352)),f329(f75(x54352),x54351)))
% 187.18/188.05 [5502]~P115(x55021)+E(f82(x55021,x55022),f78(x55021))+~P24(f329(f329(f244(x55021),f2(x55021)),x55022))
% 187.18/188.05 [5506]~P94(x55061)+E(f329(f105(x55061),f329(f108(a874),x55062)),f2(x55061))+P24(f329(f329(f243(a1),f2(a1)),f329(f108(a1),x55062)))
% 187.18/188.05 [5513]~P87(x55131)+E(f329(f75(x55131),x55132),x55132)+~P24(f329(f329(f243(x55131),f2(x55131)),x55132))
% 187.18/188.05 [5514]~P87(x55141)+E(f329(f75(x55141),x55142),x55142)+~P24(f329(f329(f244(x55141),f2(x55141)),x55142))
% 187.18/188.05 [5521]E(x55211,f2(a874))+~E(f137(a874,f329(f299(a874,x55212),x55211)),f118(a874))+P24(f329(f329(f243(a874),x55211),x55212))
% 187.18/188.05 [5531]~P72(x55311)+E(f329(f329(f6(x55311,x55311),f5(x55311)),f329(f171(x55311),x55312)),f329(f164(x55311),x55312))+~P24(f329(f135(x55311),x55312))
% 187.18/188.05 [5534]~P138(x55341)+E(f329(f105(x55341),f329(a109,x55342)),f329(f107(x55341),x55342))+~P24(f329(f329(f243(a1),f2(a1)),x55342))
% 187.18/188.05 [5561]E(x55611,x55612)+P24(f329(f329(f244(a874),x55611),x55612))+~P24(f329(f329(f243(a874),x55611),x55612))
% 187.18/188.05 [5562]E(x55621,x55622)+P24(f329(f329(f244(a1),x55621),x55622))+~P24(f329(f329(f243(a1),x55621),x55622))
% 187.18/188.05 [5565]E(x55651,f78(a1))+~E(f329(f329(f81(a1),x55652),x55651),f78(a1))+~P24(f329(f329(f244(a1),f2(a1)),x55652))
% 187.18/188.05 [5566]E(x55661,f78(a1))+~E(f329(f329(f81(a1),x55661),x55662),f78(a1))+~P24(f329(f329(f244(a1),f2(a1)),x55661))
% 187.18/188.05 [5604]~P43(x56042)+P24(f329(f329(f243(a1),f2(a1)),x56041))+~P24(f329(f329(f331(a1),x56041),x56042))
% 187.18/188.05 [5623]~P57(x56231,x56232)+P42(x56231,x56232)+~P24(f329(f62(f880(x56231,x56231)),x56232))
% 187.18/188.05 [5625]~P57(x56251,x56252)+P48(x56251,x56252)+~P24(f329(f62(f880(x56251,x56251)),x56252))
% 187.18/188.05 [5669]E(x56691,f193(f881(x56692,a869)))+~P24(f329(f62(x56692),x56691))+P24(f329(f329(f244(a874),f2(a874)),f329(f38(x56692),x56691)))
% 187.18/188.05 [5696]~P24(f329(x56961,x56962))+P24(f329(x56961,f2(a874)))+P24(f329(f329(f244(a874),f824(x56962,x56961)),x56962))
% 187.18/188.05 [5721]E(x57211,f2(a874))+~E(f329(f164(a874),x57212),f2(a874))+~P24(f329(f329(f331(a874),x57211),f329(f171(a874),x57212)))
% 187.18/188.05 [5787]E(x57871,x57872)+~P24(f329(f329(f243(a874),x57872),x57871))+~P24(f329(f329(f243(a874),x57871),x57872))
% 187.18/188.05 [5788]E(x57881,x57882)+~P24(f329(f329(f243(a1),x57882),x57881))+~P24(f329(f329(f243(a1),x57881),x57882))
% 187.18/188.05 [5789]E(f329(f38(x57891),x57892),f2(a874))+~P24(f329(f62(x57891),x57892))+P24(f329(f329(f331(x57891),f472(x57892,x57891)),x57892))
% 187.18/188.05 [5798]E(f50(x57981,x57982),f46(x57981,x57982))+P24(f329(f329(f243(a1),f2(a1)),x57981))+~P24(f329(f329(f244(a1),f2(a1)),x57982))
% 187.18/188.05 [5822]~P24(f329(x58221,f408(x58221)))+P24(f329(x58221,f329(a109,x58222)))+~P24(f329(f329(f243(a1),f2(a1)),x58222))
% 187.18/188.05 [5824]P24(f329(f329(f243(a874),x58241),f347(x58242)))+~P24(f329(f62(a874),x58242))+~P24(f329(f329(f331(a874),x58241),x58242))
% 187.18/188.05 [5825]P24(f329(f329(f244(a874),x58251),f342(x58252)))+~P24(f329(f62(a874),x58252))+~P24(f329(f329(f331(a874),x58251),x58252))
% 187.18/188.05 [5854]E(x58541,x58542)+~P24(f329(f329(f244(a874),x58541),f329(a117,x58542)))+P24(f329(f329(f244(a874),x58541),x58542))
% 187.18/188.05 [5888]E(x58881,f329(a117,x58882))+~P24(f329(f329(f243(a874),x58881),f329(a117,x58882)))+P24(f329(f329(f243(a874),x58881),x58882))
% 187.18/188.05 [5901]P24(f329(x59011,f409(x59011)))+~P24(f329(x59011,f329(a109,x59012)))+~P24(f329(f329(f243(a1),f2(a1)),x59012))
% 187.18/188.05 [5915]~P24(f329(x59151,x59152))+~P24(f329(f329(f243(a1),f2(a1)),x59152))+P24(f329(x59151,f329(f105(a1),f355(x59151))))
% 187.18/188.05 [5930]~P87(x59302)+~E(x59301,f2(x59302))+~P24(f329(f329(f244(x59302),f2(x59302)),f329(f75(x59302),x59301)))
% 187.18/188.05 [5957]~P57(x59571,x59572)+P42(x59571,f329(f284(x59571,x59571),x59572))+~P24(f329(f62(f880(x59571,x59571)),x59572))
% 187.18/188.05 [5965]~P94(x59651)+E(f329(f105(x59651),f329(f108(a874),x59652)),f329(f108(x59651),x59652))+~P24(f329(f329(f243(a1),f2(a1)),f329(f108(a1),x59652)))
% 187.18/188.05 [5969]E(f329(a117,x59691),x59692)+~P24(f329(f329(f244(a874),x59691),x59692))+P24(f329(f329(f244(a874),f329(a117,x59691)),x59692))
% 187.18/188.05 [5982]E(f329(f329(f39(a1),x59821),x59822),f2(a1))+~P24(f329(f329(f243(a1),x59821),f2(a1)))+~P24(f329(f329(f244(a1),x59822),x59821))
% 187.18/188.05 [5993]E(f45(a1,x59931,x59932),x59931)+~P24(f329(f329(f243(a1),x59931),f2(a1)))+~P24(f329(f329(f244(a1),x59932),x59931))
% 187.18/188.05 [6006]E(f47(x60061,x60062),f46(x60061,x60062))+~P24(f329(f329(f243(a1),f2(a1)),x60061))+~P24(f329(f329(f243(a1),f2(a1)),x60062))
% 187.18/188.05 [6014]E(f329(f329(f39(a1),x60141),x60142),f2(a1))+~P24(f329(f329(f243(a1),f2(a1)),x60141))+~P24(f329(f329(f244(a1),x60141),x60142))
% 187.18/188.05 [6026]E(f45(a874,f329(f108(a874),x60261),f329(f108(a874),x60262)),f329(f108(a874),x60261))+P24(f329(a198,f329(f108(a1),x60261)))+~P24(f329(a198,f329(f108(a1),x60262)))
% 187.18/188.05 [6028]E(f45(a1,x60281,x60282),x60281)+~P24(f329(f329(f243(a1),f2(a1)),x60281))+~P24(f329(f329(f244(a1),x60281),x60282))
% 187.18/188.05 [6029]E(x60291,x60292)+~P24(f329(f329(f244(a874),x60291),f329(a117,x60292)))+~P24(f329(f329(f243(a874),x60292),x60291))
% 187.18/188.05 [6046]~P78(x60461)+~P24(f329(f329(f243(x60461),x60462),f2(x60461)))+P24(f329(f329(f243(x60461),x60462),f329(f79(x60461),x60462)))
% 187.18/188.05 [6047]~P115(x60471)+~P24(f329(f329(f244(x60471),x60472),f2(x60471)))+P24(f329(f329(f244(x60471),x60472),f329(f79(x60471),x60472)))
% 187.18/188.05 [6057]~P31(x60571)+E(f329(f329(f65(x60571,x60571,f106(x60571)),f252(x60571)),x60572),f41(x60571,x60572))+~P24(f329(f62(x60571),x60572))
% 187.18/188.05 [6058]~P31(x60581)+E(f329(f329(f65(x60581,x60581,f115(x60581)),f193(x60581)),x60582),f40(x60581,x60582))+~P24(f329(f62(x60581),x60582))
% 187.18/188.05 [6072]~P115(x60721)+~P24(f329(f329(f243(a1),f2(a1)),x60722))+P24(f329(f329(f243(x60721),f2(x60721)),f329(f107(x60721),x60722)))
% 187.18/188.05 [6073]~P121(x60731)+~P24(f329(f329(f244(a874),f2(a874)),x60732))+P24(f329(f329(f244(x60731),f2(x60731)),f329(f105(x60731),x60732)))
% 187.18/188.05 [6074]~P115(x60741)+~P24(f329(f329(f244(a1),f2(a1)),x60742))+P24(f329(f329(f244(x60741),f2(x60741)),f329(f107(x60741),x60742)))
% 187.18/188.05 [6077]~P32(x60772)+~P32(x60771)+E(f329(f308(a874,a1,f105(a1)),f300(a874,f329(a109,x60771),f329(a109,x60772))),f300(a1,x60771,x60772))
% 187.18/188.05 [6083]P24(f329(x60831,x60832))+~P24(f329(f329(f243(a1),f2(a1)),x60832))+~P24(f329(x60831,f329(f105(a1),f361(x60831))))
% 187.18/188.05 [6108]E(f329(f329(f80(a874),f329(f108(a874),x61081)),f329(f108(a874),x61082)),f329(f108(a874),x61081))+P24(f329(f329(f244(a1),x61081),a83))+~P24(f329(f329(f244(a1),x61082),a83))
% 187.18/188.05 [6112]~P115(x61121)+P24(f329(f329(f244(x61121),f2(x61121)),f82(x61121,x61122)))+~P24(f329(f329(f244(x61121),f2(x61121)),x61122))
% 187.18/188.05 [6123]~P80(x61231)+~P24(f329(f329(f243(x61231),x61232),f2(x61231)))+P24(f329(f329(f243(x61231),f2(x61231)),f329(f79(x61231),x61232)))
% 187.18/188.05 [6124]~P80(x61241)+~P24(f329(f329(f244(x61241),x61242),f2(x61241)))+P24(f329(f329(f244(x61241),f2(x61241)),f329(f79(x61241),x61242)))
% 187.18/188.05 [6127]E(x61271,f252(f881(x61272,a869)))+~E(f329(f38(x61272),x61271),f329(f38(x61272),f252(f881(x61272,a869))))+~P24(f329(f62(x61272),f252(f881(x61272,a869))))
% 187.18/188.05 [6167]~P78(x61671)+P24(f329(f329(f243(x61671),x61672),f2(x61671)))+~P24(f329(f329(f243(x61671),x61672),f329(f79(x61671),x61672)))
% 187.18/188.05 [6168]~P115(x61681)+P24(f329(f329(f244(x61681),x61682),f2(x61681)))+~P24(f329(f329(f244(x61681),x61682),f329(f79(x61681),x61682)))
% 187.18/188.05 [6177]~P94(x61771)+P24(f329(f329(f331(x61771),f329(f108(x61771),x61772)),f191(x61771)))+~P24(f329(f329(f243(a1),a83),x61772))
% 187.18/188.05 [6208]E(x62081,f2(a874))+~P24(f329(f329(f244(a874),x62081),f329(a117,x62082)))+P24(f329(f329(f244(a874),f854(x62082,x62081)),x62082))
% 187.18/188.05 [6230]~P115(x62301)+~P24(f329(f329(f244(x62301),f2(x62301)),f82(x62301,x62302)))+P24(f329(f329(f244(x62301),f2(x62301)),x62302))
% 187.18/188.05 [6232]~E(f329(f108(a874),x62322),f329(f108(a874),x62321))+P24(f329(f329(f243(a1),f329(f108(a1),x62321)),f2(a1)))+~P24(f329(a198,f329(f108(a1),x62322)))
% 187.18/188.05 [6262]E(f329(f263(a1,a1),f50(x62621,x62622)),f329(f329(f39(a1),x62621),x62622))+~P24(f329(f329(f244(a1),x62621),f2(a1)))+~P24(f329(f329(f244(a1),f2(a1)),x62622))
% 187.18/188.05 [6295]E(f329(f267(a1,a1),f50(x62951,x62952)),f45(a1,x62951,x62952))+~P24(f329(f329(f244(a1),x62951),f2(a1)))+~P24(f329(f329(f244(a1),f2(a1)),x62952))
% 187.18/188.05 [6298]~P115(x62982)+~P24(f329(f329(f243(x62982),f2(x62982)),f329(f107(x62982),x62981)))+P24(f329(f329(f243(a1),f2(a1)),x62981))
% 187.18/188.05 [6299]~P121(x62992)+~P24(f329(f329(f244(x62992),f2(x62992)),f329(f105(x62992),x62991)))+P24(f329(f329(f244(a874),f2(a874)),x62991))
% 187.18/188.05 [6300]~P115(x63002)+~P24(f329(f329(f244(x63002),f2(x63002)),f329(f107(x63002),x63001)))+P24(f329(f329(f244(a1),f2(a1)),x63001))
% 187.18/188.05 [6303]E(f329(f263(a1,a1),f47(x63031,x63032)),f329(f329(f39(a1),x63031),x63032))+~P24(f329(f329(f243(a1),f2(a1)),x63032))+~P24(f329(f329(f244(a1),f2(a1)),x63031))
% 187.18/188.05 [6318]E(f329(f267(a1,a1),f47(x63181,x63182)),f45(a1,x63181,x63182))+~P24(f329(f329(f243(a1),f2(a1)),x63182))+~P24(f329(f329(f244(a1),f2(a1)),x63181))
% 187.18/188.05 [6333]~P80(x63331)+P24(f329(f329(f243(x63331),x63332),f2(x63331)))+~P24(f329(f329(f243(x63331),f2(x63331)),f329(f79(x63331),x63332)))
% 187.18/188.05 [6334]~P80(x63341)+P24(f329(f329(f244(x63341),x63342),f2(x63341)))+~P24(f329(f329(f244(x63341),f2(x63341)),f329(f79(x63341),x63342)))
% 187.18/188.05 [6359]P24(f329(f49(x63591,x63592),f50(x63591,x63592)))+~P24(f329(f329(f244(a1),x63591),f2(a1)))+~P24(f329(f329(f244(a1),f2(a1)),x63592))
% 187.18/188.05 [6384]P24(f329(f49(x63841,x63842),f47(x63841,x63842)))+~P24(f329(f329(f243(a1),f2(a1)),x63841))+~P24(f329(f329(f244(a1),f2(a1)),x63842))
% 187.18/188.05 [6427]~P80(x64271)+P24(f329(f329(f243(x64271),f329(f79(x64271),x64272)),f2(x64271)))+~P24(f329(f329(f243(x64271),f2(x64271)),x64272))
% 187.18/188.05 [6428]~P80(x64281)+P24(f329(f329(f244(x64281),f329(f79(x64281),x64282)),f2(x64281)))+~P24(f329(f329(f244(x64281),f2(x64281)),x64282))
% 187.18/188.05 [6445]E(f329(f329(f22(a874),f329(a109,x64451)),f329(a109,x64452)),f329(a109,f200(x64451,x64452)))+~P24(f329(f329(f243(a1),f2(a1)),x64452))+~P24(f329(f329(f243(a1),f2(a1)),x64451))
% 187.18/188.05 [6462]P24(f329(f329(f243(a1),f2(a1)),f200(x64621,x64622)))+~P24(f329(f329(f243(a1),f2(a1)),x64622))+~P24(f329(f329(f243(a1),f2(a1)),x64621))
% 187.18/188.05 [6500]~P24(f329(x65001,x65002))+P24(f329(x65001,f2(a874)))+P24(f329(x65001,f329(f329(f80(a874),f824(x65002,x65001)),f78(a874))))
% 187.18/188.05 [6582]E(f329(f108(a874),x65821),f329(f108(a874),x65822))+~P24(f329(f329(f243(a1),f329(f108(a1),x65822)),f2(a1)))+~P24(f329(a198,f329(f108(a1),x65821)))
% 187.18/188.05 [6592]~E(x65921,f2(a874))+~E(f705(x65922,x65921),f2(a874))+E(f329(f140(a874,a874,f80(a874),x65921),x65922),f2(a874))
% 187.18/188.05 [6618]~P24(f329(f62(x66181),f634(x66182,x66181)))+~P24(f329(f62(f881(x66181,a869)),x66182))+P24(f329(f62(x66181),f40(f881(x66181,a869),x66182)))
% 187.18/188.05 [6624]E(x66241,x66242)+P24(f329(f329(f244(a1),x66241),x66242))+~P24(f329(f329(f244(a1),x66241),f329(f329(f80(a1),x66242),f78(a1))))
% 187.18/188.05 [6625]P24(f329(f329(f243(a874),f329(a109,x66251)),f329(a109,x66252)))+~P24(f329(f329(f243(a1),f2(a1)),x66252))+~P24(f329(f329(f243(a1),x66251),x66252))
% 187.18/188.05 [6626]P24(f329(f329(f243(a874),f329(a109,x66261)),f329(a109,x66262)))+~P24(f329(f329(f244(a1),f2(a1)),x66261))+~P24(f329(f329(f243(a1),x66261),x66262))
% 187.18/188.05 [6628]P24(f329(f329(f244(a874),f329(a109,x66281)),f329(a109,x66282)))+~P24(f329(f329(f243(a1),f2(a1)),x66281))+~P24(f329(f329(f244(a1),x66281),x66282))
% 187.18/188.05 [6629]P24(f329(f329(f244(a874),f329(a109,x66291)),f329(a109,x66292)))+~P24(f329(f329(f244(a1),f2(a1)),x66292))+~P24(f329(f329(f244(a1),x66291),x66292))
% 187.18/188.05 [6640]E(f45(a874,f329(a109,x66401),f329(a109,x66402)),f329(a109,f45(a1,x66401,x66402)))+~P24(f329(f329(f243(a1),f2(a1)),x66402))+~P24(f329(f329(f243(a1),f2(a1)),x66401))
% 187.18/188.05 [6662]~P80(x66621)+~P24(f329(f329(f243(x66621),f329(f79(x66621),x66622)),f2(x66621)))+P24(f329(f329(f243(x66621),f2(x66621)),x66622))
% 187.18/188.05 [6663]~P80(x66631)+~P24(f329(f329(f244(x66631),f329(f79(x66631),x66632)),f2(x66631)))+P24(f329(f329(f244(x66631),f2(x66631)),x66632))
% 187.18/188.05 [6678]~P24(f329(f329(f244(a1),a83),x66782))+~P24(f329(f329(f244(a1),x66781),x66782))+P24(f329(f329(f244(a874),f329(f108(a874),x66781)),f329(f108(a874),x66782)))
% 187.18/188.05 [6769]~P24(f329(f329(f243(a1),f2(a1)),x67691))+P24(f329(f329(f244(a874),f329(a109,x67691)),x67692))+~P24(f329(f329(f244(a1),x67691),f329(f105(a1),x67692)))
% 187.18/188.05 [6786]E(x67861,f2(a1))+E(f45(a1,x67862,x67861),f2(a1))+E(f329(f329(f22(a1),f329(f79(a1),f329(f329(f39(a1),x67862),x67861))),f78(a1)),f329(f329(f39(a1),x67862),f329(f79(a1),x67861)))
% 187.18/188.05 [6802]~P24(f329(f329(f243(a1),f2(a1)),x68021))+~P24(f329(f329(f244(a874),f329(a109,x68021)),x68022))+P24(f329(f329(f244(a1),x68021),f329(f105(a1),x68022)))
% 187.18/188.05 [6837]~P24(f329(f329(f243(a874),f329(a109,x68371)),f329(a109,x68372)))+~P24(f329(f329(f243(a1),f2(a1)),x68372))+P24(f329(f329(f243(a1),x68371),x68372))
% 187.18/188.05 [6838]~P24(f329(f329(f243(a874),f329(a109,x68381)),f329(a109,x68382)))+~P24(f329(f329(f244(a1),f2(a1)),x68381))+P24(f329(f329(f243(a1),x68381),x68382))
% 187.18/188.05 [6866]P24(f329(f329(f243(a1),x68661),x68662))+~P24(f329(f329(f243(a874),f329(f108(a874),x68661)),f329(f108(a874),x68662)))+P24(f329(f329(f243(a1),x68661),a83))
% 187.18/188.05 [6893]P24(f329(f329(f243(a1),f2(a1)),f45(a1,x68931,x68932)))+~P24(f329(f329(f243(a1),f2(a1)),x68932))+~P24(f329(f329(f243(a1),f2(a1)),x68931))
% 187.18/188.05 [6993]P24(f329(f329(f244(a1),a83),x69931))+~P24(f329(f329(f244(a1),x69932),x69931))+~P24(f329(f329(f244(a874),f329(f108(a874),x69932)),f329(f108(a874),x69931)))
% 187.18/188.05 [7044]E(f329(f329(f264(a1,a1),f329(f329(f39(a1),x70441),x70442)),f45(a1,x70441,x70442)),f50(x70441,x70442))+~P24(f329(f329(f244(a1),x70441),f2(a1)))+~P24(f329(f329(f244(a1),f2(a1)),x70442))
% 187.18/188.05 [7065]E(f329(f329(f264(a1,a1),f329(f329(f39(a1),x70651),x70652)),f45(a1,x70651,x70652)),f47(x70651,x70652))+~P24(f329(f329(f243(a1),f2(a1)),x70652))+~P24(f329(f329(f243(a1),f2(a1)),x70651))
% 187.18/188.05 [7116]~P98(x71162)+E(x71161,f118(x71162))+E(f329(f140(x71162,x71162,f81(x71162),f329(f139(x71162),x71161)),f329(f170(x71162),x71161)),f329(f64(x71162,f81(x71162)),f329(f171(x71162),x71161)))
% 187.18/188.05 [7228]~E(x72281,f2(a874))+E(f329(f140(a874,a874,f80(a874),x72281),x72282),f2(a874))+P24(f329(f329(f331(a874),f705(x72282,x72281)),f329(f171(a874),x72282)))
% 187.18/188.05 [7275]~P24(f329(f329(f243(a1),x72751),f2(a1)))+P24(f329(f329(f243(a1),f329(f329(f39(a1),x72751),x72752)),f2(a1)))+~P24(f329(f329(f244(a1),f2(a1)),x72752))
% 187.18/188.05 [7276]~P24(f329(f329(f244(a1),x72762),f2(a1)))+P24(f329(f329(f243(a1),f329(f329(f39(a1),x72761),x72762)),f2(a1)))+~P24(f329(f329(f243(a1),f2(a1)),x72761))
% 187.18/188.05 [7277]~P24(f329(f329(f244(a1),x72772),f2(a1)))+P24(f329(f329(f244(a1),f329(f329(f39(a1),x72771),x72772)),f2(a1)))+~P24(f329(f329(f244(a1),f2(a1)),x72771))
% 187.18/188.05 [7279]~P24(f329(f329(f244(a1),x72791),f2(a1)))+P24(f329(f329(f244(a1),f329(f329(f39(a1),x72791),x72792)),f2(a1)))+~P24(f329(f329(f244(a1),f2(a1)),x72792))
% 187.18/188.05 [7285]P24(f329(f329(f331(f881(x72851,a869)),f634(x72852,x72851)),x72852))+~P24(f329(f62(f881(x72851,a869)),x72852))+P24(f329(f62(x72851),f40(f881(x72851,a869),x72852)))
% 187.18/188.05 [7383]P21(x73831,x73831,x73832,f252(f881(x73831,a869)))+~E(f329(f308(x73831,x73831,x73832),f252(f881(x73831,a869))),f252(f881(x73831,a869)))+~P24(f329(f62(x73831),f252(f881(x73831,a869))))
% 187.18/188.05 [7511]~P21(x75111,x75111,x75112,f252(f881(x75111,a869)))+E(f329(f308(x75111,x75111,x75112),f252(f881(x75111,a869))),f252(f881(x75111,a869)))+~P24(f329(f62(x75111),f252(f881(x75111,a869))))
% 187.18/188.05 [7647]E(f329(f329(f39(a1),x76471),x76472),f329(f108(a1),a102))+~P24(f329(f329(f243(a1),f329(f329(f80(a1),x76471),x76472)),f2(a1)))+~P24(f329(f329(f244(a1),f2(a1)),x76471))
% 187.18/188.05 [7708]~P24(f329(f329(f244(a1),x77082),f2(a1)))+~P24(f329(f329(f244(a1),f329(f329(f39(a1),x77081),x77082)),f2(a1)))+P24(f329(f329(f244(a1),f2(a1)),x77081))
% 187.18/188.05 [7713]E(f329(f329(f80(a1),x77131),x77132),f45(a1,x77131,x77132))+~P24(f329(f329(f243(a1),f329(f329(f80(a1),x77131),x77132)),f2(a1)))+~P24(f329(f329(f244(a1),f2(a1)),x77131))
% 187.18/188.05 [7716]P24(f329(f329(f244(a1),x77161),f2(a1)))+~P24(f329(f329(f244(a1),f329(f329(f39(a1),x77161),x77162)),f2(a1)))+~P24(f329(f329(f244(a1),f2(a1)),x77162))
% 187.18/188.05 [8112]~P60(x81121)+~P24(f329(f59(f878(x81121)),x81122))+P24(f329(f59(x81121),f329(f329(f8(f878(x81121),a869,x81121),x81122),f236(x81121))))
% 187.18/188.05 [8423]~P27(x84231)+P33(x84231,x84232)+~P24(f329(f329(f243(x84231),f329(f329(f163(x84231),x84232),f744(x84232,x84231))),f329(f329(f163(x84231),x84232),f745(x84232,x84231))))
% 187.18/188.05 [8424]~P27(x84241)+P33(x84241,x84242)+~P24(f329(f329(f243(x84241),f329(f329(f163(x84241),x84242),f751(x84242,x84241))),f329(f329(f163(x84241),x84242),f756(x84242,x84241))))
% 187.18/188.05 [8578]~P60(x85781)+P24(f329(f58(f878(x85781)),x85782))+~P24(f329(f58(x85781),f329(f329(f8(f878(x85781),a869,x85781),x85782),f236(x85781))))
% 187.18/188.05 [9744]~P60(x97441)+~P60(x97442)+E(f329(f329(f152(f875(x97441),f881(x97442,x97441)),f329(f329(f8(f881(x97442,f878(x97441)),f881(x97442,x97441),f875(x97441)),f73(f878(x97441),x97441,x97442,f240(x97441))),f329(f329(f8(f875(f880(x97442,x97441)),f881(x97442,f878(x97441)),f875(x97441)),f177(x97442,x97441)),f329(f181(x97442,x97441),f56(x97442))))),f55(x97441,f329(f194(f875(x97442)),f56(x97442)),f56(x97441))),f56(f881(x97442,x97441)))
% 187.18/188.05 [5662]E(x56621,f2(a1))+~E(f45(a1,x56622,x56621),f2(a1))+E(f329(f329(f39(a1),x56622),f329(f79(a1),x56621)),f329(f79(a1),f329(f329(f39(a1),x56622),x56621)))
% 187.18/188.05 [5680]~P43(x56802)+~P43(x56801)+P43(f329(f329(f115(f881(a1,a869)),x56801),x56802))
% 187.18/188.05 [5681]~P43(x56812)+~P43(x56811)+P43(f329(f329(f106(f881(a1,a869)),x56811),x56812))
% 187.18/188.05 [5699]~P61(x56991)+~P94(x56991)+E(f329(f79(x56991),f329(f329(f287(x56991),f78(x56991)),x56992)),f329(f329(f287(x56991),f329(f108(x56991),a102)),x56992))
% 187.18/188.05 [5814]E(x58141,f2(a1))+~E(f45(a1,x58142,x58141),f2(a1))+E(f329(f329(f39(a1),f329(f79(a1),x58142)),x58141),f329(f79(a1),f329(f329(f39(a1),x58142),x58141)))
% 187.18/188.05 [5951]~P27(x59511)+P33(x59511,x59512)+P24(f329(f329(f244(a874),f745(x59512,x59511)),f329(f194(f875(x59511)),x59512)))
% 187.18/188.05 [5952]~P27(x59521)+P33(x59521,x59522)+P24(f329(f329(f244(a874),f756(x59522,x59521)),f329(f194(f875(x59521)),x59522)))
% 187.18/188.05 [6104]~P94(x61041)+~E(f329(f108(x61041),x61042),f2(x61041))+P35(x61041,f329(f108(x61041),f329(f329(f80(a1),x61042),f329(f79(a1),a83))))
% 187.18/188.05 [6105]~P94(x61051)+~E(f329(f108(x61051),x61052),f2(x61051))+P35(x61051,f329(f108(x61051),f329(f329(f80(a1),a83),f329(f79(a1),x61052))))
% 187.18/188.05 [6107]E(f329(a51,f47(f329(f79(a1),x61071),f329(f79(a1),x61072))),f46(x61071,x61072))+P24(f329(f329(f243(a1),f2(a1)),x61071))+P24(f329(f329(f244(a1),f2(a1)),x61072))
% 187.18/188.05 [6238]~E(x62382,f2(a874))+~E(x62381,f2(a874))+P24(f329(f329(f243(a1),f329(f105(a1),x62381)),f329(f79(a1),f329(f105(a1),x62382))))
% 187.18/188.05 [6266]E(f329(f329(f80(a874),f329(f108(a874),x62661)),f329(f108(a874),x62662)),f329(f108(a874),f329(f329(f80(a1),x62661),x62662)))+P24(f329(f329(f244(a1),x62661),a83))+P24(f329(f329(f244(a1),x62662),a83))
% 187.18/188.05 [6393]~P78(x63931)+~P24(f329(f329(f243(x63931),f2(x63931)),x63932))+P24(f329(f329(f243(x63931),f329(f79(x63931),x63932)),x63932))
% 187.18/188.05 [6394]~P78(x63941)+~P24(f329(f329(f244(x63941),f2(x63941)),x63942))+P24(f329(f329(f244(x63941),f329(f79(x63941),x63942)),x63942))
% 187.18/188.05 [6568]E(f329(f329(f22(a874),f329(a109,x65681)),f329(a109,x65682)),f329(a109,f329(f329(f22(a1),x65681),x65682)))+~P24(f329(f329(f243(a1),f2(a1)),x65682))+~P24(f329(f329(f243(a1),x65682),x65681))
% 187.18/188.05 [6601]E(f329(a109,f45(a1,f329(f108(a1),x66011),f329(f108(a1),x66012))),f45(a874,f329(f108(a874),x66011),f329(f108(a874),x66012)))+P24(f329(a198,f329(f108(a1),x66011)))+P24(f329(a198,f329(f108(a1),x66012)))
% 187.18/188.05 [6619]~P78(x66191)+P24(f329(f329(f243(x66191),f2(x66191)),x66192))+~P24(f329(f329(f243(x66191),f329(f79(x66191),x66192)),x66192))
% 187.18/188.05 [6620]~P78(x66201)+P24(f329(f329(f244(x66201),f2(x66201)),x66202))+~P24(f329(f329(f244(x66201),f329(f79(x66201),x66202)),x66202))
% 187.18/188.05 [6632]~P78(x66321)+~P24(f329(f329(f243(x66321),f2(x66321)),x66322))+P24(f329(f329(f243(x66321),f2(x66321)),f329(f329(f80(x66321),x66322),x66322)))
% 187.18/188.05 [6634]~P78(x66341)+~P24(f329(f329(f244(x66341),f2(x66341)),x66342))+P24(f329(f329(f244(x66341),f2(x66341)),f329(f329(f80(x66341),x66342),x66342)))
% 187.18/188.05 [6646]E(f329(f329(f80(a874),f329(a109,x66461)),f329(a109,x66462)),f329(a109,f329(f329(f80(a1),x66461),x66462)))+~P24(f329(f329(f243(a1),f2(a1)),x66462))+~P24(f329(f329(f243(a1),f2(a1)),x66461))
% 187.18/188.05 [6657]E(x66571,f2(a874))+P24(f329(f329(f244(a874),f2(a874)),x66572))+~P24(f329(f329(f244(a874),f2(a874)),f329(f329(f254(a874),x66572),x66571)))
% 187.18/188.05 [6687]~P94(x66871)+E(f329(f108(x66871),x66872),f2(x66871))+~P35(x66871,f329(f108(x66871),f329(f329(f80(a1),a83),f329(f79(a1),x66872))))
% 187.18/188.05 [6688]~P94(x66881)+E(f329(f108(x66881),x66882),f2(x66881))+~P35(x66881,f329(f108(x66881),f329(f329(f80(a1),x66882),f329(f79(a1),a83))))
% 187.18/188.05 [6747]~P24(f329(f62(x67471),x67472))+~P24(f329(f62(x67471),f252(f881(x67471,a869))))+P24(f329(f62(x67471),f329(f79(f881(x67471,a869)),x67472)))
% 187.18/188.05 [6770]~P24(f329(f329(f244(a1),f2(a1)),x67702))+~P24(f329(f329(f243(a1),x67702),x67701))+P24(f329(f329(f244(a1),f2(a1)),f329(f329(f39(a1),x67701),x67702)))
% 187.18/188.05 [6771]~P24(f329(f329(f243(a1),x67711),f2(a1)))+~P24(f329(f329(f244(a1),x67712),f2(a1)))+P24(f329(f329(f243(a1),f2(a1)),f329(f329(f39(a1),x67711),x67712)))
% 187.18/188.05 [6810]~P24(f329(f329(f243(a1),f2(a1)),x68102))+~P24(f329(f329(f243(a1),f2(a1)),x68101))+P24(f329(f329(f243(a1),f2(a1)),f329(f329(f81(a1),x68101),x68102)))
% 187.18/188.05 [6811]~P24(f329(f329(f243(a1),f2(a1)),x68112))+~P24(f329(f329(f243(a1),f2(a1)),x68111))+P24(f329(f329(f243(a1),f2(a1)),f329(f329(f80(a1),x68111),x68112)))
% 187.18/188.05 [6812]~P24(f329(f329(f243(a1),f2(a1)),x68122))+~P24(f329(f329(f243(a1),f2(a1)),x68121))+P24(f329(f329(f243(a1),f2(a1)),f329(f329(f39(a1),x68121),x68122)))
% 187.18/188.05 [6813]~P24(f329(f329(f243(a1),f2(a1)),x68131))+~P24(f329(f329(f244(a1),f2(a1)),x68132))+P24(f329(f329(f243(a1),f2(a1)),f329(f329(f39(a1),x68131),x68132)))
% 187.18/188.05 [6814]~P24(f329(f329(f244(a874),f2(a874)),x68142))+~P24(f329(f329(f244(a874),f2(a874)),x68141))+P24(f329(f329(f244(a874),f2(a874)),f329(f329(f81(a874),x68141),x68142)))
% 187.18/188.05 [6879]E(x68791,f2(a1))+E(f45(a1,x68792,x68791),f2(a1))+E(f329(f329(f22(a1),f329(f79(a1),f329(f329(f39(a1),x68792),x68791))),f78(a1)),f329(f329(f39(a1),f329(f79(a1),x68792)),x68791))
% 187.18/188.05 [6934]P24(f329(f329(f244(a874),f2(a874)),x69341))+P24(f329(f329(f244(a874),f2(a874)),x69342))+~P24(f329(f329(f244(a874),f2(a874)),f329(f329(f80(a874),x69342),x69341)))
% 187.18/188.05 [6938]~P78(x69381)+P24(f329(f329(f243(x69381),f2(x69381)),x69382))+~P24(f329(f329(f243(x69381),f2(x69381)),f329(f329(f80(x69381),x69382),x69382)))
% 187.18/188.05 [6939]~P78(x69391)+P24(f329(f329(f244(x69391),f2(x69391)),x69392))+~P24(f329(f329(f244(x69391),f2(x69391)),f329(f329(f80(x69391),x69392),x69392)))
% 187.18/188.05 [6994]~P24(f329(f62(x69941),x69942))+P24(f329(f62(x69941),f252(f881(x69941,a869))))+~P24(f329(f62(x69941),f329(f79(f881(x69941,a869)),x69942)))
% 187.18/188.05 [7057]P24(f329(f329(f243(a1),x70571),f2(a1)))+~P24(f329(f329(f244(a1),x70572),f2(a1)))+~P24(f329(f329(f243(a1),f2(a1)),f329(f329(f39(a1),x70571),x70572)))
% 187.18/188.05 [7063]~P24(f329(f329(f244(a1),f2(a1)),x70631))+P24(f329(f329(f243(a1),x70631),x70632))+~P24(f329(f329(f244(a1),f2(a1)),f329(f329(f39(a1),x70632),x70631)))
% 187.18/188.05 [7064]~P24(f329(f329(f243(a1),f2(a1)),x70642))+P24(f329(f329(f243(a1),x70641),x70642))+~P24(f329(f329(f244(a1),f2(a1)),f329(f329(f39(a1),x70642),x70641)))
% 187.18/188.05 [7093]P24(f329(f329(f243(a1),f2(a1)),x70931))+~P24(f329(f329(f244(a1),f2(a1)),x70932))+~P24(f329(f329(f243(a1),f2(a1)),f329(f329(f39(a1),x70931),x70932)))
% 187.18/188.05 [7094]P24(f329(f329(f244(a1),f2(a1)),x70941))+~P24(f329(f329(f243(a1),f2(a1)),x70942))+~P24(f329(f329(f244(a1),f2(a1)),f329(f329(f39(a1),x70942),x70941)))
% 187.18/188.05 [7541]~P24(f329(f62(x75412),f252(f881(x75412,a869))))+~P24(f329(f62(x75411),f252(f881(x75411,a869))))+P24(f329(f62(f879(x75411,x75412)),f252(f881(f879(x75411,x75412),a869))))
% 187.18/188.05 [7542]~P24(f329(f62(x75422),f252(f881(x75422,a869))))+~P24(f329(f62(x75421),f252(f881(x75421,a869))))+P24(f329(f62(f880(x75421,x75422)),f252(f881(f880(x75421,x75422),a869))))
% 187.18/188.05 [7611]~P24(f329(f329(f244(a874),f329(a117,f2(a874))),x76111))+~P24(f329(f329(f244(a874),f329(a117,f2(a874))),x76112))+P24(f329(f329(f244(a874),x76111),f329(f329(f81(a874),x76112),x76111)))
% 187.18/188.05 [7612]~P24(f329(f329(f244(a874),f329(a117,f2(a874))),x76121))+~P24(f329(f329(f244(a874),f329(a117,f2(a874))),x76122))+P24(f329(f329(f244(a874),x76121),f329(f329(f81(a874),x76121),x76122)))
% 187.18/188.05 [7646]E(f329(f38(x76461),f252(f881(x76461,a869))),f329(a117,f2(a874)))+P24(f329(f62(x76462),f252(f881(x76462,a869))))+~P24(f329(f62(f881(x76462,x76461)),f252(f881(f881(x76462,x76461),a869))))
% 187.18/188.05 [7779]~P24(f329(f329(f243(a874),f329(a117,f2(a874))),x77791))+~P24(f329(f329(f243(a874),f329(a117,f2(a874))),x77792))+P24(f329(f329(f243(a874),f329(a117,f2(a874))),f329(f329(f81(a874),x77791),x77792)))
% 187.18/188.05 [7780]~P24(f329(f329(f244(a874),f329(a117,f2(a874))),x77802))+~P24(f329(f329(f244(a874),f329(a117,f2(a874))),x77801))+P24(f329(f329(f244(a874),f329(a117,f2(a874))),f329(f329(f81(a874),x77801),x77802)))
% 187.18/188.05 [8474]E(x84741,f118(x84742))+~P24(f329(f135(x84742),x84741))+E(f176(x84742,f329(f329(f8(a869,a869,x84742),a324),f329(f329(f7(x84742,x84742,a869),a326),f142(x84742,x84741))),x84741),f119(x84742,x84741))
% 187.18/188.05 [8569]~P43(x85692)+~P43(x85691)+E(f329(f308(a874,a1,f105(a1)),f329(f329(f115(f881(a874,a869)),f329(f308(a1,a874,a109),x85691)),f329(f308(a1,a874,a109),x85692))),f329(f329(f115(f881(a1,a869)),x85691),x85692))
% 187.18/188.05 [8570]~P43(x85702)+~P43(x85701)+E(f329(f308(a874,a1,f105(a1)),f329(f329(f106(f881(a874,a869)),f329(f308(a1,a874,a109),x85701)),f329(f308(a1,a874,a109),x85702))),f329(f329(f106(f881(a1,a869)),x85701),x85702))
% 187.18/188.05 [9224]~P94(x92241)+~E(f329(f108(x92241),x92242),f78(x92241))+P35(x92241,f329(f108(x92241),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f79(a1),x92242))))
% 187.18/188.05 [9458]~P94(x94581)+E(f329(f108(x94581),x94582),f78(x94581))+~P35(x94581,f329(f108(x94581),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f79(a1),x94582))))
% 187.18/188.05 [10189]E(x101891,f2(a1))+E(x101892,f2(a1))+E(f329(f269(a1,a1,a1,a1,f34(a1),f329(f81(a1),f82(a1,x101892))),f329(f329(f329(f101(f880(a1,a1)),f329(f329(a326,f82(a1,x101891)),f82(a1,x101892))),f53(x101891,x101892)),f329(f329(f268(a1,a1,f880(a1,a1)),f329(f329(f18(a1,f881(a1,f880(a1,a1)),f881(a1,f880(a1,a1))),f329(f329(f8(f881(a1,f881(f880(a1,a1),f880(a1,a1))),f881(f881(a1,f880(a1,a1)),f881(a1,f880(a1,a1))),a1),f18(a1,f880(a1,a1),f880(a1,a1))),f329(f329(f8(f880(a1,a1),f881(a1,f881(f880(a1,a1),f880(a1,a1))),a1),f329(f7(a1,f880(a1,a1),f881(f880(a1,a1),f880(a1,a1))),f329(f329(f8(a869,f881(f880(a1,a1),f881(f880(a1,a1),f880(a1,a1))),a1),f101(f880(a1,a1))),f329(f329(f7(a1,a1,a869),a326),f2(a1))))),f329(f329(f7(a1,a1,f880(a1,a1)),f329(f329(f8(a1,f881(a1,f880(a1,a1)),a1),f264(a1,a1)),f79(a1))),f2(a1))))),f329(f329(f7(a1,f881(a1,a1),f881(a1,f880(a1,a1))),f329(f329(f8(f881(a1,f880(a1,a1)),f881(f881(a1,a1),f881(a1,f880(a1,a1))),a1),f8(a1,f880(a1,a1),a1)),f329(f329(f8(a1,f881(a1,f880(a1,a1)),a1),f264(a1,a1)),f329(f329(f7(a1,a1,a1),f329(f329(f8(a1,f881(a1,a1),a1),f22(a1)),f79(a1))),f78(a1))))),f329(f22(a1),f329(f75(a1),x101892))))),f53(x101891,x101892)))),f46(x101891,x101892))
% 187.18/188.05 [10190]E(x101901,f2(a1))+E(x101902,f2(a1))+E(f329(f269(a1,a1,a1,a1,f34(a1),f329(f81(a1),f82(a1,x101902))),f329(f329(f329(f101(f880(a1,a1)),f329(f329(a328,f329(f329(a327,f329(f329(f244(a1),f2(a1)),x101902)),f329(f329(f243(a1),f2(a1)),x101901))),f329(f329(a327,f329(f329(f244(a1),x101902),f2(a1))),f329(f329(f244(a1),x101901),f2(a1))))),f53(x101901,x101902)),f329(f329(f268(a1,a1,f880(a1,a1)),f329(f329(f18(a1,f881(a1,f880(a1,a1)),f881(a1,f880(a1,a1))),f329(f329(f8(f881(a1,f881(f880(a1,a1),f880(a1,a1))),f881(f881(a1,f880(a1,a1)),f881(a1,f880(a1,a1))),a1),f18(a1,f880(a1,a1),f880(a1,a1))),f329(f329(f8(f880(a1,a1),f881(a1,f881(f880(a1,a1),f880(a1,a1))),a1),f329(f7(a1,f880(a1,a1),f881(f880(a1,a1),f880(a1,a1))),f329(f329(f8(a869,f881(f880(a1,a1),f881(f880(a1,a1),f880(a1,a1))),a1),f101(f880(a1,a1))),f329(f329(f7(a1,a1,a869),a326),f2(a1))))),f329(f329(f7(a1,a1,f880(a1,a1)),f329(f329(f8(a1,f881(a1,f880(a1,a1)),a1),f264(a1,a1)),f79(a1))),f2(a1))))),f329(f329(f7(a1,f881(a1,a1),f881(a1,f880(a1,a1))),f329(f329(f8(f881(a1,f880(a1,a1)),f881(f881(a1,a1),f881(a1,f880(a1,a1))),a1),f8(a1,f880(a1,a1),a1)),f329(f329(f8(a1,f881(a1,f880(a1,a1)),a1),f264(a1,a1)),f329(f329(f7(a1,a1,a1),f329(f329(f8(a1,f881(a1,a1),a1),f22(a1)),f79(a1))),f78(a1))))),f329(f22(a1),f329(f75(a1),x101902))))),f53(x101901,x101902)))),f46(x101901,x101902))
% 187.18/188.05 [10191]~P1(a5000)+P20(a871,x101911,f329(f329(f307(f873(a871)),f329(a93,x101912)),f193(f881(f873(a871),a869))))+~P20(a871,x101911,f329(f329(f307(f873(a871)),f329(f329(f329(f92(a871),f329(f329(f8(f881(a871,f881(a871,a869)),f881(a871,a869),a871),f329(f8(f881(a871,a869),a869,a871),f88(a871))),f329(f329(f8(f881(a871,a869),f881(a871,f881(a871,a869)),a871),f329(f7(a871,f881(a871,a869),f881(a871,a869)),f329(f329(f8(f881(a871,f881(a869,a869)),f881(f881(a871,a869),f881(a871,a869)),a871),f18(a871,a869,a869)),f329(f329(f8(f881(a871,a869),f881(a871,f881(a869,a869)),a871),f329(f8(a869,f881(a869,a869),a871),a332)),f199(x101912))))),a326))),x101912),a326)),f193(f881(f873(a871),a869))))
% 187.18/188.05 [5688]~P115(x56881)+~P94(x56881)+E(f329(f75(x56881),f329(f329(f254(x56881),f329(f108(x56881),a102)),x56882)),f78(x56881))
% 187.18/188.05 [6178]~P138(x61781)+~P24(f329(f329(f244(a1),x61782),f2(a1)))+E(f329(f79(x61781),f329(f105(x61781),f329(a109,f329(f79(a1),x61782)))),f329(f107(x61781),x61782))
% 187.18/188.05 [6377]P24(f329(f329(f243(a104),x63771),f78(a104)))+E(f329(f329(f80(a104),f78(a104)),f277(x63771,f329(f329(f39(a104),x63772),x63771))),f277(x63771,x63772))+P24(f329(f329(f244(a104),x63772),x63771))
% 187.18/188.05 [6979]~P93(x69791)+~P24(f329(f329(f331(x69791),x69792),f114(x69791)))+~E(f329(f329(f80(x69791),f329(f329(f80(x69791),f78(x69791)),x69792)),x69792),f2(x69791))
% 187.18/188.05 [7095]~P24(f329(f329(f243(a1),x70952),f2(a1)))+~P24(f329(f329(f244(a1),x70951),f2(a1)))+E(f329(f263(a1,a1),f329(a51,f47(f329(f79(a1),x70951),f329(f79(a1),x70952)))),f329(f329(f39(a1),x70951),x70952))
% 187.18/188.05 [7112]~P24(f329(f329(f243(a1),x71122),f2(a1)))+~P24(f329(f329(f244(a1),x71121),f2(a1)))+E(f329(f267(a1,a1),f329(a51,f47(f329(f79(a1),x71121),f329(f79(a1),x71122)))),f45(a1,x71121,x71122))
% 187.18/188.05 [7118]~P24(f329(f329(f244(a1),x71182),f2(a1)))+E(f329(f263(a1,a1),f329(a51,f50(f329(f79(a1),x71181),f329(f79(a1),x71182)))),f329(f329(f39(a1),x71181),x71182))+~P24(f329(f329(f244(a1),f2(a1)),x71181))
% 187.18/188.05 [7136]~P24(f329(f329(f244(a1),x71362),f2(a1)))+E(f329(f267(a1,a1),f329(a51,f50(f329(f79(a1),x71361),f329(f79(a1),x71362)))),f45(a1,x71361,x71362))+~P24(f329(f329(f244(a1),f2(a1)),x71361))
% 187.18/188.05 [7189]E(f329(f329(f39(a1),f329(f329(f254(a1),x71891),x71892)),x71891),f329(f329(f254(a1),x71891),f329(f329(f22(a874),x71892),f329(a117,f2(a874)))))+~P24(f329(f329(f244(a874),f2(a874)),x71892))+~P24(f329(f329(f244(a1),f2(a1)),x71891))
% 187.18/188.05 [7282]~P24(f329(f329(f244(a874),f2(a874)),x72821))+~P24(f329(f329(f244(a874),f2(a874)),x72822))+P24(f329(f329(f244(a874),f329(f329(f22(a874),x72821),x72822)),x72821))
% 187.18/188.05 [7283]~P24(f329(f329(f244(a874),f2(a874)),x72831))+~P24(f329(f329(f244(a874),f78(a874)),x72832))+P24(f329(f329(f244(a874),f329(f329(f39(a874),x72831),x72832)),x72831))
% 187.18/188.05 [7284]~P24(f329(f329(f244(a1),f2(a1)),x72841))+~P24(f329(f329(f244(a1),f78(a1)),x72842))+P24(f329(f329(f244(a1),f329(f329(f39(a1),x72841),x72842)),x72841))
% 187.18/188.05 [7433]E(x74331,f2(a874))+~E(x74332,f2(a1))+~P24(f329(f329(f244(a1),f2(a1)),f329(f329(f254(a1),f329(f75(a1),x74332)),x74331)))
% 187.18/188.05 [7858]~E(x78582,f118(f875(x78581)))+E(f329(f194(f875(f875(x78581))),f179(x78581,x78582)),f2(a874))+~P33(a874,f329(f167(a874),f329(f329(f152(f875(x78581),a874),f194(f875(x78581))),x78582)))
% 187.18/188.05 [8111]P24(f329(x81111,x81112))+~P24(f329(x81111,f329(a111,f547(x81111,x81112))))+~P24(f329(f329(f331(f881(f880(a874,a874),a869)),x81112),a103))
% 187.18/188.05 [8130]E(x81301,f118(f875(x81302)))+E(f329(f194(f875(x81302)),f329(f329(f163(f875(x81302)),x81301),f2(a874))),f329(f194(f875(f875(x81302))),f179(x81302,x81301)))+~P33(a874,f329(f167(a874),f329(f329(f152(f875(x81302),a874),f194(f875(x81302))),x81301)))
% 187.18/188.05 [8831]~P24(f329(f62(x88311),f329(f249(x88311),x88312)))+~P24(f329(f62(x88311),f252(f881(x88311,a869))))+P24(f329(f62(x88311),f329(f249(x88311),f329(f329(f8(a869,a869,x88311),a324),x88312))))
% 187.18/188.05 [8893]E(f329(f329(f264(a874,a874),f329(a117,f329(f329(f39(a874),f329(f329(f22(a874),x88931),x88932)),x88932))),f45(a874,f329(f329(f22(a874),x88931),x88932),x88932)),f85(f880(a874,a874),f48(x88931,x88932)))+~P24(f329(f329(f244(a874),f2(a874)),x88932))+~P24(f329(f329(f243(a874),x88932),x88931))
% 187.18/188.05 [9187]~P24(f329(f62(x91871),f329(f249(x91871),x91872)))+P24(f329(f62(x91871),f252(f881(x91871,a869))))+~P24(f329(f62(x91871),f329(f249(x91871),f329(f329(f8(a869,a869,x91871),a324),x91872))))
% 187.18/188.05 [9912]P22(x99121,x99122)+~P42(x99121,f329(f263(f881(f880(x99121,x99121),a869),f881(f880(x99121,x99121),a869)),x99122))+~P24(f329(f329(f243(f881(f880(x99121,x99121),a869)),f329(f329(f286(x99121,x99121,x99121),f329(f263(f881(f880(x99121,x99121),a869),f881(f880(x99121,x99121),a869)),x99122)),f329(f267(f881(f880(x99121,x99121),a869),f881(f880(x99121,x99121),a869)),x99122))),f329(f263(f881(f880(x99121,x99121),a869),f881(f880(x99121,x99121),a869)),x99122)))
% 187.18/188.05 [7215]~P24(f329(f329(f244(a874),f2(a874)),x72152))+P24(f329(f329(f244(a874),x72151),x72152))+E(f329(a117,f329(f329(f39(a874),f329(f329(f22(a874),x72151),x72152)),x72152)),f329(f329(f39(a874),x72151),x72152))
% 187.18/188.05 [7352]~P24(f329(f329(f244(a874),f2(a874)),x73522))+~P24(f329(f329(f243(a874),x73522),x73521))+E(f329(a117,f329(f329(f39(a874),f329(f329(f22(a874),x73521),x73522)),x73522)),f329(f329(f39(a874),x73521),x73522))
% 187.18/188.05 [8339]~P94(x83391)+~P93(x83391)+~P35(x83391,f329(f108(x83391),f329(f329(f22(a1),f329(f329(f80(a1),x83392),x83392)),a102)))
% 187.18/188.05 [9094]E(x90941,f2(a874))+E(f329(f329(f268(a874,a874,f880(a874,a874)),f329(f329(f8(a874,f881(a874,f880(a874,a874)),a874),f264(a874,a874)),a117)),f85(f880(a874,a874),f48(f329(f329(f22(a874),x90942),x90941),x90941))),f85(f880(a874,a874),f48(x90942,x90941)))+P24(f329(f329(f244(a874),x90942),x90941))
% 187.18/188.05 [9522]P24(f329(x95222,f655(x95222,x95221)))+P24(f329(x95221,f655(x95222,x95221)))+E(f329(f249(a1),f329(f329(f18(a1,a869,a869),f329(f329(f8(a869,f881(a869,a869),a1),a327),f329(f243(a1),f2(a1)))),x95221)),f329(f249(a1),f329(f329(f18(a1,a869,a869),f329(f329(f8(a869,f881(a869,a869),a1),a327),f329(f243(a1),f2(a1)))),x95222)))
% 187.18/188.05 [9526]~P24(f329(x95262,f655(x95262,x95261)))+~P24(f329(x95261,f655(x95262,x95261)))+E(f329(f249(a1),f329(f329(f18(a1,a869,a869),f329(f329(f8(a869,f881(a869,a869),a1),a327),f329(f243(a1),f2(a1)))),x95261)),f329(f249(a1),f329(f329(f18(a1,a869,a869),f329(f329(f8(a869,f881(a869,a869),a1),a327),f329(f243(a1),f2(a1)))),x95262)))
% 187.18/188.05 [7569]~P62(x75691)+~P94(x75691)+E(f329(f329(f287(x75691),x75692),f329(f108(x75691),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102))),x75692)
% 187.18/188.05 [9836]~P24(f329(f62(a872),x98362))+P20(a871,x98361,f329(f308(a872,f873(a871),f329(f329(f8(a870,f873(a871),a872),a93),a26)),x98362))+~P20(a871,f329(f329(f115(f881(f873(a871),a869)),x98361),f329(f308(a872,f873(a871),f329(f329(f8(a870,f873(a871),a872),a93),a26)),x98362)),f329(f308(a872,f873(a871),f329(f329(f8(a870,f873(a871),a872),a93),f329(f329(f8(f878(a870),a870,a872),f240(a870)),a28))),x98362))
% 187.18/188.05 [9223]~P94(x92231)+~E(f329(f108(x92231),x92232),f78(x92231))+P35(x92231,f329(f108(x92231),f329(f329(f80(a1),x92232),f329(f79(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))))
% 187.18/188.05 [9401]~P137(x94011)+~E(x94012,f78(x94011))+E(f329(f329(f254(x94011),x94012),f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))),f78(x94011))
% 187.18/188.05 [9402]~P137(x94021)+~E(x94022,f2(x94021))+E(f329(f329(f254(x94021),x94022),f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))),f2(x94021))
% 187.18/188.05 [9415]~P137(x94151)+~E(x94152,f329(f79(x94151),f78(x94151)))+E(f329(f329(f254(x94151),x94152),f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))),f78(x94151))
% 187.18/188.05 [9459]~P94(x94591)+E(f329(f108(x94591),x94592),f78(x94591))+~P35(x94591,f329(f108(x94591),f329(f329(f80(a1),x94592),f329(f79(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))))
% 187.18/188.05 [9846]~P115(x98462)+E(x98461,f2(x98462))+P24(f329(f329(f244(x98462),f2(x98462)),f329(f329(f254(x98462),x98461),f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102))))))
% 187.18/188.05 [9911]~P115(x99112)+~E(x99111,f2(x99112))+~P24(f329(f329(f244(x99112),f2(x99112)),f329(f329(f254(x99112),x99111),f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102))))))
% 187.18/188.05 [9937]P24(f329(f329(f243(a1),x99371),f2(a1)))+P24(f329(f329(f244(a1),x99372),x99371))+E(f329(f44(x99371),f47(x99372,f329(f329(f81(a1),f329(f108(a1),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))),x99371))),f47(x99372,x99371))
% 187.18/188.05 [9938]~P24(f329(f329(f244(a1),f2(a1)),x99381))+P24(f329(f329(f244(a1),x99382),x99381))+E(f329(f44(x99381),f47(x99382,f329(f329(f81(a1),f329(f108(a1),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))),x99381))),f47(x99382,x99381))
% 187.18/188.05 [9939]P24(f329(f329(f243(a1),x99391),f2(a1)))+P24(f329(f329(f243(a1),f2(a1)),f329(f329(f80(a1),x99392),x99391)))+E(f329(f44(x99391),f50(x99392,f329(f329(f81(a1),f329(f108(a1),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))),x99391))),f50(x99392,x99391))
% 187.18/188.05 [9940]~P24(f329(f329(f244(a1),f2(a1)),x99401))+P24(f329(f329(f243(a1),f2(a1)),f329(f329(f80(a1),x99402),x99401)))+E(f329(f44(x99401),f50(x99402,f329(f329(f81(a1),f329(f108(a1),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))),x99401))),f50(x99402,x99401))
% 187.18/188.05 [9941]~P141(x99411)+~P24(f329(f329(f243(a1),f2(a1)),x99412))+E(f329(f105(x99411),f329(a109,f329(f329(f81(a1),f329(f108(a1),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))),x99412))),f329(f329(f80(x99411),f329(f105(x99411),f329(a109,x99412))),f329(f105(x99411),f329(a109,x99412))))
% 187.18/188.05 [5024]~P143(x50241,x50242,x50243)+~E(x50243,f2(a1))+P24(f329(x50241,x50242))
% 187.18/188.05 [5147]~P27(x51471)+~P33(x51471,x51473)+P33(x51471,f168(x51471,x51472,x51473))
% 187.18/188.05 [5148]~P27(x51481)+~P33(x51481,x51483)+P33(x51481,f176(x51481,x51482,x51483))
% 187.18/188.05 [4728]~P77(x47282)+~E(x47283,f329(f79(x47282),x47281))+E(x47281,f329(f79(x47282),x47283))
% 187.18/188.05 [4730]~P77(x47301)+~E(f329(f79(x47301),x47303),x47302)+E(f329(f79(x47301),x47302),x47303)
% 187.18/188.05 [4804]~P27(x48043)+E(x48041,x48042)+~E(f329(f250(x48043),x48041),f329(f250(x48043),x48042))
% 187.18/188.05 [4805]~P104(x48053)+E(x48051,x48052)+~E(f329(f105(x48053),x48051),f329(f105(x48053),x48052))
% 187.18/188.05 [4806]~P27(x48063)+E(x48061,x48062)+~E(f329(f298(x48063),x48061),f329(f298(x48063),x48062))
% 187.18/188.05 [4807]~P27(x48073)+E(x48071,x48072)+~E(f329(f251(x48073),x48071),f329(f251(x48073),x48072))
% 187.18/188.05 [4808]~P27(x48083)+E(x48081,x48082)+~E(f329(f301(x48083),x48081),f329(f301(x48083),x48082))
% 187.18/188.05 [4809]~P77(x48093)+E(x48091,x48092)+~E(f329(f79(x48093),x48091),f329(f79(x48093),x48092))
% 187.18/188.05 [4810]~P97(x48103)+E(x48101,x48102)+~E(f329(f79(x48103),x48101),f329(f79(x48103),x48102))
% 187.18/188.05 [4811]~P93(x48113)+E(x48111,x48112)+~E(f329(f107(x48113),x48111),f329(f107(x48113),x48112))
% 187.18/188.05 [4910]~P60(x49101)+~P24(f329(x49102,x49103))+P24(f329(f58(x49101),x49102))
% 187.18/188.05 [4943]~P60(x49433)+P24(f329(x49431,x49432))+~P24(f329(f59(x49433),x49431))
% 187.18/188.05 [5043]~P144(x50431,x50433,x50432)+~E(x50432,f2(a1))+P24(f329(x50431,f2(a1)))
% 187.18/188.05 [5081]~E(x50811,f2(a874))+E(f777(x50811,x50812,x50813),f193(f881(x50813,a869)))+~E(f329(f38(x50813),x50812),f329(a117,x50811))
% 187.18/188.05 [5236]~E(x52362,f2(a874))+E(f329(f263(a874,a874),x52361),f2(a874))+~P24(f329(f48(x52363,x52362),x52361))
% 187.18/188.05 [5282]P24(f329(x52821,x52822))+~E(x52823,f329(f105(a1),x52822))+~P24(f329(x52821,f329(a109,x52823)))
% 187.18/188.05 [5753]~E(x57533,f2(a874))+~P24(f329(x57531,x57532))+P24(f329(x57531,f45(a874,x57532,x57533)))
% 187.18/188.05 [5884]~P24(f329(a25,x58843))+~P24(f329(a25,x58842))+P24(f329(a25,f30(x58841,x58842,x58843)))
% 187.18/188.05 [5916]~P60(x59163)+~P7(x59163,x59161,x59162)+P24(f329(x59161,f719(x59162,x59161,x59163)))
% 187.18/188.05 [6161]~E(x61613,f2(a874))+P24(f329(x61611,x61612))+~P24(f329(x61611,f45(a874,x61612,x61613)))
% 187.18/188.05 [6309]~P60(x63091)+P8(x63091,x63092,x63093)+~P24(f329(x63092,f726(x63093,x63092,x63091)))
% 187.18/188.05 [6836]E(x68361,f2(a874))+~P24(f329(x68362,f363(x68361,x68363,x68362)))+P24(f329(x68362,f45(a874,x68363,x68361)))
% 187.18/188.05 [6944]~P31(x69441)+~P24(f329(f329(f243(x69441),x69442),f629(x69443,x69442,x69441)))+P24(f329(f329(f243(x69441),x69442),f41(x69441,x69443)))
% 187.18/188.05 [6946]~P24(f329(x69461,x69462))+~P24(f329(x69461,f363(x69463,x69462,x69461)))+P24(f329(x69461,f45(a874,x69462,x69463)))
% 187.18/188.05 [7050]E(x70501,f118(x70502))+E(f329(f329(f149(x70502),f706(x70503,x70501,x70502)),f709(x70503,x70501,x70502)),x70501)+~P24(f329(f329(f331(f875(x70502)),x70501),f159(x70502,x70503)))
% 187.18/188.05 [7082]~P138(x70821)+~P24(f329(f329(f331(x70821),x70822),f114(x70821)))+P24(f329(f329(f331(x70821),f329(f329(f254(x70821),x70822),x70823)),f114(x70821)))
% 187.18/188.05 [7402]P42(x74021,x74022)+~P24(f329(f329(f331(x74021),x74023),f598(x74022,x74021)))+P24(f329(f329(f331(x74021),f653(x74022,x74021,x74023)),f598(x74022,x74021)))
% 187.18/188.05 [7674]E(x76741,f118(x76742))+~P24(f329(f329(f331(f875(x76742)),x76741),f159(x76742,x76743)))+P24(f329(f329(f331(f875(x76742)),f709(x76743,x76741,x76742)),f159(x76742,x76743)))
% 187.18/188.05 [7728]E(x77281,f2(a874))+E(f329(f329(f80(a874),f329(f329(f81(a874),x77281),f364(x77281,x77282,x77283))),f363(x77281,x77282,x77283)),x77282)+P24(f329(x77283,f45(a874,x77282,x77281)))
% 187.18/188.05 [7774]~P24(f329(x77743,x77742))+E(f329(f329(f80(a874),f329(f329(f81(a874),x77741),f364(x77741,x77742,x77743))),f363(x77741,x77742,x77743)),x77742)+P24(f329(x77743,f45(a874,x77742,x77741)))
% 187.18/188.05 [7914]P24(f329(f329(f244(a1),x79141),f862(x79142,x79143,x79141)))+P24(f329(f329(x79143,f329(f329(f39(a1),x79142),x79141)),f45(a1,x79142,x79141)))+~P24(f329(f329(f244(a1),x79141),f2(a1)))
% 187.18/188.05 [8191]P24(f329(f329(x81912,f329(f329(f39(a1),x81911),x81913)),f45(a1,x81911,x81913)))+~P24(f329(f329(f244(a1),x81913),f2(a1)))+P24(f329(f329(f243(a1),f862(x81911,x81912,x81913)),f2(a1)))
% 187.18/188.05 [8372]E(f329(f329(f80(a1),f329(f329(f81(a1),x83721),f863(x83722,x83723,x83721))),f862(x83722,x83723,x83721)),x83722)+P24(f329(f329(x83723,f329(f329(f39(a1),x83722),x83721)),f45(a1,x83722,x83721)))+~P24(f329(f329(f244(a1),x83721),f2(a1)))
% 187.18/188.05 [8615]~P24(f329(f329(x86151,f863(x86152,x86151,x86153)),f862(x86152,x86151,x86153)))+P24(f329(f329(x86151,f329(f329(f39(a1),x86152),x86153)),f45(a1,x86152,x86153)))+~P24(f329(f329(f244(a1),x86153),f2(a1)))
% 187.18/188.05 [8841]~P27(x88411)+~P33(x88411,x88413)+P33(x88411,f147(x88411,x88411,f5(x88411),x88412,x88413))
% 187.18/188.05 [9351]~P123(x93512)+E(x93511,f2(x93512))+~P24(f329(f329(f243(x93512),f329(f329(f80(x93512),f329(f329(f81(x93512),x93513),x93513)),f329(f329(f81(x93512),x93511),x93511))),f2(x93512)))
% 187.18/188.05 [9352]~P123(x93522)+E(x93521,f2(x93522))+~P24(f329(f329(f243(x93522),f329(f329(f80(x93522),f329(f329(f81(x93522),x93521),x93521)),f329(f329(f81(x93522),x93523),x93523))),f2(x93522)))
% 187.18/188.05 [10127]~P115(x101271)+~P24(f329(f329(f244(x101271),x101272),f2(x101271)))+P24(f329(f329(f244(x101271),f329(f329(f254(x101271),x101272),f329(a117,f329(f329(f81(a874),f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))),x101273)))),f2(x101271)))
% 187.18/188.05 [10135]~P115(x101352)+E(x101351,f2(x101352))+~P24(f329(f329(f243(x101352),f329(f329(f80(x101352),f329(f329(f254(x101352),x101353),f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102))))),f329(f329(f254(x101352),x101351),f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))))),f2(x101352)))
% 187.18/188.05 [10136]~P115(x101362)+E(x101361,f2(x101362))+~P24(f329(f329(f243(x101362),f329(f329(f80(x101362),f329(f329(f254(x101362),x101361),f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102))))),f329(f329(f254(x101362),x101363),f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))))),f2(x101362)))
% 187.18/188.05 [4760]~E(x47602,x47603)+~P69(x47601)+E(f329(f329(f22(x47601),x47602),x47603),f2(x47601))
% 187.18/188.05 [4761]~E(x47612,x47613)+~P77(x47611)+E(f329(f329(f22(x47611),x47612),x47613),f2(x47611))
% 187.18/188.05 [4774]~P139(x47741)+~E(x47743,f2(x47741))+E(f329(f329(f80(x47741),x47742),x47743),x47742)
% 187.18/188.05 [4790]~P136(x47901)+~E(x47903,f2(x47901))+E(f329(f329(f81(x47901),x47902),x47903),f2(x47901))
% 187.33/188.05 [4791]~P136(x47911)+~E(x47912,f2(x47911))+E(f329(f329(f81(x47911),x47912),x47913),f2(x47911))
% 187.33/188.05 [4813]~E(x48133,f118(x48131))+~E(x48132,f118(x48131))+E(f329(f329(f126(x48131),x48132),x48133),f118(x48131))
% 187.33/188.05 [4900]~P139(x49002)+E(x49001,f2(x49002))+~E(f329(f329(f80(x49002),x49003),x49001),x49003)
% 187.33/188.05 [4901]~P77(x49011)+~E(x49012,f329(f79(x49011),x49013))+E(f329(f329(f80(x49011),x49012),x49013),f2(x49011))
% 187.33/188.05 [4908]E(x49081,f118(x49082))+E(x49083,f2(a874))+~E(f329(f329(f174(x49082),x49083),x49081),f118(x49082))
% 187.33/188.05 [4914]~P69(x49143)+E(x49141,x49142)+~E(f329(f329(f22(x49143),x49141),x49142),f2(x49143))
% 187.33/188.05 [4915]~P77(x49153)+E(x49151,x49152)+~E(f329(f329(f22(x49153),x49151),x49152),f2(x49153))
% 187.33/188.05 [4924]~P137(x49242)+E(x49241,f2(x49242))+~E(f329(f329(f254(x49242),x49241),x49243),f2(x49242))
% 187.33/188.05 [4925]~P67(x49252)+E(x49251,f193(x49252))+~E(f329(f329(f115(x49252),x49253),x49251),f193(x49252))
% 187.33/188.05 [4926]~P67(x49262)+E(x49261,f193(x49262))+~E(f329(f329(f115(x49262),x49261),x49263),f193(x49262))
% 187.33/188.05 [4927]~P101(x49272)+E(x49271,f252(x49272))+~E(f329(f329(f106(x49272),x49273),x49271),f252(x49272))
% 187.33/188.05 [4928]~P101(x49282)+E(x49281,f252(x49282))+~E(f329(f329(f106(x49282),x49281),x49283),f252(x49282))
% 187.33/188.05 [4994]~P77(x49942)+E(x49941,f329(f79(x49942),x49943))+~E(f329(f329(f80(x49942),x49941),x49943),f2(x49942))
% 187.33/188.05 [4995]~P77(x49951)+E(f329(f79(x49951),x49952),x49953)+~E(f329(f329(f80(x49951),x49952),x49953),f2(x49951))
% 187.33/188.05 [4997]~E(x49972,x49973)+~P25(x49971)+P24(f329(f329(f243(x49971),x49972),x49973))
% 187.33/188.05 [4999]~E(x49992,x49993)+~P106(x49991)+P24(f329(f329(f243(x49991),x49992),x49993))
% 187.33/188.05 [5000]~E(x50002,x50003)+~P96(x50001)+P24(f329(f329(f91(x50001),x50002),x50003))
% 187.33/188.05 [5097]~P117(x50971)+~E(x50972,f329(f79(x50971),x50973))+E(f329(f329(f81(x50971),x50972),x50972),f329(f329(f81(x50971),x50973),x50973))
% 187.33/188.05 [5105]~P27(x51051)+~P33(x51051,x51053)+P33(x51051,f329(f329(f174(x51051),x51052),x51053))
% 187.33/188.05 [5106]~P27(x51061)+~P33(x51061,x51063)+P33(x51061,f329(f329(f136(x51061),x51062),x51063))
% 187.33/188.05 [5145]E(x51451,x51452)+E(x51453,f2(a874))+~E(f329(f329(f81(a874),x51453),x51451),f329(f329(f81(a874),x51453),x51452))
% 187.33/188.05 [5146]E(x51461,x51462)+E(x51463,f2(a874))+~E(f329(f329(f81(a874),x51461),x51463),f329(f329(f81(a874),x51462),x51463))
% 187.33/188.05 [5227]~E(x52272,x52273)+~P106(x52271)+E(f300(x52271,x52272,x52273),f329(f329(f307(x52271),x52272),f193(f881(x52271,a869))))
% 187.33/188.05 [5269]E(x52691,x52692)+~P96(x52693)+~P24(f329(f329(f91(x52693),x52691),x52692))
% 187.33/188.05 [5280]~E(x52801,x52802)+~P27(x52803)+~P24(f329(f329(f244(x52803),x52801),x52802))
% 187.33/188.05 [5281]~E(x52811,x52812)+~P106(x52813)+~P24(f329(f329(f244(x52813),x52811),x52812))
% 187.33/188.05 [5291]~P106(x52911)+E(f329(f299(x52911,x52912),x52913),f193(f881(x52911,a869)))+P24(f329(f329(f244(x52911),x52912),x52913))
% 187.33/188.05 [5338]~P106(x53381)+E(f300(x53381,x53382,x53383),f193(f881(x53381,a869)))+P24(f329(f329(f243(x53381),x53382),x53383))
% 187.33/188.05 [5339]~P106(x53391)+E(f302(x53391,x53392,x53393),f193(f881(x53391,a869)))+P24(f329(f329(f244(x53391),x53392),x53393))
% 187.33/188.05 [5340]~P106(x53401)+E(f193(f881(x53401,a869)),f300(x53401,x53402,x53403))+P24(f329(f329(f243(x53401),x53402),x53403))
% 187.33/188.05 [5341]~P106(x53411)+E(f193(f881(x53411,a869)),f302(x53411,x53412,x53413))+P24(f329(f329(f244(x53411),x53412),x53413))
% 187.33/188.05 [5349]~P102(x53491)+~E(f329(f329(f115(x53491),x53492),x53493),x53493)+P24(f329(f329(f243(x53491),x53492),x53493))
% 187.33/188.05 [5350]~P103(x53501)+~E(f329(f329(f106(x53501),x53502),x53503),x53502)+P24(f329(f329(f243(x53501),x53502),x53503))
% 187.33/188.05 [5351]~P27(x53511)+~E(f329(f329(f241(x53511),x53512),x53513),x53512)+P24(f329(f329(f243(x53511),x53512),x53513))
% 187.33/188.05 [5352]~P27(x53521)+~E(f329(f329(f242(x53521),x53522),x53523),x53523)+P24(f329(f329(f243(x53521),x53522),x53523))
% 187.33/188.05 [5372]~P27(x53721)+P33(x53721,x53722)+~P33(x53721,f329(f329(f149(x53721),x53723),x53722))
% 187.33/188.05 [5373]~P27(x53731)+P33(x53731,x53732)+~P33(x53731,f329(f329(f126(x53731),x53733),x53732))
% 187.33/188.05 [5374]~P27(x53741)+P33(x53741,x53742)+~P33(x53741,f329(f329(f126(x53741),x53742),x53743))
% 187.33/188.05 [5439]~P27(x54391)+P24(f329(f329(f243(x54391),x54393),x54392))+P24(f329(f329(f243(x54391),x54392),x54393))
% 187.33/188.05 [5444]~P27(x54441)+P24(f329(f329(f244(x54441),x54443),x54442))+P24(f329(f329(f243(x54441),x54442),x54443))
% 187.33/188.05 [5482]~P102(x54821)+E(f329(f329(f115(x54821),x54822),x54823),x54822)+~P24(f329(f329(f243(x54821),x54823),x54822))
% 187.33/188.05 [5484]~P102(x54841)+E(f329(f329(f115(x54841),x54842),x54843),x54843)+~P24(f329(f329(f243(x54841),x54842),x54843))
% 187.33/188.05 [5485]~P103(x54851)+E(f329(f329(f106(x54851),x54852),x54853),x54853)+~P24(f329(f329(f243(x54851),x54853),x54852))
% 187.33/188.05 [5487]~P103(x54871)+E(f329(f329(f106(x54871),x54872),x54873),x54872)+~P24(f329(f329(f243(x54871),x54872),x54873))
% 187.33/188.05 [5488]~P27(x54881)+E(f329(f329(f241(x54881),x54882),x54883),x54883)+~P24(f329(f329(f243(x54881),x54883),x54882))
% 187.33/188.05 [5490]~P27(x54901)+E(f329(f329(f241(x54901),x54902),x54903),x54902)+~P24(f329(f329(f243(x54901),x54902),x54903))
% 187.33/188.05 [5491]~P27(x54911)+E(f329(f329(f242(x54911),x54912),x54913),x54912)+~P24(f329(f329(f243(x54911),x54913),x54912))
% 187.33/188.05 [5493]~P27(x54931)+E(f329(f329(f242(x54931),x54932),x54933),x54933)+~P24(f329(f329(f243(x54931),x54932),x54933))
% 187.33/188.05 [5500]~P118(x55002)+E(x55001,f2(x55002))+E(f329(f329(f287(x55002),f329(f79(x55002),x55003)),f329(f79(x55002),x55001)),f329(f329(f287(x55002),x55003),x55001))
% 187.33/188.05 [5545]~P106(x55451)+E(f329(f299(x55451,x55452),x55453),f193(f881(x55451,a869)))+~P24(f329(f329(f243(x55451),x55453),x55452))
% 187.33/188.05 [5577]~P106(x55771)+E(f300(x55771,x55772,x55773),f193(f881(x55771,a869)))+~P24(f329(f329(f244(x55771),x55773),x55772))
% 187.33/188.05 [5578]~P106(x55781)+E(f303(x55781,x55782,x55783),f193(f881(x55781,a869)))+~P24(f329(f329(f243(x55781),x55783),x55782))
% 187.33/188.05 [5579]~P106(x55791)+E(f302(x55791,x55792,x55793),f193(f881(x55791,a869)))+~P24(f329(f329(f243(x55791),x55793),x55792))
% 187.33/188.05 [5630]~E(f329(f329(f22(a874),x56301),x56303),x56302)+E(x56301,f329(f329(f80(a874),x56302),x56303))+~P24(f329(f329(f243(a874),x56303),x56301))
% 187.33/188.05 [5631]~E(x56311,f329(f329(f80(a874),x56313),x56312))+E(f329(f329(f22(a874),x56311),x56312),x56313)+~P24(f329(f329(f243(a874),x56312),x56311))
% 187.33/188.05 [5677]~P24(f329(x56771,x56773))+P24(f329(x56771,f359(x56771,x56772)))+~P24(f329(f329(f243(a874),x56773),x56772))
% 187.33/188.05 [5678]~P24(f329(x56781,x56783))+P24(f329(x56781,f373(x56781,x56782)))+~P24(f329(f329(f244(a874),x56783),x56782))
% 187.33/188.05 [5686]~P106(x56861)+~E(f329(f299(x56861,x56862),x56863),f193(f881(x56861,a869)))+~P24(f329(f329(f244(x56861),x56862),x56863))
% 187.33/188.05 [5691]~P25(x56911)+~P24(f329(f329(f244(x56911),x56912),x56913))+P24(f329(f329(f243(x56911),x56912),x56913))
% 187.33/188.05 [5693]~P106(x56931)+~P24(f329(f329(f244(x56931),x56932),x56933))+P24(f329(f329(f243(x56931),x56932),x56933))
% 187.33/188.05 [5801]~P106(x58011)+~E(f300(x58011,x58012,x58013),f193(f881(x58011,a869)))+~P24(f329(f329(f243(x58011),x58012),x58013))
% 187.33/188.05 [5802]~P106(x58021)+~E(f302(x58021,x58022,x58023),f193(f881(x58021,a869)))+~P24(f329(f329(f244(x58021),x58022),x58023))
% 187.33/188.05 [5803]~P106(x58031)+~E(f193(f881(x58031,a869)),f300(x58031,x58032,x58033))+~P24(f329(f329(f243(x58031),x58032),x58033))
% 187.33/188.05 [5804]~P106(x58041)+~E(f193(f881(x58041,a869)),f302(x58041,x58042,x58043))+~P24(f329(f329(f244(x58041),x58042),x58043))
% 187.33/188.05 [5812]P24(f329(x58121,x58122))+~P24(f329(x58121,f370(x58121,x58123)))+~P24(f329(f329(f243(a874),x58122),x58123))
% 187.33/188.05 [5813]P24(f329(x58131,x58132))+~P24(f329(x58131,f374(x58131,x58133)))+~P24(f329(f329(f244(a874),x58132),x58133))
% 187.33/188.05 [5821]~E(x58211,f329(a117,x58213))+P24(f329(f329(f244(a874),x58211),f329(a117,x58212)))+~P24(f329(f329(f244(a874),x58213),x58212))
% 187.33/188.05 [5837]E(x58371,x58372)+~E(f329(f329(f81(a874),x58373),x58371),f329(f329(f81(a874),x58373),x58372))+~P24(f329(f329(f244(a874),f2(a874)),x58373))
% 187.33/188.05 [5895]E(f329(x58951,f825(x58951,x58952,x58953)),f78(a874))+~E(f329(f329(f6(x58953,a874),x58951),x58952),f78(a874))+~P24(f329(f62(x58953),x58952))
% 187.33/188.05 [5907]~P31(x59071)+P24(f329(f329(f243(x59071),x59072),f40(x59071,x59073)))+~P24(f329(f329(f331(x59071),x59072),x59073))
% 187.33/188.05 [5934]~P25(x59341)+~P24(f329(f329(f244(x59341),x59343),x59342))+~P24(f329(f329(f243(x59341),x59342),x59343))
% 187.33/188.05 [5938]~P25(x59381)+~P24(f329(f329(f244(x59381),x59383),x59382))+~P24(f329(f329(f244(x59381),x59382),x59383))
% 187.33/188.05 [5941]~P27(x59411)+~P24(f329(f329(f244(x59411),x59413),x59412))+~P24(f329(f329(f243(x59411),x59412),x59413))
% 187.33/188.05 [5942]~P27(x59421)+~P24(f329(f329(f244(x59421),x59423),x59422))+~P24(f329(f329(f244(x59421),x59422),x59423))
% 187.33/188.05 [5943]~P106(x59431)+~P24(f329(f329(f244(x59431),x59433),x59432))+~P24(f329(f329(f244(x59431),x59432),x59433))
% 187.33/188.05 [5972]~E(f329(x59722,f833(x59722,x59723,x59721)),f2(a874))+E(f329(f329(f6(x59721,a874),x59722),x59723),f2(a874))+~P24(f329(f62(x59721),x59723))
% 187.33/188.05 [5973]~E(f329(x59732,f826(x59732,x59733,x59731)),f78(a874))+E(f329(f329(f9(x59731,a874),x59732),x59733),f78(a874))+~P24(f329(f62(x59731),x59733))
% 187.33/188.05 [5986]~P26(x59861)+~P24(f329(f329(f243(x59861),x59863),x59862))+P24(f329(f329(f331(x59861),x59862),f329(f251(x59861),x59863)))
% 187.33/188.05 [5987]~P26(x59871)+~P24(f329(f329(f244(x59871),x59873),x59872))+P24(f329(f329(f331(x59871),x59872),f329(f301(x59871),x59873)))
% 187.33/188.05 [5988]~P26(x59881)+~P24(f329(f329(f244(x59881),x59882),x59883))+P24(f329(f329(f331(x59881),x59882),f329(f250(x59881),x59883)))
% 187.33/188.05 [5989]~P26(x59891)+~P24(f329(f329(f243(x59891),x59892),x59893))+P24(f329(f329(f331(x59891),x59892),f329(f298(x59891),x59893)))
% 187.33/188.05 [6001]E(f329(x60011,f856(x60011,x60012,x60013)),f329(a117,f2(a874)))+~E(f329(f329(f6(x60013,a874),x60011),x60012),f329(a117,f2(a874)))+~P24(f329(f62(x60013),x60012))
% 187.33/188.05 [6084]~P31(x60841)+~P24(f329(f329(f331(x60841),x60843),x60842))+P24(f329(f329(f243(x60841),f41(x60841,x60842)),x60843))
% 187.33/188.05 [6101]~P24(f329(f329(f243(a874),x61011),x61013))+P24(f329(f329(f243(a874),x61011),x61012))+~P24(f329(f329(f243(a874),x61013),x61012))
% 187.33/188.05 [6102]~P24(f329(f329(f243(a1),x61021),x61023))+P24(f329(f329(f243(a1),x61021),x61022))+~P24(f329(f329(f243(a1),x61023),x61022))
% 187.33/188.05 [6119]~P26(x61191)+~P24(f329(f329(f331(x61191),x61193),f329(f251(x61191),x61192)))+P24(f329(f329(f243(x61191),x61192),x61193))
% 187.33/188.05 [6120]~P26(x61201)+~P24(f329(f329(f331(x61201),x61202),f329(f298(x61201),x61203)))+P24(f329(f329(f243(x61201),x61202),x61203))
% 187.33/188.05 [6121]~P26(x61211)+~P24(f329(f329(f331(x61211),x61213),f329(f301(x61211),x61212)))+P24(f329(f329(f244(x61211),x61212),x61213))
% 187.33/188.05 [6122]~P26(x61221)+~P24(f329(f329(f331(x61221),x61222),f329(f250(x61221),x61223)))+P24(f329(f329(f244(x61221),x61222),x61223))
% 187.33/188.05 [6244]P24(f329(x62441,x62442))+~P24(f329(x62441,f556(x62441)))+~P24(f329(f329(f331(x62443),x62442),f252(f881(x62443,a869))))
% 187.33/188.05 [6343]~P63(x63431)+P24(f329(f329(f244(x63431),f2(x63431)),f847(x63433,x63432,x63431)))+P24(f329(f329(f243(x63431),x63432),x63433))
% 187.33/188.05 [6410]~P80(x64101)+~P24(f329(f329(f243(x64101),x64103),f329(f79(x64101),x64102)))+P24(f329(f329(f243(x64101),x64102),f329(f79(x64101),x64103)))
% 187.33/188.05 [6412]~P80(x64121)+~P24(f329(f329(f244(x64121),x64123),f329(f79(x64121),x64122)))+P24(f329(f329(f244(x64121),x64122),f329(f79(x64121),x64123)))
% 187.33/188.05 [6424]~P24(f329(f329(f244(a874),x64241),x64243))+~P24(f329(f329(f244(a874),x64243),x64242))+P24(f329(f329(f244(a874),f329(a117,x64241)),x64242))
% 187.33/188.05 [6450]~P121(x64501)+P24(f329(f329(f243(x64501),f329(f105(x64501),x64502)),f329(f105(x64501),x64503)))+~P24(f329(f329(f243(a874),x64502),x64503))
% 187.33/188.05 [6451]~P115(x64511)+P24(f329(f329(f243(x64511),f329(f107(x64511),x64512)),f329(f107(x64511),x64513)))+~P24(f329(f329(f243(a1),x64512),x64513))
% 187.33/188.05 [6453]~P115(x64531)+P24(f329(f329(f244(x64531),f329(f107(x64531),x64532)),f329(f107(x64531),x64533)))+~P24(f329(f329(f244(a1),x64532),x64533))
% 187.33/188.05 [6454]~P121(x64541)+P24(f329(f329(f244(x64541),f329(f105(x64541),x64542)),f329(f105(x64541),x64543)))+~P24(f329(f329(f244(a874),x64542),x64543))
% 187.33/188.05 [6460]~P27(x64601)+E(f329(f329(f115(f881(x64601,a869)),f329(f250(x64601),x64602)),f329(f299(x64601,x64602),x64603)),f329(f250(x64601),x64603))+~P24(f329(f329(f243(x64601),x64602),x64603))
% 187.33/188.05 [6491]~P80(x64911)+~P24(f329(f329(f243(x64911),x64913),x64912))+P24(f329(f329(f243(x64911),f329(f79(x64911),x64912)),f329(f79(x64911),x64913)))
% 187.33/188.05 [6493]~P97(x64931)+~P24(f329(f329(f243(x64931),x64933),x64932))+P24(f329(f329(f243(x64931),f329(f79(x64931),x64932)),f329(f79(x64931),x64933)))
% 187.33/188.05 [6494]~P80(x64941)+~P24(f329(f329(f244(x64941),x64943),x64942))+P24(f329(f329(f244(x64941),f329(f79(x64941),x64942)),f329(f79(x64941),x64943)))
% 187.33/188.05 [6526]~P27(x65261)+E(f329(f329(f115(f881(x65261,a869)),f329(f250(x65261),x65262)),f300(x65261,x65262,x65263)),f329(f298(x65261),x65263))+~P24(f329(f329(f243(x65261),x65262),x65263))
% 187.33/188.05 [6527]~P27(x65271)+E(f329(f329(f115(f881(x65271,a869)),f329(f298(x65271),x65272)),f303(x65271,x65272,x65273)),f329(f250(x65271),x65273))+~P24(f329(f329(f244(x65271),x65272),x65273))
% 187.33/188.05 [6528]~P27(x65281)+E(f329(f329(f115(f881(x65281,a869)),f329(f298(x65281),x65282)),f302(x65281,x65282,x65283)),f329(f298(x65281),x65283))+~P24(f329(f329(f243(x65281),x65282),x65283))
% 187.33/188.05 [6563]~P27(x65631)+E(f329(f329(f115(f881(x65631,a869)),f329(f299(x65631,x65632),x65633)),f329(f251(x65631),x65633)),f329(f251(x65631),x65632))+~P24(f329(f329(f243(x65631),x65632),x65633))
% 187.33/188.05 [6718]~P27(x67181)+E(f329(f329(f115(f881(x67181,a869)),f300(x67181,x67182,x67183)),f329(f301(x67181),x67183)),f329(f251(x67181),x67182))+~P24(f329(f329(f243(x67181),x67182),x67183))
% 187.33/188.05 [6719]~P27(x67191)+E(f329(f329(f115(f881(x67191,a869)),f303(x67191,x67192,x67193)),f329(f251(x67191),x67193)),f329(f301(x67191),x67192))+~P24(f329(f329(f244(x67191),x67192),x67193))
% 187.33/188.05 [6720]~P27(x67201)+E(f329(f329(f115(f881(x67201,a869)),f302(x67201,x67202,x67203)),f329(f301(x67201),x67203)),f329(f301(x67201),x67202))+~P24(f329(f329(f243(x67201),x67202),x67203))
% 187.33/188.05 [6738]P24(f329(x67381,x67382))+~P24(f329(f329(f243(a874),x67382),x67383))+P24(f329(f329(f331(a874),f370(x67381,x67383)),f300(a874,f2(a874),x67383)))
% 187.33/188.05 [6772]E(x67721,x67722)+~E(f329(f329(f163(x67723),x67721),f651(x67723,x67722,x67721)),f329(f329(f163(x67723),x67722),f651(x67723,x67722,x67721)))+~E(f329(f194(f875(x67723)),x67721),f329(f194(f875(x67723)),x67722))
% 187.33/188.05 [6777]~E(x67773,f329(f329(f39(a874),x67771),x67772))+~P24(f329(f329(f244(a874),f2(a874)),x67772))+P24(f329(f329(f244(a874),x67771),f329(f329(f81(a874),x67772),f329(a117,x67773))))
% 187.33/188.05 [6794]~P24(f329(x67941,x67943))+~P24(f329(f329(f243(a874),x67943),x67942))+P24(f329(f329(f331(a874),f359(x67941,x67942)),f300(a874,f2(a874),x67942)))
% 187.33/188.05 [6833]~P24(f329(x68331,x68333))+P24(f329(x68331,f371(x68331,x68332)))+~P24(f329(f329(f331(a874),x68333),f300(a874,f2(a874),x68332)))
% 187.33/188.05 [6852]~P121(x68523)+~P24(f329(f329(f243(x68523),f329(f105(x68523),x68521)),f329(f105(x68523),x68522)))+P24(f329(f329(f243(a874),x68521),x68522))
% 187.33/188.05 [6853]~P115(x68533)+~P24(f329(f329(f243(x68533),f329(f107(x68533),x68531)),f329(f107(x68533),x68532)))+P24(f329(f329(f243(a1),x68531),x68532))
% 187.33/188.05 [6855]~P121(x68553)+~P24(f329(f329(f244(x68553),f329(f105(x68553),x68551)),f329(f105(x68553),x68552)))+P24(f329(f329(f244(a874),x68551),x68552))
% 187.33/188.05 [6856]~P115(x68563)+~P24(f329(f329(f244(x68563),f329(f107(x68563),x68561)),f329(f107(x68563),x68562)))+P24(f329(f329(f244(a1),x68561),x68562))
% 187.33/188.05 [6873]~P121(x68731)+~P24(f329(f329(f244(x68731),f78(x68731)),x68732))+P24(f329(f329(f244(x68731),f78(x68731)),f329(f329(f254(x68731),x68732),f329(a117,x68733))))
% 187.33/188.05 [6875]~P80(x68751)+~P24(f329(f329(f243(x68751),f329(f79(x68751),x68753)),f329(f79(x68751),x68752)))+P24(f329(f329(f243(x68751),x68752),x68753))
% 187.33/188.05 [6876]~P97(x68761)+~P24(f329(f329(f243(x68761),f329(f79(x68761),x68763)),f329(f79(x68761),x68762)))+P24(f329(f329(f243(x68761),x68762),x68763))
% 187.33/188.05 [6877]~P80(x68771)+~P24(f329(f329(f244(x68771),f329(f79(x68771),x68773)),f329(f79(x68771),x68772)))+P24(f329(f329(f244(x68771),x68772),x68773))
% 187.33/188.05 [6903]P24(f329(x69031,x69032))+~P24(f329(x69031,f372(x69031,x69033)))+~P24(f329(f329(f331(a874),x69032),f300(a874,f2(a874),x69033)))
% 187.33/188.05 [6922]~P63(x69221)+P24(f329(f329(f244(x69221),f847(x69223,x69222,x69221)),f78(x69221)))+P24(f329(f329(f243(x69221),x69222),x69223))
% 187.33/188.05 [6941]~E(f45(a874,x69413,x69412),f45(a874,x69411,x69412))+E(f329(f329(f80(a874),x69411),f329(f329(f81(a874),x69412),f447(x69411,x69412,x69413))),x69413)+~P24(f329(f329(f243(a874),x69411),x69413))
% 187.33/188.05 [6960]E(f329(x69601,f762(x69601,x69602,x69603)),f206(x69602))+~P24(f329(f62(x69603),f183(x69603,x69602,x69601)))+P24(f329(f62(x69603),f252(f881(x69603,a869))))
% 187.33/188.05 [7001]E(f329(f329(f6(x70011,a874),x70012),x70013),f2(a874))+~P24(f329(f62(x70011),x70013))+P24(f329(f329(f331(x70011),f833(x70012,x70013,x70011)),x70013))
% 187.33/188.05 [7002]E(f329(f329(f9(x70021,a874),x70022),x70023),f78(a874))+~P24(f329(f62(x70021),x70023))+P24(f329(f329(f331(x70021),f826(x70022,x70023,x70021)),x70023))
% 187.33/188.05 [7024]~P27(x70241)+~P24(f329(f329(f243(x70241),x70242),x70243))+P24(f329(f329(f243(f881(x70241,a869)),f329(f250(x70241),x70242)),f329(f250(x70241),x70243)))
% 187.33/188.05 [7025]~P106(x70251)+~P24(f329(f329(f243(x70251),x70252),x70253))+P24(f329(f329(f243(f881(x70251,a869)),f329(f298(x70251),x70252)),f329(f298(x70251),x70253)))
% 187.33/188.05 [7026]~P106(x70261)+~P24(f329(f329(f243(x70261),x70263),x70262))+P24(f329(f329(f243(f881(x70261,a869)),f329(f251(x70261),x70262)),f329(f251(x70261),x70263)))
% 187.33/188.05 [7027]~P27(x70271)+~P24(f329(f329(f243(x70271),x70273),x70272))+P24(f329(f329(f243(f881(x70271,a869)),f329(f301(x70271),x70272)),f329(f301(x70271),x70273)))
% 187.33/188.05 [7028]~P27(x70281)+~P24(f329(f329(f244(x70281),x70282),x70283))+P24(f329(f329(f244(f881(x70281,a869)),f329(f250(x70281),x70282)),f329(f250(x70281),x70283)))
% 187.33/188.05 [7036]~P31(x70361)+P24(f329(f329(f243(x70361),x70362),f41(x70361,x70363)))+P24(f329(f329(f331(x70361),f629(x70363,x70362,x70361)),x70363))
% 187.33/188.05 [7042]~P80(x70421)+P24(f329(f329(f243(x70421),f329(f329(f22(x70421),x70422),x70423)),f2(x70421)))+~P24(f329(f329(f243(x70421),x70422),x70423))
% 187.33/188.05 [7043]~P80(x70431)+P24(f329(f329(f244(x70431),f329(f329(f22(x70431),x70432),x70433)),f2(x70431)))+~P24(f329(f329(f244(x70431),x70432),x70433))
% 187.33/188.05 [7085]P24(f329(x70851,x70852))+P24(f329(f329(f243(a874),f372(x70851,x70853)),x70853))+~P24(f329(f329(f331(a874),x70852),f300(a874,f2(a874),x70853)))
% 187.33/188.05 [7125]~E(f329(f329(f6(x71251,a874),x71252),x71253),f78(a874))+~P24(f329(f62(x71251),x71253))+P24(f329(f329(f331(x71251),f825(x71252,x71253,x71251)),x71253))
% 187.33/188.05 [7126]~P24(f329(x71261,x71263))+P24(f329(f329(f243(a874),f371(x71261,x71262)),x71262))+~P24(f329(f329(f331(a874),x71263),f300(a874,f2(a874),x71262)))
% 187.33/188.05 [7166]~P31(x71661)+P24(f329(f329(f331(x71661),f630(x71663,x71662,x71661)),x71662))+P24(f329(f329(f243(x71661),f40(x71661,x71662)),x71663))
% 187.33/188.05 [7197]~E(f329(f329(f6(x71971,a874),x71972),x71973),f329(a117,f2(a874)))+~P24(f329(f62(x71971),x71973))+P24(f329(f329(f331(x71971),f856(x71972,x71973,x71971)),x71973))
% 187.33/188.05 [7208]E(x72081,f2(a874))+P24(f329(x72082,f45(a874,x72083,x72081)))+P24(f329(f329(f244(a874),f363(x72081,x72083,x72082)),x72081))
% 187.33/188.05 [7313]~P24(f329(x73131,x73132))+P24(f329(x73131,f45(a874,x73132,x73133)))+P24(f329(f329(f244(a874),f363(x73133,x73132,x73131)),x73133))
% 187.33/188.05 [7437]E(x74371,f118(x74372))+~P24(f329(f329(f331(f875(x74372)),x74371),f159(x74372,x74373)))+P24(f329(f329(f331(x74372),f706(x74373,x74371,x74372)),x74373))
% 187.33/188.05 [7459]~P27(x74591)+E(f329(f329(f115(f881(x74591,a869)),f329(f329(f307(x74591),x74592),f193(f881(x74591,a869)))),f303(x74591,x74592,x74593)),f329(f299(x74591,x74592),x74593))+~P24(f329(f329(f244(x74591),x74592),x74593))
% 187.33/188.05 [7485]~P27(x74851)+E(f329(f329(f115(f881(x74851,a869)),f329(f329(f307(x74851),x74852),f193(f881(x74851,a869)))),f302(x74851,x74852,x74853)),f300(x74851,x74852,x74853))+~P24(f329(f329(f243(x74851),x74852),x74853))
% 187.33/188.05 [7591]~P27(x75911)+P24(f329(f329(f243(x75911),x75912),x75913))+~P24(f329(f329(f243(f881(x75911,a869)),f329(f301(x75911),x75913)),f329(f301(x75911),x75912)))
% 187.33/188.05 [7592]~P106(x75921)+P24(f329(f329(f243(x75921),x75922),x75923))+~P24(f329(f329(f243(f881(x75921,a869)),f329(f251(x75921),x75923)),f329(f251(x75921),x75922)))
% 187.33/188.05 [7593]~P27(x75931)+P24(f329(f329(f243(x75931),x75932),x75933))+~P24(f329(f329(f243(f881(x75931,a869)),f329(f250(x75931),x75932)),f329(f250(x75931),x75933)))
% 187.33/188.05 [7594]~P106(x75941)+P24(f329(f329(f243(x75941),x75942),x75943))+~P24(f329(f329(f243(f881(x75941,a869)),f329(f298(x75941),x75942)),f329(f298(x75941),x75943)))
% 187.33/188.05 [7595]~P27(x75951)+P24(f329(f329(f244(x75951),x75952),x75953))+~P24(f329(f329(f244(f881(x75951,a869)),f329(f250(x75951),x75952)),f329(f250(x75951),x75953)))
% 187.33/188.05 [7618]~P80(x76181)+~P24(f329(f329(f243(x76181),f329(f329(f22(x76181),x76182),x76183)),f2(x76181)))+P24(f329(f329(f243(x76181),x76182),x76183))
% 187.33/188.05 [7619]~P80(x76191)+~P24(f329(f329(f244(x76191),f329(f329(f22(x76191),x76192),x76193)),f2(x76191)))+P24(f329(f329(f244(x76191),x76192),x76193))
% 187.33/188.05 [7781]E(x77811,f2(a874))+~E(f329(f140(a874,a874,f80(a874),x77812),x77813),f2(a874))+~P24(f329(f329(f331(a874),x77811),f329(f171(a874),x77813)))
% 187.33/188.05 [7785]~P31(x77851)+~P24(f329(f329(f243(x77851),f630(x77853,x77852,x77851)),x77853))+P24(f329(f329(f243(x77851),f40(x77851,x77852)),x77853))
% 187.33/188.05 [7940]P24(f329(f329(f243(a1),f2(a1)),f864(x79401,x79402,x79403)))+P24(f329(f329(x79402,f329(f329(f39(a1),x79401),x79403)),f45(a1,x79401,x79403)))+~P24(f329(f329(f244(a1),f2(a1)),x79403))
% 187.33/188.05 [8034]E(x80341,x80342)+~E(f329(f194(f875(x80343)),x80341),f329(f194(f875(x80343)),x80342))+~P24(f329(f329(f268(x80343,x80343,a869),a326),f681(x80343,x80341,x80342)))
% 187.33/188.05 [8102]~P42(x81022,x81023)+E(x81021,f193(f881(x81022,a869)))+~P24(f329(f329(f243(f881(x81022,a869)),x81021),f329(f283(x81022,x81022,x81023),x81021)))
% 187.33/188.05 [8172]P44(x81721,x81722,x81723)+P24(f329(f329(f331(x81721),f548(x81723,x81722,x81721)),x81722))+P24(f329(f329(f331(f880(x81721,x81721)),f549(x81723,x81722,x81721)),x81723))
% 187.33/188.05 [8195]P24(f329(f329(x81952,f329(f329(f39(a1),x81951),x81953)),f45(a1,x81951,x81953)))+~P24(f329(f329(f244(a1),f2(a1)),x81953))+P24(f329(f329(f244(a1),f864(x81951,x81952,x81953)),x81953))
% 187.33/188.05 [8219]E(f329(f308(a874,a874,f329(f329(f7(a874,a874,a874),f22(a874)),x82191)),f329(f299(a874,x82192),x82193)),f193(f881(a874,a869)))+P24(f329(f329(f244(a874),x82191),x82193))+P24(f329(f329(f244(a874),x82192),x82193))
% 187.33/188.05 [8325]E(f329(f308(a874,a874,f329(f329(f7(a874,a874,a874),f22(a874)),x83251)),f329(f299(a874,x83252),x83253)),f329(f329(f307(a874),f2(a874)),f193(f881(a874,a869))))+P24(f329(f329(f244(a874),x83251),x83253))+~P24(f329(f329(f244(a874),x83252),x83253))
% 187.33/188.05 [8342]~P27(x83421)+E(f147(x83421,x83421,f5(x83421),x83422,x83423),x83423)+~P24(f329(f329(f331(x83421),x83422),f329(f171(x83421),x83423)))
% 187.33/188.05 [8356]P21(x83561,x83561,x83562,x83563)+~P24(f329(f62(x83561),x83563))+~P24(f329(f329(f243(f881(x83561,a869)),x83563),f329(f308(x83561,x83561,x83562),x83563)))
% 187.33/188.05 [8379]E(f329(f329(f80(a1),f329(f329(f81(a1),x83791),f865(x83792,x83793,x83791))),f864(x83792,x83793,x83791)),x83792)+P24(f329(f329(x83793,f329(f329(f39(a1),x83792),x83791)),f45(a1,x83792,x83791)))+~P24(f329(f329(f244(a1),f2(a1)),x83791))
% 187.33/188.05 [8621]~P24(f329(f329(x86211,f865(x86212,x86211,x86213)),f864(x86212,x86211,x86213)))+P24(f329(f329(x86211,f329(f329(f39(a1),x86212),x86213)),f45(a1,x86212,x86213)))+~P24(f329(f329(f244(a1),f2(a1)),x86213))
% 187.33/188.05 [9489]~P24(f329(f62(x94891),x94892))+~P24(f329(f329(f331(x94891),x94893),x94892))+P24(f329(f329(f244(a874),f329(f38(x94891),f329(f329(f22(f881(x94891,a869)),x94892),f329(f329(f307(x94891),x94893),f193(f881(x94891,a869)))))),f329(f38(x94891),x94892)))
% 187.33/188.05 [10088]P44(x100881,x100882,x100883)+~P24(f329(f329(f268(x100881,x100881,a869),f329(f329(f7(x100881,f881(x100881,a869),f881(x100881,a869)),f329(f329(f8(f881(a869,a869),f881(f881(x100881,a869),f881(x100881,a869)),x100881),f8(a869,a869,x100881)),f329(f329(f8(a869,f881(a869,a869),x100881),a327),f329(f329(f7(x100881,f881(x100881,a869),a869),f331(x100881)),x100882)))),f329(f329(f7(x100881,f881(x100881,a869),a869),f331(x100881)),x100882))),f549(x100883,x100882,x100881)))+P24(f329(f329(f331(x100881),f548(x100883,x100882,x100881)),x100882))
% 187.33/188.05 [5461]~P118(x54612)+E(x54611,f2(x54612))+E(f329(f329(f287(x54612),x54613),f329(f79(x54612),x54611)),f329(f79(x54612),f329(f329(f287(x54612),x54613),x54611)))
% 187.33/188.05 [5593]~E(x55933,f193(f881(x55931,a869)))+~E(x55932,f193(f881(x55931,a869)))+E(f329(f329(f115(f881(x55931,a869)),x55932),x55933),f193(f881(x55931,a869)))
% 187.33/188.05 [5651]~E(x56513,f2(a874))+~P24(f329(x56511,f2(a874)))+P24(f329(x56511,f329(f329(f39(a874),x56512),x56513)))
% 187.33/188.05 [5793]~P64(x57932)+E(x57931,f2(x57932))+E(f329(f329(f287(x57932),f329(f75(x57932),x57933)),f329(f75(x57932),x57931)),f329(f75(x57932),f329(f329(f287(x57932),x57933),x57931)))
% 187.33/188.05 [5961]~P24(f329(f62(x59611),x59613))+E(f329(f38(x59611),f329(f329(f307(x59611),x59612),x59613)),f329(a117,f329(f38(x59611),x59613)))+P24(f329(f329(f331(x59611),x59612),x59613))
% 187.33/188.05 [6033]~E(x60332,f2(a874))+P24(f329(x60331,f2(a874)))+~P24(f329(x60331,f329(f329(f39(a874),x60333),x60332)))
% 187.33/188.05 [6052]~P24(f329(f62(x60521),x60523))+E(f329(f38(x60521),f329(f329(f307(x60521),x60522),x60523)),f329(f38(x60521),x60523))+~P24(f329(f329(f331(x60521),x60522),x60523))
% 187.33/188.05 [6086]~P24(f329(f62(x60861),x60863))+E(f329(f38(x60861),f329(f329(f307(x60861),x60862),x60863)),f329(f329(f80(a874),f78(a874)),f329(f38(x60861),x60863)))+P24(f329(f329(f331(x60861),x60862),x60863))
% 187.33/188.05 [6206]E(f329(f329(f80(a874),x62061),f835(x62061,x62062,x62063)),x62062)+~P24(f329(x62063,f2(a874)))+P24(f329(x62063,f329(f329(f22(a874),x62062),x62061)))
% 187.33/188.05 [6207]E(f329(f329(f80(a874),x62071),f836(x62071,x62072,x62073)),x62072)+~P24(f329(x62073,f2(a874)))+P24(f329(x62073,f329(f329(f22(a874),x62072),x62071)))
% 187.33/188.05 [6254]~P31(x62541)+~P24(f329(f62(x62541),x62543))+E(f329(f329(f65(x62541,x62541,f115(x62541)),x62542),x62543),f329(f329(f115(x62541),x62542),f40(x62541,x62543)))
% 187.33/188.05 [6255]~P31(x62551)+~P24(f329(f62(x62551),x62553))+E(f329(f329(f65(x62551,x62551,f106(x62551)),x62552),x62553),f329(f329(f106(x62551),x62552),f41(x62551,x62553)))
% 187.33/188.05 [6261]~P94(x62611)+~E(f329(f108(x62611),x62612),f329(f108(x62611),x62613))+P35(x62611,f329(f108(x62611),f329(f329(f80(a1),x62612),f329(f79(a1),x62613))))
% 187.33/188.05 [6268]~P138(x62681)+E(f329(f329(f22(x62681),f329(f105(x62681),x62682)),f329(f105(x62681),x62683)),f329(f105(x62681),f329(f329(f22(a874),x62682),x62683)))+~P24(f329(f329(f243(a874),x62683),x62682))
% 187.33/188.05 [6353]E(f329(f329(f80(a874),x63531),f835(x63531,x63532,x63533)),x63532)+P24(f329(f329(f244(a874),x63532),x63531))+P24(f329(x63533,f329(f329(f22(a874),x63532),x63531)))
% 187.33/188.05 [6354]E(f329(f329(f80(a874),x63541),f836(x63541,x63542,x63543)),x63542)+P24(f329(f329(f244(a874),x63542),x63541))+P24(f329(x63543,f329(f329(f22(a874),x63542),x63541)))
% 187.33/188.05 [6369]~P115(x63691)+E(f329(f329(f81(x63691),f329(f75(x63691),x63692)),x63693),f329(f75(x63691),f329(f329(f81(x63691),x63692),x63693)))+~P24(f329(f329(f243(x63691),f2(x63691)),x63693))
% 187.33/188.05 [6370]~P63(x63701)+E(f329(f329(f287(x63701),f329(f75(x63701),x63702)),x63703),f329(f75(x63701),f329(f329(f287(x63701),x63702),x63703)))+~P24(f329(f329(f244(x63701),f2(x63701)),x63703))
% 187.33/188.05 [6378]~P66(x63781)+~P24(f329(f62(x63781),x63783))+E(f329(f329(f65(x63781,x63781,f106(x63781)),x63782),x63783),f10(x63781,f329(f329(f307(x63781),x63782),x63783)))
% 187.33/188.05 [6379]~P66(x63791)+~P24(f329(f62(x63791),x63793))+E(f329(f329(f65(x63791,x63791,f115(x63791)),x63792),x63793),f13(x63791,f329(f329(f307(x63791),x63792),x63793)))
% 187.33/188.05 [6380]~P27(x63801)+~P24(f329(f62(x63801),x63803))+E(f329(f329(f65(x63801,x63801,f241(x63801)),x63802),x63803),f14(x63801,f329(f329(f307(x63801),x63802),x63803)))
% 187.33/188.05 [6381]~P27(x63811)+~P24(f329(f62(x63811),x63813))+E(f329(f329(f65(x63811,x63811,f242(x63811)),x63812),x63813),f15(x63811,f329(f329(f307(x63811),x63812),x63813)))
% 187.33/188.05 [6426]E(x64261,f118(x64262))+~E(f179(x64262,x64263),f118(f875(x64262)))+~P24(f329(f329(f331(f875(x64262)),x64261),f329(f171(f875(x64262)),x64263)))
% 187.33/188.05 [6468]~P24(f329(f135(x64681),x64683))+P24(f329(f329(f331(x64681),x64682),f329(f171(x64681),x64683)))+P24(f329(f135(x64681),f329(f329(f149(x64681),x64682),x64683)))
% 187.33/188.05 [6479]~P98(x64791)+~P24(f329(f62(x64791),x64793))+E(f329(f64(x64791,f81(x64791)),f329(f329(f307(x64791),x64792),x64793)),f329(f329(f65(x64791,x64791,f81(x64791)),x64792),x64793))
% 187.33/188.05 [6502]~P27(x65021)+~P24(f329(f62(x65021),x65023))+E(f11(x65021,f241(x65021),f329(f329(f307(x65021),x65022),x65023)),f329(f329(f65(x65021,x65021,f241(x65021)),x65022),x65023))
% 187.33/188.05 [6503]~P27(x65031)+~P24(f329(f62(x65031),x65033))+E(f12(x65031,f242(x65031),f329(f329(f307(x65031),x65032),x65033)),f329(f329(f65(x65031,x65031,f242(x65031)),x65032),x65033))
% 187.33/188.05 [6505]P24(f329(x65051,f2(a874)))+~P24(f329(f329(f244(a874),x65052),x65053))+~P24(f329(x65051,f329(f329(f22(a874),x65052),x65053)))
% 187.33/188.05 [6524]~P87(x65241)+P24(f329(f329(f243(x65241),x65242),x65243))+~P24(f329(f329(f243(x65241),f329(f75(x65241),x65242)),x65243))
% 187.33/188.05 [6525]~P115(x65251)+P24(f329(f329(f244(x65251),x65252),x65253))+~P24(f329(f329(f244(x65251),f329(f75(x65251),x65252)),x65253))
% 187.33/188.05 [6542]E(x65421,f118(x65422))+E(f329(f139(x65422),f329(f329(f136(x65422),x65423),x65421)),f329(f329(f163(x65422),x65421),x65423))+~P24(f329(f329(f244(a874),x65423),f329(f194(f875(x65422)),x65421)))
% 187.33/188.05 [6594]~P24(f329(x65941,x65943))+P24(f329(x65941,f376(x65941,x65942)))+~P24(f329(f329(f331(a874),x65943),f329(f299(a874,f2(a874)),x65942)))
% 187.33/188.05 [6616]P24(f329(x66161,x66162))+~P24(f329(f329(f244(a874),x66162),x66163))+P24(f329(f329(f331(a874),f374(x66161,x66163)),f329(f299(a874,f2(a874)),x66163)))
% 187.33/188.05 [6631]~P121(x66311)+~P24(f329(f329(f243(x66311),f78(x66311)),x66312))+P24(f329(f329(f243(x66311),f78(x66311)),f329(f329(f254(x66311),x66312),x66313)))
% 187.33/188.05 [6633]~P121(x66331)+~P24(f329(f329(f243(x66331),f2(x66331)),x66332))+P24(f329(f329(f243(x66331),f2(x66331)),f329(f329(f254(x66331),x66332),x66333)))
% 187.33/188.05 [6635]~P121(x66351)+~P24(f329(f329(f244(x66351),f2(x66351)),x66352))+P24(f329(f329(f244(x66351),f2(x66351)),f329(f329(f254(x66351),x66352),x66353)))
% 187.33/188.05 [6659]~P24(f329(x66591,x66593))+~P24(f329(f329(f244(a874),x66593),x66592))+P24(f329(f329(f331(a874),f373(x66591,x66592)),f329(f299(a874,f2(a874)),x66592)))
% 187.33/188.05 [6666]P24(f329(f62(x66661),x66662))+~P24(f329(f62(x66661),x66663))+~P24(f329(f329(f243(f881(x66661,a869)),x66662),x66663))
% 187.33/188.05 [6674]P24(f329(x66741,x66742))+~P24(f329(x66741,f375(x66741,x66743)))+~P24(f329(f329(f331(a874),x66742),f329(f299(a874,f2(a874)),x66743)))
% 187.33/188.05 [6685]E(x66851,f2(a874))+P24(f329(x66852,f348(x66851,x66853,x66852)))+~P24(f329(x66852,f329(f329(f39(a874),x66853),x66851)))
% 187.33/188.05 [6693]~P123(x66932)+E(x66931,f2(x66932))+~E(f329(f329(f80(x66932),f329(f329(f81(x66932),x66933),x66933)),f329(f329(f81(x66932),x66931),x66931)),f2(x66932))
% 187.33/188.05 [6694]~P123(x66942)+E(x66941,f2(x66942))+~E(f329(f329(f80(x66942),f329(f329(f81(x66942),x66941),x66941)),f329(f329(f81(x66942),x66943),x66943)),f2(x66942))
% 187.33/188.05 [6739]E(x67391,f2(a874))+~P24(f329(x67392,f349(x67391,x67393,x67392)))+P24(f329(x67392,f329(f329(f39(a874),x67393),x67391)))
% 187.33/188.05 [6744]~P27(x67441)+~P33(x67441,x67443)+P33(x67441,f329(f329(f146(x67441,x67441,f5(x67441)),x67442),x67443))
% 187.33/188.05 [6787]P24(f329(x67871,f348(x67872,x67873,x67871)))+P24(f329(x67871,f2(a874)))+~P24(f329(x67871,f329(f329(f39(a874),x67873),x67872)))
% 187.33/188.05 [6793]~P94(x67931)+E(f329(f108(x67931),x67932),f329(f108(x67931),x67933))+~P35(x67931,f329(f108(x67931),f329(f329(f80(a1),x67932),f329(f79(a1),x67933))))
% 187.33/188.05 [6859]E(x68591,f2(a1))+E(x68592,f2(a1))+~P24(f329(f49(x68592,x68592),f329(f329(f264(a1,a1),x68593),x68591)))
% 187.33/188.05 [6860]E(x68601,f78(a1))+E(x68602,f2(a1))+~P24(f329(f49(x68602,x68602),f329(f329(f264(a1,a1),x68601),x68603)))
% 187.33/188.05 [6874]P24(f329(x68741,x68742))+P24(f329(f329(f244(a874),f375(x68741,x68743)),x68743))+~P24(f329(f329(f331(a874),x68742),f329(f299(a874,f2(a874)),x68743)))
% 187.33/188.05 [6898]~P24(f329(x68981,f835(x68983,x68982,x68981)))+~P24(f329(x68981,f2(a874)))+P24(f329(x68981,f329(f329(f22(a874),x68982),x68983)))
% 187.33/188.05 [6899]~P24(f329(x68991,f836(x68993,x68992,x68991)))+~P24(f329(x68991,f2(a874)))+P24(f329(x68991,f329(f329(f22(a874),x68992),x68993)))
% 187.33/188.05 [6900]~P24(f329(x69001,f349(x69003,x69002,x69001)))+~P24(f329(x69001,f2(a874)))+P24(f329(x69001,f329(f329(f39(a874),x69002),x69003)))
% 187.33/188.05 [6918]~P24(f329(x69181,x69183))+P24(f329(f329(f244(a874),f376(x69181,x69182)),x69182))+~P24(f329(f329(f331(a874),x69183),f329(f299(a874,f2(a874)),x69182)))
% 187.33/188.05 [6919]E(f329(f329(f22(a874),f329(f329(f22(a874),x69191),x69192)),f329(f329(f22(a874),x69193),x69192)),f329(f329(f22(a874),x69191),x69193))+~P24(f329(f329(f243(a874),x69192),x69191))+~P24(f329(f329(f243(a874),x69192),x69193))
% 187.33/188.05 [6954]~P80(x69541)+~P24(f329(f329(f243(x69541),f329(f79(x69541),x69543)),x69542))+P24(f329(f329(f243(x69541),f329(f79(x69541),x69542)),x69543))
% 187.33/188.05 [6956]~P87(x69561)+~P24(f329(f329(f243(x69561),f329(f75(x69561),x69562)),x69563))+P24(f329(f329(f243(x69561),f329(f79(x69561),x69562)),x69563))
% 187.33/188.05 [6958]~P80(x69581)+~P24(f329(f329(f244(x69581),f329(f79(x69581),x69583)),x69582))+P24(f329(f329(f244(x69581),f329(f79(x69581),x69582)),x69583))
% 187.33/188.05 [6959]~P115(x69591)+~P24(f329(f329(f244(x69591),f329(f75(x69591),x69592)),x69593))+P24(f329(f329(f244(x69591),f329(f79(x69591),x69592)),x69593))
% 187.33/188.05 [6995]~P24(f329(x69953,f835(x69952,x69951,x69953)))+P24(f329(f329(f244(a874),x69951),x69952))+P24(f329(x69953,f329(f329(f22(a874),x69951),x69952)))
% 187.33/188.05 [6996]~P24(f329(x69963,f836(x69962,x69961,x69963)))+P24(f329(f329(f244(a874),x69961),x69962))+P24(f329(x69963,f329(f329(f22(a874),x69961),x69962)))
% 187.33/188.05 [7046]~E(f637(x70463,x70462,x70461),f638(x70463,x70462,x70461))+E(f329(f329(f106(f881(x70461,a869)),x70462),f40(f881(x70461,a869),x70463)),f193(f881(x70461,a869)))+P24(f329(f329(f331(f881(x70461,a869)),x70462),x70463))
% 187.33/188.05 [7055]~P24(f329(f62(x70551),x70553))+P24(f329(f62(x70551),f41(f881(x70551,a869),x70552)))+~P24(f329(f329(f331(f881(x70551,a869)),x70553),x70552))
% 187.33/188.05 [7114]~P27(x71141)+E(f329(f329(f115(f881(x71141,a869)),f329(f299(x71141,x71142),x71143)),f329(f329(f307(x71141),x71143),f193(f881(x71141,a869)))),f300(x71141,x71142,x71143))+~P24(f329(f329(f243(x71141),x71142),x71143))
% 187.33/188.05 [7115]E(x71151,f2(a874))+P24(f329(f329(f244(a874),f350(x71151,x71153,x71152)),x71151))+P24(f329(x71152,f329(f329(f39(a874),x71153),x71151)))
% 187.33/188.05 [7150]E(x71501,x71502)+~P24(f329(f329(f243(f881(x71503,a869)),x71501),x71502))+P24(f329(f329(f244(f881(x71503,a869)),x71501),x71502))
% 187.33/188.05 [7163]E(x71631,x71632)+~E(f329(f194(f875(x71633)),x71631),f329(f194(f875(x71633)),x71632))+P24(f329(f329(f244(a874),f651(x71633,x71631,x71632)),f329(f194(f875(x71633)),x71632)))
% 187.33/188.05 [7209]P6(x72091,x72092,x72093)+~E(f329(f262(x72091,x72091),x72093),x72092)+~E(f329(f329(f286(x72091,x72091,x72091),f329(f284(x72091,x72091),x72093)),x72093),x72093)
% 187.33/188.05 [7281]~P24(f329(x72811,f2(a874)))+P24(f329(f329(f244(a874),f350(x72813,x72812,x72811)),x72813))+P24(f329(x72811,f329(f329(f39(a874),x72812),x72813)))
% 187.33/188.05 [7290]~P27(x72901)+E(f329(f329(f115(f881(x72901,a869)),f303(x72901,x72902,x72903)),f329(f329(f307(x72901),x72903),f193(f881(x72901,a869)))),f302(x72901,x72902,x72903))+~P24(f329(f329(f244(x72901),x72902),x72903))
% 187.33/188.05 [7391]~P24(f329(f62(x73911),x73913))+P24(f329(f329(f243(a874),f329(f38(x73911),x73912)),f329(f38(x73911),x73913)))+~P24(f329(f329(f243(f881(x73911,a869)),x73912),x73913))
% 187.33/188.05 [7392]~P24(f329(f62(x73921),x73923))+P24(f329(f329(f244(a874),f329(f38(x73921),x73922)),f329(f38(x73921),x73923)))+~P24(f329(f329(f244(f881(x73921,a869)),x73922),x73923))
% 187.33/188.05 [7430]~P24(f329(x74303,x74302))+P24(f329(f329(f199(x74301),x74302),f579(x74302,x74301,x74303)))+~P24(f329(f329(f199(f32(x74303,x74301)),x74302),x74302))
% 187.33/188.05 [7529]E(x75291,x75292)+~P24(f329(f329(f243(f881(x75293,a869)),x75292),x75291))+~P24(f329(f329(f243(f881(x75293,a869)),x75291),x75292))
% 187.33/188.05 [7532]~P27(x75321)+P33(x75321,x75322)+~P33(x75321,f329(f329(f146(x75321,x75321,f5(x75321)),x75323),x75322))
% 187.33/188.05 [7600]~P24(f329(f329(f244(a874),x76003),x76002))+~P24(f329(f329(f244(a874),x76003),x76001))+P24(f329(f329(f244(a874),f329(f329(f22(a874),x76001),x76002)),f329(f329(f22(a874),x76001),x76003)))
% 187.33/188.05 [7601]~P24(f329(f329(f243(a874),x76012),x76011))+~P24(f329(f329(f244(a874),x76011),x76013))+P24(f329(f329(f244(a874),f329(f329(f22(a874),x76011),x76012)),f329(f329(f22(a874),x76013),x76012)))
% 187.33/188.05 [7616]~P24(f329(f329(f244(a1),x76162),f2(a1)))+~P24(f329(f329(f243(a1),x76163),x76161))+P24(f329(f329(f243(a1),f329(f329(f39(a1),x76161),x76162)),f329(f329(f39(a1),x76163),x76162)))
% 187.33/188.05 [7634]~P24(f329(f329(f244(a874),f2(a874)),x76343))+~P24(f329(f329(f243(a874),x76343),x76342))+P24(f329(f329(f243(a874),f329(f329(f39(a874),x76341),x76342)),f329(f329(f39(a874),x76341),x76343)))
% 187.33/188.05 [7635]~P24(f329(f329(f244(a1),f2(a1)),x76352))+~P24(f329(f329(f243(a1),x76351),x76353))+P24(f329(f329(f243(a1),f329(f329(f39(a1),x76351),x76352)),f329(f329(f39(a1),x76353),x76352)))
% 187.33/188.05 [7639]~P24(f329(f329(f244(a874),f2(a874)),x76392))+~P24(f329(f329(f244(a874),x76391),x76393))+P24(f329(f329(f244(a874),f329(f329(f81(a874),x76391),x76392)),f329(f329(f81(a874),x76393),x76392)))
% 187.33/188.05 [7640]~P24(f329(f329(f244(a874),f2(a874)),x76401))+~P24(f329(f329(f244(a874),x76402),x76403))+P24(f329(f329(f244(a874),f329(f329(f81(a874),x76401),x76402)),f329(f329(f81(a874),x76401),x76403)))
% 187.33/188.05 [7641]~P24(f329(f329(f244(a1),f2(a1)),x76411))+~P24(f329(f329(f244(a1),x76412),x76413))+P24(f329(f329(f244(a1),f329(f329(f81(a1),x76411),x76412)),f329(f329(f81(a1),x76411),x76413)))
% 187.33/188.05 [7692]E(x76921,f2(a874))+E(f329(f329(f80(a874),f329(f329(f81(a874),x76921),f349(x76921,x76922,x76923))),f350(x76921,x76922,x76923)),x76922)+P24(f329(x76923,f329(f329(f39(a874),x76922),x76921)))
% 187.33/188.05 [7753]E(f329(f329(f80(a874),f329(f329(f81(a874),x77531),f349(x77531,x77532,x77533))),f350(x77531,x77532,x77533)),x77532)+~P24(f329(x77533,f2(a874)))+P24(f329(x77533,f329(f329(f39(a874),x77532),x77531)))
% 187.33/188.05 [7772]~P24(f329(f62(x77721),x77723))+P24(f329(f329(f331(x77721),f832(x77722,x77723,x77721)),x77723))+P24(f329(f329(f244(a874),f2(a874)),f329(f329(f9(x77721,a874),x77722),x77723)))
% 187.33/188.05 [7773]~P24(f329(f62(x77731),x77733))+P24(f329(f329(f331(x77731),f861(x77732,x77733,x77731)),x77733))+P24(f329(f329(f244(a874),f2(a874)),f329(f329(f9(x77731,a874),x77732),x77733)))
% 187.33/188.05 [8067]E(x80671,f193(f881(x80672,a869)))+E(x80671,f329(f329(f307(x80672),x80673),f193(f881(x80672,a869))))+~P24(f329(f329(f243(f881(x80672,a869)),x80671),f329(f329(f307(x80672),x80673),f193(f881(x80672,a869)))))
% 187.33/188.05 [8085]~P60(x80851)+P8(x80851,x80852,x80853)+P24(f329(f329(f331(f875(x80851)),f726(x80853,x80852,x80851)),f329(f171(f875(x80851)),f55(x80851,x80853,f56(x80851)))))
% 187.33/188.05 [8104]~P24(f329(f329(f244(a874),f2(a874)),x81043))+P24(f329(f329(f243(a874),x81041),x81042))+~P24(f329(f329(f243(a874),f329(f329(f81(a874),x81043),x81041)),f329(f329(f81(a874),x81043),x81042)))
% 187.33/188.05 [8105]~P24(f329(f329(f244(a874),f2(a874)),x81053))+P24(f329(f329(f243(a874),x81051),x81052))+~P24(f329(f329(f243(a874),f329(f329(f81(a874),x81051),x81053)),f329(f329(f81(a874),x81052),x81053)))
% 187.33/188.05 [8107]~P24(f329(f329(f244(a874),f2(a874)),x81073))+P24(f329(f329(f244(a874),x81071),x81072))+~P24(f329(f329(f244(a874),f329(f329(f254(a874),x81073),x81071)),f329(f329(f254(a874),x81073),x81072)))
% 187.33/188.05 [8133]~P60(x81331)+~P7(x81331,x81333,x81332)+P24(f329(f329(f331(f875(x81331)),f719(x81332,x81333,x81331)),f329(f171(f875(x81331)),f55(x81331,x81332,f56(x81331)))))
% 187.33/188.05 [8141]~P24(f329(x81411,x81413))+P24(f329(f329(f199(f32(x81411,x81412)),f579(x81413,x81412,x81411)),x81413))+~P24(f329(f329(f199(f32(x81411,x81412)),x81413),x81413))
% 187.33/188.05 [8150]~E(f329(f329(f106(f881(x81501,a869)),f638(x81503,x81502,x81501)),f637(x81503,x81502,x81501)),f193(f881(x81501,a869)))+E(f329(f329(f106(f881(x81501,a869)),x81502),f40(f881(x81501,a869),x81503)),f193(f881(x81501,a869)))+P24(f329(f329(f331(f881(x81501,a869)),x81502),x81503))
% 187.33/188.05 [8167]E(x81671,f118(x81672))+~E(f329(f140(f875(x81672),f875(x81672),f126(x81672),f118(x81672)),x81673),f118(x81672))+~P24(f329(f329(f331(f875(x81672)),x81671),f329(f171(f875(x81672)),x81673)))
% 187.33/188.05 [8224]E(x82241,f193(f881(f881(x82242,a869),a869)))+P24(f329(f329(f331(f881(x82242,a869)),f641(x82243,x82241,x82242)),x82241))+P24(f329(f329(f243(f881(x82242,a869)),f41(f881(x82242,a869),x82241)),x82243))
% 187.33/188.05 [8231]~P72(x82311)+~P76(x82311)+E(f329(f329(f6(a1,x82311),f329(f329(f8(a874,x82311,a1),x82312),a109)),f329(f308(a874,a1,f105(a1)),x82313)),f329(f329(f6(a874,x82311),x82312),x82313))
% 187.33/188.05 [8232]~P72(x82321)+~P76(x82321)+E(f329(f329(f9(a1,x82321),f329(f329(f8(a874,x82321,a1),x82322),a109)),f329(f308(a874,a1,f105(a1)),x82323)),f329(f329(f9(a874,x82321),x82322),x82323))
% 187.33/188.05 [8271]~P24(f329(f62(x82711),x82713))+~P24(f329(f329(f244(a874),f2(a874)),f329(x82712,f832(x82712,x82713,x82711))))+P24(f329(f329(f244(a874),f2(a874)),f329(f329(f9(x82711,a874),x82712),x82713)))
% 187.33/188.05 [8272]~P24(f329(f62(x82721),x82723))+~P24(f329(f329(f244(a874),f2(a874)),f329(x82722,f861(x82722,x82723,x82721))))+P24(f329(f329(f244(a874),f2(a874)),f329(f329(f9(x82721,a874),x82722),x82723)))
% 187.33/188.05 [8307]~P62(x83072)+E(x83071,f78(x83072))+E(f329(f329(f287(x83072),f329(f329(f22(x83072),f329(f329(f254(x83072),x83071),x83073)),f78(x83072))),f329(f329(f22(x83072),x83071),f78(x83072))),f329(f329(f6(a874,x83072),f329(f254(x83072),x83071)),f329(f299(a874,f2(a874)),x83073)))
% 187.33/188.05 [8365]E(x83651,f2(a874))+~P24(f329(x83653,f329(f329(f39(a874),x83652),x83651)))+P24(f329(f329(f244(a874),x83652),f329(f329(f81(a874),x83651),f329(a117,f348(x83651,x83652,x83653)))))
% 187.33/188.05 [8383]P24(f329(x83831,f2(a874)))+~P24(f329(x83831,f329(f329(f39(a874),x83832),x83833)))+P24(f329(f329(f244(a874),x83832),f329(f329(f81(a874),x83833),f329(a117,f348(x83833,x83832,x83831)))))
% 187.33/188.05 [8425]E(x84251,f2(a874))+~P24(f329(x84253,f329(f329(f39(a874),x84252),x84251)))+P24(f329(f329(f243(a874),f329(f329(f81(a874),x84251),f348(x84251,x84252,x84253))),x84252))
% 187.33/188.05 [8465]P24(f329(x84651,f2(a874)))+~P24(f329(x84651,f329(f329(f39(a874),x84653),x84652)))+P24(f329(f329(f243(a874),f329(f329(f81(a874),x84652),f348(x84652,x84653,x84651))),x84653))
% 187.33/188.05 [8468]~P27(x84681)+E(f329(f329(f146(x84681,x84681,f5(x84681)),x84682),x84683),f147(x84681,x84681,f5(x84681),x84682,x84683))+P24(f329(f329(f331(x84681),x84682),f329(f171(x84681),x84683)))
% 187.33/188.05 [8506]~E(f329(x85063,f563(x85062,x85063,x85061)),f329(x85063,f565(x85062,x85063,x85061)))+~P59(x85061,f329(x85063,f564(x85062,x85063,x85061)))+P59(x85061,f329(f329(f42(x85062,f881(x85061,f881(x85061,a869))),f252(f881(x85062,a869))),x85063))
% 187.33/188.05 [8514]E(x85141,f193(f881(f881(x85142,a869),a869)))+~P24(f329(f329(f243(f881(x85142,a869)),f641(x85143,x85141,x85142)),x85143))+P24(f329(f329(f243(f881(x85142,a869)),f41(f881(x85142,a869),x85141)),x85143))
% 187.33/188.05 [8572]~P64(x85721)+~P24(f329(f329(f244(x85721),x85722),x85723))+P24(f329(f329(f244(x85721),x85722),f329(f329(f287(x85721),f329(f329(f80(x85721),x85722),x85723)),f329(f329(f80(x85721),f78(x85721)),f78(x85721)))))
% 187.33/188.05 [8627]~P24(f329(f329(x86271,f479(x86271,x86273,x86272)),f484(x86271,x86273,x86272)))+P24(f329(f329(x86271,x86272),x86273))+~P24(f329(f317(f880(a1,a1),a52),f329(f329(f264(a1,a1),x86272),x86273)))
% 187.33/188.05 [8628]~P24(f329(f329(x86281,f485(x86281,x86283,x86282)),f486(x86281,x86283,x86282)))+P24(f329(f329(x86281,x86282),x86283))+~P24(f329(f317(f880(a1,a1),a57),f329(f329(f264(a1,a1),x86282),x86283)))
% 187.33/188.05 [8629]~P24(f329(f329(x86291,f487(x86291,x86293,x86292)),f488(x86291,x86293,x86292)))+P24(f329(f329(x86291,x86292),x86293))+~P24(f329(f317(f880(a1,a1),a232),f329(f329(f264(a1,a1),x86292),x86293)))
% 187.33/188.05 [8630]~P24(f329(f329(x86301,f492(x86301,x86303,x86302)),f493(x86301,x86303,x86302)))+P24(f329(f329(x86301,x86302),x86303))+~P24(f329(f317(f880(a874,a874),a227),f329(f329(f264(a874,a874),x86302),x86303)))
% 187.33/188.05 [8631]~P24(f329(f329(x86311,f691(x86311,x86313,x86312)),f693(x86311,x86313,x86312)))+P24(f329(f329(x86311,x86312),x86313))+~P24(f329(f317(f880(a1,a1),a182),f329(f329(f264(a1,a1),x86312),x86313)))
% 187.33/188.05 [8883]P24(f329(f329(x88831,x88832),x88833))+P24(f329(f317(f880(a874,a874),a227),f329(f329(f264(a874,a874),f492(x88831,x88833,x88832)),f493(x88831,x88833,x88832))))+~P24(f329(f317(f880(a874,a874),a227),f329(f329(f264(a874,a874),x88832),x88833)))
% 187.33/188.05 [8884]P24(f329(f329(x88841,x88842),x88843))+P24(f329(f317(f880(a1,a1),a52),f329(f329(f264(a1,a1),f479(x88841,x88843,x88842)),f484(x88841,x88843,x88842))))+~P24(f329(f317(f880(a1,a1),a52),f329(f329(f264(a1,a1),x88842),x88843)))
% 187.33/188.05 [8885]P24(f329(f329(x88851,x88852),x88853))+P24(f329(f317(f880(a1,a1),a57),f329(f329(f264(a1,a1),f485(x88851,x88853,x88852)),f486(x88851,x88853,x88852))))+~P24(f329(f317(f880(a1,a1),a57),f329(f329(f264(a1,a1),x88852),x88853)))
% 187.33/188.05 [8886]P24(f329(f329(x88861,x88862),x88863))+P24(f329(f317(f880(a1,a1),a232),f329(f329(f264(a1,a1),f487(x88861,x88863,x88862)),f488(x88861,x88863,x88862))))+~P24(f329(f317(f880(a1,a1),a232),f329(f329(f264(a1,a1),x88862),x88863)))
% 187.33/188.05 [8887]P24(f329(f329(x88871,x88872),x88873))+P24(f329(f317(f880(a1,a1),a182),f329(f329(f264(a1,a1),f691(x88871,x88873,x88872)),f693(x88871,x88873,x88872))))+~P24(f329(f317(f880(a1,a1),a182),f329(f329(f264(a1,a1),x88872),x88873)))
% 187.33/188.05 [9234]~P24(f329(f62(x92341),x92343))+P24(f329(f329(f331(f880(f881(x92341,a869),f881(x92341,a869))),f329(f329(f264(f881(x92341,a869),f881(x92341,a869)),x92342),x92343)),f304(x92341)))+~P24(f329(f329(f244(f881(x92341,a869)),x92342),x92343))
% 187.33/188.05 [9243]~P23(a871,f193(f881(f873(a871),a869)),f329(f329(f307(f873(a871)),f329(f329(f329(f92(a871),x92431),x92432),x92433)),f193(f881(f873(a871),a869))))+P20(a871,f193(f881(f873(a871),a869)),f329(f329(f307(f873(a871)),f329(f329(f329(f92(a871),x92431),x92432),x92433)),f193(f881(f873(a871),a869))))+~P20(a871,f193(f881(f873(a871),a869)),f329(f329(f307(f873(a871)),f329(a93,x92432)),f193(f881(f873(a871),a869))))
% 187.33/188.05 [9307]~P59(x93071,f329(x93073,f564(x93072,x93073,x93071)))+P59(x93071,f329(f329(f42(x93072,f881(x93071,f881(x93071,a869))),f252(f881(x93072,a869))),x93073))+~E(f329(f329(f106(f881(x93071,a869)),f258(x93071,x93071,f329(x93073,f563(x93072,x93073,x93071)))),f259(x93071,x93071,f329(x93073,f565(x93072,x93073,x93071)))),f193(f881(x93071,a869)))
% 187.33/188.05 [9504]P44(x95041,x95042,x95043)+P24(f329(f329(f331(f880(x95041,x95041)),f549(x95043,x95042,x95041)),x95043))+~P24(f329(f329(f331(f880(x95041,x95041)),f329(f329(f264(x95041,x95041),f548(x95043,x95042,x95041)),f548(x95043,x95042,x95041))),x95043))
% 187.33/188.05 [10089]P44(x100891,x100892,x100893)+~P24(f329(f329(f268(x100891,x100891,a869),f329(f329(f7(x100891,f881(x100891,a869),f881(x100891,a869)),f329(f329(f8(f881(a869,a869),f881(f881(x100891,a869),f881(x100891,a869)),x100891),f8(a869,a869,x100891)),f329(f329(f8(a869,f881(a869,a869),x100891),a327),f329(f329(f7(x100891,f881(x100891,a869),a869),f331(x100891)),x100892)))),f329(f329(f7(x100891,f881(x100891,a869),a869),f331(x100891)),x100892))),f549(x100893,x100892,x100891)))+~P24(f329(f329(f331(f880(x100891,x100891)),f329(f329(f264(x100891,x100891),f548(x100893,x100892,x100891)),f548(x100893,x100892,x100891))),x100893))
% 187.33/188.05 [5632]~P29(x56322)+E(x56321,f2(x56322))+E(f329(f329(f39(x56322),f329(f329(f81(x56322),x56323),x56321)),x56321),x56323)
% 187.33/188.05 [5633]~P29(x56332)+E(x56331,f2(x56332))+E(f329(f329(f39(x56332),f329(f329(f81(x56332),x56331),x56333)),x56331),x56333)
% 187.33/188.05 [6425]~P72(x64251)+~E(f329(x64252,f2(a874)),f2(x64251))+E(f329(f329(f6(a874,x64251),x64252),f329(f299(a874,f329(a117,f2(a874))),x64253)),f329(f329(f6(a874,x64251),x64252),f329(f299(a874,f2(a874)),x64253)))
% 187.33/188.05 [6555]~P29(x65552)+E(x65551,f2(x65552))+E(f329(f329(f39(x65552),f329(f329(f80(x65552),x65553),x65551)),x65551),f329(f329(f80(x65552),f329(f329(f39(x65552),x65553),x65551)),f78(x65552)))
% 187.33/188.05 [6556]~P29(x65562)+E(x65561,f2(x65562))+E(f329(f329(f39(x65562),f329(f329(f80(x65562),x65561),x65563)),x65561),f329(f329(f80(x65562),f329(f329(f39(x65562),x65563),x65561)),f78(x65562)))
% 187.33/188.05 [6775]~P24(f329(x67753,f2(a1)))+P24(f329(f329(f243(a874),x67751),x67752))+P24(f329(x67753,f329(f105(a1),f329(f329(f22(a874),x67752),x67751))))
% 187.33/188.05 [6880]P24(f329(f329(f244(a874),x68802),x68801))+P24(f329(f329(f243(a874),x68801),x68802))+P24(f329(x68803,f329(f105(a1),f329(f329(f22(a874),x68802),x68801))))
% 187.33/188.05 [6952]E(f329(f329(f80(a874),f329(f108(a874),x69521)),f329(f329(f80(a874),f329(f108(a874),x69522)),x69523)),f329(f329(f80(a874),f329(f108(a874),x69521)),x69523))+P24(f329(a198,f329(f108(a1),x69521)))+~P24(f329(a198,f329(f108(a1),x69522)))
% 187.33/188.05 [7033]~E(x70332,f329(f329(f39(a874),x70333),x70331))+~P24(f329(f329(f244(a874),f2(a874)),x70331))+P24(f329(f329(f243(a874),f329(f329(f81(a874),x70331),x70332)),x70333))
% 187.33/188.05 [7147]~P24(f329(f62(x71471),x71473))+~P24(f329(f62(x71471),x71472))+P24(f329(f62(x71471),f329(f329(f115(f881(x71471,a869)),x71472),x71473)))
% 187.33/188.05 [7443]~P27(x74431)+~P24(f329(f62(x74431),x74432))+E(f137(x74431,f329(f329(f22(f881(x74431,a869)),x74432),f329(f329(f307(x74431),x74433),f193(f881(x74431,a869))))),f168(x74431,x74433,f137(x74431,x74432)))
% 187.33/188.05 [7509]P24(f329(x75091,f2(a1)))+~P24(f329(f329(f244(a874),x75092),x75093))+~P24(f329(x75091,f329(f105(a1),f329(f329(f22(a874),x75092),x75093))))
% 187.33/188.05 [7526]~P24(f329(f62(x75261),x75262))+E(f329(f38(x75261),f329(f329(f22(f881(x75261,a869)),x75262),f329(f329(f307(x75261),x75263),f193(f881(x75261,a869))))),f329(f38(x75261),x75262))+P24(f329(f329(f331(x75261),x75263),x75262))
% 187.33/188.05 [7656]~P121(x76561)+~P24(f329(f329(f244(x76561),f78(x76561)),x76562))+P24(f329(f329(f244(x76561),f78(x76561)),f329(f329(f81(x76561),x76562),f329(f329(f254(x76561),x76562),x76563))))
% 187.33/188.05 [7703]~P24(f329(f62(x77031),x77033))+E(f329(f329(f22(a874),f329(f38(x77031),x77032)),f329(f38(x77031),x77033)),f329(f38(x77031),f329(f329(f22(f881(x77031,a869)),x77032),x77033)))+~P24(f329(f329(f243(f881(x77031,a869)),x77033),x77032))
% 187.33/188.05 [7762]~P24(f329(f329(f243(a874),x77622),x77623))+~P24(f329(f329(f243(a874),x77621),f329(f329(f22(a874),x77623),x77622)))+P24(f329(f329(f243(a874),f329(f329(f80(a874),x77621),x77622)),x77623))
% 187.33/188.05 [7816]P24(f329(f62(x78161),x78162))+~P24(f329(f62(x78161),x78163))+~P24(f329(f62(x78161),f329(f329(f22(f881(x78161,a869)),x78162),x78163)))
% 187.33/188.05 [7822]~P24(f329(f62(x78221),x78222))+E(f329(f38(x78221),f329(f329(f22(f881(x78221,a869)),x78222),f329(f329(f307(x78221),x78223),f193(f881(x78221,a869))))),f329(f329(f22(a874),f329(f38(x78221),x78222)),f78(a874)))+~P24(f329(f329(f331(x78221),x78223),x78222))
% 187.33/188.05 [7898]P59(x78981,x78982)+~P59(x78981,x78983)+~P24(f329(f329(f243(f881(x78981,f881(x78981,a869))),x78982),x78983))
% 187.33/188.05 [7939]~P24(f329(f329(f243(a874),x79393),x79392))+P24(f329(f329(f243(a874),x79391),f329(f329(f22(a874),x79392),x79393)))+~P24(f329(f329(f243(a874),f329(f329(f80(a874),x79391),x79393)),x79392))
% 187.33/188.05 [7957]P42(x79571,x79572)+~P42(x79571,x79573)+~P24(f329(f329(f243(f881(f880(x79571,x79571),a869)),x79572),x79573))
% 187.33/188.05 [7958]P57(x79581,x79582)+~P57(x79581,x79583)+~P24(f329(f329(f243(f881(f880(x79581,x79581),a869)),x79582),x79583))
% 187.33/188.05 [8202]~P121(x82021)+~P24(f329(f329(f244(x82021),f78(x82021)),x82022))+P24(f329(f329(f244(x82021),f329(f329(f254(x82021),x82022),x82023)),f329(f329(f81(x82021),x82022),f329(f329(f254(x82021),x82022),x82023))))
% 187.33/188.05 [8291]~P24(f329(x82911,f2(a1)))+~P24(f329(x82911,f329(f329(f22(a1),f329(f105(a1),x82912)),f329(f105(a1),x82913))))+P24(f329(x82911,f329(f105(a1),f329(f329(f22(a874),x82912),x82913))))
% 187.33/188.05 [8304]~P24(f329(f329(f243(a874),x83043),x83042))+P24(f329(x83041,f329(f329(f22(a1),f329(f105(a1),x83042)),f329(f105(a1),x83043))))+~P24(f329(x83041,f329(f105(a1),f329(f329(f22(a874),x83042),x83043))))
% 187.33/188.05 [8322]P24(f329(f329(f244(a874),x83221),x83222))+~P24(f329(x83223,f329(f329(f22(a1),f329(f105(a1),x83221)),f329(f105(a1),x83222))))+P24(f329(x83223,f329(f105(a1),f329(f329(f22(a874),x83221),x83222))))
% 187.33/188.05 [8376]~P123(x83762)+E(x83761,f2(x83762))+P24(f329(f329(f244(x83762),f2(x83762)),f329(f329(f80(x83762),f329(f329(f81(x83762),x83763),x83763)),f329(f329(f81(x83762),x83761),x83761))))
% 187.33/188.05 [8377]~P123(x83772)+E(x83771,f2(x83772))+P24(f329(f329(f244(x83772),f2(x83772)),f329(f329(f80(x83772),f329(f329(f81(x83772),x83771),x83771)),f329(f329(f81(x83772),x83773),x83773))))
% 187.33/188.05 [8486]~P24(f329(f329(f244(a874),f2(a874)),x84861))+~P24(f329(f329(f244(a1),x84862),x84863))+P24(f329(f329(f244(a1),f329(f329(f81(a1),f329(f105(a1),x84861)),x84862)),f329(f329(f81(a1),f329(f105(a1),x84861)),x84863)))
% 187.33/188.05 [8542]E(f329(f329(f106(f881(x85421,a869)),x85422),f40(f881(x85421,a869),x85423)),f193(f881(x85421,a869)))+P24(f329(f329(f331(f881(x85421,a869)),x85422),x85423))+P24(f329(f329(f331(f881(x85421,a869)),f638(x85423,x85422,x85421)),f329(f329(f307(f881(x85421,a869)),x85422),x85423)))
% 187.33/188.05 [8543]E(f329(f329(f106(f881(x85431,a869)),x85432),f40(f881(x85431,a869),x85433)),f193(f881(x85431,a869)))+P24(f329(f329(f331(f881(x85431,a869)),x85432),x85433))+P24(f329(f329(f331(f881(x85431,a869)),f637(x85433,x85432,x85431)),f329(f329(f307(f881(x85431,a869)),x85432),x85433)))
% 187.33/188.05 [8571]E(x85711,x85712)+~E(f329(f194(f875(x85713)),x85711),f329(f194(f875(x85713)),x85712))+P24(f329(f329(f331(f880(x85713,x85713)),f681(x85713,x85711,x85712)),f329(f171(f880(x85713,x85713)),f329(f329(f181(x85713,x85713),x85712),x85711))))
% 187.33/188.05 [8802]E(f305(x88021,x88022),f305(x88021,x88023))+~P24(f329(f329(f243(f881(f880(x88021,x88021),a869)),x88023),f305(x88021,x88022)))+~P24(f329(f329(f243(f881(f880(x88021,x88021),a869)),x88022),x88023))
% 187.33/188.05 [8862]~P44(x88621,f252(f881(x88621,a869)),x88623)+P24(f329(f329(f243(f881(f880(f875(x88621),f875(x88621)),a869)),f155(x88621,x88622)),f156(x88621,x88623)))+~P24(f329(f329(f243(f881(f880(x88621,x88621),a869)),x88622),x88623))
% 187.33/188.05 [9070]P42(x90701,x90702)+~P24(f329(f329(f331(x90701),x90703),f598(x90702,x90701)))+P24(f329(f329(f331(f880(x90701,x90701)),f329(f329(f264(x90701,x90701),f653(x90702,x90701,x90703)),x90703)),x90702))
% 187.33/188.05 [9104]~P24(f329(f62(x91041),x91042))+P24(f329(f62(f881(x91041,a869)),f329(f329(f61(x91041),x91042),x91043)))+~P24(f329(f329(f243(f881(f880(x91041,x91041),a869)),x91043),f329(f329(f266(x91041,x91041),x91042),f329(f16(f881(x91041,a869),x91041),x91042))))
% 187.33/188.05 [9139]P44(x91391,x91392,x91393)+P24(f329(f329(f331(x91391),f544(x91393,x91392,x91391)),x91392))+~P24(f329(f329(f243(f881(f880(x91391,x91391),a869)),x91393),f329(f329(f266(x91391,x91391),x91392),f329(f16(f881(x91391,a869),x91391),x91392))))
% 187.33/188.05 [9140]P44(x91401,x91402,x91403)+P24(f329(f329(f331(x91401),f546(x91402,x91403,x91401)),x91402))+~P24(f329(f329(f243(f881(f880(x91401,x91401),a869)),x91403),f329(f329(f266(x91401,x91401),x91402),f329(f16(f881(x91401,a869),x91401),x91402))))
% 187.33/188.05 [9175]~P64(x91751)+~P24(f329(f329(f244(x91751),x91752),x91753))+P24(f329(f329(f244(x91751),f329(f329(f287(x91751),f329(f329(f80(x91751),x91752),x91753)),f329(f329(f80(x91751),f78(x91751)),f78(x91751)))),x91753))
% 187.33/188.05 [9204]~P63(x92041)+P24(f329(f329(f243(x92041),x92042),x92043))+~P24(f329(f329(f243(x92041),f329(f329(f81(x92041),f847(x92043,x92042,x92041)),x92042)),x92043))
% 187.33/188.05 [9342]E(f329(f194(f875(f875(x93421))),f329(f134(f875(x93421),f329(f329(f8(a874,a869,f875(x93421)),f329(f244(a874),x93422)),f194(f875(x93421)))),f179(x93421,x93423))),f329(f194(f875(x93421)),f329(f329(f163(f875(x93421)),x93423),x93422)))+~P33(a874,f329(f167(a874),f329(f329(f152(f875(x93421),a874),f194(f875(x93421))),x93423)))+~P24(f329(f329(f244(a874),x93422),f329(f194(f875(f875(x93421))),x93423)))
% 187.33/188.05 [9449]~P42(x94491,x94492)+P22(x94491,f329(f329(f264(f881(f880(x94491,x94491),a869),f881(f880(x94491,x94491),a869)),x94492),x94493))+~P24(f329(f329(f243(f881(f880(x94491,x94491),a869)),f329(f329(f286(x94491,x94491,x94491),x94492),x94493)),x94492))
% 187.33/188.05 [9456]E(f329(f329(f152(f875(x94561),x94561),f329(f329(f7(f875(x94561),a874,x94561),f163(x94561)),x94562)),f329(f134(f875(x94561),f329(f329(f8(a874,a869,f875(x94561)),f329(f244(a874),x94562)),f194(f875(x94561)))),f179(x94561,x94563))),f329(f329(f163(f875(x94561)),x94563),x94562))+~P33(a874,f329(f167(a874),f329(f329(f152(f875(x94561),a874),f194(f875(x94561))),x94563)))+~P24(f329(f329(f244(a874),x94562),f329(f194(f875(f875(x94561))),x94563)))
% 187.33/188.05 [9591]P44(x95911,x95912,x95913)+~P24(f329(f329(f331(f880(x95911,x95911)),f329(f329(f264(x95911,x95911),f544(x95913,x95912,x95911)),f544(x95913,x95912,x95911))),x95913))+~P24(f329(f329(f243(f881(f880(x95911,x95911),a869)),x95913),f329(f329(f266(x95911,x95911),x95912),f329(f16(f881(x95911,a869),x95911),x95912))))
% 187.33/188.05 [9592]P44(x95921,x95922,x95923)+~P24(f329(f329(f331(f880(x95921,x95921)),f329(f329(f264(x95921,x95921),f546(x95922,x95923,x95921)),f546(x95922,x95923,x95921))),x95923))+~P24(f329(f329(f243(f881(f880(x95921,x95921),a869)),x95923),f329(f329(f266(x95921,x95921),x95922),f329(f16(f881(x95921,a869),x95921),x95922))))
% 187.33/188.05 [9767]~P138(x97671)+~P120(x97671)+E(f329(f329(f287(x97671),f329(f107(x97671),f329(f329(f73(f880(a1,a1),a1,x97672,f263(a1,a1)),f220(x97672)),x97673))),f329(f107(x97671),f329(f329(f73(f880(a1,a1),a1,x97672,f267(a1,a1)),f220(x97672)),x97673))),f233(x97672,x97671,x97673))
% 187.33/188.05 [9969]~E(x99693,f2(a874))+~E(f329(f194(f875(x99691)),f329(f329(f163(f875(x99691)),x99692),f747(x99693,x99691,x99692))),x99693)+E(f329(f329(f152(a874,f875(x99691)),f329(f329(f7(a874,f875(a874),f875(x99691)),f329(f329(f8(f881(a874,x99691),f881(f875(a874),f875(x99691)),a874),f152(a874,x99691)),f329(f7(a874,a874,x99691),f329(f329(f8(f875(x99691),f881(a874,x99691),a874),f163(x99691)),f329(f163(f875(x99691)),x99692))))),f137(a874,f329(f299(a874,f2(a874)),f329(f194(f875(f875(x99691))),x99692))))),f137(a874,f329(f299(a874,f2(a874)),x99693))),f179(x99691,x99692))
% 187.33/188.05 [9970]E(x99701,f118(f875(x99702)))+~E(f329(f194(f875(x99702)),f329(f329(f163(f875(x99702)),x99701),f747(x99703,x99702,x99701))),x99703)+E(f329(f329(f152(a874,f875(x99702)),f329(f329(f7(a874,f875(a874),f875(x99702)),f329(f329(f8(f881(a874,x99702),f881(f875(a874),f875(x99702)),a874),f152(a874,x99702)),f329(f7(a874,a874,x99702),f329(f329(f8(f875(x99702),f881(a874,x99702),a874),f163(x99702)),f329(f163(f875(x99702)),x99701))))),f137(a874,f329(f299(a874,f2(a874)),f329(f194(f875(f875(x99702))),x99701))))),f137(a874,f329(f299(a874,f2(a874)),x99703))),f179(x99702,x99701))
% 187.33/188.05 [9971]~E(x99713,f2(a874))+E(f329(f329(f152(a874,f875(x99711)),f329(f329(f7(a874,f875(a874),f875(x99711)),f329(f329(f8(f881(a874,x99711),f881(f875(a874),f875(x99711)),a874),f152(a874,x99711)),f329(f7(a874,a874,x99711),f329(f329(f8(f875(x99711),f881(a874,x99711),a874),f163(x99711)),f329(f163(f875(x99711)),x99712))))),f137(a874,f329(f299(a874,f2(a874)),f329(f194(f875(f875(x99711))),x99712))))),f137(a874,f329(f299(a874,f2(a874)),x99713))),f179(x99711,x99712))+P24(f329(f329(f244(a874),f747(x99713,x99711,x99712)),f329(f194(f875(f875(x99711))),x99712)))
% 187.33/188.05 [9972]E(x99721,f118(f875(x99722)))+E(f329(f329(f152(a874,f875(x99722)),f329(f329(f7(a874,f875(a874),f875(x99722)),f329(f329(f8(f881(a874,x99722),f881(f875(a874),f875(x99722)),a874),f152(a874,x99722)),f329(f7(a874,a874,x99722),f329(f329(f8(f875(x99722),f881(a874,x99722),a874),f163(x99722)),f329(f163(f875(x99722)),x99721))))),f137(a874,f329(f299(a874,f2(a874)),f329(f194(f875(f875(x99722))),x99721))))),f137(a874,f329(f299(a874,f2(a874)),x99723))),f179(x99722,x99721))+P24(f329(f329(f244(a874),f747(x99723,x99722,x99721)),f329(f194(f875(f875(x99722))),x99721)))
% 187.33/188.05 [7700]E(f329(f329(f80(a874),f329(f108(a874),x77001)),f329(f329(f80(a874),f329(f108(a874),x77002)),x77003)),f329(f329(f80(a874),f329(f108(a874),f329(f329(f80(a1),x77001),x77002))),x77003))+P24(f329(a198,f329(f108(a1),x77001)))+P24(f329(a198,f329(f108(a1),x77002)))
% 187.33/188.05 [8477]~P24(f329(f62(x84771),x84772))+~P24(f329(f329(f331(x84771),x84773),x84772))+E(f329(a117,f329(f38(x84771),f329(f329(f22(f881(x84771,a869)),x84772),f329(f329(f307(x84771),x84773),f193(f881(x84771,a869)))))),f329(f38(x84771),x84772))
% 187.33/188.05 [8496]~P24(f329(f62(x84961),x84962))+~P24(f329(f329(f331(x84961),x84963),x84962))+E(f329(f329(f80(a874),f78(a874)),f329(f38(x84961),f329(f329(f22(f881(x84961,a869)),x84962),f329(f329(f307(x84961),x84963),f193(f881(x84961,a869)))))),f329(f38(x84961),x84962))
% 187.33/188.05 [8580]~P27(x85801)+~P24(f329(f62(x85801),x85803))+E(f329(f329(f146(x85801,x85801,f5(x85801)),x85802),f137(x85801,f329(f329(f22(f881(x85801,a869)),x85803),f329(f329(f307(x85801),x85802),f193(f881(x85801,a869)))))),f137(x85801,f329(f329(f307(x85801),x85802),x85803)))
% 187.33/188.05 [8732]~P24(f329(f62(x87321),x87323))+~P24(f329(f62(x87321),x87322))+E(f329(f329(f80(a874),f329(f38(x87321),f329(f329(f115(f881(x87321,a869)),x87322),x87323))),f329(f38(x87321),f329(f329(f106(f881(x87321,a869)),x87322),x87323))),f329(f329(f80(a874),f329(f38(x87321),x87322)),f329(f38(x87321),x87323)))
% 187.33/188.05 [9917]~P21(x99171,f881(f881(x99171,a869),a869),f329(f329(f7(x99171,f881(f880(x99171,x99171),a869),f881(f881(x99171,a869),a869)),f329(f329(f8(f881(x99171,a869),f881(f881(f880(x99171,x99171),a869),f881(f881(x99171,a869),a869)),x99171),f61(x99171)),f329(f329(f7(x99171,f881(x99171,a869),f881(x99171,a869)),f307(x99171)),f193(f881(x99171,a869))))),x99173),x99172)+~P24(f329(f62(x99171),x99172))+E(f329(f38(f881(x99171,a869)),f329(f329(f61(x99171),x99172),x99173)),f329(f38(x99171),x99172))
% 187.33/188.05 [7973]~P94(x79731)+P24(f329(f329(f243(a1),f2(a1)),f329(f108(a1),x79733)))+E(f329(f329(f254(x79731),x79732),f329(f108(a874),f329(f329(f22(a1),f329(f329(f80(a1),x79733),x79733)),a102))),f78(x79731))
% 187.33/188.05 [9432]~P94(x94321)+~P24(f329(f329(f243(a1),f2(a1)),f329(f108(a1),x94323)))+E(f329(f329(f254(x94321),x94322),f329(f108(a874),f329(f329(f22(a1),f329(f329(f80(a1),x94323),x94323)),a102))),f329(f329(f86(x94321,x94321),f329(f329(f254(x94321),x94322),f329(f108(a874),x94323))),f329(f329(f18(x94321,x94321,x94321),f329(f329(f8(x94321,f881(x94321,x94321),x94321),f81(x94321)),f329(f81(x94321),x94322))),f5(x94321))))
% 187.33/188.05 [9826]~P24(f329(f135(x98261),x98263))+~P24(f329(f329(f331(x98261),x98262),f329(f171(x98261),x98263)))+E(f329(f329(f136(x98261),f329(f194(f875(x98261)),f176(x98261,f329(f329(f8(a869,a869,x98261),a324),f329(f329(f7(x98261,x98261,a869),a326),x98262)),f329(f167(x98261),x98263)))),f329(f167(x98261),x98263)),f329(f329(f149(x98261),x98262),f329(f167(x98261),f176(x98261,f329(f329(f8(a869,a869,x98261),a324),f329(f329(f7(x98261,x98261,a869),a326),x98262)),x98263))))
% 187.33/188.05 [9898]P24(f329(f329(f243(f881(f880(x98981,x98981),a869)),f305(x98981,x98982)),x98983))+~P24(f329(f329(f243(f881(f880(x98981,x98981),a869)),f305(x98981,f193(f881(f880(x98981,x98981),a869)))),x98983))+~P24(f329(f329(f243(f881(f880(x98981,x98981),a869)),f329(f329(f286(x98981,x98981,x98981),f329(f329(f106(f881(f880(x98981,x98981),a869)),f305(x98981,x98982)),x98983)),x98982)),x98983))
% 187.33/188.05 [9738]~P24(f329(f62(x97381),f329(f249(x97381),x97383)))+~P24(f329(f62(x97381),f329(f249(x97381),x97382)))+P24(f329(f62(x97381),f329(f249(x97381),f329(f329(f18(x97381,a869,a869),f329(f329(f8(a869,f881(a869,a869),x97381),a328),x97382)),x97383))))
% 187.33/188.05 [10031]P24(f329(f329(f243(f881(f880(x100311,x100311),a869)),f329(f329(f286(x100311,x100311,x100311),x100312),f305(x100311,x100312))),x100313))+~P24(f329(f329(f243(f881(f880(x100311,x100311),a869)),x100312),x100313))+~P24(f329(f329(f243(f881(f880(x100311,x100311),a869)),f329(f329(f286(x100311,x100311,x100311),f329(f329(f106(f881(f880(x100311,x100311),a869)),f329(f329(f286(x100311,x100311,x100311),x100312),f305(x100311,x100312))),x100313)),x100312)),x100313))
% 187.33/188.05 [9985]~P115(x99852)+E(x99851,f2(x99852))+~E(f329(f329(f80(x99852),f329(f329(f254(x99852),x99853),f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102))))),f329(f329(f254(x99852),x99851),f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102))))),f2(x99852))
% 187.33/188.05 [9986]~P115(x99862)+E(x99861,f2(x99862))+~E(f329(f329(f80(x99862),f329(f329(f254(x99862),x99861),f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102))))),f329(f329(f254(x99862),x99863),f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102))))),f2(x99862))
% 187.33/188.05 [9991]~P24(f329(f135(x99911),x99913))+~P24(f329(f329(f331(x99911),x99912),f329(f171(x99911),x99913)))+E(f329(f167(x99911),f329(f170(x99911),f329(f329(f136(x99911),f329(f194(f875(x99911)),f176(x99911,f329(f329(f8(a869,a869,x99911),a324),f329(f329(f7(x99911,x99911,a869),a326),x99912)),x99913))),x99913))),f176(x99911,f329(f329(f8(a869,a869,x99911),a324),f329(f329(f7(x99911,x99911,a869),a326),x99912)),f329(f167(x99911),x99913)))
% 187.33/188.05 [10076]~P115(x100762)+E(x100761,f2(x100762))+P24(f329(f329(f244(x100762),f2(x100762)),f329(f329(f80(x100762),f329(f329(f254(x100762),x100763),f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102))))),f329(f329(f254(x100762),x100761),f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))))))
% 187.33/188.05 [10077]~P115(x100772)+E(x100771,f2(x100772))+P24(f329(f329(f244(x100772),f2(x100772)),f329(f329(f80(x100772),f329(f329(f254(x100772),x100771),f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102))))),f329(f329(f254(x100772),x100773),f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))))))
% 187.33/188.05 [10119]~P115(x101191)+P24(f329(f329(f243(x101191),f2(x101191)),x101192))+~P24(f329(f329(f243(x101191),f2(x101191)),f329(f329(f254(x101191),x101192),f329(a117,f329(f329(f81(a874),f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))),x101193)))))
% 187.33/188.05 [5474]~P20(x54741,x54744,x54743)+P20(x54741,x54742,x54743)+~P20(x54741,x54742,x54744)
% 187.33/188.05 [4934]~E(x49342,f90(x49343,x49341))+P24(f329(x49341,x49342))+~P24(f329(x49341,x49344))
% 187.33/188.05 [6686]~P42(x66862,x66864)+~P42(x66861,x66863)+P42(f880(x66861,x66862),f322(x66861,x66862,x66863,x66864))
% 187.33/188.05 [5116]~P5(x51164,x51161)+~E(f329(x51161,x51162),f329(x51161,x51163))+P24(f329(f329(x51161,x51162),x51163))
% 187.33/188.05 [5289]~P5(x52894,x52891)+E(f329(x52891,x52892),f329(x52891,x52893))+~P24(f329(f329(x52891,x52892),x52893))
% 187.33/188.05 [5381]~P14(x53813,x53814,x53811)+E(f329(x53811,x53812),f329(f64(x53813,x53814),x53812))+~P24(f329(f62(x53813),x53812))
% 187.33/188.05 [5382]~P3(x53823,x53824,x53821)+E(f329(x53821,x53822),f329(f64(x53823,x53824),x53822))+~P24(f329(f62(x53823),x53822))
% 187.33/188.05 [5507]~P5(x55074,x55071)+~P24(f329(f329(x55071,x55073),x55072))+P24(f329(f329(x55071,x55072),x55073))
% 187.33/188.05 [5575]E(x55751,x55752)+~E(f329(f263(x55753,x55754),x55751),f329(f263(x55753,x55754),x55752))+~E(f329(f267(x55753,x55754),x55751),f329(f267(x55753,x55754),x55752))
% 187.33/188.05 [5600]E(x56001,x56002)+~P24(f329(f48(x56003,x56004),x56002))+~P24(f329(f48(x56003,x56004),x56001))
% 187.33/188.05 [5792]~P72(x57922)+E(f234(x57921,x57922,x57923,x57924),f2(x57922))+P24(f329(f62(x57921),x57924))
% 187.33/188.05 [5929]~P24(f329(f317(x59291,x59292),x59294))+P24(f329(f317(x59291,x59292),x59293))+~P24(f329(f329(x59292,x59293),x59294))
% 187.33/188.05 [7811]E(x78111,f2(a874))+~P24(f329(x78112,x78113))+P24(f329(x78112,f812(x78112,x78113,x78111,x78114)))
% 187.33/188.05 [7893]~P27(x78932)+~P24(f329(f135(x78931),x78934))+P24(f329(f135(x78931),f148(x78931,x78932,x78933,x78934)))
% 187.33/188.05 [8121]~P24(f329(f62(x81212),x81214))+~P24(f329(f62(x81211),x81213))+P24(f329(f62(f879(x81211,x81212)),f316(x81211,x81212,x81213,x81214)))
% 187.33/188.05 [8122]~P24(f329(f135(x81222),x81224))+~P24(f329(f135(x81221),x81223))+P24(f329(f135(f880(x81221,x81222)),f60(x81221,x81222,x81223,x81224)))
% 187.33/188.05 [8126]P24(f329(f329(f331(f875(x81261)),f329(f329(f126(x81261),x81262),x81263)),f159(x81261,x81264)))+~P24(f329(f329(f331(f875(x81261)),x81263),f159(x81261,x81264)))+~P24(f329(f329(f331(f875(x81261)),x81262),f159(x81261,x81264)))
% 187.33/188.05 [8409]E(x84091,f2(a874))+P24(f329(x84092,x84093))+~P24(f329(x84092,f813(x84092,x84093,x84091,x84094)))
% 187.33/188.05 [8456]~P27(x84563)+~P24(f329(f135(x84561),f148(x84561,x84563,x84564,x84562)))+P24(f329(f135(x84561),x84562))
% 187.33/188.05 [8723]~P24(f329(f329(f331(f880(x87231,x87231)),f329(f329(f264(x87231,x87231),x87232),x87234)),f305(x87231,x87233)))+P24(f329(f329(f331(x87231),x87232),f318(x87231,x87233)))+~P24(f329(f329(f331(x87231),x87234),f318(x87231,x87233)))
% 187.33/188.05 [5100]~P72(x51002)+E(f329(f329(f6(x51001,x51002),x51003),x51004),f2(x51002))+P24(f329(f62(x51001),x51004))
% 187.33/188.05 [5103]~P76(x51032)+E(f329(f329(f9(x51031,x51032),x51033),x51034),f78(x51032))+P24(f329(f62(x51031),x51034))
% 187.33/188.05 [5252]~P73(x52523)+E(x52521,x52522)+~E(f329(f329(f80(x52523),x52524),x52521),f329(f329(f80(x52523),x52524),x52522))
% 187.33/188.05 [5253]~P74(x52533)+E(x52531,x52532)+~E(f329(f329(f80(x52533),x52534),x52531),f329(f329(f80(x52533),x52534),x52532))
% 187.33/188.05 [5255]~P73(x52553)+E(x52551,x52552)+~E(f329(f329(f80(x52553),x52551),x52554),f329(f329(f80(x52553),x52552),x52554))
% 187.33/188.05 [5377]~P31(x53773)+E(x53771,f193(f881(x53772,a869)))+E(f329(f329(f42(x53772,x53773),x53771),f329(f16(x53773,x53772),x53774)),x53774)
% 187.33/188.05 [5378]~P31(x53783)+E(x53781,f193(f881(x53782,a869)))+E(f329(f329(f43(x53782,x53783),x53781),f329(f16(x53783,x53782),x53784)),x53784)
% 187.33/188.05 [5588]~P106(x55883)+E(x55881,x55882)+~E(f300(x55883,x55884,x55881),f329(f329(f307(x55883),x55882),f193(f881(x55883,a869))))
% 187.33/188.05 [5589]~P106(x55893)+E(x55891,x55892)+~E(f300(x55893,x55891,x55892),f329(f329(f307(x55893),x55894),f193(f881(x55893,a869))))
% 187.33/188.05 [5649]~P40(x56493,x56491,x56494)+P40(x56493,x56491,f329(f329(f149(x56493),x56492),x56494))+P24(f329(x56491,x56492))
% 187.33/188.05 [5752]~P36(x57521,x57522,x57524)+~P24(f329(x57522,x57523))+P36(x57521,x57522,f329(f329(f149(x57521),x57523),x57524))
% 187.33/188.05 [5885]P24(f329(x58851,x58852))+~P24(f329(f257(x58853,x58851),x58854))+~P24(f329(f329(f331(x58853),x58852),x58854))
% 187.33/188.05 [5894]~P36(x58941,x58942,x58944)+~P36(x58941,x58942,x58943)+P36(x58941,x58942,f329(f329(f126(x58941),x58943),x58944))
% 187.33/188.05 [5904]P38(x59041,x59042,x59043)+~P38(x59041,x59042,f329(f329(f149(x59041),x59044),x59043))+P24(f329(x59042,x59044))
% 187.33/188.05 [5905]P40(x59051,x59052,x59053)+~P40(x59051,x59052,f329(f329(f149(x59051),x59054),x59053))+P24(f329(x59052,x59054))
% 187.33/188.05 [5918]E(x59181,x59182)+~P24(f329(f329(f199(x59183),x59184),x59182))+~P24(f329(f329(f199(x59183),x59184),x59181))
% 187.33/188.05 [5983]P38(x59831,x59832,x59833)+P38(x59831,x59832,x59834)+~P38(x59831,x59832,f329(f329(f126(x59831),x59834),x59833))
% 187.33/188.05 [6002]~P72(x60021)+E(f329(f329(f6(a874,x60021),x60022),f329(f299(a874,x60023),f329(a117,x60024))),f2(x60021))+~P24(f329(f329(f244(a874),x60024),x60023))
% 187.33/188.05 [6007]~P30(x60071)+~E(f45(x60071,x60072,x60073),f45(x60071,x60074,x60073))+E(f45(x60071,f329(f79(x60071),x60072),x60073),f45(x60071,f329(f79(x60071),x60074),x60073))
% 187.33/188.05 [6075]P24(f329(x60751,x60752))+~E(f329(f134(x60753,x60751),x60754),x60754)+~P24(f329(f329(f331(x60753),x60752),f329(f171(x60753),x60754)))
% 187.33/188.05 [6094]~E(f329(f329(f80(a874),x60943),x60942),f329(f329(f80(a874),x60941),x60944))+~P24(f329(f329(f244(a874),x60943),x60944))+P24(f329(f329(f244(a874),x60941),x60942))
% 187.33/188.05 [6098]P38(x60981,x60982,x60983)+~P24(f329(x60982,x60984))+~P24(f329(f329(f331(x60981),x60984),f329(f171(x60981),x60983)))
% 187.33/188.05 [6134]~P36(x61343,x61341,x61344)+P24(f329(x61341,x61342))+~P24(f329(f329(f331(x61343),x61342),f329(f171(x61343),x61344)))
% 187.33/188.05 [6136]~E(f329(f134(x61361,x61362),x61363),f118(x61361))+~P24(f329(x61362,x61364))+~P24(f329(f329(f331(x61361),x61364),f329(f171(x61361),x61363)))
% 187.33/188.05 [6137]~E(f176(x61373,x61371,x61374),x61374)+P24(f329(x61371,x61372))+~P24(f329(f329(f331(x61373),x61372),f329(f171(x61373),x61374)))
% 187.33/188.05 [6171]~E(x61714,f193(f881(x61712,a869)))+~E(x61713,f193(f881(x61711,a869)))+E(f316(x61711,x61712,x61713,x61714),f193(f881(f879(x61711,x61712),a869)))
% 187.33/188.05 [6316]P24(f329(x63161,x63162))+~P24(f329(f158(x63163,x63161),x63164))+~P24(f329(f329(f331(x63163),x63162),f329(f171(x63163),x63164)))
% 187.33/188.05 [6584]~P72(x65841)+E(f329(f329(f6(a874,x65841),x65842),f300(a874,x65843,f329(a117,x65844))),f2(x65841))+~P24(f329(f329(f244(a874),f329(a117,x65844)),x65843))
% 187.33/188.05 [6725]~P27(x67251)+E(f329(f329(f22(f881(x67251,a869)),f329(f299(x67251,x67252),x67253)),f329(f299(x67251,x67252),x67254)),f329(f299(x67251,x67254),x67253))+~P24(f329(f329(f243(x67251),x67252),x67254))
% 187.33/188.05 [6797]~E(x67973,x67974)+E(x67971,f2(a874))+P24(f329(f329(f331(x67972),x67973),f329(f171(x67972),f169(x67972,x67971,x67974))))
% 187.33/188.05 [7079]~P24(f329(f329(f331(f875(x70791)),x70794),f159(x70791,x70793)))+P24(f329(f329(f331(x70791),x70792),x70793))+~P24(f329(f329(f331(x70791),x70792),f329(f171(x70791),x70794)))
% 187.33/188.05 [7086]~P42(x70861,x70862)+P24(f329(f329(f331(x70861),f639(x70862,x70861,x70863)),x70863))+~P24(f329(f329(f331(x70861),x70864),x70863))
% 187.33/188.05 [7142]~P72(x71421)+E(f329(f329(f329(f66(x71421,x71422,f80(x71421)),x71423),f2(x71421)),x71424),f329(f329(f6(x71422,x71421),x71423),x71424))+~P24(f329(f62(x71422),x71424))
% 187.33/188.05 [7144]~P76(x71441)+E(f329(f329(f329(f66(x71441,x71442,f81(x71441)),x71443),f78(x71441)),x71444),f329(f329(f9(x71442,x71441),x71443),x71444))+~P24(f329(f62(x71442),x71444))
% 187.33/188.05 [7172]P21(x71721,x71722,x71723,x71724)+~E(f329(f38(x71722),f329(f308(x71721,x71722,x71723),x71724)),f329(f38(x71721),x71724))+~P24(f329(f62(x71721),x71724))
% 187.33/188.05 [7358]~P72(x73581)+E(f329(f329(f80(x73581),f329(x73582,x73583)),f329(f329(f6(a874,x73581),x73582),f302(a874,x73583,x73584))),f329(f329(f6(a874,x73581),x73582),f300(a874,x73583,x73584)))+~P24(f329(f329(f243(a874),x73583),x73584))
% 187.33/188.05 [7368]~P72(x73681)+~P21(x73682,x73681,x73683,x73684)+E(f329(f329(f6(x73681,x73681),f34(x73681)),f329(f308(x73682,x73681,x73683),x73684)),f329(f329(f6(x73682,x73681),x73683),x73684))
% 187.33/188.05 [7369]~P76(x73691)+~P21(x73692,x73691,x73693,x73694)+E(f329(f329(f9(x73691,x73691),f34(x73691)),f329(f308(x73692,x73691,x73693),x73694)),f329(f329(f9(x73692,x73691),x73693),x73694))
% 187.33/188.05 [7423]E(f329(f38(f879(x74231,x74232)),f316(x74231,x74232,x74233,x74234)),f329(f329(f80(a874),f329(f38(x74231),x74233)),f329(f38(x74232),x74234)))+~P24(f329(f62(x74232),x74234))+~P24(f329(f62(x74231),x74233))
% 187.33/188.05 [7510]E(x75101,x75102)+P24(f329(f329(f331(x75103),x75101),f329(f171(x75103),f168(x75103,x75102,x75104))))+~P24(f329(f329(f331(x75103),x75101),f329(f171(x75103),x75104)))
% 187.33/188.05 [7737]~P72(x77371)+E(f329(f329(f80(x77371),f329(f329(f6(a874,x77371),x77372),f329(f299(a874,x77373),x77374))),f329(x77372,x77374)),f329(f329(f6(a874,x77371),x77372),f329(f299(a874,x77373),f329(a117,x77374))))+P24(f329(f329(f244(a874),x77374),x77373))
% 187.33/188.05 [7793]~P21(x77931,x77932,x77933,f252(f881(x77931,a869)))+~P24(f329(f62(x77932),x77934))+P24(f329(f62(x77931),f329(f309(x77931,x77932,x77933),x77934)))
% 187.33/188.05 [7906]P24(f329(f329(f331(f875(x79061)),f329(f329(f149(x79061),x79062),x79063)),f159(x79061,x79064)))+~P24(f329(f329(f331(f875(x79061)),x79063),f159(x79061,x79064)))+~P24(f329(f329(f331(x79061),x79062),x79064))
% 187.33/188.05 [7997]~E(f329(f308(x79973,x79971,x79974),f252(f881(x79973,a869))),f252(f881(x79971,a869)))+P24(f329(f62(x79971),x79972))+~P24(f329(f62(x79973),f329(f309(x79973,x79971,x79974),x79972)))
% 187.33/188.05 [8093]~P21(x80931,x80933,x80934,x80932)+P24(f329(f62(x80931),x80932))+~P24(f329(f62(x80933),f329(f308(x80931,x80933,x80934),x80932)))
% 187.33/188.05 [8114]~E(x81142,x81143)+P24(f329(f329(f331(f880(x81141,x81141)),f329(f329(f264(x81141,x81141),x81142),x81143)),f261(x81141,x81144)))+~P24(f329(f329(f331(x81141),x81142),x81144))
% 187.33/188.05 [8152]~P72(x81521)+E(f329(f329(f80(x81521),f329(f329(f6(a874,x81521),x81522),f300(a874,x81523,x81524))),f329(x81522,f329(a117,x81524))),f329(f329(f6(a874,x81521),x81522),f300(a874,x81523,f329(a117,x81524))))+P24(f329(f329(f244(a874),f329(a117,x81524)),x81523))
% 187.33/188.05 [8216]P24(f329(x82161,x82162))+~P24(f329(x82161,f329(f329(f163(x82163),x82164),f678(x82161,x82164,x82163))))+~P24(f329(f329(f331(x82163),x82162),f329(f171(x82163),x82164)))
% 187.33/188.05 [8355]~P24(f329(f329(f331(x83551),x83552),f318(x83551,x83554)))+P24(f329(f329(f331(f875(x83551)),f329(f329(f149(x83551),x83552),x83553)),f318(f875(x83551),f155(x83551,x83554))))+~P24(f329(f329(f331(f875(x83551)),x83553),f318(f875(x83551),f155(x83551,x83554))))
% 187.33/188.05 [8368]~P21(x83682,x83683,x83684,f642(x83684,x83683,x83682,x83681))+P21(x83682,x83683,x83684,f41(f881(x83682,a869),x83681))+E(x83681,f193(f881(f881(x83682,a869),a869)))
% 187.33/188.05 [8641]E(x86411,x86412)+~P24(f329(f329(f331(f880(x86413,x86413)),f329(f329(f264(x86413,x86413),x86411),x86412)),f305(x86413,x86414)))+P24(f329(f329(f331(x86413),x86411),f329(f262(x86413,x86413),x86414)))
% 187.33/188.05 [8905]E(x89051,f2(a874))+P24(f329(x89052,x89053))+P24(f329(f329(f331(x89054),f813(x89052,x89053,x89051,x89054)),f329(f171(x89054),f169(x89054,x89051,x89053))))
% 187.33/188.05 [8915]E(x89151,f2(a874))+~P24(f329(x89153,x89154))+P24(f329(f329(f331(x89152),f812(x89153,x89154,x89151,x89152)),f329(f171(x89152),f169(x89152,x89151,x89154))))
% 187.33/188.05 [8923]P21(x89232,x89233,x89234,f41(f881(x89232,a869),x89231))+E(x89231,f193(f881(f881(x89232,a869),a869)))+P24(f329(f329(f331(f881(x89232,a869)),f642(x89234,x89233,x89232,x89231)),x89231))
% 187.33/188.05 [9061]P24(f329(f62(x90611),x90612))+~P24(f329(f62(x90614),f329(f308(x90611,x90614,x90613),x90612)))+P24(f329(f329(f331(x90611),f430(x90613,x90614,x90612,x90611)),x90612))
% 187.33/188.05 [9153]~P31(x91532)+E(f329(f329(f65(x91531,x91532,f329(f329(f8(x91532,f881(x91532,x91532),x91531),f115(x91532)),x91533)),f193(x91532)),x91534),f329(f329(f42(x91531,x91532),x91534),x91533))+~P24(f329(f62(x91531),x91534))
% 187.33/188.05 [9154]~P31(x91542)+E(f329(f329(f65(x91541,x91542,f329(f329(f8(x91542,f881(x91542,x91542),x91541),f106(x91542)),x91543)),f252(x91542)),x91544),f329(f329(f43(x91541,x91542),x91544),x91543))+~P24(f329(f62(x91541),x91544))
% 187.33/188.05 [9237]P24(f329(x92371,x92372))+~P24(f329(x92371,f329(f329(f163(x92373),x92374),f735(x92372,x92371,x92374,x92373))))+~P24(f329(f329(f331(x92373),x92372),f329(f171(x92373),x92374)))
% 187.33/188.05 [9259]E(x92591,x92592)+~P24(f329(f329(f331(f880(x92593,x92593)),f329(f329(f264(x92593,x92593),x92591),x92592)),f305(x92593,x92594)))+P24(f329(f329(f331(f880(x92593,x92593)),f329(f329(f264(x92593,x92593),x92591),x92592)),f329(f329(f286(x92593,x92593,x92593),x92594),f305(x92593,x92594))))
% 187.33/188.05 [9308]~E(f329(f194(f875(x93081)),x93082),f329(f194(f875(x93081)),x93083))+~P24(f329(f329(f331(f880(f875(x93081),f875(x93081))),f329(f329(f264(f875(x93081),f875(x93081)),x93082),x93083)),f145(x93081,x93084)))+P24(f329(f329(f331(f880(f875(x93081),f875(x93081))),f329(f329(f264(f875(x93081),f875(x93081)),x93082),x93083)),f143(x93081,x93084)))
% 187.33/188.05 [9538]P36(x95381,f329(f329(f18(x95381,a869,a869),f329(f329(f8(a869,f881(a869,a869),x95381),a328),f329(f329(f8(a869,a869,x95381),a324),x95382))),f329(a326,x95383)),x95384)+~P24(f329(x95382,x95383))+~P40(x95381,x95382,f329(f329(f149(x95381),x95383),x95384))
% 187.33/188.05 [9699]~P36(x96991,f329(f329(f18(x96991,a869,a869),f329(f329(f8(a869,f881(a869,a869),x96991),a328),f329(f329(f8(a869,a869,x96991),a324),x96992))),f329(a326,x96993)),x96994)+~P24(f329(x96992,x96993))+P40(x96991,x96992,f329(f329(f149(x96991),x96993),x96994))
% 187.33/188.05 [9703]~P40(x97031,x97032,x97034)+~P36(x97031,f329(f329(f18(x97031,a869,a869),f329(f329(f8(a869,f881(a869,a869),x97031),a328),f329(f329(f8(a869,a869,x97031),a324),x97032))),f329(a326,x97033)),x97034)+P40(x97031,x97032,f329(f329(f149(x97031),x97033),x97034))
% 187.33/188.05 [9741]~P69(x97411)+E(f329(f329(f6(a874,x97411),f329(f329(f18(a874,x97411,x97411),f329(f329(f8(x97411,f881(x97411,x97411),a874),f22(x97411)),x97412)),f329(f329(f8(a874,x97411,a874),x97412),f329(f329(f7(a874,a874,a874),f80(a874)),f78(a874))))),f300(a874,x97413,x97414)),f2(x97411))+P24(f329(f329(f243(a874),x97413),x97414))
% 187.33/188.05 [9984]~P42(x99842,x99844)+~P21(x99842,x99841,x99843,f252(f881(x99842,a869)))+P42(x99841,f329(f308(f880(x99842,x99842),f880(x99841,x99841),f269(x99842,x99841,x99842,x99841,x99843,x99843)),x99844))
% 187.33/188.05 [10145]~E(f329(f194(f875(x101451)),x101453),f329(f194(f875(x101451)),x101452))+P24(f329(f329(f331(f880(f875(x101451),f875(x101451))),f329(f329(f264(f875(x101451),f875(x101451)),x101452),x101453)),f156(x101451,x101454)))+~P24(f329(f329(f268(x101451,x101451,a869),f329(f329(f7(x101451,f881(f880(x101451,x101451),a869),f881(x101451,a869)),f329(f329(f8(f881(x101451,f881(f881(f880(x101451,x101451),a869),a869)),f881(f881(f880(x101451,x101451),a869),f881(x101451,a869)),x101451),f7(x101451,f881(f880(x101451,x101451),a869),a869)),f329(f329(f8(f881(x101451,f880(x101451,x101451)),f881(x101451,f881(f881(f880(x101451,x101451),a869),a869)),x101451),f329(f8(f880(x101451,x101451),f881(f881(f880(x101451,x101451),a869),a869),x101451),f331(f880(x101451,x101451)))),f264(x101451,x101451)))),x101454)),f682(x101454,x101453,x101452,x101451)))
% 187.33/188.05 [5968]~E(x59684,x59682)+P24(f329(x59681,x59682))+P24(f329(f329(f199(f32(x59681,x59683)),x59682),x59684))
% 187.33/188.05 [6059]~P29(x60591)+~E(x60592,f2(x60591))+E(f329(f329(f39(x60591),f329(f329(f81(x60591),x60592),x60593)),f329(f329(f81(x60591),x60592),x60594)),f2(x60591))
% 187.33/188.05 [6097]E(x60971,f118(x60972))+E(x60973,f329(f329(f22(a874),f329(f194(f875(x60972)),x60971)),f78(a874)))+E(f142(x60972,f329(f329(f157(x60972,x60971),x60973),x60974)),f142(x60972,x60971))
% 187.33/188.05 [6125]E(x61251,x61252)+P24(f329(x61253,x61252))+~P24(f329(f329(f329(f307(x61254),x61251),x61253),x61252))
% 187.33/188.05 [6141]~P72(x61411)+~P24(f329(f135(x61412),x61414))+E(f329(f164(x61411),f329(f329(f152(x61412,x61411),x61413),x61414)),f329(f329(f6(x61412,x61411),x61413),f329(f171(x61412),x61414)))
% 187.33/188.05 [6164]~P76(x61642)+~P24(f329(f62(x61641),x61644))+E(f329(f329(f9(x61641,x61642),f329(f16(x61642,x61641),x61643)),x61644),f329(f329(f254(x61642),x61643),f329(f38(x61641),x61644)))
% 187.33/188.05 [6219]~P61(x62192)+E(x62191,f2(x62192))+E(f329(f329(f287(x62192),f329(f329(f81(x62192),x62193),x62191)),f329(f329(f81(x62192),x62194),x62191)),f329(f329(f287(x62192),x62193),x62194))
% 187.33/188.05 [6220]~P61(x62202)+E(x62201,f2(x62202))+E(f329(f329(f287(x62202),f329(f329(f81(x62202),x62201),x62203)),f329(f329(f81(x62202),x62201),x62204)),f329(f329(f287(x62202),x62203),x62204))
% 187.33/188.05 [6221]~P29(x62212)+E(x62211,f2(x62212))+E(f329(f329(f39(x62212),f329(f329(f81(x62212),x62213),x62211)),f329(f329(f81(x62212),x62214),x62211)),f329(f329(f39(x62212),x62213),x62214))
% 187.33/188.05 [6223]~P29(x62232)+E(x62231,f2(x62232))+E(f329(f329(f39(x62232),f329(f329(f81(x62232),x62231),x62233)),f329(f329(f81(x62232),x62231),x62234)),f329(f329(f39(x62232),x62233),x62234))
% 187.33/188.05 [6286]P24(f329(x62861,x62862))+~E(x62863,f329(f329(f80(a874),x62864),x62862))+~P24(f329(x62861,f329(f329(f22(a874),x62863),x62864)))
% 187.33/188.05 [6366]P23(x63661,x63662,x63663)+P34(x63661,f568(x63663,x63662,x63661),x63664)+~P24(f329(f329(f331(f873(x63661)),x63664),x63662))
% 187.33/188.05 [6368]~P24(f329(x63682,x63683))+~P24(f329(f158(x63681,x63682),x63684))+P24(f329(f158(x63681,x63682),f329(f329(f149(x63681),x63683),x63684)))
% 187.33/188.05 [6408]E(x64081,f118(x64082))+~E(x64083,f329(f329(f22(a874),f329(f194(f875(x64082)),x64081)),f78(a874)))+E(f142(x64082,f329(f329(f157(x64082,x64081),x64083),x64084)),x64084)
% 187.33/188.05 [6431]~P102(x64311)+~P24(f329(f329(f243(x64311),x64312),x64314))+P24(f329(f329(f243(x64311),x64312),f329(f329(f115(x64311),x64313),x64314)))
% 187.33/188.05 [6432]~P102(x64321)+~P24(f329(f329(f243(x64321),x64322),x64323))+P24(f329(f329(f243(x64321),x64322),f329(f329(f115(x64321),x64323),x64324)))
% 187.33/188.05 [6434]~P27(x64341)+~P24(f329(f329(f243(x64341),x64342),x64344))+P24(f329(f329(f243(x64341),x64342),f329(f329(f242(x64341),x64343),x64344)))
% 187.33/188.05 [6436]~P27(x64361)+~P24(f329(f329(f243(x64361),x64362),x64363))+P24(f329(f329(f243(x64361),x64362),f329(f329(f242(x64361),x64363),x64364)))
% 187.33/188.05 [6437]~P102(x64371)+~P24(f329(f329(f244(x64371),x64372),x64374))+P24(f329(f329(f244(x64371),x64372),f329(f329(f115(x64371),x64373),x64374)))
% 187.33/188.05 [6438]~P102(x64381)+~P24(f329(f329(f244(x64381),x64382),x64383))+P24(f329(f329(f244(x64381),x64382),f329(f329(f115(x64381),x64383),x64384)))
% 187.33/188.05 [6440]~P27(x64401)+~P24(f329(f329(f244(x64401),x64402),x64404))+P24(f329(f329(f244(x64401),x64402),f329(f329(f242(x64401),x64403),x64404)))
% 187.33/188.05 [6442]~P27(x64421)+~P24(f329(f329(f244(x64421),x64422),x64423))+P24(f329(f329(f244(x64421),x64422),f329(f329(f242(x64421),x64423),x64424)))
% 187.33/188.05 [6529]~E(f329(f329(f163(x65291),x65292),x65293),x65294)+E(f329(f329(f157(x65291,x65292),x65293),x65294),x65292)+~P24(f329(f329(f244(a874),x65293),f329(f194(f875(x65291)),x65292)))
% 187.33/188.05 [6546]E(x65461,x65462)+P24(f329(x65463,x65461))+~P24(f329(f329(f199(f32(x65463,x65464)),x65461),x65462))
% 187.33/188.05 [6570]P24(f329(x65701,x65702))+~P24(f329(x65703,x65702))+~P24(f329(f329(f243(f881(x65704,a869)),x65703),x65701))
% 187.33/188.05 [6602]~E(f329(f329(f157(x66021,x66022),x66023),x66024),x66022)+E(f329(f329(f163(x66021),x66022),x66023),x66024)+~P24(f329(f329(f244(a874),x66023),f329(f194(f875(x66021)),x66022)))
% 187.33/188.05 [6617]~P24(f329(f158(x66171,x66172),x66174))+~P24(f329(f158(x66171,x66172),x66173))+P24(f329(f158(x66171,x66172),f329(f329(f126(x66171),x66173),x66174)))
% 187.33/188.05 [6713]P34(x67131,x67132,x67133)+~P34(x67131,f329(a117,x67132),f560(x67132,x67134,x67131))+~P24(f329(f329(f331(f873(x67131)),x67133),x67134))
% 187.33/188.05 [6722]E(x67221,f193(f881(x67222,a869)))+E(x67223,f193(f881(x67224,a869)))+~E(f329(f329(f266(x67224,x67222),x67223),f329(f16(f881(x67222,a869),x67224),x67221)),f193(f881(f880(x67224,x67222),a869)))
% 187.33/188.05 [6741]E(x67411,x67412)+P24(f329(f329(f331(x67413),x67411),x67414))+~P24(f329(f329(f331(x67413),x67411),f329(f329(f307(x67413),x67412),x67414)))
% 187.33/188.05 [6758]~P27(x67581)+P24(f329(f329(f243(x67581),x67582),x67583))+~P24(f329(f329(f243(x67581),x67582),f329(f329(f241(x67581),x67584),x67583)))
% 187.33/188.05 [6760]~P27(x67601)+P24(f329(f329(f243(x67601),x67602),x67603))+~P24(f329(f329(f243(x67601),x67602),f329(f329(f241(x67601),x67603),x67604)))
% 187.33/188.05 [6762]~P103(x67621)+P24(f329(f329(f243(x67621),x67622),x67623))+~P24(f329(f329(f243(x67621),x67622),f329(f329(f106(x67621),x67624),x67623)))
% 187.33/188.05 [6764]~P103(x67641)+P24(f329(f329(f243(x67641),x67642),x67643))+~P24(f329(f329(f243(x67641),x67642),f329(f329(f106(x67641),x67643),x67644)))
% 187.33/188.05 [6765]~P27(x67651)+P24(f329(f329(f244(x67651),x67652),x67653))+~P24(f329(f329(f244(x67651),x67652),f329(f329(f241(x67651),x67654),x67653)))
% 187.33/188.05 [6766]~P27(x67661)+P24(f329(f329(f244(x67661),x67662),x67663))+~P24(f329(f329(f244(x67661),x67662),f329(f329(f241(x67661),x67663),x67664)))
% 187.33/188.05 [6788]~E(f329(f329(f163(x67881),x67883),x67884),x67882)+P24(f329(f329(f331(x67881),x67882),f329(f171(x67881),x67883)))+~P24(f329(f329(f244(a874),x67884),f329(f194(f875(x67881)),x67883)))
% 187.33/188.05 [6800]~P27(x68001)+~P33(x68001,f329(f329(f149(x68001),x68002),f329(f329(f149(x68001),x68003),x68004)))+P24(f329(f329(f243(x68001),x68002),x68003))
% 187.33/188.05 [6942]~P36(x69422,x69421,x69423)+P24(f329(x69421,f329(f329(f163(x69422),x69423),x69424)))+~P24(f329(f329(f244(a874),x69424),f329(f194(f875(x69422)),x69423)))
% 187.33/188.05 [6961]E(x69611,f2(a1))+E(f329(f329(f39(a1),x69612),x69611),x69613)+~P24(f329(f49(x69612,x69611),f329(f329(f264(a1,a1),x69613),x69614)))
% 187.33/188.05 [6982]E(f45(a1,x69822,x69821),x69823)+E(x69821,f2(a1))+~P24(f329(f49(x69822,x69821),f329(f329(f264(a1,a1),x69824),x69823)))
% 187.33/188.05 [7103]P24(f329(f329(f331(x71031),x71032),x71033))+~P24(f329(f329(f331(x71031),x71032),x71034))+~P24(f329(f329(f244(f881(x71031,a869)),x71034),x71033))
% 187.33/188.05 [7104]P24(f329(f329(f331(x71041),x71042),x71043))+~P24(f329(f329(f331(x71041),x71042),x71044))+~P24(f329(f329(f243(f881(x71041,a869)),x71044),x71043))
% 187.33/188.05 [7212]P38(x72121,x72122,x72123)+~P24(f329(x72122,f329(f329(f163(x72121),x72123),x72124)))+~P24(f329(f329(f244(a874),x72124),f329(f194(f875(x72121)),x72123)))
% 187.33/188.05 [7323]~P26(x73232)+~P24(f329(f329(f244(f881(x73231,x73232)),x73233),x73234))+P24(f329(f329(f243(f881(x73231,x73232)),x73233),x73234))
% 187.33/188.05 [7411]~P20(x74111,x74112,x74114)+P20(x74111,x74112,f329(f329(f307(f873(x74111)),x74113),x74114))+~P20(x74111,x74112,f329(f329(f307(f873(x74111)),x74113),f193(f881(f873(x74111),a869))))
% 187.33/188.05 [7456]~P24(f329(f329(f331(x74561),x74562),x74564))+P24(f329(f329(f331(x74561),x74562),f40(f881(x74561,a869),x74563)))+~P24(f329(f329(f331(f881(x74561,a869)),x74564),x74563))
% 187.33/188.05 [7468]P34(x74681,x74682,x74683)+P24(f329(f329(f331(f873(x74681)),f560(x74682,x74684,x74681)),x74684))+~P24(f329(f329(f331(f873(x74681)),x74683),x74684))
% 187.33/188.05 [7488]~P85(x74881)+~P24(f329(f329(f243(x74881),x74883),x74884))+P24(f329(f329(f243(x74881),f329(f329(f80(x74881),x74882),x74883)),f329(f329(f80(x74881),x74882),x74884)))
% 187.33/188.05 [7489]~P86(x74891)+~P24(f329(f329(f243(x74891),x74893),x74894))+P24(f329(f329(f243(x74891),f329(f329(f80(x74891),x74892),x74893)),f329(f329(f80(x74891),x74892),x74894)))
% 187.33/188.05 [7490]~P85(x74901)+~P24(f329(f329(f243(x74901),x74902),x74904))+P24(f329(f329(f243(x74901),f329(f329(f80(x74901),x74902),x74903)),f329(f329(f80(x74901),x74904),x74903)))
% 187.33/188.05 [7491]~P86(x74911)+~P24(f329(f329(f243(x74911),x74912),x74914))+P24(f329(f329(f243(x74911),f329(f329(f80(x74911),x74912),x74913)),f329(f329(f80(x74911),x74914),x74913)))
% 187.33/188.05 [7492]~P84(x74921)+~P24(f329(f329(f244(x74921),x74923),x74924))+P24(f329(f329(f244(x74921),f329(f329(f80(x74921),x74922),x74923)),f329(f329(f80(x74921),x74922),x74924)))
% 187.33/188.05 [7493]~P85(x74931)+~P24(f329(f329(f244(x74931),x74933),x74934))+P24(f329(f329(f244(x74931),f329(f329(f80(x74931),x74932),x74933)),f329(f329(f80(x74931),x74932),x74934)))
% 187.33/188.05 [7494]~P84(x74941)+~P24(f329(f329(f244(x74941),x74942),x74944))+P24(f329(f329(f244(x74941),f329(f329(f80(x74941),x74942),x74943)),f329(f329(f80(x74941),x74944),x74943)))
% 187.33/188.05 [7495]~P85(x74951)+~P24(f329(f329(f244(x74951),x74952),x74954))+P24(f329(f329(f244(x74951),f329(f329(f80(x74951),x74952),x74953)),f329(f329(f80(x74951),x74954),x74953)))
% 187.33/188.05 [7504]~P107(x75041)+~P95(x75041)+E(f329(f329(f22(x75041),f329(f329(f81(x75041),x75042),f329(f108(x75041),x75043))),f329(f329(f81(x75041),x75044),f329(f108(x75041),x75043))),f329(f329(f81(x75041),f329(f329(f22(x75041),x75042),x75044)),f329(f108(x75041),x75043)))
% 187.33/188.05 [7505]~P135(x75051)+~P95(x75051)+E(f329(f329(f80(x75051),f329(f329(f81(x75051),x75052),f329(f108(x75051),x75053))),f329(f329(f81(x75051),x75054),f329(f108(x75051),x75053))),f329(f329(f81(x75051),f329(f329(f80(x75051),x75052),x75054)),f329(f108(x75051),x75053)))
% 187.33/188.05 [7540]~P72(x75401)+E(f329(f329(f80(x75401),f329(x75402,x75403)),f329(f329(f6(a874,x75401),x75402),f300(a874,f329(a117,x75403),x75404))),f329(f329(f6(a874,x75401),x75402),f300(a874,x75403,x75404)))+~P24(f329(f329(f243(a874),x75403),x75404))
% 187.33/188.05 [7551]~P21(x75512,x75511,x75513,f329(f171(x75512),x75514))+~P24(f329(f135(x75512),x75514))+P24(f329(f135(x75511),f329(f329(f152(x75512,x75511),x75513),x75514)))
% 187.33/188.05 [7598]~P24(f329(f329(f243(a874),x75982),x75984))+~P24(f329(f329(f243(a874),x75981),x75983))+P24(f329(f329(f243(a874),f329(f329(f81(a874),x75981),x75982)),f329(f329(f81(a874),x75983),x75984)))
% 187.33/188.05 [7599]~P24(f329(f329(f243(a874),x75992),x75994))+~P24(f329(f329(f243(a874),x75991),x75993))+P24(f329(f329(f243(a874),f329(f329(f80(a874),x75991),x75992)),f329(f329(f80(a874),x75993),x75994)))
% 187.33/188.05 [7602]~P24(f329(f329(f244(a874),x76022),x76024))+~P24(f329(f329(f244(a874),x76021),x76023))+P24(f329(f329(f244(a874),f329(f329(f80(a874),x76021),x76022)),f329(f329(f80(a874),x76023),x76024)))
% 187.33/188.05 [7603]~P24(f329(f329(f243(a1),x76032),x76034))+~P24(f329(f329(f244(a1),x76031),x76033))+P24(f329(f329(f244(a1),f329(f329(f80(a1),x76031),x76032)),f329(f329(f80(a1),x76033),x76034)))
% 187.33/188.05 [7651]P24(f329(f329(f331(x76511),x76512),x76513))+~P24(f329(f329(f331(x76511),x76512),f41(f881(x76511,a869),x76514)))+~P24(f329(f329(f331(f881(x76511,a869)),x76513),x76514))
% 187.33/188.05 [7667]~P24(f329(x76671,f676(x76671,x76673,x76672)))+P24(f329(x76671,f329(f329(f163(x76672),x76673),x76674)))+~P24(f329(f329(f244(a874),x76674),f329(f194(f875(x76672)),x76673)))
% 187.33/188.05 [7673]P24(f329(x76731,x76732))+~P24(f329(f329(f331(x76734),x76732),f329(f171(x76734),x76733)))+P24(f329(f329(f244(a874),f678(x76731,x76733,x76734)),f329(f194(f875(x76734)),x76733)))
% 187.33/188.05 [7693]~P24(f329(f329(f199(x76932),x76933),x76934))+~P24(f329(f329(f199(f32(x76931,x76932)),x76934),x76933))+P24(f329(f329(f199(f32(x76931,x76932)),x76933),x76933))
% 187.33/188.05 [7722]~P26(x77221)+~P24(f329(f329(f244(f881(x77222,x77221)),x77224),x77223))+~P24(f329(f329(f243(f881(x77222,x77221)),x77223),x77224))
% 187.33/188.05 [7770]~P24(f329(x77704,x77702))+~P24(f329(f329(f331(x77701),x77702),x77703))+P24(f329(f329(f331(x77701),x77702),f329(f329(f106(f881(x77701,a869)),x77703),f329(f249(x77701),x77704))))
% 187.33/188.05 [7915]~P24(f329(f329(f331(x79151),x79153),x79154))+~P24(f329(f329(f244(f881(x79151,a869)),x79152),x79154))+P24(f329(f329(f244(f881(x79151,a869)),x79152),f329(f329(f307(x79151),x79153),x79154)))
% 187.33/188.05 [7917]E(f329(f329(f106(f881(x79171,a869)),x79172),x79173),f193(f881(x79171,a869)))+~E(f329(f329(f106(f881(x79171,a869)),f40(f881(x79171,a869),x79174)),x79173),f193(f881(x79171,a869)))+~P24(f329(f329(f331(f881(x79171,a869)),x79172),x79174))
% 187.33/188.05 [7993]P24(f329(f329(f331(x79931),x79932),x79933))+~P24(f329(f329(f243(f881(x79931,a869)),x79933),f329(f329(f307(x79931),x79932),x79934)))+P24(f329(f329(f243(f881(x79931,a869)),x79933),x79934))
% 187.33/188.05 [8015]P24(f329(f329(f331(x80152),f676(x80151,x80153,x80152)),f329(f171(x80152),x80153)))+P24(f329(x80151,f329(f329(f163(x80152),x80153),x80154)))+~P24(f329(f329(f244(a874),x80154),f329(f194(f875(x80152)),x80153)))
% 187.33/188.05 [8023]~P24(f329(f329(f243(f881(x80231,a869)),x80232),x80234))+P24(f329(f329(f243(f881(x80231,a869)),x80232),x80233))+~P24(f329(f329(f243(f881(x80231,a869)),x80234),x80233))
% 187.33/188.05 [8024]~P24(f329(f329(f244(f881(x80241,a869)),x80242),x80244))+~P24(f329(f329(f243(f881(x80241,a869)),x80244),x80243))+P24(f329(f329(f244(f881(x80241,a869)),x80242),x80243))
% 187.33/188.05 [8025]~P24(f329(f329(f243(f881(x80251,a869)),x80252),x80254))+~P24(f329(f329(f244(f881(x80251,a869)),x80254),x80253))+P24(f329(f329(f244(f881(x80251,a869)),x80252),x80253))
% 187.33/188.05 [8026]~P24(f329(f329(f244(f881(x80261,a869)),x80262),x80264))+P24(f329(f329(f244(f881(x80261,a869)),x80262),x80263))+~P24(f329(f329(f244(f881(x80261,a869)),x80264),x80263))
% 187.33/188.05 [8066]~P24(f329(f329(f331(x80661),x80664),x80663))+~P24(f329(f329(f244(f881(x80661,a869)),x80662),f329(f329(f307(x80661),x80664),x80663)))+P24(f329(f329(f244(f881(x80661,a869)),x80662),x80663))
% 187.33/188.05 [8078]~P85(x80781)+P24(f329(f329(f243(x80781),x80782),x80783))+~P24(f329(f329(f243(x80781),f329(f329(f80(x80781),x80784),x80782)),f329(f329(f80(x80781),x80784),x80783)))
% 187.33/188.05 [8080]~P85(x80801)+P24(f329(f329(f243(x80801),x80802),x80803))+~P24(f329(f329(f243(x80801),f329(f329(f80(x80801),x80802),x80804)),f329(f329(f80(x80801),x80803),x80804)))
% 187.33/188.05 [8082]~P85(x80821)+P24(f329(f329(f244(x80821),x80822),x80823))+~P24(f329(f329(f244(x80821),f329(f329(f80(x80821),x80824),x80822)),f329(f329(f80(x80821),x80824),x80823)))
% 187.33/188.05 [8084]~P85(x80841)+P24(f329(f329(f244(x80841),x80842),x80843))+~P24(f329(f329(f244(x80841),f329(f329(f80(x80841),x80842),x80844)),f329(f329(f80(x80841),x80843),x80844)))
% 187.33/188.05 [8132]P24(f329(x81321,x81322))+~E(f329(f329(f136(x81323),f329(f194(f875(x81323)),f176(x81323,x81321,x81324))),x81324),f118(x81323))+~P24(f329(f329(f331(x81323),x81322),f329(f171(x81323),x81324)))
% 187.33/188.05 [8258]P24(f329(x82581,x82582))+~P24(f329(f329(f331(x82583),x82582),f329(f171(x82583),x82584)))+P24(f329(f329(f244(a874),f329(f194(f875(x82583)),f329(f134(x82583,x82581),x82584))),f329(f194(f875(x82583)),x82584)))
% 187.33/188.05 [8384]E(x83841,x83842)+P24(f329(f329(f199(x83843),x83841),f606(x83842,x83841,x83843,x83844)))+~P24(f329(f329(f199(f32(x83844,x83843)),x83841),x83842))
% 187.33/188.05 [8415]~P24(f329(x84154,x84152))+P24(f329(f329(f199(x84151),x84152),f606(x84153,x84152,x84151,x84154)))+~P24(f329(f329(f199(f32(x84154,x84151)),x84152),x84153))
% 187.33/188.05 [8734]~P24(f329(x87341,f783(x87341,x87343,x87342,x87344)))+P24(f329(x87341,f329(f329(f163(x87342),x87343),x87344)))+~P24(f329(f329(f244(a874),x87344),f329(f194(f875(x87342)),x87343)))
% 187.33/188.05 [8757]~P21(x87574,x87573,x87571,f252(f881(x87574,a869)))+E(f329(x87571,f511(x87572,x87571,x87573,x87574)),x87572)+~P24(f329(f329(f331(x87573),x87572),f329(f308(x87574,x87573,x87571),f252(f881(x87574,a869)))))
% 187.33/188.05 [8822]E(f176(x88221,x88222,x88223),f329(f329(f174(x88221),x88224),x88223))+P24(f329(f329(f244(a874),f758(x88222,x88223,x88221,x88224)),x88224))+P24(f329(f329(f244(a874),x88224),f329(f194(f875(x88221)),x88223)))
% 187.33/188.05 [8825]E(f176(x88251,x88252,x88253),f329(f329(f174(x88251),x88254),x88253))+P24(f329(f329(f244(a874),f758(x88252,x88253,x88251,x88254)),x88254))+P24(f329(x88252,f329(f329(f163(x88251),x88253),x88254)))
% 187.33/188.05 [8854]P24(f329(x88541,x88542))+~P24(f329(f329(f331(x88544),x88542),f329(f171(x88544),x88543)))+P24(f329(f329(f244(a874),f735(x88542,x88541,x88543,x88544)),f329(f194(f875(x88544)),x88543)))
% 187.33/188.05 [8857]E(f176(x88571,x88572,x88573),f329(f329(f174(x88571),x88574),x88573))+P24(f329(f329(f244(a874),x88574),f329(f194(f875(x88571)),x88573)))+P24(f329(f329(f244(a874),f758(x88572,x88573,x88571,x88574)),f329(f194(f875(x88571)),x88573)))
% 187.33/188.05 [8864]E(f176(x88641,x88642,x88643),f329(f329(f174(x88641),x88644),x88643))+P24(f329(x88642,f329(f329(f163(x88641),x88643),x88644)))+P24(f329(f329(f244(a874),f758(x88642,x88643,x88641,x88644)),f329(f194(f875(x88641)),x88643)))
% 187.33/188.05 [8890]~P121(x88904)+P24(f329(f329(f331(x88901),f662(x88902,x88903,x88901,x88904)),x88903))+P24(f329(f329(f244(x88904),f2(x88904)),f329(f329(f9(x88901,x88904),x88902),x88903)))
% 187.33/188.05 [8891]~P121(x88914)+P24(f329(f329(f331(x88911),f663(x88912,x88913,x88911,x88914)),x88913))+P24(f329(f329(f243(x88914),f2(x88914)),f329(f329(f9(x88911,x88914),x88912),x88913)))
% 187.33/188.05 [8925]~P24(f329(f62(x89251),x89254))+P24(f329(f329(f331(x89251),f535(x89252,x89253,x89254,x89251)),x89254))+P24(f329(f62(f880(x89251,x89253)),f329(f329(f266(x89251,x89253),x89254),x89252)))
% 187.33/188.05 [8959]P24(f329(f329(f331(x89592),f783(x89591,x89593,x89592,x89594)),f329(f171(x89592),x89593)))+P24(f329(x89591,f329(f329(f163(x89592),x89593),x89594)))+~P24(f329(f329(f244(a874),x89594),f329(f194(f875(x89592)),x89593)))
% 187.33/188.05 [8974]E(x89741,x89742)+P24(f329(f329(f199(f32(x89743,x89744)),f606(x89741,x89742,x89744,x89743)),x89741))+~P24(f329(f329(f199(f32(x89743,x89744)),x89742),x89741))
% 187.33/188.05 [8995]~P24(f329(x89951,x89954))+P24(f329(f329(f199(f32(x89951,x89952)),f606(x89953,x89954,x89952,x89951)),x89953))+~P24(f329(f329(f199(f32(x89951,x89952)),x89954),x89953))
% 187.33/188.05 [9090]P24(f329(f329(f243(a874),x90904),f329(f194(f875(x90902)),f176(x90902,x90903,x90901))))+P24(f329(f329(f244(a874),f759(x90901,x90902,x90903,x90904)),x90904))+~P24(f329(f329(f243(a874),x90904),f329(f194(f875(x90902)),x90901)))
% 187.33/188.05 [9194]~E(f329(f329(f177(x91941,x91942),x91943),f770(x91944,x91943,x91942,x91941)),f329(f329(f177(x91941,x91942),x91944),f770(x91944,x91943,x91942,x91941)))+E(f329(f177(x91941,x91942),x91943),f329(f177(x91941,x91942),x91944))+~E(f329(f171(x91941),f329(f329(f152(f880(x91941,x91942),x91941),f263(x91941,x91942)),x91943)),f329(f171(x91941),f329(f329(f152(f880(x91941,x91942),x91941),f263(x91941,x91942)),x91944)))
% 187.33/188.05 [9240]E(f176(x92401,x92402,x92403),f329(f329(f174(x92401),x92404),x92403))+~P24(f329(x92402,f329(f329(f163(x92401),x92403),f758(x92402,x92403,x92401,x92404))))+P24(f329(f329(f244(a874),x92404),f329(f194(f875(x92401)),x92403)))
% 187.33/188.05 [9246]E(f176(x92461,x92462,x92463),f329(f329(f174(x92461),x92464),x92463))+~P24(f329(x92462,f329(f329(f163(x92461),x92463),f758(x92462,x92463,x92461,x92464))))+P24(f329(x92462,f329(f329(f163(x92461),x92463),x92464)))
% 187.33/188.05 [9253]~P24(f329(f62(x92531),x92533))+~P24(f329(f62(x92532),f329(x92534,f535(x92534,x92532,x92533,x92531))))+P24(f329(f62(f880(x92531,x92532)),f329(f329(f266(x92531,x92532),x92533),x92534)))
% 187.33/188.05 [9261]~P121(x92611)+~P24(f329(f329(f243(x92611),f2(x92611)),f329(x92613,f663(x92613,x92614,x92612,x92611))))+P24(f329(f329(f243(x92611),f2(x92611)),f329(f329(f9(x92612,x92611),x92613),x92614)))
% 187.33/188.05 [9262]~P121(x92621)+~P24(f329(f329(f244(x92621),f2(x92621)),f329(x92623,f662(x92623,x92624,x92622,x92621))))+P24(f329(f329(f244(x92621),f2(x92621)),f329(f329(f9(x92622,x92621),x92623),x92624)))
% 187.33/188.05 [9268]~E(f329(f194(f875(x92684)),x92682),f329(f194(f875(x92684)),x92683))+P24(f329(f329(f331(f880(f875(x92684),f875(x92684))),f329(f329(f264(f875(x92684),f875(x92684)),x92683),x92682)),f156(x92684,x92681)))+P24(f329(f329(f244(a874),f664(x92681,x92682,x92683,x92684)),f329(f194(f875(x92684)),x92683)))
% 187.33/188.05 [9322]~P24(f329(x93223,f329(f329(f163(x93222),x93224),f759(x93224,x93222,x93223,x93221))))+P24(f329(f329(f243(a874),x93221),f329(f194(f875(x93222)),f176(x93222,x93223,x93224))))+~P24(f329(f329(f243(a874),x93221),f329(f194(f875(x93222)),x93224)))
% 187.33/188.05 [9398]E(f329(f329(f174(x93981),f677(x93982,x93983,x93984,x93981)),x93983),f329(f329(f174(x93981),f677(x93982,x93983,x93984,x93981)),x93984))+~P24(f329(f329(f331(f880(f875(x93981),f875(x93981))),f329(f329(f264(f875(x93981),f875(x93981)),x93984),x93983)),f145(x93981,x93982)))+P24(f329(f329(f244(a874),f329(f194(f875(x93981)),x93984)),f329(f194(f875(x93981)),x93983)))
% 187.33/188.05 [9452]~P24(f329(f329(f244(a874),f2(a874)),x94523))+~P24(f329(f329(f244(a874),x94524),x94521))+P24(f329(f329(f244(a874),f329(f329(f80(a874),f329(f329(f81(a874),x94521),f45(a874,x94522,x94523))),x94524)),f329(f329(f81(a874),x94521),x94523)))
% 187.33/188.05 [9644]~P26(x96442)+~P24(f329(f329(f243(x96442),f329(x96443,f669(x96444,x96443,x96441,x96442))),f329(x96444,f669(x96444,x96443,x96441,x96442))))+P24(f329(f329(f243(f881(x96441,x96442)),x96443),x96444))
% 187.33/188.05 [9748]~P69(x97481)+E(f329(f329(f6(a874,x97481),f329(f329(f18(a874,x97481,x97481),f329(f329(f8(x97481,f881(x97481,x97481),a874),f22(x97481)),x97482)),f329(f329(f8(a874,x97481,a874),x97482),f329(f329(f7(a874,a874,a874),f80(a874)),f78(a874))))),f300(a874,x97483,x97484)),f329(f329(f22(x97481),f329(x97482,x97483)),f329(x97482,f329(f329(f80(a874),x97484),f78(a874)))))+~P24(f329(f329(f243(a874),x97483),x97484))
% 187.33/188.05 [6792]E(f329(f329(f126(x67921),x67922),x67923),x67924)+~E(x67923,f329(f329(f136(x67921),f329(f194(f875(x67921)),x67922)),x67924))+~E(f329(f329(f174(x67921),f329(f194(f875(x67921)),x67922)),x67924),x67922)
% 187.33/188.05 [6848]~P62(x68482)+E(x68481,f2(x68482))+E(f329(f329(f287(x68482),f329(f329(f254(x68482),x68483),x68484)),f329(f329(f254(x68482),x68481),x68484)),f329(f329(f254(x68482),f329(f329(f287(x68482),x68483),x68481)),x68484))
% 187.33/188.05 [6984]~E(f329(f194(f875(x69841)),x69843),f329(f194(f875(x69842)),x69844))+~P24(f329(f135(x69841),x69843))+E(f183(x69841,x69842,f329(f177(x69841,x69842),f329(f329(f181(x69841,x69842),x69843),x69844))),f329(f171(x69841),x69843))
% 187.33/188.05 [7003]~P103(x70031)+~P24(f329(f329(f243(x70031),x70033),x70034))+P24(f329(f329(f243(x70031),f329(f329(f106(x70031),x70032),x70033)),x70034))
% 187.33/188.05 [7004]~P103(x70041)+~P24(f329(f329(f243(x70041),x70042),x70044))+P24(f329(f329(f243(x70041),f329(f329(f106(x70041),x70042),x70043)),x70044))
% 187.33/188.05 [7006]~P27(x70061)+~P24(f329(f329(f243(x70061),x70063),x70064))+P24(f329(f329(f243(x70061),f329(f329(f241(x70061),x70062),x70063)),x70064))
% 187.33/188.05 [7008]~P27(x70081)+~P24(f329(f329(f243(x70081),x70082),x70084))+P24(f329(f329(f243(x70081),f329(f329(f241(x70081),x70082),x70083)),x70084))
% 187.33/188.05 [7009]~P103(x70091)+~P24(f329(f329(f244(x70091),x70093),x70094))+P24(f329(f329(f244(x70091),f329(f329(f106(x70091),x70092),x70093)),x70094))
% 187.33/188.05 [7010]~P103(x70101)+~P24(f329(f329(f244(x70101),x70102),x70104))+P24(f329(f329(f244(x70101),f329(f329(f106(x70101),x70102),x70103)),x70104))
% 187.33/188.05 [7012]~P27(x70121)+~P24(f329(f329(f244(x70121),x70123),x70124))+P24(f329(f329(f244(x70121),f329(f329(f241(x70121),x70122),x70123)),x70124))
% 187.33/188.05 [7014]~P27(x70141)+~P24(f329(f329(f244(x70141),x70142),x70144))+P24(f329(f329(f244(x70141),f329(f329(f241(x70141),x70142),x70143)),x70144))
% 187.33/188.05 [7034]~P24(f329(x70343,x70344))+~P24(f329(x70342,x70344))+P24(f329(f329(f329(f106(f881(x70341,a869)),x70342),x70343),x70344))
% 187.33/188.05 [7158]P20(x71581,x71582,x71583)+~P20(x71581,x71584,x71583)+~P24(f329(f329(f243(f881(f873(x71581),a869)),x71584),x71582))
% 187.33/188.05 [7159]P20(x71591,x71592,x71593)+~P20(x71591,x71592,x71594)+~P24(f329(f329(f243(f881(f873(x71591),a869)),x71593),x71594))
% 187.33/188.05 [7530]~P72(x75301)+E(f329(f329(f80(x75301),f329(x75302,x75303)),f329(f329(f6(a874,x75301),x75302),f329(f299(a874,f329(a117,x75303)),x75304))),f329(f329(f6(a874,x75301),x75302),f329(f299(a874,x75303),x75304)))+~P24(f329(f329(f244(a874),x75303),x75304))
% 187.33/188.05 [7559]~P27(x75591)+P24(f329(f329(f243(x75591),x75592),x75593))+~P24(f329(f329(f243(x75591),f329(f329(f242(x75591),x75594),x75592)),x75593))
% 187.33/188.05 [7561]~P27(x75611)+P24(f329(f329(f243(x75611),x75612),x75613))+~P24(f329(f329(f243(x75611),f329(f329(f242(x75611),x75612),x75614)),x75613))
% 187.33/188.05 [7563]~P102(x75631)+P24(f329(f329(f243(x75631),x75632),x75633))+~P24(f329(f329(f243(x75631),f329(f329(f115(x75631),x75634),x75632)),x75633))
% 187.33/188.05 [7565]~P102(x75651)+P24(f329(f329(f243(x75651),x75652),x75653))+~P24(f329(f329(f243(x75651),f329(f329(f115(x75651),x75652),x75654)),x75653))
% 187.33/188.05 [7566]~P27(x75661)+P24(f329(f329(f244(x75661),x75662),x75663))+~P24(f329(f329(f244(x75661),f329(f329(f242(x75661),x75664),x75662)),x75663))
% 187.33/188.05 [7567]~P27(x75671)+P24(f329(f329(f244(x75671),x75672),x75673))+~P24(f329(f329(f244(x75671),f329(f329(f242(x75671),x75672),x75674)),x75673))
% 187.33/188.05 [7643]~P24(f329(f329(f331(x76431),x76432),x76434))+P24(f329(f329(f331(x76431),x76432),x76433))+P24(f329(f329(f331(x76431),x76432),f329(f329(f22(f881(x76431,a869)),x76434),x76433)))
% 187.33/188.05 [7729]P24(f329(x77291,x77292))+P24(f329(x77293,x77292))+~P24(f329(f329(f329(f115(f881(x77294,a869)),x77293),x77291),x77292))
% 187.33/188.05 [7740]~P24(f329(f329(f331(x77401),x77402),x77404))+~P24(f329(f329(f331(x77401),x77402),x77403))+P24(f329(f329(f331(x77401),x77402),f329(f329(f106(f881(x77401,a869)),x77403),x77404)))
% 187.33/188.05 [7794]~P102(x77941)+~P24(f329(f62(x77941),x77944))+E(f329(f329(f65(x77941,x77941,f115(x77941)),x77942),f329(f329(f307(x77941),x77943),x77944)),f329(f329(f115(x77941),x77943),f329(f329(f65(x77941,x77941,f115(x77941)),x77942),x77944)))
% 187.33/188.05 [7795]~P103(x77951)+~P24(f329(f62(x77951),x77954))+E(f329(f329(f65(x77951,x77951,f106(x77951)),x77952),f329(f329(f307(x77951),x77953),x77954)),f329(f329(f106(x77951),x77953),f329(f329(f65(x77951,x77951,f106(x77951)),x77952),x77954)))
% 187.33/188.05 [7796]~P27(x77961)+~P24(f329(f62(x77961),x77964))+E(f329(f329(f65(x77961,x77961,f241(x77961)),x77962),f329(f329(f307(x77961),x77963),x77964)),f329(f329(f241(x77961),x77963),f329(f329(f65(x77961,x77961,f241(x77961)),x77962),x77964)))
% 187.33/188.05 [7797]~P27(x77971)+~P24(f329(f62(x77971),x77974))+E(f329(f329(f65(x77971,x77971,f242(x77971)),x77972),f329(f329(f307(x77971),x77973),x77974)),f329(f329(f242(x77971),x77973),f329(f329(f65(x77971,x77971,f242(x77971)),x77972),x77974)))
% 187.33/188.05 [7798]~P107(x77981)+~P95(x77981)+E(f329(f329(f22(x77981),f329(f329(f81(x77981),f329(f108(x77981),x77982)),x77983)),f329(f329(f81(x77981),f329(f108(x77981),x77982)),x77984)),f329(f329(f81(x77981),f329(f108(x77981),x77982)),f329(f329(f22(x77981),x77983),x77984)))
% 187.33/188.05 [7799]~P135(x77991)+~P95(x77991)+E(f329(f329(f80(x77991),f329(f329(f81(x77991),f329(f108(x77991),x77992)),x77993)),f329(f329(f81(x77991),f329(f108(x77991),x77992)),x77994)),f329(f329(f81(x77991),f329(f108(x77991),x77992)),f329(f329(f80(x77991),x77993),x77994)))
% 187.33/188.05 [7913]E(x79131,x79132)+P24(f329(f329(f331(x79133),x79131),f329(f171(x79133),x79134)))+~P24(f329(f329(f331(x79133),x79131),f329(f171(x79133),f329(f329(f149(x79133),x79132),x79134))))
% 187.33/188.05 [7938]~P60(x79381)+~E(f329(f194(f875(x79382)),x79383),f329(f194(f875(x79381)),f56(x79381)))+E(f329(f329(f177(x79381,x79382),f329(f329(f181(x79381,x79382),f56(x79381)),x79383)),x79384),f329(f236(x79382),f734(x79384,x79383,x79382,x79381)))
% 187.33/188.05 [8091]P54(x80911,x80912,x80913)+~P54(x80911,x80912,x80914)+~P24(f329(f329(f243(f881(f880(x80911,x80912),a869)),x80913),x80914))
% 187.33/188.05 [8135]P24(f329(f329(f331(x81351),x81352),x81353))+P24(f329(f329(f331(x81351),x81352),x81354))+~P24(f329(f329(f331(x81351),x81352),f329(f329(f115(f881(x81351,a869)),x81354),x81353)))
% 187.33/188.05 [8146]~P44(x81461,x81464,x81463)+~P24(f329(f329(f331(x81461),x81462),x81464))+P24(f329(f329(f331(f880(x81461,x81461)),f329(f329(f264(x81461,x81461),x81462),x81462)),x81463))
% 187.33/188.05 [8161]~P24(f329(f62(x81612),x81614))+~P24(f329(f62(x81611),x81613))+P24(f329(f62(f880(x81611,x81612)),f329(f329(f266(x81611,x81612),x81613),f329(f16(f881(x81612,a869),x81611),x81614))))
% 187.33/188.05 [8162]~P24(f329(f329(f331(x81621),x81622),x81624))+~P24(f329(f329(f243(f881(x81621,a869)),x81623),x81624))+P24(f329(f329(f243(f881(x81621,a869)),f329(f329(f307(x81621),x81622),x81623)),x81624))
% 187.33/188.05 [8170]~P76(x81702)+~P141(x81702)+E(f329(f329(f9(x81701,x81702),f329(f329(f8(a874,x81702,x81701),f105(x81702)),x81703)),x81704),f329(f105(x81702),f329(f329(f9(x81701,a874),x81703),x81704)))
% 187.33/188.05 [8171]~P76(x81712)+~P138(x81712)+E(f329(f329(f9(x81711,x81712),f329(f329(f8(a1,x81712,x81711),f107(x81712)),x81713)),x81714),f329(f107(x81712),f329(f329(f9(x81711,a1),x81713),x81714)))
% 187.33/188.05 [8197]E(f329(f329(f22(f881(x81971,a869)),x81972),f329(f329(f22(f881(x81971,a869)),x81973),x81974)),x81974)+~P24(f329(f329(f243(f881(x81971,a869)),x81972),x81973))+~P24(f329(f329(f243(f881(x81971,a869)),x81974),x81972))
% 187.33/188.05 [8292]~P24(f329(f62(x82921),x82924))+E(f329(f329(f22(a874),f329(f329(f6(x82921,a874),x82922),x82923)),f329(f329(f6(x82921,a874),x82922),x82924)),f329(f329(f6(x82921,a874),x82922),f329(f329(f22(f881(x82921,a869)),x82923),x82924)))+~P24(f329(f329(f243(f881(x82921,a869)),x82924),x82923))
% 187.33/188.05 [8449]~P6(x84491,x84494,x84493)+~P24(f329(f329(f331(x84491),x84492),x84494))+P24(f329(f329(f331(x84491),x84492),f329(f283(x84491,x84491,x84493),f329(f329(f307(x84491),x84492),f193(f881(x84491,a869))))))
% 187.33/188.05 [8512]~P24(f329(f329(f243(f881(x85121,a869)),x85122),x85123))+~P24(f329(f329(f243(f881(x85121,a869)),x85122),x85124))+P24(f329(f329(f243(f881(x85121,a869)),x85122),f329(f329(f106(f881(x85121,a869)),x85123),x85124)))
% 187.33/188.05 [8609]E(x86091,f193(f881(x86092,a869)))+P24(f329(f62(x86093),x86094))+~P24(f329(f62(f880(x86093,x86092)),f329(f329(f266(x86093,x86092),x86094),f329(f16(f881(x86092,a869),x86093),x86091))))
% 187.33/188.05 [8610]E(x86101,f193(f881(x86102,a869)))+P24(f329(f62(x86103),x86104))+~P24(f329(f62(f880(x86102,x86103)),f329(f329(f266(x86102,x86103),x86101),f329(f16(f881(x86103,a869),x86102),x86104))))
% 187.33/188.05 [8677]P24(f329(f329(f331(x86771),x86772),f318(x86771,x86773)))+~P24(f329(f329(f331(x86771),x86774),f318(x86771,x86773)))+~P24(f329(f329(f331(f880(x86771,x86771)),f329(f329(f264(x86771,x86771),x86772),x86774)),x86773))
% 187.33/188.05 [8729]~P42(x87291,x87294)+P24(f329(f329(f331(f880(x87291,x87291)),f329(f329(f264(x87291,x87291),x87293),x87292)),f305(x87291,x87294)))+P42(x87291,f329(f329(f307(f880(x87291,x87291)),f329(f329(f264(x87291,x87291),x87292),x87293)),x87294))
% 187.33/188.05 [8730]~P57(x87301,x87304)+P24(f329(f329(f331(f880(x87301,x87301)),f329(f329(f264(x87301,x87301),x87303),x87302)),f305(x87301,x87304)))+P57(x87301,f329(f329(f307(f880(x87301,x87301)),f329(f329(f264(x87301,x87301),x87302),x87303)),x87304))
% 187.33/188.05 [8807]~E(x88072,x88073)+~P24(f329(f329(f331(x88071),x88072),f329(f171(x88071),x88074)))+P24(f329(f329(f331(f880(x88071,x88071)),f329(f329(f264(x88071,x88071),x88072),x88073)),f329(f171(f880(x88071,x88071)),f329(f329(f181(x88071,x88071),x88074),x88074))))
% 187.33/188.05 [8888]~E(x88883,x88884)+P24(f329(f329(f268(x88881,x88881,a869),a326),x88882))+~P24(f329(f329(f331(f880(x88881,x88881)),x88882),f329(f171(f880(x88881,x88881)),f329(f329(f181(x88881,x88881),x88883),x88884))))
% 187.33/188.05 [8916]~P24(f329(x89164,x89162))+P24(f329(f329(f329(f329(a201,x89161),x89162),x89163),f866(x89163,x89162,x89161,x89164)))+~P24(f329(f329(f329(f329(a201,f32(x89164,x89161)),x89162),x89163),x89162))
% 187.33/188.05 [8943]P24(f329(f329(f331(f880(f875(x89431),f875(x89431))),f329(f329(f264(f875(x89431),f875(x89431)),x89432),x89433)),f145(x89431,x89434)))+~E(f329(f329(f174(x89431),f329(f194(f875(x89431)),x89432)),x89433),x89432)+~P24(f329(f329(f244(a874),f329(f194(f875(x89431)),x89432)),f329(f194(f875(x89431)),x89433)))
% 187.33/188.05 [9042]~P24(f329(f62(x90421),x90424))+P24(f329(f329(f331(x90421),f429(x90422,x90423,x90424,x90421)),x90424))+P24(f329(f62(x90423),f329(f329(f42(x90421,f881(x90423,a869)),x90424),x90422)))
% 187.33/188.05 [9043]~P24(f329(f62(x90431),x90434))+P24(f329(f329(f331(x90431),f470(x90432,x90433,x90434,x90431)),x90434))+P24(f329(f62(x90433),f329(f329(f42(x90431,f881(x90433,a869)),x90434),x90432)))
% 187.33/188.05 [9124]P24(f329(f329(f331(f880(x91241,x91241)),x91242),f329(f329(f286(x91241,x91241,x91241),x91243),f305(x91241,x91243))))+~P24(f329(f329(f244(a874),f2(a874)),x91244))+~P24(f329(f329(f331(f880(x91241,x91241)),x91242),f329(f329(f188(f880(x91241,x91241),a869),x91244),x91243)))
% 187.33/188.05 [9132]~P42(x91321,x91322)+~P24(f329(f329(f331(f880(x91321,x91321)),f329(f329(f264(x91321,x91321),x91324),x91323)),x91322))+~P24(f329(f329(f331(f880(x91321,x91321)),f329(f329(f264(x91321,x91321),x91323),x91324)),x91322))
% 187.33/188.05 [9260]~P24(f329(f62(x92601),x92604))+E(f329(f329(f6(x92601,a874),f329(f329(f8(f881(x92602,a869),a874,x92601),f38(x92602)),x92603)),x92604),f329(f38(f880(x92601,x92602)),f329(f329(f266(x92601,x92602),x92604),x92603)))+P24(f329(f329(f331(x92601),f536(x92603,x92602,x92604,x92601)),x92604))
% 187.33/188.05 [9264]~P24(f329(f135(x92641),x92642))+P24(f329(f135(x92641),f329(f329(f157(x92641,x92642),x92643),x92644)))+P24(f329(f329(f331(x92641),x92644),f329(f329(f22(f881(x92641,a869)),f329(f171(x92641),x92642)),f329(f329(f307(x92641),f329(f329(f163(x92641),x92642),x92643)),f193(f881(x92641,a869))))))
% 187.33/188.05 [9280]~P24(f329(f62(x92802),x92803))+~P24(f329(f62(x92801),f329(x92804,f429(x92804,x92801,x92803,x92802))))+P24(f329(f62(x92801),f329(f329(f42(x92802,f881(x92801,a869)),x92803),x92804)))
% 187.33/188.05 [9281]~P24(f329(f62(x92812),x92813))+~P24(f329(f62(x92811),f329(x92814,f470(x92814,x92811,x92813,x92812))))+P24(f329(f62(x92811),f329(f329(f42(x92812,f881(x92811,a869)),x92813),x92814)))
% 187.33/188.05 [9360]~P24(f329(f329(f331(f880(x93601,x93601)),x93602),f329(f329(f286(x93601,x93601,x93601),x93604),f305(x93601,x93604))))+P24(f329(f329(f331(f880(x93601,x93601)),x93602),f329(f329(f286(x93601,x93601,x93601),x93603),f305(x93601,x93603))))+~P24(f329(f329(f243(f881(f880(x93601,x93601),a869)),x93604),x93603))
% 187.33/188.05 [9367]E(f329(f329(f174(x93671),f677(x93674,x93673,x93672,x93671)),x93673),f329(f329(f174(x93671),f677(x93674,x93673,x93672,x93671)),x93672))+~P24(f329(f329(f331(f880(f875(x93671),f875(x93671))),f329(f329(f264(f875(x93671),f875(x93671)),x93672),x93673)),f145(x93671,x93674)))+E(f329(f329(f174(x93671),f329(f194(f875(x93671)),x93672)),x93673),x93672)
% 187.33/188.05 [9383]~P24(f329(f62(x93831),x93834))+E(f329(f329(f6(x93831,a874),f329(f329(f8(f881(x93832,a869),a874,x93831),f38(x93832)),x93833)),x93834),f329(f38(f880(x93831,x93832)),f329(f329(f266(x93831,x93832),x93834),x93833)))+~P24(f329(f62(x93832),f329(x93833,f536(x93833,x93832,x93834,x93831))))
% 187.33/188.05 [9387]~E(f329(f194(f875(x93871)),x93873),f329(f194(f875(x93871)),x93872))+P24(f329(f329(f331(f880(f875(x93871),f875(x93871))),f329(f329(f264(f875(x93871),f875(x93871)),x93872),x93873)),f156(x93871,x93874)))+P24(f329(f329(f331(f880(x93871,x93871)),f682(x93874,x93873,x93872,x93871)),f329(f171(f880(x93871,x93871)),f329(f329(f181(x93871,x93871),x93872),x93873))))
% 187.33/188.05 [9464]~P24(f329(f329(f331(f880(f875(x94641),f875(x94641))),f329(f329(f264(f875(x94641),f875(x94641)),x94642),x94643)),f145(x94641,x94644)))+E(f329(f329(f174(x94641),f329(f194(f875(x94641)),x94642)),x94643),x94642)+P24(f329(f329(f244(a874),f677(x94644,x94643,x94642,x94641)),f329(f329(f241(a874),f329(f194(f875(x94641)),x94642)),f329(f194(f875(x94641)),x94643))))
% 187.33/188.05 [9465]E(f329(f177(x94651,x94652),x94653),f329(f177(x94651,x94652),x94654))+~E(f329(f171(x94651),f329(f329(f152(f880(x94651,x94652),x94651),f263(x94651,x94652)),x94653)),f329(f171(x94651),f329(f329(f152(f880(x94651,x94652),x94651),f263(x94651,x94652)),x94654)))+P24(f329(f329(f331(x94651),f770(x94653,x94654,x94652,x94651)),f329(f171(x94651),f329(f329(f152(f880(x94651,x94652),x94651),f263(x94651,x94652)),x94654))))
% 187.33/188.05 [9481]~P24(f329(x94811,x94814))+P24(f329(f329(f329(f329(a201,f32(x94811,x94812)),f866(x94813,x94814,x94812,x94811)),x94813),x94814))+~P24(f329(f329(f329(f329(a201,f32(x94811,x94812)),x94814),x94813),x94814))
% 187.33/188.05 [9486]~P24(f329(f329(f331(f880(f875(x94861),f875(x94861))),f329(f329(f264(f875(x94861),f875(x94861)),x94862),x94863)),f145(x94861,x94864)))+P24(f329(f329(f244(a874),f329(f194(f875(x94861)),x94862)),f329(f194(f875(x94861)),x94863)))+P24(f329(f329(f244(a874),f677(x94864,x94863,x94862,x94861)),f329(f329(f241(a874),f329(f194(f875(x94861)),x94862)),f329(f194(f875(x94861)),x94863))))
% 187.33/188.05 [9785]~P24(f329(f329(f329(x97851,f723(x97851,x97854,x97853,x97852)),f724(x97851,x97854,x97853,x97852)),f725(x97851,x97854,x97853,x97852)))+P24(f329(f329(f329(x97851,x97852),x97853),x97854))+~P24(f329(f317(f880(f881(a1,f878(f875(a325))),f880(a1,a1)),a315),f329(f329(f264(f881(a1,f878(f875(a325))),f880(a1,a1)),x97852),f329(f329(f264(a1,a1),x97853),x97854))))
% 187.33/188.05 [9865]P24(f329(f329(f329(x98651,x98652),x98653),x98654))+P24(f329(f317(f880(f881(a1,f878(f875(a325))),f880(a1,a1)),a315),f329(f329(f264(f881(a1,f878(f875(a325))),f880(a1,a1)),f723(x98651,x98654,x98653,x98652)),f329(f329(f264(a1,a1),f724(x98651,x98654,x98653,x98652)),f725(x98651,x98654,x98653,x98652)))))+~P24(f329(f317(f880(f881(a1,f878(f875(a325))),f880(a1,a1)),a315),f329(f329(f264(f881(a1,f878(f875(a325))),f880(a1,a1)),x98652),f329(f329(f264(a1,a1),x98653),x98654))))
% 187.33/188.05 [9904]~P24(f329(f329(f331(f880(f875(x99041),f875(x99041))),f329(f329(f264(f875(x99041),f875(x99041)),x99042),x99043)),f145(x99041,x99044)))+E(f329(f329(f174(x99041),f329(f194(f875(x99041)),x99042)),x99043),x99042)+P24(f329(f329(f331(f880(x99041,x99041)),f329(f329(f264(x99041,x99041),f329(f329(f163(x99041),x99042),f677(x99044,x99043,x99042,x99041))),f329(f329(f163(x99041),x99043),f677(x99044,x99043,x99042,x99041)))),x99044))
% 187.33/188.05 [9905]~P24(f329(f329(f331(f880(f875(x99051),f875(x99051))),f329(f329(f264(f875(x99051),f875(x99051)),x99052),x99053)),f145(x99051,x99054)))+P24(f329(f329(f244(a874),f329(f194(f875(x99051)),x99052)),f329(f194(f875(x99051)),x99053)))+P24(f329(f329(f331(f880(x99051,x99051)),f329(f329(f264(x99051,x99051),f329(f329(f163(x99051),x99052),f677(x99054,x99053,x99052,x99051))),f329(f329(f163(x99051),x99053),f677(x99054,x99053,x99052,x99051)))),x99054))
% 187.33/188.05 [9962]~E(f329(f194(f875(x99621)),x99622),f329(f194(f875(x99621)),x99623))+P24(f329(f329(f331(f880(f875(x99621),f875(x99621))),f329(f329(f264(f875(x99621),f875(x99621)),x99622),x99623)),f156(x99621,x99624)))+~P24(f329(f329(f331(f880(x99621,x99621)),f329(f329(f264(x99621,x99621),f329(f329(f163(x99621),x99622),f664(x99624,x99623,x99622,x99621))),f329(f329(f163(x99621),x99623),f664(x99624,x99623,x99622,x99621)))),x99624))
% 187.33/188.05 [10097]~P72(x100971)+~P24(f329(f62(x100972),x100974))+E(f329(f164(x100971),f329(f329(f152(x100972,x100971),x100973),f90(f875(x100972),f329(f329(f18(f875(x100972),a869,a869),f329(f329(f8(a869,f881(a869,a869),f875(x100972)),a327),f329(f329(f7(f875(x100972),f881(x100972,a869),a869),f329(f329(f8(f881(x100972,a869),f881(f881(x100972,a869),a869),f875(x100972)),a326),f171(x100972))),x100974))),f135(x100972))))),f234(x100972,x100971,x100973,x100974))
% 187.33/188.05 [7370]~P61(x73702)+E(x73701,f2(x73702))+E(f329(f329(f287(x73702),f329(f329(f80(x73702),x73703),f329(f329(f81(x73702),x73704),x73701))),x73701),f329(f329(f80(x73702),x73704),f329(f329(f287(x73702),x73703),x73701)))
% 187.33/188.05 [7371]~P29(x73712)+E(x73711,f2(x73712))+E(f329(f329(f39(x73712),f329(f329(f80(x73712),x73713),f329(f329(f81(x73712),x73714),x73711))),x73711),f329(f329(f80(x73712),x73714),f329(f329(f39(x73712),x73713),x73711)))
% 187.33/188.05 [7372]~P29(x73722)+E(x73721,f2(x73722))+E(f329(f329(f39(x73722),f329(f329(f80(x73722),x73723),f329(f329(f81(x73722),x73721),x73724))),x73721),f329(f329(f80(x73722),x73724),f329(f329(f39(x73722),x73723),x73721)))
% 187.33/188.05 [7606]~P62(x76062)+E(x76061,f2(x76062))+E(f329(f329(f287(x76062),f329(f329(f22(x76062),x76063),f329(f329(f81(x76062),x76061),x76064))),x76061),f329(f329(f22(x76062),f329(f329(f287(x76062),x76063),x76061)),x76064))
% 187.33/188.05 [7607]~P61(x76072)+E(x76071,f2(x76072))+E(f329(f329(f287(x76072),f329(f329(f80(x76072),x76073),f329(f329(f81(x76072),x76074),x76071))),x76071),f329(f329(f80(x76072),f329(f329(f287(x76072),x76073),x76071)),x76074))
% 187.33/188.05 [7608]~P62(x76082)+E(x76081,f2(x76082))+E(f329(f329(f287(x76082),f329(f329(f80(x76082),x76083),f329(f329(f81(x76082),x76081),x76084))),x76081),f329(f329(f80(x76082),f329(f329(f287(x76082),x76083),x76081)),x76084))
% 187.33/188.05 [8320]~P24(f329(f158(x83201,x83203),x83204))+~P24(f329(f158(x83201,x83202),x83204))+P24(f329(f158(x83201,f329(f329(f106(f881(x83201,a869)),x83202),x83203)),x83204))
% 187.33/188.05 [8691]~E(f329(f329(f286(x86911,x86911,x86911),x86912),x86914),f193(f881(f880(x86911,x86911),a869)))+~E(f329(f329(f286(x86911,x86911,x86911),x86912),x86913),f193(f881(f880(x86911,x86911),a869)))+E(f329(f329(f286(x86911,x86911,x86911),x86912),f329(f329(f115(f881(f880(x86911,x86911),a869)),x86913),x86914)),f193(f881(f880(x86911,x86911),a869)))
% 187.33/188.05 [8808]~P24(f329(f329(f243(f881(x88081,a869)),x88083),x88084))+~P24(f329(f329(f243(f881(x88081,a869)),x88082),x88084))+P24(f329(f329(f243(f881(x88081,a869)),f329(f329(f115(f881(x88081,a869)),x88082),x88083)),x88084))
% 187.33/188.05 [9188]~P24(f329(f62(x91881),x91884))+~P24(f329(f62(x91881),x91883))+E(f329(f329(f22(a874),f329(f329(f80(a874),f329(f329(f6(x91881,a874),x91882),x91883)),f329(f329(f6(x91881,a874),x91882),x91884))),f329(f329(f6(x91881,a874),x91882),f329(f329(f106(f881(x91881,a869)),x91883),x91884))),f329(f329(f6(x91881,a874),x91882),f329(f329(f115(f881(x91881,a869)),x91883),x91884)))
% 187.33/188.05 [9277]~P24(f329(f329(f331(x92771),x92773),x92772))+~P24(f329(f329(f243(f881(x92771,a869)),x92772),f329(f329(f307(x92771),x92773),x92774)))+P24(f329(f329(f243(f881(x92771,a869)),f329(f329(f22(f881(x92771,a869)),x92772),f329(f329(f307(x92771),x92773),f193(f881(x92771,a869))))),x92774))
% 187.33/188.05 [9436]~P24(f329(f329(f331(x94361),x94363),x94362))+P24(f329(f329(f243(f881(x94361,a869)),x94362),f329(f329(f307(x94361),x94363),x94364)))+~P24(f329(f329(f243(f881(x94361,a869)),f329(f329(f22(f881(x94361,a869)),x94362),f329(f329(f307(x94361),x94363),f193(f881(x94361,a869))))),x94364))
% 187.33/188.05 [9527]~P24(f329(f329(f243(a874),x95271),x95273))+~P24(f329(f329(f244(a874),x95272),x95274))+P24(f329(f329(f331(f880(f880(a874,a874),f880(a874,a874))),f329(f329(f264(f880(a874,a874),f880(a874,a874)),f329(f329(f264(a874,a874),x95271),x95272)),f329(f329(f264(a874,a874),x95273),x95274))),a35))
% 187.33/188.05 [9528]~P24(f329(f329(f243(a874),x95282),x95284))+~P24(f329(f329(f243(a874),x95281),x95283))+P24(f329(f329(f331(f880(f880(a874,a874),f880(a874,a874))),f329(f329(f264(f880(a874,a874),f880(a874,a874)),f329(f329(f264(a874,a874),x95281),x95282)),f329(f329(f264(a874,a874),x95283),x95284))),a70))
% 187.33/188.05 [9824]~P24(f329(f329(f331(f875(x98241)),x98244),f159(x98241,x98243)))+~P24(f329(f329(f331(f875(x98241)),x98244),f159(x98241,x98242)))+P24(f329(f158(x98241,f329(f329(f106(f881(x98241,a869)),f329(f329(f7(x98241,f881(x98241,a869),a869),f331(x98241)),x98242)),f329(f329(f7(x98241,f881(x98241,a869),a869),f331(x98241)),x98243))),x98244))
% 187.33/188.05 [9927]~P21(x99271,f881(f881(x99271,a869),a869),f329(f329(f7(x99271,f881(f880(x99271,x99271),a869),f881(f881(x99271,a869),a869)),f329(f329(f8(f881(x99271,a869),f881(f881(f880(x99271,x99271),a869),f881(f881(x99271,a869),a869)),x99271),f61(x99271)),f329(f329(f7(x99271,f881(x99271,a869),f881(x99271,a869)),f307(x99271)),f193(f881(x99271,a869))))),x99273),x99272)+~P24(f329(f329(f331(x99271),x99274),x99272))+E(f329(f329(f22(f881(f881(x99271,a869),a869)),f329(f329(f61(x99271),x99272),x99273)),f329(f329(f61(x99271),f329(f329(f307(x99271),x99274),f193(f881(x99271,a869)))),x99273)),f329(f329(f61(x99271),f329(f329(f22(f881(x99271,a869)),x99272),f329(f329(f307(x99271),x99274),f193(f881(x99271,a869))))),x99273))
% 187.33/188.05 [10061]~P44(x100611,x100612,x100614)+~P24(f329(f329(f331(f880(x100611,x100611)),x100613),x100614))+P24(f329(f329(f268(x100611,x100611,a869),f329(f329(f7(x100611,f881(x100611,a869),f881(x100611,a869)),f329(f329(f8(f881(a869,a869),f881(f881(x100611,a869),f881(x100611,a869)),x100611),f8(a869,a869,x100611)),f329(f329(f8(a869,f881(a869,a869),x100611),a327),f329(f329(f7(x100611,f881(x100611,a869),a869),f331(x100611)),x100612)))),f329(f329(f7(x100611,f881(x100611,a869),a869),f331(x100611)),x100612))),x100613))
% 187.33/188.05 [10073]P24(f329(f62(x100731),x100732))+~P24(f329(f62(x100733),f329(f308(x100731,x100733,x100734),x100732)))+~P24(f329(f62(x100731),f329(f249(x100731),f329(f329(f18(x100731,a869,a869),f329(f329(f8(a869,f881(a869,a869),x100731),a327),f329(f329(f7(x100731,f881(x100731,a869),a869),f331(x100731)),x100732))),f329(f329(f7(x100731,x100733,a869),f329(f329(f8(x100733,f881(x100733,a869),x100731),a326),x100734)),f329(x100734,f430(x100734,x100733,x100732,x100731)))))))
% 187.33/188.05 [8073]~P62(x80732)+E(x80731,f2(x80732))+E(f329(f329(f287(x80732),f329(f329(f22(x80732),f329(f329(f81(x80732),x80731),x80733)),x80734)),x80731),f329(f329(f22(x80732),x80733),f329(f329(f287(x80732),x80734),x80731)))
% 187.33/188.05 [8074]~P62(x80742)+E(x80741,f2(x80742))+E(f329(f329(f287(x80742),f329(f329(f80(x80742),f329(f329(f81(x80742),x80741),x80743)),x80744)),x80741),f329(f329(f80(x80742),x80743),f329(f329(f287(x80742),x80744),x80741)))
% 187.33/188.05 [8973]~E(f329(f329(f286(x89731,x89731,x89731),x89733),x89734),f193(f881(f880(x89731,x89731),a869)))+~E(f329(f329(f286(x89731,x89731,x89731),x89732),x89734),f193(f881(f880(x89731,x89731),a869)))+E(f329(f329(f286(x89731,x89731,x89731),f329(f329(f115(f881(f880(x89731,x89731),a869)),x89732),x89733)),x89734),f193(f881(f880(x89731,x89731),a869)))
% 187.33/188.05 [10004]~P142(x100041)+~P142(x100042)+E(f329(f329(f314(x100041),f329(f329(f7(x100041,a104,f878(f875(a325))),f329(f329(f8(f881(x100042,f878(f875(a325))),f881(a104,f878(f875(a325))),x100041),f314(x100042)),f329(f329(f8(f881(x100042,f880(x100041,x100042)),f881(x100042,f878(f875(a325))),x100041),f329(f8(f880(x100041,x100042),f878(f875(a325)),x100042),x100043)),f264(x100041,x100042)))),x100044)),x100044),f329(f329(f314(f880(x100041,x100042)),x100043),x100044))
% 187.33/188.05 [9733]~P24(f329(f158(x97331,x97333),x97334))+~P24(f329(f158(x97331,x97332),x97334))+P24(f329(f158(x97331,f329(f329(f18(x97331,a869,a869),f329(f329(f8(a869,f881(a869,a869),x97331),a327),x97332)),x97333)),x97334))
% 187.33/188.05 [9996]P24(f329(x99961,f431(x99962,x99963,x99961,x99964)))+~P24(f329(f62(x99964),f329(f249(x99964),x99961)))+P24(f329(f62(x99963),f329(f249(x99963),f329(f329(f8(f881(x99964,a869),a869,x99963),f87(x99964)),f329(f329(f8(f881(x99964,a869),f881(x99964,a869),x99963),f329(f18(x99964,a869,a869),f329(f329(f8(a869,f881(a869,a869),x99964),a327),x99961))),x99962)))))
% 187.33/188.05 [10017]~P24(f329(f62(x100172),f329(f249(x100172),x100173)))+~P24(f329(f62(x100171),f329(f249(x100171),f329(f329(f7(x100171,x100172,a869),x100174),f431(x100174,x100171,x100173,x100172)))))+P24(f329(f62(x100171),f329(f249(x100171),f329(f329(f8(f881(x100172,a869),a869,x100171),f87(x100172)),f329(f329(f8(f881(x100172,a869),f881(x100172,a869),x100171),f329(f18(x100172,a869,a869),f329(f329(f8(a869,f881(a869,a869),x100172),a327),x100173))),x100174)))))
% 187.33/188.05 [5009]~E(x50092,x50094)+E(f169(x50091,x50092,x50093),f169(x50091,x50094,x50095))+~E(x50092,f2(a874))
% 187.33/188.05 [5272]E(x52721,x52722)+~E(f169(x52724,x52723,x52721),f169(x52724,x52725,x52722))+E(x52723,f2(a874))
% 187.33/188.05 [6510]E(x65101,x65102)+~E(f329(x65103,x65101),f329(x65103,x65102))+~P21(x65104,x65105,x65103,f252(f881(x65104,a869)))
% 187.33/188.05 [6670]~E(f329(x66703,x66705),f206(x66702))+~E(f329(x66704,x66705),f206(x66702))+E(f329(f184(x66701,x66702,x66703,x66704),x66705),f206(x66702))
% 187.33/188.05 [7406]E(x74061,x74062)+~P21(x74063,x74064,x74065,f252(f881(x74063,a869)))+~E(f329(f308(x74063,x74064,x74065),x74061),f329(f308(x74063,x74064,x74065),x74062))
% 187.33/188.05 [7660]P21(x76602,x76603,f502(x76604,x76603,x76602,x76601),x76601)+~E(f329(f308(x76603,x76602,x76605),x76604),x76601)+E(x76601,f193(f881(x76602,a869)))
% 187.33/188.05 [8208]~P24(f329(f329(x82083,x82082),x82085))+~P24(f329(f329(x82083,x82084),x82082))+P24(f329(f329(f331(x82081),x82082),f293(x82081,x82083,x82084,x82085)))
% 187.33/188.05 [8209]~P24(f329(f329(x82093,x82092),x82095))+~P24(f329(f329(x82093,x82094),x82092))+P24(f329(f329(f331(x82091),x82092),f296(x82091,x82093,x82094,x82095)))
% 187.33/188.05 [8766]~P21(x87661,x87663,x87665,f252(f881(x87661,a869)))+~P21(x87663,x87662,x87664,f252(f881(x87663,a869)))+P21(x87661,x87662,f329(f73(x87663,x87662,x87661,x87664),x87665),f252(f881(x87661,a869)))
% 187.33/188.05 [9336]P24(f329(f329(f331(f880(x93361,x93361)),f329(f329(f264(x93361,x93361),x93362),x93363)),f305(x93361,x93364)))+~P24(f329(f329(f331(f880(x93361,x93361)),f329(f329(f264(x93361,x93361),x93362),x93365)),f305(x93361,x93364)))+~P24(f329(f329(f331(f880(x93361,x93361)),f329(f329(f264(x93361,x93361),x93365),x93363)),f305(x93361,x93364)))
% 187.33/188.05 [9374]~P27(x93742)+~P24(f329(f135(x93741),x93745))+P24(f329(f135(x93741),f147(x93741,x93742,x93743,x93744,x93745)))
% 187.33/188.05 [5343]~E(x53432,f118(x53431))+E(f329(f329(f126(x53431),x53432),x53433),f329(f329(f149(x53431),x53434),x53435))+~E(x53433,f329(f329(f149(x53431),x53434),x53435))
% 187.33/188.05 [5344]~E(x53442,f118(x53441))+E(f329(f329(f126(x53441),x53442),x53443),f329(f329(f149(x53441),x53444),x53445))+~E(f329(f329(f149(x53441),x53444),x53445),x53443)
% 187.33/188.05 [6466]~E(f329(f194(f875(x64661)),x64665),f329(f194(f875(x64662)),x64664))+E(f329(f329(f152(f880(x64661,x64662),x64662),f267(x64661,x64662)),x64663),x64664)+~E(f329(f329(f181(x64661,x64662),x64665),x64664),x64663)
% 187.33/188.05 [6467]~E(f329(f194(f875(x64671)),x64674),f329(f194(f875(x64672)),x64675))+E(f329(f329(f152(f880(x64671,x64672),x64671),f263(x64671,x64672)),x64673),x64674)+~E(f329(f329(f181(x64671,x64672),x64674),x64675),x64673)
% 187.33/188.05 [6943]~P27(x69431)+~P33(x69431,f329(f329(f152(x69432,x69431),x69433),x69435))+P33(x69431,f329(f329(f152(x69432,x69431),x69433),f329(f134(x69432,x69434),x69435)))
% 187.33/188.05 [6990]~P24(f329(x69903,x69905))+~P24(f329(f329(x69902,x69904),x69905))+P24(f329(f329(f97(x69901,x69902,x69903),x69904),x69905))
% 187.33/188.05 [7087]~P27(x70871)+P33(x70871,f329(f329(f152(x70872,x70871),x70873),f168(x70872,x70874,x70875)))+~P33(x70871,f329(f329(f152(x70872,x70871),x70873),x70875))
% 187.33/188.05 [7110]~P54(x71103,x71102,x71105)+~P54(x71101,x71103,x71104)+P54(x71101,x71102,f329(f329(f286(x71101,x71103,x71102),x71104),x71105))
% 187.33/188.05 [7202]E(x72021,x72022)+~P21(x72023,x72024,x72025,f252(f881(x72023,a869)))+~E(f329(f329(f152(x72023,x72024),x72025),x72021),f329(f329(f152(x72023,x72024),x72025),x72022))
% 187.33/188.05 [7356]~P24(f329(f329(f243(a874),x73561),f329(x73563,x73565)))+P24(f329(f329(f243(a874),x73561),f153(x73562,x73563,x73564)))+~P24(f329(f329(f331(x73562),x73565),f329(f171(x73562),x73564)))
% 187.33/188.05 [7357]~P24(f329(f329(f244(a874),x73571),f329(x73573,x73575)))+P24(f329(f329(f244(a874),x73571),f153(x73572,x73573,x73574)))+~P24(f329(f329(f331(x73572),x73575),f329(f171(x73572),x73574)))
% 187.33/188.05 [7763]P24(f329(x77631,x77632))+~P24(f329(x77631,x77633))+~P24(f329(f329(f331(x77634),x77632),f329(f171(x77634),f169(x77634,x77635,x77633))))
% 187.33/188.05 [7764]P24(f329(x77641,x77642))+~P24(f329(x77641,x77643))+~P24(f329(f329(f331(x77644),x77643),f329(f171(x77644),f169(x77644,x77645,x77642))))
% 187.33/188.05 [7769]~P106(x77691)+P24(f329(f329(f243(f881(x77691,a869)),f300(x77691,x77692,x77693)),f300(x77691,x77694,x77695)))+P24(f329(f329(f243(x77691),x77692),x77693))
% 187.33/188.05 [7792]~P31(x77921)+P24(f329(f329(f243(x77921),f329(f329(f43(x77922,x77921),x77923),x77924)),f329(x77924,x77925)))+~P24(f329(f329(f331(x77922),x77925),x77923))
% 187.33/188.05 [7859]~P21(x78591,x78592,x78594,x78593)+E(f329(f77(x78591,x78592,x78593,x78594),f329(x78594,x78595)),x78595)+~P24(f329(f329(f331(x78591),x78595),x78593))
% 187.33/188.05 [8061]~P24(f329(x80611,x80615))+P24(f329(x80611,f848(x80611,x80612,x80613,x80614)))+~P24(f329(f329(f331(x80614),x80615),x80613))
% 187.33/188.05 [8062]~P24(f329(x80621,x80625))+P24(f329(x80621,f848(x80621,x80622,x80623,x80624)))+~P24(f329(f329(f331(x80624),x80625),x80622))
% 187.33/188.05 [8159]P24(f329(f62(x81591),x81592))+~P24(f329(f62(x81593),x81594))+~P24(f329(f329(f243(f881(x81591,a869)),x81592),f329(f308(x81593,x81591,x81595),x81594)))
% 187.33/188.05 [8324]E(x83241,x83242)+~P21(x83243,x83244,x83245,f329(f329(f115(f881(x83243,a869)),f329(f171(x83243),x83241)),f329(f171(x83243),x83242)))+~E(f329(f329(f152(x83243,x83244),x83245),x83241),f329(f329(f152(x83243,x83244),x83245),x83242))
% 187.33/188.05 [8378]~P106(x83781)+~P24(f329(f329(f244(f881(x83781,a869)),f300(x83781,x83784,x83785)),f300(x83781,x83782,x83783)))+P24(f329(f329(f243(x83781),x83782),x83783))
% 187.33/188.05 [8447]~P21(x84471,x84474,x84475,f252(f881(x84471,a869)))+~P24(f329(f329(f331(x84474),f329(x84475,x84472)),f329(f308(x84471,x84474,x84475),x84473)))+P24(f329(f329(f331(x84471),x84472),x84473))
% 187.33/188.05 [8525]P24(f329(x85251,x85252))+~P24(f329(x85251,f859(x85251,x85253,x85254,x85255)))+~P24(f329(f329(f331(x85255),x85252),x85254))
% 187.33/188.05 [8526]P24(f329(x85261,x85262))+~P24(f329(x85261,f859(x85261,x85263,x85264,x85265)))+~P24(f329(f329(f331(x85265),x85262),x85263))
% 187.33/188.05 [8805]~P21(x88052,x88053,x88051,x88054)+E(f329(x88051,f329(f77(x88052,x88053,x88054,x88051),x88055)),x88055)+~P24(f329(f329(f331(x88053),x88055),f329(f308(x88052,x88053,x88051),x88054)))
% 187.33/188.05 [8910]E(x89101,f118(x89102))+E(f329(f329(f149(x89102),x89103),f694(x89104,x89103,x89105,x89101,x89102)),x89101)+~E(f329(f329(f126(x89102),x89101),x89105),f329(f329(f149(x89102),x89103),x89104))
% 187.33/188.05 [8911]E(x89111,f118(x89112))+E(f329(f329(f149(x89112),x89113),f695(x89114,x89111,x89115,x89113,x89112)),x89111)+~E(f329(f329(f126(x89112),x89111),x89114),f329(f329(f149(x89112),x89113),x89115))
% 187.33/188.05 [8929]E(f329(f329(f149(x89292),x89293),f694(x89294,x89293,x89291,x89295,x89292)),x89295)+~E(f329(f329(f126(x89292),x89295),x89291),f329(f329(f149(x89292),x89293),x89294))+E(x89291,f329(f329(f149(x89292),x89293),x89294))
% 187.33/188.05 [8930]E(f329(f329(f149(x89301),x89302),f695(x89304,x89305,x89303,x89302,x89301)),x89305)+~E(f329(f329(f126(x89301),x89305),x89304),f329(f329(f149(x89301),x89302),x89303))+E(f329(f329(f149(x89301),x89302),x89303),x89304)
% 187.33/188.05 [9012]~E(f329(f308(x90123,x90122,x90124),f252(f881(x90123,a869))),f252(f881(x90122,a869)))+~E(f329(f308(x90121,x90123,x90125),f252(f881(x90121,a869))),f252(f881(x90123,a869)))+E(f329(f308(x90121,x90122,f329(f73(x90123,x90122,x90121,x90124),x90125)),f252(f881(x90121,a869))),f252(f881(x90122,a869)))
% 187.33/188.05 [9241]E(f329(f308(x92411,x92412,x92413),f775(x92414,x92413,x92411,x92415,x92412)),x92415)+~P24(f329(f62(x92412),x92415))+~P24(f329(f329(f243(f881(x92412,a869)),x92415),f329(f308(x92411,x92412,x92413),x92414)))
% 187.33/188.05 [9380]E(x93801,f118(x93802))+~E(f329(f329(f126(x93802),x93801),x93803),f329(f329(f149(x93802),x93805),x93804))+E(f329(f329(f126(x93802),f695(x93803,x93801,x93804,x93805,x93802)),x93803),x93804)
% 187.33/188.05 [9381]E(x93811,f118(x93812))+~E(f329(f329(f126(x93812),x93811),x93815),f329(f329(f149(x93812),x93814),x93813))+E(f329(f329(f126(x93812),f694(x93813,x93814,x93815,x93811,x93812)),x93815),x93813)
% 187.33/188.05 [9388]E(f329(f329(f126(x93882),f694(x93884,x93883,x93881,x93885,x93882)),x93881),x93884)+~E(f329(f329(f126(x93882),x93885),x93881),f329(f329(f149(x93882),x93883),x93884))+E(x93881,f329(f329(f149(x93882),x93883),x93884))
% 187.33/188.05 [9389]~E(f329(f329(f126(x93891),x93895),x93894),f329(f329(f149(x93891),x93892),x93893))+E(f329(f329(f126(x93891),f695(x93894,x93895,x93893,x93892,x93891)),x93894),x93893)+E(f329(f329(f149(x93891),x93892),x93893),x93894)
% 187.33/188.05 [9390]E(f329(f329(f126(x93901),x93905),f697(x93903,x93902,x93904,x93905,x93901)),x93902)+E(f329(f329(f126(x93901),x93902),f696(x93903,x93902,x93904,x93905,x93901)),x93905)+~E(f329(f329(f126(x93901),x93905),x93904),f329(f329(f126(x93901),x93902),x93903))
% 187.33/188.05 [9422]~P27(x94221)+P33(x94221,f329(f329(f152(x94222,x94221),x94223),f147(x94222,x94221,x94223,x94224,x94225)))+~P33(x94221,f329(f329(f152(x94222,x94221),x94223),x94225))
% 187.33/188.05 [9433]~P58(x94335,x94331,x94334,x94333)+P24(f329(f329(x94331,x94332),f518(x94333,x94334,x94331,x94335,x94332)))+~P24(f329(f329(f331(x94335),x94332),x94334))
% 187.33/188.05 [9487]~P24(f329(f62(x94875),x94874))+P24(f329(f62(x94871),f775(x94872,x94873,x94871,x94874,x94875)))+~P24(f329(f329(f243(f881(x94875,a869)),x94874),f329(f308(x94871,x94875,x94873),x94872)))
% 187.33/188.05 [9539]~P24(f329(f329(f331(f880(x95391,x95391)),f329(f329(f264(x95391,x95391),x95395),x95393)),f305(x95391,x95394)))+P24(f329(f329(f331(f880(x95391,x95391)),f329(f329(f264(x95391,x95391),x95392),x95393)),f329(f329(f286(x95391,x95391,x95391),x95394),f305(x95391,x95394))))+~P24(f329(f329(f331(f880(x95391,x95391)),f329(f329(f264(x95391,x95391),x95392),x95395)),f329(f329(f286(x95391,x95391,x95391),x95394),f305(x95391,x95394))))
% 187.33/188.05 [9540]~P24(f329(f329(f331(f880(x95401,x95401)),f329(f329(f264(x95401,x95401),x95402),x95405)),f305(x95401,x95404)))+P24(f329(f329(f331(f880(x95401,x95401)),f329(f329(f264(x95401,x95401),x95402),x95403)),f329(f329(f286(x95401,x95401,x95401),x95404),f305(x95401,x95404))))+~P24(f329(f329(f331(f880(x95401,x95401)),f329(f329(f264(x95401,x95401),x95405),x95403)),f329(f329(f286(x95401,x95401,x95401),x95404),f305(x95401,x95404))))
% 187.33/188.05 [9543]P24(f329(f329(f331(f880(f875(x95431),f875(x95431))),f329(f329(f264(f875(x95431),f875(x95431)),x95432),x95433)),f156(x95431,f305(x95431,x95434))))+~P24(f329(f329(f331(f880(f875(x95431),f875(x95431))),f329(f329(f264(f875(x95431),f875(x95431)),x95432),x95435)),f156(x95431,f305(x95431,x95434))))+~P24(f329(f329(f331(f880(f875(x95431),f875(x95431))),f329(f329(f264(f875(x95431),f875(x95431)),x95435),x95433)),f156(x95431,f305(x95431,x95434))))
% 187.33/188.05 [9547]E(f329(f329(f126(x95471),x95472),f696(x95473,x95472,x95474,x95475,x95471)),x95475)+E(f329(f329(f126(x95471),f697(x95473,x95472,x95474,x95475,x95471)),x95473),x95474)+~E(f329(f329(f126(x95471),x95472),x95473),f329(f329(f126(x95471),x95475),x95474))
% 187.33/188.05 [9548]E(f329(f329(f126(x95481),x95482),f697(x95483,x95484,x95485,x95482,x95481)),x95484)+E(f329(f329(f126(x95481),f696(x95483,x95484,x95485,x95482,x95481)),x95485),x95483)+~E(f329(f329(f126(x95481),x95482),x95485),f329(f329(f126(x95481),x95484),x95483))
% 187.33/188.05 [9602]P24(f329(f329(f331(f880(x96021,x96021)),f329(f329(f264(x96021,x96021),x96022),x96023)),f329(f329(f286(x96021,x96021,x96021),x96024),f305(x96021,x96024))))+~P24(f329(f329(f331(f880(x96021,x96021)),f329(f329(f264(x96021,x96021),x96022),x96025)),f329(f329(f286(x96021,x96021,x96021),x96024),f305(x96021,x96024))))+~P24(f329(f329(f331(f880(x96021,x96021)),f329(f329(f264(x96021,x96021),x96025),x96023)),f329(f329(f286(x96021,x96021,x96021),x96024),f305(x96021,x96024))))
% 187.33/188.05 [9629]P39(x96291,x96292,x96293,x96294,x96295)+~E(f329(f194(f875(x96291)),x96294),f329(f194(f875(x96292)),x96295))+~P24(f329(f329(f268(x96291,x96292,a869),x96293),f737(x96295,x96294,x96293,x96292,x96291)))
% 187.33/188.05 [9630]P39(x96301,x96302,x96303,x96304,x96305)+~E(f329(f194(f875(x96301)),x96304),f329(f194(f875(x96302)),x96305))+~P24(f329(f329(f268(x96301,x96302,a869),x96303),f738(x96303,x96305,x96304,x96302,x96301)))
% 187.33/188.05 [9635]E(f329(f329(f126(x96351),f696(x96352,x96353,x96354,x96355,x96351)),x96354),x96352)+~E(f329(f329(f126(x96351),x96353),x96352),f329(f329(f126(x96351),x96355),x96354))+E(f329(f329(f126(x96351),f697(x96352,x96353,x96354,x96355,x96351)),x96352),x96354)
% 187.33/188.05 [9650]~P27(x96502)+E(f329(f329(f146(x96501,x96502,x96503),x96504),x96505),f329(f329(f149(x96501),x96504),x96505))+P24(f329(f329(f331(x96501),f787(x96504,x96503,x96505,x96501,x96502)),f329(f171(x96501),x96505)))
% 187.33/188.05 [9655]~P58(x96551,x96554,x96553,x96552)+~P24(f329(f329(f331(x96551),x96555),x96553))+P24(f329(f329(f331(x96551),f518(x96552,x96553,x96554,x96551,x96555)),x96552))
% 187.33/188.05 [9704]~P24(f329(f62(x97045),x97044))+~P24(f329(f329(f243(f881(x97045,a869)),x97044),f329(f308(x97041,x97045,x97043),x97042)))+P24(f329(f329(f243(f881(x97041,a869)),f775(x97042,x97043,x97041,x97044,x97045)),x97042))
% 187.33/188.05 [9776]~P24(f329(f329(f331(f880(f881(x97761,a869),f881(x97761,a869))),f329(f329(f264(f881(x97761,a869),f881(x97761,a869)),x97764),x97763)),f321(x97761,x97762)))+~P24(f329(f329(f331(x97761),x97765),x97764))+P24(f329(f329(f331(x97761),f586(x97762,x97763,x97764,x97761,x97765)),x97763))
% 187.33/188.05 [9788]~P27(x97882)+E(f329(f329(f146(x97881,x97882,x97883),x97884),x97885),f329(f329(f149(x97881),x97884),x97885))+~P24(f329(f329(f243(x97882),f329(x97883,x97884)),f329(x97883,f787(x97884,x97883,x97885,x97881,x97882))))
% 187.33/188.05 [9979]P39(x99791,x99792,x99793,x99794,x99795)+~E(f329(f194(f875(x99791)),x99794),f329(f194(f875(x99792)),x99795))+~P24(f329(f329(x99793,f329(f329(f163(x99791),x99794),f739(x99795,x99794,x99793,x99792,x99791))),f329(f329(f163(x99792),x99795),f739(x99795,x99794,x99793,x99792,x99791))))
% 187.33/188.05 [9980]P39(x99801,x99802,x99803,x99804,x99805)+~E(f329(f194(f875(x99801)),x99804),f329(f194(f875(x99802)),x99805))+~P24(f329(f329(x99803,f329(f329(f163(x99801),x99804),f774(x99803,x99805,x99802,x99804,x99801))),f329(f329(f163(x99802),x99805),f774(x99803,x99805,x99802,x99804,x99801))))
% 187.33/188.05 [6538]~P13(x65382,x65385,x65381)+~P24(f329(f62(x65382),x65384))+E(f329(x65381,f329(f329(f307(x65382),x65383),x65384)),f329(f329(f65(x65382,x65382,x65385),x65383),x65384))
% 187.33/188.05 [6539]~E(x65393,x65394)+~E(x65392,x65395)+E(f329(f329(f307(x65391),x65392),f329(f329(f307(x65391),x65393),f193(f881(x65391,a869)))),f329(f329(f307(x65391),x65394),f329(f329(f307(x65391),x65395),f193(f881(x65391,a869)))))
% 187.33/188.05 [6550]P24(f329(x65502,x65505))+E(f176(x65501,x65502,f329(f329(f126(x65501),x65503),x65504)),f176(x65501,x65502,x65503))+~P24(f329(f329(f331(x65501),x65505),f329(f171(x65501),x65503)))
% 187.33/188.05 [6587]E(f329(x65871,x65872),f193(f881(x65873,a869)))+~E(f329(f329(f42(x65874,f881(x65873,a869)),x65875),x65871),f193(f881(x65873,a869)))+~P24(f329(f329(f331(x65874),x65872),x65875))
% 187.33/188.05 [6588]E(f329(x65881,x65882),f252(f881(x65883,a869)))+~E(f329(f329(f43(x65884,f881(x65883,a869)),x65885),x65881),f252(f881(x65883,a869)))+~P24(f329(f329(f331(x65884),x65882),x65885))
% 187.33/188.05 [6892]~P24(f329(f329(f199(x68921),x68923),x68925))+~P24(f329(f329(f199(x68922),x68925),x68924))+P24(f329(f329(f199(f33(x68921,x68922)),x68923),x68924))
% 187.33/188.05 [7097]~E(x70972,x70974)+~P139(x70971)+E(f329(f329(f80(x70971),f329(f329(f81(x70971),x70972),x70973)),f329(f329(f81(x70971),x70974),x70975)),f329(f329(f80(x70971),f329(f329(f81(x70971),x70972),x70975)),f329(f329(f81(x70971),x70974),x70973)))
% 187.33/188.05 [7157]~P31(x71571)+~P24(f329(f329(f331(x71574),x71573),x71575))+P24(f329(f329(f243(x71571),f329(x71572,x71573)),f329(f329(f42(x71574,x71571),x71575),x71572)))
% 187.33/188.05 [7207]~P26(x72071)+P24(f329(f329(f243(x72071),f329(x72072,x72073)),f329(x72074,x72073)))+~P24(f329(f329(f243(f881(x72075,x72071)),x72072),x72074))
% 187.33/188.05 [7324]E(x73241,x73242)+E(x73243,x73241)+~E(f329(f329(f307(x73244),x73241),f329(f329(f307(x73244),x73245),f193(f881(x73244,a869)))),f329(f329(f307(x73244),x73242),f329(f329(f307(x73244),x73243),f193(f881(x73244,a869)))))
% 187.33/188.05 [7325]E(x73251,x73252)+E(x73253,x73251)+~E(f329(f329(f307(x73254),x73253),f329(f329(f307(x73254),x73252),f193(f881(x73254,a869)))),f329(f329(f307(x73254),x73255),f329(f329(f307(x73254),x73251),f193(f881(x73254,a869)))))
% 187.33/188.05 [7326]E(x73261,x73262)+E(x73261,x73263)+~E(f329(f329(f307(x73264),x73263),f329(f329(f307(x73264),x73262),f193(f881(x73264,a869)))),f329(f329(f307(x73264),x73265),f329(f329(f307(x73264),x73261),f193(f881(x73264,a869)))))
% 187.33/188.05 [7327]E(x73271,x73272)+E(x73271,x73273)+~E(f329(f329(f307(x73274),x73271),f329(f329(f307(x73274),x73275),f193(f881(x73274,a869)))),f329(f329(f307(x73274),x73272),f329(f329(f307(x73274),x73273),f193(f881(x73274,a869)))))
% 187.33/188.05 [7869]P21(x78691,x78692,x78693,x78694)+~P21(x78691,x78692,x78693,x78695)+~P24(f329(f329(f243(f881(x78691,a869)),x78694),x78695))
% 187.33/188.05 [7876]~P24(f329(f329(f243(a874),x78765),x78763))+~P24(f329(f329(f329(f329(a201,x78761),x78762),x78765),x78764))+P24(f329(f329(f329(f329(a201,x78761),x78762),x78763),x78764))
% 187.33/188.05 [7972]P24(f329(x79721,x79722))+~P24(f329(f329(f199(x79724),x79722),x79725))+P24(f329(f329(f199(f30(x79721,x79723,x79724)),x79722),x79725))
% 187.33/188.05 [8000]~P24(f329(x80001,x80004))+~P24(f329(f329(f199(x80002),x80004),x80005))+P24(f329(f329(f199(f30(x80001,x80002,x80003)),x80004),x80005))
% 187.33/188.05 [8051]E(x80511,x80512)+~E(f329(f308(x80513,x80514,x80515),x80511),f329(f308(x80513,x80514,x80515),x80512))+~P21(x80513,x80514,x80515,f329(f329(f115(f881(x80513,a869)),x80511),x80512))
% 187.33/188.05 [8125]P24(f329(x81252,x81254))+E(f329(f329(f136(x81251),f329(f194(f875(x81251)),f176(x81251,x81252,x81253))),x81253),f329(f329(f149(x81251),x81254),x81255))+~E(f329(f329(f126(x81251),f176(x81251,x81252,x81253)),f329(f329(f149(x81251),x81254),x81255)),x81253)
% 187.33/188.05 [8156]~P21(x81561,x81562,x81563,x81565)+~P21(x81561,x81562,x81563,x81564)+P21(x81561,x81562,x81563,f329(f329(f106(f881(x81561,a869)),x81564),x81565))
% 187.33/188.05 [8265]~P72(x82651)+E(f329(f329(f80(x82651),f329(x82652,x82653)),f329(f164(x82651),f329(f329(f152(x82654,x82651),x82652),f168(x82654,x82653,x82655)))),f329(f164(x82651),f329(f329(f152(x82654,x82651),x82652),x82655)))+~P24(f329(f329(f331(x82654),x82653),f329(f171(x82654),x82655)))
% 187.33/188.05 [8354]~P27(x83541)+~P33(x83541,f329(f329(f152(x83542,x83541),x83543),x83545))+P33(x83541,f329(f329(f152(x83542,x83541),x83543),f329(f329(f146(x83542,x83541,x83543),x83544),x83545)))
% 187.33/188.05 [8432]P24(f329(x84321,x84322))+P24(f329(f329(f199(x84323),x84322),x84324))+~P24(f329(f329(f199(f30(x84321,x84325,x84323)),x84322),x84324))
% 187.33/188.05 [8443]~P31(x84431)+P24(f329(f329(f243(x84431),f329(f329(f42(x84432,x84431),x84433),x84434)),f329(f329(f42(x84432,x84431),x84435),x84434)))+~P24(f329(f329(f243(f881(x84432,a869)),x84433),x84435))
% 187.33/188.05 [8444]~P31(x84441)+P24(f329(f329(f243(x84441),f329(f329(f43(x84442,x84441),x84443),x84444)),f329(f329(f43(x84442,x84441),x84445),x84444)))+~P24(f329(f329(f243(f881(x84442,a869)),x84445),x84443))
% 187.33/188.05 [8455]~P24(f329(x84554,x84552))+P24(f329(f329(f199(x84551),x84552),x84553))+~P24(f329(f329(f199(f30(x84554,x84551,x84555)),x84552),x84553))
% 187.33/188.05 [8479]~P27(x84793)+P24(f329(f135(x84791),x84792))+~P24(f329(f135(x84791),f329(f329(f146(x84791,x84793,x84794),x84795),x84792)))
% 187.33/188.05 [8489]P24(f329(f329(f199(x84891),x84892),x84893))+P24(f329(f329(f199(x84894),x84892),x84893))+~P24(f329(f329(f199(f30(x84895,x84891,x84894)),x84892),x84893))
% 187.33/188.05 [8620]~P27(x86201)+~P24(f329(f329(f331(x86202),x86203),f329(f171(x86202),x86204)))+~P24(f329(f135(x86202),f329(f329(f146(x86202,x86201,x86205),x86203),x86204)))
% 187.33/188.05 [8701]~P27(x87011)+P33(x87011,f329(f329(f152(x87012,x87011),x87013),x87014))+~P33(x87011,f329(f329(f152(x87012,x87011),x87013),f329(f329(f146(x87012,x87011,x87013),x87015),x87014)))
% 187.33/188.05 [8793]~P27(x87932)+E(f329(f329(f146(x87931,x87932,x87933),x87934),x87935),f147(x87931,x87932,x87933,x87934,x87935))+P24(f329(f329(f331(x87932),f329(x87933,x87934)),f329(f308(x87931,x87932,x87933),f329(f171(x87931),x87935))))
% 187.33/188.05 [8867]~P27(x88672)+E(f147(x88671,x88672,x88673,x88674,x88675),x88675)+~P24(f329(f329(f331(x88672),f329(x88673,x88674)),f329(f308(x88671,x88672,x88673),f329(f171(x88671),x88675))))
% 187.33/188.05 [8882]~P21(x88822,x88821,x88823,x88825)+P24(f329(f329(f244(f881(x88821,a869)),f329(f308(x88822,x88821,x88823),x88824)),f329(f308(x88822,x88821,x88823),x88825)))+~P24(f329(f329(f244(f881(x88822,a869)),x88824),x88825))
% 187.33/188.05 [9054]~P21(x90541,x90542,x90543,f252(f881(x90541,a869)))+~P24(f329(f329(f243(f881(x90542,a869)),x90544),f329(f308(x90541,x90542,x90543),x90545)))+P24(f329(f329(f243(f881(x90541,a869)),f329(f309(x90541,x90542,x90543),x90544)),x90545))
% 187.33/188.05 [9074]~E(f329(f308(x90743,x90741,x90744),f252(f881(x90743,a869))),f252(f881(x90741,a869)))+P24(f329(f329(f243(f881(x90741,a869)),x90742),f329(f308(x90743,x90741,x90744),x90745)))+~P24(f329(f329(f243(f881(x90743,a869)),f329(f309(x90743,x90741,x90744),x90742)),x90745))
% 187.33/188.05 [9098]~E(f329(f236(x90982),x90984),f329(f329(f177(x90981,x90982),x90985),x90983))+~P24(f329(f135(x90981),f329(f329(f152(f880(x90981,x90982),x90981),f263(x90981,x90982)),x90985)))+P24(f329(f329(f331(f880(x90981,x90982)),f329(f329(f264(x90981,x90982),x90983),x90984)),f329(f171(f880(x90981,x90982)),x90985)))
% 187.33/188.05 [9180]~P21(x91801,x91804,x91805,f252(f881(x91801,a869)))+~P24(f329(f329(f243(f881(x91804,a869)),f329(f308(x91801,x91804,x91805),x91802)),f329(f308(x91801,x91804,x91805),x91803)))+P24(f329(f329(f243(f881(x91801,a869)),x91802),x91803))
% 187.33/188.05 [9247]E(f329(f236(x92471),x92472),f329(f329(f177(x92473,x92471),x92474),x92475))+~P24(f329(f135(x92473),f329(f329(f152(f880(x92473,x92471),x92473),f263(x92473,x92471)),x92474)))+~P24(f329(f329(f331(f880(x92473,x92471)),f329(f329(f264(x92473,x92471),x92475),x92472)),f329(f171(f880(x92473,x92471)),x92474)))
% 187.33/188.05 [9249]E(f329(f329(f177(x92491,x92492),x92493),x92494),f329(f236(x92492),x92495))+~P24(f329(f135(x92491),f329(f329(f152(f880(x92491,x92492),x92491),f263(x92491,x92492)),x92493)))+~P24(f329(f329(f331(f880(x92491,x92492)),f329(f329(f264(x92491,x92492),x92494),x92495)),f329(f171(f880(x92491,x92492)),x92493)))
% 187.33/188.05 [9304]~P83(x93041)+~E(f329(x93043,f755(x93043,x93044,x93045,x93042,x93041)),f2(x93041))+E(f329(f164(x93041),f329(f329(f152(x93042,x93041),x93043),f329(f134(x93042,x93044),x93045))),f329(f164(x93041),f329(f329(f152(x93042,x93041),x93043),x93045)))
% 187.33/188.05 [9480]~P12(x94801,x94802,x94803)+~P24(f329(f62(x94801),x94805))+P24(f329(f67(x94801,x94802,x94803,x94804,x94805),f329(f329(f65(x94801,x94802,x94803),x94804),x94805)))
% 187.33/188.05 [9560]P24(f329(x95601,f656(x95602,x95601,x95603,x95604,x95605)))+~P24(f329(f329(f243(f881(x95605,a869)),x95604),x95603))+P24(f329(f329(f243(f881(x95605,a869)),f329(f329(f106(f881(x95605,a869)),x95604),f329(f249(x95605),x95601))),f329(f329(f106(f881(x95605,a869)),x95603),f329(f249(x95605),x95602))))
% 187.33/188.05 [9574]~P83(x95741)+~P24(f329(x95744,f755(x95743,x95744,x95745,x95742,x95741)))+E(f329(f164(x95741),f329(f329(f152(x95742,x95741),x95743),f329(f134(x95742,x95744),x95745))),f329(f164(x95741),f329(f329(f152(x95742,x95741),x95743),x95745)))
% 187.33/188.05 [9653]~P31(x96535)+P24(f329(f329(f331(x96531),f626(x96532,x96533,x96531,x96534,x96535)),x96533))+P24(f329(f329(f243(x96535),x96534),f329(f329(f43(x96531,x96535),x96533),x96532)))
% 187.33/188.05 [9656]~P83(x96561)+E(f329(f164(x96561),f329(f329(f152(x96562,x96561),x96563),f329(f134(x96562,x96564),x96565))),f329(f164(x96561),f329(f329(f152(x96562,x96561),x96563),x96565)))+P24(f329(f329(f331(x96562),f755(x96563,x96564,x96565,x96562,x96561)),f329(f171(x96562),x96565)))
% 187.33/188.05 [9666]~P24(f329(x96665,f656(x96665,x96663,x96664,x96662,x96661)))+~P24(f329(f329(f243(f881(x96661,a869)),x96662),x96664))+P24(f329(f329(f243(f881(x96661,a869)),f329(f329(f106(f881(x96661,a869)),x96662),f329(f249(x96661),x96663))),f329(f329(f106(f881(x96661,a869)),x96664),f329(f249(x96661),x96665))))
% 187.33/188.05 [9700]P39(x97001,x97002,x97003,x97004,x97005)+~E(f329(f194(f875(x97002)),x97005),f329(f194(f875(x97001)),x97004))+P24(f329(f329(f244(a874),f739(x97005,x97004,x97003,x97002,x97001)),f329(f194(f875(x97001)),x97004)))
% 187.33/188.05 [9701]P39(x97011,x97012,x97013,x97014,x97015)+~E(f329(f194(f875(x97012)),x97015),f329(f194(f875(x97011)),x97014))+P24(f329(f329(f244(a874),f774(x97013,x97015,x97012,x97014,x97011)),f329(f194(f875(x97011)),x97014)))
% 187.33/188.05 [9735]P24(f329(f329(f331(x97351),f656(x97352,x97353,x97354,x97355,x97351)),x97355))+~P24(f329(f329(f243(f881(x97351,a869)),x97355),x97354))+P24(f329(f329(f243(f881(x97351,a869)),f329(f329(f106(f881(x97351,a869)),x97355),f329(f249(x97351),x97353))),f329(f329(f106(f881(x97351,a869)),x97354),f329(f249(x97351),x97352))))
% 187.33/188.05 [9789]~P31(x97891)+~P24(f329(f329(f243(x97891),x97892),f329(x97895,f626(x97895,x97894,x97893,x97892,x97891))))+P24(f329(f329(f243(x97891),x97892),f329(f329(f43(x97893,x97891),x97894),x97895)))
% 187.33/188.05 [9822]~P76(x98221)+~P24(f329(f62(x98222),x98225))+E(f329(f329(f329(f66(x98221,x98222,f81(x98221)),f329(f329(f18(x98222,x98221,x98221),f329(f329(f8(x98221,f881(x98221,x98221),x98222),f81(x98221)),x98223)),x98224)),f78(x98221)),x98225),f329(f329(f81(x98221),f329(f329(f329(f66(x98221,x98222,f81(x98221)),x98223),f78(x98221)),x98225)),f329(f329(f329(f66(x98221,x98222,f81(x98221)),x98224),f78(x98221)),x98225)))
% 187.33/188.05 [9886]~P24(f329(f329(f331(f880(f881(x98861,a869),f881(x98861,a869))),f329(f329(f264(f881(x98861,a869),f881(x98861,a869)),x98865),x98864)),f321(x98861,x98863)))+~P24(f329(f329(f331(x98861),x98862),x98865))+P24(f329(f329(f331(f880(x98861,x98861)),f329(f329(f264(x98861,x98861),x98862),f586(x98863,x98864,x98865,x98861,x98862))),x98863))
% 187.33/188.05 [10014]~P24(f329(f329(f331(f880(f875(x100141),f875(x100141))),f329(f329(f264(f875(x100141),f875(x100141)),f329(f329(f126(x100141),x100145),x100142)),f329(f329(f126(x100141),x100145),x100143))),f145(x100141,x100144)))+P24(f329(f329(f331(f880(f875(x100141),f875(x100141))),f329(f329(f264(f875(x100141),f875(x100141)),x100142),x100143)),f145(x100141,x100144)))+P24(f329(f329(f331(f880(x100141,x100141)),f329(f329(f264(x100141,x100141),f703(x100144,x100143,x100142,x100145,x100141)),f703(x100144,x100143,x100142,x100145,x100141))),x100144))
% 187.33/188.05 [7137]~E(f329(f194(f875(x71371)),x71373),f329(f194(f875(x71372)),x71374))+E(f329(f329(f177(x71371,x71372),f329(f329(f181(x71371,x71372),x71373),x71374)),x71375),f206(x71372))+P24(f329(f329(f331(x71371),x71375),f329(f171(x71371),x71373)))
% 187.33/188.05 [7210]~E(x72103,x72105)+E(f329(f329(f163(x72101),f329(f329(f157(x72101,x72102),x72103),x72104)),x72105),x72104)+~P24(f329(f329(f244(a874),x72103),f329(f194(f875(x72101)),x72102)))
% 187.33/188.05 [7319]~E(f329(f329(f126(x73191),x73192),x73194),f329(f329(f126(x73191),x73193),x73195))+E(f329(f329(f174(x73191),f329(f194(f875(x73191)),x73192)),x73193),x73192)+P24(f329(f329(f243(a874),f329(f194(f875(x73191)),x73193)),f329(f194(f875(x73191)),x73192)))
% 187.33/188.05 [7336]~E(x73365,x73362)+P24(f329(x73361,x73362))+P24(f329(f329(f329(f329(a201,f32(x73361,x73363)),x73362),x73364),x73365))
% 187.33/188.05 [7830]~E(f329(f329(f126(x78301),x78302),x78304),f329(f329(f126(x78301),x78303),x78305))+E(f329(f329(f174(x78301),f329(f194(f875(x78301)),x78302)),x78303),x78302)+~P24(f329(f329(f243(a874),f329(f194(f875(x78301)),x78302)),f329(f194(f875(x78301)),x78303)))
% 187.33/188.05 [7854]~P24(f329(f62(x78541),f329(x78544,x78545)))+~P24(f329(f329(f331(x78542),x78545),x78543))+P24(f329(f62(x78541),f329(f329(f43(x78542,f881(x78541,a869)),x78543),x78544)))
% 187.33/188.05 [7907]~E(f329(f194(f875(x79071)),x79072),f329(f194(f875(x79073)),x79074))+~E(f329(f329(f177(x79071,x79073),f329(f329(f181(x79071,x79073),x79072),x79074)),x79075),f206(x79073))+~P24(f329(f329(f331(x79071),x79075),f329(f171(x79071),x79072)))
% 187.33/188.05 [8036]~P44(x80361,x80363,x80365)+~P44(x80361,x80362,x80364)+P44(x80361,f329(f329(f115(f881(x80361,a869)),x80362),x80363),f329(f329(f115(f881(f880(x80361,x80361),a869)),x80364),x80365))
% 187.33/188.05 [8037]~P44(x80371,x80373,x80375)+~P44(x80371,x80372,x80374)+P44(x80371,f329(f329(f106(f881(x80371,a869)),x80372),x80373),f329(f329(f106(f881(f880(x80371,x80371),a869)),x80374),x80375))
% 187.33/188.05 [8119]E(x81191,x81192)+P24(f329(x81193,x81191))+~P24(f329(f329(f329(f329(a201,f32(x81193,x81194)),x81191),x81195),x81192))
% 187.33/188.05 [8392]E(f329(f329(f264(x83921,x83922),f329(f329(f163(x83921),x83923),x83924)),f329(f329(f163(x83922),x83925),x83924)),f329(f329(f163(f880(x83921,x83922)),f329(f329(f181(x83921,x83922),x83923),x83925)),x83924))+~P24(f329(f329(f244(a874),x83924),f329(f194(f875(x83921)),x83923)))+~P24(f329(f329(f244(a874),x83924),f329(f194(f875(x83922)),x83925)))
% 187.33/188.05 [8553]~P44(x85531,x85533,x85534)+P24(f329(f329(f331(x85531),x85532),x85533))+~P24(f329(f329(f331(f880(x85531,x85531)),f329(f329(f264(x85531,x85531),x85535),x85532)),x85534))
% 187.33/188.05 [8554]~P44(x85541,x85543,x85544)+P24(f329(f329(f331(x85541),x85542),x85543))+~P24(f329(f329(f331(f880(x85541,x85541)),f329(f329(f264(x85541,x85541),x85542),x85545)),x85544))
% 187.33/188.05 [8555]~P6(x85551,x85553,x85554)+P24(f329(f329(f331(x85551),x85552),x85553))+~P24(f329(f329(f331(f880(x85551,x85551)),f329(f329(f264(x85551,x85551),x85555),x85552)),x85554))
% 187.33/188.05 [8556]~P6(x85561,x85563,x85564)+P24(f329(f329(f331(x85561),x85562),x85563))+~P24(f329(f329(f331(f880(x85561,x85561)),f329(f329(f264(x85561,x85561),x85562),x85565)),x85564))
% 187.33/188.05 [8815]~P6(x88151,x88155,x88152)+E(f329(f283(x88151,x88151,x88152),f329(f329(f307(x88151),x88153),f193(f881(x88151,a869)))),f329(f283(x88151,x88151,x88152),f329(f329(f307(x88151),x88154),f193(f881(x88151,a869)))))+~P24(f329(f329(f331(f880(x88151,x88151)),f329(f329(f264(x88151,x88151),x88153),x88154)),x88152))
% 187.33/188.05 [8897]~P24(f329(f329(f329(f329(a201,x88972),x88973),x88974),x88975))+~P24(f329(f329(f329(f329(a201,f32(x88971,x88972)),x88975),x88974),x88973))+P24(f329(f329(f329(f329(a201,f32(x88971,x88972)),x88973),x88974),x88973))
% 187.33/188.05 [9009]P24(f329(x90091,x90092))+~P24(f329(f329(f331(x90093),x90092),x90095))+P24(f329(f329(f331(x90093),f859(x90091,x90094,x90095,x90093)),f329(f329(f115(f881(x90093,a869)),x90095),x90094)))
% 187.33/188.05 [9010]P24(f329(x90101,x90102))+~P24(f329(f329(f331(x90103),x90102),x90104))+P24(f329(f329(f331(x90103),f859(x90101,x90104,x90105,x90103)),f329(f329(f115(f881(x90103,a869)),x90105),x90104)))
% 187.33/188.05 [9018]~P24(f329(x90182,x90185))+~P24(f329(f329(f331(x90181),x90185),x90184))+P24(f329(f329(f331(x90181),f848(x90182,x90183,x90184,x90181)),f329(f329(f115(f881(x90181,a869)),x90184),x90183)))
% 187.33/188.05 [9019]~P24(f329(x90192,x90195))+~P24(f329(f329(f331(x90191),x90195),x90193))+P24(f329(f329(f331(x90191),f848(x90192,x90193,x90194,x90191)),f329(f329(f115(f881(x90191,a869)),x90194),x90193)))
% 187.33/188.05 [9034]~P24(f329(f329(f243(f881(x90341,a869)),x90343),x90345))+~P24(f329(f329(f243(f881(x90341,a869)),x90342),x90344))+P24(f329(f329(f243(f881(x90341,a869)),f329(f329(f115(f881(x90341,a869)),x90342),x90343)),f329(f329(f115(f881(x90341,a869)),x90344),x90345)))
% 187.33/188.05 [9035]~P24(f329(f329(f243(f881(x90351,a869)),x90355),x90353))+~P24(f329(f329(f243(f881(x90351,a869)),x90352),x90354))+P24(f329(f329(f243(f881(x90351,a869)),f329(f329(f22(f881(x90351,a869)),x90352),x90353)),f329(f329(f22(f881(x90351,a869)),x90354),x90355)))
% 187.33/188.05 [9036]~P24(f329(f329(f243(f881(x90361,a869)),x90363),x90365))+~P24(f329(f329(f243(f881(x90361,a869)),x90362),x90364))+P24(f329(f329(f243(f881(x90361,a869)),f329(f329(f106(f881(x90361,a869)),x90362),x90363)),f329(f329(f106(f881(x90361,a869)),x90364),x90365)))
% 187.33/188.05 [9123]~E(f329(f194(f875(x91231)),x91233),f329(f194(f875(x91232)),x91234))+E(f329(f329(f177(x91231,x91232),f329(f329(f181(x91231,x91232),x91233),x91234)),x91235),f329(f236(x91232),f712(x91235,x91234,x91232,x91233,x91231)))+~P24(f329(f329(f331(x91231),x91235),f329(f171(x91231),x91233)))
% 187.33/188.05 [9127]P24(f329(f329(f331(f880(x91271,x91271)),f329(f329(f264(x91271,x91271),x91272),x91273)),f323(x91271,x91274,x91275)))+~P24(f329(f329(f243(a874),f329(x91274,x91272)),f329(x91274,x91273)))+~P24(f329(f329(f331(f880(x91271,x91271)),f329(f329(f264(x91271,x91271),x91272),x91273)),x91275))
% 187.33/188.05 [9314]P24(f329(f329(f331(f880(x93141,x93141)),f329(f329(f264(x93141,x93141),x93142),x93143)),f305(x93141,x93144)))+~P24(f329(f329(f331(f880(x93141,x93141)),f329(f329(f264(x93141,x93141),x93142),x93145)),f305(x93141,x93144)))+~P24(f329(f329(f331(f880(x93141,x93141)),f329(f329(f264(x93141,x93141),x93145),x93143)),x93144))
% 187.33/188.05 [9315]P24(f329(f329(f331(f880(x93151,x93151)),f329(f329(f264(x93151,x93151),x93152),x93153)),f305(x93151,x93154)))+~P24(f329(f329(f331(f880(x93151,x93151)),f329(f329(f264(x93151,x93151),x93155),x93153)),f305(x93151,x93154)))+~P24(f329(f329(f331(f880(x93151,x93151)),f329(f329(f264(x93151,x93151),x93152),x93155)),x93154))
% 187.33/188.05 [9411]E(x94111,x94112)+E(f329(a117,f608(x94113,x94114,x94111,x94112,x94115)),x94114)+~P24(f329(f329(f331(f880(x94115,x94115)),f329(f329(f264(x94115,x94115),x94112),x94111)),f329(f329(f188(f880(x94115,x94115),a869),x94114),x94113)))
% 187.33/188.05 [9412]E(x94121,x94122)+E(f329(a117,f610(x94123,x94124,x94121,x94122,x94125)),x94124)+~P24(f329(f329(f331(f880(x94125,x94125)),f329(f329(f264(x94125,x94125),x94122),x94121)),f329(f329(f188(f880(x94125,x94125),a869),x94124),x94123)))
% 187.33/188.05 [9413]E(x94131,f2(a874))+E(f329(a117,f608(x94132,x94131,x94133,x94134,x94135)),x94131)+~P24(f329(f329(f331(f880(x94135,x94135)),f329(f329(f264(x94135,x94135),x94134),x94133)),f329(f329(f188(f880(x94135,x94135),a869),x94131),x94132)))
% 187.33/188.05 [9414]E(x94141,f2(a874))+E(f329(a117,f610(x94142,x94141,x94143,x94144,x94145)),x94141)+~P24(f329(f329(f331(f880(x94145,x94145)),f329(f329(f264(x94145,x94145),x94144),x94143)),f329(f329(f188(f880(x94145,x94145),a869),x94141),x94142)))
% 187.33/188.05 [9430]P24(f329(f329(f331(f880(x94301,x94301)),f329(f329(f264(x94301,x94301),x94302),x94303)),f329(f329(f286(x94301,x94301,x94301),x94304),f305(x94301,x94304))))+~P24(f329(f329(f331(f880(x94301,x94301)),f329(f329(f264(x94301,x94301),x94302),x94305)),x94304))+~P24(f329(f329(f331(f880(x94301,x94301)),f329(f329(f264(x94301,x94301),x94305),x94303)),x94304))
% 187.33/188.05 [9437]~P24(f329(f329(f331(f880(x94371,x94371)),f329(f329(f264(x94371,x94371),x94372),x94375)),f305(x94371,x94374)))+P24(f329(f329(f331(f880(x94371,x94371)),f329(f329(f264(x94371,x94371),x94372),x94373)),f329(f329(f286(x94371,x94371,x94371),x94374),f305(x94371,x94374))))+~P24(f329(f329(f331(f880(x94371,x94371)),f329(f329(f264(x94371,x94371),x94375),x94373)),x94374))
% 187.33/188.05 [9476]~P6(x94761,x94765,x94762)+~P24(f329(f329(f331(f880(x94761,x94761)),f329(f329(f264(x94761,x94761),x94763),x94764)),x94762))+P24(f329(f329(f243(f881(x94761,a869)),f329(f283(x94761,x94761,x94762),f329(f329(f307(x94761),x94763),f193(f881(x94761,a869))))),f329(f283(x94761,x94761,x94762),f329(f329(f307(x94761),x94764),f193(f881(x94761,a869))))))
% 187.33/188.05 [9499]E(x94991,x94992)+P24(f329(f329(f329(f329(a201,x94993),x94991),x94994),f867(x94992,x94994,x94991,x94993,x94995)))+~P24(f329(f329(f329(f329(a201,f32(x94995,x94993)),x94991),x94994),x94992))
% 187.33/188.05 [9503]~P24(f329(x95035,x95032))+P24(f329(f329(f329(f329(a201,x95031),x95032),x95033),f867(x95034,x95033,x95032,x95031,x95035)))+~P24(f329(f329(f329(f329(a201,f32(x95035,x95031)),x95032),x95033),x95034))
% 187.33/188.05 [9532]P24(f329(f329(f331(f880(x95321,x95321)),f329(f329(f264(x95321,x95321),x95322),x95323)),f329(f329(f286(x95321,x95321,x95321),x95324),f305(x95321,x95324))))+~P24(f329(f329(f331(f880(x95321,x95321)),f329(f329(f264(x95321,x95321),x95322),x95325)),f329(f329(f286(x95321,x95321,x95321),x95324),f305(x95321,x95324))))+~P24(f329(f329(f331(f880(x95321,x95321)),f329(f329(f264(x95321,x95321),x95325),x95323)),x95324))
% 187.33/188.05 [9533]P24(f329(f329(f331(f880(x95331,x95331)),f329(f329(f264(x95331,x95331),x95332),x95333)),f329(f329(f286(x95331,x95331,x95331),x95334),f305(x95331,x95334))))+~P24(f329(f329(f331(f880(x95331,x95331)),f329(f329(f264(x95331,x95331),x95335),x95333)),f329(f329(f286(x95331,x95331,x95331),x95334),f305(x95331,x95334))))+~P24(f329(f329(f331(f880(x95331,x95331)),f329(f329(f264(x95331,x95331),x95332),x95335)),x95334))
% 187.33/188.05 [9583]~P24(f329(f67(x95831,x95831,x95834,x95832,x95833),x95835))+P24(f329(f329(f331(x95831),x95832),x95833))+P24(f329(f63(x95831,x95834,f329(f329(f307(x95831),x95832),x95833)),x95835))
% 187.33/188.05 [9622]~E(f329(f308(x96223,x96222,x96225),x96224),x96221)+E(x96221,f193(f881(x96222,a869)))+P24(f329(f329(f243(f881(x96223,a869)),f329(f308(x96222,x96223,f502(x96224,x96223,x96222,x96221)),x96221)),x96224))
% 187.33/188.05 [9669]~P31(x96695)+P24(f329(f329(f331(x96691),f437(x96692,x96693,x96694,x96691,x96695)),x96694))+P24(f329(f329(f243(x96695),f329(f329(f42(x96691,x96695),x96694),x96693)),x96692))
% 187.33/188.05 [9721]P39(x97211,x97212,x97213,x97214,x97215)+~E(f329(f194(f875(x97211)),x97214),f329(f194(f875(x97212)),x97215))+P24(f329(f329(f331(f880(x97211,x97212)),f737(x97215,x97214,x97213,x97212,x97211)),f329(f171(f880(x97211,x97212)),f329(f329(f181(x97211,x97212),x97214),x97215))))
% 187.33/188.05 [9722]P39(x97221,x97222,x97223,x97224,x97225)+~E(f329(f194(f875(x97221)),x97224),f329(f194(f875(x97222)),x97225))+P24(f329(f329(f331(f880(x97221,x97222)),f738(x97223,x97225,x97224,x97222,x97221)),f329(f171(f880(x97221,x97222)),f329(f329(f181(x97221,x97222),x97224),x97225))))
% 187.33/188.05 [9853]E(x98531,x98532)+P24(f329(f329(f329(f329(a201,f32(x98533,x98534)),f867(x98531,x98535,x98532,x98534,x98533)),x98535),x98531))+~P24(f329(f329(f329(f329(a201,f32(x98533,x98534)),x98532),x98535),x98531))
% 187.33/188.05 [9855]~P24(f329(x98551,x98555))+P24(f329(f329(f329(f329(a201,f32(x98551,x98552)),f867(x98553,x98554,x98555,x98552,x98551)),x98554),x98553))+~P24(f329(f329(f329(f329(a201,f32(x98551,x98552)),x98555),x98554),x98553))
% 187.33/188.05 [9863]E(x98631,x98632)+P24(f329(f329(f331(f880(x98633,x98633)),f329(f329(f264(x98633,x98633),x98631),f611(x98634,x98635,x98632,x98631,x98633))),x98634))+~P24(f329(f329(f331(f880(x98633,x98633)),f329(f329(f264(x98633,x98633),x98631),x98632)),f329(f329(f188(f880(x98633,x98633),a869),x98635),x98634)))
% 187.33/188.05 [9864]E(x98641,f2(a874))+P24(f329(f329(f331(f880(x98642,x98642)),f329(f329(f264(x98642,x98642),x98643),f611(x98644,x98641,x98645,x98643,x98642))),x98644))+~P24(f329(f329(f331(f880(x98642,x98642)),f329(f329(f264(x98642,x98642),x98643),x98645)),f329(f329(f188(f880(x98642,x98642),a869),x98641),x98644)))
% 187.33/188.05 [9907]~P31(x99071)+~P24(f329(f329(f243(x99071),f329(x99074,f437(x99075,x99074,x99073,x99072,x99071))),x99075))+P24(f329(f329(f243(x99071),f329(f329(f42(x99072,x99071),x99073),x99074)),x99075))
% 187.33/188.05 [9949]E(x99491,x99492)+P24(f329(f329(f331(f880(x99493,x99493)),f329(f329(f264(x99493,x99493),f609(x99494,x99495,x99491,x99492,x99493)),x99491)),x99494))+~P24(f329(f329(f331(f880(x99493,x99493)),f329(f329(f264(x99493,x99493),x99492),x99491)),f329(f329(f188(f880(x99493,x99493),a869),x99495),x99494)))
% 187.33/188.05 [9950]E(x99501,f2(a874))+P24(f329(f329(f331(f880(x99502,x99502)),f329(f329(f264(x99502,x99502),f609(x99503,x99501,x99504,x99505,x99502)),x99504)),x99503))+~P24(f329(f329(f331(f880(x99502,x99502)),f329(f329(f264(x99502,x99502),x99505),x99504)),f329(f329(f188(f880(x99502,x99502),a869),x99501),x99503)))
% 187.33/188.05 [9954]E(x99541,x99542)+P24(f329(f329(f331(f880(x99543,x99543)),f329(f329(f264(x99543,x99543),x99541),f609(x99544,x99545,x99542,x99541,x99543))),f329(f329(f188(f880(x99543,x99543),a869),f608(x99544,x99545,x99542,x99541,x99543)),x99544)))+~P24(f329(f329(f331(f880(x99543,x99543)),f329(f329(f264(x99543,x99543),x99541),x99542)),f329(f329(f188(f880(x99543,x99543),a869),x99545),x99544)))
% 187.33/188.05 [9955]E(x99551,f2(a874))+P24(f329(f329(f331(f880(x99552,x99552)),f329(f329(f264(x99552,x99552),x99553),f609(x99554,x99551,x99555,x99553,x99552))),f329(f329(f188(f880(x99552,x99552),a869),f608(x99554,x99551,x99555,x99553,x99552)),x99554)))+~P24(f329(f329(f331(f880(x99552,x99552)),f329(f329(f264(x99552,x99552),x99553),x99555)),f329(f329(f188(f880(x99552,x99552),a869),x99551),x99554)))
% 187.33/188.05 [10005]E(x100051,x100052)+P24(f329(f329(f331(f880(x100053,x100053)),f329(f329(f264(x100053,x100053),f611(x100054,x100055,x100051,x100052,x100053)),x100051)),f329(f329(f188(f880(x100053,x100053),a869),f610(x100054,x100055,x100051,x100052,x100053)),x100054)))+~P24(f329(f329(f331(f880(x100053,x100053)),f329(f329(f264(x100053,x100053),x100052),x100051)),f329(f329(f188(f880(x100053,x100053),a869),x100055),x100054)))
% 187.33/188.05 [10006]E(x100061,f2(a874))+P24(f329(f329(f331(f880(x100062,x100062)),f329(f329(f264(x100062,x100062),f611(x100063,x100061,x100064,x100065,x100062)),x100064)),f329(f329(f188(f880(x100062,x100062),a869),f610(x100063,x100061,x100064,x100065,x100062)),x100063)))+~P24(f329(f329(f331(f880(x100062,x100062)),f329(f329(f264(x100062,x100062),x100065),x100064)),f329(f329(f188(f880(x100062,x100062),a869),x100061),x100063)))
% 187.33/188.05 [10039]~P72(x100392)+~P24(f329(f62(x100391),x100395))+E(f329(f329(f6(x100391,x100392),f329(f329(f7(x100391,x100392,x100392),f329(f329(f18(x100391,x100392,f881(x100392,x100392)),f329(f329(f8(a869,f881(x100392,f881(x100392,x100392)),x100391),f101(x100392)),f329(f329(f7(x100391,f881(x100391,a869),a869),f331(x100391)),x100393))),x100394)),f2(x100392))),x100395),f329(f329(f6(x100391,x100392),x100394),f329(f329(f106(f881(x100391,a869)),x100395),x100393)))
% 187.33/188.05 [8617]~P72(x86171)+~P24(f329(f62(x86174),x86175))+E(f329(f329(f80(x86171),f329(x86172,x86173)),f329(f329(f6(x86174,x86171),x86172),f329(f329(f22(f881(x86174,a869)),x86175),f329(f329(f307(x86174),x86173),f193(f881(x86174,a869)))))),f329(f329(f6(x86174,x86171),x86172),f329(f329(f307(x86174),x86173),x86175)))
% 187.33/188.05 [8618]~P76(x86181)+~P24(f329(f62(x86184),x86185))+E(f329(f329(f81(x86181),f329(x86182,x86183)),f329(f329(f9(x86184,x86181),x86182),f329(f329(f22(f881(x86184,a869)),x86185),f329(f329(f307(x86184),x86183),f193(f881(x86184,a869)))))),f329(f329(f9(x86184,x86181),x86182),f329(f329(f307(x86184),x86183),x86185)))
% 187.33/188.05 [8938]~P27(x89382)+~P33(x89382,f329(f167(x89382),f329(f329(f152(x89381,x89382),x89384),x89385)))+E(f329(f134(x89381,f329(f329(f8(x89382,a869,x89381),f329(f244(x89382),x89383)),x89384)),x89385),f176(x89381,f329(f329(f8(x89382,a869,x89381),f329(f244(x89382),x89383)),x89384),x89385))
% 187.33/188.05 [8963]~P72(x89631)+E(f329(f329(f80(x89631),f329(f329(f6(a874,x89631),x89632),f300(a874,x89633,x89634))),f329(f329(f6(a874,x89631),x89632),f300(a874,f329(f329(f80(a874),x89634),f78(a874)),f329(f329(f80(a874),x89634),x89635)))),f329(f329(f6(a874,x89631),x89632),f300(a874,x89633,f329(f329(f80(a874),x89634),x89635))))+~P24(f329(f329(f243(a874),x89633),f329(f329(f80(a874),x89634),f78(a874))))
% 187.33/188.05 [8964]~P24(f329(f329(f331(x89641),x89644),x89645))+~P24(f329(f329(f243(f881(x89641,a869)),f329(f171(x89641),x89642)),x89645))+P24(f329(f329(f243(f881(x89641,a869)),f329(f171(x89641),f329(f329(f157(x89641,x89642),x89643),x89644))),x89645))
% 187.33/188.05 [9190]~P31(x91902)+~P24(f329(f62(x91901),x91905))+E(f329(f329(f65(x91901,x91902,f329(f329(f8(x91902,f881(x91902,x91902),x91901),f115(x91902)),x91903)),x91904),x91905),f329(f329(f115(x91902),x91904),f329(f329(f42(x91901,x91902),x91905),x91903)))
% 187.33/188.05 [9191]~P31(x91912)+~P24(f329(f62(x91911),x91915))+E(f329(f329(f65(x91911,x91912,f329(f329(f8(x91912,f881(x91912,x91912),x91911),f106(x91912)),x91913)),x91914),x91915),f329(f329(f106(x91912),x91914),f329(f329(f43(x91911,x91912),x91915),x91913)))
% 187.33/188.05 [9238]E(f329(x92381,x92382),f329(x92381,x92383))+P24(f329(f329(f244(a874),f329(x92381,x92382)),f329(x92381,x92383)))+~P24(f329(f329(f331(f880(x92384,x92384)),f329(f329(f264(x92384,x92384),x92382),x92383)),f151(x92384,f329(f329(f149(f881(x92384,a874)),x92381),x92385))))
% 187.33/188.05 [9271]~E(f329(x92714,x92712),f329(x92714,x92713))+~P24(f329(f329(f331(f880(x92711,x92711)),f329(f329(f264(x92711,x92711),x92712),x92713)),f151(x92711,x92715)))+P24(f329(f329(f331(f880(x92711,x92711)),f329(f329(f264(x92711,x92711),x92712),x92713)),f151(x92711,f329(f329(f149(f881(x92711,a874)),x92714),x92715))))
% 187.33/188.05 [9293]~P21(x92931,x92932,x92933,x92935)+P21(x92931,x92932,x92933,f329(f329(f307(x92931),x92934),x92935))+P24(f329(f329(f331(x92932),f329(x92933,x92934)),f329(f308(x92931,x92932,x92933),f329(f329(f22(f881(x92931,a869)),x92935),f329(f329(f307(x92931),x92934),f193(f881(x92931,a869)))))))
% 187.33/188.05 [9297]P24(f329(x92972,x92975))+~P24(f329(f329(f331(x92971),x92975),f329(f171(x92971),x92973)))+E(f329(f329(f136(x92971),f329(f194(f875(x92971)),f176(x92971,x92972,f329(f329(f126(x92971),x92973),x92974)))),f329(f329(f126(x92971),x92973),x92974)),f329(f329(f126(x92971),f329(f329(f136(x92971),f329(f194(f875(x92971)),f176(x92971,x92972,x92973))),x92973)),x92974))
% 187.33/188.05 [9300]~P24(f329(f329(f331(f880(x93001,x93001)),f329(f329(f264(x93001,x93001),x93002),x93003)),f151(x93001,x93005)))+~P24(f329(f329(f243(a874),f329(x93004,x93002)),f329(x93004,x93003)))+P24(f329(f329(f331(f880(x93001,x93001)),f329(f329(f264(x93001,x93001),x93002),x93003)),f151(x93001,f329(f329(f149(f881(x93001,a874)),x93004),x93005))))
% 187.33/188.05 [9365]P24(f329(f329(f331(f880(x93654,x93654)),f329(f329(f264(x93654,x93654),x93652),x93653)),f151(x93654,x93655)))+P24(f329(f329(f244(a874),f329(x93651,x93652)),f329(x93651,x93653)))+~P24(f329(f329(f331(f880(x93654,x93654)),f329(f329(f264(x93654,x93654),x93652),x93653)),f151(x93654,f329(f329(f149(f881(x93654,a874)),x93651),x93655))))
% 187.33/188.05 [9506]~P24(f329(f329(f331(f880(f875(x95061),f875(x95061))),f329(f329(f264(f875(x95061),f875(x95061)),x95062),x95064)),f156(x95061,x95065)))+~P24(f329(f329(f244(a874),x95063),f329(f194(f875(x95061)),x95062)))+P24(f329(f329(f331(f880(x95061,x95061)),f329(f329(f264(x95061,x95061),f329(f329(f163(x95061),x95062),x95063)),f329(f329(f163(x95061),x95064),x95063))),x95065))
% 187.33/188.05 [9749]E(x97491,f2(a1))+~P24(f329(f49(x97493,x97491),f329(f329(f264(a1,a1),x97494),x97495)))+P24(f329(f49(f329(f329(f81(a1),x97492),x97493),x97491),f329(f329(f264(a1,a1),f329(f329(f80(a1),f329(f329(f81(a1),x97492),x97494)),f329(f329(f39(a1),f329(f329(f81(a1),x97492),x97495)),x97491))),f45(a1,f329(f329(f81(a1),x97492),x97495),x97491))))
% 187.33/188.05 [9751]~P24(f329(f329(f244(a874),f2(a874)),x97513))+~P24(f329(f48(x97512,x97513),f329(f329(f264(a874,a874),x97514),x97515)))+P24(f329(f48(f329(f329(f81(a874),x97511),x97512),x97513),f329(f329(f264(a874,a874),f329(f329(f80(a874),f329(f329(f81(a874),x97511),x97514)),f329(f329(f39(a874),f329(f329(f81(a874),x97511),x97515)),x97513))),f45(a874,f329(f329(f81(a874),x97511),x97515),x97513))))
% 187.33/188.05 [10062]~P72(x100622)+~P24(f329(f62(x100621),x100624))+E(f329(f329(f6(x100621,x100622),x100623),f329(f249(x100621),f329(f329(f18(x100621,a869,a869),f329(f329(f8(a869,f881(a869,a869),x100621),a327),f329(f329(f7(x100621,f881(x100621,a869),a869),f331(x100621)),x100624))),f329(f329(f7(x100621,f881(x100621,a869),a869),f331(x100621)),x100625)))),f329(f329(f6(x100621,x100622),f329(f329(f7(x100621,x100622,x100622),f329(f329(f18(x100621,x100622,f881(x100622,x100622)),f329(f329(f8(a869,f881(x100622,f881(x100622,x100622)),x100621),f101(x100622)),f329(f329(f7(x100621,f881(x100621,a869),a869),f331(x100621)),x100625))),x100623)),f2(x100622))),x100624))
% 187.33/188.05 [8247]~E(f329(f329(f126(x82471),x82472),x82475),f329(f329(f126(x82471),x82473),x82474))+E(f329(f329(f126(x82471),f329(f329(f136(x82471),f329(f194(f875(x82471)),x82472)),x82473)),x82474),x82475)+P24(f329(f329(f243(a874),f329(f194(f875(x82471)),x82473)),f329(f194(f875(x82471)),x82472)))
% 187.33/188.05 [8446]~E(f329(f329(f126(x84462),x84463),x84461),f329(f329(f126(x84462),x84464),x84465))+E(x84461,f329(f329(f126(x84462),f329(f329(f136(x84462),f329(f194(f875(x84462)),x84463)),x84464)),x84465))+~P24(f329(f329(f243(a874),f329(f194(f875(x84462)),x84463)),f329(f194(f875(x84462)),x84464)))
% 187.33/188.05 [8536]~E(f329(f329(f80(a874),f329(f329(f81(a874),x85363),x85364)),x85361),f329(f329(f80(a874),f329(f329(f81(a874),x85362),x85364)),x85365))+~P24(f329(f329(f243(a874),x85363),x85362))+E(x85361,f329(f329(f80(a874),f329(f329(f81(a874),f329(f329(f22(a874),x85362),x85363)),x85364)),x85365))
% 187.33/188.05 [8537]~E(f329(f329(f80(a874),f329(f329(f81(a874),x85371),x85373)),x85374),f329(f329(f80(a874),f329(f329(f81(a874),x85372),x85373)),x85375))+~P24(f329(f329(f243(a874),x85372),x85371))+E(f329(f329(f80(a874),f329(f329(f81(a874),f329(f329(f22(a874),x85371),x85372)),x85373)),x85374),x85375)
% 187.33/188.05 [8694]E(f329(f329(f80(a874),f329(f329(f81(a874),x86941),x86942)),x86943),f329(f329(f80(a874),f329(f329(f81(a874),x86944),x86942)),x86945))+~P24(f329(f329(f243(a874),x86944),x86941))+~E(x86945,f329(f329(f80(a874),f329(f329(f81(a874),f329(f329(f22(a874),x86941),x86944)),x86942)),x86943))
% 187.33/188.05 [8695]E(f329(f329(f80(a874),f329(f329(f81(a874),x86951),x86952)),x86953),f329(f329(f80(a874),f329(f329(f81(a874),x86954),x86952)),x86955))+~P24(f329(f329(f243(a874),x86954),x86951))+~E(f329(f329(f80(a874),f329(f329(f81(a874),f329(f329(f22(a874),x86951),x86954)),x86952)),x86953),x86955)
% 187.33/188.05 [9559]~P61(x95592)+~P24(f329(f62(x95591),x95595))+E(f329(f329(f9(x95591,x95592),f329(f329(f18(x95591,x95592,x95592),f329(f329(f8(x95592,f881(x95592,x95592),x95591),f287(x95592)),x95593)),x95594)),x95595),f329(f329(f287(x95592),f329(f329(f9(x95591,x95592),x95593),x95595)),f329(f329(f9(x95591,x95592),x95594),x95595)))
% 187.33/188.05 [9684]~E(f612(x96845,x96844,x96843,x96842,x96841),f613(x96845,x96844,x96843,x96842,x96841))+P24(f329(f329(f331(f880(x96841,x96841)),f329(f329(f264(x96841,x96841),x96842),x96843)),f305(x96841,x96844)))+~P24(f329(f329(f331(f880(x96841,x96841)),f329(f329(f264(x96841,x96841),x96842),x96843)),f305(x96841,f329(f329(f115(f881(f880(x96841,x96841),a869)),x96844),x96845))))
% 187.33/188.05 [9685]~E(f614(x96855,x96854,x96853,x96852,x96851),f615(x96855,x96854,x96853,x96852,x96851))+P24(f329(f329(f331(f880(x96851,x96851)),f329(f329(f264(x96851,x96851),x96852),x96853)),f305(x96851,x96854)))+~P24(f329(f329(f331(f880(x96851,x96851)),f329(f329(f264(x96851,x96851),x96852),x96853)),f305(x96851,f329(f329(f115(f881(f880(x96851,x96851),a869)),x96854),x96855))))
% 187.33/188.05 [9897]P24(f329(f329(f331(f880(x98971,x98971)),f329(f329(f264(x98971,x98971),x98972),f613(x98975,x98974,x98973,x98972,x98971))),f305(x98971,x98974)))+P24(f329(f329(f331(f880(x98971,x98971)),f329(f329(f264(x98971,x98971),x98972),x98973)),f305(x98971,x98974)))+~P24(f329(f329(f331(f880(x98971,x98971)),f329(f329(f264(x98971,x98971),x98972),x98973)),f305(x98971,f329(f329(f115(f881(f880(x98971,x98971),a869)),x98974),x98975))))
% 187.33/188.05 [9976]P24(f329(f329(f331(f880(x99761,x99761)),f329(f329(f264(x99761,x99761),f615(x99765,x99764,x99763,x99762,x99761)),x99763)),f305(x99761,x99764)))+P24(f329(f329(f331(f880(x99761,x99761)),f329(f329(f264(x99761,x99761),x99762),x99763)),f305(x99761,x99764)))+~P24(f329(f329(f331(f880(x99761,x99761)),f329(f329(f264(x99761,x99761),x99762),x99763)),f305(x99761,f329(f329(f115(f881(f880(x99761,x99761),a869)),x99764),x99765))))
% 187.33/188.05 [10012]P24(f329(f329(f331(f880(x100121,x100121)),f329(f329(f264(x100121,x100121),x100122),x100123)),f305(x100121,x100124)))+P24(f329(f329(f331(f880(x100121,x100121)),f329(f329(f264(x100121,x100121),f613(x100125,x100124,x100123,x100122,x100121)),f612(x100125,x100124,x100123,x100122,x100121))),x100125))+~P24(f329(f329(f331(f880(x100121,x100121)),f329(f329(f264(x100121,x100121),x100122),x100123)),f305(x100121,f329(f329(f115(f881(f880(x100121,x100121),a869)),x100124),x100125))))
% 187.33/188.05 [10013]P24(f329(f329(f331(f880(x100131,x100131)),f329(f329(f264(x100131,x100131),x100132),x100133)),f305(x100131,x100134)))+P24(f329(f329(f331(f880(x100131,x100131)),f329(f329(f264(x100131,x100131),f614(x100135,x100134,x100133,x100132,x100131)),f615(x100135,x100134,x100133,x100132,x100131))),x100135))+~P24(f329(f329(f331(f880(x100131,x100131)),f329(f329(f264(x100131,x100131),x100132),x100133)),f305(x100131,f329(f329(f115(f881(f880(x100131,x100131),a869)),x100134),x100135))))
% 187.33/188.05 [10133]~P24(f329(f329(f331(f880(f875(x101331),f875(x101331))),f329(f329(f264(f875(x101331),f875(x101331)),x101334),x101335)),f156(x101331,x101332)))+~P24(f329(f329(f331(f880(x101331,x101331)),x101333),f329(f171(f880(x101331,x101331)),f329(f329(f181(x101331,x101331),x101334),x101335))))+P24(f329(f329(f268(x101331,x101331,a869),f329(f329(f7(x101331,f881(f880(x101331,x101331),a869),f881(x101331,a869)),f329(f329(f8(f881(x101331,f881(f881(f880(x101331,x101331),a869),a869)),f881(f881(f880(x101331,x101331),a869),f881(x101331,a869)),x101331),f7(x101331,f881(f880(x101331,x101331),a869),a869)),f329(f329(f8(f881(x101331,f880(x101331,x101331)),f881(x101331,f881(f881(f880(x101331,x101331),a869),a869)),x101331),f329(f8(f880(x101331,x101331),f881(f881(f880(x101331,x101331),a869),a869),x101331),f331(f880(x101331,x101331)))),f264(x101331,x101331)))),x101332)),x101333))
% 187.33/188.05 [9587]~P24(f329(f329(f243(a874),x95873),x95872))+~P24(f329(f329(f243(a874),f329(f329(f80(a874),f329(f329(f81(a874),x95873),x95874)),x95871)),f329(f329(f80(a874),f329(f329(f81(a874),x95872),x95874)),x95875)))+P24(f329(f329(f243(a874),x95871),f329(f329(f80(a874),f329(f329(f81(a874),f329(f329(f22(a874),x95872),x95873)),x95874)),x95875)))
% 187.33/188.05 [9588]~P24(f329(f329(f243(a874),x95883),x95882))+~P24(f329(f329(f244(a874),f329(f329(f80(a874),f329(f329(f81(a874),x95883),x95884)),x95881)),f329(f329(f80(a874),f329(f329(f81(a874),x95882),x95884)),x95885)))+P24(f329(f329(f244(a874),x95881),f329(f329(f80(a874),f329(f329(f81(a874),f329(f329(f22(a874),x95882),x95883)),x95884)),x95885)))
% 187.33/188.05 [9606]~P24(f329(f329(f243(a874),x96061),x96064))+P24(f329(f329(f243(a874),f329(f329(f80(a874),f329(f329(f81(a874),x96061),x96062)),x96063)),f329(f329(f80(a874),f329(f329(f81(a874),x96064),x96062)),x96065)))+~P24(f329(f329(f243(a874),x96063),f329(f329(f80(a874),f329(f329(f81(a874),f329(f329(f22(a874),x96064),x96061)),x96062)),x96065)))
% 187.33/188.05 [9607]~P24(f329(f329(f243(a874),x96071),x96074))+P24(f329(f329(f244(a874),f329(f329(f80(a874),f329(f329(f81(a874),x96071),x96072)),x96073)),f329(f329(f80(a874),f329(f329(f81(a874),x96074),x96072)),x96075)))+~P24(f329(f329(f244(a874),x96073),f329(f329(f80(a874),f329(f329(f81(a874),f329(f329(f22(a874),x96074),x96071)),x96072)),x96075)))
% 187.33/188.05 [9719]~P24(f329(f329(f243(a874),x97192),x97191))+~P24(f329(f329(f243(a874),f329(f329(f80(a874),f329(f329(f81(a874),x97191),x97193)),x97194)),f329(f329(f80(a874),f329(f329(f81(a874),x97192),x97193)),x97195)))+P24(f329(f329(f243(a874),f329(f329(f80(a874),f329(f329(f81(a874),f329(f329(f22(a874),x97191),x97192)),x97193)),x97194)),x97195))
% 187.33/188.05 [9720]~P24(f329(f329(f243(a874),x97202),x97201))+~P24(f329(f329(f244(a874),f329(f329(f80(a874),f329(f329(f81(a874),x97201),x97203)),x97204)),f329(f329(f80(a874),f329(f329(f81(a874),x97202),x97203)),x97205)))+P24(f329(f329(f244(a874),f329(f329(f80(a874),f329(f329(f81(a874),f329(f329(f22(a874),x97201),x97202)),x97203)),x97204)),x97205))
% 187.33/188.05 [9773]~P24(f329(f329(f243(a874),x97734),x97731))+P24(f329(f329(f243(a874),f329(f329(f80(a874),f329(f329(f81(a874),x97731),x97732)),x97733)),f329(f329(f80(a874),f329(f329(f81(a874),x97734),x97732)),x97735)))+~P24(f329(f329(f243(a874),f329(f329(f80(a874),f329(f329(f81(a874),f329(f329(f22(a874),x97731),x97734)),x97732)),x97733)),x97735))
% 187.33/188.05 [9774]~P24(f329(f329(f243(a874),x97744),x97741))+P24(f329(f329(f244(a874),f329(f329(f80(a874),f329(f329(f81(a874),x97741),x97742)),x97743)),f329(f329(f80(a874),f329(f329(f81(a874),x97744),x97742)),x97745)))+~P24(f329(f329(f244(a874),f329(f329(f80(a874),f329(f329(f81(a874),f329(f329(f22(a874),x97741),x97744)),x97742)),x97743)),x97745))
% 187.33/188.05 [9997]~P9(x99971,x99972,x99975,x99973)+~P24(f329(f329(f331(f880(x99971,x99971)),x99974),x99975))+P24(f329(f329(f268(x99971,x99971,a869),f329(f329(f7(x99971,f881(x99971,x99972),f881(x99971,a869)),f329(f329(f8(f881(x99972,a869),f881(f881(x99971,x99972),f881(x99971,a869)),x99971),f8(x99972,a869,x99971)),f329(f329(f8(x99972,f881(x99972,a869),x99971),a326),x99973))),x99973)),x99974))
% 187.33/188.05 [6780]~E(f329(x67804,x67805),f206(x67802))+E(f329(f184(x67801,x67802,x67803,x67804),x67805),f329(f236(x67802),x67806))+~E(f329(x67803,x67805),f329(f236(x67802),x67806))
% 187.33/188.05 [6881]~E(f329(x68813,x68816),f206(x68811))+E(f329(f238(f878(x68811),x68812,f206(x68811),x68813),f329(x68814,x68815)),f206(x68811))+~E(f329(x68814,x68815),f329(f236(x68812),x68816))
% 187.33/188.05 [7467]E(f329(x74671,x74672),f206(x74673))+~E(f329(f184(x74675,x74673,x74676,x74671),x74672),f329(f236(x74673),x74674))+E(f329(x74671,x74672),f329(f236(x74673),x74674))
% 187.33/188.05 [7503]~E(f329(f184(x75036,x75033,x75035,x75031),x75032),f329(f236(x75033),x75034))+E(f329(x75031,x75032),f329(f236(x75033),x75034))+E(f329(x75035,x75032),f329(f236(x75033),x75034))
% 187.33/188.05 [8405]~P15(x84056,x84051,x84052,x84054)+E(f329(f73(x84051,x84051,x84051,f329(x84052,x84053)),f329(x84054,x84055)),f329(f73(x84051,x84051,x84051,f329(x84054,x84055)),f329(x84052,x84053)))+~P24(f329(f62(x84056),x84055))
% 187.33/188.05 [8827]~P21(x88271,x88273,x88275,x88276)+~P21(x88273,x88272,x88274,f329(f308(x88271,x88273,x88275),x88276))+P21(x88271,x88272,f329(f73(x88273,x88272,x88271,x88274),x88275),x88276)
% 187.33/188.05 [9396]~P24(f329(f329(x93963,x93962),x93966))+~P24(f329(f329(x93964,x93965),x93962))+P24(f329(f329(f331(x93961),x93962),f297(x93961,x93963,x93964,x93965,x93966)))
% 187.33/188.05 [9397]~P24(f329(f329(x93974,x93972),x93976))+~P24(f329(f329(x93973,x93975),x93972))+P24(f329(f329(f331(x93971),x93972),f294(x93971,x93973,x93974,x93975,x93976)))
% 187.33/188.05 [9507]E(x95071,x95072)+E(x95073,x95074)+~P24(f329(f329(f331(f880(f875(x95075),f875(x95075))),f329(f329(f264(f875(x95075),f875(x95075)),f329(f329(f149(x95075),x95073),x95071)),f329(f329(f149(x95075),x95074),x95072))),f155(x95075,x95076)))
% 187.33/188.05 [9516]~E(x95162,x95164)+P24(f329(f329(f331(f880(f875(x95161),f875(x95161))),f329(f329(f264(f875(x95161),f875(x95161)),f329(f329(f149(x95161),x95162),x95163)),f329(f329(f149(x95161),x95164),x95165))),f143(x95161,x95166)))+~P24(f329(f329(f331(f880(f875(x95161),f875(x95161))),f329(f329(f264(f875(x95161),f875(x95161)),x95163),x95165)),f143(x95161,x95166)))
% 187.33/188.05 [9517]~E(x95172,x95174)+P24(f329(f329(f331(f880(f875(x95171),f875(x95171))),f329(f329(f264(f875(x95171),f875(x95171)),f329(f329(f149(x95171),x95172),x95173)),f329(f329(f149(x95171),x95174),x95175))),f145(x95171,x95176)))+~P24(f329(f329(f331(f880(f875(x95171),f875(x95171))),f329(f329(f264(f875(x95171),f875(x95171)),x95173),x95175)),f145(x95171,x95176)))
% 187.33/188.05 [9518]~E(x95182,x95184)+P24(f329(f329(f331(f880(f875(x95181),f875(x95181))),f329(f329(f264(f875(x95181),f875(x95181)),f329(f329(f149(x95181),x95182),x95183)),f329(f329(f149(x95181),x95184),x95185))),f155(x95181,x95186)))+~P24(f329(f329(f331(f880(f875(x95181),f875(x95181))),f329(f329(f264(f875(x95181),f875(x95181)),x95183),x95185)),f155(x95181,x95186)))
% 187.33/188.05 [9519]~E(x95192,x95194)+P24(f329(f329(f331(f880(f875(x95191),f875(x95191))),f329(f329(f264(f875(x95191),f875(x95191)),f329(f329(f126(x95191),x95192),x95193)),f329(f329(f126(x95191),x95194),x95195))),f155(x95191,x95196)))+~P24(f329(f329(f331(f880(f875(x95191),f875(x95191))),f329(f329(f264(f875(x95191),f875(x95191)),x95193),x95195)),f155(x95191,x95196)))
% 187.33/188.05 [9520]~E(x95203,x95205)+P24(f329(f329(f331(f880(f875(x95201),f875(x95201))),f329(f329(f264(f875(x95201),f875(x95201)),f329(f329(f126(x95201),x95202),x95203)),f329(f329(f126(x95201),x95204),x95205))),f155(x95201,x95206)))+~P24(f329(f329(f331(f880(f875(x95201),f875(x95201))),f329(f329(f264(f875(x95201),f875(x95201)),x95202),x95204)),f155(x95201,x95206)))
% 187.33/188.05 [9575]E(x95751,x95752)+P24(f329(f329(f331(f880(f875(x95753),f875(x95753))),f329(f329(f264(f875(x95753),f875(x95753)),x95751),x95752)),f155(x95753,x95754)))+~P24(f329(f329(f331(f880(f875(x95753),f875(x95753))),f329(f329(f264(f875(x95753),f875(x95753)),f329(f329(f149(x95753),x95755),x95751)),f329(f329(f149(x95753),x95756),x95752))),f155(x95753,x95754)))
% 187.33/188.05 [9723]~E(x97233,x97235)+P24(f329(f329(f331(f880(f875(x97231),f875(x97231))),f329(f329(f264(f875(x97231),f875(x97231)),f329(f329(f126(x97231),x97232),f329(f329(f149(x97231),x97233),f118(x97231)))),f329(f329(f126(x97231),x97234),f329(f329(f149(x97231),x97235),f118(x97231))))),f155(x97231,x97236)))+~P24(f329(f329(f331(f880(f875(x97231),f875(x97231))),f329(f329(f264(f875(x97231),f875(x97231)),x97232),x97234)),f155(x97231,x97236)))
% 187.33/188.05 [9739]E(f329(x97391,x97392),f206(x97393))+~E(f329(f238(f878(x97396),x97393,f206(x97396),x97394),f329(x97391,x97392)),f206(x97396))+E(f329(x97394,f769(x97392,x97391,x97394,x97395,x97396,x97393)),f206(x97396))
% 187.33/188.05 [9740]E(f329(x97401,x97402),f206(x97403))+~E(f329(f238(f878(x97406),x97403,f206(x97406),x97404),f329(x97401,x97402)),f206(x97406))+E(f329(f236(x97403),f769(x97402,x97401,x97404,x97405,x97406,x97403)),f329(x97401,x97402))
% 187.33/188.05 [9777]E(x97771,x97772)+E(x97773,x97774)+~P24(f329(f329(f331(f880(f875(x97775),f875(x97775))),f329(f329(f264(f875(x97775),f875(x97775)),f329(f329(f126(x97775),x97773),f329(f329(f149(x97775),x97771),f118(x97775)))),f329(f329(f126(x97775),x97774),f329(f329(f149(x97775),x97772),f118(x97775))))),f155(x97775,x97776)))
% 187.33/188.05 [9802]E(x98021,x98022)+~P24(f329(f329(f331(f880(f875(x98023),f875(x98023))),f329(f329(f264(f875(x98023),f875(x98023)),f329(f329(f126(x98023),x98021),f329(f329(f149(x98023),x98025),f118(x98023)))),f329(f329(f126(x98023),x98022),f329(f329(f149(x98023),x98026),f118(x98023))))),f155(x98023,x98024)))+P24(f329(f329(f331(f880(f875(x98023),f875(x98023))),f329(f329(f264(f875(x98023),f875(x98023)),x98021),x98022)),f155(x98023,x98024)))
% 187.33/188.05 [9839]~P24(f329(f329(f331(f880(f881(x98391,a869),f881(x98391,a869))),f329(f329(f264(f881(x98391,a869),f881(x98391,a869)),x98392),x98394)),f321(x98391,x98396)))+~P24(f329(f329(f331(f880(f881(x98391,a869),f881(x98391,a869))),f329(f329(f264(f881(x98391,a869),f881(x98391,a869)),x98393),x98395)),f321(x98391,x98396)))+P24(f329(f329(f331(f880(f881(x98391,a869),f881(x98391,a869))),f329(f329(f264(f881(x98391,a869),f881(x98391,a869)),f329(f329(f115(f881(x98391,a869)),x98392),x98393)),f329(f329(f115(f881(x98391,a869)),x98394),x98395))),f321(x98391,x98396)))
% 187.33/188.05 [5228]~E(f329(x52283,x52286),x52285)+~E(x52284,f329(f236(x52281),x52286))+E(f329(f329(f207(x52281,x52282),x52283),x52284),f329(f236(x52282),x52285))
% 187.33/188.05 [5641]~E(f329(f329(f126(x56411),x56416),x56413),x56415)+E(f329(f329(f126(x56411),x56412),x56413),f329(f329(f149(x56411),x56414),x56415))+~E(x56412,f329(f329(f149(x56411),x56414),x56416))
% 187.33/188.05 [5642]~E(f329(f329(f126(x56421),x56426),x56423),x56425)+E(f329(f329(f126(x56421),x56422),x56423),f329(f329(f126(x56421),x56424),x56425))+~E(x56422,f329(f329(f126(x56421),x56424),x56426))
% 187.33/188.05 [5644]E(f329(f329(f126(x56441),x56442),x56443),f329(f329(f149(x56441),x56444),x56445))+~E(f329(f329(f149(x56441),x56444),x56446),x56442)+~E(x56445,f329(f329(f126(x56441),x56446),x56443))
% 187.33/188.05 [5646]~E(f329(f329(f126(x56461),x56462),x56466),x56464)+E(f329(f329(f126(x56461),x56462),x56463),f329(f329(f126(x56461),x56464),x56465))+~E(x56463,f329(f329(f126(x56461),x56466),x56465))
% 187.33/188.05 [6774]E(f329(x67741,x67742),f329(x67743,x67742))+~E(f329(f329(f152(x67744,x67745),x67741),x67746),f329(f329(f152(x67744,x67745),x67743),x67746))+~P24(f329(f329(f331(x67744),x67742),f329(f171(x67744),x67746)))
% 187.33/188.05 [7160]~P15(x71604,x71605,x71606,x71601)+E(f329(f329(x71601,x71602),x71603),f329(f329(f65(x71604,x71605,x71606),x71603),x71602))+~P24(f329(f62(x71604),x71602))
% 187.33/188.05 [7226]~E(x72262,f329(x72264,x72266))+~P24(f329(f329(f331(x72263),x72266),x72265))+P24(f329(f329(f331(x72261),x72262),f329(f308(x72263,x72261,x72264),x72265)))
% 187.33/188.05 [7227]~E(f329(x72274,x72272),x72276)+~P24(f329(f329(f331(x72273),x72276),x72275))+P24(f329(f329(f331(x72271),x72272),f329(f309(x72271,x72273,x72274),x72275)))
% 187.33/188.05 [7683]~P37(x76831,x76832,x76834,x76836)+P37(x76831,x76832,f329(f329(f149(x76831),x76833),x76834),f329(f329(f149(x76831),x76835),x76836))+~P24(f329(f329(x76832,x76833),x76835))
% 187.33/188.05 [8702]~P56(x87024,x87025,x87021,x87022,x87026)+E(f329(x87021,f329(x87022,x87023)),x87023)+~P24(f329(f329(f331(x87025),x87023),x87026))
% 187.33/188.05 [9509]E(x95091,x95092)+E(f329(f194(f875(x95093)),x95094),f329(f194(f875(x95093)),x95095))+~P24(f329(f329(f331(f880(f875(x95093),f875(x95093))),f329(f329(f264(f875(x95093),f875(x95093)),f329(f329(f149(x95093),x95091),x95094)),f329(f329(f149(x95093),x95092),x95095))),f143(x95093,x95096)))
% 187.33/188.05 [9571]~P12(x95711,x95712,x95713)+E(f329(f329(f65(x95711,x95712,x95713),x95714),x95715),x95716)+~P24(f329(f67(x95711,x95712,x95713,x95714,x95715),x95716))
% 187.33/188.05 [9578]E(f329(f194(f875(x95781)),x95782),f329(f194(f875(x95781)),x95783))+P24(f329(f329(f331(f880(f875(x95781),f875(x95781))),f329(f329(f264(f875(x95781),f875(x95781)),x95782),x95783)),f143(x95781,x95784)))+~P24(f329(f329(f331(f880(f875(x95781),f875(x95781))),f329(f329(f264(f875(x95781),f875(x95781)),f329(f329(f149(x95781),x95785),x95782)),f329(f329(f149(x95781),x95786),x95783))),f143(x95781,x95784)))
% 187.33/188.05 [9600]~P24(f329(f329(f331(f880(x96001,x96001)),f329(f329(f264(x96001,x96001),x96002),x96004)),f305(x96001,x96006)))+P24(f329(f329(f331(f880(f875(x96001),f875(x96001))),f329(f329(f264(f875(x96001),f875(x96001)),f329(f329(f149(x96001),x96002),x96003)),f329(f329(f149(x96001),x96004),x96005))),f305(f875(x96001),f155(x96001,x96006))))+~P24(f329(f329(f331(f880(f875(x96001),f875(x96001))),f329(f329(f264(f875(x96001),f875(x96001)),x96003),x96005)),f305(f875(x96001),f155(x96001,x96006))))
% 187.33/188.05 [9783]~P24(f329(x97832,x97836))+~E(f329(f134(x97831,x97832),x97833),f329(f329(f149(x97831),x97834),x97835))+~P24(f329(f329(f331(x97831),x97836),f329(f171(x97831),f788(x97835,x97834,x97833,x97832,x97831))))
% 187.33/188.05 [9784]~P24(f329(x97844,x97846))+~E(f329(f329(f149(x97841),x97842),x97843),f329(f134(x97841,x97844),x97845))+~P24(f329(f329(f331(x97841),x97846),f329(f171(x97841),f786(x97845,x97844,x97843,x97842,x97841))))
% 187.33/188.05 [10090]~P72(x100902)+E(f329(f329(f6(x100901,x100902),f329(f329(f8(f881(x100903,a869),x100902,x100901),f329(f6(x100903,x100902),x100904)),f329(f329(f8(f881(x100903,a869),f881(x100903,a869),x100901),f249(x100903)),f329(f329(f8(f881(x100903,a869),f881(x100903,a869),x100901),f329(f18(x100903,a869,a869),f329(f329(f8(a869,f881(a869,a869),x100903),a327),f329(f329(f7(x100903,f881(x100903,a869),a869),f331(x100903)),x100905)))),f329(f7(x100903,x100901,a869),f329(f329(f8(x100901,f881(x100901,a869),x100903),a326),x100906)))))),f329(f308(x100903,x100901,x100906),x100905)),f329(f329(f6(x100903,x100902),x100904),x100905))+~P24(f329(f62(x100903),x100905))
% 187.33/188.05 [6832]~P27(x68323)+P24(f329(x68322,x68325))+E(f329(f134(x68321,x68322),f329(f329(f146(x68321,x68323,x68324),x68325),x68326)),f329(f134(x68321,x68322),x68326))
% 187.33/188.05 [6834]P24(f329(x68341,x68342))+~E(f165(x68343,x68341,x68344),f329(f329(f264(f875(x68343),f875(x68343)),x68345),x68346))+~P24(f329(f329(f331(x68343),x68342),f329(f171(x68343),x68345)))
% 187.33/188.05 [6878]~P24(f329(x68782,x68786))+~E(f165(x68781,x68782,x68783),f329(f329(f264(f875(x68781),f875(x68781)),x68784),x68785))+~P24(f329(f329(f331(x68781),x68786),f329(f171(x68781),x68785)))
% 187.33/188.05 [7547]~P11(x75471,x75472,x75473)+~P24(f329(f62(x75471),x75476))+E(f329(f329(f65(x75471,x75472,x75473),x75474),f329(f329(f307(x75471),x75475),x75476)),f329(f329(f65(x75471,x75472,x75473),f329(f329(x75473,x75475),x75474)),x75476))
% 187.33/188.05 [7597]~P27(x75972)+~P24(f329(f329(f243(x75972),f329(x75973,x75974)),f329(x75973,x75975)))+E(f329(f329(f146(x75971,x75972,x75973),x75974),f329(f329(f149(x75971),x75975),x75976)),f329(f329(f149(x75971),x75974),f329(f329(f149(x75971),x75975),x75976)))
% 187.33/188.05 [7714]E(x77141,x77142)+~E(f329(f329(f266(x77143,x77144),x77141),f329(f16(f881(x77144,a869),x77143),x77145)),f329(f329(f266(x77143,x77144),x77142),f329(f16(f881(x77144,a869),x77143),x77145)))+~P24(f329(f329(f331(x77144),x77146),x77145))
% 187.33/188.05 [7782]~P11(x77821,x77822,x77823)+~P24(f329(f62(x77821),x77826))+E(f329(f329(f65(x77821,x77822,x77823),x77824),f329(f329(f307(x77821),x77825),x77826)),f329(f329(x77823,x77825),f329(f329(f65(x77821,x77822,x77823),x77824),x77826)))
% 187.33/188.05 [7899]~P12(x78991,x78992,x78993)+~P24(f329(f62(x78991),x78996))+E(f329(f329(f65(x78991,x78992,x78993),f329(f329(x78993,x78994),x78995)),x78996),f329(f329(x78993,x78994),f329(f329(f65(x78991,x78992,x78993),x78995),x78996)))
% 187.33/188.05 [7968]~P16(x79682,x79685,x79686,x79681)+~P24(f329(f62(x79682),x79684))+E(f329(x79681,f329(f329(f307(x79682),x79683),x79684)),f329(f73(x79685,x79685,x79685,f329(x79681,x79684)),f329(x79686,x79683)))
% 187.33/188.05 [8006]~P27(x80062)+P24(f329(f329(f243(x80062),f329(x80063,x80064)),f329(x80063,x80065)))+E(f329(f329(f146(x80061,x80062,x80063),x80064),f329(f329(f149(x80061),x80065),x80066)),f329(f329(f149(x80061),x80065),f329(f329(f146(x80061,x80062,x80063),x80064),x80066)))
% 187.33/188.05 [8148]~E(f329(f194(f875(x81481)),x81485),f329(f194(f875(x81482)),x81486))+~E(f329(f194(f875(x81481)),x81483),f329(f194(f875(x81482)),x81484))+E(f329(f329(f126(f880(x81481,x81482)),f329(f329(f181(x81481,x81482),x81483),x81484)),f329(f329(f181(x81481,x81482),x81485),x81486)),f329(f329(f181(x81481,x81482),f329(f329(f126(x81481),x81483),x81485)),f329(f329(f126(x81482),x81484),x81486)))
% 187.33/188.05 [8262]~E(x82622,f329(f308(x82623,x82621,x82624),x82626))+P24(f329(f329(f243(f881(x82621,a869)),x82622),f329(f308(x82623,x82621,x82624),x82625)))+~P24(f329(f329(f243(f881(x82623,a869)),x82626),x82625))
% 187.33/188.05 [8363]~P27(x83635)+E(f329(x83631,x83632),f329(x83631,x83633))+E(f329(f329(f146(x83634,x83635,x83631),x83632),f329(f329(f146(x83634,x83635,x83631),x83633),x83636)),f329(f329(f146(x83634,x83635,x83631),x83633),f329(f329(f146(x83634,x83635,x83631),x83632),x83636)))
% 187.33/188.05 [8398]~P21(x83983,x83981,x83984,x83985)+P21(x83983,x83981,f329(f329(f329(f72(x83983,x83981),x83984),x83986),x83982),x83985)+P24(f329(f329(f331(x83981),x83982),f329(f308(x83983,x83981,x83984),x83985)))
% 187.33/188.05 [8545]~P24(f329(f329(f331(x85452),x85454),f329(x85456,x85453)))+~P24(f329(f329(f331(x85451),x85453),x85455))+P24(f329(f329(f331(f880(x85451,x85452)),f329(f329(f264(x85451,x85452),x85453),x85454)),f329(f329(f266(x85451,x85452),x85455),x85456)))
% 187.33/188.05 [9007]~P72(x90072)+~P21(x90074,x90071,x90075,x90076)+E(f329(f329(f6(x90071,x90072),x90073),f329(f308(x90074,x90071,x90075),x90076)),f329(f329(f6(x90074,x90072),f329(f73(x90071,x90072,x90074,x90073),x90075)),x90076))
% 187.33/188.05 [9008]~P76(x90082)+~P21(x90084,x90081,x90085,x90086)+E(f329(f329(f9(x90081,x90082),x90083),f329(f308(x90084,x90081,x90085),x90086)),f329(f329(f9(x90084,x90082),f329(f73(x90081,x90082,x90084,x90083),x90085)),x90086))
% 187.33/188.05 [9056]~P39(x90562,x90565,x90561,x90563,x90566)+P24(f329(f329(x90561,f329(f329(f163(x90562),x90563),x90564)),f329(f329(f163(x90565),x90566),x90564)))+~P24(f329(f329(f244(a874),x90564),f329(f194(f875(x90565)),x90566)))
% 187.33/188.05 [9057]~P39(x90572,x90575,x90571,x90573,x90576)+P24(f329(f329(x90571,f329(f329(f163(x90572),x90573),x90574)),f329(f329(f163(x90575),x90576),x90574)))+~P24(f329(f329(f244(a874),x90574),f329(f194(f875(x90572)),x90573)))
% 187.33/188.05 [9267]~P15(x92673,x92671,x92676,x92672)+~P24(f329(f62(x92673),x92674))+E(f329(f73(x92671,x92671,x92671,f329(x92672,f329(f329(f22(f881(x92673,a869)),x92674),f329(f329(f307(x92673),x92675),f193(f881(x92673,a869)))))),f329(x92676,x92675)),f329(x92672,f329(f329(f307(x92673),x92675),x92674)))
% 187.33/188.05 [9877]~E(f329(f308(x98772,x98774,x98776),f252(f881(x98772,a869))),f252(f881(x98774,a869)))+~E(f329(f308(x98771,x98773,x98775),f252(f881(x98771,a869))),f252(f881(x98773,a869)))+E(f329(f308(f880(x98771,x98772),f880(x98773,x98774),f269(x98771,x98773,x98772,x98774,x98775,x98776)),f252(f881(f880(x98771,x98772),a869))),f252(f881(f880(x98773,x98774),a869)))
% 187.33/188.05 [9925]~P21(x99253,x99254,x99255,f329(x99256,f645(x99256,x99255,x99254,x99253,x99252,x99251)))+P21(x99253,x99254,x99255,f329(f329(f43(x99252,f881(x99253,a869)),x99251),x99256))+E(x99251,f193(f881(x99252,a869)))
% 187.33/188.05 [9983]P21(x99836,x99835,x99834,f329(f329(f43(x99832,f881(x99836,a869)),x99831),x99833))+E(x99831,f193(f881(x99832,a869)))+P24(f329(f329(f331(x99832),f645(x99833,x99834,x99835,x99836,x99832,x99831)),x99831))
% 187.33/188.05 [9988]P24(f329(f329(f331(x99881),f581(x99882,x99883,x99884,x99885,x99886,x99881)),x99886))+P24(f329(f329(f243(f881(f880(x99881,x99884),a869)),f329(f329(f266(x99881,x99884),x99886),x99883)),f329(f329(f266(x99881,x99884),x99885),x99882)))+~P24(f329(f329(f243(f881(x99881,a869)),x99886),x99885))
% 187.33/188.05 [10026]P20(x100266,x100265,f329(f329(f307(f873(x100266)),f329(f329(f329(f92(x100266),x100261),x100263),x100262)),f193(f881(f873(x100266),a869))))+~P20(x100266,x100265,f329(f329(f307(f873(x100266)),f329(f329(f329(f92(x100266),x100264),x100263),x100262)),f193(f881(f873(x100266),a869))))+P24(f329(f329(x100261,f461(x100261,x100262,x100263,x100264,x100265,x100266)),f471(x100261,x100262,x100263,x100264,x100265,x100266)))
% 187.33/188.05 [10027]P20(x100276,x100275,f329(f329(f307(f873(x100276)),f329(f329(f329(f92(x100276),x100274),x100273),x100272)),f193(f881(f873(x100276),a869))))+~P20(x100276,x100275,f329(f329(f307(f873(x100276)),f329(f329(f329(f92(x100276),x100274),x100273),x100271)),f193(f881(f873(x100276),a869))))+P24(f329(f329(x100271,f500(x100272,x100271,x100273,x100274,x100275,x100276)),f513(x100272,x100271,x100273,x100274,x100275,x100276)))
% 187.33/188.05 [10065]~P20(x100651,x100652,f329(f329(f307(f873(x100651)),f329(f329(f329(f92(x100651),x100653),x100654),x100656)),f193(f881(f873(x100651),a869))))+P20(x100651,x100652,f329(f329(f307(f873(x100651)),f329(f329(f329(f92(x100651),x100653),x100654),x100655)),f193(f881(f873(x100651),a869))))+~P24(f329(f329(x100655,f500(x100655,x100656,x100654,x100653,x100652,x100651)),f513(x100655,x100656,x100654,x100653,x100652,x100651)))
% 187.33/188.05 [10066]~P20(x100661,x100662,f329(f329(f307(f873(x100661)),f329(f329(f329(f92(x100661),x100666),x100664),x100665)),f193(f881(f873(x100661),a869))))+P20(x100661,x100662,f329(f329(f307(f873(x100661)),f329(f329(f329(f92(x100661),x100663),x100664),x100665)),f193(f881(f873(x100661),a869))))+~P24(f329(f329(x100666,f461(x100663,x100665,x100664,x100666,x100662,x100661)),f471(x100663,x100665,x100664,x100666,x100662,x100661)))
% 187.33/188.05 [10101]~P24(f329(f329(f243(f881(x101012,a869)),f329(x101014,f581(x101016,x101014,x101012,x101015,x101013,x101011))),f329(x101016,f581(x101016,x101014,x101012,x101015,x101013,x101011))))+~P24(f329(f329(f243(f881(x101011,a869)),x101013),x101015))+P24(f329(f329(f243(f881(f880(x101011,x101012),a869)),f329(f329(f266(x101011,x101012),x101013),x101014)),f329(f329(f266(x101011,x101012),x101015),x101016)))
% 187.33/188.05 [7734]~P24(f329(x77341,x77345))+~P24(f329(x77346,x77344))+P24(f329(x77341,f329(f267(x77342,x77343),f329(f329(f264(x77342,x77343),x77344),x77345))))
% 187.33/188.05 [7735]~P24(f329(x77351,x77354))+~P24(f329(x77356,x77355))+P24(f329(x77351,f329(f263(x77352,x77353),f329(f329(f264(x77352,x77353),x77354),x77355))))
% 187.33/188.05 [7758]~E(f329(f194(f875(x77581)),x77583),f329(f194(f875(x77584)),x77585))+~E(f329(f329(f177(x77581,x77584),f329(f329(f181(x77581,x77584),x77583),x77585)),x77582),f329(f236(x77584),x77586))+P24(f329(f329(f331(x77581),x77582),f329(f171(x77581),x77583)))
% 187.33/188.05 [7787]~P24(f329(f329(x77874,x77876),x77875))+~P24(f329(f329(f331(x77871),x77876),x77873))+P24(f329(f329(f329(f42(x77871,f881(x77872,a869)),x77873),x77874),x77875))
% 187.33/188.05 [8097]~P24(f329(f329(f331(x80971),x80972),f329(x80975,x80976)))+~P24(f329(f329(f331(x80973),x80976),x80974))+P24(f329(f329(f331(x80971),x80972),f329(f329(f42(x80973,f881(x80971,a869)),x80974),x80975)))
% 187.33/188.05 [8140]P24(f329(f329(x81401,x81402),x81403))+~P24(f329(f329(x81404,x81402),x81403))+~P24(f329(f329(f243(f881(x81405,f881(x81406,a869))),x81404),x81401))
% 187.33/188.05 [8286]P24(f329(f329(x82861,x82862),x82863))+~P24(f329(f329(f331(x82864),x82862),x82865))+~P24(f329(f329(f329(f43(x82864,f881(x82866,a869)),x82865),x82861),x82863))
% 187.33/188.05 [8422]P24(f329(f329(f331(x84221),x84222),f329(x84223,x84224)))+~P24(f329(f329(f331(x84225),x84224),x84226))+~P24(f329(f329(f331(x84221),x84222),f329(f329(f43(x84225,f881(x84221,a869)),x84226),x84223)))
% 187.33/188.05 [8614]~P24(f329(f329(f329(f329(a201,x86141),x86143),x86144),x86146))+~P24(f329(f329(f329(f329(a201,x86142),x86146),x86144),x86145))+P24(f329(f329(f329(f329(a201,f33(x86141,x86142)),x86143),x86144),x86145))
% 187.33/188.05 [8684]~P9(x86844,x86845,x86846,x86841)+E(f329(x86841,x86842),f329(x86841,x86843))+~P24(f329(f329(f331(f880(x86844,x86844)),f329(f329(f264(x86844,x86844),x86842),x86843)),x86846))
% 187.33/188.05 [8715]P24(f329(f329(f243(f881(x87151,a869)),x87152),f329(x87153,x87154)))+~P24(f329(f329(f331(x87155),x87154),x87156))+~P24(f329(f329(f243(f881(x87151,a869)),x87152),f329(f329(f43(x87155,f881(x87151,a869)),x87156),x87153)))
% 187.33/188.05 [8743]~P54(x87433,x87434,f329(f284(x87434,x87433),x87435))+E(x87431,f193(f881(x87432,a869)))+E(f329(f329(f43(x87432,f881(x87433,a869)),x87431),f329(f329(f8(f881(x87434,a869),f881(x87433,a869),x87432),f283(x87434,x87433,x87435)),x87436)),f329(f283(x87434,x87433,x87435),f329(f329(f43(x87432,f881(x87434,a869)),x87431),x87436)))
% 187.33/188.05 [8818]P24(f329(f329(f331(x88181),x88182),f329(f283(x88183,x88181,x88184),x88185)))+~P24(f329(f329(f331(x88183),x88186),x88185))+~P24(f329(f329(f331(f880(x88183,x88181)),f329(f329(f264(x88183,x88181),x88186),x88182)),x88184))
% 187.33/188.05 [8937]P24(f329(x89371,x89372))+~P24(f329(f329(f329(f329(a201,x89374),x89372),x89375),x89376))+P24(f329(f329(f329(f329(a201,f30(x89371,x89373,x89374)),x89372),x89375),x89376))
% 187.33/188.05 [8954]~P24(f329(x89541,x89544))+~P24(f329(f329(f329(f329(a201,x89542),x89544),x89545),x89546))+P24(f329(f329(f329(f329(a201,f30(x89541,x89542,x89543)),x89544),x89545),x89546))
% 187.33/188.05 [9129]P24(f329(f329(f243(f881(x91291,a869)),f329(f283(x91292,x91291,x91293),x91294)),f329(f283(x91292,x91291,x91295),x91296)))+~P24(f329(f329(f243(f881(x91292,a869)),x91294),x91296))+~P24(f329(f329(f243(f881(f880(x91292,x91291),a869)),x91293),x91295))
% 187.33/188.05 [9217]P24(f329(x92171,x92172))+P24(f329(f329(f329(f329(a201,x92173),x92172),x92174),x92175))+~P24(f329(f329(f329(f329(a201,f30(x92171,x92176,x92173)),x92172),x92174),x92175))
% 187.33/188.05 [9222]~P24(f329(x92225,x92222))+P24(f329(f329(f329(f329(a201,x92221),x92222),x92223),x92224))+~P24(f329(f329(f329(f329(a201,f30(x92225,x92221,x92226)),x92222),x92223),x92224))
% 187.33/188.05 [9274]P24(f329(f329(f329(f329(a201,x92741),x92742),x92743),x92744))+P24(f329(f329(f329(f329(a201,x92745),x92742),x92743),x92744))+~P24(f329(f329(f329(f329(a201,f30(x92746,x92741,x92745)),x92742),x92743),x92744))
% 187.33/188.05 [9316]~P24(f329(f329(f331(x93162),x93166),x93164))+~P24(f329(f329(f243(f881(x93161,a869)),x93163),x93165))+P24(f329(f329(f243(f881(f880(x93161,x93162),a869)),f329(f329(f266(x93161,x93162),x93163),f329(f16(f881(x93162,a869),x93161),x93164))),f329(f329(f266(x93161,x93162),x93165),f329(f16(f881(x93162,a869),x93161),x93164))))
% 187.33/188.05 [9329]~P39(x93291,x93292,x93293,x93295,x93296)+P24(f329(f329(f268(x93291,x93292,a869),x93293),x93294))+~P24(f329(f329(f331(f880(x93291,x93292)),x93294),f329(f171(f880(x93291,x93292)),f329(f329(f181(x93291,x93292),x93295),x93296))))
% 187.33/188.05 [9462]~E(x94623,x94625)+P24(f329(f329(f331(f880(f875(x94621),f875(x94621))),f329(f329(f264(f875(x94621),f875(x94621)),f329(f329(f149(x94621),x94622),x94623)),f329(f329(f149(x94621),x94624),x94625))),f155(x94621,x94626)))+~P24(f329(f329(f331(f880(x94621,x94621)),f329(f329(f264(x94621,x94621),x94622),x94624)),x94626))
% 187.33/188.05 [9468]~E(f329(f194(f875(x94681)),x94685),f329(f194(f875(x94682)),x94686))+E(f186(x94681,x94682,f187(x94681,x94682,x94683,f329(f329(f22(f881(x94681,a869)),x94684),f329(f171(x94681),x94685))),x94685,x94686),f187(x94681,x94682,f186(x94681,x94682,x94683,x94685,x94686),x94684))+~P24(f329(f329(f243(f881(x94681,a869)),f329(f171(x94681),x94685)),x94684))
% 187.33/188.05 [9469]~E(f329(f194(f875(x94691)),x94693),f329(f194(f875(x94691)),x94695))+P24(f329(f329(f331(f880(f875(x94691),f875(x94691))),f329(f329(f264(f875(x94691),f875(x94691)),f329(f329(f149(x94691),x94692),x94693)),f329(f329(f149(x94691),x94694),x94695))),f143(x94691,x94696)))+~P24(f329(f329(f331(f880(x94691,x94691)),f329(f329(f264(x94691,x94691),x94692),x94694)),x94696))
% 187.33/188.05 [9500]P24(f329(f329(f331(f880(x95001,x95001)),f329(f329(f264(x95001,x95001),x95002),x95003)),f329(f329(f188(f880(x95001,x95001),a869),f329(a117,x95004)),x95005)))+~P24(f329(f329(f331(f880(x95001,x95001)),f329(f329(f264(x95001,x95001),x95006),x95003)),x95005))+~P24(f329(f329(f331(f880(x95001,x95001)),f329(f329(f264(x95001,x95001),x95002),x95006)),f329(f329(f188(f880(x95001,x95001),a869),x95004),x95005)))
% 187.33/188.05 [9501]P24(f329(f329(f331(f880(x95011,x95011)),f329(f329(f264(x95011,x95011),x95012),x95013)),f329(f329(f188(f880(x95011,x95011),a869),f329(a117,x95014)),x95015)))+~P24(f329(f329(f331(f880(x95011,x95011)),f329(f329(f264(x95011,x95011),x95012),x95016)),x95015))+~P24(f329(f329(f331(f880(x95011,x95011)),f329(f329(f264(x95011,x95011),x95016),x95013)),f329(f329(f188(f880(x95011,x95011),a869),x95014),x95015)))
% 187.33/188.05 [9505]~P24(f329(f329(f331(x95054),x95055),x95056))+P24(f329(f329(f243(f881(x95051,a869)),x95052),x95053))+~P24(f329(f329(f243(f881(f880(x95051,x95054),a869)),f329(f329(f266(x95051,x95054),x95052),f329(f16(f881(x95054,a869),x95051),x95056))),f329(f329(f266(x95051,x95054),x95053),f329(f16(f881(x95054,a869),x95051),x95056))))
% 187.33/188.05 [9549]E(x95491,x95492)+~P24(f329(f329(f331(f880(f875(x95493),f875(x95493))),f329(f329(f264(f875(x95493),f875(x95493)),f329(f329(f149(x95493),x95491),x95495)),f329(f329(f149(x95493),x95492),x95496))),f143(x95493,x95494)))+P24(f329(f329(f331(f880(x95493,x95493)),f329(f329(f264(x95493,x95493),x95491),x95492)),x95494))
% 187.33/188.05 [9550]E(x95501,x95502)+~P24(f329(f329(f331(f880(f875(x95503),f875(x95503))),f329(f329(f264(f875(x95503),f875(x95503)),f329(f329(f149(x95503),x95501),x95505)),f329(f329(f149(x95503),x95502),x95506))),f145(x95503,x95504)))+P24(f329(f329(f331(f880(x95503,x95503)),f329(f329(f264(x95503,x95503),x95501),x95502)),x95504))
% 187.33/188.05 [9551]E(x95511,x95512)+~P24(f329(f329(f331(f880(f875(x95513),f875(x95513))),f329(f329(f264(f875(x95513),f875(x95513)),f329(f329(f149(x95513),x95511),x95515)),f329(f329(f149(x95513),x95512),x95516))),f155(x95513,x95514)))+P24(f329(f329(f331(f880(x95513,x95513)),f329(f329(f264(x95513,x95513),x95511),x95512)),x95514))
% 187.33/188.05 [9586]P24(f329(f329(f331(f880(f875(x95861),f875(x95861))),f329(f329(f264(f875(x95861),f875(x95861)),f329(f329(f149(x95861),x95862),x95863)),f329(f329(f149(x95861),x95864),x95865))),f156(x95861,x95866)))+~P24(f329(f329(f331(f880(f875(x95861),f875(x95861))),f329(f329(f264(f875(x95861),f875(x95861)),x95863),x95865)),f156(x95861,x95866)))+~P24(f329(f329(f331(f880(x95861,x95861)),f329(f329(f264(x95861,x95861),x95862),x95864)),x95866))
% 187.33/188.05 [9604]P24(f329(x96041,x96042))+~P24(f329(x96041,f434(x96041,x96043,x96044,x96045,x96046)))+~P24(f329(f329(f331(x96046),x96042),f329(f329(f42(x96045,f881(x96046,a869)),x96044),x96043)))
% 187.33/188.05 [9609]~P24(f329(f329(f331(f880(f875(x96091),f875(x96091))),f329(f329(f264(f875(x96091),f875(x96091)),f329(f329(f149(x96091),x96092),x96095)),f329(f329(f149(x96091),x96093),x96096))),f143(x96091,x96094)))+P24(f329(f329(f331(f880(f875(x96091),f875(x96091))),f329(f329(f264(f875(x96091),f875(x96091)),x96095),x96096)),f143(x96091,x96094)))+P24(f329(f329(f331(f880(x96091,x96091)),f329(f329(f264(x96091,x96091),x96092),x96093)),x96094))
% 187.33/188.05 [9610]~P24(f329(f329(f331(f880(f875(x96101),f875(x96101))),f329(f329(f264(f875(x96101),f875(x96101)),f329(f329(f149(x96101),x96102),x96105)),f329(f329(f149(x96101),x96103),x96106))),f145(x96101,x96104)))+P24(f329(f329(f331(f880(f875(x96101),f875(x96101))),f329(f329(f264(f875(x96101),f875(x96101)),x96105),x96106)),f145(x96101,x96104)))+P24(f329(f329(f331(f880(x96101,x96101)),f329(f329(f264(x96101,x96101),x96102),x96103)),x96104))
% 187.33/188.05 [9611]~P24(f329(f329(f331(f880(f875(x96111),f875(x96111))),f329(f329(f264(f875(x96111),f875(x96111)),f329(f329(f149(x96111),x96112),x96115)),f329(f329(f149(x96111),x96113),x96116))),f155(x96111,x96114)))+P24(f329(f329(f331(f880(f875(x96111),f875(x96111))),f329(f329(f264(f875(x96111),f875(x96111)),x96115),x96116)),f155(x96111,x96114)))+P24(f329(f329(f331(f880(x96111,x96111)),f329(f329(f264(x96111,x96111),x96112),x96113)),x96114))
% 187.33/188.05 [9694]P24(f329(x96941,x96942))+P24(f329(f329(f331(x96943),f435(x96941,x96944,x96945,x96943,x96946)),x96945))+~P24(f329(f329(f331(x96946),x96942),f329(f329(f42(x96943,f881(x96946,a869)),x96945),x96944)))
% 187.33/188.05 [9706]~E(x97062,x97064)+P24(f329(f329(f331(f880(f875(x97061),f875(x97061))),f329(f329(f264(f875(x97061),f875(x97061)),f329(f329(f126(x97061),x97062),f329(f329(f149(x97061),x97063),f118(x97061)))),f329(f329(f126(x97061),x97064),f329(f329(f149(x97061),x97065),f118(x97061))))),f155(x97061,x97066)))+~P24(f329(f329(f331(f880(x97061,x97061)),f329(f329(f264(x97061,x97061),x97063),x97065)),x97066))
% 187.33/188.05 [9793]E(x97931,x97932)+~P24(f329(f329(f331(f880(f875(x97933),f875(x97933))),f329(f329(f264(f875(x97933),f875(x97933)),f329(f329(f126(x97933),x97935),f329(f329(f149(x97933),x97931),f118(x97933)))),f329(f329(f126(x97933),x97936),f329(f329(f149(x97933),x97932),f118(x97933))))),f155(x97933,x97934)))+P24(f329(f329(f331(f880(x97933,x97933)),f329(f329(f264(x97933,x97933),x97931),x97932)),x97934))
% 187.33/188.05 [9821]~P24(f329(f329(f331(f880(f875(x98211),f875(x98211))),f329(f329(f264(f875(x98211),f875(x98211)),f329(f329(f126(x98211),x98215),f329(f329(f149(x98211),x98212),f118(x98211)))),f329(f329(f126(x98211),x98216),f329(f329(f149(x98211),x98213),f118(x98211))))),f155(x98211,x98214)))+P24(f329(f329(f331(f880(f875(x98211),f875(x98211))),f329(f329(f264(f875(x98211),f875(x98211)),x98215),x98216)),f155(x98211,x98214)))+P24(f329(f329(f331(f880(x98211,x98211)),f329(f329(f264(x98211,x98211),x98212),x98213)),x98214))
% 187.33/188.05 [9840]P24(f329(x98401,x98402))+P24(f329(f329(f331(x98403),f434(x98401,x98404,x98405,x98406,x98403)),f329(x98404,f435(x98401,x98404,x98405,x98406,x98403))))+~P24(f329(f329(f331(x98403),x98402),f329(f329(f42(x98406,f881(x98403,a869)),x98405),x98404)))
% 187.33/188.05 [8833]~P12(x88333,x88334,x88331)+~P24(f329(f62(x88333),x88336))+E(f329(f329(x88331,x88332),f329(f329(f65(x88333,x88334,x88331),x88335),f329(f329(f22(f881(x88333,a869)),x88336),f329(f329(f307(x88333),x88332),f193(f881(x88333,a869)))))),f329(f329(f65(x88333,x88334,x88331),x88335),f329(f329(f307(x88333),x88332),x88336)))
% 187.33/188.05 [8920]~E(f329(f329(f177(x89201,x89202),x89204),x89205),f329(f236(x89202),x89206))+~P24(f329(f329(x89203,x89205),x89206))+E(f329(f329(f177(x89201,x89202),f329(f134(f880(x89201,x89202),f329(f268(x89201,x89202,a869),x89203)),x89204)),x89205),f329(f236(x89202),x89206))
% 187.33/188.05 [9136]~P24(f329(f329(f331(x91365),x91363),x91366))+P24(f329(f329(f243(f881(x91361,a869)),f329(x91362,x91363)),x91364))+~P24(f329(f329(f243(f881(x91361,a869)),f329(f329(f42(x91365,f881(x91361,a869)),x91366),x91362)),x91364))
% 187.33/188.05 [9766]~P6(x97661,x97665,x97664)+P24(f329(f329(f331(f880(x97661,x97661)),f329(f329(f264(x97661,x97661),x97662),x97663)),x97664))+~P24(f329(f329(f331(x97661),x97666),f329(f329(f106(f881(x97661,a869)),f329(f283(x97661,x97661,x97664),f329(f329(f307(x97661),x97662),f193(f881(x97661,a869))))),f329(f283(x97661,x97661,x97664),f329(f329(f307(x97661),x97663),f193(f881(x97661,a869)))))))
% 187.33/188.05 [8581]~P107(x85812)+~E(f329(f329(f80(x85812),f329(f329(f81(x85812),x85814),x85815)),x85811),f329(f329(f80(x85812),f329(f329(f81(x85812),x85813),x85815)),x85816))+E(x85811,f329(f329(f80(x85812),f329(f329(f81(x85812),f329(f329(f22(x85812),x85813),x85814)),x85815)),x85816))
% 187.33/188.05 [8582]~P107(x85821)+~E(f329(f329(f80(x85821),f329(f329(f81(x85821),x85822),x85824)),x85825),f329(f329(f80(x85821),f329(f329(f81(x85821),x85823),x85824)),x85826))+E(f329(f329(f80(x85821),f329(f329(f81(x85821),f329(f329(f22(x85821),x85822),x85823)),x85824)),x85825),x85826)
% 187.33/188.05 [8746]~P107(x87461)+E(f329(f329(f80(x87461),f329(f329(f81(x87461),x87462),x87463)),x87464),f329(f329(f80(x87461),f329(f329(f81(x87461),x87465),x87463)),x87466))+~E(x87466,f329(f329(f80(x87461),f329(f329(f81(x87461),f329(f329(f22(x87461),x87462),x87465)),x87463)),x87464))
% 187.33/188.05 [8747]~P107(x87471)+E(f329(f329(f80(x87471),f329(f329(f81(x87471),x87472),x87473)),x87474),f329(f329(f80(x87471),f329(f329(f81(x87471),x87475),x87473)),x87476))+~E(f329(f329(f80(x87471),f329(f329(f81(x87471),f329(f329(f22(x87471),x87472),x87475)),x87473)),x87474),x87476)
% 187.33/188.05 [9076]~P24(f329(f329(x90764,x90765),x90766))+~P24(f329(f329(x90763,x90765),x90766))+P24(f329(f329(f329(f329(f106(f881(x90761,f881(x90762,a869))),x90763),x90764),x90765),x90766))
% 187.33/188.05 [9337]P24(f329(f329(x93371,x93372),x93373))+P24(f329(f329(x93374,x93372),x93373))+~P24(f329(f329(f329(f329(f115(f881(x93375,f881(x93376,a869))),x93374),x93371),x93372),x93373))
% 187.33/188.05 [9624]~P108(x96241)+~P24(f329(f329(f243(x96241),f329(f329(f80(x96241),f329(f329(f81(x96241),x96244),x96245)),x96242)),f329(f329(f80(x96241),f329(f329(f81(x96241),x96243),x96245)),x96246)))+P24(f329(f329(f243(x96241),x96242),f329(f329(f80(x96241),f329(f329(f81(x96241),f329(f329(f22(x96241),x96243),x96244)),x96245)),x96246)))
% 187.33/188.05 [9625]~P108(x96251)+~P24(f329(f329(f244(x96251),f329(f329(f80(x96251),f329(f329(f81(x96251),x96254),x96255)),x96252)),f329(f329(f80(x96251),f329(f329(f81(x96251),x96253),x96255)),x96256)))+P24(f329(f329(f244(x96251),x96252),f329(f329(f80(x96251),f329(f329(f81(x96251),f329(f329(f22(x96251),x96253),x96254)),x96255)),x96256)))
% 187.33/188.05 [9648]~P108(x96481)+P24(f329(f329(f243(x96481),f329(f329(f80(x96481),f329(f329(f81(x96481),x96482),x96483)),x96484)),f329(f329(f80(x96481),f329(f329(f81(x96481),x96485),x96483)),x96486)))+~P24(f329(f329(f243(x96481),x96484),f329(f329(f80(x96481),f329(f329(f81(x96481),f329(f329(f22(x96481),x96485),x96482)),x96483)),x96486)))
% 187.33/188.05 [9649]~P108(x96491)+P24(f329(f329(f244(x96491),f329(f329(f80(x96491),f329(f329(f81(x96491),x96492),x96493)),x96494)),f329(f329(f80(x96491),f329(f329(f81(x96491),x96495),x96493)),x96496)))+~P24(f329(f329(f244(x96491),x96494),f329(f329(f80(x96491),f329(f329(f81(x96491),f329(f329(f22(x96491),x96495),x96492)),x96493)),x96496)))
% 187.33/188.05 [9754]~P108(x97541)+~P24(f329(f329(f243(x97541),f329(f329(f80(x97541),f329(f329(f81(x97541),x97542),x97544)),x97545)),f329(f329(f80(x97541),f329(f329(f81(x97541),x97543),x97544)),x97546)))+P24(f329(f329(f243(x97541),f329(f329(f80(x97541),f329(f329(f81(x97541),f329(f329(f22(x97541),x97542),x97543)),x97544)),x97545)),x97546))
% 187.33/188.05 [9755]~P108(x97551)+~P24(f329(f329(f244(x97551),f329(f329(f80(x97551),f329(f329(f81(x97551),x97552),x97554)),x97555)),f329(f329(f80(x97551),f329(f329(f81(x97551),x97553),x97554)),x97556)))+P24(f329(f329(f244(x97551),f329(f329(f80(x97551),f329(f329(f81(x97551),f329(f329(f22(x97551),x97552),x97553)),x97554)),x97555)),x97556))
% 187.33/188.05 [9804]~P108(x98041)+P24(f329(f329(f243(x98041),f329(f329(f80(x98041),f329(f329(f81(x98041),x98042),x98043)),x98044)),f329(f329(f80(x98041),f329(f329(f81(x98041),x98045),x98043)),x98046)))+~P24(f329(f329(f243(x98041),f329(f329(f80(x98041),f329(f329(f81(x98041),f329(f329(f22(x98041),x98042),x98045)),x98043)),x98044)),x98046))
% 187.33/188.05 [9805]~P108(x98051)+P24(f329(f329(f244(x98051),f329(f329(f80(x98051),f329(f329(f81(x98051),x98052),x98053)),x98054)),f329(f329(f80(x98051),f329(f329(f81(x98051),x98055),x98053)),x98056)))+~P24(f329(f329(f244(x98051),f329(f329(f80(x98051),f329(f329(f81(x98051),f329(f329(f22(x98051),x98052),x98055)),x98053)),x98054)),x98056))
% 187.33/188.05 [9977]~P72(x99772)+~P24(f329(f62(x99771),x99776))+E(f329(f329(f6(x99771,x99772),f329(f329(f18(x99771,x99772,x99772),f329(f329(f18(x99771,x99772,f881(x99772,x99772)),f329(f329(f8(a869,f881(x99772,f881(x99772,x99772)),x99771),f101(x99772)),x99773)),x99774)),x99775)),x99776),f329(f329(f80(x99772),f329(f329(f6(x99771,x99772),x99774),f329(f329(f106(f881(x99771,a869)),x99776),f329(f249(x99771),x99773)))),f329(f329(f6(x99771,x99772),x99775),f329(f329(f106(f881(x99771,a869)),x99776),f329(f79(f881(x99771,a869)),f329(f249(x99771),x99773))))))
% 187.33/188.05 [10035]P24(f329(f329(f331(x100352),x100354),x100356))+P24(f329(f329(f331(x100352),x100355),x100356))+E(f329(f309(x100351,x100352,f329(f329(f7(x100351,x100352,x100352),f329(f329(f7(x100351,x100352,f881(x100352,x100352)),f329(f329(f8(a869,f881(x100352,f881(x100352,x100352)),x100351),f101(x100352)),f329(f329(f7(x100351,f881(x100351,a869),a869),f331(x100351)),x100353))),x100354)),x100355)),x100356),f193(f881(x100351,a869)))
% 187.33/188.05 [10036]P24(f329(f329(f331(x100362),x100365),x100366))+~P24(f329(f329(f331(x100362),x100364),x100366))+E(f329(f309(x100361,x100362,f329(f329(f7(x100361,x100362,x100362),f329(f329(f7(x100361,x100362,f881(x100362,x100362)),f329(f329(f8(a869,f881(x100362,f881(x100362,x100362)),x100361),f101(x100362)),f329(f329(f7(x100361,f881(x100361,a869),a869),f331(x100361)),x100363))),x100364)),x100365)),x100366),x100363)
% 187.33/188.05 [10037]P24(f329(f329(f331(x100372),x100374),x100376))+~P24(f329(f329(f331(x100372),x100375),x100376))+E(f329(f309(x100371,x100372,f329(f329(f7(x100371,x100372,x100372),f329(f329(f7(x100371,x100372,f881(x100372,x100372)),f329(f329(f8(a869,f881(x100372,f881(x100372,x100372)),x100371),f101(x100372)),f329(f329(f7(x100371,f881(x100371,a869),a869),f331(x100371)),x100373))),x100374)),x100375)),x100376),f329(f79(f881(x100371,a869)),x100373))
% 187.33/188.05 [10038]~P24(f329(f329(f331(x100382),x100384),x100386))+~P24(f329(f329(f331(x100382),x100385),x100386))+E(f329(f309(x100381,x100382,f329(f329(f7(x100381,x100382,x100382),f329(f329(f7(x100381,x100382,f881(x100382,x100382)),f329(f329(f8(a869,f881(x100382,f881(x100382,x100382)),x100381),f101(x100382)),f329(f329(f7(x100381,f881(x100381,a869),a869),f331(x100381)),x100383))),x100384)),x100385)),x100386),f252(f881(x100381,a869)))
% 187.33/188.05 [10167]P20(x101671,x101672,f329(f329(f307(f873(x101671)),f329(f329(f329(f92(x101671),f329(x101673,x101674)),f329(a26,x101674)),f329(x101675,x101674))),f193(f881(f873(x101671),a869))))+~P24(f329(f329(f331(a872),x101674),x101676))+~P20(x101671,f329(f329(f115(f881(f873(x101671),a869)),x101672),f329(f308(a872,f873(x101671),f329(f329(f18(a872,f881(x101671,f881(a871,a869)),f873(x101671)),f329(f329(f18(a872,a870,f881(f881(x101671,f881(a871,a869)),f873(x101671))),f329(f329(f8(f881(x101671,f881(a871,a869)),f881(a870,f881(f881(x101671,f881(a871,a869)),f873(x101671))),a872),f92(x101671)),x101673)),a26)),x101675)),x101676)),f329(f308(a872,f873(x101671),f329(f329(f18(a872,f881(x101671,f881(a871,a869)),f873(x101671)),f329(f329(f18(a872,a870,f881(f881(x101671,f881(a871,a869)),f873(x101671))),f329(f329(f8(f881(x101671,f881(a871,a869)),f881(a870,f881(f881(x101671,f881(a871,a869)),f873(x101671))),a872),f92(x101671)),x101673)),f329(f329(f8(f878(a870),a870,a872),f240(a870)),a28))),x101675)),x101676))
% 187.33/188.05 [8611]E(x86111,x86112)+~P56(x86114,x86115,x86113,x86116,x86117)+~E(f329(x86113,x86111),f329(x86113,x86112))
% 187.33/188.05 [6986]E(f329(f238(f878(x69861),x69862,f206(x69861),x69863),f329(x69864,x69865)),f329(f236(x69861),x69866))+~E(f329(x69864,x69865),f329(f236(x69862),x69867))+~E(f329(x69863,x69867),f329(f236(x69861),x69866))
% 187.33/188.05 [8639]~P4(x86396,x86395,x86397,x86394,x86391)+E(f329(f329(x86391,x86392),x86393),x86394)+P24(f329(f62(x86395),x86393))
% 187.33/188.05 [9490]P47(x94901,x94902,x94903,x94904,x94905,f329(f329(x94903,x94906),x94907))+~E(f329(f329(x94903,x94906),x94907),x94904)+~E(x94905,f193(f881(x94901,a869)))
% 187.33/188.05 [9670]~P24(f329(x96706,x96703))+~P24(f329(f329(f331(f880(x96702,x96702)),f329(f329(f264(x96702,x96702),x96704),x96705)),f329(x96707,x96703)))+P24(f329(f329(f331(f880(f880(x96701,x96702),f880(x96701,x96702))),f329(f329(f264(f880(x96701,x96702),f880(x96701,x96702)),f329(f329(f264(x96701,x96702),x96703),x96704)),f329(f329(f264(x96701,x96702),x96703),x96705))),f281(x96701,x96702,x96706,x96707)))
% 187.33/188.05 [10092]~P47(x100922,x100927,x100923,x100926,x100921,f329(f329(x100923,x100925),x100924))+E(f329(f329(x100923,f701(x100924,x100925,x100921,x100926,x100923,x100927,x100922)),f710(x100924,x100925,x100921,x100926,x100923,x100927,x100922)),f329(f329(x100923,x100925),x100924))+E(x100921,f193(f881(x100922,a869)))
% 187.33/188.05 [10093]~P47(x100937,x100936,x100931,x100934,x100935,f329(f329(x100931,x100932),x100933))+E(f329(f329(x100931,f701(x100933,x100932,x100935,x100934,x100931,x100936,x100937)),f710(x100933,x100932,x100935,x100934,x100931,x100936,x100937)),f329(f329(x100931,x100932),x100933))+E(f329(f329(x100931,x100932),x100933),x100934)
% 187.33/188.05 [9174]~P39(x91741,x91742,x91743,x91745,x91747)+P39(x91741,x91742,x91743,f329(f329(f149(x91741),x91744),x91745),f329(f329(f149(x91742),x91746),x91747))+~P24(f329(f329(x91743,x91744),x91746))
% 187.33/188.05 [9192]P39(x91921,x91922,x91923,x91924,x91925)+~P39(x91921,x91922,x91923,f329(f329(f126(x91921),x91926),x91924),f329(f329(f126(x91922),x91927),x91925))+~E(f329(f194(f875(x91921)),x91926),f329(f194(f875(x91922)),x91927))
% 187.33/188.05 [9193]P39(x91931,x91932,x91933,x91934,x91935)+~P39(x91931,x91932,x91933,f329(f329(f126(x91931),x91934),x91936),f329(f329(f126(x91932),x91935),x91937))+~E(f329(f194(f875(x91931)),x91934),f329(f194(f875(x91932)),x91935))
% 187.33/188.05 [9399]~P39(x93991,x93992,x93993,x93995,x93997)+~P39(x93991,x93992,x93993,x93994,x93996)+P39(x93991,x93992,x93993,f329(f329(f126(x93991),x93994),x93995),f329(f329(f126(x93992),x93996),x93997))
% 187.33/188.05 [9743]~P24(f329(f67(x97431,x97434,x97435,x97436,x97433),x97437))+P24(f329(f67(x97431,x97434,x97435,x97436,f329(f329(f307(x97431),x97432),x97433)),f329(f329(x97435,x97432),x97437)))+P24(f329(f329(f331(x97431),x97432),x97433))
% 187.33/188.05 [9875]~P21(x98753,x98751,x98754,f252(f881(x98753,a869)))+E(f329(f329(f177(x98751,x98752),f329(f329(f152(f880(x98753,x98752),f880(x98751,x98752)),f329(f268(x98753,x98752,f880(x98751,x98752)),f329(f329(f8(x98751,f881(x98752,f880(x98751,x98752)),x98753),f264(x98751,x98752)),x98754))),x98755)),f329(x98754,x98756)),f329(f236(x98752),x98757))+~E(f329(f329(f177(x98753,x98752),x98755),x98756),f329(f236(x98752),x98757))
% 187.33/188.05 [10113]~P47(x101132,x101137,x101136,x101135,x101131,f329(f329(x101136,x101134),x101133))+E(x101131,f193(f881(x101132,a869)))+P24(f329(f329(f331(x101132),f701(x101133,x101134,x101131,x101135,x101136,x101137,x101132)),x101131))
% 187.33/188.05 [10114]~P47(x101145,x101147,x101141,x101144,x101146,f329(f329(x101141,x101142),x101143))+E(f329(f329(x101141,x101142),x101143),x101144)+P24(f329(f329(f331(x101145),f701(x101143,x101142,x101146,x101144,x101141,x101147,x101145)),x101146))
% 187.33/188.05 [6773]~E(x67735,x67737)+~E(x67736,x67734)+E(f329(f329(f329(f329(f72(x67731,f878(x67732)),x67733),x67734),f329(f236(x67732),x67735)),x67736),f329(f236(x67732),x67737))
% 187.33/188.05 [6902]E(x69021,x69022)+~E(f329(x69025,x69021),f329(f236(x69024),x69027))+E(f329(f329(f329(f329(f72(x69023,f878(x69024)),x69025),x69022),f329(f236(x69024),x69026)),x69021),f329(f236(x69024),x69027))
% 187.33/188.05 [7622]E(x76221,x76222)+~E(x76223,x76224)+~E(f329(f329(f329(f329(f72(x76225,f878(x76226)),x76227),x76224),f329(f236(x76226),x76221)),x76223),f329(f236(x76226),x76222))
% 187.33/188.05 [7689]E(x76891,x76892)+E(f329(x76893,x76894),f329(f236(x76895),x76891))+~E(f329(f329(f329(f329(f72(x76896,f878(x76895)),x76893),x76897),f329(f236(x76895),x76892)),x76894),f329(f236(x76895),x76891))
% 187.33/188.05 [7690]E(x76901,x76902)+E(f329(x76903,x76901),f329(f236(x76904),x76905))+~E(f329(f329(f329(f329(f72(x76906,f878(x76904)),x76903),x76902),f329(f236(x76904),x76907)),x76901),f329(f236(x76904),x76905))
% 187.33/188.05 [8858]~P17(x88584,x88585,x88586,x88587,x88581)+~P24(f329(f62(x88585),x88583))+E(f329(f329(x88581,x88582),x88583),f329(f329(f329(f66(x88584,x88585,x88586),x88582),x88587),x88583))
% 187.33/188.05 [8859]~P4(x88594,x88595,x88596,x88597,x88591)+~P24(f329(f62(x88595),x88593))+E(f329(f329(x88591,x88592),x88593),f329(f329(f329(f66(x88594,x88595,x88596),x88592),x88597),x88593))
% 187.33/188.05 [9455]~P20(x94551,x94552,f329(f329(f307(f873(x94551)),f329(f329(f329(f92(x94551),x94553),x94554),x94557)),f193(f881(f873(x94551),a869))))+P20(x94551,x94552,f329(f329(f307(f873(x94551)),f329(f329(f329(f92(x94551),x94553),f33(x94554,x94555)),x94556)),f193(f881(f873(x94551),a869))))+~P20(x94551,x94552,f329(f329(f307(f873(x94551)),f329(f329(f329(f92(x94551),x94557),x94555),x94556)),f193(f881(f873(x94551),a869))))
% 187.33/188.05 [9643]~P19(x96433,x96434,x96435,x96437,x96436,x96431)+~P24(f329(f62(x96434),x96432))+E(f329(x96431,x96432),f329(f329(f329(f66(x96433,x96434,x96435),x96436),x96437),x96432))
% 187.33/188.05 [9799]P47(x97991,x97992,x97993,x97994,x97995,f329(f329(x97993,x97996),x97997))+~P47(x97991,x97992,x97993,x97994,f329(f329(f22(f881(x97991,a869)),x97995),f329(f329(f307(x97991),x97996),f193(f881(x97991,a869)))),x97997)+~P24(f329(f329(f331(x97991),x97996),x97995))
% 187.33/188.05 [10067]~P20(x100671,x100672,f329(f329(f307(f873(x100671)),f329(f329(f329(f92(x100671),f97(x100671,x100673,x100674)),x100675),x100677)),f193(f881(f873(x100671),a869))))+P20(x100671,x100672,f329(f329(f307(f873(x100671)),f329(f329(f329(f92(x100671),x100673),f30(x100674,x100675,x100676)),x100677)),f193(f881(f873(x100671),a869))))+~P20(x100671,x100672,f329(f329(f307(f873(x100671)),f329(f329(f329(f92(x100671),f97(x100671,x100673,f329(f73(a869,a869,a871,a324),x100674))),x100676),x100677)),f193(f881(f873(x100671),a869))))
% 187.33/188.05 [10138]~P47(x101382,x101383,x101384,x101385,x101381,f329(f329(x101384,x101387),x101386))+P47(x101382,x101383,x101384,x101385,f329(f329(f22(f881(x101382,a869)),x101381),f329(f329(f307(x101382),f701(x101386,x101387,x101381,x101385,x101384,x101383,x101382)),f193(f881(x101382,a869)))),f710(x101386,x101387,x101381,x101385,x101384,x101383,x101382))+E(x101381,f193(f881(x101382,a869)))
% 187.33/188.05 [10139]~P47(x101395,x101396,x101391,x101394,x101397,f329(f329(x101391,x101392),x101393))+P47(x101395,x101396,x101391,x101394,f329(f329(f22(f881(x101395,a869)),x101397),f329(f329(f307(x101395),f701(x101393,x101392,x101397,x101394,x101391,x101396,x101395)),f193(f881(x101395,a869)))),f710(x101393,x101392,x101397,x101394,x101391,x101396,x101395))+E(f329(f329(x101391,x101392),x101393),x101394)
% 187.33/188.05 [9181]E(f186(x91811,x91812,x91813,x91814,f329(f329(f157(x91812,x91815),x91816),x91817)),f186(x91811,x91812,x91813,x91814,x91815))+~P24(f329(f329(f244(a874),x91816),f329(f194(f875(x91812)),x91815)))+~P24(f329(f329(f243(a874),f329(f194(f875(x91811)),x91814)),x91816))
% 187.33/188.05 [9477]P24(f329(f329(f243(f881(f880(x94771,x94772),a869)),f329(f329(f286(x94771,x94773,x94772),x94774),x94775)),f329(f329(f286(x94771,x94773,x94772),x94776),x94777)))+~P24(f329(f329(f243(f881(f880(x94773,x94772),a869)),x94775),x94777))+~P24(f329(f329(f243(f881(f880(x94771,x94773),a869)),x94774),x94776))
% 187.33/188.05 [9810]~P24(f329(f329(f331(x98101),x98106),x98105))+P24(f329(f67(x98101,x98102,x98103,x98104,x98105),f329(f329(x98103,x98106),x98107)))+~P24(f329(f67(x98101,x98102,x98103,x98104,f329(f329(f22(f881(x98101,a869)),x98105),f329(f329(f307(x98101),x98106),f193(f881(x98101,a869))))),x98107))
% 187.33/188.05 [10198]~P134(x101981)+~P21(f880(x101982,x101983),x101981,f329(f268(x101982,x101983,x101981),f329(f329(f7(x101982,f881(x101983,x101981),f881(x101983,x101981)),f329(f329(f8(f881(x101981,x101981),f881(f881(x101983,x101981),f881(x101983,x101981)),x101982),f8(x101981,x101981,x101983)),f329(f329(f8(x101981,f881(x101981,x101981),x101982),f81(x101981)),x101984))),x101985)),f329(f329(f266(x101982,x101983),x101986),f329(f16(f881(x101983,a869),x101982),x101987)))+E(f329(f329(f6(x101981,x101981),f34(x101981)),f329(f249(x101981),f329(f329(f8(f881(x101982,a869),a869,x101981),f87(x101982)),f329(f329(f8(f881(x101982,f881(x101983,a869)),f881(x101982,a869),x101981),f329(f8(f881(x101983,a869),a869,x101982),f87(x101983))),f329(f329(f7(x101981,f881(x101982,f881(x101983,a869)),f881(x101982,f881(x101983,a869))),f329(f329(f8(f881(x101982,f881(f881(x101983,a869),f881(x101983,a869))),f881(f881(x101982,f881(x101983,a869)),f881(x101982,f881(x101983,a869))),x101981),f18(x101982,f881(x101983,a869),f881(x101983,a869))),f329(f329(f8(f881(x101982,f881(x101983,f881(a869,a869))),f881(x101982,f881(f881(x101983,a869),f881(x101983,a869))),x101981),f329(f8(f881(x101983,f881(a869,a869)),f881(f881(x101983,a869),f881(x101983,a869)),x101982),f18(x101983,a869,a869))),f329(f329(f8(f881(x101982,f881(x101983,a869)),f881(x101982,f881(x101983,f881(a869,a869))),x101981),f329(f8(f881(x101983,a869),f881(x101983,f881(a869,a869)),x101982),f329(f8(a869,f881(a869,a869),x101983),a327))),f329(f329(f7(x101981,f881(x101982,f881(x101983,x101981)),f881(x101982,f881(x101983,a869))),f329(f329(f8(f881(f881(x101983,x101981),f881(x101983,a869)),f881(f881(x101982,f881(x101983,x101981)),f881(x101982,f881(x101983,a869))),x101981),f8(f881(x101983,x101981),f881(x101983,a869),x101982)),f329(f329(f8(f881(x101981,a869),f881(f881(x101983,x101981),f881(x101983,a869)),x101981),f8(x101981,a869,x101983)),a326))),f329(f329(f7(x101982,f881(x101983,x101981),f881(x101983,x101981)),f329(f329(f8(f881(x101981,x101981),f881(f881(x101983,x101981),f881(x101983,x101981)),x101982),f8(x101981,x101981,x101983)),f329(f329(f8(x101981,f881(x101981,x101981),x101982),f81(x101981)),x101984))),x101985)))))),f329(f329(f7(x101982,f881(x101983,a869),f881(x101983,a869)),f329(f329(f8(f881(a869,a869),f881(f881(x101983,a869),f881(x101983,a869)),x101982),f8(a869,a869,x101983)),f329(f329(f8(a869,f881(a869,a869),x101982),a327),f329(f329(f7(x101982,f881(x101982,a869),a869),f331(x101982)),x101986)))),f329(f329(f7(x101983,f881(x101983,a869),a869),f331(x101983)),x101987))))))),f329(f329(f81(x101981),f329(f329(f6(x101982,x101981),x101984),x101986)),f329(f329(f6(x101983,x101981),x101985),x101987)))
% 187.33/188.05 [9641]~P24(f329(f329(x96414,x96416),x96418))+~P24(f329(f329(x96415,x96418),x96417))+P24(f329(f329(f265(x96411,x96412,x96413,x96414,x96415),x96416),x96417))
% 187.33/188.05 [9244]~P15(x92448,x92441,x92443,x92445)+~P24(f329(f62(x92448),x92446))+E(f329(f73(x92441,x92441,x92442,f329(x92443,x92444)),f329(f73(x92441,x92441,x92442,f329(x92445,x92446)),x92447)),f329(f73(x92441,x92441,x92442,f329(x92445,x92446)),f329(f73(x92441,x92441,x92442,f329(x92443,x92444)),x92447)))
% 187.33/188.05 [9631]~P18(x96317,x96312,x96315,x96318,x96316,x96311)+~P24(f329(f62(x96312),x96314))+E(f329(x96311,f329(f329(f307(x96312),x96313),x96314)),f329(f329(x96315,f329(x96316,x96313)),f329(x96311,x96314)))
% 187.33/188.05 [9752]~P21(x97522,x97524,x97526,x97528)+~P21(x97521,x97523,x97525,x97527)+P21(f880(x97521,x97522),f880(x97523,x97524),f269(x97521,x97523,x97522,x97524,x97525,x97526),f329(f329(f266(x97521,x97522),x97527),f329(f16(f881(x97522,a869),x97521),x97528)))
% 187.33/188.05 [9423]P24(f329(f329(f331(f880(x94231,x94232)),f329(f329(f264(x94231,x94232),x94233),x94234)),f329(f329(f286(x94231,x94235,x94232),x94236),x94237)))+~P24(f329(f329(f331(f880(x94231,x94235)),f329(f329(f264(x94231,x94235),x94233),x94238)),x94236))+~P24(f329(f329(f331(f880(x94235,x94232)),f329(f329(f264(x94235,x94232),x94238),x94234)),x94237))
% 187.33/188.05 [9612]~P24(f329(f329(f243(f881(f880(x96123,x96122),a869)),x96125),f329(f329(f266(x96123,x96122),x96128),f329(f16(f881(x96122,a869),x96123),x96127))))+~P24(f329(f329(f243(f881(f880(x96121,x96123),a869)),x96124),f329(f329(f266(x96121,x96123),x96126),f329(f16(f881(x96123,a869),x96121),x96128))))+P24(f329(f329(f243(f881(f880(x96121,x96122),a869)),f329(f329(f286(x96121,x96123,x96122),x96124),x96125)),f329(f329(f266(x96121,x96122),x96126),f329(f16(f881(x96122,a869),x96121),x96127))))
% 187.33/188.05 [9665]~E(x96653,x96655)+P24(f329(f329(f331(f880(f880(x96651,x96652),f880(x96651,x96652))),f329(f329(f264(f880(x96651,x96652),f880(x96651,x96652)),f329(f329(f264(x96651,x96652),x96653),x96654)),f329(f329(f264(x96651,x96652),x96655),x96656))),f322(x96651,x96652,x96657,x96658)))+~P24(f329(f329(f331(f880(x96652,x96652)),f329(f329(f264(x96652,x96652),x96654),x96656)),x96658))
% 187.33/188.05 [9775]E(x97751,x97752)+~P24(f329(f329(f331(f880(f880(x97753,x97755),f880(x97753,x97755))),f329(f329(f264(f880(x97753,x97755),f880(x97753,x97755)),f329(f329(f264(x97753,x97755),x97751),x97756)),f329(f329(f264(x97753,x97755),x97752),x97757))),f322(x97753,x97755,x97754,x97758)))+P24(f329(f329(f331(f880(x97753,x97753)),f329(f329(f264(x97753,x97753),x97751),x97752)),x97754))
% 187.33/188.05 [9792]~P24(f329(f329(f331(f880(f880(x97921,x97925),f880(x97921,x97925))),f329(f329(f264(f880(x97921,x97925),f880(x97921,x97925)),f329(f329(f264(x97921,x97925),x97922),x97926)),f329(f329(f264(x97921,x97925),x97923),x97927))),f322(x97921,x97925,x97924,x97928)))+P24(f329(f329(f331(f880(x97921,x97921)),f329(f329(f264(x97921,x97921),x97922),x97923)),x97924))+P24(f329(f329(f331(f880(x97925,x97925)),f329(f329(f264(x97925,x97925),x97926),x97927)),x97928))
% 187.33/188.05 [9695]~P19(x96957,x96955,x96951,x96958,x96952,x96954)+~P24(f329(f62(x96955),x96956))+E(f329(f329(x96951,f329(x96952,x96953)),f329(x96954,f329(f329(f22(f881(x96955,a869)),x96956),f329(f329(f307(x96955),x96953),f193(f881(x96955,a869)))))),f329(x96954,f329(f329(f307(x96955),x96953),x96956)))
% 187.33/188.05 [9200]~P24(f329(f329(f329(x92005,x92008),x92006),x92007))+~P24(f329(f329(f331(x92001),x92008),x92004))+P24(f329(f329(f329(f329(f42(x92001,f881(x92002,f881(x92003,a869))),x92004),x92005),x92006),x92007))
% 187.33/188.05 [9410]P24(f329(f329(f329(x94101,x94102),x94103),x94104))+~P24(f329(f329(f331(x94105),x94102),x94106))+~P24(f329(f329(f329(f329(f43(x94105,f881(x94107,f881(x94108,a869))),x94106),x94101),x94103),x94104))
% 187.33/188.05 [9605]~P17(x96053,x96052,x96054,x96058,x96051)+~P24(f329(f62(x96052),x96057))+E(f329(f329(x96051,f329(f329(f18(x96052,x96053,x96053),f329(f329(f8(x96053,f881(x96053,x96053),x96052),x96054),x96055)),x96056)),x96057),f329(f329(x96054,f329(f329(x96051,x96055),x96057)),f329(f329(x96051,x96056),x96057)))
% 187.33/188.05 [9883]~E(f329(f308(x98832,x98834,x98836),x98838),x988310)+~E(f329(f308(x98831,x98833,x98835),x98837),x98839)+E(f329(f308(f880(x98831,x98832),f880(x98833,x98834),f269(x98831,x98833,x98832,x98834,x98835,x98836)),f329(f329(f266(x98831,x98832),x98837),f329(f16(f881(x98832,a869),x98831),x98838))),f329(f329(f266(x98833,x98834),x98839),f329(f16(f881(x98834,a869),x98833),x988310)))
% 187.33/188.05 [6483]~P1(a5000)+~P2(a5000)+~P24(f329(a25,x64831))+P20(a871,f193(f881(f873(a871),a869)),f329(f329(f307(f873(a871)),f329(a93,x64831)),f193(f881(f873(a871),a869))))
% 187.33/188.05 [4820]~P27(x48202)+~P33(x48202,x48201)+P33(x48202,f119(x48202,x48201))+E(x48201,f118(x48202))
% 187.33/188.05 [4821]~P27(x48212)+~P33(x48212,x48211)+P33(x48212,f743(x48211,x48212))+E(x48211,f118(x48212))
% 187.33/188.05 [5054]~P31(x50542)+E(f10(x50542,x50541),f41(x50542,x50541))+E(x50541,f193(f881(x50542,a869)))+~P24(f329(f62(x50542),x50541))
% 187.33/188.05 [5055]~P31(x50552)+E(f13(x50552,x50551),f40(x50552,x50551))+E(x50551,f193(f881(x50552,a869)))+~P24(f329(f62(x50552),x50551))
% 187.33/188.05 [5216]~P27(x52162)+~P33(x52162,x52161)+E(x52161,f118(x52162))+E(f329(f329(f149(x52162),f761(x52161,x52162)),f743(x52161,x52162)),x52161)
% 187.33/188.05 [6011]~P66(x60112)+E(x60111,f193(f881(x60112,a869)))+P24(f329(f329(f243(x60112),f10(x60112,x60111)),f13(x60112,x60111)))+~P24(f329(f62(x60112),x60111))
% 187.33/188.05 [6023]~P43(x60232)+~P43(x60231)+E(x60231,x60232)+~E(f329(f308(a1,a874,a109),x60231),f329(f308(a1,a874,a109),x60232))
% 187.33/188.05 [9058]~P115(x90581)+~P24(f329(f329(f331(x90581),x90582),f114(x90581)))+P24(f329(f329(f244(x90581),f329(f329(f80(x90581),f329(f329(f80(x90581),f78(x90581)),x90582)),x90582)),f2(x90581)))+~P24(f329(f329(f244(x90581),x90582),f2(x90581)))
% 187.33/188.05 [9299]~P115(x92991)+~P24(f329(f329(f331(x92991),x92992),f114(x92991)))+~P24(f329(f329(f244(x92991),f329(f329(f80(x92991),f329(f329(f80(x92991),f78(x92991)),x92992)),x92992)),f2(x92991)))+P24(f329(f329(f244(x92991),x92992),f2(x92991)))
% 187.33/188.05 [4876]~P134(x48762)+~P111(x48762)+E(x48761,f2(a874))+E(f329(f329(f254(x48762),f2(x48762)),x48761),f2(x48762))
% 187.33/188.05 [4880]~P134(x48801)+~P111(x48801)+~E(x48802,f2(a874))+E(f329(f329(f254(x48801),f2(x48801)),x48802),f78(x48801))
% 187.33/188.05 [5041]~P137(x50412)+E(x50411,f78(x50412))+E(x50411,f329(f79(x50412),f78(x50412)))+~E(f329(f329(f81(x50412),x50411),x50411),f78(x50412))
% 187.33/188.05 [5299]~P91(x52992)+E(x52991,f2(x52992))+E(f82(x52992,x52991),f329(f79(x52992),f78(x52992)))+P24(f329(f329(f244(x52992),f2(x52992)),x52991))
% 187.33/188.05 [5532]~P91(x55322)+E(f82(x55322,x55321),f78(x55322))+E(x55321,f2(x55322))+~P24(f329(f329(f244(x55322),f2(x55322)),x55321))
% 187.33/188.05 [5541]E(x55411,x55412)+~E(f329(f108(a874),x55411),f329(f108(a874),x55412))+P24(f329(a198,f329(f108(a1),x55412)))+P24(f329(a198,f329(f108(a1),x55411)))
% 187.33/188.05 [5591]~P93(x55911)+~E(x55912,f2(x55911))+E(f329(f329(f80(x55911),x55912),x55912),f2(x55911))+~P24(f329(f329(f331(x55911),x55912),f114(x55911)))
% 187.33/188.05 [5629]E(x56291,f2(a1))+~E(f329(f329(f39(a1),x56292),x56291),f2(a1))+P24(f329(f329(f244(a1),x56291),x56292))+P24(f329(f329(f244(a1),x56292),x56291))
% 187.33/188.05 [5660]E(x56601,f2(a1))+~E(f329(f329(f39(a1),x56602),x56601),f2(a1))+P24(f329(f329(f243(a1),x56602),f2(a1)))+P24(f329(f329(f244(a1),x56602),x56601))
% 187.33/188.05 [5694]E(x56941,f2(a1))+~E(f329(f329(f39(a1),x56942),x56941),f2(a1))+P24(f329(f329(f243(a1),f2(a1)),x56942))+P24(f329(f329(f244(a1),x56941),x56942))
% 187.33/188.05 [5730]~P93(x57302)+E(x57301,f2(x57302))+~E(f329(f329(f80(x57302),x57301),x57301),f2(x57302))+~P24(f329(f329(f331(x57302),x57301),f114(x57302)))
% 187.33/188.05 [5790]E(f329(f108(a874),x57901),f329(f108(a874),x57902))+~E(f329(f108(a1),x57902),f2(a1))+P24(f329(a198,f329(f108(a1),x57902)))+~P24(f329(a198,f329(f108(a1),x57901)))
% 187.33/188.05 [5817]~E(f329(f108(a874),x58172),f329(f108(a874),x58171))+E(f329(f108(a1),x58171),f2(a1))+P24(f329(a198,f329(f108(a1),x58171)))+~P24(f329(a198,f329(f108(a1),x58172)))
% 187.33/188.05 [5826]~P27(x58262)+E(x58261,f193(f881(x58262,a869)))+~P24(f329(f62(x58262),x58261))+P24(f329(f329(f331(x58262),f14(x58262,x58261)),x58261))
% 187.33/188.05 [5827]~P27(x58272)+E(x58271,f193(f881(x58272,a869)))+~P24(f329(f62(x58272),x58271))+P24(f329(f329(f331(x58272),f15(x58272,x58271)),x58271))
% 187.33/188.05 [5991]~P115(x59911)+~P94(x59911)+P24(f329(f329(f243(x59911),f2(x59911)),f329(f108(x59911),x59912)))+~P24(f329(f329(f243(a1),a83),x59912))
% 187.33/188.05 [5992]~P115(x59921)+~P94(x59921)+P24(f329(f329(f244(x59921),f2(x59921)),f329(f108(x59921),x59922)))+~P24(f329(f329(f244(a1),a83),x59922))
% 187.33/188.05 [6010]~P115(x60101)+~P94(x60101)+E(f329(f75(x60101),f329(f108(x60101),x60102)),f329(f108(x60101),x60102))+P24(f329(f329(f244(x60101),f329(f108(x60101),x60102)),f2(x60101)))
% 187.33/188.05 [6050]E(x60501,x60502)+~E(f329(a109,x60501),f329(a109,x60502))+~P24(f329(f329(f243(a1),f2(a1)),x60502))+~P24(f329(f329(f243(a1),f2(a1)),x60501))
% 187.33/188.05 [6246]~P94(x62462)+~P115(x62462)+~P24(f329(f329(f243(x62462),f2(x62462)),f329(f108(x62462),x62461)))+P24(f329(f329(f243(a1),a83),x62461))
% 187.33/188.05 [6247]~P94(x62472)+~P115(x62472)+~P24(f329(f329(f244(x62472),f2(x62472)),f329(f108(x62472),x62471)))+P24(f329(f329(f244(a1),a83),x62471))
% 187.33/188.05 [6252]~P115(x62521)+~P94(x62521)+P24(f329(f329(f243(x62521),f329(f108(x62521),x62522)),f2(x62521)))+~P24(f329(f329(f243(a1),x62522),a83))
% 187.33/188.05 [6253]~P115(x62531)+~P94(x62531)+P24(f329(f329(f244(x62531),f329(f108(x62531),x62532)),f2(x62531)))+~P24(f329(f329(f244(a1),x62532),a83))
% 187.33/188.05 [6561]~P94(x65612)+~P115(x65612)+~P24(f329(f329(f243(x65612),f329(f108(x65612),x65611)),f2(x65612)))+P24(f329(f329(f243(a1),x65611),a83))
% 187.33/188.05 [6562]~P94(x65622)+~P115(x65622)+~P24(f329(f329(f244(x65622),f329(f108(x65622),x65621)),f2(x65622)))+P24(f329(f329(f244(a1),x65621),a83))
% 187.33/188.05 [6653]~P115(x66531)+~P94(x66531)+E(f329(f75(x66531),f329(f108(x66531),x66532)),f329(f79(x66531),f329(f108(x66531),x66532)))+~P24(f329(f329(f244(x66531),f329(f108(x66531),x66532)),f2(x66531)))
% 187.33/188.05 [6671]E(f329(f108(a874),x66711),f329(f108(a874),x66712))+~E(f329(f108(a1),x66712),f2(a1))+~P24(f329(f329(f243(a1),f329(f108(a1),x66711)),f2(a1)))+~P24(f329(a198,f329(f108(a1),x66711)))
% 187.33/188.05 [7553]~P27(x75532)+E(x75531,f193(f881(x75532,a869)))+~P24(f329(f62(x75532),x75531))+P24(f329(f329(f243(x75532),f11(x75532,f241(x75532),x75531)),f12(x75532,f242(x75532),x75531)))
% 187.33/188.05 [7875]~P32(x78751)+~P43(x78752)+P24(f329(f329(f331(a1),x78751),x78752))+~P24(f329(f329(f331(a874),f329(a109,x78751)),f329(f308(a1,a874,a109),x78752)))
% 187.33/188.05 [8151]~P60(x81512)+P24(f329(x81511,f206(x81512)))+~P24(f329(f58(f878(x81512)),x81511))+P24(f329(f58(x81512),f329(f329(f8(f878(x81512),a869,x81512),x81511),f236(x81512))))
% 187.33/188.05 [8619]~P60(x86191)+~P24(f329(x86192,f206(x86191)))+P24(f329(f59(f878(x86191)),x86192))+~P24(f329(f59(x86191),f329(f329(f8(f878(x86191),a869,x86191),x86192),f236(x86191))))
% 187.33/188.05 [5823]~P138(x58232)+E(x58231,f2(a1))+E(f329(f79(x58232),f329(f107(x58232),f329(f79(a1),x58231))),f329(f107(x58232),x58231))+~P24(f329(f329(f244(a1),x58231),f2(a1)))
% 187.33/188.05 [5896]~P93(x58961)+~P94(x58961)+~P35(x58961,f329(f108(x58961),x58962))+P35(x58961,f329(f108(x58961),f329(f329(f80(a1),x58962),x58962)))
% 187.33/188.05 [6234]~P78(x62342)+E(x62341,f193(f881(x62342,a869)))+E(f15(x62342,f329(f308(x62342,x62342,f79(x62342)),x62341)),f329(f79(x62342),f14(x62342,x62341)))+~P24(f329(f62(x62342),x62341))
% 187.33/188.05 [6235]~P78(x62352)+E(x62351,f193(f881(x62352,a869)))+E(f14(x62352,f329(f308(x62352,x62352,f79(x62352)),x62351)),f329(f79(x62352),f15(x62352,x62351)))+~P24(f329(f62(x62352),x62351))
% 187.33/188.05 [6267]~P93(x62671)+~P94(x62671)+P35(x62671,f329(f108(x62671),x62672))+~P35(x62671,f329(f108(x62671),f329(f329(f80(a1),x62672),x62672)))
% 187.33/188.05 [6355]E(x63551,f2(a1))+E(f329(a51,f50(f329(f79(a1),x63551),f329(f79(a1),x63552))),f46(x63551,x63552))+P24(f329(f329(f243(a1),f2(a1)),x63552))+~P24(f329(f329(f243(a1),f2(a1)),x63551))
% 187.33/188.05 [7376]~P1(a5000)+~P24(f329(a25,x73761))+P20(a871,x73762,f329(f329(f307(f873(a871)),f329(a93,x73761)),f193(f881(f873(a871),a869))))+P24(f329(f329(f331(a872),f383(x73761,x73762)),f183(a872,a870,a28)))
% 187.33/188.05 [8650]~P1(a5000)+~P24(f329(a25,x86502))+P20(a871,x86501,f329(f329(f307(f873(a871)),f329(a93,x86502)),f193(f881(f873(a871),a869))))+~P20(a871,x86501,f329(f329(f307(f873(a871)),f329(a93,f329(a26,f383(x86502,x86501)))),f193(f881(f873(a871),a869))))
% 187.33/188.05 [8664]~P43(x86642)+~P43(x86641)+P24(f329(f329(f244(f881(a874,a869)),f329(f308(a1,a874,a109),x86641)),f329(f308(a1,a874,a109),x86642)))+~P24(f329(f329(f244(f881(a1,a869)),x86641),x86642))
% 187.33/188.05 [8876]~E(f764(x88762,x88761),f765(x88762,x88761))+~P24(f329(f135(x88761),f766(x88762,x88761)))+~P24(f329(f135(f875(x88761)),x88762))+P24(f329(f135(x88761),f329(f140(f875(x88761),f875(x88761),f126(x88761),f118(x88761)),x88762)))
% 187.33/188.05 [8975]~P43(x89752)+~P43(x89751)+~P24(f329(f329(f243(f881(a874,a869)),f329(f308(a1,a874,a109),x89751)),f329(f308(a1,a874,a109),x89752)))+P24(f329(f329(f243(f881(a1,a869)),x89751),x89752))
% 187.33/188.05 [8976]~P43(x89762)+~P43(x89761)+~P24(f329(f329(f244(f881(a874,a869)),f329(f308(a1,a874,a109),x89761)),f329(f308(a1,a874,a109),x89762)))+P24(f329(f329(f244(f881(a1,a869)),x89761),x89762))
% 187.33/188.05 [8982]~E(f764(x89822,x89821),f765(x89822,x89821))+~P24(f329(f135(f875(x89821)),x89822))+P24(f329(f135(x89821),f329(f140(f875(x89821),f875(x89821),f126(x89821),f118(x89821)),x89822)))+P24(f329(f329(f331(f875(x89821)),f766(x89822,x89821)),f329(f171(f875(x89821)),x89822)))
% 187.33/188.05 [9025]~P24(f329(f135(x90251),f766(x90252,x90251)))+~P24(f329(f135(f875(x90251)),x90252))+P24(f329(f135(x90251),f329(f140(f875(x90251),f875(x90251),f126(x90251),f118(x90251)),x90252)))+P24(f329(f329(f331(f875(x90251)),f765(x90252,x90251)),f329(f171(f875(x90251)),x90252)))
% 187.33/188.05 [9026]~P24(f329(f135(x90261),f766(x90262,x90261)))+~P24(f329(f135(f875(x90261)),x90262))+P24(f329(f135(x90261),f329(f140(f875(x90261),f875(x90261),f126(x90261),f118(x90261)),x90262)))+P24(f329(f329(f331(f875(x90261)),f764(x90262,x90261)),f329(f171(f875(x90261)),x90262)))
% 187.33/188.05 [9101]~P24(f329(f135(f875(x91011)),x91012))+P24(f329(f135(x91011),f329(f140(f875(x91011),f875(x91011),f126(x91011),f118(x91011)),x91012)))+P24(f329(f329(f331(f875(x91011)),f765(x91012,x91011)),f329(f171(f875(x91011)),x91012)))+P24(f329(f329(f331(f875(x91011)),f766(x91012,x91011)),f329(f171(f875(x91011)),x91012)))
% 187.33/188.05 [9102]~P24(f329(f135(f875(x91021)),x91022))+P24(f329(f135(x91021),f329(f140(f875(x91021),f875(x91021),f126(x91021),f118(x91021)),x91022)))+P24(f329(f329(f331(f875(x91021)),f764(x91022,x91021)),f329(f171(f875(x91021)),x91022)))+P24(f329(f329(f331(f875(x91021)),f766(x91022,x91021)),f329(f171(f875(x91021)),x91022)))
% 187.33/188.05 [9115]~E(f329(f329(f106(f881(x91151,a869)),f329(f171(x91151),f765(x91152,x91151))),f329(f171(x91151),f764(x91152,x91151))),f193(f881(x91151,a869)))+~P24(f329(f135(x91151),f766(x91152,x91151)))+~P24(f329(f135(f875(x91151)),x91152))+P24(f329(f135(x91151),f329(f140(f875(x91151),f875(x91151),f126(x91151),f118(x91151)),x91152)))
% 187.33/188.05 [9177]~E(f329(f329(f106(f881(x91771,a869)),f329(f171(x91771),f765(x91772,x91771))),f329(f171(x91771),f764(x91772,x91771))),f193(f881(x91771,a869)))+~P24(f329(f135(f875(x91771)),x91772))+P24(f329(f135(x91771),f329(f140(f875(x91771),f875(x91771),f126(x91771),f118(x91771)),x91772)))+P24(f329(f329(f331(f875(x91771)),f766(x91772,x91771)),f329(f171(f875(x91771)),x91772)))
% 187.33/188.05 [9447]E(x94471,f2(a1))+E(x94472,f2(a1))+E(f329(f329(f86(a1,f880(a1,a1)),f329(f329(a225,x94472),x94471)),f329(f329(f18(a1,a1,f880(a1,a1)),f329(f329(f8(a1,f881(a1,f880(a1,a1)),a1),f264(a1,a1)),f329(f39(a1),x94472))),f329(f39(a1),x94471))),f223(x94472,x94471))+P24(f329(f329(f244(a1),x94471),f2(a1)))
% 187.33/188.05 [8212]~P94(x82122)+~P115(x82122)+~P24(f329(f329(f243(x82122),f329(f108(x82122),x82121)),f78(x82122)))+P24(f329(f329(f243(a1),x82121),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))
% 187.33/188.05 [8213]~P94(x82132)+~P115(x82132)+~P24(f329(f329(f244(x82132),f329(f108(x82132),x82131)),f78(x82132)))+P24(f329(f329(f244(a1),x82131),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))
% 187.33/188.05 [8491]~P115(x84911)+~P94(x84911)+P24(f329(f329(f243(x84911),f329(f108(x84911),x84912)),f78(x84911)))+~P24(f329(f329(f243(a1),x84912),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))
% 187.33/188.05 [8492]~P115(x84921)+~P94(x84921)+P24(f329(f329(f244(x84921),f329(f108(x84921),x84922)),f78(x84921)))+~P24(f329(f329(f244(a1),x84922),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))
% 187.33/188.05 [8689]~P94(x86892)+~P115(x86892)+~P24(f329(f329(f243(x86892),f78(x86892)),f329(f108(x86892),x86891)))+P24(f329(f329(f243(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),x86891))
% 187.33/188.05 [8690]~P94(x86902)+~P115(x86902)+~P24(f329(f329(f244(x86902),f78(x86902)),f329(f108(x86902),x86901)))+P24(f329(f329(f244(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),x86901))
% 187.33/188.05 [9064]~P115(x90641)+~P94(x90641)+P24(f329(f329(f243(x90641),f78(x90641)),f329(f108(x90641),x90642)))+~P24(f329(f329(f243(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),x90642))
% 187.33/188.05 [9065]~P115(x90651)+~P94(x90651)+P24(f329(f329(f244(x90651),f78(x90651)),f329(f108(x90651),x90652)))+~P24(f329(f329(f244(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),x90652))
% 187.33/188.05 [9577]~P137(x95772)+E(x95771,f78(x95772))+E(x95771,f329(f79(x95772),f78(x95772)))+~E(f329(f329(f254(x95772),x95771),f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))),f78(x95772))
% 187.33/188.05 [9851]~P63(x98511)+~P94(x98511)+~P24(f329(f329(f244(x98511),f2(x98511)),x98512))+P24(f329(f329(f244(x98511),f2(x98511)),f329(f329(f287(x98511),x98512),f329(f108(x98511),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102))))))
% 187.33/188.05 [9913]~P63(x99131)+~P94(x99131)+P24(f329(f329(f244(x99131),f2(x99131)),x99132))+~P24(f329(f329(f244(x99131),f2(x99131)),f329(f329(f287(x99131),x99132),f329(f108(x99131),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102))))))
% 187.33/188.05 [10166]~P138(x101662)+E(x101661,f2(a1))+P24(f329(f329(f244(a1),x101661),f2(a1)))+E(f329(f329(f268(a1,a1,x101662),f329(f329(f7(a1,f881(a1,f881(x101662,x101662)),f881(a1,x101662)),f329(f329(f8(f881(f881(x101662,x101662),x101662),f881(f881(a1,f881(x101662,x101662)),f881(a1,x101662)),a1),f8(f881(x101662,x101662),x101662,a1)),f329(f329(f8(x101662,f881(f881(x101662,x101662),x101662),a1),f86(x101662,x101662)),f107(x101662)))),f329(f329(f7(a1,f881(x101662,x101662),f881(x101662,x101662)),f329(f329(f8(f881(x101662,f881(x101662,x101662)),f881(f881(x101662,x101662),f881(x101662,x101662)),a1),f18(x101662,x101662,x101662)),f329(f329(f7(a1,f881(x101662,x101662),f881(x101662,f881(x101662,x101662))),f329(f329(f8(f881(x101662,f881(x101662,x101662)),f881(f881(x101662,x101662),f881(x101662,f881(x101662,x101662))),a1),f8(x101662,f881(x101662,x101662),x101662)),f329(f329(f8(a869,f881(x101662,f881(x101662,x101662)),a1),f101(x101662)),f329(f329(f7(a1,a1,a869),a326),f2(a1))))),f329(f329(f18(x101662,x101662,x101662),f80(x101662)),f5(x101662))))),f329(f329(f7(x101662,x101662,x101662),f329(f329(f8(x101662,f881(x101662,x101662),x101662),f80(x101662)),f329(f329(f18(x101662,x101662,x101662),f80(x101662)),f5(x101662)))),f78(x101662))))),f46(x101661,f329(f108(a1),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102))))),f329(f107(x101662),x101661))
% 187.33/188.05 [5211]~P60(x52113)+~P40(x52113,x52112,f56(x52113))+E(x52111,f778(x52112,x52113))+~P24(f329(x52112,x52111))
% 187.33/188.05 [5369]~P60(x53691)+P40(x53691,x53692,f56(x53691))+~E(f779(x53692,x53691,x53693),x53693)+~P24(f329(x53692,x53693))
% 187.33/188.05 [4847]~P93(x48473)+~P94(x48473)+E(x48471,x48472)+~E(f329(f108(x48473),x48471),f329(f108(x48473),x48472))
% 187.33/188.05 [5990]~P60(x59901)+P40(x59901,x59902,f56(x59901))+~P24(f329(x59902,x59903))+P24(f329(x59902,f779(x59902,x59901,x59903)))
% 187.33/188.05 [6000]~P24(f329(x60001,x60002))+~P24(f329(x60001,x60003))+~P24(f329(f329(f243(a874),x60003),f824(x60002,x60001)))+P24(f329(x60001,f2(a874)))
% 187.33/188.05 [6418]P144(x64182,x64183,x64181)+E(x64181,f2(a1))+P24(f329(f329(f243(a1),f2(a1)),f809(x64181,x64183,x64182)))+P24(f329(f329(f244(a1),x64181),f2(a1)))
% 187.33/188.05 [6419]P143(x64192,x64193,x64191)+E(x64191,f2(a1))+P24(f329(f329(f243(a1),f2(a1)),f817(x64191,x64193,x64192)))+P24(f329(f329(f244(a1),x64191),f2(a1)))
% 187.33/188.05 [6540]P143(x65401,x65402,x65403)+~P24(f329(x65401,x65402))+P24(f329(f329(f243(a1),f2(a1)),f817(x65403,x65402,x65401)))+P24(f329(f329(f244(a1),x65403),f2(a1)))
% 187.33/188.05 [6567]P144(x65671,x65672,x65673)+P24(f329(f329(f243(a1),f2(a1)),f809(x65673,x65672,x65671)))+~P24(f329(x65671,f2(a1)))+P24(f329(f329(f244(a1),x65673),f2(a1)))
% 187.33/188.05 [6595]P144(x65952,x65953,x65951)+E(x65951,f2(a1))+~P24(f329(x65952,f810(x65951,x65953,x65952)))+P24(f329(f329(f244(a1),x65951),f2(a1)))
% 187.33/188.05 [6596]P143(x65962,x65963,x65961)+E(x65961,f2(a1))+~P24(f329(x65962,f817(x65961,x65963,x65962)))+P24(f329(f329(f244(a1),x65961),f2(a1)))
% 187.33/188.05 [6696]~P27(x66961)+~P31(x66961)+~P24(f329(f329(f244(x66961),x66962),f40(x66961,x66963)))+P24(f329(f329(f244(x66961),x66962),f600(x66963,x66962,x66961)))
% 187.33/188.05 [6705]P143(x67051,x67052,x67053)+~P24(f329(x67051,x67052))+~P24(f329(x67051,f817(x67053,x67052,x67051)))+P24(f329(f329(f244(a1),x67053),f2(a1)))
% 187.33/188.05 [6737]P144(x67371,x67372,x67373)+~P24(f329(x67371,f810(x67373,x67372,x67371)))+~P24(f329(x67371,f2(a1)))+P24(f329(f329(f244(a1),x67373),f2(a1)))
% 187.33/188.05 [6991]P144(x69912,x69913,x69911)+E(x69911,f2(a1))+P24(f329(f329(f243(a1),f2(a1)),f809(x69911,x69913,x69912)))+P24(f329(f329(f244(a1),x69911),f808(x69911,x69913,x69912)))
% 187.33/188.05 [6992]P143(x69922,x69923,x69921)+E(x69921,f2(a1))+P24(f329(f329(f243(a1),f2(a1)),f817(x69921,x69923,x69922)))+P24(f329(f329(f244(a1),x69921),f816(x69921,x69923,x69922)))
% 187.33/188.05 [7109]P143(x71091,x71092,x71093)+~P24(f329(x71091,x71092))+P24(f329(f329(f243(a1),f2(a1)),f817(x71093,x71092,x71091)))+P24(f329(f329(f244(a1),x71093),f816(x71093,x71092,x71091)))
% 187.33/188.05 [7128]P144(x71281,x71282,x71283)+P24(f329(f329(f243(a1),f2(a1)),f809(x71283,x71282,x71281)))+P24(f329(f329(f244(a1),x71283),f808(x71283,x71282,x71281)))+~P24(f329(x71281,f2(a1)))
% 187.33/188.05 [7161]P144(x71612,x71613,x71611)+E(x71611,f2(a1))+~P24(f329(x71612,f810(x71611,x71613,x71612)))+P24(f329(f329(f244(a1),x71611),f808(x71611,x71613,x71612)))
% 187.33/188.05 [7162]P143(x71622,x71623,x71621)+E(x71621,f2(a1))+~P24(f329(x71622,f817(x71621,x71623,x71622)))+P24(f329(f329(f244(a1),x71621),f816(x71621,x71623,x71622)))
% 187.33/188.05 [7203]P144(x72032,x72033,x72031)+E(x72031,f2(a1))+P24(f329(f329(f243(a1),f2(a1)),f809(x72031,x72033,x72032)))+~P24(f329(x72032,f815(x72031,x72033,x72032)))
% 187.33/188.05 [7204]P143(x72042,x72043,x72041)+E(x72041,f2(a1))+P24(f329(f329(f243(a1),f2(a1)),f817(x72041,x72043,x72042)))+~P24(f329(x72042,f816(x72041,x72043,x72042)))
% 187.33/188.05 [7292]P143(x72921,x72922,x72923)+~P24(f329(x72921,x72922))+~P24(f329(x72921,f817(x72923,x72922,x72921)))+P24(f329(f329(f244(a1),x72923),f816(x72923,x72922,x72921)))
% 187.33/188.05 [7308]P144(x73081,x73082,x73083)+~P24(f329(x73081,f810(x73083,x73082,x73081)))+P24(f329(f329(f244(a1),x73083),f808(x73083,x73082,x73081)))+~P24(f329(x73081,f2(a1)))
% 187.33/188.05 [7312]P143(x73121,x73122,x73123)+~P24(f329(x73121,x73122))+P24(f329(f329(f243(a1),f2(a1)),f817(x73123,x73122,x73121)))+~P24(f329(x73121,f816(x73123,x73122,x73121)))
% 187.33/188.05 [7330]P144(x73301,x73302,x73303)+P24(f329(f329(f243(a1),f2(a1)),f809(x73303,x73302,x73301)))+~P24(f329(x73301,f815(x73303,x73302,x73301)))+~P24(f329(x73301,f2(a1)))
% 187.33/188.05 [7354]P144(x73542,x73543,x73541)+E(x73541,f2(a1))+~P24(f329(x73542,f810(x73541,x73543,x73542)))+~P24(f329(x73542,f815(x73541,x73543,x73542)))
% 187.33/188.05 [7355]P143(x73552,x73553,x73551)+E(x73551,f2(a1))+~P24(f329(x73552,f817(x73551,x73553,x73552)))+~P24(f329(x73552,f816(x73551,x73553,x73552)))
% 187.33/188.05 [7448]P143(x74481,x74482,x74483)+~P24(f329(x74481,x74482))+~P24(f329(x74481,f817(x74483,x74482,x74481)))+~P24(f329(x74481,f816(x74483,x74482,x74481)))
% 187.33/188.05 [7465]P144(x74651,x74652,x74653)+~P24(f329(x74651,f810(x74653,x74652,x74651)))+~P24(f329(x74651,f815(x74653,x74652,x74651)))+~P24(f329(x74651,f2(a1)))
% 187.33/188.05 [7513]P144(x75132,x75133,x75131)+E(x75131,f2(a1))+P24(f329(f329(f243(a1),f2(a1)),f809(x75131,x75133,x75132)))+P24(f329(f329(f243(a1),f808(x75131,x75133,x75132)),f2(a1)))
% 187.33/188.05 [7514]P143(x75142,x75143,x75141)+E(x75141,f2(a1))+P24(f329(f329(f243(a1),f2(a1)),f817(x75141,x75143,x75142)))+P24(f329(f329(f243(a1),f816(x75141,x75143,x75142)),f2(a1)))
% 187.33/188.05 [7515]~P89(x75151)+~P24(f329(f329(f243(x75151),x75153),f2(x75151)))+~P24(f329(f329(f243(x75151),x75152),f2(x75151)))+P24(f329(f329(f243(x75151),f329(f329(f80(x75151),x75152),x75153)),f2(x75151)))
% 187.33/188.05 [7516]~P138(x75161)+~P24(f329(f329(f331(x75161),x75163),f114(x75161)))+~P24(f329(f329(f331(x75161),x75162),f114(x75161)))+P24(f329(f329(f331(x75161),f329(f329(f22(x75161),x75162),x75163)),f114(x75161)))
% 187.33/188.05 [7517]~P138(x75171)+~P24(f329(f329(f331(x75171),x75173),f114(x75171)))+~P24(f329(f329(f331(x75171),x75172),f114(x75171)))+P24(f329(f329(f331(x75171),f329(f329(f81(x75171),x75172),x75173)),f114(x75171)))
% 187.33/188.05 [7518]~P141(x75181)+~P24(f329(f329(f331(x75181),x75183),f191(x75181)))+~P24(f329(f329(f331(x75181),x75182),f191(x75181)))+P24(f329(f329(f331(x75181),f329(f329(f81(x75181),x75182),x75183)),f191(x75181)))
% 187.33/188.05 [7519]~P138(x75191)+~P24(f329(f329(f331(x75191),x75193),f114(x75191)))+~P24(f329(f329(f331(x75191),x75192),f114(x75191)))+P24(f329(f329(f331(x75191),f329(f329(f80(x75191),x75192),x75193)),f114(x75191)))
% 187.33/188.05 [7520]~P141(x75201)+~P24(f329(f329(f331(x75201),x75203),f191(x75201)))+~P24(f329(f329(f331(x75201),x75202),f191(x75201)))+P24(f329(f329(f331(x75201),f329(f329(f80(x75201),x75202),x75203)),f191(x75201)))
% 187.33/188.05 [7521]~P89(x75211)+~P24(f329(f329(f243(x75211),x75213),f2(x75211)))+~P24(f329(f329(f244(x75211),x75212),f2(x75211)))+P24(f329(f329(f244(x75211),f329(f329(f80(x75211),x75212),x75213)),f2(x75211)))
% 187.33/188.05 [7522]~P89(x75221)+~P24(f329(f329(f243(x75221),x75222),f2(x75221)))+~P24(f329(f329(f244(x75221),x75223),f2(x75221)))+P24(f329(f329(f244(x75221),f329(f329(f80(x75221),x75222),x75223)),f2(x75221)))
% 187.33/188.05 [7523]~P89(x75231)+~P24(f329(f329(f244(x75231),x75233),f2(x75231)))+~P24(f329(f329(f244(x75231),x75232),f2(x75231)))+P24(f329(f329(f244(x75231),f329(f329(f80(x75231),x75232),x75233)),f2(x75231)))
% 187.33/188.05 [7549]P144(x75493,x75492,x75491)+E(x75491,f2(a1))+E(f329(f329(f80(a1),f329(f329(f81(a1),x75491),f810(x75491,x75492,x75493))),f809(x75491,x75492,x75493)),x75492)+P24(f329(f329(f244(a1),x75491),f2(a1)))
% 187.33/188.05 [7550]P143(x75503,x75502,x75501)+E(x75501,f2(a1))+E(f329(f329(f80(a1),f329(f329(f81(a1),x75501),f818(x75501,x75502,x75503))),f817(x75501,x75502,x75503)),x75502)+P24(f329(f329(f244(a1),x75501),f2(a1)))
% 187.33/188.05 [7632]P143(x76321,x76322,x76323)+~P24(f329(x76321,x76322))+P24(f329(f329(f243(a1),f2(a1)),f817(x76323,x76322,x76321)))+P24(f329(f329(f243(a1),f816(x76323,x76322,x76321)),f2(a1)))
% 187.33/188.05 [7661]P144(x76611,x76612,x76613)+P24(f329(f329(f243(a1),f2(a1)),f809(x76613,x76612,x76611)))+~P24(f329(x76611,f2(a1)))+P24(f329(f329(f243(a1),f808(x76613,x76612,x76611)),f2(a1)))
% 187.33/188.05 [7671]P143(x76713,x76712,x76711)+~P24(f329(x76713,x76712))+E(f329(f329(f80(a1),f329(f329(f81(a1),x76711),f818(x76711,x76712,x76713))),f817(x76711,x76712,x76713)),x76712)+P24(f329(f329(f244(a1),x76711),f2(a1)))
% 187.33/188.05 [7678]P144(x76782,x76783,x76781)+E(x76781,f2(a1))+~P24(f329(x76782,f810(x76781,x76783,x76782)))+P24(f329(f329(f243(a1),f808(x76781,x76783,x76782)),f2(a1)))
% 187.33/188.05 [7679]P143(x76792,x76793,x76791)+E(x76791,f2(a1))+~P24(f329(x76792,f817(x76791,x76793,x76792)))+P24(f329(f329(f243(a1),f816(x76791,x76793,x76792)),f2(a1)))
% 187.33/188.05 [7684]P144(x76843,x76842,x76841)+E(f329(f329(f80(a1),f329(f329(f81(a1),x76841),f810(x76841,x76842,x76843))),f809(x76841,x76842,x76843)),x76842)+~P24(f329(x76843,f2(a1)))+P24(f329(f329(f244(a1),x76841),f2(a1)))
% 187.33/188.05 [7741]P143(x77411,x77412,x77413)+~P24(f329(x77411,x77412))+~P24(f329(x77411,f817(x77413,x77412,x77411)))+P24(f329(f329(f243(a1),f816(x77413,x77412,x77411)),f2(a1)))
% 187.33/188.05 [7745]P144(x77451,x77452,x77453)+~P24(f329(x77451,f810(x77453,x77452,x77451)))+~P24(f329(x77451,f2(a1)))+P24(f329(f329(f243(a1),f808(x77453,x77452,x77451)),f2(a1)))
% 187.33/188.05 [7817]~P123(x78171)+~P24(f329(f329(f243(x78171),f329(f329(f81(x78171),x78173),x78172)),f2(x78171)))+P24(f329(f329(f243(x78171),x78172),f2(x78171)))+P24(f329(f329(f243(x78171),x78173),f2(x78171)))
% 187.33/188.05 [7818]~P63(x78181)+~P24(f329(f329(f243(x78181),f329(f329(f287(x78181),x78183),x78182)),f2(x78181)))+P24(f329(f329(f243(x78181),x78182),f2(x78181)))+P24(f329(f329(f243(x78181),x78183),f2(x78181)))
% 187.33/188.05 [7819]~P63(x78191)+~P24(f329(f329(f244(x78191),f329(f329(f287(x78191),x78193),x78192)),f2(x78191)))+P24(f329(f329(f244(x78191),x78192),f2(x78191)))+P24(f329(f329(f244(x78191),x78193),f2(x78191)))
% 187.33/188.05 [7933]P144(x79333,x79332,x79331)+E(x79331,f2(a1))+E(f329(f329(f80(a1),f329(f329(f81(a1),x79331),f810(x79331,x79332,x79333))),f809(x79331,x79332,x79333)),x79332)+P24(f329(f329(f244(a1),x79331),f808(x79331,x79332,x79333)))
% 187.33/188.05 [7934]P143(x79343,x79342,x79341)+E(x79341,f2(a1))+E(f329(f329(f80(a1),f329(f329(f81(a1),x79341),f818(x79341,x79342,x79343))),f817(x79341,x79342,x79343)),x79342)+P24(f329(f329(f244(a1),x79341),f816(x79341,x79342,x79343)))
% 187.33/188.05 [7946]P144(x79463,x79462,x79461)+E(x79461,f2(a1))+E(f329(f329(f80(a1),f329(f329(f81(a1),x79461),f815(x79461,x79462,x79463))),f808(x79461,x79462,x79463)),x79462)+P24(f329(f329(f243(a1),f2(a1)),f809(x79461,x79462,x79463)))
% 187.33/188.05 [7947]P143(x79473,x79472,x79471)+E(x79471,f2(a1))+E(f329(f329(f80(a1),f329(f329(f81(a1),x79471),f819(x79471,x79472,x79473))),f816(x79471,x79472,x79473)),x79472)+P24(f329(f329(f243(a1),f2(a1)),f817(x79471,x79472,x79473)))
% 187.33/188.05 [7991]P143(x79913,x79912,x79911)+~P24(f329(x79913,x79912))+E(f329(f329(f80(a1),f329(f329(f81(a1),x79911),f818(x79911,x79912,x79913))),f817(x79911,x79912,x79913)),x79912)+P24(f329(f329(f244(a1),x79911),f816(x79911,x79912,x79913)))
% 187.33/188.05 [8003]P144(x80033,x80032,x80031)+E(f329(f329(f80(a1),f329(f329(f81(a1),x80031),f810(x80031,x80032,x80033))),f809(x80031,x80032,x80033)),x80032)+P24(f329(f329(f244(a1),x80031),f808(x80031,x80032,x80033)))+~P24(f329(x80033,f2(a1)))
% 187.33/188.05 [8009]P143(x80093,x80092,x80091)+~P24(f329(x80093,x80092))+E(f329(f329(f80(a1),f329(f329(f81(a1),x80091),f819(x80091,x80092,x80093))),f816(x80091,x80092,x80093)),x80092)+P24(f329(f329(f243(a1),f2(a1)),f817(x80091,x80092,x80093)))
% 187.33/188.05 [8017]P144(x80173,x80172,x80171)+E(f329(f329(f80(a1),f329(f329(f81(a1),x80171),f815(x80171,x80172,x80173))),f808(x80171,x80172,x80173)),x80172)+P24(f329(f329(f243(a1),f2(a1)),f809(x80171,x80172,x80173)))+~P24(f329(x80173,f2(a1)))
% 187.33/188.05 [8028]P144(x80283,x80282,x80281)+E(x80281,f2(a1))+E(f329(f329(f80(a1),f329(f329(f81(a1),x80281),f810(x80281,x80282,x80283))),f809(x80281,x80282,x80283)),x80282)+~P24(f329(x80283,f815(x80281,x80282,x80283)))
% 187.33/188.05 [8029]P143(x80293,x80292,x80291)+E(x80291,f2(a1))+E(f329(f329(f80(a1),f329(f329(f81(a1),x80291),f818(x80291,x80292,x80293))),f817(x80291,x80292,x80293)),x80292)+~P24(f329(x80293,f816(x80291,x80292,x80293)))
% 187.33/188.05 [8030]P144(x80303,x80302,x80301)+E(x80301,f2(a1))+E(f329(f329(f80(a1),f329(f329(f81(a1),x80301),f815(x80301,x80302,x80303))),f808(x80301,x80302,x80303)),x80302)+~P24(f329(x80303,f810(x80301,x80302,x80303)))
% 187.33/188.05 [8031]P143(x80313,x80312,x80311)+E(x80311,f2(a1))+E(f329(f329(f80(a1),f329(f329(f81(a1),x80311),f819(x80311,x80312,x80313))),f816(x80311,x80312,x80313)),x80312)+~P24(f329(x80313,f817(x80311,x80312,x80313)))
% 187.33/188.05 [8089]P143(x80893,x80892,x80891)+~P24(f329(x80893,x80892))+E(f329(f329(f80(a1),f329(f329(f81(a1),x80891),f818(x80891,x80892,x80893))),f817(x80891,x80892,x80893)),x80892)+~P24(f329(x80893,f816(x80891,x80892,x80893)))
% 187.33/188.05 [8090]P143(x80903,x80902,x80901)+~P24(f329(x80903,x80902))+E(f329(f329(f80(a1),f329(f329(f81(a1),x80901),f819(x80901,x80902,x80903))),f816(x80901,x80902,x80903)),x80902)+~P24(f329(x80903,f817(x80901,x80902,x80903)))
% 187.33/188.05 [8100]P144(x81003,x81002,x81001)+E(f329(f329(f80(a1),f329(f329(f81(a1),x81001),f810(x81001,x81002,x81003))),f809(x81001,x81002,x81003)),x81002)+~P24(f329(x81003,f815(x81001,x81002,x81003)))+~P24(f329(x81003,f2(a1)))
% 187.33/188.05 [8101]P144(x81013,x81012,x81011)+E(f329(f329(f80(a1),f329(f329(f81(a1),x81011),f815(x81011,x81012,x81013))),f808(x81011,x81012,x81013)),x81012)+~P24(f329(x81013,f810(x81011,x81012,x81013)))+~P24(f329(x81013,f2(a1)))
% 187.33/188.05 [8205]P144(x82053,x82052,x82051)+E(x82051,f2(a1))+E(f329(f329(f80(a1),f329(f329(f81(a1),x82051),f810(x82051,x82052,x82053))),f809(x82051,x82052,x82053)),x82052)+P24(f329(f329(f243(a1),f808(x82051,x82052,x82053)),f2(a1)))
% 187.33/188.05 [8206]P143(x82063,x82062,x82061)+E(x82061,f2(a1))+E(f329(f329(f80(a1),f329(f329(f81(a1),x82061),f818(x82061,x82062,x82063))),f817(x82061,x82062,x82063)),x82062)+P24(f329(f329(f243(a1),f816(x82061,x82062,x82063)),f2(a1)))
% 187.33/188.05 [8246]P143(x82463,x82462,x82461)+~P24(f329(x82463,x82462))+E(f329(f329(f80(a1),f329(f329(f81(a1),x82461),f818(x82461,x82462,x82463))),f817(x82461,x82462,x82463)),x82462)+P24(f329(f329(f243(a1),f816(x82461,x82462,x82463)),f2(a1)))
% 187.33/188.05 [8251]P144(x82513,x82512,x82511)+E(f329(f329(f80(a1),f329(f329(f81(a1),x82511),f810(x82511,x82512,x82513))),f809(x82511,x82512,x82513)),x82512)+~P24(f329(x82513,f2(a1)))+P24(f329(f329(f243(a1),f808(x82511,x82512,x82513)),f2(a1)))
% 187.33/188.05 [8380]P144(x83803,x83802,x83801)+E(x83801,f2(a1))+E(f329(f329(f80(a1),f329(f329(f81(a1),x83801),f815(x83801,x83802,x83803))),f808(x83801,x83802,x83803)),x83802)+E(f329(f329(f80(a1),f329(f329(f81(a1),x83801),f810(x83801,x83802,x83803))),f809(x83801,x83802,x83803)),x83802)
% 187.33/188.05 [8381]P143(x83813,x83812,x83811)+E(x83811,f2(a1))+E(f329(f329(f80(a1),f329(f329(f81(a1),x83811),f819(x83811,x83812,x83813))),f816(x83811,x83812,x83813)),x83812)+E(f329(f329(f80(a1),f329(f329(f81(a1),x83811),f818(x83811,x83812,x83813))),f817(x83811,x83812,x83813)),x83812)
% 187.33/188.05 [8404]P143(x84043,x84042,x84041)+~P24(f329(x84043,x84042))+E(f329(f329(f80(a1),f329(f329(f81(a1),x84041),f819(x84041,x84042,x84043))),f816(x84041,x84042,x84043)),x84042)+E(f329(f329(f80(a1),f329(f329(f81(a1),x84041),f818(x84041,x84042,x84043))),f817(x84041,x84042,x84043)),x84042)
% 187.33/188.05 [8417]P144(x84173,x84172,x84171)+E(f329(f329(f80(a1),f329(f329(f81(a1),x84171),f815(x84171,x84172,x84173))),f808(x84171,x84172,x84173)),x84172)+E(f329(f329(f80(a1),f329(f329(f81(a1),x84171),f810(x84171,x84172,x84173))),f809(x84171,x84172,x84173)),x84172)+~P24(f329(x84173,f2(a1)))
% 187.33/188.05 [9069]~P123(x90691)+~E(x90693,f2(x90691))+~E(x90692,f2(x90691))+P24(f329(f329(f243(x90691),f329(f329(f80(x90691),f329(f329(f81(x90691),x90692),x90692)),f329(f329(f81(x90691),x90693),x90693))),f2(x90691)))
% 187.33/188.05 [10116]~P115(x101161)+~E(x101163,f2(x101161))+~E(x101162,f2(x101161))+P24(f329(f329(f243(x101161),f329(f329(f80(x101161),f329(f329(f254(x101161),x101162),f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102))))),f329(f329(f254(x101161),x101163),f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))))),f2(x101161)))
% 187.33/188.05 [4795]~E(x47953,x47951)+~P118(x47952)+E(x47951,f2(x47952))+E(f329(f329(f287(x47952),x47953),x47951),f78(x47952))
% 187.33/188.05 [4848]~P67(x48481)+~E(x48483,f193(x48481))+~E(x48482,f193(x48481))+E(f329(f329(f115(x48481),x48482),x48483),f193(x48481))
% 187.33/188.05 [4849]~P101(x48491)+~E(x48493,f252(x48491))+~E(x48492,f252(x48491))+E(f329(f329(f106(x48491),x48492),x48493),f252(x48491))
% 187.33/188.05 [4935]~P118(x49353)+E(x49351,x49352)+E(x49352,f2(x49353))+~E(f329(f329(f287(x49353),x49351),x49352),f78(x49353))
% 187.33/188.05 [4954]~P127(x49542)+E(x49541,f2(x49542))+E(x49543,f2(x49542))+~E(f329(f329(f81(x49542),x49543),x49541),f2(x49542))
% 187.33/188.05 [4955]~P136(x49552)+E(x49551,f2(x49552))+E(x49553,f2(x49552))+~E(f329(f329(f81(x49552),x49553),x49551),f2(x49552))
% 187.33/188.05 [5336]~P117(x53363)+E(x53361,x53362)+E(x53361,f329(f79(x53363),x53362))+~E(f329(f329(f81(x53363),x53361),x53361),f329(f329(f81(x53363),x53362),x53362))
% 187.33/188.05 [5376]~P97(x53761)+E(f329(f79(x53761),x53762),x53763)+~E(f329(f329(f115(x53761),x53762),x53763),f252(x53761))+~E(f329(f329(f106(x53761),x53762),x53763),f193(x53761))
% 187.33/188.05 [5455]~P115(x54553)+E(x54551,x54552)+P24(f329(f329(f244(x54553),x54552),x54551))+P24(f329(f329(f244(x54553),x54551),x54552))
% 187.33/188.05 [5456]~P27(x54563)+E(x54561,x54562)+P24(f329(f329(f244(x54563),x54562),x54561))+P24(f329(f329(f244(x54563),x54561),x54562))
% 187.33/188.05 [5457]~E(x54572,x54573)+~P27(x54571)+P24(f329(f329(f244(x54571),x54572),x54573))+P24(f329(f329(f243(x54571),x54572),x54573))
% 187.33/188.05 [5710]~P106(x57103)+E(x57101,x57102)+~P24(f329(f329(f243(x57103),x57102),x57101))+P24(f329(f329(f244(x57103),x57102),x57101))
% 187.33/188.05 [5712]~P27(x57123)+E(x57121,x57122)+~P24(f329(f329(f243(x57123),x57121),x57122))+P24(f329(f329(f244(x57123),x57121),x57122))
% 187.33/188.05 [5718]~P106(x57183)+E(x57181,x57182)+~P24(f329(f329(f243(x57183),x57181),x57182))+P24(f329(f329(f244(x57183),x57181),x57182))
% 187.33/188.05 [5820]P143(x58201,x58202,x58203)+~P24(f329(x58201,x58202))+P24(f329(f329(f244(a1),x58203),f2(a1)))+P24(f329(f329(f244(a1),f2(a1)),x58203))
% 187.33/188.05 [5867]P144(x58671,x58672,x58673)+~P24(f329(x58671,f2(a1)))+P24(f329(f329(f244(a1),x58673),f2(a1)))+P24(f329(f329(f244(a1),f2(a1)),x58673))
% 187.33/188.05 [5871]~P66(x58711)+E(f329(f329(f115(x58711),x58712),f10(x58711,x58713)),x58712)+~P24(f329(f62(x58711),x58713))+~P24(f329(f329(f331(x58711),x58712),x58713))
% 187.33/188.05 [5872]~P66(x58721)+E(f329(f329(f106(x58721),x58722),f13(x58721,x58723)),x58722)+~P24(f329(f62(x58721),x58723))+~P24(f329(f329(f331(x58721),x58722),x58723))
% 187.33/188.05 [5908]~P66(x59081)+E(f329(f329(f115(x59081),x59082),f13(x59081,x59083)),f13(x59081,x59083))+~P24(f329(f62(x59081),x59083))+~P24(f329(f329(f331(x59081),x59082),x59083))
% 187.33/188.05 [5909]~P66(x59091)+E(f329(f329(f106(x59091),x59092),f10(x59091,x59093)),f10(x59091,x59093))+~P24(f329(f62(x59091),x59093))+~P24(f329(f329(f331(x59091),x59092),x59093))
% 187.33/188.05 [5910]~P27(x59101)+E(f329(f329(f241(x59101),x59102),f14(x59101,x59103)),f14(x59101,x59103))+~P24(f329(f62(x59101),x59103))+~P24(f329(f329(f331(x59101),x59102),x59103))
% 187.33/188.05 [5911]~P27(x59111)+E(f329(f329(f242(x59111),x59112),f15(x59111,x59113)),f15(x59111,x59113))+~P24(f329(f62(x59111),x59113))+~P24(f329(f329(f331(x59111),x59112),x59113))
% 187.33/188.05 [5956]E(x59561,x59562)+~P106(x59563)+~P24(f329(f329(f243(x59563),x59562),x59561))+~P24(f329(f329(f243(x59563),x59561),x59562))
% 187.33/188.05 [6095]~P25(x60951)+P24(f329(f329(f244(x60951),x60953),x60952))+~P24(f329(f329(f243(x60951),x60953),x60952))+P24(f329(f329(f243(x60951),x60952),x60953))
% 187.33/188.05 [6116]~P27(x61161)+~P24(f329(f62(x61161),x61163))+P24(f329(f329(f243(x61161),x61162),f15(x61161,x61163)))+~P24(f329(f329(f331(x61161),x61162),x61163))
% 187.33/188.05 [6169]~P27(x61691)+E(f329(f329(f241(x61691),x61692),f12(x61691,f242(x61691),x61693)),x61692)+~P24(f329(f62(x61691),x61693))+~P24(f329(f329(f331(x61691),x61692),x61693))
% 187.33/188.05 [6170]~P27(x61701)+E(f329(f329(f242(x61701),x61702),f11(x61701,f241(x61701),x61703)),x61702)+~P24(f329(f62(x61701),x61703))+~P24(f329(f329(f331(x61701),x61702),x61703))
% 187.33/188.05 [6308]E(x63081,x63082)+~E(f329(f329(f22(a874),x63081),x63083),f329(f329(f22(a874),x63082),x63083))+~P24(f329(f329(f243(a874),x63083),x63081))+~P24(f329(f329(f243(a874),x63083),x63082))
% 187.33/188.05 [6335]~P27(x63351)+~P24(f329(f62(x63351),x63352))+~P24(f329(f329(f331(x63351),x63353),x63352))+P24(f329(f329(f243(x63351),f14(x63351,x63352)),x63353))
% 187.33/188.05 [6397]P144(x63972,x63973,x63971)+E(x63971,f2(a1))+P24(f329(f329(f244(a1),x63971),f808(x63971,x63973,x63972)))+P24(f329(f329(f244(a1),f2(a1)),x63971))
% 187.33/188.05 [6398]P143(x63982,x63983,x63981)+E(x63981,f2(a1))+P24(f329(f329(f244(a1),x63981),f816(x63981,x63983,x63982)))+P24(f329(f329(f244(a1),f2(a1)),x63981))
% 187.33/188.05 [6399]~P27(x63991)+E(f329(f329(f241(x63991),x63992),f11(x63991,f241(x63991),x63993)),f11(x63991,f241(x63991),x63993))+~P24(f329(f62(x63991),x63993))+~P24(f329(f329(f331(x63991),x63992),x63993))
% 187.33/188.05 [6400]~P27(x64001)+E(f329(f329(f242(x64001),x64002),f12(x64001,f242(x64001),x64003)),f12(x64001,f242(x64001),x64003))+~P24(f329(f62(x64001),x64003))+~P24(f329(f329(f331(x64001),x64002),x64003))
% 187.33/188.05 [6406]~P24(f329(x64061,x64062))+P24(f329(x64061,f473(x64062,x64061,x64063)))+P24(f329(x64061,f2(a874)))+~P24(f329(f329(f244(a874),x64062),x64063))
% 187.33/188.05 [6461]~P24(f329(x64611,x64612))+~P24(f329(f62(x64613),x64612))+P24(f329(x64611,f599(x64611,x64612,x64613)))+P24(f329(x64611,f193(f881(x64613,a869))))
% 187.33/188.05 [6474]~P115(x64741)+~P94(x64741)+P24(f329(f329(f243(x64741),f329(f108(x64741),x64742)),f329(f108(x64741),x64743)))+~P24(f329(f329(f243(a1),x64742),x64743))
% 187.33/188.05 [6475]~P115(x64751)+~P94(x64751)+P24(f329(f329(f244(x64751),f329(f108(x64751),x64752)),f329(f108(x64751),x64753)))+~P24(f329(f329(f244(a1),x64752),x64753))
% 187.33/188.05 [6478]~P24(f329(x64781,x64783))+~P24(f329(f62(x64782),x64783))+P24(f329(f62(x64782),f599(x64781,x64783,x64782)))+P24(f329(x64781,f193(f881(x64782,a869))))
% 187.33/188.05 [6512]P143(x65121,x65122,x65123)+~P24(f329(x65121,x65122))+P24(f329(f329(f244(a1),x65123),f816(x65123,x65122,x65121)))+P24(f329(f329(f244(a1),f2(a1)),x65123))
% 187.33/188.05 [6547]P144(x65471,x65472,x65473)+P24(f329(f329(f244(a1),x65473),f808(x65473,x65472,x65471)))+~P24(f329(x65471,f2(a1)))+P24(f329(f329(f244(a1),f2(a1)),x65473))
% 187.33/188.05 [6578]~P26(x65781)+~P95(x65781)+E(f329(f329(f241(x65781),f329(f108(x65781),x65782)),f329(f108(x65781),x65783)),f329(f108(x65781),x65783))+P24(f329(f329(f243(x65781),f329(f108(x65781),x65782)),f329(f108(x65781),x65783)))
% 187.33/188.05 [6579]~P26(x65791)+~P95(x65791)+E(f329(f329(f242(x65791),f329(f108(x65791),x65792)),f329(f108(x65791),x65793)),f329(f108(x65791),x65792))+P24(f329(f329(f243(x65791),f329(f108(x65791),x65792)),f329(f108(x65791),x65793)))
% 187.33/188.05 [6637]P144(x66372,x66373,x66371)+E(x66371,f2(a1))+~P24(f329(x66372,f815(x66371,x66373,x66372)))+P24(f329(f329(f244(a1),f2(a1)),x66371))
% 187.33/188.05 [6638]P143(x66382,x66383,x66381)+E(x66381,f2(a1))+~P24(f329(x66382,f816(x66381,x66383,x66382)))+P24(f329(f329(f244(a1),f2(a1)),x66381))
% 187.33/188.05 [6642]P24(f329(x66421,x66422))+~P24(f329(f62(x66423),x66422))+P24(f329(x66421,f557(x66421,x66422,x66423)))+~P24(f329(x66421,f193(f881(x66423,a869))))
% 187.33/188.05 [6661]P24(f329(x66611,x66612))+P24(f329(f62(x66613),f557(x66611,x66612,x66613)))+~P24(f329(f62(x66613),x66612))+~P24(f329(x66611,f193(f881(x66613,a869))))
% 187.33/188.05 [6726]P143(x67261,x67262,x67263)+~P24(f329(x67261,x67262))+~P24(f329(x67261,f816(x67263,x67262,x67261)))+P24(f329(f329(f244(a1),f2(a1)),x67263))
% 187.33/188.05 [6756]P144(x67561,x67562,x67563)+~P24(f329(x67561,f815(x67563,x67562,x67561)))+~P24(f329(x67561,f2(a1)))+P24(f329(f329(f244(a1),f2(a1)),x67563))
% 187.33/188.05 [6864]~P94(x68643)+~P115(x68643)+~P24(f329(f329(f243(x68643),f329(f108(x68643),x68641)),f329(f108(x68643),x68642)))+P24(f329(f329(f243(a1),x68641),x68642))
% 187.33/188.05 [6865]~P94(x68653)+~P115(x68653)+~P24(f329(f329(f244(x68653),f329(f108(x68653),x68651)),f329(f108(x68653),x68652)))+P24(f329(f329(f244(a1),x68651),x68652))
% 187.33/188.05 [6894]~P27(x68941)+~P33(x68941,x68943)+P33(x68941,f329(f329(f149(x68941),x68942),x68943))+~P24(f329(f329(f243(x68941),x68942),f746(x68943,x68942,x68941)))
% 187.33/188.05 [6895]~P27(x68951)+~P33(x68951,x68953)+P33(x68951,f329(f329(f149(x68951),x68952),x68953))+~P24(f329(f329(f243(x68951),x68952),f748(x68953,x68952,x68951)))
% 187.33/188.05 [6896]~P27(x68961)+~P33(x68961,x68963)+P33(x68961,f329(f329(f149(x68961),x68962),x68963))+~P24(f329(f329(f243(x68961),x68962),f781(x68962,x68963,x68961)))
% 187.33/188.05 [6980]P144(x69802,x69803,x69801)+E(x69801,f2(a1))+P24(f329(f329(f244(a1),x69801),f2(a1)))+P24(f329(f329(f244(a1),f809(x69801,x69803,x69802)),x69801))
% 187.33/188.05 [6981]P143(x69812,x69813,x69811)+E(x69811,f2(a1))+P24(f329(f329(f244(a1),x69811),f2(a1)))+P24(f329(f329(f244(a1),f817(x69811,x69813,x69812)),x69811))
% 187.33/188.05 [7022]P144(x70222,x70223,x70221)+E(x70221,f2(a1))+P24(f329(f329(f243(a1),f808(x70221,x70223,x70222)),f2(a1)))+P24(f329(f329(f244(a1),f2(a1)),x70221))
% 187.33/188.05 [7023]P143(x70232,x70233,x70231)+E(x70231,f2(a1))+P24(f329(f329(f243(a1),f816(x70231,x70233,x70232)),f2(a1)))+P24(f329(f329(f244(a1),f2(a1)),x70231))
% 187.33/188.05 [7045]~P27(x70451)+~P33(x70451,x70453)+E(f329(f329(f146(x70451,x70451,f5(x70451)),x70452),f168(x70451,x70452,x70453)),x70453)+~P24(f329(f329(f331(x70451),x70452),f329(f171(x70451),x70453)))
% 187.33/188.05 [7092]P143(x70921,x70922,x70923)+~P24(f329(x70921,x70922))+P24(f329(f329(f244(a1),x70923),f2(a1)))+P24(f329(f329(f244(a1),f817(x70923,x70922,x70921)),x70923))
% 187.33/188.05 [7098]~P26(x70981)+~P95(x70981)+E(f329(f329(f241(x70981),f329(f108(x70981),x70982)),f329(f108(x70981),x70983)),f329(f108(x70981),x70982))+~P24(f329(f329(f243(x70981),f329(f108(x70981),x70982)),f329(f108(x70981),x70983)))
% 187.33/188.05 [7099]~P26(x70991)+~P95(x70991)+E(f329(f329(f242(x70991),f329(f108(x70991),x70992)),f329(f108(x70991),x70993)),f329(f108(x70991),x70993))+~P24(f329(f329(f243(x70991),f329(f108(x70991),x70992)),f329(f108(x70991),x70993)))
% 187.33/188.05 [7113]P144(x71131,x71132,x71133)+~P24(f329(x71131,f2(a1)))+P24(f329(f329(f244(a1),x71133),f2(a1)))+P24(f329(f329(f244(a1),f809(x71133,x71132,x71131)),x71133))
% 187.33/188.05 [7121]P143(x71211,x71212,x71213)+~P24(f329(x71211,x71212))+P24(f329(f329(f243(a1),f816(x71213,x71212,x71211)),f2(a1)))+P24(f329(f329(f244(a1),f2(a1)),x71213))
% 187.33/188.05 [7145]P144(x71451,x71452,x71453)+~P24(f329(x71451,f2(a1)))+P24(f329(f329(f243(a1),f808(x71453,x71452,x71451)),f2(a1)))+P24(f329(f329(f244(a1),f2(a1)),x71453))
% 187.33/188.05 [7173]~P24(f329(x71731,x71732))+P24(f329(x71731,f2(a874)))+~P24(f329(f329(f244(a874),x71732),x71733))+P24(f329(f329(f244(a874),f473(x71732,x71731,x71733)),x71733))
% 187.33/188.05 [7190]~P27(x71901)+~P33(x71901,x71903)+P33(x71901,f329(f329(f149(x71901),x71902),x71903))+P24(f329(f329(f331(x71901),f746(x71903,x71902,x71901)),f329(f171(x71901),x71903)))
% 187.33/188.05 [7191]~P27(x71911)+~P33(x71911,x71913)+P33(x71911,f329(f329(f149(x71911),x71912),x71913))+P24(f329(f329(f331(x71911),f748(x71913,x71912,x71911)),f329(f171(x71911),x71913)))
% 187.33/188.05 [7192]~P27(x71921)+~P33(x71921,x71923)+P33(x71921,f329(f329(f149(x71921),x71922),x71923))+P24(f329(f329(f331(x71921),f781(x71922,x71923,x71921)),f329(f171(x71921),x71923)))
% 187.33/188.05 [7296]~P27(x72961)+~P31(x72961)+~P24(f329(f329(f244(x72961),x72963),f40(x72961,x72962)))+P24(f329(f329(f331(x72961),f600(x72962,x72963,x72961)),x72962))
% 187.33/188.05 [7463]~P27(x74631)+~P31(x74631)+~P24(f329(f329(f244(x74631),f41(x74631,x74633)),x74632))+P24(f329(f329(f331(x74631),f601(x74632,x74633,x74631)),x74633))
% 187.33/188.05 [7464]~P27(x74641)+~P31(x74641)+~P24(f329(f329(f244(x74641),f41(x74641,x74643)),x74642))+P24(f329(f329(f244(x74641),f601(x74642,x74643,x74641)),x74642))
% 187.33/188.05 [7479]P144(x74792,x74793,x74791)+E(x74791,f2(a1))+P24(f329(f329(f244(a1),x74791),f808(x74791,x74793,x74792)))+P24(f329(f329(f244(a1),f809(x74791,x74793,x74792)),x74791))
% 187.33/188.05 [7480]P143(x74802,x74803,x74801)+E(x74801,f2(a1))+P24(f329(f329(f244(a1),x74801),f816(x74801,x74803,x74802)))+P24(f329(f329(f244(a1),f817(x74801,x74803,x74802)),x74801))
% 187.33/188.05 [7570]P144(x75703,x75702,x75701)+E(x75701,f2(a1))+E(f329(f329(f80(a1),f329(f329(f81(a1),x75701),f815(x75701,x75702,x75703))),f808(x75701,x75702,x75703)),x75702)+P24(f329(f329(f244(a1),f2(a1)),x75701))
% 187.33/188.05 [7571]P143(x75713,x75712,x75711)+E(x75711,f2(a1))+E(f329(f329(f80(a1),f329(f329(f81(a1),x75711),f819(x75711,x75712,x75713))),f816(x75711,x75712,x75713)),x75712)+P24(f329(f329(f244(a1),f2(a1)),x75711))
% 187.33/188.05 [7573]~P123(x75731)+~P24(f329(f329(f243(x75731),x75733),f2(x75731)))+P24(f329(f329(f243(x75731),f329(f329(f81(x75731),x75732),x75733)),f2(x75731)))+~P24(f329(f329(f243(x75731),f2(x75731)),x75732))
% 187.33/188.05 [7574]~P123(x75741)+~P24(f329(f329(f243(x75741),x75742),f2(x75741)))+P24(f329(f329(f243(x75741),f329(f329(f81(x75741),x75742),x75743)),f2(x75741)))+~P24(f329(f329(f243(x75741),f2(x75741)),x75743))
% 187.33/188.05 [7576]~P130(x75761)+~P24(f329(f329(f243(x75761),x75763),f2(x75761)))+P24(f329(f329(f243(x75761),f329(f329(f81(x75761),x75762),x75763)),f2(x75761)))+~P24(f329(f329(f243(x75761),f2(x75761)),x75762))
% 187.33/188.05 [7578]~P130(x75781)+~P24(f329(f329(f243(x75781),x75782),f2(x75781)))+P24(f329(f329(f243(x75781),f329(f329(f81(x75781),x75782),x75783)),f2(x75781)))+~P24(f329(f329(f243(x75781),f2(x75781)),x75783))
% 187.33/188.05 [7579]~P63(x75791)+~P24(f329(f329(f243(x75791),x75793),f2(x75791)))+P24(f329(f329(f243(x75791),f329(f329(f287(x75791),x75792),x75793)),f2(x75791)))+~P24(f329(f329(f243(x75791),f2(x75791)),x75792))
% 187.33/188.05 [7580]~P63(x75801)+~P24(f329(f329(f243(x75801),x75802),f2(x75801)))+P24(f329(f329(f243(x75801),f329(f329(f287(x75801),x75802),x75803)),f2(x75801)))+~P24(f329(f329(f243(x75801),f2(x75801)),x75803))
% 187.33/188.05 [7581]~P64(x75811)+~P24(f329(f329(f243(x75811),x75812),f2(x75811)))+P24(f329(f329(f243(x75811),f329(f329(f287(x75811),x75812),x75813)),f2(x75811)))+~P24(f329(f329(f244(x75811),f2(x75811)),x75813))
% 187.33/188.05 [7582]~P64(x75821)+~P24(f329(f329(f244(x75821),x75823),f2(x75821)))+P24(f329(f329(f243(x75821),f329(f329(f287(x75821),x75822),x75823)),f2(x75821)))+~P24(f329(f329(f243(x75821),f2(x75821)),x75822))
% 187.33/188.05 [7584]~P129(x75841)+~P24(f329(f329(f244(x75841),x75843),f2(x75841)))+P24(f329(f329(f244(x75841),f329(f329(f81(x75841),x75842),x75843)),f2(x75841)))+~P24(f329(f329(f244(x75841),f2(x75841)),x75842))
% 187.33/188.05 [7585]~P129(x75851)+~P24(f329(f329(f244(x75851),x75852),f2(x75851)))+P24(f329(f329(f244(x75851),f329(f329(f81(x75851),x75852),x75853)),f2(x75851)))+~P24(f329(f329(f244(x75851),f2(x75851)),x75853))
% 187.33/188.05 [7586]~P63(x75861)+~P24(f329(f329(f244(x75861),x75863),f2(x75861)))+P24(f329(f329(f244(x75861),f329(f329(f287(x75861),x75862),x75863)),f2(x75861)))+~P24(f329(f329(f244(x75861),f2(x75861)),x75862))
% 187.33/188.05 [7587]~P63(x75871)+~P24(f329(f329(f244(x75871),x75872),f2(x75871)))+P24(f329(f329(f244(x75871),f329(f329(f287(x75871),x75872),x75873)),f2(x75871)))+~P24(f329(f329(f244(x75871),f2(x75871)),x75873))
% 187.33/188.05 [7588]~P64(x75881)+~P24(f329(f329(f244(x75881),x75883),f2(x75881)))+P24(f329(f329(f244(x75881),f329(f329(f287(x75881),x75882),x75883)),f2(x75881)))+~P24(f329(f329(f244(x75881),f2(x75881)),x75882))
% 187.33/188.05 [7589]~P64(x75891)+~P24(f329(f329(f244(x75891),x75892),f2(x75891)))+P24(f329(f329(f244(x75891),f329(f329(f287(x75891),x75892),x75893)),f2(x75891)))+~P24(f329(f329(f244(x75891),f2(x75891)),x75893))
% 187.33/188.05 [7604]P143(x76041,x76042,x76043)+~P24(f329(x76041,x76042))+P24(f329(f329(f244(a1),x76043),f816(x76043,x76042,x76041)))+P24(f329(f329(f244(a1),f817(x76043,x76042,x76041)),x76043))
% 187.33/188.05 [7617]P144(x76171,x76172,x76173)+P24(f329(f329(f244(a1),x76173),f808(x76173,x76172,x76171)))+~P24(f329(x76171,f2(a1)))+P24(f329(f329(f244(a1),f809(x76173,x76172,x76171)),x76173))
% 187.33/188.05 [7668]P144(x76682,x76683,x76681)+E(x76681,f2(a1))+~P24(f329(x76682,f815(x76681,x76683,x76682)))+P24(f329(f329(f244(a1),f809(x76681,x76683,x76682)),x76681))
% 187.33/188.05 [7669]P143(x76692,x76693,x76691)+E(x76691,f2(a1))+~P24(f329(x76692,f816(x76691,x76693,x76692)))+P24(f329(f329(f244(a1),f817(x76691,x76693,x76692)),x76691))
% 187.33/188.05 [7681]P143(x76813,x76812,x76811)+~P24(f329(x76813,x76812))+E(f329(f329(f80(a1),f329(f329(f81(a1),x76811),f819(x76811,x76812,x76813))),f816(x76811,x76812,x76813)),x76812)+P24(f329(f329(f244(a1),f2(a1)),x76811))
% 187.33/188.05 [7699]P144(x76993,x76992,x76991)+E(f329(f329(f80(a1),f329(f329(f81(a1),x76991),f815(x76991,x76992,x76993))),f808(x76991,x76992,x76993)),x76992)+~P24(f329(x76993,f2(a1)))+P24(f329(f329(f244(a1),f2(a1)),x76991))
% 187.33/188.05 [7725]~P24(f329(x77251,x77253))+~P24(f329(f62(x77252),x77253))+P24(f329(f329(f331(x77252),f602(x77251,x77253,x77252)),f599(x77251,x77253,x77252)))+P24(f329(x77251,f193(f881(x77252,a869))))
% 187.33/188.05 [7736]P143(x77361,x77362,x77363)+~P24(f329(x77361,x77362))+~P24(f329(x77361,f816(x77363,x77362,x77361)))+P24(f329(f329(f244(a1),f817(x77363,x77362,x77361)),x77363))
% 187.33/188.05 [7742]P144(x77421,x77422,x77423)+~P24(f329(x77421,f815(x77423,x77422,x77421)))+~P24(f329(x77421,f2(a1)))+P24(f329(f329(f244(a1),f809(x77423,x77422,x77421)),x77423))
% 187.33/188.05 [7848]~P123(x78481)+~P24(f329(f329(f243(x78481),f329(f329(f81(x78481),x78483),x78482)),f2(x78481)))+P24(f329(f329(f243(x78481),x78482),f2(x78481)))+P24(f329(f329(f243(x78481),f2(x78481)),x78482))
% 187.33/188.05 [7849]~P123(x78491)+~P24(f329(f329(f243(x78491),f329(f329(f81(x78491),x78492),x78493)),f2(x78491)))+P24(f329(f329(f243(x78491),x78492),f2(x78491)))+P24(f329(f329(f243(x78491),f2(x78491)),x78492))
% 187.33/188.05 [7850]~P63(x78501)+~P24(f329(f329(f243(x78501),f329(f329(f287(x78501),x78503),x78502)),f2(x78501)))+P24(f329(f329(f243(x78501),x78502),f2(x78501)))+P24(f329(f329(f243(x78501),f2(x78501)),x78502))
% 187.33/188.05 [7851]~P63(x78511)+~P24(f329(f329(f243(x78511),f329(f329(f287(x78511),x78512),x78513)),f2(x78511)))+P24(f329(f329(f243(x78511),x78512),f2(x78511)))+P24(f329(f329(f243(x78511),f2(x78511)),x78512))
% 187.33/188.05 [7852]~P63(x78521)+~P24(f329(f329(f244(x78521),f329(f329(f287(x78521),x78523),x78522)),f2(x78521)))+P24(f329(f329(f244(x78521),x78522),f2(x78521)))+P24(f329(f329(f244(x78521),f2(x78521)),x78522))
% 187.33/188.05 [7853]~P63(x78531)+~P24(f329(f329(f244(x78531),f329(f329(f287(x78531),x78532),x78533)),f2(x78531)))+P24(f329(f329(f244(x78531),x78532),f2(x78531)))+P24(f329(f329(f244(x78531),f2(x78531)),x78532))
% 187.33/188.05 [7877]~P123(x78771)+~P24(f329(f329(f243(x78771),f329(f329(f81(x78771),x78772),x78773)),f2(x78771)))+P24(f329(f329(f243(x78771),f2(x78771)),x78772))+P24(f329(f329(f243(x78771),f2(x78771)),x78773))
% 187.33/188.05 [7878]~P63(x78781)+~P24(f329(f329(f243(x78781),f329(f329(f287(x78781),x78782),x78783)),f2(x78781)))+P24(f329(f329(f243(x78781),f2(x78781)),x78782))+P24(f329(f329(f243(x78781),f2(x78781)),x78783))
% 187.33/188.05 [7879]~P63(x78791)+~P24(f329(f329(f244(x78791),f329(f329(f287(x78791),x78792),x78793)),f2(x78791)))+P24(f329(f329(f244(x78791),f2(x78791)),x78792))+P24(f329(f329(f244(x78791),f2(x78791)),x78793))
% 187.33/188.05 [7900]P144(x79002,x79003,x79001)+E(x79001,f2(a1))+P24(f329(f329(f243(a1),f808(x79001,x79003,x79002)),f2(a1)))+P24(f329(f329(f244(a1),f809(x79001,x79003,x79002)),x79001))
% 187.33/188.05 [7901]P143(x79012,x79013,x79011)+E(x79011,f2(a1))+P24(f329(f329(f243(a1),f816(x79011,x79013,x79012)),f2(a1)))+P24(f329(f329(f244(a1),f817(x79011,x79013,x79012)),x79011))
% 187.33/188.05 [7908]~P121(x79081)+~P24(f329(f329(f244(x79081),x79082),f78(x79081)))+P24(f329(f329(f244(x79081),f329(f329(f254(x79081),x79082),f329(a117,x79083))),f78(x79081)))+~P24(f329(f329(f244(x79081),f2(x79081)),x79082))
% 187.33/188.05 [7963]~P27(x79631)+~E(x79633,f118(x79631))+~P33(x79631,f329(f167(x79631),x79633))+E(f329(f140(x79631,x79631,f329(f7(x79631,x79631,x79631),f242(x79631)),x79632),f329(f167(x79631),x79633)),x79632)
% 187.33/188.05 [7965]P143(x79651,x79652,x79653)+~P24(f329(x79651,x79652))+P24(f329(f329(f243(a1),f816(x79653,x79652,x79651)),f2(a1)))+P24(f329(f329(f244(a1),f817(x79653,x79652,x79651)),x79653))
% 187.33/188.05 [7975]P144(x79751,x79752,x79753)+~P24(f329(x79751,f2(a1)))+P24(f329(f329(f243(a1),f808(x79753,x79752,x79751)),f2(a1)))+P24(f329(f329(f244(a1),f809(x79753,x79752,x79751)),x79753))
% 187.33/188.05 [8200]P144(x82003,x82002,x82001)+E(x82001,f2(a1))+E(f329(f329(f80(a1),f329(f329(f81(a1),x82001),f815(x82001,x82002,x82003))),f808(x82001,x82002,x82003)),x82002)+P24(f329(f329(f244(a1),f809(x82001,x82002,x82003)),x82001))
% 187.33/188.05 [8201]P143(x82013,x82012,x82011)+E(x82011,f2(a1))+E(f329(f329(f80(a1),f329(f329(f81(a1),x82011),f819(x82011,x82012,x82013))),f816(x82011,x82012,x82013)),x82012)+P24(f329(f329(f244(a1),f817(x82011,x82012,x82013)),x82011))
% 187.33/188.05 [8237]P143(x82373,x82372,x82371)+~P24(f329(x82373,x82372))+E(f329(f329(f80(a1),f329(f329(f81(a1),x82371),f819(x82371,x82372,x82373))),f816(x82371,x82372,x82373)),x82372)+P24(f329(f329(f244(a1),f817(x82371,x82372,x82373)),x82371))
% 187.33/188.05 [8238]~P72(x82381)+~P76(x82381)+~P43(x82383)+E(f329(f329(f6(a874,x82381),f329(f329(f8(a1,x82381,a874),x82382),f105(a1))),f329(f308(a1,a874,a109),x82383)),f329(f329(f6(a1,x82381),x82382),x82383))
% 187.33/188.05 [8239]~P72(x82391)+~P76(x82391)+~P43(x82393)+E(f329(f329(f9(a874,x82391),f329(f329(f8(a1,x82391,a874),x82392),f105(a1))),f329(f308(a1,a874,a109),x82393)),f329(f329(f9(a1,x82391),x82392),x82393))
% 187.33/188.05 [8248]P144(x82483,x82482,x82481)+E(f329(f329(f80(a1),f329(f329(f81(a1),x82481),f815(x82481,x82482,x82483))),f808(x82481,x82482,x82483)),x82482)+~P24(f329(x82483,f2(a1)))+P24(f329(f329(f244(a1),f809(x82481,x82482,x82483)),x82481))
% 187.33/188.05 [8267]~E(x82672,f2(a874))+~E(f329(f263(a874,a874),x82673),f2(a874))+~E(x82671,f329(f329(f80(a874),f329(f329(f81(a874),f329(f263(a874,a874),x82673)),x82672)),f329(f267(a874,a874),x82673)))+P24(f329(f48(x82671,x82672),x82673))
% 187.33/188.05 [8321]P24(f329(x83211,x83212))+~P24(f329(f329(f331(x83213),f534(x83211,x83212,x83213)),f557(x83211,x83212,x83213)))+~P24(f329(f62(x83213),x83212))+~P24(f329(x83211,f193(f881(x83213,a869))))
% 187.33/188.05 [8939]P24(f329(x89391,x89392))+~P24(f329(f62(x89393),x89392))+~P24(f329(x89391,f329(f329(f307(x89393),f534(x89391,x89392,x89393)),f557(x89391,x89392,x89393))))+~P24(f329(x89391,f193(f881(x89393,a869))))
% 187.33/188.05 [9173]P24(f329(f329(f243(a1),x91731),f2(a1)))+~P24(f329(f329(f244(a1),f329(f329(f80(a1),f329(f329(f81(a1),x91733),x91731)),x91732)),f2(a1)))+~P24(f329(f329(f243(a1),f2(a1)),x91732))+~P24(f329(f329(f244(a1),f2(a1)),x91733))
% 187.33/188.05 [5781]~P66(x57812)+E(x57811,f193(f881(x57812,a869)))+~P24(f329(f62(x57812),x57811))+E(f10(x57812,f329(f329(f307(x57812),x57813),x57811)),f329(f329(f106(x57812),x57813),f10(x57812,x57811)))
% 187.33/188.05 [5782]~P66(x57822)+E(x57821,f193(f881(x57822,a869)))+~P24(f329(f62(x57822),x57821))+E(f13(x57822,f329(f329(f307(x57822),x57823),x57821)),f329(f329(f115(x57822),x57823),f13(x57822,x57821)))
% 187.33/188.05 [5783]~P27(x57832)+E(x57831,f193(f881(x57832,a869)))+~P24(f329(f62(x57832),x57831))+E(f14(x57832,f329(f329(f307(x57832),x57833),x57831)),f329(f329(f241(x57832),x57833),f14(x57832,x57831)))
% 187.33/188.05 [5784]~P27(x57842)+E(x57841,f193(f881(x57842,a869)))+~P24(f329(f62(x57842),x57841))+E(f15(x57842,f329(f329(f307(x57842),x57843),x57841)),f329(f329(f242(x57842),x57843),f15(x57842,x57841)))
% 187.33/188.05 [6092]~P123(x60921)+~E(x60923,f2(x60921))+~E(x60922,f2(x60921))+E(f329(f329(f80(x60921),f329(f329(f81(x60921),x60922),x60922)),f329(f329(f81(x60921),x60923),x60923)),f2(x60921))
% 187.33/188.05 [6163]~P98(x61632)+E(x61631,f193(f881(x61632,a869)))+~P24(f329(f62(x61632),x61631))+E(f329(f64(x61632,f81(x61632)),f329(f329(f307(x61632),x61633),x61631)),f329(f329(f81(x61632),x61633),f329(f64(x61632,f81(x61632)),x61631)))
% 187.33/188.05 [6287]~P27(x62872)+E(x62871,f193(f881(x62872,a869)))+~P24(f329(f62(x62872),x62871))+E(f11(x62872,f241(x62872),f329(f329(f307(x62872),x62873),x62871)),f329(f329(f241(x62872),x62873),f11(x62872,f241(x62872),x62871)))
% 187.33/188.05 [6288]~P27(x62882)+E(x62881,f193(f881(x62882,a869)))+~P24(f329(f62(x62882),x62881))+E(f12(x62882,f242(x62882),f329(f329(f307(x62882),x62883),x62881)),f329(f329(f242(x62882),x62883),f12(x62882,f242(x62882),x62881)))
% 187.33/188.05 [6791]~P70(x67911)+~P24(f329(f62(x67911),x67913))+E(f329(f64(x67911,f81(x67911)),f329(f329(f307(x67911),x67912),x67913)),f329(f329(f65(x67911,x67911,f81(x67911)),x67912),x67913))+P24(f329(f329(f331(x67911),x67912),x67913))
% 187.33/188.05 [6872]~E(f329(f329(f80(a1),x68722),f329(f329(f81(a1),x68723),x68721)),x68723)+~P24(f329(f329(f244(a1),f2(a1)),x68723))+P24(f329(f329(f243(a1),f78(a1)),x68721))+~P24(f329(f329(f244(a1),x68722),x68723))
% 187.33/188.05 [6901]~E(f329(f329(f80(a1),x69012),f329(f329(f81(a1),x69013),x69011)),x69013)+P24(f329(f329(f243(a1),x69011),f78(a1)))+~P24(f329(f329(f243(a1),f2(a1)),x69012))+~P24(f329(f329(f244(a1),f2(a1)),x69013))
% 187.33/188.05 [6917]E(x69171,f2(a874))+~P24(f329(f48(x69173,x69171),x69172))+~P24(f329(f329(f244(a874),f2(a874)),x69171))+P24(f329(f329(f244(a874),f329(f267(a874,a874),x69172)),x69171))
% 187.33/188.05 [6947]~P133(x69471)+~P24(f329(f329(f243(x69471),x69472),f2(x69471)))+~P24(f329(f329(f243(x69471),x69473),f2(x69471)))+E(f329(f329(f81(x69471),f329(f75(x69471),x69472)),f329(f75(x69471),x69473)),f329(f75(x69471),f329(f329(f81(x69471),x69472),x69473)))
% 187.33/188.05 [6999]~P133(x69991)+~P24(f329(f329(f243(x69991),x69992),f2(x69991)))+E(f329(f329(f81(x69991),f329(f75(x69991),x69992)),f329(f75(x69991),x69993)),f329(f75(x69991),f329(f329(f81(x69991),x69992),x69993)))+~P24(f329(f329(f243(x69991),f2(x69991)),x69993))
% 187.33/188.05 [7000]~P133(x70001)+~P24(f329(f329(f243(x70001),x70003),f2(x70001)))+E(f329(f329(f81(x70001),f329(f75(x70001),x70002)),f329(f75(x70001),x70003)),f329(f75(x70001),f329(f329(f81(x70001),x70002),x70003)))+~P24(f329(f329(f243(x70001),f2(x70001)),x70002))
% 187.33/188.05 [7054]~P133(x70541)+E(f329(f329(f81(x70541),f329(f75(x70541),x70542)),f329(f75(x70541),x70543)),f329(f75(x70541),f329(f329(f81(x70541),x70542),x70543)))+~P24(f329(f329(f243(x70541),f2(x70541)),x70542))+~P24(f329(f329(f243(x70541),f2(x70541)),x70543))
% 187.33/188.05 [7071]~P108(x70711)+~P24(f329(f329(f243(x70711),x70713),f2(x70711)))+~P24(f329(f329(f243(x70711),x70712),f2(x70711)))+P24(f329(f329(f243(x70711),f2(x70711)),f329(f329(f81(x70711),x70712),x70713)))
% 187.33/188.05 [7072]~P123(x70721)+~P24(f329(f329(f243(x70721),x70723),f2(x70721)))+~P24(f329(f329(f243(x70721),x70722),f2(x70721)))+P24(f329(f329(f243(x70721),f2(x70721)),f329(f329(f81(x70721),x70722),x70723)))
% 187.33/188.05 [7073]~P63(x70731)+~P24(f329(f329(f243(x70731),x70733),f2(x70731)))+~P24(f329(f329(f243(x70731),x70732),f2(x70731)))+P24(f329(f329(f243(x70731),f2(x70731)),f329(f329(f287(x70731),x70732),x70733)))
% 187.33/188.05 [7074]~P64(x70741)+~P24(f329(f329(f244(x70741),x70743),f2(x70741)))+~P24(f329(f329(f243(x70741),x70742),f2(x70741)))+P24(f329(f329(f243(x70741),f2(x70741)),f329(f329(f287(x70741),x70742),x70743)))
% 187.33/188.05 [7075]~P123(x70751)+~P24(f329(f329(f244(x70751),x70753),f2(x70751)))+~P24(f329(f329(f244(x70751),x70752),f2(x70751)))+P24(f329(f329(f244(x70751),f2(x70751)),f329(f329(f81(x70751),x70752),x70753)))
% 187.33/188.05 [7076]~P63(x70761)+~P24(f329(f329(f244(x70761),x70763),f2(x70761)))+~P24(f329(f329(f244(x70761),x70762),f2(x70761)))+P24(f329(f329(f244(x70761),f2(x70761)),f329(f329(f287(x70761),x70762),x70763)))
% 187.33/188.05 [7077]~P64(x70771)+~P24(f329(f329(f244(x70771),x70773),f2(x70771)))+~P24(f329(f329(f244(x70771),x70772),f2(x70771)))+P24(f329(f329(f244(x70771),f2(x70771)),f329(f329(f287(x70771),x70772),x70773)))
% 187.33/188.05 [7078]~P121(x70781)+~P24(f329(f329(f244(a874),f2(a874)),x70783))+~P24(f329(f329(f244(x70781),f78(x70781)),x70782))+P24(f329(f329(f244(x70781),f78(x70781)),f329(f329(f254(x70781),x70782),x70783)))
% 187.33/188.05 [7174]~P108(x71741)+~P24(f329(f329(f243(x71741),f2(x71741)),x71743))+~P24(f329(f329(f243(x71741),f2(x71741)),x71742))+P24(f329(f329(f243(x71741),f2(x71741)),f329(f329(f81(x71741),x71742),x71743)))
% 187.33/188.05 [7175]~P123(x71751)+~P24(f329(f329(f243(x71751),f2(x71751)),x71753))+~P24(f329(f329(f243(x71751),f2(x71751)),x71752))+P24(f329(f329(f243(x71751),f2(x71751)),f329(f329(f81(x71751),x71752),x71753)))
% 187.33/188.05 [7176]~P130(x71761)+~P24(f329(f329(f243(x71761),f2(x71761)),x71763))+~P24(f329(f329(f243(x71761),f2(x71761)),x71762))+P24(f329(f329(f243(x71761),f2(x71761)),f329(f329(f81(x71761),x71762),x71763)))
% 187.33/188.05 [7178]~P63(x71781)+~P24(f329(f329(f243(x71781),f2(x71781)),x71783))+~P24(f329(f329(f243(x71781),f2(x71781)),x71782))+P24(f329(f329(f243(x71781),f2(x71781)),f329(f329(f287(x71781),x71782),x71783)))
% 187.33/188.05 [7179]~P64(x71791)+~P24(f329(f329(f244(x71791),f2(x71791)),x71793))+~P24(f329(f329(f243(x71791),f2(x71791)),x71792))+P24(f329(f329(f243(x71791),f2(x71791)),f329(f329(f287(x71791),x71792),x71793)))
% 187.33/188.05 [7180]~P121(x71801)+~P24(f329(f329(f244(x71801),f78(x71801)),x71803))+~P24(f329(f329(f244(x71801),f78(x71801)),x71802))+P24(f329(f329(f244(x71801),f78(x71801)),f329(f329(f81(x71801),x71802),x71803)))
% 187.33/188.05 [7181]~P129(x71811)+~P24(f329(f329(f244(x71811),f2(x71811)),x71813))+~P24(f329(f329(f244(x71811),f2(x71811)),x71812))+P24(f329(f329(f244(x71811),f2(x71811)),f329(f329(f81(x71811),x71812),x71813)))
% 187.33/188.05 [7184]~P89(x71841)+~P24(f329(f329(f244(x71841),f2(x71841)),x71843))+~P24(f329(f329(f244(x71841),f2(x71841)),x71842))+P24(f329(f329(f244(x71841),f2(x71841)),f329(f329(f80(x71841),x71842),x71843)))
% 187.33/188.05 [7185]~P63(x71851)+~P24(f329(f329(f244(x71851),f2(x71851)),x71853))+~P24(f329(f329(f244(x71851),f2(x71851)),x71852))+P24(f329(f329(f244(x71851),f2(x71851)),f329(f329(f287(x71851),x71852),x71853)))
% 187.33/188.05 [7186]~P64(x71861)+~P24(f329(f329(f244(x71861),f2(x71861)),x71863))+~P24(f329(f329(f244(x71861),f2(x71861)),x71862))+P24(f329(f329(f244(x71861),f2(x71861)),f329(f329(f287(x71861),x71862),x71863)))
% 187.33/188.05 [7257]~P66(x72571)+~P24(f329(f62(x72571),x72573))+E(f10(x72571,f329(f329(f307(x72571),x72572),x72573)),x72572)+~E(f329(f329(f22(f881(x72571,a869)),x72573),f329(f329(f307(x72571),x72572),f193(f881(x72571,a869)))),f193(f881(x72571,a869)))
% 187.33/188.05 [7258]~P66(x72581)+~P24(f329(f62(x72581),x72583))+E(f13(x72581,f329(f329(f307(x72581),x72582),x72583)),x72582)+~E(f329(f329(f22(f881(x72581,a869)),x72583),f329(f329(f307(x72581),x72582),f193(f881(x72581,a869)))),f193(f881(x72581,a869)))
% 187.33/188.05 [7259]~P27(x72591)+~P24(f329(f62(x72591),x72593))+E(f14(x72591,f329(f329(f307(x72591),x72592),x72593)),x72592)+~E(f329(f329(f22(f881(x72591,a869)),x72593),f329(f329(f307(x72591),x72592),f193(f881(x72591,a869)))),f193(f881(x72591,a869)))
% 187.33/188.05 [7260]~P27(x72601)+~P24(f329(f62(x72601),x72603))+E(f15(x72601,f329(f329(f307(x72601),x72602),x72603)),x72602)+~E(f329(f329(f22(f881(x72601,a869)),x72603),f329(f329(f307(x72601),x72602),f193(f881(x72601,a869)))),f193(f881(x72601,a869)))
% 187.33/188.05 [7261]~P123(x72611)+P24(f329(f329(f243(x72611),x72612),f2(x72611)))+P24(f329(f329(f243(x72611),f2(x72611)),x72613))+~P24(f329(f329(f243(x72611),f2(x72611)),f329(f329(f81(x72611),x72613),x72612)))
% 187.33/188.05 [7262]~P123(x72621)+P24(f329(f329(f243(x72621),x72622),f2(x72621)))+P24(f329(f329(f243(x72621),f2(x72621)),x72623))+~P24(f329(f329(f243(x72621),f2(x72621)),f329(f329(f81(x72621),x72622),x72623)))
% 187.33/188.05 [7263]~P63(x72631)+P24(f329(f329(f243(x72631),x72632),f2(x72631)))+P24(f329(f329(f243(x72631),f2(x72631)),x72633))+~P24(f329(f329(f243(x72631),f2(x72631)),f329(f329(f287(x72631),x72633),x72632)))
% 187.33/188.05 [7264]~P63(x72641)+P24(f329(f329(f243(x72641),x72642),f2(x72641)))+P24(f329(f329(f243(x72641),f2(x72641)),x72643))+~P24(f329(f329(f243(x72641),f2(x72641)),f329(f329(f287(x72641),x72642),x72643)))
% 187.33/188.05 [7265]~P123(x72651)+P24(f329(f329(f243(x72651),x72652),f2(x72651)))+P24(f329(f329(f243(x72651),f2(x72651)),x72652))+~P24(f329(f329(f243(x72651),f2(x72651)),f329(f329(f81(x72651),x72653),x72652)))
% 187.33/188.05 [7266]~P123(x72661)+P24(f329(f329(f243(x72661),x72662),f2(x72661)))+P24(f329(f329(f243(x72661),f2(x72661)),x72662))+~P24(f329(f329(f243(x72661),f2(x72661)),f329(f329(f81(x72661),x72662),x72663)))
% 187.33/188.05 [7267]~P63(x72671)+P24(f329(f329(f243(x72671),x72672),f2(x72671)))+P24(f329(f329(f243(x72671),f2(x72671)),x72672))+~P24(f329(f329(f243(x72671),f2(x72671)),f329(f329(f287(x72671),x72673),x72672)))
% 187.33/188.05 [7268]~P63(x72681)+P24(f329(f329(f243(x72681),x72682),f2(x72681)))+P24(f329(f329(f243(x72681),f2(x72681)),x72682))+~P24(f329(f329(f243(x72681),f2(x72681)),f329(f329(f287(x72681),x72682),x72683)))
% 187.33/188.05 [7269]~P63(x72691)+P24(f329(f329(f244(x72691),x72692),f2(x72691)))+P24(f329(f329(f244(x72691),f2(x72691)),x72693))+~P24(f329(f329(f244(x72691),f2(x72691)),f329(f329(f287(x72691),x72693),x72692)))
% 187.33/188.05 [7270]~P63(x72701)+P24(f329(f329(f244(x72701),x72702),f2(x72701)))+P24(f329(f329(f244(x72701),f2(x72701)),x72703))+~P24(f329(f329(f244(x72701),f2(x72701)),f329(f329(f287(x72701),x72702),x72703)))
% 187.33/188.05 [7271]~P63(x72711)+P24(f329(f329(f244(x72711),x72712),f2(x72711)))+P24(f329(f329(f244(x72711),f2(x72711)),x72712))+~P24(f329(f329(f244(x72711),f2(x72711)),f329(f329(f287(x72711),x72713),x72712)))
% 187.33/188.05 [7272]~P63(x72721)+P24(f329(f329(f244(x72721),x72722),f2(x72721)))+P24(f329(f329(f244(x72721),f2(x72721)),x72722))+~P24(f329(f329(f244(x72721),f2(x72721)),f329(f329(f287(x72721),x72722),x72723)))
% 187.33/188.05 [7362]~E(f329(f329(f106(f881(x73621,a869)),f329(f171(x73621),x73622)),f329(f171(x73621),x73623)),f193(f881(x73621,a869)))+~P24(f329(f135(x73621),x73623))+~P24(f329(f135(x73621),x73622))+P24(f329(f135(x73621),f329(f329(f126(x73621),x73622),x73623)))
% 187.33/188.05 [7363]~P27(x73631)+~P24(f329(f62(x73631),x73633))+E(f11(x73631,f241(x73631),f329(f329(f307(x73631),x73632),x73633)),x73632)+~E(f329(f329(f22(f881(x73631,a869)),x73633),f329(f329(f307(x73631),x73632),f193(f881(x73631,a869)))),f193(f881(x73631,a869)))
% 187.33/188.05 [7364]~P27(x73641)+~P24(f329(f62(x73641),x73643))+E(f12(x73641,f242(x73641),f329(f329(f307(x73641),x73642),x73643)),x73642)+~E(f329(f329(f22(f881(x73641,a869)),x73643),f329(f329(f307(x73641),x73642),f193(f881(x73641,a869)))),f193(f881(x73641,a869)))
% 187.33/188.05 [7381]~P87(x73811)+~P24(f329(f329(f243(x73811),x73812),x73813))+~P24(f329(f329(f243(x73811),f329(f79(x73811),x73812)),x73813))+P24(f329(f329(f243(x73811),f329(f75(x73811),x73812)),x73813))
% 187.33/188.05 [7382]~P115(x73821)+~P24(f329(f329(f244(x73821),x73822),x73823))+~P24(f329(f329(f244(x73821),f329(f79(x73821),x73822)),x73823))+P24(f329(f329(f244(x73821),f329(f75(x73821),x73822)),x73823))
% 187.33/188.05 [7453]~P129(x74531)+P24(f329(f329(f244(x74531),f2(x74531)),x74532))+~P24(f329(f329(f244(x74531),f2(x74531)),x74533))+~P24(f329(f329(f244(x74531),f2(x74531)),f329(f329(f81(x74531),x74533),x74532)))
% 187.33/188.05 [7454]~P129(x74541)+P24(f329(f329(f244(x74541),f2(x74541)),x74542))+~P24(f329(f329(f244(x74541),f2(x74541)),x74543))+~P24(f329(f329(f244(x74541),f2(x74541)),f329(f329(f81(x74541),x74542),x74543)))
% 187.33/188.05 [7760]E(x77601,x77602)+~P24(f329(f62(x77603),x77601))+~P24(f329(f329(f243(a874),f329(f38(x77603),x77601)),f329(f38(x77603),x77602)))+~P24(f329(f329(f243(f881(x77603,a869)),x77602),x77601))
% 187.33/188.05 [7904]~P24(f329(f329(f244(a1),x79041),f2(a1)))+~P24(f329(f329(f244(a1),f2(a1)),x79042))+~P24(f329(f329(f243(a1),x79042),x79043))+P24(f329(f329(f243(a1),f329(f329(f39(a1),x79041),x79042)),f329(f329(f39(a1),x79041),x79043)))
% 187.33/188.05 [7916]~P24(f329(f329(f243(a1),f2(a1)),x79161))+~P24(f329(f329(f244(a1),f2(a1)),x79163))+~P24(f329(f329(f243(a1),x79163),x79162))+P24(f329(f329(f243(a1),f329(f329(f39(a1),x79161),x79162)),f329(f329(f39(a1),x79161),x79163)))
% 187.33/188.05 [8056]E(f329(x80561,f411(x80562,x80561,x80563)),x80562)+~P24(f329(f329(f243(a1),x80562),f329(x80561,x80563)))+P24(f329(f329(f244(a874),f412(x80562,x80561,x80563)),x80563))+~P24(f329(f329(f243(a1),f329(x80561,f2(a874))),x80562))
% 187.33/188.05 [8057]E(f329(x80571,f418(x80572,x80571,x80573)),x80572)+~P24(f329(f329(f243(a1),x80572),f329(x80571,x80573)))+P24(f329(f329(f244(a874),f419(x80572,x80571,x80573)),x80573))+~P24(f329(f329(f243(a1),f329(x80571,f2(a874))),x80572))
% 187.33/188.05 [8160]~P24(f329(f62(x81601),x81603))+~P24(f329(f329(f244(a874),f329(f38(x81601),x81602)),f329(f38(x81601),x81603)))+~P24(f329(f329(f243(f881(x81601,a869)),x81602),x81603))+P24(f329(f329(f244(f881(x81601,a869)),x81602),x81603))
% 187.33/188.05 [8189]E(f329(f329(f80(a1),f384(x81893,x81891,x81892)),f385(x81893,x81891,x81892)),x81891)+E(f329(f329(f22(a1),x81891),x81892),x81891)+~P24(f329(f329(f244(a1),f2(a1)),x81892))+~P24(f329(f329(f331(a1),f329(f329(f22(a1),x81891),f78(a1))),x81893))
% 187.33/188.05 [8190]E(f329(f329(f22(a1),f392(x81903,x81901,x81902)),f393(x81903,x81901,x81902)),x81901)+E(f329(f329(f80(a1),x81901),x81902),x81901)+~P24(f329(f329(f244(a1),f2(a1)),x81902))+~P24(f329(f329(f331(a1),f329(f329(f80(a1),x81901),f78(a1))),x81903))
% 187.33/188.05 [8243]~P24(f329(f329(f243(a874),x82433),x82431))+P24(f329(f329(f243(a874),x82431),x82432))+~P24(f329(f329(f243(a874),x82433),x82432))+~P24(f329(f329(f243(a874),f329(f329(f22(a874),x82431),x82433)),f329(f329(f22(a874),x82432),x82433)))
% 187.33/188.05 [8244]~P24(f329(f329(f243(a874),x82443),x82441))+P24(f329(f329(f244(a874),x82441),x82442))+~P24(f329(f329(f243(a874),x82443),x82442))+~P24(f329(f329(f244(a874),f329(f329(f22(a874),x82441),x82443)),f329(f329(f22(a874),x82442),x82443)))
% 187.33/188.05 [8260]~P27(x82602)+E(x82601,f118(x82602))+~P33(x82602,f329(f167(x82602),x82601))+E(f329(f140(x82602,x82602,f329(f7(x82602,x82602,x82602),f242(x82602)),x82603),f329(f167(x82602),x82601)),f329(f329(f242(x82602),f329(f329(f163(x82602),x82601),f2(a874))),x82603))
% 187.33/188.05 [8326]E(f329(f329(f22(a1),x83261),x83262),x83261)+~P24(f329(f329(f244(a1),f2(a1)),x83262))+P24(f329(f329(f331(a1),f384(x83263,x83261,x83262)),x83263))+~P24(f329(f329(f331(a1),f329(f329(f22(a1),x83261),f78(a1))),x83263))
% 187.33/188.05 [8327]E(f329(f329(f80(a1),x83271),x83272),x83271)+~P24(f329(f329(f244(a1),f2(a1)),x83272))+P24(f329(f329(f331(a1),f392(x83273,x83271,x83272)),x83273))+~P24(f329(f329(f331(a1),f329(f329(f80(a1),x83271),f78(a1))),x83273))
% 187.33/188.05 [8402]~P24(f329(f329(f243(a1),x84021),f329(x84022,x84023)))+P24(f329(f329(f244(a874),f412(x84021,x84022,x84023)),x84023))+P24(f329(f329(f243(a874),f411(x84021,x84022,x84023)),x84023))+~P24(f329(f329(f243(a1),f329(x84022,f2(a874))),x84021))
% 187.33/188.05 [8403]~P24(f329(f329(f243(a1),x84031),f329(x84032,x84033)))+P24(f329(f329(f244(a874),f419(x84031,x84032,x84033)),x84033))+P24(f329(f329(f243(a874),f418(x84031,x84032,x84033)),x84033))+~P24(f329(f329(f243(a1),f329(x84032,f2(a874))),x84031))
% 187.33/188.05 [8482]E(f329(f329(f22(a1),x84821),x84822),x84821)+~P24(f329(f329(f244(a1),f2(a1)),x84822))+P24(f329(f329(f331(a1),f385(x84823,x84821,x84822)),f300(a1,f78(a1),x84822)))+~P24(f329(f329(f331(a1),f329(f329(f22(a1),x84821),f78(a1))),x84823))
% 187.33/188.05 [8483]E(f329(f329(f80(a1),x84831),x84832),x84831)+~P24(f329(f329(f244(a1),f2(a1)),x84832))+P24(f329(f329(f331(a1),f393(x84833,x84831,x84832)),f300(a1,f78(a1),x84832)))+~P24(f329(f329(f331(a1),f329(f329(f80(a1),x84831),f78(a1))),x84833))
% 187.33/188.05 [8612]~P121(x86121)+~P24(f329(f329(f244(x86121),x86122),f78(x86121)))+~P24(f329(f329(f244(x86121),f2(x86121)),x86122))+P24(f329(f329(f244(x86121),f329(f329(f81(x86121),x86122),f329(f329(f254(x86121),x86122),x86123))),f329(f329(f254(x86121),x86122),x86123)))
% 187.33/188.05 [8696]~P24(f329(x86961,x86962))+P24(f329(x86961,f2(a874)))+~P24(f329(f329(f244(a874),x86962),x86963))+~P24(f329(x86961,f45(a874,f329(a117,f473(x86962,x86961,x86963)),x86963)))
% 187.33/188.05 [8834]E(f493(x88341,x88342,x88343),f2(a874))+P24(f329(f329(x88341,x88343),x88342))+P24(f329(f329(x88341,f493(x88341,x88342,x88343)),f45(a874,f492(x88341,x88342,x88343),f493(x88341,x88342,x88343))))+~P24(f329(f317(f880(a874,a874),a227),f329(f329(f264(a874,a874),x88343),x88342)))
% 187.33/188.05 [8872]~P21(x88721,x88721,x88722,x88723)+E(f329(f308(x88721,x88721,x88722),x88723),x88723)+~P24(f329(f62(x88721),x88723))+~P24(f329(f329(f243(f881(x88721,a869)),f329(f308(x88721,x88721,x88722),x88723)),x88723))
% 187.33/188.05 [9114]P24(f329(f329(x91141,x91142),x91143))+~P24(f329(f329(f244(a1),f488(x91141,x91143,x91142)),f2(a1)))+P24(f329(f329(x91141,f329(f79(a1),f487(x91141,x91143,x91142))),f329(f79(a1),f488(x91141,x91143,x91142))))+~P24(f329(f317(f880(a1,a1),a232),f329(f329(f264(a1,a1),x91142),x91143)))
% 187.33/188.05 [9303]P24(f329(f329(x93031,x93032),x93033))+P24(f329(f329(x93031,f329(f329(f80(a1),f691(x93031,x93033,x93032)),f78(a1))),f693(x93031,x93033,x93032)))+~P24(f329(f329(f243(a1),f691(x93031,x93033,x93032)),f693(x93031,x93033,x93032)))+~P24(f329(f317(f880(a1,a1),a182),f329(f329(f264(a1,a1),x93032),x93033)))
% 187.33/188.05 [9728]~P60(x97282)+~P60(x97281)+~P24(f329(f58(f880(x97281,x97282)),x97283))+P24(f329(f58(x97281),f329(f329(f8(f881(x97282,a869),a869,x97281),f58(x97282)),f329(f329(f8(f881(x97282,f880(x97281,x97282)),f881(x97282,a869),x97281),f329(f8(f880(x97281,x97282),a869,x97282),x97283)),f264(x97281,x97282)))))
% 187.33/188.05 [9729]~P60(x97292)+~P60(x97291)+~P24(f329(f59(f880(x97291,x97292)),x97293))+P24(f329(f59(x97291),f329(f329(f8(f881(x97292,a869),a869,x97291),f59(x97292)),f329(f329(f8(f881(x97292,f880(x97291,x97292)),f881(x97292,a869),x97291),f329(f8(f880(x97291,x97292),a869,x97292),x97293)),f264(x97291,x97292)))))
% 187.33/188.05 [9831]~P60(x98312)+~P60(x98311)+P24(f329(f58(f880(x98311,x98312)),x98313))+~P24(f329(f58(x98311),f329(f329(f8(f881(x98312,a869),a869,x98311),f58(x98312)),f329(f329(f8(f881(x98312,f880(x98311,x98312)),f881(x98312,a869),x98311),f329(f8(f880(x98311,x98312),a869,x98312),x98313)),f264(x98311,x98312)))))
% 187.33/188.05 [9832]~P60(x98322)+~P60(x98321)+P24(f329(f59(f880(x98321,x98322)),x98323))+~P24(f329(f59(x98321),f329(f329(f8(f881(x98322,a869),a869,x98321),f59(x98322)),f329(f329(f8(f881(x98322,f880(x98321,x98322)),f881(x98322,a869),x98321),f329(f8(f880(x98321,x98322),a869,x98322),x98323)),f264(x98321,x98322)))))
% 187.33/188.05 [10002]E(f329(x100021,f411(x100022,x100021,x100023)),x100022)+~P24(f329(f329(f243(a1),x100022),f329(x100021,x100023)))+~P24(f329(f329(f243(a1),f329(f75(a1),f329(f329(f22(a1),f329(x100021,f329(f329(f80(a874),f412(x100022,x100021,x100023)),f78(a874)))),f329(x100021,f412(x100022,x100021,x100023))))),f78(a1)))+~P24(f329(f329(f243(a1),f329(x100021,f2(a874))),x100022))
% 187.33/188.05 [10003]E(f329(x100031,f418(x100032,x100031,x100033)),x100032)+~P24(f329(f329(f243(a1),x100032),f329(x100031,x100033)))+~P24(f329(f329(f243(a1),f329(f75(a1),f329(f329(f22(a1),f329(x100031,f329(f329(f80(a874),f419(x100032,x100031,x100033)),f78(a874)))),f329(x100031,f419(x100032,x100031,x100033))))),f78(a1)))+~P24(f329(f329(f243(a1),f329(x100031,f2(a874))),x100032))
% 187.33/188.05 [10007]~P24(f329(f329(f243(a1),x100071),f329(x100072,x100073)))+~P24(f329(f329(f243(a1),f329(f75(a1),f329(f329(f22(a1),f329(x100072,f329(f329(f80(a874),f412(x100071,x100072,x100073)),f78(a874)))),f329(x100072,f412(x100071,x100072,x100073))))),f78(a1)))+P24(f329(f329(f243(a874),f411(x100071,x100072,x100073)),x100073))+~P24(f329(f329(f243(a1),f329(x100072,f2(a874))),x100071))
% 187.33/188.05 [10008]~P24(f329(f329(f243(a1),x100081),f329(x100082,x100083)))+~P24(f329(f329(f243(a1),f329(f75(a1),f329(f329(f22(a1),f329(x100082,f329(f329(f80(a874),f419(x100081,x100082,x100083)),f78(a874)))),f329(x100082,f419(x100081,x100082,x100083))))),f78(a1)))+P24(f329(f329(f243(a874),f418(x100081,x100082,x100083)),x100083))+~P24(f329(f329(f243(a1),f329(x100082,f2(a874))),x100081))
% 187.33/188.05 [10063]E(x100631,x100632)+~E(f329(f140(f875(x100633),f875(x100633),f126(x100633),f118(x100633)),x100631),f329(f140(f875(x100633),f875(x100633),f126(x100633),f118(x100633)),x100632))+~E(f329(f194(f875(f875(x100633))),x100631),f329(f194(f875(f875(x100633))),x100632))+~P24(f329(f329(f268(f875(x100633),f875(x100633),a869),f329(f329(f7(f875(x100633),f881(f875(x100633),a874),f881(f875(x100633),a869)),f329(f329(f8(f881(a874,a869),f881(f881(f875(x100633),a874),f881(f875(x100633),a869)),f875(x100633)),f8(a874,a869,f875(x100633))),f329(f329(f8(a874,f881(a874,a869),f875(x100633)),a326),f194(f875(x100633))))),f194(f875(x100633)))),f740(x100631,x100632,x100633)))
% 187.33/188.05 [10064]E(x100641,x100642)+~E(f329(f140(f875(x100643),f875(x100643),f126(x100643),f118(x100643)),x100641),f329(f140(f875(x100643),f875(x100643),f126(x100643),f118(x100643)),x100642))+~E(f329(f194(f875(f875(x100643))),x100641),f329(f194(f875(f875(x100643))),x100642))+~P24(f329(f329(f268(f875(x100643),f875(x100643),a869),f329(f329(f7(f875(x100643),f881(f875(x100643),a874),f881(f875(x100643),a869)),f329(f329(f8(f881(a874,a869),f881(f881(f875(x100643),a874),f881(f875(x100643),a869)),f875(x100643)),f8(a874,a869,f875(x100643))),f329(f329(f8(a874,f881(a874,a869),f875(x100643)),a326),f194(f875(x100643))))),f194(f875(x100643)))),f741(x100642,x100641,x100643)))
% 187.33/188.05 [6778]~E(f78(a874),f2(a874))+~P24(f329(f62(x67781),x67783))+~P24(f329(f62(x67781),x67782))+E(f329(f329(f80(a874),f329(f38(x67781),x67782)),f329(f38(x67781),x67783)),f329(f38(x67781),f329(f329(f115(f881(x67781,a869)),x67782),x67783)))
% 187.33/188.05 [7193]~P103(x71931)+~P24(f329(f62(x71931),x71932))+~P24(f329(f329(f331(x71931),x71933),x71932))+P24(f329(f329(f243(x71931),f329(f64(x71931,f106(x71931)),x71932)),x71933))
% 187.33/188.05 [7194]~P27(x71941)+~P24(f329(f62(x71941),x71942))+~P24(f329(f329(f331(x71941),x71943),x71942))+P24(f329(f329(f243(x71941),f329(f64(x71941,f241(x71941)),x71942)),x71943))
% 187.33/188.05 [7447]~P24(f329(f62(x74471),x74473))+~P24(f329(f62(x74471),x74472))+~E(f329(f329(f106(f881(x74471,a869)),x74472),x74473),f193(f881(x74471,a869)))+E(f329(f329(f80(a874),f329(f38(x74471),x74472)),f329(f38(x74471),x74473)),f329(f38(x74471),f329(f329(f115(f881(x74471,a869)),x74472),x74473)))
% 187.33/188.05 [8249]~P42(x82491,x82493)+~P42(x82491,x82492)+~E(f329(f329(f106(f881(x82491,a869)),f329(f262(x82491,x82491),x82492)),f329(f260(x82491,x82491),x82493)),f193(f881(x82491,a869)))+P42(x82491,f329(f329(f115(f881(f880(x82491,x82491),a869)),x82492),x82493))
% 187.33/188.05 [8341]E(x83411,f329(f329(f39(a874),x83412),x83413))+~P24(f329(f329(f244(a874),f2(a874)),x83413))+~P24(f329(f329(f244(a874),x83412),f329(f329(f81(a874),x83413),f329(a117,x83411))))+~P24(f329(f329(f243(a874),f329(f329(f81(a874),x83413),x83411)),x83412))
% 187.33/188.05 [8480]~P24(f329(f62(x84801),x84802))+~P24(f329(f62(x84801),x84803))+E(f329(f329(f80(a874),f329(f38(x84801),x84802)),f329(f38(x84801),x84803)),f329(f38(x84801),f329(f329(f115(f881(x84801,a869)),x84802),x84803)))+P24(f329(f329(f331(x84801),f837(x84803,x84802,x84801)),f329(f329(f106(f881(x84801,a869)),x84802),x84803)))
% 187.33/188.05 [8846]~P123(x88462)+~E(x88461,f2(x88462))+~E(x88463,f2(x88462))+~P24(f329(f329(f244(x88462),f2(x88462)),f329(f329(f80(x88462),f329(f329(f81(x88462),x88463),x88463)),f329(f329(f81(x88462),x88461),x88461))))
% 187.33/188.05 [9382]~P42(x93821,x93823)+~P42(x93821,x93822)+P42(x93821,f329(f329(f115(f881(f880(x93821,x93821),a869)),x93822),x93823))+~P24(f329(f329(f243(f881(f880(x93821,x93821),a869)),f329(f329(f286(x93821,x93821,x93821),x93822),x93823)),x93822))
% 187.33/188.05 [9508]~P24(f329(x95081,x95083))+~P24(f329(f62(x95082),x95083))+P24(f329(x95081,f193(f881(x95082,a869))))+~P24(f329(x95081,f329(f329(f22(f881(x95082,a869)),f599(x95081,x95083,x95082)),f329(f329(f307(x95082),f602(x95081,x95083,x95082)),f193(f881(x95082,a869))))))
% 187.33/188.05 [9758]~P60(x97581)+~P60(x97582)+P7(x97581,f329(f329(f8(f881(x97582,x97581),a869,f875(x97581)),x97583),f329(f329(f8(f881(x97582,f878(x97581)),f881(x97582,x97581),f875(x97581)),f73(f878(x97581),x97581,x97582,f240(x97581))),f329(f329(f8(f875(f880(x97582,x97581)),f881(x97582,f878(x97581)),f875(x97581)),f177(x97582,x97581)),f329(f181(x97582,x97581),f56(x97582))))),f329(f194(f875(x97582)),f56(x97582)))+~P24(f329(f58(f881(x97582,x97581)),x97583))
% 187.33/188.05 [9759]~P60(x97591)+~P60(x97592)+P8(x97591,f329(f329(f8(f881(x97592,x97591),a869,f875(x97591)),x97593),f329(f329(f8(f881(x97592,f878(x97591)),f881(x97592,x97591),f875(x97591)),f73(f878(x97591),x97591,x97592,f240(x97591))),f329(f329(f8(f875(f880(x97592,x97591)),f881(x97592,f878(x97591)),f875(x97591)),f177(x97592,x97591)),f329(f181(x97592,x97591),f56(x97592))))),f329(f194(f875(x97592)),f56(x97592)))+~P24(f329(f59(f881(x97592,x97591)),x97593))
% 187.33/188.05 [9856]~P60(x98561)+~P60(x98562)+~P7(x98562,f329(f329(f8(f881(x98561,x98562),a869,f875(x98562)),x98563),f329(f329(f8(f881(x98561,f878(x98562)),f881(x98561,x98562),f875(x98562)),f73(f878(x98562),x98562,x98561,f240(x98562))),f329(f329(f8(f875(f880(x98561,x98562)),f881(x98561,f878(x98562)),f875(x98562)),f177(x98561,x98562)),f329(f181(x98561,x98562),f56(x98561))))),f329(f194(f875(x98561)),f56(x98561)))+P24(f329(f58(f881(x98561,x98562)),x98563))
% 187.33/188.05 [9857]~P60(x98571)+~P60(x98572)+~P8(x98572,f329(f329(f8(f881(x98571,x98572),a869,f875(x98572)),x98573),f329(f329(f8(f881(x98571,f878(x98572)),f881(x98571,x98572),f875(x98572)),f73(f878(x98572),x98572,x98571,f240(x98572))),f329(f329(f8(f875(f880(x98571,x98572)),f881(x98571,f878(x98572)),f875(x98572)),f177(x98571,x98572)),f329(f181(x98571,x98572),f56(x98571))))),f329(f194(f875(x98571)),f56(x98571)))+P24(f329(f59(f881(x98571,x98572)),x98573))
% 187.33/188.05 [8647]~P24(f329(f329(f244(a1),f2(a1)),x86473))+P24(f329(f329(f243(a1),f2(a1)),x86471))+~P24(f329(f329(f244(a1),x86472),x86473))+~P24(f329(f329(f243(a1),f2(a1)),f329(f329(f80(a1),f329(f329(f81(a1),x86473),x86471)),x86472)))
% 187.33/188.05 [8670]~P66(x86701)+~P24(f329(f62(x86701),x86702))+E(f329(f329(f22(f881(x86701,a869)),x86702),f329(f329(f307(x86701),x86703),f193(f881(x86701,a869)))),f193(f881(x86701,a869)))+E(f329(f329(f106(x86701),x86703),f10(x86701,f329(f329(f22(f881(x86701,a869)),x86702),f329(f329(f307(x86701),x86703),f193(f881(x86701,a869)))))),f10(x86701,f329(f329(f307(x86701),x86703),x86702)))
% 187.33/188.05 [8671]~P66(x86711)+~P24(f329(f62(x86711),x86712))+E(f329(f329(f22(f881(x86711,a869)),x86712),f329(f329(f307(x86711),x86713),f193(f881(x86711,a869)))),f193(f881(x86711,a869)))+E(f329(f329(f115(x86711),x86713),f13(x86711,f329(f329(f22(f881(x86711,a869)),x86712),f329(f329(f307(x86711),x86713),f193(f881(x86711,a869)))))),f13(x86711,f329(f329(f307(x86711),x86713),x86712)))
% 187.33/188.05 [8672]~P27(x86721)+~P24(f329(f62(x86721),x86722))+E(f329(f329(f22(f881(x86721,a869)),x86722),f329(f329(f307(x86721),x86723),f193(f881(x86721,a869)))),f193(f881(x86721,a869)))+E(f329(f329(f241(x86721),x86723),f14(x86721,f329(f329(f22(f881(x86721,a869)),x86722),f329(f329(f307(x86721),x86723),f193(f881(x86721,a869)))))),f14(x86721,f329(f329(f307(x86721),x86723),x86722)))
% 187.33/188.05 [8673]~P27(x86731)+~P24(f329(f62(x86731),x86732))+E(f329(f329(f22(f881(x86731,a869)),x86732),f329(f329(f307(x86731),x86733),f193(f881(x86731,a869)))),f193(f881(x86731,a869)))+E(f329(f329(f242(x86731),x86733),f15(x86731,f329(f329(f22(f881(x86731,a869)),x86732),f329(f329(f307(x86731),x86733),f193(f881(x86731,a869)))))),f15(x86731,f329(f329(f307(x86731),x86733),x86732)))
% 187.33/188.05 [8737]~P27(x87371)+~P24(f329(f62(x87371),x87372))+E(f329(f329(f22(f881(x87371,a869)),x87372),f329(f329(f307(x87371),x87373),f193(f881(x87371,a869)))),f193(f881(x87371,a869)))+E(f329(f329(f241(x87371),x87373),f11(x87371,f241(x87371),f329(f329(f22(f881(x87371,a869)),x87372),f329(f329(f307(x87371),x87373),f193(f881(x87371,a869)))))),f11(x87371,f241(x87371),f329(f329(f307(x87371),x87373),x87372)))
% 187.33/188.05 [8738]~P27(x87381)+~P24(f329(f62(x87381),x87382))+E(f329(f329(f22(f881(x87381,a869)),x87382),f329(f329(f307(x87381),x87383),f193(f881(x87381,a869)))),f193(f881(x87381,a869)))+E(f329(f329(f242(x87381),x87383),f12(x87381,f242(x87381),f329(f329(f22(f881(x87381,a869)),x87382),f329(f329(f307(x87381),x87383),f193(f881(x87381,a869)))))),f12(x87381,f242(x87381),f329(f329(f307(x87381),x87383),x87382)))
% 187.33/188.05 [9323]E(x93231,x93232)+~E(f329(f140(f875(x93233),f875(x93233),f126(x93233),f118(x93233)),x93231),f329(f140(f875(x93233),f875(x93233),f126(x93233),f118(x93233)),x93232))+~E(f329(f194(f875(f875(x93233))),x93231),f329(f194(f875(f875(x93233))),x93232))+P24(f329(f329(f331(f880(f875(x93233),f875(x93233))),f740(x93231,x93232,x93233)),f329(f171(f880(f875(x93233),f875(x93233))),f329(f329(f181(f875(x93233),f875(x93233)),x93232),x93231))))
% 187.33/188.05 [9324]E(x93241,x93242)+~E(f329(f140(f875(x93243),f875(x93243),f126(x93243),f118(x93243)),x93241),f329(f140(f875(x93243),f875(x93243),f126(x93243),f118(x93243)),x93242))+~E(f329(f194(f875(f875(x93243))),x93241),f329(f194(f875(f875(x93243))),x93242))+P24(f329(f329(f331(f880(f875(x93243),f875(x93243))),f741(x93242,x93241,x93243)),f329(f171(f880(f875(x93243),f875(x93243))),f329(f329(f181(f875(x93243),f875(x93243)),x93241),x93242))))
% 187.33/188.05 [10148]~P100(x101482)+E(x101481,f193(f881(x101482,a869)))+~P24(f329(f62(x101482),x101481))+E(f10(x101482,f329(f249(x101482),f329(f329(f8(f881(x101482,a869),a869,x101482),f87(x101482)),f329(f329(f7(x101482,f881(x101482,a869),f881(x101482,a869)),f329(f329(f8(f881(x101482,f881(a869,a869)),f881(f881(x101482,a869),f881(x101482,a869)),x101482),f18(x101482,a869,a869)),f329(f329(f8(f881(x101482,a869),f881(x101482,f881(a869,a869)),x101482),f329(f8(a869,f881(a869,a869),x101482),a327)),f329(f329(f7(x101482,f881(x101482,x101482),f881(x101482,a869)),f329(f329(f8(f881(x101482,a869),f881(f881(x101482,x101482),f881(x101482,a869)),x101482),f8(x101482,a869,x101482)),a326)),f329(f115(x101482),x101483))))),f329(f329(f7(x101482,f881(x101482,a869),a869),f331(x101482)),x101481))))),f329(f329(f115(x101482),x101483),f10(x101482,x101481)))
% 187.33/188.05 [10149]~P100(x101492)+E(x101491,f193(f881(x101492,a869)))+~P24(f329(f62(x101492),x101491))+E(f13(x101492,f329(f249(x101492),f329(f329(f8(f881(x101492,a869),a869,x101492),f87(x101492)),f329(f329(f7(x101492,f881(x101492,a869),f881(x101492,a869)),f329(f329(f8(f881(x101492,f881(a869,a869)),f881(f881(x101492,a869),f881(x101492,a869)),x101492),f18(x101492,a869,a869)),f329(f329(f8(f881(x101492,a869),f881(x101492,f881(a869,a869)),x101492),f329(f8(a869,f881(a869,a869),x101492),a327)),f329(f329(f7(x101492,f881(x101492,x101492),f881(x101492,a869)),f329(f329(f8(f881(x101492,a869),f881(f881(x101492,x101492),f881(x101492,a869)),x101492),f8(x101492,a869,x101492)),a326)),f329(f106(x101492),x101493))))),f329(f329(f7(x101492,f881(x101492,a869),a869),f331(x101492)),x101491))))),f329(f329(f106(x101492),x101493),f13(x101492,x101491)))
% 187.33/188.05 [10150]~P79(x101502)+E(x101501,f193(f881(x101502,a869)))+~P24(f329(f62(x101502),x101501))+E(f14(x101502,f329(f249(x101502),f329(f329(f8(f881(x101502,a869),a869,x101502),f87(x101502)),f329(f329(f7(x101502,f881(x101502,a869),f881(x101502,a869)),f329(f329(f8(f881(x101502,f881(a869,a869)),f881(f881(x101502,a869),f881(x101502,a869)),x101502),f18(x101502,a869,a869)),f329(f329(f8(f881(x101502,a869),f881(x101502,f881(a869,a869)),x101502),f329(f8(a869,f881(a869,a869),x101502),a327)),f329(f329(f7(x101502,f881(x101502,x101502),f881(x101502,a869)),f329(f329(f8(f881(x101502,a869),f881(f881(x101502,x101502),f881(x101502,a869)),x101502),f8(x101502,a869,x101502)),a326)),f329(f80(x101502),x101503))))),f329(f329(f7(x101502,f881(x101502,a869),a869),f331(x101502)),x101501))))),f329(f329(f80(x101502),x101503),f14(x101502,x101501)))
% 187.33/188.05 [10151]~P79(x101512)+E(x101511,f193(f881(x101512,a869)))+~P24(f329(f62(x101512),x101511))+E(f15(x101512,f329(f249(x101512),f329(f329(f8(f881(x101512,a869),a869,x101512),f87(x101512)),f329(f329(f7(x101512,f881(x101512,a869),f881(x101512,a869)),f329(f329(f8(f881(x101512,f881(a869,a869)),f881(f881(x101512,a869),f881(x101512,a869)),x101512),f18(x101512,a869,a869)),f329(f329(f8(f881(x101512,a869),f881(x101512,f881(a869,a869)),x101512),f329(f8(a869,f881(a869,a869),x101512),a327)),f329(f329(f7(x101512,f881(x101512,x101512),f881(x101512,a869)),f329(f329(f8(f881(x101512,a869),f881(f881(x101512,x101512),f881(x101512,a869)),x101512),f8(x101512,a869,x101512)),a326)),f329(f80(x101512),x101513))))),f329(f329(f7(x101512,f881(x101512,a869),a869),f331(x101512)),x101511))))),f329(f329(f80(x101512),x101513),f15(x101512,x101511)))
% 187.33/188.05 [10152]~P27(x101522)+E(x101521,f193(f881(x101522,a869)))+~P24(f329(f62(x101522),x101521))+E(f12(x101522,f242(x101522),f329(f249(x101522),f329(f329(f8(f881(x101522,a869),a869,x101522),f87(x101522)),f329(f329(f7(x101522,f881(x101522,a869),f881(x101522,a869)),f329(f329(f8(f881(x101522,f881(a869,a869)),f881(f881(x101522,a869),f881(x101522,a869)),x101522),f18(x101522,a869,a869)),f329(f329(f8(f881(x101522,a869),f881(x101522,f881(a869,a869)),x101522),f329(f8(a869,f881(a869,a869),x101522),a327)),f329(f329(f7(x101522,f881(x101522,x101522),f881(x101522,a869)),f329(f329(f8(f881(x101522,a869),f881(f881(x101522,x101522),f881(x101522,a869)),x101522),f8(x101522,a869,x101522)),a326)),f329(f241(x101522),x101523))))),f329(f329(f7(x101522,f881(x101522,a869),a869),f331(x101522)),x101521))))),f329(f329(f241(x101522),x101523),f12(x101522,f242(x101522),x101521)))
% 187.33/188.05 [10153]~P27(x101532)+E(x101531,f193(f881(x101532,a869)))+~P24(f329(f62(x101532),x101531))+E(f11(x101532,f241(x101532),f329(f249(x101532),f329(f329(f8(f881(x101532,a869),a869,x101532),f87(x101532)),f329(f329(f7(x101532,f881(x101532,a869),f881(x101532,a869)),f329(f329(f8(f881(x101532,f881(a869,a869)),f881(f881(x101532,a869),f881(x101532,a869)),x101532),f18(x101532,a869,a869)),f329(f329(f8(f881(x101532,a869),f881(x101532,f881(a869,a869)),x101532),f329(f8(a869,f881(a869,a869),x101532),a327)),f329(f329(f7(x101532,f881(x101532,x101532),f881(x101532,a869)),f329(f329(f8(f881(x101532,a869),f881(f881(x101532,x101532),f881(x101532,a869)),x101532),f8(x101532,a869,x101532)),a326)),f329(f242(x101532),x101533))))),f329(f329(f7(x101532,f881(x101532,a869),a869),f331(x101532)),x101531))))),f329(f329(f242(x101532),x101533),f11(x101532,f241(x101532),x101531)))
% 187.33/188.05 [9906]~P115(x99061)+~E(x99063,f2(x99061))+~E(x99062,f2(x99061))+E(f329(f329(f80(x99061),f329(f329(f254(x99061),x99062),f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102))))),f329(f329(f254(x99061),x99063),f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102))))),f2(x99061))
% 187.33/188.05 [10047]~P121(x100471)+~P24(f329(f329(f243(x100471),f2(x100471)),x100473))+P24(f329(f329(f243(x100471),x100472),x100473))+~P24(f329(f329(f243(x100471),f329(f329(f254(x100471),x100472),f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102))))),f329(f329(f254(x100471),x100473),f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102))))))
% 187.33/188.05 [10094]~P115(x100942)+~E(x100941,f2(x100942))+~E(x100943,f2(x100942))+~P24(f329(f329(f244(x100942),f2(x100942)),f329(f329(f80(x100942),f329(f329(f254(x100942),x100943),f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102))))),f329(f329(f254(x100942),x100941),f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))))))
% 187.33/188.05 [9285]E(x92851,x92852)+~E(f665(x92851,x92852,x92854,x92853),f667(x92851,x92852,x92854,x92853))+P24(f329(f329(f331(f880(f875(x92853),f875(x92853))),f329(f329(f264(f875(x92853),f875(x92853)),x92852),x92851)),f145(x92853,x92854)))+P24(f329(f329(f331(f880(f875(x92853),f875(x92853))),f329(f329(f264(f875(x92853),f875(x92853)),x92851),x92852)),f145(x92853,x92854)))
% 187.33/188.05 [4834]~P61(x48342)+~E(x48344,f2(x48342))+~E(x48341,f2(x48342))+E(x48341,f329(f329(f287(x48342),x48343),x48344))
% 187.33/188.05 [4835]~P61(x48351)+~E(x48353,f2(x48351))+~E(x48354,f2(x48351))+E(f329(f329(f287(x48351),x48352),x48353),x48354)
% 187.33/188.05 [4944]~P61(x49442)+E(x49441,f2(x49442))+~E(x49443,f2(x49442))+~E(x49441,f329(f329(f287(x49442),x49444),x49443))
% 187.33/188.05 [4945]~P61(x49452)+E(x49451,f2(x49452))+~E(x49453,f2(x49452))+~E(f329(f329(f287(x49452),x49454),x49453),x49451)
% 187.33/188.05 [5123]~P118(x51232)+E(x51231,f2(x51232))+~E(f329(f329(f287(x51232),x51233),x51231),x51234)+E(x51233,f329(f329(f81(x51232),x51234),x51231))
% 187.33/188.05 [5125]~P118(x51252)+E(x51251,f2(x51252))+~E(f329(f329(f81(x51252),x51253),x51251),x51254)+E(x51253,f329(f329(f287(x51252),x51254),x51251))
% 187.33/188.05 [5126]~P61(x51262)+E(x51261,f2(x51262))+~E(f329(f329(f287(x51262),x51263),x51261),x51264)+E(x51263,f329(f329(f81(x51262),x51264),x51261))
% 187.33/188.05 [5127]~P61(x51272)+E(x51271,f2(x51272))+~E(f329(f329(f81(x51272),x51273),x51271),x51274)+E(x51273,f329(f329(f287(x51272),x51274),x51271))
% 187.33/188.05 [5128]~P118(x51282)+E(x51281,f2(x51282))+~E(x51283,f329(f329(f287(x51282),x51284),x51281))+E(f329(f329(f81(x51282),x51283),x51281),x51284)
% 187.33/188.05 [5130]~P118(x51302)+E(x51301,f2(x51302))+~E(x51303,f329(f329(f81(x51302),x51304),x51301))+E(f329(f329(f287(x51302),x51303),x51301),x51304)
% 187.33/188.05 [5131]~P61(x51312)+E(x51311,f2(x51312))+~E(x51313,f329(f329(f287(x51312),x51314),x51311))+E(f329(f329(f81(x51312),x51313),x51311),x51314)
% 187.33/188.05 [5132]~P61(x51322)+E(x51321,f2(x51322))+~E(x51323,f329(f329(f81(x51322),x51324),x51321))+E(f329(f329(f287(x51322),x51323),x51321),x51324)
% 187.33/188.05 [5165]~P61(x51652)+~E(x51651,f2(x51652))+~E(f329(f329(f81(x51652),x51651),x51654),x51653)+E(x51651,f329(f329(f287(x51652),x51653),x51654))
% 187.33/188.05 [5166]~P61(x51661)+~E(x51664,f2(x51661))+~E(x51662,f329(f329(f81(x51661),x51664),x51663))+E(f329(f329(f287(x51661),x51662),x51663),x51664)
% 187.33/188.05 [5239]~E(x52393,x52394)+~E(x52392,x52393)+~P106(x52391)+E(f300(x52391,x52392,x52393),f329(f329(f307(x52391),x52394),f193(f881(x52391,a869))))
% 187.33/188.05 [5445]~E(f119(x54452,x54451),x54453)+~E(f142(x54452,x54451),x54454)+E(x54451,f118(x54452))+E(f329(f329(f126(x54452),x54453),f329(f329(f149(x54452),x54454),f118(x54452))),x54451)
% 187.33/188.05 [6060]~P121(x60603)+E(x60601,x60602)+~E(f329(f329(f254(x60603),x60604),x60601),f329(f329(f254(x60603),x60604),x60602))+~P24(f329(f329(f244(x60603),f78(x60603)),x60604))
% 187.33/188.05 [6061]E(x60611,x60612)+~E(f329(f329(f307(x60613),x60614),x60611),f329(f329(f307(x60613),x60614),x60612))+P24(f329(f329(f331(x60613),x60614),x60612))+P24(f329(f329(f331(x60613),x60614),x60611))
% 187.33/188.05 [6099]E(f329(x60991,x60992),f78(a874))+~E(f329(f329(f9(x60993,a874),x60991),x60994),f78(a874))+~P24(f329(f62(x60993),x60994))+~P24(f329(f329(f331(x60993),x60992),x60994))
% 187.33/188.05 [6100]E(f329(x61001,x61002),f2(a874))+~E(f329(f329(f6(x61003,a874),x61001),x61004),f2(a874))+~P24(f329(f62(x61003),x61004))+~P24(f329(f329(f331(x61003),x61002),x61004))
% 187.33/188.05 [6320]~P106(x63201)+~P24(f329(f329(f243(x63201),x63204),x63203))+P24(f329(f329(f243(x63201),x63202),x63203))+~P24(f329(f329(f243(x63201),x63202),x63204))
% 187.33/188.05 [6321]~P25(x63211)+~P24(f329(f329(f243(x63211),x63212),x63214))+P24(f329(f329(f243(x63211),x63212),x63213))+~P24(f329(f329(f243(x63211),x63214),x63213))
% 187.33/188.05 [6322]~P106(x63221)+~P24(f329(f329(f244(x63221),x63224),x63223))+P24(f329(f329(f244(x63221),x63222),x63223))+~P24(f329(f329(f243(x63221),x63222),x63224))
% 187.33/188.05 [6323]~P106(x63231)+~P24(f329(f329(f244(x63231),x63232),x63234))+P24(f329(f329(f244(x63231),x63232),x63233))+~P24(f329(f329(f243(x63231),x63234),x63233))
% 187.33/188.05 [6324]~P106(x63241)+~P24(f329(f329(f244(x63241),x63244),x63243))+P24(f329(f329(f244(x63241),x63242),x63243))+~P24(f329(f329(f244(x63241),x63242),x63244))
% 187.33/188.05 [6325]~P25(x63251)+~P24(f329(f329(f244(x63251),x63252),x63254))+P24(f329(f329(f244(x63251),x63252),x63253))+~P24(f329(f329(f243(x63251),x63254),x63253))
% 187.33/188.05 [6326]~P25(x63261)+~P24(f329(f329(f244(x63261),x63264),x63263))+P24(f329(f329(f244(x63261),x63262),x63263))+~P24(f329(f329(f243(x63261),x63262),x63264))
% 187.33/188.05 [6327]~P25(x63271)+~P24(f329(f329(f244(x63271),x63272),x63274))+P24(f329(f329(f244(x63271),x63272),x63273))+~P24(f329(f329(f244(x63271),x63274),x63273))
% 187.33/188.05 [6407]~P40(x64074,x64073,x64072)+E(x64071,f807(x64072,x64073,x64074))+~P24(f329(x64073,x64071))+~P24(f329(f329(f331(x64074),x64071),f329(f171(x64074),x64072)))
% 187.33/188.05 [6553]~P31(x65531)+~P24(f329(f329(f243(x65531),x65532),f41(x65531,x65534)))+P24(f329(f329(f243(x65531),x65532),x65533))+~P24(f329(f329(f331(x65531),x65533),x65534))
% 187.33/188.05 [6699]~P27(x66991)+~P33(x66991,f329(f329(f149(x66991),x66992),x66994))+~P24(f329(f329(f331(x66991),x66993),f329(f171(x66991),x66994)))+P24(f329(f329(f243(x66991),x66992),x66993))
% 187.33/188.05 [6789]~P31(x67891)+~P24(f329(f329(f243(x67891),f40(x67891,x67894)),x67893))+P24(f329(f329(f243(x67891),x67892),x67893))+~P24(f329(f329(f331(x67891),x67892),x67894))
% 187.33/188.05 [7196]~P27(x71961)+E(f329(f329(f115(f881(x71961,a869)),f329(f299(x71961,x71962),x71963)),f329(f299(x71961,x71963),x71964)),f329(f299(x71961,x71962),x71964))+~P24(f329(f329(f243(x71961),x71963),x71964))+~P24(f329(f329(f243(x71961),x71962),x71963))
% 187.33/188.05 [7233]P40(x72331,x72332,x72333)+~E(f811(x72333,x72332,x72331,x72334),x72334)+~P24(f329(x72332,x72334))+~P24(f329(f329(f331(x72331),x72334),f329(f171(x72331),x72333)))
% 187.33/188.05 [7307]~P27(x73071)+E(f329(f329(f115(f881(x73071,a869)),f329(f299(x73071,x73072),x73073)),f300(x73071,x73073,x73074)),f300(x73071,x73072,x73074))+~P24(f329(f329(f243(x73071),x73073),x73074))+~P24(f329(f329(f243(x73071),x73072),x73073))
% 187.33/188.05 [7373]~P27(x73731)+E(f329(f329(f115(f881(x73731,a869)),f303(x73731,x73732,x73733)),f329(f299(x73731,x73733),x73734)),f303(x73731,x73732,x73734))+~P24(f329(f329(f243(x73731),x73733),x73734))+~P24(f329(f329(f244(x73731),x73732),x73733))
% 187.33/188.05 [7394]~P27(x73941)+E(f329(f329(f115(f881(x73941,a869)),f300(x73941,x73942,x73943)),f303(x73941,x73943,x73944)),f329(f299(x73941,x73942),x73944))+~P24(f329(f329(f243(x73941),x73942),x73943))+~P24(f329(f329(f244(x73941),x73943),x73944))
% 187.33/188.05 [7426]~P27(x74261)+E(f329(f329(f115(f881(x74261,a869)),f300(x74261,x74262,x74263)),f302(x74261,x74263,x74264)),f300(x74261,x74262,x74264))+~P24(f329(f329(f243(x74261),x74263),x74264))+~P24(f329(f329(f243(x74261),x74262),x74263))
% 187.33/188.05 [7427]~P27(x74271)+E(f329(f329(f115(f881(x74271,a869)),f303(x74271,x74272,x74273)),f300(x74271,x74273,x74274)),f302(x74271,x74272,x74274))+~P24(f329(f329(f243(x74271),x74273),x74274))+~P24(f329(f329(f244(x74271),x74272),x74273))
% 187.33/188.05 [7428]~P27(x74281)+E(f329(f329(f115(f881(x74281,a869)),f302(x74281,x74282,x74283)),f303(x74281,x74283,x74284)),f303(x74281,x74282,x74284))+~P24(f329(f329(f243(x74281),x74282),x74283))+~P24(f329(f329(f244(x74281),x74283),x74284))
% 187.33/188.05 [7429]~P27(x74291)+E(f329(f329(f115(f881(x74291,a869)),f302(x74291,x74292,x74293)),f302(x74291,x74293,x74294)),f302(x74291,x74292,x74294))+~P24(f329(f329(f243(x74291),x74293),x74294))+~P24(f329(f329(f243(x74291),x74292),x74293))
% 187.33/188.05 [8233]P21(x82331,x82332,f516(x82333,x82332,x82334,x82331),x82334)+~P24(f329(f62(x82332),x82333))+~P24(f329(f62(x82331),x82334))+~P24(f329(f329(f243(a874),f329(f38(x82331),x82334)),f329(f38(x82332),x82333)))
% 187.33/188.05 [8254]P40(x82541,x82542,x82543)+~P24(f329(x82542,x82544))+P24(f329(x82542,f811(x82543,x82542,x82541,x82544)))+~P24(f329(f329(f331(x82541),x82544),f329(f171(x82541),x82543)))
% 187.33/188.05 [8305]~P76(x83051)+~E(f329(x83053,f828(x83053,x83054,x83052,x83051)),f78(x83051))+E(f329(f329(f329(f66(x83051,x83052,f81(x83051)),x83053),f78(x83051)),x83054),f78(x83051))+~P24(f329(f62(x83052),x83054))
% 187.33/188.05 [8579]~P121(x85791)+~P24(f329(f329(f243(x85791),f2(x85791)),x85793))+P24(f329(f329(f243(x85791),x85792),x85793))+~P24(f329(f329(f243(x85791),f329(f329(f254(x85791),x85792),f329(a117,x85794))),f329(f329(f254(x85791),x85793),f329(a117,x85794))))
% 187.33/188.05 [8873]P40(x88731,x88732,x88733)+~P24(f329(x88732,x88734))+~P24(f329(f329(f331(x88731),x88734),f329(f171(x88731),x88733)))+P24(f329(f329(f331(x88731),f811(x88733,x88732,x88731,x88734)),f329(f171(x88731),x88733)))
% 187.33/188.05 [8960]~P76(x89601)+E(f329(f329(f329(f66(x89601,x89602,f81(x89601)),x89603),f78(x89601)),x89604),f78(x89601))+~P24(f329(f62(x89602),x89604))+P24(f329(f329(f331(x89602),f828(x89603,x89604,x89602,x89601)),x89604))
% 187.33/188.05 [9448]~P24(f329(f329(f243(a1),x94484),f2(a1)))+P24(f329(f329(f243(a1),f329(f329(f80(a1),f329(f329(f81(a1),x94481),f45(a1,x94482,x94483))),x94484)),f2(a1)))+~P24(f329(f329(f244(a1),f2(a1)),x94483))+~P24(f329(f329(f244(a1),x94481),x94484))
% 187.33/188.05 [9899]~P24(f329(f62(x98991),x98992))+~P24(f329(f329(f331(x98991),x98994),x98992))+~P24(f329(f329(f331(x98991),x98993),x98992))+P24(f329(f329(f244(a874),f329(f38(x98991),f329(f329(f22(f881(x98991,a869)),f329(f329(f22(f881(x98991,a869)),x98992),f329(f329(f307(x98991),x98993),f193(f881(x98991,a869))))),f329(f329(f307(x98991),x98994),f193(f881(x98991,a869)))))),f329(f38(x98991),x98992)))
% 187.33/188.05 [6906]~P103(x69061)+~P24(f329(f329(f243(x69061),x69062),x69064))+~P24(f329(f329(f243(x69061),x69062),x69063))+P24(f329(f329(f243(x69061),x69062),f329(f329(f106(x69061),x69063),x69064)))
% 187.33/188.05 [6909]~P27(x69091)+~P24(f329(f329(f243(x69091),x69092),x69094))+~P24(f329(f329(f243(x69091),x69092),x69093))+P24(f329(f329(f243(x69091),x69092),f329(f329(f241(x69091),x69093),x69094)))
% 187.33/188.05 [6910]~P27(x69101)+~P24(f329(f329(f244(x69101),x69102),x69104))+~P24(f329(f329(f244(x69101),x69102),x69103))+P24(f329(f329(f244(x69101),x69102),f329(f329(f241(x69101),x69103),x69104)))
% 187.33/188.05 [6929]~P62(x69292)+E(x69291,f2(x69292))+E(f329(f329(f287(x69292),f329(f329(f254(x69292),x69291),x69293)),f329(f329(f254(x69292),x69291),x69294)),f329(f329(f254(x69292),x69291),f329(f329(f22(a874),x69293),x69294)))+~P24(f329(f329(f243(a874),x69294),x69293))
% 187.33/188.05 [6974]~P27(x69741)+~P33(x69741,f329(f329(f149(x69741),x69743),x69744))+P33(x69741,f329(f329(f149(x69741),x69742),f329(f329(f149(x69741),x69743),x69744)))+~P24(f329(f329(f243(x69741),x69742),x69743))
% 187.33/188.05 [7015]~P89(x70151)+~P24(f329(f329(f243(x70151),f2(x70151)),x70154))+~P24(f329(f329(f243(x70151),x70152),x70153))+P24(f329(f329(f243(x70151),x70152),f329(f329(f80(x70151),x70153),x70154)))
% 187.33/188.05 [7016]~P89(x70161)+~P24(f329(f329(f243(x70161),f2(x70161)),x70163))+~P24(f329(f329(f243(x70161),x70162),x70164))+P24(f329(f329(f243(x70161),x70162),f329(f329(f80(x70161),x70163),x70164)))
% 187.33/188.05 [7017]~P121(x70171)+~P24(f329(f329(f244(x70171),f2(x70171)),x70173))+~P24(f329(f329(f244(x70171),x70172),x70174))+P24(f329(f329(f244(x70171),x70172),f329(f329(f80(x70171),x70173),x70174)))
% 187.33/188.05 [7018]~P89(x70181)+~P24(f329(f329(f243(x70181),x70182),x70184))+~P24(f329(f329(f244(x70181),f2(x70181)),x70183))+P24(f329(f329(f244(x70181),x70182),f329(f329(f80(x70181),x70183),x70184)))
% 187.33/188.05 [7019]~P89(x70191)+~P24(f329(f329(f243(x70191),f2(x70191)),x70193))+~P24(f329(f329(f244(x70191),x70192),x70194))+P24(f329(f329(f244(x70191),x70192),f329(f329(f80(x70191),x70193),x70194)))
% 187.33/188.05 [7058]~P27(x70581)+P24(f329(f329(f243(x70581),x70582),x70583))+P24(f329(f329(f243(x70581),x70582),x70584))+~P24(f329(f329(f243(x70581),x70582),f329(f329(f242(x70581),x70584),x70583)))
% 187.33/188.05 [7059]~P27(x70591)+P24(f329(f329(f244(x70591),x70592),x70593))+P24(f329(f329(f244(x70591),x70592),x70594))+~P24(f329(f329(f244(x70591),x70592),f329(f329(f242(x70591),x70594),x70593)))
% 187.33/188.05 [7346]~P106(x73462)+~P60(x73461)+~P24(f329(f329(f244(f881(x73461,x73462)),x73463),x73464))+P24(f329(f329(f243(f881(x73461,x73462)),x73463),x73464))
% 187.33/188.05 [7718]~P64(x77181)+~P24(f329(f329(f244(x77181),x77184),f2(x77181)))+~P24(f329(f329(f243(x77181),x77183),f329(f329(f287(x77181),x77182),x77184)))+P24(f329(f329(f243(x77181),x77182),f329(f329(f81(x77181),x77183),x77184)))
% 187.33/188.05 [7719]~P64(x77191)+~P24(f329(f329(f244(x77191),x77194),f2(x77191)))+~P24(f329(f329(f243(x77191),x77193),f329(f329(f81(x77191),x77192),x77194)))+P24(f329(f329(f243(x77191),x77192),f329(f329(f287(x77191),x77193),x77194)))
% 187.33/188.05 [7720]~P64(x77201)+~P24(f329(f329(f244(x77201),x77204),f2(x77201)))+~P24(f329(f329(f244(x77201),x77203),f329(f329(f287(x77201),x77202),x77204)))+P24(f329(f329(f244(x77201),x77202),f329(f329(f81(x77201),x77203),x77204)))
% 187.33/188.05 [7721]~P64(x77211)+~P24(f329(f329(f244(x77211),x77214),f2(x77211)))+~P24(f329(f329(f244(x77211),x77213),f329(f329(f81(x77211),x77212),x77214)))+P24(f329(f329(f244(x77211),x77212),f329(f329(f287(x77211),x77213),x77214)))
% 187.33/188.05 [7831]~P108(x78311)+~P24(f329(f329(f243(x78311),x78312),f2(x78311)))+~P24(f329(f329(f243(x78311),x78314),x78313))+P24(f329(f329(f243(x78311),f329(f329(f81(x78311),x78312),x78313)),f329(f329(f81(x78311),x78312),x78314)))
% 187.33/188.05 [7832]~P123(x78321)+~P24(f329(f329(f244(x78321),x78322),f2(x78321)))+~P24(f329(f329(f243(x78321),x78324),x78323))+P24(f329(f329(f243(x78321),f329(f329(f81(x78321),x78322),x78323)),f329(f329(f81(x78321),x78322),x78324)))
% 187.33/188.05 [7833]~P108(x78331)+~P24(f329(f329(f243(x78331),x78333),f2(x78331)))+~P24(f329(f329(f243(x78331),x78334),x78332))+P24(f329(f329(f243(x78331),f329(f329(f81(x78331),x78332),x78333)),f329(f329(f81(x78331),x78334),x78333)))
% 187.33/188.05 [7834]~P63(x78341)+~P24(f329(f329(f243(x78341),x78343),f2(x78341)))+~P24(f329(f329(f243(x78341),x78344),x78342))+P24(f329(f329(f243(x78341),f329(f329(f287(x78341),x78342),x78343)),f329(f329(f287(x78341),x78344),x78343)))
% 187.33/188.05 [7838]~P123(x78381)+~P24(f329(f329(f244(x78381),x78383),f2(x78381)))+~P24(f329(f329(f244(x78381),x78384),x78382))+P24(f329(f329(f244(x78381),f329(f329(f81(x78381),x78382),x78383)),f329(f329(f81(x78381),x78384),x78383)))
% 187.33/188.05 [7839]~P123(x78391)+~P24(f329(f329(f244(x78391),x78392),f2(x78391)))+~P24(f329(f329(f244(x78391),x78394),x78393))+P24(f329(f329(f244(x78391),f329(f329(f81(x78391),x78392),x78393)),f329(f329(f81(x78391),x78392),x78394)))
% 187.33/188.05 [7840]~P64(x78401)+~P24(f329(f329(f244(x78401),x78403),f2(x78401)))+~P24(f329(f329(f244(x78401),x78404),x78402))+P24(f329(f329(f244(x78401),f329(f329(f287(x78401),x78402),x78403)),f329(f329(f287(x78401),x78404),x78403)))
% 187.33/188.05 [7841]~P121(x78411)+~P24(f329(f329(f244(x78411),f78(x78411)),x78412))+~P24(f329(f329(f243(a874),x78413),x78414))+P24(f329(f329(f243(x78411),f329(f329(f254(x78411),x78412),x78413)),f329(f329(f254(x78411),x78412),x78414)))
% 187.33/188.05 [7842]~P121(x78421)+~P24(f329(f329(f243(x78421),f78(x78421)),x78422))+~P24(f329(f329(f243(a874),x78423),x78424))+P24(f329(f329(f243(x78421),f329(f329(f254(x78421),x78422),x78423)),f329(f329(f254(x78421),x78422),x78424)))
% 187.33/188.05 [7844]~P121(x78441)+~P24(f329(f329(f244(x78441),f78(x78441)),x78442))+~P24(f329(f329(f244(a874),x78443),x78444))+P24(f329(f329(f244(x78441),f329(f329(f254(x78441),x78442),x78443)),f329(f329(f254(x78441),x78442),x78444)))
% 187.33/188.05 [7871]P24(f329(f329(f244(a874),f2(a874)),f329(x78711,x78712)))+~P24(f329(f62(x78713),x78714))+~P24(f329(f329(f331(x78713),x78712),x78714))+~P24(f329(f329(f244(a874),f2(a874)),f329(f329(f9(x78713,a874),x78711),x78714)))
% 187.33/188.05 [7880]~P123(x78801)+~P24(f329(f329(f244(x78801),f2(x78801)),x78802))+~P24(f329(f329(f243(x78801),x78803),x78804))+P24(f329(f329(f243(x78801),f329(f329(f81(x78801),x78802),x78803)),f329(f329(f81(x78801),x78802),x78804)))
% 187.33/188.05 [7881]~P132(x78811)+~P24(f329(f329(f243(x78811),x78813),x78814))+~P24(f329(f329(f243(x78811),f2(x78811)),x78812))+P24(f329(f329(f243(x78811),f329(f329(f81(x78811),x78812),x78813)),f329(f329(f81(x78811),x78812),x78814)))
% 187.33/188.05 [7882]~P131(x78821)+~P24(f329(f329(f243(x78821),x78823),x78824))+~P24(f329(f329(f243(x78821),f2(x78821)),x78822))+P24(f329(f329(f243(x78821),f329(f329(f81(x78821),x78822),x78823)),f329(f329(f81(x78821),x78822),x78824)))
% 187.33/188.05 [7883]~P132(x78831)+~P24(f329(f329(f243(x78831),x78832),x78834))+~P24(f329(f329(f243(x78831),f2(x78831)),x78833))+P24(f329(f329(f243(x78831),f329(f329(f81(x78831),x78832),x78833)),f329(f329(f81(x78831),x78834),x78833)))
% 187.33/188.05 [7884]~P121(x78841)+~P24(f329(f329(f243(x78841),x78842),x78844))+~P24(f329(f329(f243(x78841),f2(x78841)),x78842))+P24(f329(f329(f243(x78841),f329(f329(f254(x78841),x78842),x78843)),f329(f329(f254(x78841),x78844),x78843)))
% 187.33/188.05 [7885]~P63(x78851)+~P24(f329(f329(f243(x78851),x78852),x78854))+~P24(f329(f329(f243(x78851),f2(x78851)),x78853))+P24(f329(f329(f243(x78851),f329(f329(f287(x78851),x78852),x78853)),f329(f329(f287(x78851),x78854),x78853)))
% 187.33/188.05 [7887]~P129(x78871)+~P24(f329(f329(f244(x78871),x78873),x78874))+~P24(f329(f329(f244(x78871),f2(x78871)),x78872))+P24(f329(f329(f244(x78871),f329(f329(f81(x78871),x78872),x78873)),f329(f329(f81(x78871),x78872),x78874)))
% 187.33/188.05 [7888]~P116(x78881)+~P24(f329(f329(f244(x78881),x78883),x78884))+~P24(f329(f329(f244(x78881),f2(x78881)),x78882))+P24(f329(f329(f244(x78881),f329(f329(f81(x78881),x78882),x78883)),f329(f329(f81(x78881),x78882),x78884)))
% 187.33/188.05 [7889]~P123(x78891)+~P24(f329(f329(f244(x78891),x78892),x78894))+~P24(f329(f329(f244(x78891),f2(x78891)),x78893))+P24(f329(f329(f244(x78891),f329(f329(f81(x78891),x78892),x78893)),f329(f329(f81(x78891),x78894),x78893)))
% 187.33/188.05 [7890]~P129(x78901)+~P24(f329(f329(f244(x78901),x78902),x78904))+~P24(f329(f329(f244(x78901),f2(x78901)),x78903))+P24(f329(f329(f244(x78901),f329(f329(f81(x78901),x78902),x78903)),f329(f329(f81(x78901),x78904),x78903)))
% 187.33/188.05 [7891]~P123(x78911)+~P24(f329(f329(f244(x78911),x78913),x78914))+~P24(f329(f329(f244(x78911),f2(x78911)),x78912))+P24(f329(f329(f244(x78911),f329(f329(f81(x78911),x78912),x78913)),f329(f329(f81(x78911),x78912),x78914)))
% 187.33/188.05 [7892]~P64(x78921)+~P24(f329(f329(f244(x78921),x78922),x78924))+~P24(f329(f329(f244(x78921),f2(x78921)),x78923))+P24(f329(f329(f244(x78921),f329(f329(f287(x78921),x78922),x78923)),f329(f329(f287(x78921),x78924),x78923)))
% 187.33/188.05 [7935]~P26(x79352)+P24(f329(f329(f244(f881(x79351,x79352)),x79354),x79353))+~P24(f329(f329(f243(f881(x79351,x79352)),x79354),x79353))+P24(f329(f329(f243(f881(x79351,x79352)),x79353),x79354))
% 187.33/188.05 [7977]P24(f329(f329(f331(x79771),x79772),x79773))+P24(f329(f329(f331(x79771),x79772),x79774))+~P24(f329(f329(f243(f881(x79771,a869)),x79774),x79773))+P24(f329(f329(f244(f881(x79771,a869)),x79774),f329(f329(f307(x79771),x79772),x79773)))
% 187.33/188.05 [8138]P24(f329(f329(f331(x81381),x81382),x81383))+P24(f329(f329(f331(x81381),x81382),x81384))+~P24(f329(f329(f244(f881(x81381,a869)),x81384),f329(f329(f307(x81381),x81382),x81383)))+P24(f329(f329(f243(f881(x81381,a869)),x81384),x81383))
% 187.33/188.05 [8147]~P60(x81471)+P7(x81471,x81472,x81473)+~P24(f329(x81472,x81474))+~P24(f329(f329(f331(f875(x81471)),x81474),f329(f171(f875(x81471)),f55(x81471,x81473,f56(x81471)))))
% 187.33/188.05 [8157]~P8(x81573,x81571,x81574)+~P60(x81573)+P24(f329(x81571,x81572))+~P24(f329(f329(f331(f875(x81573)),x81572),f329(f171(f875(x81573)),f55(x81573,x81574,f56(x81573)))))
% 187.33/188.05 [8210]~P123(x82101)+P24(f329(f329(f244(x82101),x82103),x82102))+P24(f329(f329(f244(x82101),x82102),x82103))+~P24(f329(f329(f244(x82101),f329(f329(f81(x82101),x82104),x82102)),f329(f329(f81(x82101),x82104),x82103)))
% 187.33/188.05 [8211]~P123(x82111)+P24(f329(f329(f244(x82111),x82113),x82112))+P24(f329(f329(f244(x82111),x82112),x82113))+~P24(f329(f329(f244(x82111),f329(f329(f81(x82111),x82112),x82114)),f329(f329(f81(x82111),x82113),x82114)))
% 187.33/188.05 [8222]~P123(x82221)+P24(f329(f329(f244(x82221),x82224),f2(x82221)))+P24(f329(f329(f244(x82221),x82222),x82223))+~P24(f329(f329(f244(x82221),f329(f329(f81(x82221),x82222),x82224)),f329(f329(f81(x82221),x82223),x82224)))
% 187.33/188.05 [8223]~P123(x82231)+P24(f329(f329(f244(x82231),x82234),f2(x82231)))+P24(f329(f329(f244(x82231),x82232),x82233))+~P24(f329(f329(f244(x82231),f329(f329(f81(x82231),x82234),x82232)),f329(f329(f81(x82231),x82234),x82233)))
% 187.33/188.05 [8227]~P123(x82271)+P24(f329(f329(f244(x82271),x82272),x82273))+P24(f329(f329(f244(x82271),f2(x82271)),x82274))+~P24(f329(f329(f244(x82271),f329(f329(f81(x82271),x82274),x82273)),f329(f329(f81(x82271),x82274),x82272)))
% 187.33/188.05 [8228]~P123(x82281)+P24(f329(f329(f244(x82281),x82282),x82283))+P24(f329(f329(f244(x82281),f2(x82281)),x82284))+~P24(f329(f329(f244(x82281),f329(f329(f81(x82281),x82283),x82284)),f329(f329(f81(x82281),x82282),x82284)))
% 187.33/188.05 [8241]~P123(x82411)+P24(f329(f329(f244(x82411),x82412),f2(x82411)))+P24(f329(f329(f244(x82411),f2(x82411)),x82412))+~P24(f329(f329(f244(x82411),f329(f329(f81(x82411),x82413),x82412)),f329(f329(f81(x82411),x82414),x82412)))
% 187.33/188.05 [8242]~P123(x82421)+P24(f329(f329(f244(x82421),x82422),f2(x82421)))+P24(f329(f329(f244(x82421),f2(x82421)),x82422))+~P24(f329(f329(f244(x82421),f329(f329(f81(x82421),x82422),x82423)),f329(f329(f81(x82421),x82422),x82424)))
% 187.33/188.05 [8268]~P123(x82681)+~P24(f329(f329(f244(x82681),x82684),f2(x82681)))+P24(f329(f329(f243(x82681),x82682),x82683))+~P24(f329(f329(f243(x82681),f329(f329(f81(x82681),x82684),x82683)),f329(f329(f81(x82681),x82684),x82682)))
% 187.33/188.05 [8269]~P123(x82691)+~P24(f329(f329(f244(x82691),x82694),f2(x82691)))+P24(f329(f329(f244(x82691),x82692),x82693))+~P24(f329(f329(f244(x82691),f329(f329(f81(x82691),x82694),x82693)),f329(f329(f81(x82691),x82694),x82692)))
% 187.33/188.05 [8281]~P121(x82813)+~P24(f329(f329(f244(x82813),f78(x82813)),x82814))+P24(f329(f329(f243(a874),x82811),x82812))+~P24(f329(f329(f243(x82813),f329(f329(f254(x82813),x82814),x82811)),f329(f329(f254(x82813),x82814),x82812)))
% 187.33/188.05 [8283]~P121(x82833)+~P24(f329(f329(f244(x82833),f78(x82833)),x82834))+P24(f329(f329(f244(a874),x82831),x82832))+~P24(f329(f329(f244(x82833),f329(f329(f254(x82833),x82834),x82831)),f329(f329(f254(x82833),x82834),x82832)))
% 187.33/188.05 [8293]~P123(x82931)+P24(f329(f329(f243(x82931),x82932),x82933))+~P24(f329(f329(f244(x82931),f2(x82931)),x82934))+~P24(f329(f329(f243(x82931),f329(f329(f81(x82931),x82934),x82932)),f329(f329(f81(x82931),x82934),x82933)))
% 187.33/188.05 [8294]~P129(x82941)+P24(f329(f329(f243(x82941),x82942),x82943))+~P24(f329(f329(f244(x82941),f2(x82941)),x82944))+~P24(f329(f329(f243(x82941),f329(f329(f81(x82941),x82944),x82942)),f329(f329(f81(x82941),x82944),x82943)))
% 187.33/188.05 [8295]~P129(x82951)+P24(f329(f329(f243(x82951),x82952),x82953))+~P24(f329(f329(f244(x82951),f2(x82951)),x82954))+~P24(f329(f329(f243(x82951),f329(f329(f81(x82951),x82952),x82954)),f329(f329(f81(x82951),x82953),x82954)))
% 187.33/188.05 [8296]~P123(x82961)+P24(f329(f329(f244(x82961),x82962),x82963))+~P24(f329(f329(f244(x82961),f2(x82961)),x82964))+~P24(f329(f329(f244(x82961),f329(f329(f81(x82961),x82964),x82962)),f329(f329(f81(x82961),x82964),x82963)))
% 187.33/188.05 [8297]~P129(x82971)+P24(f329(f329(f244(x82971),x82972),x82973))+~P24(f329(f329(f243(x82971),f2(x82971)),x82974))+~P24(f329(f329(f244(x82971),f329(f329(f81(x82971),x82974),x82972)),f329(f329(f81(x82971),x82974),x82973)))
% 187.33/188.05 [8298]~P125(x82981)+P24(f329(f329(f244(x82981),x82982),x82983))+~P24(f329(f329(f243(x82981),f2(x82981)),x82984))+~P24(f329(f329(f244(x82981),f329(f329(f81(x82981),x82984),x82982)),f329(f329(f81(x82981),x82984),x82983)))
% 187.33/188.05 [8299]~P121(x82991)+~P24(f329(f329(f243(x82991),f2(x82991)),x82993))+P24(f329(f329(f244(x82991),x82992),x82993))+~P24(f329(f329(f244(x82991),f329(f329(f254(x82991),x82992),x82994)),f329(f329(f254(x82991),x82993),x82994)))
% 187.33/188.05 [8300]~P129(x83001)+P24(f329(f329(f244(x83001),x83002),x83003))+~P24(f329(f329(f243(x83001),f2(x83001)),x83004))+~P24(f329(f329(f244(x83001),f329(f329(f81(x83001),x83002),x83004)),f329(f329(f81(x83001),x83003),x83004)))
% 187.33/188.05 [8301]~P125(x83011)+P24(f329(f329(f244(x83011),x83012),x83013))+~P24(f329(f329(f243(x83011),f2(x83011)),x83014))+~P24(f329(f329(f244(x83011),f329(f329(f81(x83011),x83012),x83014)),f329(f329(f81(x83011),x83013),x83014)))
% 187.33/188.05 [8344]P24(f329(f329(f331(x83441),x83442),x83443))+~P24(f329(f329(f243(f881(x83441,a869)),x83443),x83444))+~P24(f329(f329(f244(f881(x83441,a869)),x83443),x83444))+P24(f329(f329(f244(f881(x83441,a869)),x83443),f329(f329(f307(x83441),x83442),x83444)))
% 187.33/188.05 [8602]~P60(x86021)+~P96(x86022)+~E(f329(x86023,f804(x86024,x86023,x86021,x86022)),f329(x86024,f804(x86024,x86023,x86021,x86022)))+P24(f329(f329(f91(f881(x86021,x86022)),x86023),x86024))
% 187.33/188.05 [8717]E(f329(f329(f22(a1),f396(x87171,x87172,x87173,x87174)),f397(x87171,x87172,x87173,x87174)),x87174)+~P24(f329(f329(f244(a1),f2(a1)),x87173))+~P24(f329(f329(f243(a1),x87171),x87174))+P24(f329(f329(f243(a1),x87171),f329(f329(f80(a1),x87174),x87173)))
% 187.33/188.05 [8718]E(f329(f329(f22(a1),f405(x87181,x87182,x87183,x87184)),f406(x87181,x87182,x87183,x87184)),x87184)+~P24(f329(f329(f244(a1),f2(a1)),x87183))+~P24(f329(f329(f244(a1),x87181),x87184))+P24(f329(f329(f244(a1),x87181),f329(f329(f80(a1),x87184),x87183)))
% 187.33/188.05 [8853]~E(f329(f329(f163(x88531),x88533),f692(x88534,x88533,x88531,x88532)),f329(f329(f163(x88531),x88534),f692(x88534,x88533,x88531,x88532)))+E(f329(f329(f174(x88531),x88532),x88533),f329(f329(f174(x88531),x88532),x88534))+~P24(f329(f329(f243(a874),x88532),f329(f194(f875(x88531)),x88533)))+~P24(f329(f329(f243(a874),x88532),f329(f194(f875(x88531)),x88534)))
% 187.33/188.05 [8926]~P24(f329(f329(f244(a1),f2(a1)),x89263))+~P24(f329(f329(f243(a1),x89261),x89264))+P24(f329(f329(f331(a1),f396(x89261,x89262,x89263,x89264)),x89262))+P24(f329(f329(f243(a1),x89261),f329(f329(f80(a1),x89264),x89263)))
% 187.33/188.05 [8927]~P24(f329(f329(f244(a1),f2(a1)),x89273))+~P24(f329(f329(f244(a1),x89271),x89274))+P24(f329(f329(f331(a1),f405(x89271,x89272,x89273,x89274)),x89272))+P24(f329(f329(f244(a1),x89271),f329(f329(f80(a1),x89274),x89273)))
% 187.33/188.05 [8969]~P103(x89691)+~P24(f329(f62(x89691),x89693))+~P24(f329(f329(f331(x89691),x89694),x89693))+P24(f329(f329(f243(x89691),f329(f329(f65(x89691,x89691,f106(x89691)),x89692),x89693)),f329(f329(f106(x89691),x89694),x89692)))
% 187.33/188.05 [8970]~P27(x89701)+~P24(f329(f62(x89701),x89703))+~P24(f329(f329(f331(x89701),x89704),x89703))+P24(f329(f329(f243(x89701),f329(f329(f65(x89701,x89701,f241(x89701)),x89702),x89703)),f329(f329(f241(x89701),x89704),x89702)))
% 187.33/188.05 [9017]E(f329(f329(f174(x90171),x90172),x90173),f329(f329(f174(x90171),x90172),x90174))+P24(f329(f329(f244(a874),f692(x90173,x90174,x90171,x90172)),x90172))+~P24(f329(f329(f243(a874),x90172),f329(f194(f875(x90171)),x90173)))+~P24(f329(f329(f243(a874),x90172),f329(f194(f875(x90171)),x90174)))
% 187.33/188.05 [9022]~P24(f329(f329(f244(a1),f2(a1)),x90223))+~P24(f329(f329(f243(a1),x90221),x90222))+P24(f329(f329(f331(a1),f397(x90221,x90224,x90223,x90222)),f300(a1,f78(a1),x90223)))+P24(f329(f329(f243(a1),x90221),f329(f329(f80(a1),x90222),x90223)))
% 187.33/188.05 [9023]~P24(f329(f329(f244(a1),f2(a1)),x90233))+~P24(f329(f329(f244(a1),x90231),x90232))+P24(f329(f329(f331(a1),f406(x90231,x90234,x90233,x90232)),f300(a1,f78(a1),x90233)))+P24(f329(f329(f244(a1),x90231),f329(f329(f80(a1),x90232),x90233)))
% 187.33/188.05 [9186]~E(f329(f177(x91861,x91862),x91863),f329(f177(x91861,x91862),x91864))+E(f329(f171(f880(x91861,x91862)),x91863),f329(f171(f880(x91861,x91862)),x91864))+~P24(f329(f135(x91861),f329(f329(f152(f880(x91861,x91862),x91861),f263(x91861,x91862)),x91864)))+~P24(f329(f135(x91861),f329(f329(f152(f880(x91861,x91862),x91861),f263(x91861,x91862)),x91863)))
% 187.33/188.05 [9198]E(f329(f177(x91981,x91982),x91983),f329(f177(x91981,x91982),x91984))+~E(f329(f171(f880(x91981,x91982)),x91983),f329(f171(f880(x91981,x91982)),x91984))+~P24(f329(f135(x91981),f329(f329(f152(f880(x91981,x91982),x91981),f263(x91981,x91982)),x91984)))+~P24(f329(f135(x91981),f329(f329(f152(f880(x91981,x91982),x91981),f263(x91981,x91982)),x91983)))
% 187.33/188.05 [9343]~P27(x93431)+~P24(f329(f62(x93431),x93434))+P24(f329(f329(f331(x93431),f644(x93432,x93433,x93434,x93431)),x93434))+P24(f329(f329(f243(x93431),f329(f329(f65(x93431,x93431,f242(x93431)),x93432),x93434)),f329(f329(f242(x93431),x93433),x93432)))
% 187.33/188.05 [9344]~P102(x93441)+~P24(f329(f62(x93441),x93444))+P24(f329(f329(f331(x93441),f649(x93442,x93443,x93444,x93441)),x93444))+P24(f329(f329(f243(x93441),f329(f329(f65(x93441,x93441,f115(x93441)),x93442),x93444)),f329(f329(f115(x93441),x93443),x93442)))
% 187.33/188.05 [9466]~P102(x94661)+~P24(f329(f62(x94661),x94663))+~P24(f329(f329(f243(x94661),f649(x94662,x94664,x94663,x94661)),x94664))+P24(f329(f329(f243(x94661),f329(f329(f65(x94661,x94661,f115(x94661)),x94662),x94663)),f329(f329(f115(x94661),x94664),x94662)))
% 187.33/188.05 [9467]~P27(x94671)+~P24(f329(f62(x94671),x94673))+~P24(f329(f329(f243(x94671),f644(x94672,x94674,x94673,x94671)),x94674))+P24(f329(f329(f243(x94671),f329(f329(f65(x94671,x94671,f242(x94671)),x94672),x94673)),f329(f329(f242(x94671),x94674),x94672)))
% 187.33/188.05 [9470]~P24(f329(f329(f243(a1),f2(a1)),x94704))+~P24(f329(f329(f244(a1),f2(a1)),x94703))+~P24(f329(f329(f244(a1),x94704),x94701))+P24(f329(f329(f244(a1),f329(f329(f80(a1),f329(f329(f81(a1),x94701),f45(a1,x94702,x94703))),x94704)),f329(f329(f81(a1),x94701),x94703)))
% 187.33/188.05 [9868]E(x98681,x98682)+P24(f329(f329(f331(f880(f875(x98683),f875(x98683))),f329(f329(f264(f875(x98683),f875(x98683)),x98682),x98681)),f145(x98683,x98684)))+P24(f329(f329(f331(f880(f875(x98683),f875(x98683))),f329(f329(f264(f875(x98683),f875(x98683)),x98681),x98682)),f145(x98683,x98684)))+~P24(f329(f329(f331(f880(x98683,x98683)),f329(f329(f264(x98683,x98683),f665(x98681,x98682,x98684,x98683)),f667(x98681,x98682,x98684,x98683))),x98684))
% 187.33/188.05 [9869]E(x98691,x98692)+P24(f329(f329(f331(f880(f875(x98693),f875(x98693))),f329(f329(f264(f875(x98693),f875(x98693)),x98692),x98691)),f145(x98693,x98694)))+P24(f329(f329(f331(f880(f875(x98693),f875(x98693))),f329(f329(f264(f875(x98693),f875(x98693)),x98691),x98692)),f145(x98693,x98694)))+~P24(f329(f329(f331(f880(x98693,x98693)),f329(f329(f264(x98693,x98693),f667(x98691,x98692,x98694,x98693)),f665(x98691,x98692,x98694,x98693))),x98694))
% 187.33/188.05 [7416]~P102(x74161)+~P24(f329(f329(f243(x74161),x74163),x74164))+~P24(f329(f329(f243(x74161),x74162),x74164))+P24(f329(f329(f243(x74161),f329(f329(f115(x74161),x74162),x74163)),x74164))
% 187.33/188.05 [7419]~P27(x74191)+~P24(f329(f329(f243(x74191),x74193),x74194))+~P24(f329(f329(f243(x74191),x74192),x74194))+P24(f329(f329(f243(x74191),f329(f329(f242(x74191),x74192),x74193)),x74194))
% 187.33/188.05 [7420]~P27(x74201)+~P24(f329(f329(f244(x74201),x74203),x74204))+~P24(f329(f329(f244(x74201),x74202),x74204))+P24(f329(f329(f244(x74201),f329(f329(f242(x74201),x74202),x74203)),x74204))
% 187.33/188.05 [7743]~E(x77431,x77433)+E(f137(a874,f329(f299(a874,x77431),x77432)),f329(f329(f149(a874),x77433),x77434))+~E(f137(a874,f329(f299(a874,f329(f329(f80(a874),x77431),f78(a874))),x77432)),x77434)+~P24(f329(f329(f244(a874),x77431),x77432))
% 187.33/188.05 [7754]~P27(x77541)+P24(f329(f329(f243(x77541),x77542),x77543))+P24(f329(f329(f243(x77541),x77544),x77543))+~P24(f329(f329(f243(x77541),f329(f329(f241(x77541),x77544),x77542)),x77543))
% 187.33/188.05 [7755]~P27(x77551)+P24(f329(f329(f244(x77551),x77552),x77553))+P24(f329(f329(f244(x77551),x77554),x77553))+~P24(f329(f329(f244(x77551),f329(f329(f241(x77551),x77554),x77552)),x77553))
% 187.33/188.05 [8038]~P63(x80381)+~P24(f329(f329(f244(x80381),f2(x80381)),x80383))+~P24(f329(f329(f243(x80381),x80382),f329(f329(f287(x80381),x80384),x80383)))+P24(f329(f329(f243(x80381),f329(f329(f81(x80381),x80382),x80383)),x80384))
% 187.33/188.05 [8039]~P64(x80391)+~P24(f329(f329(f244(x80391),f2(x80391)),x80393))+~P24(f329(f329(f243(x80391),x80392),f329(f329(f287(x80391),x80394),x80393)))+P24(f329(f329(f243(x80391),f329(f329(f81(x80391),x80392),x80393)),x80394))
% 187.33/188.05 [8040]~P63(x80401)+~P24(f329(f329(f244(x80401),f2(x80401)),x80403))+~P24(f329(f329(f243(x80401),x80402),f329(f329(f81(x80401),x80404),x80403)))+P24(f329(f329(f243(x80401),f329(f329(f287(x80401),x80402),x80403)),x80404))
% 187.33/188.05 [8042]~P64(x80421)+~P24(f329(f329(f244(x80421),f2(x80421)),x80423))+~P24(f329(f329(f243(x80421),x80422),f329(f329(f81(x80421),x80424),x80423)))+P24(f329(f329(f243(x80421),f329(f329(f287(x80421),x80422),x80423)),x80424))
% 187.33/188.05 [8043]~P63(x80431)+~P24(f329(f329(f244(x80431),f2(x80431)),x80433))+~P24(f329(f329(f244(x80431),x80432),f329(f329(f287(x80431),x80434),x80433)))+P24(f329(f329(f244(x80431),f329(f329(f81(x80431),x80432),x80433)),x80434))
% 187.33/188.05 [8044]~P64(x80441)+~P24(f329(f329(f244(x80441),f2(x80441)),x80443))+~P24(f329(f329(f244(x80441),x80442),f329(f329(f287(x80441),x80444),x80443)))+P24(f329(f329(f244(x80441),f329(f329(f81(x80441),x80442),x80443)),x80444))
% 187.33/188.05 [8045]~P63(x80451)+~P24(f329(f329(f244(x80451),f2(x80451)),x80453))+~P24(f329(f329(f244(x80451),x80452),f329(f329(f81(x80451),x80454),x80453)))+P24(f329(f329(f244(x80451),f329(f329(f287(x80451),x80452),x80453)),x80454))
% 187.33/188.05 [8047]~P64(x80471)+~P24(f329(f329(f244(x80471),f2(x80471)),x80473))+~P24(f329(f329(f244(x80471),x80472),f329(f329(f81(x80471),x80474),x80473)))+P24(f329(f329(f244(x80471),f329(f329(f287(x80471),x80472),x80473)),x80474))
% 187.33/188.05 [8179]~P63(x81791)+~P24(f329(f329(f244(x81791),f2(x81791)),x81794))+P24(f329(f329(f243(x81791),x81792),f329(f329(f81(x81791),x81793),x81794)))+~P24(f329(f329(f243(x81791),f329(f329(f287(x81791),x81792),x81794)),x81793))
% 187.33/188.05 [8180]~P63(x81801)+~P24(f329(f329(f244(x81801),f2(x81801)),x81804))+P24(f329(f329(f243(x81801),x81802),f329(f329(f287(x81801),x81803),x81804)))+~P24(f329(f329(f243(x81801),f329(f329(f81(x81801),x81802),x81804)),x81803))
% 187.33/188.05 [8182]~P64(x81821)+~P24(f329(f329(f244(x81821),f2(x81821)),x81824))+P24(f329(f329(f243(x81821),x81822),f329(f329(f81(x81821),x81823),x81824)))+~P24(f329(f329(f243(x81821),f329(f329(f287(x81821),x81822),x81824)),x81823))
% 187.33/188.05 [8183]~P64(x81831)+~P24(f329(f329(f244(x81831),f2(x81831)),x81834))+P24(f329(f329(f243(x81831),x81832),f329(f329(f287(x81831),x81833),x81834)))+~P24(f329(f329(f243(x81831),f329(f329(f81(x81831),x81832),x81834)),x81833))
% 187.33/188.05 [8184]~P63(x81841)+~P24(f329(f329(f244(x81841),f2(x81841)),x81844))+P24(f329(f329(f244(x81841),x81842),f329(f329(f81(x81841),x81843),x81844)))+~P24(f329(f329(f244(x81841),f329(f329(f287(x81841),x81842),x81844)),x81843))
% 187.33/188.05 [8185]~P63(x81851)+~P24(f329(f329(f244(x81851),f2(x81851)),x81854))+P24(f329(f329(f244(x81851),x81852),f329(f329(f287(x81851),x81853),x81854)))+~P24(f329(f329(f244(x81851),f329(f329(f81(x81851),x81852),x81854)),x81853))
% 187.33/188.05 [8187]~P64(x81871)+~P24(f329(f329(f244(x81871),f2(x81871)),x81874))+P24(f329(f329(f244(x81871),x81872),f329(f329(f81(x81871),x81873),x81874)))+~P24(f329(f329(f244(x81871),f329(f329(f287(x81871),x81872),x81874)),x81873))
% 187.33/188.05 [8188]~P64(x81881)+~P24(f329(f329(f244(x81881),f2(x81881)),x81884))+P24(f329(f329(f244(x81881),x81882),f329(f329(f287(x81881),x81883),x81884)))+~P24(f329(f329(f244(x81881),f329(f329(f81(x81881),x81882),x81884)),x81883))
% 187.33/188.05 [8348]~P64(x83481)+~P24(f329(f329(f244(x83481),x83483),f2(x83481)))+~P24(f329(f329(f243(x83481),f329(f329(f287(x83481),x83484),x83483)),x83482))+P24(f329(f329(f243(x83481),f329(f329(f81(x83481),x83482),x83483)),x83484))
% 187.33/188.05 [8349]~P64(x83491)+~P24(f329(f329(f244(x83491),x83493),f2(x83491)))+~P24(f329(f329(f243(x83491),f329(f329(f81(x83491),x83494),x83493)),x83492))+P24(f329(f329(f243(x83491),f329(f329(f287(x83491),x83492),x83493)),x83494))
% 187.33/188.05 [8350]~P64(x83501)+~P24(f329(f329(f244(x83501),x83503),f2(x83501)))+~P24(f329(f329(f244(x83501),f329(f329(f287(x83501),x83504),x83503)),x83502))+P24(f329(f329(f244(x83501),f329(f329(f81(x83501),x83502),x83503)),x83504))
% 187.33/188.05 [8351]~P64(x83511)+~P24(f329(f329(f244(x83511),x83513),f2(x83511)))+~P24(f329(f329(f244(x83511),f329(f329(f81(x83511),x83514),x83513)),x83512))+P24(f329(f329(f244(x83511),f329(f329(f287(x83511),x83512),x83513)),x83514))
% 187.33/188.05 [8361]~P24(f329(x83611,x83614))+~P24(f329(f329(f244(a874),x83612),f329(f329(f81(a874),x83613),f329(a117,x83614))))+P24(f329(x83611,f329(f329(f39(a874),x83612),x83613)))+~P24(f329(f329(f243(a874),f329(f329(f81(a874),x83613),x83614)),x83612))
% 187.33/188.05 [8576]~P102(x85761)+~P24(f329(f62(x85761),x85764))+~P24(f329(f329(f331(x85761),x85762),x85764))+P24(f329(f329(f243(x85761),f329(f329(f115(x85761),x85762),x85763)),f329(f329(f65(x85761,x85761,f115(x85761)),x85763),x85764)))
% 187.33/188.05 [8577]~P27(x85771)+~P24(f329(f62(x85771),x85774))+~P24(f329(f329(f331(x85771),x85772),x85774))+P24(f329(f329(f243(x85771),f329(f329(f242(x85771),x85772),x85773)),f329(f329(f65(x85771,x85771,f242(x85771)),x85773),x85774)))
% 187.33/188.05 [8719]~P24(f329(f62(x87191),x87192))+E(f329(f38(x87191),f329(f329(f22(f881(x87191,a869)),x87192),f329(f329(f307(x87191),x87193),x87194))),f329(f329(f22(a874),f329(f38(x87191),f329(f329(f22(f881(x87191,a869)),x87192),x87194))),f78(a874)))+P24(f329(f329(f331(x87191),x87193),x87194))+~P24(f329(f329(f331(x87191),x87193),x87192))
% 187.33/188.05 [8789]E(f329(f329(f80(a1),f398(x87891,x87892,x87893,x87894)),f399(x87891,x87892,x87893,x87894)),x87894)+~P24(f329(f329(f244(a1),f2(a1)),x87893))+~P24(f329(f329(f243(a1),x87894),x87891))+P24(f329(f329(f243(a1),f329(f329(f22(a1),x87894),x87893)),x87891))
% 187.33/188.05 [8790]E(f329(f329(f80(a1),f403(x87901,x87902,x87903,x87904)),f404(x87901,x87902,x87903,x87904)),x87904)+~P24(f329(f329(f244(a1),f2(a1)),x87903))+~P24(f329(f329(f244(a1),x87904),x87901))+P24(f329(f329(f244(a1),f329(f329(f22(a1),x87904),x87903)),x87901))
% 187.33/188.05 [9002]~P24(f329(f329(f244(a1),f2(a1)),x90023))+~P24(f329(f329(f243(a1),x90024),x90021))+P24(f329(f329(f331(a1),f398(x90021,x90022,x90023,x90024)),x90022))+P24(f329(f329(f243(a1),f329(f329(f22(a1),x90024),x90023)),x90021))
% 187.33/188.05 [9003]~P24(f329(f329(f244(a1),f2(a1)),x90033))+~P24(f329(f329(f244(a1),x90034),x90031))+P24(f329(f329(f331(a1),f403(x90031,x90032,x90033,x90034)),x90032))+P24(f329(f329(f244(a1),f329(f329(f22(a1),x90034),x90033)),x90031))
% 187.33/188.05 [9088]~P24(f329(f329(f244(a1),f2(a1)),x90882))+~P24(f329(f329(f243(a1),x90881),x90883))+P24(f329(f329(f331(a1),f399(x90883,x90884,x90882,x90881)),f300(a1,f78(a1),x90882)))+P24(f329(f329(f243(a1),f329(f329(f22(a1),x90881),x90882)),x90883))
% 187.33/188.05 [9089]~P24(f329(f329(f244(a1),f2(a1)),x90892))+~P24(f329(f329(f244(a1),x90891),x90893))+P24(f329(f329(f331(a1),f404(x90893,x90894,x90892,x90891)),f300(a1,f78(a1),x90892)))+P24(f329(f329(f244(a1),f329(f329(f22(a1),x90891),x90892)),x90893))
% 187.33/188.05 [9105]~P24(f329(f329(f243(a1),f2(a1)),x91054))+~P24(f329(f329(f244(a1),f2(a1)),x91053))+~P24(f329(f329(f244(a1),x91054),x91051))+P24(f329(f329(f243(a1),f2(a1)),f329(f329(f80(a1),f329(f329(f81(a1),x91051),f45(a1,x91052,x91053))),x91054)))
% 187.33/188.05 [9169]~P103(x91691)+~P24(f329(f62(x91691),x91694))+~P24(f329(f329(f243(x91691),x91692),f648(x91693,x91692,x91694,x91691)))+P24(f329(f329(f243(x91691),f329(f329(f106(x91691),x91692),x91693)),f329(f329(f65(x91691,x91691,f106(x91691)),x91693),x91694)))
% 187.33/188.05 [9170]~P27(x91701)+~P24(f329(f62(x91701),x91704))+~P24(f329(f329(f243(x91701),x91702),f643(x91703,x91702,x91704,x91701)))+P24(f329(f329(f243(x91701),f329(f329(f241(x91701),x91702),x91703)),f329(f329(f65(x91701,x91701,f241(x91701)),x91703),x91704)))
% 187.33/188.05 [9185]~P24(f329(f329(f243(a1),x91854),f2(a1)))+~P24(f329(f329(f244(a1),f2(a1)),x91852))+~P24(f329(f329(f244(a1),x91851),x91854))+P24(f329(f329(f244(a1),f329(f329(f81(a1),x91851),x91852)),f329(f329(f80(a1),f329(f329(f81(a1),x91851),f45(a1,x91853,x91852))),x91854)))
% 187.33/188.05 [9207]P24(f329(f62(x92071),x92072))+~P24(f329(f62(x92071),x92073))+~P24(f329(f329(f331(f881(x92071,a869)),x92072),f329(f329(f61(x92071),x92073),x92074)))+~P24(f329(f329(f243(f881(f880(x92071,x92071),a869)),x92074),f329(f329(f266(x92071,x92071),x92073),f329(f16(f881(x92071,a869),x92071),x92073))))
% 187.33/188.05 [9235]~P27(x92351)+~P24(f329(f62(x92351),x92354))+P24(f329(f329(f331(x92351),f643(x92352,x92353,x92354,x92351)),x92354))+P24(f329(f329(f243(x92351),f329(f329(f241(x92351),x92353),x92352)),f329(f329(f65(x92351,x92351,f241(x92351)),x92352),x92354)))
% 187.33/188.05 [9236]~P103(x92361)+~P24(f329(f62(x92361),x92364))+P24(f329(f329(f331(x92361),f648(x92362,x92363,x92364,x92361)),x92364))+P24(f329(f329(f243(x92361),f329(f329(f106(x92361),x92363),x92362)),f329(f329(f65(x92361,x92361,f106(x92361)),x92362),x92364)))
% 187.33/188.05 [9633]~P24(f329(f62(x96332),x96334))+~P24(f329(f62(x96331),x96333))+~P24(f329(f329(f243(a874),f329(f38(x96332),x96334)),f329(f38(x96331),x96333)))+P24(f329(f329(f243(f881(x96331,a869)),f329(f308(x96332,x96331,f516(x96333,x96331,x96334,x96332)),x96334)),x96333))
% 187.33/188.05 [9284]~P24(f329(f329(f331(x92841),x92842),x92844))+P24(f329(f329(f331(x92841),x92842),x92843))+~P24(f329(f329(f244(f881(x92841,a869)),x92844),f329(f329(f307(x92841),x92842),x92843)))+P24(f329(f329(f244(f881(x92841,a869)),f329(f329(f22(f881(x92841,a869)),x92844),f329(f329(f307(x92841),x92842),f193(f881(x92841,a869))))),x92843))
% 187.33/188.05 [9444]~P24(f329(f329(f331(x94441),x94442),x94444))+P24(f329(f329(f331(x94441),x94442),x94443))+P24(f329(f329(f244(f881(x94441,a869)),x94444),f329(f329(f307(x94441),x94442),x94443)))+~P24(f329(f329(f244(f881(x94441,a869)),f329(f329(f22(f881(x94441,a869)),x94444),f329(f329(f307(x94441),x94442),f193(f881(x94441,a869))))),x94443))
% 187.33/188.05 [9473]P24(f329(f329(f331(x94731),x94732),x94733))+~P24(f329(f329(f243(f881(x94731,a869)),x94734),x94733))+P24(f329(f329(f244(f881(x94731,a869)),x94734),f329(f329(f307(x94731),x94732),x94733)))+~P24(f329(f329(f244(f881(x94731,a869)),f329(f329(f22(f881(x94731,a869)),x94734),f329(f329(f307(x94731),x94732),f193(f881(x94731,a869))))),x94733))
% 187.33/188.05 [9478]~P24(f329(f329(f331(x94781),x94783),x94782))+~P24(f329(f329(f244(f881(x94781,a869)),x94782),x94784))+P24(f329(f329(f244(f881(x94781,a869)),x94782),f329(f329(f307(x94781),x94783),x94784)))+~P24(f329(f329(f244(f881(x94781,a869)),f329(f329(f22(f881(x94781,a869)),x94782),f329(f329(f307(x94781),x94783),f193(f881(x94781,a869))))),x94784))
% 187.33/188.05 [9492]~P24(f329(f329(f243(f881(x94921,a869)),x94922),x94924))+~P24(f329(f329(f244(f881(x94921,a869)),x94922),x94924))+P24(f329(f329(f244(f881(x94921,a869)),x94922),f329(f329(f307(x94921),x94923),x94924)))+~P24(f329(f329(f244(f881(x94921,a869)),f329(f329(f22(f881(x94921,a869)),x94922),f329(f329(f307(x94921),x94923),f193(f881(x94921,a869))))),x94924))
% 187.33/188.05 [9536]~P106(x95362)+~P60(x95361)+~P24(f329(f329(f243(f881(x95361,x95362)),x95363),x95364))+P24(f329(f59(x95361),f329(f329(f18(x95361,x95362,a869),f329(f329(f8(x95362,f881(x95362,a869),x95361),f243(x95362)),x95363)),x95364)))
% 187.33/188.05 [9680]~P106(x96802)+~P60(x96801)+P24(f329(f329(f243(f881(x96801,x96802)),x96803),x96804))+~P24(f329(f59(x96801),f329(f329(f18(x96801,x96802,a869),f329(f329(f8(x96802,f881(x96802,a869),x96801),f243(x96802)),x96803)),x96804)))
% 187.33/188.05 [9852]E(f329(f329(f163(x98521),f329(f329(f163(f875(x98521)),f179(x98521,x98522)),x98523)),x98524),f329(f329(f163(x98521),f329(f329(f163(f875(x98521)),x98522),x98524)),x98523))+~P24(f329(f329(f244(a874),x98523),f329(f194(f875(f875(x98521))),f179(x98521,x98522))))+~P33(a874,f329(f167(a874),f329(f329(f152(f875(x98521),a874),f194(f875(x98521))),x98522)))+~P24(f329(f329(f244(a874),x98524),f329(f194(f875(f875(x98521))),f329(f134(f875(x98521),f329(f329(f8(a874,a869,f875(x98521)),f329(f244(a874),x98523)),f194(f875(x98521)))),x98522))))
% 187.33/188.05 [9881]~P24(f329(f329(f331(f880(a874,a874)),x98814),x98811))+~P24(f329(f329(f331(f880(f880(a874,a874),f880(a874,a874))),f329(f329(f264(f880(a874,a874),f880(a874,a874)),x98814),x98812)),a35))+~P24(f329(f329(f331(f880(f881(f880(a874,a874),a869),f881(f880(a874,a874),a869))),f329(f329(f264(f881(f880(a874,a874),a869),f881(f880(a874,a874),a869)),x98811),x98813)),a36))+P24(f329(f329(f331(f880(f881(f880(a874,a874),a869),f881(f880(a874,a874),a869))),f329(f329(f264(f881(f880(a874,a874),a869),f881(f880(a874,a874),a869)),x98811),f329(f329(f307(f880(a874,a874)),x98812),x98813))),a36))
% 187.33/188.05 [9882]~P24(f329(f329(f331(f880(a874,a874)),x98824),x98821))+~P24(f329(f329(f331(f880(f880(a874,a874),f880(a874,a874))),f329(f329(f264(f880(a874,a874),f880(a874,a874)),x98824),x98822)),a70))+~P24(f329(f329(f331(f880(f881(f880(a874,a874),a869),f881(f880(a874,a874),a869))),f329(f329(f264(f881(f880(a874,a874),a869),f881(f880(a874,a874),a869)),x98821),x98823)),a71))+P24(f329(f329(f331(f880(f881(f880(a874,a874),a869),f881(f880(a874,a874),a869))),f329(f329(f264(f881(f880(a874,a874),a869),f881(f880(a874,a874),a869)),x98821),f329(f329(f307(f880(a874,a874)),x98822),x98823))),a71))
% 187.33/188.05 [9765]~P106(x97652)+~P60(x97651)+~P24(f329(f329(f244(f881(x97651,x97652)),x97653),x97654))+P24(f329(f58(x97651),f329(f329(f8(a869,a869,x97651),a324),f329(f329(f18(x97651,x97652,a869),f329(f329(f8(x97652,f881(x97652,a869),x97651),a326),x97653)),x97654))))
% 187.33/188.05 [9895]~P24(f329(f329(f331(f880(a874,a874)),x98954),x98953))+~P24(f329(f329(f331(f880(f880(a874,a874),f880(a874,a874))),f329(f329(f264(f880(a874,a874),f880(a874,a874)),x98951),x98954)),a70))+~P24(f329(f329(f331(f880(f881(f880(a874,a874),a869),f881(f880(a874,a874),a869))),f329(f329(f264(f881(f880(a874,a874),a869),f881(f880(a874,a874),a869)),x98952),x98953)),a69))+P24(f329(f329(f331(f880(f881(f880(a874,a874),a869),f881(f880(a874,a874),a869))),f329(f329(f264(f881(f880(a874,a874),a869),f881(f880(a874,a874),a869)),f329(f329(f307(f880(a874,a874)),x98951),x98952)),x98953)),a69))
% 187.33/188.05 [9896]~P24(f329(f329(f331(f880(a874,a874)),x98964),x98963))+~P24(f329(f329(f331(f880(f880(a874,a874),f880(a874,a874))),f329(f329(f264(f880(a874,a874),f880(a874,a874)),x98961),x98964)),a35))+~P24(f329(f329(f331(f880(f881(f880(a874,a874),a869),f881(f880(a874,a874),a869))),f329(f329(f264(f881(f880(a874,a874),a869),f881(f880(a874,a874),a869)),x98962),x98963)),a37))+P24(f329(f329(f331(f880(f881(f880(a874,a874),a869),f881(f880(a874,a874),a869))),f329(f329(f264(f881(f880(a874,a874),a869),f881(f880(a874,a874),a869)),f329(f329(f307(f880(a874,a874)),x98961),x98962)),x98963)),a37))
% 187.33/188.05 [6009]~P5(x60094,x60091)+~P24(f329(f329(x60091,x60092),x60095))+P24(f329(f329(x60091,x60092),x60093))+~P24(f329(f329(x60091,x60095),x60093))
% 187.33/188.05 [5271]~P69(x52715)+E(x52711,x52712)+~E(x52713,x52714)+~E(f329(f329(f22(x52715),x52713),x52714),f329(f329(f22(x52715),x52711),x52712))
% 187.33/188.05 [6117]~P13(x61175,x61171,x61173)+E(f329(f329(x61171,x61172),f329(x61173,x61174)),f329(x61173,x61174))+~P24(f329(f62(x61175),x61174))+~P24(f329(f329(f331(x61175),x61172),x61174))
% 187.33/188.05 [6311]~P80(x63111)+~E(f329(f329(f22(x63111),x63114),x63115),f329(f329(f22(x63111),x63112),x63113))+~P24(f329(f329(f243(x63111),x63114),x63115))+P24(f329(f329(f243(x63111),x63112),x63113))
% 187.33/188.05 [6313]~P80(x63131)+~E(f329(f329(f22(x63131),x63134),x63135),f329(f329(f22(x63131),x63132),x63133))+~P24(f329(f329(f244(x63131),x63134),x63135))+P24(f329(f329(f244(x63131),x63132),x63133))
% 187.33/188.05 [7274]~E(x72742,f329(f329(f149(x72741),x72744),x72745))+P24(f329(f329(f331(f875(x72741)),x72742),f159(x72741,x72743)))+~P24(f329(f329(f331(f875(x72741)),x72745),f159(x72741,x72743)))+~P24(f329(f329(f331(x72741),x72744),x72743))
% 187.33/188.05 [7694]~E(f329(f194(f875(x76941)),x76943),f329(f194(f875(x76942)),x76944))+~E(f329(f329(f152(f880(x76941,x76942),x76942),f267(x76941,x76942)),x76945),x76944)+~E(f329(f329(f152(f880(x76941,x76942),x76941),f263(x76941,x76942)),x76945),x76943)+E(f329(f329(f181(x76941,x76942),x76943),x76944),x76945)
% 187.33/188.05 [8035]~P106(x80351)+P24(f329(f329(f244(f881(x80351,a869)),f300(x80351,x80352,x80353)),f300(x80351,x80354,x80355)))+~P24(f329(f329(f243(x80351),x80354),x80355))+P24(f329(f329(f243(x80351),x80352),x80353))
% 187.33/188.05 [8131]~P106(x81311)+P24(f329(f329(f243(f881(x81311,a869)),f300(x81311,x81312,x81313)),f300(x81311,x81314,x81315)))+~P24(f329(f329(f243(x81311),x81313),x81315))+~P24(f329(f329(f243(x81311),x81314),x81312))
% 187.33/188.05 [8256]~P27(x82561)+P24(f329(f329(f243(x82561),x82562),x82563))+P24(f329(f329(f243(x82561),x82564),x82563))+~P24(f329(f329(f243(f881(x82561,a869)),f329(f299(x82561,x82563),x82562)),f329(f299(x82561,x82564),x82565)))
% 187.33/188.05 [8257]~P27(x82571)+P24(f329(f329(f243(x82571),x82572),x82573))+P24(f329(f329(f243(x82571),x82572),x82574))+~P24(f329(f329(f243(f881(x82571,a869)),f329(f299(x82571,x82573),x82572)),f329(f299(x82571,x82575),x82574)))
% 187.33/188.05 [8497]~P106(x84971)+~P24(f329(f329(f243(f881(x84971,a869)),f300(x84971,x84974,x84972)),f300(x84971,x84975,x84973)))+P24(f329(f329(f243(x84971),x84972),x84973))+~P24(f329(f329(f243(x84971),x84974),x84972))
% 187.33/188.05 [8498]~P106(x84981)+~P24(f329(f329(f244(f881(x84981,a869)),f300(x84981,x84984,x84982)),f300(x84981,x84985,x84983)))+P24(f329(f329(f243(x84981),x84982),x84983))+~P24(f329(f329(f243(x84981),x84984),x84982))
% 187.33/188.05 [8499]~P106(x84991)+~P24(f329(f329(f243(f881(x84991,a869)),f300(x84991,x84993,x84994)),f300(x84991,x84992,x84995)))+P24(f329(f329(f243(x84991),x84992),x84993))+~P24(f329(f329(f243(x84991),x84993),x84994))
% 187.33/188.05 [8500]~P106(x85001)+~P24(f329(f329(f244(f881(x85001,a869)),f300(x85001,x85003,x85004)),f300(x85001,x85002,x85005)))+P24(f329(f329(f243(x85001),x85002),x85003))+~P24(f329(f329(f243(x85001),x85003),x85004))
% 187.33/188.05 [6008]~P13(x60082,x60085,x60083)+E(x60081,f193(f881(x60082,a869)))+~P24(f329(f62(x60082),x60081))+E(f329(x60083,f329(f329(f307(x60082),x60084),x60081)),f329(f329(x60085,x60084),f329(x60083,x60081)))
% 187.33/188.05 [6776]~E(x67761,x67762)+~E(f329(f329(f106(f881(x67763,a869)),x67764),x67765),f193(f881(x67763,a869)))+~P24(f329(f329(f331(x67763),x67762),x67765))+~P24(f329(f329(f331(x67763),x67761),x67764))
% 187.33/188.05 [6858]~P14(x68582,x68585,x68581)+~P24(f329(f62(x68582),x68584))+E(f329(x68581,f329(f329(f307(x68582),x68583),x68584)),f329(f329(f65(x68582,x68582,x68585),x68583),x68584))+P24(f329(f329(f331(x68582),x68583),x68584))
% 187.33/188.05 [6925]~P72(x69252)+~P24(f329(f62(x69251),x69255))+E(f329(f329(f6(x69251,x69252),x69253),f329(f329(f307(x69251),x69254),x69255)),f329(f329(f80(x69252),f329(x69253,x69254)),f329(f329(f6(x69251,x69252),x69253),x69255)))+P24(f329(f329(f331(x69251),x69254),x69255))
% 187.33/188.05 [6927]~P76(x69272)+~P24(f329(f62(x69271),x69275))+E(f329(f329(f9(x69271,x69272),x69273),f329(f329(f307(x69271),x69274),x69275)),f329(f329(f81(x69272),f329(x69273,x69274)),f329(f329(f9(x69271,x69272),x69273),x69275)))+P24(f329(f329(f331(x69271),x69274),x69275))
% 187.33/188.05 [7432]~P14(x74322,x74325,x74321)+~P24(f329(f62(x74322),x74324))+E(f329(x74321,f329(f329(f307(x74322),x74323),x74324)),x74323)+~E(f329(f329(f22(f881(x74322,a869)),x74324),f329(f329(f307(x74322),x74323),f193(f881(x74322,a869)))),f193(f881(x74322,a869)))
% 187.33/188.05 [7747]~P24(f329(x77471,x77473))+~P24(f329(f329(f199(x77472),x77473),x77475))+~P24(f329(f329(f199(f32(x77471,x77472)),x77475),x77474))+P24(f329(f329(f199(f32(x77471,x77472)),x77473),x77474))
% 187.33/188.05 [7801]~P102(x78011)+~P24(f329(f329(f243(x78011),x78013),x78015))+~P24(f329(f329(f243(x78011),x78012),x78014))+P24(f329(f329(f243(x78011),f329(f329(f115(x78011),x78012),x78013)),f329(f329(f115(x78011),x78014),x78015)))
% 187.33/188.05 [7802]~P103(x78021)+~P24(f329(f329(f243(x78021),x78023),x78025))+~P24(f329(f329(f243(x78021),x78022),x78024))+P24(f329(f329(f243(x78021),f329(f329(f106(x78021),x78022),x78023)),f329(f329(f106(x78021),x78024),x78025)))
% 187.33/188.05 [7803]~P86(x78031)+~P24(f329(f329(f243(x78031),x78033),x78035))+~P24(f329(f329(f243(x78031),x78032),x78034))+P24(f329(f329(f243(x78031),f329(f329(f80(x78031),x78032),x78033)),f329(f329(f80(x78031),x78034),x78035)))
% 187.33/188.05 [7804]~P27(x78041)+~P24(f329(f329(f243(x78041),x78043),x78045))+~P24(f329(f329(f243(x78041),x78042),x78044))+P24(f329(f329(f243(x78041),f329(f329(f241(x78041),x78042),x78043)),f329(f329(f241(x78041),x78044),x78045)))
% 187.33/188.05 [7805]~P27(x78051)+~P24(f329(f329(f243(x78051),x78053),x78055))+~P24(f329(f329(f243(x78051),x78052),x78054))+P24(f329(f329(f243(x78051),f329(f329(f242(x78051),x78052),x78053)),f329(f329(f242(x78051),x78054),x78055)))
% 187.33/188.05 [7806]~P84(x78061)+~P24(f329(f329(f243(x78061),x78063),x78065))+~P24(f329(f329(f244(x78061),x78062),x78064))+P24(f329(f329(f244(x78061),f329(f329(f80(x78061),x78062),x78063)),f329(f329(f80(x78061),x78064),x78065)))
% 187.33/188.05 [7807]~P84(x78071)+~P24(f329(f329(f243(x78071),x78072),x78074))+~P24(f329(f329(f244(x78071),x78073),x78075))+P24(f329(f329(f244(x78071),f329(f329(f80(x78071),x78072),x78073)),f329(f329(f80(x78071),x78074),x78075)))
% 187.33/188.05 [7808]~P84(x78081)+~P24(f329(f329(f244(x78081),x78083),x78085))+~P24(f329(f329(f244(x78081),x78082),x78084))+P24(f329(f329(f244(x78081),f329(f329(f80(x78081),x78082),x78083)),f329(f329(f80(x78081),x78084),x78085)))
% 187.33/188.05 [7945]~P139(x79455)+E(x79451,x79452)+E(x79453,x79454)+~E(f329(f329(f80(x79455),f329(f329(f81(x79455),x79453),x79451)),f329(f329(f81(x79455),x79454),x79452)),f329(f329(f80(x79455),f329(f329(f81(x79455),x79453),x79452)),f329(f329(f81(x79455),x79454),x79451)))
% 187.33/188.05 [8086]P34(x80861,x80862,x80863)+~P23(x80861,x80864,x80865)+~P34(x80861,x80862,f569(x80865,x80864,x80861,x80862))+~P24(f329(f329(f331(f873(x80861)),x80863),x80865))
% 187.33/188.05 [8154]~P27(x81544)+~P24(f329(f135(x81541),x81543))+P24(f329(f329(f331(x81541),x81542),f329(f171(x81541),x81543)))+P24(f329(f135(x81541),f329(f329(f146(x81541,x81544,x81545),x81542),x81543)))
% 187.33/188.05 [8302]~P69(x83021)+E(f329(f329(f22(x83021),f329(f329(f6(a874,x83021),x83022),f329(f299(a874,x83023),x83024))),f329(f329(f6(a874,x83021),x83022),f329(f299(a874,x83023),x83025))),f329(f329(f6(a874,x83021),x83022),f329(f299(a874,x83025),x83024)))+~P24(f329(f329(f243(a874),x83025),x83024))+~P24(f329(f329(f243(a874),x83023),x83025))
% 187.33/188.05 [8303]~P72(x83031)+E(f329(f329(f80(x83031),f329(f329(f6(a874,x83031),x83032),f329(f299(a874,x83033),x83034))),f329(f329(f6(a874,x83031),x83032),f329(f299(a874,x83034),x83035))),f329(f329(f6(a874,x83031),x83032),f329(f299(a874,x83033),x83035)))+~P24(f329(f329(f243(a874),x83034),x83035))+~P24(f329(f329(f243(a874),x83033),x83034))
% 187.33/188.05 [8633]~P62(x86332)+E(x86331,f2(x86332))+E(x86333,f2(x86332))+E(f329(f329(f287(x86332),f329(f329(f22(x86332),f329(f329(f81(x86332),x86334),x86331)),f329(f329(f81(x86332),x86335),x86333))),f329(f329(f81(x86332),x86333),x86331)),f329(f329(f22(x86332),f329(f329(f287(x86332),x86334),x86333)),f329(f329(f287(x86332),x86335),x86331)))
% 187.33/188.05 [8634]~P62(x86342)+E(x86341,f2(x86342))+E(x86343,f2(x86342))+E(f329(f329(f287(x86342),f329(f329(f80(x86342),f329(f329(f81(x86342),x86344),x86341)),f329(f329(f81(x86342),x86345),x86343))),f329(f329(f81(x86342),x86343),x86341)),f329(f329(f80(x86342),f329(f329(f287(x86342),x86344),x86343)),f329(f329(f287(x86342),x86345),x86341)))
% 187.33/188.05 [8643]~E(x86432,f329(x86433,x86431))+E(x86431,f511(x86432,x86433,x86434,x86435))+~P21(x86435,x86434,x86433,f252(f881(x86435,a869)))+~P24(f329(f329(f331(x86434),x86432),f329(f308(x86435,x86434,x86433),f252(f881(x86435,a869)))))
% 187.33/188.05 [8838]~P115(x88381)+~P24(f329(f329(f244(x88381),f329(f75(x88381),x88382)),x88384))+P24(f329(f329(f244(x88381),f329(f329(f81(x88381),f329(f75(x88381),x88382)),f329(f75(x88381),x88383))),f329(f329(f81(x88381),x88384),x88385)))+~P24(f329(f329(f244(x88381),f329(f75(x88381),x88383)),x88385))
% 187.33/188.05 [8855]~P23(x88551,x88555,x88554)+P34(x88551,x88552,x88553)+P24(f329(f329(f331(f873(x88551)),f569(x88554,x88555,x88551,x88552)),x88555))+~P24(f329(f329(f331(f873(x88551)),x88553),x88554))
% 187.33/188.05 [8961]~P21(x89611,x89613,x89615,x89612)+~P24(f329(f62(x89613),x89614))+P24(f329(f329(f243(a874),f329(f38(x89611),x89612)),f329(f38(x89613),x89614)))+~P24(f329(f329(f243(f881(x89613,a869)),f329(f308(x89611,x89613,x89615),x89612)),x89614))
% 187.33/188.05 [9031]~P72(x90312)+~P21(x90311,x90311,x90314,x90315)+~P24(f329(f62(x90311),x90315))+E(f329(f329(f6(x90311,x90312),f329(f73(x90311,x90312,x90311,x90313),x90314)),x90315),f329(f329(f6(x90311,x90312),x90313),f329(f308(x90311,x90311,x90314),x90315)))
% 187.33/188.05 [9032]~P76(x90322)+~P21(x90321,x90321,x90324,x90325)+~P24(f329(f62(x90321),x90325))+E(f329(f329(f9(x90321,x90322),f329(f73(x90321,x90322,x90321,x90323),x90324)),x90325),f329(f329(f9(x90321,x90322),x90323),f329(f308(x90321,x90321,x90324),x90325)))
% 187.33/188.05 [9146]~P42(x91461,x91462)+~P24(f329(f329(f331(x91461),x91463),x91464))+~P24(f329(f329(f331(x91461),x91465),x91464))+~P24(f329(f329(f331(f880(x91461,x91461)),f329(f329(f264(x91461,x91461),x91465),f639(x91462,x91461,x91464))),x91462))
% 187.33/188.05 [9184]~P21(x91842,x91843,x91845,x91841)+E(x91841,f193(f881(x91842,a869)))+E(f329(f308(x91843,x91842,f514(x91844,x91843,x91842,x91841)),x91844),x91841)+~P24(f329(f329(f243(f881(x91843,a869)),f329(f308(x91842,x91843,x91845),x91841)),x91844))
% 187.33/188.05 [9662]~P27(x96625)+~P31(x96625)+P24(f329(f329(f331(x96621),f436(x96622,x96623,x96621,x96624,x96625)),x96623))+~P24(f329(f329(f244(x96625),x96624),f329(f329(f42(x96621,x96625),x96623),x96622)))
% 187.33/188.05 [9667]~P27(x96671)+~P31(x96671)+P24(f329(f329(f244(x96671),x96672),f329(x96673,f436(x96673,x96674,x96675,x96672,x96671))))+~P24(f329(f329(f244(x96671),x96672),f329(f329(f42(x96675,x96671),x96674),x96673)))
% 187.33/188.05 [9745]~P70(x97451)+~P24(f329(f67(x97451,x97451,f81(x97451),x97452,x97453),x97455))+P24(f329(f329(f331(x97451),x97452),x97453))+P24(f329(f67(x97451,x97451,f81(x97451),x97454,f329(f329(f307(x97451),x97452),x97453)),f329(f329(f81(x97451),x97454),x97455)))
% 187.33/188.05 [9963]~P72(x99632)+~P24(f329(f62(x99631),x99635))+E(f329(f329(f6(x99631,x99632),f329(f329(f7(x99631,x99632,x99632),f329(f329(f18(x99631,x99632,f881(x99632,x99632)),f329(f329(f8(a869,f881(x99632,f881(x99632,x99632)),x99631),f101(x99632)),f329(a326,x99633))),x99634)),f2(x99632))),x99635),f2(x99632))+P24(f329(f329(f331(x99631),x99633),x99635))
% 187.33/188.05 [9964]~P76(x99642)+~P24(f329(f62(x99641),x99645))+E(f329(f329(f9(x99641,x99642),f329(f329(f7(x99641,x99642,x99642),f329(f329(f18(x99641,x99642,f881(x99642,x99642)),f329(f329(f8(a869,f881(x99642,f881(x99642,x99642)),x99641),f101(x99642)),f329(a326,x99643))),x99644)),f78(x99642))),x99645),f78(x99642))+P24(f329(f329(f331(x99641),x99643),x99645))
% 187.33/188.05 [9965]~P72(x99652)+~P24(f329(f62(x99651),x99655))+E(f329(f329(f6(x99651,x99652),f329(f329(f7(x99651,x99652,x99652),f329(f329(f18(x99651,x99652,f881(x99652,x99652)),f329(f329(f8(a869,f881(x99652,f881(x99652,x99652)),x99651),f101(x99652)),f329(a326,x99653))),x99654)),f2(x99652))),x99655),f329(x99654,x99653))+~P24(f329(f329(f331(x99651),x99653),x99655))
% 187.33/188.05 [9966]~P76(x99662)+~P24(f329(f62(x99661),x99665))+E(f329(f329(f9(x99661,x99662),f329(f329(f7(x99661,x99662,x99662),f329(f329(f18(x99661,x99662,f881(x99662,x99662)),f329(f329(f8(a869,f881(x99662,f881(x99662,x99662)),x99661),f101(x99662)),f329(a326,x99663))),x99664)),f78(x99662))),x99665),f329(x99664,x99663))+~P24(f329(f329(f331(x99661),x99663),x99665))
% 187.33/188.05 [10021]~P72(x100212)+~P24(f329(f62(x100211),x100215))+E(f329(f329(f6(x100211,x100212),f329(f329(f7(x100211,x100212,x100212),f329(f329(f18(x100211,x100212,f881(x100212,x100212)),f329(f329(f8(a869,f881(x100212,f881(x100212,x100212)),x100211),f101(x100212)),f329(f329(f7(x100211,x100211,a869),a326),x100213))),x100214)),f2(x100212))),x100215),f2(x100212))+P24(f329(f329(f331(x100211),x100213),x100215))
% 187.33/188.05 [10022]~P76(x100222)+~P24(f329(f62(x100221),x100225))+E(f329(f329(f9(x100221,x100222),f329(f329(f7(x100221,x100222,x100222),f329(f329(f18(x100221,x100222,f881(x100222,x100222)),f329(f329(f8(a869,f881(x100222,f881(x100222,x100222)),x100221),f101(x100222)),f329(f329(f7(x100221,x100221,a869),a326),x100223))),x100224)),f78(x100222))),x100225),f78(x100222))+P24(f329(f329(f331(x100221),x100223),x100225))
% 187.33/188.05 [10024]~P72(x100242)+~P24(f329(f62(x100241),x100245))+E(f329(f329(f6(x100241,x100242),f329(f329(f7(x100241,x100242,x100242),f329(f329(f18(x100241,x100242,f881(x100242,x100242)),f329(f329(f8(a869,f881(x100242,f881(x100242,x100242)),x100241),f101(x100242)),f329(f329(f7(x100241,x100241,a869),a326),x100243))),x100244)),f2(x100242))),x100245),f329(x100244,x100243))+~P24(f329(f329(f331(x100241),x100243),x100245))
% 187.33/188.05 [10025]~P76(x100252)+~P24(f329(f62(x100251),x100255))+E(f329(f329(f9(x100251,x100252),f329(f329(f7(x100251,x100252,x100252),f329(f329(f18(x100251,x100252,f881(x100252,x100252)),f329(f329(f8(a869,f881(x100252,f881(x100252,x100252)),x100251),f101(x100252)),f329(f329(f7(x100251,x100251,a869),a326),x100253))),x100254)),f78(x100252))),x100255),f329(x100254,x100253))+~P24(f329(f329(f331(x100251),x100253),x100255))
% 187.33/188.05 [7800]~P69(x78002)+~P24(f329(f62(x78001),x78004))+E(f329(f329(f6(x78001,x78002),x78003),f329(f329(f22(f881(x78001,a869)),x78004),f329(f329(f307(x78001),x78005),f193(f881(x78001,a869))))),f329(f329(f6(x78001,x78002),x78003),x78004))+P24(f329(f329(f331(x78001),x78005),x78004))
% 187.33/188.05 [8308]~P107(x83082)+~P24(f329(f62(x83081),x83084))+E(f329(f329(f6(x83081,x83082),x83083),f329(f329(f22(f881(x83081,a869)),x83084),f329(f329(f307(x83081),x83085),f193(f881(x83081,a869))))),f329(f329(f22(x83082),f329(f329(f6(x83081,x83082),x83083),x83084)),f329(x83083,x83085)))+~P24(f329(f329(f331(x83081),x83085),x83084))
% 187.33/188.05 [8309]~P69(x83092)+~P24(f329(f62(x83091),x83094))+E(f329(f329(f6(x83091,x83092),x83093),f329(f329(f22(f881(x83091,a869)),x83094),f329(f329(f307(x83091),x83095),f193(f881(x83091,a869))))),f329(f329(f22(x83092),f329(f329(f6(x83091,x83092),x83093),x83094)),f329(x83093,x83095)))+~P24(f329(f329(f331(x83091),x83095),x83094))
% 187.33/188.05 [8340]~P69(x83401)+~P24(f329(f62(x83402),x83404))+E(f329(f329(f22(x83401),f329(f329(f6(x83402,x83401),x83403),x83404)),f329(f329(f6(x83402,x83401),x83403),x83405)),f329(f329(f6(x83402,x83401),x83403),f329(f329(f22(f881(x83402,a869)),x83404),x83405)))+~P24(f329(f329(f243(f881(x83402,a869)),x83405),x83404))
% 187.33/188.05 [8360]P24(f329(f62(x83601),f329(x83602,x83603)))+~P24(f329(f62(x83604),x83605))+~P24(f329(f329(f331(x83604),x83603),x83605))+~P24(f329(f62(x83601),f329(f329(f42(x83604,f881(x83601,a869)),x83605),x83602)))
% 187.33/188.05 [8801]~P6(x88011,x88015,x88014)+~E(f329(f283(x88011,x88011,x88014),f329(f329(f307(x88011),x88012),f193(f881(x88011,a869)))),f329(f283(x88011,x88011,x88014),f329(f329(f307(x88011),x88013),f193(f881(x88011,a869)))))+~P24(f329(f329(f331(x88011),x88013),x88015))+P24(f329(f329(f331(f880(x88011,x88011)),f329(f329(f264(x88011,x88011),x88012),x88013)),x88014))
% 187.33/188.05 [9103]~P24(f329(x91031,x91035))+P24(f329(x91031,f838(x91031,x91032,x91033,x91034)))+P24(f329(x91031,f831(x91031,x91032,x91033,x91034)))+~P24(f329(f329(f331(x91034),x91035),f329(f329(f115(f881(x91034,a869)),x91033),x91032)))
% 187.33/188.05 [9289]~P24(f329(x92891,x92895))+P24(f329(x92891,f831(x92891,x92892,x92893,x92894)))+P24(f329(f329(f331(x92894),f838(x92891,x92892,x92893,x92894)),x92892))+~P24(f329(f329(f331(x92894),x92895),f329(f329(f115(f881(x92894,a869)),x92893),x92892)))
% 187.33/188.05 [9290]~P24(f329(x92901,x92905))+P24(f329(x92901,f838(x92901,x92902,x92903,x92904)))+P24(f329(f329(f331(x92904),f831(x92901,x92902,x92903,x92904)),x92903))+~P24(f329(f329(f331(x92904),x92905),f329(f329(f115(f881(x92904,a869)),x92903),x92902)))
% 187.33/188.05 [9296]P24(f329(x92961,x92962))+~P24(f329(x92961,f351(x92961,x92963,x92964,x92965)))+~P24(f329(x92961,f868(x92961,x92963,x92964,x92965)))+~P24(f329(f329(f331(x92965),x92962),f329(f329(f115(f881(x92965,a869)),x92964),x92963)))
% 187.33/188.05 [9338]E(x93381,x93382)+~P24(f329(f329(f331(f880(x93383,x93383)),f329(f329(f264(x93383,x93383),x93381),x93382)),f305(x93383,x93385)))+P24(f329(f329(f331(x93383),x93381),x93384))+~P24(f329(f329(f243(f881(f880(x93383,x93383),a869)),x93385),f329(f329(f266(x93383,x93383),x93384),f329(f16(f881(x93383,a869),x93383),x93384))))
% 187.33/188.05 [9357]P24(f329(x93571,x93572))+~P24(f329(x93571,f868(x93571,x93574,x93575,x93573)))+P24(f329(f329(f331(x93573),f351(x93571,x93574,x93575,x93573)),x93574))+~P24(f329(f329(f331(x93573),x93572),f329(f329(f115(f881(x93573,a869)),x93575),x93574)))
% 187.33/188.05 [9358]P24(f329(x93581,x93582))+~P24(f329(x93581,f351(x93581,x93584,x93585,x93583)))+P24(f329(f329(f331(x93583),f868(x93581,x93584,x93585,x93583)),x93585))+~P24(f329(f329(f331(x93583),x93582),f329(f329(f115(f881(x93583,a869)),x93585),x93584)))
% 187.33/188.05 [9418]P24(f329(x94181,x94182))+P24(f329(f329(f331(x94183),f351(x94181,x94184,x94185,x94183)),x94184))+P24(f329(f329(f331(x94183),f868(x94181,x94184,x94185,x94183)),x94185))+~P24(f329(f329(f331(x94183),x94182),f329(f329(f115(f881(x94183,a869)),x94185),x94184)))
% 187.33/188.05 [9420]~P24(f329(x94202,x94205))+P24(f329(f329(f331(x94201),f838(x94202,x94203,x94204,x94201)),x94203))+P24(f329(f329(f331(x94201),f831(x94202,x94203,x94204,x94201)),x94204))+~P24(f329(f329(f331(x94201),x94205),f329(f329(f115(f881(x94201,a869)),x94204),x94203)))
% 187.33/188.05 [9569]~P6(x95691,x95695,x95694)+~P24(f329(f329(f331(x95691),x95693),x95695))+P24(f329(f329(f331(f880(x95691,x95691)),f329(f329(f264(x95691,x95691),x95692),x95693)),x95694))+~P24(f329(f329(f243(f881(x95691,a869)),f329(f283(x95691,x95691,x95694),f329(f329(f307(x95691),x95693),f193(f881(x95691,a869))))),f329(f283(x95691,x95691,x95694),f329(f329(f307(x95691),x95692),f193(f881(x95691,a869))))))
% 187.33/188.05 [9692]~P27(x96925)+~P31(x96925)+P24(f329(f329(f331(x96921),f625(x96922,x96923,x96924,x96921,x96925)),x96924))+~P24(f329(f329(f244(x96925),f329(f329(f43(x96921,x96925),x96924),x96923)),x96922))
% 187.33/188.05 [9725]~P86(x97255)+~P83(x97255)+P24(f329(f329(f331(x97251),f714(x97252,x97253,x97254,x97251,x97255)),f329(f171(x97251),x97254)))+P24(f329(f329(f243(x97255),f329(f164(x97255),f329(f329(f152(x97251,x97255),x97253),x97254))),f329(f164(x97255),f329(f329(f152(x97251,x97255),x97252),x97254))))
% 187.33/188.05 [9841]~P27(x98411)+~P31(x98411)+P24(f329(f329(f244(x98411),f329(x98412,f625(x98413,x98412,x98414,x98415,x98411))),x98413))+~P24(f329(f329(f244(x98411),f329(f329(f43(x98415,x98411),x98414),x98412)),x98413))
% 187.33/188.05 [9981]~P86(x99811)+~P83(x99811)+~P24(f329(f329(f243(x99811),f329(x99813,f714(x99815,x99813,x99814,x99812,x99811))),f329(x99815,f714(x99815,x99813,x99814,x99812,x99811))))+P24(f329(f329(f243(x99811),f329(f164(x99811),f329(f329(f152(x99812,x99811),x99813),x99814))),f329(f164(x99811),f329(f329(f152(x99812,x99811),x99815),x99814))))
% 187.33/188.05 [8652]~P72(x86521)+~P24(f329(f62(x86524),x86525))+~P24(f329(f329(f331(x86524),x86523),x86525))+E(f329(f329(f80(x86521),f329(x86522,x86523)),f329(f329(f6(x86524,x86521),x86522),f329(f329(f22(f881(x86524,a869)),x86525),f329(f329(f307(x86524),x86523),f193(f881(x86524,a869)))))),f329(f329(f6(x86524,x86521),x86522),x86525))
% 187.33/188.05 [8653]~P76(x86531)+~P24(f329(f62(x86534),x86535))+~P24(f329(f329(f331(x86534),x86533),x86535))+E(f329(f329(f81(x86531),f329(x86532,x86533)),f329(f329(f9(x86534,x86531),x86532),f329(f329(f22(f881(x86534,a869)),x86535),f329(f329(f307(x86534),x86533),f193(f881(x86534,a869)))))),f329(f329(f9(x86534,x86531),x86532),x86535))
% 187.33/188.05 [8708]~P14(x87081,x87084,x87085)+~P24(f329(f62(x87081),x87082))+E(f329(f329(f22(f881(x87081,a869)),x87082),f329(f329(f307(x87081),x87083),f193(f881(x87081,a869)))),f193(f881(x87081,a869)))+E(f329(f329(x87084,x87083),f329(x87085,f329(f329(f22(f881(x87081,a869)),x87082),f329(f329(f307(x87081),x87083),f193(f881(x87081,a869)))))),f329(x87085,f329(f329(f307(x87081),x87083),x87082)))
% 187.33/188.05 [9084]~P76(x90841)+~P24(f329(f62(x90842),x90845))+~P24(f329(f62(x90842),x90844))+E(f329(f329(f81(x90841),f329(f329(f9(x90842,x90841),x90843),f329(f329(f115(f881(x90842,a869)),x90844),x90845))),f329(f329(f9(x90842,x90841),x90843),f329(f329(f106(f881(x90842,a869)),x90844),x90845))),f329(f329(f81(x90841),f329(f329(f9(x90842,x90841),x90843),x90844)),f329(f329(f9(x90842,x90841),x90843),x90845)))
% 187.33/188.05 [9085]~P72(x90851)+~P24(f329(f62(x90852),x90855))+~P24(f329(f62(x90852),x90854))+E(f329(f329(f80(x90851),f329(f329(f6(x90852,x90851),x90853),f329(f329(f115(f881(x90852,a869)),x90854),x90855))),f329(f329(f6(x90852,x90851),x90853),f329(f329(f106(f881(x90852,a869)),x90854),x90855))),f329(f329(f80(x90851),f329(f329(f6(x90852,x90851),x90853),x90854)),f329(f329(f6(x90852,x90851),x90853),x90855)))
% 187.33/188.05 [9226]~P69(x92261)+~P24(f329(f62(x92262),x92265))+~P24(f329(f62(x92262),x92264))+E(f329(f329(f22(x92261),f329(f329(f80(x92261),f329(f329(f6(x92262,x92261),x92263),x92264)),f329(f329(f6(x92262,x92261),x92263),x92265))),f329(f329(f6(x92262,x92261),x92263),f329(f329(f106(f881(x92262,a869)),x92264),x92265))),f329(f329(f6(x92262,x92261),x92263),f329(f329(f115(f881(x92262,a869)),x92264),x92265)))
% 187.33/188.05 [9429]~P21(x94291,x94292,x94293,x94295)+~P21(x94291,x94292,x94293,x94294)+P21(x94291,x94292,x94293,f329(f329(f115(f881(x94291,a869)),x94294),x94295))+~E(f329(f329(f106(f881(x94292,a869)),f329(f308(x94291,x94292,x94293),f329(f329(f22(f881(x94291,a869)),x94294),x94295))),f329(f308(x94291,x94292,x94293),f329(f329(f22(f881(x94291,a869)),x94295),x94294))),f193(f881(x94292,a869)))
% 187.33/188.05 [9544]E(x95441,f2(a1))+~P24(f329(f329(f244(a1),f2(a1)),x95443))+~P24(f329(f49(x95442,x95441),f329(f329(f264(a1,a1),x95444),x95445)))+P24(f329(f49(x95442,f329(f329(f81(a1),x95441),x95443)),f329(f329(f264(a1,a1),f329(f329(f39(a1),x95444),x95443)),f329(f329(f80(a1),f329(f329(f81(a1),x95441),f45(a1,x95444,x95443))),x95445))))
% 187.33/188.05 [9552]~P24(f329(f329(f244(a874),f2(a874)),x95523))+~P24(f329(f329(f244(a874),f2(a874)),x95522))+~P24(f329(f48(x95521,x95522),f329(f329(f264(a874,a874),x95524),x95525)))+P24(f329(f48(x95521,f329(f329(f81(a874),x95522),x95523)),f329(f329(f264(a874,a874),f329(f329(f39(a874),x95524),x95523)),f329(f329(f80(a874),f329(f329(f81(a874),x95522),f45(a874,x95524,x95523))),x95525))))
% 187.33/188.05 [9601]~P76(x96011)+~P24(f329(f62(x96012),x96015))+~P24(f329(f62(x96012),x96014))+E(f329(f329(f81(x96011),f329(f329(f329(f66(x96011,x96012,f81(x96011)),x96013),f78(x96011)),f329(f329(f115(f881(x96012,a869)),x96014),x96015))),f329(f329(f329(f66(x96011,x96012,f81(x96011)),x96013),f78(x96011)),f329(f329(f106(f881(x96012,a869)),x96014),x96015))),f329(f329(f81(x96011),f329(f329(f329(f66(x96011,x96012,f81(x96011)),x96013),f78(x96011)),x96014)),f329(f329(f329(f66(x96011,x96012,f81(x96011)),x96013),f78(x96011)),x96015)))
% 187.33/188.05 [9603]~E(f329(f329(f174(x96031),x96035),x96032),f329(f329(f174(x96031),x96035),x96033))+P24(f329(f329(f331(f880(f875(x96031),f875(x96031))),f329(f329(f264(f875(x96031),f875(x96031)),x96032),x96033)),f145(x96031,x96034)))+~P24(f329(f329(f244(a874),x96035),f329(f329(f241(a874),f329(f194(f875(x96031)),x96032)),f329(f194(f875(x96031)),x96033))))+~P24(f329(f329(f331(f880(x96031,x96031)),f329(f329(f264(x96031,x96031),f329(f329(f163(x96031),x96032),x96035)),f329(f329(f163(x96031),x96033),x96035))),x96034))
% 187.33/188.05 [9713]~P86(x97135)+~P141(x97135)+P24(f329(f329(f331(x97131),f368(x97132,x97133,x97134,x97131,x97135)),x97134))+P24(f329(f329(f243(x97135),f329(f329(f6(x97131,x97135),x97133),x97134)),f329(f329(f81(x97135),f329(f105(x97135),f329(f38(x97131),x97134))),x97132)))
% 187.33/188.05 [9909]~P86(x99091)+~P141(x99091)+~P24(f329(f329(f243(x99091),f329(x99093,f368(x99095,x99093,x99094,x99092,x99091))),x99095))+P24(f329(f329(f243(x99091),f329(f329(f6(x99092,x99091),x99093),x99094)),f329(f329(f81(x99091),f329(f105(x99091),f329(f38(x99092),x99094))),x99095)))
% 187.33/188.05 [8680]E(f329(f329(f126(x86801),x86802),x86803),f329(f329(f126(x86801),x86804),x86805))+~E(f329(f329(f174(x86801),f329(f194(f875(x86801)),x86802)),x86804),x86802)+~E(f329(f329(f126(x86801),f329(f329(f136(x86801),f329(f194(f875(x86801)),x86802)),x86804)),x86805),x86803)+P24(f329(f329(f243(a874),f329(f194(f875(x86801)),x86804)),f329(f194(f875(x86801)),x86802)))
% 187.33/188.05 [8800]E(f329(f329(f126(x88001),x88002),x88003),f329(f329(f126(x88001),x88004),x88005))+~E(f329(f329(f174(x88001),f329(f194(f875(x88001)),x88002)),x88004),x88002)+~E(x88003,f329(f329(f126(x88001),f329(f329(f136(x88001),f329(f194(f875(x88001)),x88002)),x88004)),x88005))+~P24(f329(f329(f243(a874),f329(f194(f875(x88001)),x88002)),f329(f194(f875(x88001)),x88004)))
% 187.33/188.05 [10043]~P24(f329(x100435,x100434))+~P24(f329(f62(x100432),f329(f249(x100432),x100435)))+P24(f329(f62(x100431),f329(f249(x100431),f329(f329(f7(x100431,x100432,a869),x100433),x100434))))+~P24(f329(f62(x100431),f329(f249(x100431),f329(f329(f8(f881(x100432,a869),a869,x100431),f87(x100432)),f329(f329(f8(f881(x100432,a869),f881(x100432,a869),x100431),f329(f18(x100432,a869,a869),f329(f329(f8(a869,f881(a869,a869),x100432),a327),x100435))),x100433)))))
% 187.33/188.05 [8475]~P15(x84755,x84751,x84756,x84752)+E(f329(f73(x84751,x84751,x84751,f329(x84752,x84753)),f329(x84752,x84754)),f329(f73(x84751,x84751,x84751,f329(x84752,x84754)),f329(x84752,x84753)))+~P24(f329(f62(x84755),x84754))+~P24(f329(f62(x84755),x84753))
% 187.33/188.05 [7856]~P21(x78561,x78562,x78564,x78563)+~E(f329(x78564,x78566),x78565)+E(f329(f77(x78561,x78562,x78563,x78564),x78565),x78566)+~P24(f329(f329(f331(x78561),x78566),x78563))
% 187.33/188.05 [8055]~P16(x80556,x80551,x80554,x80552)+E(f329(f73(x80551,x80551,x80551,f329(x80552,x80553)),f329(x80554,x80555)),f329(x80552,x80553))+~P24(f329(f62(x80556),x80553))+~P24(f329(f329(f331(x80556),x80555),x80553))
% 187.33/188.05 [9275]~P15(x92753,x92751,x92756,x92752)+E(f329(f73(x92751,x92751,x92751,f329(x92752,f329(f329(f22(f881(x92753,a869)),x92754),f329(f329(f307(x92753),x92755),f193(f881(x92753,a869)))))),f329(x92756,x92755)),f329(x92752,x92754))+~P24(f329(f62(x92753),x92754))+~P24(f329(f329(f331(x92753),x92755),x92754))
% 187.33/188.05 [6930]~P30(x69301)+~E(f45(x69301,x69303,x69304),f45(x69301,x69306,x69304))+~E(f45(x69301,x69302,x69304),f45(x69301,x69305,x69304))+E(f45(x69301,f329(f329(f22(x69301),x69302),x69303),x69304),f45(x69301,f329(f329(f22(x69301),x69305),x69306),x69304))
% 187.33/188.05 [6931]~P29(x69311)+~E(f45(x69311,x69313,x69314),f45(x69311,x69316,x69314))+~E(f45(x69311,x69312,x69314),f45(x69311,x69315,x69314))+E(f45(x69311,f329(f329(f81(x69311),x69312),x69313),x69314),f45(x69311,f329(f329(f81(x69311),x69315),x69316),x69314))
% 187.33/188.05 [6932]~P29(x69321)+~E(f45(x69321,x69323,x69324),f45(x69321,x69326,x69324))+~E(f45(x69321,x69322,x69324),f45(x69321,x69325,x69324))+E(f45(x69321,f329(f329(f80(x69321),x69322),x69323),x69324),f45(x69321,f329(f329(f80(x69321),x69325),x69326),x69324))
% 187.33/188.05 [7749]~P12(x77491,x77492,x77493)+~P24(f329(f62(x77491),x77496))+E(f329(f329(f65(x77491,x77492,x77493),x77494),f329(f329(f307(x77491),x77495),x77496)),f329(f329(f65(x77491,x77492,x77493),f329(f329(x77493,x77495),x77494)),x77496))+P24(f329(f329(f331(x77491),x77495),x77496))
% 187.33/188.05 [7814]~P31(x78141)+P24(f329(f329(f243(x78141),x78142),f329(x78143,x78144)))+~P24(f329(f329(f331(x78145),x78144),x78146))+~P24(f329(f329(f243(x78141),x78142),f329(f329(f43(x78145,x78141),x78146),x78143)))
% 187.33/188.05 [7974]~P12(x79741,x79742,x79743)+~P24(f329(f62(x79741),x79746))+E(f329(f329(f65(x79741,x79742,x79743),x79744),f329(f329(f307(x79741),x79745),x79746)),f329(f329(x79743,x79745),f329(f329(f65(x79741,x79742,x79743),x79744),x79746)))+P24(f329(f329(f331(x79741),x79745),x79746))
% 187.33/188.05 [8071]~P27(x80713)+~P24(f329(x80712,x80715))+~P33(x80713,f329(f329(f152(x80711,x80713),x80714),x80716))+E(f329(f134(x80711,x80712),f329(f329(f146(x80711,x80713,x80714),x80715),x80716)),f329(f329(f146(x80711,x80713,x80714),x80715),f329(f134(x80711,x80712),x80716)))
% 187.33/188.05 [8094]E(x80941,x80942)+E(x80943,f2(a1))+~P24(f329(f49(x80944,x80943),f329(f329(f264(a1,a1),x80945),x80942)))+~P24(f329(f49(x80944,x80943),f329(f329(f264(a1,a1),x80946),x80941)))
% 187.33/188.05 [8095]E(x80951,x80952)+E(x80953,f2(a1))+~P24(f329(f49(x80954,x80953),f329(f329(f264(a1,a1),x80952),x80955)))+~P24(f329(f49(x80954,x80953),f329(f329(f264(a1,a1),x80951),x80956)))
% 187.33/188.05 [8115]~P15(x81152,x81155,x81156,x81151)+~P24(f329(f62(x81152),x81154))+E(f329(x81151,f329(f329(f307(x81152),x81153),x81154)),f329(f73(x81155,x81155,x81155,f329(x81151,x81154)),f329(x81156,x81153)))+P24(f329(f329(f331(x81152),x81153),x81154))
% 187.33/188.05 [8343]~P16(x83435,x83431,x83436,x83432)+E(f329(f73(x83431,x83431,x83431,f329(x83432,x83433)),f329(x83432,x83434)),f329(x83432,x83433))+~P24(f329(f62(x83435),x83433))+~P24(f329(f329(f243(f881(x83435,a869)),x83434),x83433))
% 187.33/188.05 [9475]~P21(x94751,x94752,x94754,x94753)+~P24(f329(f329(f331(x94752),x94755),f329(f308(x94751,x94752,x94754),x94753)))+P24(f329(f329(f331(x94751),f329(f77(x94751,x94752,x94753,x94754),x94755)),x94756))+~P24(f329(f329(f243(f881(x94751,a869)),x94753),x94756))
% 187.33/188.05 [9854]~P72(x98542)+~E(f573(x98541,x98543,x98545,x98546,x98544,x98542),f574(x98541,x98543,x98545,x98546,x98544,x98542))+~P24(f329(f62(x98544),x98546))+E(f329(f329(f6(x98541,x98542),x98543),f329(f308(x98544,x98541,x98545),x98546)),f329(f329(f6(x98544,x98542),f329(f73(x98541,x98542,x98544,x98543),x98545)),x98546))
% 187.33/188.05 [9891]~P72(x98916)+E(f329(x98911,f573(x98912,x98913,x98911,x98914,x98915,x98916)),f329(x98911,f574(x98912,x98913,x98911,x98914,x98915,x98916)))+E(f329(f329(f6(x98912,x98916),x98913),f329(f308(x98915,x98912,x98911),x98914)),f329(f329(f6(x98915,x98916),f329(f73(x98912,x98916,x98915,x98913),x98911)),x98914))+~P24(f329(f62(x98915),x98914))
% 187.33/188.05 [9931]~P72(x99312)+~E(f329(x99313,f329(x99315,f574(x99311,x99313,x99315,x99316,x99314,x99312))),f2(x99312))+~P24(f329(f62(x99314),x99316))+E(f329(f329(f6(x99311,x99312),x99313),f329(f308(x99314,x99311,x99315),x99316)),f329(f329(f6(x99314,x99312),f329(f73(x99311,x99312,x99314,x99313),x99315)),x99316))
% 187.33/188.05 [9989]~P72(x99892)+~P24(f329(f62(x99894),x99896))+E(f329(f329(f6(x99891,x99892),x99893),f329(f308(x99894,x99891,x99895),x99896)),f329(f329(f6(x99894,x99892),f329(f73(x99891,x99892,x99894,x99893),x99895)),x99896))+P24(f329(f329(f331(x99894),f574(x99891,x99893,x99895,x99896,x99894,x99892)),x99896))
% 187.33/188.05 [9990]~P72(x99902)+~P24(f329(f62(x99904),x99906))+E(f329(f329(f6(x99901,x99902),x99903),f329(f308(x99904,x99901,x99905),x99906)),f329(f329(f6(x99904,x99902),f329(f73(x99901,x99902,x99904,x99903),x99905)),x99906))+P24(f329(f329(f331(x99904),f573(x99901,x99903,x99905,x99906,x99904,x99902)),x99906))
% 187.33/188.05 [10102]~P76(x101021)+~P24(f329(f62(x101022),x101026))+E(f329(f329(f329(f66(x101021,x101022,f81(x101021)),f329(f329(f18(x101022,f881(x101023,a869),x101021),f329(f329(f7(x101022,x101021,f881(f881(x101023,a869),x101021)),f329(f329(f8(f881(x101023,x101021),f881(x101021,f881(f881(x101023,a869),x101021)),x101022),f66(x101021,x101023,f81(x101021))),x101024)),f78(x101021))),x101025)),f78(x101021)),x101026),f329(f329(f329(f66(x101021,f880(x101022,x101023),f81(x101021)),f329(f268(x101022,x101023,x101021),x101024)),f78(x101021)),f329(f329(f266(x101022,x101023),x101026),x101025)))+P24(f329(f329(f331(x101022),f539(x101024,x101025,x101023,x101026,x101022,x101021)),x101026))
% 187.33/188.05 [10120]~P76(x101201)+~P24(f329(f62(x101202),x101206))+E(f329(f329(f329(f66(x101201,x101202,f81(x101201)),f329(f329(f18(x101202,f881(x101203,a869),x101201),f329(f329(f7(x101202,x101201,f881(f881(x101203,a869),x101201)),f329(f329(f8(f881(x101203,x101201),f881(x101201,f881(f881(x101203,a869),x101201)),x101202),f66(x101201,x101203,f81(x101201))),x101204)),f78(x101201))),x101205)),f78(x101201)),x101206),f329(f329(f329(f66(x101201,f880(x101202,x101203),f81(x101201)),f329(f268(x101202,x101203,x101201),x101204)),f78(x101201)),f329(f329(f266(x101202,x101203),x101206),x101205)))+~P24(f329(f62(x101203),f329(x101205,f539(x101204,x101205,x101203,x101206,x101202,x101201))))
% 187.33/188.05 [8255]~P16(x82552,x82555,x82556,x82551)+~P24(f329(f62(x82552),x82554))+~P24(f329(f62(x82552),x82553))+E(f329(x82551,f329(f329(f115(f881(x82552,a869)),x82553),x82554)),f329(f73(x82555,x82555,x82555,f329(x82551,x82553)),f329(x82551,x82554)))
% 187.33/188.05 [8476]~P31(x84761)+P24(f329(f329(f243(x84761),f329(x84762,x84763)),x84764))+~P24(f329(f329(f331(x84765),x84763),x84766))+~P24(f329(f329(f243(x84761),f329(f329(f42(x84765,x84761),x84766),x84762)),x84764))
% 187.33/188.05 [8879]~P21(x88792,x88791,x88793,x88796)+E(f329(f329(f22(f881(x88791,a869)),f329(f308(x88792,x88791,x88793),x88794)),f329(f308(x88792,x88791,x88793),x88795)),f329(f308(x88792,x88791,x88793),f329(f329(f22(f881(x88792,a869)),x88794),x88795)))+~P24(f329(f329(f243(f881(x88792,a869)),x88795),x88796))+~P24(f329(f329(f243(f881(x88792,a869)),x88794),x88796))
% 187.33/188.05 [8880]~P21(x88802,x88801,x88803,x88806)+E(f329(f329(f106(f881(x88801,a869)),f329(f308(x88802,x88801,x88803),x88804)),f329(f308(x88802,x88801,x88803),x88805)),f329(f308(x88802,x88801,x88803),f329(f329(f106(f881(x88802,a869)),x88804),x88805)))+~P24(f329(f329(f243(f881(x88802,a869)),x88805),x88806))+~P24(f329(f329(f243(f881(x88802,a869)),x88804),x88806))
% 187.33/188.05 [8919]~P24(f329(x89191,x89193))+~P24(f329(f329(f329(f329(a201,x89192),x89193),x89194),x89196))+~P24(f329(f329(f329(f329(a201,f32(x89191,x89192)),x89196),x89194),x89195))+P24(f329(f329(f329(f329(a201,f32(x89191,x89192)),x89193),x89194),x89195))
% 187.33/188.05 [9148]E(x91481,x91482)+~P54(x91483,x91484,x91485)+~P24(f329(f329(f331(f880(x91483,x91484)),f329(f329(f264(x91483,x91484),x91486),x91482)),x91485))+~P24(f329(f329(f331(f880(x91483,x91484)),f329(f329(f264(x91483,x91484),x91486),x91481)),x91485))
% 187.33/188.05 [9926]~P70(x99261)+~E(f329(x99263,f477(x99264,x99266,x99263,x99265,x99262,x99261)),f329(x99266,f477(x99264,x99266,x99263,x99265,x99262,x99261)))+~P24(f329(f62(x99262),x99265))+E(f329(f329(f329(f66(x99261,x99262,f81(x99261)),x99263),x99264),x99265),f329(f329(f329(f66(x99261,x99262,f81(x99261)),x99266),x99264),x99265))
% 187.33/188.05 [9987]~P70(x99871)+~P24(f329(f62(x99872),x99875))+E(f329(f329(f329(f66(x99871,x99872,f81(x99871)),x99873),x99874),x99875),f329(f329(f329(f66(x99871,x99872,f81(x99871)),x99876),x99874),x99875))+P24(f329(f329(f331(x99872),f477(x99874,x99873,x99876,x99875,x99872,x99871)),x99875))
% 187.33/188.05 [8693]~P70(x86931)+~P24(f329(f62(x86932),x86936))+P24(f329(f329(f331(x86932),x86935),x86936))+E(f329(f329(f329(f66(x86931,x86932,f81(x86931)),x86933),x86934),f329(f329(f307(x86932),x86935),x86936)),f329(f329(f81(x86931),f329(x86933,x86935)),f329(f329(f329(f66(x86931,x86932,f81(x86931)),x86933),x86934),x86936)))
% 187.33/188.05 [8739]~P6(x87391,x87396,x87393)+~P9(x87391,f881(x87392,a869),x87393,x87395)+~P24(f329(f329(f331(x87391),x87394),x87396))+E(f329(f329(f42(x87391,f881(x87392,a869)),f329(f283(x87391,x87391,x87393),f329(f329(f307(x87391),x87394),f193(f881(x87391,a869))))),x87395),f329(x87395,x87394))
% 187.33/188.05 [8856]~P12(x88563,x88564,x88561)+~P24(f329(f62(x88563),x88566))+~P24(f329(f329(f331(x88563),x88562),x88566))+E(f329(f329(x88561,x88562),f329(f329(f65(x88563,x88564,x88561),x88565),f329(f329(f22(f881(x88563,a869)),x88566),f329(f329(f307(x88563),x88562),f193(f881(x88563,a869)))))),f329(f329(f65(x88563,x88564,x88561),x88565),x88566))
% 187.33/188.05 [9161]~P15(x91613,x91611,x91616,x91612)+~P24(f329(f62(x91613),x91615))+~P24(f329(f62(x91613),x91614))+E(f329(f73(x91611,x91611,x91611,f329(x91612,f329(f329(f115(f881(x91613,a869)),x91614),x91615))),f329(x91612,f329(f329(f106(f881(x91613,a869)),x91614),x91615))),f329(f73(x91611,x91611,x91611,f329(x91612,x91614)),f329(x91612,x91615)))
% 187.33/188.05 [9496]~E(x94963,f329(f329(f157(x94961,x94962),x94965),x94966))+P24(f329(f329(f331(f880(f875(x94961),f875(x94961))),f329(f329(f264(f875(x94961),f875(x94961)),x94962),x94963)),f155(x94961,x94964)))+~P24(f329(f329(f244(a874),x94965),f329(f194(f875(x94961)),x94962)))+~P24(f329(f329(f331(f880(x94961,x94961)),f329(f329(f264(x94961,x94961),f329(f329(f163(x94961),x94962),x94965)),x94966)),x94964))
% 187.33/188.05 [10000]~P72(x100002)+~P24(f329(f62(x100001),x100006))+P24(f329(f329(f331(x100001),f537(x100004,x100005,x100003,x100006,x100001,x100002)),x100006))+E(f329(f329(f6(x100001,x100002),f329(f329(f18(x100001,f881(x100003,a869),x100002),f329(f329(f8(f881(x100003,x100002),f881(f881(x100003,a869),x100002),x100001),f6(x100003,x100002)),x100004)),x100005)),x100006),f329(f329(f6(f880(x100001,x100003),x100002),f329(f268(x100001,x100003,x100002),x100004)),f329(f329(f266(x100001,x100003),x100006),x100005)))
% 187.33/188.05 [10001]~P76(x100012)+~P24(f329(f62(x100011),x100016))+P24(f329(f329(f331(x100011),f538(x100014,x100015,x100013,x100016,x100011,x100012)),x100016))+E(f329(f329(f9(x100011,x100012),f329(f329(f18(x100011,f881(x100013,a869),x100012),f329(f329(f8(f881(x100013,x100012),f881(f881(x100013,a869),x100012),x100011),f9(x100013,x100012)),x100014)),x100015)),x100016),f329(f329(f9(f880(x100011,x100013),x100012),f329(f268(x100011,x100013,x100012),x100014)),f329(f329(f266(x100011,x100013),x100016),x100015)))
% 187.33/188.05 [10040]~P72(x100402)+~P24(f329(f62(x100401),x100406))+~P24(f329(f62(x100403),f329(x100405,f537(x100404,x100405,x100403,x100406,x100401,x100402))))+E(f329(f329(f6(x100401,x100402),f329(f329(f18(x100401,f881(x100403,a869),x100402),f329(f329(f8(f881(x100403,x100402),f881(f881(x100403,a869),x100402),x100401),f6(x100403,x100402)),x100404)),x100405)),x100406),f329(f329(f6(f880(x100401,x100403),x100402),f329(f268(x100401,x100403,x100402),x100404)),f329(f329(f266(x100401,x100403),x100406),x100405)))
% 187.33/188.05 [10041]~P76(x100412)+~P24(f329(f62(x100411),x100416))+~P24(f329(f62(x100413),f329(x100415,f538(x100414,x100415,x100413,x100416,x100411,x100412))))+E(f329(f329(f9(x100411,x100412),f329(f329(f18(x100411,f881(x100413,a869),x100412),f329(f329(f8(f881(x100413,x100412),f881(f881(x100413,a869),x100412),x100411),f9(x100413,x100412)),x100414)),x100415)),x100416),f329(f329(f9(f880(x100411,x100413),x100412),f329(f268(x100411,x100413,x100412),x100414)),f329(f329(f266(x100411,x100413),x100416),x100415)))
% 187.33/188.05 [10023]~P76(x100232)+~P24(f329(f62(x100231),x100236))+P24(f329(f329(f331(x100231),x100233),x100236))+E(f329(f329(f9(x100231,x100232),f329(f329(f7(x100231,x100232,x100232),f329(f329(f18(x100231,x100232,f881(x100232,x100232)),f329(f329(f8(a869,f881(x100232,f881(x100232,x100232)),x100231),f101(x100232)),f329(f329(f7(x100231,x100231,a869),a326),x100233))),x100234)),x100235)),x100236),f329(f329(f254(x100232),x100235),f329(f38(x100231),x100236)))
% 187.33/188.05 [10028]~P76(x100282)+~P24(f329(f62(x100281),x100286))+~P24(f329(f329(f331(x100281),x100283),x100286))+E(f329(f329(f9(x100281,x100282),f329(f329(f7(x100281,x100282,x100282),f329(f329(f18(x100281,x100282,f881(x100282,x100282)),f329(f329(f8(a869,f881(x100282,f881(x100282,x100282)),x100281),f101(x100282)),f329(f329(f7(x100281,x100281,a869),a326),x100283))),x100284)),x100285)),x100286),f329(f329(f81(x100282),f329(x100284,x100283)),f329(f329(f254(x100282),x100285),f329(f329(f22(a874),f329(f38(x100281),x100286)),f78(a874)))))
% 187.33/188.05 [10095]~P24(f329(f62(x100951),x100955))+~P24(f329(f62(x100952),x100953))+P24(f329(f329(f331(x100952),f427(x100956,x100954,x100953,x100952,x100955,x100951)),x100953))+E(f329(f329(f6(x100951,a874),f329(f329(f8(f881(x100952,a869),a874,x100951),f38(x100952)),f329(f329(f8(f881(x100952,a869),f881(x100952,a869),x100951),f249(x100952)),f329(f329(f8(f881(x100952,a869),f881(x100952,a869),x100951),f329(f18(x100952,a869,a869),f329(f329(f8(a869,f881(a869,a869),x100952),a327),f329(f329(f7(x100952,f881(x100952,a869),a869),f331(x100952)),x100953)))),x100954)))),x100955),f329(f329(f81(a874),x100956),f329(f38(x100952),x100953)))
% 187.33/188.05 [10096]~P24(f329(f62(x100961),x100965))+~P24(f329(f62(x100962),x100963))+P24(f329(f329(f331(x100962),f428(x100966,x100964,x100963,x100962,x100965,x100961)),x100963))+E(f329(f329(f6(x100961,a874),f329(f329(f8(f881(x100962,a869),a874,x100961),f38(x100962)),f329(f329(f8(f881(x100962,a869),f881(x100962,a869),x100961),f249(x100962)),f329(f329(f8(f881(x100962,a869),f881(x100962,a869),x100961),f329(f18(x100962,a869,a869),f329(f329(f8(a869,f881(a869,a869),x100962),a327),f329(f329(f7(x100962,f881(x100962,a869),a869),f331(x100962)),x100963)))),x100964)))),x100965),f329(f329(f6(x100962,a874),x100966),x100963))
% 187.33/188.05 [10126]~P24(f329(f62(x101262),x101263))+~P24(f329(f62(x101261),x101265))+~E(f329(f38(x101261),f329(f249(x101261),f329(f329(f18(x101261,a869,a869),f329(f329(f8(a869,f881(a869,a869),x101261),a327),f329(f329(f7(x101261,f881(x101261,a869),a869),f331(x101261)),x101265))),f329(f329(f7(x101261,x101262,a869),x101264),f427(x101266,x101264,x101263,x101262,x101265,x101261))))),x101266)+E(f329(f329(f6(x101261,a874),f329(f329(f8(f881(x101262,a869),a874,x101261),f38(x101262)),f329(f329(f8(f881(x101262,a869),f881(x101262,a869),x101261),f249(x101262)),f329(f329(f8(f881(x101262,a869),f881(x101262,a869),x101261),f329(f18(x101262,a869,a869),f329(f329(f8(a869,f881(a869,a869),x101262),a327),f329(f329(f7(x101262,f881(x101262,a869),a869),f331(x101262)),x101263)))),x101264)))),x101265),f329(f329(f81(a874),x101266),f329(f38(x101262),x101263)))
% 187.33/188.05 [10128]~P24(f329(f62(x101282),x101283))+~P24(f329(f62(x101281),x101285))+~E(f329(f38(x101281),f329(f249(x101281),f329(f329(f18(x101281,a869,a869),f329(f329(f8(a869,f881(a869,a869),x101281),a327),f329(f329(f7(x101281,f881(x101281,a869),a869),f331(x101281)),x101285))),f329(f329(f7(x101281,x101282,a869),x101284),f428(x101286,x101284,x101283,x101282,x101285,x101281))))),f329(x101286,f428(x101286,x101284,x101283,x101282,x101285,x101281)))+E(f329(f329(f6(x101281,a874),f329(f329(f8(f881(x101282,a869),a874,x101281),f38(x101282)),f329(f329(f8(f881(x101282,a869),f881(x101282,a869),x101281),f249(x101282)),f329(f329(f8(f881(x101282,a869),f881(x101282,a869),x101281),f329(f18(x101282,a869,a869),f329(f329(f8(a869,f881(a869,a869),x101282),a327),f329(f329(f7(x101282,f881(x101282,a869),a869),f331(x101282)),x101283)))),x101284)))),x101285),f329(f329(f6(x101282,a874),x101286),x101283))
% 187.33/188.05 [9780]E(x97801,x97802)+~P12(x97803,x97804,x97805)+~P24(f329(f67(x97803,x97804,x97805,x97806,x97807),x97802))+~P24(f329(f67(x97803,x97804,x97805,x97806,x97807),x97801))
% 187.33/188.05 [9572]P24(f329(x95721,x95722))+~P24(f329(f329(f331(x95727),x95722),f329(x95726,x95724)))+~P24(f329(x95721,f432(x95721,x95726,x95725,x95723,x95727)))+~P24(f329(f329(f331(x95723),x95724),x95725))
% 187.33/188.05 [10015]~P12(x100157,x100156,x100151)+E(f329(f329(x100151,x100152),f623(x100152,x100153,x100154,x100155,x100151,x100156,x100157)),x100153)+~P24(f329(f67(x100157,x100156,x100151,x100155,x100154),x100153))+~P24(f329(f329(f331(x100157),x100152),x100154))
% 187.33/188.05 [10080]~P12(x100801,x100802,x100803)+~P24(f329(f67(x100801,x100802,x100803,x100804,x100805),x100807))+P24(f329(f67(x100801,x100802,x100803,x100804,f329(f329(f22(f881(x100801,a869)),x100805),f329(f329(f307(x100801),x100806),f193(f881(x100801,a869))))),f623(x100806,x100807,x100805,x100804,x100803,x100802,x100801)))+~P24(f329(f329(f331(x100801),x100806),x100805))
% 187.33/188.05 [9471]~P70(x94711)+~P21(x94715,x94712,x94716,x94717)+~P24(f329(f62(x94715),x94717))+E(f329(f329(f329(f66(x94711,x94712,f81(x94711)),x94713),x94714),f329(f308(x94715,x94712,x94716),x94717)),f329(f329(f329(f66(x94711,x94715,f81(x94711)),f329(f73(x94712,x94711,x94715,x94713),x94716)),x94714),x94717))
% 187.33/188.05 [9596]~E(f329(f329(f307(x95961),x95965),x95966),f329(f329(f307(x95961),x95962),x95963))+~P24(f329(f67(x95961,x95961,x95964,x95962,x95963),x95967))+P24(f329(f329(f331(x95961),x95962),x95963))+P24(f329(f63(x95961,x95964,f329(f329(f307(x95961),x95965),x95966)),x95967))
% 187.33/188.05 [9679]P24(f329(x96791,x96792))+~P24(f329(f329(f331(x96793),x96792),f329(x96794,x96797)))+~P24(f329(f329(f331(x96796),x96797),x96795))+P24(f329(f329(f331(x96793),f432(x96791,x96794,x96795,x96796,x96793)),f329(f329(f42(x96796,f881(x96793,a869)),x96795),x96794)))
% 187.33/188.05 [9693]~P21(x96932,x96931,x96935,x96934)+~P21(x96931,x96933,x96936,f329(f308(x96932,x96931,x96935),x96934))+E(f329(f329(f73(x96931,x96932,x96933,f77(x96932,x96931,x96934,x96935)),f77(x96931,x96933,f329(f308(x96932,x96931,x96935),x96934),x96936)),x96937),f329(f77(x96932,x96933,x96934,f329(f73(x96931,x96933,x96932,x96936),x96935)),x96937))+~P24(f329(f329(f331(x96933),x96937),f329(f308(x96931,x96933,x96936),f329(f308(x96932,x96931,x96935),x96934))))
% 187.33/188.05 [10016]~P12(x100167,x100166,x100161)+E(f329(f329(x100161,x100162),f646(x100163,x100164,x100162,x100165,x100161,x100166,x100167)),x100163)+P24(f329(f329(f331(x100167),x100162),x100164))+~P24(f329(f67(x100167,x100166,x100161,x100165,f329(f329(f307(x100167),x100162),x100164)),x100163))
% 187.33/188.05 [10079]~P12(x100791,x100794,x100795)+P24(f329(f67(x100791,x100794,x100795,x100796,x100793),f646(x100797,x100793,x100792,x100796,x100795,x100794,x100791)))+P24(f329(f329(f331(x100791),x100792),x100793))+~P24(f329(f67(x100791,x100794,x100795,x100796,f329(f329(f307(x100791),x100792),x100793)),x100797))
% 187.33/188.05 [9762]E(x97621,f2(a1))+~P24(f329(f49(x97623,x97621),f329(f329(f264(a1,a1),x97625),x97627)))+~P24(f329(f49(x97622,x97621),f329(f329(f264(a1,a1),x97624),x97626)))+P24(f329(f49(f329(f329(f80(a1),x97622),x97623),x97621),f329(f329(f264(a1,a1),f329(f329(f80(a1),f329(f329(f80(a1),x97624),x97625)),f329(f329(f39(a1),f329(f329(f80(a1),x97626),x97627)),x97621))),f45(a1,f329(f329(f80(a1),x97626),x97627),x97621))))
% 187.33/188.05 [9764]~P24(f329(f329(f244(a874),f2(a874)),x97643))+~P24(f329(f48(x97642,x97643),f329(f329(f264(a874,a874),x97645),x97647)))+~P24(f329(f48(x97641,x97643),f329(f329(f264(a874,a874),x97644),x97646)))+P24(f329(f48(f329(f329(f80(a874),x97641),x97642),x97643),f329(f329(f264(a874,a874),f329(f329(f80(a874),f329(f329(f80(a874),x97644),x97645)),f329(f329(f39(a874),f329(f329(f80(a874),x97646),x97647)),x97643))),f45(a874,f329(f329(f80(a874),x97646),x97647),x97643))))
% 187.33/188.05 [10125]~P72(x101252)+~P24(f329(f62(x101253),x101255))+~P24(f329(f62(x101251),x101257))+E(f329(f329(f6(x101251,x101252),f329(f329(f18(x101251,f881(x101253,a869),x101252),f329(f329(f8(f881(x101253,x101252),f881(f881(x101253,a869),x101252),x101251),f6(x101253,x101252)),x101254)),f329(f329(f8(f881(x101253,a869),f881(x101253,a869),x101251),f249(x101253)),f329(f329(f8(f881(x101253,a869),f881(x101253,a869),x101251),f329(f18(x101253,a869,a869),f329(f329(f8(a869,f881(a869,a869),x101253),a327),f329(f329(f7(x101253,f881(x101253,a869),a869),f331(x101253)),x101255)))),x101256)))),x101257),f329(f329(f6(x101253,x101252),f329(f329(f18(x101253,f881(x101251,a869),x101252),f329(f329(f8(f881(x101251,x101252),f881(f881(x101251,a869),x101252),x101253),f6(x101251,x101252)),f329(f7(x101251,x101253,x101252),x101254))),f329(f329(f8(f881(x101251,a869),f881(x101251,a869),x101253),f249(x101251)),f329(f329(f8(f881(x101251,a869),f881(x101251,a869),x101253),f329(f18(x101251,a869,a869),f329(f329(f8(a869,f881(a869,a869),x101251),a327),f329(f329(f7(x101251,f881(x101251,a869),a869),f331(x101251)),x101257)))),f329(f7(x101251,x101253,a869),x101256))))),x101255))
% 187.33/188.05 [9632]~P18(x96327,x96326,x96321,x96328,x96322,x96324)+E(f329(f329(x96321,f329(x96322,x96323)),f329(x96324,x96325)),f329(x96324,x96325))+~P24(f329(f62(x96326),x96325))+~P24(f329(f329(f331(x96326),x96323),x96325))
% 187.33/188.05 [9636]~P10(x96366,x96361,x96362,x96368,x96363,x96364)+~P6(x96366,x96367,x96368)+P9(x96361,x96362,x96363,f329(x96364,x96365))+~P24(f329(f329(f331(x96366),x96365),x96367))
% 187.33/188.05 [8072]~P34(x80728,x80727,f329(f329(f329(f92(x80728),x80724),x80726),x80721))+P24(f329(f329(x80721,x80722),x80723))+~P24(f329(f329(x80724,x80722),x80725))+~P24(f329(f329(f329(f329(a201,x80726),x80725),x80727),x80723))
% 187.33/188.05 [9257]~P15(x92577,x92571,x92578,x92573)+~P24(f329(f62(x92577),x92575))+~P24(f329(f62(x92577),x92574))+E(f329(f73(x92571,x92571,x92572,f329(x92573,x92574)),f329(f73(x92571,x92571,x92572,f329(x92573,x92575)),x92576)),f329(f73(x92571,x92571,x92572,f329(x92573,x92575)),f329(f73(x92571,x92571,x92572,f329(x92573,x92574)),x92576)))
% 187.33/188.05 [9265]~P39(x92651,x92652,x92653,x92654,x92657)+P39(x92651,x92652,x92653,f329(f329(f157(x92651,x92654),x92655),x92656),f329(f329(f157(x92652,x92657),x92655),x92658))+~P24(f329(f329(x92653,x92656),x92658))+~P24(f329(f329(f244(a874),x92655),f329(f194(f875(x92651)),x92654)))
% 187.33/188.05 [9266]~P39(x92661,x92662,x92663,x92664,x92667)+P39(x92661,x92662,x92663,f329(f329(f157(x92661,x92664),x92665),x92666),f329(f329(f157(x92662,x92667),x92665),x92668))+~P24(f329(f329(x92663,x92666),x92668))+~P24(f329(f329(f244(a874),x92665),f329(f194(f875(x92662)),x92667)))
% 187.33/188.05 [9345]~P21(x93452,x93452,x93455,x93456)+~P17(x93453,x93452,x93457,x93458,x93451)+~P24(f329(f62(x93452),x93456))+E(f329(f329(x93451,f329(f73(x93452,x93453,x93452,x93454),x93455)),x93456),f329(f329(x93451,x93454),f329(f308(x93452,x93452,x93455),x93456)))
% 187.33/188.05 [9634]~P19(x96347,x96342,x96345,x96348,x96346,x96341)+~P24(f329(f62(x96342),x96344))+E(f329(x96341,f329(f329(f307(x96342),x96343),x96344)),f329(f329(x96345,f329(x96346,x96343)),f329(x96341,x96344)))+P24(f329(f329(f331(x96342),x96343),x96344))
% 187.33/188.05 [9645]~P18(x96456,x96455,x96451,x96457,x96458,x96452)+E(f329(f329(x96451,f329(x96452,x96453)),f329(x96452,x96454)),f329(x96452,x96454))+~P24(f329(f62(x96455),x96454))+~P24(f329(f329(f243(f881(x96455,a869)),x96453),x96454))
% 187.33/188.05 [9242]P24(f329(f329(f331(f880(f875(x92421),f875(x92421))),f329(f329(f264(f875(x92421),f875(x92421)),x92422),x92423)),f155(x92421,x92424)))+~E(x92423,f329(f329(f126(x92421),x92425),f329(f329(f149(x92421),x92426),x92427)))+~E(x92422,f329(f329(f126(x92421),x92425),f329(f329(f149(x92421),x92428),x92427)))+~P24(f329(f329(f331(f880(x92421,x92421)),f329(f329(f264(x92421,x92421),x92428),x92426)),x92424))
% 187.33/188.05 [9639]~P18(x96396,x96392,x96395,x96397,x96398,x96391)+~P24(f329(f62(x96392),x96394))+~P24(f329(f62(x96392),x96393))+E(f329(x96391,f329(f329(f115(f881(x96392,a869)),x96393),x96394)),f329(f329(x96395,f329(x96391,x96393)),f329(x96391,x96394)))
% 187.33/188.05 [10163]~P21(x101634,x101632,x101635,x101638)+E(f329(f329(f43(x101631,f881(x101632,a869)),x101633),f329(f329(f8(f881(x101634,a869),f881(x101632,a869),x101631),f308(x101634,x101632,x101635)),x101636)),f329(f308(x101634,x101632,x101635),f329(f329(f43(x101631,f881(x101634,a869)),x101633),x101636)))+~P24(f329(f329(f331(x101631),x101637),x101633))+P24(f329(f329(f331(x101631),f633(x101637,x101636,x101633,x101631,x101638,x101635,x101632,x101634)),x101633))
% 187.33/188.05 [10187]~P21(x101874,x101872,x101875,x101877)+E(f329(f329(f43(x101871,f881(x101872,a869)),x101873),f329(f329(f8(f881(x101874,a869),f881(x101872,a869),x101871),f308(x101874,x101872,x101875)),x101876)),f329(f308(x101874,x101872,x101875),f329(f329(f43(x101871,f881(x101874,a869)),x101873),x101876)))+~P24(f329(f329(f331(x101871),x101878),x101873))+~P24(f329(f329(f243(f881(x101874,a869)),f329(x101876,f633(x101878,x101876,x101873,x101871,x101877,x101875,x101872,x101874))),x101877))
% 187.33/188.05 [9702]~P19(x97027,x97025,x97021,x97028,x97022,x97024)+~P24(f329(f62(x97025),x97026))+~P24(f329(f329(f331(x97025),x97023),x97026))+E(f329(f329(x97021,f329(x97022,x97023)),f329(x97024,f329(f329(f22(f881(x97025,a869)),x97026),f329(f329(f307(x97025),x97023),f193(f881(x97025,a869)))))),f329(x97024,x97026))
% 187.33/188.05 [9711]~P19(x97116,x97113,x97111,x97117,x97118,x97112)+~P24(f329(f62(x97113),x97115))+~P24(f329(f62(x97113),x97114))+E(f329(f329(x97111,f329(x97112,f329(f329(f115(f881(x97113,a869)),x97114),x97115))),f329(x97112,f329(f329(f106(f881(x97113,a869)),x97114),x97115))),f329(f329(x97111,f329(x97112,x97114)),f329(x97112,x97115)))
% 187.33/188.05 [9803]P47(x98031,x98032,x98033,x98034,x98035,f329(f329(x98033,x98036),x98037))+~P47(x98031,x98032,x98033,x98034,f329(f329(f22(f881(x98031,a869)),x98035),f329(f329(f307(x98031),x98038),f193(f881(x98031,a869)))),x98039)+~E(f329(f329(x98033,x98036),x98037),f329(f329(x98033,x98038),x98039))+~P24(f329(f329(f331(x98031),x98038),x98035))
% 187.33/188.05 [10202]P20(x102021,x102022,f329(f329(f307(f873(x102021)),f329(f329(f329(f92(x102021),f329(x102023,f365(x102024,x102025,x102026,x102027,x102023,x102022,x102021,x102028,x102029))),f329(x102027,f365(x102024,x102025,x102026,x102027,x102023,x102022,x102021,x102028,x102029))),f329(x102026,f365(x102024,x102025,x102026,x102027,x102023,x102022,x102021,x102028,x102029)))),f193(f881(f873(x102021),a869))))+~P24(f329(f62(x102029),x102028))+~P20(x102021,x102022,f329(f308(x102029,f873(x102021),f329(f329(f18(x102029,f881(x102021,f881(a871,a869)),f873(x102021)),f329(f329(f18(x102029,a870,f881(f881(x102021,f881(a871,a869)),f873(x102021))),f329(f329(f8(f881(x102021,f881(a871,a869)),f881(a870,f881(f881(x102021,f881(a871,a869)),f873(x102021))),x102029),f92(x102021)),x102023)),x102027)),x102026)),x102028))+P20(x102021,x102022,f329(f308(x102029,f873(x102021),f329(f329(f18(x102029,f881(x102021,f881(a871,a869)),f873(x102021)),f329(f329(f18(x102029,a870,f881(f881(x102021,f881(a871,a869)),f873(x102021))),f329(f329(f8(f881(x102021,f881(a871,a869)),f881(a870,f881(f881(x102021,f881(a871,a869)),f873(x102021))),x102029),f92(x102021)),x102025)),x102027)),x102024)),x102028))
% 187.33/188.05 [10203]~P20(x102031,x102032,f329(f329(f307(f873(x102031)),f329(f329(f329(f92(x102031),f329(x102034,f365(x102036,x102034,x102038,x102035,x102039,x102032,x102031,x102037,x102033))),f329(x102035,f365(x102036,x102034,x102038,x102035,x102039,x102032,x102031,x102037,x102033))),f329(x102036,f365(x102036,x102034,x102038,x102035,x102039,x102032,x102031,x102037,x102033)))),f193(f881(f873(x102031),a869))))+~P24(f329(f62(x102033),x102037))+~P20(x102031,x102032,f329(f308(x102033,f873(x102031),f329(f329(f18(x102033,f881(x102031,f881(a871,a869)),f873(x102031)),f329(f329(f18(x102033,a870,f881(f881(x102031,f881(a871,a869)),f873(x102031))),f329(f329(f8(f881(x102031,f881(a871,a869)),f881(a870,f881(f881(x102031,f881(a871,a869)),f873(x102031))),x102033),f92(x102031)),x102039)),x102035)),x102038)),x102037))+P20(x102031,x102032,f329(f308(x102033,f873(x102031),f329(f329(f18(x102033,f881(x102031,f881(a871,a869)),f873(x102031)),f329(f329(f18(x102033,a870,f881(f881(x102031,f881(a871,a869)),f873(x102031))),f329(f329(f8(f881(x102031,f881(a871,a869)),f881(a870,f881(f881(x102031,f881(a871,a869)),f873(x102031))),x102033),f92(x102031)),x102034)),x102035)),x102036)),x102037))
% 187.33/188.05 [9737]~P10(x97376,x97377,x97378,x97379,x973710,x97371)+E(f329(f329(x97371,x97372),x97373),f329(f329(x97371,x97374),x97375))+~P24(f329(f329(f331(f880(x97377,x97377)),f329(f329(f264(x97377,x97377),x97373),x97375)),x973710))+~P24(f329(f329(f331(f880(x97376,x97376)),f329(f329(f264(x97376,x97376),x97372),x97374)),x97379))
% 187.33/188.05 [9347]~P66(x93472)+E(x93471,f193(f881(x93472,a869)))+~P24(f329(f62(x93472),x93471))+P24(f329(f329(f331(x93472),f10(x93472,x93471)),x93471))+~P24(f329(f329(f331(x93472),f329(f329(f106(x93472),f654(x93471,x93472)),f668(x93471,x93472))),f329(f329(f307(x93472),f654(x93471,x93472)),f329(f329(f307(x93472),f668(x93471,x93472)),f193(f881(x93472,a869))))))
% 187.33/188.05 [9348]~P66(x93482)+E(x93481,f193(f881(x93482,a869)))+~P24(f329(f62(x93482),x93481))+P24(f329(f329(f331(x93482),f13(x93482,x93481)),x93481))+~P24(f329(f329(f331(x93482),f329(f329(f115(x93482),f679(x93481,x93482)),f688(x93481,x93482))),f329(f329(f307(x93482),f679(x93481,x93482)),f329(f329(f307(x93482),f688(x93481,x93482)),f193(f881(x93482,a869))))))
% 187.33/188.05 [9379]~P70(x93792)+E(x93791,f193(f881(x93792,a869)))+~P24(f329(f62(x93792),x93791))+P24(f329(f329(f331(x93792),f329(f64(x93792,f81(x93792)),x93791)),x93791))+~P24(f329(f329(f331(x93792),f329(f329(f81(x93792),f821(x93791,x93792)),f823(x93791,x93792))),f329(f329(f307(x93792),f821(x93791,x93792)),f329(f329(f307(x93792),f823(x93791,x93792)),f193(f881(x93792,a869))))))
% 187.33/188.05 [9385]~P27(x93852)+E(x93851,f193(f881(x93852,a869)))+~P24(f329(f62(x93852),x93851))+P24(f329(f329(f331(x93852),f11(x93852,f241(x93852),x93851)),x93851))+~P24(f329(f329(f331(x93852),f329(f329(f241(x93852),f458(x93851,x93852)),f460(x93851,x93852))),f329(f329(f307(x93852),f458(x93851,x93852)),f329(f329(f307(x93852),f460(x93851,x93852)),f193(f881(x93852,a869))))))
% 187.33/188.05 [9386]~P27(x93862)+E(x93861,f193(f881(x93862,a869)))+~P24(f329(f62(x93862),x93861))+P24(f329(f329(f331(x93862),f12(x93862,f242(x93862),x93861)),x93861))+~P24(f329(f329(f331(x93862),f329(f329(f242(x93862),f466(x93861,x93862)),f467(x93861,x93862))),f329(f329(f307(x93862),f466(x93861,x93862)),f329(f329(f307(x93862),f467(x93861,x93862)),f193(f881(x93862,a869))))))
% 187.33/188.05 [6498]~P89(x64982)+E(x64981,f2(x64982))+~E(f329(f329(f80(x64982),x64983),x64981),f2(x64982))+~P24(f329(f329(f243(x64982),f2(x64982)),x64983))+~P24(f329(f329(f243(x64982),f2(x64982)),x64981))
% 187.33/188.05 [6499]~P89(x64992)+E(x64991,f2(x64992))+~E(f329(f329(f80(x64992),x64991),x64993),f2(x64992))+~P24(f329(f329(f243(x64992),f2(x64992)),x64993))+~P24(f329(f329(f243(x64992),f2(x64992)),x64991))
% 187.33/188.05 [7032]~P27(x70322)+~P33(x70322,x70321)+E(x70321,f118(x70322))+~P24(f329(f329(f331(x70322),x70323),f329(f171(x70322),f743(x70321,x70322))))+P24(f329(f329(f243(x70322),f761(x70321,x70322)),x70323))
% 187.33/188.05 [7198]~P27(x71981)+E(f14(x71981,x71982),x71983)+~P24(f329(f62(x71981),x71982))+~P24(f329(f329(f243(x71981),x71983),f475(x71983,x71982,x71981)))+~P24(f329(f329(f331(x71981),x71983),x71982))
% 187.33/188.05 [7229]~P27(x72291)+~P33(x72291,x72292)+~P33(x72291,x72293)+P33(x72291,f329(f329(f126(x72291),x72292),x72293))+P24(f329(f329(f331(x72291),f749(x72293,x72292,x72291)),f329(f171(x72291),x72292)))
% 187.33/188.05 [7230]~P27(x72301)+~P33(x72301,x72302)+~P33(x72301,x72303)+P33(x72301,f329(f329(f126(x72301),x72302),x72303))+P24(f329(f329(f331(x72301),f750(x72303,x72302,x72301)),f329(f171(x72301),x72303)))
% 187.33/188.05 [7286]~P27(x72861)+E(f14(x72861,x72862),x72863)+~P24(f329(f62(x72861),x72862))+P24(f329(f329(f331(x72861),f475(x72863,x72862,x72861)),x72862))+~P24(f329(f329(f331(x72861),x72863),x72862))
% 187.33/188.05 [7287]~P27(x72871)+E(f15(x72871,x72872),x72873)+~P24(f329(f62(x72871),x72872))+P24(f329(f329(f331(x72871),f476(x72873,x72872,x72871)),x72872))+~P24(f329(f329(f331(x72871),x72873),x72872))
% 187.33/188.05 [7874]~P27(x78741)+E(f15(x78741,x78742),x78743)+~P24(f329(f62(x78741),x78742))+~P24(f329(f329(f331(x78741),x78743),x78742))+~P24(f329(f329(f243(x78741),f476(x78743,x78742,x78741)),x78743))
% 187.33/188.05 [8203]~P27(x82031)+~P33(x82031,x82032)+~P33(x82031,x82033)+P33(x82031,f329(f329(f126(x82031),x82032),x82033))+~P24(f329(f329(f243(x82031),f749(x82033,x82032,x82031)),f750(x82033,x82032,x82031)))
% 187.33/188.05 [8985]~P66(x89852)+E(x89851,f193(f881(x89852,a869)))+~E(f329(f329(f106(x89852),f329(x89853,f722(x89851,x89853,x89852))),f329(x89853,f736(x89851,x89853,x89852))),f329(x89853,f329(f329(f106(x89852),f722(x89851,x89853,x89852)),f736(x89851,x89853,x89852))))+E(f10(x89852,f329(f308(x89852,x89852,x89853),x89851)),f329(x89853,f10(x89852,x89851)))+~P24(f329(f62(x89852),x89851))
% 187.33/188.05 [8986]~P66(x89862)+E(x89861,f193(f881(x89862,a869)))+~E(f329(f329(f115(x89862),f329(x89863,f742(x89861,x89863,x89862))),f329(x89863,f754(x89861,x89863,x89862))),f329(x89863,f329(f329(f115(x89862),f742(x89861,x89863,x89862)),f754(x89861,x89863,x89862))))+E(f13(x89862,f329(f308(x89862,x89862,x89863),x89861)),f329(x89863,f13(x89862,x89861)))+~P24(f329(f62(x89862),x89861))
% 187.33/188.05 [8987]~P27(x89872)+E(x89871,f193(f881(x89872,a869)))+~E(f329(f329(f241(x89872),f329(x89873,f452(x89871,x89873,x89872))),f329(x89873,f455(x89871,x89873,x89872))),f329(x89873,f329(f329(f241(x89872),f452(x89871,x89873,x89872)),f455(x89871,x89873,x89872))))+E(f14(x89872,f329(f308(x89872,x89872,x89873),x89871)),f329(x89873,f14(x89872,x89871)))+~P24(f329(f62(x89872),x89871))
% 187.33/188.05 [8988]~P27(x89882)+E(x89881,f193(f881(x89882,a869)))+~E(f329(f329(f242(x89882),f329(x89883,f456(x89881,x89883,x89882))),f329(x89883,f469(x89881,x89883,x89882))),f329(x89883,f329(f329(f242(x89882),f456(x89881,x89883,x89882)),f469(x89881,x89883,x89882))))+E(f15(x89882,f329(f308(x89882,x89882,x89883),x89881)),f329(x89883,f15(x89882,x89881)))+~P24(f329(f62(x89882),x89881))
% 187.33/188.05 [9059]~P27(x90592)+E(x90591,f193(f881(x90592,a869)))+~E(f329(f329(f241(x90592),f329(x90593,f457(x90591,x90593,x90592))),f329(x90593,f462(x90591,x90593,x90592))),f329(x90593,f329(f329(f241(x90592),f457(x90591,x90593,x90592)),f462(x90591,x90593,x90592))))+E(f11(x90592,f241(x90592),f329(f308(x90592,x90592,x90593),x90591)),f329(x90593,f11(x90592,f241(x90592),x90591)))+~P24(f329(f62(x90592),x90591))
% 187.33/188.05 [9060]~P27(x90602)+E(x90601,f193(f881(x90602,a869)))+~E(f329(f329(f242(x90602),f329(x90603,f463(x90601,x90603,x90602))),f329(x90603,f468(x90601,x90603,x90602))),f329(x90603,f329(f329(f242(x90602),f463(x90601,x90603,x90602)),f468(x90601,x90603,x90602))))+E(f12(x90602,f242(x90602),f329(f308(x90602,x90602,x90603),x90601)),f329(x90603,f12(x90602,f242(x90602),x90601)))+~P24(f329(f62(x90602),x90601))
% 187.33/188.05 [6514]~P70(x65142)+E(x65141,f193(f881(x65142,a869)))+~P24(f329(f62(x65142),x65141))+E(f329(f64(x65142,f81(x65142)),f329(f329(f307(x65142),x65143),x65141)),f329(f329(f81(x65142),x65143),f329(f64(x65142,f81(x65142)),x65141)))+P24(f329(f329(f331(x65142),x65143),x65141))
% 187.33/188.05 [7038]~P66(x70382)+E(f329(f329(f115(x70382),f13(x70382,x70381)),f13(x70382,x70383)),f13(x70382,x70383))+E(x70381,f193(f881(x70382,a869)))+~P24(f329(f62(x70382),x70383))+~P24(f329(f329(f243(f881(x70382,a869)),x70381),x70383))
% 187.33/188.05 [7039]~P66(x70392)+E(f329(f329(f106(x70392),f10(x70392,x70391)),f10(x70392,x70393)),f10(x70392,x70393))+E(x70391,f193(f881(x70392,a869)))+~P24(f329(f62(x70392),x70393))+~P24(f329(f329(f243(f881(x70392,a869)),x70391),x70393))
% 187.33/188.05 [7040]~P27(x70402)+E(f329(f329(f241(x70402),f14(x70402,x70401)),f14(x70402,x70403)),f14(x70402,x70403))+E(x70401,f193(f881(x70402,a869)))+~P24(f329(f62(x70402),x70403))+~P24(f329(f329(f243(f881(x70402,a869)),x70401),x70403))
% 187.33/188.05 [7041]~P27(x70412)+E(f329(f329(f242(x70412),f15(x70412,x70411)),f15(x70412,x70413)),f15(x70412,x70413))+E(x70411,f193(f881(x70412,a869)))+~P24(f329(f62(x70412),x70413))+~P24(f329(f329(f243(f881(x70412,a869)),x70411),x70413))
% 187.33/188.05 [7338]~P27(x73382)+E(x73381,f193(f881(x73382,a869)))+~P24(f329(f62(x73382),x73383))+P24(f329(f329(f243(x73382),f14(x73382,x73383)),f14(x73382,x73381)))+~P24(f329(f329(f243(f881(x73382,a869)),x73381),x73383))
% 187.33/188.05 [7339]~P27(x73392)+E(x73391,f193(f881(x73392,a869)))+~P24(f329(f62(x73392),x73393))+P24(f329(f329(f243(x73392),f15(x73392,x73391)),f15(x73392,x73393)))+~P24(f329(f329(f243(f881(x73392,a869)),x73391),x73393))
% 187.33/188.05 [7398]~P66(x73981)+E(f10(x73981,x73982),x73983)+~P24(f329(f62(x73981),x73982))+~E(f329(f329(f22(f881(x73981,a869)),x73982),f329(f329(f307(x73981),x73983),f193(f881(x73981,a869)))),f193(f881(x73981,a869)))+~P24(f329(f329(f331(x73981),x73983),x73982))
% 187.33/188.05 [7399]~P66(x73991)+E(f13(x73991,x73992),x73993)+~P24(f329(f62(x73991),x73992))+~E(f329(f329(f22(f881(x73991,a869)),x73992),f329(f329(f307(x73991),x73993),f193(f881(x73991,a869)))),f193(f881(x73991,a869)))+~P24(f329(f329(f331(x73991),x73993),x73992))
% 187.33/188.05 [7400]~P27(x74001)+E(f14(x74001,x74002),x74003)+~P24(f329(f62(x74001),x74002))+~E(f329(f329(f22(f881(x74001,a869)),x74002),f329(f329(f307(x74001),x74003),f193(f881(x74001,a869)))),f193(f881(x74001,a869)))+~P24(f329(f329(f331(x74001),x74003),x74002))
% 187.33/188.05 [7401]~P27(x74011)+E(f15(x74011,x74012),x74013)+~P24(f329(f62(x74011),x74012))+~E(f329(f329(f22(f881(x74011,a869)),x74012),f329(f329(f307(x74011),x74013),f193(f881(x74011,a869)))),f193(f881(x74011,a869)))+~P24(f329(f329(f331(x74011),x74013),x74012))
% 187.33/188.05 [7500]~P27(x75001)+E(f11(x75001,f241(x75001),x75002),x75003)+~P24(f329(f62(x75001),x75002))+~E(f329(f329(f22(f881(x75001,a869)),x75002),f329(f329(f307(x75001),x75003),f193(f881(x75001,a869)))),f193(f881(x75001,a869)))+~P24(f329(f329(f331(x75001),x75003),x75002))
% 187.33/188.05 [7501]~P27(x75011)+E(f12(x75011,f242(x75011),x75012),x75013)+~P24(f329(f62(x75011),x75012))+~E(f329(f329(f22(f881(x75011,a869)),x75012),f329(f329(f307(x75011),x75013),f193(f881(x75011,a869)))),f193(f881(x75011,a869)))+~P24(f329(f329(f331(x75011),x75013),x75012))
% 187.33/188.05 [7537]~P103(x75372)+E(x75371,f193(f881(x75372,a869)))+~P24(f329(f62(x75372),x75371))+~P24(f329(f329(f243(x75372),x75373),f820(x75373,x75371,x75372)))+P24(f329(f329(f243(x75372),x75373),f329(f64(x75372,f106(x75372)),x75371)))
% 187.33/188.05 [7538]~P27(x75382)+E(x75381,f193(f881(x75382,a869)))+~P24(f329(f62(x75382),x75381))+~P24(f329(f329(f243(x75382),x75383),f448(x75383,x75381,x75382)))+P24(f329(f329(f243(x75382),x75383),f329(f64(x75382,f241(x75382)),x75381)))
% 187.33/188.05 [7539]~P27(x75392)+E(x75391,f193(f881(x75392,a869)))+~P24(f329(f62(x75392),x75391))+~P24(f329(f329(f244(x75392),x75393),f449(x75393,x75391,x75392)))+P24(f329(f329(f244(x75392),x75393),f329(f64(x75392,f241(x75392)),x75391)))
% 187.33/188.05 [7624]~P103(x76242)+E(x76241,f193(f881(x76242,a869)))+~P24(f329(f62(x76242),x76241))+P24(f329(f329(f331(x76242),f820(x76243,x76241,x76242)),x76241))+P24(f329(f329(f243(x76242),x76243),f329(f64(x76242,f106(x76242)),x76241)))
% 187.33/188.05 [7625]~P27(x76252)+E(x76251,f193(f881(x76252,a869)))+~P24(f329(f62(x76252),x76251))+P24(f329(f329(f331(x76252),f448(x76253,x76251,x76252)),x76251))+P24(f329(f329(f243(x76252),x76253),f329(f64(x76252,f241(x76252)),x76251)))
% 187.33/188.05 [7626]~P27(x76262)+E(x76261,f193(f881(x76262,a869)))+~P24(f329(f62(x76262),x76261))+P24(f329(f329(f331(x76262),f449(x76263,x76261,x76262)),x76261))+P24(f329(f329(f244(x76262),x76263),f329(f64(x76262,f241(x76262)),x76261)))
% 187.33/188.05 [7751]~P27(x77512)+E(x77511,f193(f881(x77512,a869)))+E(f329(f329(f241(x77512),f11(x77512,f241(x77512),x77511)),f11(x77512,f241(x77512),x77513)),f11(x77512,f241(x77512),x77513))+~P24(f329(f62(x77512),x77513))+~P24(f329(f329(f243(f881(x77512,a869)),x77511),x77513))
% 187.33/188.05 [7752]~P27(x77522)+E(x77521,f193(f881(x77522,a869)))+E(f329(f329(f242(x77522),f12(x77522,f242(x77522),x77521)),f12(x77522,f242(x77522),x77523)),f12(x77522,f242(x77522),x77523))+~P24(f329(f62(x77522),x77523))+~P24(f329(f329(f243(f881(x77522,a869)),x77521),x77523))
% 187.33/188.05 [7953]~E(f635(x79531,x79533,x79532),f636(x79531,x79533,x79532))+~E(f329(f38(x79532),f632(x79531,x79533,x79532)),x79531)+E(f329(f329(f81(a874),x79531),f329(f38(f881(x79532,a869)),x79533)),f329(f38(x79532),f40(f881(x79532,a869),x79533)))+~P24(f329(f62(x79532),f40(f881(x79532,a869),x79533)))+~P24(f329(f62(f881(x79532,a869)),x79533))
% 187.33/188.05 [8136]~P27(x81362)+E(x81361,f193(f881(x81362,a869)))+~P24(f329(f62(x81362),x81363))+P24(f329(f329(f243(x81362),f329(f64(x81362,f241(x81362)),x81363)),f329(f64(x81362,f241(x81362)),x81361)))+~P24(f329(f329(f243(f881(x81362,a869)),x81361),x81363))
% 187.33/188.05 [8445]~E(f635(x84451,x84453,x84452),f636(x84451,x84453,x84452))+E(f329(f329(f81(a874),x84451),f329(f38(f881(x84452,a869)),x84453)),f329(f38(x84452),f40(f881(x84452,a869),x84453)))+P24(f329(f329(f331(f881(x84452,a869)),f632(x84451,x84453,x84452)),x84453))+~P24(f329(f62(x84452),f40(f881(x84452,a869),x84453)))+~P24(f329(f62(f881(x84452,a869)),x84453))
% 187.33/188.05 [8472]~E(f329(f38(x84722),f632(x84721,x84723,x84722)),x84721)+E(f329(f329(f81(a874),x84721),f329(f38(f881(x84722,a869)),x84723)),f329(f38(x84722),f40(f881(x84722,a869),x84723)))+P24(f329(f329(f331(f881(x84722,a869)),f636(x84721,x84723,x84722)),x84723))+~P24(f329(f62(x84722),f40(f881(x84722,a869),x84723)))+~P24(f329(f62(f881(x84722,a869)),x84723))
% 187.33/188.05 [8473]~E(f329(f38(x84732),f632(x84731,x84733,x84732)),x84731)+E(f329(f329(f81(a874),x84731),f329(f38(f881(x84732,a869)),x84733)),f329(f38(x84732),f40(f881(x84732,a869),x84733)))+P24(f329(f329(f331(f881(x84732,a869)),f635(x84731,x84733,x84732)),x84733))+~P24(f329(f62(x84732),f40(f881(x84732,a869),x84733)))+~P24(f329(f62(f881(x84732,a869)),x84733))
% 187.33/188.05 [8501]~E(f329(f38(x85012),f632(x85011,x85013,x85012)),x85011)+~E(f329(f329(f106(f881(x85012,a869)),f636(x85011,x85013,x85012)),f635(x85011,x85013,x85012)),f193(f881(x85012,a869)))+E(f329(f329(f81(a874),x85011),f329(f38(f881(x85012,a869)),x85013)),f329(f38(x85012),f40(f881(x85012,a869),x85013)))+~P24(f329(f62(f881(x85012,a869)),x85013))+~P24(f329(f62(x85012),f40(f881(x85012,a869),x85013)))
% 187.33/188.05 [8744]E(f329(f329(f81(a874),x87441),f329(f38(f881(x87442,a869)),x87443)),f329(f38(x87442),f40(f881(x87442,a869),x87443)))+P24(f329(f329(f331(f881(x87442,a869)),f632(x87441,x87443,x87442)),x87443))+P24(f329(f329(f331(f881(x87442,a869)),f636(x87441,x87443,x87442)),x87443))+~P24(f329(f62(f881(x87442,a869)),x87443))+~P24(f329(f62(x87442),f40(f881(x87442,a869),x87443)))
% 187.33/188.05 [8745]E(f329(f329(f81(a874),x87451),f329(f38(f881(x87452,a869)),x87453)),f329(f38(x87452),f40(f881(x87452,a869),x87453)))+P24(f329(f329(f331(f881(x87452,a869)),f632(x87451,x87453,x87452)),x87453))+P24(f329(f329(f331(f881(x87452,a869)),f635(x87451,x87453,x87452)),x87453))+~P24(f329(f62(f881(x87452,a869)),x87453))+~P24(f329(f62(x87452),f40(f881(x87452,a869),x87453)))
% 187.33/188.05 [8770]~E(f329(f329(f106(f881(x87702,a869)),f636(x87701,x87703,x87702)),f635(x87701,x87703,x87702)),f193(f881(x87702,a869)))+E(f329(f329(f81(a874),x87701),f329(f38(f881(x87702,a869)),x87703)),f329(f38(x87702),f40(f881(x87702,a869),x87703)))+~P24(f329(f62(f881(x87702,a869)),x87703))+P24(f329(f329(f331(f881(x87702,a869)),f632(x87701,x87703,x87702)),x87703))+~P24(f329(f62(x87702),f40(f881(x87702,a869),x87703)))
% 187.33/188.05 [9033]~P98(x90332)+E(x90331,f193(f881(x90332,a869)))+~E(f329(f329(f81(x90332),f329(x90333,f829(x90331,x90333,x90332))),f329(x90333,f830(x90331,x90333,x90332))),f329(x90333,f329(f329(f81(x90332),f829(x90331,x90333,x90332)),f830(x90331,x90333,x90332))))+~P24(f329(f62(x90332),x90331))+E(f329(f64(x90332,f81(x90332)),f329(f308(x90332,x90332,x90333),x90331)),f329(x90333,f329(f64(x90332,f81(x90332)),x90331)))
% 187.33/188.05 [9961]P24(f329(f329(x99611,x99612),x99613))+P24(f329(f329(f244(a1),f485(x99611,x99613,x99612)),f486(x99611,x99613,x99612)))+P24(f329(f329(f243(a1),f486(x99611,x99613,x99612)),f2(a1)))+P24(f329(f329(x99611,f485(x99611,x99613,x99612)),f329(f329(f81(a1),f329(f108(a1),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))),f486(x99611,x99613,x99612))))+~P24(f329(f317(f880(a1,a1),a57),f329(f329(f264(a1,a1),x99612),x99613)))
% 187.33/188.05 [9967]P24(f329(f329(x99671,x99672),x99673))+P24(f329(f329(f243(a1),f484(x99671,x99673,x99672)),f2(a1)))+P24(f329(f329(x99671,f479(x99671,x99673,x99672)),f329(f329(f81(a1),f329(f108(a1),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))),f484(x99671,x99673,x99672))))+P24(f329(f329(f243(a1),f2(a1)),f329(f329(f80(a1),f479(x99671,x99673,x99672)),f484(x99671,x99673,x99672))))+~P24(f329(f317(f880(a1,a1),a52),f329(f329(f264(a1,a1),x99672),x99673)))
% 187.33/188.05 [7924]~P115(x79241)+~P24(f329(f329(f243(x79241),x79242),f78(x79241)))+~P24(f329(f329(f243(x79241),f2(x79241)),x79242))+~P24(f329(f329(f243(x79241),f2(x79241)),x79243))+P24(f329(f329(f243(x79241),f329(f329(f81(x79241),x79242),x79243)),x79243))
% 187.33/188.05 [7925]~P115(x79251)+~P24(f329(f329(f243(x79251),x79253),f78(x79251)))+~P24(f329(f329(f243(x79251),f2(x79251)),x79253))+~P24(f329(f329(f243(x79251),f2(x79251)),x79252))+P24(f329(f329(f243(x79251),f329(f329(f81(x79251),x79252),x79253)),x79252))
% 187.33/188.05 [8287]~P27(x82872)+E(x82871,f193(f881(x82872,a869)))+~P24(f329(f62(x82872),x82871))+P24(f329(f329(f243(x82872),f440(x82873,x82871,x82872)),x82873))+~P24(f329(f329(f243(x82872),f329(f64(x82872,f241(x82872)),x82871)),x82873))
% 187.33/188.05 [8288]~P27(x82882)+E(x82881,f193(f881(x82882,a869)))+~P24(f329(f62(x82882),x82881))+P24(f329(f329(f331(x82882),f440(x82883,x82881,x82882)),x82881))+~P24(f329(f329(f243(x82882),f329(f64(x82882,f241(x82882)),x82881)),x82883))
% 187.33/188.05 [8289]~P27(x82892)+E(x82891,f193(f881(x82892,a869)))+~P24(f329(f62(x82892),x82891))+P24(f329(f329(f331(x82892),f450(x82893,x82891,x82892)),x82891))+~P24(f329(f329(f244(x82892),f329(f64(x82892,f241(x82892)),x82891)),x82893))
% 187.33/188.05 [8290]~P27(x82902)+E(x82901,f193(f881(x82902,a869)))+~P24(f329(f62(x82902),x82901))+P24(f329(f329(f244(x82902),f450(x82903,x82901,x82902)),x82903))+~P24(f329(f329(f244(x82902),f329(f64(x82902,f241(x82902)),x82901)),x82903))
% 187.33/188.05 [8374]~P24(f329(x83741,x83743))+P24(f329(x83741,f400(x83741,x83742)))+P24(f329(x83741,f395(x83741,x83742)))+~P24(f329(f329(f244(a1),f2(a1)),x83742))+P24(f329(x83741,f329(f329(f22(a1),f395(x83741,x83742)),f329(f329(f81(a1),f401(x83741,x83742)),x83742))))
% 187.33/188.05 [8596]~P24(f329(x85961,x85963))+P24(f329(x85961,f395(x85961,x85962)))+~P24(f329(f329(f244(a1),f2(a1)),x85962))+P24(f329(f329(f331(a1),f400(x85961,x85962)),f300(a1,f78(a1),x85962)))+P24(f329(x85961,f329(f329(f22(a1),f395(x85961,x85962)),f329(f329(f81(a1),f401(x85961,x85962)),x85962))))
% 187.33/188.05 [8792]~P24(f329(x87921,x87923))+~P24(f329(x87921,f395(x87921,x87922)))+P24(f329(x87921,f400(x87921,x87922)))+~P24(f329(f329(f244(a1),f2(a1)),x87922))+~P24(f329(x87921,f329(f329(f22(a1),f395(x87921,x87922)),f329(f329(f81(a1),f401(x87921,x87922)),x87922))))
% 187.33/188.05 [8917]~P24(f329(x89171,x89173))+~P24(f329(x89171,f395(x89171,x89172)))+~P24(f329(f329(f244(a1),f2(a1)),x89172))+P24(f329(f329(f331(a1),f400(x89171,x89172)),f300(a1,f78(a1),x89172)))+~P24(f329(x89171,f329(f329(f22(a1),f395(x89171,x89172)),f329(f329(f81(a1),f401(x89171,x89172)),x89172))))
% 187.33/188.05 [8704]~P66(x87041)+~P24(f329(f62(x87041),x87042))+E(f329(f329(f22(f881(x87041,a869)),x87042),f329(f329(f307(x87041),x87043),f193(f881(x87041,a869)))),f193(f881(x87041,a869)))+~P24(f329(f329(f331(x87041),x87043),x87042))+E(f329(f329(f106(x87041),x87043),f10(x87041,f329(f329(f22(f881(x87041,a869)),x87042),f329(f329(f307(x87041),x87043),f193(f881(x87041,a869)))))),f10(x87041,x87042))
% 187.33/188.05 [8705]~P66(x87051)+~P24(f329(f62(x87051),x87052))+E(f329(f329(f22(f881(x87051,a869)),x87052),f329(f329(f307(x87051),x87053),f193(f881(x87051,a869)))),f193(f881(x87051,a869)))+~P24(f329(f329(f331(x87051),x87053),x87052))+E(f329(f329(f115(x87051),x87053),f13(x87051,f329(f329(f22(f881(x87051,a869)),x87052),f329(f329(f307(x87051),x87053),f193(f881(x87051,a869)))))),f13(x87051,x87052))
% 187.33/188.05 [8706]~P27(x87061)+~P24(f329(f62(x87061),x87062))+E(f329(f329(f22(f881(x87061,a869)),x87062),f329(f329(f307(x87061),x87063),f193(f881(x87061,a869)))),f193(f881(x87061,a869)))+~P24(f329(f329(f331(x87061),x87063),x87062))+E(f329(f329(f241(x87061),x87063),f14(x87061,f329(f329(f22(f881(x87061,a869)),x87062),f329(f329(f307(x87061),x87063),f193(f881(x87061,a869)))))),f14(x87061,x87062))
% 187.33/188.05 [8707]~P27(x87071)+~P24(f329(f62(x87071),x87072))+E(f329(f329(f22(f881(x87071,a869)),x87072),f329(f329(f307(x87071),x87073),f193(f881(x87071,a869)))),f193(f881(x87071,a869)))+~P24(f329(f329(f331(x87071),x87073),x87072))+E(f329(f329(f242(x87071),x87073),f15(x87071,f329(f329(f22(f881(x87071,a869)),x87072),f329(f329(f307(x87071),x87073),f193(f881(x87071,a869)))))),f15(x87071,x87072))
% 187.33/188.05 [8764]~P27(x87641)+~P24(f329(f62(x87641),x87642))+E(f329(f329(f22(f881(x87641,a869)),x87642),f329(f329(f307(x87641),x87643),f193(f881(x87641,a869)))),f193(f881(x87641,a869)))+~P24(f329(f329(f331(x87641),x87643),x87642))+E(f329(f329(f241(x87641),x87643),f11(x87641,f241(x87641),f329(f329(f22(f881(x87641,a869)),x87642),f329(f329(f307(x87641),x87643),f193(f881(x87641,a869)))))),f11(x87641,f241(x87641),x87642))
% 187.33/188.05 [8765]~P27(x87651)+~P24(f329(f62(x87651),x87652))+E(f329(f329(f22(f881(x87651,a869)),x87652),f329(f329(f307(x87651),x87653),f193(f881(x87651,a869)))),f193(f881(x87651,a869)))+~P24(f329(f329(f331(x87651),x87653),x87652))+E(f329(f329(f242(x87651),x87653),f12(x87651,f242(x87651),f329(f329(f22(f881(x87651,a869)),x87652),f329(f329(f307(x87651),x87653),f193(f881(x87651,a869)))))),f12(x87651,f242(x87651),x87652))
% 187.33/188.05 [8779]~P66(x87791)+~P24(f329(f62(x87791),x87793))+~P24(f329(f62(x87791),x87792))+E(f329(f329(f106(f881(x87791,a869)),x87792),x87793),f193(f881(x87791,a869)))+E(f329(f329(f115(x87791),f13(x87791,f329(f329(f115(f881(x87791,a869)),x87792),x87793))),f13(x87791,f329(f329(f106(f881(x87791,a869)),x87792),x87793))),f329(f329(f115(x87791),f13(x87791,x87792)),f13(x87791,x87793)))
% 187.33/188.05 [8780]~P66(x87801)+~P24(f329(f62(x87801),x87803))+~P24(f329(f62(x87801),x87802))+E(f329(f329(f106(f881(x87801,a869)),x87802),x87803),f193(f881(x87801,a869)))+E(f329(f329(f106(x87801),f10(x87801,f329(f329(f115(f881(x87801,a869)),x87802),x87803))),f10(x87801,f329(f329(f106(f881(x87801,a869)),x87802),x87803))),f329(f329(f106(x87801),f10(x87801,x87802)),f10(x87801,x87803)))
% 187.33/188.05 [8781]~P27(x87811)+~P24(f329(f62(x87811),x87813))+~P24(f329(f62(x87811),x87812))+E(f329(f329(f106(f881(x87811,a869)),x87812),x87813),f193(f881(x87811,a869)))+E(f329(f329(f241(x87811),f14(x87811,f329(f329(f115(f881(x87811,a869)),x87812),x87813))),f14(x87811,f329(f329(f106(f881(x87811,a869)),x87812),x87813))),f329(f329(f241(x87811),f14(x87811,x87812)),f14(x87811,x87813)))
% 187.33/188.05 [8782]~P27(x87821)+~P24(f329(f62(x87821),x87823))+~P24(f329(f62(x87821),x87822))+E(f329(f329(f106(f881(x87821,a869)),x87822),x87823),f193(f881(x87821,a869)))+E(f329(f329(f242(x87821),f15(x87821,f329(f329(f115(f881(x87821,a869)),x87822),x87823))),f15(x87821,f329(f329(f106(f881(x87821,a869)),x87822),x87823))),f329(f329(f242(x87821),f15(x87821,x87822)),f15(x87821,x87823)))
% 187.33/188.05 [9005]~P27(x90051)+~P24(f329(f62(x90051),x90053))+~P24(f329(f62(x90051),x90052))+E(f329(f329(f106(f881(x90051,a869)),x90052),x90053),f193(f881(x90051,a869)))+E(f329(f329(f241(x90051),f11(x90051,f241(x90051),f329(f329(f115(f881(x90051,a869)),x90052),x90053))),f11(x90051,f241(x90051),f329(f329(f106(f881(x90051,a869)),x90052),x90053))),f329(f329(f241(x90051),f11(x90051,f241(x90051),x90052)),f11(x90051,f241(x90051),x90053)))
% 187.33/188.05 [9006]~P27(x90061)+~P24(f329(f62(x90061),x90063))+~P24(f329(f62(x90061),x90062))+E(f329(f329(f106(f881(x90061,a869)),x90062),x90063),f193(f881(x90061,a869)))+E(f329(f329(f242(x90061),f12(x90061,f242(x90061),f329(f329(f115(f881(x90061,a869)),x90062),x90063))),f12(x90061,f242(x90061),f329(f329(f106(f881(x90061,a869)),x90062),x90063))),f329(f329(f242(x90061),f12(x90061,f242(x90061),x90062)),f12(x90061,f242(x90061),x90063)))
% 187.33/188.05 [9800]~P121(x98003)+E(x98001,x98002)+~P24(f329(f329(f243(x98003),f2(x98003)),x98002))+~P24(f329(f329(f243(x98003),f2(x98003)),x98001))+~E(f329(f329(f254(x98003),x98001),f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))),f329(f329(f254(x98003),x98002),f329(f108(a874),f329(f329(f80(a1),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)),f329(f329(f22(a1),f329(f329(f80(a1),a83),a83)),a102)))))
% 187.33/188.05 [6315]E(f825(x63151,x63152,x63153),x63154)+E(f329(x63151,x63154),f2(a874))+~E(f329(f329(f6(x63153,a874),x63151),x63152),f78(a874))+~P24(f329(f62(x63153),x63152))+~P24(f329(f329(f331(x63153),x63154),x63152))
% 187.33/188.05 [6376]E(f856(x63761,x63762,x63763),x63764)+E(f329(x63761,x63764),f2(a874))+~E(f329(f329(f6(x63763,a874),x63761),x63762),f329(a117,f2(a874)))+~P24(f329(f62(x63763),x63762))+~P24(f329(f329(f331(x63763),x63764),x63762))
% 187.33/188.05 [6482]~P27(x64821)+~P31(x64821)+P24(f329(f329(f244(x64821),x64822),f40(x64821,x64823)))+~P24(f329(f329(f244(x64821),x64822),x64824))+~P24(f329(f329(f331(x64821),x64824),x64823))
% 187.33/188.05 [6656]~P27(x66561)+~P31(x66561)+~P24(f329(f329(f244(x66561),x66564),x66563))+P24(f329(f329(f244(x66561),f41(x66561,x66562)),x66563))+~P24(f329(f329(f331(x66561),x66564),x66562))
% 187.33/188.05 [6916]~P121(x69163)+E(x69161,x69162)+~E(f329(f329(f254(x69163),x69161),f329(a117,x69164)),f329(f329(f254(x69163),x69162),f329(a117,x69164)))+~P24(f329(f329(f243(x69163),f2(x69163)),x69162))+~P24(f329(f329(f243(x69163),f2(x69163)),x69161))
% 187.33/188.05 [7127]~E(f834(x71272,x71273,x71271,x71274),x71274)+~E(f329(x71272,x71274),f78(a874))+E(f329(f329(f6(x71271,a874),x71272),x71273),f78(a874))+~P24(f329(f62(x71271),x71273))+~P24(f329(f329(f331(x71271),x71274),x71273))
% 187.33/188.05 [7134]~P109(x71344)+~P127(x71344)+E(f329(x71341,f827(x71341,x71342,x71343,x71344)),f2(x71344))+~E(f329(f329(f9(x71343,x71344),x71341),x71342),f2(x71344))+~P24(f329(f62(x71343),x71342))
% 187.33/188.05 [7220]~E(f858(x72202,x72203,x72201,x72204),x72204)+~E(f329(x72202,x72204),f329(a117,f2(a874)))+E(f329(f329(f6(x72201,a874),x72202),x72203),f329(a117,f2(a874)))+~P24(f329(f62(x72201),x72203))+~P24(f329(f329(f331(x72201),x72204),x72203))
% 187.33/188.05 [7964]~E(f329(x79642,x79644),f78(a874))+~E(f329(x79642,f834(x79642,x79643,x79641,x79644)),f2(a874))+E(f329(f329(f6(x79641,a874),x79642),x79643),f78(a874))+~P24(f329(f62(x79641),x79643))+~P24(f329(f329(f331(x79641),x79644),x79643))
% 187.33/188.05 [8008]~E(f329(x80082,x80084),f329(a117,f2(a874)))+~E(f329(x80082,f858(x80082,x80083,x80081,x80084)),f2(a874))+E(f329(f329(f6(x80081,a874),x80082),x80083),f329(a117,f2(a874)))+~P24(f329(f62(x80081),x80083))+~P24(f329(f329(f331(x80081),x80084),x80083))
% 187.33/188.05 [8566]~P27(x85661)+~P33(x85661,x85664)+P33(x85661,x85662)+~E(x85662,f329(f329(f149(x85661),x85663),x85664))+~P24(f329(f329(f243(x85661),x85663),f763(x85662,x85661,x85664,x85663)))
% 187.33/188.05 [8600]E(x86001,x86002)+E(f329(f329(f22(a1),f377(x86003,x86002,x86004,x86001)),f378(x86003,x86002,x86004,x86001)),x86001)+~E(f329(f329(f80(a1),x86001),x86004),x86002)+~P24(f329(f329(f244(a1),f2(a1)),x86004))+~P24(f329(f329(f331(a1),x86002),x86003))
% 187.33/188.05 [8601]E(x86011,x86012)+E(f329(f329(f80(a1),f386(x86013,x86012,x86014,x86011)),f387(x86013,x86012,x86014,x86011)),x86011)+~E(f329(f329(f22(a1),x86011),x86014),x86012)+~P24(f329(f329(f244(a1),f2(a1)),x86014))+~P24(f329(f329(f331(a1),x86012),x86013))
% 187.33/188.05 [8777]E(f329(x87771,f583(x87772,x87771,x87773,x87774)),x87772)+P24(f329(f329(f243(a874),x87774),f584(x87772,x87771,x87773,x87774)))+~P24(f329(f329(f243(a1),x87772),f329(x87771,x87773)))+~P24(f329(f329(f244(a874),x87774),x87773))+~P24(f329(f329(f243(a1),f329(x87771,x87774)),x87772))
% 187.33/188.05 [8778]~P27(x87781)+~P33(x87781,x87783)+P33(x87781,x87782)+~E(x87782,f329(f329(f149(x87781),x87784),x87783))+P24(f329(f329(f331(x87781),f763(x87782,x87781,x87783,x87784)),f329(f171(x87781),x87783)))
% 187.33/188.05 [8796]~P109(x87964)+~P127(x87964)+~E(f329(f329(f9(x87961,x87964),x87962),x87963),f2(x87964))+~P24(f329(f62(x87961),x87963))+P24(f329(f329(f331(x87961),f827(x87962,x87963,x87961,x87964)),x87963))
% 187.33/188.05 [8830]~E(f329(x88302,x88304),f78(a874))+E(f329(f329(f6(x88301,a874),x88302),x88303),f78(a874))+~P24(f329(f62(x88301),x88303))+~P24(f329(f329(f331(x88301),x88304),x88303))+P24(f329(f329(f331(x88301),f834(x88302,x88303,x88301,x88304)),x88303))
% 187.33/188.05 [8839]E(x88391,x88392)+~E(f329(f329(f80(a1),x88392),x88394),x88391)+~P24(f329(f329(f244(a1),f2(a1)),x88394))+~P24(f329(f329(f331(a1),x88391),x88393))+P24(f329(f329(f331(a1),f377(x88393,x88391,x88394,x88392)),x88393))
% 187.33/188.05 [8840]E(x88401,x88402)+~E(f329(f329(f22(a1),x88402),x88404),x88401)+~P24(f329(f329(f244(a1),f2(a1)),x88404))+~P24(f329(f329(f331(a1),x88401),x88403))+P24(f329(f329(f331(a1),f386(x88403,x88401,x88404,x88402)),x88403))
% 187.33/188.05 [8842]~E(f329(x88422,x88424),f329(a117,f2(a874)))+E(f329(f329(f6(x88421,a874),x88422),x88423),f329(a117,f2(a874)))+~P24(f329(f62(x88421),x88423))+~P24(f329(f329(f331(x88421),x88424),x88423))+P24(f329(f329(f331(x88421),f858(x88422,x88423,x88421,x88424)),x88423))
% 187.33/188.05 [8847]P58(x88472,x88473,x88474,x88471)+E(x88471,f193(f881(x88472,a869)))+~P24(f329(f62(x88472),x88474))+~P24(f329(f62(x88472),x88471))+P24(f329(f329(f331(x88472),f517(x88471,x88474,x88473,x88472)),x88474))
% 187.33/188.05 [8931]E(x89311,x89312)+~E(f329(f329(f80(a1),x89312),x89314),x89311)+~P24(f329(f329(f244(a1),f2(a1)),x89314))+~P24(f329(f329(f331(a1),x89311),x89313))+P24(f329(f329(f331(a1),f378(x89313,x89311,x89314,x89312)),f300(a1,f78(a1),x89314)))
% 187.33/188.05 [8932]E(x89321,x89322)+~E(f329(f329(f22(a1),x89322),x89324),x89321)+~P24(f329(f329(f244(a1),f2(a1)),x89324))+~P24(f329(f329(f331(a1),x89321),x89323))+P24(f329(f329(f331(a1),f387(x89323,x89321,x89324,x89322)),f300(a1,f78(a1),x89324)))
% 187.33/188.05 [9011]P24(f329(f329(f243(a874),x90111),f583(x90112,x90113,x90114,x90111)))+~P24(f329(f329(f243(a1),x90112),f329(x90113,x90114)))+P24(f329(f329(f243(a874),x90111),f584(x90112,x90113,x90114,x90111)))+~P24(f329(f329(f244(a874),x90111),x90114))+~P24(f329(f329(f243(a1),f329(x90113,x90111)),x90112))
% 187.33/188.05 [9121]E(f329(x91211,f583(x91212,x91211,x91213,x91214)),x91212)+~P24(f329(f329(f243(a1),x91212),f329(x91211,x91213)))+P24(f329(f329(f244(a874),f584(x91212,x91211,x91213,x91214)),x91213))+~P24(f329(f329(f244(a874),x91214),x91213))+~P24(f329(f329(f243(a1),f329(x91211,x91214)),x91212))
% 187.33/188.05 [9254]~P24(f329(f329(f243(a1),x92542),f329(x92543,x92544)))+P24(f329(f329(f243(a874),x92541),f584(x92542,x92543,x92544,x92541)))+P24(f329(f329(f243(a874),f583(x92542,x92543,x92544,x92541)),x92544))+~P24(f329(f329(f244(a874),x92541),x92544))+~P24(f329(f329(f243(a1),f329(x92543,x92541)),x92542))
% 187.33/188.05 [9255]~P24(f329(f329(f243(a1),x92552),f329(x92553,x92554)))+P24(f329(f329(f243(a874),x92551),f583(x92552,x92553,x92554,x92551)))+P24(f329(f329(f244(a874),f584(x92552,x92553,x92554,x92551)),x92554))+~P24(f329(f329(f244(a874),x92551),x92554))+~P24(f329(f329(f243(a1),f329(x92553,x92551)),x92552))
% 187.33/188.05 [9362]~P24(f329(f329(f243(a1),x93621),f329(x93622,x93623)))+P24(f329(f329(f244(a874),f584(x93621,x93622,x93623,x93624)),x93623))+~P24(f329(f329(f244(a874),x93624),x93623))+~P24(f329(f329(f243(a1),f329(x93622,x93624)),x93621))+P24(f329(f329(f243(a874),f583(x93621,x93622,x93623,x93624)),x93623))
% 187.33/188.05 [9439]E(x94391,f193(f881(x94392,a869)))+~P24(f329(f62(x94392),x94394))+~P24(f329(f62(x94392),x94391))+P24(f329(f329(f331(f880(f881(x94392,a869),f881(x94392,a869))),f329(f329(f264(f881(x94392,a869),f881(x94392,a869)),x94394),x94391)),f321(x94392,x94393)))+P24(f329(f329(f331(x94392),f526(x94393,x94391,x94394,x94392)),x94394))
% 187.33/188.05 [9440]E(x94401,f193(f881(x94402,a869)))+~P24(f329(f62(x94402),x94404))+~P24(f329(f62(x94402),x94401))+P24(f329(f329(f331(f880(f881(x94402,a869),f881(x94402,a869))),f329(f329(f264(f881(x94402,a869),f881(x94402,a869)),x94404),x94401)),f321(x94402,x94403)))+P24(f329(f329(f331(x94402),f585(x94403,x94401,x94404,x94402)),x94404))
% 187.33/188.05 [10103]E(f329(x101031,f583(x101032,x101031,x101033,x101034)),x101032)+~P24(f329(f329(f243(a1),x101032),f329(x101031,x101033)))+~P24(f329(f329(f243(a1),f329(f75(a1),f329(f329(f22(a1),f329(x101031,f329(f329(f80(a874),f584(x101032,x101031,x101033,x101034)),f78(a874)))),f329(x101031,f584(x101032,x101031,x101033,x101034))))),f78(a1)))+~P24(f329(f329(f244(a874),x101034),x101033))+~P24(f329(f329(f243(a1),f329(x101031,x101034)),x101032))
% 187.33/188.05 [10104]~P24(f329(f329(f243(a1),x101042),f329(x101043,x101044)))+P24(f329(f329(f243(a874),x101041),f583(x101042,x101043,x101044,x101041)))+~P24(f329(f329(f243(a1),f329(f75(a1),f329(f329(f22(a1),f329(x101043,f329(f329(f80(a874),f584(x101042,x101043,x101044,x101041)),f78(a874)))),f329(x101043,f584(x101042,x101043,x101044,x101041))))),f78(a1)))+~P24(f329(f329(f244(a874),x101041),x101044))+~P24(f329(f329(f243(a1),f329(x101043,x101041)),x101042))
% 187.33/188.05 [10105]~P24(f329(f329(f243(a1),x101051),f329(x101052,x101053)))+~P24(f329(f329(f243(a1),f329(f75(a1),f329(f329(f22(a1),f329(x101052,f329(f329(f80(a874),f584(x101051,x101052,x101053,x101054)),f78(a874)))),f329(x101052,f584(x101051,x101052,x101053,x101054))))),f78(a1)))+~P24(f329(f329(f244(a874),x101054),x101053))+~P24(f329(f329(f243(a1),f329(x101052,x101054)),x101051))+P24(f329(f329(f243(a874),f583(x101051,x101052,x101053,x101054)),x101053))
% 187.33/188.05 [7187]~P63(x71871)+P24(f329(f329(f244(x71871),x71872),f2(x71871)))+~P24(f329(f329(f243(x71871),x71873),f2(x71871)))+P24(f329(f329(f244(x71871),f2(x71871)),x71872))+P24(f329(f329(f243(x71871),x71873),f329(f329(f287(x71871),x71874),x71872)))
% 187.33/188.05 [7188]~P63(x71881)+P24(f329(f329(f244(x71881),x71882),f2(x71881)))+~P24(f329(f329(f244(x71881),x71883),f2(x71881)))+P24(f329(f329(f244(x71881),f2(x71881)),x71882))+P24(f329(f329(f244(x71881),x71883),f329(f329(f287(x71881),x71884),x71882)))
% 187.33/188.05 [7438]~P63(x74381)+P24(f329(f329(f243(x74381),x74382),f2(x74381)))+P24(f329(f329(f244(x74381),x74383),f2(x74381)))+P24(f329(f329(f244(x74381),f2(x74381)),x74383))+~P24(f329(f329(f243(x74381),x74382),f329(f329(f287(x74381),x74384),x74383)))
% 187.33/188.05 [7439]~P63(x74391)+P24(f329(f329(f244(x74391),x74392),f2(x74391)))+P24(f329(f329(f244(x74391),x74393),f2(x74391)))+P24(f329(f329(f244(x74391),f2(x74391)),x74393))+~P24(f329(f329(f244(x74391),x74392),f329(f329(f287(x74391),x74394),x74393)))
% 187.33/188.05 [7557]E(x75571,x75572)+~E(f329(f329(f163(x75573),x75574),x75571),f329(f329(f163(x75573),x75574),x75572))+~P24(f329(f135(x75573),x75574))+~P24(f329(f329(f244(a874),x75572),f329(f194(f875(x75573)),x75574)))+~P24(f329(f329(f244(a874),x75571),f329(f194(f875(x75573)),x75574)))
% 187.33/188.05 [7926]~P63(x79261)+~P24(f329(f329(f243(x79261),x79263),f2(x79261)))+P24(f329(f329(f244(x79261),f2(x79261)),x79262))+~P24(f329(f329(f243(x79261),x79264),f329(f329(f81(x79261),x79263),x79262)))+P24(f329(f329(f243(x79261),x79263),f329(f329(f287(x79261),x79264),x79262)))
% 187.33/188.05 [7927]~P63(x79271)+~P24(f329(f329(f244(x79271),x79273),f2(x79271)))+P24(f329(f329(f244(x79271),f2(x79271)),x79272))+~P24(f329(f329(f244(x79271),x79274),f329(f329(f81(x79271),x79273),x79272)))+P24(f329(f329(f244(x79271),x79273),f329(f329(f287(x79271),x79274),x79272)))
% 187.33/188.05 [7928]~P63(x79281)+~P24(f329(f329(f244(x79281),x79282),f2(x79281)))+P24(f329(f329(f244(x79281),f2(x79281)),x79282))+~P24(f329(f329(f243(x79281),x79284),f329(f329(f81(x79281),x79283),x79282)))+P24(f329(f329(f243(x79281),x79283),f329(f329(f287(x79281),x79284),x79282)))
% 187.33/188.05 [7929]~P63(x79291)+~P24(f329(f329(f244(x79291),x79292),f2(x79291)))+P24(f329(f329(f244(x79291),f2(x79291)),x79292))+~P24(f329(f329(f243(x79291),x79294),f329(f329(f287(x79291),x79293),x79292)))+P24(f329(f329(f243(x79291),x79293),f329(f329(f81(x79291),x79294),x79292)))
% 187.33/188.05 [7930]~P63(x79301)+~P24(f329(f329(f244(x79301),x79302),f2(x79301)))+P24(f329(f329(f244(x79301),f2(x79301)),x79302))+~P24(f329(f329(f244(x79301),x79304),f329(f329(f81(x79301),x79303),x79302)))+P24(f329(f329(f244(x79301),x79303),f329(f329(f287(x79301),x79304),x79302)))
% 187.33/188.05 [7931]~P63(x79311)+~P24(f329(f329(f244(x79311),x79312),f2(x79311)))+P24(f329(f329(f244(x79311),f2(x79311)),x79312))+~P24(f329(f329(f244(x79311),x79314),f329(f329(f287(x79311),x79313),x79312)))+P24(f329(f329(f244(x79311),x79313),f329(f329(f81(x79311),x79314),x79312)))
% 187.33/188.05 [8076]~P27(x80761)+~P33(x80761,x80762)+~P24(f329(f329(f243(a874),x80763),x80764))+P24(f329(f329(f243(x80761),f329(f329(f163(x80761),x80762),x80763)),f329(f329(f163(x80761),x80762),x80764)))+~P24(f329(f329(f244(a874),x80764),f329(f194(f875(x80761)),x80762)))
% 187.33/188.05 [8127]~P121(x81271)+~P24(f329(f329(f243(x81271),x81272),f78(x81271)))+~P24(f329(f329(f243(x81271),f2(x81271)),x81272))+~P24(f329(f329(f243(a874),x81274),x81273))+P24(f329(f329(f243(x81271),f329(f329(f254(x81271),x81272),x81273)),f329(f329(f254(x81271),x81272),x81274)))
% 187.33/188.05 [8128]~P121(x81281)+~P24(f329(f329(f244(x81281),x81282),f78(x81281)))+~P24(f329(f329(f244(x81281),f2(x81281)),x81282))+~P24(f329(f329(f244(a874),x81284),x81283))+P24(f329(f329(f244(x81281),f329(f329(f254(x81281),x81282),x81283)),f329(f329(f254(x81281),x81282),x81284)))
% 187.33/188.05 [8129]~P121(x81291)+~P24(f329(f329(f243(x81291),f2(x81291)),x81292))+~P24(f329(f329(f244(a874),f2(a874)),x81293))+~P24(f329(f329(f244(x81291),x81292),x81294))+P24(f329(f329(f244(x81291),f329(f329(f254(x81291),x81292),x81293)),f329(f329(f254(x81291),x81294),x81293)))
% 187.33/188.05 [8149]~P27(x81491)+~P33(x81491,f329(f167(x81491),x81492))+~P24(f329(f329(f243(a874),x81494),x81493))+P24(f329(f329(f243(x81491),f329(f329(f163(x81491),x81492),x81493)),f329(f329(f163(x81491),x81492),x81494)))+~P24(f329(f329(f244(a874),x81493),f329(f194(f875(x81491)),x81492)))
% 187.33/188.05 [8396]~P63(x83961)+~P24(f329(f329(f243(x83961),x83962),f2(x83961)))+~P24(f329(f329(f243(x83961),x83963),x83964))+~P24(f329(f329(f244(x83961),f2(x83961)),f329(f329(f81(x83961),x83963),x83964)))+P24(f329(f329(f243(x83961),f329(f329(f287(x83961),x83962),x83963)),f329(f329(f287(x83961),x83962),x83964)))
% 187.33/188.05 [8397]~P64(x83971)+~P24(f329(f329(f244(x83971),x83972),f2(x83971)))+~P24(f329(f329(f244(x83971),x83973),x83974))+~P24(f329(f329(f244(x83971),f2(x83971)),f329(f329(f81(x83971),x83973),x83974)))+P24(f329(f329(f244(x83971),f329(f329(f287(x83971),x83972),x83973)),f329(f329(f287(x83971),x83972),x83974)))
% 187.33/188.05 [8407]~P64(x84071)+~P24(f329(f329(f243(x84071),x84074),x84073))+~P24(f329(f329(f243(x84071),f2(x84071)),x84072))+~P24(f329(f329(f244(x84071),f2(x84071)),f329(f329(f81(x84071),x84073),x84074)))+P24(f329(f329(f243(x84071),f329(f329(f287(x84071),x84072),x84073)),f329(f329(f287(x84071),x84072),x84074)))
% 187.33/188.05 [8408]~P64(x84081)+~P24(f329(f329(f244(x84081),x84084),x84083))+~P24(f329(f329(f244(x84081),f2(x84081)),x84082))+~P24(f329(f329(f244(x84081),f2(x84081)),f329(f329(f81(x84081),x84083),x84084)))+P24(f329(f329(f244(x84081),f329(f329(f287(x84081),x84082),x84083)),f329(f329(f287(x84081),x84082),x84084)))
% 187.33/188.05 [8516]P24(f329(x85161,x85162))+~P24(f329(f62(x85164),x85162))+P24(f329(x85161,f426(x85161,x85163,x85162,x85164)))+~P24(f329(x85161,f193(f881(x85164,a869))))+~P24(f329(f329(f243(f881(x85164,a869)),x85162),x85163))
% 187.33/188.05 [8524]P24(f329(x85241,x85242))+P24(f329(f62(x85243),f426(x85241,x85244,x85242,x85243)))+~P24(f329(f62(x85243),x85242))+~P24(f329(x85241,f193(f881(x85243,a869))))+~P24(f329(f329(f243(f881(x85243,a869)),x85242),x85244))
% 187.33/188.05 [8772]E(f329(f329(f80(a1),f388(x87721,x87722,x87723,x87724)),f389(x87721,x87722,x87723,x87724)),x87724)+~P24(f329(f329(f244(a1),f2(a1)),x87723))+~P24(f329(f329(f244(a1),x87722),x87724))+~P24(f329(f329(f331(a1),x87722),x87721))+P24(f329(f329(f244(a1),x87722),f329(f329(f22(a1),x87724),x87723)))
% 187.33/188.05 [8991]~P24(f329(f329(f244(a1),f2(a1)),x89913))+~P24(f329(f329(f244(a1),x89912),x89914))+~P24(f329(f329(f331(a1),x89912),x89911))+P24(f329(f329(f331(a1),f388(x89911,x89912,x89913,x89914)),x89911))+P24(f329(f329(f244(a1),x89912),f329(f329(f22(a1),x89914),x89913)))
% 187.33/188.05 [9004]P24(f329(x90041,x90042))+~P24(f329(f62(x90043),x90042))+P24(f329(f329(f331(x90043),f415(x90041,x90044,x90042,x90043)),x90044))+~P24(f329(x90041,f193(f881(x90043,a869))))+~P24(f329(f329(f243(f881(x90043,a869)),x90042),x90044))
% 187.33/188.05 [9021]E(f329(f329(f80(a1),f379(x90211,x90212,x90213,x90214)),f380(x90211,x90212,x90213,x90214)),x90214)+~P24(f329(f329(f244(a1),f2(a1)),x90213))+~P24(f329(f329(f243(a1),x90212),x90214))+P24(f329(f329(f243(a1),x90212),f329(f329(f22(a1),x90214),x90213)))+~P24(f329(f329(f331(a1),f329(f329(f22(a1),x90212),f78(a1))),x90211))
% 187.33/188.05 [9073]~P24(f329(f329(f244(a1),f2(a1)),x90733))+~P24(f329(f329(f244(a1),x90731),x90732))+~P24(f329(f329(f331(a1),x90731),x90734))+P24(f329(f329(f331(a1),f389(x90734,x90731,x90733,x90732)),f300(a1,f78(a1),x90733)))+P24(f329(f329(f244(a1),x90731),f329(f329(f22(a1),x90732),x90733)))
% 187.33/188.05 [9168]~P24(f329(f329(f244(a1),f2(a1)),x91683))+~P24(f329(f329(f243(a1),x91682),x91684))+P24(f329(f329(f331(a1),f379(x91681,x91682,x91683,x91684)),x91681))+P24(f329(f329(f243(a1),x91682),f329(f329(f22(a1),x91684),x91683)))+~P24(f329(f329(f331(a1),f329(f329(f22(a1),x91682),f78(a1))),x91681))
% 187.33/188.05 [9208]~P24(f329(f329(f244(a1),f2(a1)),x92083))+~P24(f329(f329(f243(a1),x92081),x92082))+P24(f329(f329(f331(a1),f380(x92084,x92081,x92083,x92082)),f300(a1,f78(a1),x92083)))+P24(f329(f329(f243(a1),x92081),f329(f329(f22(a1),x92082),x92083)))+~P24(f329(f329(f331(a1),f329(f329(f22(a1),x92081),f78(a1))),x92084))
% 187.33/188.05 [9442]P24(f329(x94421,x94422))+~P24(f329(f329(f331(x94423),f415(x94421,x94424,x94422,x94423)),f426(x94421,x94424,x94422,x94423)))+~P24(f329(f62(x94423),x94422))+~P24(f329(x94421,f193(f881(x94423,a869))))+~P24(f329(f329(f243(f881(x94423,a869)),x94422),x94424))
% 187.33/188.05 [9659]P24(f329(x96591,x96592))+~P24(f329(f62(x96593),x96592))+~P24(f329(x96591,f329(f329(f307(x96593),f415(x96591,x96594,x96592,x96593)),f426(x96591,x96594,x96592,x96593))))+~P24(f329(x96591,f193(f881(x96593,a869))))+~P24(f329(f329(f243(f881(x96593,a869)),x96592),x96594))
% 187.33/188.05 [7695]~P63(x76951)+P24(f329(f329(f244(x76951),x76952),f2(x76951)))+~P24(f329(f329(f243(x76951),f2(x76951)),x76954))+P24(f329(f329(f244(x76951),f2(x76951)),x76952))+P24(f329(f329(f243(x76951),f329(f329(f287(x76951),x76953),x76952)),x76954))
% 187.33/188.05 [7696]~P63(x76961)+P24(f329(f329(f244(x76961),x76962),f2(x76961)))+P24(f329(f329(f244(x76961),f2(x76961)),x76962))+~P24(f329(f329(f244(x76961),f2(x76961)),x76964))+P24(f329(f329(f244(x76961),f329(f329(f287(x76961),x76963),x76962)),x76964))
% 187.33/188.05 [7980]~P24(f329(f329(f243(a1),x79804),f2(a1)))+~E(x79802,f329(f329(f80(a1),f329(f329(f81(a1),x79801),x79803)),x79804))+P24(f329(f329(f244(a1),f2(a1)),x79801))+~P24(f329(f329(f244(a1),x79801),x79804))+P24(f329(f49(x79802,x79801),f329(f329(f264(a1,a1),x79803),x79804)))
% 187.33/188.05 [8019]~P24(f329(x80191,x80194))+P24(f329(x80191,f366(x80192,x80191,x80193)))+~P24(f329(f329(f243(a1),f2(a1)),x80192))+~P24(f329(f329(f244(a1),f2(a1)),x80193))+P24(f329(x80191,f329(f329(f22(a1),x80194),f329(f329(f81(a1),x80192),x80193))))
% 187.33/188.05 [8020]~P24(f329(x80201,x80204))+P24(f329(x80201,f369(x80202,x80201,x80203)))+~P24(f329(f329(f243(a1),f2(a1)),x80202))+~P24(f329(f329(f244(a1),f2(a1)),x80203))+P24(f329(x80201,f329(f329(f80(a1),x80204),f329(f329(f81(a1),x80202),x80203))))
% 187.33/188.05 [8021]~P63(x80211)+P24(f329(f329(f244(x80211),x80212),f2(x80211)))+P24(f329(f329(f244(x80211),f2(x80211)),x80212))+P24(f329(f329(f243(x80211),f2(x80211)),x80213))+~P24(f329(f329(f243(x80211),f329(f329(f287(x80211),x80214),x80212)),x80213))
% 187.33/188.05 [8022]~P63(x80221)+P24(f329(f329(f244(x80221),x80222),f2(x80221)))+P24(f329(f329(f244(x80221),f2(x80221)),x80222))+P24(f329(f329(f244(x80221),f2(x80221)),x80223))+~P24(f329(f329(f244(x80221),f329(f329(f287(x80221),x80224),x80222)),x80223))
% 187.33/188.05 [8070]~E(x80701,f329(f329(f80(a1),f329(f329(f81(a1),x80702),x80703)),x80704))+~P24(f329(f329(f243(a1),f2(a1)),x80704))+~P24(f329(f329(f244(a1),f2(a1)),x80702))+~P24(f329(f329(f244(a1),x80704),x80702))+P24(f329(f49(x80701,x80702),f329(f329(f264(a1,a1),x80703),x80704)))
% 187.33/188.05 [8193]~P63(x81931)+P24(f329(f329(f244(x81931),x81932),f2(x81931)))+~P24(f329(f329(f243(x81931),f2(x81931)),x81934))+~P24(f329(f329(f243(x81931),x81933),f329(f329(f81(x81931),x81934),x81932)))+P24(f329(f329(f243(x81931),f329(f329(f287(x81931),x81933),x81932)),x81934))
% 187.33/188.05 [8194]~P63(x81941)+P24(f329(f329(f244(x81941),x81942),f2(x81941)))+~P24(f329(f329(f244(x81941),f2(x81941)),x81944))+~P24(f329(f329(f244(x81941),x81943),f329(f329(f81(x81941),x81944),x81942)))+P24(f329(f329(f244(x81941),f329(f329(f287(x81941),x81943),x81942)),x81944))
% 187.33/188.05 [8275]~P63(x82751)+P24(f329(f329(f244(x82751),x82752),f2(x82751)))+~P24(f329(f329(f243(x82751),x82753),f2(x82751)))+P24(f329(f329(f243(x82751),x82753),f329(f329(f287(x82751),x82754),x82752)))+~P24(f329(f329(f243(x82751),f329(f329(f81(x82751),x82753),x82752)),x82754))
% 187.33/188.05 [8276]~P63(x82761)+P24(f329(f329(f244(x82761),x82762),f2(x82761)))+~P24(f329(f329(f244(x82761),x82763),f2(x82761)))+P24(f329(f329(f244(x82761),x82763),f329(f329(f287(x82761),x82764),x82762)))+~P24(f329(f329(f244(x82761),f329(f329(f81(x82761),x82763),x82762)),x82764))
% 187.33/188.05 [8434]~P63(x84341)+~P24(f329(f329(f244(x84341),x84342),f2(x84341)))+P24(f329(f329(f244(x84341),f2(x84341)),x84342))+~P24(f329(f329(f243(x84341),f329(f329(f287(x84341),x84344),x84342)),x84343))+P24(f329(f329(f243(x84341),f329(f329(f81(x84341),x84343),x84342)),x84344))
% 187.33/188.05 [8435]~P63(x84351)+~P24(f329(f329(f244(x84351),x84352),f2(x84351)))+P24(f329(f329(f244(x84351),f2(x84351)),x84352))+~P24(f329(f329(f243(x84351),f329(f329(f81(x84351),x84354),x84352)),x84353))+P24(f329(f329(f243(x84351),f329(f329(f287(x84351),x84353),x84352)),x84354))
% 187.33/188.05 [8436]~P63(x84361)+~P24(f329(f329(f244(x84361),x84362),f2(x84361)))+P24(f329(f329(f244(x84361),f2(x84361)),x84362))+~P24(f329(f329(f244(x84361),f329(f329(f287(x84361),x84364),x84362)),x84363))+P24(f329(f329(f244(x84361),f329(f329(f81(x84361),x84363),x84362)),x84364))
% 187.33/188.05 [8437]~P63(x84371)+~P24(f329(f329(f244(x84371),x84372),f2(x84371)))+P24(f329(f329(f244(x84371),f2(x84371)),x84372))+~P24(f329(f329(f244(x84371),f329(f329(f81(x84371),x84374),x84372)),x84373))+P24(f329(f329(f244(x84371),f329(f329(f287(x84371),x84373),x84372)),x84374))
% 187.33/188.05 [8459]~P63(x84591)+~P24(f329(f329(f243(x84591),f2(x84591)),x84594))+P24(f329(f329(f244(x84591),f2(x84591)),x84592))+~P24(f329(f329(f243(x84591),f329(f329(f81(x84591),x84594),x84592)),x84593))+P24(f329(f329(f243(x84591),f329(f329(f287(x84591),x84593),x84592)),x84594))
% 187.33/188.05 [8460]~P63(x84601)+~P24(f329(f329(f244(x84601),f2(x84601)),x84604))+P24(f329(f329(f244(x84601),f2(x84601)),x84602))+~P24(f329(f329(f244(x84601),f329(f329(f81(x84601),x84604),x84602)),x84603))+P24(f329(f329(f244(x84601),f329(f329(f287(x84601),x84603),x84602)),x84604))
% 187.33/188.05 [8532]~P63(x85321)+~P24(f329(f329(f244(x85321),x85324),f2(x85321)))+~P24(f329(f329(f243(x85321),x85323),f329(f329(f81(x85321),x85322),x85324)))+P24(f329(f329(f243(x85321),x85322),f329(f329(f287(x85321),x85323),x85324)))+~P24(f329(f329(f243(x85321),f329(f329(f81(x85321),x85322),x85324)),x85323))
% 187.33/188.05 [8533]~P63(x85331)+~P24(f329(f329(f243(x85331),x85332),f2(x85331)))+~P24(f329(f329(f243(x85331),x85333),f329(f329(f81(x85331),x85332),x85334)))+P24(f329(f329(f243(x85331),x85332),f329(f329(f287(x85331),x85333),x85334)))+~P24(f329(f329(f243(x85331),f329(f329(f81(x85331),x85332),x85334)),x85333))
% 187.33/188.05 [8534]~P63(x85341)+~P24(f329(f329(f244(x85341),x85344),f2(x85341)))+~P24(f329(f329(f244(x85341),x85343),f329(f329(f81(x85341),x85342),x85344)))+P24(f329(f329(f244(x85341),x85342),f329(f329(f287(x85341),x85343),x85344)))+~P24(f329(f329(f244(x85341),f329(f329(f81(x85341),x85342),x85344)),x85343))
% 187.33/188.05 [8535]~P63(x85351)+~P24(f329(f329(f244(x85351),x85352),f2(x85351)))+~P24(f329(f329(f244(x85351),x85353),f329(f329(f81(x85351),x85352),x85354)))+P24(f329(f329(f244(x85351),x85352),f329(f329(f287(x85351),x85353),x85354)))+~P24(f329(f329(f244(x85351),f329(f329(f81(x85351),x85352),x85354)),x85353))
% 187.33/188.05 [8648]~P63(x86481)+~P24(f329(f329(f244(x86481),x86483),f2(x86481)))+~P24(f329(f329(f243(x86481),x86482),f329(f329(f81(x86481),x86484),x86483)))+~P24(f329(f329(f243(x86481),f329(f329(f81(x86481),x86484),x86483)),x86482))+P24(f329(f329(f243(x86481),f329(f329(f287(x86481),x86482),x86483)),x86484))
% 187.33/188.05 [8649]~P63(x86491)+~P24(f329(f329(f244(x86491),x86493),f2(x86491)))+~P24(f329(f329(f244(x86491),x86492),f329(f329(f81(x86491),x86494),x86493)))+~P24(f329(f329(f244(x86491),f329(f329(f81(x86491),x86494),x86493)),x86492))+P24(f329(f329(f244(x86491),f329(f329(f287(x86491),x86492),x86493)),x86494))
% 187.33/188.05 [8665]~P63(x86651)+~P24(f329(f329(f243(x86651),f2(x86651)),x86654))+~P24(f329(f329(f243(x86651),x86652),f329(f329(f81(x86651),x86654),x86653)))+~P24(f329(f329(f243(x86651),f329(f329(f81(x86651),x86654),x86653)),x86652))+P24(f329(f329(f243(x86651),f329(f329(f287(x86651),x86652),x86653)),x86654))
% 187.33/188.05 [8666]~P63(x86661)+~P24(f329(f329(f244(x86661),f2(x86661)),x86664))+~P24(f329(f329(f244(x86661),x86662),f329(f329(f81(x86661),x86664),x86663)))+~P24(f329(f329(f244(x86661),f329(f329(f81(x86661),x86664),x86663)),x86662))+P24(f329(f329(f244(x86661),f329(f329(f287(x86661),x86662),x86663)),x86664))
% 187.33/188.05 [8832]E(f329(f329(f22(a1),f390(x88321,x88322,x88323,x88324)),f391(x88321,x88322,x88323,x88324)),x88324)+~P24(f329(f329(f244(a1),f2(a1)),x88323))+~P24(f329(f329(f331(a1),x88322),x88321))+~P24(f329(f329(f244(a1),x88324),x88322))+P24(f329(f329(f244(a1),f329(f329(f80(a1),x88324),x88323)),x88322))
% 187.33/188.05 [8912]~P24(f329(x89121,x89122))+~P24(f329(f329(f243(a1),f2(a1)),x89123))+~P24(f329(f329(f244(a1),f2(a1)),x89124))+~P24(f329(x89121,f329(f329(f22(a1),f366(x89123,x89121,x89124)),x89124)))+P24(f329(x89121,f329(f329(f22(a1),x89122),f329(f329(f81(a1),x89123),x89124))))
% 187.33/188.05 [8913]~P24(f329(x89131,x89132))+~P24(f329(f329(f243(a1),f2(a1)),x89133))+~P24(f329(f329(f244(a1),f2(a1)),x89134))+~P24(f329(x89131,f329(f329(f80(a1),f369(x89133,x89131,x89134)),x89134)))+P24(f329(x89131,f329(f329(f80(a1),x89132),f329(f329(f81(a1),x89133),x89134))))
% 187.33/188.05 [9067]~P24(f329(f329(f244(a1),f2(a1)),x90673))+~P24(f329(f329(f331(a1),x90672),x90671))+~P24(f329(f329(f244(a1),x90674),x90672))+P24(f329(f329(f331(a1),f390(x90671,x90672,x90673,x90674)),x90671))+P24(f329(f329(f244(a1),f329(f329(f80(a1),x90674),x90673)),x90672))
% 187.33/188.05 [9087]E(f329(f329(f22(a1),f381(x90871,x90872,x90873,x90874)),f382(x90871,x90872,x90873,x90874)),x90874)+~P24(f329(f329(f244(a1),f2(a1)),x90873))+~P24(f329(f329(f243(a1),x90874),x90872))+~P24(f329(f329(f331(a1),f329(f329(f80(a1),x90872),f78(a1))),x90871))+P24(f329(f329(f243(a1),f329(f329(f80(a1),x90874),x90873)),x90872))
% 187.33/188.05 [9113]~P24(f329(f329(f244(a1),f2(a1)),x91132))+~P24(f329(f329(f331(a1),x91133),x91134))+~P24(f329(f329(f244(a1),x91131),x91133))+P24(f329(f329(f331(a1),f391(x91134,x91133,x91132,x91131)),f300(a1,f78(a1),x91132)))+P24(f329(f329(f244(a1),f329(f329(f80(a1),x91131),x91132)),x91133))
% 187.33/188.05 [9203]~P24(f329(f329(f244(a1),f2(a1)),x92033))+~P24(f329(f329(f243(a1),x92034),x92032))+P24(f329(f329(f331(a1),f381(x92031,x92032,x92033,x92034)),x92031))+~P24(f329(f329(f331(a1),f329(f329(f80(a1),x92032),f78(a1))),x92031))+P24(f329(f329(f243(a1),f329(f329(f80(a1),x92034),x92033)),x92032))
% 187.33/188.05 [9250]~P24(f329(f329(f244(a1),f2(a1)),x92502))+~P24(f329(f329(f243(a1),x92501),x92503))+P24(f329(f329(f331(a1),f382(x92504,x92503,x92502,x92501)),f300(a1,f78(a1),x92502)))+~P24(f329(f329(f331(a1),f329(f329(f80(a1),x92503),f78(a1))),x92504))+P24(f329(f329(f243(a1),f329(f329(f80(a1),x92501),x92502)),x92503))
% 187.33/188.05 [9535]~P42(x95351,x95353)+~P22(x95351,x95354)+P42(x95351,f329(f329(f115(f881(f880(x95351,x95351),a869)),x95352),x95353))+~P24(f329(f329(f243(f881(f880(x95351,x95351),a869)),x95352),f329(f263(f881(f880(x95351,x95351),a869),f881(f880(x95351,x95351),a869)),x95354)))+~P24(f329(f329(f243(f881(f880(x95351,x95351),a869)),x95353),f329(f267(f881(f880(x95351,x95351),a869),f881(f880(x95351,x95351),a869)),x95354)))
% 187.33/188.05 [9828]~E(f329(f723(x98281,x98284,x98283,x98282),f725(x98281,x98284,x98283,x98282)),f206(f875(a325)))+P24(f329(f329(f244(a1),f724(x98281,x98284,x98283,x98282)),f725(x98281,x98284,x98283,x98282)))+P24(f329(f329(f329(x98281,x98282),x98283),x98284))+P24(f329(f329(f329(x98281,f723(x98281,x98284,x98283,x98282)),f724(x98281,x98284,x98283,x98282)),f329(f329(f80(a1),f725(x98281,x98284,x98283,x98282)),f78(a1))))+~P24(f329(f317(f880(f881(a1,f878(f875(a325))),f880(a1,a1)),a315),f329(f329(f264(f881(a1,f878(f875(a325))),f880(a1,a1)),x98282),f329(f329(f264(a1,a1),x98283),x98284))))
% 187.33/188.05 [9930]~P14(x99302,x99304,x99303)+E(x99301,f193(f881(x99302,a869)))+~P24(f329(f62(x99302),x99301))+P24(f329(f329(f331(x99302),f329(x99303,x99301)),x99301))+~P24(f329(f329(f331(x99302),f329(f329(x99304,f482(x99301,x99303,x99304,x99302)),f490(x99301,x99303,x99304,x99302))),f329(f329(f307(x99302),f482(x99301,x99303,x99304,x99302)),f329(f329(f307(x99302),f490(x99301,x99303,x99304,x99302)),f193(f881(x99302,a869))))))
% 187.33/188.05 [9861]~P106(x98612)+~P60(x98611)+~P24(f329(f329(f243(f881(x98611,x98612)),x98613),x98614))+P24(f329(f329(f244(f881(x98611,x98612)),x98613),x98614))+~P24(f329(f58(x98611),f329(f329(f8(a869,a869,x98611),a324),f329(f329(f18(x98611,x98612,a869),f329(f329(f8(x98612,f881(x98612,a869),x98611),a326),x98613)),x98614))))
% 187.33/188.05 [9450]~P54(x94501,x94501,x94504)+P24(f329(f329(f331(f880(x94501,x94501)),f329(f329(f264(x94501,x94501),x94502),x94503)),f305(x94501,x94504)))+P24(f329(f329(f331(f880(x94501,x94501)),f329(f329(f264(x94501,x94501),x94503),x94502)),f305(x94501,x94504)))+~P24(f329(f329(f331(f880(x94501,x94501)),f329(f329(f264(x94501,x94501),x94505),x94502)),f305(x94501,x94504)))+~P24(f329(f329(f331(f880(x94501,x94501)),f329(f329(f264(x94501,x94501),x94505),x94503)),f305(x94501,x94504)))
% 187.33/188.05 [5598]E(x55981,f2(a874))+~E(f329(f38(x55982),x55985),x55981)+E(f329(f38(x55982),x55983),f329(a117,x55981))+~E(x55983,f329(f329(f307(x55982),x55984),x55985))+P24(f329(f329(f331(x55982),x55984),x55985))
% 187.33/188.05 [5724]~P62(x57242)+E(x57241,f2(x57242))+E(x57243,f2(x57242))+~E(f329(f329(f287(x57242),x57244),x57243),f329(f329(f287(x57242),x57245),x57241))+E(f329(f329(f81(x57242),x57244),x57241),f329(f329(f81(x57242),x57245),x57243))
% 187.33/188.05 [5725]~P62(x57252)+E(x57251,f2(x57252))+E(x57253,f2(x57252))+~E(f329(f329(f81(x57252),x57254),x57253),f329(f329(f81(x57252),x57255),x57251))+E(f329(f329(f287(x57252),x57254),x57251),f329(f329(f287(x57252),x57255),x57253))
% 187.33/188.05 [5791]~E(f329(f38(x57911),x57915),x57913)+~E(x57915,f193(f881(x57911,a869)))+E(f329(f38(x57911),x57912),f329(a117,x57913))+~E(x57912,f329(f329(f307(x57911),x57914),x57915))+P24(f329(f329(f331(x57911),x57914),x57915))
% 187.33/188.05 [6018]~P109(x60182)+~E(f329(x60183,x60185),f2(x60182))+E(f329(f329(f9(x60181,x60182),x60183),x60184),f2(x60182))+~P24(f329(f62(x60181),x60184))+~P24(f329(f329(f331(x60181),x60185),x60184))
% 187.33/188.05 [6389]~P27(x63893)+E(x63891,x63892)+~E(f329(f299(x63893,x63894),x63891),f329(f299(x63893,x63895),x63892))+~P24(f329(f329(f244(x63893),x63895),x63892))+~P24(f329(f329(f244(x63893),x63894),x63891))
% 187.33/188.05 [6390]~P27(x63903)+E(x63901,x63902)+~E(f329(f299(x63903,x63901),x63904),f329(f299(x63903,x63902),x63905))+~P24(f329(f329(f244(x63903),x63902),x63905))+~P24(f329(f329(f244(x63903),x63901),x63904))
% 187.33/188.05 [7455]~P27(x74551)+~P33(x74551,f329(f329(f126(x74551),x74554),x74555))+~P24(f329(f329(f331(x74551),x74553),f329(f171(x74551),x74555)))+~P24(f329(f329(f331(x74551),x74552),f329(f171(x74551),x74554)))+P24(f329(f329(f243(x74551),x74552),x74553))
% 187.33/188.05 [8568]~P106(x85681)+~P24(f329(f329(f244(f881(x85681,a869)),f300(x85681,x85685,x85682)),f300(x85681,x85684,x85683)))+~P24(f329(f329(f243(x85681),x85685),x85682))+P24(f329(f329(f244(x85681),x85682),x85683))+P24(f329(f329(f244(x85681),x85684),x85685))
% 187.33/188.05 [9973]~P13(x99732,x99735,x99733)+E(x99731,f193(f881(x99732,a869)))+~E(f329(f329(x99735,f329(x99734,f525(x99731,x99734,x99733,x99735,x99732))),f329(x99734,f532(x99731,x99734,x99733,x99735,x99732))),f329(x99734,f329(f329(x99735,f525(x99731,x99734,x99733,x99735,x99732)),f532(x99731,x99734,x99733,x99735,x99732))))+E(f329(x99733,f329(f308(x99732,x99732,x99734),x99731)),f329(x99734,f329(x99733,x99731)))+~P24(f329(f62(x99732),x99731))
% 187.33/188.05 [6386]~P14(x63862,x63865,x63863)+E(x63861,f193(f881(x63862,a869)))+~P24(f329(f62(x63862),x63861))+E(f329(x63863,f329(f329(f307(x63862),x63864),x63861)),f329(f329(x63865,x63864),f329(x63863,x63861)))+P24(f329(f329(f331(x63862),x63864),x63861))
% 187.33/188.05 [7211]~P13(x72112,x72113,x72114)+E(f329(f329(x72113,f329(x72114,x72111)),f329(x72114,x72115)),f329(x72114,x72115))+E(x72111,f193(f881(x72112,a869)))+~P24(f329(f62(x72112),x72115))+~P24(f329(f329(f243(f881(x72112,a869)),x72111),x72115))
% 187.33/188.05 [7431]~P60(x74314)+~P96(x74315)+E(f329(x74311,x74312),f329(x74313,x74312))+~P24(f329(f329(f331(x74314),x74312),f329(f171(x74314),f56(x74314))))+~P24(f329(f329(f91(f881(x74314,x74315)),x74311),x74313))
% 187.33/188.05 [7590]~P14(x75904,x75905,x75901)+E(f329(x75901,x75902),x75903)+~P24(f329(f62(x75904),x75902))+~E(f329(f329(f22(f881(x75904,a869)),x75902),f329(f329(f307(x75904),x75903),f193(f881(x75904,a869)))),f193(f881(x75904,a869)))+~P24(f329(f329(f331(x75904),x75903),x75902))
% 187.33/188.05 [7677]E(x76771,x76772)+~E(f329(f194(f875(x76773)),x76772),f329(f194(f875(x76774)),x76775))+~E(f329(f194(f875(x76773)),x76771),f329(f194(f875(x76774)),x76775))+~E(f329(f177(x76774,x76773),f329(f329(f181(x76774,x76773),x76775),x76771)),f329(f177(x76774,x76773),f329(f329(f181(x76774,x76773),x76775),x76772)))+~P24(f329(f135(x76774),x76775))
% 187.33/188.05 [8539]E(x85391,x85392)+~P6(x85393,x85394,x85395)+E(f329(f329(f106(f881(x85393,a869)),x85391),x85392),f193(f881(x85393,a869)))+~P24(f329(f329(f331(f881(x85393,a869)),x85392),f329(f329(f61(x85393),x85394),x85395)))+~P24(f329(f329(f331(f881(x85393,a869)),x85391),f329(f329(f61(x85393),x85394),x85395)))
% 187.33/188.05 [9332]~P72(x93322)+~E(f329(x93323,f850(x93323,x93324,x93325,x93321,x93322)),f2(x93322))+E(f329(f329(f6(x93321,x93322),x93323),x93324),f329(f329(f6(x93321,x93322),x93323),x93325))+~P24(f329(f62(x93321),x93325))+~P24(f329(f329(f243(f881(x93321,a869)),x93324),x93325))
% 187.33/188.06 [9333]~P72(x93332)+~E(f329(x93333,f853(x93333,x93334,x93335,x93331,x93332)),f2(x93332))+E(f329(f329(f6(x93331,x93332),x93333),x93334),f329(f329(f6(x93331,x93332),x93333),x93335))+~P24(f329(f62(x93331),x93335))+~P24(f329(f329(f243(f881(x93331,a869)),x93334),x93335))
% 187.33/188.06 [9334]~P76(x93342)+~E(f329(x93343,f849(x93343,x93344,x93345,x93341,x93342)),f78(x93342))+E(f329(f329(f9(x93341,x93342),x93343),x93344),f329(f329(f9(x93341,x93342),x93343),x93345))+~P24(f329(f62(x93341),x93345))+~P24(f329(f329(f243(f881(x93341,a869)),x93344),x93345))
% 187.33/188.06 [9335]~P76(x93352)+~E(f329(x93353,f851(x93353,x93354,x93355,x93351,x93352)),f78(x93352))+E(f329(f329(f9(x93351,x93352),x93353),x93354),f329(f329(f9(x93351,x93352),x93353),x93355))+~P24(f329(f62(x93351),x93355))+~P24(f329(f329(f243(f881(x93351,a869)),x93354),x93355))
% 187.33/188.06 [9808]~P89(x98081)+~P24(f329(f62(x98082),x98085))+~P24(f329(f329(f243(x98081),f2(x98081)),f329(x98083,f839(x98083,x98084,x98085,x98082,x98081))))+P24(f329(f329(f243(x98081),f329(f329(f6(x98082,x98081),x98083),x98084)),f329(f329(f6(x98082,x98081),x98083),x98085)))+~P24(f329(f329(f243(f881(x98082,a869)),x98084),x98085))
% 187.33/188.06 [7452]E(x74521,f2(a874))+P24(f329(x74522,x74523))+~E(x74524,f329(f329(f80(a874),f329(f329(f81(a874),x74521),x74523)),x74525))+~P24(f329(f329(f244(a874),x74525),x74521))+~P24(f329(x74522,f329(f329(f39(a874),x74524),x74521)))
% 187.33/188.06 [7531]E(x75311,f2(a874))+P24(f329(x75312,x75313))+~P24(f329(x75312,f45(a874,x75314,x75311)))+~E(x75314,f329(f329(f80(a874),f329(f329(f81(a874),x75311),x75315)),x75313))+~P24(f329(f329(f244(a874),x75313),x75311))
% 187.33/188.06 [7827]~P62(x78273)+E(f329(x78271,x78272),f2(x78273))+~P24(f329(f62(x78274),x78275))+E(f329(f329(f9(x78274,x78273),x78271),f329(f329(f22(f881(x78274,a869)),x78275),f329(f329(f307(x78274),x78272),f193(f881(x78274,a869))))),f329(f329(f9(x78274,x78273),x78271),x78275))+P24(f329(f329(f331(x78274),x78272),x78275))
% 187.33/188.06 [8234]~P72(x82341)+~P24(f329(f62(x82342),x82345))+~P24(f329(f62(x82342),x82344))+~E(f329(f329(f106(f881(x82342,a869)),x82344),x82345),f193(f881(x82342,a869)))+E(f329(f329(f80(x82341),f329(f329(f6(x82342,x82341),x82343),x82344)),f329(f329(f6(x82342,x82341),x82343),x82345)),f329(f329(f6(x82342,x82341),x82343),f329(f329(f115(f881(x82342,a869)),x82344),x82345)))
% 187.33/188.06 [8236]~P76(x82361)+~P24(f329(f62(x82362),x82365))+~P24(f329(f62(x82362),x82364))+~E(f329(f329(f106(f881(x82362,a869)),x82364),x82365),f193(f881(x82362,a869)))+E(f329(f329(f81(x82361),f329(f329(f9(x82362,x82361),x82363),x82364)),f329(f329(f9(x82362,x82361),x82363),x82365)),f329(f329(f9(x82362,x82361),x82363),f329(f329(f115(f881(x82362,a869)),x82364),x82365)))
% 187.33/188.06 [8329]~P62(x83293)+E(f329(x83291,x83292),f2(x83293))+~P24(f329(f62(x83294),x83295))+E(f329(f329(f9(x83294,x83293),x83291),f329(f329(f22(f881(x83294,a869)),x83295),f329(f329(f307(x83294),x83292),f193(f881(x83294,a869))))),f329(f329(f287(x83293),f329(f329(f9(x83294,x83293),x83291),x83295)),f329(x83291,x83292)))+~P24(f329(f329(f331(x83294),x83292),x83295))
% 187.33/188.06 [9046]~P6(x90461,x90465,x90464)+~E(f329(f329(f61(x90461),f329(f329(f307(x90461),x90462),f193(f881(x90461,a869)))),x90464),f329(f329(f61(x90461),f329(f329(f307(x90461),x90463),f193(f881(x90461,a869)))),x90464))+~P24(f329(f329(f331(x90461),x90463),x90465))+~P24(f329(f329(f331(x90461),x90462),x90465))+P24(f329(f329(f331(f880(x90461,x90461)),f329(f329(f264(x90461,x90461),x90462),x90463)),x90464))
% 187.33/188.06 [9066]~P6(x90661,x90665,x90663)+E(f329(f329(f61(x90661),f329(f329(f307(x90661),x90662),f193(f881(x90661,a869)))),x90663),f329(f329(f61(x90661),f329(f329(f307(x90661),x90664),f193(f881(x90661,a869)))),x90663))+~P24(f329(f329(f331(x90661),x90664),x90665))+~P24(f329(f329(f331(x90661),x90662),x90665))+~P24(f329(f329(f331(f880(x90661,x90661)),f329(f329(f264(x90661,x90661),x90662),x90664)),x90663))
% 187.33/188.06 [9361]~P76(x93611)+~P24(f329(f62(x93612),x93615))+~P24(f329(f62(x93612),x93614))+~E(f329(f329(f106(f881(x93612,a869)),x93614),x93615),f193(f881(x93612,a869)))+E(f329(f329(f81(x93611),f329(f329(f329(f66(x93611,x93612,f81(x93611)),x93613),f78(x93611)),x93614)),f329(f329(f329(f66(x93611,x93612,f81(x93611)),x93613),f78(x93611)),x93615)),f329(f329(f329(f66(x93611,x93612,f81(x93611)),x93613),f78(x93611)),f329(f329(f115(f881(x93612,a869)),x93614),x93615)))
% 187.33/188.06 [9370]~P72(x93701)+~E(f329(x93703,f840(x93703,x93705,x93704,x93702,x93701)),f2(x93701))+~P24(f329(f62(x93702),x93704))+~P24(f329(f62(x93702),x93705))+E(f329(f329(f80(x93701),f329(f329(f6(x93702,x93701),x93703),x93704)),f329(f329(f6(x93702,x93701),x93703),x93705)),f329(f329(f6(x93702,x93701),x93703),f329(f329(f115(f881(x93702,a869)),x93704),x93705)))
% 187.33/188.06 [9371]~P72(x93711)+~E(f329(x93713,f843(x93713,x93715,x93714,x93712,x93711)),f2(x93711))+~P24(f329(f62(x93712),x93714))+~P24(f329(f62(x93712),x93715))+E(f329(f329(f80(x93711),f329(f329(f6(x93712,x93711),x93713),x93714)),f329(f329(f6(x93712,x93711),x93713),x93715)),f329(f329(f6(x93712,x93711),x93713),f329(f329(f115(f881(x93712,a869)),x93714),x93715)))
% 187.33/188.06 [9372]~P76(x93721)+~E(f329(x93723,f841(x93723,x93725,x93724,x93722,x93721)),f78(x93721))+~P24(f329(f62(x93722),x93724))+~P24(f329(f62(x93722),x93725))+E(f329(f329(f81(x93721),f329(f329(f9(x93722,x93721),x93723),x93724)),f329(f329(f9(x93722,x93721),x93723),x93725)),f329(f329(f9(x93722,x93721),x93723),f329(f329(f115(f881(x93722,a869)),x93724),x93725)))
% 187.33/188.06 [9373]~P76(x93731)+~E(f329(x93733,f842(x93733,x93735,x93734,x93732,x93731)),f78(x93731))+~P24(f329(f62(x93732),x93734))+~P24(f329(f62(x93732),x93735))+E(f329(f329(f81(x93731),f329(f329(f9(x93732,x93731),x93733),x93734)),f329(f329(f9(x93732,x93731),x93733),x93735)),f329(f329(f9(x93732,x93731),x93733),f329(f329(f115(f881(x93732,a869)),x93734),x93735)))
% 187.33/188.06 [9579]~P76(x95791)+~E(f329(x95793,f822(x95793,x95795,x95794,x95792,x95791)),f78(x95791))+~P24(f329(f62(x95792),x95794))+~P24(f329(f62(x95792),x95795))+E(f329(f329(f81(x95791),f329(f329(f329(f66(x95791,x95792,f81(x95791)),x95793),f78(x95791)),x95794)),f329(f329(f329(f66(x95791,x95792,f81(x95791)),x95793),f78(x95791)),x95795)),f329(f329(f329(f66(x95791,x95792,f81(x95791)),x95793),f78(x95791)),f329(f329(f115(f881(x95792,a869)),x95794),x95795)))
% 187.33/188.06 [9686]~P72(x96862)+E(f329(f329(f6(x96861,x96862),x96863),x96864),f329(f329(f6(x96861,x96862),x96863),x96865))+~P24(f329(f62(x96861),x96865))+~P24(f329(f329(f243(f881(x96861,a869)),x96864),x96865))+P24(f329(f329(f331(x96861),f850(x96863,x96864,x96865,x96861,x96862)),f329(f329(f22(f881(x96861,a869)),x96865),x96864)))
% 187.33/188.06 [9687]~P72(x96872)+E(f329(f329(f6(x96871,x96872),x96873),x96874),f329(f329(f6(x96871,x96872),x96873),x96875))+~P24(f329(f62(x96871),x96875))+~P24(f329(f329(f243(f881(x96871,a869)),x96874),x96875))+P24(f329(f329(f331(x96871),f853(x96873,x96874,x96875,x96871,x96872)),f329(f329(f22(f881(x96871,a869)),x96875),x96874)))
% 187.33/188.06 [9688]~P76(x96882)+E(f329(f329(f9(x96881,x96882),x96883),x96884),f329(f329(f9(x96881,x96882),x96883),x96885))+~P24(f329(f62(x96881),x96885))+~P24(f329(f329(f243(f881(x96881,a869)),x96884),x96885))+P24(f329(f329(f331(x96881),f849(x96883,x96884,x96885,x96881,x96882)),f329(f329(f22(f881(x96881,a869)),x96885),x96884)))
% 187.33/188.06 [9689]~P76(x96892)+E(f329(f329(f9(x96891,x96892),x96893),x96894),f329(f329(f9(x96891,x96892),x96893),x96895))+~P24(f329(f62(x96891),x96895))+~P24(f329(f329(f243(f881(x96891,a869)),x96894),x96895))+P24(f329(f329(f331(x96891),f851(x96893,x96894,x96895,x96891,x96892)),f329(f329(f22(f881(x96891,a869)),x96895),x96894)))
% 187.33/188.06 [9707]~P72(x97071)+~P24(f329(f62(x97072),x97074))+~P24(f329(f62(x97072),x97075))+E(f329(f329(f80(x97071),f329(f329(f6(x97072,x97071),x97073),x97074)),f329(f329(f6(x97072,x97071),x97073),x97075)),f329(f329(f6(x97072,x97071),x97073),f329(f329(f115(f881(x97072,a869)),x97074),x97075)))+P24(f329(f329(f331(x97072),f840(x97073,x97075,x97074,x97072,x97071)),f329(f329(f106(f881(x97072,a869)),x97074),x97075)))
% 187.33/188.06 [9708]~P72(x97081)+~P24(f329(f62(x97082),x97084))+~P24(f329(f62(x97082),x97085))+E(f329(f329(f80(x97081),f329(f329(f6(x97082,x97081),x97083),x97084)),f329(f329(f6(x97082,x97081),x97083),x97085)),f329(f329(f6(x97082,x97081),x97083),f329(f329(f115(f881(x97082,a869)),x97084),x97085)))+P24(f329(f329(f331(x97082),f843(x97083,x97085,x97084,x97082,x97081)),f329(f329(f106(f881(x97082,a869)),x97084),x97085)))
% 187.33/188.06 [9709]~P76(x97091)+~P24(f329(f62(x97092),x97094))+~P24(f329(f62(x97092),x97095))+E(f329(f329(f81(x97091),f329(f329(f9(x97092,x97091),x97093),x97094)),f329(f329(f9(x97092,x97091),x97093),x97095)),f329(f329(f9(x97092,x97091),x97093),f329(f329(f115(f881(x97092,a869)),x97094),x97095)))+P24(f329(f329(f331(x97092),f841(x97093,x97095,x97094,x97092,x97091)),f329(f329(f106(f881(x97092,a869)),x97094),x97095)))
% 187.33/188.06 [9710]~P76(x97101)+~P24(f329(f62(x97102),x97104))+~P24(f329(f62(x97102),x97105))+E(f329(f329(f81(x97101),f329(f329(f9(x97102,x97101),x97103),x97104)),f329(f329(f9(x97102,x97101),x97103),x97105)),f329(f329(f9(x97102,x97101),x97103),f329(f329(f115(f881(x97102,a869)),x97104),x97105)))+P24(f329(f329(f331(x97102),f842(x97103,x97105,x97104,x97102,x97101)),f329(f329(f106(f881(x97102,a869)),x97104),x97105)))
% 187.33/188.06 [9717]~P89(x97175)+~P24(f329(f62(x97171),x97174))+P24(f329(f329(f243(x97175),f329(f329(f6(x97171,x97175),x97172),x97173)),f329(f329(f6(x97171,x97175),x97172),x97174)))+~P24(f329(f329(f243(f881(x97171,a869)),x97173),x97174))+P24(f329(f329(f331(x97171),f839(x97172,x97173,x97174,x97171,x97175)),f329(f329(f22(f881(x97171,a869)),x97174),x97173)))
% 187.33/188.06 [9771]~P76(x97711)+~P24(f329(f62(x97712),x97714))+~P24(f329(f62(x97712),x97715))+E(f329(f329(f81(x97711),f329(f329(f329(f66(x97711,x97712,f81(x97711)),x97713),f78(x97711)),x97714)),f329(f329(f329(f66(x97711,x97712,f81(x97711)),x97713),f78(x97711)),x97715)),f329(f329(f329(f66(x97711,x97712,f81(x97711)),x97713),f78(x97711)),f329(f329(f115(f881(x97712,a869)),x97714),x97715)))+P24(f329(f329(f331(x97712),f822(x97713,x97715,x97714,x97712,x97711)),f329(f329(f106(f881(x97712,a869)),x97714),x97715)))
% 187.33/188.06 [8733]~P14(x87331,x87334,x87335)+~P24(f329(f62(x87331),x87332))+E(f329(f329(f22(f881(x87331,a869)),x87332),f329(f329(f307(x87331),x87333),f193(f881(x87331,a869)))),f193(f881(x87331,a869)))+~P24(f329(f329(f331(x87331),x87333),x87332))+E(f329(f329(x87334,x87333),f329(x87335,f329(f329(f22(f881(x87331,a869)),x87332),f329(f329(f307(x87331),x87333),f193(f881(x87331,a869)))))),f329(x87335,x87332))
% 187.33/188.06 [8806]~P14(x88061,x88064,x88065)+~P24(f329(f62(x88061),x88063))+~P24(f329(f62(x88061),x88062))+E(f329(f329(f106(f881(x88061,a869)),x88062),x88063),f193(f881(x88061,a869)))+E(f329(f329(x88064,f329(x88065,f329(f329(f115(f881(x88061,a869)),x88062),x88063))),f329(x88065,f329(f329(f106(f881(x88061,a869)),x88062),x88063))),f329(f329(x88064,f329(x88065,x88062)),f329(x88065,x88063)))
% 187.33/188.06 [9375]~P24(f329(f329(f243(a1),x93754),f2(a1)))+~P24(f329(f329(f244(a1),x93753),x93755))+P24(f329(f329(f243(a1),x93751),x93752))+~P24(f329(f329(f244(a1),x93753),x93754))+~P24(f329(f329(f243(a1),f329(f329(f80(a1),f329(f329(f81(a1),x93753),x93752)),x93755)),f329(f329(f80(a1),f329(f329(f81(a1),x93753),x93751)),x93754)))
% 187.33/188.06 [9377]~P24(f329(f329(f243(a1),f2(a1)),x93775))+P24(f329(f329(f243(a1),x93771),x93772))+~P24(f329(f329(f244(a1),x93773),x93774))+~P24(f329(f329(f244(a1),x93775),x93774))+~P24(f329(f329(f243(a1),f329(f329(f80(a1),f329(f329(f81(a1),x93774),x93771)),x93775)),f329(f329(f80(a1),f329(f329(f81(a1),x93774),x93772)),x93773)))
% 187.33/188.06 [9488]~P62(x94885)+E(f329(x94881,f852(x94881,x94882,x94883,x94884,x94885)),f2(x94885))+~P24(f329(f62(x94884),x94883))+~P24(f329(f62(x94884),x94882))+E(f329(f329(f287(x94885),f329(f329(f81(x94885),f329(f329(f9(x94884,x94885),x94881),x94883)),f329(f329(f9(x94884,x94885),x94881),x94882))),f329(f329(f9(x94884,x94885),x94881),f329(f329(f106(f881(x94884,a869)),x94883),x94882))),f329(f329(f9(x94884,x94885),x94881),f329(f329(f115(f881(x94884,a869)),x94883),x94882)))
% 187.33/188.06 [9763]~P62(x97631)+~P24(f329(f62(x97632),x97634))+~P24(f329(f62(x97632),x97635))+E(f329(f329(f287(x97631),f329(f329(f81(x97631),f329(f329(f9(x97632,x97631),x97633),x97634)),f329(f329(f9(x97632,x97631),x97633),x97635))),f329(f329(f9(x97632,x97631),x97633),f329(f329(f106(f881(x97632,a869)),x97634),x97635))),f329(f329(f9(x97632,x97631),x97633),f329(f329(f115(f881(x97632,a869)),x97634),x97635)))+P24(f329(f329(f331(x97632),f852(x97633,x97635,x97634,x97632,x97631)),f329(f329(f106(f881(x97632,a869)),x97634),x97635)))
% 187.33/188.06 [9086]E(f329(f329(f126(x90861),x90862),x90863),f329(f329(f126(x90861),x90864),x90865))+~E(f329(f329(f174(x90861),f329(f194(f875(x90861)),x90864)),x90862),x90864)+~E(f329(f329(f174(x90861),f329(f194(f875(x90861)),x90862)),x90864),x90862)+~E(x90865,f329(f329(f126(x90861),f329(f329(f136(x90861),f329(f194(f875(x90861)),x90864)),x90862)),x90863))+~E(f329(f329(f126(x90861),f329(f329(f136(x90861),f329(f194(f875(x90861)),x90862)),x90864)),x90865),x90863)
% 187.33/188.06 [9485]~P27(x94852)+E(f329(f329(f146(x94851,x94852,x94853),x94854),f168(x94851,x94854,x94855)),x94855)+~P33(x94852,f329(f329(f152(x94851,x94852),x94853),x94855))+~P24(f329(f329(f331(x94851),x94854),f329(f171(x94851),x94855)))+~E(f329(f139(x94851),f329(f134(x94851,f329(f329(f8(x94852,a869,x94851),f329(a326,f329(x94853,x94854))),x94853)),x94855)),x94854)
% 187.33/188.06 [9825]~P70(x98251)+~P24(f329(f67(x98251,x98251,f81(x98251),x98252,x98253),x98255))+~P24(f329(f329(f331(x98251),x98254),x98253))+P24(f329(f329(f331(x98251),x98252),x98253))+P24(f329(f67(x98251,x98251,f81(x98251),x98254,f329(f329(f307(x98251),x98252),f329(f329(f22(f881(x98251,a869)),x98253),f329(f329(f307(x98251),x98254),f193(f881(x98251,a869)))))),x98255))
% 187.33/188.06 [7219]E(x72191,x72192)+~P21(x72194,x72195,x72193,x72196)+~E(f329(x72193,x72191),f329(x72193,x72192))+~P24(f329(f329(f331(x72194),x72192),x72196))+~P24(f329(f329(f331(x72194),x72191),x72196))
% 187.33/188.06 [6477]~P139(x64774)+E(x64771,x64772)+~E(x64775,x64776)+E(x64773,f2(x64774))+~E(f329(f329(f80(x64774),x64775),f329(f329(f81(x64774),x64773),x64771)),f329(f329(f80(x64774),x64776),f329(f329(f81(x64774),x64773),x64772)))
% 187.33/188.06 [7512]~P27(x75121)+~P31(x75121)+~P24(f329(f329(f244(x75121),x75122),f329(x75125,x75126)))+~P24(f329(f329(f331(x75123),x75126),x75124))+P24(f329(f329(f244(x75121),x75122),f329(f329(f42(x75123,x75121),x75124),x75125)))
% 187.33/188.06 [8204]~P27(x82041)+~P31(x82041)+~P24(f329(f329(f244(x82041),f329(x82044,x82046)),x82045))+~P24(f329(f329(f331(x82042),x82046),x82043))+P24(f329(f329(f244(x82041),f329(f329(f43(x82042,x82041),x82043),x82044)),x82045))
% 187.33/188.06 [8466]~P15(x84662,x84665,x84666,x84661)+~P24(f329(f62(x84662),x84664))+~P24(f329(f62(x84662),x84663))+~E(f329(f329(f106(f881(x84662,a869)),x84663),x84664),f193(f881(x84662,a869)))+E(f329(x84661,f329(f329(f115(f881(x84662,a869)),x84663),x84664)),f329(f73(x84665,x84665,x84665,f329(x84661,x84663)),f329(x84661,x84664)))
% 187.33/188.06 [8776]E(x87761,x87762)+~P56(x87764,x87765,x87766,x87763,x87767)+~E(f329(x87763,x87761),f329(x87763,x87762))+~P24(f329(f329(f331(x87765),x87762),x87767))+~P24(f329(f329(f331(x87765),x87761),x87767))
% 187.33/188.06 [10071]~P24(f329(x100712,x100714))+~E(x100715,f329(f134(x100711,x100712),x100717))+E(f329(f134(x100711,x100712),x100713),f329(f329(f149(x100711),x100714),x100715))+~E(x100713,f329(f329(f126(x100711),x100716),f329(f329(f149(x100711),x100714),x100717)))+P24(f329(x100712,f790(x100715,x100714,x100713,x100712,x100711,x100716,x100717)))
% 187.33/188.06 [10072]~P24(f329(x100724,x100722))+~E(x100723,f329(f134(x100721,x100724),x100727))+E(f329(f329(f149(x100721),x100722),x100723),f329(f134(x100721,x100724),x100725))+~E(x100725,f329(f329(f126(x100721),x100726),f329(f329(f149(x100721),x100722),x100727)))+P24(f329(x100724,f789(x100725,x100724,x100723,x100722,x100721,x100726,x100727)))
% 187.33/188.06 [10106]~P24(f329(x101062,x101064))+~E(x101065,f329(f134(x101061,x101062),x101067))+E(f329(f134(x101061,x101062),x101063),f329(f329(f149(x101061),x101064),x101065))+~E(x101063,f329(f329(f126(x101061),x101066),f329(f329(f149(x101061),x101064),x101067)))+P24(f329(f329(f331(x101061),f790(x101065,x101064,x101063,x101062,x101061,x101066,x101067)),f329(f171(x101061),x101066)))
% 187.33/188.06 [10107]~P24(f329(x101074,x101072))+~E(x101073,f329(f134(x101071,x101074),x101077))+E(f329(f329(f149(x101071),x101072),x101073),f329(f134(x101071,x101074),x101075))+~E(x101075,f329(f329(f126(x101071),x101076),f329(f329(f149(x101071),x101072),x101077)))+P24(f329(f329(f331(x101071),f789(x101075,x101074,x101073,x101072,x101071,x101076,x101077)),f329(f171(x101071),x101076)))
% 187.33/188.06 [10110]~P6(x101101,x101107,x101106)+~P9(x101101,f881(x101105,a869),x101106,x101104)+P24(f329(f329(f331(x101101),f506(x101102,x101103,x101104,x101105,x101106,x101107,x101101)),x101107))+~P24(f329(f329(f331(f881(x101101,a869)),x101103),f329(f329(f61(x101101),x101107),x101106)))+P24(f329(f329(f331(f881(x101105,a869)),f329(f329(f42(x101101,f881(x101105,a869)),x101103),x101104)),x101102))
% 187.33/188.06 [10155]~P6(x101552,x101556,x101557)+~P9(x101552,f881(x101551,a869),x101557,x101554)+~P24(f329(f329(f331(f881(x101552,a869)),x101553),f329(f329(f61(x101552),x101556),x101557)))+~P24(f329(f329(f331(f881(x101551,a869)),f329(x101554,f506(x101555,x101553,x101554,x101551,x101557,x101556,x101552))),x101555))+P24(f329(f329(f331(f881(x101551,a869)),f329(f329(f42(x101552,f881(x101551,a869)),x101553),x101554)),x101555))
% 187.33/188.06 [8373]~P76(x83732)+~P21(x83731,x83735,x83738,x83734)+~E(x83733,f329(f73(x83735,x83732,x83731,x83736),x83738))+~E(x83737,f329(f308(x83731,x83735,x83738),x83734))+E(f329(f329(f9(x83731,x83732),x83733),x83734),f329(f329(f9(x83735,x83732),x83736),x83737))
% 187.33/188.06 [10159]~P76(x101592)+~P21(x101595,x101591,x101598,x101597)+~E(f329(x101596,f575(x101593,x101596,x101594,x101597,x101598,x101591,x101595,x101592)),f329(f329(f73(x101591,x101592,x101595,x101593),x101598),f575(x101593,x101596,x101594,x101597,x101598,x101591,x101595,x101592)))+~E(x101594,f329(f308(x101595,x101591,x101598),x101597))+E(f329(f329(f9(x101591,x101592),x101593),x101594),f329(f329(f9(x101595,x101592),x101596),x101597))
% 187.33/188.06 [10161]~P72(x101612)+~P21(x101611,x101615,x101618,x101614)+~E(x101617,f329(f308(x101611,x101615,x101618),x101614))+E(f329(f329(f6(x101611,x101612),x101613),x101614),f329(f329(f6(x101615,x101612),x101616),x101617))+P24(f329(f329(f331(x101611),f589(x101616,x101613,x101617,x101614,x101618,x101615,x101611,x101612)),x101614))
% 187.33/188.06 [10162]~P76(x101622)+~P21(x101621,x101625,x101628,x101624)+~E(x101627,f329(f308(x101621,x101625,x101628),x101624))+E(f329(f329(f9(x101621,x101622),x101623),x101624),f329(f329(f9(x101625,x101622),x101626),x101627))+P24(f329(f329(f331(x101621),f575(x101626,x101623,x101627,x101624,x101628,x101625,x101621,x101622)),x101624))
% 187.33/188.06 [10168]~P72(x101682)+~P21(x101685,x101681,x101688,x101687)+~E(x101684,f329(f308(x101685,x101681,x101688),x101687))+~E(f329(x101686,f589(x101683,x101686,x101684,x101687,x101688,x101681,x101685,x101682)),f329(x101683,f329(x101688,f589(x101683,x101686,x101684,x101687,x101688,x101681,x101685,x101682))))+E(f329(f329(f6(x101681,x101682),x101683),x101684),f329(f329(f6(x101685,x101682),x101686),x101687))
% 187.33/188.06 [9541]~E(f329(f194(f875(x95412)),x95415),f329(f194(f875(x95411)),x95413))+~E(f329(f194(f875(x95412)),x95414),f329(f194(f875(x95411)),x95413))+~E(f329(f329(f329(f72(x95411,f878(x95412)),f329(f177(x95411,x95412),f329(f329(f181(x95411,x95412),x95413),x95414))),x95416),f329(f236(x95412),x95417)),f329(f329(f329(f72(x95411,f878(x95412)),f329(f177(x95411,x95412),f329(f329(f181(x95411,x95412),x95413),x95415))),x95416),f329(f236(x95412),x95418)))+E(f329(f177(x95411,x95412),f329(f329(f181(x95411,x95412),x95413),x95414)),f329(f177(x95411,x95412),f329(f329(f181(x95411,x95412),x95413),x95415)))+P24(f329(f329(f331(x95411),x95416),f329(f171(x95411),x95413)))
% 187.33/188.06 [9654]~P19(x96546,x96542,x96545,x96547,x96548,x96541)+~P24(f329(f62(x96542),x96544))+~P24(f329(f62(x96542),x96543))+~E(f329(f329(f106(f881(x96542,a869)),x96543),x96544),f193(f881(x96542,a869)))+E(f329(x96541,f329(f329(f115(f881(x96542,a869)),x96543),x96544)),f329(f329(x96545,f329(x96541,x96543)),f329(x96541,x96544)))
% 187.33/188.06 [10058]~P19(x100588,x100582,x100585,x100587,x100586,x100581)+~E(f329(x100586,f647(x100584,x100583,x100581,x100586,x100587,x100585,x100582)),x100587)+~P24(f329(f62(x100582),x100583))+~P24(f329(f62(x100582),x100584))+E(f329(x100581,f329(f329(f115(f881(x100582,a869)),x100583),x100584)),f329(f329(x100585,f329(x100581,x100583)),f329(x100581,x100584)))
% 187.33/188.06 [10115]~P19(x101158,x101152,x101155,x101157,x101156,x101151)+~P24(f329(f62(x101152),x101153))+~P24(f329(f62(x101152),x101154))+E(f329(x101151,f329(f329(f115(f881(x101152,a869)),x101153),x101154)),f329(f329(x101155,f329(x101151,x101153)),f329(x101151,x101154)))+P24(f329(f329(f331(x101152),f647(x101154,x101153,x101151,x101156,x101157,x101155,x101152)),f329(f329(f106(f881(x101152,a869)),x101153),x101154)))
% 187.33/188.06 [9813]~P6(x98134,x98138,x98135)+~P6(x98131,x98139,x98133)+~P10(x98131,x98134,f881(x98132,a869),x98133,x98135,x98137)+P9(x98131,f881(x98132,a869),x98133,f329(f329(f8(f881(x98134,f881(x98132,a869)),f881(x98132,a869),x98131),f329(f42(x98134,f881(x98132,a869)),f329(f283(x98134,x98134,x98135),f329(f329(f307(x98134),x98136),f193(f881(x98134,a869)))))),x98137))+~P24(f329(f329(f331(x98134),x98136),x98138))
% 187.33/188.06 [5405]~P27(x54053)+~P33(x54053,x54051)+E(x54051,f760(x54052,x54053))+~E(f329(f171(x54053),x54051),x54052)+~P24(f329(f62(x54053),x54052))+~P24(f329(f135(x54053),x54051))
% 187.33/188.06 [5025]~P127(x50252)+~P128(x50252)+~P140(x50252)+~P111(x50252)+E(x50251,f2(x50252))+~E(f329(f329(f254(x50252),x50251),x50253),f2(x50252))
% 187.33/188.06 [5026]~P127(x50262)+~P128(x50262)+~P140(x50262)+~P111(x50262)+~E(x50261,f2(a874))+~E(f329(f329(f254(x50262),x50263),x50261),f2(x50262))
% 187.33/188.06 [6459]~P89(x64591)+~E(x64593,f2(x64591))+~E(x64592,f2(x64591))+E(f329(f329(f80(x64591),x64592),x64593),f2(x64591))+~P24(f329(f329(f243(x64591),f2(x64591)),x64593))+~P24(f329(f329(f243(x64591),f2(x64591)),x64592))
% 187.33/188.06 [8837]~E(f329(f263(a874,a874),x88373),f2(a874))+~E(x88371,f329(f329(f80(a874),f329(f329(f81(a874),f329(f263(a874,a874),x88373)),x88372)),f329(f267(a874,a874),x88373)))+P24(f329(f48(x88371,x88372),x88373))+~P24(f329(f329(f243(a874),f329(f267(a874,a874),x88373)),f2(a874)))+P24(f329(f329(f244(a874),f2(a874)),x88372))+~P24(f329(f329(f244(a874),x88372),f329(f267(a874,a874),x88373)))
% 187.33/188.06 [8845]E(x88451,f2(a874))+~E(x88452,f329(f329(f80(a874),f329(f329(f81(a874),f329(f263(a874,a874),x88453)),x88451)),f329(f267(a874,a874),x88453)))+P24(f329(f48(x88452,x88451),x88453))+~P24(f329(f329(f244(a874),f2(a874)),x88451))+~P24(f329(f329(f243(a874),f2(a874)),f329(f267(a874,a874),x88453)))+~P24(f329(f329(f244(a874),f329(f267(a874,a874),x88453)),x88451))
% 187.33/188.06 [8863]~E(f329(f263(a874,a874),x88633),f2(a874))+~E(x88631,f329(f329(f80(a874),f329(f329(f81(a874),f329(f263(a874,a874),x88633)),x88632)),f329(f267(a874,a874),x88633)))+P24(f329(f48(x88631,x88632),x88633))+~P24(f329(f329(f244(a874),f2(a874)),x88632))+~P24(f329(f329(f243(a874),f2(a874)),f329(f267(a874,a874),x88633)))+~P24(f329(f329(f244(a874),f329(f267(a874,a874),x88633)),x88632))
% 187.33/188.06 [6842]~P66(x68422)+E(x68421,f193(f881(x68422,a869)))+E(x68423,f193(f881(x68422,a869)))+~P24(f329(f62(x68422),x68421))+~P24(f329(f62(x68422),x68423))+E(f10(x68422,f329(f329(f115(f881(x68422,a869)),x68423),x68421)),f329(f329(f106(x68422),f10(x68422,x68423)),f10(x68422,x68421)))
% 187.33/188.06 [6843]~P66(x68432)+E(x68431,f193(f881(x68432,a869)))+E(x68433,f193(f881(x68432,a869)))+~P24(f329(f62(x68432),x68431))+~P24(f329(f62(x68432),x68433))+E(f13(x68432,f329(f329(f115(f881(x68432,a869)),x68433),x68431)),f329(f329(f115(x68432),f13(x68432,x68433)),f13(x68432,x68431)))
% 187.33/188.06 [6844]~P27(x68442)+E(x68441,f193(f881(x68442,a869)))+E(x68443,f193(f881(x68442,a869)))+~P24(f329(f62(x68442),x68441))+~P24(f329(f62(x68442),x68443))+E(f14(x68442,f329(f329(f115(f881(x68442,a869)),x68443),x68441)),f329(f329(f241(x68442),f14(x68442,x68443)),f14(x68442,x68441)))
% 187.33/188.06 [6845]~P27(x68452)+E(x68451,f193(f881(x68452,a869)))+E(x68453,f193(f881(x68452,a869)))+~P24(f329(f62(x68452),x68451))+~P24(f329(f62(x68452),x68453))+E(f15(x68452,f329(f329(f115(f881(x68452,a869)),x68453),x68451)),f329(f329(f242(x68452),f15(x68452,x68453)),f15(x68452,x68451)))
% 187.33/188.06 [7487]~P98(x74872)+E(x74871,f193(f881(x74872,a869)))+E(x74873,f193(f881(x74872,a869)))+~P24(f329(f62(x74872),x74871))+~P24(f329(f62(x74872),x74873))+E(f329(f329(f81(x74872),f329(f64(x74872,f81(x74872)),x74873)),f329(f64(x74872,f81(x74872)),x74871)),f329(f64(x74872,f81(x74872)),f329(f329(f115(f881(x74872,a869)),x74873),x74871)))
% 187.33/188.06 [7644]~P27(x76442)+E(x76441,f193(f881(x76442,a869)))+E(x76443,f193(f881(x76442,a869)))+~P24(f329(f62(x76442),x76441))+~P24(f329(f62(x76442),x76443))+E(f329(f329(f241(x76442),f11(x76442,f241(x76442),x76443)),f11(x76442,f241(x76442),x76441)),f11(x76442,f241(x76442),f329(f329(f115(f881(x76442,a869)),x76443),x76441)))
% 187.33/188.06 [7645]~P27(x76452)+E(x76451,f193(f881(x76452,a869)))+E(x76453,f193(f881(x76452,a869)))+~P24(f329(f62(x76452),x76451))+~P24(f329(f62(x76452),x76453))+E(f329(f329(f242(x76452),f12(x76452,f242(x76452),x76453)),f12(x76452,f242(x76452),x76451)),f12(x76452,f242(x76452),f329(f329(f115(f881(x76452,a869)),x76453),x76451)))
% 187.33/188.06 [8686]~P24(f329(x86861,x86863))+P24(f329(x86861,f402(x86861,x86862)))+P24(f329(x86861,f395(x86861,x86862)))+~P24(f329(f329(f244(a1),f2(a1)),x86862))+~P24(f329(f329(f331(a1),x86863),f300(a1,f78(a1),x86862)))+P24(f329(x86861,f329(f329(f22(a1),f395(x86861,x86862)),f329(f329(f81(a1),f401(x86861,x86862)),x86862))))
% 187.33/188.06 [8984]~P24(f329(x89841,x89843))+~P24(f329(x89841,f395(x89841,x89842)))+P24(f329(x89841,f402(x89841,x89842)))+~P24(f329(f329(f244(a1),f2(a1)),x89842))+~P24(f329(f329(f331(a1),x89843),f300(a1,f78(a1),x89842)))+~P24(f329(x89841,f329(f329(f22(a1),f395(x89841,x89842)),f329(f329(f81(a1),f401(x89841,x89842)),x89842))))
% 187.33/188.06 [10193]~P100(x101932)+E(x101931,f193(f881(x101932,a869)))+E(x101933,f193(f881(x101932,a869)))+~P24(f329(f62(x101932),x101931))+~P24(f329(f62(x101932),x101933))+E(f10(x101932,f329(f249(x101932),f329(f329(f8(f881(x101932,a869),a869,x101932),f87(x101932)),f329(f329(f8(f881(x101932,f881(x101932,a869)),f881(x101932,a869),x101932),f329(f8(f881(x101932,a869),a869,x101932),f87(x101932))),f329(f329(f7(x101932,f881(x101932,f881(x101932,a869)),f881(x101932,f881(x101932,a869))),f329(f329(f8(f881(x101932,f881(f881(x101932,a869),f881(x101932,a869))),f881(f881(x101932,f881(x101932,a869)),f881(x101932,f881(x101932,a869))),x101932),f18(x101932,f881(x101932,a869),f881(x101932,a869))),f329(f329(f8(f881(x101932,f881(x101932,f881(a869,a869))),f881(x101932,f881(f881(x101932,a869),f881(x101932,a869))),x101932),f329(f8(f881(x101932,f881(a869,a869)),f881(f881(x101932,a869),f881(x101932,a869)),x101932),f18(x101932,a869,a869))),f329(f329(f8(f881(x101932,f881(x101932,a869)),f881(x101932,f881(x101932,f881(a869,a869))),x101932),f329(f8(f881(x101932,a869),f881(x101932,f881(a869,a869)),x101932),f329(f8(a869,f881(a869,a869),x101932),a327))),f329(f329(f7(x101932,f881(x101932,f881(x101932,x101932)),f881(x101932,f881(x101932,a869))),f329(f329(f8(f881(f881(x101932,x101932),f881(x101932,a869)),f881(f881(x101932,f881(x101932,x101932)),f881(x101932,f881(x101932,a869))),x101932),f8(f881(x101932,x101932),f881(x101932,a869),x101932)),f329(f329(f8(f881(x101932,a869),f881(f881(x101932,x101932),f881(x101932,a869)),x101932),f8(x101932,a869,x101932)),a326))),f115(x101932)))))),f329(f329(f7(x101932,f881(x101932,a869),f881(x101932,a869)),f329(f329(f8(f881(a869,a869),f881(f881(x101932,a869),f881(x101932,a869)),x101932),f8(a869,a869,x101932)),f329(f329(f8(a869,f881(a869,a869),x101932),a327),f329(f329(f7(x101932,f881(x101932,a869),a869),f331(x101932)),x101933)))),f329(f329(f7(x101932,f881(x101932,a869),a869),f331(x101932)),x101931))))))),f329(f329(f115(x101932),f10(x101932,x101933)),f10(x101932,x101931)))
% 187.33/188.06 [10194]~P100(x101942)+E(x101941,f193(f881(x101942,a869)))+E(x101943,f193(f881(x101942,a869)))+~P24(f329(f62(x101942),x101941))+~P24(f329(f62(x101942),x101943))+E(f13(x101942,f329(f249(x101942),f329(f329(f8(f881(x101942,a869),a869,x101942),f87(x101942)),f329(f329(f8(f881(x101942,f881(x101942,a869)),f881(x101942,a869),x101942),f329(f8(f881(x101942,a869),a869,x101942),f87(x101942))),f329(f329(f7(x101942,f881(x101942,f881(x101942,a869)),f881(x101942,f881(x101942,a869))),f329(f329(f8(f881(x101942,f881(f881(x101942,a869),f881(x101942,a869))),f881(f881(x101942,f881(x101942,a869)),f881(x101942,f881(x101942,a869))),x101942),f18(x101942,f881(x101942,a869),f881(x101942,a869))),f329(f329(f8(f881(x101942,f881(x101942,f881(a869,a869))),f881(x101942,f881(f881(x101942,a869),f881(x101942,a869))),x101942),f329(f8(f881(x101942,f881(a869,a869)),f881(f881(x101942,a869),f881(x101942,a869)),x101942),f18(x101942,a869,a869))),f329(f329(f8(f881(x101942,f881(x101942,a869)),f881(x101942,f881(x101942,f881(a869,a869))),x101942),f329(f8(f881(x101942,a869),f881(x101942,f881(a869,a869)),x101942),f329(f8(a869,f881(a869,a869),x101942),a327))),f329(f329(f7(x101942,f881(x101942,f881(x101942,x101942)),f881(x101942,f881(x101942,a869))),f329(f329(f8(f881(f881(x101942,x101942),f881(x101942,a869)),f881(f881(x101942,f881(x101942,x101942)),f881(x101942,f881(x101942,a869))),x101942),f8(f881(x101942,x101942),f881(x101942,a869),x101942)),f329(f329(f8(f881(x101942,a869),f881(f881(x101942,x101942),f881(x101942,a869)),x101942),f8(x101942,a869,x101942)),a326))),f106(x101942)))))),f329(f329(f7(x101942,f881(x101942,a869),f881(x101942,a869)),f329(f329(f8(f881(a869,a869),f881(f881(x101942,a869),f881(x101942,a869)),x101942),f8(a869,a869,x101942)),f329(f329(f8(a869,f881(a869,a869),x101942),a327),f329(f329(f7(x101942,f881(x101942,a869),a869),f331(x101942)),x101943)))),f329(f329(f7(x101942,f881(x101942,a869),a869),f331(x101942)),x101941))))))),f329(f329(f106(x101942),f13(x101942,x101943)),f13(x101942,x101941)))
% 187.33/188.06 [10195]~P27(x101952)+E(x101951,f193(f881(x101952,a869)))+E(x101953,f193(f881(x101952,a869)))+~P24(f329(f62(x101952),x101951))+~P24(f329(f62(x101952),x101953))+E(f12(x101952,f242(x101952),f329(f249(x101952),f329(f329(f8(f881(x101952,a869),a869,x101952),f87(x101952)),f329(f329(f8(f881(x101952,f881(x101952,a869)),f881(x101952,a869),x101952),f329(f8(f881(x101952,a869),a869,x101952),f87(x101952))),f329(f329(f7(x101952,f881(x101952,f881(x101952,a869)),f881(x101952,f881(x101952,a869))),f329(f329(f8(f881(x101952,f881(f881(x101952,a869),f881(x101952,a869))),f881(f881(x101952,f881(x101952,a869)),f881(x101952,f881(x101952,a869))),x101952),f18(x101952,f881(x101952,a869),f881(x101952,a869))),f329(f329(f8(f881(x101952,f881(x101952,f881(a869,a869))),f881(x101952,f881(f881(x101952,a869),f881(x101952,a869))),x101952),f329(f8(f881(x101952,f881(a869,a869)),f881(f881(x101952,a869),f881(x101952,a869)),x101952),f18(x101952,a869,a869))),f329(f329(f8(f881(x101952,f881(x101952,a869)),f881(x101952,f881(x101952,f881(a869,a869))),x101952),f329(f8(f881(x101952,a869),f881(x101952,f881(a869,a869)),x101952),f329(f8(a869,f881(a869,a869),x101952),a327))),f329(f329(f7(x101952,f881(x101952,f881(x101952,x101952)),f881(x101952,f881(x101952,a869))),f329(f329(f8(f881(f881(x101952,x101952),f881(x101952,a869)),f881(f881(x101952,f881(x101952,x101952)),f881(x101952,f881(x101952,a869))),x101952),f8(f881(x101952,x101952),f881(x101952,a869),x101952)),f329(f329(f8(f881(x101952,a869),f881(f881(x101952,x101952),f881(x101952,a869)),x101952),f8(x101952,a869,x101952)),a326))),f241(x101952)))))),f329(f329(f7(x101952,f881(x101952,a869),f881(x101952,a869)),f329(f329(f8(f881(a869,a869),f881(f881(x101952,a869),f881(x101952,a869)),x101952),f8(a869,a869,x101952)),f329(f329(f8(a869,f881(a869,a869),x101952),a327),f329(f329(f7(x101952,f881(x101952,a869),a869),f331(x101952)),x101953)))),f329(f329(f7(x101952,f881(x101952,a869),a869),f331(x101952)),x101951))))))),f329(f329(f241(x101952),f12(x101952,f242(x101952),x101953)),f12(x101952,f242(x101952),x101951)))
% 187.33/188.06 [10196]~P27(x101962)+E(x101961,f193(f881(x101962,a869)))+E(x101963,f193(f881(x101962,a869)))+~P24(f329(f62(x101962),x101961))+~P24(f329(f62(x101962),x101963))+E(f11(x101962,f241(x101962),f329(f249(x101962),f329(f329(f8(f881(x101962,a869),a869,x101962),f87(x101962)),f329(f329(f8(f881(x101962,f881(x101962,a869)),f881(x101962,a869),x101962),f329(f8(f881(x101962,a869),a869,x101962),f87(x101962))),f329(f329(f7(x101962,f881(x101962,f881(x101962,a869)),f881(x101962,f881(x101962,a869))),f329(f329(f8(f881(x101962,f881(f881(x101962,a869),f881(x101962,a869))),f881(f881(x101962,f881(x101962,a869)),f881(x101962,f881(x101962,a869))),x101962),f18(x101962,f881(x101962,a869),f881(x101962,a869))),f329(f329(f8(f881(x101962,f881(x101962,f881(a869,a869))),f881(x101962,f881(f881(x101962,a869),f881(x101962,a869))),x101962),f329(f8(f881(x101962,f881(a869,a869)),f881(f881(x101962,a869),f881(x101962,a869)),x101962),f18(x101962,a869,a869))),f329(f329(f8(f881(x101962,f881(x101962,a869)),f881(x101962,f881(x101962,f881(a869,a869))),x101962),f329(f8(f881(x101962,a869),f881(x101962,f881(a869,a869)),x101962),f329(f8(a869,f881(a869,a869),x101962),a327))),f329(f329(f7(x101962,f881(x101962,f881(x101962,x101962)),f881(x101962,f881(x101962,a869))),f329(f329(f8(f881(f881(x101962,x101962),f881(x101962,a869)),f881(f881(x101962,f881(x101962,x101962)),f881(x101962,f881(x101962,a869))),x101962),f8(f881(x101962,x101962),f881(x101962,a869),x101962)),f329(f329(f8(f881(x101962,a869),f881(f881(x101962,x101962),f881(x101962,a869)),x101962),f8(x101962,a869,x101962)),a326))),f242(x101962)))))),f329(f329(f7(x101962,f881(x101962,a869),f881(x101962,a869)),f329(f329(f8(f881(a869,a869),f881(f881(x101962,a869),f881(x101962,a869)),x101962),f8(a869,a869,x101962)),f329(f329(f8(a869,f881(a869,a869),x101962),a327),f329(f329(f7(x101962,f881(x101962,a869),a869),f331(x101962)),x101963)))),f329(f329(f7(x101962,f881(x101962,a869),a869),f331(x101962)),x101961))))))),f329(f329(f242(x101962),f11(x101962,f241(x101962),x101963)),f11(x101962,f241(x101962),x101961)))
% 187.33/188.06 [7170]~P121(x71703)+E(x71701,x71702)+~E(f329(f329(f254(x71703),x71701),x71704),f329(f329(f254(x71703),x71702),x71704))+~P24(f329(f329(f243(x71703),f2(x71703)),x71702))+~P24(f329(f329(f243(x71703),f2(x71703)),x71701))+~P24(f329(f329(f244(a874),f2(a874)),x71704))
% 187.33/188.06 [7444]~P27(x74442)+E(x74441,f193(f881(x74442,a869)))+~P24(f329(f62(x74442),x74441))+~P24(f329(f329(f331(x74442),x74444),x74441))+P24(f329(f329(f243(x74442),x74443),x74444))+~P24(f329(f329(f243(x74442),x74443),f329(f64(x74442,f241(x74442)),x74441)))
% 187.33/188.06 [7445]~P103(x74452)+E(x74451,f193(f881(x74452,a869)))+~P24(f329(f62(x74452),x74451))+~P24(f329(f329(f331(x74452),x74454),x74451))+P24(f329(f329(f243(x74452),x74453),x74454))+~P24(f329(f329(f243(x74452),x74453),f329(f64(x74452,f106(x74452)),x74451)))
% 187.33/188.06 [7446]~P27(x74462)+E(x74461,f193(f881(x74462,a869)))+~P24(f329(f62(x74462),x74461))+~P24(f329(f329(f331(x74462),x74464),x74461))+P24(f329(f329(f244(x74462),x74463),x74464))+~P24(f329(f329(f244(x74462),x74463),f329(f64(x74462,f241(x74462)),x74461)))
% 187.33/188.06 [7344]E(x73441,f2(a1))+E(f329(f329(f39(a1),x73442),x73441),x73443)+~P24(f329(f329(f243(a1),x73444),f2(a1)))+~E(x73442,f329(f329(f80(a1),f329(f329(f81(a1),x73441),x73443)),x73444))+P24(f329(f329(f244(a1),f2(a1)),x73441))+~P24(f329(f329(f244(a1),x73441),x73444))
% 187.33/188.06 [7359]E(f45(a1,x73592,x73591),x73593)+E(x73591,f2(a1))+~P24(f329(f329(f243(a1),x73593),f2(a1)))+~E(x73592,f329(f329(f80(a1),f329(f329(f81(a1),x73591),x73594)),x73593))+P24(f329(f329(f244(a1),f2(a1)),x73591))+~P24(f329(f329(f244(a1),x73591),x73593))
% 187.33/188.06 [7486]E(x74861,f2(a1))+E(f329(f329(f39(a1),x74862),x74861),x74863)+~E(x74862,f329(f329(f80(a1),f329(f329(f81(a1),x74861),x74863)),x74864))+~P24(f329(f329(f243(a1),f2(a1)),x74864))+~P24(f329(f329(f244(a1),f2(a1)),x74861))+~P24(f329(f329(f244(a1),x74864),x74861))
% 187.33/188.06 [7508]E(f45(a1,x75082,x75081),x75083)+E(x75081,f2(a1))+~E(x75082,f329(f329(f80(a1),f329(f329(f81(a1),x75081),x75084)),x75083))+~P24(f329(f329(f243(a1),f2(a1)),x75083))+~P24(f329(f329(f244(a1),f2(a1)),x75081))+~P24(f329(f329(f244(a1),x75083),x75081))
% 187.33/188.06 [7648]~P27(x76482)+E(x76481,f193(f881(x76482,a869)))+~P24(f329(f62(x76482),x76481))+~P24(f329(f329(f331(x76482),x76484),x76481))+~P24(f329(f329(f243(x76482),x76484),x76483))+P24(f329(f329(f243(x76482),f329(f64(x76482,f241(x76482)),x76481)),x76483))
% 187.33/188.06 [7649]~P27(x76492)+E(x76491,f193(f881(x76492,a869)))+~P24(f329(f62(x76492),x76491))+~P24(f329(f329(f244(x76492),x76494),x76493))+~P24(f329(f329(f331(x76492),x76494),x76491))+P24(f329(f329(f244(x76492),f329(f64(x76492,f241(x76492)),x76491)),x76493))
% 187.33/188.06 [8229]~P24(f329(f329(f243(a1),x82294),f2(a1)))+~E(x82291,f329(f329(f80(a1),f329(f329(f81(a1),x82292),x82293)),x82294))+~P24(f329(f329(f243(a1),f2(a1)),x82294))+~P24(f329(f329(f244(a1),x82294),x82292))+~P24(f329(f329(f244(a1),x82292),x82294))+P24(f329(f49(x82291,x82292),f329(f329(f264(a1,a1),x82293),x82294)))
% 187.33/188.06 [9178]~P60(x91783)+~P60(x91784)+E(x91781,x91782)+~E(f329(f194(f875(x91783)),x91782),f329(f194(f875(x91784)),f56(x91784)))+~E(f329(f194(f875(x91783)),x91781),f329(f194(f875(x91784)),f56(x91784)))+~E(f329(f73(f878(x91783),x91783,x91784,f240(x91783)),f329(f177(x91784,x91783),f329(f329(f181(x91784,x91783),f56(x91784)),x91781))),f329(f73(f878(x91783),x91783,x91784,f240(x91783)),f329(f177(x91784,x91783),f329(f329(f181(x91784,x91783),f56(x91784)),x91782))))
% 187.33/188.06 [8393]~P106(x83931)+P24(f329(f329(f244(f881(x83931,a869)),f300(x83931,x83932,x83933)),f300(x83931,x83934,x83935)))+~P24(f329(f329(f243(x83931),x83934),x83932))+~P24(f329(f329(f243(x83931),x83934),x83935))+~P24(f329(f329(f243(x83931),x83933),x83935))+~P24(f329(f329(f244(x83931),x83933),x83935))
% 187.33/188.06 [8394]~P106(x83941)+P24(f329(f329(f244(f881(x83941,a869)),f300(x83941,x83942,x83943)),f300(x83941,x83944,x83945)))+~P24(f329(f329(f243(x83941),x83943),x83945))+~P24(f329(f329(f243(x83941),x83944),x83945))+~P24(f329(f329(f243(x83941),x83944),x83942))+~P24(f329(f329(f244(x83941),x83944),x83942))
% 187.33/188.06 [9245]P58(x92452,x92453,x92454,x92451)+E(x92451,f193(f881(x92452,a869)))+~P24(f329(f62(x92452),x92454))+~P24(f329(f62(x92452),x92451))+~P24(f329(f329(x92453,f517(x92451,x92454,x92453,x92452)),x92455))+~P24(f329(f329(f331(x92452),x92455),x92451))
% 187.33/188.06 [9393]~E(x93933,x93935)+~P72(x93931)+~P76(x93931)+~P43(x93933)+E(f329(f329(f6(a1,x93931),x93932),x93933),f329(f329(f6(a1,x93931),x93934),x93935))+P24(f329(f329(f243(a1),f2(a1)),f416(x93932,x93934,x93933,x93935,x93931)))
% 187.33/188.06 [9394]~E(x93943,x93945)+~P72(x93941)+~P76(x93941)+~P43(x93943)+E(f329(f329(f9(a1,x93941),x93942),x93943),f329(f329(f9(a1,x93941),x93944),x93945))+P24(f329(f329(f243(a1),f2(a1)),f417(x93942,x93944,x93943,x93945,x93941)))
% 187.33/188.06 [9562]~E(x95625,x95623)+~P72(x95621)+~P76(x95621)+~P43(x95625)+~E(f329(x95622,f416(x95624,x95622,x95625,x95623,x95621)),f329(x95624,f416(x95624,x95622,x95625,x95623,x95621)))+E(f329(f329(f6(a1,x95621),x95622),x95623),f329(f329(f6(a1,x95621),x95624),x95625))
% 187.33/188.06 [9563]~E(x95635,x95633)+~P72(x95631)+~P76(x95631)+~P43(x95635)+~E(f329(x95632,f417(x95634,x95632,x95635,x95633,x95631)),f329(x95634,f417(x95634,x95632,x95635,x95633,x95631)))+E(f329(f329(f9(a1,x95631),x95632),x95633),f329(f329(f9(a1,x95631),x95634),x95635))
% 187.33/188.06 [9651]~P80(x96513)+E(f329(x96511,x96512),f2(x96513))+~E(f329(f329(f6(x96514,x96513),x96511),x96515),f2(x96513))+~P24(f329(f62(x96514),x96515))+P24(f329(f329(f331(x96514),f844(x96512,x96511,x96515,x96514,x96513)),x96515))+~P24(f329(f329(f331(x96514),x96512),x96515))
% 187.33/188.06 [9787]~P80(x97873)+E(f329(x97871,x97872),f2(x97873))+~E(f329(f329(f6(x97874,x97873),x97871),x97875),f2(x97873))+~P24(f329(f62(x97874),x97875))+~P24(f329(f329(f331(x97874),x97872),x97875))+~P24(f329(f329(f243(x97873),f2(x97873)),f329(x97871,f844(x97872,x97871,x97875,x97874,x97873))))
% 187.33/188.06 [8310]~P132(x83101)+~P24(f329(f329(f243(x83101),x83103),x83105))+~P24(f329(f329(f243(x83101),x83102),x83104))+~P24(f329(f329(f243(x83101),f2(x83101)),x83103))+~P24(f329(f329(f243(x83101),f2(x83101)),x83104))+P24(f329(f329(f243(x83101),f329(f329(f81(x83101),x83102),x83103)),f329(f329(f81(x83101),x83104),x83105)))
% 187.33/188.06 [8311]~P132(x83111)+~P24(f329(f329(f243(x83111),x83113),x83115))+~P24(f329(f329(f243(x83111),x83112),x83114))+~P24(f329(f329(f243(x83111),f2(x83111)),x83113))+~P24(f329(f329(f243(x83111),f2(x83111)),x83112))+P24(f329(f329(f243(x83111),f329(f329(f81(x83111),x83112),x83113)),f329(f329(f81(x83111),x83114),x83115)))
% 187.33/188.06 [8312]~P64(x83121)+~P24(f329(f329(f244(x83121),f2(x83121)),x83125))+~P24(f329(f329(f243(x83121),x83125),x83123))+~P24(f329(f329(f243(x83121),x83122),x83124))+~P24(f329(f329(f243(x83121),f2(x83121)),x83122))+P24(f329(f329(f243(x83121),f329(f329(f287(x83121),x83122),x83123)),f329(f329(f287(x83121),x83124),x83125)))
% 187.33/188.06 [8313]~P129(x83131)+~P24(f329(f329(f243(x83131),x83133),x83135))+~P24(f329(f329(f243(x83131),f2(x83131)),x83132))+~P24(f329(f329(f244(x83131),x83132),x83134))+~P24(f329(f329(f244(x83131),f2(x83131)),x83133))+P24(f329(f329(f244(x83131),f329(f329(f81(x83131),x83132),x83133)),f329(f329(f81(x83131),x83134),x83135)))
% 187.33/188.06 [8314]~P129(x83141)+~P24(f329(f329(f243(x83141),x83142),x83144))+~P24(f329(f329(f243(x83141),f2(x83141)),x83143))+~P24(f329(f329(f244(x83141),x83143),x83145))+~P24(f329(f329(f244(x83141),f2(x83141)),x83142))+P24(f329(f329(f244(x83141),f329(f329(f81(x83141),x83142),x83143)),f329(f329(f81(x83141),x83144),x83145)))
% 187.33/188.06 [8315]~P129(x83151)+~P24(f329(f329(f243(x83151),f2(x83151)),x83153))+~P24(f329(f329(f243(x83151),f2(x83151)),x83152))+~P24(f329(f329(f244(x83151),x83153),x83155))+~P24(f329(f329(f244(x83151),x83152),x83154))+P24(f329(f329(f244(x83151),f329(f329(f81(x83151),x83152),x83153)),f329(f329(f81(x83151),x83154),x83155)))
% 187.33/188.06 [8316]~P129(x83161)+~P24(f329(f329(f243(x83161),f2(x83161)),x83163))+~P24(f329(f329(f244(x83161),x83163),x83165))+~P24(f329(f329(f244(x83161),x83162),x83164))+~P24(f329(f329(f244(x83161),f2(x83161)),x83164))+P24(f329(f329(f244(x83161),f329(f329(f81(x83161),x83162),x83163)),f329(f329(f81(x83161),x83164),x83165)))
% 187.33/188.06 [8317]~P64(x83171)+~P24(f329(f329(f243(x83171),x83175),x83173))+~P24(f329(f329(f243(x83171),f2(x83171)),x83172))+~P24(f329(f329(f244(x83171),x83172),x83174))+~P24(f329(f329(f244(x83171),f2(x83171)),x83175))+P24(f329(f329(f244(x83171),f329(f329(f287(x83171),x83172),x83173)),f329(f329(f287(x83171),x83174),x83175)))
% 187.33/188.06 [8318]~P64(x83181)+~P24(f329(f329(f243(x83181),x83182),x83184))+~P24(f329(f329(f244(x83181),x83185),x83183))+~P24(f329(f329(f244(x83181),f2(x83181)),x83185))+~P24(f329(f329(f244(x83181),f2(x83181)),x83182))+P24(f329(f329(f244(x83181),f329(f329(f287(x83181),x83182),x83183)),f329(f329(f287(x83181),x83184),x83185)))
% 187.33/188.06 [9690]~P72(x96905)+~P84(x96905)+E(x96901,f193(f881(x96902,a869)))+~P24(f329(f62(x96902),x96901))+P24(f329(f329(f331(x96902),f767(x96903,x96904,x96901,x96902,x96905)),x96901))+P24(f329(f329(f244(x96905),f329(f329(f6(x96902,x96905),x96904),x96901)),f329(f329(f6(x96902,x96905),x96903),x96901)))
% 187.33/188.06 [9809]~P72(x98091)+~P86(x98091)+~P24(f329(f62(x98092),x98095))+~P24(f329(f329(f243(x98091),f2(x98091)),f329(x98093,f845(x98093,x98094,x98095,x98092,x98091))))+P24(f329(f329(f243(x98091),f329(f329(f6(x98092,x98091),x98093),x98094)),f329(f329(f6(x98092,x98091),x98093),x98095)))+~P24(f329(f329(f243(f881(x98092,a869)),x98094),x98095))
% 187.33/188.06 [9978]~P72(x99783)+~P84(x99783)+E(x99781,f193(f881(x99782,a869)))+~P24(f329(f62(x99782),x99781))+~P24(f329(f329(f244(x99783),f329(x99784,f767(x99785,x99784,x99781,x99782,x99783))),f329(x99785,f767(x99785,x99784,x99781,x99782,x99783))))+P24(f329(f329(f244(x99783),f329(f329(f6(x99782,x99783),x99784),x99781)),f329(f329(f6(x99782,x99783),x99785),x99781)))
% 187.33/188.06 [7029]~P13(x70292,x70295,x70294)+E(x70291,f193(f881(x70292,a869)))+E(x70293,f193(f881(x70292,a869)))+~P24(f329(f62(x70292),x70291))+~P24(f329(f62(x70292),x70293))+E(f329(x70294,f329(f329(f115(f881(x70292,a869)),x70293),x70291)),f329(f329(x70295,f329(x70294,x70293)),f329(x70294,x70291)))
% 187.33/188.06 [7614]~P144(x76141,x76143,x76144)+P24(f329(x76141,x76142))+~P24(f329(f329(f244(a1),x76144),f2(a1)))+~P24(f329(f329(f243(a1),x76145),f2(a1)))+~E(x76143,f329(f329(f80(a1),f329(f329(f81(a1),x76144),x76142)),x76145))+~P24(f329(f329(f244(a1),x76144),x76145))
% 187.33/188.06 [7615]~P143(x76151,x76153,x76154)+P24(f329(x76151,x76152))+~P24(f329(f329(f244(a1),x76154),f2(a1)))+~P24(f329(f329(f243(a1),x76152),f2(a1)))+~E(x76153,f329(f329(f80(a1),f329(f329(f81(a1),x76154),x76155)),x76152))+~P24(f329(f329(f244(a1),x76154),x76152))
% 187.33/188.06 [7657]~P144(x76571,x76573,x76574)+P24(f329(x76571,x76572))+~E(x76573,f329(f329(f80(a1),f329(f329(f81(a1),x76574),x76572)),x76575))+~P24(f329(f329(f243(a1),f2(a1)),x76575))+~P24(f329(f329(f244(a1),f2(a1)),x76574))+~P24(f329(f329(f244(a1),x76575),x76574))
% 187.33/188.06 [7658]~P143(x76581,x76583,x76584)+P24(f329(x76581,x76582))+~E(x76583,f329(f329(f80(a1),f329(f329(f81(a1),x76584),x76585)),x76582))+~P24(f329(f329(f243(a1),f2(a1)),x76582))+~P24(f329(f329(f244(a1),f2(a1)),x76584))+~P24(f329(f329(f244(a1),x76582),x76584))
% 187.33/188.06 [8607]P24(f329(f329(x86071,x86072),x86073))+~P24(f329(f329(x86071,f329(f329(f39(a1),x86074),x86075)),f45(a1,x86074,x86075)))+~P24(f329(f329(f244(a1),x86075),f2(a1)))+~P24(f329(f329(f243(a1),x86073),f2(a1)))+~E(x86074,f329(f329(f80(a1),f329(f329(f81(a1),x86075),x86072)),x86073))+~P24(f329(f329(f244(a1),x86075),x86073))
% 187.33/188.06 [8616]P24(f329(f329(x86161,x86162),x86163))+~P24(f329(f329(x86161,f329(f329(f39(a1),x86164),x86165)),f45(a1,x86164,x86165)))+~E(x86164,f329(f329(f80(a1),f329(f329(f81(a1),x86165),x86162)),x86163))+~P24(f329(f329(f243(a1),f2(a1)),x86163))+~P24(f329(f329(f244(a1),f2(a1)),x86165))+~P24(f329(f329(f244(a1),x86163),x86165))
% 187.33/188.06 [8851]E(x88511,x88512)+~P55(x88513,x88515,x88514)+~P24(f329(f329(f331(x88513),x88512),x88515))+~P24(f329(f329(f331(x88513),x88511),x88515))+P24(f329(f329(f331(f880(x88513,x88513)),f329(f329(f264(x88513,x88513),x88511),x88512)),x88514))+P24(f329(f329(f331(f880(x88513,x88513)),f329(f329(f264(x88513,x88513),x88512),x88511)),x88514))
% 187.33/188.06 [9718]~P72(x97185)+~P86(x97185)+~P24(f329(f62(x97181),x97184))+P24(f329(f329(f243(x97185),f329(f329(f6(x97181,x97185),x97182),x97183)),f329(f329(f6(x97181,x97185),x97182),x97184)))+~P24(f329(f329(f243(f881(x97181,a869)),x97183),x97184))+P24(f329(f329(f331(x97181),f845(x97182,x97183,x97184,x97181,x97185)),f329(f329(f22(f881(x97181,a869)),x97184),x97183)))
% 187.33/188.06 [9817]E(x98171,f193(f881(x98172,a869)))+~P24(f329(f62(x98172),x98173))+~P24(f329(f62(x98172),x98171))+P24(f329(f329(f331(f880(f881(x98172,a869),f881(x98172,a869))),f329(f329(f264(f881(x98172,a869),f881(x98172,a869)),x98173),x98171)),f321(x98172,x98174)))+~P24(f329(f329(f331(x98172),x98175),x98171))+~P24(f329(f329(f331(f880(x98172,x98172)),f329(f329(f264(x98172,x98172),f526(x98174,x98171,x98173,x98172)),x98175)),x98174))
% 187.33/188.06 [9818]E(x98181,f193(f881(x98182,a869)))+~P24(f329(f62(x98182),x98183))+~P24(f329(f62(x98182),x98181))+P24(f329(f329(f331(f880(f881(x98182,a869),f881(x98182,a869))),f329(f329(f264(f881(x98182,a869),f881(x98182,a869)),x98183),x98181)),f321(x98182,x98184)))+~P24(f329(f329(f331(x98182),x98185),x98181))+~P24(f329(f329(f331(f880(x98182,x98182)),f329(f329(f264(x98182,x98182),f585(x98184,x98181,x98183,x98182)),x98185)),x98184))
% 187.33/188.06 [9982]~P80(x99821)+~E(f329(f329(f6(x99825,x99821),x99822),x99826),x99824)+~P24(f329(f62(x99825),x99826))+P24(f329(f329(f331(x99825),f846(x99823,x99824,x99822,x99826,x99825,x99821)),x99826))+P24(f329(f329(f243(x99821),f329(x99822,x99823)),x99824))+~P24(f329(f329(f331(x99825),x99823),x99826))
% 187.33/188.06 [10029]~P80(x100291)+~E(f329(f329(f6(x100295,x100291),x100292),x100296),x100294)+~P24(f329(f62(x100295),x100296))+~P24(f329(f329(f331(x100295),x100293),x100296))+~P24(f329(f329(f243(x100291),f2(x100291)),f329(x100292,f846(x100293,x100294,x100292,x100296,x100295,x100291))))+P24(f329(f329(f243(x100291),f329(x100292,x100293)),x100294))
% 187.33/188.06 [10141]~E(x101415,x101418)+~E(x101414,x101417)+~P26(x101411)+~P72(x101412)+E(f329(f329(f6(x101411,x101412),x101413),f329(f299(x101411,x101414),x101415)),f329(f329(f6(x101411,x101412),x101416),f329(f299(x101411,x101417),x101418)))+P24(f329(f329(f243(x101411),x101414),f588(x101413,x101416,x101415,x101418,x101414,x101417,x101411,x101412)))
% 187.33/188.06 [10158]~E(x101587,x101584)+~E(x101588,x101585)+~P26(x101581)+~P72(x101582)+~E(f329(x101583,f588(x101586,x101583,x101588,x101585,x101587,x101584,x101581,x101582)),f329(x101586,f588(x101586,x101583,x101588,x101585,x101587,x101584,x101581,x101582)))+E(f329(f329(f6(x101581,x101582),x101583),f329(f299(x101581,x101584),x101585)),f329(f329(f6(x101581,x101582),x101586),f329(f299(x101581,x101587),x101588)))
% 187.33/188.06 [10160]~E(x101604,x101607)+~E(x101605,x101608)+~P26(x101601)+~P72(x101602)+E(f329(f329(f6(x101601,x101602),x101603),f329(f299(x101601,x101604),x101605)),f329(f329(f6(x101601,x101602),x101606),f329(f299(x101601,x101607),x101608)))+P24(f329(f329(f244(x101601),f588(x101603,x101606,x101605,x101608,x101604,x101607,x101601,x101602)),x101605))
% 187.33/188.06 [9823]~P6(x98235,x98239,x98236)+~P6(x98231,x982310,x98233)+~P10(x98231,x98235,f881(x98232,a869),x98233,x98236,x98238)+~P24(f329(f329(f331(x98235),x98237),x98239))+~P24(f329(f329(f331(x98231),x98234),x982310))+E(f329(f329(f42(x98231,f881(x98232,a869)),f329(f283(x98231,x98231,x98233),f329(f329(f307(x98231),x98234),f193(f881(x98231,a869))))),f329(f329(f8(f881(x98235,f881(x98232,a869)),f881(x98232,a869),x98231),f329(f42(x98235,f881(x98232,a869)),f329(f283(x98235,x98235,x98236),f329(f329(f307(x98235),x98237),f193(f881(x98235,a869)))))),x98238)),f329(f329(x98238,x98234),x98237))
% 187.33/188.06 [5571]~P27(x55713)+~P33(x55713,x55712)+~P33(x55713,x55711)+E(x55711,x55712)+~E(f329(f171(x55713),x55711),f329(f171(x55713),x55712))+~P24(f329(f135(x55713),x55712))+~P24(f329(f135(x55713),x55711))
% 187.33/188.06 [4907]~P127(x49072)+~P128(x49072)+~P140(x49072)+~P111(x49072)+~E(x49073,f2(x49072))+E(x49071,f2(a874))+E(f329(f329(f254(x49072),x49073),x49071),f2(x49072))
% 187.33/188.06 [9119]E(x91191,f2(a874))+~E(x91192,f329(f329(f80(a874),f329(f329(f81(a874),f329(f263(a874,a874),x91193)),x91191)),f329(f267(a874,a874),x91193)))+P24(f329(f48(x91192,x91191),x91193))+~P24(f329(f329(f243(a874),f329(f267(a874,a874),x91193)),f2(a874)))+~P24(f329(f329(f243(a874),f2(a874)),f329(f267(a874,a874),x91193)))+~P24(f329(f329(f244(a874),x91191),f329(f267(a874,a874),x91193)))+~P24(f329(f329(f244(a874),f329(f267(a874,a874),x91193)),x91191))
% 187.33/188.06 [9128]~E(f329(f263(a874,a874),x91283),f2(a874))+~E(x91281,f329(f329(f80(a874),f329(f329(f81(a874),f329(f263(a874,a874),x91283)),x91282)),f329(f267(a874,a874),x91283)))+P24(f329(f48(x91281,x91282),x91283))+~P24(f329(f329(f243(a874),f329(f267(a874,a874),x91283)),f2(a874)))+~P24(f329(f329(f243(a874),f2(a874)),f329(f267(a874,a874),x91283)))+~P24(f329(f329(f244(a874),x91282),f329(f267(a874,a874),x91283)))+~P24(f329(f329(f244(a874),f329(f267(a874,a874),x91283)),x91282))
% 187.33/188.06 [7976]~P70(x79762)+E(x79761,f193(f881(x79762,a869)))+E(x79763,f193(f881(x79762,a869)))+~P24(f329(f62(x79762),x79761))+~P24(f329(f62(x79762),x79763))+~E(f329(f329(f106(f881(x79762,a869)),x79763),x79761),f193(f881(x79762,a869)))+E(f329(f329(f81(x79762),f329(f64(x79762,f81(x79762)),x79763)),f329(f64(x79762,f81(x79762)),x79761)),f329(f64(x79762,f81(x79762)),f329(f329(f115(f881(x79762,a869)),x79763),x79761)))
% 187.33/188.06 [7757]E(x77571,f2(a1))+E(f329(f329(f39(a1),x77572),x77571),x77573)+~P24(f329(f329(f243(a1),x77574),f2(a1)))+~E(x77572,f329(f329(f80(a1),f329(f329(f81(a1),x77571),x77573)),x77574))+~P24(f329(f329(f243(a1),f2(a1)),x77574))+~P24(f329(f329(f244(a1),x77574),x77571))+~P24(f329(f329(f244(a1),x77571),x77574))
% 187.33/188.06 [7766]E(f45(a1,x77662,x77661),x77663)+E(x77661,f2(a1))+~P24(f329(f329(f243(a1),x77663),f2(a1)))+~E(x77662,f329(f329(f80(a1),f329(f329(f81(a1),x77661),x77664)),x77663))+~P24(f329(f329(f243(a1),f2(a1)),x77663))+~P24(f329(f329(f244(a1),x77663),x77661))+~P24(f329(f329(f244(a1),x77661),x77663))
% 187.33/188.06 [7666]~P14(x76662,x76665,x76664)+E(x76661,f193(f881(x76662,a869)))+E(x76663,f193(f881(x76662,a869)))+~P24(f329(f62(x76662),x76661))+~P24(f329(f62(x76662),x76663))+~E(f329(f329(f106(f881(x76662,a869)),x76663),x76661),f193(f881(x76662,a869)))+E(f329(x76664,f329(f329(f115(f881(x76662,a869)),x76663),x76661)),f329(f329(x76665,f329(x76664,x76663)),f329(x76664,x76661)))
% 187.33/188.06 [9366]~P21(x93663,x93661,x93665,x93664)+~P21(x93661,x93663,x93666,x93662)+E(f329(f38(x93661),x93662),f329(f38(x93663),x93664))+~P24(f329(f62(x93663),x93664))+~P24(f329(f62(x93661),x93662))+~P24(f329(f329(f243(f881(x93663,a869)),f329(f308(x93661,x93663,x93666),x93662)),x93664))+~P24(f329(f329(f243(f881(x93661,a869)),f329(f308(x93663,x93661,x93665),x93664)),x93662))
% 187.33/188.06 [9310]~P24(f329(f329(f244(a1),f329(f329(f80(a1),f329(f329(f81(a1),x93105),x93101)),x93106)),f2(a1)))+~E(f329(f329(f80(a1),f329(f329(f81(a1),x93103),x93102)),x93104),f329(f329(f80(a1),f329(f329(f81(a1),x93105),x93101)),x93106))+~P24(f329(f329(f243(a1),f2(a1)),x93106))+~P24(f329(f329(f244(a1),f2(a1)),x93105))+~P24(f329(f329(f243(a1),x93105),x93103))+~P24(f329(f329(f244(a1),x93104),x93103))+P24(f329(f329(f243(a1),x93101),x93102))
% 187.33/188.06 [9072]~E(f329(f329(f80(a1),f329(f329(f81(a1),x90723),x90721)),x90724),f329(f329(f80(a1),f329(f329(f81(a1),x90725),x90722)),x90726))+~P24(f329(f329(f243(a1),f2(a1)),x90724))+~P24(f329(f329(f244(a1),f2(a1)),x90725))+~P24(f329(f329(f243(a1),x90725),x90723))+~P24(f329(f329(f244(a1),x90726),x90725))+P24(f329(f329(f243(a1),x90721),x90722))+~P24(f329(f329(f243(a1),f2(a1)),f329(f329(f80(a1),f329(f329(f81(a1),x90725),x90722)),x90726)))
% 187.33/188.06 [9251]~P126(x92511)+~E(f329(f329(f80(x92511),x92512),x92514),f78(x92511))+~P24(f329(f329(f243(x92511),x92515),x92516))+~P24(f329(f329(f243(x92511),x92513),x92516))+~P24(f329(f329(f243(x92511),f2(x92511)),x92514))+~P24(f329(f329(f243(x92511),f2(x92511)),x92512))+P24(f329(f329(f243(x92511),f329(f329(f80(x92511),f329(f329(f81(x92511),x92512),x92513)),f329(f329(f81(x92511),x92514),x92515))),x92516))
% 187.33/188.06 [9252]~P124(x92521)+~E(f329(f329(f80(x92521),x92522),x92524),f78(x92521))+~P24(f329(f329(f243(x92521),f2(x92521)),x92524))+~P24(f329(f329(f243(x92521),f2(x92521)),x92522))+~P24(f329(f329(f244(x92521),x92525),x92526))+~P24(f329(f329(f244(x92521),x92523),x92526))+P24(f329(f329(f244(x92521),f329(f329(f80(x92521),f329(f329(f81(x92521),x92522),x92523)),f329(f329(f81(x92521),x92524),x92525))),x92526))
% 187.33/188.06 [10074]~P6(x100747,x100746,x100745)+E(x100741,x100742)+~P9(x100747,f881(x100744,a869),x100745,x100743)+E(f329(x100743,f504(x100741,x100742,x100743,x100744,x100745,x100746,x100747)),f329(x100743,f505(x100741,x100742,x100743,x100744,x100745,x100746,x100747)))+~E(f329(f329(f42(x100747,f881(x100744,a869)),x100741),x100743),f329(f329(f42(x100747,f881(x100744,a869)),x100742),x100743))+~P24(f329(f329(f331(f881(x100747,a869)),x100742),f329(f329(f61(x100747),x100746),x100745)))+~P24(f329(f329(f331(f881(x100747,a869)),x100741),f329(f329(f61(x100747),x100746),x100745)))
% 187.33/188.06 [10108]~P6(x101083,x101087,x101086)+E(x101081,x101082)+~P9(x101083,f881(x101085,a869),x101086,x101084)+~E(f329(f329(f42(x101083,f881(x101085,a869)),x101081),x101084),f329(f329(f42(x101083,f881(x101085,a869)),x101082),x101084))+P24(f329(f329(f331(x101083),f505(x101081,x101082,x101084,x101085,x101086,x101087,x101083)),x101087))+~P24(f329(f329(f331(f881(x101083,a869)),x101082),f329(f329(f61(x101083),x101087),x101086)))+~P24(f329(f329(f331(f881(x101083,a869)),x101081),f329(f329(f61(x101083),x101087),x101086)))
% 187.33/188.06 [10109]~P6(x101093,x101097,x101096)+E(x101091,x101092)+~P9(x101093,f881(x101095,a869),x101096,x101094)+~E(f329(f329(f42(x101093,f881(x101095,a869)),x101091),x101094),f329(f329(f42(x101093,f881(x101095,a869)),x101092),x101094))+P24(f329(f329(f331(x101093),f504(x101091,x101092,x101094,x101095,x101096,x101097,x101093)),x101097))+~P24(f329(f329(f331(f881(x101093,a869)),x101092),f329(f329(f61(x101093),x101097),x101096)))+~P24(f329(f329(f331(f881(x101093,a869)),x101091),f329(f329(f61(x101093),x101097),x101096)))
% 187.33/188.06 [10177]E(x101771,x101772)+~P6(x101773,x101776,x101777)+~P9(x101773,f881(x101774,a869),x101777,x101775)+~E(f329(f329(f42(x101773,f881(x101774,a869)),x101771),x101775),f329(f329(f42(x101773,f881(x101774,a869)),x101772),x101775))+~P24(f329(f329(f331(f880(x101773,x101773)),f329(f329(f264(x101773,x101773),f505(x101771,x101772,x101775,x101774,x101777,x101776,x101773)),f504(x101771,x101772,x101775,x101774,x101777,x101776,x101773))),x101777))+~P24(f329(f329(f331(f881(x101773,a869)),x101772),f329(f329(f61(x101773),x101776),x101777)))+~P24(f329(f329(f331(f881(x101773,a869)),x101771),f329(f329(f61(x101773),x101776),x101777)))
% 187.33/188.06 [9071]~P6(x90711,x90717,x90714)+~E(x90715,x90716)+~P24(f329(f329(f331(x90711),x90713),x90716))+~P24(f329(f329(f331(x90711),x90712),x90715))+~P24(f329(f329(f331(f881(x90711,a869)),x90716),f329(f329(f61(x90711),x90717),x90714)))+~P24(f329(f329(f331(f881(x90711,a869)),x90715),f329(f329(f61(x90711),x90717),x90714)))+P24(f329(f329(f331(f880(x90711,x90711)),f329(f329(f264(x90711,x90711),x90712),x90713)),x90714))
% 187.33/188.06 [9206]E(x92061,x92062)+~P6(x92063,x92064,x92065)+~P24(f329(f329(f331(x92063),x92066),x92062))+~P24(f329(f329(f331(x92063),x92067),x92061))+~P24(f329(f329(f331(f881(x92063,a869)),x92062),f329(f329(f61(x92063),x92064),x92065)))+~P24(f329(f329(f331(f881(x92063,a869)),x92061),f329(f329(f61(x92063),x92064),x92065)))+~P24(f329(f329(f331(f880(x92063,x92063)),f329(f329(f264(x92063,x92063),x92067),x92066)),x92065))
% 187.33/188.06 [10200]~P6(x102009,x102008,x102007)+~P6(x102001,x1020011,x1020010)+~P10(x102001,x102009,f881(x102006,a869),x1020010,x102007,x102005)+P24(f329(f329(f331(x102001),f507(x102002,x102003,x102004,x102005,x102006,x102007,x102008,x102009,x1020010,x1020011,x102001)),x1020011))+~P24(f329(f329(f331(f881(x102009,a869)),x102003),f329(f329(f61(x102009),x102008),x102007)))+~P24(f329(f329(f331(f881(x102001,a869)),x102004),f329(f329(f61(x102001),x1020011),x1020010)))+P24(f329(f329(f331(f881(x102006,a869)),f329(f329(f42(x102001,f881(x102006,a869)),x102004),f329(f329(f8(f881(x102009,f881(x102006,a869)),f881(x102006,a869),x102001),f329(f42(x102009,f881(x102006,a869)),x102003)),x102005))),x102002))
% 187.33/188.06 [10201]~P6(x1020111,x1020110,x102019)+~P6(x102011,x102018,x102017)+~P10(x1020111,x102011,f881(x102016,a869),x102019,x102017,x102015)+P24(f329(f329(f331(x102011),f508(x102012,x102013,x102014,x102015,x102016,x102017,x102018,x102011,x102019,x1020110,x1020111)),x102018))+~P24(f329(f329(f331(f881(x1020111,a869)),x102014),f329(f329(f61(x1020111),x1020110),x102019)))+~P24(f329(f329(f331(f881(x102011,a869)),x102013),f329(f329(f61(x102011),x102018),x102017)))+P24(f329(f329(f331(f881(x102016,a869)),f329(f329(f42(x1020111,f881(x102016,a869)),x102014),f329(f329(f8(f881(x102011,f881(x102016,a869)),f881(x102016,a869),x1020111),f329(f42(x102011,f881(x102016,a869)),x102013)),x102015))),x102012))
% 187.33/188.06 [10204]~P6(x102042,x102048,x102049)+~P6(x102044,x1020410,x1020411)+~P10(x102042,x102044,f881(x102041,a869),x102049,x1020411,x102046)+~P24(f329(f329(f331(f881(x102042,a869)),x102043),f329(f329(f61(x102042),x102048),x102049)))+~P24(f329(f329(f331(f881(x102044,a869)),x102045),f329(f329(f61(x102044),x1020410),x1020411)))+~P24(f329(f329(f331(f881(x102041,a869)),f329(f329(x102046,f507(x102047,x102045,x102043,x102046,x102041,x1020411,x1020410,x102044,x102049,x102048,x102042)),f508(x102047,x102045,x102043,x102046,x102041,x1020411,x1020410,x102044,x102049,x102048,x102042))),x102047))+P24(f329(f329(f331(f881(x102041,a869)),f329(f329(f42(x102042,f881(x102041,a869)),x102043),f329(f329(f8(f881(x102044,f881(x102041,a869)),f881(x102041,a869),x102042),f329(f42(x102044,f881(x102041,a869)),x102045)),x102046))),x102047))
% 187.33/188.06 [9106]E(x91061,x91062)+~P27(x91064)+~P21(x91063,x91064,x91065,f329(f329(f115(f881(x91063,a869)),f329(f171(x91063),x91061)),f329(f171(x91063),x91062)))+~E(f329(f171(x91063),x91061),f329(f171(x91063),x91062))+~P33(x91064,f329(f329(f152(x91063,x91064),x91065),x91062))+~P33(x91064,f329(f329(f152(x91063,x91064),x91065),x91061))+~P24(f329(f135(x91064),f329(f329(f152(x91063,x91064),x91065),x91062)))+~P24(f329(f135(x91064),f329(f329(f152(x91063,x91064),x91065),x91061)))
% 187.33/188.06 %EqnAxiom
% 187.33/188.06 [1]E(x11,x11)
% 187.33/188.06 [2]E(x22,x21)+~E(x21,x22)
% 187.33/188.06 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 187.33/188.06 [4]~E(x41,x42)+E(f2(x41),f2(x42))
% 187.33/188.06 [5]~E(x51,x52)+E(f105(x51),f105(x52))
% 187.33/188.06 [6]~E(x61,x62)+E(f22(x61),f22(x62))
% 187.33/188.06 [7]~E(x71,x72)+E(f193(x71),f193(x72))
% 187.33/188.06 [8]~E(x81,x82)+E(f329(x81,x83),f329(x82,x83))
% 187.33/188.06 [9]~E(x91,x92)+E(f329(x93,x91),f329(x93,x92))
% 187.33/188.06 [10]~E(x101,x102)+E(f31(x101),f31(x102))
% 187.33/188.06 [11]~E(x111,x112)+E(f875(x111),f875(x112))
% 187.33/188.06 [12]~E(x121,x122)+E(f106(x121),f106(x122))
% 187.33/188.06 [13]~E(x131,x132)+E(f241(x131),f241(x132))
% 187.33/188.06 [14]~E(x141,x142)+E(f115(x141),f115(x142))
% 187.33/188.06 [15]~E(x151,x152)+E(f242(x151),f242(x152))
% 187.33/188.06 [16]~E(x161,x162)+E(f107(x161),f107(x162))
% 187.33/188.06 [17]~E(x171,x172)+E(f34(x171),f34(x172))
% 187.33/188.06 [18]~E(x181,x182)+E(f84(x181),f84(x182))
% 187.33/188.06 [19]~E(x191,x192)+E(f149(x191),f149(x192))
% 187.33/188.06 [20]~E(x201,x202)+E(f77(x201,x203,x204,x205),f77(x202,x203,x204,x205))
% 187.33/188.06 [21]~E(x211,x212)+E(f77(x213,x211,x214,x215),f77(x213,x212,x214,x215))
% 187.33/188.06 [22]~E(x221,x222)+E(f77(x223,x224,x221,x225),f77(x223,x224,x222,x225))
% 187.33/188.06 [23]~E(x231,x232)+E(f77(x233,x234,x235,x231),f77(x233,x234,x235,x232))
% 187.33/188.06 [24]~E(x241,x242)+E(f508(x241,x243,x244,x245,x246,x247,x248,x249,x2410,x2411,x2412),f508(x242,x243,x244,x245,x246,x247,x248,x249,x2410,x2411,x2412))
% 187.33/188.06 [25]~E(x251,x252)+E(f508(x253,x251,x254,x255,x256,x257,x258,x259,x2510,x2511,x2512),f508(x253,x252,x254,x255,x256,x257,x258,x259,x2510,x2511,x2512))
% 187.33/188.06 [26]~E(x261,x262)+E(f508(x263,x264,x261,x265,x266,x267,x268,x269,x2610,x2611,x2612),f508(x263,x264,x262,x265,x266,x267,x268,x269,x2610,x2611,x2612))
% 187.33/188.06 [27]~E(x271,x272)+E(f508(x273,x274,x275,x271,x276,x277,x278,x279,x2710,x2711,x2712),f508(x273,x274,x275,x272,x276,x277,x278,x279,x2710,x2711,x2712))
% 187.33/188.06 [28]~E(x281,x282)+E(f508(x283,x284,x285,x286,x281,x287,x288,x289,x2810,x2811,x2812),f508(x283,x284,x285,x286,x282,x287,x288,x289,x2810,x2811,x2812))
% 187.33/188.06 [29]~E(x291,x292)+E(f508(x293,x294,x295,x296,x297,x291,x298,x299,x2910,x2911,x2912),f508(x293,x294,x295,x296,x297,x292,x298,x299,x2910,x2911,x2912))
% 187.33/188.06 [30]~E(x301,x302)+E(f508(x303,x304,x305,x306,x307,x308,x301,x309,x3010,x3011,x3012),f508(x303,x304,x305,x306,x307,x308,x302,x309,x3010,x3011,x3012))
% 187.33/188.06 [31]~E(x311,x312)+E(f508(x313,x314,x315,x316,x317,x318,x319,x311,x3110,x3111,x3112),f508(x313,x314,x315,x316,x317,x318,x319,x312,x3110,x3111,x3112))
% 187.33/188.06 [32]~E(x321,x322)+E(f508(x323,x324,x325,x326,x327,x328,x329,x3210,x321,x3211,x3212),f508(x323,x324,x325,x326,x327,x328,x329,x3210,x322,x3211,x3212))
% 187.33/188.06 [33]~E(x331,x332)+E(f508(x333,x334,x335,x336,x337,x338,x339,x3310,x3311,x331,x3312),f508(x333,x334,x335,x336,x337,x338,x339,x3310,x3311,x332,x3312))
% 187.33/188.06 [34]~E(x341,x342)+E(f508(x343,x344,x345,x346,x347,x348,x349,x3410,x3411,x3412,x341),f508(x343,x344,x345,x346,x347,x348,x349,x3410,x3411,x3412,x342))
% 187.33/188.06 [35]~E(x351,x352)+E(f78(x351),f78(x352))
% 187.33/188.06 [36]~E(x361,x362)+E(f880(x361,x363),f880(x362,x363))
% 187.33/188.06 [37]~E(x371,x372)+E(f880(x373,x371),f880(x373,x372))
% 187.33/188.06 [38]~E(x381,x382)+E(f507(x381,x383,x384,x385,x386,x387,x388,x389,x3810,x3811,x3812),f507(x382,x383,x384,x385,x386,x387,x388,x389,x3810,x3811,x3812))
% 187.33/188.06 [39]~E(x391,x392)+E(f507(x393,x391,x394,x395,x396,x397,x398,x399,x3910,x3911,x3912),f507(x393,x392,x394,x395,x396,x397,x398,x399,x3910,x3911,x3912))
% 187.33/188.06 [40]~E(x401,x402)+E(f507(x403,x404,x401,x405,x406,x407,x408,x409,x4010,x4011,x4012),f507(x403,x404,x402,x405,x406,x407,x408,x409,x4010,x4011,x4012))
% 187.33/188.06 [41]~E(x411,x412)+E(f507(x413,x414,x415,x411,x416,x417,x418,x419,x4110,x4111,x4112),f507(x413,x414,x415,x412,x416,x417,x418,x419,x4110,x4111,x4112))
% 187.33/188.06 [42]~E(x421,x422)+E(f507(x423,x424,x425,x426,x421,x427,x428,x429,x4210,x4211,x4212),f507(x423,x424,x425,x426,x422,x427,x428,x429,x4210,x4211,x4212))
% 187.33/188.06 [43]~E(x431,x432)+E(f507(x433,x434,x435,x436,x437,x431,x438,x439,x4310,x4311,x4312),f507(x433,x434,x435,x436,x437,x432,x438,x439,x4310,x4311,x4312))
% 187.33/188.06 [44]~E(x441,x442)+E(f507(x443,x444,x445,x446,x447,x448,x441,x449,x4410,x4411,x4412),f507(x443,x444,x445,x446,x447,x448,x442,x449,x4410,x4411,x4412))
% 187.33/188.06 [45]~E(x451,x452)+E(f507(x453,x454,x455,x456,x457,x458,x459,x451,x4510,x4511,x4512),f507(x453,x454,x455,x456,x457,x458,x459,x452,x4510,x4511,x4512))
% 187.33/188.06 [46]~E(x461,x462)+E(f507(x463,x464,x465,x466,x467,x468,x469,x4610,x461,x4611,x4612),f507(x463,x464,x465,x466,x467,x468,x469,x4610,x462,x4611,x4612))
% 187.33/188.06 [47]~E(x471,x472)+E(f507(x473,x474,x475,x476,x477,x478,x479,x4710,x4711,x471,x4712),f507(x473,x474,x475,x476,x477,x478,x479,x4710,x4711,x472,x4712))
% 187.33/188.06 [48]~E(x481,x482)+E(f507(x483,x484,x485,x486,x487,x488,x489,x4810,x4811,x4812,x481),f507(x483,x484,x485,x486,x487,x488,x489,x4810,x4811,x4812,x482))
% 187.33/188.06 [49]~E(x491,x492)+E(f4(x491),f4(x492))
% 187.33/188.06 [50]~E(x501,x502)+E(f331(x501),f331(x502))
% 187.33/188.06 [51]~E(x511,x512)+E(f881(x511,x513),f881(x512,x513))
% 187.33/188.06 [52]~E(x521,x522)+E(f881(x523,x521),f881(x523,x522))
% 187.33/188.06 [53]~E(x531,x532)+E(f116(x531),f116(x532))
% 187.33/188.06 [54]~E(x541,x542)+E(f7(x541,x543,x544),f7(x542,x543,x544))
% 187.33/188.06 [55]~E(x551,x552)+E(f7(x553,x551,x554),f7(x553,x552,x554))
% 187.33/188.06 [56]~E(x561,x562)+E(f7(x563,x564,x561),f7(x563,x564,x562))
% 187.33/188.06 [57]~E(x571,x572)+E(f873(x571),f873(x572))
% 187.33/188.06 [58]~E(x581,x582)+E(f878(x581),f878(x582))
% 187.33/188.06 [59]~E(x591,x592)+E(f243(x591),f243(x592))
% 187.33/188.06 [60]~E(x601,x602)+E(f876(x601),f876(x602))
% 187.33/188.06 [61]~E(x611,x612)+E(f765(x611,x613),f765(x612,x613))
% 187.33/188.06 [62]~E(x621,x622)+E(f765(x623,x621),f765(x623,x622))
% 187.33/188.06 [63]~E(x631,x632)+E(f244(x631),f244(x632))
% 187.33/188.06 [64]~E(x641,x642)+E(f292(x641,x643,x644),f292(x642,x643,x644))
% 187.33/188.06 [65]~E(x651,x652)+E(f292(x653,x651,x654),f292(x653,x652,x654))
% 187.33/188.06 [66]~E(x661,x662)+E(f292(x663,x664,x661),f292(x663,x664,x662))
% 187.33/188.06 [67]~E(x671,x672)+E(f108(x671),f108(x672))
% 187.33/188.06 [68]~E(x681,x682)+E(f79(x681),f79(x682))
% 187.33/188.06 [69]~E(x691,x692)+E(f119(x691,x693),f119(x692,x693))
% 187.33/188.06 [70]~E(x701,x702)+E(f119(x703,x701),f119(x703,x702))
% 187.33/188.06 [71]~E(x711,x712)+E(f194(x711),f194(x712))
% 187.33/188.06 [72]~E(x721,x722)+E(f41(x721,x723),f41(x722,x723))
% 187.33/188.06 [73]~E(x731,x732)+E(f41(x733,x731),f41(x733,x732))
% 187.33/188.06 [74]~E(x741,x742)+E(f73(x741,x743,x744,x745),f73(x742,x743,x744,x745))
% 187.33/188.06 [75]~E(x751,x752)+E(f73(x753,x751,x754,x755),f73(x753,x752,x754,x755))
% 187.33/188.06 [76]~E(x761,x762)+E(f73(x763,x764,x761,x765),f73(x763,x764,x762,x765))
% 187.33/188.06 [77]~E(x771,x772)+E(f73(x773,x774,x775,x771),f73(x773,x774,x775,x772))
% 187.33/188.06 [78]~E(x781,x782)+E(f13(x781,x783),f13(x782,x783))
% 187.33/188.06 [79]~E(x791,x792)+E(f13(x793,x791),f13(x793,x792))
% 187.33/188.06 [80]~E(x801,x802)+E(f642(x801,x803,x804,x805),f642(x802,x803,x804,x805))
% 187.33/188.06 [81]~E(x811,x812)+E(f642(x813,x811,x814,x815),f642(x813,x812,x814,x815))
% 187.33/188.06 [82]~E(x821,x822)+E(f642(x823,x824,x821,x825),f642(x823,x824,x822,x825))
% 187.33/188.06 [83]~E(x831,x832)+E(f642(x833,x834,x835,x831),f642(x833,x834,x835,x832))
% 187.33/188.06 [84]~E(x841,x842)+E(f291(x841,x843,x844),f291(x842,x843,x844))
% 187.33/188.06 [85]~E(x851,x852)+E(f291(x853,x851,x854),f291(x853,x852,x854))
% 187.33/188.06 [86]~E(x861,x862)+E(f291(x863,x864,x861),f291(x863,x864,x862))
% 187.33/188.06 [87]~E(x871,x872)+E(f45(x871,x873,x874),f45(x872,x873,x874))
% 187.33/188.06 [88]~E(x881,x882)+E(f45(x883,x881,x884),f45(x883,x882,x884))
% 187.33/188.06 [89]~E(x891,x892)+E(f45(x893,x894,x891),f45(x893,x894,x892))
% 187.33/188.06 [90]~E(x901,x902)+E(f80(x901),f80(x902))
% 187.33/188.06 [91]~E(x911,x912)+E(f16(x911,x913),f16(x912,x913))
% 187.33/188.06 [92]~E(x921,x922)+E(f16(x923,x921),f16(x923,x922))
% 187.33/188.06 [93]~E(x931,x932)+E(f184(x931,x933,x934,x935),f184(x932,x933,x934,x935))
% 187.33/188.06 [94]~E(x941,x942)+E(f184(x943,x941,x944,x945),f184(x943,x942,x944,x945))
% 187.33/188.06 [95]~E(x951,x952)+E(f184(x953,x954,x951,x955),f184(x953,x954,x952,x955))
% 187.33/188.06 [96]~E(x961,x962)+E(f184(x963,x964,x965,x961),f184(x963,x964,x965,x962))
% 187.33/188.06 [97]~E(x971,x972)+E(f39(x971),f39(x972))
% 187.33/188.06 [98]~E(x981,x982)+E(f33(x981,x983),f33(x982,x983))
% 187.33/188.06 [99]~E(x991,x992)+E(f33(x993,x991),f33(x993,x992))
% 187.33/188.06 [100]~E(x1001,x1002)+E(f48(x1001,x1003),f48(x1002,x1003))
% 187.33/188.06 [101]~E(x1011,x1012)+E(f48(x1013,x1011),f48(x1013,x1012))
% 187.33/188.06 [102]~E(x1021,x1022)+E(f62(x1021),f62(x1022))
% 187.33/188.06 [103]~E(x1031,x1032)+E(f631(x1031,x1033,x1034),f631(x1032,x1033,x1034))
% 187.33/188.06 [104]~E(x1041,x1042)+E(f631(x1043,x1041,x1044),f631(x1043,x1042,x1044))
% 187.33/188.06 [105]~E(x1051,x1052)+E(f631(x1053,x1054,x1051),f631(x1053,x1054,x1052))
% 187.33/188.06 [106]~E(x1061,x1062)+E(f61(x1061),f61(x1062))
% 187.33/188.06 [107]~E(x1071,x1072)+E(f264(x1071,x1073),f264(x1072,x1073))
% 187.33/188.06 [108]~E(x1081,x1082)+E(f264(x1083,x1081),f264(x1083,x1082))
% 187.33/188.06 [109]~E(x1091,x1092)+E(f118(x1091),f118(x1092))
% 187.33/188.06 [110]~E(x1101,x1102)+E(f577(x1101,x1103,x1104),f577(x1102,x1103,x1104))
% 187.33/188.06 [111]~E(x1111,x1112)+E(f577(x1113,x1111,x1114),f577(x1113,x1112,x1114))
% 187.33/188.06 [112]~E(x1121,x1122)+E(f577(x1123,x1124,x1121),f577(x1123,x1124,x1122))
% 187.33/188.06 [113]~E(x1131,x1132)+E(f164(x1131),f164(x1132))
% 187.33/188.06 [114]~E(x1141,x1142)+E(f30(x1141,x1143,x1144),f30(x1142,x1143,x1144))
% 187.33/188.06 [115]~E(x1151,x1152)+E(f30(x1153,x1151,x1154),f30(x1153,x1152,x1154))
% 187.33/188.06 [116]~E(x1161,x1162)+E(f30(x1163,x1164,x1161),f30(x1163,x1164,x1162))
% 187.33/188.06 [117]~E(x1171,x1172)+E(f171(x1171),f171(x1172))
% 187.33/188.06 [118]~E(x1181,x1182)+E(f152(x1181,x1183),f152(x1182,x1183))
% 187.33/188.06 [119]~E(x1191,x1192)+E(f152(x1193,x1191),f152(x1193,x1192))
% 187.33/188.06 [120]~E(x1201,x1202)+E(f308(x1201,x1203,x1204),f308(x1202,x1203,x1204))
% 187.33/188.06 [121]~E(x1211,x1212)+E(f308(x1213,x1211,x1214),f308(x1213,x1212,x1214))
% 187.33/188.06 [122]~E(x1221,x1222)+E(f308(x1223,x1224,x1221),f308(x1223,x1224,x1222))
% 187.33/188.06 [123]~E(x1231,x1232)+E(f11(x1231,x1233,x1234),f11(x1232,x1233,x1234))
% 187.33/188.06 [124]~E(x1241,x1242)+E(f11(x1243,x1241,x1244),f11(x1243,x1242,x1244))
% 187.33/188.06 [125]~E(x1251,x1252)+E(f11(x1253,x1254,x1251),f11(x1253,x1254,x1252))
% 187.33/188.06 [126]~E(x1261,x1262)+E(f126(x1261),f126(x1262))
% 187.33/188.06 [127]~E(x1271,x1272)+E(f181(x1271,x1273),f181(x1272,x1273))
% 187.33/188.06 [128]~E(x1281,x1282)+E(f181(x1283,x1281),f181(x1283,x1282))
% 187.33/188.06 [129]~E(x1291,x1292)+E(f65(x1291,x1293,x1294),f65(x1292,x1293,x1294))
% 187.33/188.06 [130]~E(x1301,x1302)+E(f65(x1303,x1301,x1304),f65(x1303,x1302,x1304))
% 187.33/188.06 [131]~E(x1311,x1312)+E(f65(x1313,x1314,x1311),f65(x1313,x1314,x1312))
% 187.33/188.06 [132]~E(x1321,x1322)+E(f289(x1321,x1323),f289(x1322,x1323))
% 187.33/188.06 [133]~E(x1331,x1332)+E(f289(x1333,x1331),f289(x1333,x1332))
% 187.33/188.06 [134]~E(x1341,x1342)+E(f307(x1341),f307(x1342))
% 187.33/188.06 [135]~E(x1351,x1352)+E(f8(x1351,x1353,x1354),f8(x1352,x1353,x1354))
% 187.33/188.06 [136]~E(x1361,x1362)+E(f8(x1363,x1361,x1364),f8(x1363,x1362,x1364))
% 187.33/188.06 [137]~E(x1371,x1372)+E(f8(x1373,x1374,x1371),f8(x1373,x1374,x1372))
% 187.33/188.06 [138]~E(x1381,x1382)+E(f301(x1381),f301(x1382))
% 187.33/188.06 [139]~E(x1391,x1392)+E(f140(x1391,x1393,x1394,x1395),f140(x1392,x1393,x1394,x1395))
% 187.33/188.06 [140]~E(x1401,x1402)+E(f140(x1403,x1401,x1404,x1405),f140(x1403,x1402,x1404,x1405))
% 187.33/188.06 [141]~E(x1411,x1412)+E(f140(x1413,x1414,x1411,x1415),f140(x1413,x1414,x1412,x1415))
% 187.33/188.06 [142]~E(x1421,x1422)+E(f140(x1423,x1424,x1425,x1421),f140(x1423,x1424,x1425,x1422))
% 187.33/188.06 [143]~E(x1431,x1432)+E(f81(x1431),f81(x1432))
% 187.33/188.06 [144]~E(x1441,x1442)+E(f303(x1441,x1443,x1444),f303(x1442,x1443,x1444))
% 187.33/188.06 [145]~E(x1451,x1452)+E(f303(x1453,x1451,x1454),f303(x1453,x1452,x1454))
% 187.33/188.06 [146]~E(x1461,x1462)+E(f303(x1463,x1464,x1461),f303(x1463,x1464,x1462))
% 187.33/188.06 [147]~E(x1471,x1472)+E(f14(x1471,x1473),f14(x1472,x1473))
% 187.33/188.06 [148]~E(x1481,x1482)+E(f14(x1483,x1481),f14(x1483,x1482))
% 187.33/188.06 [149]~E(x1491,x1492)+E(f305(x1491,x1493),f305(x1492,x1493))
% 187.33/188.06 [150]~E(x1501,x1502)+E(f305(x1503,x1501),f305(x1503,x1502))
% 187.33/188.06 [151]~E(x1511,x1512)+E(f236(x1511),f236(x1512))
% 187.33/188.06 [152]~E(x1521,x1522)+E(f299(x1521,x1523),f299(x1522,x1523))
% 187.33/188.06 [153]~E(x1531,x1532)+E(f299(x1533,x1531),f299(x1533,x1532))
% 187.33/188.06 [154]~E(x1541,x1542)+E(f290(x1541,x1543,x1544),f290(x1542,x1543,x1544))
% 187.33/188.06 [155]~E(x1551,x1552)+E(f290(x1553,x1551,x1554),f290(x1553,x1552,x1554))
% 187.33/188.06 [156]~E(x1561,x1562)+E(f290(x1563,x1564,x1561),f290(x1563,x1564,x1562))
% 187.33/188.06 [157]~E(x1571,x1572)+E(f139(x1571),f139(x1572))
% 187.33/188.06 [158]~E(x1581,x1582)+E(f10(x1581,x1583),f10(x1582,x1583))
% 187.33/188.06 [159]~E(x1591,x1592)+E(f10(x1593,x1591),f10(x1593,x1592))
% 187.33/188.06 [160]~E(x1601,x1602)+E(f295(x1601,x1603,x1604),f295(x1602,x1603,x1604))
% 187.33/188.06 [161]~E(x1611,x1612)+E(f295(x1613,x1611,x1614),f295(x1613,x1612,x1614))
% 187.33/188.06 [162]~E(x1621,x1622)+E(f295(x1623,x1624,x1621),f295(x1623,x1624,x1622))
% 187.33/188.06 [163]~E(x1631,x1632)+E(f110(x1631),f110(x1632))
% 187.33/188.06 [164]~E(x1641,x1642)+E(f112(x1641),f112(x1642))
% 187.33/188.06 [165]~E(x1651,x1652)+E(f330(x1651),f330(x1652))
% 187.33/188.06 [166]~E(x1661,x1662)+E(f12(x1661,x1663,x1664),f12(x1662,x1663,x1664))
% 187.33/188.06 [167]~E(x1671,x1672)+E(f12(x1673,x1671,x1674),f12(x1673,x1672,x1674))
% 187.33/188.06 [168]~E(x1681,x1682)+E(f12(x1683,x1684,x1681),f12(x1683,x1684,x1682))
% 187.33/188.06 [169]~E(x1691,x1692)+E(f549(x1691,x1693,x1694),f549(x1692,x1693,x1694))
% 187.33/188.06 [170]~E(x1701,x1702)+E(f549(x1703,x1701,x1704),f549(x1703,x1702,x1704))
% 187.33/188.06 [171]~E(x1711,x1712)+E(f549(x1713,x1714,x1711),f549(x1713,x1714,x1712))
% 187.33/188.06 [172]~E(x1721,x1722)+E(f75(x1721),f75(x1722))
% 187.33/188.06 [173]~E(x1731,x1732)+E(f287(x1731),f287(x1732))
% 187.33/188.06 [174]~E(x1741,x1742)+E(f5(x1741),f5(x1742))
% 187.33/188.06 [175]~E(x1751,x1752)+E(f145(x1751,x1753),f145(x1752,x1753))
% 187.33/188.06 [176]~E(x1761,x1762)+E(f145(x1763,x1761),f145(x1763,x1762))
% 187.33/188.06 [177]~E(x1771,x1772)+E(f249(x1771),f249(x1772))
% 187.33/188.06 [178]~E(x1781,x1782)+E(f40(x1781,x1783),f40(x1782,x1783))
% 187.33/188.06 [179]~E(x1791,x1792)+E(f40(x1793,x1791),f40(x1793,x1792))
% 187.33/188.06 [180]~E(x1801,x1802)+E(f263(x1801,x1803),f263(x1802,x1803))
% 187.33/188.06 [181]~E(x1811,x1812)+E(f263(x1813,x1811),f263(x1813,x1812))
% 187.33/188.06 [182]~E(x1821,x1822)+E(f317(x1821,x1823),f317(x1822,x1823))
% 187.33/188.06 [183]~E(x1831,x1832)+E(f317(x1833,x1831),f317(x1833,x1832))
% 187.33/188.06 [184]~E(x1841,x1842)+E(f56(x1841),f56(x1842))
% 187.33/188.06 [185]~E(x1851,x1852)+E(f101(x1851),f101(x1852))
% 187.33/188.06 [186]~E(x1861,x1862)+E(f154(x1861,x1863,x1864,x1865),f154(x1862,x1863,x1864,x1865))
% 187.33/188.06 [187]~E(x1871,x1872)+E(f154(x1873,x1871,x1874,x1875),f154(x1873,x1872,x1874,x1875))
% 187.33/188.06 [188]~E(x1881,x1882)+E(f154(x1883,x1884,x1881,x1885),f154(x1883,x1884,x1882,x1885))
% 187.33/188.06 [189]~E(x1891,x1892)+E(f154(x1893,x1894,x1895,x1891),f154(x1893,x1894,x1895,x1892))
% 187.33/188.06 [190]~E(x1901,x1902)+E(f9(x1901,x1903),f9(x1902,x1903))
% 187.33/188.06 [191]~E(x1911,x1912)+E(f9(x1913,x1911),f9(x1913,x1912))
% 187.33/188.06 [192]~E(x1921,x1922)+E(f269(x1921,x1923,x1924,x1925,x1926,x1927),f269(x1922,x1923,x1924,x1925,x1926,x1927))
% 187.33/188.06 [193]~E(x1931,x1932)+E(f269(x1933,x1931,x1934,x1935,x1936,x1937),f269(x1933,x1932,x1934,x1935,x1936,x1937))
% 187.33/188.06 [194]~E(x1941,x1942)+E(f269(x1943,x1944,x1941,x1945,x1946,x1947),f269(x1943,x1944,x1942,x1945,x1946,x1947))
% 187.33/188.06 [195]~E(x1951,x1952)+E(f269(x1953,x1954,x1955,x1951,x1956,x1957),f269(x1953,x1954,x1955,x1952,x1956,x1957))
% 187.33/188.06 [196]~E(x1961,x1962)+E(f269(x1963,x1964,x1965,x1966,x1961,x1967),f269(x1963,x1964,x1965,x1966,x1962,x1967))
% 187.33/188.06 [197]~E(x1971,x1972)+E(f269(x1973,x1974,x1975,x1976,x1977,x1971),f269(x1973,x1974,x1975,x1976,x1977,x1972))
% 187.33/188.06 [198]~E(x1981,x1982)+E(f174(x1981),f174(x1982))
% 187.33/188.06 [199]~E(x1991,x1992)+E(f6(x1991,x1993),f6(x1992,x1993))
% 187.33/188.06 [200]~E(x2001,x2002)+E(f6(x2003,x2001),f6(x2003,x2002))
% 187.33/188.06 [201]~E(x2011,x2012)+E(f195(x2011,x2013,x2014,x2015),f195(x2012,x2013,x2014,x2015))
% 187.33/188.06 [202]~E(x2021,x2022)+E(f195(x2023,x2021,x2024,x2025),f195(x2023,x2022,x2024,x2025))
% 187.33/188.06 [203]~E(x2031,x2032)+E(f195(x2033,x2034,x2031,x2035),f195(x2033,x2034,x2032,x2035))
% 187.33/188.06 [204]~E(x2041,x2042)+E(f195(x2043,x2044,x2045,x2041),f195(x2043,x2044,x2045,x2042))
% 187.33/188.06 [205]~E(x2051,x2052)+E(f816(x2051,x2053,x2054),f816(x2052,x2053,x2054))
% 187.33/188.06 [206]~E(x2061,x2062)+E(f816(x2063,x2061,x2064),f816(x2063,x2062,x2064))
% 187.33/188.06 [207]~E(x2071,x2072)+E(f816(x2073,x2074,x2071),f816(x2073,x2074,x2072))
% 187.33/188.06 [208]~E(x2081,x2082)+E(f728(x2081,x2083),f728(x2082,x2083))
% 187.33/188.06 [209]~E(x2091,x2092)+E(f728(x2093,x2091),f728(x2093,x2092))
% 187.33/188.06 [210]~E(x2101,x2102)+E(f86(x2101,x2103),f86(x2102,x2103))
% 187.33/188.06 [211]~E(x2111,x2112)+E(f86(x2113,x2111),f86(x2113,x2112))
% 187.33/188.06 [212]~E(x2121,x2122)+E(f604(x2121,x2123,x2124,x2125),f604(x2122,x2123,x2124,x2125))
% 187.33/188.06 [213]~E(x2131,x2132)+E(f604(x2133,x2131,x2134,x2135),f604(x2133,x2132,x2134,x2135))
% 187.33/188.06 [214]~E(x2141,x2142)+E(f604(x2143,x2144,x2141,x2145),f604(x2143,x2144,x2142,x2145))
% 187.33/188.06 [215]~E(x2151,x2152)+E(f604(x2153,x2154,x2155,x2151),f604(x2153,x2154,x2155,x2152))
% 187.33/188.06 [216]~E(x2161,x2162)+E(f142(x2161,x2163),f142(x2162,x2163))
% 187.33/188.06 [217]~E(x2171,x2172)+E(f142(x2173,x2171),f142(x2173,x2172))
% 187.33/188.06 [218]~E(x2181,x2182)+E(f804(x2181,x2183,x2184,x2185),f804(x2182,x2183,x2184,x2185))
% 187.33/188.06 [219]~E(x2191,x2192)+E(f804(x2193,x2191,x2194,x2195),f804(x2193,x2192,x2194,x2195))
% 187.33/188.06 [220]~E(x2201,x2202)+E(f804(x2203,x2204,x2201,x2205),f804(x2203,x2204,x2202,x2205))
% 187.33/188.06 [221]~E(x2211,x2212)+E(f804(x2213,x2214,x2215,x2211),f804(x2213,x2214,x2215,x2212))
% 187.33/188.06 [222]~E(x2221,x2222)+E(f251(x2221),f251(x2222))
% 187.33/188.06 [223]~E(x2231,x2232)+E(f54(x2231,x2233),f54(x2232,x2233))
% 187.33/188.06 [224]~E(x2241,x2242)+E(f54(x2243,x2241),f54(x2243,x2242))
% 187.33/188.06 [225]~E(x2251,x2252)+E(f316(x2251,x2253,x2254,x2255),f316(x2252,x2253,x2254,x2255))
% 187.33/188.06 [226]~E(x2261,x2262)+E(f316(x2263,x2261,x2264,x2265),f316(x2263,x2262,x2264,x2265))
% 187.33/188.06 [227]~E(x2271,x2272)+E(f316(x2273,x2274,x2271,x2275),f316(x2273,x2274,x2272,x2275))
% 187.33/188.06 [228]~E(x2281,x2282)+E(f316(x2283,x2284,x2285,x2281),f316(x2283,x2284,x2285,x2282))
% 187.33/188.06 [229]~E(x2291,x2292)+E(f457(x2291,x2293,x2294),f457(x2292,x2293,x2294))
% 187.33/188.06 [230]~E(x2301,x2302)+E(f457(x2303,x2301,x2304),f457(x2303,x2302,x2304))
% 187.33/188.06 [231]~E(x2311,x2312)+E(f457(x2313,x2314,x2311),f457(x2313,x2314,x2312))
% 187.33/188.06 [232]~E(x2321,x2322)+E(f72(x2321,x2323),f72(x2322,x2323))
% 187.33/188.06 [233]~E(x2331,x2332)+E(f72(x2333,x2331),f72(x2333,x2332))
% 187.33/188.06 [234]~E(x2341,x2342)+E(f150(x2341,x2343),f150(x2342,x2343))
% 187.33/188.06 [235]~E(x2351,x2352)+E(f150(x2353,x2351),f150(x2353,x2352))
% 187.33/188.06 [236]~E(x2361,x2362)+E(f300(x2361,x2363,x2364),f300(x2362,x2363,x2364))
% 187.33/188.06 [237]~E(x2371,x2372)+E(f300(x2373,x2371,x2374),f300(x2373,x2372,x2374))
% 187.33/188.06 [238]~E(x2381,x2382)+E(f300(x2383,x2384,x2381),f300(x2383,x2384,x2382))
% 187.33/188.06 [239]~E(x2391,x2392)+E(f258(x2391,x2393,x2394),f258(x2392,x2393,x2394))
% 187.33/188.06 [240]~E(x2401,x2402)+E(f258(x2403,x2401,x2404),f258(x2403,x2402,x2404))
% 187.33/188.06 [241]~E(x2411,x2412)+E(f258(x2413,x2414,x2411),f258(x2413,x2414,x2412))
% 187.33/188.06 [242]~E(x2421,x2422)+E(f163(x2421),f163(x2422))
% 187.33/188.06 [243]~E(x2431,x2432)+E(f42(x2431,x2433),f42(x2432,x2433))
% 187.33/188.06 [244]~E(x2441,x2442)+E(f42(x2443,x2441),f42(x2443,x2442))
% 187.33/188.06 [245]~E(x2451,x2452)+E(f38(x2451),f38(x2452))
% 187.33/188.06 [246]~E(x2461,x2462)+E(f165(x2461,x2463,x2464),f165(x2462,x2463,x2464))
% 187.33/188.06 [247]~E(x2471,x2472)+E(f165(x2473,x2471,x2474),f165(x2473,x2472,x2474))
% 187.33/188.06 [248]~E(x2481,x2482)+E(f165(x2483,x2484,x2481),f165(x2483,x2484,x2482))
% 187.33/188.06 [249]~E(x2491,x2492)+E(f254(x2491),f254(x2492))
% 187.33/188.06 [250]~E(x2501,x2502)+E(f155(x2501,x2503),f155(x2502,x2503))
% 187.33/188.06 [251]~E(x2511,x2512)+E(f155(x2513,x2511),f155(x2513,x2512))
% 187.33/188.06 [252]~E(x2521,x2522)+E(f134(x2521,x2523),f134(x2522,x2523))
% 187.33/188.06 [253]~E(x2531,x2532)+E(f134(x2533,x2531),f134(x2533,x2532))
% 187.33/188.06 [254]~E(x2541,x2542)+E(f135(x2541),f135(x2542))
% 187.33/188.06 [255]~E(x2551,x2552)+E(f284(x2551,x2553),f284(x2552,x2553))
% 187.33/188.06 [256]~E(x2561,x2562)+E(f284(x2563,x2561),f284(x2563,x2562))
% 187.33/188.06 [257]~E(x2571,x2572)+E(f252(x2571),f252(x2572))
% 187.33/188.06 [258]~E(x2581,x2582)+E(f67(x2581,x2583,x2584,x2585,x2586),f67(x2582,x2583,x2584,x2585,x2586))
% 187.33/188.06 [259]~E(x2591,x2592)+E(f67(x2593,x2591,x2594,x2595,x2596),f67(x2593,x2592,x2594,x2595,x2596))
% 187.33/188.06 [260]~E(x2601,x2602)+E(f67(x2603,x2604,x2601,x2605,x2606),f67(x2603,x2604,x2602,x2605,x2606))
% 187.33/188.06 [261]~E(x2611,x2612)+E(f67(x2613,x2614,x2615,x2611,x2616),f67(x2613,x2614,x2615,x2612,x2616))
% 187.33/188.06 [262]~E(x2621,x2622)+E(f67(x2623,x2624,x2625,x2626,x2621),f67(x2623,x2624,x2625,x2626,x2622))
% 187.33/188.06 [263]~E(x2631,x2632)+E(f579(x2631,x2633,x2634),f579(x2632,x2633,x2634))
% 187.33/188.06 [264]~E(x2641,x2642)+E(f579(x2643,x2641,x2644),f579(x2643,x2642,x2644))
% 187.33/188.06 [265]~E(x2651,x2652)+E(f579(x2653,x2654,x2651),f579(x2653,x2654,x2652))
% 187.33/188.06 [266]~E(x2661,x2662)+E(f639(x2661,x2663,x2664),f639(x2662,x2663,x2664))
% 187.33/188.06 [267]~E(x2671,x2672)+E(f639(x2673,x2671,x2674),f639(x2673,x2672,x2674))
% 187.33/188.06 [268]~E(x2681,x2682)+E(f639(x2683,x2684,x2681),f639(x2683,x2684,x2682))
% 187.33/188.06 [269]~E(x2691,x2692)+E(f250(x2691),f250(x2692))
% 187.33/188.06 [270]~E(x2701,x2702)+E(f196(x2701),f196(x2702))
% 187.33/188.06 [271]~E(x2711,x2712)+E(f178(x2711,x2713),f178(x2712,x2713))
% 187.33/188.06 [272]~E(x2721,x2722)+E(f178(x2723,x2721),f178(x2723,x2722))
% 187.33/188.06 [273]~E(x2731,x2732)+E(f120(x2731),f120(x2732))
% 187.33/188.06 [274]~E(x2741,x2742)+E(f737(x2741,x2743,x2744,x2745,x2746),f737(x2742,x2743,x2744,x2745,x2746))
% 187.33/188.06 [275]~E(x2751,x2752)+E(f737(x2753,x2751,x2754,x2755,x2756),f737(x2753,x2752,x2754,x2755,x2756))
% 187.33/188.06 [276]~E(x2761,x2762)+E(f737(x2763,x2764,x2761,x2765,x2766),f737(x2763,x2764,x2762,x2765,x2766))
% 187.33/188.06 [277]~E(x2771,x2772)+E(f737(x2773,x2774,x2775,x2771,x2776),f737(x2773,x2774,x2775,x2772,x2776))
% 187.33/188.06 [278]~E(x2781,x2782)+E(f737(x2783,x2784,x2785,x2786,x2781),f737(x2783,x2784,x2785,x2786,x2782))
% 187.33/188.06 [279]~E(x2791,x2792)+E(f493(x2791,x2793,x2794),f493(x2792,x2793,x2794))
% 187.33/188.06 [280]~E(x2801,x2802)+E(f493(x2803,x2801,x2804),f493(x2803,x2802,x2804))
% 187.33/188.06 [281]~E(x2811,x2812)+E(f493(x2813,x2814,x2811),f493(x2813,x2814,x2812))
% 187.33/188.06 [282]~E(x2821,x2822)+E(f188(x2821,x2823),f188(x2822,x2823))
% 187.33/188.06 [283]~E(x2831,x2832)+E(f188(x2833,x2831),f188(x2833,x2832))
% 187.33/188.06 [284]~E(x2841,x2842)+E(f49(x2841,x2843),f49(x2842,x2843))
% 187.33/188.06 [285]~E(x2851,x2852)+E(f49(x2853,x2851),f49(x2853,x2852))
% 187.33/188.06 [286]~E(x2861,x2862)+E(f492(x2861,x2863,x2864),f492(x2862,x2863,x2864))
% 187.33/188.06 [287]~E(x2871,x2872)+E(f492(x2873,x2871,x2874),f492(x2873,x2872,x2874))
% 187.33/188.06 [288]~E(x2881,x2882)+E(f492(x2883,x2884,x2881),f492(x2883,x2884,x2882))
% 187.33/188.06 [289]~E(x2891,x2892)+E(f879(x2891,x2893),f879(x2892,x2893))
% 187.33/188.06 [290]~E(x2901,x2902)+E(f879(x2903,x2901),f879(x2903,x2902))
% 187.33/188.06 [291]~E(x2911,x2912)+E(f384(x2911,x2913,x2914),f384(x2912,x2913,x2914))
% 187.33/188.06 [292]~E(x2921,x2922)+E(f384(x2923,x2921,x2924),f384(x2923,x2922,x2924))
% 187.33/188.06 [293]~E(x2931,x2932)+E(f384(x2933,x2934,x2931),f384(x2933,x2934,x2932))
% 187.33/188.06 [294]~E(x2941,x2942)+E(f137(x2941,x2943),f137(x2942,x2943))
% 187.33/188.06 [295]~E(x2951,x2952)+E(f137(x2953,x2951),f137(x2953,x2952))
% 187.33/188.06 [296]~E(x2961,x2962)+E(f168(x2961,x2963,x2964),f168(x2962,x2963,x2964))
% 187.33/188.06 [297]~E(x2971,x2972)+E(f168(x2973,x2971,x2974),f168(x2973,x2972,x2974))
% 187.33/188.06 [298]~E(x2981,x2982)+E(f168(x2983,x2984,x2981),f168(x2983,x2984,x2982))
% 187.33/188.06 [299]~E(x2991,x2992)+E(f166(x2991),f166(x2992))
% 187.33/188.06 [300]~E(x3001,x3002)+E(f229(x3001,x3003,x3004),f229(x3002,x3003,x3004))
% 187.33/188.06 [301]~E(x3011,x3012)+E(f229(x3013,x3011,x3014),f229(x3013,x3012,x3014))
% 187.33/188.06 [302]~E(x3021,x3022)+E(f229(x3023,x3024,x3021),f229(x3023,x3024,x3022))
% 187.33/188.06 [303]~E(x3031,x3032)+E(f607(x3031,x3033,x3034),f607(x3032,x3033,x3034))
% 187.33/188.06 [304]~E(x3041,x3042)+E(f607(x3043,x3041,x3044),f607(x3043,x3042,x3044))
% 187.33/188.06 [305]~E(x3051,x3052)+E(f607(x3053,x3054,x3051),f607(x3053,x3054,x3052))
% 187.33/188.06 [306]~E(x3061,x3062)+E(f87(x3061),f87(x3062))
% 187.33/188.06 [307]~E(x3071,x3072)+E(f170(x3071),f170(x3072))
% 187.33/188.06 [308]~E(x3081,x3082)+E(f822(x3081,x3083,x3084,x3085,x3086),f822(x3082,x3083,x3084,x3085,x3086))
% 187.33/188.06 [309]~E(x3091,x3092)+E(f822(x3093,x3091,x3094,x3095,x3096),f822(x3093,x3092,x3094,x3095,x3096))
% 187.33/188.06 [310]~E(x3101,x3102)+E(f822(x3103,x3104,x3101,x3105,x3106),f822(x3103,x3104,x3102,x3105,x3106))
% 187.33/188.06 [311]~E(x3111,x3112)+E(f822(x3113,x3114,x3115,x3111,x3116),f822(x3113,x3114,x3115,x3112,x3116))
% 187.33/188.06 [312]~E(x3121,x3122)+E(f822(x3123,x3124,x3125,x3126,x3121),f822(x3123,x3124,x3125,x3126,x3122))
% 187.33/188.06 [313]~E(x3131,x3132)+E(f47(x3131,x3133),f47(x3132,x3133))
% 187.33/188.06 [314]~E(x3141,x3142)+E(f47(x3143,x3141),f47(x3143,x3142))
% 187.33/188.06 [315]~E(x3151,x3152)+E(f18(x3151,x3153,x3154),f18(x3152,x3153,x3154))
% 187.33/188.06 [316]~E(x3161,x3162)+E(f18(x3163,x3161,x3164),f18(x3163,x3162,x3164))
% 187.33/188.06 [317]~E(x3171,x3172)+E(f18(x3173,x3174,x3171),f18(x3173,x3174,x3172))
% 187.33/188.06 [318]~E(x3181,x3182)+E(f167(x3181),f167(x3182))
% 187.33/188.06 [319]~E(x3191,x3192)+E(f220(x3191),f220(x3192))
% 187.33/188.06 [320]~E(x3201,x3202)+E(f262(x3201,x3203),f262(x3202,x3203))
% 187.33/188.06 [321]~E(x3211,x3212)+E(f262(x3213,x3211),f262(x3213,x3212))
% 187.33/188.06 [322]~E(x3221,x3222)+E(f363(x3221,x3223,x3224),f363(x3222,x3223,x3224))
% 187.33/188.06 [323]~E(x3231,x3232)+E(f363(x3233,x3231,x3234),f363(x3233,x3232,x3234))
% 187.33/188.06 [324]~E(x3241,x3242)+E(f363(x3243,x3244,x3241),f363(x3243,x3244,x3242))
% 187.33/188.06 [325]~E(x3251,x3252)+E(f15(x3251,x3253),f15(x3252,x3253))
% 187.33/188.06 [326]~E(x3261,x3262)+E(f15(x3263,x3261),f15(x3263,x3262))
% 187.33/188.06 [327]~E(x3271,x3272)+E(f66(x3271,x3273,x3274),f66(x3272,x3273,x3274))
% 187.33/188.06 [328]~E(x3281,x3282)+E(f66(x3283,x3281,x3284),f66(x3283,x3282,x3284))
% 187.33/188.06 [329]~E(x3291,x3292)+E(f66(x3293,x3294,x3291),f66(x3293,x3294,x3292))
% 187.33/188.06 [330]~E(x3301,x3302)+E(f43(x3301,x3303),f43(x3302,x3303))
% 187.33/188.06 [331]~E(x3311,x3312)+E(f43(x3313,x3311),f43(x3313,x3312))
% 187.33/188.06 [332]~E(x3321,x3322)+E(f50(x3321,x3323),f50(x3322,x3323))
% 187.33/188.06 [333]~E(x3331,x3332)+E(f50(x3333,x3331),f50(x3333,x3332))
% 187.33/188.06 [334]~E(x3341,x3342)+E(f177(x3341,x3343),f177(x3342,x3343))
% 187.33/188.06 [335]~E(x3351,x3352)+E(f177(x3353,x3351),f177(x3353,x3352))
% 187.33/188.06 [336]~E(x3361,x3362)+E(f158(x3361,x3363),f158(x3362,x3363))
% 187.33/188.06 [337]~E(x3371,x3372)+E(f158(x3373,x3371),f158(x3373,x3372))
% 187.33/188.06 [338]~E(x3381,x3382)+E(f385(x3381,x3383,x3384),f385(x3382,x3383,x3384))
% 187.33/188.06 [339]~E(x3391,x3392)+E(f385(x3393,x3391,x3394),f385(x3393,x3392,x3394))
% 187.33/188.06 [340]~E(x3401,x3402)+E(f385(x3403,x3404,x3401),f385(x3403,x3404,x3402))
% 187.33/188.06 [341]~E(x3411,x3412)+E(f320(x3411,x3413),f320(x3412,x3413))
% 187.33/188.06 [342]~E(x3421,x3422)+E(f320(x3423,x3421),f320(x3423,x3422))
% 187.33/188.06 [343]~E(x3431,x3432)+E(f770(x3431,x3433,x3434,x3435),f770(x3432,x3433,x3434,x3435))
% 187.33/188.06 [344]~E(x3441,x3442)+E(f770(x3443,x3441,x3444,x3445),f770(x3443,x3442,x3444,x3445))
% 187.33/188.06 [345]~E(x3451,x3452)+E(f770(x3453,x3454,x3451,x3455),f770(x3453,x3454,x3452,x3455))
% 187.33/188.06 [346]~E(x3461,x3462)+E(f770(x3463,x3464,x3465,x3461),f770(x3463,x3464,x3465,x3462))
% 187.33/188.06 [347]~E(x3471,x3472)+E(f321(x3471,x3473),f321(x3472,x3473))
% 187.33/188.06 [348]~E(x3481,x3482)+E(f321(x3483,x3481),f321(x3483,x3482))
% 187.33/188.06 [349]~E(x3491,x3492)+E(f266(x3491,x3493),f266(x3492,x3493))
% 187.33/188.06 [350]~E(x3501,x3502)+E(f266(x3503,x3501),f266(x3503,x3502))
% 187.33/188.06 [351]~E(x3511,x3512)+E(f369(x3511,x3513,x3514),f369(x3512,x3513,x3514))
% 187.33/188.06 [352]~E(x3521,x3522)+E(f369(x3523,x3521,x3524),f369(x3523,x3522,x3524))
% 187.33/188.06 [353]~E(x3531,x3532)+E(f369(x3533,x3534,x3531),f369(x3533,x3534,x3532))
% 187.33/188.06 [354]~E(x3541,x3542)+E(f808(x3541,x3543,x3544),f808(x3542,x3543,x3544))
% 187.33/188.06 [355]~E(x3551,x3552)+E(f808(x3553,x3551,x3554),f808(x3553,x3552,x3554))
% 187.33/188.06 [356]~E(x3561,x3562)+E(f808(x3563,x3564,x3561),f808(x3563,x3564,x3562))
% 187.33/188.06 [357]~E(x3571,x3572)+E(f82(x3571,x3573),f82(x3572,x3573))
% 187.33/188.06 [358]~E(x3581,x3582)+E(f82(x3583,x3581),f82(x3583,x3582))
% 187.33/188.06 [359]~E(x3591,x3592)+E(f758(x3591,x3593,x3594,x3595),f758(x3592,x3593,x3594,x3595))
% 187.33/188.06 [360]~E(x3601,x3602)+E(f758(x3603,x3601,x3604,x3605),f758(x3603,x3602,x3604,x3605))
% 187.33/188.06 [361]~E(x3611,x3612)+E(f758(x3613,x3614,x3611,x3615),f758(x3613,x3614,x3612,x3615))
% 187.33/188.06 [362]~E(x3621,x3622)+E(f758(x3623,x3624,x3625,x3621),f758(x3623,x3624,x3625,x3622))
% 187.33/188.06 [363]~E(x3631,x3632)+E(f32(x3631,x3633),f32(x3632,x3633))
% 187.33/188.06 [364]~E(x3641,x3642)+E(f32(x3643,x3641),f32(x3643,x3642))
% 187.33/188.06 [365]~E(x3651,x3652)+E(f253(x3651,x3653,x3654),f253(x3652,x3653,x3654))
% 187.33/188.06 [366]~E(x3661,x3662)+E(f253(x3663,x3661,x3664),f253(x3663,x3662,x3664))
% 187.33/188.06 [367]~E(x3671,x3672)+E(f253(x3673,x3674,x3671),f253(x3673,x3674,x3672))
% 187.33/188.06 [368]~E(x3681,x3682)+E(f428(x3681,x3683,x3684,x3685,x3686,x3687),f428(x3682,x3683,x3684,x3685,x3686,x3687))
% 187.33/188.06 [369]~E(x3691,x3692)+E(f428(x3693,x3691,x3694,x3695,x3696,x3697),f428(x3693,x3692,x3694,x3695,x3696,x3697))
% 187.33/188.06 [370]~E(x3701,x3702)+E(f428(x3703,x3704,x3701,x3705,x3706,x3707),f428(x3703,x3704,x3702,x3705,x3706,x3707))
% 187.33/188.06 [371]~E(x3711,x3712)+E(f428(x3713,x3714,x3715,x3711,x3716,x3717),f428(x3713,x3714,x3715,x3712,x3716,x3717))
% 187.33/188.06 [372]~E(x3721,x3722)+E(f428(x3723,x3724,x3725,x3726,x3721,x3727),f428(x3723,x3724,x3725,x3726,x3722,x3727))
% 187.33/188.06 [373]~E(x3731,x3732)+E(f428(x3733,x3734,x3735,x3736,x3737,x3731),f428(x3733,x3734,x3735,x3736,x3737,x3732))
% 187.33/188.06 [374]~E(x3741,x3742)+E(f683(x3741,x3743),f683(x3742,x3743))
% 187.33/188.06 [375]~E(x3751,x3752)+E(f683(x3753,x3751),f683(x3753,x3752))
% 187.33/188.06 [376]~E(x3761,x3762)+E(f719(x3761,x3763,x3764),f719(x3762,x3763,x3764))
% 187.33/188.06 [377]~E(x3771,x3772)+E(f719(x3773,x3771,x3774),f719(x3773,x3772,x3774))
% 187.33/188.06 [378]~E(x3781,x3782)+E(f719(x3783,x3784,x3781),f719(x3783,x3784,x3782))
% 187.33/188.06 [379]~E(x3791,x3792)+E(f588(x3791,x3793,x3794,x3795,x3796,x3797,x3798,x3799),f588(x3792,x3793,x3794,x3795,x3796,x3797,x3798,x3799))
% 187.33/188.06 [380]~E(x3801,x3802)+E(f588(x3803,x3801,x3804,x3805,x3806,x3807,x3808,x3809),f588(x3803,x3802,x3804,x3805,x3806,x3807,x3808,x3809))
% 187.33/188.06 [381]~E(x3811,x3812)+E(f588(x3813,x3814,x3811,x3815,x3816,x3817,x3818,x3819),f588(x3813,x3814,x3812,x3815,x3816,x3817,x3818,x3819))
% 187.33/188.06 [382]~E(x3821,x3822)+E(f588(x3823,x3824,x3825,x3821,x3826,x3827,x3828,x3829),f588(x3823,x3824,x3825,x3822,x3826,x3827,x3828,x3829))
% 187.33/188.06 [383]~E(x3831,x3832)+E(f588(x3833,x3834,x3835,x3836,x3831,x3837,x3838,x3839),f588(x3833,x3834,x3835,x3836,x3832,x3837,x3838,x3839))
% 187.33/188.06 [384]~E(x3841,x3842)+E(f588(x3843,x3844,x3845,x3846,x3847,x3841,x3848,x3849),f588(x3843,x3844,x3845,x3846,x3847,x3842,x3848,x3849))
% 187.33/188.06 [385]~E(x3851,x3852)+E(f588(x3853,x3854,x3855,x3856,x3857,x3858,x3851,x3859),f588(x3853,x3854,x3855,x3856,x3857,x3858,x3852,x3859))
% 187.33/188.06 [386]~E(x3861,x3862)+E(f588(x3863,x3864,x3865,x3866,x3867,x3868,x3869,x3861),f588(x3863,x3864,x3865,x3866,x3867,x3868,x3869,x3862))
% 187.33/188.06 [387]~E(x3871,x3872)+E(f176(x3871,x3873,x3874),f176(x3872,x3873,x3874))
% 187.33/188.06 [388]~E(x3881,x3882)+E(f176(x3883,x3881,x3884),f176(x3883,x3882,x3884))
% 187.33/188.06 [389]~E(x3891,x3892)+E(f176(x3893,x3894,x3891),f176(x3893,x3894,x3892))
% 187.33/188.06 [390]~E(x3901,x3902)+E(f125(x3901),f125(x3902))
% 187.33/188.06 [391]~E(x3911,x3912)+E(f199(x3911),f199(x3912))
% 187.33/188.06 [392]~E(x3921,x3922)+E(f336(x3921),f336(x3922))
% 187.33/188.06 [393]~E(x3931,x3932)+E(f863(x3931,x3933,x3934),f863(x3932,x3933,x3934))
% 187.33/188.06 [394]~E(x3941,x3942)+E(f863(x3943,x3941,x3944),f863(x3943,x3942,x3944))
% 187.33/188.06 [395]~E(x3951,x3952)+E(f863(x3953,x3954,x3951),f863(x3953,x3954,x3952))
% 187.33/188.06 [396]~E(x3961,x3962)+E(f85(x3961,x3963),f85(x3962,x3963))
% 187.33/188.06 [397]~E(x3971,x3972)+E(f85(x3973,x3971),f85(x3973,x3972))
% 187.33/188.06 [398]~E(x3981,x3982)+E(f485(x3981,x3983,x3984),f485(x3982,x3983,x3984))
% 187.33/188.06 [399]~E(x3991,x3992)+E(f485(x3993,x3991,x3994),f485(x3993,x3992,x3994))
% 187.33/188.06 [400]~E(x4001,x4002)+E(f485(x4003,x4004,x4001),f485(x4003,x4004,x4002))
% 187.33/188.06 [401]~E(x4011,x4012)+E(f90(x4011,x4013),f90(x4012,x4013))
% 187.33/188.06 [402]~E(x4021,x4022)+E(f90(x4023,x4021),f90(x4023,x4022))
% 187.33/188.06 [403]~E(x4031,x4032)+E(f206(x4031),f206(x4032))
% 187.33/188.06 [404]~E(x4041,x4042)+E(f151(x4041,x4043),f151(x4042,x4043))
% 187.33/188.06 [405]~E(x4051,x4052)+E(f151(x4053,x4051),f151(x4053,x4052))
% 187.33/188.06 [406]~E(x4061,x4062)+E(f143(x4061,x4063),f143(x4062,x4063))
% 187.33/188.06 [407]~E(x4071,x4072)+E(f143(x4073,x4071),f143(x4073,x4072))
% 187.33/188.06 [408]~E(x4081,x4082)+E(f207(x4081,x4083),f207(x4082,x4083))
% 187.33/188.06 [409]~E(x4091,x4092)+E(f207(x4093,x4091),f207(x4093,x4092))
% 187.33/188.06 [410]~E(x4101,x4102)+E(f234(x4101,x4103,x4104,x4105),f234(x4102,x4103,x4104,x4105))
% 187.33/188.06 [411]~E(x4111,x4112)+E(f234(x4113,x4111,x4114,x4115),f234(x4113,x4112,x4114,x4115))
% 187.33/188.06 [412]~E(x4121,x4122)+E(f234(x4123,x4124,x4121,x4125),f234(x4123,x4124,x4122,x4125))
% 187.33/188.06 [413]~E(x4131,x4132)+E(f234(x4133,x4134,x4135,x4131),f234(x4133,x4134,x4135,x4132))
% 187.33/188.06 [414]~E(x4141,x4142)+E(f286(x4141,x4143,x4144),f286(x4142,x4143,x4144))
% 187.33/188.06 [415]~E(x4151,x4152)+E(f286(x4153,x4151,x4154),f286(x4153,x4152,x4154))
% 187.33/188.06 [416]~E(x4161,x4162)+E(f286(x4163,x4164,x4161),f286(x4163,x4164,x4162))
% 187.33/188.06 [417]~E(x4171,x4172)+E(f204(x4171,x4173,x4174,x4175),f204(x4172,x4173,x4174,x4175))
% 187.33/188.06 [418]~E(x4181,x4182)+E(f204(x4183,x4181,x4184,x4185),f204(x4183,x4182,x4184,x4185))
% 187.33/188.06 [419]~E(x4191,x4192)+E(f204(x4193,x4194,x4191,x4195),f204(x4193,x4194,x4192,x4195))
% 187.33/188.06 [420]~E(x4201,x4202)+E(f204(x4203,x4204,x4205,x4201),f204(x4203,x4204,x4205,x4202))
% 187.33/188.06 [421]~E(x4211,x4212)+E(f662(x4211,x4213,x4214,x4215),f662(x4212,x4213,x4214,x4215))
% 187.33/188.06 [422]~E(x4221,x4222)+E(f662(x4223,x4221,x4224,x4225),f662(x4223,x4222,x4224,x4225))
% 187.33/188.06 [423]~E(x4231,x4232)+E(f662(x4233,x4234,x4231,x4235),f662(x4233,x4234,x4232,x4235))
% 187.33/188.06 [424]~E(x4241,x4242)+E(f662(x4243,x4244,x4245,x4241),f662(x4243,x4244,x4245,x4242))
% 187.33/188.06 [425]~E(x4251,x4252)+E(f433(x4251,x4253,x4254,x4255,x4256),f433(x4252,x4253,x4254,x4255,x4256))
% 187.33/188.06 [426]~E(x4261,x4262)+E(f433(x4263,x4261,x4264,x4265,x4266),f433(x4263,x4262,x4264,x4265,x4266))
% 187.33/188.06 [427]~E(x4271,x4272)+E(f433(x4273,x4274,x4271,x4275,x4276),f433(x4273,x4274,x4272,x4275,x4276))
% 187.33/188.06 [428]~E(x4281,x4282)+E(f433(x4283,x4284,x4285,x4281,x4286),f433(x4283,x4284,x4285,x4282,x4286))
% 187.33/188.06 [429]~E(x4291,x4292)+E(f433(x4293,x4294,x4295,x4296,x4291),f433(x4293,x4294,x4295,x4296,x4292))
% 187.33/188.06 [430]~E(x4301,x4302)+E(f267(x4301,x4303),f267(x4302,x4303))
% 187.33/188.06 [431]~E(x4311,x4312)+E(f267(x4313,x4311),f267(x4313,x4312))
% 187.33/188.06 [432]~E(x4321,x4322)+E(f755(x4321,x4323,x4324,x4325,x4326),f755(x4322,x4323,x4324,x4325,x4326))
% 187.33/188.06 [433]~E(x4331,x4332)+E(f755(x4333,x4331,x4334,x4335,x4336),f755(x4333,x4332,x4334,x4335,x4336))
% 187.33/188.06 [434]~E(x4341,x4342)+E(f755(x4343,x4344,x4341,x4345,x4346),f755(x4343,x4344,x4342,x4345,x4346))
% 187.33/188.06 [435]~E(x4351,x4352)+E(f755(x4353,x4354,x4355,x4351,x4356),f755(x4353,x4354,x4355,x4352,x4356))
% 187.33/188.06 [436]~E(x4361,x4362)+E(f755(x4363,x4364,x4365,x4366,x4361),f755(x4363,x4364,x4365,x4366,x4362))
% 187.33/188.06 [437]~E(x4371,x4372)+E(f302(x4371,x4373,x4374),f302(x4372,x4373,x4374))
% 187.33/188.06 [438]~E(x4381,x4382)+E(f302(x4383,x4381,x4384),f302(x4383,x4382,x4384))
% 187.33/188.06 [439]~E(x4391,x4392)+E(f302(x4393,x4394,x4391),f302(x4393,x4394,x4392))
% 187.33/188.06 [440]~E(x4401,x4402)+E(f862(x4401,x4403,x4404),f862(x4402,x4403,x4404))
% 187.33/188.06 [441]~E(x4411,x4412)+E(f862(x4413,x4411,x4414),f862(x4413,x4412,x4414))
% 187.33/188.06 [442]~E(x4421,x4422)+E(f862(x4423,x4424,x4421),f862(x4423,x4424,x4422))
% 187.33/188.06 [443]~E(x4431,x4432)+E(f268(x4431,x4433,x4434),f268(x4432,x4433,x4434))
% 187.33/188.06 [444]~E(x4441,x4442)+E(f268(x4443,x4441,x4444),f268(x4443,x4442,x4444))
% 187.33/188.06 [445]~E(x4451,x4452)+E(f268(x4453,x4454,x4451),f268(x4453,x4454,x4452))
% 187.33/188.06 [446]~E(x4461,x4462)+E(f179(x4461,x4463),f179(x4462,x4463))
% 187.33/188.06 [447]~E(x4471,x4472)+E(f179(x4473,x4471),f179(x4473,x4472))
% 187.33/188.06 [448]~E(x4481,x4482)+E(f306(x4481),f306(x4482))
% 187.33/188.06 [449]~E(x4491,x4492)+E(f293(x4491,x4493,x4494,x4495),f293(x4492,x4493,x4494,x4495))
% 187.33/188.06 [450]~E(x4501,x4502)+E(f293(x4503,x4501,x4504,x4505),f293(x4503,x4502,x4504,x4505))
% 187.33/188.06 [451]~E(x4511,x4512)+E(f293(x4513,x4514,x4511,x4515),f293(x4513,x4514,x4512,x4515))
% 187.33/188.06 [452]~E(x4521,x4522)+E(f293(x4523,x4524,x4525,x4521),f293(x4523,x4524,x4525,x4522))
% 187.33/188.06 [453]~E(x4531,x4532)+E(f551(x4531,x4533),f551(x4532,x4533))
% 187.33/188.06 [454]~E(x4541,x4542)+E(f551(x4543,x4541),f551(x4543,x4542))
% 187.33/188.06 [455]~E(x4551,x4552)+E(f584(x4551,x4553,x4554,x4555),f584(x4552,x4553,x4554,x4555))
% 187.33/188.06 [456]~E(x4561,x4562)+E(f584(x4563,x4561,x4564,x4565),f584(x4563,x4562,x4564,x4565))
% 187.33/188.06 [457]~E(x4571,x4572)+E(f584(x4573,x4574,x4571,x4575),f584(x4573,x4574,x4572,x4575))
% 187.33/188.06 [458]~E(x4581,x4582)+E(f584(x4583,x4584,x4585,x4581),f584(x4583,x4584,x4585,x4582))
% 187.33/188.06 [459]~E(x4591,x4592)+E(f245(x4591,x4593),f245(x4592,x4593))
% 187.33/188.06 [460]~E(x4601,x4602)+E(f245(x4603,x4601),f245(x4603,x4602))
% 187.33/188.06 [461]~E(x4611,x4612)+E(f283(x4611,x4613,x4614),f283(x4612,x4613,x4614))
% 187.33/188.06 [462]~E(x4621,x4622)+E(f283(x4623,x4621,x4624),f283(x4623,x4622,x4624))
% 187.33/188.06 [463]~E(x4631,x4632)+E(f283(x4633,x4634,x4631),f283(x4633,x4634,x4632))
% 187.33/188.06 [464]~E(x4641,x4642)+E(f136(x4641),f136(x4642))
% 187.33/188.06 [465]~E(x4651,x4652)+E(f285(x4651,x4653),f285(x4652,x4653))
% 187.33/188.06 [466]~E(x4661,x4662)+E(f285(x4663,x4661),f285(x4663,x4662))
% 187.33/188.06 [467]~E(x4671,x4672)+E(f815(x4671,x4673,x4674),f815(x4672,x4673,x4674))
% 187.33/188.06 [468]~E(x4681,x4682)+E(f815(x4683,x4681,x4684),f815(x4683,x4682,x4684))
% 187.33/188.06 [469]~E(x4691,x4692)+E(f815(x4693,x4694,x4691),f815(x4693,x4694,x4692))
% 187.33/188.06 [470]~E(x4701,x4702)+E(f157(x4701,x4703),f157(x4702,x4703))
% 187.33/188.06 [471]~E(x4711,x4712)+E(f157(x4713,x4711),f157(x4713,x4712))
% 187.33/188.06 [472]~E(x4721,x4722)+E(f803(x4721,x4723,x4724),f803(x4722,x4723,x4724))
% 187.33/188.06 [473]~E(x4731,x4732)+E(f803(x4733,x4731,x4734),f803(x4733,x4732,x4734))
% 187.33/188.06 [474]~E(x4741,x4742)+E(f803(x4743,x4744,x4741),f803(x4743,x4744,x4742))
% 187.33/188.06 [475]~E(x4751,x4752)+E(f456(x4751,x4753,x4754),f456(x4752,x4753,x4754))
% 187.33/188.06 [476]~E(x4761,x4762)+E(f456(x4763,x4761,x4764),f456(x4763,x4762,x4764))
% 187.33/188.06 [477]~E(x4771,x4772)+E(f456(x4773,x4774,x4771),f456(x4773,x4774,x4772))
% 187.33/188.06 [478]~E(x4781,x4782)+E(f46(x4781,x4783),f46(x4782,x4783))
% 187.33/188.06 [479]~E(x4791,x4792)+E(f46(x4793,x4791),f46(x4793,x4792))
% 187.33/188.06 [480]~E(x4801,x4802)+E(f224(x4801,x4803),f224(x4802,x4803))
% 187.33/188.06 [481]~E(x4811,x4812)+E(f224(x4813,x4811),f224(x4813,x4812))
% 187.33/188.06 [482]~E(x4821,x4822)+E(f92(x4821),f92(x4822))
% 187.33/188.06 [483]~E(x4831,x4832)+E(f810(x4831,x4833,x4834),f810(x4832,x4833,x4834))
% 187.33/188.06 [484]~E(x4841,x4842)+E(f810(x4843,x4841,x4844),f810(x4843,x4842,x4844))
% 187.33/188.06 [485]~E(x4851,x4852)+E(f810(x4853,x4854,x4851),f810(x4853,x4854,x4852))
% 187.33/188.06 [486]~E(x4861,x4862)+E(f304(x4861),f304(x4862))
% 187.33/188.06 [487]~E(x4871,x4872)+E(f337(x4871),f337(x4872))
% 187.33/188.06 [488]~E(x4881,x4882)+E(f55(x4881,x4883,x4884),f55(x4882,x4883,x4884))
% 187.33/188.06 [489]~E(x4891,x4892)+E(f55(x4893,x4891,x4894),f55(x4893,x4892,x4894))
% 187.33/188.06 [490]~E(x4901,x4902)+E(f55(x4903,x4904,x4901),f55(x4903,x4904,x4902))
% 187.33/188.06 [491]~E(x4911,x4912)+E(f309(x4911,x4913,x4914),f309(x4912,x4913,x4914))
% 187.33/188.06 [492]~E(x4921,x4922)+E(f309(x4923,x4921,x4924),f309(x4923,x4922,x4924))
% 187.33/188.06 [493]~E(x4931,x4932)+E(f309(x4933,x4934,x4931),f309(x4933,x4934,x4932))
% 187.33/188.06 [494]~E(x4941,x4942)+E(f183(x4941,x4943,x4944),f183(x4942,x4943,x4944))
% 187.33/188.06 [495]~E(x4951,x4952)+E(f183(x4953,x4951,x4954),f183(x4953,x4952,x4954))
% 187.33/188.06 [496]~E(x4961,x4962)+E(f183(x4963,x4964,x4961),f183(x4963,x4964,x4962))
% 187.33/188.06 [497]~E(x4971,x4972)+E(f513(x4971,x4973,x4974,x4975,x4976,x4977),f513(x4972,x4973,x4974,x4975,x4976,x4977))
% 187.33/188.06 [498]~E(x4981,x4982)+E(f513(x4983,x4981,x4984,x4985,x4986,x4987),f513(x4983,x4982,x4984,x4985,x4986,x4987))
% 187.33/188.06 [499]~E(x4991,x4992)+E(f513(x4993,x4994,x4991,x4995,x4996,x4997),f513(x4993,x4994,x4992,x4995,x4996,x4997))
% 187.33/188.06 [500]~E(x5001,x5002)+E(f513(x5003,x5004,x5005,x5001,x5006,x5007),f513(x5003,x5004,x5005,x5002,x5006,x5007))
% 187.33/188.06 [501]~E(x5011,x5012)+E(f513(x5013,x5014,x5015,x5016,x5011,x5017),f513(x5013,x5014,x5015,x5016,x5012,x5017))
% 187.33/188.06 [502]~E(x5021,x5022)+E(f513(x5023,x5024,x5025,x5026,x5027,x5021),f513(x5023,x5024,x5025,x5026,x5027,x5022))
% 187.33/188.06 [503]~E(x5031,x5032)+E(f817(x5031,x5033,x5034),f817(x5032,x5033,x5034))
% 187.33/188.06 [504]~E(x5041,x5042)+E(f817(x5043,x5041,x5044),f817(x5043,x5042,x5044))
% 187.33/188.06 [505]~E(x5051,x5052)+E(f817(x5053,x5054,x5051),f817(x5053,x5054,x5052))
% 187.33/188.06 [506]~E(x5061,x5062)+E(f159(x5061,x5063),f159(x5062,x5063))
% 187.33/188.06 [507]~E(x5071,x5072)+E(f159(x5073,x5071),f159(x5073,x5072))
% 187.33/188.06 [508]~E(x5081,x5082)+E(f820(x5081,x5083,x5084),f820(x5082,x5083,x5084))
% 187.33/188.06 [509]~E(x5091,x5092)+E(f820(x5093,x5091,x5094),f820(x5093,x5092,x5094))
% 187.33/188.06 [510]~E(x5101,x5102)+E(f820(x5103,x5104,x5101),f820(x5103,x5104,x5102))
% 187.33/188.06 [511]~E(x5111,x5112)+E(f462(x5111,x5113,x5114),f462(x5112,x5113,x5114))
% 187.33/188.06 [512]~E(x5121,x5122)+E(f462(x5123,x5121,x5124),f462(x5123,x5122,x5124))
% 187.33/188.06 [513]~E(x5131,x5132)+E(f462(x5133,x5134,x5131),f462(x5133,x5134,x5132))
% 187.33/188.06 [514]~E(x5141,x5142)+E(f867(x5141,x5143,x5144,x5145,x5146),f867(x5142,x5143,x5144,x5145,x5146))
% 187.33/188.06 [515]~E(x5151,x5152)+E(f867(x5153,x5151,x5154,x5155,x5156),f867(x5153,x5152,x5154,x5155,x5156))
% 187.33/188.06 [516]~E(x5161,x5162)+E(f867(x5163,x5164,x5161,x5165,x5166),f867(x5163,x5164,x5162,x5165,x5166))
% 187.33/188.06 [517]~E(x5171,x5172)+E(f867(x5173,x5174,x5175,x5171,x5176),f867(x5173,x5174,x5175,x5172,x5176))
% 187.33/188.06 [518]~E(x5181,x5182)+E(f867(x5183,x5184,x5185,x5186,x5181),f867(x5183,x5184,x5185,x5186,x5182))
% 187.33/188.06 [519]~E(x5191,x5192)+E(f809(x5191,x5193,x5194),f809(x5192,x5193,x5194))
% 187.33/188.06 [520]~E(x5201,x5202)+E(f809(x5203,x5201,x5204),f809(x5203,x5202,x5204))
% 187.33/188.06 [521]~E(x5211,x5212)+E(f809(x5213,x5214,x5211),f809(x5213,x5214,x5212))
% 187.33/188.06 [522]~E(x5221,x5222)+E(f650(x5221,x5223,x5224),f650(x5222,x5223,x5224))
% 187.33/188.06 [523]~E(x5231,x5232)+E(f650(x5233,x5231,x5234),f650(x5233,x5232,x5234))
% 187.33/188.06 [524]~E(x5241,x5242)+E(f650(x5243,x5244,x5241),f650(x5243,x5244,x5242))
% 187.33/188.06 [525]~E(x5251,x5252)+E(f64(x5251,x5253),f64(x5252,x5253))
% 187.33/188.06 [526]~E(x5261,x5262)+E(f64(x5263,x5261),f64(x5263,x5262))
% 187.33/188.06 [527]~E(x5271,x5272)+E(f636(x5271,x5273,x5274),f636(x5272,x5273,x5274))
% 187.33/188.06 [528]~E(x5281,x5282)+E(f636(x5283,x5281,x5284),f636(x5283,x5282,x5284))
% 187.33/188.06 [529]~E(x5291,x5292)+E(f636(x5293,x5294,x5291),f636(x5293,x5294,x5292))
% 187.33/188.06 [530]~E(x5301,x5302)+E(f568(x5301,x5303,x5304),f568(x5302,x5303,x5304))
% 187.33/188.06 [531]~E(x5311,x5312)+E(f568(x5313,x5311,x5314),f568(x5313,x5312,x5314))
% 187.33/188.06 [532]~E(x5321,x5322)+E(f568(x5323,x5324,x5321),f568(x5323,x5324,x5322))
% 187.33/188.06 [533]~E(x5331,x5332)+E(f235(x5331,x5333),f235(x5332,x5333))
% 187.33/188.06 [534]~E(x5341,x5342)+E(f235(x5343,x5341),f235(x5343,x5342))
% 187.33/188.06 [535]~E(x5351,x5352)+E(f517(x5351,x5353,x5354,x5355),f517(x5352,x5353,x5354,x5355))
% 187.33/188.06 [536]~E(x5361,x5362)+E(f517(x5363,x5361,x5364,x5365),f517(x5363,x5362,x5364,x5365))
% 187.33/188.06 [537]~E(x5371,x5372)+E(f517(x5373,x5374,x5371,x5375),f517(x5373,x5374,x5372,x5375))
% 187.33/188.06 [538]~E(x5381,x5382)+E(f517(x5383,x5384,x5385,x5381),f517(x5383,x5384,x5385,x5382))
% 187.33/188.06 [539]~E(x5391,x5392)+E(f60(x5391,x5393,x5394,x5395),f60(x5392,x5393,x5394,x5395))
% 187.33/188.06 [540]~E(x5401,x5402)+E(f60(x5403,x5401,x5404,x5405),f60(x5403,x5402,x5404,x5405))
% 187.33/188.06 [541]~E(x5411,x5412)+E(f60(x5413,x5414,x5411,x5415),f60(x5413,x5414,x5412,x5415))
% 187.33/188.06 [542]~E(x5421,x5422)+E(f60(x5423,x5424,x5425,x5421),f60(x5423,x5424,x5425,x5422))
% 187.33/188.06 [543]~E(x5431,x5432)+E(f575(x5431,x5433,x5434,x5435,x5436,x5437,x5438,x5439),f575(x5432,x5433,x5434,x5435,x5436,x5437,x5438,x5439))
% 187.33/188.06 [544]~E(x5441,x5442)+E(f575(x5443,x5441,x5444,x5445,x5446,x5447,x5448,x5449),f575(x5443,x5442,x5444,x5445,x5446,x5447,x5448,x5449))
% 187.33/188.06 [545]~E(x5451,x5452)+E(f575(x5453,x5454,x5451,x5455,x5456,x5457,x5458,x5459),f575(x5453,x5454,x5452,x5455,x5456,x5457,x5458,x5459))
% 187.33/188.06 [546]~E(x5461,x5462)+E(f575(x5463,x5464,x5465,x5461,x5466,x5467,x5468,x5469),f575(x5463,x5464,x5465,x5462,x5466,x5467,x5468,x5469))
% 187.33/188.06 [547]~E(x5471,x5472)+E(f575(x5473,x5474,x5475,x5476,x5471,x5477,x5478,x5479),f575(x5473,x5474,x5475,x5476,x5472,x5477,x5478,x5479))
% 187.33/188.06 [548]~E(x5481,x5482)+E(f575(x5483,x5484,x5485,x5486,x5487,x5481,x5488,x5489),f575(x5483,x5484,x5485,x5486,x5487,x5482,x5488,x5489))
% 187.33/188.06 [549]~E(x5491,x5492)+E(f575(x5493,x5494,x5495,x5496,x5497,x5498,x5491,x5499),f575(x5493,x5494,x5495,x5496,x5497,x5498,x5492,x5499))
% 187.33/188.06 [550]~E(x5501,x5502)+E(f575(x5503,x5504,x5505,x5506,x5507,x5508,x5509,x5501),f575(x5503,x5504,x5505,x5506,x5507,x5508,x5509,x5502))
% 187.33/188.06 [551]~E(x5511,x5512)+E(f148(x5511,x5513,x5514,x5515),f148(x5512,x5513,x5514,x5515))
% 187.33/188.06 [552]~E(x5521,x5522)+E(f148(x5523,x5521,x5524,x5525),f148(x5523,x5522,x5524,x5525))
% 187.33/188.06 [553]~E(x5531,x5532)+E(f148(x5533,x5534,x5531,x5535),f148(x5533,x5534,x5532,x5535))
% 187.33/188.06 [554]~E(x5541,x5542)+E(f148(x5543,x5544,x5545,x5541),f148(x5543,x5544,x5545,x5542))
% 187.33/188.06 [555]~E(x5551,x5552)+E(f318(x5551,x5553),f318(x5552,x5553))
% 187.33/188.06 [556]~E(x5561,x5562)+E(f318(x5563,x5561),f318(x5563,x5562))
% 187.33/188.06 [557]~E(x5571,x5572)+E(f417(x5571,x5573,x5574,x5575,x5576),f417(x5572,x5573,x5574,x5575,x5576))
% 187.33/188.06 [558]~E(x5581,x5582)+E(f417(x5583,x5581,x5584,x5585,x5586),f417(x5583,x5582,x5584,x5585,x5586))
% 187.33/188.06 [559]~E(x5591,x5592)+E(f417(x5593,x5594,x5591,x5595,x5596),f417(x5593,x5594,x5592,x5595,x5596))
% 187.33/188.06 [560]~E(x5601,x5602)+E(f417(x5603,x5604,x5605,x5601,x5606),f417(x5603,x5604,x5605,x5602,x5606))
% 187.33/188.06 [561]~E(x5611,x5612)+E(f417(x5613,x5614,x5615,x5616,x5611),f417(x5613,x5614,x5615,x5616,x5612))
% 187.33/188.06 [562]~E(x5621,x5622)+E(f187(x5621,x5623,x5624,x5625),f187(x5622,x5623,x5624,x5625))
% 187.33/188.06 [563]~E(x5631,x5632)+E(f187(x5633,x5631,x5634,x5635),f187(x5633,x5632,x5634,x5635))
% 187.33/188.06 [564]~E(x5641,x5642)+E(f187(x5643,x5644,x5641,x5645),f187(x5643,x5644,x5642,x5645))
% 187.33/188.06 [565]~E(x5651,x5652)+E(f187(x5653,x5654,x5655,x5651),f187(x5653,x5654,x5655,x5652))
% 187.33/188.06 [566]~E(x5661,x5662)+E(f273(x5661,x5663),f273(x5662,x5663))
% 187.33/188.06 [567]~E(x5671,x5672)+E(f273(x5673,x5671),f273(x5673,x5672))
% 187.33/188.06 [568]~E(x5681,x5682)+E(f364(x5681,x5683,x5684),f364(x5682,x5683,x5684))
% 187.33/188.06 [569]~E(x5691,x5692)+E(f364(x5693,x5691,x5694),f364(x5693,x5692,x5694))
% 187.33/188.06 [570]~E(x5701,x5702)+E(f364(x5703,x5704,x5701),f364(x5703,x5704,x5702))
% 187.33/188.06 [571]~E(x5711,x5712)+E(f858(x5711,x5713,x5714,x5715),f858(x5712,x5713,x5714,x5715))
% 187.33/188.06 [572]~E(x5721,x5722)+E(f858(x5723,x5721,x5724,x5725),f858(x5723,x5722,x5724,x5725))
% 187.33/188.06 [573]~E(x5731,x5732)+E(f858(x5733,x5734,x5731,x5735),f858(x5733,x5734,x5732,x5735))
% 187.33/188.06 [574]~E(x5741,x5742)+E(f858(x5743,x5744,x5745,x5741),f858(x5743,x5744,x5745,x5742))
% 187.33/188.06 [575]~E(x5751,x5752)+E(f608(x5751,x5753,x5754,x5755,x5756),f608(x5752,x5753,x5754,x5755,x5756))
% 187.33/188.06 [576]~E(x5761,x5762)+E(f608(x5763,x5761,x5764,x5765,x5766),f608(x5763,x5762,x5764,x5765,x5766))
% 187.33/188.06 [577]~E(x5771,x5772)+E(f608(x5773,x5774,x5771,x5775,x5776),f608(x5773,x5774,x5772,x5775,x5776))
% 187.33/188.06 [578]~E(x5781,x5782)+E(f608(x5783,x5784,x5785,x5781,x5786),f608(x5783,x5784,x5785,x5782,x5786))
% 187.33/188.06 [579]~E(x5791,x5792)+E(f608(x5793,x5794,x5795,x5796,x5791),f608(x5793,x5794,x5795,x5796,x5792))
% 187.33/188.06 [580]~E(x5801,x5802)+E(f395(x5801,x5803),f395(x5802,x5803))
% 187.33/188.06 [581]~E(x5811,x5812)+E(f395(x5813,x5811),f395(x5813,x5812))
% 187.33/188.06 [582]~E(x5821,x5822)+E(f91(x5821),f91(x5822))
% 187.33/188.06 [583]~E(x5831,x5832)+E(f63(x5831,x5833,x5834),f63(x5832,x5833,x5834))
% 187.33/188.06 [584]~E(x5841,x5842)+E(f63(x5843,x5841,x5844),f63(x5843,x5842,x5844))
% 187.33/188.06 [585]~E(x5851,x5852)+E(f63(x5853,x5854,x5851),f63(x5853,x5854,x5852))
% 187.33/188.06 [586]~E(x5861,x5862)+E(f691(x5861,x5863,x5864),f691(x5862,x5863,x5864))
% 187.33/188.06 [587]~E(x5871,x5872)+E(f691(x5873,x5871,x5874),f691(x5873,x5872,x5874))
% 187.33/188.06 [588]~E(x5881,x5882)+E(f691(x5883,x5884,x5881),f691(x5883,x5884,x5882))
% 187.33/188.06 [589]~E(x5891,x5892)+E(f412(x5891,x5893,x5894),f412(x5892,x5893,x5894))
% 187.33/188.06 [590]~E(x5901,x5902)+E(f412(x5903,x5901,x5904),f412(x5903,x5902,x5904))
% 187.33/188.06 [591]~E(x5911,x5912)+E(f412(x5913,x5914,x5911),f412(x5913,x5914,x5912))
% 187.33/188.06 [592]~E(x5921,x5922)+E(f777(x5921,x5923,x5924),f777(x5922,x5923,x5924))
% 187.33/188.06 [593]~E(x5931,x5932)+E(f777(x5933,x5931,x5934),f777(x5933,x5932,x5934))
% 187.33/188.06 [594]~E(x5941,x5942)+E(f777(x5943,x5944,x5941),f777(x5943,x5944,x5942))
% 187.33/188.06 [595]~E(x5951,x5952)+E(f583(x5951,x5953,x5954,x5955),f583(x5952,x5953,x5954,x5955))
% 187.33/188.06 [596]~E(x5961,x5962)+E(f583(x5963,x5961,x5964,x5965),f583(x5963,x5962,x5964,x5965))
% 187.33/188.06 [597]~E(x5971,x5972)+E(f583(x5973,x5974,x5971,x5975),f583(x5973,x5974,x5972,x5975))
% 187.33/188.06 [598]~E(x5981,x5982)+E(f583(x5983,x5984,x5985,x5981),f583(x5983,x5984,x5985,x5982))
% 187.33/188.06 [599]~E(x5991,x5992)+E(f841(x5991,x5993,x5994,x5995,x5996),f841(x5992,x5993,x5994,x5995,x5996))
% 187.33/188.06 [600]~E(x6001,x6002)+E(f841(x6003,x6001,x6004,x6005,x6006),f841(x6003,x6002,x6004,x6005,x6006))
% 187.33/188.06 [601]~E(x6011,x6012)+E(f841(x6013,x6014,x6011,x6015,x6016),f841(x6013,x6014,x6012,x6015,x6016))
% 187.33/188.06 [602]~E(x6021,x6022)+E(f841(x6023,x6024,x6025,x6021,x6026),f841(x6023,x6024,x6025,x6022,x6026))
% 187.33/188.06 [603]~E(x6031,x6032)+E(f841(x6033,x6034,x6035,x6036,x6031),f841(x6033,x6034,x6035,x6036,x6032))
% 187.33/188.06 [604]~E(x6041,x6042)+E(f256(x6041,x6043,x6044),f256(x6042,x6043,x6044))
% 187.33/188.06 [605]~E(x6051,x6052)+E(f256(x6053,x6051,x6054),f256(x6053,x6052,x6054))
% 187.33/188.06 [606]~E(x6061,x6062)+E(f256(x6063,x6064,x6061),f256(x6063,x6064,x6062))
% 187.33/188.06 [607]~E(x6071,x6072)+E(f427(x6071,x6073,x6074,x6075,x6076,x6077),f427(x6072,x6073,x6074,x6075,x6076,x6077))
% 187.33/188.06 [608]~E(x6081,x6082)+E(f427(x6083,x6081,x6084,x6085,x6086,x6087),f427(x6083,x6082,x6084,x6085,x6086,x6087))
% 187.33/188.06 [609]~E(x6091,x6092)+E(f427(x6093,x6094,x6091,x6095,x6096,x6097),f427(x6093,x6094,x6092,x6095,x6096,x6097))
% 187.33/188.06 [610]~E(x6101,x6102)+E(f427(x6103,x6104,x6105,x6101,x6106,x6107),f427(x6103,x6104,x6105,x6102,x6106,x6107))
% 187.33/188.06 [611]~E(x6111,x6112)+E(f427(x6113,x6114,x6115,x6116,x6111,x6117),f427(x6113,x6114,x6115,x6116,x6112,x6117))
% 187.33/188.06 [612]~E(x6121,x6122)+E(f427(x6123,x6124,x6125,x6126,x6127,x6121),f427(x6123,x6124,x6125,x6126,x6127,x6122))
% 187.33/188.06 [613]~E(x6131,x6132)+E(f175(x6131,x6133,x6134),f175(x6132,x6133,x6134))
% 187.33/188.06 [614]~E(x6141,x6142)+E(f175(x6143,x6141,x6144),f175(x6143,x6142,x6144))
% 187.33/188.06 [615]~E(x6151,x6152)+E(f175(x6153,x6154,x6151),f175(x6153,x6154,x6152))
% 187.33/188.06 [616]~E(x6161,x6162)+E(f658(x6161,x6163,x6164,x6165),f658(x6162,x6163,x6164,x6165))
% 187.33/188.06 [617]~E(x6171,x6172)+E(f658(x6173,x6171,x6174,x6175),f658(x6173,x6172,x6174,x6175))
% 187.33/188.06 [618]~E(x6181,x6182)+E(f658(x6183,x6184,x6181,x6185),f658(x6183,x6184,x6182,x6185))
% 187.33/188.06 [619]~E(x6191,x6192)+E(f658(x6193,x6194,x6195,x6191),f658(x6193,x6194,x6195,x6192))
% 187.33/188.06 [620]~E(x6201,x6202)+E(f138(x6201,x6203,x6204),f138(x6202,x6203,x6204))
% 187.33/188.06 [621]~E(x6211,x6212)+E(f138(x6213,x6211,x6214),f138(x6213,x6212,x6214))
% 187.33/188.06 [622]~E(x6221,x6222)+E(f138(x6223,x6224,x6221),f138(x6223,x6224,x6222))
% 187.33/188.06 [623]~E(x6231,x6232)+E(f298(x6231),f298(x6232))
% 187.33/188.06 [624]~E(x6241,x6242)+E(f774(x6241,x6243,x6244,x6245,x6246),f774(x6242,x6243,x6244,x6245,x6246))
% 187.33/188.06 [625]~E(x6251,x6252)+E(f774(x6253,x6251,x6254,x6255,x6256),f774(x6253,x6252,x6254,x6255,x6256))
% 187.33/188.06 [626]~E(x6261,x6262)+E(f774(x6263,x6264,x6261,x6265,x6266),f774(x6263,x6264,x6262,x6265,x6266))
% 187.33/188.06 [627]~E(x6271,x6272)+E(f774(x6273,x6274,x6275,x6271,x6276),f774(x6273,x6274,x6275,x6272,x6276))
% 187.33/188.06 [628]~E(x6281,x6282)+E(f774(x6283,x6284,x6285,x6286,x6281),f774(x6283,x6284,x6285,x6286,x6282))
% 187.33/188.06 [629]~E(x6291,x6292)+E(f400(x6291,x6293),f400(x6292,x6293))
% 187.33/188.06 [630]~E(x6301,x6302)+E(f400(x6303,x6301),f400(x6303,x6302))
% 187.33/188.06 [631]~E(x6311,x6312)+E(f401(x6311,x6313),f401(x6312,x6313))
% 187.33/188.06 [632]~E(x6321,x6322)+E(f401(x6323,x6321),f401(x6323,x6322))
% 187.33/188.06 [633]~E(x6331,x6332)+E(f763(x6331,x6333,x6334,x6335),f763(x6332,x6333,x6334,x6335))
% 187.33/188.06 [634]~E(x6341,x6342)+E(f763(x6343,x6341,x6344,x6345),f763(x6343,x6342,x6344,x6345))
% 187.33/188.06 [635]~E(x6351,x6352)+E(f763(x6353,x6354,x6351,x6355),f763(x6353,x6354,x6352,x6355))
% 187.33/188.06 [636]~E(x6361,x6362)+E(f763(x6363,x6364,x6365,x6361),f763(x6363,x6364,x6365,x6362))
% 187.33/188.06 [637]~E(x6371,x6372)+E(f169(x6371,x6373,x6374),f169(x6372,x6373,x6374))
% 187.33/188.06 [638]~E(x6381,x6382)+E(f169(x6383,x6381,x6384),f169(x6383,x6382,x6384))
% 187.33/188.06 [639]~E(x6391,x6392)+E(f169(x6393,x6394,x6391),f169(x6393,x6394,x6392))
% 187.33/188.06 [640]~E(x6401,x6402)+E(f866(x6401,x6403,x6404,x6405),f866(x6402,x6403,x6404,x6405))
% 187.33/188.06 [641]~E(x6411,x6412)+E(f866(x6413,x6411,x6414,x6415),f866(x6413,x6412,x6414,x6415))
% 187.33/188.06 [642]~E(x6421,x6422)+E(f866(x6423,x6424,x6421,x6425),f866(x6423,x6424,x6422,x6425))
% 187.33/188.06 [643]~E(x6431,x6432)+E(f866(x6433,x6434,x6435,x6431),f866(x6433,x6434,x6435,x6432))
% 187.33/188.06 [644]~E(x6441,x6442)+E(f730(x6441,x6443,x6444),f730(x6442,x6443,x6444))
% 187.33/188.06 [645]~E(x6451,x6452)+E(f730(x6453,x6451,x6454),f730(x6453,x6452,x6454))
% 187.33/188.06 [646]~E(x6461,x6462)+E(f730(x6463,x6464,x6461),f730(x6463,x6464,x6462))
% 187.33/188.06 [647]~E(x6471,x6472)+E(f775(x6471,x6473,x6474,x6475,x6476),f775(x6472,x6473,x6474,x6475,x6476))
% 187.33/188.06 [648]~E(x6481,x6482)+E(f775(x6483,x6481,x6484,x6485,x6486),f775(x6483,x6482,x6484,x6485,x6486))
% 187.33/188.06 [649]~E(x6491,x6492)+E(f775(x6493,x6494,x6491,x6495,x6496),f775(x6493,x6494,x6492,x6495,x6496))
% 187.33/188.06 [650]~E(x6501,x6502)+E(f775(x6503,x6504,x6505,x6501,x6506),f775(x6503,x6504,x6505,x6502,x6506))
% 187.33/188.06 [651]~E(x6511,x6512)+E(f775(x6513,x6514,x6515,x6516,x6511),f775(x6513,x6514,x6515,x6516,x6512))
% 187.33/188.06 [652]~E(x6521,x6522)+E(f482(x6521,x6523,x6524,x6525),f482(x6522,x6523,x6524,x6525))
% 187.33/188.06 [653]~E(x6531,x6532)+E(f482(x6533,x6531,x6534,x6535),f482(x6533,x6532,x6534,x6535))
% 187.33/188.06 [654]~E(x6541,x6542)+E(f482(x6543,x6544,x6541,x6545),f482(x6543,x6544,x6542,x6545))
% 187.33/188.06 [655]~E(x6551,x6552)+E(f482(x6553,x6554,x6555,x6551),f482(x6553,x6554,x6555,x6552))
% 187.33/188.06 [656]~E(x6561,x6562)+E(f261(x6561,x6563),f261(x6562,x6563))
% 187.33/188.06 [657]~E(x6571,x6572)+E(f261(x6573,x6571),f261(x6573,x6572))
% 187.33/188.06 [658]~E(x6581,x6582)+E(f114(x6581),f114(x6582))
% 187.33/188.06 [659]~E(x6591,x6592)+E(f97(x6591,x6593,x6594),f97(x6592,x6593,x6594))
% 187.33/188.06 [660]~E(x6601,x6602)+E(f97(x6603,x6601,x6604),f97(x6603,x6602,x6604))
% 187.33/188.06 [661]~E(x6611,x6612)+E(f97(x6613,x6614,x6611),f97(x6613,x6614,x6612))
% 187.33/188.06 [662]~E(x6621,x6622)+E(f282(x6621),f282(x6622))
% 187.33/188.06 [663]~E(x6631,x6632)+E(f377(x6631,x6633,x6634,x6635),f377(x6632,x6633,x6634,x6635))
% 187.33/188.06 [664]~E(x6641,x6642)+E(f377(x6643,x6641,x6644,x6645),f377(x6643,x6642,x6644,x6645))
% 187.33/188.06 [665]~E(x6651,x6652)+E(f377(x6653,x6654,x6651,x6655),f377(x6653,x6654,x6652,x6655))
% 187.33/188.06 [666]~E(x6661,x6662)+E(f377(x6663,x6664,x6665,x6661),f377(x6663,x6664,x6665,x6662))
% 187.33/188.06 [667]~E(x6671,x6672)+E(f205(x6671,x6673,x6674,x6675),f205(x6672,x6673,x6674,x6675))
% 187.33/188.06 [668]~E(x6681,x6682)+E(f205(x6683,x6681,x6684,x6685),f205(x6683,x6682,x6684,x6685))
% 187.33/188.06 [669]~E(x6691,x6692)+E(f205(x6693,x6694,x6691,x6695),f205(x6693,x6694,x6692,x6695))
% 187.33/188.06 [670]~E(x6701,x6702)+E(f205(x6703,x6704,x6705,x6701),f205(x6703,x6704,x6705,x6702))
% 187.33/188.06 [671]~E(x6711,x6712)+E(f240(x6711),f240(x6712))
% 187.33/188.06 [672]~E(x6721,x6722)+E(f418(x6721,x6723,x6724),f418(x6722,x6723,x6724))
% 187.33/188.06 [673]~E(x6731,x6732)+E(f418(x6733,x6731,x6734),f418(x6733,x6732,x6734))
% 187.33/188.06 [674]~E(x6741,x6742)+E(f418(x6743,x6744,x6741),f418(x6743,x6744,x6742))
% 187.33/188.06 [675]~E(x6751,x6752)+E(f651(x6751,x6753,x6754),f651(x6752,x6753,x6754))
% 187.33/188.06 [676]~E(x6761,x6762)+E(f651(x6763,x6761,x6764),f651(x6763,x6762,x6764))
% 187.33/188.06 [677]~E(x6771,x6772)+E(f651(x6773,x6774,x6771),f651(x6773,x6774,x6772))
% 187.33/188.06 [678]~E(x6781,x6782)+E(f864(x6781,x6783,x6784),f864(x6782,x6783,x6784))
% 187.33/188.06 [679]~E(x6791,x6792)+E(f864(x6793,x6791,x6794),f864(x6793,x6792,x6794))
% 187.33/188.06 [680]~E(x6801,x6802)+E(f864(x6803,x6804,x6801),f864(x6803,x6804,x6802))
% 187.33/188.06 [681]~E(x6811,x6812)+E(f559(x6811,x6813,x6814),f559(x6812,x6813,x6814))
% 187.33/188.06 [682]~E(x6821,x6822)+E(f559(x6823,x6821,x6824),f559(x6823,x6822,x6824))
% 187.33/188.06 [683]~E(x6831,x6832)+E(f559(x6833,x6834,x6831),f559(x6833,x6834,x6832))
% 187.33/188.06 [684]~E(x6841,x6842)+E(f53(x6841,x6843),f53(x6842,x6843))
% 187.33/188.06 [685]~E(x6851,x6852)+E(f53(x6853,x6851),f53(x6853,x6852))
% 187.33/188.06 [686]~E(x6861,x6862)+E(f503(x6861,x6863,x6864),f503(x6862,x6863,x6864))
% 187.33/188.06 [687]~E(x6871,x6872)+E(f503(x6873,x6871,x6874),f503(x6873,x6872,x6874))
% 187.33/188.06 [688]~E(x6881,x6882)+E(f503(x6883,x6884,x6881),f503(x6883,x6884,x6882))
% 187.33/188.06 [689]~E(x6891,x6892)+E(f29(x6891,x6893,x6894),f29(x6892,x6893,x6894))
% 187.33/188.06 [690]~E(x6901,x6902)+E(f29(x6903,x6901,x6904),f29(x6903,x6902,x6904))
% 187.33/188.06 [691]~E(x6911,x6912)+E(f29(x6913,x6914,x6911),f29(x6913,x6914,x6912))
% 187.33/188.06 [692]~E(x6921,x6922)+E(f223(x6921,x6923),f223(x6922,x6923))
% 187.33/188.06 [693]~E(x6931,x6932)+E(f223(x6933,x6931),f223(x6933,x6932))
% 187.33/188.06 [694]~E(x6941,x6942)+E(f488(x6941,x6943,x6944),f488(x6942,x6943,x6944))
% 187.33/188.06 [695]~E(x6951,x6952)+E(f488(x6953,x6951,x6954),f488(x6953,x6952,x6954))
% 187.33/188.06 [696]~E(x6961,x6962)+E(f488(x6963,x6964,x6961),f488(x6963,x6964,x6962))
% 187.33/188.06 [697]~E(x6971,x6972)+E(f537(x6971,x6973,x6974,x6975,x6976,x6977),f537(x6972,x6973,x6974,x6975,x6976,x6977))
% 187.33/188.06 [698]~E(x6981,x6982)+E(f537(x6983,x6981,x6984,x6985,x6986,x6987),f537(x6983,x6982,x6984,x6985,x6986,x6987))
% 187.33/188.06 [699]~E(x6991,x6992)+E(f537(x6993,x6994,x6991,x6995,x6996,x6997),f537(x6993,x6994,x6992,x6995,x6996,x6997))
% 187.33/188.06 [700]~E(x7001,x7002)+E(f537(x7003,x7004,x7005,x7001,x7006,x7007),f537(x7003,x7004,x7005,x7002,x7006,x7007))
% 187.33/188.06 [701]~E(x7011,x7012)+E(f537(x7013,x7014,x7015,x7016,x7011,x7017),f537(x7013,x7014,x7015,x7016,x7012,x7017))
% 187.33/188.06 [702]~E(x7021,x7022)+E(f537(x7023,x7024,x7025,x7026,x7027,x7021),f537(x7023,x7024,x7025,x7026,x7027,x7022))
% 187.33/188.06 [703]~E(x7031,x7032)+E(f484(x7031,x7033,x7034),f484(x7032,x7033,x7034))
% 187.33/188.06 [704]~E(x7041,x7042)+E(f484(x7043,x7041,x7044),f484(x7043,x7042,x7044))
% 187.33/188.06 [705]~E(x7051,x7052)+E(f484(x7053,x7054,x7051),f484(x7053,x7054,x7052))
% 187.33/188.06 [706]~E(x7061,x7062)+E(f446(x7061),f446(x7062))
% 187.33/188.06 [707]~E(x7071,x7072)+E(f419(x7071,x7073,x7074),f419(x7072,x7073,x7074))
% 187.33/188.06 [708]~E(x7081,x7082)+E(f419(x7083,x7081,x7084),f419(x7083,x7082,x7084))
% 187.33/188.06 [709]~E(x7091,x7092)+E(f419(x7093,x7094,x7091),f419(x7093,x7094,x7092))
% 187.33/188.06 [710]~E(x7101,x7102)+E(f275(x7101,x7103),f275(x7102,x7103))
% 187.33/188.06 [711]~E(x7111,x7112)+E(f275(x7113,x7111),f275(x7113,x7112))
% 187.33/188.06 [712]~E(x7121,x7122)+E(f561(x7121,x7123),f561(x7122,x7123))
% 187.33/188.06 [713]~E(x7131,x7132)+E(f561(x7133,x7131),f561(x7133,x7132))
% 187.33/188.06 [714]~E(x7141,x7142)+E(f470(x7141,x7143,x7144,x7145),f470(x7142,x7143,x7144,x7145))
% 187.33/188.06 [715]~E(x7151,x7152)+E(f470(x7153,x7151,x7154,x7155),f470(x7153,x7152,x7154,x7155))
% 187.33/188.06 [716]~E(x7161,x7162)+E(f470(x7163,x7164,x7161,x7165),f470(x7163,x7164,x7162,x7165))
% 187.33/188.06 [717]~E(x7171,x7172)+E(f470(x7173,x7174,x7175,x7171),f470(x7173,x7174,x7175,x7172))
% 187.33/188.06 [718]~E(x7181,x7182)+E(f357(x7181,x7183),f357(x7182,x7183))
% 187.33/188.06 [719]~E(x7191,x7192)+E(f357(x7193,x7191),f357(x7193,x7192))
% 187.33/188.06 [720]~E(x7201,x7202)+E(f96(x7201,x7203,x7204,x7205),f96(x7202,x7203,x7204,x7205))
% 187.33/188.06 [721]~E(x7211,x7212)+E(f96(x7213,x7211,x7214,x7215),f96(x7213,x7212,x7214,x7215))
% 187.33/188.06 [722]~E(x7221,x7222)+E(f96(x7223,x7224,x7221,x7225),f96(x7223,x7224,x7222,x7225))
% 187.33/188.06 [723]~E(x7231,x7232)+E(f96(x7233,x7234,x7235,x7231),f96(x7233,x7234,x7235,x7232))
% 187.33/188.06 [724]~E(x7241,x7242)+E(f546(x7241,x7243,x7244),f546(x7242,x7243,x7244))
% 187.33/188.06 [725]~E(x7251,x7252)+E(f546(x7253,x7251,x7254),f546(x7253,x7252,x7254))
% 187.33/188.06 [726]~E(x7261,x7262)+E(f546(x7263,x7264,x7261),f546(x7263,x7264,x7262))
% 187.33/188.06 [727]~E(x7271,x7272)+E(f153(x7271,x7273,x7274),f153(x7272,x7273,x7274))
% 187.33/188.06 [728]~E(x7281,x7282)+E(f153(x7283,x7281,x7284),f153(x7283,x7282,x7284))
% 187.33/188.06 [729]~E(x7291,x7292)+E(f153(x7293,x7294,x7291),f153(x7293,x7294,x7292))
% 187.33/188.06 [730]~E(x7301,x7302)+E(f373(x7301,x7303),f373(x7302,x7303))
% 187.33/188.06 [731]~E(x7311,x7312)+E(f373(x7313,x7311),f373(x7313,x7312))
% 187.33/188.06 [732]~E(x7321,x7322)+E(f684(x7321,x7323),f684(x7322,x7323))
% 187.33/188.06 [733]~E(x7331,x7332)+E(f684(x7333,x7331),f684(x7333,x7332))
% 187.33/188.06 [734]~E(x7341,x7342)+E(f838(x7341,x7343,x7344,x7345),f838(x7342,x7343,x7344,x7345))
% 187.33/188.06 [735]~E(x7351,x7352)+E(f838(x7353,x7351,x7354,x7355),f838(x7353,x7352,x7354,x7355))
% 187.33/188.06 [736]~E(x7361,x7362)+E(f838(x7363,x7364,x7361,x7365),f838(x7363,x7364,x7362,x7365))
% 187.33/188.06 [737]~E(x7371,x7372)+E(f838(x7373,x7374,x7375,x7371),f838(x7373,x7374,x7375,x7372))
% 187.33/188.06 [738]~E(x7381,x7382)+E(f701(x7381,x7383,x7384,x7385,x7386,x7387,x7388),f701(x7382,x7383,x7384,x7385,x7386,x7387,x7388))
% 187.33/188.06 [739]~E(x7391,x7392)+E(f701(x7393,x7391,x7394,x7395,x7396,x7397,x7398),f701(x7393,x7392,x7394,x7395,x7396,x7397,x7398))
% 187.33/188.06 [740]~E(x7401,x7402)+E(f701(x7403,x7404,x7401,x7405,x7406,x7407,x7408),f701(x7403,x7404,x7402,x7405,x7406,x7407,x7408))
% 187.33/188.06 [741]~E(x7411,x7412)+E(f701(x7413,x7414,x7415,x7411,x7416,x7417,x7418),f701(x7413,x7414,x7415,x7412,x7416,x7417,x7418))
% 187.33/188.06 [742]~E(x7421,x7422)+E(f701(x7423,x7424,x7425,x7426,x7421,x7427,x7428),f701(x7423,x7424,x7425,x7426,x7422,x7427,x7428))
% 187.33/188.06 [743]~E(x7431,x7432)+E(f701(x7433,x7434,x7435,x7436,x7437,x7431,x7438),f701(x7433,x7434,x7435,x7436,x7437,x7432,x7438))
% 187.33/188.06 [744]~E(x7441,x7442)+E(f701(x7443,x7444,x7445,x7446,x7447,x7448,x7441),f701(x7443,x7444,x7445,x7446,x7447,x7448,x7442))
% 187.33/188.06 [745]~E(x7451,x7452)+E(f215(x7451,x7453,x7454,x7455,x7456,x7457,x7458),f215(x7452,x7453,x7454,x7455,x7456,x7457,x7458))
% 187.33/188.06 [746]~E(x7461,x7462)+E(f215(x7463,x7461,x7464,x7465,x7466,x7467,x7468),f215(x7463,x7462,x7464,x7465,x7466,x7467,x7468))
% 187.33/188.06 [747]~E(x7471,x7472)+E(f215(x7473,x7474,x7471,x7475,x7476,x7477,x7478),f215(x7473,x7474,x7472,x7475,x7476,x7477,x7478))
% 187.33/188.06 [748]~E(x7481,x7482)+E(f215(x7483,x7484,x7485,x7481,x7486,x7487,x7488),f215(x7483,x7484,x7485,x7482,x7486,x7487,x7488))
% 187.33/188.06 [749]~E(x7491,x7492)+E(f215(x7493,x7494,x7495,x7496,x7491,x7497,x7498),f215(x7493,x7494,x7495,x7496,x7492,x7497,x7498))
% 187.33/188.06 [750]~E(x7501,x7502)+E(f215(x7503,x7504,x7505,x7506,x7507,x7501,x7508),f215(x7503,x7504,x7505,x7506,x7507,x7502,x7508))
% 187.33/188.06 [751]~E(x7511,x7512)+E(f215(x7513,x7514,x7515,x7516,x7517,x7518,x7511),f215(x7513,x7514,x7515,x7516,x7517,x7518,x7512))
% 187.33/188.06 [752]~E(x7521,x7522)+E(f121(x7521,x7523,x7524),f121(x7522,x7523,x7524))
% 187.33/188.06 [753]~E(x7531,x7532)+E(f121(x7533,x7531,x7534),f121(x7533,x7532,x7534))
% 187.33/188.06 [754]~E(x7541,x7542)+E(f121(x7543,x7544,x7541),f121(x7543,x7544,x7542))
% 187.33/188.06 [755]~E(x7551,x7552)+E(f699(x7551,x7553,x7554,x7555),f699(x7552,x7553,x7554,x7555))
% 187.33/188.06 [756]~E(x7561,x7562)+E(f699(x7563,x7561,x7564,x7565),f699(x7563,x7562,x7564,x7565))
% 187.33/188.06 [757]~E(x7571,x7572)+E(f699(x7573,x7574,x7571,x7575),f699(x7573,x7574,x7572,x7575))
% 187.33/188.06 [758]~E(x7581,x7582)+E(f699(x7583,x7584,x7585,x7581),f699(x7583,x7584,x7585,x7582))
% 187.33/188.06 [759]~E(x7591,x7592)+E(f694(x7591,x7593,x7594,x7595,x7596),f694(x7592,x7593,x7594,x7595,x7596))
% 187.33/188.06 [760]~E(x7601,x7602)+E(f694(x7603,x7601,x7604,x7605,x7606),f694(x7603,x7602,x7604,x7605,x7606))
% 187.33/188.06 [761]~E(x7611,x7612)+E(f694(x7613,x7614,x7611,x7615,x7616),f694(x7613,x7614,x7612,x7615,x7616))
% 187.33/188.06 [762]~E(x7621,x7622)+E(f694(x7623,x7624,x7625,x7621,x7626),f694(x7623,x7624,x7625,x7622,x7626))
% 187.33/188.06 [763]~E(x7631,x7632)+E(f694(x7633,x7634,x7635,x7636,x7631),f694(x7633,x7634,x7635,x7636,x7632))
% 187.33/188.06 [764]~E(x7641,x7642)+E(f200(x7641,x7643),f200(x7642,x7643))
% 187.33/188.06 [765]~E(x7651,x7652)+E(f200(x7653,x7651),f200(x7653,x7652))
% 187.33/188.06 [766]~E(x7661,x7662)+E(f413(x7661,x7663,x7664),f413(x7662,x7663,x7664))
% 187.33/188.06 [767]~E(x7671,x7672)+E(f413(x7673,x7671,x7674),f413(x7673,x7672,x7674))
% 187.33/188.06 [768]~E(x7681,x7682)+E(f413(x7683,x7684,x7681),f413(x7683,x7684,x7682))
% 187.33/188.06 [769]~E(x7691,x7692)+E(f88(x7691),f88(x7692))
% 187.33/188.06 [770]~E(x7701,x7702)+E(f750(x7701,x7703,x7704),f750(x7702,x7703,x7704))
% 187.33/188.06 [771]~E(x7711,x7712)+E(f750(x7713,x7711,x7714),f750(x7713,x7712,x7714))
% 187.33/188.06 [772]~E(x7721,x7722)+E(f750(x7723,x7724,x7721),f750(x7723,x7724,x7722))
% 187.33/188.06 [773]~E(x7731,x7732)+E(f654(x7731,x7733),f654(x7732,x7733))
% 187.33/188.06 [774]~E(x7741,x7742)+E(f654(x7743,x7741),f654(x7743,x7742))
% 187.33/188.06 [775]~E(x7751,x7752)+E(f535(x7751,x7753,x7754,x7755),f535(x7752,x7753,x7754,x7755))
% 187.33/188.06 [776]~E(x7761,x7762)+E(f535(x7763,x7761,x7764,x7765),f535(x7763,x7762,x7764,x7765))
% 187.33/188.06 [777]~E(x7771,x7772)+E(f535(x7773,x7774,x7771,x7775),f535(x7773,x7774,x7772,x7775))
% 187.33/188.06 [778]~E(x7781,x7782)+E(f535(x7783,x7784,x7785,x7781),f535(x7783,x7784,x7785,x7782))
% 187.33/188.06 [779]~E(x7791,x7792)+E(f829(x7791,x7793,x7794),f829(x7792,x7793,x7794))
% 187.33/188.06 [780]~E(x7801,x7802)+E(f829(x7803,x7801,x7804),f829(x7803,x7802,x7804))
% 187.33/188.06 [781]~E(x7811,x7812)+E(f829(x7813,x7814,x7811),f829(x7813,x7814,x7812))
% 187.33/188.06 [782]~E(x7821,x7822)+E(f161(x7821,x7823,x7824,x7825),f161(x7822,x7823,x7824,x7825))
% 187.33/188.06 [783]~E(x7831,x7832)+E(f161(x7833,x7831,x7834,x7835),f161(x7833,x7832,x7834,x7835))
% 187.33/188.06 [784]~E(x7841,x7842)+E(f161(x7843,x7844,x7841,x7845),f161(x7843,x7844,x7842,x7845))
% 187.33/188.06 [785]~E(x7851,x7852)+E(f161(x7853,x7854,x7855,x7851),f161(x7853,x7854,x7855,x7852))
% 187.33/188.06 [786]~E(x7861,x7862)+E(f769(x7861,x7863,x7864,x7865,x7866,x7867),f769(x7862,x7863,x7864,x7865,x7866,x7867))
% 187.33/188.06 [787]~E(x7871,x7872)+E(f769(x7873,x7871,x7874,x7875,x7876,x7877),f769(x7873,x7872,x7874,x7875,x7876,x7877))
% 187.33/188.06 [788]~E(x7881,x7882)+E(f769(x7883,x7884,x7881,x7885,x7886,x7887),f769(x7883,x7884,x7882,x7885,x7886,x7887))
% 187.33/188.06 [789]~E(x7891,x7892)+E(f769(x7893,x7894,x7895,x7891,x7896,x7897),f769(x7893,x7894,x7895,x7892,x7896,x7897))
% 187.33/188.06 [790]~E(x7901,x7902)+E(f769(x7903,x7904,x7905,x7906,x7901,x7907),f769(x7903,x7904,x7905,x7906,x7902,x7907))
% 187.33/188.06 [791]~E(x7911,x7912)+E(f769(x7913,x7914,x7915,x7916,x7917,x7911),f769(x7913,x7914,x7915,x7916,x7917,x7912))
% 187.33/188.06 [792]~E(x7921,x7922)+E(f451(x7921,x7923,x7924,x7925),f451(x7922,x7923,x7924,x7925))
% 187.33/188.06 [793]~E(x7931,x7932)+E(f451(x7933,x7931,x7934,x7935),f451(x7933,x7932,x7934,x7935))
% 187.33/188.06 [794]~E(x7941,x7942)+E(f451(x7943,x7944,x7941,x7945),f451(x7943,x7944,x7942,x7945))
% 187.33/188.06 [795]~E(x7951,x7952)+E(f451(x7953,x7954,x7955,x7951),f451(x7953,x7954,x7955,x7952))
% 187.33/188.06 [796]~E(x7961,x7962)+E(f696(x7961,x7963,x7964,x7965,x7966),f696(x7962,x7963,x7964,x7965,x7966))
% 187.33/188.06 [797]~E(x7971,x7972)+E(f696(x7973,x7971,x7974,x7975,x7976),f696(x7973,x7972,x7974,x7975,x7976))
% 187.33/188.06 [798]~E(x7981,x7982)+E(f696(x7983,x7984,x7981,x7985,x7986),f696(x7983,x7984,x7982,x7985,x7986))
% 187.33/188.06 [799]~E(x7991,x7992)+E(f696(x7993,x7994,x7995,x7991,x7996),f696(x7993,x7994,x7995,x7992,x7996))
% 187.33/188.06 [800]~E(x8001,x8002)+E(f696(x8003,x8004,x8005,x8006,x8001),f696(x8003,x8004,x8005,x8006,x8002))
% 187.33/188.06 [801]~E(x8011,x8012)+E(f237(x8011,x8013,x8014),f237(x8012,x8013,x8014))
% 187.33/188.06 [802]~E(x8021,x8022)+E(f237(x8023,x8021,x8024),f237(x8023,x8022,x8024))
% 187.33/188.06 [803]~E(x8031,x8032)+E(f237(x8033,x8034,x8031),f237(x8033,x8034,x8032))
% 187.33/188.06 [804]~E(x8041,x8042)+E(f355(x8041),f355(x8042))
% 187.33/188.06 [805]~E(x8051,x8052)+E(f392(x8051,x8053,x8054),f392(x8052,x8053,x8054))
% 187.33/188.06 [806]~E(x8061,x8062)+E(f392(x8063,x8061,x8064),f392(x8063,x8062,x8064))
% 187.33/188.06 [807]~E(x8071,x8072)+E(f392(x8073,x8074,x8071),f392(x8073,x8074,x8072))
% 187.33/188.06 [808]~E(x8081,x8082)+E(f611(x8081,x8083,x8084,x8085,x8086),f611(x8082,x8083,x8084,x8085,x8086))
% 187.33/188.06 [809]~E(x8091,x8092)+E(f611(x8093,x8091,x8094,x8095,x8096),f611(x8093,x8092,x8094,x8095,x8096))
% 187.33/188.06 [810]~E(x8101,x8102)+E(f611(x8103,x8104,x8101,x8105,x8106),f611(x8103,x8104,x8102,x8105,x8106))
% 187.33/188.06 [811]~E(x8111,x8112)+E(f611(x8113,x8114,x8115,x8111,x8116),f611(x8113,x8114,x8115,x8112,x8116))
% 187.33/188.06 [812]~E(x8121,x8122)+E(f611(x8123,x8124,x8125,x8126,x8121),f611(x8123,x8124,x8125,x8126,x8122))
% 187.33/188.06 [813]~E(x8131,x8132)+E(f323(x8131,x8133,x8134),f323(x8132,x8133,x8134))
% 187.33/188.06 [814]~E(x8141,x8142)+E(f323(x8143,x8141,x8144),f323(x8143,x8142,x8144))
% 187.33/188.06 [815]~E(x8151,x8152)+E(f323(x8153,x8154,x8151),f323(x8153,x8154,x8152))
% 187.33/188.06 [816]~E(x8161,x8162)+E(f423(x8161,x8163,x8164,x8165),f423(x8162,x8163,x8164,x8165))
% 187.33/188.06 [817]~E(x8171,x8172)+E(f423(x8173,x8171,x8174,x8175),f423(x8173,x8172,x8174,x8175))
% 187.33/188.06 [818]~E(x8181,x8182)+E(f423(x8183,x8184,x8181,x8185),f423(x8183,x8184,x8182,x8185))
% 187.33/188.06 [819]~E(x8191,x8192)+E(f423(x8193,x8194,x8195,x8191),f423(x8193,x8194,x8195,x8192))
% 187.33/188.06 [820]~E(x8201,x8202)+E(f764(x8201,x8203),f764(x8202,x8203))
% 187.33/188.06 [821]~E(x8211,x8212)+E(f764(x8213,x8211),f764(x8213,x8212))
% 187.33/188.06 [822]~E(x8221,x8222)+E(f440(x8221,x8223,x8224),f440(x8222,x8223,x8224))
% 187.33/188.06 [823]~E(x8231,x8232)+E(f440(x8233,x8231,x8234),f440(x8233,x8232,x8234))
% 187.33/188.06 [824]~E(x8241,x8242)+E(f440(x8243,x8244,x8241),f440(x8243,x8244,x8242))
% 187.33/188.06 [825]~E(x8251,x8252)+E(f425(x8251,x8253),f425(x8252,x8253))
% 187.33/188.06 [826]~E(x8261,x8262)+E(f425(x8263,x8261),f425(x8263,x8262))
% 187.33/188.06 [827]~E(x8271,x8272)+E(f557(x8271,x8273,x8274),f557(x8272,x8273,x8274))
% 187.33/188.06 [828]~E(x8281,x8282)+E(f557(x8283,x8281,x8284),f557(x8283,x8282,x8284))
% 187.33/188.06 [829]~E(x8291,x8292)+E(f557(x8293,x8294,x8291),f557(x8293,x8294,x8292))
% 187.33/188.06 [830]~E(x8301,x8302)+E(f156(x8301,x8303),f156(x8302,x8303))
% 187.33/188.06 [831]~E(x8311,x8312)+E(f156(x8313,x8311),f156(x8313,x8312))
% 187.33/188.06 [832]~E(x8321,x8322)+E(f635(x8321,x8323,x8324),f635(x8322,x8323,x8324))
% 187.33/188.06 [833]~E(x8331,x8332)+E(f635(x8333,x8331,x8334),f635(x8333,x8332,x8334))
% 187.33/188.06 [834]~E(x8341,x8342)+E(f635(x8343,x8344,x8341),f635(x8343,x8344,x8342))
% 187.33/188.06 [835]~E(x8351,x8352)+E(f818(x8351,x8353,x8354),f818(x8352,x8353,x8354))
% 187.33/188.06 [836]~E(x8361,x8362)+E(f818(x8363,x8361,x8364),f818(x8363,x8362,x8364))
% 187.33/188.06 [837]~E(x8371,x8372)+E(f818(x8373,x8374,x8371),f818(x8373,x8374,x8372))
% 187.33/188.06 [838]~E(x8381,x8382)+E(f851(x8381,x8383,x8384,x8385,x8386),f851(x8382,x8383,x8384,x8385,x8386))
% 187.33/188.06 [839]~E(x8391,x8392)+E(f851(x8393,x8391,x8394,x8395,x8396),f851(x8393,x8392,x8394,x8395,x8396))
% 187.33/188.06 [840]~E(x8401,x8402)+E(f851(x8403,x8404,x8401,x8405,x8406),f851(x8403,x8404,x8402,x8405,x8406))
% 187.33/188.06 [841]~E(x8411,x8412)+E(f851(x8413,x8414,x8415,x8411,x8416),f851(x8413,x8414,x8415,x8412,x8416))
% 187.33/188.06 [842]~E(x8421,x8422)+E(f851(x8423,x8424,x8425,x8426,x8421),f851(x8423,x8424,x8425,x8426,x8422))
% 187.33/188.06 [843]~E(x8431,x8432)+E(f459(x8431,x8433,x8434,x8435,x8436,x8437,x8438),f459(x8432,x8433,x8434,x8435,x8436,x8437,x8438))
% 187.33/188.06 [844]~E(x8441,x8442)+E(f459(x8443,x8441,x8444,x8445,x8446,x8447,x8448),f459(x8443,x8442,x8444,x8445,x8446,x8447,x8448))
% 187.33/188.06 [845]~E(x8451,x8452)+E(f459(x8453,x8454,x8451,x8455,x8456,x8457,x8458),f459(x8453,x8454,x8452,x8455,x8456,x8457,x8458))
% 187.33/188.06 [846]~E(x8461,x8462)+E(f459(x8463,x8464,x8465,x8461,x8466,x8467,x8468),f459(x8463,x8464,x8465,x8462,x8466,x8467,x8468))
% 187.33/188.06 [847]~E(x8471,x8472)+E(f459(x8473,x8474,x8475,x8476,x8471,x8477,x8478),f459(x8473,x8474,x8475,x8476,x8472,x8477,x8478))
% 187.33/188.06 [848]~E(x8481,x8482)+E(f459(x8483,x8484,x8485,x8486,x8487,x8481,x8488),f459(x8483,x8484,x8485,x8486,x8487,x8482,x8488))
% 187.33/188.06 [849]~E(x8491,x8492)+E(f459(x8493,x8494,x8495,x8496,x8497,x8498,x8491),f459(x8493,x8494,x8495,x8496,x8497,x8498,x8492))
% 187.33/188.06 [850]~E(x8501,x8502)+E(f802(x8501,x8503,x8504),f802(x8502,x8503,x8504))
% 187.33/188.06 [851]~E(x8511,x8512)+E(f802(x8513,x8511,x8514),f802(x8513,x8512,x8514))
% 187.33/188.06 [852]~E(x8521,x8522)+E(f802(x8523,x8524,x8521),f802(x8523,x8524,x8522))
% 187.33/188.06 [853]~E(x8531,x8532)+E(f146(x8531,x8533,x8534),f146(x8532,x8533,x8534))
% 187.33/188.06 [854]~E(x8541,x8542)+E(f146(x8543,x8541,x8544),f146(x8543,x8542,x8544))
% 187.33/188.06 [855]~E(x8551,x8552)+E(f146(x8553,x8554,x8551),f146(x8553,x8554,x8552))
% 187.33/188.06 [856]~E(x8561,x8562)+E(f592(x8561,x8563,x8564),f592(x8562,x8563,x8564))
% 187.33/188.06 [857]~E(x8571,x8572)+E(f592(x8573,x8571,x8574),f592(x8573,x8572,x8574))
% 187.33/188.06 [858]~E(x8581,x8582)+E(f592(x8583,x8584,x8581),f592(x8583,x8584,x8582))
% 187.33/188.06 [859]~E(x8591,x8592)+E(f58(x8591),f58(x8592))
% 187.33/188.06 [860]~E(x8601,x8602)+E(f598(x8601,x8603),f598(x8602,x8603))
% 187.33/188.06 [861]~E(x8611,x8612)+E(f598(x8613,x8611),f598(x8613,x8612))
% 187.33/188.06 [862]~E(x8621,x8622)+E(f162(x8621,x8623,x8624,x8625),f162(x8622,x8623,x8624,x8625))
% 187.33/188.06 [863]~E(x8631,x8632)+E(f162(x8633,x8631,x8634,x8635),f162(x8633,x8632,x8634,x8635))
% 187.33/188.06 [864]~E(x8641,x8642)+E(f162(x8643,x8644,x8641,x8645),f162(x8643,x8644,x8642,x8645))
% 187.33/188.06 [865]~E(x8651,x8652)+E(f162(x8653,x8654,x8655,x8651),f162(x8653,x8654,x8655,x8652))
% 187.33/188.06 [866]~E(x8661,x8662)+E(f185(x8661,x8663,x8664),f185(x8662,x8663,x8664))
% 187.33/188.06 [867]~E(x8671,x8672)+E(f185(x8673,x8671,x8674),f185(x8673,x8672,x8674))
% 187.33/188.06 [868]~E(x8681,x8682)+E(f185(x8683,x8684,x8681),f185(x8683,x8684,x8682))
% 187.33/188.06 [869]~E(x8691,x8692)+E(f372(x8691,x8693),f372(x8692,x8693))
% 187.33/188.06 [870]~E(x8701,x8702)+E(f372(x8703,x8701),f372(x8703,x8702))
% 187.33/188.06 [871]~E(x8711,x8712)+E(f278(x8711,x8713,x8714,x8715),f278(x8712,x8713,x8714,x8715))
% 187.33/188.06 [872]~E(x8721,x8722)+E(f278(x8723,x8721,x8724,x8725),f278(x8723,x8722,x8724,x8725))
% 187.33/188.06 [873]~E(x8731,x8732)+E(f278(x8733,x8734,x8731,x8735),f278(x8733,x8734,x8732,x8735))
% 187.33/188.06 [874]~E(x8741,x8742)+E(f278(x8743,x8744,x8745,x8741),f278(x8743,x8744,x8745,x8742))
% 187.33/188.06 [875]~E(x8751,x8752)+E(f344(x8751,x8753,x8754,x8755),f344(x8752,x8753,x8754,x8755))
% 187.33/188.06 [876]~E(x8761,x8762)+E(f344(x8763,x8761,x8764,x8765),f344(x8763,x8762,x8764,x8765))
% 187.33/188.06 [877]~E(x8771,x8772)+E(f344(x8773,x8774,x8771,x8775),f344(x8773,x8774,x8772,x8775))
% 187.33/188.06 [878]~E(x8781,x8782)+E(f344(x8783,x8784,x8785,x8781),f344(x8783,x8784,x8785,x8782))
% 187.33/188.06 [879]~E(x8791,x8792)+E(f68(x8791,x8793,x8794),f68(x8792,x8793,x8794))
% 187.33/188.06 [880]~E(x8801,x8802)+E(f68(x8803,x8801,x8804),f68(x8803,x8802,x8804))
% 187.33/188.06 [881]~E(x8811,x8812)+E(f68(x8813,x8814,x8811),f68(x8813,x8814,x8812))
% 187.33/188.06 [882]~E(x8821,x8822)+E(f668(x8821,x8823),f668(x8822,x8823))
% 187.33/188.06 [883]~E(x8831,x8832)+E(f668(x8833,x8831),f668(x8833,x8832))
% 187.33/188.06 [884]~E(x8841,x8842)+E(f378(x8841,x8843,x8844,x8845),f378(x8842,x8843,x8844,x8845))
% 187.33/188.06 [885]~E(x8851,x8852)+E(f378(x8853,x8851,x8854,x8855),f378(x8853,x8852,x8854,x8855))
% 187.33/188.06 [886]~E(x8861,x8862)+E(f378(x8863,x8864,x8861,x8865),f378(x8863,x8864,x8862,x8865))
% 187.33/188.06 [887]~E(x8871,x8872)+E(f378(x8873,x8874,x8875,x8871),f378(x8873,x8874,x8875,x8872))
% 187.33/188.06 [888]~E(x8881,x8882)+E(f555(x8881,x8883,x8884),f555(x8882,x8883,x8884))
% 187.33/188.06 [889]~E(x8891,x8892)+E(f555(x8893,x8891,x8894),f555(x8893,x8892,x8894))
% 187.33/188.06 [890]~E(x8901,x8902)+E(f555(x8903,x8904,x8901),f555(x8903,x8904,x8902))
% 187.33/188.06 [891]~E(x8911,x8912)+E(f44(x8911),f44(x8912))
% 187.33/188.06 [892]~E(x8921,x8922)+E(f197(x8921,x8923),f197(x8922,x8923))
% 187.33/188.06 [893]~E(x8931,x8932)+E(f197(x8933,x8931),f197(x8933,x8932))
% 187.33/188.06 [894]~E(x8941,x8942)+E(f415(x8941,x8943,x8944,x8945),f415(x8942,x8943,x8944,x8945))
% 187.33/188.06 [895]~E(x8951,x8952)+E(f415(x8953,x8951,x8954,x8955),f415(x8953,x8952,x8954,x8955))
% 187.33/188.06 [896]~E(x8961,x8962)+E(f415(x8963,x8964,x8961,x8965),f415(x8963,x8964,x8962,x8965))
% 187.33/188.06 [897]~E(x8971,x8972)+E(f415(x8973,x8974,x8975,x8971),f415(x8973,x8974,x8975,x8972))
% 187.33/188.06 [898]~E(x8981,x8982)+E(f123(x8981,x8983),f123(x8982,x8983))
% 187.33/188.06 [899]~E(x8991,x8992)+E(f123(x8993,x8991),f123(x8993,x8992))
% 187.33/188.06 [900]~E(x9001,x9002)+E(f359(x9001,x9003),f359(x9002,x9003))
% 187.33/188.06 [901]~E(x9011,x9012)+E(f359(x9013,x9011),f359(x9013,x9012))
% 187.33/188.06 [902]~E(x9021,x9022)+E(f260(x9021,x9023),f260(x9022,x9023))
% 187.33/188.06 [903]~E(x9031,x9032)+E(f260(x9033,x9031),f260(x9033,x9032))
% 187.33/188.06 [904]~E(x9041,x9042)+E(f656(x9041,x9043,x9044,x9045,x9046),f656(x9042,x9043,x9044,x9045,x9046))
% 187.33/188.06 [905]~E(x9051,x9052)+E(f656(x9053,x9051,x9054,x9055,x9056),f656(x9053,x9052,x9054,x9055,x9056))
% 187.33/188.06 [906]~E(x9061,x9062)+E(f656(x9063,x9064,x9061,x9065,x9066),f656(x9063,x9064,x9062,x9065,x9066))
% 187.33/188.06 [907]~E(x9071,x9072)+E(f656(x9073,x9074,x9075,x9071,x9076),f656(x9073,x9074,x9075,x9072,x9076))
% 187.33/188.06 [908]~E(x9081,x9082)+E(f656(x9083,x9084,x9085,x9086,x9081),f656(x9083,x9084,x9085,x9086,x9082))
% 187.33/188.06 [909]~E(x9091,x9092)+E(f335(x9091),f335(x9092))
% 187.33/188.06 [910]~E(x9101,x9102)+E(f487(x9101,x9103,x9104),f487(x9102,x9103,x9104))
% 187.33/188.06 [911]~E(x9111,x9112)+E(f487(x9113,x9111,x9114),f487(x9113,x9112,x9114))
% 187.33/188.06 [912]~E(x9121,x9122)+E(f487(x9123,x9124,x9121),f487(x9123,x9124,x9122))
% 187.33/188.06 [913]~E(x9131,x9132)+E(f600(x9131,x9133,x9134),f600(x9132,x9133,x9134))
% 187.33/188.06 [914]~E(x9141,x9142)+E(f600(x9143,x9141,x9144),f600(x9143,x9142,x9144))
% 187.33/188.06 [915]~E(x9151,x9152)+E(f600(x9153,x9154,x9151),f600(x9153,x9154,x9152))
% 187.33/188.06 [916]~E(x9161,x9162)+E(f402(x9161,x9163),f402(x9162,x9163))
% 187.33/188.06 [917]~E(x9171,x9172)+E(f402(x9173,x9171),f402(x9173,x9172))
% 187.33/188.06 [918]~E(x9181,x9182)+E(f825(x9181,x9183,x9184),f825(x9182,x9183,x9184))
% 187.33/188.06 [919]~E(x9191,x9192)+E(f825(x9193,x9191,x9194),f825(x9193,x9192,x9194))
% 187.33/188.06 [920]~E(x9201,x9202)+E(f825(x9203,x9204,x9201),f825(x9203,x9204,x9202))
% 187.33/188.06 [921]~E(x9211,x9212)+E(f516(x9211,x9213,x9214,x9215),f516(x9212,x9213,x9214,x9215))
% 187.33/188.06 [922]~E(x9221,x9222)+E(f516(x9223,x9221,x9224,x9225),f516(x9223,x9222,x9224,x9225))
% 187.33/188.06 [923]~E(x9231,x9232)+E(f516(x9233,x9234,x9231,x9235),f516(x9233,x9234,x9232,x9235))
% 187.33/188.06 [924]~E(x9241,x9242)+E(f516(x9243,x9244,x9245,x9241),f516(x9243,x9244,x9245,x9242))
% 187.33/188.06 [925]~E(x9251,x9252)+E(f836(x9251,x9253,x9254),f836(x9252,x9253,x9254))
% 187.33/188.06 [926]~E(x9261,x9262)+E(f836(x9263,x9261,x9264),f836(x9263,x9262,x9264))
% 187.33/188.06 [927]~E(x9271,x9272)+E(f836(x9273,x9274,x9271),f836(x9273,x9274,x9272))
% 187.33/188.06 [928]~E(x9281,x9282)+E(f578(x9281,x9283,x9284),f578(x9282,x9283,x9284))
% 187.33/188.06 [929]~E(x9291,x9292)+E(f578(x9293,x9291,x9294),f578(x9293,x9292,x9294))
% 187.33/188.06 [930]~E(x9301,x9302)+E(f578(x9303,x9304,x9301),f578(x9303,x9304,x9302))
% 187.33/188.06 [931]~E(x9311,x9312)+E(f130(x9311,x9313),f130(x9312,x9313))
% 187.33/188.06 [932]~E(x9321,x9322)+E(f130(x9323,x9321),f130(x9323,x9322))
% 187.33/188.06 [933]~E(x9331,x9332)+E(f540(x9331,x9333,x9334,x9335,x9336),f540(x9332,x9333,x9334,x9335,x9336))
% 187.33/188.06 [934]~E(x9341,x9342)+E(f540(x9343,x9341,x9344,x9345,x9346),f540(x9343,x9342,x9344,x9345,x9346))
% 187.33/188.06 [935]~E(x9351,x9352)+E(f540(x9353,x9354,x9351,x9355,x9356),f540(x9353,x9354,x9352,x9355,x9356))
% 187.33/188.06 [936]~E(x9361,x9362)+E(f540(x9363,x9364,x9365,x9361,x9366),f540(x9363,x9364,x9365,x9362,x9366))
% 187.33/188.06 [937]~E(x9371,x9372)+E(f540(x9373,x9374,x9375,x9376,x9371),f540(x9373,x9374,x9375,x9376,x9372))
% 187.33/188.06 [938]~E(x9381,x9382)+E(f848(x9381,x9383,x9384,x9385),f848(x9382,x9383,x9384,x9385))
% 187.33/188.06 [939]~E(x9391,x9392)+E(f848(x9393,x9391,x9394,x9395),f848(x9393,x9392,x9394,x9395))
% 187.33/188.06 [940]~E(x9401,x9402)+E(f848(x9403,x9404,x9401,x9405),f848(x9403,x9404,x9402,x9405))
% 187.33/188.06 [941]~E(x9411,x9412)+E(f848(x9413,x9414,x9415,x9411),f848(x9413,x9414,x9415,x9412))
% 187.33/188.06 [942]~E(x9421,x9422)+E(f270(x9421,x9423,x9424,x9425),f270(x9422,x9423,x9424,x9425))
% 187.33/188.06 [943]~E(x9431,x9432)+E(f270(x9433,x9431,x9434,x9435),f270(x9433,x9432,x9434,x9435))
% 187.33/188.06 [944]~E(x9441,x9442)+E(f270(x9443,x9444,x9441,x9445),f270(x9443,x9444,x9442,x9445))
% 187.33/188.06 [945]~E(x9451,x9452)+E(f270(x9453,x9454,x9455,x9451),f270(x9453,x9454,x9455,x9452))
% 187.33/188.06 [946]~E(x9461,x9462)+E(f682(x9461,x9463,x9464,x9465),f682(x9462,x9463,x9464,x9465))
% 187.33/188.06 [947]~E(x9471,x9472)+E(f682(x9473,x9471,x9474,x9475),f682(x9473,x9472,x9474,x9475))
% 187.33/188.06 [948]~E(x9481,x9482)+E(f682(x9483,x9484,x9481,x9485),f682(x9483,x9484,x9482,x9485))
% 187.33/188.06 [949]~E(x9491,x9492)+E(f682(x9493,x9494,x9495,x9491),f682(x9493,x9494,x9495,x9492))
% 187.33/188.06 [950]~E(x9501,x9502)+E(f685(x9501,x9503,x9504,x9505),f685(x9502,x9503,x9504,x9505))
% 187.33/188.06 [951]~E(x9511,x9512)+E(f685(x9513,x9511,x9514,x9515),f685(x9513,x9512,x9514,x9515))
% 187.33/188.06 [952]~E(x9521,x9522)+E(f685(x9523,x9524,x9521,x9525),f685(x9523,x9524,x9522,x9525))
% 187.33/188.06 [953]~E(x9531,x9532)+E(f685(x9533,x9534,x9535,x9531),f685(x9533,x9534,x9535,x9532))
% 187.33/188.06 [954]~E(x9541,x9542)+E(f147(x9541,x9543,x9544,x9545,x9546),f147(x9542,x9543,x9544,x9545,x9546))
% 187.33/188.06 [955]~E(x9551,x9552)+E(f147(x9553,x9551,x9554,x9555,x9556),f147(x9553,x9552,x9554,x9555,x9556))
% 187.33/188.06 [956]~E(x9561,x9562)+E(f147(x9563,x9564,x9561,x9565,x9566),f147(x9563,x9564,x9562,x9565,x9566))
% 187.33/188.06 [957]~E(x9571,x9572)+E(f147(x9573,x9574,x9575,x9571,x9576),f147(x9573,x9574,x9575,x9572,x9576))
% 187.33/188.06 [958]~E(x9581,x9582)+E(f147(x9583,x9584,x9585,x9586,x9581),f147(x9583,x9584,x9585,x9586,x9582))
% 187.33/188.06 [959]~E(x9591,x9592)+E(f455(x9591,x9593,x9594),f455(x9592,x9593,x9594))
% 187.33/188.06 [960]~E(x9601,x9602)+E(f455(x9603,x9601,x9604),f455(x9603,x9602,x9604))
% 187.33/188.06 [961]~E(x9611,x9612)+E(f455(x9613,x9614,x9611),f455(x9613,x9614,x9612))
% 187.33/188.06 [962]~E(x9621,x9622)+E(f771(x9621,x9623,x9624,x9625,x9626),f771(x9622,x9623,x9624,x9625,x9626))
% 187.33/188.06 [963]~E(x9631,x9632)+E(f771(x9633,x9631,x9634,x9635,x9636),f771(x9633,x9632,x9634,x9635,x9636))
% 187.33/188.06 [964]~E(x9641,x9642)+E(f771(x9643,x9644,x9641,x9645,x9646),f771(x9643,x9644,x9642,x9645,x9646))
% 187.33/188.06 [965]~E(x9651,x9652)+E(f771(x9653,x9654,x9655,x9651,x9656),f771(x9653,x9654,x9655,x9652,x9656))
% 187.33/188.06 [966]~E(x9661,x9662)+E(f771(x9663,x9664,x9665,x9666,x9661),f771(x9663,x9664,x9665,x9666,x9662))
% 187.33/188.06 [967]~E(x9671,x9672)+E(f576(x9671,x9673,x9674),f576(x9672,x9673,x9674))
% 187.33/188.06 [968]~E(x9681,x9682)+E(f576(x9683,x9681,x9684),f576(x9683,x9682,x9684))
% 187.33/188.06 [969]~E(x9691,x9692)+E(f576(x9693,x9694,x9691),f576(x9693,x9694,x9692))
% 187.33/188.06 [970]~E(x9701,x9702)+E(f491(x9701,x9703),f491(x9702,x9703))
% 187.33/188.06 [971]~E(x9711,x9712)+E(f491(x9713,x9711),f491(x9713,x9712))
% 187.33/188.06 [972]~E(x9721,x9722)+E(f648(x9721,x9723,x9724,x9725),f648(x9722,x9723,x9724,x9725))
% 187.33/188.06 [973]~E(x9731,x9732)+E(f648(x9733,x9731,x9734,x9735),f648(x9733,x9732,x9734,x9735))
% 187.33/188.06 [974]~E(x9741,x9742)+E(f648(x9743,x9744,x9741,x9745),f648(x9743,x9744,x9742,x9745))
% 187.33/188.06 [975]~E(x9751,x9752)+E(f648(x9753,x9754,x9755,x9751),f648(x9753,x9754,x9755,x9752))
% 187.33/188.06 [976]~E(x9761,x9762)+E(f647(x9761,x9763,x9764,x9765,x9766,x9767,x9768),f647(x9762,x9763,x9764,x9765,x9766,x9767,x9768))
% 187.33/188.06 [977]~E(x9771,x9772)+E(f647(x9773,x9771,x9774,x9775,x9776,x9777,x9778),f647(x9773,x9772,x9774,x9775,x9776,x9777,x9778))
% 187.33/188.06 [978]~E(x9781,x9782)+E(f647(x9783,x9784,x9781,x9785,x9786,x9787,x9788),f647(x9783,x9784,x9782,x9785,x9786,x9787,x9788))
% 187.33/188.06 [979]~E(x9791,x9792)+E(f647(x9793,x9794,x9795,x9791,x9796,x9797,x9798),f647(x9793,x9794,x9795,x9792,x9796,x9797,x9798))
% 187.33/188.06 [980]~E(x9801,x9802)+E(f647(x9803,x9804,x9805,x9806,x9801,x9807,x9808),f647(x9803,x9804,x9805,x9806,x9802,x9807,x9808))
% 187.33/188.06 [981]~E(x9811,x9812)+E(f647(x9813,x9814,x9815,x9816,x9817,x9811,x9818),f647(x9813,x9814,x9815,x9816,x9817,x9812,x9818))
% 187.33/188.06 [982]~E(x9821,x9822)+E(f647(x9823,x9824,x9825,x9826,x9827,x9828,x9821),f647(x9823,x9824,x9825,x9826,x9827,x9828,x9822))
% 187.33/188.06 [983]~E(x9831,x9832)+E(f432(x9831,x9833,x9834,x9835,x9836),f432(x9832,x9833,x9834,x9835,x9836))
% 187.33/188.06 [984]~E(x9841,x9842)+E(f432(x9843,x9841,x9844,x9845,x9846),f432(x9843,x9842,x9844,x9845,x9846))
% 187.33/188.06 [985]~E(x9851,x9852)+E(f432(x9853,x9854,x9851,x9855,x9856),f432(x9853,x9854,x9852,x9855,x9856))
% 187.33/188.06 [986]~E(x9861,x9862)+E(f432(x9863,x9864,x9865,x9861,x9866),f432(x9863,x9864,x9865,x9862,x9866))
% 187.33/188.06 [987]~E(x9871,x9872)+E(f432(x9873,x9874,x9875,x9876,x9871),f432(x9873,x9874,x9875,x9876,x9872))
% 187.33/188.06 [988]~E(x9881,x9882)+E(f352(x9881,x9883,x9884,x9885),f352(x9882,x9883,x9884,x9885))
% 187.33/188.06 [989]~E(x9891,x9892)+E(f352(x9893,x9891,x9894,x9895),f352(x9893,x9892,x9894,x9895))
% 187.33/188.06 [990]~E(x9901,x9902)+E(f352(x9903,x9904,x9901,x9905),f352(x9903,x9904,x9902,x9905))
% 187.33/188.06 [991]~E(x9911,x9912)+E(f352(x9913,x9914,x9915,x9911),f352(x9913,x9914,x9915,x9912))
% 187.33/188.06 [992]~E(x9921,x9922)+E(f757(x9921,x9923,x9924),f757(x9922,x9923,x9924))
% 187.33/188.06 [993]~E(x9931,x9932)+E(f757(x9933,x9931,x9934),f757(x9933,x9932,x9934))
% 187.33/188.06 [994]~E(x9941,x9942)+E(f757(x9943,x9944,x9941),f757(x9943,x9944,x9942))
% 187.33/188.06 [995]~E(x9951,x9952)+E(f541(x9951,x9953,x9954,x9955,x9956),f541(x9952,x9953,x9954,x9955,x9956))
% 187.33/188.06 [996]~E(x9961,x9962)+E(f541(x9963,x9961,x9964,x9965,x9966),f541(x9963,x9962,x9964,x9965,x9966))
% 187.33/188.06 [997]~E(x9971,x9972)+E(f541(x9973,x9974,x9971,x9975,x9976),f541(x9973,x9974,x9972,x9975,x9976))
% 187.33/188.06 [998]~E(x9981,x9982)+E(f541(x9983,x9984,x9985,x9981,x9986),f541(x9983,x9984,x9985,x9982,x9986))
% 187.33/188.06 [999]~E(x9991,x9992)+E(f541(x9993,x9994,x9995,x9996,x9991),f541(x9993,x9994,x9995,x9996,x9992))
% 187.33/188.06 [1000]~E(x10001,x10002)+E(f748(x10001,x10003,x10004),f748(x10002,x10003,x10004))
% 187.33/188.06 [1001]~E(x10011,x10012)+E(f748(x10013,x10011,x10014),f748(x10013,x10012,x10014))
% 187.33/188.06 [1002]~E(x10021,x10022)+E(f748(x10023,x10024,x10021),f748(x10023,x10024,x10022))
% 187.33/188.06 [1003]~E(x10031,x10032)+E(f238(x10031,x10033,x10034,x10035),f238(x10032,x10033,x10034,x10035))
% 187.33/188.06 [1004]~E(x10041,x10042)+E(f238(x10043,x10041,x10044,x10045),f238(x10043,x10042,x10044,x10045))
% 187.33/188.06 [1005]~E(x10051,x10052)+E(f238(x10053,x10054,x10051,x10055),f238(x10053,x10054,x10052,x10055))
% 187.33/188.06 [1006]~E(x10061,x10062)+E(f238(x10063,x10064,x10065,x10061),f238(x10063,x10064,x10065,x10062))
% 187.33/188.06 [1007]~E(x10071,x10072)+E(f189(x10071,x10073,x10074),f189(x10072,x10073,x10074))
% 187.33/188.06 [1008]~E(x10081,x10082)+E(f189(x10083,x10081,x10084),f189(x10083,x10082,x10084))
% 187.33/188.06 [1009]~E(x10091,x10092)+E(f189(x10093,x10094,x10091),f189(x10093,x10094,x10092))
% 187.33/188.06 [1010]~E(x10101,x10102)+E(f823(x10101,x10103),f823(x10102,x10103))
% 187.33/188.06 [1011]~E(x10111,x10112)+E(f823(x10113,x10111),f823(x10113,x10112))
% 187.33/188.06 [1012]~E(x10121,x10122)+E(f186(x10121,x10123,x10124,x10125,x10126),f186(x10122,x10123,x10124,x10125,x10126))
% 187.33/188.06 [1013]~E(x10131,x10132)+E(f186(x10133,x10131,x10134,x10135,x10136),f186(x10133,x10132,x10134,x10135,x10136))
% 187.33/188.06 [1014]~E(x10141,x10142)+E(f186(x10143,x10144,x10141,x10145,x10146),f186(x10143,x10144,x10142,x10145,x10146))
% 187.33/188.06 [1015]~E(x10151,x10152)+E(f186(x10153,x10154,x10155,x10151,x10156),f186(x10153,x10154,x10155,x10152,x10156))
% 187.33/188.06 [1016]~E(x10161,x10162)+E(f186(x10163,x10164,x10165,x10166,x10161),f186(x10163,x10164,x10165,x10166,x10162))
% 187.33/188.06 [1017]~E(x10171,x10172)+E(f768(x10171,x10173,x10174,x10175,x10176,x10177,x10178),f768(x10172,x10173,x10174,x10175,x10176,x10177,x10178))
% 187.33/188.06 [1018]~E(x10181,x10182)+E(f768(x10183,x10181,x10184,x10185,x10186,x10187,x10188),f768(x10183,x10182,x10184,x10185,x10186,x10187,x10188))
% 187.33/188.06 [1019]~E(x10191,x10192)+E(f768(x10193,x10194,x10191,x10195,x10196,x10197,x10198),f768(x10193,x10194,x10192,x10195,x10196,x10197,x10198))
% 187.33/188.06 [1020]~E(x10201,x10202)+E(f768(x10203,x10204,x10205,x10201,x10206,x10207,x10208),f768(x10203,x10204,x10205,x10202,x10206,x10207,x10208))
% 187.33/188.06 [1021]~E(x10211,x10212)+E(f768(x10213,x10214,x10215,x10216,x10211,x10217,x10218),f768(x10213,x10214,x10215,x10216,x10212,x10217,x10218))
% 187.33/188.06 [1022]~E(x10221,x10222)+E(f768(x10223,x10224,x10225,x10226,x10227,x10221,x10228),f768(x10223,x10224,x10225,x10226,x10227,x10222,x10228))
% 187.33/188.06 [1023]~E(x10231,x10232)+E(f768(x10233,x10234,x10235,x10236,x10237,x10238,x10231),f768(x10233,x10234,x10235,x10236,x10237,x10238,x10232))
% 187.33/188.06 [1024]~E(x10241,x10242)+E(f733(x10241,x10243),f733(x10242,x10243))
% 187.33/188.06 [1025]~E(x10251,x10252)+E(f733(x10253,x10251),f733(x10253,x10252))
% 187.33/188.06 [1026]~E(x10261,x10262)+E(f386(x10261,x10263,x10264,x10265),f386(x10262,x10263,x10264,x10265))
% 187.33/188.06 [1027]~E(x10271,x10272)+E(f386(x10273,x10271,x10274,x10275),f386(x10273,x10272,x10274,x10275))
% 187.33/188.06 [1028]~E(x10281,x10282)+E(f386(x10283,x10284,x10281,x10285),f386(x10283,x10284,x10282,x10285))
% 187.33/188.06 [1029]~E(x10291,x10292)+E(f386(x10293,x10294,x10295,x10291),f386(x10293,x10294,x10295,x10292))
% 187.33/188.06 [1030]~E(x10301,x10302)+E(f489(x10301,x10303,x10304),f489(x10302,x10303,x10304))
% 187.33/188.06 [1031]~E(x10311,x10312)+E(f489(x10313,x10311,x10314),f489(x10313,x10312,x10314))
% 187.33/188.06 [1032]~E(x10321,x10322)+E(f489(x10323,x10324,x10321),f489(x10323,x10324,x10322))
% 187.33/188.06 [1033]~E(x10331,x10332)+E(f393(x10331,x10333,x10334),f393(x10332,x10333,x10334))
% 187.33/188.06 [1034]~E(x10341,x10342)+E(f393(x10343,x10341,x10344),f393(x10343,x10342,x10344))
% 187.33/188.06 [1035]~E(x10351,x10352)+E(f393(x10353,x10354,x10351),f393(x10353,x10354,x10352))
% 187.33/188.06 [1036]~E(x10361,x10362)+E(f483(x10361,x10363,x10364),f483(x10362,x10363,x10364))
% 187.33/188.06 [1037]~E(x10371,x10372)+E(f483(x10373,x10371,x10374),f483(x10373,x10372,x10374))
% 187.33/188.06 [1038]~E(x10381,x10382)+E(f483(x10383,x10384,x10381),f483(x10383,x10384,x10382))
% 187.33/188.06 [1039]~E(x10391,x10392)+E(f801(x10391,x10393,x10394,x10395,x10396),f801(x10392,x10393,x10394,x10395,x10396))
% 187.33/188.06 [1040]~E(x10401,x10402)+E(f801(x10403,x10401,x10404,x10405,x10406),f801(x10403,x10402,x10404,x10405,x10406))
% 187.33/188.06 [1041]~E(x10411,x10412)+E(f801(x10413,x10414,x10411,x10415,x10416),f801(x10413,x10414,x10412,x10415,x10416))
% 187.33/188.06 [1042]~E(x10421,x10422)+E(f801(x10423,x10424,x10425,x10421,x10426),f801(x10423,x10424,x10425,x10422,x10426))
% 187.33/188.06 [1043]~E(x10431,x10432)+E(f801(x10433,x10434,x10435,x10436,x10431),f801(x10433,x10434,x10435,x10436,x10432))
% 187.33/188.06 [1044]~E(x10441,x10442)+E(f795(x10441,x10443,x10444),f795(x10442,x10443,x10444))
% 187.33/188.06 [1045]~E(x10451,x10452)+E(f795(x10453,x10451,x10454),f795(x10453,x10452,x10454))
% 187.33/188.06 [1046]~E(x10461,x10462)+E(f795(x10463,x10464,x10461),f795(x10463,x10464,x10462))
% 187.33/188.06 [1047]~E(x10471,x10472)+E(f190(x10471,x10473,x10474,x10475),f190(x10472,x10473,x10474,x10475))
% 187.33/188.06 [1048]~E(x10481,x10482)+E(f190(x10483,x10481,x10484,x10485),f190(x10483,x10482,x10484,x10485))
% 187.33/188.06 [1049]~E(x10491,x10492)+E(f190(x10493,x10494,x10491,x10495),f190(x10493,x10494,x10492,x10495))
% 187.33/188.06 [1050]~E(x10501,x10502)+E(f190(x10503,x10504,x10505,x10501),f190(x10503,x10504,x10505,x10502))
% 187.33/188.06 [1051]~E(x10511,x10512)+E(f495(x10511),f495(x10512))
% 187.33/188.06 [1052]~E(x10521,x10522)+E(f391(x10521,x10523,x10524,x10525),f391(x10522,x10523,x10524,x10525))
% 187.33/188.06 [1053]~E(x10531,x10532)+E(f391(x10533,x10531,x10534,x10535),f391(x10533,x10532,x10534,x10535))
% 187.33/188.06 [1054]~E(x10541,x10542)+E(f391(x10543,x10544,x10541,x10545),f391(x10543,x10544,x10542,x10545))
% 187.33/188.06 [1055]~E(x10551,x10552)+E(f391(x10553,x10554,x10555,x10551),f391(x10553,x10554,x10555,x10552))
% 187.33/188.06 [1056]~E(x10561,x10562)+E(f606(x10561,x10563,x10564,x10565),f606(x10562,x10563,x10564,x10565))
% 187.33/188.06 [1057]~E(x10571,x10572)+E(f606(x10573,x10571,x10574,x10575),f606(x10573,x10572,x10574,x10575))
% 187.33/188.06 [1058]~E(x10581,x10582)+E(f606(x10583,x10584,x10581,x10585),f606(x10583,x10584,x10582,x10585))
% 187.33/188.06 [1059]~E(x10591,x10592)+E(f606(x10593,x10594,x10595,x10591),f606(x10593,x10594,x10595,x10592))
% 187.33/188.06 [1060]~E(x10601,x10602)+E(f844(x10601,x10603,x10604,x10605,x10606),f844(x10602,x10603,x10604,x10605,x10606))
% 187.33/188.06 [1061]~E(x10611,x10612)+E(f844(x10613,x10611,x10614,x10615,x10616),f844(x10613,x10612,x10614,x10615,x10616))
% 187.33/188.06 [1062]~E(x10621,x10622)+E(f844(x10623,x10624,x10621,x10625,x10626),f844(x10623,x10624,x10622,x10625,x10626))
% 187.33/188.06 [1063]~E(x10631,x10632)+E(f844(x10633,x10634,x10635,x10631,x10636),f844(x10633,x10634,x10635,x10632,x10636))
% 187.33/188.06 [1064]~E(x10641,x10642)+E(f844(x10643,x10644,x10645,x10646,x10641),f844(x10643,x10644,x10645,x10646,x10642))
% 187.33/188.06 [1065]~E(x10651,x10652)+E(f214(x10651,x10653,x10654,x10655),f214(x10652,x10653,x10654,x10655))
% 187.33/188.06 [1066]~E(x10661,x10662)+E(f214(x10663,x10661,x10664,x10665),f214(x10663,x10662,x10664,x10665))
% 187.33/188.06 [1067]~E(x10671,x10672)+E(f214(x10673,x10674,x10671,x10675),f214(x10673,x10674,x10672,x10675))
% 187.33/188.06 [1068]~E(x10681,x10682)+E(f214(x10683,x10684,x10685,x10681),f214(x10683,x10684,x10685,x10682))
% 187.33/188.06 [1069]~E(x10691,x10692)+E(f786(x10691,x10693,x10694,x10695,x10696),f786(x10692,x10693,x10694,x10695,x10696))
% 187.33/188.06 [1070]~E(x10701,x10702)+E(f786(x10703,x10701,x10704,x10705,x10706),f786(x10703,x10702,x10704,x10705,x10706))
% 187.33/188.06 [1071]~E(x10711,x10712)+E(f786(x10713,x10714,x10711,x10715,x10716),f786(x10713,x10714,x10712,x10715,x10716))
% 187.33/188.06 [1072]~E(x10721,x10722)+E(f786(x10723,x10724,x10725,x10721,x10726),f786(x10723,x10724,x10725,x10722,x10726))
% 187.33/188.06 [1073]~E(x10731,x10732)+E(f786(x10733,x10734,x10735,x10736,x10731),f786(x10733,x10734,x10735,x10736,x10732))
% 187.33/188.06 [1074]~E(x10741,x10742)+E(f751(x10741,x10743),f751(x10742,x10743))
% 187.33/188.06 [1075]~E(x10751,x10752)+E(f751(x10753,x10751),f751(x10753,x10752))
% 187.33/188.06 [1076]~E(x10761,x10762)+E(f717(x10761,x10763),f717(x10762,x10763))
% 187.33/188.06 [1077]~E(x10771,x10772)+E(f717(x10773,x10771),f717(x10773,x10772))
% 187.33/188.06 [1078]~E(x10781,x10782)+E(f785(x10781,x10783,x10784,x10785,x10786),f785(x10782,x10783,x10784,x10785,x10786))
% 187.33/188.06 [1079]~E(x10791,x10792)+E(f785(x10793,x10791,x10794,x10795,x10796),f785(x10793,x10792,x10794,x10795,x10796))
% 187.33/188.06 [1080]~E(x10801,x10802)+E(f785(x10803,x10804,x10801,x10805,x10806),f785(x10803,x10804,x10802,x10805,x10806))
% 187.33/188.06 [1081]~E(x10811,x10812)+E(f785(x10813,x10814,x10815,x10811,x10816),f785(x10813,x10814,x10815,x10812,x10816))
% 187.33/188.06 [1082]~E(x10821,x10822)+E(f785(x10823,x10824,x10825,x10826,x10821),f785(x10823,x10824,x10825,x10826,x10822))
% 187.33/188.06 [1083]~E(x10831,x10832)+E(f697(x10831,x10833,x10834,x10835,x10836),f697(x10832,x10833,x10834,x10835,x10836))
% 187.33/188.06 [1084]~E(x10841,x10842)+E(f697(x10843,x10841,x10844,x10845,x10846),f697(x10843,x10842,x10844,x10845,x10846))
% 187.33/188.06 [1085]~E(x10851,x10852)+E(f697(x10853,x10854,x10851,x10855,x10856),f697(x10853,x10854,x10852,x10855,x10856))
% 187.33/188.06 [1086]~E(x10861,x10862)+E(f697(x10863,x10864,x10865,x10861,x10866),f697(x10863,x10864,x10865,x10862,x10866))
% 187.33/188.06 [1087]~E(x10871,x10872)+E(f697(x10873,x10874,x10875,x10876,x10871),f697(x10873,x10874,x10875,x10876,x10872))
% 187.33/188.06 [1088]~E(x10881,x10882)+E(f127(x10881),f127(x10882))
% 187.33/188.06 [1089]~E(x10891,x10892)+E(f677(x10891,x10893,x10894,x10895),f677(x10892,x10893,x10894,x10895))
% 187.33/188.06 [1090]~E(x10901,x10902)+E(f677(x10903,x10901,x10904,x10905),f677(x10903,x10902,x10904,x10905))
% 187.33/188.06 [1091]~E(x10911,x10912)+E(f677(x10913,x10914,x10911,x10915),f677(x10913,x10914,x10912,x10915))
% 187.33/188.06 [1092]~E(x10921,x10922)+E(f677(x10923,x10924,x10925,x10921),f677(x10923,x10924,x10925,x10922))
% 187.33/188.06 [1093]~E(x10931,x10932)+E(f569(x10931,x10933,x10934,x10935),f569(x10932,x10933,x10934,x10935))
% 187.33/188.06 [1094]~E(x10941,x10942)+E(f569(x10943,x10941,x10944,x10945),f569(x10943,x10942,x10944,x10945))
% 187.33/188.06 [1095]~E(x10951,x10952)+E(f569(x10953,x10954,x10951,x10955),f569(x10953,x10954,x10952,x10955))
% 187.33/188.06 [1096]~E(x10961,x10962)+E(f569(x10963,x10964,x10965,x10961),f569(x10963,x10964,x10965,x10962))
% 187.33/188.06 [1097]~E(x10971,x10972)+E(f657(x10971,x10973,x10974,x10975),f657(x10972,x10973,x10974,x10975))
% 187.33/188.06 [1098]~E(x10981,x10982)+E(f657(x10983,x10981,x10984,x10985),f657(x10983,x10982,x10984,x10985))
% 187.33/188.06 [1099]~E(x10991,x10992)+E(f657(x10993,x10994,x10991,x10995),f657(x10993,x10994,x10992,x10995))
% 187.33/188.06 [1100]~E(x11001,x11002)+E(f657(x11003,x11004,x11005,x11001),f657(x11003,x11004,x11005,x11002))
% 187.33/188.06 [1101]~E(x11011,x11012)+E(f745(x11011,x11013),f745(x11012,x11013))
% 187.33/188.06 [1102]~E(x11021,x11022)+E(f745(x11023,x11021),f745(x11023,x11022))
% 187.33/188.06 [1103]~E(x11031,x11032)+E(f226(x11031,x11033),f226(x11032,x11033))
% 187.33/188.06 [1104]~E(x11041,x11042)+E(f226(x11043,x11041),f226(x11043,x11042))
% 187.33/188.06 [1105]~E(x11051,x11052)+E(f341(x11051,x11053),f341(x11052,x11053))
% 187.33/188.06 [1106]~E(x11061,x11062)+E(f341(x11063,x11061),f341(x11063,x11062))
% 187.33/188.06 [1107]~E(x11071,x11072)+E(f141(x11071,x11073),f141(x11072,x11073))
% 187.33/188.06 [1108]~E(x11081,x11082)+E(f141(x11083,x11081),f141(x11083,x11082))
% 187.33/188.06 [1109]~E(x11091,x11092)+E(f435(x11091,x11093,x11094,x11095,x11096),f435(x11092,x11093,x11094,x11095,x11096))
% 187.33/188.06 [1110]~E(x11101,x11102)+E(f435(x11103,x11101,x11104,x11105,x11106),f435(x11103,x11102,x11104,x11105,x11106))
% 187.33/188.06 [1111]~E(x11111,x11112)+E(f435(x11113,x11114,x11111,x11115,x11116),f435(x11113,x11114,x11112,x11115,x11116))
% 187.33/188.06 [1112]~E(x11121,x11122)+E(f435(x11123,x11124,x11125,x11121,x11126),f435(x11123,x11124,x11125,x11122,x11126))
% 187.33/188.06 [1113]~E(x11131,x11132)+E(f435(x11133,x11134,x11135,x11136,x11131),f435(x11133,x11134,x11135,x11136,x11132))
% 187.33/188.06 [1114]~E(x11141,x11142)+E(f379(x11141,x11143,x11144,x11145),f379(x11142,x11143,x11144,x11145))
% 187.33/188.06 [1115]~E(x11151,x11152)+E(f379(x11153,x11151,x11154,x11155),f379(x11153,x11152,x11154,x11155))
% 187.33/188.06 [1116]~E(x11161,x11162)+E(f379(x11163,x11164,x11161,x11165),f379(x11163,x11164,x11162,x11165))
% 187.33/188.06 [1117]~E(x11171,x11172)+E(f379(x11173,x11174,x11175,x11171),f379(x11173,x11174,x11175,x11172))
% 187.33/188.06 [1118]~E(x11181,x11182)+E(f735(x11181,x11183,x11184,x11185),f735(x11182,x11183,x11184,x11185))
% 187.33/188.06 [1119]~E(x11191,x11192)+E(f735(x11193,x11191,x11194,x11195),f735(x11193,x11192,x11194,x11195))
% 187.33/188.06 [1120]~E(x11201,x11202)+E(f735(x11203,x11204,x11201,x11205),f735(x11203,x11204,x11202,x11205))
% 187.33/188.06 [1121]~E(x11211,x11212)+E(f735(x11213,x11214,x11215,x11211),f735(x11213,x11214,x11215,x11212))
% 187.33/188.06 [1122]~E(x11221,x11222)+E(f632(x11221,x11223,x11224),f632(x11222,x11223,x11224))
% 187.33/188.06 [1123]~E(x11231,x11232)+E(f632(x11233,x11231,x11234),f632(x11233,x11232,x11234))
% 187.33/188.06 [1124]~E(x11241,x11242)+E(f632(x11243,x11244,x11241),f632(x11243,x11244,x11242))
% 187.33/188.06 [1125]~E(x11251,x11252)+E(f544(x11251,x11253,x11254),f544(x11252,x11253,x11254))
% 187.33/188.06 [1126]~E(x11261,x11262)+E(f544(x11263,x11261,x11264),f544(x11263,x11262,x11264))
% 187.33/188.06 [1127]~E(x11271,x11272)+E(f544(x11273,x11274,x11271),f544(x11273,x11274,x11272))
% 187.33/188.06 [1128]~E(x11281,x11282)+E(f191(x11281),f191(x11282))
% 187.33/188.06 [1129]~E(x11291,x11292)+E(f637(x11291,x11293,x11294),f637(x11292,x11293,x11294))
% 187.33/188.06 [1130]~E(x11301,x11302)+E(f637(x11303,x11301,x11304),f637(x11303,x11302,x11304))
% 187.33/188.06 [1131]~E(x11311,x11312)+E(f637(x11313,x11314,x11311),f637(x11313,x11314,x11312))
% 187.33/188.06 [1132]~E(x11321,x11322)+E(f727(x11321,x11323),f727(x11322,x11323))
% 187.33/188.06 [1133]~E(x11331,x11332)+E(f727(x11333,x11331),f727(x11333,x11332))
% 187.33/188.06 [1134]~E(x11341,x11342)+E(f59(x11341),f59(x11342))
% 187.33/188.06 [1135]~E(x11351,x11352)+E(f172(x11351,x11353,x11354),f172(x11352,x11353,x11354))
% 187.33/188.06 [1136]~E(x11361,x11362)+E(f172(x11363,x11361,x11364),f172(x11363,x11362,x11364))
% 187.33/188.06 [1137]~E(x11371,x11372)+E(f172(x11373,x11374,x11371),f172(x11373,x11374,x11372))
% 187.33/188.06 [1138]~E(x11381,x11382)+E(f595(x11381,x11383),f595(x11382,x11383))
% 187.33/188.06 [1139]~E(x11391,x11392)+E(f595(x11393,x11391),f595(x11393,x11392))
% 187.33/188.06 [1140]~E(x11401,x11402)+E(f596(x11401,x11403,x11404),f596(x11402,x11403,x11404))
% 187.33/188.06 [1141]~E(x11411,x11412)+E(f596(x11413,x11411,x11414),f596(x11413,x11412,x11414))
% 187.33/188.06 [1142]~E(x11421,x11422)+E(f596(x11423,x11424,x11421),f596(x11423,x11424,x11422))
% 187.33/188.06 [1143]~E(x11431,x11432)+E(f839(x11431,x11433,x11434,x11435,x11436),f839(x11432,x11433,x11434,x11435,x11436))
% 187.33/188.06 [1144]~E(x11441,x11442)+E(f839(x11443,x11441,x11444,x11445,x11446),f839(x11443,x11442,x11444,x11445,x11446))
% 187.33/188.06 [1145]~E(x11451,x11452)+E(f839(x11453,x11454,x11451,x11455,x11456),f839(x11453,x11454,x11452,x11455,x11456))
% 187.33/188.06 [1146]~E(x11461,x11462)+E(f839(x11463,x11464,x11465,x11461,x11466),f839(x11463,x11464,x11465,x11462,x11466))
% 187.33/188.06 [1147]~E(x11471,x11472)+E(f839(x11473,x11474,x11475,x11476,x11471),f839(x11473,x11474,x11475,x11476,x11472))
% 187.33/188.06 [1148]~E(x11481,x11482)+E(f629(x11481,x11483,x11484),f629(x11482,x11483,x11484))
% 187.33/188.06 [1149]~E(x11491,x11492)+E(f629(x11493,x11491,x11494),f629(x11493,x11492,x11494))
% 187.33/188.06 [1150]~E(x11501,x11502)+E(f629(x11503,x11504,x11501),f629(x11503,x11504,x11502))
% 187.33/188.06 [1151]~E(x11511,x11512)+E(f706(x11511,x11513,x11514),f706(x11512,x11513,x11514))
% 187.33/188.06 [1152]~E(x11521,x11522)+E(f706(x11523,x11521,x11524),f706(x11523,x11522,x11524))
% 187.33/188.06 [1153]~E(x11531,x11532)+E(f706(x11533,x11534,x11531),f706(x11533,x11534,x11532))
% 187.33/188.06 [1154]~E(x11541,x11542)+E(f630(x11541,x11543,x11544),f630(x11542,x11543,x11544))
% 187.33/188.06 [1155]~E(x11551,x11552)+E(f630(x11553,x11551,x11554),f630(x11553,x11552,x11554))
% 187.33/188.06 [1156]~E(x11561,x11562)+E(f630(x11563,x11564,x11561),f630(x11563,x11564,x11562))
% 187.33/188.06 [1157]~E(x11571,x11572)+E(f824(x11571,x11573),f824(x11572,x11573))
% 187.33/188.06 [1158]~E(x11581,x11582)+E(f824(x11583,x11581),f824(x11583,x11582))
% 187.33/188.06 [1159]~E(x11591,x11592)+E(f280(x11591,x11593),f280(x11592,x11593))
% 187.33/188.06 [1160]~E(x11601,x11602)+E(f280(x11603,x11601),f280(x11603,x11602))
% 187.33/188.06 [1161]~E(x11611,x11612)+E(f865(x11611,x11613,x11614),f865(x11612,x11613,x11614))
% 187.33/188.06 [1162]~E(x11621,x11622)+E(f865(x11623,x11621,x11624),f865(x11623,x11622,x11624))
% 187.33/188.06 [1163]~E(x11631,x11632)+E(f865(x11633,x11634,x11631),f865(x11633,x11634,x11632))
% 187.33/188.06 [1164]~E(x11641,x11642)+E(f704(x11641),f704(x11642))
% 187.33/188.06 [1165]~E(x11651,x11652)+E(f202(x11651,x11653,x11654,x11655),f202(x11652,x11653,x11654,x11655))
% 187.33/188.06 [1166]~E(x11661,x11662)+E(f202(x11663,x11661,x11664,x11665),f202(x11663,x11662,x11664,x11665))
% 187.33/188.06 [1167]~E(x11671,x11672)+E(f202(x11673,x11674,x11671,x11675),f202(x11673,x11674,x11672,x11675))
% 187.33/188.06 [1168]~E(x11681,x11682)+E(f202(x11683,x11684,x11685,x11681),f202(x11683,x11684,x11685,x11682))
% 187.33/188.06 [1169]~E(x11691,x11692)+E(f467(x11691,x11693),f467(x11692,x11693))
% 187.33/188.06 [1170]~E(x11701,x11702)+E(f467(x11703,x11701),f467(x11703,x11702))
% 187.33/188.06 [1171]~E(x11711,x11712)+E(f99(x11711,x11713,x11714,x11715),f99(x11712,x11713,x11714,x11715))
% 187.33/188.06 [1172]~E(x11721,x11722)+E(f99(x11723,x11721,x11724,x11725),f99(x11723,x11722,x11724,x11725))
% 187.33/188.06 [1173]~E(x11731,x11732)+E(f99(x11733,x11734,x11731,x11735),f99(x11733,x11734,x11732,x11735))
% 187.33/188.06 [1174]~E(x11741,x11742)+E(f99(x11743,x11744,x11745,x11741),f99(x11743,x11744,x11745,x11742))
% 187.33/188.06 [1175]~E(x11751,x11752)+E(f565(x11751,x11753,x11754),f565(x11752,x11753,x11754))
% 187.33/188.06 [1176]~E(x11761,x11762)+E(f565(x11763,x11761,x11764),f565(x11763,x11762,x11764))
% 187.33/188.06 [1177]~E(x11771,x11772)+E(f565(x11773,x11774,x11771),f565(x11773,x11774,x11772))
% 187.33/188.06 [1178]~E(x11781,x11782)+E(f784(x11781,x11783,x11784,x11785,x11786),f784(x11782,x11783,x11784,x11785,x11786))
% 187.33/188.06 [1179]~E(x11791,x11792)+E(f784(x11793,x11791,x11794,x11795,x11796),f784(x11793,x11792,x11794,x11795,x11796))
% 187.33/188.06 [1180]~E(x11801,x11802)+E(f784(x11803,x11804,x11801,x11805,x11806),f784(x11803,x11804,x11802,x11805,x11806))
% 187.33/188.06 [1181]~E(x11811,x11812)+E(f784(x11813,x11814,x11815,x11811,x11816),f784(x11813,x11814,x11815,x11812,x11816))
% 187.33/188.06 [1182]~E(x11821,x11822)+E(f784(x11823,x11824,x11825,x11826,x11821),f784(x11823,x11824,x11825,x11826,x11822))
% 187.33/188.06 [1183]~E(x11831,x11832)+E(f574(x11831,x11833,x11834,x11835,x11836,x11837),f574(x11832,x11833,x11834,x11835,x11836,x11837))
% 187.33/188.06 [1184]~E(x11841,x11842)+E(f574(x11843,x11841,x11844,x11845,x11846,x11847),f574(x11843,x11842,x11844,x11845,x11846,x11847))
% 187.33/188.06 [1185]~E(x11851,x11852)+E(f574(x11853,x11854,x11851,x11855,x11856,x11857),f574(x11853,x11854,x11852,x11855,x11856,x11857))
% 187.33/188.06 [1186]~E(x11861,x11862)+E(f574(x11863,x11864,x11865,x11861,x11866,x11867),f574(x11863,x11864,x11865,x11862,x11866,x11867))
% 187.33/188.06 [1187]~E(x11871,x11872)+E(f574(x11873,x11874,x11875,x11876,x11871,x11877),f574(x11873,x11874,x11875,x11876,x11872,x11877))
% 187.33/188.06 [1188]~E(x11881,x11882)+E(f574(x11883,x11884,x11885,x11886,x11887,x11881),f574(x11883,x11884,x11885,x11886,x11887,x11882))
% 187.33/188.06 [1189]~E(x11891,x11892)+E(f288(x11891,x11893),f288(x11892,x11893))
% 187.33/188.06 [1190]~E(x11901,x11902)+E(f288(x11903,x11901),f288(x11903,x11902))
% 187.33/188.06 [1191]~E(x11911,x11912)+E(f208(x11911,x11913),f208(x11912,x11913))
% 187.33/188.06 [1192]~E(x11921,x11922)+E(f208(x11923,x11921),f208(x11923,x11922))
% 187.33/188.06 [1193]~E(x11931,x11932)+E(f591(x11931,x11933,x11934,x11935,x11936),f591(x11932,x11933,x11934,x11935,x11936))
% 187.33/188.06 [1194]~E(x11941,x11942)+E(f591(x11943,x11941,x11944,x11945,x11946),f591(x11943,x11942,x11944,x11945,x11946))
% 187.33/188.06 [1195]~E(x11951,x11952)+E(f591(x11953,x11954,x11951,x11955,x11956),f591(x11953,x11954,x11952,x11955,x11956))
% 187.33/188.06 [1196]~E(x11961,x11962)+E(f591(x11963,x11964,x11965,x11961,x11966),f591(x11963,x11964,x11965,x11962,x11966))
% 187.33/188.06 [1197]~E(x11971,x11972)+E(f591(x11973,x11974,x11975,x11976,x11971),f591(x11973,x11974,x11975,x11976,x11972))
% 187.33/188.06 [1198]~E(x11981,x11982)+E(f311(x11981,x11983,x11984),f311(x11982,x11983,x11984))
% 187.33/188.06 [1199]~E(x11991,x11992)+E(f311(x11993,x11991,x11994),f311(x11993,x11992,x11994))
% 187.33/188.06 [1200]~E(x12001,x12002)+E(f311(x12003,x12004,x12001),f311(x12003,x12004,x12002))
% 187.33/188.06 [1201]~E(x12011,x12012)+E(f617(x12011,x12013,x12014,x12015,x12016),f617(x12012,x12013,x12014,x12015,x12016))
% 187.33/188.06 [1202]~E(x12021,x12022)+E(f617(x12023,x12021,x12024,x12025,x12026),f617(x12023,x12022,x12024,x12025,x12026))
% 187.33/188.06 [1203]~E(x12031,x12032)+E(f617(x12033,x12034,x12031,x12035,x12036),f617(x12033,x12034,x12032,x12035,x12036))
% 187.33/188.06 [1204]~E(x12041,x12042)+E(f617(x12043,x12044,x12045,x12041,x12046),f617(x12043,x12044,x12045,x12042,x12046))
% 187.33/188.06 [1205]~E(x12051,x12052)+E(f617(x12053,x12054,x12055,x12056,x12051),f617(x12053,x12054,x12055,x12056,x12052))
% 187.33/188.06 [1206]~E(x12061,x12062)+E(f313(x12061,x12063,x12064),f313(x12062,x12063,x12064))
% 187.33/188.06 [1207]~E(x12071,x12072)+E(f313(x12073,x12071,x12074),f313(x12073,x12072,x12074))
% 187.33/188.06 [1208]~E(x12081,x12082)+E(f313(x12083,x12084,x12081),f313(x12083,x12084,x12082))
% 187.33/188.06 [1209]~E(x12091,x12092)+E(f494(x12091,x12093,x12094,x12095,x12096),f494(x12092,x12093,x12094,x12095,x12096))
% 187.33/188.06 [1210]~E(x12101,x12102)+E(f494(x12103,x12101,x12104,x12105,x12106),f494(x12103,x12102,x12104,x12105,x12106))
% 187.33/188.06 [1211]~E(x12111,x12112)+E(f494(x12113,x12114,x12111,x12115,x12116),f494(x12113,x12114,x12112,x12115,x12116))
% 187.33/188.06 [1212]~E(x12121,x12122)+E(f494(x12123,x12124,x12125,x12121,x12126),f494(x12123,x12124,x12125,x12122,x12126))
% 187.33/188.06 [1213]~E(x12131,x12132)+E(f494(x12133,x12134,x12135,x12136,x12131),f494(x12133,x12134,x12135,x12136,x12132))
% 187.33/188.06 [1214]~E(x12141,x12142)+E(f345(x12141,x12143,x12144,x12145),f345(x12142,x12143,x12144,x12145))
% 187.33/188.06 [1215]~E(x12151,x12152)+E(f345(x12153,x12151,x12154,x12155),f345(x12153,x12152,x12154,x12155))
% 187.33/188.06 [1216]~E(x12161,x12162)+E(f345(x12163,x12164,x12161,x12165),f345(x12163,x12164,x12162,x12165))
% 187.33/188.06 [1217]~E(x12171,x12172)+E(f345(x12173,x12174,x12175,x12171),f345(x12173,x12174,x12175,x12172))
% 187.33/188.06 [1218]~E(x12181,x12182)+E(f100(x12181,x12183,x12184,x12185),f100(x12182,x12183,x12184,x12185))
% 187.33/188.06 [1219]~E(x12191,x12192)+E(f100(x12193,x12191,x12194,x12195),f100(x12193,x12192,x12194,x12195))
% 187.33/188.06 [1220]~E(x12201,x12202)+E(f100(x12203,x12204,x12201,x12205),f100(x12203,x12204,x12202,x12205))
% 187.33/188.06 [1221]~E(x12211,x12212)+E(f100(x12213,x12214,x12215,x12211),f100(x12213,x12214,x12215,x12212))
% 187.33/188.06 [1222]~E(x12221,x12222)+E(f814(x12221,x12223,x12224,x12225,x12226),f814(x12222,x12223,x12224,x12225,x12226))
% 187.33/188.06 [1223]~E(x12231,x12232)+E(f814(x12233,x12231,x12234,x12235,x12236),f814(x12233,x12232,x12234,x12235,x12236))
% 187.33/188.06 [1224]~E(x12241,x12242)+E(f814(x12243,x12244,x12241,x12245,x12246),f814(x12243,x12244,x12242,x12245,x12246))
% 187.33/188.06 [1225]~E(x12251,x12252)+E(f814(x12253,x12254,x12255,x12251,x12256),f814(x12253,x12254,x12255,x12252,x12256))
% 187.33/188.06 [1226]~E(x12261,x12262)+E(f814(x12263,x12264,x12265,x12266,x12261),f814(x12263,x12264,x12265,x12266,x12262))
% 187.33/188.06 [1227]~E(x12271,x12272)+E(f681(x12271,x12273,x12274),f681(x12272,x12273,x12274))
% 187.33/188.06 [1228]~E(x12281,x12282)+E(f681(x12283,x12281,x12284),f681(x12283,x12282,x12284))
% 187.33/188.06 [1229]~E(x12291,x12292)+E(f681(x12293,x12294,x12291),f681(x12293,x12294,x12292))
% 187.33/188.06 [1230]~E(x12301,x12302)+E(f593(x12301,x12303,x12304),f593(x12302,x12303,x12304))
% 187.33/188.06 [1231]~E(x12311,x12312)+E(f593(x12313,x12311,x12314),f593(x12313,x12312,x12314))
% 187.33/188.06 [1232]~E(x12321,x12322)+E(f593(x12323,x12324,x12321),f593(x12323,x12324,x12322))
% 187.33/188.06 [1233]~E(x12331,x12332)+E(f414(x12331,x12333,x12334),f414(x12332,x12333,x12334))
% 187.33/188.06 [1234]~E(x12341,x12342)+E(f414(x12343,x12341,x12344),f414(x12343,x12342,x12344))
% 187.33/188.06 [1235]~E(x12351,x12352)+E(f414(x12353,x12354,x12351),f414(x12353,x12354,x12352))
% 187.33/188.06 [1236]~E(x12361,x12362)+E(f74(x12361,x12363),f74(x12362,x12363))
% 187.33/188.06 [1237]~E(x12371,x12372)+E(f74(x12373,x12371),f74(x12373,x12372))
% 187.33/188.06 [1238]~E(x12381,x12382)+E(f852(x12381,x12383,x12384,x12385,x12386),f852(x12382,x12383,x12384,x12385,x12386))
% 187.33/188.06 [1239]~E(x12391,x12392)+E(f852(x12393,x12391,x12394,x12395,x12396),f852(x12393,x12392,x12394,x12395,x12396))
% 187.33/188.06 [1240]~E(x12401,x12402)+E(f852(x12403,x12404,x12401,x12405,x12406),f852(x12403,x12404,x12402,x12405,x12406))
% 187.33/188.06 [1241]~E(x12411,x12412)+E(f852(x12413,x12414,x12415,x12411,x12416),f852(x12413,x12414,x12415,x12412,x12416))
% 187.33/188.06 [1242]~E(x12421,x12422)+E(f852(x12423,x12424,x12425,x12426,x12421),f852(x12423,x12424,x12425,x12426,x12422))
% 187.33/188.06 [1243]~E(x12431,x12432)+E(f679(x12431,x12433),f679(x12432,x12433))
% 187.33/188.06 [1244]~E(x12441,x12442)+E(f679(x12443,x12441),f679(x12443,x12442))
% 187.33/188.06 [1245]~E(x12451,x12452)+E(f610(x12451,x12453,x12454,x12455,x12456),f610(x12452,x12453,x12454,x12455,x12456))
% 187.33/188.06 [1246]~E(x12461,x12462)+E(f610(x12463,x12461,x12464,x12465,x12466),f610(x12463,x12462,x12464,x12465,x12466))
% 187.33/188.06 [1247]~E(x12471,x12472)+E(f610(x12473,x12474,x12471,x12475,x12476),f610(x12473,x12474,x12472,x12475,x12476))
% 187.33/188.06 [1248]~E(x12481,x12482)+E(f610(x12483,x12484,x12485,x12481,x12486),f610(x12483,x12484,x12485,x12482,x12486))
% 187.33/188.06 [1249]~E(x12491,x12492)+E(f610(x12493,x12494,x12495,x12496,x12491),f610(x12493,x12494,x12495,x12496,x12492))
% 187.33/188.06 [1250]~E(x12501,x12502)+E(f676(x12501,x12503,x12504),f676(x12502,x12503,x12504))
% 187.33/188.06 [1251]~E(x12511,x12512)+E(f676(x12513,x12511,x12514),f676(x12513,x12512,x12514))
% 187.33/188.06 [1252]~E(x12521,x12522)+E(f676(x12523,x12524,x12521),f676(x12523,x12524,x12522))
% 187.33/188.06 [1253]~E(x12531,x12532)+E(f133(x12531),f133(x12532))
% 187.33/188.06 [1254]~E(x12541,x12542)+E(f351(x12541,x12543,x12544,x12545),f351(x12542,x12543,x12544,x12545))
% 187.33/188.06 [1255]~E(x12551,x12552)+E(f351(x12553,x12551,x12554,x12555),f351(x12553,x12552,x12554,x12555))
% 187.33/188.06 [1256]~E(x12561,x12562)+E(f351(x12563,x12564,x12561,x12565),f351(x12563,x12564,x12562,x12565))
% 187.33/188.06 [1257]~E(x12571,x12572)+E(f351(x12573,x12574,x12575,x12571),f351(x12573,x12574,x12575,x12572))
% 187.33/188.06 [1258]~E(x12581,x12582)+E(f408(x12581),f408(x12582))
% 187.33/188.06 [1259]~E(x12591,x12592)+E(f399(x12591,x12593,x12594,x12595),f399(x12592,x12593,x12594,x12595))
% 187.33/188.06 [1260]~E(x12601,x12602)+E(f399(x12603,x12601,x12604,x12605),f399(x12603,x12602,x12604,x12605))
% 187.33/188.06 [1261]~E(x12611,x12612)+E(f399(x12613,x12614,x12611,x12615),f399(x12613,x12614,x12612,x12615))
% 187.33/188.06 [1262]~E(x12621,x12622)+E(f399(x12623,x12624,x12625,x12621),f399(x12623,x12624,x12625,x12622))
% 187.33/188.06 [1263]~E(x12631,x12632)+E(f652(x12631,x12633,x12634),f652(x12632,x12633,x12634))
% 187.33/188.06 [1264]~E(x12641,x12642)+E(f652(x12643,x12641,x12644),f652(x12643,x12642,x12644))
% 187.33/188.06 [1265]~E(x12651,x12652)+E(f652(x12653,x12654,x12651),f652(x12653,x12654,x12652))
% 187.33/188.06 [1266]~E(x12661,x12662)+E(f819(x12661,x12663,x12664),f819(x12662,x12663,x12664))
% 187.33/188.06 [1267]~E(x12671,x12672)+E(f819(x12673,x12671,x12674),f819(x12673,x12672,x12674))
% 187.33/188.06 [1268]~E(x12681,x12682)+E(f819(x12683,x12684,x12681),f819(x12683,x12684,x12682))
% 187.33/188.06 [1269]~E(x12691,x12692)+E(f673(x12691,x12693,x12694,x12695,x12696),f673(x12692,x12693,x12694,x12695,x12696))
% 187.33/188.06 [1270]~E(x12701,x12702)+E(f673(x12703,x12701,x12704,x12705,x12706),f673(x12703,x12702,x12704,x12705,x12706))
% 187.33/188.06 [1271]~E(x12711,x12712)+E(f673(x12713,x12714,x12711,x12715,x12716),f673(x12713,x12714,x12712,x12715,x12716))
% 187.33/188.06 [1272]~E(x12721,x12722)+E(f673(x12723,x12724,x12725,x12721,x12726),f673(x12723,x12724,x12725,x12722,x12726))
% 187.33/188.06 [1273]~E(x12731,x12732)+E(f673(x12733,x12734,x12735,x12736,x12731),f673(x12733,x12734,x12735,x12736,x12732))
% 187.33/188.06 [1274]~E(x12741,x12742)+E(f496(x12741),f496(x12742))
% 187.33/188.06 [1275]~E(x12751,x12752)+E(f259(x12751,x12753,x12754),f259(x12752,x12753,x12754))
% 187.33/188.06 [1276]~E(x12761,x12762)+E(f259(x12763,x12761,x12764),f259(x12763,x12762,x12764))
% 187.33/188.06 [1277]~E(x12771,x12772)+E(f259(x12773,x12774,x12771),f259(x12773,x12774,x12772))
% 187.33/188.06 [1278]~E(x12781,x12782)+E(f589(x12781,x12783,x12784,x12785,x12786,x12787,x12788,x12789),f589(x12782,x12783,x12784,x12785,x12786,x12787,x12788,x12789))
% 187.33/188.06 [1279]~E(x12791,x12792)+E(f589(x12793,x12791,x12794,x12795,x12796,x12797,x12798,x12799),f589(x12793,x12792,x12794,x12795,x12796,x12797,x12798,x12799))
% 187.33/188.06 [1280]~E(x12801,x12802)+E(f589(x12803,x12804,x12801,x12805,x12806,x12807,x12808,x12809),f589(x12803,x12804,x12802,x12805,x12806,x12807,x12808,x12809))
% 187.33/188.06 [1281]~E(x12811,x12812)+E(f589(x12813,x12814,x12815,x12811,x12816,x12817,x12818,x12819),f589(x12813,x12814,x12815,x12812,x12816,x12817,x12818,x12819))
% 187.33/188.06 [1282]~E(x12821,x12822)+E(f589(x12823,x12824,x12825,x12826,x12821,x12827,x12828,x12829),f589(x12823,x12824,x12825,x12826,x12822,x12827,x12828,x12829))
% 187.33/188.06 [1283]~E(x12831,x12832)+E(f589(x12833,x12834,x12835,x12836,x12837,x12831,x12838,x12839),f589(x12833,x12834,x12835,x12836,x12837,x12832,x12838,x12839))
% 187.33/188.06 [1284]~E(x12841,x12842)+E(f589(x12843,x12844,x12845,x12846,x12847,x12848,x12841,x12849),f589(x12843,x12844,x12845,x12846,x12847,x12848,x12842,x12849))
% 187.33/188.06 [1285]~E(x12851,x12852)+E(f589(x12853,x12854,x12855,x12856,x12857,x12858,x12859,x12851),f589(x12853,x12854,x12855,x12856,x12857,x12858,x12859,x12852))
% 187.33/188.06 [1286]~E(x12861,x12862)+E(f835(x12861,x12863,x12864),f835(x12862,x12863,x12864))
% 187.33/188.06 [1287]~E(x12871,x12872)+E(f835(x12873,x12871,x12874),f835(x12873,x12872,x12874))
% 187.33/188.06 [1288]~E(x12881,x12882)+E(f835(x12883,x12884,x12881),f835(x12883,x12884,x12882))
% 187.33/188.06 [1289]~E(x12891,x12892)+E(f644(x12891,x12893,x12894,x12895),f644(x12892,x12893,x12894,x12895))
% 187.33/188.06 [1290]~E(x12901,x12902)+E(f644(x12903,x12901,x12904,x12905),f644(x12903,x12902,x12904,x12905))
% 187.33/188.06 [1291]~E(x12911,x12912)+E(f644(x12913,x12914,x12911,x12915),f644(x12913,x12914,x12912,x12915))
% 187.33/188.06 [1292]~E(x12921,x12922)+E(f644(x12923,x12924,x12925,x12921),f644(x12923,x12924,x12925,x12922))
% 187.33/188.06 [1293]~E(x12931,x12932)+E(f450(x12931,x12933,x12934),f450(x12932,x12933,x12934))
% 187.33/188.06 [1294]~E(x12941,x12942)+E(f450(x12943,x12941,x12944),f450(x12943,x12942,x12944))
% 187.33/188.06 [1295]~E(x12951,x12952)+E(f450(x12953,x12954,x12951),f450(x12953,x12954,x12952))
% 187.33/188.06 [1296]~E(x12961,x12962)+E(f660(x12961,x12963,x12964,x12965,x12966,x12967),f660(x12962,x12963,x12964,x12965,x12966,x12967))
% 187.33/188.06 [1297]~E(x12971,x12972)+E(f660(x12973,x12971,x12974,x12975,x12976,x12977),f660(x12973,x12972,x12974,x12975,x12976,x12977))
% 187.33/188.06 [1298]~E(x12981,x12982)+E(f660(x12983,x12984,x12981,x12985,x12986,x12987),f660(x12983,x12984,x12982,x12985,x12986,x12987))
% 187.33/188.06 [1299]~E(x12991,x12992)+E(f660(x12993,x12994,x12995,x12991,x12996,x12997),f660(x12993,x12994,x12995,x12992,x12996,x12997))
% 187.33/188.06 [1300]~E(x13001,x13002)+E(f660(x13003,x13004,x13005,x13006,x13001,x13007),f660(x13003,x13004,x13005,x13006,x13002,x13007))
% 187.33/188.06 [1301]~E(x13011,x13012)+E(f660(x13013,x13014,x13015,x13016,x13017,x13011),f660(x13013,x13014,x13015,x13016,x13017,x13012))
% 187.33/188.06 [1302]~E(x13021,x13022)+E(f661(x13021,x13023,x13024,x13025,x13026,x13027),f661(x13022,x13023,x13024,x13025,x13026,x13027))
% 187.33/188.06 [1303]~E(x13031,x13032)+E(f661(x13033,x13031,x13034,x13035,x13036,x13037),f661(x13033,x13032,x13034,x13035,x13036,x13037))
% 187.33/188.06 [1304]~E(x13041,x13042)+E(f661(x13043,x13044,x13041,x13045,x13046,x13047),f661(x13043,x13044,x13042,x13045,x13046,x13047))
% 187.33/188.06 [1305]~E(x13051,x13052)+E(f661(x13053,x13054,x13055,x13051,x13056,x13057),f661(x13053,x13054,x13055,x13052,x13056,x13057))
% 187.33/188.06 [1306]~E(x13061,x13062)+E(f661(x13063,x13064,x13065,x13066,x13061,x13067),f661(x13063,x13064,x13065,x13066,x13062,x13067))
% 187.33/188.06 [1307]~E(x13071,x13072)+E(f661(x13073,x13074,x13075,x13076,x13077,x13071),f661(x13073,x13074,x13075,x13076,x13077,x13072))
% 187.33/188.06 [1308]~E(x13081,x13082)+E(f731(x13081,x13083,x13084),f731(x13082,x13083,x13084))
% 187.33/188.06 [1309]~E(x13091,x13092)+E(f731(x13093,x13091,x13094),f731(x13093,x13092,x13094))
% 187.33/188.06 [1310]~E(x13101,x13102)+E(f731(x13103,x13104,x13101),f731(x13103,x13104,x13102))
% 187.33/188.06 [1311]~E(x13111,x13112)+E(f534(x13111,x13113,x13114),f534(x13112,x13113,x13114))
% 187.33/188.06 [1312]~E(x13121,x13122)+E(f534(x13123,x13121,x13124),f534(x13123,x13122,x13124))
% 187.33/188.06 [1313]~E(x13131,x13132)+E(f534(x13133,x13134,x13131),f534(x13133,x13134,x13132))
% 187.33/188.06 [1314]~E(x13141,x13142)+E(f449(x13141,x13143,x13144),f449(x13142,x13143,x13144))
% 187.33/188.06 [1315]~E(x13151,x13152)+E(f449(x13153,x13151,x13154),f449(x13153,x13152,x13154))
% 187.33/188.06 [1316]~E(x13161,x13162)+E(f449(x13163,x13164,x13161),f449(x13163,x13164,x13162))
% 187.33/188.06 [1317]~E(x13171,x13172)+E(f312(x13171,x13173,x13174),f312(x13172,x13173,x13174))
% 187.33/188.06 [1318]~E(x13181,x13182)+E(f312(x13183,x13181,x13184),f312(x13183,x13182,x13184))
% 187.33/188.06 [1319]~E(x13191,x13192)+E(f312(x13193,x13194,x13191),f312(x13193,x13194,x13192))
% 187.33/188.06 [1320]~E(x13201,x13202)+E(f794(x13201,x13203,x13204),f794(x13202,x13203,x13204))
% 187.33/188.06 [1321]~E(x13211,x13212)+E(f794(x13213,x13211,x13214),f794(x13213,x13212,x13214))
% 187.33/188.06 [1322]~E(x13221,x13222)+E(f794(x13223,x13224,x13221),f794(x13223,x13224,x13222))
% 187.33/188.06 [1323]~E(x13231,x13232)+E(f397(x13231,x13233,x13234,x13235),f397(x13232,x13233,x13234,x13235))
% 187.33/188.06 [1324]~E(x13241,x13242)+E(f397(x13243,x13241,x13244,x13245),f397(x13243,x13242,x13244,x13245))
% 187.33/188.06 [1325]~E(x13251,x13252)+E(f397(x13253,x13254,x13251,x13255),f397(x13253,x13254,x13252,x13255))
% 187.33/188.06 [1326]~E(x13261,x13262)+E(f397(x13263,x13264,x13265,x13261),f397(x13263,x13264,x13265,x13262))
% 187.33/188.06 [1327]~E(x13271,x13272)+E(f602(x13271,x13273,x13274),f602(x13272,x13273,x13274))
% 187.33/188.06 [1328]~E(x13281,x13282)+E(f602(x13283,x13281,x13284),f602(x13283,x13282,x13284))
% 187.33/188.06 [1329]~E(x13291,x13292)+E(f602(x13293,x13294,x13291),f602(x13293,x13294,x13292))
% 187.33/188.06 [1330]~E(x13301,x13302)+E(f239(x13301,x13303,x13304,x13305,x13306),f239(x13302,x13303,x13304,x13305,x13306))
% 187.33/188.06 [1331]~E(x13311,x13312)+E(f239(x13313,x13311,x13314,x13315,x13316),f239(x13313,x13312,x13314,x13315,x13316))
% 187.33/188.06 [1332]~E(x13321,x13322)+E(f239(x13323,x13324,x13321,x13325,x13326),f239(x13323,x13324,x13322,x13325,x13326))
% 187.33/188.06 [1333]~E(x13331,x13332)+E(f239(x13333,x13334,x13335,x13331,x13336),f239(x13333,x13334,x13335,x13332,x13336))
% 187.33/188.06 [1334]~E(x13341,x13342)+E(f239(x13343,x13344,x13345,x13346,x13341),f239(x13343,x13344,x13345,x13346,x13342))
% 187.33/188.06 [1335]~E(x13351,x13352)+E(f698(x13351,x13353,x13354,x13355),f698(x13352,x13353,x13354,x13355))
% 187.33/188.06 [1336]~E(x13361,x13362)+E(f698(x13363,x13361,x13364,x13365),f698(x13363,x13362,x13364,x13365))
% 187.33/188.06 [1337]~E(x13371,x13372)+E(f698(x13373,x13374,x13371,x13375),f698(x13373,x13374,x13372,x13375))
% 187.33/188.06 [1338]~E(x13381,x13382)+E(f698(x13383,x13384,x13385,x13381),f698(x13383,x13384,x13385,x13382))
% 187.33/188.06 [1339]~E(x13391,x13392)+E(f831(x13391,x13393,x13394,x13395),f831(x13392,x13393,x13394,x13395))
% 187.33/188.06 [1340]~E(x13401,x13402)+E(f831(x13403,x13401,x13404,x13405),f831(x13403,x13402,x13404,x13405))
% 187.33/188.06 [1341]~E(x13411,x13412)+E(f831(x13413,x13414,x13411,x13415),f831(x13413,x13414,x13412,x13415))
% 187.33/188.06 [1342]~E(x13421,x13422)+E(f831(x13423,x13424,x13425,x13421),f831(x13423,x13424,x13425,x13422))
% 187.33/188.06 [1343]~E(x13431,x13432)+E(f522(x13431,x13433,x13434,x13435),f522(x13432,x13433,x13434,x13435))
% 187.33/188.06 [1344]~E(x13441,x13442)+E(f522(x13443,x13441,x13444,x13445),f522(x13443,x13442,x13444,x13445))
% 187.33/188.06 [1345]~E(x13451,x13452)+E(f522(x13453,x13454,x13451,x13455),f522(x13453,x13454,x13452,x13455))
% 187.33/188.06 [1346]~E(x13461,x13462)+E(f522(x13463,x13464,x13465,x13461),f522(x13463,x13464,x13465,x13462))
% 187.33/188.06 [1347]~E(x13471,x13472)+E(f211(x13471,x13473),f211(x13472,x13473))
% 187.33/188.06 [1348]~E(x13481,x13482)+E(f211(x13483,x13481),f211(x13483,x13482))
% 187.33/188.06 [1349]~E(x13491,x13492)+E(f754(x13491,x13493,x13494),f754(x13492,x13493,x13494))
% 187.33/188.06 [1350]~E(x13501,x13502)+E(f754(x13503,x13501,x13504),f754(x13503,x13502,x13504))
% 187.33/188.06 [1351]~E(x13511,x13512)+E(f754(x13513,x13514,x13511),f754(x13513,x13514,x13512))
% 187.33/188.06 [1352]~E(x13521,x13522)+E(f659(x13521,x13523,x13524,x13525,x13526,x13527),f659(x13522,x13523,x13524,x13525,x13526,x13527))
% 187.33/188.06 [1353]~E(x13531,x13532)+E(f659(x13533,x13531,x13534,x13535,x13536,x13537),f659(x13533,x13532,x13534,x13535,x13536,x13537))
% 187.33/188.06 [1354]~E(x13541,x13542)+E(f659(x13543,x13544,x13541,x13545,x13546,x13547),f659(x13543,x13544,x13542,x13545,x13546,x13547))
% 187.33/188.06 [1355]~E(x13551,x13552)+E(f659(x13553,x13554,x13555,x13551,x13556,x13557),f659(x13553,x13554,x13555,x13552,x13556,x13557))
% 187.33/188.06 [1356]~E(x13561,x13562)+E(f659(x13563,x13564,x13565,x13566,x13561,x13567),f659(x13563,x13564,x13565,x13566,x13562,x13567))
% 187.33/188.06 [1357]~E(x13571,x13572)+E(f659(x13573,x13574,x13575,x13576,x13577,x13571),f659(x13573,x13574,x13575,x13576,x13577,x13572))
% 187.33/188.06 [1358]~E(x13581,x13582)+E(f846(x13581,x13583,x13584,x13585,x13586,x13587),f846(x13582,x13583,x13584,x13585,x13586,x13587))
% 187.33/188.06 [1359]~E(x13591,x13592)+E(f846(x13593,x13591,x13594,x13595,x13596,x13597),f846(x13593,x13592,x13594,x13595,x13596,x13597))
% 187.33/188.06 [1360]~E(x13601,x13602)+E(f846(x13603,x13604,x13601,x13605,x13606,x13607),f846(x13603,x13604,x13602,x13605,x13606,x13607))
% 187.33/188.06 [1361]~E(x13611,x13612)+E(f846(x13613,x13614,x13615,x13611,x13616,x13617),f846(x13613,x13614,x13615,x13612,x13616,x13617))
% 187.33/188.06 [1362]~E(x13621,x13622)+E(f846(x13623,x13624,x13625,x13626,x13621,x13627),f846(x13623,x13624,x13625,x13626,x13622,x13627))
% 187.33/188.06 [1363]~E(x13631,x13632)+E(f846(x13633,x13634,x13635,x13636,x13637,x13631),f846(x13633,x13634,x13635,x13636,x13637,x13632))
% 187.33/188.06 [1364]~E(x13641,x13642)+E(f538(x13641,x13643,x13644,x13645,x13646,x13647),f538(x13642,x13643,x13644,x13645,x13646,x13647))
% 187.33/188.06 [1365]~E(x13651,x13652)+E(f538(x13653,x13651,x13654,x13655,x13656,x13657),f538(x13653,x13652,x13654,x13655,x13656,x13657))
% 187.33/188.06 [1366]~E(x13661,x13662)+E(f538(x13663,x13664,x13661,x13665,x13666,x13667),f538(x13663,x13664,x13662,x13665,x13666,x13667))
% 187.33/188.06 [1367]~E(x13671,x13672)+E(f538(x13673,x13674,x13675,x13671,x13676,x13677),f538(x13673,x13674,x13675,x13672,x13676,x13677))
% 187.33/188.06 [1368]~E(x13681,x13682)+E(f538(x13683,x13684,x13685,x13686,x13681,x13687),f538(x13683,x13684,x13685,x13686,x13682,x13687))
% 187.33/188.06 [1369]~E(x13691,x13692)+E(f538(x13693,x13694,x13695,x13696,x13697,x13691),f538(x13693,x13694,x13695,x13696,x13697,x13692))
% 187.33/188.06 [1370]~E(x13701,x13702)+E(f766(x13701,x13703),f766(x13702,x13703))
% 187.33/188.06 [1371]~E(x13711,x13712)+E(f766(x13713,x13711),f766(x13713,x13712))
% 187.33/188.06 [1372]~E(x13721,x13722)+E(f625(x13721,x13723,x13724,x13725,x13726),f625(x13722,x13723,x13724,x13725,x13726))
% 187.33/188.06 [1373]~E(x13731,x13732)+E(f625(x13733,x13731,x13734,x13735,x13736),f625(x13733,x13732,x13734,x13735,x13736))
% 187.33/188.06 [1374]~E(x13741,x13742)+E(f625(x13743,x13744,x13741,x13745,x13746),f625(x13743,x13744,x13742,x13745,x13746))
% 187.33/188.06 [1375]~E(x13751,x13752)+E(f625(x13753,x13754,x13755,x13751,x13756),f625(x13753,x13754,x13755,x13752,x13756))
% 187.33/188.06 [1376]~E(x13761,x13762)+E(f625(x13763,x13764,x13765,x13766,x13761),f625(x13763,x13764,x13765,x13766,x13762))
% 187.33/188.06 [1377]~E(x13771,x13772)+E(f128(x13771,x13773,x13774),f128(x13772,x13773,x13774))
% 187.33/188.06 [1378]~E(x13781,x13782)+E(f128(x13783,x13781,x13784),f128(x13783,x13782,x13784))
% 187.33/188.06 [1379]~E(x13791,x13792)+E(f128(x13793,x13794,x13791),f128(x13793,x13794,x13792))
% 187.33/188.06 [1380]~E(x13801,x13802)+E(f536(x13801,x13803,x13804,x13805),f536(x13802,x13803,x13804,x13805))
% 187.33/188.06 [1381]~E(x13811,x13812)+E(f536(x13813,x13811,x13814,x13815),f536(x13813,x13812,x13814,x13815))
% 187.33/188.06 [1382]~E(x13821,x13822)+E(f536(x13823,x13824,x13821,x13825),f536(x13823,x13824,x13822,x13825))
% 187.33/188.06 [1383]~E(x13831,x13832)+E(f536(x13833,x13834,x13835,x13831),f536(x13833,x13834,x13835,x13832))
% 187.33/188.06 [1384]~E(x13841,x13842)+E(f274(x13841),f274(x13842))
% 187.33/188.06 [1385]~E(x13851,x13852)+E(f322(x13851,x13853,x13854,x13855),f322(x13852,x13853,x13854,x13855))
% 187.33/188.06 [1386]~E(x13861,x13862)+E(f322(x13863,x13861,x13864,x13865),f322(x13863,x13862,x13864,x13865))
% 187.33/188.06 [1387]~E(x13871,x13872)+E(f322(x13873,x13874,x13871,x13875),f322(x13873,x13874,x13872,x13875))
% 187.33/188.06 [1388]~E(x13881,x13882)+E(f322(x13883,x13884,x13885,x13881),f322(x13883,x13884,x13885,x13882))
% 187.33/188.06 [1389]~E(x13891,x13892)+E(f257(x13891,x13893),f257(x13892,x13893))
% 187.33/188.06 [1390]~E(x13901,x13902)+E(f257(x13903,x13901),f257(x13903,x13902))
% 187.33/188.06 [1391]~E(x13911,x13912)+E(f519(x13911,x13913,x13914,x13915),f519(x13912,x13913,x13914,x13915))
% 187.33/188.06 [1392]~E(x13921,x13922)+E(f519(x13923,x13921,x13924,x13925),f519(x13923,x13922,x13924,x13925))
% 187.33/188.06 [1393]~E(x13931,x13932)+E(f519(x13933,x13934,x13931,x13935),f519(x13933,x13934,x13932,x13935))
% 187.33/188.06 [1394]~E(x13941,x13942)+E(f519(x13943,x13944,x13945,x13941),f519(x13943,x13944,x13945,x13942))
% 187.33/188.06 [1395]~E(x13951,x13952)+E(f218(x13951,x13953,x13954,x13955),f218(x13952,x13953,x13954,x13955))
% 187.33/188.06 [1396]~E(x13961,x13962)+E(f218(x13963,x13961,x13964,x13965),f218(x13963,x13962,x13964,x13965))
% 187.33/188.06 [1397]~E(x13971,x13972)+E(f218(x13973,x13974,x13971,x13975),f218(x13973,x13974,x13972,x13975))
% 187.33/188.06 [1398]~E(x13981,x13982)+E(f218(x13983,x13984,x13985,x13981),f218(x13983,x13984,x13985,x13982))
% 187.33/188.06 [1399]~E(x13991,x13992)+E(f374(x13991,x13993),f374(x13992,x13993))
% 187.33/188.06 [1400]~E(x14001,x14002)+E(f374(x14003,x14001),f374(x14003,x14002))
% 187.33/188.06 [1401]~E(x14011,x14012)+E(f411(x14011,x14013,x14014),f411(x14012,x14013,x14014))
% 187.33/188.06 [1402]~E(x14021,x14022)+E(f411(x14023,x14021,x14024),f411(x14023,x14022,x14024))
% 187.33/188.06 [1403]~E(x14031,x14032)+E(f411(x14033,x14034,x14031),f411(x14033,x14034,x14032))
% 187.33/188.06 [1404]~E(x14041,x14042)+E(f94(x14041,x14043,x14044),f94(x14042,x14043,x14044))
% 187.33/188.06 [1405]~E(x14051,x14052)+E(f94(x14053,x14051,x14054),f94(x14053,x14052,x14054))
% 187.33/188.06 [1406]~E(x14061,x14062)+E(f94(x14063,x14064,x14061),f94(x14063,x14064,x14062))
% 187.33/188.06 [1407]~E(x14071,x14072)+E(f753(x14071,x14073,x14074),f753(x14072,x14073,x14074))
% 187.33/188.06 [1408]~E(x14081,x14082)+E(f753(x14083,x14081,x14084),f753(x14083,x14082,x14084))
% 187.33/188.06 [1409]~E(x14091,x14092)+E(f753(x14093,x14094,x14091),f753(x14093,x14094,x14092))
% 187.33/188.06 [1410]~E(x14101,x14102)+E(f526(x14101,x14103,x14104,x14105),f526(x14102,x14103,x14104,x14105))
% 187.33/188.06 [1411]~E(x14111,x14112)+E(f526(x14113,x14111,x14114,x14115),f526(x14113,x14112,x14114,x14115))
% 187.33/188.06 [1412]~E(x14121,x14122)+E(f526(x14123,x14124,x14121,x14125),f526(x14123,x14124,x14122,x14125))
% 187.33/188.06 [1413]~E(x14131,x14132)+E(f526(x14133,x14134,x14135,x14131),f526(x14133,x14134,x14135,x14132))
% 187.33/188.06 [1414]~E(x14141,x14142)+E(f469(x14141,x14143,x14144),f469(x14142,x14143,x14144))
% 187.33/188.06 [1415]~E(x14151,x14152)+E(f469(x14153,x14151,x14154),f469(x14153,x14152,x14154))
% 187.33/188.06 [1416]~E(x14161,x14162)+E(f469(x14163,x14164,x14161),f469(x14163,x14164,x14162))
% 187.33/188.06 [1417]~E(x14171,x14172)+E(f365(x14171,x14173,x14174,x14175,x14176,x14177,x14178,x14179,x141710),f365(x14172,x14173,x14174,x14175,x14176,x14177,x14178,x14179,x141710))
% 187.33/188.06 [1418]~E(x14181,x14182)+E(f365(x14183,x14181,x14184,x14185,x14186,x14187,x14188,x14189,x141810),f365(x14183,x14182,x14184,x14185,x14186,x14187,x14188,x14189,x141810))
% 187.33/188.06 [1419]~E(x14191,x14192)+E(f365(x14193,x14194,x14191,x14195,x14196,x14197,x14198,x14199,x141910),f365(x14193,x14194,x14192,x14195,x14196,x14197,x14198,x14199,x141910))
% 187.33/188.06 [1420]~E(x14201,x14202)+E(f365(x14203,x14204,x14205,x14201,x14206,x14207,x14208,x14209,x142010),f365(x14203,x14204,x14205,x14202,x14206,x14207,x14208,x14209,x142010))
% 187.33/188.06 [1421]~E(x14211,x14212)+E(f365(x14213,x14214,x14215,x14216,x14211,x14217,x14218,x14219,x142110),f365(x14213,x14214,x14215,x14216,x14212,x14217,x14218,x14219,x142110))
% 187.33/188.06 [1422]~E(x14221,x14222)+E(f365(x14223,x14224,x14225,x14226,x14227,x14221,x14228,x14229,x142210),f365(x14223,x14224,x14225,x14226,x14227,x14222,x14228,x14229,x142210))
% 187.33/188.06 [1423]~E(x14231,x14232)+E(f365(x14233,x14234,x14235,x14236,x14237,x14238,x14231,x14239,x142310),f365(x14233,x14234,x14235,x14236,x14237,x14238,x14232,x14239,x142310))
% 187.33/188.06 [1424]~E(x14241,x14242)+E(f365(x14243,x14244,x14245,x14246,x14247,x14248,x14249,x14241,x142410),f365(x14243,x14244,x14245,x14246,x14247,x14248,x14249,x14242,x142410))
% 187.33/188.06 [1425]~E(x14251,x14252)+E(f365(x14253,x14254,x14255,x14256,x14257,x14258,x14259,x142510,x14251),f365(x14253,x14254,x14255,x14256,x14257,x14258,x14259,x142510,x14252))
% 187.33/188.06 [1426]~E(x14261,x14262)+E(f476(x14261,x14263,x14264),f476(x14262,x14263,x14264))
% 187.33/188.06 [1427]~E(x14271,x14272)+E(f476(x14273,x14271,x14274),f476(x14273,x14272,x14274))
% 187.33/188.06 [1428]~E(x14281,x14282)+E(f476(x14283,x14284,x14281),f476(x14283,x14284,x14282))
% 187.33/188.06 [1429]~E(x14291,x14292)+E(f655(x14291,x14293),f655(x14292,x14293))
% 187.33/188.06 [1430]~E(x14301,x14302)+E(f655(x14303,x14301),f655(x14303,x14302))
% 187.33/188.06 [1431]~E(x14311,x14312)+E(f477(x14311,x14313,x14314,x14315,x14316,x14317),f477(x14312,x14313,x14314,x14315,x14316,x14317))
% 187.33/188.06 [1432]~E(x14321,x14322)+E(f477(x14323,x14321,x14324,x14325,x14326,x14327),f477(x14323,x14322,x14324,x14325,x14326,x14327))
% 187.33/188.06 [1433]~E(x14331,x14332)+E(f477(x14333,x14334,x14331,x14335,x14336,x14337),f477(x14333,x14334,x14332,x14335,x14336,x14337))
% 187.33/188.06 [1434]~E(x14341,x14342)+E(f477(x14343,x14344,x14345,x14341,x14346,x14347),f477(x14343,x14344,x14345,x14342,x14346,x14347))
% 187.33/188.06 [1435]~E(x14351,x14352)+E(f477(x14353,x14354,x14355,x14356,x14351,x14357),f477(x14353,x14354,x14355,x14356,x14352,x14357))
% 187.33/188.06 [1436]~E(x14361,x14362)+E(f477(x14363,x14364,x14365,x14366,x14367,x14361),f477(x14363,x14364,x14365,x14366,x14367,x14362))
% 187.33/188.06 [1437]~E(x14371,x14372)+E(f439(x14371,x14373,x14374,x14375,x14376),f439(x14372,x14373,x14374,x14375,x14376))
% 187.33/188.06 [1438]~E(x14381,x14382)+E(f439(x14383,x14381,x14384,x14385,x14386),f439(x14383,x14382,x14384,x14385,x14386))
% 187.33/188.06 [1439]~E(x14391,x14392)+E(f439(x14393,x14394,x14391,x14395,x14396),f439(x14393,x14394,x14392,x14395,x14396))
% 187.33/188.06 [1440]~E(x14401,x14402)+E(f439(x14403,x14404,x14405,x14401,x14406),f439(x14403,x14404,x14405,x14402,x14406))
% 187.33/188.06 [1441]~E(x14411,x14412)+E(f439(x14413,x14414,x14415,x14416,x14411),f439(x14413,x14414,x14415,x14416,x14412))
% 187.33/188.06 [1442]~E(x14421,x14422)+E(f228(x14421,x14423),f228(x14422,x14423))
% 187.33/188.06 [1443]~E(x14431,x14432)+E(f228(x14433,x14431),f228(x14433,x14432))
% 187.33/188.06 [1444]~E(x14441,x14442)+E(f474(x14441,x14443,x14444),f474(x14442,x14443,x14444))
% 187.33/188.06 [1445]~E(x14451,x14452)+E(f474(x14453,x14451,x14454),f474(x14453,x14452,x14454))
% 187.33/188.06 [1446]~E(x14461,x14462)+E(f474(x14463,x14464,x14461),f474(x14463,x14464,x14462))
% 187.33/188.06 [1447]~E(x14471,x14472)+E(f664(x14471,x14473,x14474,x14475),f664(x14472,x14473,x14474,x14475))
% 187.33/188.06 [1448]~E(x14481,x14482)+E(f664(x14483,x14481,x14484,x14485),f664(x14483,x14482,x14484,x14485))
% 187.33/188.06 [1449]~E(x14491,x14492)+E(f664(x14493,x14494,x14491,x14495),f664(x14493,x14494,x14492,x14495))
% 187.33/188.06 [1450]~E(x14501,x14502)+E(f664(x14503,x14504,x14505,x14501),f664(x14503,x14504,x14505,x14502))
% 187.33/188.06 [1451]~E(x14511,x14512)+E(f420(x14511),f420(x14512))
% 187.33/188.06 [1452]~E(x14521,x14522)+E(f713(x14521,x14523,x14524,x14525,x14526),f713(x14522,x14523,x14524,x14525,x14526))
% 187.33/188.06 [1453]~E(x14531,x14532)+E(f713(x14533,x14531,x14534,x14535,x14536),f713(x14533,x14532,x14534,x14535,x14536))
% 187.33/188.06 [1454]~E(x14541,x14542)+E(f713(x14543,x14544,x14541,x14545,x14546),f713(x14543,x14544,x14542,x14545,x14546))
% 187.33/188.06 [1455]~E(x14551,x14552)+E(f713(x14553,x14554,x14555,x14551,x14556),f713(x14553,x14554,x14555,x14552,x14556))
% 187.33/188.06 [1456]~E(x14561,x14562)+E(f713(x14563,x14564,x14565,x14566,x14561),f713(x14563,x14564,x14565,x14566,x14562))
% 187.33/188.06 [1457]~E(x14571,x14572)+E(f734(x14571,x14573,x14574,x14575),f734(x14572,x14573,x14574,x14575))
% 187.33/188.06 [1458]~E(x14581,x14582)+E(f734(x14583,x14581,x14584,x14585),f734(x14583,x14582,x14584,x14585))
% 187.33/188.06 [1459]~E(x14591,x14592)+E(f734(x14593,x14594,x14591,x14595),f734(x14593,x14594,x14592,x14595))
% 187.33/188.06 [1460]~E(x14601,x14602)+E(f734(x14603,x14604,x14605,x14601),f734(x14603,x14604,x14605,x14602))
% 187.33/188.06 [1461]~E(x14611,x14612)+E(f849(x14611,x14613,x14614,x14615,x14616),f849(x14612,x14613,x14614,x14615,x14616))
% 187.33/188.06 [1462]~E(x14621,x14622)+E(f849(x14623,x14621,x14624,x14625,x14626),f849(x14623,x14622,x14624,x14625,x14626))
% 187.33/188.06 [1463]~E(x14631,x14632)+E(f849(x14633,x14634,x14631,x14635,x14636),f849(x14633,x14634,x14632,x14635,x14636))
% 187.33/188.06 [1464]~E(x14641,x14642)+E(f849(x14643,x14644,x14645,x14641,x14646),f849(x14643,x14644,x14645,x14642,x14646))
% 187.33/188.06 [1465]~E(x14651,x14652)+E(f849(x14653,x14654,x14655,x14656,x14651),f849(x14653,x14654,x14655,x14656,x14652))
% 187.33/188.06 [1466]~E(x14661,x14662)+E(f633(x14661,x14663,x14664,x14665,x14666,x14667,x14668,x14669),f633(x14662,x14663,x14664,x14665,x14666,x14667,x14668,x14669))
% 187.33/188.06 [1467]~E(x14671,x14672)+E(f633(x14673,x14671,x14674,x14675,x14676,x14677,x14678,x14679),f633(x14673,x14672,x14674,x14675,x14676,x14677,x14678,x14679))
% 187.33/188.06 [1468]~E(x14681,x14682)+E(f633(x14683,x14684,x14681,x14685,x14686,x14687,x14688,x14689),f633(x14683,x14684,x14682,x14685,x14686,x14687,x14688,x14689))
% 187.33/188.06 [1469]~E(x14691,x14692)+E(f633(x14693,x14694,x14695,x14691,x14696,x14697,x14698,x14699),f633(x14693,x14694,x14695,x14692,x14696,x14697,x14698,x14699))
% 187.33/188.06 [1470]~E(x14701,x14702)+E(f633(x14703,x14704,x14705,x14706,x14701,x14707,x14708,x14709),f633(x14703,x14704,x14705,x14706,x14702,x14707,x14708,x14709))
% 187.33/188.06 [1471]~E(x14711,x14712)+E(f633(x14713,x14714,x14715,x14716,x14717,x14711,x14718,x14719),f633(x14713,x14714,x14715,x14716,x14717,x14712,x14718,x14719))
% 187.33/188.06 [1472]~E(x14721,x14722)+E(f633(x14723,x14724,x14725,x14726,x14727,x14728,x14721,x14729),f633(x14723,x14724,x14725,x14726,x14727,x14728,x14722,x14729))
% 187.33/188.06 [1473]~E(x14731,x14732)+E(f633(x14733,x14734,x14735,x14736,x14737,x14738,x14739,x14731),f633(x14733,x14734,x14735,x14736,x14737,x14738,x14739,x14732))
% 187.33/188.06 [1474]~E(x14741,x14742)+E(f210(x14741),f210(x14742))
% 187.33/188.06 [1475]~E(x14751,x14752)+E(f383(x14751,x14753),f383(x14752,x14753))
% 187.33/188.06 [1476]~E(x14761,x14762)+E(f383(x14763,x14761),f383(x14763,x14762))
% 187.33/188.06 [1477]~E(x14771,x14772)+E(f725(x14771,x14773,x14774,x14775),f725(x14772,x14773,x14774,x14775))
% 187.33/188.06 [1478]~E(x14781,x14782)+E(f725(x14783,x14781,x14784,x14785),f725(x14783,x14782,x14784,x14785))
% 187.33/188.06 [1479]~E(x14791,x14792)+E(f725(x14793,x14794,x14791,x14795),f725(x14793,x14794,x14792,x14795))
% 187.33/188.06 [1480]~E(x14801,x14802)+E(f725(x14803,x14804,x14805,x14801),f725(x14803,x14804,x14805,x14802))
% 187.33/188.06 [1481]~E(x14811,x14812)+E(f371(x14811,x14813),f371(x14812,x14813))
% 187.33/188.06 [1482]~E(x14821,x14822)+E(f371(x14823,x14821),f371(x14823,x14822))
% 187.33/188.06 [1483]~E(x14831,x14832)+E(f641(x14831,x14833,x14834),f641(x14832,x14833,x14834))
% 187.33/188.06 [1484]~E(x14841,x14842)+E(f641(x14843,x14841,x14844),f641(x14843,x14842,x14844))
% 187.33/188.06 [1485]~E(x14851,x14852)+E(f641(x14853,x14854,x14851),f641(x14853,x14854,x14852))
% 187.33/188.06 [1486]~E(x14861,x14862)+E(f486(x14861,x14863,x14864),f486(x14862,x14863,x14864))
% 187.33/188.06 [1487]~E(x14871,x14872)+E(f486(x14873,x14871,x14874),f486(x14873,x14872,x14874))
% 187.33/188.06 [1488]~E(x14881,x14882)+E(f486(x14883,x14884,x14881),f486(x14883,x14884,x14882))
% 187.33/188.06 [1489]~E(x14891,x14892)+E(f394(x14891,x14893,x14894,x14895),f394(x14892,x14893,x14894,x14895))
% 187.33/188.06 [1490]~E(x14901,x14902)+E(f394(x14903,x14901,x14904,x14905),f394(x14903,x14902,x14904,x14905))
% 187.33/188.06 [1491]~E(x14911,x14912)+E(f394(x14913,x14914,x14911,x14915),f394(x14913,x14914,x14912,x14915))
% 187.33/188.06 [1492]~E(x14921,x14922)+E(f394(x14923,x14924,x14925,x14921),f394(x14923,x14924,x14925,x14922))
% 187.33/188.06 [1493]~E(x14931,x14932)+E(f620(x14931,x14933,x14934,x14935),f620(x14932,x14933,x14934,x14935))
% 187.33/188.06 [1494]~E(x14941,x14942)+E(f620(x14943,x14941,x14944,x14945),f620(x14943,x14942,x14944,x14945))
% 187.33/188.06 [1495]~E(x14951,x14952)+E(f620(x14953,x14954,x14951,x14955),f620(x14953,x14954,x14952,x14955))
% 187.33/188.06 [1496]~E(x14961,x14962)+E(f620(x14963,x14964,x14965,x14961),f620(x14963,x14964,x14965,x14962))
% 187.33/188.06 [1497]~E(x14971,x14972)+E(f460(x14971,x14973),f460(x14972,x14973))
% 187.33/188.06 [1498]~E(x14981,x14982)+E(f460(x14983,x14981),f460(x14983,x14982))
% 187.33/188.06 [1499]~E(x14991,x14992)+E(f346(x14991,x14993),f346(x14992,x14993))
% 187.33/188.06 [1500]~E(x15001,x15002)+E(f346(x15003,x15001),f346(x15003,x15002))
% 187.33/188.06 [1501]~E(x15011,x15012)+E(f594(x15011,x15013,x15014),f594(x15012,x15013,x15014))
% 187.33/188.06 [1502]~E(x15021,x15022)+E(f594(x15023,x15021,x15024),f594(x15023,x15022,x15024))
% 187.33/188.06 [1503]~E(x15031,x15032)+E(f594(x15033,x15034,x15031),f594(x15033,x15034,x15032))
% 187.33/188.06 [1504]~E(x15041,x15042)+E(f678(x15041,x15043,x15044),f678(x15042,x15043,x15044))
% 187.33/188.06 [1505]~E(x15051,x15052)+E(f678(x15053,x15051,x15054),f678(x15053,x15052,x15054))
% 187.33/188.06 [1506]~E(x15061,x15062)+E(f678(x15063,x15064,x15061),f678(x15063,x15064,x15062))
% 187.33/188.06 [1507]~E(x15071,x15072)+E(f160(x15071,x15073),f160(x15072,x15073))
% 187.33/188.06 [1508]~E(x15081,x15082)+E(f160(x15083,x15081),f160(x15083,x15082))
% 187.33/188.06 [1509]~E(x15091,x15092)+E(f772(x15091,x15093,x15094,x15095,x15096,x15097,x15098,x15099),f772(x15092,x15093,x15094,x15095,x15096,x15097,x15098,x15099))
% 187.33/188.06 [1510]~E(x15101,x15102)+E(f772(x15103,x15101,x15104,x15105,x15106,x15107,x15108,x15109),f772(x15103,x15102,x15104,x15105,x15106,x15107,x15108,x15109))
% 187.33/188.06 [1511]~E(x15111,x15112)+E(f772(x15113,x15114,x15111,x15115,x15116,x15117,x15118,x15119),f772(x15113,x15114,x15112,x15115,x15116,x15117,x15118,x15119))
% 187.33/188.06 [1512]~E(x15121,x15122)+E(f772(x15123,x15124,x15125,x15121,x15126,x15127,x15128,x15129),f772(x15123,x15124,x15125,x15122,x15126,x15127,x15128,x15129))
% 187.33/188.06 [1513]~E(x15131,x15132)+E(f772(x15133,x15134,x15135,x15136,x15131,x15137,x15138,x15139),f772(x15133,x15134,x15135,x15136,x15132,x15137,x15138,x15139))
% 187.33/188.06 [1514]~E(x15141,x15142)+E(f772(x15143,x15144,x15145,x15146,x15147,x15141,x15148,x15149),f772(x15143,x15144,x15145,x15146,x15147,x15142,x15148,x15149))
% 187.33/188.06 [1515]~E(x15151,x15152)+E(f772(x15153,x15154,x15155,x15156,x15157,x15158,x15151,x15159),f772(x15153,x15154,x15155,x15156,x15157,x15158,x15152,x15159))
% 187.33/188.06 [1516]~E(x15161,x15162)+E(f772(x15163,x15164,x15165,x15166,x15167,x15168,x15169,x15161),f772(x15163,x15164,x15165,x15166,x15167,x15168,x15169,x15162))
% 187.33/188.06 [1517]~E(x15171,x15172)+E(f406(x15171,x15173,x15174,x15175),f406(x15172,x15173,x15174,x15175))
% 187.33/188.06 [1518]~E(x15181,x15182)+E(f406(x15183,x15181,x15184,x15185),f406(x15183,x15182,x15184,x15185))
% 187.33/188.06 [1519]~E(x15191,x15192)+E(f406(x15193,x15194,x15191,x15195),f406(x15193,x15194,x15192,x15195))
% 187.33/188.06 [1520]~E(x15201,x15202)+E(f406(x15203,x15204,x15205,x15201),f406(x15203,x15204,x15205,x15202))
% 187.33/188.06 [1521]~E(x15211,x15212)+E(f744(x15211,x15213),f744(x15212,x15213))
% 187.33/188.06 [1522]~E(x15221,x15222)+E(f744(x15223,x15221),f744(x15223,x15222))
% 187.33/188.06 [1523]~E(x15231,x15232)+E(f403(x15231,x15233,x15234,x15235),f403(x15232,x15233,x15234,x15235))
% 187.33/188.06 [1524]~E(x15241,x15242)+E(f403(x15243,x15241,x15244,x15245),f403(x15243,x15242,x15244,x15245))
% 187.33/188.06 [1525]~E(x15251,x15252)+E(f403(x15253,x15254,x15251,x15255),f403(x15253,x15254,x15252,x15255))
% 187.33/188.06 [1526]~E(x15261,x15262)+E(f403(x15263,x15264,x15265,x15261),f403(x15263,x15264,x15265,x15262))
% 187.33/188.06 [1527]~E(x15271,x15272)+E(f17(x15271,x15273,x15274,x15275),f17(x15272,x15273,x15274,x15275))
% 187.33/188.06 [1528]~E(x15281,x15282)+E(f17(x15283,x15281,x15284,x15285),f17(x15283,x15282,x15284,x15285))
% 187.33/188.06 [1529]~E(x15291,x15292)+E(f17(x15293,x15294,x15291,x15295),f17(x15293,x15294,x15292,x15295))
% 187.33/188.06 [1530]~E(x15301,x15302)+E(f17(x15303,x15304,x15305,x15301),f17(x15303,x15304,x15305,x15302))
% 187.33/188.06 [1531]~E(x15311,x15312)+E(f787(x15311,x15313,x15314,x15315,x15316),f787(x15312,x15313,x15314,x15315,x15316))
% 187.33/188.06 [1532]~E(x15321,x15322)+E(f787(x15323,x15321,x15324,x15325,x15326),f787(x15323,x15322,x15324,x15325,x15326))
% 187.33/188.06 [1533]~E(x15331,x15332)+E(f787(x15333,x15334,x15331,x15335,x15336),f787(x15333,x15334,x15332,x15335,x15336))
% 187.33/188.06 [1534]~E(x15341,x15342)+E(f787(x15343,x15344,x15345,x15341,x15346),f787(x15343,x15344,x15345,x15342,x15346))
% 187.33/188.06 [1535]~E(x15351,x15352)+E(f787(x15353,x15354,x15355,x15356,x15351),f787(x15353,x15354,x15355,x15356,x15352))
% 187.33/188.06 [1536]~E(x15361,x15362)+E(f638(x15361,x15363,x15364),f638(x15362,x15363,x15364))
% 187.33/188.06 [1537]~E(x15371,x15372)+E(f638(x15373,x15371,x15374),f638(x15373,x15372,x15374))
% 187.33/188.06 [1538]~E(x15381,x15382)+E(f638(x15383,x15384,x15381),f638(x15383,x15384,x15382))
% 187.33/188.06 [1539]~E(x15391,x15392)+E(f669(x15391,x15393,x15394,x15395),f669(x15392,x15393,x15394,x15395))
% 187.33/188.06 [1540]~E(x15401,x15402)+E(f669(x15403,x15401,x15404,x15405),f669(x15403,x15402,x15404,x15405))
% 187.33/188.06 [1541]~E(x15411,x15412)+E(f669(x15413,x15414,x15411,x15415),f669(x15413,x15414,x15412,x15415))
% 187.33/188.06 [1542]~E(x15421,x15422)+E(f669(x15423,x15424,x15425,x15421),f669(x15423,x15424,x15425,x15422))
% 187.33/188.06 [1543]~E(x15431,x15432)+E(f354(x15431),f354(x15432))
% 187.33/188.06 [1544]~E(x15441,x15442)+E(f473(x15441,x15443,x15444),f473(x15442,x15443,x15444))
% 187.33/188.06 [1545]~E(x15451,x15452)+E(f473(x15453,x15451,x15454),f473(x15453,x15452,x15454))
% 187.33/188.06 [1546]~E(x15461,x15462)+E(f473(x15463,x15464,x15461),f473(x15463,x15464,x15462))
% 187.33/188.06 [1547]~E(x15471,x15472)+E(f599(x15471,x15473,x15474),f599(x15472,x15473,x15474))
% 187.33/188.06 [1548]~E(x15481,x15482)+E(f599(x15483,x15481,x15484),f599(x15483,x15482,x15484))
% 187.33/188.06 [1549]~E(x15491,x15492)+E(f599(x15493,x15494,x15491),f599(x15493,x15494,x15492))
% 187.33/188.06 [1550]~E(x15501,x15502)+E(f333(x15501,x15503,x15504,x15505),f333(x15502,x15503,x15504,x15505))
% 187.33/188.06 [1551]~E(x15511,x15512)+E(f333(x15513,x15511,x15514,x15515),f333(x15513,x15512,x15514,x15515))
% 187.33/188.06 [1552]~E(x15521,x15522)+E(f333(x15523,x15524,x15521,x15525),f333(x15523,x15524,x15522,x15525))
% 187.33/188.06 [1553]~E(x15531,x15532)+E(f333(x15533,x15534,x15535,x15531),f333(x15533,x15534,x15535,x15532))
% 187.33/188.06 [1554]~E(x15541,x15542)+E(f255(x15541,x15543,x15544),f255(x15542,x15543,x15544))
% 187.33/188.06 [1555]~E(x15551,x15552)+E(f255(x15553,x15551,x15554),f255(x15553,x15552,x15554))
% 187.33/188.06 [1556]~E(x15561,x15562)+E(f255(x15563,x15564,x15561),f255(x15563,x15564,x15562))
% 187.33/188.06 [1557]~E(x15571,x15572)+E(f746(x15571,x15573,x15574),f746(x15572,x15573,x15574))
% 187.33/188.06 [1558]~E(x15581,x15582)+E(f746(x15583,x15581,x15584),f746(x15583,x15582,x15584))
% 187.33/188.06 [1559]~E(x15591,x15592)+E(f746(x15593,x15594,x15591),f746(x15593,x15594,x15592))
% 187.33/188.06 [1560]~E(x15601,x15602)+E(f640(x15601,x15603,x15604),f640(x15602,x15603,x15604))
% 187.33/188.06 [1561]~E(x15611,x15612)+E(f640(x15613,x15611,x15614),f640(x15613,x15612,x15614))
% 187.33/188.06 [1562]~E(x15621,x15622)+E(f640(x15623,x15624,x15621),f640(x15623,x15624,x15622))
% 187.33/188.06 [1563]~E(x15631,x15632)+E(f475(x15631,x15633,x15634),f475(x15632,x15633,x15634))
% 187.33/188.06 [1564]~E(x15641,x15642)+E(f475(x15643,x15641,x15644),f475(x15643,x15642,x15644))
% 187.33/188.06 [1565]~E(x15651,x15652)+E(f475(x15653,x15654,x15651),f475(x15653,x15654,x15652))
% 187.33/188.06 [1566]~E(x15661,x15662)+E(f811(x15661,x15663,x15664,x15665),f811(x15662,x15663,x15664,x15665))
% 187.33/188.06 [1567]~E(x15671,x15672)+E(f811(x15673,x15671,x15674,x15675),f811(x15673,x15672,x15674,x15675))
% 187.33/188.06 [1568]~E(x15681,x15682)+E(f811(x15683,x15684,x15681,x15685),f811(x15683,x15684,x15682,x15685))
% 187.33/188.06 [1569]~E(x15691,x15692)+E(f811(x15693,x15694,x15695,x15691),f811(x15693,x15694,x15695,x15692))
% 187.33/188.06 [1570]~E(x15701,x15702)+E(f343(x15701,x15703,x15704,x15705),f343(x15702,x15703,x15704,x15705))
% 187.33/188.06 [1571]~E(x15711,x15712)+E(f343(x15713,x15711,x15714,x15715),f343(x15713,x15712,x15714,x15715))
% 187.33/188.06 [1572]~E(x15721,x15722)+E(f343(x15723,x15724,x15721,x15725),f343(x15723,x15724,x15722,x15725))
% 187.33/188.06 [1573]~E(x15731,x15732)+E(f343(x15733,x15734,x15735,x15731),f343(x15733,x15734,x15735,x15732))
% 187.33/188.06 [1574]~E(x15741,x15742)+E(f690(x15741),f690(x15742))
% 187.33/188.06 [1575]~E(x15751,x15752)+E(f539(x15751,x15753,x15754,x15755,x15756,x15757),f539(x15752,x15753,x15754,x15755,x15756,x15757))
% 187.33/188.06 [1576]~E(x15761,x15762)+E(f539(x15763,x15761,x15764,x15765,x15766,x15767),f539(x15763,x15762,x15764,x15765,x15766,x15767))
% 187.33/188.06 [1577]~E(x15771,x15772)+E(f539(x15773,x15774,x15771,x15775,x15776,x15777),f539(x15773,x15774,x15772,x15775,x15776,x15777))
% 187.33/188.06 [1578]~E(x15781,x15782)+E(f539(x15783,x15784,x15785,x15781,x15786,x15787),f539(x15783,x15784,x15785,x15782,x15786,x15787))
% 187.33/188.06 [1579]~E(x15791,x15792)+E(f539(x15793,x15794,x15795,x15796,x15791,x15797),f539(x15793,x15794,x15795,x15796,x15792,x15797))
% 187.33/188.06 [1580]~E(x15801,x15802)+E(f539(x15803,x15804,x15805,x15806,x15807,x15801),f539(x15803,x15804,x15805,x15806,x15807,x15802))
% 187.33/188.06 [1581]~E(x15811,x15812)+E(f271(x15811,x15813,x15814,x15815,x15816),f271(x15812,x15813,x15814,x15815,x15816))
% 187.33/188.06 [1582]~E(x15821,x15822)+E(f271(x15823,x15821,x15824,x15825,x15826),f271(x15823,x15822,x15824,x15825,x15826))
% 187.33/188.06 [1583]~E(x15831,x15832)+E(f271(x15833,x15834,x15831,x15835,x15836),f271(x15833,x15834,x15832,x15835,x15836))
% 187.33/188.06 [1584]~E(x15841,x15842)+E(f271(x15843,x15844,x15845,x15841,x15846),f271(x15843,x15844,x15845,x15842,x15846))
% 187.33/188.06 [1585]~E(x15851,x15852)+E(f271(x15853,x15854,x15855,x15856,x15851),f271(x15853,x15854,x15855,x15856,x15852))
% 187.33/188.06 [1586]~E(x15861,x15862)+E(f203(x15861,x15863,x15864,x15865),f203(x15862,x15863,x15864,x15865))
% 187.33/188.06 [1587]~E(x15871,x15872)+E(f203(x15873,x15871,x15874,x15875),f203(x15873,x15872,x15874,x15875))
% 187.33/188.06 [1588]~E(x15881,x15882)+E(f203(x15883,x15884,x15881,x15885),f203(x15883,x15884,x15882,x15885))
% 187.33/188.06 [1589]~E(x15891,x15892)+E(f203(x15893,x15894,x15895,x15891),f203(x15893,x15894,x15895,x15892))
% 187.33/188.06 [1590]~E(x15901,x15902)+E(f560(x15901,x15903,x15904),f560(x15902,x15903,x15904))
% 187.33/188.06 [1591]~E(x15911,x15912)+E(f560(x15913,x15911,x15914),f560(x15913,x15912,x15914))
% 187.33/188.06 [1592]~E(x15921,x15922)+E(f560(x15923,x15924,x15921),f560(x15923,x15924,x15922))
% 187.33/188.06 [1593]~E(x15931,x15932)+E(f710(x15931,x15933,x15934,x15935,x15936,x15937,x15938),f710(x15932,x15933,x15934,x15935,x15936,x15937,x15938))
% 187.33/188.06 [1594]~E(x15941,x15942)+E(f710(x15943,x15941,x15944,x15945,x15946,x15947,x15948),f710(x15943,x15942,x15944,x15945,x15946,x15947,x15948))
% 187.33/188.06 [1595]~E(x15951,x15952)+E(f710(x15953,x15954,x15951,x15955,x15956,x15957,x15958),f710(x15953,x15954,x15952,x15955,x15956,x15957,x15958))
% 187.33/188.06 [1596]~E(x15961,x15962)+E(f710(x15963,x15964,x15965,x15961,x15966,x15967,x15968),f710(x15963,x15964,x15965,x15962,x15966,x15967,x15968))
% 187.33/188.06 [1597]~E(x15971,x15972)+E(f710(x15973,x15974,x15975,x15976,x15971,x15977,x15978),f710(x15973,x15974,x15975,x15976,x15972,x15977,x15978))
% 187.33/188.06 [1598]~E(x15981,x15982)+E(f710(x15983,x15984,x15985,x15986,x15987,x15981,x15988),f710(x15983,x15984,x15985,x15986,x15987,x15982,x15988))
% 187.33/188.06 [1599]~E(x15991,x15992)+E(f710(x15993,x15994,x15995,x15996,x15997,x15998,x15991),f710(x15993,x15994,x15995,x15996,x15997,x15998,x15992))
% 187.33/188.06 [1600]~E(x16001,x16002)+E(f129(x16001),f129(x16002))
% 187.33/188.06 [1601]~E(x16011,x16012)+E(f370(x16011,x16013),f370(x16012,x16013))
% 187.33/188.06 [1602]~E(x16021,x16022)+E(f370(x16023,x16021),f370(x16023,x16022))
% 187.33/188.06 [1603]~E(x16031,x16032)+E(f711(x16031,x16033,x16034,x16035,x16036),f711(x16032,x16033,x16034,x16035,x16036))
% 187.33/188.06 [1604]~E(x16041,x16042)+E(f711(x16043,x16041,x16044,x16045,x16046),f711(x16043,x16042,x16044,x16045,x16046))
% 187.33/188.06 [1605]~E(x16051,x16052)+E(f711(x16053,x16054,x16051,x16055,x16056),f711(x16053,x16054,x16052,x16055,x16056))
% 187.33/188.06 [1606]~E(x16061,x16062)+E(f711(x16063,x16064,x16065,x16061,x16066),f711(x16063,x16064,x16065,x16062,x16066))
% 187.33/188.06 [1607]~E(x16071,x16072)+E(f711(x16073,x16074,x16075,x16076,x16071),f711(x16073,x16074,x16075,x16076,x16072))
% 187.33/188.06 [1608]~E(x16081,x16082)+E(f857(x16081,x16083,x16084),f857(x16082,x16083,x16084))
% 187.33/188.06 [1609]~E(x16091,x16092)+E(f857(x16093,x16091,x16094),f857(x16093,x16092,x16094))
% 187.33/188.06 [1610]~E(x16101,x16102)+E(f857(x16103,x16104,x16101),f857(x16103,x16104,x16102))
% 187.33/188.06 [1611]~E(x16111,x16112)+E(f752(x16111,x16113,x16114),f752(x16112,x16113,x16114))
% 187.33/188.06 [1612]~E(x16121,x16122)+E(f752(x16123,x16121,x16124),f752(x16123,x16122,x16124))
% 187.33/188.06 [1613]~E(x16131,x16132)+E(f752(x16133,x16134,x16131),f752(x16133,x16134,x16132))
% 187.33/188.06 [1614]~E(x16141,x16142)+E(f76(x16141,x16143,x16144,x16145,x16146),f76(x16142,x16143,x16144,x16145,x16146))
% 187.33/188.06 [1615]~E(x16151,x16152)+E(f76(x16153,x16151,x16154,x16155,x16156),f76(x16153,x16152,x16154,x16155,x16156))
% 187.33/188.06 [1616]~E(x16161,x16162)+E(f76(x16163,x16164,x16161,x16165,x16166),f76(x16163,x16164,x16162,x16165,x16166))
% 187.33/188.06 [1617]~E(x16171,x16172)+E(f76(x16173,x16174,x16175,x16171,x16176),f76(x16173,x16174,x16175,x16172,x16176))
% 187.33/188.06 [1618]~E(x16181,x16182)+E(f76(x16183,x16184,x16185,x16186,x16181),f76(x16183,x16184,x16185,x16186,x16182))
% 187.33/188.06 [1619]~E(x16191,x16192)+E(f800(x16191,x16193,x16194),f800(x16192,x16193,x16194))
% 187.33/188.06 [1620]~E(x16201,x16202)+E(f800(x16203,x16201,x16204),f800(x16203,x16202,x16204))
% 187.33/188.06 [1621]~E(x16211,x16212)+E(f800(x16213,x16214,x16211),f800(x16213,x16214,x16212))
% 187.33/188.06 [1622]~E(x16221,x16222)+E(f464(x16221,x16223),f464(x16222,x16223))
% 187.33/188.06 [1623]~E(x16231,x16232)+E(f464(x16233,x16231),f464(x16233,x16232))
% 187.33/188.06 [1624]~E(x16241,x16242)+E(f653(x16241,x16243,x16244),f653(x16242,x16243,x16244))
% 187.33/188.06 [1625]~E(x16251,x16252)+E(f653(x16253,x16251,x16254),f653(x16253,x16252,x16254))
% 187.33/188.06 [1626]~E(x16261,x16262)+E(f653(x16263,x16264,x16261),f653(x16263,x16264,x16262))
% 187.33/188.06 [1627]~E(x16271,x16272)+E(f558(x16271,x16273,x16274,x16275,x16276),f558(x16272,x16273,x16274,x16275,x16276))
% 187.33/188.06 [1628]~E(x16281,x16282)+E(f558(x16283,x16281,x16284,x16285,x16286),f558(x16283,x16282,x16284,x16285,x16286))
% 187.33/188.06 [1629]~E(x16291,x16292)+E(f558(x16293,x16294,x16291,x16295,x16296),f558(x16293,x16294,x16292,x16295,x16296))
% 187.33/188.06 [1630]~E(x16301,x16302)+E(f558(x16303,x16304,x16305,x16301,x16306),f558(x16303,x16304,x16305,x16302,x16306))
% 187.33/188.06 [1631]~E(x16311,x16312)+E(f558(x16313,x16314,x16315,x16316,x16311),f558(x16313,x16314,x16315,x16316,x16312))
% 187.33/188.06 [1632]~E(x16321,x16322)+E(f233(x16321,x16323,x16324),f233(x16322,x16323,x16324))
% 187.33/188.06 [1633]~E(x16331,x16332)+E(f233(x16333,x16331,x16334),f233(x16333,x16332,x16334))
% 187.33/188.06 [1634]~E(x16341,x16342)+E(f233(x16343,x16344,x16341),f233(x16343,x16344,x16342))
% 187.33/188.06 [1635]~E(x16351,x16352)+E(f621(x16351,x16353,x16354,x16355,x16356),f621(x16352,x16353,x16354,x16355,x16356))
% 187.33/188.06 [1636]~E(x16361,x16362)+E(f621(x16363,x16361,x16364,x16365,x16366),f621(x16363,x16362,x16364,x16365,x16366))
% 187.33/188.06 [1637]~E(x16371,x16372)+E(f621(x16373,x16374,x16371,x16375,x16376),f621(x16373,x16374,x16372,x16375,x16376))
% 187.33/188.06 [1638]~E(x16381,x16382)+E(f621(x16383,x16384,x16385,x16381,x16386),f621(x16383,x16384,x16385,x16382,x16386))
% 187.33/188.06 [1639]~E(x16391,x16392)+E(f621(x16393,x16394,x16395,x16396,x16391),f621(x16393,x16394,x16395,x16396,x16392))
% 187.33/188.06 [1640]~E(x16401,x16402)+E(f481(x16401,x16403,x16404),f481(x16402,x16403,x16404))
% 187.33/188.06 [1641]~E(x16411,x16412)+E(f481(x16413,x16411,x16414),f481(x16413,x16412,x16414))
% 187.33/188.06 [1642]~E(x16421,x16422)+E(f481(x16423,x16424,x16421),f481(x16423,x16424,x16422))
% 187.33/188.06 [1643]~E(x16431,x16432)+E(f832(x16431,x16433,x16434),f832(x16432,x16433,x16434))
% 187.33/188.06 [1644]~E(x16441,x16442)+E(f832(x16443,x16441,x16444),f832(x16443,x16442,x16444))
% 187.33/188.06 [1645]~E(x16451,x16452)+E(f832(x16453,x16454,x16451),f832(x16453,x16454,x16452))
% 187.33/188.06 [1646]~E(x16461,x16462)+E(f510(x16461,x16463,x16464,x16465),f510(x16462,x16463,x16464,x16465))
% 187.33/188.06 [1647]~E(x16471,x16472)+E(f510(x16473,x16471,x16474,x16475),f510(x16473,x16472,x16474,x16475))
% 187.33/188.06 [1648]~E(x16481,x16482)+E(f510(x16483,x16484,x16481,x16485),f510(x16483,x16484,x16482,x16485))
% 187.33/188.06 [1649]~E(x16491,x16492)+E(f510(x16493,x16494,x16495,x16491),f510(x16493,x16494,x16495,x16492))
% 187.33/188.06 [1650]~E(x16501,x16502)+E(f497(x16501,x16503,x16504,x16505),f497(x16502,x16503,x16504,x16505))
% 187.33/188.06 [1651]~E(x16511,x16512)+E(f497(x16513,x16511,x16514,x16515),f497(x16513,x16512,x16514,x16515))
% 187.33/188.06 [1652]~E(x16521,x16522)+E(f497(x16523,x16524,x16521,x16525),f497(x16523,x16524,x16522,x16525))
% 187.33/188.06 [1653]~E(x16531,x16532)+E(f497(x16533,x16534,x16535,x16531),f497(x16533,x16534,x16535,x16532))
% 187.33/188.06 [1654]~E(x16541,x16542)+E(f776(x16541,x16543,x16544,x16545,x16546),f776(x16542,x16543,x16544,x16545,x16546))
% 187.33/188.06 [1655]~E(x16551,x16552)+E(f776(x16553,x16551,x16554,x16555,x16556),f776(x16553,x16552,x16554,x16555,x16556))
% 187.33/188.06 [1656]~E(x16561,x16562)+E(f776(x16563,x16564,x16561,x16565,x16566),f776(x16563,x16564,x16562,x16565,x16566))
% 187.33/188.06 [1657]~E(x16571,x16572)+E(f776(x16573,x16574,x16575,x16571,x16576),f776(x16573,x16574,x16575,x16572,x16576))
% 187.33/188.06 [1658]~E(x16581,x16582)+E(f776(x16583,x16584,x16585,x16586,x16581),f776(x16583,x16584,x16585,x16586,x16582))
% 187.33/188.06 [1659]~E(x16591,x16592)+E(f548(x16591,x16593,x16594),f548(x16592,x16593,x16594))
% 187.33/188.06 [1660]~E(x16601,x16602)+E(f548(x16603,x16601,x16604),f548(x16603,x16602,x16604))
% 187.33/188.06 [1661]~E(x16611,x16612)+E(f548(x16613,x16614,x16611),f548(x16613,x16614,x16612))
% 187.33/188.06 [1662]~E(x16621,x16622)+E(f618(x16621,x16623),f618(x16622,x16623))
% 187.33/188.06 [1663]~E(x16631,x16632)+E(f618(x16633,x16631),f618(x16633,x16632))
% 187.33/188.06 [1664]~E(x16641,x16642)+E(f387(x16641,x16643,x16644,x16645),f387(x16642,x16643,x16644,x16645))
% 187.33/188.06 [1665]~E(x16651,x16652)+E(f387(x16653,x16651,x16654,x16655),f387(x16653,x16652,x16654,x16655))
% 187.33/188.06 [1666]~E(x16661,x16662)+E(f387(x16663,x16664,x16661,x16665),f387(x16663,x16664,x16662,x16665))
% 187.33/188.06 [1667]~E(x16671,x16672)+E(f387(x16673,x16674,x16675,x16671),f387(x16673,x16674,x16675,x16672))
% 187.33/188.06 [1668]~E(x16681,x16682)+E(f742(x16681,x16683,x16684),f742(x16682,x16683,x16684))
% 187.33/188.06 [1669]~E(x16691,x16692)+E(f742(x16693,x16691,x16694),f742(x16693,x16692,x16694))
% 187.33/188.06 [1670]~E(x16701,x16702)+E(f742(x16703,x16704,x16701),f742(x16703,x16704,x16702))
% 187.33/188.06 [1671]~E(x16711,x16712)+E(f447(x16711,x16713,x16714),f447(x16712,x16713,x16714))
% 187.33/188.06 [1672]~E(x16721,x16722)+E(f447(x16723,x16721,x16724),f447(x16723,x16722,x16724))
% 187.33/188.06 [1673]~E(x16731,x16732)+E(f447(x16733,x16734,x16731),f447(x16733,x16734,x16732))
% 187.33/188.06 [1674]~E(x16741,x16742)+E(f530(x16741,x16743,x16744,x16745),f530(x16742,x16743,x16744,x16745))
% 187.33/188.06 [1675]~E(x16751,x16752)+E(f530(x16753,x16751,x16754,x16755),f530(x16753,x16752,x16754,x16755))
% 187.33/188.06 [1676]~E(x16761,x16762)+E(f530(x16763,x16764,x16761,x16765),f530(x16763,x16764,x16762,x16765))
% 187.33/188.06 [1677]~E(x16771,x16772)+E(f530(x16773,x16774,x16775,x16771),f530(x16773,x16774,x16775,x16772))
% 187.33/188.06 [1678]~E(x16781,x16782)+E(f854(x16781,x16783),f854(x16782,x16783))
% 187.33/188.06 [1679]~E(x16791,x16792)+E(f854(x16793,x16791),f854(x16793,x16792))
% 187.33/188.06 [1680]~E(x16801,x16802)+E(f452(x16801,x16803,x16804),f452(x16802,x16803,x16804))
% 187.33/188.06 [1681]~E(x16811,x16812)+E(f452(x16813,x16811,x16814),f452(x16813,x16812,x16814))
% 187.33/188.06 [1682]~E(x16821,x16822)+E(f452(x16823,x16824,x16821),f452(x16823,x16824,x16822))
% 187.33/188.06 [1683]~E(x16831,x16832)+E(f480(x16831,x16833),f480(x16832,x16833))
% 187.33/188.06 [1684]~E(x16841,x16842)+E(f480(x16843,x16841),f480(x16843,x16842))
% 187.33/188.06 [1685]~E(x16851,x16852)+E(f444(x16851,x16853,x16854,x16855),f444(x16852,x16853,x16854,x16855))
% 187.33/188.06 [1686]~E(x16861,x16862)+E(f444(x16863,x16861,x16864,x16865),f444(x16863,x16862,x16864,x16865))
% 187.33/188.06 [1687]~E(x16871,x16872)+E(f444(x16873,x16874,x16871,x16875),f444(x16873,x16874,x16872,x16875))
% 187.33/188.06 [1688]~E(x16881,x16882)+E(f444(x16883,x16884,x16885,x16881),f444(x16883,x16884,x16885,x16882))
% 187.33/188.06 [1689]~E(x16891,x16892)+E(f277(x16891,x16893),f277(x16892,x16893))
% 187.33/188.06 [1690]~E(x16901,x16902)+E(f277(x16903,x16901),f277(x16903,x16902))
% 187.33/188.06 [1691]~E(x16911,x16912)+E(f821(x16911,x16913),f821(x16912,x16913))
% 187.33/188.06 [1692]~E(x16921,x16922)+E(f821(x16923,x16921),f821(x16923,x16922))
% 187.33/188.06 [1693]~E(x16931,x16932)+E(f479(x16931,x16933,x16934),f479(x16932,x16933,x16934))
% 187.33/188.06 [1694]~E(x16941,x16942)+E(f479(x16943,x16941,x16944),f479(x16943,x16942,x16944))
% 187.33/188.06 [1695]~E(x16951,x16952)+E(f479(x16953,x16954,x16951),f479(x16953,x16954,x16952))
% 187.33/188.06 [1696]~E(x16961,x16962)+E(f628(x16961,x16963,x16964,x16965,x16966,x16967,x16968),f628(x16962,x16963,x16964,x16965,x16966,x16967,x16968))
% 187.33/188.06 [1697]~E(x16971,x16972)+E(f628(x16973,x16971,x16974,x16975,x16976,x16977,x16978),f628(x16973,x16972,x16974,x16975,x16976,x16977,x16978))
% 187.33/188.06 [1698]~E(x16981,x16982)+E(f628(x16983,x16984,x16981,x16985,x16986,x16987,x16988),f628(x16983,x16984,x16982,x16985,x16986,x16987,x16988))
% 187.33/188.06 [1699]~E(x16991,x16992)+E(f628(x16993,x16994,x16995,x16991,x16996,x16997,x16998),f628(x16993,x16994,x16995,x16992,x16996,x16997,x16998))
% 187.33/188.06 [1700]~E(x17001,x17002)+E(f628(x17003,x17004,x17005,x17006,x17001,x17007,x17008),f628(x17003,x17004,x17005,x17006,x17002,x17007,x17008))
% 187.33/188.06 [1701]~E(x17011,x17012)+E(f628(x17013,x17014,x17015,x17016,x17017,x17011,x17018),f628(x17013,x17014,x17015,x17016,x17017,x17012,x17018))
% 187.33/188.06 [1702]~E(x17021,x17022)+E(f628(x17023,x17024,x17025,x17026,x17027,x17028,x17021),f628(x17023,x17024,x17025,x17026,x17027,x17028,x17022))
% 187.33/188.06 [1703]~E(x17031,x17032)+E(f434(x17031,x17033,x17034,x17035,x17036),f434(x17032,x17033,x17034,x17035,x17036))
% 187.33/188.06 [1704]~E(x17041,x17042)+E(f434(x17043,x17041,x17044,x17045,x17046),f434(x17043,x17042,x17044,x17045,x17046))
% 187.33/188.06 [1705]~E(x17051,x17052)+E(f434(x17053,x17054,x17051,x17055,x17056),f434(x17053,x17054,x17052,x17055,x17056))
% 187.33/188.06 [1706]~E(x17061,x17062)+E(f434(x17063,x17064,x17065,x17061,x17066),f434(x17063,x17064,x17065,x17062,x17066))
% 187.33/188.06 [1707]~E(x17071,x17072)+E(f434(x17073,x17074,x17075,x17076,x17071),f434(x17073,x17074,x17075,x17076,x17072))
% 187.33/188.06 [1708]~E(x17081,x17082)+E(f779(x17081,x17083,x17084),f779(x17082,x17083,x17084))
% 187.33/188.06 [1709]~E(x17091,x17092)+E(f779(x17093,x17091,x17094),f779(x17093,x17092,x17094))
% 187.33/188.06 [1710]~E(x17101,x17102)+E(f779(x17103,x17104,x17101),f779(x17103,x17104,x17102))
% 187.33/188.06 [1711]~E(x17111,x17112)+E(f356(x17111),f356(x17112))
% 187.33/188.06 [1712]~E(x17121,x17122)+E(f590(x17121,x17123),f590(x17122,x17123))
% 187.33/188.06 [1713]~E(x17131,x17132)+E(f590(x17133,x17131),f590(x17133,x17132))
% 187.33/188.06 [1714]~E(x17141,x17142)+E(f761(x17141,x17143),f761(x17142,x17143))
% 187.33/188.06 [1715]~E(x17151,x17152)+E(f761(x17153,x17151),f761(x17153,x17152))
% 187.33/188.06 [1716]~E(x17161,x17162)+E(f422(x17161,x17163,x17164,x17165),f422(x17162,x17163,x17164,x17165))
% 187.33/188.06 [1717]~E(x17171,x17172)+E(f422(x17173,x17171,x17174,x17175),f422(x17173,x17172,x17174,x17175))
% 187.33/188.06 [1718]~E(x17181,x17182)+E(f422(x17183,x17184,x17181,x17185),f422(x17183,x17184,x17182,x17185))
% 187.33/188.06 [1719]~E(x17191,x17192)+E(f422(x17193,x17194,x17195,x17191),f422(x17193,x17194,x17195,x17192))
% 187.33/188.06 [1720]~E(x17201,x17202)+E(f471(x17201,x17203,x17204,x17205,x17206,x17207),f471(x17202,x17203,x17204,x17205,x17206,x17207))
% 187.33/188.06 [1721]~E(x17211,x17212)+E(f471(x17213,x17211,x17214,x17215,x17216,x17217),f471(x17213,x17212,x17214,x17215,x17216,x17217))
% 187.33/188.06 [1722]~E(x17221,x17222)+E(f471(x17223,x17224,x17221,x17225,x17226,x17227),f471(x17223,x17224,x17222,x17225,x17226,x17227))
% 187.33/188.06 [1723]~E(x17231,x17232)+E(f471(x17233,x17234,x17235,x17231,x17236,x17237),f471(x17233,x17234,x17235,x17232,x17236,x17237))
% 187.33/188.06 [1724]~E(x17241,x17242)+E(f471(x17243,x17244,x17245,x17246,x17241,x17247),f471(x17243,x17244,x17245,x17246,x17242,x17247))
% 187.33/188.06 [1725]~E(x17251,x17252)+E(f471(x17253,x17254,x17255,x17256,x17257,x17251),f471(x17253,x17254,x17255,x17256,x17257,x17252))
% 187.33/188.06 [1726]~E(x17261,x17262)+E(f410(x17261,x17263),f410(x17262,x17263))
% 187.33/188.06 [1727]~E(x17271,x17272)+E(f410(x17273,x17271),f410(x17273,x17272))
% 187.33/188.06 [1728]~E(x17281,x17282)+E(f686(x17281,x17283,x17284,x17285),f686(x17282,x17283,x17284,x17285))
% 187.33/188.06 [1729]~E(x17291,x17292)+E(f686(x17293,x17291,x17294,x17295),f686(x17293,x17292,x17294,x17295))
% 187.33/188.06 [1730]~E(x17301,x17302)+E(f686(x17303,x17304,x17301,x17305),f686(x17303,x17304,x17302,x17305))
% 187.33/188.06 [1731]~E(x17311,x17312)+E(f686(x17313,x17314,x17315,x17311),f686(x17313,x17314,x17315,x17312))
% 187.33/188.06 [1732]~E(x17321,x17322)+E(f868(x17321,x17323,x17324,x17325),f868(x17322,x17323,x17324,x17325))
% 187.33/188.06 [1733]~E(x17331,x17332)+E(f868(x17333,x17331,x17334,x17335),f868(x17333,x17332,x17334,x17335))
% 187.33/188.06 [1734]~E(x17341,x17342)+E(f868(x17343,x17344,x17341,x17345),f868(x17343,x17344,x17342,x17345))
% 187.33/188.06 [1735]~E(x17351,x17352)+E(f868(x17353,x17354,x17355,x17351),f868(x17353,x17354,x17355,x17352))
% 187.33/188.06 [1736]~E(x17361,x17362)+E(f722(x17361,x17363,x17364),f722(x17362,x17363,x17364))
% 187.33/188.06 [1737]~E(x17371,x17372)+E(f722(x17373,x17371,x17374),f722(x17373,x17372,x17374))
% 187.33/188.06 [1738]~E(x17381,x17382)+E(f722(x17383,x17384,x17381),f722(x17383,x17384,x17382))
% 187.33/188.06 [1739]~E(x17391,x17392)+E(f613(x17391,x17393,x17394,x17395,x17396),f613(x17392,x17393,x17394,x17395,x17396))
% 187.33/188.06 [1740]~E(x17401,x17402)+E(f613(x17403,x17401,x17404,x17405,x17406),f613(x17403,x17402,x17404,x17405,x17406))
% 187.33/188.06 [1741]~E(x17411,x17412)+E(f613(x17413,x17414,x17411,x17415,x17416),f613(x17413,x17414,x17412,x17415,x17416))
% 187.33/188.06 [1742]~E(x17421,x17422)+E(f613(x17423,x17424,x17425,x17421,x17426),f613(x17423,x17424,x17425,x17422,x17426))
% 187.33/188.06 [1743]~E(x17431,x17432)+E(f613(x17433,x17434,x17435,x17436,x17431),f613(x17433,x17434,x17435,x17436,x17432))
% 187.33/188.06 [1744]~E(x17441,x17442)+E(f723(x17441,x17443,x17444,x17445),f723(x17442,x17443,x17444,x17445))
% 187.33/188.06 [1745]~E(x17451,x17452)+E(f723(x17453,x17451,x17454,x17455),f723(x17453,x17452,x17454,x17455))
% 187.33/188.06 [1746]~E(x17461,x17462)+E(f723(x17463,x17464,x17461,x17465),f723(x17463,x17464,x17462,x17465))
% 187.33/188.06 [1747]~E(x17471,x17472)+E(f723(x17473,x17474,x17475,x17471),f723(x17473,x17474,x17475,x17472))
% 187.33/188.06 [1748]~E(x17481,x17482)+E(f840(x17481,x17483,x17484,x17485,x17486),f840(x17482,x17483,x17484,x17485,x17486))
% 187.33/188.06 [1749]~E(x17491,x17492)+E(f840(x17493,x17491,x17494,x17495,x17496),f840(x17493,x17492,x17494,x17495,x17496))
% 187.33/188.06 [1750]~E(x17501,x17502)+E(f840(x17503,x17504,x17501,x17505,x17506),f840(x17503,x17504,x17502,x17505,x17506))
% 187.33/188.06 [1751]~E(x17511,x17512)+E(f840(x17513,x17514,x17515,x17511,x17516),f840(x17513,x17514,x17515,x17512,x17516))
% 187.33/188.06 [1752]~E(x17521,x17522)+E(f840(x17523,x17524,x17525,x17526,x17521),f840(x17523,x17524,x17525,x17526,x17522))
% 187.33/188.06 [1753]~E(x17531,x17532)+E(f396(x17531,x17533,x17534,x17535),f396(x17532,x17533,x17534,x17535))
% 187.33/188.06 [1754]~E(x17541,x17542)+E(f396(x17543,x17541,x17544,x17545),f396(x17543,x17542,x17544,x17545))
% 187.33/188.06 [1755]~E(x17551,x17552)+E(f396(x17553,x17554,x17551,x17555),f396(x17553,x17554,x17552,x17555))
% 187.33/188.06 [1756]~E(x17561,x17562)+E(f396(x17563,x17564,x17565,x17561),f396(x17563,x17564,x17565,x17562))
% 187.33/188.06 [1757]~E(x17571,x17572)+E(f465(x17571,x17573),f465(x17572,x17573))
% 187.33/188.06 [1758]~E(x17581,x17582)+E(f465(x17583,x17581),f465(x17583,x17582))
% 187.33/188.06 [1759]~E(x17591,x17592)+E(f398(x17591,x17593,x17594,x17595),f398(x17592,x17593,x17594,x17595))
% 187.33/188.06 [1760]~E(x17601,x17602)+E(f398(x17603,x17601,x17604,x17605),f398(x17603,x17602,x17604,x17605))
% 187.33/188.06 [1761]~E(x17611,x17612)+E(f398(x17613,x17614,x17611,x17615),f398(x17613,x17614,x17612,x17615))
% 187.33/188.06 [1762]~E(x17621,x17622)+E(f398(x17623,x17624,x17625,x17621),f398(x17623,x17624,x17625,x17622))
% 187.33/188.06 [1763]~E(x17631,x17632)+E(f348(x17631,x17633,x17634),f348(x17632,x17633,x17634))
% 187.33/188.06 [1764]~E(x17641,x17642)+E(f348(x17643,x17641,x17644),f348(x17643,x17642,x17644))
% 187.33/188.06 [1765]~E(x17651,x17652)+E(f348(x17653,x17654,x17651),f348(x17653,x17654,x17652))
% 187.33/188.06 [1766]~E(x17661,x17662)+E(f672(x17661,x17663,x17664,x17665,x17666),f672(x17662,x17663,x17664,x17665,x17666))
% 187.33/188.06 [1767]~E(x17671,x17672)+E(f672(x17673,x17671,x17674,x17675,x17676),f672(x17673,x17672,x17674,x17675,x17676))
% 187.33/188.06 [1768]~E(x17681,x17682)+E(f672(x17683,x17684,x17681,x17685,x17686),f672(x17683,x17684,x17682,x17685,x17686))
% 187.33/188.06 [1769]~E(x17691,x17692)+E(f672(x17693,x17694,x17695,x17691,x17696),f672(x17693,x17694,x17695,x17692,x17696))
% 187.33/188.06 [1770]~E(x17701,x17702)+E(f672(x17703,x17704,x17705,x17706,x17701),f672(x17703,x17704,x17705,x17706,x17702))
% 187.33/188.06 [1771]~E(x17711,x17712)+E(f709(x17711,x17713,x17714),f709(x17712,x17713,x17714))
% 187.33/188.06 [1772]~E(x17721,x17722)+E(f709(x17723,x17721,x17724),f709(x17723,x17722,x17724))
% 187.33/188.06 [1773]~E(x17731,x17732)+E(f709(x17733,x17734,x17731),f709(x17733,x17734,x17732))
% 187.33/188.06 [1774]~E(x17741,x17742)+E(f429(x17741,x17743,x17744,x17745),f429(x17742,x17743,x17744,x17745))
% 187.33/188.06 [1775]~E(x17751,x17752)+E(f429(x17753,x17751,x17754,x17755),f429(x17753,x17752,x17754,x17755))
% 187.33/188.06 [1776]~E(x17761,x17762)+E(f429(x17763,x17764,x17761,x17765),f429(x17763,x17764,x17762,x17765))
% 187.33/188.06 [1777]~E(x17771,x17772)+E(f429(x17773,x17774,x17775,x17771),f429(x17773,x17774,x17775,x17772))
% 187.33/188.06 [1778]~E(x17781,x17782)+E(f573(x17781,x17783,x17784,x17785,x17786,x17787),f573(x17782,x17783,x17784,x17785,x17786,x17787))
% 187.33/188.06 [1779]~E(x17791,x17792)+E(f573(x17793,x17791,x17794,x17795,x17796,x17797),f573(x17793,x17792,x17794,x17795,x17796,x17797))
% 187.33/188.06 [1780]~E(x17801,x17802)+E(f573(x17803,x17804,x17801,x17805,x17806,x17807),f573(x17803,x17804,x17802,x17805,x17806,x17807))
% 187.33/188.06 [1781]~E(x17811,x17812)+E(f573(x17813,x17814,x17815,x17811,x17816,x17817),f573(x17813,x17814,x17815,x17812,x17816,x17817))
% 187.33/188.06 [1782]~E(x17821,x17822)+E(f573(x17823,x17824,x17825,x17826,x17821,x17827),f573(x17823,x17824,x17825,x17826,x17822,x17827))
% 187.33/188.06 [1783]~E(x17831,x17832)+E(f573(x17833,x17834,x17835,x17836,x17837,x17831),f573(x17833,x17834,x17835,x17836,x17837,x17832))
% 187.33/188.06 [1784]~E(x17841,x17842)+E(f626(x17841,x17843,x17844,x17845,x17846),f626(x17842,x17843,x17844,x17845,x17846))
% 187.33/188.06 [1785]~E(x17851,x17852)+E(f626(x17853,x17851,x17854,x17855,x17856),f626(x17853,x17852,x17854,x17855,x17856))
% 187.33/188.06 [1786]~E(x17861,x17862)+E(f626(x17863,x17864,x17861,x17865,x17866),f626(x17863,x17864,x17862,x17865,x17866))
% 187.33/188.06 [1787]~E(x17871,x17872)+E(f626(x17873,x17874,x17875,x17871,x17876),f626(x17873,x17874,x17875,x17872,x17876))
% 187.33/188.06 [1788]~E(x17881,x17882)+E(f626(x17883,x17884,x17885,x17886,x17881),f626(x17883,x17884,x17885,x17886,x17882))
% 187.33/188.06 [1789]~E(x17891,x17892)+E(f265(x17891,x17893,x17894,x17895,x17896),f265(x17892,x17893,x17894,x17895,x17896))
% 187.33/188.06 [1790]~E(x17901,x17902)+E(f265(x17903,x17901,x17904,x17905,x17906),f265(x17903,x17902,x17904,x17905,x17906))
% 187.33/188.06 [1791]~E(x17911,x17912)+E(f265(x17913,x17914,x17911,x17915,x17916),f265(x17913,x17914,x17912,x17915,x17916))
% 187.33/188.06 [1792]~E(x17921,x17922)+E(f265(x17923,x17924,x17925,x17921,x17926),f265(x17923,x17924,x17925,x17922,x17926))
% 187.33/188.06 [1793]~E(x17931,x17932)+E(f265(x17933,x17934,x17935,x17936,x17931),f265(x17933,x17934,x17935,x17936,x17932))
% 187.33/188.06 [1794]~E(x17941,x17942)+E(f212(x17941),f212(x17942))
% 187.33/188.06 [1795]~E(x17951,x17952)+E(f707(x17951,x17953,x17954),f707(x17952,x17953,x17954))
% 187.33/188.06 [1796]~E(x17961,x17962)+E(f707(x17963,x17961,x17964),f707(x17963,x17962,x17964))
% 187.33/188.06 [1797]~E(x17971,x17972)+E(f707(x17973,x17974,x17971),f707(x17973,x17974,x17972))
% 187.33/188.06 [1798]~E(x17981,x17982)+E(f714(x17981,x17983,x17984,x17985,x17986),f714(x17982,x17983,x17984,x17985,x17986))
% 187.33/188.06 [1799]~E(x17991,x17992)+E(f714(x17993,x17991,x17994,x17995,x17996),f714(x17993,x17992,x17994,x17995,x17996))
% 187.33/188.06 [1800]~E(x18001,x18002)+E(f714(x18003,x18004,x18001,x18005,x18006),f714(x18003,x18004,x18002,x18005,x18006))
% 187.33/188.06 [1801]~E(x18011,x18012)+E(f714(x18013,x18014,x18015,x18011,x18016),f714(x18013,x18014,x18015,x18012,x18016))
% 187.33/188.06 [1802]~E(x18021,x18022)+E(f714(x18023,x18024,x18025,x18026,x18021),f714(x18023,x18024,x18025,x18026,x18022))
% 187.33/188.06 [1803]~E(x18031,x18032)+E(f687(x18031,x18033,x18034,x18035),f687(x18032,x18033,x18034,x18035))
% 187.33/188.06 [1804]~E(x18041,x18042)+E(f687(x18043,x18041,x18044,x18045),f687(x18043,x18042,x18044,x18045))
% 187.33/188.06 [1805]~E(x18051,x18052)+E(f687(x18053,x18054,x18051,x18055),f687(x18053,x18054,x18052,x18055))
% 187.33/188.06 [1806]~E(x18061,x18062)+E(f687(x18063,x18064,x18065,x18061),f687(x18063,x18064,x18065,x18062))
% 187.33/188.06 [1807]~E(x18071,x18072)+E(f675(x18071,x18073,x18074),f675(x18072,x18073,x18074))
% 187.33/188.06 [1808]~E(x18081,x18082)+E(f675(x18083,x18081,x18084),f675(x18083,x18082,x18084))
% 187.33/188.06 [1809]~E(x18091,x18092)+E(f675(x18093,x18094,x18091),f675(x18093,x18094,x18092))
% 187.33/188.06 [1810]~E(x18101,x18102)+E(f131(x18101,x18103,x18104,x18105,x18106),f131(x18102,x18103,x18104,x18105,x18106))
% 187.33/188.06 [1811]~E(x18111,x18112)+E(f131(x18113,x18111,x18114,x18115,x18116),f131(x18113,x18112,x18114,x18115,x18116))
% 187.33/188.06 [1812]~E(x18121,x18122)+E(f131(x18123,x18124,x18121,x18125,x18126),f131(x18123,x18124,x18122,x18125,x18126))
% 187.33/188.06 [1813]~E(x18131,x18132)+E(f131(x18133,x18134,x18135,x18131,x18136),f131(x18133,x18134,x18135,x18132,x18136))
% 187.33/188.06 [1814]~E(x18141,x18142)+E(f131(x18143,x18144,x18145,x18146,x18141),f131(x18143,x18144,x18145,x18146,x18142))
% 187.33/188.06 [1815]~E(x18151,x18152)+E(f533(x18151,x18153),f533(x18152,x18153))
% 187.33/188.06 [1816]~E(x18161,x18162)+E(f533(x18163,x18161),f533(x18163,x18162))
% 187.33/188.06 [1817]~E(x18171,x18172)+E(f773(x18171,x18173,x18174,x18175),f773(x18172,x18173,x18174,x18175))
% 187.33/188.06 [1818]~E(x18181,x18182)+E(f773(x18183,x18181,x18184,x18185),f773(x18183,x18182,x18184,x18185))
% 187.33/188.06 [1819]~E(x18191,x18192)+E(f773(x18193,x18194,x18191,x18195),f773(x18193,x18194,x18192,x18195))
% 187.33/188.06 [1820]~E(x18201,x18202)+E(f773(x18203,x18204,x18205,x18201),f773(x18203,x18204,x18205,x18202))
% 187.33/188.06 [1821]~E(x18211,x18212)+E(f416(x18211,x18213,x18214,x18215,x18216),f416(x18212,x18213,x18214,x18215,x18216))
% 187.33/188.06 [1822]~E(x18221,x18222)+E(f416(x18223,x18221,x18224,x18225,x18226),f416(x18223,x18222,x18224,x18225,x18226))
% 187.33/188.06 [1823]~E(x18231,x18232)+E(f416(x18233,x18234,x18231,x18235,x18236),f416(x18233,x18234,x18232,x18235,x18236))
% 187.33/188.06 [1824]~E(x18241,x18242)+E(f416(x18243,x18244,x18245,x18241,x18246),f416(x18243,x18244,x18245,x18242,x18246))
% 187.33/188.06 [1825]~E(x18251,x18252)+E(f416(x18253,x18254,x18255,x18256,x18251),f416(x18253,x18254,x18255,x18256,x18252))
% 187.33/188.06 [1826]~E(x18261,x18262)+E(f527(x18261,x18263,x18264,x18265),f527(x18262,x18263,x18264,x18265))
% 187.33/188.06 [1827]~E(x18271,x18272)+E(f527(x18273,x18271,x18274,x18275),f527(x18273,x18272,x18274,x18275))
% 187.33/188.06 [1828]~E(x18281,x18282)+E(f527(x18283,x18284,x18281,x18285),f527(x18283,x18284,x18282,x18285))
% 187.33/188.06 [1829]~E(x18291,x18292)+E(f527(x18293,x18294,x18295,x18291),f527(x18293,x18294,x18295,x18292))
% 187.33/188.06 [1830]~E(x18301,x18302)+E(f646(x18301,x18303,x18304,x18305,x18306,x18307,x18308),f646(x18302,x18303,x18304,x18305,x18306,x18307,x18308))
% 187.33/188.06 [1831]~E(x18311,x18312)+E(f646(x18313,x18311,x18314,x18315,x18316,x18317,x18318),f646(x18313,x18312,x18314,x18315,x18316,x18317,x18318))
% 187.33/188.06 [1832]~E(x18321,x18322)+E(f646(x18323,x18324,x18321,x18325,x18326,x18327,x18328),f646(x18323,x18324,x18322,x18325,x18326,x18327,x18328))
% 187.33/188.06 [1833]~E(x18331,x18332)+E(f646(x18333,x18334,x18335,x18331,x18336,x18337,x18338),f646(x18333,x18334,x18335,x18332,x18336,x18337,x18338))
% 187.33/188.06 [1834]~E(x18341,x18342)+E(f646(x18343,x18344,x18345,x18346,x18341,x18347,x18348),f646(x18343,x18344,x18345,x18346,x18342,x18347,x18348))
% 187.33/188.06 [1835]~E(x18351,x18352)+E(f646(x18353,x18354,x18355,x18356,x18357,x18351,x18358),f646(x18353,x18354,x18355,x18356,x18357,x18352,x18358))
% 187.33/188.06 [1836]~E(x18361,x18362)+E(f646(x18363,x18364,x18365,x18366,x18367,x18368,x18361),f646(x18363,x18364,x18365,x18366,x18367,x18368,x18362))
% 187.33/188.06 [1837]~E(x18371,x18372)+E(f585(x18371,x18373,x18374,x18375),f585(x18372,x18373,x18374,x18375))
% 187.33/188.06 [1838]~E(x18381,x18382)+E(f585(x18383,x18381,x18384,x18385),f585(x18383,x18382,x18384,x18385))
% 187.33/188.06 [1839]~E(x18391,x18392)+E(f585(x18393,x18394,x18391,x18395),f585(x18393,x18394,x18392,x18395))
% 187.33/188.06 [1840]~E(x18401,x18402)+E(f585(x18403,x18404,x18405,x18401),f585(x18403,x18404,x18405,x18402))
% 187.33/188.06 [1841]~E(x18411,x18412)+E(f553(x18411,x18413),f553(x18412,x18413))
% 187.33/188.06 [1842]~E(x18421,x18422)+E(f553(x18423,x18421),f553(x18423,x18422))
% 187.33/188.06 [1843]~E(x18431,x18432)+E(f502(x18431,x18433,x18434,x18435),f502(x18432,x18433,x18434,x18435))
% 187.33/188.06 [1844]~E(x18441,x18442)+E(f502(x18443,x18441,x18444,x18445),f502(x18443,x18442,x18444,x18445))
% 187.33/188.06 [1845]~E(x18451,x18452)+E(f502(x18453,x18454,x18451,x18455),f502(x18453,x18454,x18452,x18455))
% 187.33/188.06 [1846]~E(x18461,x18462)+E(f502(x18463,x18464,x18465,x18461),f502(x18463,x18464,x18465,x18462))
% 187.33/188.06 [1847]~E(x18471,x18472)+E(f693(x18471,x18473,x18474),f693(x18472,x18473,x18474))
% 187.33/188.06 [1848]~E(x18481,x18482)+E(f693(x18483,x18481,x18484),f693(x18483,x18482,x18484))
% 187.33/188.06 [1849]~E(x18491,x18492)+E(f693(x18493,x18494,x18491),f693(x18493,x18494,x18492))
% 187.33/188.06 [1850]~E(x18501,x18502)+E(f490(x18501,x18503,x18504,x18505),f490(x18502,x18503,x18504,x18505))
% 187.33/188.06 [1851]~E(x18511,x18512)+E(f490(x18513,x18511,x18514,x18515),f490(x18513,x18512,x18514,x18515))
% 187.33/188.06 [1852]~E(x18521,x18522)+E(f490(x18523,x18524,x18521,x18525),f490(x18523,x18524,x18522,x18525))
% 187.33/188.06 [1853]~E(x18531,x18532)+E(f490(x18533,x18534,x18535,x18531),f490(x18533,x18534,x18535,x18532))
% 187.33/188.06 [1854]~E(x18541,x18542)+E(f791(x18541,x18543,x18544,x18545,x18546),f791(x18542,x18543,x18544,x18545,x18546))
% 187.33/188.06 [1855]~E(x18551,x18552)+E(f791(x18553,x18551,x18554,x18555,x18556),f791(x18553,x18552,x18554,x18555,x18556))
% 187.33/188.06 [1856]~E(x18561,x18562)+E(f791(x18563,x18564,x18561,x18565,x18566),f791(x18563,x18564,x18562,x18565,x18566))
% 187.33/188.06 [1857]~E(x18571,x18572)+E(f791(x18573,x18574,x18575,x18571,x18576),f791(x18573,x18574,x18575,x18572,x18576))
% 187.33/188.06 [1858]~E(x18581,x18582)+E(f791(x18583,x18584,x18585,x18586,x18581),f791(x18583,x18584,x18585,x18586,x18582))
% 187.33/188.06 [1859]~E(x18591,x18592)+E(f296(x18591,x18593,x18594,x18595),f296(x18592,x18593,x18594,x18595))
% 187.33/188.06 [1860]~E(x18601,x18602)+E(f296(x18603,x18601,x18604,x18605),f296(x18603,x18602,x18604,x18605))
% 187.33/188.06 [1861]~E(x18611,x18612)+E(f296(x18613,x18614,x18611,x18615),f296(x18613,x18614,x18612,x18615))
% 187.33/188.06 [1862]~E(x18621,x18622)+E(f296(x18623,x18624,x18625,x18621),f296(x18623,x18624,x18625,x18622))
% 187.33/188.06 [1863]~E(x18631,x18632)+E(f552(x18631,x18633),f552(x18632,x18633))
% 187.33/188.06 [1864]~E(x18641,x18642)+E(f552(x18643,x18641),f552(x18643,x18642))
% 187.33/188.06 [1865]~E(x18651,x18652)+E(f708(x18651,x18653,x18654),f708(x18652,x18653,x18654))
% 187.33/188.06 [1866]~E(x18661,x18662)+E(f708(x18663,x18661,x18664),f708(x18663,x18662,x18664))
% 187.33/188.06 [1867]~E(x18671,x18672)+E(f708(x18673,x18674,x18671),f708(x18673,x18674,x18672))
% 187.33/188.06 [1868]~E(x18681,x18682)+E(f781(x18681,x18683,x18684),f781(x18682,x18683,x18684))
% 187.33/188.06 [1869]~E(x18691,x18692)+E(f781(x18693,x18691,x18694),f781(x18693,x18692,x18694))
% 187.33/188.06 [1870]~E(x18701,x18702)+E(f781(x18703,x18704,x18701),f781(x18703,x18704,x18702))
% 187.33/188.06 [1871]~E(x18711,x18712)+E(f334(x18711),f334(x18712))
% 187.33/188.06 [1872]~E(x18721,x18722)+E(f778(x18721,x18723),f778(x18722,x18723))
% 187.33/188.06 [1873]~E(x18731,x18732)+E(f778(x18733,x18731),f778(x18733,x18732))
% 187.33/188.06 [1874]~E(x18741,x18742)+E(f144(x18741,x18743),f144(x18742,x18743))
% 187.33/188.06 [1875]~E(x18751,x18752)+E(f144(x18753,x18751),f144(x18753,x18752))
% 187.33/188.06 [1876]~E(x18761,x18762)+E(f780(x18761,x18763,x18764),f780(x18762,x18763,x18764))
% 187.33/188.06 [1877]~E(x18771,x18772)+E(f780(x18773,x18771,x18774),f780(x18773,x18772,x18774))
% 187.33/188.06 [1878]~E(x18781,x18782)+E(f780(x18783,x18784,x18781),f780(x18783,x18784,x18782))
% 187.33/188.06 [1879]~E(x18791,x18792)+E(f368(x18791,x18793,x18794,x18795,x18796),f368(x18792,x18793,x18794,x18795,x18796))
% 187.33/188.06 [1880]~E(x18801,x18802)+E(f368(x18803,x18801,x18804,x18805,x18806),f368(x18803,x18802,x18804,x18805,x18806))
% 187.33/188.06 [1881]~E(x18811,x18812)+E(f368(x18813,x18814,x18811,x18815,x18816),f368(x18813,x18814,x18812,x18815,x18816))
% 187.33/188.06 [1882]~E(x18821,x18822)+E(f368(x18823,x18824,x18825,x18821,x18826),f368(x18823,x18824,x18825,x18822,x18826))
% 187.33/188.06 [1883]~E(x18831,x18832)+E(f368(x18833,x18834,x18835,x18836,x18831),f368(x18833,x18834,x18835,x18836,x18832))
% 187.33/188.06 [1884]~E(x18841,x18842)+E(f500(x18841,x18843,x18844,x18845,x18846,x18847),f500(x18842,x18843,x18844,x18845,x18846,x18847))
% 187.33/188.06 [1885]~E(x18851,x18852)+E(f500(x18853,x18851,x18854,x18855,x18856,x18857),f500(x18853,x18852,x18854,x18855,x18856,x18857))
% 187.33/188.06 [1886]~E(x18861,x18862)+E(f500(x18863,x18864,x18861,x18865,x18866,x18867),f500(x18863,x18864,x18862,x18865,x18866,x18867))
% 187.33/188.06 [1887]~E(x18871,x18872)+E(f500(x18873,x18874,x18875,x18871,x18876,x18877),f500(x18873,x18874,x18875,x18872,x18876,x18877))
% 187.33/188.06 [1888]~E(x18881,x18882)+E(f500(x18883,x18884,x18885,x18886,x18881,x18887),f500(x18883,x18884,x18885,x18886,x18882,x18887))
% 187.33/188.06 [1889]~E(x18891,x18892)+E(f500(x18893,x18894,x18895,x18896,x18897,x18891),f500(x18893,x18894,x18895,x18896,x18897,x18892))
% 187.33/188.06 [1890]~E(x18901,x18902)+E(f826(x18901,x18903,x18904),f826(x18902,x18903,x18904))
% 187.33/188.06 [1891]~E(x18911,x18912)+E(f826(x18913,x18911,x18914),f826(x18913,x18912,x18914))
% 187.33/188.06 [1892]~E(x18921,x18922)+E(f826(x18923,x18924,x18921),f826(x18923,x18924,x18922))
% 187.33/188.06 [1893]~E(x18931,x18932)+E(f792(x18931,x18933,x18934),f792(x18932,x18933,x18934))
% 187.33/188.06 [1894]~E(x18941,x18942)+E(f792(x18943,x18941,x18944),f792(x18943,x18942,x18944))
% 187.33/188.06 [1895]~E(x18951,x18952)+E(f792(x18953,x18954,x18951),f792(x18953,x18954,x18952))
% 187.33/188.06 [1896]~E(x18961,x18962)+E(f712(x18961,x18963,x18964,x18965,x18966),f712(x18962,x18963,x18964,x18965,x18966))
% 187.33/188.06 [1897]~E(x18971,x18972)+E(f712(x18973,x18971,x18974,x18975,x18976),f712(x18973,x18972,x18974,x18975,x18976))
% 187.33/188.06 [1898]~E(x18981,x18982)+E(f712(x18983,x18984,x18981,x18985,x18986),f712(x18983,x18984,x18982,x18985,x18986))
% 187.33/188.06 [1899]~E(x18991,x18992)+E(f712(x18993,x18994,x18995,x18991,x18996),f712(x18993,x18994,x18995,x18992,x18996))
% 187.33/188.06 [1900]~E(x19001,x19002)+E(f712(x19003,x19004,x19005,x19006,x19001),f712(x19003,x19004,x19005,x19006,x19002))
% 187.33/188.06 [1901]~E(x19011,x19012)+E(f805(x19011),f805(x19012))
% 187.33/188.06 [1902]~E(x19021,x19022)+E(f426(x19021,x19023,x19024,x19025),f426(x19022,x19023,x19024,x19025))
% 187.33/188.06 [1903]~E(x19031,x19032)+E(f426(x19033,x19031,x19034,x19035),f426(x19033,x19032,x19034,x19035))
% 187.33/188.06 [1904]~E(x19041,x19042)+E(f426(x19043,x19044,x19041,x19045),f426(x19043,x19044,x19042,x19045))
% 187.33/188.06 [1905]~E(x19051,x19052)+E(f426(x19053,x19054,x19055,x19051),f426(x19053,x19054,x19055,x19052))
% 187.33/188.06 [1906]~E(x19061,x19062)+E(f453(x19061,x19063),f453(x19062,x19063))
% 187.33/188.06 [1907]~E(x19071,x19072)+E(f453(x19073,x19071),f453(x19073,x19072))
% 187.33/188.06 [1908]~E(x19081,x19082)+E(f350(x19081,x19083,x19084),f350(x19082,x19083,x19084))
% 187.33/188.06 [1909]~E(x19091,x19092)+E(f350(x19093,x19091,x19094),f350(x19093,x19092,x19094))
% 187.33/188.06 [1910]~E(x19101,x19102)+E(f350(x19103,x19104,x19101),f350(x19103,x19104,x19102))
% 187.33/188.06 [1911]~E(x19111,x19112)+E(f564(x19111,x19113,x19114),f564(x19112,x19113,x19114))
% 187.33/188.06 [1912]~E(x19121,x19122)+E(f564(x19123,x19121,x19124),f564(x19123,x19122,x19124))
% 187.33/188.06 [1913]~E(x19131,x19132)+E(f564(x19133,x19134,x19131),f564(x19133,x19134,x19132))
% 187.33/188.06 [1914]~E(x19141,x19142)+E(f281(x19141,x19143,x19144,x19145),f281(x19142,x19143,x19144,x19145))
% 187.33/188.06 [1915]~E(x19151,x19152)+E(f281(x19153,x19151,x19154,x19155),f281(x19153,x19152,x19154,x19155))
% 187.33/188.06 [1916]~E(x19161,x19162)+E(f281(x19163,x19164,x19161,x19165),f281(x19163,x19164,x19162,x19165))
% 187.33/188.06 [1917]~E(x19171,x19172)+E(f281(x19173,x19174,x19175,x19171),f281(x19173,x19174,x19175,x19172))
% 187.33/188.06 [1918]~E(x19181,x19182)+E(f663(x19181,x19183,x19184,x19185),f663(x19182,x19183,x19184,x19185))
% 187.33/188.06 [1919]~E(x19191,x19192)+E(f663(x19193,x19191,x19194,x19195),f663(x19193,x19192,x19194,x19195))
% 187.33/188.06 [1920]~E(x19201,x19202)+E(f663(x19203,x19204,x19201,x19205),f663(x19203,x19204,x19202,x19205))
% 187.33/188.06 [1921]~E(x19211,x19212)+E(f663(x19213,x19214,x19215,x19211),f663(x19213,x19214,x19215,x19212))
% 187.33/188.06 [1922]~E(x19221,x19222)+E(f666(x19221,x19223),f666(x19222,x19223))
% 187.33/188.06 [1923]~E(x19231,x19232)+E(f666(x19233,x19231),f666(x19233,x19232))
% 187.33/188.06 [1924]~E(x19241,x19242)+E(f741(x19241,x19243,x19244),f741(x19242,x19243,x19244))
% 187.33/188.06 [1925]~E(x19251,x19252)+E(f741(x19253,x19251,x19254),f741(x19253,x19252,x19254))
% 187.33/188.06 [1926]~E(x19261,x19262)+E(f741(x19263,x19264,x19261),f741(x19263,x19264,x19262))
% 187.33/188.06 [1927]~E(x19271,x19272)+E(f622(x19271,x19273,x19274,x19275,x19276),f622(x19272,x19273,x19274,x19275,x19276))
% 187.33/188.06 [1928]~E(x19281,x19282)+E(f622(x19283,x19281,x19284,x19285,x19286),f622(x19283,x19282,x19284,x19285,x19286))
% 187.33/188.06 [1929]~E(x19291,x19292)+E(f622(x19293,x19294,x19291,x19295,x19296),f622(x19293,x19294,x19292,x19295,x19296))
% 187.33/188.06 [1930]~E(x19301,x19302)+E(f622(x19303,x19304,x19305,x19301,x19306),f622(x19303,x19304,x19305,x19302,x19306))
% 187.33/188.06 [1931]~E(x19311,x19312)+E(f622(x19313,x19314,x19315,x19316,x19311),f622(x19313,x19314,x19315,x19316,x19312))
% 187.33/188.06 [1932]~E(x19321,x19322)+E(f724(x19321,x19323,x19324,x19325),f724(x19322,x19323,x19324,x19325))
% 187.33/188.06 [1933]~E(x19331,x19332)+E(f724(x19333,x19331,x19334,x19335),f724(x19333,x19332,x19334,x19335))
% 187.33/188.06 [1934]~E(x19341,x19342)+E(f724(x19343,x19344,x19341,x19345),f724(x19343,x19344,x19342,x19345))
% 187.33/188.06 [1935]~E(x19351,x19352)+E(f724(x19353,x19354,x19355,x19351),f724(x19353,x19354,x19355,x19352))
% 187.33/188.06 [1936]~E(x19361,x19362)+E(f747(x19361,x19363,x19364),f747(x19362,x19363,x19364))
% 187.33/188.06 [1937]~E(x19371,x19372)+E(f747(x19373,x19371,x19374),f747(x19373,x19372,x19374))
% 187.33/188.06 [1938]~E(x19381,x19382)+E(f747(x19383,x19384,x19381),f747(x19383,x19384,x19382))
% 187.33/188.06 [1939]~E(x19391,x19392)+E(f297(x19391,x19393,x19394,x19395,x19396),f297(x19392,x19393,x19394,x19395,x19396))
% 187.33/188.06 [1940]~E(x19401,x19402)+E(f297(x19403,x19401,x19404,x19405,x19406),f297(x19403,x19402,x19404,x19405,x19406))
% 187.33/188.06 [1941]~E(x19411,x19412)+E(f297(x19413,x19414,x19411,x19415,x19416),f297(x19413,x19414,x19412,x19415,x19416))
% 187.33/188.06 [1942]~E(x19421,x19422)+E(f297(x19423,x19424,x19425,x19421,x19426),f297(x19423,x19424,x19425,x19422,x19426))
% 187.33/188.06 [1943]~E(x19431,x19432)+E(f297(x19433,x19434,x19435,x19436,x19431),f297(x19433,x19434,x19435,x19436,x19432))
% 187.33/188.06 [1944]~E(x19441,x19442)+E(f231(x19441,x19443,x19444),f231(x19442,x19443,x19444))
% 187.33/188.06 [1945]~E(x19451,x19452)+E(f231(x19453,x19451,x19454),f231(x19453,x19452,x19454))
% 187.33/188.06 [1946]~E(x19461,x19462)+E(f231(x19463,x19464,x19461),f231(x19463,x19464,x19462))
% 187.33/188.06 [1947]~E(x19471,x19472)+E(f720(x19471,x19473,x19474),f720(x19472,x19473,x19474))
% 187.33/188.06 [1948]~E(x19481,x19482)+E(f720(x19483,x19481,x19484),f720(x19483,x19482,x19484))
% 187.33/188.06 [1949]~E(x19491,x19492)+E(f720(x19493,x19494,x19491),f720(x19493,x19494,x19492))
% 187.33/188.06 [1950]~E(x19501,x19502)+E(f404(x19501,x19503,x19504,x19505),f404(x19502,x19503,x19504,x19505))
% 187.33/188.06 [1951]~E(x19511,x19512)+E(f404(x19513,x19511,x19514,x19515),f404(x19513,x19512,x19514,x19515))
% 187.33/188.06 [1952]~E(x19521,x19522)+E(f404(x19523,x19524,x19521,x19525),f404(x19523,x19524,x19522,x19525))
% 187.33/188.06 [1953]~E(x19531,x19532)+E(f404(x19533,x19534,x19535,x19531),f404(x19533,x19534,x19535,x19532))
% 187.33/188.06 [1954]~E(x19541,x19542)+E(f665(x19541,x19543,x19544,x19545),f665(x19542,x19543,x19544,x19545))
% 187.33/188.06 [1955]~E(x19551,x19552)+E(f665(x19553,x19551,x19554,x19555),f665(x19553,x19552,x19554,x19555))
% 187.33/188.06 [1956]~E(x19561,x19562)+E(f665(x19563,x19564,x19561,x19565),f665(x19563,x19564,x19562,x19565))
% 187.33/188.06 [1957]~E(x19571,x19572)+E(f665(x19573,x19574,x19575,x19571),f665(x19573,x19574,x19575,x19572))
% 187.33/188.06 [1958]~E(x19581,x19582)+E(f563(x19581,x19583,x19584),f563(x19582,x19583,x19584))
% 187.33/188.06 [1959]~E(x19591,x19592)+E(f563(x19593,x19591,x19594),f563(x19593,x19592,x19594))
% 187.33/188.06 [1960]~E(x19601,x19602)+E(f563(x19603,x19604,x19601),f563(x19603,x19604,x19602))
% 187.33/188.06 [1961]~E(x19611,x19612)+E(f382(x19611,x19613,x19614,x19615),f382(x19612,x19613,x19614,x19615))
% 187.33/188.06 [1962]~E(x19621,x19622)+E(f382(x19623,x19621,x19624,x19625),f382(x19623,x19622,x19624,x19625))
% 187.33/188.06 [1963]~E(x19631,x19632)+E(f382(x19633,x19634,x19631,x19635),f382(x19633,x19634,x19632,x19635))
% 187.33/188.06 [1964]~E(x19641,x19642)+E(f382(x19643,x19644,x19645,x19641),f382(x19643,x19644,x19645,x19642))
% 187.33/188.06 [1965]~E(x19651,x19652)+E(f756(x19651,x19653),f756(x19652,x19653))
% 187.33/188.06 [1966]~E(x19661,x19662)+E(f756(x19663,x19661),f756(x19663,x19662))
% 187.33/188.06 [1967]~E(x19671,x19672)+E(f788(x19671,x19673,x19674,x19675,x19676),f788(x19672,x19673,x19674,x19675,x19676))
% 187.33/188.06 [1968]~E(x19681,x19682)+E(f788(x19683,x19681,x19684,x19685,x19686),f788(x19683,x19682,x19684,x19685,x19686))
% 187.33/188.06 [1969]~E(x19691,x19692)+E(f788(x19693,x19694,x19691,x19695,x19696),f788(x19693,x19694,x19692,x19695,x19696))
% 187.33/188.06 [1970]~E(x19701,x19702)+E(f788(x19703,x19704,x19705,x19701,x19706),f788(x19703,x19704,x19705,x19702,x19706))
% 187.33/188.06 [1971]~E(x19711,x19712)+E(f788(x19713,x19714,x19715,x19716,x19711),f788(x19713,x19714,x19715,x19716,x19712))
% 187.33/188.06 [1972]~E(x19721,x19722)+E(f834(x19721,x19723,x19724,x19725),f834(x19722,x19723,x19724,x19725))
% 187.33/188.06 [1973]~E(x19731,x19732)+E(f834(x19733,x19731,x19734,x19735),f834(x19733,x19732,x19734,x19735))
% 187.33/188.06 [1974]~E(x19741,x19742)+E(f834(x19743,x19744,x19741,x19745),f834(x19743,x19744,x19742,x19745))
% 187.33/188.06 [1975]~E(x19751,x19752)+E(f834(x19753,x19754,x19755,x19751),f834(x19753,x19754,x19755,x19752))
% 187.33/188.06 [1976]~E(x19761,x19762)+E(f580(x19761,x19763,x19764),f580(x19762,x19763,x19764))
% 187.33/188.06 [1977]~E(x19771,x19772)+E(f580(x19773,x19771,x19774),f580(x19773,x19772,x19774))
% 187.33/188.06 [1978]~E(x19781,x19782)+E(f580(x19783,x19784,x19781),f580(x19783,x19784,x19782))
% 187.33/188.06 [1979]~E(x19791,x19792)+E(f828(x19791,x19793,x19794,x19795),f828(x19792,x19793,x19794,x19795))
% 187.33/188.06 [1980]~E(x19801,x19802)+E(f828(x19803,x19801,x19804,x19805),f828(x19803,x19802,x19804,x19805))
% 187.33/188.06 [1981]~E(x19811,x19812)+E(f828(x19813,x19814,x19811,x19815),f828(x19813,x19814,x19812,x19815))
% 187.33/188.06 [1982]~E(x19821,x19822)+E(f828(x19823,x19824,x19825,x19821),f828(x19823,x19824,x19825,x19822))
% 187.33/188.06 [1983]~E(x19831,x19832)+E(f442(x19831,x19833,x19834),f442(x19832,x19833,x19834))
% 187.33/188.06 [1984]~E(x19841,x19842)+E(f442(x19843,x19841,x19844),f442(x19843,x19842,x19844))
% 187.33/188.06 [1985]~E(x19851,x19852)+E(f442(x19853,x19854,x19851),f442(x19853,x19854,x19852))
% 187.33/188.06 [1986]~E(x19861,x19862)+E(f605(x19861,x19863,x19864,x19865),f605(x19862,x19863,x19864,x19865))
% 187.33/188.06 [1987]~E(x19871,x19872)+E(f605(x19873,x19871,x19874,x19875),f605(x19873,x19872,x19874,x19875))
% 187.33/188.06 [1988]~E(x19881,x19882)+E(f605(x19883,x19884,x19881,x19885),f605(x19883,x19884,x19882,x19885))
% 187.33/188.06 [1989]~E(x19891,x19892)+E(f605(x19893,x19894,x19895,x19891),f605(x19893,x19894,x19895,x19892))
% 187.33/188.06 [1990]~E(x19901,x19902)+E(f21(x19901,x19903),f21(x19902,x19903))
% 187.33/188.06 [1991]~E(x19911,x19912)+E(f21(x19913,x19911),f21(x19913,x19912))
% 187.33/188.06 [1992]~E(x19921,x19922)+E(f740(x19921,x19923,x19924),f740(x19922,x19923,x19924))
% 187.33/188.06 [1993]~E(x19931,x19932)+E(f740(x19933,x19931,x19934),f740(x19933,x19932,x19934))
% 187.33/188.06 [1994]~E(x19941,x19942)+E(f740(x19943,x19944,x19941),f740(x19943,x19944,x19942))
% 187.33/188.06 [1995]~E(x19951,x19952)+E(f310(x19951,x19953),f310(x19952,x19953))
% 187.33/188.06 [1996]~E(x19961,x19962)+E(f310(x19963,x19961),f310(x19963,x19962))
% 187.33/188.06 [1997]~E(x19971,x19972)+E(f612(x19971,x19973,x19974,x19975,x19976),f612(x19972,x19973,x19974,x19975,x19976))
% 187.33/188.06 [1998]~E(x19981,x19982)+E(f612(x19983,x19981,x19984,x19985,x19986),f612(x19983,x19982,x19984,x19985,x19986))
% 187.33/188.06 [1999]~E(x19991,x19992)+E(f612(x19993,x19994,x19991,x19995,x19996),f612(x19993,x19994,x19992,x19995,x19996))
% 187.33/188.06 [2000]~E(x20001,x20002)+E(f612(x20003,x20004,x20005,x20001,x20006),f612(x20003,x20004,x20005,x20002,x20006))
% 187.33/188.06 [2001]~E(x20011,x20012)+E(f612(x20013,x20014,x20015,x20016,x20011),f612(x20013,x20014,x20015,x20016,x20012))
% 187.33/188.06 [2002]~E(x20021,x20022)+E(f349(x20021,x20023,x20024),f349(x20022,x20023,x20024))
% 187.33/188.06 [2003]~E(x20031,x20032)+E(f349(x20033,x20031,x20034),f349(x20033,x20032,x20034))
% 187.33/188.06 [2004]~E(x20041,x20042)+E(f349(x20043,x20044,x20041),f349(x20043,x20044,x20042))
% 187.33/188.06 [2005]~E(x20051,x20052)+E(f570(x20051,x20053,x20054),f570(x20052,x20053,x20054))
% 187.33/188.06 [2006]~E(x20061,x20062)+E(f570(x20063,x20061,x20064),f570(x20063,x20062,x20064))
% 187.33/188.06 [2007]~E(x20071,x20072)+E(f570(x20073,x20074,x20071),f570(x20073,x20074,x20072))
% 187.33/188.06 [2008]~E(x20081,x20082)+E(f688(x20081,x20083),f688(x20082,x20083))
% 187.33/188.06 [2009]~E(x20091,x20092)+E(f688(x20093,x20091),f688(x20093,x20092))
% 187.33/188.06 [2010]~E(x20101,x20102)+E(f700(x20101,x20103,x20104,x20105),f700(x20102,x20103,x20104,x20105))
% 187.33/188.06 [2011]~E(x20111,x20112)+E(f700(x20113,x20111,x20114,x20115),f700(x20113,x20112,x20114,x20115))
% 187.33/188.06 [2012]~E(x20121,x20122)+E(f700(x20123,x20124,x20121,x20125),f700(x20123,x20124,x20122,x20125))
% 187.33/188.06 [2013]~E(x20131,x20132)+E(f700(x20133,x20134,x20135,x20131),f700(x20133,x20134,x20135,x20132))
% 187.33/188.06 [2014]~E(x20141,x20142)+E(f478(x20141,x20143,x20144),f478(x20142,x20143,x20144))
% 187.33/188.06 [2015]~E(x20151,x20152)+E(f478(x20153,x20151,x20154),f478(x20153,x20152,x20154))
% 187.33/188.06 [2016]~E(x20161,x20162)+E(f478(x20163,x20164,x20161),f478(x20163,x20164,x20162))
% 187.33/188.06 [2017]~E(x20171,x20172)+E(f859(x20171,x20173,x20174,x20175),f859(x20172,x20173,x20174,x20175))
% 187.33/188.06 [2018]~E(x20181,x20182)+E(f859(x20183,x20181,x20184,x20185),f859(x20183,x20182,x20184,x20185))
% 187.33/188.06 [2019]~E(x20191,x20192)+E(f859(x20193,x20194,x20191,x20195),f859(x20193,x20194,x20192,x20195))
% 187.33/188.06 [2020]~E(x20201,x20202)+E(f859(x20203,x20204,x20205,x20201),f859(x20203,x20204,x20205,x20202))
% 187.33/188.06 [2021]~E(x20211,x20212)+E(f405(x20211,x20213,x20214,x20215),f405(x20212,x20213,x20214,x20215))
% 187.33/188.06 [2022]~E(x20221,x20222)+E(f405(x20223,x20221,x20224,x20225),f405(x20223,x20222,x20224,x20225))
% 187.33/188.06 [2023]~E(x20231,x20232)+E(f405(x20233,x20234,x20231,x20235),f405(x20233,x20234,x20232,x20235))
% 187.33/188.06 [2024]~E(x20241,x20242)+E(f405(x20243,x20244,x20245,x20241),f405(x20243,x20244,x20245,x20242))
% 187.33/188.06 [2025]~E(x20251,x20252)+E(f360(x20251,x20253),f360(x20252,x20253))
% 187.33/188.06 [2026]~E(x20261,x20262)+E(f360(x20263,x20261),f360(x20263,x20262))
% 187.33/188.06 [2027]~E(x20271,x20272)+E(f702(x20271,x20273,x20274,x20275),f702(x20272,x20273,x20274,x20275))
% 187.33/188.06 [2028]~E(x20281,x20282)+E(f702(x20283,x20281,x20284,x20285),f702(x20283,x20282,x20284,x20285))
% 187.33/188.06 [2029]~E(x20291,x20292)+E(f702(x20293,x20294,x20291,x20295),f702(x20293,x20294,x20292,x20295))
% 187.33/188.06 [2030]~E(x20301,x20302)+E(f702(x20303,x20304,x20305,x20301),f702(x20303,x20304,x20305,x20302))
% 187.33/188.06 [2031]~E(x20311,x20312)+E(f361(x20311),f361(x20312))
% 187.33/188.06 [2032]~E(x20321,x20322)+E(f437(x20321,x20323,x20324,x20325,x20326),f437(x20322,x20323,x20324,x20325,x20326))
% 187.33/188.06 [2033]~E(x20331,x20332)+E(f437(x20333,x20331,x20334,x20335,x20336),f437(x20333,x20332,x20334,x20335,x20336))
% 187.33/188.06 [2034]~E(x20341,x20342)+E(f437(x20343,x20344,x20341,x20345,x20346),f437(x20343,x20344,x20342,x20345,x20346))
% 187.33/188.06 [2035]~E(x20351,x20352)+E(f437(x20353,x20354,x20355,x20351,x20356),f437(x20353,x20354,x20355,x20352,x20356))
% 187.33/188.06 [2036]~E(x20361,x20362)+E(f437(x20363,x20364,x20365,x20366,x20361),f437(x20363,x20364,x20365,x20366,x20362))
% 187.33/188.06 [2037]~E(x20371,x20372)+E(f571(x20371,x20373,x20374,x20375,x20376,x20377),f571(x20372,x20373,x20374,x20375,x20376,x20377))
% 187.33/188.06 [2038]~E(x20381,x20382)+E(f571(x20383,x20381,x20384,x20385,x20386,x20387),f571(x20383,x20382,x20384,x20385,x20386,x20387))
% 187.33/188.06 [2039]~E(x20391,x20392)+E(f571(x20393,x20394,x20391,x20395,x20396,x20397),f571(x20393,x20394,x20392,x20395,x20396,x20397))
% 187.33/188.06 [2040]~E(x20401,x20402)+E(f571(x20403,x20404,x20405,x20401,x20406,x20407),f571(x20403,x20404,x20405,x20402,x20406,x20407))
% 187.33/188.06 [2041]~E(x20411,x20412)+E(f571(x20413,x20414,x20415,x20416,x20411,x20417),f571(x20413,x20414,x20415,x20416,x20412,x20417))
% 187.33/188.06 [2042]~E(x20421,x20422)+E(f571(x20423,x20424,x20425,x20426,x20427,x20421),f571(x20423,x20424,x20425,x20426,x20427,x20422))
% 187.33/188.06 [2043]~E(x20431,x20432)+E(f511(x20431,x20433,x20434,x20435),f511(x20432,x20433,x20434,x20435))
% 187.33/188.06 [2044]~E(x20441,x20442)+E(f511(x20443,x20441,x20444,x20445),f511(x20443,x20442,x20444,x20445))
% 187.33/188.06 [2045]~E(x20451,x20452)+E(f511(x20453,x20454,x20451,x20455),f511(x20453,x20454,x20452,x20455))
% 187.33/188.06 [2046]~E(x20461,x20462)+E(f511(x20463,x20464,x20465,x20461),f511(x20463,x20464,x20465,x20462))
% 187.33/188.06 [2047]~E(x20471,x20472)+E(f643(x20471,x20473,x20474,x20475),f643(x20472,x20473,x20474,x20475))
% 187.33/188.06 [2048]~E(x20481,x20482)+E(f643(x20483,x20481,x20484,x20485),f643(x20483,x20482,x20484,x20485))
% 187.33/188.06 [2049]~E(x20491,x20492)+E(f643(x20493,x20494,x20491,x20495),f643(x20493,x20494,x20492,x20495))
% 187.33/188.06 [2050]~E(x20501,x20502)+E(f643(x20503,x20504,x20505,x20501),f643(x20503,x20504,x20505,x20502))
% 187.33/188.06 [2051]~E(x20511,x20512)+E(f649(x20511,x20513,x20514,x20515),f649(x20512,x20513,x20514,x20515))
% 187.33/188.06 [2052]~E(x20521,x20522)+E(f649(x20523,x20521,x20524,x20525),f649(x20523,x20522,x20524,x20525))
% 187.33/188.06 [2053]~E(x20531,x20532)+E(f649(x20533,x20534,x20531,x20535),f649(x20533,x20534,x20532,x20535))
% 187.33/188.06 [2054]~E(x20541,x20542)+E(f649(x20543,x20544,x20545,x20541),f649(x20543,x20544,x20545,x20542))
% 187.33/188.06 [2055]~E(x20551,x20552)+E(f615(x20551,x20553,x20554,x20555,x20556),f615(x20552,x20553,x20554,x20555,x20556))
% 187.33/188.06 [2056]~E(x20561,x20562)+E(f615(x20563,x20561,x20564,x20565,x20566),f615(x20563,x20562,x20564,x20565,x20566))
% 187.33/188.06 [2057]~E(x20571,x20572)+E(f615(x20573,x20574,x20571,x20575,x20576),f615(x20573,x20574,x20572,x20575,x20576))
% 187.33/188.06 [2058]~E(x20581,x20582)+E(f615(x20583,x20584,x20585,x20581,x20586),f615(x20583,x20584,x20585,x20582,x20586))
% 187.33/188.06 [2059]~E(x20591,x20592)+E(f615(x20593,x20594,x20595,x20596,x20591),f615(x20593,x20594,x20595,x20596,x20592))
% 187.33/188.06 [2060]~E(x20601,x20602)+E(f667(x20601,x20603,x20604,x20605),f667(x20602,x20603,x20604,x20605))
% 187.33/188.06 [2061]~E(x20611,x20612)+E(f667(x20613,x20611,x20614,x20615),f667(x20613,x20612,x20614,x20615))
% 187.33/188.06 [2062]~E(x20621,x20622)+E(f667(x20623,x20624,x20621,x20625),f667(x20623,x20624,x20622,x20625))
% 187.33/188.06 [2063]~E(x20631,x20632)+E(f667(x20633,x20634,x20635,x20631),f667(x20633,x20634,x20635,x20632))
% 187.33/188.06 [2064]~E(x20641,x20642)+E(f609(x20641,x20643,x20644,x20645,x20646),f609(x20642,x20643,x20644,x20645,x20646))
% 187.33/188.06 [2065]~E(x20651,x20652)+E(f609(x20653,x20651,x20654,x20655,x20656),f609(x20653,x20652,x20654,x20655,x20656))
% 187.33/188.06 [2066]~E(x20661,x20662)+E(f609(x20663,x20664,x20661,x20665,x20666),f609(x20663,x20664,x20662,x20665,x20666))
% 187.33/188.06 [2067]~E(x20671,x20672)+E(f609(x20673,x20674,x20675,x20671,x20676),f609(x20673,x20674,x20675,x20672,x20676))
% 187.33/188.06 [2068]~E(x20681,x20682)+E(f609(x20683,x20684,x20685,x20686,x20681),f609(x20683,x20684,x20685,x20686,x20682))
% 187.33/188.06 [2069]~E(x20691,x20692)+E(f572(x20691,x20693,x20694,x20695,x20696,x20697),f572(x20692,x20693,x20694,x20695,x20696,x20697))
% 187.33/188.06 [2070]~E(x20701,x20702)+E(f572(x20703,x20701,x20704,x20705,x20706,x20707),f572(x20703,x20702,x20704,x20705,x20706,x20707))
% 187.33/188.06 [2071]~E(x20711,x20712)+E(f572(x20713,x20714,x20711,x20715,x20716,x20717),f572(x20713,x20714,x20712,x20715,x20716,x20717))
% 187.33/188.06 [2072]~E(x20721,x20722)+E(f572(x20723,x20724,x20725,x20721,x20726,x20727),f572(x20723,x20724,x20725,x20722,x20726,x20727))
% 187.33/188.06 [2073]~E(x20731,x20732)+E(f572(x20733,x20734,x20735,x20736,x20731,x20737),f572(x20733,x20734,x20735,x20736,x20732,x20737))
% 187.33/188.06 [2074]~E(x20741,x20742)+E(f572(x20743,x20744,x20745,x20746,x20747,x20741),f572(x20743,x20744,x20745,x20746,x20747,x20742))
% 187.33/188.06 [2075]~E(x20751,x20752)+E(f367(x20751,x20753,x20754),f367(x20752,x20753,x20754))
% 187.33/188.06 [2076]~E(x20761,x20762)+E(f367(x20763,x20761,x20764),f367(x20763,x20762,x20764))
% 187.33/188.06 [2077]~E(x20771,x20772)+E(f367(x20773,x20774,x20771),f367(x20773,x20774,x20772))
% 187.33/188.06 [2078]~E(x20781,x20782)+E(f830(x20781,x20783,x20784),f830(x20782,x20783,x20784))
% 187.33/188.06 [2079]~E(x20791,x20792)+E(f830(x20793,x20791,x20794),f830(x20793,x20792,x20794))
% 187.33/188.06 [2080]~E(x20801,x20802)+E(f830(x20803,x20804,x20801),f830(x20803,x20804,x20802))
% 187.33/188.06 [2081]~E(x20811,x20812)+E(f587(x20811,x20813,x20814),f587(x20812,x20813,x20814))
% 187.33/188.06 [2082]~E(x20821,x20822)+E(f587(x20823,x20821,x20824),f587(x20823,x20822,x20824))
% 187.33/188.06 [2083]~E(x20831,x20832)+E(f587(x20833,x20834,x20831),f587(x20833,x20834,x20832))
% 187.33/188.06 [2084]~E(x20841,x20842)+E(f726(x20841,x20843,x20844),f726(x20842,x20843,x20844))
% 187.33/188.06 [2085]~E(x20851,x20852)+E(f726(x20853,x20851,x20854),f726(x20853,x20852,x20854))
% 187.33/188.06 [2086]~E(x20861,x20862)+E(f726(x20863,x20864,x20861),f726(x20863,x20864,x20862))
% 187.33/188.06 [2087]~E(x20871,x20872)+E(f739(x20871,x20873,x20874,x20875,x20876),f739(x20872,x20873,x20874,x20875,x20876))
% 187.33/188.06 [2088]~E(x20881,x20882)+E(f739(x20883,x20881,x20884,x20885,x20886),f739(x20883,x20882,x20884,x20885,x20886))
% 187.33/188.06 [2089]~E(x20891,x20892)+E(f739(x20893,x20894,x20891,x20895,x20896),f739(x20893,x20894,x20892,x20895,x20896))
% 187.33/188.06 [2090]~E(x20901,x20902)+E(f739(x20903,x20904,x20905,x20901,x20906),f739(x20903,x20904,x20905,x20902,x20906))
% 187.33/188.06 [2091]~E(x20911,x20912)+E(f739(x20913,x20914,x20915,x20916,x20911),f739(x20913,x20914,x20915,x20916,x20912))
% 187.33/188.06 [2092]~E(x20921,x20922)+E(f95(x20921),f95(x20922))
% 187.33/188.06 [2093]~E(x20931,x20932)+E(f695(x20931,x20933,x20934,x20935,x20936),f695(x20932,x20933,x20934,x20935,x20936))
% 187.33/188.06 [2094]~E(x20941,x20942)+E(f695(x20943,x20941,x20944,x20945,x20946),f695(x20943,x20942,x20944,x20945,x20946))
% 187.33/188.06 [2095]~E(x20951,x20952)+E(f695(x20953,x20954,x20951,x20955,x20956),f695(x20953,x20954,x20952,x20955,x20956))
% 187.33/188.06 [2096]~E(x20961,x20962)+E(f695(x20963,x20964,x20965,x20961,x20966),f695(x20963,x20964,x20965,x20962,x20966))
% 187.33/188.06 [2097]~E(x20971,x20972)+E(f695(x20973,x20974,x20975,x20976,x20971),f695(x20973,x20974,x20975,x20976,x20972))
% 187.33/188.06 [2098]~E(x20981,x20982)+E(f505(x20981,x20983,x20984,x20985,x20986,x20987,x20988),f505(x20982,x20983,x20984,x20985,x20986,x20987,x20988))
% 187.33/188.06 [2099]~E(x20991,x20992)+E(f505(x20993,x20991,x20994,x20995,x20996,x20997,x20998),f505(x20993,x20992,x20994,x20995,x20996,x20997,x20998))
% 187.33/188.06 [2100]~E(x21001,x21002)+E(f505(x21003,x21004,x21001,x21005,x21006,x21007,x21008),f505(x21003,x21004,x21002,x21005,x21006,x21007,x21008))
% 187.33/188.06 [2101]~E(x21011,x21012)+E(f505(x21013,x21014,x21015,x21011,x21016,x21017,x21018),f505(x21013,x21014,x21015,x21012,x21016,x21017,x21018))
% 187.33/188.06 [2102]~E(x21021,x21022)+E(f505(x21023,x21024,x21025,x21026,x21021,x21027,x21028),f505(x21023,x21024,x21025,x21026,x21022,x21027,x21028))
% 187.33/188.06 [2103]~E(x21031,x21032)+E(f505(x21033,x21034,x21035,x21036,x21037,x21031,x21038),f505(x21033,x21034,x21035,x21036,x21037,x21032,x21038))
% 187.33/188.06 [2104]~E(x21041,x21042)+E(f505(x21043,x21044,x21045,x21046,x21047,x21048,x21041),f505(x21043,x21044,x21045,x21046,x21047,x21048,x21042))
% 187.33/188.06 [2105]~E(x21051,x21052)+E(f843(x21051,x21053,x21054,x21055,x21056),f843(x21052,x21053,x21054,x21055,x21056))
% 187.33/188.06 [2106]~E(x21061,x21062)+E(f843(x21063,x21061,x21064,x21065,x21066),f843(x21063,x21062,x21064,x21065,x21066))
% 187.33/188.06 [2107]~E(x21071,x21072)+E(f843(x21073,x21074,x21071,x21075,x21076),f843(x21073,x21074,x21072,x21075,x21076))
% 187.33/188.06 [2108]~E(x21081,x21082)+E(f843(x21083,x21084,x21085,x21081,x21086),f843(x21083,x21084,x21085,x21082,x21086))
% 187.33/188.06 [2109]~E(x21091,x21092)+E(f843(x21093,x21094,x21095,x21096,x21091),f843(x21093,x21094,x21095,x21096,x21092))
% 187.33/188.06 [2110]~E(x21101,x21102)+E(f670(x21101,x21103,x21104,x21105,x21106),f670(x21102,x21103,x21104,x21105,x21106))
% 187.33/188.06 [2111]~E(x21111,x21112)+E(f670(x21113,x21111,x21114,x21115,x21116),f670(x21113,x21112,x21114,x21115,x21116))
% 187.33/188.06 [2112]~E(x21121,x21122)+E(f670(x21123,x21124,x21121,x21125,x21126),f670(x21123,x21124,x21122,x21125,x21126))
% 187.33/188.06 [2113]~E(x21131,x21132)+E(f670(x21133,x21134,x21135,x21131,x21136),f670(x21133,x21134,x21135,x21132,x21136))
% 187.33/188.06 [2114]~E(x21141,x21142)+E(f670(x21143,x21144,x21145,x21146,x21141),f670(x21143,x21144,x21145,x21146,x21142))
% 187.33/188.06 [2115]~E(x21151,x21152)+E(f294(x21151,x21153,x21154,x21155,x21156),f294(x21152,x21153,x21154,x21155,x21156))
% 187.33/188.06 [2116]~E(x21161,x21162)+E(f294(x21163,x21161,x21164,x21165,x21166),f294(x21163,x21162,x21164,x21165,x21166))
% 187.33/188.06 [2117]~E(x21171,x21172)+E(f294(x21173,x21174,x21171,x21175,x21176),f294(x21173,x21174,x21172,x21175,x21176))
% 187.33/188.06 [2118]~E(x21181,x21182)+E(f294(x21183,x21184,x21185,x21181,x21186),f294(x21183,x21184,x21185,x21182,x21186))
% 187.33/188.06 [2119]~E(x21191,x21192)+E(f294(x21193,x21194,x21195,x21196,x21191),f294(x21193,x21194,x21195,x21196,x21192))
% 187.33/188.06 [2120]~E(x21201,x21202)+E(f353(x21201),f353(x21202))
% 187.33/188.06 [2121]~E(x21211,x21212)+E(f524(x21211,x21213,x21214),f524(x21212,x21213,x21214))
% 187.33/188.06 [2122]~E(x21221,x21222)+E(f524(x21223,x21221,x21224),f524(x21223,x21222,x21224))
% 187.33/188.06 [2123]~E(x21231,x21232)+E(f524(x21233,x21234,x21231),f524(x21233,x21234,x21232))
% 187.33/188.06 [2124]~E(x21241,x21242)+E(f132(x21241,x21243,x21244,x21245),f132(x21242,x21243,x21244,x21245))
% 187.33/188.06 [2125]~E(x21251,x21252)+E(f132(x21253,x21251,x21254,x21255),f132(x21253,x21252,x21254,x21255))
% 187.33/188.06 [2126]~E(x21261,x21262)+E(f132(x21263,x21264,x21261,x21265),f132(x21263,x21264,x21262,x21265))
% 187.33/188.06 [2127]~E(x21271,x21272)+E(f132(x21273,x21274,x21275,x21271),f132(x21273,x21274,x21275,x21272))
% 187.33/188.06 [2128]~E(x21281,x21282)+E(f556(x21281),f556(x21282))
% 187.33/188.06 [2129]~E(x21291,x21292)+E(f783(x21291,x21293,x21294,x21295),f783(x21292,x21293,x21294,x21295))
% 187.33/188.06 [2130]~E(x21301,x21302)+E(f783(x21303,x21301,x21304,x21305),f783(x21303,x21302,x21304,x21305))
% 187.33/188.06 [2131]~E(x21311,x21312)+E(f783(x21313,x21314,x21311,x21315),f783(x21313,x21314,x21312,x21315))
% 187.33/188.06 [2132]~E(x21321,x21322)+E(f783(x21323,x21324,x21325,x21321),f783(x21323,x21324,x21325,x21322))
% 187.33/188.06 [2133]~E(x21331,x21332)+E(f466(x21331,x21333),f466(x21332,x21333))
% 187.33/188.06 [2134]~E(x21341,x21342)+E(f466(x21343,x21341),f466(x21343,x21342))
% 187.33/188.06 [2135]~E(x21351,x21352)+E(f705(x21351,x21353),f705(x21352,x21353))
% 187.33/188.06 [2136]~E(x21361,x21362)+E(f705(x21363,x21361),f705(x21363,x21362))
% 187.33/188.06 [2137]~E(x21371,x21372)+E(f430(x21371,x21373,x21374,x21375),f430(x21372,x21373,x21374,x21375))
% 187.33/188.06 [2138]~E(x21381,x21382)+E(f430(x21383,x21381,x21384,x21385),f430(x21383,x21382,x21384,x21385))
% 187.33/188.06 [2139]~E(x21391,x21392)+E(f430(x21393,x21394,x21391,x21395),f430(x21393,x21394,x21392,x21395))
% 187.33/188.06 [2140]~E(x21401,x21402)+E(f430(x21403,x21404,x21405,x21401),f430(x21403,x21404,x21405,x21402))
% 187.33/188.06 [2141]~E(x21411,x21412)+E(f850(x21411,x21413,x21414,x21415,x21416),f850(x21412,x21413,x21414,x21415,x21416))
% 187.33/188.06 [2142]~E(x21421,x21422)+E(f850(x21423,x21421,x21424,x21425,x21426),f850(x21423,x21422,x21424,x21425,x21426))
% 187.33/188.06 [2143]~E(x21431,x21432)+E(f850(x21433,x21434,x21431,x21435,x21436),f850(x21433,x21434,x21432,x21435,x21436))
% 187.33/188.06 [2144]~E(x21441,x21442)+E(f850(x21443,x21444,x21445,x21441,x21446),f850(x21443,x21444,x21445,x21442,x21446))
% 187.33/188.06 [2145]~E(x21451,x21452)+E(f850(x21453,x21454,x21455,x21456,x21451),f850(x21453,x21454,x21455,x21456,x21452))
% 187.33/188.06 [2146]~E(x21461,x21462)+E(f807(x21461,x21463,x21464),f807(x21462,x21463,x21464))
% 187.33/188.06 [2147]~E(x21471,x21472)+E(f807(x21473,x21471,x21474),f807(x21473,x21472,x21474))
% 187.33/188.06 [2148]~E(x21481,x21482)+E(f807(x21483,x21484,x21481),f807(x21483,x21484,x21482))
% 187.33/188.06 [2149]~E(x21491,x21492)+E(f790(x21491,x21493,x21494,x21495,x21496,x21497,x21498),f790(x21492,x21493,x21494,x21495,x21496,x21497,x21498))
% 187.33/188.06 [2150]~E(x21501,x21502)+E(f790(x21503,x21501,x21504,x21505,x21506,x21507,x21508),f790(x21503,x21502,x21504,x21505,x21506,x21507,x21508))
% 187.33/188.06 [2151]~E(x21511,x21512)+E(f790(x21513,x21514,x21511,x21515,x21516,x21517,x21518),f790(x21513,x21514,x21512,x21515,x21516,x21517,x21518))
% 187.33/188.06 [2152]~E(x21521,x21522)+E(f790(x21523,x21524,x21525,x21521,x21526,x21527,x21528),f790(x21523,x21524,x21525,x21522,x21526,x21527,x21528))
% 187.33/188.06 [2153]~E(x21531,x21532)+E(f790(x21533,x21534,x21535,x21536,x21531,x21537,x21538),f790(x21533,x21534,x21535,x21536,x21532,x21537,x21538))
% 187.33/188.06 [2154]~E(x21541,x21542)+E(f790(x21543,x21544,x21545,x21546,x21547,x21541,x21548),f790(x21543,x21544,x21545,x21546,x21547,x21542,x21548))
% 187.33/188.06 [2155]~E(x21551,x21552)+E(f790(x21553,x21554,x21555,x21556,x21557,x21558,x21551),f790(x21553,x21554,x21555,x21556,x21557,x21558,x21552))
% 187.33/188.06 [2156]~E(x21561,x21562)+E(f340(x21561,x21563,x21564,x21565,x21566),f340(x21562,x21563,x21564,x21565,x21566))
% 187.33/188.06 [2157]~E(x21571,x21572)+E(f340(x21573,x21571,x21574,x21575,x21576),f340(x21573,x21572,x21574,x21575,x21576))
% 187.33/188.06 [2158]~E(x21581,x21582)+E(f340(x21583,x21584,x21581,x21585,x21586),f340(x21583,x21584,x21582,x21585,x21586))
% 187.33/188.06 [2159]~E(x21591,x21592)+E(f340(x21593,x21594,x21595,x21591,x21596),f340(x21593,x21594,x21595,x21592,x21596))
% 187.33/188.06 [2160]~E(x21601,x21602)+E(f340(x21603,x21604,x21605,x21606,x21601),f340(x21603,x21604,x21605,x21606,x21602))
% 187.33/188.06 [2161]~E(x21611,x21612)+E(f545(x21611),f545(x21612))
% 187.33/188.06 [2162]~E(x21621,x21622)+E(f338(x21621,x21623),f338(x21622,x21623))
% 187.33/188.06 [2163]~E(x21631,x21632)+E(f338(x21633,x21631),f338(x21633,x21632))
% 187.33/188.06 [2164]~E(x21641,x21642)+E(f512(x21641,x21643,x21644,x21645,x21646),f512(x21642,x21643,x21644,x21645,x21646))
% 187.33/188.06 [2165]~E(x21651,x21652)+E(f512(x21653,x21651,x21654,x21655,x21656),f512(x21653,x21652,x21654,x21655,x21656))
% 187.33/188.06 [2166]~E(x21661,x21662)+E(f512(x21663,x21664,x21661,x21665,x21666),f512(x21663,x21664,x21662,x21665,x21666))
% 187.33/188.06 [2167]~E(x21671,x21672)+E(f512(x21673,x21674,x21675,x21671,x21676),f512(x21673,x21674,x21675,x21672,x21676))
% 187.33/188.06 [2168]~E(x21681,x21682)+E(f512(x21683,x21684,x21685,x21686,x21681),f512(x21683,x21684,x21685,x21686,x21682))
% 187.33/188.06 [2169]~E(x21691,x21692)+E(f614(x21691,x21693,x21694,x21695,x21696),f614(x21692,x21693,x21694,x21695,x21696))
% 187.33/188.06 [2170]~E(x21701,x21702)+E(f614(x21703,x21701,x21704,x21705,x21706),f614(x21703,x21702,x21704,x21705,x21706))
% 187.33/188.06 [2171]~E(x21711,x21712)+E(f614(x21713,x21714,x21711,x21715,x21716),f614(x21713,x21714,x21712,x21715,x21716))
% 187.33/188.06 [2172]~E(x21721,x21722)+E(f614(x21723,x21724,x21725,x21721,x21726),f614(x21723,x21724,x21725,x21722,x21726))
% 187.33/188.06 [2173]~E(x21731,x21732)+E(f614(x21733,x21734,x21735,x21736,x21731),f614(x21733,x21734,x21735,x21736,x21732))
% 187.33/188.06 [2174]~E(x21741,x21742)+E(f718(x21741,x21743),f718(x21742,x21743))
% 187.33/188.06 [2175]~E(x21751,x21752)+E(f718(x21753,x21751),f718(x21753,x21752))
% 187.33/188.06 [2176]~E(x21761,x21762)+E(f692(x21761,x21763,x21764,x21765),f692(x21762,x21763,x21764,x21765))
% 187.33/188.06 [2177]~E(x21771,x21772)+E(f692(x21773,x21771,x21774,x21775),f692(x21773,x21772,x21774,x21775))
% 187.33/188.06 [2178]~E(x21781,x21782)+E(f692(x21783,x21784,x21781,x21785),f692(x21783,x21784,x21782,x21785))
% 187.33/188.06 [2179]~E(x21791,x21792)+E(f692(x21793,x21794,x21795,x21791),f692(x21793,x21794,x21795,x21792))
% 187.33/188.06 [2180]~E(x21801,x21802)+E(f276(x21801,x21803),f276(x21802,x21803))
% 187.33/188.06 [2181]~E(x21811,x21812)+E(f276(x21813,x21811),f276(x21813,x21812))
% 187.33/188.06 [2182]~E(x21821,x21822)+E(f390(x21821,x21823,x21824,x21825),f390(x21822,x21823,x21824,x21825))
% 187.33/188.06 [2183]~E(x21831,x21832)+E(f390(x21833,x21831,x21834,x21835),f390(x21833,x21832,x21834,x21835))
% 187.33/188.06 [2184]~E(x21841,x21842)+E(f390(x21843,x21844,x21841,x21845),f390(x21843,x21844,x21842,x21845))
% 187.33/188.06 [2185]~E(x21851,x21852)+E(f390(x21853,x21854,x21855,x21851),f390(x21853,x21854,x21855,x21852))
% 187.33/188.06 [2186]~E(x21861,x21862)+E(f314(x21861),f314(x21862))
% 187.33/188.06 [2187]~E(x21871,x21872)+E(f458(x21871,x21873),f458(x21872,x21873))
% 187.33/188.06 [2188]~E(x21881,x21882)+E(f458(x21883,x21881),f458(x21883,x21882))
% 187.33/188.06 [2189]~E(x21891,x21892)+E(f603(x21891,x21893,x21894,x21895),f603(x21892,x21893,x21894,x21895))
% 187.33/188.06 [2190]~E(x21901,x21902)+E(f603(x21903,x21901,x21904,x21905),f603(x21903,x21902,x21904,x21905))
% 187.33/188.06 [2191]~E(x21911,x21912)+E(f603(x21913,x21914,x21911,x21915),f603(x21913,x21914,x21912,x21915))
% 187.33/188.06 [2192]~E(x21921,x21922)+E(f603(x21923,x21924,x21925,x21921),f603(x21923,x21924,x21925,x21922))
% 187.33/188.06 [2193]~E(x21931,x21932)+E(f671(x21931,x21933,x21934,x21935,x21936),f671(x21932,x21933,x21934,x21935,x21936))
% 187.33/188.06 [2194]~E(x21941,x21942)+E(f671(x21943,x21941,x21944,x21945,x21946),f671(x21943,x21942,x21944,x21945,x21946))
% 187.33/188.06 [2195]~E(x21951,x21952)+E(f671(x21953,x21954,x21951,x21955,x21956),f671(x21953,x21954,x21952,x21955,x21956))
% 187.33/188.06 [2196]~E(x21961,x21962)+E(f671(x21963,x21964,x21965,x21961,x21966),f671(x21963,x21964,x21965,x21962,x21966))
% 187.33/188.06 [2197]~E(x21971,x21972)+E(f671(x21973,x21974,x21975,x21976,x21971),f671(x21973,x21974,x21975,x21976,x21972))
% 187.33/188.06 [2198]~E(x21981,x21982)+E(f375(x21981,x21983),f375(x21982,x21983))
% 187.33/188.06 [2199]~E(x21991,x21992)+E(f375(x21993,x21991),f375(x21993,x21992))
% 187.33/188.06 [2200]~E(x22001,x22002)+E(f550(x22001),f550(x22002))
% 187.33/188.06 [2201]~E(x22011,x22012)+E(f217(x22011,x22013,x22014,x22015),f217(x22012,x22013,x22014,x22015))
% 187.33/188.06 [2202]~E(x22021,x22022)+E(f217(x22023,x22021,x22024,x22025),f217(x22023,x22022,x22024,x22025))
% 187.33/188.06 [2203]~E(x22031,x22032)+E(f217(x22033,x22034,x22031,x22035),f217(x22033,x22034,x22032,x22035))
% 187.33/188.06 [2204]~E(x22041,x22042)+E(f217(x22043,x22044,x22045,x22041),f217(x22043,x22044,x22045,x22042))
% 187.33/188.06 [2205]~E(x22051,x22052)+E(f209(x22051),f209(x22052))
% 187.33/188.06 [2206]~E(x22061,x22062)+E(f542(x22061,x22063,x22064,x22065,x22066,x22067,x22068,x22069),f542(x22062,x22063,x22064,x22065,x22066,x22067,x22068,x22069))
% 187.33/188.06 [2207]~E(x22071,x22072)+E(f542(x22073,x22071,x22074,x22075,x22076,x22077,x22078,x22079),f542(x22073,x22072,x22074,x22075,x22076,x22077,x22078,x22079))
% 187.33/188.06 [2208]~E(x22081,x22082)+E(f542(x22083,x22084,x22081,x22085,x22086,x22087,x22088,x22089),f542(x22083,x22084,x22082,x22085,x22086,x22087,x22088,x22089))
% 187.33/188.06 [2209]~E(x22091,x22092)+E(f542(x22093,x22094,x22095,x22091,x22096,x22097,x22098,x22099),f542(x22093,x22094,x22095,x22092,x22096,x22097,x22098,x22099))
% 187.33/188.06 [2210]~E(x22101,x22102)+E(f542(x22103,x22104,x22105,x22106,x22101,x22107,x22108,x22109),f542(x22103,x22104,x22105,x22106,x22102,x22107,x22108,x22109))
% 187.33/188.06 [2211]~E(x22111,x22112)+E(f542(x22113,x22114,x22115,x22116,x22117,x22111,x22118,x22119),f542(x22113,x22114,x22115,x22116,x22117,x22112,x22118,x22119))
% 187.33/188.06 [2212]~E(x22121,x22122)+E(f542(x22123,x22124,x22125,x22126,x22127,x22128,x22121,x22129),f542(x22123,x22124,x22125,x22126,x22127,x22128,x22122,x22129))
% 187.33/188.06 [2213]~E(x22131,x22132)+E(f542(x22133,x22134,x22135,x22136,x22137,x22138,x22139,x22131),f542(x22133,x22134,x22135,x22136,x22137,x22138,x22139,x22132))
% 187.33/188.06 [2214]~E(x22141,x22142)+E(f624(x22141,x22143,x22144,x22145,x22146),f624(x22142,x22143,x22144,x22145,x22146))
% 187.33/188.06 [2215]~E(x22151,x22152)+E(f624(x22153,x22151,x22154,x22155,x22156),f624(x22153,x22152,x22154,x22155,x22156))
% 187.33/188.06 [2216]~E(x22161,x22162)+E(f624(x22163,x22164,x22161,x22165,x22166),f624(x22163,x22164,x22162,x22165,x22166))
% 187.33/188.06 [2217]~E(x22171,x22172)+E(f624(x22173,x22174,x22175,x22171,x22176),f624(x22173,x22174,x22175,x22172,x22176))
% 187.33/188.06 [2218]~E(x22181,x22182)+E(f624(x22183,x22184,x22185,x22186,x22181),f624(x22183,x22184,x22185,x22186,x22182))
% 187.33/188.06 [2219]~E(x22191,x22192)+E(f509(x22191,x22193,x22194,x22195),f509(x22192,x22193,x22194,x22195))
% 187.33/188.06 [2220]~E(x22201,x22202)+E(f509(x22203,x22201,x22204,x22205),f509(x22203,x22202,x22204,x22205))
% 187.33/188.06 [2221]~E(x22211,x22212)+E(f509(x22213,x22214,x22211,x22215),f509(x22213,x22214,x22212,x22215))
% 187.33/188.06 [2222]~E(x22221,x22222)+E(f509(x22223,x22224,x22225,x22221),f509(x22223,x22224,x22225,x22222))
% 187.33/188.06 [2223]~E(x22231,x22232)+E(f98(x22231,x22233,x22234),f98(x22232,x22233,x22234))
% 187.33/188.06 [2224]~E(x22241,x22242)+E(f98(x22243,x22241,x22244),f98(x22243,x22242,x22244))
% 187.33/188.06 [2225]~E(x22251,x22252)+E(f98(x22253,x22254,x22251),f98(x22253,x22254,x22252))
% 187.33/188.06 [2226]~E(x22261,x22262)+E(f847(x22261,x22263,x22264),f847(x22262,x22263,x22264))
% 187.33/188.06 [2227]~E(x22271,x22272)+E(f847(x22273,x22271,x22274),f847(x22273,x22272,x22274))
% 187.33/188.06 [2228]~E(x22281,x22282)+E(f847(x22283,x22284,x22281),f847(x22283,x22284,x22282))
% 187.33/188.06 [2229]~E(x22291,x22292)+E(f736(x22291,x22293,x22294),f736(x22292,x22293,x22294))
% 187.33/188.06 [2230]~E(x22301,x22302)+E(f736(x22303,x22301,x22304),f736(x22303,x22302,x22304))
% 187.33/188.06 [2231]~E(x22311,x22312)+E(f736(x22313,x22314,x22311),f736(x22313,x22314,x22312))
% 187.33/188.06 [2232]~E(x22321,x22322)+E(f581(x22321,x22323,x22324,x22325,x22326,x22327),f581(x22322,x22323,x22324,x22325,x22326,x22327))
% 187.33/188.06 [2233]~E(x22331,x22332)+E(f581(x22333,x22331,x22334,x22335,x22336,x22337),f581(x22333,x22332,x22334,x22335,x22336,x22337))
% 187.33/188.06 [2234]~E(x22341,x22342)+E(f581(x22343,x22344,x22341,x22345,x22346,x22347),f581(x22343,x22344,x22342,x22345,x22346,x22347))
% 187.33/188.06 [2235]~E(x22351,x22352)+E(f581(x22353,x22354,x22355,x22351,x22356,x22357),f581(x22353,x22354,x22355,x22352,x22356,x22357))
% 187.33/188.06 [2236]~E(x22361,x22362)+E(f581(x22363,x22364,x22365,x22366,x22361,x22367),f581(x22363,x22364,x22365,x22366,x22362,x22367))
% 187.33/188.06 [2237]~E(x22371,x22372)+E(f581(x22373,x22374,x22375,x22376,x22377,x22371),f581(x22373,x22374,x22375,x22376,x22377,x22372))
% 187.33/188.06 [2238]~E(x22381,x22382)+E(f806(x22381,x22383),f806(x22382,x22383))
% 187.33/188.06 [2239]~E(x22391,x22392)+E(f806(x22393,x22391),f806(x22393,x22392))
% 187.33/188.06 [2240]~E(x22401,x22402)+E(f122(x22401,x22403,x22404),f122(x22402,x22403,x22404))
% 187.33/188.06 [2241]~E(x22411,x22412)+E(f122(x22413,x22411,x22414),f122(x22413,x22412,x22414))
% 187.33/188.06 [2242]~E(x22421,x22422)+E(f122(x22423,x22424,x22421),f122(x22423,x22424,x22422))
% 187.33/188.06 [2243]~E(x22431,x22432)+E(f856(x22431,x22433,x22434),f856(x22432,x22433,x22434))
% 187.33/188.06 [2244]~E(x22441,x22442)+E(f856(x22443,x22441,x22444),f856(x22443,x22442,x22444))
% 187.33/188.06 [2245]~E(x22451,x22452)+E(f856(x22453,x22454,x22451),f856(x22453,x22454,x22452))
% 187.33/188.06 [2246]~E(x22461,x22462)+E(f845(x22461,x22463,x22464,x22465,x22466),f845(x22462,x22463,x22464,x22465,x22466))
% 187.33/188.06 [2247]~E(x22471,x22472)+E(f845(x22473,x22471,x22474,x22475,x22476),f845(x22473,x22472,x22474,x22475,x22476))
% 187.33/188.06 [2248]~E(x22481,x22482)+E(f845(x22483,x22484,x22481,x22485,x22486),f845(x22483,x22484,x22482,x22485,x22486))
% 187.33/188.06 [2249]~E(x22491,x22492)+E(f845(x22493,x22494,x22495,x22491,x22496),f845(x22493,x22494,x22495,x22492,x22496))
% 187.33/188.06 [2250]~E(x22501,x22502)+E(f845(x22503,x22504,x22505,x22506,x22501),f845(x22503,x22504,x22505,x22506,x22502))
% 187.33/188.06 [2251]~E(x22511,x22512)+E(f407(x22511),f407(x22512))
% 187.33/188.06 [2252]~E(x22521,x22522)+E(f431(x22521,x22523,x22524,x22525),f431(x22522,x22523,x22524,x22525))
% 187.33/188.06 [2253]~E(x22531,x22532)+E(f431(x22533,x22531,x22534,x22535),f431(x22533,x22532,x22534,x22535))
% 187.33/188.06 [2254]~E(x22541,x22542)+E(f431(x22543,x22544,x22541,x22545),f431(x22543,x22544,x22542,x22545))
% 187.33/188.06 [2255]~E(x22551,x22552)+E(f431(x22553,x22554,x22555,x22551),f431(x22553,x22554,x22555,x22552))
% 187.33/188.06 [2256]~E(x22561,x22562)+E(f342(x22561),f342(x22562))
% 187.33/188.06 [2257]~E(x22571,x22572)+E(f566(x22571,x22573,x22574,x22575,x22576,x22577),f566(x22572,x22573,x22574,x22575,x22576,x22577))
% 187.33/188.06 [2258]~E(x22581,x22582)+E(f566(x22583,x22581,x22584,x22585,x22586,x22587),f566(x22583,x22582,x22584,x22585,x22586,x22587))
% 187.33/188.06 [2259]~E(x22591,x22592)+E(f566(x22593,x22594,x22591,x22595,x22596,x22597),f566(x22593,x22594,x22592,x22595,x22596,x22597))
% 187.33/188.06 [2260]~E(x22601,x22602)+E(f566(x22603,x22604,x22605,x22601,x22606,x22607),f566(x22603,x22604,x22605,x22602,x22606,x22607))
% 187.33/188.06 [2261]~E(x22611,x22612)+E(f566(x22613,x22614,x22615,x22616,x22611,x22617),f566(x22613,x22614,x22615,x22616,x22612,x22617))
% 187.33/188.06 [2262]~E(x22621,x22622)+E(f566(x22623,x22624,x22625,x22626,x22627,x22621),f566(x22623,x22624,x22625,x22626,x22627,x22622))
% 187.33/188.06 [2263]~E(x22631,x22632)+E(f554(x22631,x22633),f554(x22632,x22633))
% 187.33/188.06 [2264]~E(x22641,x22642)+E(f554(x22643,x22641),f554(x22643,x22642))
% 187.33/188.06 [2265]~E(x22651,x22652)+E(f721(x22651,x22653,x22654,x22655),f721(x22652,x22653,x22654,x22655))
% 187.33/188.06 [2266]~E(x22661,x22662)+E(f721(x22663,x22661,x22664,x22665),f721(x22663,x22662,x22664,x22665))
% 187.33/188.06 [2267]~E(x22671,x22672)+E(f721(x22673,x22674,x22671,x22675),f721(x22673,x22674,x22672,x22675))
% 187.33/188.06 [2268]~E(x22681,x22682)+E(f721(x22683,x22684,x22685,x22681),f721(x22683,x22684,x22685,x22682))
% 187.33/188.06 [2269]~E(x22691,x22692)+E(f760(x22691,x22693),f760(x22692,x22693))
% 187.33/188.06 [2270]~E(x22701,x22702)+E(f760(x22703,x22701),f760(x22703,x22702))
% 187.33/188.06 [2271]~E(x22711,x22712)+E(f782(x22711,x22713,x22714,x22715),f782(x22712,x22713,x22714,x22715))
% 187.33/188.06 [2272]~E(x22721,x22722)+E(f782(x22723,x22721,x22724,x22725),f782(x22723,x22722,x22724,x22725))
% 187.33/188.06 [2273]~E(x22731,x22732)+E(f782(x22733,x22734,x22731,x22735),f782(x22733,x22734,x22732,x22735))
% 187.33/188.06 [2274]~E(x22741,x22742)+E(f782(x22743,x22744,x22745,x22741),f782(x22743,x22744,x22745,x22742))
% 187.33/188.06 [2275]~E(x22751,x22752)+E(f634(x22751,x22753),f634(x22752,x22753))
% 187.33/188.06 [2276]~E(x22761,x22762)+E(f634(x22763,x22761),f634(x22763,x22762))
% 187.33/188.06 [2277]~E(x22771,x22772)+E(f793(x22771,x22773,x22774),f793(x22772,x22773,x22774))
% 187.33/188.06 [2278]~E(x22781,x22782)+E(f793(x22783,x22781,x22784),f793(x22783,x22782,x22784))
% 187.33/188.06 [2279]~E(x22791,x22792)+E(f793(x22793,x22794,x22791),f793(x22793,x22794,x22792))
% 187.33/188.06 [2280]~E(x22801,x22802)+E(f827(x22801,x22803,x22804,x22805),f827(x22802,x22803,x22804,x22805))
% 187.33/188.06 [2281]~E(x22811,x22812)+E(f827(x22813,x22811,x22814,x22815),f827(x22813,x22812,x22814,x22815))
% 187.33/188.06 [2282]~E(x22821,x22822)+E(f827(x22823,x22824,x22821,x22825),f827(x22823,x22824,x22822,x22825))
% 187.33/188.06 [2283]~E(x22831,x22832)+E(f827(x22833,x22834,x22835,x22831),f827(x22833,x22834,x22835,x22832))
% 187.33/188.06 [2284]~E(x22841,x22842)+E(f689(x22841,x22843),f689(x22842,x22843))
% 187.33/188.06 [2285]~E(x22851,x22852)+E(f689(x22853,x22851),f689(x22853,x22852))
% 187.33/188.06 [2286]~E(x22861,x22862)+E(f797(x22861,x22863,x22864),f797(x22862,x22863,x22864))
% 187.33/188.06 [2287]~E(x22871,x22872)+E(f797(x22873,x22871,x22874),f797(x22873,x22872,x22874))
% 187.33/188.06 [2288]~E(x22881,x22882)+E(f797(x22883,x22884,x22881),f797(x22883,x22884,x22882))
% 187.33/188.06 [2289]~E(x22891,x22892)+E(f448(x22891,x22893,x22894),f448(x22892,x22893,x22894))
% 187.33/188.06 [2290]~E(x22901,x22902)+E(f448(x22903,x22901,x22904),f448(x22903,x22902,x22904))
% 187.33/188.06 [2291]~E(x22911,x22912)+E(f448(x22913,x22914,x22911),f448(x22913,x22914,x22912))
% 187.33/188.06 [2292]~E(x22921,x22922)+E(f532(x22921,x22923,x22924,x22925,x22926),f532(x22922,x22923,x22924,x22925,x22926))
% 187.33/188.06 [2293]~E(x22931,x22932)+E(f532(x22933,x22931,x22934,x22935,x22936),f532(x22933,x22932,x22934,x22935,x22936))
% 187.33/188.06 [2294]~E(x22941,x22942)+E(f532(x22943,x22944,x22941,x22945,x22946),f532(x22943,x22944,x22942,x22945,x22946))
% 187.33/188.06 [2295]~E(x22951,x22952)+E(f532(x22953,x22954,x22955,x22951,x22956),f532(x22953,x22954,x22955,x22952,x22956))
% 187.33/188.06 [2296]~E(x22961,x22962)+E(f532(x22963,x22964,x22965,x22966,x22961),f532(x22963,x22964,x22965,x22966,x22962))
% 187.33/188.06 [2297]~E(x22971,x22972)+E(f358(x22971,x22973),f358(x22972,x22973))
% 187.33/188.06 [2298]~E(x22981,x22982)+E(f358(x22983,x22981),f358(x22983,x22982))
% 187.33/188.06 [2299]~E(x22991,x22992)+E(f520(x22991,x22993),f520(x22992,x22993))
% 187.33/188.06 [2300]~E(x23001,x23002)+E(f520(x23003,x23001),f520(x23003,x23002))
% 187.33/188.06 [2301]~E(x23011,x23012)+E(f767(x23011,x23013,x23014,x23015,x23016),f767(x23012,x23013,x23014,x23015,x23016))
% 187.33/188.06 [2302]~E(x23021,x23022)+E(f767(x23023,x23021,x23024,x23025,x23026),f767(x23023,x23022,x23024,x23025,x23026))
% 187.33/188.06 [2303]~E(x23031,x23032)+E(f767(x23033,x23034,x23031,x23035,x23036),f767(x23033,x23034,x23032,x23035,x23036))
% 187.33/188.06 [2304]~E(x23041,x23042)+E(f767(x23043,x23044,x23045,x23041,x23046),f767(x23043,x23044,x23045,x23042,x23046))
% 187.33/188.06 [2305]~E(x23051,x23052)+E(f767(x23053,x23054,x23055,x23056,x23051),f767(x23053,x23054,x23055,x23056,x23052))
% 187.33/188.06 [2306]~E(x23061,x23062)+E(f619(x23061,x23063,x23064,x23065),f619(x23062,x23063,x23064,x23065))
% 187.33/188.06 [2307]~E(x23071,x23072)+E(f619(x23073,x23071,x23074,x23075),f619(x23073,x23072,x23074,x23075))
% 187.33/188.06 [2308]~E(x23081,x23082)+E(f619(x23083,x23084,x23081,x23085),f619(x23083,x23084,x23082,x23085))
% 187.33/188.06 [2309]~E(x23091,x23092)+E(f619(x23093,x23094,x23095,x23091),f619(x23093,x23094,x23095,x23092))
% 187.33/188.06 [2310]~E(x23101,x23102)+E(f445(x23101,x23103,x23104,x23105,x23106),f445(x23102,x23103,x23104,x23105,x23106))
% 187.33/188.06 [2311]~E(x23111,x23112)+E(f445(x23113,x23111,x23114,x23115,x23116),f445(x23113,x23112,x23114,x23115,x23116))
% 187.33/188.06 [2312]~E(x23121,x23122)+E(f445(x23123,x23124,x23121,x23125,x23126),f445(x23123,x23124,x23122,x23125,x23126))
% 187.33/188.06 [2313]~E(x23131,x23132)+E(f445(x23133,x23134,x23135,x23131,x23136),f445(x23133,x23134,x23135,x23132,x23136))
% 187.33/188.06 [2314]~E(x23141,x23142)+E(f445(x23143,x23144,x23145,x23146,x23141),f445(x23143,x23144,x23145,x23146,x23142))
% 187.33/188.06 [2315]~E(x23151,x23152)+E(f749(x23151,x23153,x23154),f749(x23152,x23153,x23154))
% 187.33/188.06 [2316]~E(x23161,x23162)+E(f749(x23163,x23161,x23164),f749(x23163,x23162,x23164))
% 187.33/188.06 [2317]~E(x23171,x23172)+E(f749(x23173,x23174,x23171),f749(x23173,x23174,x23172))
% 187.33/188.06 [2318]~E(x23181,x23182)+E(f366(x23181,x23183,x23184),f366(x23182,x23183,x23184))
% 187.33/188.06 [2319]~E(x23191,x23192)+E(f366(x23193,x23191,x23194),f366(x23193,x23192,x23194))
% 187.33/188.06 [2320]~E(x23201,x23202)+E(f366(x23203,x23204,x23201),f366(x23203,x23204,x23202))
% 187.33/188.06 [2321]~E(x23211,x23212)+E(f173(x23211,x23213,x23214),f173(x23212,x23213,x23214))
% 187.33/188.06 [2322]~E(x23221,x23222)+E(f173(x23223,x23221,x23224),f173(x23223,x23222,x23224))
% 187.33/188.06 [2323]~E(x23231,x23232)+E(f173(x23233,x23234,x23231),f173(x23233,x23234,x23232))
% 187.33/188.06 [2324]~E(x23241,x23242)+E(f216(x23241),f216(x23242))
% 187.33/188.06 [2325]~E(x23251,x23252)+E(f759(x23251,x23253,x23254,x23255),f759(x23252,x23253,x23254,x23255))
% 187.33/188.06 [2326]~E(x23261,x23262)+E(f759(x23263,x23261,x23264,x23265),f759(x23263,x23262,x23264,x23265))
% 187.33/188.06 [2327]~E(x23271,x23272)+E(f759(x23273,x23274,x23271,x23275),f759(x23273,x23274,x23272,x23275))
% 187.33/188.06 [2328]~E(x23281,x23282)+E(f759(x23283,x23284,x23285,x23281),f759(x23283,x23284,x23285,x23282))
% 187.33/188.06 [2329]~E(x23291,x23292)+E(f499(x23291),f499(x23292))
% 187.33/188.06 [2330]~E(x23301,x23302)+E(f567(x23301,x23303,x23304,x23305,x23306,x23307),f567(x23302,x23303,x23304,x23305,x23306,x23307))
% 187.33/188.06 [2331]~E(x23311,x23312)+E(f567(x23313,x23311,x23314,x23315,x23316,x23317),f567(x23313,x23312,x23314,x23315,x23316,x23317))
% 187.33/188.06 [2332]~E(x23321,x23322)+E(f567(x23323,x23324,x23321,x23325,x23326,x23327),f567(x23323,x23324,x23322,x23325,x23326,x23327))
% 187.33/188.06 [2333]~E(x23331,x23332)+E(f567(x23333,x23334,x23335,x23331,x23336,x23337),f567(x23333,x23334,x23335,x23332,x23336,x23337))
% 187.33/188.06 [2334]~E(x23341,x23342)+E(f567(x23343,x23344,x23345,x23346,x23341,x23347),f567(x23343,x23344,x23345,x23346,x23342,x23347))
% 187.33/188.06 [2335]~E(x23351,x23352)+E(f567(x23353,x23354,x23355,x23356,x23357,x23351),f567(x23353,x23354,x23355,x23356,x23357,x23352))
% 187.33/188.06 [2336]~E(x23361,x23362)+E(f381(x23361,x23363,x23364,x23365),f381(x23362,x23363,x23364,x23365))
% 187.33/188.06 [2337]~E(x23371,x23372)+E(f381(x23373,x23371,x23374,x23375),f381(x23373,x23372,x23374,x23375))
% 187.33/188.06 [2338]~E(x23381,x23382)+E(f381(x23383,x23384,x23381,x23385),f381(x23383,x23384,x23382,x23385))
% 187.33/188.06 [2339]~E(x23391,x23392)+E(f381(x23393,x23394,x23395,x23391),f381(x23393,x23394,x23395,x23392))
% 187.33/188.06 [2340]~E(x23401,x23402)+E(f732(x23401,x23403),f732(x23402,x23403))
% 187.33/188.06 [2341]~E(x23411,x23412)+E(f732(x23413,x23411),f732(x23413,x23412))
% 187.33/188.06 [2342]~E(x23421,x23422)+E(f443(x23421,x23423,x23424,x23425),f443(x23422,x23423,x23424,x23425))
% 187.33/188.06 [2343]~E(x23431,x23432)+E(f443(x23433,x23431,x23434,x23435),f443(x23433,x23432,x23434,x23435))
% 187.33/188.06 [2344]~E(x23441,x23442)+E(f443(x23443,x23444,x23441,x23445),f443(x23443,x23444,x23442,x23445))
% 187.33/188.06 [2345]~E(x23451,x23452)+E(f443(x23453,x23454,x23455,x23451),f443(x23453,x23454,x23455,x23452))
% 187.33/188.06 [2346]~E(x23461,x23462)+E(f219(x23461,x23463,x23464,x23465,x23466,x23467,x23468),f219(x23462,x23463,x23464,x23465,x23466,x23467,x23468))
% 187.33/188.06 [2347]~E(x23471,x23472)+E(f219(x23473,x23471,x23474,x23475,x23476,x23477,x23478),f219(x23473,x23472,x23474,x23475,x23476,x23477,x23478))
% 187.33/188.06 [2348]~E(x23481,x23482)+E(f219(x23483,x23484,x23481,x23485,x23486,x23487,x23488),f219(x23483,x23484,x23482,x23485,x23486,x23487,x23488))
% 187.33/188.06 [2349]~E(x23491,x23492)+E(f219(x23493,x23494,x23495,x23491,x23496,x23497,x23498),f219(x23493,x23494,x23495,x23492,x23496,x23497,x23498))
% 187.33/188.06 [2350]~E(x23501,x23502)+E(f219(x23503,x23504,x23505,x23506,x23501,x23507,x23508),f219(x23503,x23504,x23505,x23506,x23502,x23507,x23508))
% 187.33/188.06 [2351]~E(x23511,x23512)+E(f219(x23513,x23514,x23515,x23516,x23517,x23511,x23518),f219(x23513,x23514,x23515,x23516,x23517,x23512,x23518))
% 187.33/188.06 [2352]~E(x23521,x23522)+E(f219(x23523,x23524,x23525,x23526,x23527,x23528,x23521),f219(x23523,x23524,x23525,x23526,x23527,x23528,x23522))
% 187.33/188.06 [2353]~E(x23531,x23532)+E(f529(x23531,x23533,x23534,x23535),f529(x23532,x23533,x23534,x23535))
% 187.33/188.06 [2354]~E(x23541,x23542)+E(f529(x23543,x23541,x23544,x23545),f529(x23543,x23542,x23544,x23545))
% 187.33/188.06 [2355]~E(x23551,x23552)+E(f529(x23553,x23554,x23551,x23555),f529(x23553,x23554,x23552,x23555))
% 187.33/188.06 [2356]~E(x23561,x23562)+E(f529(x23563,x23564,x23565,x23561),f529(x23563,x23564,x23565,x23562))
% 187.33/188.06 [2357]~E(x23571,x23572)+E(f528(x23571,x23573,x23574,x23575),f528(x23572,x23573,x23574,x23575))
% 187.33/188.06 [2358]~E(x23581,x23582)+E(f528(x23583,x23581,x23584,x23585),f528(x23583,x23582,x23584,x23585))
% 187.33/188.06 [2359]~E(x23591,x23592)+E(f528(x23593,x23594,x23591,x23595),f528(x23593,x23594,x23592,x23595))
% 187.33/188.06 [2360]~E(x23601,x23602)+E(f528(x23603,x23604,x23605,x23601),f528(x23603,x23604,x23605,x23602))
% 187.33/188.06 [2361]~E(x23611,x23612)+E(f523(x23611,x23613),f523(x23612,x23613))
% 187.33/188.06 [2362]~E(x23621,x23622)+E(f523(x23623,x23621),f523(x23623,x23622))
% 187.33/188.06 [2363]~E(x23631,x23632)+E(f525(x23631,x23633,x23634,x23635,x23636),f525(x23632,x23633,x23634,x23635,x23636))
% 187.33/188.06 [2364]~E(x23641,x23642)+E(f525(x23643,x23641,x23644,x23645,x23646),f525(x23643,x23642,x23644,x23645,x23646))
% 187.33/188.06 [2365]~E(x23651,x23652)+E(f525(x23653,x23654,x23651,x23655,x23656),f525(x23653,x23654,x23652,x23655,x23656))
% 187.33/188.06 [2366]~E(x23661,x23662)+E(f525(x23663,x23664,x23665,x23661,x23666),f525(x23663,x23664,x23665,x23662,x23666))
% 187.33/188.06 [2367]~E(x23671,x23672)+E(f525(x23673,x23674,x23675,x23676,x23671),f525(x23673,x23674,x23675,x23676,x23672))
% 187.33/188.06 [2368]~E(x23681,x23682)+E(f518(x23681,x23683,x23684,x23685,x23686),f518(x23682,x23683,x23684,x23685,x23686))
% 187.33/188.06 [2369]~E(x23691,x23692)+E(f518(x23693,x23691,x23694,x23695,x23696),f518(x23693,x23692,x23694,x23695,x23696))
% 187.33/188.06 [2370]~E(x23701,x23702)+E(f518(x23703,x23704,x23701,x23705,x23706),f518(x23703,x23704,x23702,x23705,x23706))
% 187.33/188.06 [2371]~E(x23711,x23712)+E(f518(x23713,x23714,x23715,x23711,x23716),f518(x23713,x23714,x23715,x23712,x23716))
% 187.33/188.06 [2372]~E(x23721,x23722)+E(f518(x23723,x23724,x23725,x23726,x23721),f518(x23723,x23724,x23725,x23726,x23722))
% 187.33/188.06 [2373]~E(x23731,x23732)+E(f833(x23731,x23733,x23734),f833(x23732,x23733,x23734))
% 187.33/188.06 [2374]~E(x23741,x23742)+E(f833(x23743,x23741,x23744),f833(x23743,x23742,x23744))
% 187.33/188.06 [2375]~E(x23751,x23752)+E(f833(x23753,x23754,x23751),f833(x23753,x23754,x23752))
% 187.33/188.06 [2376]~E(x23761,x23762)+E(f389(x23761,x23763,x23764,x23765),f389(x23762,x23763,x23764,x23765))
% 187.33/188.06 [2377]~E(x23771,x23772)+E(f389(x23773,x23771,x23774,x23775),f389(x23773,x23772,x23774,x23775))
% 187.33/188.06 [2378]~E(x23781,x23782)+E(f389(x23783,x23784,x23781,x23785),f389(x23783,x23784,x23782,x23785))
% 187.33/188.06 [2379]~E(x23791,x23792)+E(f389(x23793,x23794,x23795,x23791),f389(x23793,x23794,x23795,x23792))
% 187.33/188.06 [2380]~E(x23801,x23802)+E(f601(x23801,x23803,x23804),f601(x23802,x23803,x23804))
% 187.33/188.06 [2381]~E(x23811,x23812)+E(f601(x23813,x23811,x23814),f601(x23813,x23812,x23814))
% 187.33/188.06 [2382]~E(x23821,x23822)+E(f601(x23823,x23824,x23821),f601(x23823,x23824,x23822))
% 187.33/188.06 [2383]~E(x23831,x23832)+E(f627(x23831,x23833,x23834,x23835,x23836),f627(x23832,x23833,x23834,x23835,x23836))
% 187.33/188.06 [2384]~E(x23841,x23842)+E(f627(x23843,x23841,x23844,x23845,x23846),f627(x23843,x23842,x23844,x23845,x23846))
% 187.33/188.06 [2385]~E(x23851,x23852)+E(f627(x23853,x23854,x23851,x23855,x23856),f627(x23853,x23854,x23852,x23855,x23856))
% 187.33/188.06 [2386]~E(x23861,x23862)+E(f627(x23863,x23864,x23865,x23861,x23866),f627(x23863,x23864,x23865,x23862,x23866))
% 187.33/188.06 [2387]~E(x23871,x23872)+E(f627(x23873,x23874,x23875,x23876,x23871),f627(x23873,x23874,x23875,x23876,x23872))
% 187.33/188.06 [2388]~E(x23881,x23882)+E(f743(x23881,x23883),f743(x23882,x23883))
% 187.33/188.06 [2389]~E(x23891,x23892)+E(f743(x23893,x23891),f743(x23893,x23892))
% 187.33/188.06 [2390]~E(x23901,x23902)+E(f623(x23901,x23903,x23904,x23905,x23906,x23907,x23908),f623(x23902,x23903,x23904,x23905,x23906,x23907,x23908))
% 187.33/188.06 [2391]~E(x23911,x23912)+E(f623(x23913,x23911,x23914,x23915,x23916,x23917,x23918),f623(x23913,x23912,x23914,x23915,x23916,x23917,x23918))
% 187.33/188.06 [2392]~E(x23921,x23922)+E(f623(x23923,x23924,x23921,x23925,x23926,x23927,x23928),f623(x23923,x23924,x23922,x23925,x23926,x23927,x23928))
% 187.33/188.06 [2393]~E(x23931,x23932)+E(f623(x23933,x23934,x23935,x23931,x23936,x23937,x23938),f623(x23933,x23934,x23935,x23932,x23936,x23937,x23938))
% 187.33/188.06 [2394]~E(x23941,x23942)+E(f623(x23943,x23944,x23945,x23946,x23941,x23947,x23948),f623(x23943,x23944,x23945,x23946,x23942,x23947,x23948))
% 187.33/188.06 [2395]~E(x23951,x23952)+E(f623(x23953,x23954,x23955,x23956,x23957,x23951,x23958),f623(x23953,x23954,x23955,x23956,x23957,x23952,x23958))
% 187.33/188.06 [2396]~E(x23961,x23962)+E(f623(x23963,x23964,x23965,x23966,x23967,x23968,x23961),f623(x23963,x23964,x23965,x23966,x23967,x23968,x23962))
% 187.33/188.06 [2397]~E(x23971,x23972)+E(f842(x23971,x23973,x23974,x23975,x23976),f842(x23972,x23973,x23974,x23975,x23976))
% 187.33/188.06 [2398]~E(x23981,x23982)+E(f842(x23983,x23981,x23984,x23985,x23986),f842(x23983,x23982,x23984,x23985,x23986))
% 187.33/188.06 [2399]~E(x23991,x23992)+E(f842(x23993,x23994,x23991,x23995,x23996),f842(x23993,x23994,x23992,x23995,x23996))
% 187.33/188.06 [2400]~E(x24001,x24002)+E(f842(x24003,x24004,x24005,x24001,x24006),f842(x24003,x24004,x24005,x24002,x24006))
% 187.33/188.06 [2401]~E(x24011,x24012)+E(f842(x24013,x24014,x24015,x24016,x24011),f842(x24013,x24014,x24015,x24016,x24012))
% 187.33/188.06 [2402]~E(x24021,x24022)+E(f860(x24021,x24023,x24024),f860(x24022,x24023,x24024))
% 187.33/188.06 [2403]~E(x24031,x24032)+E(f860(x24033,x24031,x24034),f860(x24033,x24032,x24034))
% 187.33/188.06 [2404]~E(x24041,x24042)+E(f860(x24043,x24044,x24041),f860(x24043,x24044,x24042))
% 187.33/188.06 [2405]~E(x24051,x24052)+E(f703(x24051,x24053,x24054,x24055,x24056),f703(x24052,x24053,x24054,x24055,x24056))
% 187.33/188.06 [2406]~E(x24061,x24062)+E(f703(x24063,x24061,x24064,x24065,x24066),f703(x24063,x24062,x24064,x24065,x24066))
% 187.33/188.06 [2407]~E(x24071,x24072)+E(f703(x24073,x24074,x24071,x24075,x24076),f703(x24073,x24074,x24072,x24075,x24076))
% 187.33/188.06 [2408]~E(x24081,x24082)+E(f703(x24083,x24084,x24085,x24081,x24086),f703(x24083,x24084,x24085,x24082,x24086))
% 187.33/188.06 [2409]~E(x24091,x24092)+E(f703(x24093,x24094,x24095,x24096,x24091),f703(x24093,x24094,x24095,x24096,x24092))
% 187.33/188.06 [2410]~E(x24101,x24102)+E(f645(x24101,x24103,x24104,x24105,x24106,x24107),f645(x24102,x24103,x24104,x24105,x24106,x24107))
% 187.33/188.06 [2411]~E(x24111,x24112)+E(f645(x24113,x24111,x24114,x24115,x24116,x24117),f645(x24113,x24112,x24114,x24115,x24116,x24117))
% 187.33/188.06 [2412]~E(x24121,x24122)+E(f645(x24123,x24124,x24121,x24125,x24126,x24127),f645(x24123,x24124,x24122,x24125,x24126,x24127))
% 187.33/188.06 [2413]~E(x24131,x24132)+E(f645(x24133,x24134,x24135,x24131,x24136,x24137),f645(x24133,x24134,x24135,x24132,x24136,x24137))
% 187.33/188.06 [2414]~E(x24141,x24142)+E(f645(x24143,x24144,x24145,x24146,x24141,x24147),f645(x24143,x24144,x24145,x24146,x24142,x24147))
% 187.33/188.06 [2415]~E(x24151,x24152)+E(f645(x24153,x24154,x24155,x24156,x24157,x24151),f645(x24153,x24154,x24155,x24156,x24157,x24152))
% 187.33/188.06 [2416]~E(x24161,x24162)+E(f543(x24161,x24163,x24164,x24165,x24166,x24167,x24168,x24169),f543(x24162,x24163,x24164,x24165,x24166,x24167,x24168,x24169))
% 187.33/188.06 [2417]~E(x24171,x24172)+E(f543(x24173,x24171,x24174,x24175,x24176,x24177,x24178,x24179),f543(x24173,x24172,x24174,x24175,x24176,x24177,x24178,x24179))
% 187.33/188.06 [2418]~E(x24181,x24182)+E(f543(x24183,x24184,x24181,x24185,x24186,x24187,x24188,x24189),f543(x24183,x24184,x24182,x24185,x24186,x24187,x24188,x24189))
% 187.33/188.06 [2419]~E(x24191,x24192)+E(f543(x24193,x24194,x24195,x24191,x24196,x24197,x24198,x24199),f543(x24193,x24194,x24195,x24192,x24196,x24197,x24198,x24199))
% 187.33/188.06 [2420]~E(x24201,x24202)+E(f543(x24203,x24204,x24205,x24206,x24201,x24207,x24208,x24209),f543(x24203,x24204,x24205,x24206,x24202,x24207,x24208,x24209))
% 187.33/188.06 [2421]~E(x24211,x24212)+E(f543(x24213,x24214,x24215,x24216,x24217,x24211,x24218,x24219),f543(x24213,x24214,x24215,x24216,x24217,x24212,x24218,x24219))
% 187.33/188.06 [2422]~E(x24221,x24222)+E(f543(x24223,x24224,x24225,x24226,x24227,x24228,x24221,x24229),f543(x24223,x24224,x24225,x24226,x24227,x24228,x24222,x24229))
% 187.33/188.06 [2423]~E(x24231,x24232)+E(f543(x24233,x24234,x24235,x24236,x24237,x24238,x24239,x24231),f543(x24233,x24234,x24235,x24236,x24237,x24238,x24239,x24232))
% 187.33/188.06 [2424]~E(x24241,x24242)+E(f436(x24241,x24243,x24244,x24245,x24246),f436(x24242,x24243,x24244,x24245,x24246))
% 187.33/188.06 [2425]~E(x24251,x24252)+E(f436(x24253,x24251,x24254,x24255,x24256),f436(x24253,x24252,x24254,x24255,x24256))
% 187.33/188.06 [2426]~E(x24261,x24262)+E(f436(x24263,x24264,x24261,x24265,x24266),f436(x24263,x24264,x24262,x24265,x24266))
% 187.33/188.06 [2427]~E(x24271,x24272)+E(f436(x24273,x24274,x24275,x24271,x24276),f436(x24273,x24274,x24275,x24272,x24276))
% 187.33/188.06 [2428]~E(x24281,x24282)+E(f436(x24283,x24284,x24285,x24286,x24281),f436(x24283,x24284,x24285,x24286,x24282))
% 187.33/188.06 [2429]~E(x24291,x24292)+E(f812(x24291,x24293,x24294,x24295),f812(x24292,x24293,x24294,x24295))
% 187.33/188.06 [2430]~E(x24301,x24302)+E(f812(x24303,x24301,x24304,x24305),f812(x24303,x24302,x24304,x24305))
% 187.33/188.06 [2431]~E(x24311,x24312)+E(f812(x24313,x24314,x24311,x24315),f812(x24313,x24314,x24312,x24315))
% 187.33/188.06 [2432]~E(x24321,x24322)+E(f812(x24323,x24324,x24325,x24321),f812(x24323,x24324,x24325,x24322))
% 187.33/188.06 [2433]~E(x24331,x24332)+E(f230(x24331,x24333,x24334,x24335),f230(x24332,x24333,x24334,x24335))
% 187.33/188.06 [2434]~E(x24341,x24342)+E(f230(x24343,x24341,x24344,x24345),f230(x24343,x24342,x24344,x24345))
% 187.33/188.06 [2435]~E(x24351,x24352)+E(f230(x24353,x24354,x24351,x24355),f230(x24353,x24354,x24352,x24355))
% 187.33/188.06 [2436]~E(x24361,x24362)+E(f230(x24363,x24364,x24365,x24361),f230(x24363,x24364,x24365,x24362))
% 187.33/188.06 [2437]~E(x24371,x24372)+E(f506(x24371,x24373,x24374,x24375,x24376,x24377,x24378),f506(x24372,x24373,x24374,x24375,x24376,x24377,x24378))
% 187.33/188.06 [2438]~E(x24381,x24382)+E(f506(x24383,x24381,x24384,x24385,x24386,x24387,x24388),f506(x24383,x24382,x24384,x24385,x24386,x24387,x24388))
% 187.33/188.06 [2439]~E(x24391,x24392)+E(f506(x24393,x24394,x24391,x24395,x24396,x24397,x24398),f506(x24393,x24394,x24392,x24395,x24396,x24397,x24398))
% 187.33/188.06 [2440]~E(x24401,x24402)+E(f506(x24403,x24404,x24405,x24401,x24406,x24407,x24408),f506(x24403,x24404,x24405,x24402,x24406,x24407,x24408))
% 187.33/188.06 [2441]~E(x24411,x24412)+E(f506(x24413,x24414,x24415,x24416,x24411,x24417,x24418),f506(x24413,x24414,x24415,x24416,x24412,x24417,x24418))
% 187.33/188.06 [2442]~E(x24421,x24422)+E(f506(x24423,x24424,x24425,x24426,x24427,x24421,x24428),f506(x24423,x24424,x24425,x24426,x24427,x24422,x24428))
% 187.33/188.06 [2443]~E(x24431,x24432)+E(f506(x24433,x24434,x24435,x24436,x24437,x24438,x24431),f506(x24433,x24434,x24435,x24436,x24437,x24438,x24432))
% 187.33/188.06 [2444]~E(x24441,x24442)+E(f498(x24441,x24443,x24444,x24445,x24446),f498(x24442,x24443,x24444,x24445,x24446))
% 187.33/188.06 [2445]~E(x24451,x24452)+E(f498(x24453,x24451,x24454,x24455,x24456),f498(x24453,x24452,x24454,x24455,x24456))
% 187.33/188.06 [2446]~E(x24461,x24462)+E(f498(x24463,x24464,x24461,x24465,x24466),f498(x24463,x24464,x24462,x24465,x24466))
% 187.33/188.06 [2447]~E(x24471,x24472)+E(f498(x24473,x24474,x24475,x24471,x24476),f498(x24473,x24474,x24475,x24472,x24476))
% 187.33/188.06 [2448]~E(x24481,x24482)+E(f498(x24483,x24484,x24485,x24486,x24481),f498(x24483,x24484,x24485,x24486,x24482))
% 187.33/188.06 [2449]~E(x24491,x24492)+E(f124(x24491,x24493,x24494,x24495),f124(x24492,x24493,x24494,x24495))
% 187.33/188.06 [2450]~E(x24501,x24502)+E(f124(x24503,x24501,x24504,x24505),f124(x24503,x24502,x24504,x24505))
% 187.33/188.06 [2451]~E(x24511,x24512)+E(f124(x24513,x24514,x24511,x24515),f124(x24513,x24514,x24512,x24515))
% 187.33/188.06 [2452]~E(x24521,x24522)+E(f124(x24523,x24524,x24525,x24521),f124(x24523,x24524,x24525,x24522))
% 187.33/188.06 [2453]~E(x24531,x24532)+E(f463(x24531,x24533,x24534),f463(x24532,x24533,x24534))
% 187.33/188.06 [2454]~E(x24541,x24542)+E(f463(x24543,x24541,x24544),f463(x24543,x24542,x24544))
% 187.33/188.06 [2455]~E(x24551,x24552)+E(f463(x24553,x24554,x24551),f463(x24553,x24554,x24552))
% 187.33/188.06 [2456]~E(x24561,x24562)+E(f515(x24561,x24563,x24564),f515(x24562,x24563,x24564))
% 187.33/188.06 [2457]~E(x24571,x24572)+E(f515(x24573,x24571,x24574),f515(x24573,x24572,x24574))
% 187.33/188.06 [2458]~E(x24581,x24582)+E(f515(x24583,x24584,x24581),f515(x24583,x24584,x24582))
% 187.33/188.06 [2459]~E(x24591,x24592)+E(f715(x24591,x24593,x24594,x24595,x24596),f715(x24592,x24593,x24594,x24595,x24596))
% 187.33/188.06 [2460]~E(x24601,x24602)+E(f715(x24603,x24601,x24604,x24605,x24606),f715(x24603,x24602,x24604,x24605,x24606))
% 187.33/188.06 [2461]~E(x24611,x24612)+E(f715(x24613,x24614,x24611,x24615,x24616),f715(x24613,x24614,x24612,x24615,x24616))
% 187.33/188.06 [2462]~E(x24621,x24622)+E(f715(x24623,x24624,x24625,x24621,x24626),f715(x24623,x24624,x24625,x24622,x24626))
% 187.33/188.06 [2463]~E(x24631,x24632)+E(f715(x24633,x24634,x24635,x24636,x24631),f715(x24633,x24634,x24635,x24636,x24632))
% 187.33/188.06 [2464]~E(x24641,x24642)+E(f180(x24641),f180(x24642))
% 187.33/188.06 [2465]~E(x24651,x24652)+E(f454(x24651,x24653),f454(x24652,x24653))
% 187.33/188.06 [2466]~E(x24661,x24662)+E(f454(x24663,x24661),f454(x24663,x24662))
% 187.33/188.06 [2467]~E(x24671,x24672)+E(f762(x24671,x24673,x24674),f762(x24672,x24673,x24674))
% 187.33/188.06 [2468]~E(x24681,x24682)+E(f762(x24683,x24681,x24684),f762(x24683,x24682,x24684))
% 187.33/188.06 [2469]~E(x24691,x24692)+E(f762(x24693,x24694,x24691),f762(x24693,x24694,x24692))
% 187.33/188.06 [2470]~E(x24701,x24702)+E(f388(x24701,x24703,x24704,x24705),f388(x24702,x24703,x24704,x24705))
% 187.33/188.06 [2471]~E(x24711,x24712)+E(f388(x24713,x24711,x24714,x24715),f388(x24713,x24712,x24714,x24715))
% 187.33/188.06 [2472]~E(x24721,x24722)+E(f388(x24723,x24724,x24721,x24725),f388(x24723,x24724,x24722,x24725))
% 187.33/188.06 [2473]~E(x24731,x24732)+E(f388(x24733,x24734,x24735,x24731),f388(x24733,x24734,x24735,x24732))
% 187.33/188.06 [2474]~E(x24741,x24742)+E(f504(x24741,x24743,x24744,x24745,x24746,x24747,x24748),f504(x24742,x24743,x24744,x24745,x24746,x24747,x24748))
% 187.33/188.06 [2475]~E(x24751,x24752)+E(f504(x24753,x24751,x24754,x24755,x24756,x24757,x24758),f504(x24753,x24752,x24754,x24755,x24756,x24757,x24758))
% 187.33/188.06 [2476]~E(x24761,x24762)+E(f504(x24763,x24764,x24761,x24765,x24766,x24767,x24768),f504(x24763,x24764,x24762,x24765,x24766,x24767,x24768))
% 187.33/188.06 [2477]~E(x24771,x24772)+E(f504(x24773,x24774,x24775,x24771,x24776,x24777,x24778),f504(x24773,x24774,x24775,x24772,x24776,x24777,x24778))
% 187.33/188.06 [2478]~E(x24781,x24782)+E(f504(x24783,x24784,x24785,x24786,x24781,x24787,x24788),f504(x24783,x24784,x24785,x24786,x24782,x24787,x24788))
% 187.33/188.06 [2479]~E(x24791,x24792)+E(f504(x24793,x24794,x24795,x24796,x24797,x24791,x24798),f504(x24793,x24794,x24795,x24796,x24797,x24792,x24798))
% 187.33/188.06 [2480]~E(x24801,x24802)+E(f504(x24803,x24804,x24805,x24806,x24807,x24808,x24801),f504(x24803,x24804,x24805,x24806,x24807,x24808,x24802))
% 187.33/188.06 [2481]~E(x24811,x24812)+E(f582(x24811,x24813,x24814),f582(x24812,x24813,x24814))
% 187.33/188.06 [2482]~E(x24821,x24822)+E(f582(x24823,x24821,x24824),f582(x24823,x24822,x24824))
% 187.33/188.06 [2483]~E(x24831,x24832)+E(f582(x24833,x24834,x24831),f582(x24833,x24834,x24832))
% 187.33/188.06 [2484]~E(x24841,x24842)+E(f461(x24841,x24843,x24844,x24845,x24846,x24847),f461(x24842,x24843,x24844,x24845,x24846,x24847))
% 187.33/188.06 [2485]~E(x24851,x24852)+E(f461(x24853,x24851,x24854,x24855,x24856,x24857),f461(x24853,x24852,x24854,x24855,x24856,x24857))
% 187.33/188.06 [2486]~E(x24861,x24862)+E(f461(x24863,x24864,x24861,x24865,x24866,x24867),f461(x24863,x24864,x24862,x24865,x24866,x24867))
% 187.33/188.06 [2487]~E(x24871,x24872)+E(f461(x24873,x24874,x24875,x24871,x24876,x24877),f461(x24873,x24874,x24875,x24872,x24876,x24877))
% 187.33/188.06 [2488]~E(x24881,x24882)+E(f461(x24883,x24884,x24885,x24886,x24881,x24887),f461(x24883,x24884,x24885,x24886,x24882,x24887))
% 187.33/188.06 [2489]~E(x24891,x24892)+E(f461(x24893,x24894,x24895,x24896,x24897,x24891),f461(x24893,x24894,x24895,x24896,x24897,x24892))
% 187.33/188.06 [2490]~E(x24901,x24902)+E(f738(x24901,x24903,x24904,x24905,x24906),f738(x24902,x24903,x24904,x24905,x24906))
% 187.33/188.06 [2491]~E(x24911,x24912)+E(f738(x24913,x24911,x24914,x24915,x24916),f738(x24913,x24912,x24914,x24915,x24916))
% 187.33/188.06 [2492]~E(x24921,x24922)+E(f738(x24923,x24924,x24921,x24925,x24926),f738(x24923,x24924,x24922,x24925,x24926))
% 187.33/188.06 [2493]~E(x24931,x24932)+E(f738(x24933,x24934,x24935,x24931,x24936),f738(x24933,x24934,x24935,x24932,x24936))
% 187.33/188.06 [2494]~E(x24941,x24942)+E(f738(x24943,x24944,x24945,x24946,x24941),f738(x24943,x24944,x24945,x24946,x24942))
% 187.33/188.06 [2495]~E(x24951,x24952)+E(f347(x24951),f347(x24952))
% 187.33/188.06 [2496]~E(x24961,x24962)+E(f531(x24961,x24963,x24964,x24965),f531(x24962,x24963,x24964,x24965))
% 187.33/188.06 [2497]~E(x24971,x24972)+E(f531(x24973,x24971,x24974,x24975),f531(x24973,x24972,x24974,x24975))
% 187.33/188.06 [2498]~E(x24981,x24982)+E(f531(x24983,x24984,x24981,x24985),f531(x24983,x24984,x24982,x24985))
% 187.33/188.06 [2499]~E(x24991,x24992)+E(f531(x24993,x24994,x24995,x24991),f531(x24993,x24994,x24995,x24992))
% 187.33/188.06 [2500]~E(x25001,x25002)+E(f799(x25001,x25003,x25004),f799(x25002,x25003,x25004))
% 187.33/188.06 [2501]~E(x25011,x25012)+E(f799(x25013,x25011,x25014),f799(x25013,x25012,x25014))
% 187.33/188.06 [2502]~E(x25021,x25022)+E(f799(x25023,x25024,x25021),f799(x25023,x25024,x25022))
% 187.33/188.06 [2503]~E(x25031,x25032)+E(f853(x25031,x25033,x25034,x25035,x25036),f853(x25032,x25033,x25034,x25035,x25036))
% 187.33/188.06 [2504]~E(x25041,x25042)+E(f853(x25043,x25041,x25044,x25045,x25046),f853(x25043,x25042,x25044,x25045,x25046))
% 187.33/188.06 [2505]~E(x25051,x25052)+E(f853(x25053,x25054,x25051,x25055,x25056),f853(x25053,x25054,x25052,x25055,x25056))
% 187.33/188.06 [2506]~E(x25061,x25062)+E(f853(x25063,x25064,x25065,x25061,x25066),f853(x25063,x25064,x25065,x25062,x25066))
% 187.33/188.06 [2507]~E(x25071,x25072)+E(f853(x25073,x25074,x25075,x25076,x25071),f853(x25073,x25074,x25075,x25076,x25072))
% 187.33/188.06 [2508]~E(x25081,x25082)+E(f547(x25081,x25083),f547(x25082,x25083))
% 187.33/188.06 [2509]~E(x25091,x25092)+E(f547(x25093,x25091),f547(x25093,x25092))
% 187.33/188.06 [2510]~E(x25101,x25102)+E(f380(x25101,x25103,x25104,x25105),f380(x25102,x25103,x25104,x25105))
% 187.33/188.06 [2511]~E(x25111,x25112)+E(f380(x25113,x25111,x25114,x25115),f380(x25113,x25112,x25114,x25115))
% 187.33/188.06 [2512]~E(x25121,x25122)+E(f380(x25123,x25124,x25121,x25125),f380(x25123,x25124,x25122,x25125))
% 187.33/188.06 [2513]~E(x25131,x25132)+E(f380(x25133,x25134,x25135,x25131),f380(x25133,x25134,x25135,x25132))
% 187.33/188.06 [2514]~E(x25141,x25142)+E(f222(x25141,x25143),f222(x25142,x25143))
% 187.33/188.06 [2515]~E(x25151,x25152)+E(f222(x25153,x25151),f222(x25153,x25152))
% 187.33/188.06 [2516]~E(x25161,x25162)+E(f421(x25161,x25163),f421(x25162,x25163))
% 187.33/188.06 [2517]~E(x25171,x25172)+E(f421(x25173,x25171),f421(x25173,x25172))
% 187.33/188.06 [2518]~E(x25181,x25182)+E(f376(x25181,x25183),f376(x25182,x25183))
% 187.33/188.06 [2519]~E(x25191,x25192)+E(f376(x25193,x25191),f376(x25193,x25192))
% 187.33/188.06 [2520]~E(x25201,x25202)+E(f716(x25201,x25203),f716(x25202,x25203))
% 187.33/188.06 [2521]~E(x25211,x25212)+E(f716(x25213,x25211),f716(x25213,x25212))
% 187.33/188.06 [2522]~E(x25221,x25222)+E(f813(x25221,x25223,x25224,x25225),f813(x25222,x25223,x25224,x25225))
% 187.33/188.06 [2523]~E(x25231,x25232)+E(f813(x25233,x25231,x25234,x25235),f813(x25233,x25232,x25234,x25235))
% 187.33/188.06 [2524]~E(x25241,x25242)+E(f813(x25243,x25244,x25241,x25245),f813(x25243,x25244,x25242,x25245))
% 187.33/188.06 [2525]~E(x25251,x25252)+E(f813(x25253,x25254,x25255,x25251),f813(x25253,x25254,x25255,x25252))
% 187.33/188.06 [2526]~E(x25261,x25262)+E(f501(x25261,x25263),f501(x25262,x25263))
% 187.33/188.06 [2527]~E(x25271,x25272)+E(f501(x25273,x25271),f501(x25273,x25272))
% 187.33/188.06 [2528]~E(x25281,x25282)+E(f674(x25281,x25283,x25284),f674(x25282,x25283,x25284))
% 187.33/188.06 [2529]~E(x25291,x25292)+E(f674(x25293,x25291,x25294),f674(x25293,x25292,x25294))
% 187.33/188.06 [2530]~E(x25301,x25302)+E(f674(x25303,x25304,x25301),f674(x25303,x25304,x25302))
% 187.33/188.06 [2531]~E(x25311,x25312)+E(f213(x25311,x25313,x25314,x25315),f213(x25312,x25313,x25314,x25315))
% 187.33/188.06 [2532]~E(x25321,x25322)+E(f213(x25323,x25321,x25324,x25325),f213(x25323,x25322,x25324,x25325))
% 187.33/188.06 [2533]~E(x25331,x25332)+E(f213(x25333,x25334,x25331,x25335),f213(x25333,x25334,x25332,x25335))
% 187.33/188.06 [2534]~E(x25341,x25342)+E(f213(x25343,x25344,x25345,x25341),f213(x25343,x25344,x25345,x25342))
% 187.33/188.06 [2535]~E(x25351,x25352)+E(f279(x25351,x25353,x25354),f279(x25352,x25353,x25354))
% 187.33/188.06 [2536]~E(x25361,x25362)+E(f279(x25363,x25361,x25364),f279(x25363,x25362,x25364))
% 187.33/188.06 [2537]~E(x25371,x25372)+E(f279(x25373,x25374,x25371),f279(x25373,x25374,x25372))
% 187.33/188.06 [2538]~E(x25381,x25382)+E(f424(x25381,x25383),f424(x25382,x25383))
% 187.33/188.06 [2539]~E(x25391,x25392)+E(f424(x25393,x25391),f424(x25393,x25392))
% 187.33/188.06 [2540]~E(x25401,x25402)+E(f586(x25401,x25403,x25404,x25405,x25406),f586(x25402,x25403,x25404,x25405,x25406))
% 187.33/188.06 [2541]~E(x25411,x25412)+E(f586(x25413,x25411,x25414,x25415,x25416),f586(x25413,x25412,x25414,x25415,x25416))
% 187.33/188.06 [2542]~E(x25421,x25422)+E(f586(x25423,x25424,x25421,x25425,x25426),f586(x25423,x25424,x25422,x25425,x25426))
% 187.33/188.06 [2543]~E(x25431,x25432)+E(f586(x25433,x25434,x25435,x25431,x25436),f586(x25433,x25434,x25435,x25432,x25436))
% 187.33/188.06 [2544]~E(x25441,x25442)+E(f586(x25443,x25444,x25445,x25446,x25441),f586(x25443,x25444,x25445,x25446,x25442))
% 187.33/188.06 [2545]~E(x25451,x25452)+E(f441(x25451,x25453,x25454,x25455,x25456),f441(x25452,x25453,x25454,x25455,x25456))
% 187.33/188.06 [2546]~E(x25461,x25462)+E(f441(x25463,x25461,x25464,x25465,x25466),f441(x25463,x25462,x25464,x25465,x25466))
% 187.33/188.06 [2547]~E(x25471,x25472)+E(f441(x25473,x25474,x25471,x25475,x25476),f441(x25473,x25474,x25472,x25475,x25476))
% 187.33/188.06 [2548]~E(x25481,x25482)+E(f441(x25483,x25484,x25485,x25481,x25486),f441(x25483,x25484,x25485,x25482,x25486))
% 187.33/188.06 [2549]~E(x25491,x25492)+E(f441(x25493,x25494,x25495,x25496,x25491),f441(x25493,x25494,x25495,x25496,x25492))
% 187.33/188.06 [2550]~E(x25501,x25502)+E(f616(x25501,x25503,x25504,x25505,x25506),f616(x25502,x25503,x25504,x25505,x25506))
% 187.33/188.06 [2551]~E(x25511,x25512)+E(f616(x25513,x25511,x25514,x25515,x25516),f616(x25513,x25512,x25514,x25515,x25516))
% 187.33/188.06 [2552]~E(x25521,x25522)+E(f616(x25523,x25524,x25521,x25525,x25526),f616(x25523,x25524,x25522,x25525,x25526))
% 187.33/188.06 [2553]~E(x25531,x25532)+E(f616(x25533,x25534,x25535,x25531,x25536),f616(x25533,x25534,x25535,x25532,x25536))
% 187.33/188.06 [2554]~E(x25541,x25542)+E(f616(x25543,x25544,x25545,x25546,x25541),f616(x25543,x25544,x25545,x25546,x25542))
% 187.33/188.06 [2555]~E(x25551,x25552)+E(f861(x25551,x25553,x25554),f861(x25552,x25553,x25554))
% 187.33/188.06 [2556]~E(x25561,x25562)+E(f861(x25563,x25561,x25564),f861(x25563,x25562,x25564))
% 187.33/188.06 [2557]~E(x25571,x25572)+E(f861(x25573,x25574,x25571),f861(x25573,x25574,x25572))
% 187.33/188.06 [2558]~E(x25581,x25582)+E(f789(x25581,x25583,x25584,x25585,x25586,x25587,x25588),f789(x25582,x25583,x25584,x25585,x25586,x25587,x25588))
% 187.33/188.06 [2559]~E(x25591,x25592)+E(f789(x25593,x25591,x25594,x25595,x25596,x25597,x25598),f789(x25593,x25592,x25594,x25595,x25596,x25597,x25598))
% 187.33/188.06 [2560]~E(x25601,x25602)+E(f789(x25603,x25604,x25601,x25605,x25606,x25607,x25608),f789(x25603,x25604,x25602,x25605,x25606,x25607,x25608))
% 187.33/188.06 [2561]~E(x25611,x25612)+E(f789(x25613,x25614,x25615,x25611,x25616,x25617,x25618),f789(x25613,x25614,x25615,x25612,x25616,x25617,x25618))
% 187.33/188.06 [2562]~E(x25621,x25622)+E(f789(x25623,x25624,x25625,x25626,x25621,x25627,x25628),f789(x25623,x25624,x25625,x25626,x25622,x25627,x25628))
% 187.33/188.06 [2563]~E(x25631,x25632)+E(f789(x25633,x25634,x25635,x25636,x25637,x25631,x25638),f789(x25633,x25634,x25635,x25636,x25637,x25632,x25638))
% 187.33/188.06 [2564]~E(x25641,x25642)+E(f789(x25643,x25644,x25645,x25646,x25647,x25648,x25641),f789(x25643,x25644,x25645,x25646,x25647,x25648,x25642))
% 187.33/188.06 [2565]~E(x25651,x25652)+E(f468(x25651,x25653,x25654),f468(x25652,x25653,x25654))
% 187.33/188.06 [2566]~E(x25661,x25662)+E(f468(x25663,x25661,x25664),f468(x25663,x25662,x25664))
% 187.33/188.06 [2567]~E(x25671,x25672)+E(f468(x25673,x25674,x25671),f468(x25673,x25674,x25672))
% 187.33/188.06 [2568]~E(x25681,x25682)+E(f246(x25681,x25683),f246(x25682,x25683))
% 187.33/188.06 [2569]~E(x25691,x25692)+E(f246(x25693,x25691),f246(x25693,x25692))
% 187.33/188.06 [2570]~E(x25701,x25702)+E(f562(x25701,x25703,x25704,x25705),f562(x25702,x25703,x25704,x25705))
% 187.33/188.06 [2571]~E(x25711,x25712)+E(f562(x25713,x25711,x25714,x25715),f562(x25713,x25712,x25714,x25715))
% 187.33/188.06 [2572]~E(x25721,x25722)+E(f562(x25723,x25724,x25721,x25725),f562(x25723,x25724,x25722,x25725))
% 187.33/188.06 [2573]~E(x25731,x25732)+E(f562(x25733,x25734,x25735,x25731),f562(x25733,x25734,x25735,x25732))
% 187.33/188.06 [2574]~E(x25741,x25742)+E(f597(x25741,x25743),f597(x25742,x25743))
% 187.33/188.06 [2575]~E(x25751,x25752)+E(f597(x25753,x25751),f597(x25753,x25752))
% 187.33/188.06 [2576]~E(x25761,x25762)+E(f438(x25761,x25763,x25764,x25765,x25766),f438(x25762,x25763,x25764,x25765,x25766))
% 187.33/188.06 [2577]~E(x25771,x25772)+E(f438(x25773,x25771,x25774,x25775,x25776),f438(x25773,x25772,x25774,x25775,x25776))
% 187.33/188.06 [2578]~E(x25781,x25782)+E(f438(x25783,x25784,x25781,x25785,x25786),f438(x25783,x25784,x25782,x25785,x25786))
% 187.33/188.06 [2579]~E(x25791,x25792)+E(f438(x25793,x25794,x25795,x25791,x25796),f438(x25793,x25794,x25795,x25792,x25796))
% 187.33/188.06 [2580]~E(x25801,x25802)+E(f438(x25803,x25804,x25805,x25806,x25801),f438(x25803,x25804,x25805,x25806,x25802))
% 187.33/188.06 [2581]~E(x25811,x25812)+E(f798(x25811,x25813,x25814),f798(x25812,x25813,x25814))
% 187.33/188.06 [2582]~E(x25821,x25822)+E(f798(x25823,x25821,x25824),f798(x25823,x25822,x25824))
% 187.33/188.06 [2583]~E(x25831,x25832)+E(f798(x25833,x25834,x25831),f798(x25833,x25834,x25832))
% 187.33/188.06 [2584]~E(x25841,x25842)+E(f514(x25841,x25843,x25844,x25845),f514(x25842,x25843,x25844,x25845))
% 187.33/188.06 [2585]~E(x25851,x25852)+E(f514(x25853,x25851,x25854,x25855),f514(x25853,x25852,x25854,x25855))
% 187.33/188.06 [2586]~E(x25861,x25862)+E(f514(x25863,x25864,x25861,x25865),f514(x25863,x25864,x25862,x25865))
% 187.33/188.06 [2587]~E(x25871,x25872)+E(f514(x25873,x25874,x25875,x25871),f514(x25873,x25874,x25875,x25872))
% 187.33/188.06 [2588]~E(x25881,x25882)+E(f729(x25881,x25883),f729(x25882,x25883))
% 187.33/188.06 [2589]~E(x25891,x25892)+E(f729(x25893,x25891),f729(x25893,x25892))
% 187.33/188.06 [2590]~E(x25901,x25902)+E(f272(x25901,x25903,x25904,x25905,x25906),f272(x25902,x25903,x25904,x25905,x25906))
% 187.33/188.06 [2591]~E(x25911,x25912)+E(f272(x25913,x25911,x25914,x25915,x25916),f272(x25913,x25912,x25914,x25915,x25916))
% 187.33/188.06 [2592]~E(x25921,x25922)+E(f272(x25923,x25924,x25921,x25925,x25926),f272(x25923,x25924,x25922,x25925,x25926))
% 187.33/188.06 [2593]~E(x25931,x25932)+E(f272(x25933,x25934,x25935,x25931,x25936),f272(x25933,x25934,x25935,x25932,x25936))
% 187.33/188.06 [2594]~E(x25941,x25942)+E(f272(x25943,x25944,x25945,x25946,x25941),f272(x25943,x25944,x25945,x25946,x25942))
% 187.33/188.06 [2595]~E(x25951,x25952)+E(f855(x25951,x25953),f855(x25952,x25953))
% 187.33/188.06 [2596]~E(x25961,x25962)+E(f855(x25963,x25961),f855(x25963,x25962))
% 187.33/188.06 [2597]~E(x25971,x25972)+E(f521(x25971,x25973),f521(x25972,x25973))
% 187.33/188.06 [2598]~E(x25981,x25982)+E(f521(x25983,x25981),f521(x25983,x25982))
% 187.33/188.06 [2599]~E(x25991,x25992)+E(f362(x25991,x25993),f362(x25992,x25993))
% 187.33/188.06 [2600]~E(x26001,x26002)+E(f362(x26003,x26001),f362(x26003,x26002))
% 187.33/188.06 [2601]~E(x26011,x26012)+E(f339(x26011,x26013),f339(x26012,x26013))
% 187.33/188.06 [2602]~E(x26021,x26022)+E(f339(x26023,x26021),f339(x26023,x26022))
% 187.33/188.06 [2603]~E(x26031,x26032)+E(f409(x26031),f409(x26032))
% 187.33/188.06 [2604]~E(x26041,x26042)+E(f796(x26041,x26043,x26044),f796(x26042,x26043,x26044))
% 187.33/188.06 [2605]~E(x26051,x26052)+E(f796(x26053,x26051,x26054),f796(x26053,x26052,x26054))
% 187.33/188.06 [2606]~E(x26061,x26062)+E(f796(x26063,x26064,x26061),f796(x26063,x26064,x26062))
% 187.33/188.06 [2607]~E(x26071,x26072)+E(f472(x26071,x26073),f472(x26072,x26073))
% 187.33/188.06 [2608]~E(x26081,x26082)+E(f472(x26083,x26081),f472(x26083,x26082))
% 187.33/188.06 [2609]~E(x26091,x26092)+E(f837(x26091,x26093,x26094),f837(x26092,x26093,x26094))
% 187.33/188.06 [2610]~E(x26101,x26102)+E(f837(x26103,x26101,x26104),f837(x26103,x26102,x26104))
% 187.33/188.06 [2611]~E(x26111,x26112)+E(f837(x26113,x26114,x26111),f837(x26113,x26114,x26112))
% 187.33/188.06 [2612]~P1(x26121)+P1(x26122)+~E(x26121,x26122)
% 187.33/188.06 [2613]~P2(x26131)+P2(x26132)+~E(x26131,x26132)
% 187.33/188.06 [2614]~P24(x26141)+P24(x26142)+~E(x26141,x26142)
% 187.33/188.06 [2615]~P25(x26151)+P25(x26152)+~E(x26151,x26152)
% 187.33/188.06 [2616]P42(x26162,x26163)+~E(x26161,x26162)+~P42(x26161,x26163)
% 187.33/188.06 [2617]P42(x26173,x26172)+~E(x26171,x26172)+~P42(x26173,x26171)
% 187.33/188.06 [2618]~P31(x26181)+P31(x26182)+~E(x26181,x26182)
% 187.33/188.06 [2619]P144(x26192,x26193,x26194)+~E(x26191,x26192)+~P144(x26191,x26193,x26194)
% 187.33/188.06 [2620]P144(x26203,x26202,x26204)+~E(x26201,x26202)+~P144(x26203,x26201,x26204)
% 187.33/188.06 [2621]P144(x26213,x26214,x26212)+~E(x26211,x26212)+~P144(x26213,x26214,x26211)
% 187.33/188.06 [2622]~P26(x26221)+P26(x26222)+~E(x26221,x26222)
% 187.33/188.06 [2623]~P133(x26231)+P133(x26232)+~E(x26231,x26232)
% 187.33/188.06 [2624]~P94(x26241)+P94(x26242)+~E(x26241,x26242)
% 187.33/188.06 [2625]~P109(x26251)+P109(x26252)+~E(x26251,x26252)
% 187.33/188.06 [2626]~P27(x26261)+P27(x26262)+~E(x26261,x26262)
% 187.33/188.06 [2627]~P89(x26271)+P89(x26272)+~E(x26271,x26272)
% 187.33/188.06 [2628]P21(x26282,x26283,x26284,x26285)+~E(x26281,x26282)+~P21(x26281,x26283,x26284,x26285)
% 187.33/188.06 [2629]P21(x26293,x26292,x26294,x26295)+~E(x26291,x26292)+~P21(x26293,x26291,x26294,x26295)
% 187.33/188.06 [2630]P21(x26303,x26304,x26302,x26305)+~E(x26301,x26302)+~P21(x26303,x26304,x26301,x26305)
% 187.33/188.06 [2631]P21(x26313,x26314,x26315,x26312)+~E(x26311,x26312)+~P21(x26313,x26314,x26315,x26311)
% 187.33/188.06 [2632]~P106(x26321)+P106(x26322)+~E(x26321,x26322)
% 187.33/188.06 [2633]P57(x26332,x26333)+~E(x26331,x26332)+~P57(x26331,x26333)
% 187.33/188.06 [2634]P57(x26343,x26342)+~E(x26341,x26342)+~P57(x26343,x26341)
% 187.33/188.06 [2635]~P29(x26351)+P29(x26352)+~E(x26351,x26352)
% 187.33/188.06 [2636]P6(x26362,x26363,x26364)+~E(x26361,x26362)+~P6(x26361,x26363,x26364)
% 187.33/188.06 [2637]P6(x26373,x26372,x26374)+~E(x26371,x26372)+~P6(x26373,x26371,x26374)
% 187.33/188.06 [2638]P6(x26383,x26384,x26382)+~E(x26381,x26382)+~P6(x26383,x26384,x26381)
% 187.33/188.06 [2639]~P28(x26391)+P28(x26392)+~E(x26391,x26392)
% 187.33/188.06 [2640]~P64(x26401)+P64(x26402)+~E(x26401,x26402)
% 187.33/188.06 [2641]~P65(x26411)+P65(x26412)+~E(x26411,x26412)
% 187.33/188.06 [2642]~P121(x26421)+P121(x26422)+~E(x26421,x26422)
% 187.33/188.06 [2643]~P66(x26431)+P66(x26432)+~E(x26431,x26432)
% 187.33/188.06 [2644]~P43(x26441)+P43(x26442)+~E(x26441,x26442)
% 187.33/188.06 [2645]~P61(x26451)+P61(x26452)+~E(x26451,x26452)
% 187.33/188.06 [2646]~P102(x26461)+P102(x26462)+~E(x26461,x26462)
% 187.33/188.06 [2647]P15(x26472,x26473,x26474,x26475)+~E(x26471,x26472)+~P15(x26471,x26473,x26474,x26475)
% 187.33/188.06 [2648]P15(x26483,x26482,x26484,x26485)+~E(x26481,x26482)+~P15(x26483,x26481,x26484,x26485)
% 187.33/188.06 [2649]P15(x26493,x26494,x26492,x26495)+~E(x26491,x26492)+~P15(x26493,x26494,x26491,x26495)
% 187.33/188.06 [2650]P15(x26503,x26504,x26505,x26502)+~E(x26501,x26502)+~P15(x26503,x26504,x26505,x26501)
% 187.33/188.06 [2651]P46(x26512,x26513)+~E(x26511,x26512)+~P46(x26511,x26513)
% 187.33/188.06 [2652]P46(x26523,x26522)+~E(x26521,x26522)+~P46(x26523,x26521)
% 187.33/188.06 [2653]~P67(x26531)+P67(x26532)+~E(x26531,x26532)
% 187.33/188.06 [2654]~P68(x26541)+P68(x26542)+~E(x26541,x26542)
% 187.33/188.06 [2655]~P123(x26551)+P123(x26552)+~E(x26551,x26552)
% 187.33/188.06 [2656]~P92(x26561)+P92(x26562)+~E(x26561,x26562)
% 187.33/188.06 [2657]P44(x26572,x26573,x26574)+~E(x26571,x26572)+~P44(x26571,x26573,x26574)
% 187.33/188.06 [2658]P44(x26583,x26582,x26584)+~E(x26581,x26582)+~P44(x26583,x26581,x26584)
% 187.33/188.06 [2659]P44(x26593,x26594,x26592)+~E(x26591,x26592)+~P44(x26593,x26594,x26591)
% 187.33/188.06 [2660]~P103(x26601)+P103(x26602)+~E(x26601,x26602)
% 187.33/188.06 [2661]P34(x26612,x26613,x26614)+~E(x26611,x26612)+~P34(x26611,x26613,x26614)
% 187.33/188.06 [2662]P34(x26623,x26622,x26624)+~E(x26621,x26622)+~P34(x26623,x26621,x26624)
% 187.33/188.06 [2663]P34(x26633,x26634,x26632)+~E(x26631,x26632)+~P34(x26633,x26634,x26631)
% 187.33/188.06 [2664]~P76(x26641)+P76(x26642)+~E(x26641,x26642)
% 187.33/188.06 [2665]~P100(x26651)+P100(x26652)+~E(x26651,x26652)
% 187.33/188.06 [2666]P54(x26662,x26663,x26664)+~E(x26661,x26662)+~P54(x26661,x26663,x26664)
% 187.33/188.06 [2667]P54(x26673,x26672,x26674)+~E(x26671,x26672)+~P54(x26673,x26671,x26674)
% 187.33/188.06 [2668]P54(x26683,x26684,x26682)+~E(x26681,x26682)+~P54(x26683,x26684,x26681)
% 187.33/188.06 [2669]~P107(x26691)+P107(x26692)+~E(x26691,x26692)
% 187.33/188.06 [2670]~P80(x26701)+P80(x26702)+~E(x26701,x26702)
% 187.33/188.06 [2671]~P69(x26711)+P69(x26712)+~E(x26711,x26712)
% 187.33/188.06 [2672]~P95(x26721)+P95(x26722)+~E(x26721,x26722)
% 187.33/188.06 [2673]~P70(x26731)+P70(x26732)+~E(x26731,x26732)
% 187.33/188.06 [2674]P40(x26742,x26743,x26744)+~E(x26741,x26742)+~P40(x26741,x26743,x26744)
% 187.33/188.06 [2675]P40(x26753,x26752,x26754)+~E(x26751,x26752)+~P40(x26753,x26751,x26754)
% 187.33/188.06 [2676]P40(x26763,x26764,x26762)+~E(x26761,x26762)+~P40(x26763,x26764,x26761)
% 187.33/188.06 [2677]P38(x26772,x26773,x26774)+~E(x26771,x26772)+~P38(x26771,x26773,x26774)
% 187.33/188.06 [2678]P38(x26783,x26782,x26784)+~E(x26781,x26782)+~P38(x26783,x26781,x26784)
% 187.33/188.06 [2679]P38(x26793,x26794,x26792)+~E(x26791,x26792)+~P38(x26793,x26794,x26791)
% 187.33/188.06 [2680]~P134(x26801)+P134(x26802)+~E(x26801,x26802)
% 187.33/188.06 [2681]P55(x26812,x26813,x26814)+~E(x26811,x26812)+~P55(x26811,x26813,x26814)
% 187.33/188.06 [2682]P55(x26823,x26822,x26824)+~E(x26821,x26822)+~P55(x26823,x26821,x26824)
% 187.33/188.06 [2683]P55(x26833,x26834,x26832)+~E(x26831,x26832)+~P55(x26833,x26834,x26831)
% 187.33/188.06 [2684]~P60(x26841)+P60(x26842)+~E(x26841,x26842)
% 187.33/188.06 [2685]~P72(x26851)+P72(x26852)+~E(x26851,x26852)
% 187.33/188.06 [2686]~P111(x26861)+P111(x26862)+~E(x26861,x26862)
% 187.33/188.06 [2687]P143(x26872,x26873,x26874)+~E(x26871,x26872)+~P143(x26871,x26873,x26874)
% 187.33/188.06 [2688]P143(x26883,x26882,x26884)+~E(x26881,x26882)+~P143(x26883,x26881,x26884)
% 187.33/188.06 [2689]P143(x26893,x26894,x26892)+~E(x26891,x26892)+~P143(x26893,x26894,x26891)
% 187.33/188.06 [2690]~P87(x26901)+P87(x26902)+~E(x26901,x26902)
% 187.33/188.06 [2691]~P108(x26911)+P108(x26912)+~E(x26911,x26912)
% 187.33/188.06 [2692]~P63(x26921)+P63(x26922)+~E(x26921,x26922)
% 187.33/188.06 [2693]~P84(x26931)+P84(x26932)+~E(x26931,x26932)
% 187.33/188.06 [2694]~P122(x26941)+P122(x26942)+~E(x26941,x26942)
% 187.33/188.06 [2695]P36(x26952,x26953,x26954)+~E(x26951,x26952)+~P36(x26951,x26953,x26954)
% 187.33/188.06 [2696]P36(x26963,x26962,x26964)+~E(x26961,x26962)+~P36(x26963,x26961,x26964)
% 187.33/188.06 [2697]P36(x26973,x26974,x26972)+~E(x26971,x26972)+~P36(x26973,x26974,x26971)
% 187.33/188.06 [2698]~P81(x26981)+P81(x26982)+~E(x26981,x26982)
% 187.33/188.06 [2699]~P135(x26991)+P135(x26992)+~E(x26991,x26992)
% 187.33/188.06 [2700]~P49(x27001)+P49(x27002)+~E(x27001,x27002)
% 187.33/188.06 [2701]~P71(x27011)+P71(x27012)+~E(x27011,x27012)
% 187.33/188.06 [2702]P39(x27022,x27023,x27024,x27025,x27026)+~E(x27021,x27022)+~P39(x27021,x27023,x27024,x27025,x27026)
% 187.33/188.06 [2703]P39(x27033,x27032,x27034,x27035,x27036)+~E(x27031,x27032)+~P39(x27033,x27031,x27034,x27035,x27036)
% 187.33/188.06 [2704]P39(x27043,x27044,x27042,x27045,x27046)+~E(x27041,x27042)+~P39(x27043,x27044,x27041,x27045,x27046)
% 187.33/188.06 [2705]P39(x27053,x27054,x27055,x27052,x27056)+~E(x27051,x27052)+~P39(x27053,x27054,x27055,x27051,x27056)
% 187.33/188.06 [2706]P39(x27063,x27064,x27065,x27066,x27062)+~E(x27061,x27062)+~P39(x27063,x27064,x27065,x27066,x27061)
% 187.33/188.06 [2707]~P30(x27071)+P30(x27072)+~E(x27071,x27072)
% 187.33/188.06 [2708]~P73(x27081)+P73(x27082)+~E(x27081,x27082)
% 187.33/188.06 [2709]~P85(x27091)+P85(x27092)+~E(x27091,x27092)
% 187.33/188.06 [2710]P37(x27102,x27103,x27104,x27105)+~E(x27101,x27102)+~P37(x27101,x27103,x27104,x27105)
% 187.33/188.06 [2711]P37(x27113,x27112,x27114,x27115)+~E(x27111,x27112)+~P37(x27113,x27111,x27114,x27115)
% 187.33/188.06 [2712]P37(x27123,x27124,x27122,x27125)+~E(x27121,x27122)+~P37(x27123,x27124,x27121,x27125)
% 187.33/188.06 [2713]P37(x27133,x27134,x27135,x27132)+~E(x27131,x27132)+~P37(x27133,x27134,x27135,x27131)
% 187.33/188.06 [2714]~P74(x27141)+P74(x27142)+~E(x27141,x27142)
% 187.33/188.06 [2715]P33(x27152,x27153)+~E(x27151,x27152)+~P33(x27151,x27153)
% 187.33/188.06 [2716]P33(x27163,x27162)+~E(x27161,x27162)+~P33(x27163,x27161)
% 187.33/188.06 [2717]~P98(x27171)+P98(x27172)+~E(x27171,x27172)
% 187.33/188.06 [2718]~P32(x27181)+P32(x27182)+~E(x27181,x27182)
% 187.33/188.06 [2719]~P115(x27191)+P115(x27192)+~E(x27191,x27192)
% 187.33/188.06 [2720]P35(x27202,x27203)+~E(x27201,x27202)+~P35(x27201,x27203)
% 187.33/188.06 [2721]P35(x27213,x27212)+~E(x27211,x27212)+~P35(x27213,x27211)
% 187.33/188.06 [2722]~P86(x27221)+P86(x27222)+~E(x27221,x27222)
% 187.33/188.06 [2723]P59(x27232,x27233)+~E(x27231,x27232)+~P59(x27231,x27233)
% 187.33/188.06 [2724]P59(x27243,x27242)+~E(x27241,x27242)+~P59(x27243,x27241)
% 187.33/188.06 [2725]~P137(x27251)+P137(x27252)+~E(x27251,x27252)
% 187.33/188.06 [2726]~P77(x27261)+P77(x27262)+~E(x27261,x27262)
% 187.33/188.06 [2727]~P82(x27271)+P82(x27272)+~E(x27271,x27272)
% 187.33/188.06 [2728]~P129(x27281)+P129(x27282)+~E(x27281,x27282)
% 187.33/188.06 [2729]~P93(x27291)+P93(x27292)+~E(x27291,x27292)
% 187.33/188.06 [2730]P4(x27302,x27303,x27304,x27305,x27306)+~E(x27301,x27302)+~P4(x27301,x27303,x27304,x27305,x27306)
% 187.33/188.06 [2731]P4(x27313,x27312,x27314,x27315,x27316)+~E(x27311,x27312)+~P4(x27313,x27311,x27314,x27315,x27316)
% 187.33/188.06 [2732]P4(x27323,x27324,x27322,x27325,x27326)+~E(x27321,x27322)+~P4(x27323,x27324,x27321,x27325,x27326)
% 187.33/188.06 [2733]P4(x27333,x27334,x27335,x27332,x27336)+~E(x27331,x27332)+~P4(x27333,x27334,x27335,x27331,x27336)
% 187.33/188.06 [2734]P4(x27343,x27344,x27345,x27346,x27342)+~E(x27341,x27342)+~P4(x27343,x27344,x27345,x27346,x27341)
% 187.33/188.06 [2735]P20(x27352,x27353,x27354)+~E(x27351,x27352)+~P20(x27351,x27353,x27354)
% 187.33/188.06 [2736]P20(x27363,x27362,x27364)+~E(x27361,x27362)+~P20(x27363,x27361,x27364)
% 187.33/188.06 [2737]P20(x27373,x27374,x27372)+~E(x27371,x27372)+~P20(x27373,x27374,x27371)
% 187.33/188.06 [2738]~P132(x27381)+P132(x27382)+~E(x27381,x27382)
% 187.33/188.06 [2739]~P90(x27391)+P90(x27392)+~E(x27391,x27392)
% 187.33/188.06 [2740]P10(x27402,x27403,x27404,x27405,x27406,x27407)+~E(x27401,x27402)+~P10(x27401,x27403,x27404,x27405,x27406,x27407)
% 187.33/188.06 [2741]P10(x27413,x27412,x27414,x27415,x27416,x27417)+~E(x27411,x27412)+~P10(x27413,x27411,x27414,x27415,x27416,x27417)
% 187.33/188.06 [2742]P10(x27423,x27424,x27422,x27425,x27426,x27427)+~E(x27421,x27422)+~P10(x27423,x27424,x27421,x27425,x27426,x27427)
% 187.33/188.06 [2743]P10(x27433,x27434,x27435,x27432,x27436,x27437)+~E(x27431,x27432)+~P10(x27433,x27434,x27435,x27431,x27436,x27437)
% 187.33/188.06 [2744]P10(x27443,x27444,x27445,x27446,x27442,x27447)+~E(x27441,x27442)+~P10(x27443,x27444,x27445,x27446,x27441,x27447)
% 187.33/188.06 [2745]P10(x27453,x27454,x27455,x27456,x27457,x27452)+~E(x27451,x27452)+~P10(x27453,x27454,x27455,x27456,x27457,x27451)
% 187.33/188.06 [2746]~P139(x27461)+P139(x27462)+~E(x27461,x27462)
% 187.33/188.06 [2747]~P117(x27471)+P117(x27472)+~E(x27471,x27472)
% 187.33/188.06 [2748]~P110(x27481)+P110(x27482)+~E(x27481,x27482)
% 187.33/188.06 [2749]~P138(x27491)+P138(x27492)+~E(x27491,x27492)
% 187.33/188.06 [2750]~P101(x27501)+P101(x27502)+~E(x27501,x27502)
% 187.33/188.06 [2751]~P78(x27511)+P78(x27512)+~E(x27511,x27512)
% 187.33/188.06 [2752]~P141(x27521)+P141(x27522)+~E(x27521,x27522)
% 187.33/188.06 [2753]P18(x27532,x27533,x27534,x27535,x27536,x27537)+~E(x27531,x27532)+~P18(x27531,x27533,x27534,x27535,x27536,x27537)
% 187.33/188.06 [2754]P18(x27543,x27542,x27544,x27545,x27546,x27547)+~E(x27541,x27542)+~P18(x27543,x27541,x27544,x27545,x27546,x27547)
% 187.33/188.06 [2755]P18(x27553,x27554,x27552,x27555,x27556,x27557)+~E(x27551,x27552)+~P18(x27553,x27554,x27551,x27555,x27556,x27557)
% 187.33/188.06 [2756]P18(x27563,x27564,x27565,x27562,x27566,x27567)+~E(x27561,x27562)+~P18(x27563,x27564,x27565,x27561,x27566,x27567)
% 187.33/188.06 [2757]P18(x27573,x27574,x27575,x27576,x27572,x27577)+~E(x27571,x27572)+~P18(x27573,x27574,x27575,x27576,x27571,x27577)
% 187.33/188.06 [2758]P18(x27583,x27584,x27585,x27586,x27587,x27582)+~E(x27581,x27582)+~P18(x27583,x27584,x27585,x27586,x27587,x27581)
% 187.33/188.06 [2759]~P118(x27591)+P118(x27592)+~E(x27591,x27592)
% 187.33/188.06 [2760]P14(x27602,x27603,x27604)+~E(x27601,x27602)+~P14(x27601,x27603,x27604)
% 187.33/188.06 [2761]P14(x27613,x27612,x27614)+~E(x27611,x27612)+~P14(x27613,x27611,x27614)
% 187.33/188.06 [2762]P14(x27623,x27624,x27622)+~E(x27621,x27622)+~P14(x27623,x27624,x27621)
% 187.33/188.06 [2763]P5(x27632,x27633)+~E(x27631,x27632)+~P5(x27631,x27633)
% 187.33/188.06 [2764]P5(x27643,x27642)+~E(x27641,x27642)+~P5(x27643,x27641)
% 187.33/188.06 [2765]~P124(x27651)+P124(x27652)+~E(x27651,x27652)
% 187.33/188.06 [2766]~P127(x27661)+P127(x27662)+~E(x27661,x27662)
% 187.33/188.06 [2767]P50(x27672,x27673)+~E(x27671,x27672)+~P50(x27671,x27673)
% 187.33/188.06 [2768]P50(x27683,x27682)+~E(x27681,x27682)+~P50(x27683,x27681)
% 187.33/188.06 [2769]~P97(x27691)+P97(x27692)+~E(x27691,x27692)
% 187.33/188.06 [2770]~P88(x27701)+P88(x27702)+~E(x27701,x27702)
% 187.33/188.06 [2771]P19(x27712,x27713,x27714,x27715,x27716,x27717)+~E(x27711,x27712)+~P19(x27711,x27713,x27714,x27715,x27716,x27717)
% 187.33/188.06 [2772]P19(x27723,x27722,x27724,x27725,x27726,x27727)+~E(x27721,x27722)+~P19(x27723,x27721,x27724,x27725,x27726,x27727)
% 187.33/188.06 [2773]P19(x27733,x27734,x27732,x27735,x27736,x27737)+~E(x27731,x27732)+~P19(x27733,x27734,x27731,x27735,x27736,x27737)
% 187.33/188.06 [2774]P19(x27743,x27744,x27745,x27742,x27746,x27747)+~E(x27741,x27742)+~P19(x27743,x27744,x27745,x27741,x27746,x27747)
% 187.33/188.06 [2775]P19(x27753,x27754,x27755,x27756,x27752,x27757)+~E(x27751,x27752)+~P19(x27753,x27754,x27755,x27756,x27751,x27757)
% 187.33/188.06 [2776]P19(x27763,x27764,x27765,x27766,x27767,x27762)+~E(x27761,x27762)+~P19(x27763,x27764,x27765,x27766,x27767,x27761)
% 187.33/188.06 [2777]~P142(x27771)+P142(x27772)+~E(x27771,x27772)
% 187.33/188.06 [2778]~P83(x27781)+P83(x27782)+~E(x27781,x27782)
% 187.33/188.06 [2779]~P128(x27791)+P128(x27792)+~E(x27791,x27792)
% 187.33/188.06 [2780]P12(x27802,x27803,x27804)+~E(x27801,x27802)+~P12(x27801,x27803,x27804)
% 187.33/188.06 [2781]P12(x27813,x27812,x27814)+~E(x27811,x27812)+~P12(x27813,x27811,x27814)
% 187.33/188.06 [2782]P12(x27823,x27824,x27822)+~E(x27821,x27822)+~P12(x27823,x27824,x27821)
% 187.33/188.06 [2783]~P62(x27831)+P62(x27832)+~E(x27831,x27832)
% 187.33/188.06 [2784]~P136(x27841)+P136(x27842)+~E(x27841,x27842)
% 187.33/188.06 [2785]P13(x27852,x27853,x27854)+~E(x27851,x27852)+~P13(x27851,x27853,x27854)
% 187.33/188.06 [2786]P13(x27863,x27862,x27864)+~E(x27861,x27862)+~P13(x27863,x27861,x27864)
% 187.33/188.06 [2787]P13(x27873,x27874,x27872)+~E(x27871,x27872)+~P13(x27873,x27874,x27871)
% 187.33/188.06 [2788]~P96(x27881)+P96(x27882)+~E(x27881,x27882)
% 187.33/188.06 [2789]P47(x27892,x27893,x27894,x27895,x27896,x27897)+~E(x27891,x27892)+~P47(x27891,x27893,x27894,x27895,x27896,x27897)
% 187.33/188.06 [2790]P47(x27903,x27902,x27904,x27905,x27906,x27907)+~E(x27901,x27902)+~P47(x27903,x27901,x27904,x27905,x27906,x27907)
% 187.33/188.06 [2791]P47(x27913,x27914,x27912,x27915,x27916,x27917)+~E(x27911,x27912)+~P47(x27913,x27914,x27911,x27915,x27916,x27917)
% 187.33/188.06 [2792]P47(x27923,x27924,x27925,x27922,x27926,x27927)+~E(x27921,x27922)+~P47(x27923,x27924,x27925,x27921,x27926,x27927)
% 187.33/188.06 [2793]P47(x27933,x27934,x27935,x27936,x27932,x27937)+~E(x27931,x27932)+~P47(x27933,x27934,x27935,x27936,x27931,x27937)
% 187.33/188.06 [2794]P47(x27943,x27944,x27945,x27946,x27947,x27942)+~E(x27941,x27942)+~P47(x27943,x27944,x27945,x27946,x27947,x27941)
% 187.33/188.06 [2795]~P140(x27951)+P140(x27952)+~E(x27951,x27952)
% 187.33/188.06 [2796]P45(x27962,x27963,x27964,x27965)+~E(x27961,x27962)+~P45(x27961,x27963,x27964,x27965)
% 187.33/188.06 [2797]P45(x27973,x27972,x27974,x27975)+~E(x27971,x27972)+~P45(x27973,x27971,x27974,x27975)
% 187.33/188.06 [2798]P45(x27983,x27984,x27982,x27985)+~E(x27981,x27982)+~P45(x27983,x27984,x27981,x27985)
% 187.33/188.06 [2799]P45(x27993,x27994,x27995,x27992)+~E(x27991,x27992)+~P45(x27993,x27994,x27995,x27991)
% 187.33/188.06 [2800]~P130(x28001)+P130(x28002)+~E(x28001,x28002)
% 187.33/188.06 [2801]P11(x28012,x28013,x28014)+~E(x28011,x28012)+~P11(x28011,x28013,x28014)
% 187.33/188.06 [2802]P11(x28023,x28022,x28024)+~E(x28021,x28022)+~P11(x28023,x28021,x28024)
% 187.33/188.06 [2803]P11(x28033,x28034,x28032)+~E(x28031,x28032)+~P11(x28033,x28034,x28031)
% 187.33/188.06 [2804]~P119(x28041)+P119(x28042)+~E(x28041,x28042)
% 187.33/188.06 [2805]P9(x28052,x28053,x28054,x28055)+~E(x28051,x28052)+~P9(x28051,x28053,x28054,x28055)
% 187.33/188.06 [2806]P9(x28063,x28062,x28064,x28065)+~E(x28061,x28062)+~P9(x28063,x28061,x28064,x28065)
% 187.33/188.06 [2807]P9(x28073,x28074,x28072,x28075)+~E(x28071,x28072)+~P9(x28073,x28074,x28071,x28075)
% 187.33/188.06 [2808]P9(x28083,x28084,x28085,x28082)+~E(x28081,x28082)+~P9(x28083,x28084,x28085,x28081)
% 187.33/188.06 [2809]P17(x28092,x28093,x28094,x28095,x28096)+~E(x28091,x28092)+~P17(x28091,x28093,x28094,x28095,x28096)
% 187.33/188.06 [2810]P17(x28103,x28102,x28104,x28105,x28106)+~E(x28101,x28102)+~P17(x28103,x28101,x28104,x28105,x28106)
% 187.33/188.06 [2811]P17(x28113,x28114,x28112,x28115,x28116)+~E(x28111,x28112)+~P17(x28113,x28114,x28111,x28115,x28116)
% 187.33/188.06 [2812]P17(x28123,x28124,x28125,x28122,x28126)+~E(x28121,x28122)+~P17(x28123,x28124,x28125,x28121,x28126)
% 187.33/188.06 [2813]P17(x28133,x28134,x28135,x28136,x28132)+~E(x28131,x28132)+~P17(x28133,x28134,x28135,x28136,x28131)
% 187.33/188.06 [2814]P48(x28142,x28143)+~E(x28141,x28142)+~P48(x28141,x28143)
% 187.33/188.06 [2815]P48(x28153,x28152)+~E(x28151,x28152)+~P48(x28153,x28151)
% 187.33/188.06 [2816]~P116(x28161)+P116(x28162)+~E(x28161,x28162)
% 187.33/188.06 [2817]P56(x28172,x28173,x28174,x28175,x28176)+~E(x28171,x28172)+~P56(x28171,x28173,x28174,x28175,x28176)
% 187.33/188.06 [2818]P56(x28183,x28182,x28184,x28185,x28186)+~E(x28181,x28182)+~P56(x28183,x28181,x28184,x28185,x28186)
% 187.33/188.06 [2819]P56(x28193,x28194,x28192,x28195,x28196)+~E(x28191,x28192)+~P56(x28193,x28194,x28191,x28195,x28196)
% 187.33/188.06 [2820]P56(x28203,x28204,x28205,x28202,x28206)+~E(x28201,x28202)+~P56(x28203,x28204,x28205,x28201,x28206)
% 187.33/188.06 [2821]P56(x28213,x28214,x28215,x28216,x28212)+~E(x28211,x28212)+~P56(x28213,x28214,x28215,x28216,x28211)
% 187.33/188.06 [2822]P23(x28222,x28223,x28224)+~E(x28221,x28222)+~P23(x28221,x28223,x28224)
% 187.33/188.06 [2823]P23(x28233,x28232,x28234)+~E(x28231,x28232)+~P23(x28233,x28231,x28234)
% 187.33/188.06 [2824]P23(x28243,x28244,x28242)+~E(x28241,x28242)+~P23(x28243,x28244,x28241)
% 187.33/188.06 [2825]P8(x28252,x28253,x28254)+~E(x28251,x28252)+~P8(x28251,x28253,x28254)
% 187.33/188.06 [2826]P8(x28263,x28262,x28264)+~E(x28261,x28262)+~P8(x28263,x28261,x28264)
% 187.33/188.06 [2827]P8(x28273,x28274,x28272)+~E(x28271,x28272)+~P8(x28273,x28274,x28271)
% 187.33/188.06 [2828]~P104(x28281)+P104(x28282)+~E(x28281,x28282)
% 187.33/188.06 [2829]~P112(x28291)+P112(x28292)+~E(x28291,x28292)
% 187.33/188.06 [2830]~P131(x28301)+P131(x28302)+~E(x28301,x28302)
% 187.33/188.06 [2831]~P120(x28311)+P120(x28312)+~E(x28311,x28312)
% 187.33/188.06 [2832]P16(x28322,x28323,x28324,x28325)+~E(x28321,x28322)+~P16(x28321,x28323,x28324,x28325)
% 187.33/188.06 [2833]P16(x28333,x28332,x28334,x28335)+~E(x28331,x28332)+~P16(x28333,x28331,x28334,x28335)
% 187.33/188.06 [2834]P16(x28343,x28344,x28342,x28345)+~E(x28341,x28342)+~P16(x28343,x28344,x28341,x28345)
% 187.33/188.06 [2835]P16(x28353,x28354,x28355,x28352)+~E(x28351,x28352)+~P16(x28353,x28354,x28355,x28351)
% 187.33/188.06 [2836]P58(x28362,x28363,x28364,x28365)+~E(x28361,x28362)+~P58(x28361,x28363,x28364,x28365)
% 187.33/188.06 [2837]P58(x28373,x28372,x28374,x28375)+~E(x28371,x28372)+~P58(x28373,x28371,x28374,x28375)
% 187.33/188.06 [2838]P58(x28383,x28384,x28382,x28385)+~E(x28381,x28382)+~P58(x28383,x28384,x28381,x28385)
% 187.33/188.06 [2839]P58(x28393,x28394,x28395,x28392)+~E(x28391,x28392)+~P58(x28393,x28394,x28395,x28391)
% 187.33/188.06 [2840]~P75(x28401)+P75(x28402)+~E(x28401,x28402)
% 187.33/188.06 [2841]~P105(x28411)+P105(x28412)+~E(x28411,x28412)
% 187.33/188.06 [2842]P22(x28422,x28423)+~E(x28421,x28422)+~P22(x28421,x28423)
% 187.33/188.06 [2843]P22(x28433,x28432)+~E(x28431,x28432)+~P22(x28433,x28431)
% 187.33/188.06 [2844]~P99(x28441)+P99(x28442)+~E(x28441,x28442)
% 187.33/188.06 [2845]P7(x28452,x28453,x28454)+~E(x28451,x28452)+~P7(x28451,x28453,x28454)
% 187.33/188.06 [2846]P7(x28463,x28462,x28464)+~E(x28461,x28462)+~P7(x28463,x28461,x28464)
% 187.33/188.06 [2847]P7(x28473,x28474,x28472)+~E(x28471,x28472)+~P7(x28473,x28474,x28471)
% 187.33/188.06 [2848]~P125(x28481)+P125(x28482)+~E(x28481,x28482)
% 187.33/188.06 [2849]~P114(x28491)+P114(x28492)+~E(x28491,x28492)
% 187.33/188.06 [2850]~P79(x28501)+P79(x28502)+~E(x28501,x28502)
% 187.33/188.06 [2851]~P126(x28511)+P126(x28512)+~E(x28511,x28512)
% 187.33/188.06 [2852]P53(x28522,x28523)+~E(x28521,x28522)+~P53(x28521,x28523)
% 187.33/188.06 [2853]P53(x28533,x28532)+~E(x28531,x28532)+~P53(x28533,x28531)
% 187.33/188.06 [2854]P51(x28542,x28543,x28544)+~E(x28541,x28542)+~P51(x28541,x28543,x28544)
% 187.33/188.06 [2855]P51(x28553,x28552,x28554)+~E(x28551,x28552)+~P51(x28553,x28551,x28554)
% 187.33/188.06 [2856]P51(x28563,x28564,x28562)+~E(x28561,x28562)+~P51(x28563,x28564,x28561)
% 187.33/188.06 [2857]~P91(x28571)+P91(x28572)+~E(x28571,x28572)
% 187.33/188.06 [2858]~P41(x28581)+P41(x28582)+~E(x28581,x28582)
% 187.33/188.06 [2859]~P113(x28591)+P113(x28592)+~E(x28591,x28592)
% 187.33/188.06 [2860]P52(x28602,x28603,x28604)+~E(x28601,x28602)+~P52(x28601,x28603,x28604)
% 187.33/188.06 [2861]P52(x28613,x28612,x28614)+~E(x28611,x28612)+~P52(x28613,x28611,x28614)
% 187.33/188.06 [2862]P52(x28623,x28624,x28622)+~E(x28621,x28622)+~P52(x28623,x28624,x28621)
% 187.33/188.06 [2863]P3(x28632,x28633,x28634)+~E(x28631,x28632)+~P3(x28631,x28633,x28634)
% 187.33/188.06 [2864]P3(x28643,x28642,x28644)+~E(x28641,x28642)+~P3(x28643,x28641,x28644)
% 187.33/188.06 [2865]P3(x28653,x28654,x28652)+~E(x28651,x28652)+~P3(x28653,x28654,x28651)
% 187.33/188.06
% 187.33/188.06 %-------------------------------------------
% 187.33/188.09 cnf(10208,plain,
% 187.33/188.09 (~E(f329(a117,x102081),x102081)),
% 187.33/188.09 inference(rename_variables,[],[4459])).
% 187.33/188.09 cnf(10211,plain,
% 187.33/188.09 (E(f329(f260(x102111,x102111),f261(x102111,x102112)),x102112)),
% 187.33/188.09 inference(rename_variables,[],[3234])).
% 187.33/188.09 cnf(10218,plain,
% 187.33/188.09 (~E(f329(a117,x102181),x102181)),
% 187.33/188.09 inference(rename_variables,[],[4459])).
% 187.33/188.09 cnf(10229,plain,
% 187.33/188.09 (~E(f329(a117,x102291),x102291)),
% 187.33/188.09 inference(rename_variables,[],[4459])).
% 187.33/188.09 cnf(10234,plain,
% 187.33/188.09 (~P24(f329(f63(x102341,x102342,f193(f881(x102341,a869))),x102343))),
% 187.33/188.09 inference(rename_variables,[],[4544])).
% 187.33/188.09 cnf(10237,plain,
% 187.33/188.09 (~P24(f329(f63(x102371,x102372,f193(f881(x102371,a869))),x102373))),
% 187.33/188.09 inference(rename_variables,[],[4544])).
% 187.33/188.09 cnf(10240,plain,
% 187.33/188.09 (~E(f329(a117,x102401),x102401)),
% 187.33/188.09 inference(rename_variables,[],[4459])).
% 187.33/188.09 cnf(10243,plain,
% 187.33/188.09 (~P24(f329(f329(f244(a874),x102431),f2(a874)))),
% 187.33/188.09 inference(rename_variables,[],[4524])).
% 187.33/188.09 cnf(10246,plain,
% 187.33/188.09 (~P24(f329(f329(f244(a874),x102461),f2(a874)))),
% 187.33/188.09 inference(rename_variables,[],[4524])).
% 187.33/188.09 cnf(10259,plain,
% 187.33/188.09 (~P24(f329(f193(f881(x102591,a869)),x102592))),
% 187.33/188.09 inference(scs_inference,[],[4459,10208,10218,10229,3065,3234,3108,3169,3115,3260,4524,10243,4521,4479,4527,3251,4511,4544,10234,4548,4568,4594,4643,4645,4675,4692,4699,4700,4739,4769,4775,4860,4885,4886,4921,4946,4947,4969,4970,4983,4987,5010,5017])).
% 187.33/188.09 cnf(10263,plain,
% 187.33/188.09 (~P24(f329(f329(f243(a874),f329(a117,x102631)),x102631))),
% 187.33/188.09 inference(rename_variables,[],[4529])).
% 187.33/188.09 cnf(10266,plain,
% 187.33/188.09 (~E(f329(f329(f149(x102661),x102662),x102663),x102663)),
% 187.33/188.09 inference(rename_variables,[],[4484])).
% 187.33/188.09 cnf(10272,plain,
% 187.33/188.09 (~P24(f329(f329(f244(a874),x102721),f2(a874)))),
% 187.33/188.09 inference(rename_variables,[],[4524])).
% 187.33/188.09 cnf(10274,plain,
% 187.33/188.09 (E(f45(a874,f329(f260(x102741,x102741),f261(x102741,f329(f329(f81(a874),x102742),x102743))),x102742),f2(a874))),
% 187.33/188.09 inference(scs_inference,[],[4459,10208,10218,10229,3065,3234,10211,3108,3169,3136,3115,4484,3260,4524,10243,10246,4521,4479,4529,4527,3251,4511,4544,10234,4548,4568,4594,4643,4645,4675,4692,4699,4700,4739,4769,4775,4860,4885,4886,4921,4946,4947,4969,4970,4983,4987,5010,5017,5035,5038,5039,5040,5045])).
% 187.33/188.09 cnf(10275,plain,
% 187.33/188.09 (E(f329(f260(x102751,x102751),f261(x102751,x102752)),x102752)),
% 187.33/188.09 inference(rename_variables,[],[3234])).
% 187.33/188.09 cnf(10278,plain,
% 187.33/188.09 (E(f329(f260(x102781,x102781),f261(x102781,x102782)),x102782)),
% 187.33/188.09 inference(rename_variables,[],[3234])).
% 187.33/188.09 cnf(10285,plain,
% 187.33/188.09 (~P24(f329(f329(f244(a874),f329(f329(f80(a874),x102851),x102852)),x102852))),
% 187.33/188.09 inference(rename_variables,[],[4546])).
% 187.33/188.09 cnf(10288,plain,
% 187.33/188.09 (~P24(f329(f329(f244(a874),f329(f329(f80(a874),x102881),x102882)),x102882))),
% 187.33/188.09 inference(rename_variables,[],[4546])).
% 187.33/188.09 cnf(10295,plain,
% 187.33/188.09 (~E(x102951,f329(a117,x102951))),
% 187.33/188.09 inference(scs_inference,[],[4459,10208,10218,10229,3065,3234,10211,10275,3108,3169,3136,3115,4484,3347,3260,4524,10243,10246,4521,4479,4529,4110,4527,3251,4511,4544,10234,4548,4546,10285,4568,4594,4643,4645,4675,4692,4699,4700,4739,4769,4775,4860,4885,4886,4921,4946,4947,4969,4970,4983,4987,5010,5017,5035,5038,5039,5040,5045,5046,5068,5093,5094,5104,5109,5115,5160])).
% 187.33/188.09 cnf(10309,plain,
% 187.33/188.09 (~P24(f329(f329(f244(a874),x103091),x103091))),
% 187.33/188.09 inference(rename_variables,[],[4520])).
% 187.33/188.09 cnf(10312,plain,
% 187.33/188.09 (P24(f329(f329(f243(a874),f45(a874,x103121,x103122)),x103121))),
% 187.33/188.09 inference(rename_variables,[],[3738])).
% 187.33/188.09 cnf(10333,plain,
% 187.33/188.09 (E(f329(f38(a874),f329(f250(a874),x103331)),x103331)),
% 187.33/188.09 inference(rename_variables,[],[3166])).
% 187.33/188.09 cnf(10341,plain,
% 187.33/188.09 (~E(f329(a117,x103411),x103411)),
% 187.33/188.09 inference(rename_variables,[],[4459])).
% 187.33/188.09 cnf(10344,plain,
% 187.33/188.09 (~E(f329(a117,x103441),x103441)),
% 187.33/188.09 inference(rename_variables,[],[4459])).
% 187.33/188.09 cnf(10347,plain,
% 187.33/188.09 (~E(f329(a117,x103471),x103471)),
% 187.33/188.09 inference(rename_variables,[],[4459])).
% 187.33/188.09 cnf(10349,plain,
% 187.33/188.09 (P24(f329(a198,a102))),
% 187.33/188.09 inference(scs_inference,[],[4459,10208,10218,10229,10240,10341,10344,3065,3234,10211,10275,3108,3169,3136,3115,3205,4484,3166,4553,3188,3347,3260,4524,10243,10246,3869,3281,4521,4479,4520,10309,3373,3800,3738,4529,10263,4110,4527,4510,3251,4511,4515,4544,10234,4548,4546,10285,4568,4594,4643,4645,4675,4692,4699,4700,4739,4769,4775,4860,4885,4886,4921,4946,4947,4969,4970,4983,4987,5010,5017,5035,5038,5039,5040,5045,5046,5068,5093,5094,5104,5109,5115,5160,5161,5169,5178,5183,5185,5195,5197,5203,5207,5222,5229,5232,5233,5234,5238,5274,5287,5295,5297,5298,5302,5303,5304])).
% 187.33/188.09 cnf(10352,plain,
% 187.33/188.09 (P24(f329(f329(f244(a874),x103521),f329(a117,x103521)))),
% 187.33/188.09 inference(rename_variables,[],[3347])).
% 187.33/188.09 cnf(10361,plain,
% 187.33/188.09 (P24(f329(f329(f243(a874),x103611),x103611))),
% 187.33/188.09 inference(rename_variables,[],[3276])).
% 187.33/188.09 cnf(10368,plain,
% 187.33/188.09 (E(f329(f260(x103681,x103681),f261(x103681,x103682)),x103682)),
% 187.33/188.09 inference(rename_variables,[],[3234])).
% 187.33/188.09 cnf(10371,plain,
% 187.33/188.09 (E(f329(f260(x103711,x103711),f261(x103711,x103712)),x103712)),
% 187.33/188.09 inference(rename_variables,[],[3234])).
% 187.33/188.09 cnf(10390,plain,
% 187.33/188.09 (P24(f329(f329(f243(a1),x103901),x103901))),
% 187.33/188.09 inference(rename_variables,[],[3277])).
% 187.33/188.09 cnf(10399,plain,
% 187.33/188.09 (~P24(f329(f329(f244(a874),x103991),x103991))),
% 187.33/188.09 inference(rename_variables,[],[4520])).
% 187.33/188.09 cnf(10404,plain,
% 187.33/188.09 (~E(f329(f329(f329(f72(x104041,f878(x104042)),x104043),x104044),f329(f236(x104042),x104045)),f329(f16(f878(x104042),x104041),f206(x104042)))),
% 187.33/188.09 inference(rename_variables,[],[4541])).
% 187.33/188.09 cnf(10408,plain,
% 187.33/188.09 (E(f329(f329(f80(a874),x104081),f806(x104081,x104081)),x104081)),
% 187.33/188.09 inference(scs_inference,[],[4459,10208,10218,10229,10240,10341,10344,3065,3234,10211,10275,10278,10368,3108,3169,3136,3115,3205,4541,4484,3166,4066,4553,3188,3347,10352,3260,4524,10243,10246,3720,3869,3308,3281,4521,4479,4019,3276,10361,3277,3280,4520,10309,3373,3800,3738,10312,4529,10263,4110,4527,4510,3251,4511,4515,4544,10234,4548,3760,4546,10285,4568,4594,4643,4645,4675,4692,4699,4700,4739,4769,4775,4860,4885,4886,4921,4946,4947,4969,4970,4983,4987,5010,5017,5035,5038,5039,5040,5045,5046,5068,5093,5094,5104,5109,5115,5160,5161,5169,5178,5183,5185,5195,5197,5203,5207,5222,5229,5232,5233,5234,5238,5274,5287,5295,5297,5298,5302,5303,5304,5312,5315,5319,5320,5321,5328,5332,5333,5334,5342,5346,5347,5348,5353,5366,5375,5387,5389,5397,5398,5402,5406,5431,5437,5447,5448])).
% 187.33/188.09 cnf(10431,plain,
% 187.33/188.09 (~E(f329(f329(f149(x104311),x104312),x104313),x104313)),
% 187.33/188.09 inference(rename_variables,[],[4484])).
% 187.33/188.09 cnf(10434,plain,
% 187.33/188.09 (~E(f329(a26,x104341),f33(x104342,x104343))),
% 187.33/188.09 inference(rename_variables,[],[4474])).
% 187.33/188.09 cnf(10445,plain,
% 187.33/188.09 (P24(f329(f329(f243(a1),x104451),x104451))),
% 187.33/188.09 inference(rename_variables,[],[3277])).
% 187.33/188.09 cnf(10450,plain,
% 187.33/188.09 (~E(f329(a117,x104501),x104501)),
% 187.33/188.09 inference(rename_variables,[],[4459])).
% 187.33/188.09 cnf(10457,plain,
% 187.33/188.09 (P24(f329(f329(f243(a874),x104571),x104571))),
% 187.33/188.09 inference(rename_variables,[],[3276])).
% 187.33/188.09 cnf(10470,plain,
% 187.33/188.09 (P24(f329(f329(f244(a874),x104701),f329(a117,x104701)))),
% 187.33/188.09 inference(rename_variables,[],[3347])).
% 187.33/188.09 cnf(10475,plain,
% 187.33/188.09 (E(f329(f329(f126(x104751),f118(x104751)),x104752),x104752)),
% 187.33/188.09 inference(rename_variables,[],[3229])).
% 187.33/188.09 cnf(10493,plain,
% 187.33/188.09 (~P24(f329(f63(x104931,x104932,f193(f881(x104931,a869))),x104933))),
% 187.33/188.09 inference(rename_variables,[],[4544])).
% 187.33/188.09 cnf(10512,plain,
% 187.33/188.09 (~P24(f329(f329(f244(a874),x105121),x105121))),
% 187.33/188.09 inference(rename_variables,[],[4520])).
% 187.33/188.09 cnf(10524,plain,
% 187.33/188.09 (E(f329(f329(f254(a874),f329(f108(a874),a102)),x105241),f329(f329(f254(a874),f2(a874)),x105241))),
% 187.33/188.09 inference(scs_inference,[],[4459,10208,10218,10229,10240,10341,10344,10347,4474,3065,3234,10211,10275,10278,10368,3108,3169,3136,3115,3205,3229,10475,4541,4484,10266,3166,4066,4553,3188,3644,3347,10352,10470,3260,4524,10243,10246,10272,4536,3720,3869,3306,3308,3281,4521,4479,4019,3276,10361,10457,3277,10390,3280,4520,10309,10399,3373,3800,3738,10312,4529,10263,4110,4527,4510,3251,3255,4512,4511,4515,4544,10234,10237,4548,3760,4546,10285,4568,4594,4643,4645,4675,4692,4699,4700,4739,4769,4775,4860,4885,4886,4921,4946,4947,4969,4970,4983,4987,5010,5017,5035,5038,5039,5040,5045,5046,5068,5093,5094,5104,5109,5115,5160,5161,5169,5178,5183,5185,5195,5197,5203,5207,5222,5229,5232,5233,5234,5238,5274,5287,5295,5297,5298,5302,5303,5304,5312,5315,5319,5320,5321,5328,5332,5333,5334,5342,5346,5347,5348,5353,5366,5375,5387,5389,5397,5398,5402,5406,5431,5437,5447,5448,5463,5475,5497,5503,5519,5520,5523,5542,5550,5551,5556,5557,5567,5569,5581,5585,5594,5595,5597,5612,5617,5627,5628,5640,5647,5661,5665,5668,5674,5675,5676,5679,5684,5722,5723,5726,5728,5731,5732,5733,5735,5737,5739,5744,5751,5766,5780,5785,5786,5799,5800,5805,5809])).
% 187.33/188.09 cnf(10527,plain,
% 187.33/188.09 (~E(f329(a26,x105271),f33(x105272,x105273))),
% 187.33/188.09 inference(rename_variables,[],[4474])).
% 187.33/188.09 cnf(10536,plain,
% 187.33/188.09 (~P24(f329(f329(f244(a874),x105361),x105361))),
% 187.33/188.09 inference(rename_variables,[],[4520])).
% 187.33/188.09 cnf(10541,plain,
% 187.33/188.09 (P24(f329(f329(f244(a874),x105411),f329(a117,x105411)))),
% 187.33/188.09 inference(rename_variables,[],[3347])).
% 187.33/188.09 cnf(10544,plain,
% 187.33/188.09 (~P24(f329(f63(x105441,x105442,f193(f881(x105441,a869))),x105443))),
% 187.33/188.09 inference(rename_variables,[],[4544])).
% 187.33/188.09 cnf(10547,plain,
% 187.33/188.09 (~P24(f329(f63(x105471,x105472,f193(f881(x105471,a869))),x105473))),
% 187.33/188.09 inference(rename_variables,[],[4544])).
% 187.33/188.09 cnf(10552,plain,
% 187.33/188.09 (~P24(f329(f63(x105521,x105522,f193(f881(x105521,a869))),x105523))),
% 187.33/188.09 inference(rename_variables,[],[4544])).
% 187.33/188.09 cnf(10562,plain,
% 187.33/188.09 (~E(f329(f167(x105621),f329(a117,f329(f329(f126(x105621),f329(f167(x105621),x105622)),f329(f329(f149(x105621),x105623),f118(x105621))))),f329(f329(f149(x105621),x105623),x105622))),
% 187.33/188.09 inference(scs_inference,[],[4459,10208,10218,10229,10240,10341,10344,10347,10450,4474,10434,3065,3234,10211,10275,10278,10368,3108,3169,3136,3115,3205,3229,10475,4541,4484,10266,3166,4066,4553,3188,3644,3347,10352,10470,10541,3260,4524,10243,10246,10272,4536,3720,3869,3306,3308,3281,4521,4479,4019,3276,10361,10457,3277,10390,3280,4520,10309,10399,10512,3373,3800,3738,10312,4529,10263,4110,4527,4510,3251,3255,4512,4511,4515,4544,10234,10237,10493,10544,10547,4548,3760,4546,10285,4568,4594,4643,4645,4675,4692,4699,4700,4739,4769,4775,4860,4885,4886,4921,4946,4947,4969,4970,4983,4987,5010,5017,5035,5038,5039,5040,5045,5046,5068,5093,5094,5104,5109,5115,5160,5161,5169,5178,5183,5185,5195,5197,5203,5207,5222,5229,5232,5233,5234,5238,5274,5287,5295,5297,5298,5302,5303,5304,5312,5315,5319,5320,5321,5328,5332,5333,5334,5342,5346,5347,5348,5353,5366,5375,5387,5389,5397,5398,5402,5406,5431,5437,5447,5448,5463,5475,5497,5503,5519,5520,5523,5542,5550,5551,5556,5557,5567,5569,5581,5585,5594,5595,5597,5612,5617,5627,5628,5640,5647,5661,5665,5668,5674,5675,5676,5679,5684,5722,5723,5726,5728,5731,5732,5733,5735,5737,5739,5744,5751,5766,5780,5785,5786,5799,5800,5805,5809,5811,5816,5857,5869,5878,5882,5893,5897,5898,5906,5920,5926,5944,5947,5959,5985])).
% 187.33/188.09 cnf(10563,plain,
% 187.33/188.09 (~E(f329(a117,x105631),x105631)),
% 187.33/188.09 inference(rename_variables,[],[4459])).
% 187.33/188.09 cnf(10581,plain,
% 187.33/188.09 (P24(f329(f329(f244(a104),f329(a3,x105811)),f329(a3,f329(a117,x105811))))),
% 187.33/188.09 inference(scs_inference,[],[4459,10208,10218,10229,10240,10341,10344,10347,10450,4474,10434,3065,3234,10211,10275,10278,10368,3108,3169,3136,3115,3205,3229,10475,4541,4484,10266,3166,4066,4553,3188,3644,3347,10352,10470,10541,3733,3260,4524,10243,10246,10272,4536,3720,3869,3306,3308,3281,4521,4479,4019,3276,10361,10457,3277,10390,3280,4520,10309,10399,10512,3373,3800,3738,10312,4529,10263,4110,4527,4510,3251,3255,4512,4511,4515,4544,10234,10237,10493,10544,10547,4548,3760,4546,10285,4568,4594,4643,4645,4675,4692,4699,4700,4739,4769,4775,4860,4885,4886,4921,4946,4947,4969,4970,4983,4987,5010,5017,5035,5038,5039,5040,5045,5046,5068,5093,5094,5104,5109,5115,5160,5161,5169,5178,5183,5185,5195,5197,5203,5207,5222,5229,5232,5233,5234,5238,5274,5287,5295,5297,5298,5302,5303,5304,5312,5315,5319,5320,5321,5328,5332,5333,5334,5342,5346,5347,5348,5353,5366,5375,5387,5389,5397,5398,5402,5406,5431,5437,5447,5448,5463,5475,5497,5503,5519,5520,5523,5542,5550,5551,5556,5557,5567,5569,5581,5585,5594,5595,5597,5612,5617,5627,5628,5640,5647,5661,5665,5668,5674,5675,5676,5679,5684,5722,5723,5726,5728,5731,5732,5733,5735,5737,5739,5744,5751,5766,5780,5785,5786,5799,5800,5805,5809,5811,5816,5857,5869,5878,5882,5893,5897,5898,5906,5920,5926,5944,5947,5959,5985,5999,6024,6044,6045,6048,6062,6064,6066,6068])).
% 187.33/188.09 cnf(10588,plain,
% 187.33/188.09 (P24(f329(f329(f243(a874),x105881),x105881))),
% 187.33/188.09 inference(rename_variables,[],[3276])).
% 187.33/188.09 cnf(10591,plain,
% 187.33/188.09 (P24(f329(f329(f243(a874),x105911),f329(f329(f81(a874),x105911),x105911)))),
% 187.33/188.09 inference(rename_variables,[],[3547])).
% 187.33/188.09 cnf(10593,plain,
% 187.33/188.09 (P24(f329(f329(f244(a874),x105931),f329(f329(f81(a874),f329(a117,x105931)),f329(a117,x105931))))),
% 187.33/188.09 inference(scs_inference,[],[4459,10208,10218,10229,10240,10341,10344,10347,10450,4474,10434,3065,3234,10211,10275,10278,10368,3108,3169,3136,3115,3205,3229,10475,4541,4484,10266,3166,4066,4553,3188,3644,3347,10352,10470,10541,3733,3260,4524,10243,10246,10272,4536,3720,3869,3306,3308,3281,4521,4479,4019,3276,10361,10457,3277,10390,3280,4520,10309,10399,10512,3373,3800,3738,10312,4529,10263,4110,4527,4510,3251,3255,4512,4511,4515,4544,10234,10237,10493,10544,10547,3547,10591,4548,3760,4546,10285,4568,4594,4643,4645,4675,4692,4699,4700,4739,4769,4775,4860,4885,4886,4921,4946,4947,4969,4970,4983,4987,5010,5017,5035,5038,5039,5040,5045,5046,5068,5093,5094,5104,5109,5115,5160,5161,5169,5178,5183,5185,5195,5197,5203,5207,5222,5229,5232,5233,5234,5238,5274,5287,5295,5297,5298,5302,5303,5304,5312,5315,5319,5320,5321,5328,5332,5333,5334,5342,5346,5347,5348,5353,5366,5375,5387,5389,5397,5398,5402,5406,5431,5437,5447,5448,5463,5475,5497,5503,5519,5520,5523,5542,5550,5551,5556,5557,5567,5569,5581,5585,5594,5595,5597,5612,5617,5627,5628,5640,5647,5661,5665,5668,5674,5675,5676,5679,5684,5722,5723,5726,5728,5731,5732,5733,5735,5737,5739,5744,5751,5766,5780,5785,5786,5799,5800,5805,5809,5811,5816,5857,5869,5878,5882,5893,5897,5898,5906,5920,5926,5944,5947,5959,5985,5999,6024,6044,6045,6048,6062,6064,6066,6068,6081,6082,6085,6087,6090])).
% 187.33/188.09 cnf(10594,plain,
% 187.33/188.09 (P24(f329(f329(f243(a874),x105941),f329(f329(f81(a874),x105941),x105941)))),
% 187.33/188.09 inference(rename_variables,[],[3547])).
% 187.33/188.09 cnf(10597,plain,
% 187.33/188.09 (P24(f329(f329(f244(a874),x105971),f329(a117,f329(f329(f80(a874),x105972),x105971))))),
% 187.33/188.09 inference(rename_variables,[],[3731])).
% 187.33/188.09 cnf(10602,plain,
% 187.33/188.09 (P24(f329(f329(f244(a874),x106021),f329(a117,x106021)))),
% 187.33/188.09 inference(rename_variables,[],[3347])).
% 187.33/188.09 cnf(10605,plain,
% 187.33/188.09 (P24(f329(f329(f244(a874),x106051),f329(a117,x106051)))),
% 187.33/188.09 inference(rename_variables,[],[3347])).
% 187.33/188.09 cnf(10608,plain,
% 187.33/188.09 (P24(f329(f329(f331(x106081),x106082),f252(f881(x106081,a869))))),
% 187.33/188.09 inference(rename_variables,[],[3437])).
% 187.33/188.09 cnf(10625,plain,
% 187.33/188.09 (~P24(f329(f329(f243(a874),f329(a117,x106251)),x106251))),
% 187.33/188.09 inference(rename_variables,[],[4529])).
% 187.33/188.09 cnf(10628,plain,
% 187.33/188.09 (~P24(f329(f329(f243(a874),f329(a117,x106281)),x106281))),
% 187.33/188.09 inference(rename_variables,[],[4529])).
% 187.33/188.09 cnf(10631,plain,
% 187.33/188.09 (~P24(f329(f329(f244(a874),f329(f329(f80(a874),x106311),x106312)),x106312))),
% 187.33/188.09 inference(rename_variables,[],[4546])).
% 187.33/188.09 cnf(10634,plain,
% 187.33/188.09 (~P24(f329(f329(f244(a874),f329(f329(f80(a874),x106341),x106342)),x106342))),
% 187.33/188.09 inference(rename_variables,[],[4546])).
% 187.33/188.09 cnf(10637,plain,
% 187.33/188.09 (P24(f329(f252(f881(x106371,a869)),x106372))),
% 187.33/188.09 inference(rename_variables,[],[3341])).
% 187.33/188.09 cnf(10640,plain,
% 187.33/188.09 (E(f329(f38(a874),f329(f250(a874),x106401)),x106401)),
% 187.33/188.09 inference(rename_variables,[],[3166])).
% 187.33/188.09 cnf(10643,plain,
% 187.33/188.09 (P24(f329(f329(f244(a874),x106431),f329(a117,x106431)))),
% 187.33/188.09 inference(rename_variables,[],[3347])).
% 187.33/188.09 cnf(10650,plain,
% 187.33/188.09 (P24(f329(f329(f243(a874),x106501),x106501))),
% 187.33/188.09 inference(rename_variables,[],[3276])).
% 187.33/188.09 cnf(10655,plain,
% 187.33/188.09 (P24(f329(f329(f243(a1),x106551),x106551))),
% 187.33/188.09 inference(rename_variables,[],[3277])).
% 187.33/188.09 cnf(10664,plain,
% 187.33/188.09 (E(f329(f260(x106641,x106641),f261(x106641,x106642)),x106642)),
% 187.33/188.09 inference(rename_variables,[],[3234])).
% 187.33/188.09 cnf(10667,plain,
% 187.33/188.09 (P24(f329(f252(f881(x106671,a869)),x106672))),
% 187.33/188.09 inference(rename_variables,[],[3341])).
% 187.33/188.09 cnf(10670,plain,
% 187.33/188.09 (P24(f329(f329(f243(a874),f2(a874)),x106701))),
% 187.33/188.09 inference(rename_variables,[],[3300])).
% 187.33/188.09 cnf(10673,plain,
% 187.33/188.09 (P24(f329(f329(f243(f881(x106731,a869)),f193(f881(x106731,a869))),x106732))),
% 187.33/188.09 inference(rename_variables,[],[3729])).
% 187.33/188.09 cnf(10676,plain,
% 187.33/188.09 (P24(f329(f252(f881(x106761,a869)),x106762))),
% 187.33/188.09 inference(rename_variables,[],[3341])).
% 187.33/188.09 cnf(10678,plain,
% 187.33/188.09 (~P24(f329(f329(f243(a874),f329(f329(f81(a874),f329(a117,x106781)),f329(a117,x106781))),x106781))),
% 187.33/188.09 inference(scs_inference,[],[4459,10208,10218,10229,10240,10341,10344,10347,10450,4474,10434,3065,3234,10211,10275,10278,10368,10371,3108,3169,3136,3115,3205,3229,10475,4541,4484,10266,3166,10333,4066,4553,3188,3644,3583,3347,10352,10470,10541,10602,10605,3733,3260,4524,10243,10246,10272,4536,3720,3491,3869,3306,3308,3281,4521,4479,4019,3276,10361,10457,10588,3277,10390,10445,3280,4520,10309,10399,10512,3437,3341,10637,10667,3373,3800,3738,10312,4529,10263,10625,3300,4110,4527,4510,3251,3255,4512,4511,4515,4544,10234,10237,10493,10544,10547,4551,3729,3547,10591,10594,4548,3760,4546,10285,10288,10631,3731,4568,4594,4643,4645,4675,4692,4699,4700,4739,4769,4775,4860,4885,4886,4921,4946,4947,4969,4970,4983,4987,5010,5017,5035,5038,5039,5040,5045,5046,5068,5093,5094,5104,5109,5115,5160,5161,5169,5178,5183,5185,5195,5197,5203,5207,5222,5229,5232,5233,5234,5238,5274,5287,5295,5297,5298,5302,5303,5304,5312,5315,5319,5320,5321,5328,5332,5333,5334,5342,5346,5347,5348,5353,5366,5375,5387,5389,5397,5398,5402,5406,5431,5437,5447,5448,5463,5475,5497,5503,5519,5520,5523,5542,5550,5551,5556,5557,5567,5569,5581,5585,5594,5595,5597,5612,5617,5627,5628,5640,5647,5661,5665,5668,5674,5675,5676,5679,5684,5722,5723,5726,5728,5731,5732,5733,5735,5737,5739,5744,5751,5766,5780,5785,5786,5799,5800,5805,5809,5811,5816,5857,5869,5878,5882,5893,5897,5898,5906,5920,5926,5944,5947,5959,5985,5999,6024,6044,6045,6048,6062,6064,6066,6068,6081,6082,6085,6087,6090,6091,6103,6109,6110,6111,6113,6115,6158,6159,6166,6172,6176,6212,6214,6216,6218,6227,6229,6231,6237,6239,6245,6248,6256,6263,6264,6265,6270,6292,6293,6294,6296,6302])).
% 187.33/188.09 cnf(10679,plain,
% 187.33/188.09 (P24(f329(f329(f243(a874),x106791),f329(f329(f81(a874),x106791),x106791)))),
% 187.33/188.09 inference(rename_variables,[],[3547])).
% 187.33/188.09 cnf(10683,plain,
% 187.33/188.09 (E(f329(f167(x106831),f172(x106832,f329(f329(f126(x106831),f329(f167(x106831),x106833)),f329(f329(f149(x106831),x106834),f118(x106831))),f118(x106832))),f329(f329(f149(x106831),x106834),x106833))),
% 187.33/188.09 inference(scs_inference,[],[4459,10208,10218,10229,10240,10341,10344,10347,10450,4474,10434,3065,3234,10211,10275,10278,10368,10371,3212,3108,3169,3136,3115,3205,3229,10475,4541,4484,10266,3166,10333,4066,4553,3188,3644,3583,3347,10352,10470,10541,10602,10605,3733,3260,4524,10243,10246,10272,4536,3720,3491,3869,3306,3308,3281,4521,4479,4019,3276,10361,10457,10588,3277,10390,10445,3280,4520,10309,10399,10512,3437,3341,10637,10667,3373,3800,3738,10312,4529,10263,10625,3300,4110,4527,4510,3251,3255,4512,4511,4515,4544,10234,10237,10493,10544,10547,4551,3729,3547,10591,10594,4548,3760,4546,10285,10288,10631,3731,4568,4594,4643,4645,4675,4692,4699,4700,4739,4769,4775,4860,4885,4886,4921,4946,4947,4969,4970,4983,4987,5010,5017,5035,5038,5039,5040,5045,5046,5068,5093,5094,5104,5109,5115,5160,5161,5169,5178,5183,5185,5195,5197,5203,5207,5222,5229,5232,5233,5234,5238,5274,5287,5295,5297,5298,5302,5303,5304,5312,5315,5319,5320,5321,5328,5332,5333,5334,5342,5346,5347,5348,5353,5366,5375,5387,5389,5397,5398,5402,5406,5431,5437,5447,5448,5463,5475,5497,5503,5519,5520,5523,5542,5550,5551,5556,5557,5567,5569,5581,5585,5594,5595,5597,5612,5617,5627,5628,5640,5647,5661,5665,5668,5674,5675,5676,5679,5684,5722,5723,5726,5728,5731,5732,5733,5735,5737,5739,5744,5751,5766,5780,5785,5786,5799,5800,5805,5809,5811,5816,5857,5869,5878,5882,5893,5897,5898,5906,5920,5926,5944,5947,5959,5985,5999,6024,6044,6045,6048,6062,6064,6066,6068,6081,6082,6085,6087,6090,6091,6103,6109,6110,6111,6113,6115,6158,6159,6166,6172,6176,6212,6214,6216,6218,6227,6229,6231,6237,6239,6245,6248,6256,6263,6264,6265,6270,6292,6293,6294,6296,6302,6307,6341])).
% 187.33/188.09 cnf(10688,plain,
% 187.33/188.09 (~P24(f329(f329(f243(a874),f329(a117,f329(a117,f329(f329(f80(a874),x106881),x106882)))),f329(a117,x106882)))),
% 187.33/188.09 inference(scs_inference,[],[4459,10208,10218,10229,10240,10341,10344,10347,10450,4474,10434,3065,3234,10211,10275,10278,10368,10371,3212,3108,3169,3136,3115,3205,3229,10475,4541,4484,10266,3166,10333,4066,4553,3188,3644,3583,3347,10352,10470,10541,10602,10605,10643,3733,3260,4524,10243,10246,10272,4536,3720,3491,3869,3306,3308,3281,4521,4479,4019,3276,10361,10457,10588,3277,10390,10445,3280,4520,10309,10399,10512,3437,3341,10637,10667,3373,3800,3738,10312,4529,10263,10625,3300,4110,4527,4510,3251,3255,4512,4511,4515,4544,10234,10237,10493,10544,10547,4551,3729,3547,10591,10594,4548,3760,4546,10285,10288,10631,3731,4568,4594,4643,4645,4675,4692,4699,4700,4739,4769,4775,4860,4885,4886,4921,4946,4947,4969,4970,4983,4987,5010,5017,5035,5038,5039,5040,5045,5046,5068,5093,5094,5104,5109,5115,5160,5161,5169,5178,5183,5185,5195,5197,5203,5207,5222,5229,5232,5233,5234,5238,5274,5287,5295,5297,5298,5302,5303,5304,5312,5315,5319,5320,5321,5328,5332,5333,5334,5342,5346,5347,5348,5353,5366,5375,5387,5389,5397,5398,5402,5406,5431,5437,5447,5448,5463,5475,5497,5503,5519,5520,5523,5542,5550,5551,5556,5557,5567,5569,5581,5585,5594,5595,5597,5612,5617,5627,5628,5640,5647,5661,5665,5668,5674,5675,5676,5679,5684,5722,5723,5726,5728,5731,5732,5733,5735,5737,5739,5744,5751,5766,5780,5785,5786,5799,5800,5805,5809,5811,5816,5857,5869,5878,5882,5893,5897,5898,5906,5920,5926,5944,5947,5959,5985,5999,6024,6044,6045,6048,6062,6064,6066,6068,6081,6082,6085,6087,6090,6091,6103,6109,6110,6111,6113,6115,6158,6159,6166,6172,6176,6212,6214,6216,6218,6227,6229,6231,6237,6239,6245,6248,6256,6263,6264,6265,6270,6292,6293,6294,6296,6302,6307,6341,6342,6344])).
% 187.33/188.09 cnf(10696,plain,
% 187.33/188.09 (~P24(f329(f329(f244(a104),f329(a3,x106961)),f329(a3,f2(a874))))),
% 187.33/188.09 inference(scs_inference,[],[4459,10208,10218,10229,10240,10341,10344,10347,10450,4474,10434,3065,3234,10211,10275,10278,10368,10371,3212,3108,3169,3136,3115,3205,3229,10475,4541,4484,10266,3166,10333,4066,4553,3188,3644,3583,3347,10352,10470,10541,10602,10605,10643,3733,3260,4524,10243,10246,10272,4536,3720,3491,3869,3306,3308,3281,4521,4479,4019,3276,10361,10457,10588,3277,10390,10445,3280,4520,10309,10399,10512,3437,3341,10637,10667,3373,3800,3738,10312,4529,10263,10625,10628,3300,4110,4527,4510,3251,3255,4512,4511,4515,4544,10234,10237,10493,10544,10547,4551,3729,3547,10591,10594,4548,3760,4546,10285,10288,10631,3731,4568,4594,4643,4645,4675,4692,4699,4700,4739,4769,4775,4860,4885,4886,4921,4946,4947,4969,4970,4983,4987,5010,5017,5035,5038,5039,5040,5045,5046,5068,5093,5094,5104,5109,5115,5160,5161,5169,5178,5183,5185,5195,5197,5203,5207,5222,5229,5232,5233,5234,5238,5274,5287,5295,5297,5298,5302,5303,5304,5312,5315,5319,5320,5321,5328,5332,5333,5334,5342,5346,5347,5348,5353,5366,5375,5387,5389,5397,5398,5402,5406,5431,5437,5447,5448,5463,5475,5497,5503,5519,5520,5523,5542,5550,5551,5556,5557,5567,5569,5581,5585,5594,5595,5597,5612,5617,5627,5628,5640,5647,5661,5665,5668,5674,5675,5676,5679,5684,5722,5723,5726,5728,5731,5732,5733,5735,5737,5739,5744,5751,5766,5780,5785,5786,5799,5800,5805,5809,5811,5816,5857,5869,5878,5882,5893,5897,5898,5906,5920,5926,5944,5947,5959,5985,5999,6024,6044,6045,6048,6062,6064,6066,6068,6081,6082,6085,6087,6090,6091,6103,6109,6110,6111,6113,6115,6158,6159,6166,6172,6176,6212,6214,6216,6218,6227,6229,6231,6237,6239,6245,6248,6256,6263,6264,6265,6270,6292,6293,6294,6296,6302,6307,6341,6342,6344,6345,6346,6348,6349])).
% 187.33/188.09 cnf(10719,plain,
% 187.33/188.09 (P24(f329(f329(f243(a874),x107191),x107191))),
% 187.33/188.09 inference(rename_variables,[],[3276])).
% 187.33/188.09 cnf(10730,plain,
% 187.33/188.09 (~P24(f329(f329(f193(f881(x107301,f881(x107302,a869))),x107303),x107304))),
% 187.33/188.09 inference(rename_variables,[],[4549])).
% 187.33/188.09 cnf(10737,plain,
% 187.33/188.09 (P24(f329(f329(f244(a874),x107371),f329(a117,x107371)))),
% 187.33/188.09 inference(rename_variables,[],[3347])).
% 187.33/188.09 cnf(10739,plain,
% 187.33/188.09 (P24(f329(f329(f244(a1),f329(f329(f22(a1),x107391),f78(a1))),x107391))),
% 187.33/188.09 inference(scs_inference,[],[4459,10208,10218,10229,10240,10341,10344,10347,10450,4474,10434,3065,3234,10211,10275,10278,10368,10371,3212,3108,3169,3136,3115,3205,3229,10475,4541,4484,10266,3166,10333,4066,3921,4553,3188,3644,3583,3347,10352,10470,10541,10602,10605,10643,3733,3260,4524,10243,10246,10272,4536,3720,3491,3869,3306,3308,3281,4521,4479,4019,3276,10361,10457,10588,10650,10719,3277,10390,10445,10655,3280,4520,10309,10399,10512,3437,4532,3341,10637,10667,3373,3800,3738,10312,4529,10263,10625,10628,3300,4110,4527,4510,4513,3251,3255,4512,4511,4515,4544,10234,10237,10493,10544,10547,4551,3729,3547,10591,10594,4548,4549,3760,4546,10285,10288,10631,3731,4568,4594,4643,4645,4675,4692,4699,4700,4739,4769,4775,4860,4885,4886,4921,4946,4947,4969,4970,4983,4987,5010,5017,5035,5038,5039,5040,5045,5046,5068,5093,5094,5104,5109,5115,5160,5161,5169,5178,5183,5185,5195,5197,5203,5207,5222,5229,5232,5233,5234,5238,5274,5287,5295,5297,5298,5302,5303,5304,5312,5315,5319,5320,5321,5328,5332,5333,5334,5342,5346,5347,5348,5353,5366,5375,5387,5389,5397,5398,5402,5406,5431,5437,5447,5448,5463,5475,5497,5503,5519,5520,5523,5542,5550,5551,5556,5557,5567,5569,5581,5585,5594,5595,5597,5612,5617,5627,5628,5640,5647,5661,5665,5668,5674,5675,5676,5679,5684,5722,5723,5726,5728,5731,5732,5733,5735,5737,5739,5744,5751,5766,5780,5785,5786,5799,5800,5805,5809,5811,5816,5857,5869,5878,5882,5893,5897,5898,5906,5920,5926,5944,5947,5959,5985,5999,6024,6044,6045,6048,6062,6064,6066,6068,6081,6082,6085,6087,6090,6091,6103,6109,6110,6111,6113,6115,6158,6159,6166,6172,6176,6212,6214,6216,6218,6227,6229,6231,6237,6239,6245,6248,6256,6263,6264,6265,6270,6292,6293,6294,6296,6302,6307,6341,6342,6344,6345,6346,6348,6349,6350,6351,6358,6391,6392,6401,6422,6423,6443,6446,6457,6458,6464,6495,6497,6511,6549,6551,6552,6606])).
% 187.33/188.09 cnf(10740,plain,
% 187.33/188.09 (P24(f329(f329(f243(a1),x107401),x107401))),
% 187.33/188.09 inference(rename_variables,[],[3277])).
% 187.33/188.09 cnf(10745,plain,
% 187.33/188.09 (~P24(f329(f329(f244(a874),x107451),f2(a874)))),
% 187.33/188.09 inference(rename_variables,[],[4524])).
% 187.33/188.09 cnf(10758,plain,
% 187.33/188.09 (~P24(f329(f329(f244(a874),x107581),f2(a874)))),
% 187.33/188.09 inference(rename_variables,[],[4524])).
% 187.33/188.09 cnf(10761,plain,
% 187.33/188.09 (~P24(f329(f329(f244(f881(x107611,a869)),x107612),f193(f881(x107611,a869))))),
% 187.33/188.09 inference(rename_variables,[],[4542])).
% 187.33/188.09 cnf(10764,plain,
% 187.33/188.09 (P24(f329(f329(f243(a874),x107641),x107641))),
% 187.33/188.09 inference(rename_variables,[],[3276])).
% 187.33/188.09 cnf(10767,plain,
% 187.33/188.09 (P24(f329(f329(f243(a874),x107671),x107671))),
% 187.33/188.09 inference(rename_variables,[],[3276])).
% 187.33/188.09 cnf(10781,plain,
% 187.33/188.09 (~P24(f329(f329(f244(a874),x107811),f329(f329(f22(a874),x107811),x107812)))),
% 187.33/188.09 inference(scs_inference,[],[4323,4459,10208,10218,10229,10240,10341,10344,10347,10450,4474,10434,3065,3234,10211,10275,10278,10368,10371,3212,3108,3169,3136,3115,3205,3229,10475,4541,4484,10266,3166,10333,4066,3921,4553,3188,3644,3583,3347,10352,10470,10541,10602,10605,10643,3733,3260,4524,10243,10246,10272,10745,4536,3720,3491,3869,3306,3308,3281,4521,4479,4019,4542,3276,10361,10457,10588,10650,10719,10764,10767,3277,10390,10445,10655,3280,4520,10309,10399,10512,10536,3437,4532,3341,10637,10667,3373,3800,3738,10312,4529,10263,10625,10628,3300,4110,4527,4510,4513,3251,3255,4512,4511,4515,4544,10234,10237,10493,10544,10547,4551,3729,3547,10591,10594,4548,4549,3760,4546,10285,10288,10631,3731,4568,4594,4643,4645,4675,4692,4699,4700,4739,4769,4775,4860,4885,4886,4921,4946,4947,4969,4970,4983,4987,5010,5017,5035,5038,5039,5040,5045,5046,5068,5093,5094,5104,5109,5115,5160,5161,5169,5178,5183,5185,5195,5197,5203,5207,5222,5229,5232,5233,5234,5238,5274,5287,5295,5297,5298,5302,5303,5304,5312,5315,5319,5320,5321,5328,5332,5333,5334,5342,5346,5347,5348,5353,5366,5375,5387,5389,5397,5398,5402,5406,5431,5437,5447,5448,5463,5475,5497,5503,5519,5520,5523,5542,5550,5551,5556,5557,5567,5569,5581,5585,5594,5595,5597,5612,5617,5627,5628,5640,5647,5661,5665,5668,5674,5675,5676,5679,5684,5722,5723,5726,5728,5731,5732,5733,5735,5737,5739,5744,5751,5766,5780,5785,5786,5799,5800,5805,5809,5811,5816,5857,5869,5878,5882,5893,5897,5898,5906,5920,5926,5944,5947,5959,5985,5999,6024,6044,6045,6048,6062,6064,6066,6068,6081,6082,6085,6087,6090,6091,6103,6109,6110,6111,6113,6115,6158,6159,6166,6172,6176,6212,6214,6216,6218,6227,6229,6231,6237,6239,6245,6248,6256,6263,6264,6265,6270,6292,6293,6294,6296,6302,6307,6341,6342,6344,6345,6346,6348,6349,6350,6351,6358,6391,6392,6401,6422,6423,6443,6446,6457,6458,6464,6495,6497,6511,6549,6551,6552,6606,6630,6672,6692,6701,6702,6703,6704,6723,6724,6730,6743,6746,6748,6750,6751,6752,6754,6768])).
% 187.33/188.09 cnf(10782,plain,
% 187.33/188.09 (~P24(f329(f329(f244(a874),x107821),x107821))),
% 187.33/188.09 inference(rename_variables,[],[4520])).
% 187.33/188.09 cnf(10791,plain,
% 187.33/188.09 (~P24(f329(f329(f331(x107911),x107912),f193(f881(x107911,a869))))),
% 187.33/188.09 inference(rename_variables,[],[4532])).
% 187.33/188.09 cnf(10800,plain,
% 187.33/188.09 (P24(f329(f329(f243(a874),x108001),x108001))),
% 187.33/188.09 inference(rename_variables,[],[3276])).
% 187.33/188.09 cnf(10803,plain,
% 187.33/188.09 (~P24(f329(f329(f331(x108031),x108032),f193(f881(x108031,a869))))),
% 187.33/188.09 inference(rename_variables,[],[4532])).
% 187.33/188.09 cnf(10806,plain,
% 187.33/188.09 (P24(f329(f329(f243(f881(x108061,a869)),f329(f308(x108062,x108061,x108063),f329(f309(x108062,x108061,x108063),x108064))),x108064))),
% 187.33/188.09 inference(rename_variables,[],[4170])).
% 187.33/188.09 cnf(10815,plain,
% 187.33/188.09 (E(f329(f308(x108151,x108151,f5(x108151)),x108152),x108152)),
% 187.33/188.09 inference(rename_variables,[],[3337])).
% 187.33/188.09 cnf(10820,plain,
% 187.33/188.09 (P24(f329(f329(f243(a874),f2(a874)),x108201))),
% 187.33/188.09 inference(rename_variables,[],[3300])).
% 187.33/188.09 cnf(10823,plain,
% 187.33/188.09 (P24(f329(f329(f243(a874),x108231),x108231))),
% 187.33/188.09 inference(rename_variables,[],[3276])).
% 187.33/188.09 cnf(10826,plain,
% 187.33/188.09 (~P24(f329(f329(f244(a874),x108261),x108261))),
% 187.33/188.09 inference(rename_variables,[],[4520])).
% 187.33/188.09 cnf(10829,plain,
% 187.33/188.09 (~P24(f329(f329(f193(f881(x108291,f881(x108292,a869))),x108293),x108294))),
% 187.33/188.09 inference(rename_variables,[],[4549])).
% 187.33/188.09 cnf(10836,plain,
% 187.33/188.09 (~P24(f329(f329(f244(a874),x108361),x108361))),
% 187.33/188.09 inference(rename_variables,[],[4520])).
% 187.33/188.09 cnf(10847,plain,
% 187.33/188.09 (P24(f329(f329(f243(a874),x108471),f329(f329(f81(a874),x108471),x108471)))),
% 187.33/188.09 inference(rename_variables,[],[3547])).
% 187.33/188.09 cnf(10853,plain,
% 187.33/188.09 (P24(f329(f329(f244(a874),x108531),f329(a117,f329(f329(f80(a874),x108532),x108531))))),
% 187.33/188.09 inference(rename_variables,[],[3731])).
% 187.33/188.09 cnf(10860,plain,
% 187.33/188.09 (P24(f329(f329(f243(a874),x108601),x108601))),
% 187.33/188.09 inference(rename_variables,[],[3276])).
% 187.33/188.09 cnf(10863,plain,
% 187.33/188.09 (P24(f329(f329(f243(a1),x108631),x108631))),
% 187.33/188.09 inference(rename_variables,[],[3277])).
% 187.33/188.09 cnf(10866,plain,
% 187.33/188.09 (~E(f329(a117,x108661),x108661)),
% 187.33/188.09 inference(rename_variables,[],[4459])).
% 187.33/188.09 cnf(10871,plain,
% 187.33/188.09 (P24(f329(f329(f331(x108711),x108712),f252(f881(x108711,a869))))),
% 187.33/188.09 inference(rename_variables,[],[3437])).
% 187.33/188.09 cnf(10876,plain,
% 187.33/188.09 (~P24(f329(f329(f244(a874),x108761),f2(a874)))),
% 187.33/188.09 inference(rename_variables,[],[4524])).
% 187.33/188.09 cnf(10878,plain,
% 187.33/188.09 (P24(f329(f329(f243(f881(x108781,a869)),x108782),f40(f881(x108781,a869),f329(f306(x108781),x108782))))),
% 187.33/188.09 inference(scs_inference,[],[4323,4459,10208,10218,10229,10240,10341,10344,10347,10450,10563,4474,10434,3065,3234,10211,10275,10278,10368,10371,3212,3108,3169,3136,3115,3337,3205,3229,10475,4541,4484,10266,3166,10333,4066,3921,4553,3188,3482,3644,3583,3347,10352,10470,10541,10602,10605,10643,10737,3733,3260,4524,10243,10246,10272,10745,10758,4536,3720,3491,3869,3306,3308,3281,4521,4479,3645,4019,4542,3276,10361,10457,10588,10650,10719,10764,10767,10800,10823,3277,10390,10445,10655,10740,3280,4520,10309,10399,10512,10536,10782,10826,3437,10608,4532,10791,10803,3341,10637,10667,3373,3800,3738,10312,4529,10263,10625,10628,3300,10670,4110,4527,4510,4513,3251,3255,4512,4511,4515,4544,10234,10237,10493,10544,10547,4551,3729,3547,10591,10594,10679,10847,4548,4549,10730,4170,3760,4546,10285,10288,10631,3731,10597,4568,4594,4643,4645,4675,4692,4699,4700,4739,4769,4775,4860,4885,4886,4921,4946,4947,4969,4970,4983,4987,5010,5017,5035,5038,5039,5040,5045,5046,5068,5093,5094,5104,5109,5115,5160,5161,5169,5178,5183,5185,5195,5197,5203,5207,5222,5229,5232,5233,5234,5238,5274,5287,5295,5297,5298,5302,5303,5304,5312,5315,5319,5320,5321,5328,5332,5333,5334,5342,5346,5347,5348,5353,5366,5375,5387,5389,5397,5398,5402,5406,5431,5437,5447,5448,5463,5475,5497,5503,5519,5520,5523,5542,5550,5551,5556,5557,5567,5569,5581,5585,5594,5595,5597,5612,5617,5627,5628,5640,5647,5661,5665,5668,5674,5675,5676,5679,5684,5722,5723,5726,5728,5731,5732,5733,5735,5737,5739,5744,5751,5766,5780,5785,5786,5799,5800,5805,5809,5811,5816,5857,5869,5878,5882,5893,5897,5898,5906,5920,5926,5944,5947,5959,5985,5999,6024,6044,6045,6048,6062,6064,6066,6068,6081,6082,6085,6087,6090,6091,6103,6109,6110,6111,6113,6115,6158,6159,6166,6172,6176,6212,6214,6216,6218,6227,6229,6231,6237,6239,6245,6248,6256,6263,6264,6265,6270,6292,6293,6294,6296,6302,6307,6341,6342,6344,6345,6346,6348,6349,6350,6351,6358,6391,6392,6401,6422,6423,6443,6446,6457,6458,6464,6495,6497,6511,6549,6551,6552,6606,6630,6672,6692,6701,6702,6703,6704,6723,6724,6730,6743,6746,6748,6750,6751,6752,6754,6768,6779,6781,6782,6795,6799,6850,6861,6863,6867,6884,6885,6921,6933,6964,6998,7052,7080,7135,7156,7165,7168,7223,7231,7289,7291,7306,7316,7317,7318,7337,7343,7345,7395,7405,7408,7424,7476,7478,7481])).
% 187.33/188.09 cnf(10891,plain,
% 187.33/188.09 (P24(f329(f329(f243(a874),f2(a874)),x108911))),
% 187.33/188.09 inference(rename_variables,[],[3300])).
% 187.33/188.09 cnf(10898,plain,
% 187.33/188.09 (P24(f329(f329(f243(a874),x108981),x108981))),
% 187.33/188.09 inference(rename_variables,[],[3276])).
% 187.33/188.09 cnf(10907,plain,
% 187.33/188.09 (~P24(f329(f329(f331(x109071),x109072),f193(f881(x109071,a869))))),
% 187.33/188.09 inference(rename_variables,[],[4532])).
% 187.33/188.09 cnf(10909,plain,
% 187.33/188.09 (P24(f329(f329(f243(f881(x109091,a869)),f41(f881(x109091,a869),f329(f306(x109091),x109092))),x109092))),
% 187.33/188.09 inference(scs_inference,[],[4323,4459,10208,10218,10229,10240,10341,10344,10347,10450,10563,4474,10434,3065,3234,10211,10275,10278,10368,10371,3212,3108,3169,3136,3115,3337,3205,3229,10475,4541,4484,10266,3166,10333,4066,3921,4553,3188,3482,3644,3583,3796,3347,10352,10470,10541,10602,10605,10643,10737,3733,3260,4524,10243,10246,10272,10745,10758,4536,3720,3491,3869,3306,3308,3281,4521,4479,3645,4019,4542,3276,10361,10457,10588,10650,10719,10764,10767,10800,10823,10860,3277,10390,10445,10655,10740,3280,4520,10309,10399,10512,10536,10782,10826,3437,10608,10871,4532,10791,10803,3341,10637,10667,3373,3800,3738,10312,4529,10263,10625,10628,3300,10670,10820,4110,4527,3808,4510,4513,3251,3255,4512,4511,4515,4544,10234,10237,10493,10544,10547,4551,3729,3547,10591,10594,10679,10847,4548,4549,10730,4170,3760,4546,10285,10288,10631,3731,10597,4568,4594,4643,4645,4675,4692,4699,4700,4739,4769,4775,4860,4885,4886,4921,4946,4947,4969,4970,4983,4987,5010,5017,5035,5038,5039,5040,5045,5046,5068,5093,5094,5104,5109,5115,5160,5161,5169,5178,5183,5185,5195,5197,5203,5207,5222,5229,5232,5233,5234,5238,5274,5287,5295,5297,5298,5302,5303,5304,5312,5315,5319,5320,5321,5328,5332,5333,5334,5342,5346,5347,5348,5353,5366,5375,5387,5389,5397,5398,5402,5406,5431,5437,5447,5448,5463,5475,5497,5503,5519,5520,5523,5542,5550,5551,5556,5557,5567,5569,5581,5585,5594,5595,5597,5612,5617,5627,5628,5640,5647,5661,5665,5668,5674,5675,5676,5679,5684,5722,5723,5726,5728,5731,5732,5733,5735,5737,5739,5744,5751,5766,5780,5785,5786,5799,5800,5805,5809,5811,5816,5857,5869,5878,5882,5893,5897,5898,5906,5920,5926,5944,5947,5959,5985,5999,6024,6044,6045,6048,6062,6064,6066,6068,6081,6082,6085,6087,6090,6091,6103,6109,6110,6111,6113,6115,6158,6159,6166,6172,6176,6212,6214,6216,6218,6227,6229,6231,6237,6239,6245,6248,6256,6263,6264,6265,6270,6292,6293,6294,6296,6302,6307,6341,6342,6344,6345,6346,6348,6349,6350,6351,6358,6391,6392,6401,6422,6423,6443,6446,6457,6458,6464,6495,6497,6511,6549,6551,6552,6606,6630,6672,6692,6701,6702,6703,6704,6723,6724,6730,6743,6746,6748,6750,6751,6752,6754,6768,6779,6781,6782,6795,6799,6850,6861,6863,6867,6884,6885,6921,6933,6964,6998,7052,7080,7135,7156,7165,7168,7223,7231,7289,7291,7306,7316,7317,7318,7337,7343,7345,7395,7405,7408,7424,7476,7478,7481,7524,7525,7543,7610,7629,7652,7676,7691,7706,7717,7726,7727,7756,7759])).
% 187.33/188.09 cnf(10914,plain,
% 187.33/188.09 (P24(f329(f329(f331(f875(x109141)),x109142),f159(x109141,f252(f881(x109141,a869)))))),
% 187.33/188.09 inference(scs_inference,[],[4323,4459,10208,10218,10229,10240,10341,10344,10347,10450,10563,4474,10434,3065,3234,10211,10275,10278,10368,10371,3212,3108,3169,3136,3115,3337,3205,3229,10475,4541,4484,10266,3166,10333,4066,3921,4553,3188,3482,3644,3583,3796,3347,10352,10470,10541,10602,10605,10643,10737,3733,3260,4524,10243,10246,10272,10745,10758,4536,3720,3491,3869,3306,3308,3281,4521,4479,3645,4019,4542,3276,10361,10457,10588,10650,10719,10764,10767,10800,10823,10860,3277,10390,10445,10655,10740,3280,4520,10309,10399,10512,10536,10782,10826,3437,10608,10871,4532,10791,10803,3341,10637,10667,3373,3800,3738,10312,4529,10263,10625,10628,3300,10670,10820,4110,4527,3808,4510,4513,3251,3255,4512,4511,4515,4544,10234,10237,10493,10544,10547,4551,3729,3547,10591,10594,10679,10847,4548,4549,10730,4170,3760,4546,10285,10288,10631,3731,10597,4003,4568,4594,4643,4645,4675,4692,4699,4700,4739,4769,4775,4860,4885,4886,4921,4946,4947,4969,4970,4983,4987,5010,5017,5035,5038,5039,5040,5045,5046,5068,5093,5094,5104,5109,5115,5160,5161,5169,5178,5183,5185,5195,5197,5203,5207,5222,5229,5232,5233,5234,5238,5274,5287,5295,5297,5298,5302,5303,5304,5312,5315,5319,5320,5321,5328,5332,5333,5334,5342,5346,5347,5348,5353,5366,5375,5387,5389,5397,5398,5402,5406,5431,5437,5447,5448,5463,5475,5497,5503,5519,5520,5523,5542,5550,5551,5556,5557,5567,5569,5581,5585,5594,5595,5597,5612,5617,5627,5628,5640,5647,5661,5665,5668,5674,5675,5676,5679,5684,5722,5723,5726,5728,5731,5732,5733,5735,5737,5739,5744,5751,5766,5780,5785,5786,5799,5800,5805,5809,5811,5816,5857,5869,5878,5882,5893,5897,5898,5906,5920,5926,5944,5947,5959,5985,5999,6024,6044,6045,6048,6062,6064,6066,6068,6081,6082,6085,6087,6090,6091,6103,6109,6110,6111,6113,6115,6158,6159,6166,6172,6176,6212,6214,6216,6218,6227,6229,6231,6237,6239,6245,6248,6256,6263,6264,6265,6270,6292,6293,6294,6296,6302,6307,6341,6342,6344,6345,6346,6348,6349,6350,6351,6358,6391,6392,6401,6422,6423,6443,6446,6457,6458,6464,6495,6497,6511,6549,6551,6552,6606,6630,6672,6692,6701,6702,6703,6704,6723,6724,6730,6743,6746,6748,6750,6751,6752,6754,6768,6779,6781,6782,6795,6799,6850,6861,6863,6867,6884,6885,6921,6933,6964,6998,7052,7080,7135,7156,7165,7168,7223,7231,7289,7291,7306,7316,7317,7318,7337,7343,7345,7395,7405,7408,7424,7476,7478,7481,7524,7525,7543,7610,7629,7652,7676,7691,7706,7717,7726,7727,7756,7759,7761,7771])).
% 187.33/188.09 cnf(10915,plain,
% 187.33/188.09 (P24(f329(f329(f331(x109151),x109152),f252(f881(x109151,a869))))),
% 187.33/188.09 inference(rename_variables,[],[3437])).
% 187.33/188.09 cnf(10918,plain,
% 187.33/188.09 (~P24(f329(f329(f331(f880(f875(x109181),f875(x109181))),f329(f329(f264(f875(x109181),f875(x109181)),x109182),f118(x109181))),f143(x109181,x109183)))),
% 187.33/188.09 inference(rename_variables,[],[4553])).
% 187.33/188.09 cnf(10924,plain,
% 187.33/188.09 (~P24(f329(f329(f331(f880(x109241,x109241)),x109242),f261(x109241,f193(f881(x109241,a869)))))),
% 187.33/188.09 inference(scs_inference,[],[4323,4459,10208,10218,10229,10240,10341,10344,10347,10450,10563,4474,10434,3065,3234,10211,10275,10278,10368,10371,3212,3108,3169,3136,3115,3337,3205,3229,10475,4541,4484,10266,3166,10333,4066,3921,4553,3188,3482,3644,3583,3796,3347,10352,10470,10541,10602,10605,10643,10737,3733,3260,4524,10243,10246,10272,10745,10758,4536,3720,3491,3869,3306,3308,3281,4521,4479,3645,4019,4542,3276,10361,10457,10588,10650,10719,10764,10767,10800,10823,10860,3277,10390,10445,10655,10740,3280,4520,10309,10399,10512,10536,10782,10826,3437,10608,10871,4532,10791,10803,10907,3341,10637,10667,3373,3800,3738,10312,4529,10263,10625,10628,3300,10670,10820,4110,4527,3808,4510,4513,3251,3255,4512,4511,4515,4544,10234,10237,10493,10544,10547,4551,3729,3547,10591,10594,10679,10847,4548,4549,10730,4170,3760,4546,10285,10288,10631,3731,10597,4003,4568,4594,4643,4645,4675,4692,4699,4700,4739,4769,4775,4860,4885,4886,4921,4946,4947,4969,4970,4983,4987,5010,5017,5035,5038,5039,5040,5045,5046,5068,5093,5094,5104,5109,5115,5160,5161,5169,5178,5183,5185,5195,5197,5203,5207,5222,5229,5232,5233,5234,5238,5274,5287,5295,5297,5298,5302,5303,5304,5312,5315,5319,5320,5321,5328,5332,5333,5334,5342,5346,5347,5348,5353,5366,5375,5387,5389,5397,5398,5402,5406,5431,5437,5447,5448,5463,5475,5497,5503,5519,5520,5523,5542,5550,5551,5556,5557,5567,5569,5581,5585,5594,5595,5597,5612,5617,5627,5628,5640,5647,5661,5665,5668,5674,5675,5676,5679,5684,5722,5723,5726,5728,5731,5732,5733,5735,5737,5739,5744,5751,5766,5780,5785,5786,5799,5800,5805,5809,5811,5816,5857,5869,5878,5882,5893,5897,5898,5906,5920,5926,5944,5947,5959,5985,5999,6024,6044,6045,6048,6062,6064,6066,6068,6081,6082,6085,6087,6090,6091,6103,6109,6110,6111,6113,6115,6158,6159,6166,6172,6176,6212,6214,6216,6218,6227,6229,6231,6237,6239,6245,6248,6256,6263,6264,6265,6270,6292,6293,6294,6296,6302,6307,6341,6342,6344,6345,6346,6348,6349,6350,6351,6358,6391,6392,6401,6422,6423,6443,6446,6457,6458,6464,6495,6497,6511,6549,6551,6552,6606,6630,6672,6692,6701,6702,6703,6704,6723,6724,6730,6743,6746,6748,6750,6751,6752,6754,6768,6779,6781,6782,6795,6799,6850,6861,6863,6867,6884,6885,6921,6933,6964,6998,7052,7080,7135,7156,7165,7168,7223,7231,7289,7291,7306,7316,7317,7318,7337,7343,7345,7395,7405,7408,7424,7476,7478,7481,7524,7525,7543,7610,7629,7652,7676,7691,7706,7717,7726,7727,7756,7759,7761,7771,7809,7820,7845,7903])).
% 187.33/188.09 cnf(10925,plain,
% 187.33/188.09 (~P24(f329(f329(f331(x109251),x109252),f193(f881(x109251,a869))))),
% 187.33/188.09 inference(rename_variables,[],[4532])).
% 187.33/188.09 cnf(10927,plain,
% 187.33/188.09 (~P24(f329(f329(f331(x109271),x109272),f329(f309(x109271,x109273,x109274),f193(f881(x109273,a869)))))),
% 187.33/188.09 inference(scs_inference,[],[4323,4459,10208,10218,10229,10240,10341,10344,10347,10450,10563,4474,10434,3065,3234,10211,10275,10278,10368,10371,3212,3108,3169,3136,3115,3337,3205,3229,10475,4541,4484,10266,3166,10333,4066,3921,4553,3188,3482,3644,3583,3796,3347,10352,10470,10541,10602,10605,10643,10737,3733,3260,4524,10243,10246,10272,10745,10758,4536,3720,3491,3869,3306,3308,3281,4521,4479,3645,4019,4542,3276,10361,10457,10588,10650,10719,10764,10767,10800,10823,10860,3277,10390,10445,10655,10740,3280,4520,10309,10399,10512,10536,10782,10826,3437,10608,10871,4532,10791,10803,10907,10925,3341,10637,10667,3373,3800,3738,10312,4529,10263,10625,10628,3300,10670,10820,4110,4527,3808,4510,4513,3251,3255,4512,4511,4515,4544,10234,10237,10493,10544,10547,4551,3729,3547,10591,10594,10679,10847,4548,4549,10730,4170,3760,4546,10285,10288,10631,3731,10597,4003,4568,4594,4643,4645,4675,4692,4699,4700,4739,4769,4775,4860,4885,4886,4921,4946,4947,4969,4970,4983,4987,5010,5017,5035,5038,5039,5040,5045,5046,5068,5093,5094,5104,5109,5115,5160,5161,5169,5178,5183,5185,5195,5197,5203,5207,5222,5229,5232,5233,5234,5238,5274,5287,5295,5297,5298,5302,5303,5304,5312,5315,5319,5320,5321,5328,5332,5333,5334,5342,5346,5347,5348,5353,5366,5375,5387,5389,5397,5398,5402,5406,5431,5437,5447,5448,5463,5475,5497,5503,5519,5520,5523,5542,5550,5551,5556,5557,5567,5569,5581,5585,5594,5595,5597,5612,5617,5627,5628,5640,5647,5661,5665,5668,5674,5675,5676,5679,5684,5722,5723,5726,5728,5731,5732,5733,5735,5737,5739,5744,5751,5766,5780,5785,5786,5799,5800,5805,5809,5811,5816,5857,5869,5878,5882,5893,5897,5898,5906,5920,5926,5944,5947,5959,5985,5999,6024,6044,6045,6048,6062,6064,6066,6068,6081,6082,6085,6087,6090,6091,6103,6109,6110,6111,6113,6115,6158,6159,6166,6172,6176,6212,6214,6216,6218,6227,6229,6231,6237,6239,6245,6248,6256,6263,6264,6265,6270,6292,6293,6294,6296,6302,6307,6341,6342,6344,6345,6346,6348,6349,6350,6351,6358,6391,6392,6401,6422,6423,6443,6446,6457,6458,6464,6495,6497,6511,6549,6551,6552,6606,6630,6672,6692,6701,6702,6703,6704,6723,6724,6730,6743,6746,6748,6750,6751,6752,6754,6768,6779,6781,6782,6795,6799,6850,6861,6863,6867,6884,6885,6921,6933,6964,6998,7052,7080,7135,7156,7165,7168,7223,7231,7289,7291,7306,7316,7317,7318,7337,7343,7345,7395,7405,7408,7424,7476,7478,7481,7524,7525,7543,7610,7629,7652,7676,7691,7706,7717,7726,7727,7756,7759,7761,7771,7809,7820,7845,7903,7937])).
% 187.33/188.09 cnf(10928,plain,
% 187.33/188.09 (~P24(f329(f329(f331(x109281),x109282),f193(f881(x109281,a869))))),
% 187.33/188.09 inference(rename_variables,[],[4532])).
% 187.33/188.09 cnf(10931,plain,
% 187.33/188.09 (P24(f329(f329(f243(f881(x109311,a869)),x109312),f329(f329(f307(x109311),x109313),x109312)))),
% 187.33/188.09 inference(rename_variables,[],[3727])).
% 187.33/188.09 cnf(10934,plain,
% 187.33/188.09 (P24(f329(f329(f243(a874),x109341),x109341))),
% 187.33/188.09 inference(rename_variables,[],[3276])).
% 187.33/188.09 cnf(10937,plain,
% 187.33/188.09 (P24(f329(f329(f243(f881(x109371,a869)),x109372),f329(f329(f307(x109371),x109373),x109372)))),
% 187.33/188.09 inference(rename_variables,[],[3727])).
% 187.33/188.09 cnf(10952,plain,
% 187.33/188.09 (P24(f329(f329(f243(f881(x109521,a869)),x109522),f329(f329(f307(x109521),x109523),x109522)))),
% 187.33/188.09 inference(rename_variables,[],[3727])).
% 187.33/188.09 cnf(10957,plain,
% 187.33/188.09 (~P24(f329(f63(x109571,x109572,f193(f881(x109571,a869))),x109573))),
% 187.33/188.09 inference(rename_variables,[],[4544])).
% 187.33/188.09 cnf(10970,plain,
% 187.33/188.09 (P24(f329(f329(f244(a874),x109701),f329(a117,x109701)))),
% 187.33/188.09 inference(rename_variables,[],[3347])).
% 187.33/188.09 cnf(10980,plain,
% 187.33/188.09 (~E(f329(f308(x109801,f881(x109801,a869),x109802),x109803),f329(f306(x109801),x109803))),
% 187.33/188.09 inference(rename_variables,[],[4530])).
% 187.33/188.09 cnf(10983,plain,
% 187.33/188.09 (~P24(f329(f329(f331(x109831),x109832),f193(f881(x109831,a869))))),
% 187.33/188.09 inference(rename_variables,[],[4532])).
% 187.33/188.09 cnf(10986,plain,
% 187.33/188.09 (P24(f329(f329(f331(f880(x109861,x109861)),f329(f329(f264(x109861,x109861),x109862),x109862)),f305(x109861,x109863)))),
% 187.33/188.09 inference(rename_variables,[],[3921])).
% 187.33/188.09 cnf(10989,plain,
% 187.33/188.09 (P24(f329(f329(f243(f881(x109891,a869)),f329(f171(x109891),f175(x109891,x109892,x109893))),f329(f171(x109891),x109892)))),
% 187.33/188.09 inference(rename_variables,[],[3982])).
% 187.33/188.09 cnf(10992,plain,
% 187.33/188.09 (P24(f329(f329(f243(f881(x109921,a869)),x109922),f252(f881(x109921,a869))))),
% 187.33/188.09 inference(rename_variables,[],[3663])).
% 187.33/188.09 cnf(11008,plain,
% 187.33/188.09 (P24(f329(f329(f243(f881(x110081,a869)),f193(f881(x110081,a869))),x110082))),
% 187.33/188.09 inference(rename_variables,[],[3729])).
% 187.33/188.09 cnf(11019,plain,
% 187.33/188.09 (~P24(f329(f329(f331(f880(f875(x110191),f875(x110191))),f329(f329(f264(f875(x110191),f875(x110191)),x110192),f118(x110191))),f145(x110191,x110193)))),
% 187.33/188.09 inference(rename_variables,[],[4554])).
% 187.33/188.09 cnf(11030,plain,
% 187.33/188.09 (~E(f329(a117,x110301),x110301)),
% 187.33/188.09 inference(rename_variables,[],[4459])).
% 187.33/188.09 cnf(11033,plain,
% 187.33/188.09 (~E(f329(a117,x110331),x110331)),
% 187.33/188.09 inference(rename_variables,[],[4459])).
% 187.33/188.09 cnf(11035,plain,
% 187.33/188.09 (P24(f329(f329(f331(f880(f875(x110351),f875(x110351))),f329(f329(f264(f875(x110351),f875(x110351)),f118(x110351)),f118(x110351))),f329(f329(f286(f875(x110351),f875(x110351),f875(x110351)),f156(x110351,x110352)),f305(f875(x110351),f156(x110351,x110352)))))),
% 187.33/188.09 inference(scs_inference,[],[4323,4459,10208,10218,10229,10240,10341,10344,10347,10450,10563,10866,11030,4474,10434,3065,3118,3234,10211,10275,10278,10368,10371,3212,3740,3108,3169,3136,3115,3337,3205,3229,10475,4541,3919,4484,10266,4530,3166,10333,4066,3921,10986,4553,10918,4554,3188,3482,3644,3583,3796,3347,10352,10470,10541,10602,10605,10643,10737,3733,3260,4524,10243,10246,10272,10745,10758,10876,4536,3720,3491,3869,3306,3308,3281,4521,4479,4030,3982,3645,4019,3663,4542,3276,10361,10457,10588,10650,10719,10764,10767,10800,10823,10860,10898,3277,10390,10445,10655,10740,3280,4520,10309,10399,10512,10536,10782,10826,3437,10608,10871,10915,4532,10791,10803,10907,10925,10928,3341,10637,10667,3373,3800,3738,10312,4529,10263,10625,10628,3300,10670,10820,4110,4527,3808,4510,4513,3251,3255,4512,4511,4515,4544,10234,10237,10493,10544,10547,10552,4551,3886,3727,10931,10937,3729,10673,3547,10591,10594,10679,10847,4548,4549,10730,4170,3760,4546,10285,10288,10631,3731,10597,4003,4568,4594,4643,4645,4675,4692,4699,4700,4739,4769,4775,4860,4885,4886,4921,4946,4947,4969,4970,4983,4987,5010,5017,5035,5038,5039,5040,5045,5046,5068,5093,5094,5104,5109,5115,5160,5161,5169,5178,5183,5185,5195,5197,5203,5207,5222,5229,5232,5233,5234,5238,5274,5287,5295,5297,5298,5302,5303,5304,5312,5315,5319,5320,5321,5328,5332,5333,5334,5342,5346,5347,5348,5353,5366,5375,5387,5389,5397,5398,5402,5406,5431,5437,5447,5448,5463,5475,5497,5503,5519,5520,5523,5542,5550,5551,5556,5557,5567,5569,5581,5585,5594,5595,5597,5612,5617,5627,5628,5640,5647,5661,5665,5668,5674,5675,5676,5679,5684,5722,5723,5726,5728,5731,5732,5733,5735,5737,5739,5744,5751,5766,5780,5785,5786,5799,5800,5805,5809,5811,5816,5857,5869,5878,5882,5893,5897,5898,5906,5920,5926,5944,5947,5959,5985,5999,6024,6044,6045,6048,6062,6064,6066,6068,6081,6082,6085,6087,6090,6091,6103,6109,6110,6111,6113,6115,6158,6159,6166,6172,6176,6212,6214,6216,6218,6227,6229,6231,6237,6239,6245,6248,6256,6263,6264,6265,6270,6292,6293,6294,6296,6302,6307,6341,6342,6344,6345,6346,6348,6349,6350,6351,6358,6391,6392,6401,6422,6423,6443,6446,6457,6458,6464,6495,6497,6511,6549,6551,6552,6606,6630,6672,6692,6701,6702,6703,6704,6723,6724,6730,6743,6746,6748,6750,6751,6752,6754,6768,6779,6781,6782,6795,6799,6850,6861,6863,6867,6884,6885,6921,6933,6964,6998,7052,7080,7135,7156,7165,7168,7223,7231,7289,7291,7306,7316,7317,7318,7337,7343,7345,7395,7405,7408,7424,7476,7478,7481,7524,7525,7543,7610,7629,7652,7676,7691,7706,7717,7726,7727,7756,7759,7761,7771,7809,7820,7845,7903,7937,7969,8016,8032,8048,8049,8124,8177,8196,8220,8240,8264,8362,8364,8370,8386,8390,8406,8429,8440,8442,8457,8463,8467,8490,8504,8505,8521,8522,8527,8528,8529,8530,8531,8549,8550,8551,8559,8573,8575,8587,8591,8593,8594,8595,8603])).
% 187.33/188.09 cnf(11045,plain,
% 187.33/188.09 (P21(x110451,x110451,f5(x110451),x110452)),
% 187.33/188.09 inference(rename_variables,[],[3521])).
% 187.33/188.09 cnf(11050,plain,
% 187.33/188.09 (~E(f329(f308(x110501,f881(x110501,a869),x110502),x110503),f329(f306(x110501),x110503))),
% 187.33/188.09 inference(rename_variables,[],[4530])).
% 187.33/188.09 cnf(11055,plain,
% 187.33/188.09 (P24(f329(f329(f243(f881(x110551,a869)),x110552),f252(f881(x110551,a869))))),
% 187.33/188.09 inference(rename_variables,[],[3663])).
% 187.33/188.09 cnf(11069,plain,
% 187.33/188.09 (~P24(f329(f329(f331(x110691),x110692),f193(f881(x110691,a869))))),
% 187.33/188.09 inference(rename_variables,[],[4532])).
% 187.33/188.09 cnf(11072,plain,
% 187.33/188.09 (~P24(f329(f329(f243(a874),f329(a117,x110721)),x110721))),
% 187.33/188.09 inference(rename_variables,[],[4529])).
% 187.33/188.09 cnf(11077,plain,
% 187.33/188.09 (~P24(f329(f329(f331(x110771),x110772),f193(f881(x110771,a869))))),
% 187.33/188.09 inference(rename_variables,[],[4532])).
% 187.33/188.09 cnf(11089,plain,
% 187.33/188.09 (~P24(f329(f329(f331(a874),f329(a117,f329(f140(a874,a874,f80(a874),f2(a874)),x110891))),f329(f171(a874),x110891)))),
% 187.33/188.09 inference(scs_inference,[],[4323,3521,4459,10208,10218,10229,10240,10341,10344,10347,10450,10563,10866,11030,4474,10434,10527,3065,3118,3234,10211,10275,10278,10368,10371,3212,3740,3108,3169,3136,3115,3337,3205,3229,10475,4541,3919,4484,10266,4530,10980,3384,3166,10333,4066,3921,10986,4553,10918,4554,3188,3482,3644,3583,3796,3347,10352,10470,10541,10602,10605,10643,10737,10970,3733,3260,4524,10243,10246,10272,10745,10758,10876,4536,3720,3491,3869,3306,3308,3281,4521,4479,4030,3982,3645,4019,3663,10992,4542,3276,10361,10457,10588,10650,10719,10764,10767,10800,10823,10860,10898,3277,10390,10445,10655,10740,3280,4520,10309,10399,10512,10536,10782,10826,3437,10608,10871,10915,4532,10791,10803,10907,10925,10928,10983,11069,3341,10637,10667,3373,3800,3738,10312,4529,10263,10625,10628,11072,3300,10670,10820,4110,4527,3808,4510,4513,3251,3255,4512,4511,4515,4544,10234,10237,10493,10544,10547,10552,4551,3886,3727,10931,10937,3729,10673,3547,10591,10594,10679,10847,4548,4549,10730,4170,3760,4546,10285,10288,10631,3731,10597,4003,4568,4594,4643,4645,4675,4692,4699,4700,4739,4769,4775,4860,4885,4886,4921,4946,4947,4969,4970,4983,4987,5010,5017,5035,5038,5039,5040,5045,5046,5068,5093,5094,5104,5109,5115,5160,5161,5169,5178,5183,5185,5195,5197,5203,5207,5222,5229,5232,5233,5234,5238,5274,5287,5295,5297,5298,5302,5303,5304,5312,5315,5319,5320,5321,5328,5332,5333,5334,5342,5346,5347,5348,5353,5366,5375,5387,5389,5397,5398,5402,5406,5431,5437,5447,5448,5463,5475,5497,5503,5519,5520,5523,5542,5550,5551,5556,5557,5567,5569,5581,5585,5594,5595,5597,5612,5617,5627,5628,5640,5647,5661,5665,5668,5674,5675,5676,5679,5684,5722,5723,5726,5728,5731,5732,5733,5735,5737,5739,5744,5751,5766,5780,5785,5786,5799,5800,5805,5809,5811,5816,5857,5869,5878,5882,5893,5897,5898,5906,5920,5926,5944,5947,5959,5985,5999,6024,6044,6045,6048,6062,6064,6066,6068,6081,6082,6085,6087,6090,6091,6103,6109,6110,6111,6113,6115,6158,6159,6166,6172,6176,6212,6214,6216,6218,6227,6229,6231,6237,6239,6245,6248,6256,6263,6264,6265,6270,6292,6293,6294,6296,6302,6307,6341,6342,6344,6345,6346,6348,6349,6350,6351,6358,6391,6392,6401,6422,6423,6443,6446,6457,6458,6464,6495,6497,6511,6549,6551,6552,6606,6630,6672,6692,6701,6702,6703,6704,6723,6724,6730,6743,6746,6748,6750,6751,6752,6754,6768,6779,6781,6782,6795,6799,6850,6861,6863,6867,6884,6885,6921,6933,6964,6998,7052,7080,7135,7156,7165,7168,7223,7231,7289,7291,7306,7316,7317,7318,7337,7343,7345,7395,7405,7408,7424,7476,7478,7481,7524,7525,7543,7610,7629,7652,7676,7691,7706,7717,7726,7727,7756,7759,7761,7771,7809,7820,7845,7903,7937,7969,8016,8032,8048,8049,8124,8177,8196,8220,8240,8264,8362,8364,8370,8386,8390,8406,8429,8440,8442,8457,8463,8467,8490,8504,8505,8521,8522,8527,8528,8529,8530,8531,8549,8550,8551,8559,8573,8575,8587,8591,8593,8594,8595,8603,8608,8635,8636,8668,8681,8685,8703,8725,8726,8727,8728,8740,8741,8763,8773,8783,8784,8785,8786,8788,8809,8810,8821])).
% 187.33/188.09 cnf(11090,plain,
% 187.33/188.09 (~P24(f329(f329(f243(a874),f329(a117,x110901)),x110901))),
% 187.33/188.09 inference(rename_variables,[],[4529])).
% 187.33/188.09 cnf(11093,plain,
% 187.33/188.09 (~P24(f329(f329(f331(x110931),x110932),f193(f881(x110931,a869))))),
% 187.33/188.09 inference(rename_variables,[],[4532])).
% 187.33/188.09 cnf(11101,plain,
% 187.33/188.09 (E(f329(f134(x111011,f252(f881(x111012,a869))),f784(x111013,x111014,f329(f329(f149(x111011),x111014),x111013),f252(f881(x111012,a869)),x111011)),x111013)),
% 187.33/188.09 inference(scs_inference,[],[4323,3521,4459,10208,10218,10229,10240,10341,10344,10347,10450,10563,10866,11030,4474,10434,10527,3065,3118,3234,10211,10275,10278,10368,10371,3212,3740,3108,3169,3136,3115,3337,3205,3229,10475,4541,3919,4484,10266,4530,10980,3384,3166,10333,4066,3921,10986,4553,10918,4554,3188,3482,3644,3583,3796,3347,10352,10470,10541,10602,10605,10643,10737,10970,3733,3260,4524,10243,10246,10272,10745,10758,10876,4536,3720,3491,3869,3306,3308,3281,4521,4479,4030,3982,3645,4019,3663,10992,4542,3276,10361,10457,10588,10650,10719,10764,10767,10800,10823,10860,10898,3277,10390,10445,10655,10740,3280,4520,10309,10399,10512,10536,10782,10826,3437,10608,10871,10915,4532,10791,10803,10907,10925,10928,10983,11069,11077,3341,10637,10667,3373,3800,3738,10312,4529,10263,10625,10628,11072,3300,10670,10820,4110,4527,3808,4510,4513,3251,3255,4512,4511,4515,4544,10234,10237,10493,10544,10547,10552,4551,3886,3727,10931,10937,3729,10673,3547,10591,10594,10679,10847,4548,4549,10730,4170,3760,4546,10285,10288,10631,3731,10597,4003,4568,4594,4643,4645,4675,4692,4699,4700,4739,4769,4775,4860,4885,4886,4921,4946,4947,4969,4970,4983,4987,5010,5017,5035,5038,5039,5040,5045,5046,5068,5093,5094,5104,5109,5115,5160,5161,5169,5178,5183,5185,5195,5197,5203,5207,5222,5229,5232,5233,5234,5238,5274,5287,5295,5297,5298,5302,5303,5304,5312,5315,5319,5320,5321,5328,5332,5333,5334,5342,5346,5347,5348,5353,5366,5375,5387,5389,5397,5398,5402,5406,5431,5437,5447,5448,5463,5475,5497,5503,5519,5520,5523,5542,5550,5551,5556,5557,5567,5569,5581,5585,5594,5595,5597,5612,5617,5627,5628,5640,5647,5661,5665,5668,5674,5675,5676,5679,5684,5722,5723,5726,5728,5731,5732,5733,5735,5737,5739,5744,5751,5766,5780,5785,5786,5799,5800,5805,5809,5811,5816,5857,5869,5878,5882,5893,5897,5898,5906,5920,5926,5944,5947,5959,5985,5999,6024,6044,6045,6048,6062,6064,6066,6068,6081,6082,6085,6087,6090,6091,6103,6109,6110,6111,6113,6115,6158,6159,6166,6172,6176,6212,6214,6216,6218,6227,6229,6231,6237,6239,6245,6248,6256,6263,6264,6265,6270,6292,6293,6294,6296,6302,6307,6341,6342,6344,6345,6346,6348,6349,6350,6351,6358,6391,6392,6401,6422,6423,6443,6446,6457,6458,6464,6495,6497,6511,6549,6551,6552,6606,6630,6672,6692,6701,6702,6703,6704,6723,6724,6730,6743,6746,6748,6750,6751,6752,6754,6768,6779,6781,6782,6795,6799,6850,6861,6863,6867,6884,6885,6921,6933,6964,6998,7052,7080,7135,7156,7165,7168,7223,7231,7289,7291,7306,7316,7317,7318,7337,7343,7345,7395,7405,7408,7424,7476,7478,7481,7524,7525,7543,7610,7629,7652,7676,7691,7706,7717,7726,7727,7756,7759,7761,7771,7809,7820,7845,7903,7937,7969,8016,8032,8048,8049,8124,8177,8196,8220,8240,8264,8362,8364,8370,8386,8390,8406,8429,8440,8442,8457,8463,8467,8490,8504,8505,8521,8522,8527,8528,8529,8530,8531,8549,8550,8551,8559,8573,8575,8587,8591,8593,8594,8595,8603,8608,8635,8636,8668,8681,8685,8703,8725,8726,8727,8728,8740,8741,8763,8773,8783,8784,8785,8786,8788,8809,8810,8821,8865,8871,8877,8889,8894])).
% 187.33/188.09 cnf(11103,plain,
% 187.33/188.09 (E(f329(x111031,f711(f329(x111031,x111032),f329(f236(x111033),x111032),x111031,x111034,x111033)),f329(x111031,x111032))),
% 187.33/188.09 inference(scs_inference,[],[4323,3521,4459,10208,10218,10229,10240,10341,10344,10347,10450,10563,10866,11030,4474,10434,10527,3065,3118,3234,10211,10275,10278,10368,10371,3212,3740,3108,3169,3136,3115,3337,3205,3229,10475,3383,4541,3919,4484,10266,4530,10980,3384,3166,10333,4066,3921,10986,4553,10918,4554,3188,3482,3644,3583,3796,3347,10352,10470,10541,10602,10605,10643,10737,10970,3733,3260,4524,10243,10246,10272,10745,10758,10876,4536,3720,3491,3869,3306,3308,3281,4521,4479,4030,3982,3645,4019,3663,10992,4542,3276,10361,10457,10588,10650,10719,10764,10767,10800,10823,10860,10898,3277,10390,10445,10655,10740,3280,4520,10309,10399,10512,10536,10782,10826,3437,10608,10871,10915,4532,10791,10803,10907,10925,10928,10983,11069,11077,3341,10637,10667,3373,3800,3738,10312,4529,10263,10625,10628,11072,3300,10670,10820,4110,4527,3808,4510,4513,3251,3255,4512,4511,4515,4544,10234,10237,10493,10544,10547,10552,4551,3886,3727,10931,10937,3729,10673,3547,10591,10594,10679,10847,4548,4549,10730,4170,3760,4546,10285,10288,10631,3731,10597,4003,4568,4594,4643,4645,4675,4692,4699,4700,4739,4769,4775,4860,4885,4886,4921,4946,4947,4969,4970,4983,4987,5010,5017,5035,5038,5039,5040,5045,5046,5068,5093,5094,5104,5109,5115,5160,5161,5169,5178,5183,5185,5195,5197,5203,5207,5222,5229,5232,5233,5234,5238,5274,5287,5295,5297,5298,5302,5303,5304,5312,5315,5319,5320,5321,5328,5332,5333,5334,5342,5346,5347,5348,5353,5366,5375,5387,5389,5397,5398,5402,5406,5431,5437,5447,5448,5463,5475,5497,5503,5519,5520,5523,5542,5550,5551,5556,5557,5567,5569,5581,5585,5594,5595,5597,5612,5617,5627,5628,5640,5647,5661,5665,5668,5674,5675,5676,5679,5684,5722,5723,5726,5728,5731,5732,5733,5735,5737,5739,5744,5751,5766,5780,5785,5786,5799,5800,5805,5809,5811,5816,5857,5869,5878,5882,5893,5897,5898,5906,5920,5926,5944,5947,5959,5985,5999,6024,6044,6045,6048,6062,6064,6066,6068,6081,6082,6085,6087,6090,6091,6103,6109,6110,6111,6113,6115,6158,6159,6166,6172,6176,6212,6214,6216,6218,6227,6229,6231,6237,6239,6245,6248,6256,6263,6264,6265,6270,6292,6293,6294,6296,6302,6307,6341,6342,6344,6345,6346,6348,6349,6350,6351,6358,6391,6392,6401,6422,6423,6443,6446,6457,6458,6464,6495,6497,6511,6549,6551,6552,6606,6630,6672,6692,6701,6702,6703,6704,6723,6724,6730,6743,6746,6748,6750,6751,6752,6754,6768,6779,6781,6782,6795,6799,6850,6861,6863,6867,6884,6885,6921,6933,6964,6998,7052,7080,7135,7156,7165,7168,7223,7231,7289,7291,7306,7316,7317,7318,7337,7343,7345,7395,7405,7408,7424,7476,7478,7481,7524,7525,7543,7610,7629,7652,7676,7691,7706,7717,7726,7727,7756,7759,7761,7771,7809,7820,7845,7903,7937,7969,8016,8032,8048,8049,8124,8177,8196,8220,8240,8264,8362,8364,8370,8386,8390,8406,8429,8440,8442,8457,8463,8467,8490,8504,8505,8521,8522,8527,8528,8529,8530,8531,8549,8550,8551,8559,8573,8575,8587,8591,8593,8594,8595,8603,8608,8635,8636,8668,8681,8685,8703,8725,8726,8727,8728,8740,8741,8763,8773,8783,8784,8785,8786,8788,8809,8810,8821,8865,8871,8877,8889,8894,8896])).
% 187.33/188.09 cnf(11112,plain,
% 187.33/188.09 (P24(f329(f329(f331(f880(x111121,x111121)),f329(f329(f264(x111121,x111121),x111122),x111122)),f305(x111121,x111123)))),
% 187.33/188.09 inference(rename_variables,[],[3921])).
% 187.33/188.09 cnf(11117,plain,
% 187.33/188.09 (~P24(f329(f329(f331(f880(f875(x111171),f875(x111171))),f329(f329(f264(f875(x111171),f875(x111171)),x111172),f118(x111171))),f143(x111171,x111173)))),
% 187.33/188.09 inference(rename_variables,[],[4553])).
% 187.33/188.09 cnf(11120,plain,
% 187.33/188.09 (~P24(f329(f329(f331(f880(f875(x111201),f875(x111201))),f329(f329(f264(f875(x111201),f875(x111201)),x111202),f118(x111201))),f145(x111201,x111203)))),
% 187.33/188.09 inference(rename_variables,[],[4554])).
% 187.33/188.09 cnf(11123,plain,
% 187.33/188.09 (~P24(f329(f329(f331(f880(f875(x111231),f875(x111231))),f329(f329(f264(f875(x111231),f875(x111231)),x111232),f118(x111231))),f155(x111231,x111233)))),
% 187.33/188.09 inference(rename_variables,[],[4555])).
% 187.33/188.09 cnf(11125,plain,
% 187.33/188.09 (~P24(f329(f329(f331(f880(f875(x111251),f875(x111251))),f329(f329(f264(f875(x111251),f875(x111251)),f118(x111251)),x111252)),f329(f284(f875(x111251),f875(x111251)),f143(x111251,x111253))))),
% 187.33/188.09 inference(scs_inference,[],[4323,3521,4459,10208,10218,10229,10240,10341,10344,10347,10450,10563,10866,11030,4474,10434,10527,3065,3118,3234,10211,10275,10278,10368,10371,3212,3740,3108,3169,3136,3115,3337,3205,3229,10475,3383,4541,3919,4484,10266,4530,10980,3384,3166,10333,4066,3921,10986,4553,10918,11117,4554,11019,4555,3188,3482,3644,3583,3796,3347,10352,10470,10541,10602,10605,10643,10737,10970,3733,3260,4524,10243,10246,10272,10745,10758,10876,4536,3720,3491,3869,3306,3308,3281,4521,4479,4030,3982,3645,4019,3663,10992,4542,3276,10361,10457,10588,10650,10719,10764,10767,10800,10823,10860,10898,3277,10390,10445,10655,10740,3280,4520,10309,10399,10512,10536,10782,10826,3437,10608,10871,10915,4532,10791,10803,10907,10925,10928,10983,11069,11077,3341,10637,10667,3373,3800,3738,10312,4529,10263,10625,10628,11072,3300,10670,10820,4110,4527,3808,4510,4513,3251,3255,4512,4511,4515,4544,10234,10237,10493,10544,10547,10552,4551,3886,3727,10931,10937,3729,10673,3547,10591,10594,10679,10847,4548,4549,10730,4170,3760,4546,10285,10288,10631,3731,10597,4003,4568,4594,4643,4645,4675,4692,4699,4700,4739,4769,4775,4860,4885,4886,4921,4946,4947,4969,4970,4983,4987,5010,5017,5035,5038,5039,5040,5045,5046,5068,5093,5094,5104,5109,5115,5160,5161,5169,5178,5183,5185,5195,5197,5203,5207,5222,5229,5232,5233,5234,5238,5274,5287,5295,5297,5298,5302,5303,5304,5312,5315,5319,5320,5321,5328,5332,5333,5334,5342,5346,5347,5348,5353,5366,5375,5387,5389,5397,5398,5402,5406,5431,5437,5447,5448,5463,5475,5497,5503,5519,5520,5523,5542,5550,5551,5556,5557,5567,5569,5581,5585,5594,5595,5597,5612,5617,5627,5628,5640,5647,5661,5665,5668,5674,5675,5676,5679,5684,5722,5723,5726,5728,5731,5732,5733,5735,5737,5739,5744,5751,5766,5780,5785,5786,5799,5800,5805,5809,5811,5816,5857,5869,5878,5882,5893,5897,5898,5906,5920,5926,5944,5947,5959,5985,5999,6024,6044,6045,6048,6062,6064,6066,6068,6081,6082,6085,6087,6090,6091,6103,6109,6110,6111,6113,6115,6158,6159,6166,6172,6176,6212,6214,6216,6218,6227,6229,6231,6237,6239,6245,6248,6256,6263,6264,6265,6270,6292,6293,6294,6296,6302,6307,6341,6342,6344,6345,6346,6348,6349,6350,6351,6358,6391,6392,6401,6422,6423,6443,6446,6457,6458,6464,6495,6497,6511,6549,6551,6552,6606,6630,6672,6692,6701,6702,6703,6704,6723,6724,6730,6743,6746,6748,6750,6751,6752,6754,6768,6779,6781,6782,6795,6799,6850,6861,6863,6867,6884,6885,6921,6933,6964,6998,7052,7080,7135,7156,7165,7168,7223,7231,7289,7291,7306,7316,7317,7318,7337,7343,7345,7395,7405,7408,7424,7476,7478,7481,7524,7525,7543,7610,7629,7652,7676,7691,7706,7717,7726,7727,7756,7759,7761,7771,7809,7820,7845,7903,7937,7969,8016,8032,8048,8049,8124,8177,8196,8220,8240,8264,8362,8364,8370,8386,8390,8406,8429,8440,8442,8457,8463,8467,8490,8504,8505,8521,8522,8527,8528,8529,8530,8531,8549,8550,8551,8559,8573,8575,8587,8591,8593,8594,8595,8603,8608,8635,8636,8668,8681,8685,8703,8725,8726,8727,8728,8740,8741,8763,8773,8783,8784,8785,8786,8788,8809,8810,8821,8865,8871,8877,8889,8894,8896,8899,8900,8904,8914,8997,9028,9029,9030,9045])).
% 187.33/188.09 cnf(11128,plain,
% 187.33/188.09 (~P24(f329(f329(f244(f881(x111281,a869)),x111282),f193(f881(x111281,a869))))),
% 187.33/188.09 inference(rename_variables,[],[4542])).
% 187.33/188.09 cnf(11130,plain,
% 187.33/188.09 (~P24(f329(f329(f331(x111301),x111302),f329(f308(x111303,x111301,x111304),f193(f881(x111303,a869)))))),
% 187.33/188.09 inference(scs_inference,[],[4323,3521,4459,10208,10218,10229,10240,10341,10344,10347,10450,10563,10866,11030,4474,10434,10527,3065,3118,3234,10211,10275,10278,10368,10371,3212,3740,3108,3169,3136,3115,3337,3205,3229,10475,3383,4541,3919,4484,10266,4530,10980,3384,3166,10333,4066,3921,10986,4553,10918,11117,4554,11019,4555,3188,3482,3644,3583,3796,3347,10352,10470,10541,10602,10605,10643,10737,10970,3733,3260,4524,10243,10246,10272,10745,10758,10876,4536,3720,3491,3869,3306,3308,3281,4521,4479,4030,3982,3645,4019,3663,10992,4542,10761,3276,10361,10457,10588,10650,10719,10764,10767,10800,10823,10860,10898,3277,10390,10445,10655,10740,3280,4520,10309,10399,10512,10536,10782,10826,3437,10608,10871,10915,4532,10791,10803,10907,10925,10928,10983,11069,11077,11093,3341,10637,10667,3373,3800,3738,10312,4529,10263,10625,10628,11072,3300,10670,10820,4110,4527,3808,4510,4513,3251,3255,4512,4511,4515,4544,10234,10237,10493,10544,10547,10552,4551,3886,3727,10931,10937,3729,10673,3547,10591,10594,10679,10847,4548,4549,10730,4170,3760,4546,10285,10288,10631,3731,10597,4003,4568,4594,4643,4645,4675,4692,4699,4700,4739,4769,4775,4860,4885,4886,4921,4946,4947,4969,4970,4983,4987,5010,5017,5035,5038,5039,5040,5045,5046,5068,5093,5094,5104,5109,5115,5160,5161,5169,5178,5183,5185,5195,5197,5203,5207,5222,5229,5232,5233,5234,5238,5274,5287,5295,5297,5298,5302,5303,5304,5312,5315,5319,5320,5321,5328,5332,5333,5334,5342,5346,5347,5348,5353,5366,5375,5387,5389,5397,5398,5402,5406,5431,5437,5447,5448,5463,5475,5497,5503,5519,5520,5523,5542,5550,5551,5556,5557,5567,5569,5581,5585,5594,5595,5597,5612,5617,5627,5628,5640,5647,5661,5665,5668,5674,5675,5676,5679,5684,5722,5723,5726,5728,5731,5732,5733,5735,5737,5739,5744,5751,5766,5780,5785,5786,5799,5800,5805,5809,5811,5816,5857,5869,5878,5882,5893,5897,5898,5906,5920,5926,5944,5947,5959,5985,5999,6024,6044,6045,6048,6062,6064,6066,6068,6081,6082,6085,6087,6090,6091,6103,6109,6110,6111,6113,6115,6158,6159,6166,6172,6176,6212,6214,6216,6218,6227,6229,6231,6237,6239,6245,6248,6256,6263,6264,6265,6270,6292,6293,6294,6296,6302,6307,6341,6342,6344,6345,6346,6348,6349,6350,6351,6358,6391,6392,6401,6422,6423,6443,6446,6457,6458,6464,6495,6497,6511,6549,6551,6552,6606,6630,6672,6692,6701,6702,6703,6704,6723,6724,6730,6743,6746,6748,6750,6751,6752,6754,6768,6779,6781,6782,6795,6799,6850,6861,6863,6867,6884,6885,6921,6933,6964,6998,7052,7080,7135,7156,7165,7168,7223,7231,7289,7291,7306,7316,7317,7318,7337,7343,7345,7395,7405,7408,7424,7476,7478,7481,7524,7525,7543,7610,7629,7652,7676,7691,7706,7717,7726,7727,7756,7759,7761,7771,7809,7820,7845,7903,7937,7969,8016,8032,8048,8049,8124,8177,8196,8220,8240,8264,8362,8364,8370,8386,8390,8406,8429,8440,8442,8457,8463,8467,8490,8504,8505,8521,8522,8527,8528,8529,8530,8531,8549,8550,8551,8559,8573,8575,8587,8591,8593,8594,8595,8603,8608,8635,8636,8668,8681,8685,8703,8725,8726,8727,8728,8740,8741,8763,8773,8783,8784,8785,8786,8788,8809,8810,8821,8865,8871,8877,8889,8894,8896,8899,8900,8904,8914,8997,9028,9029,9030,9045,9063,9068])).
% 187.33/188.09 cnf(11131,plain,
% 187.33/188.09 (~P24(f329(f329(f331(x111311),x111312),f193(f881(x111311,a869))))),
% 187.33/188.09 inference(rename_variables,[],[4532])).
% 187.33/188.09 cnf(11135,plain,
% 187.33/188.09 (P24(f329(f329(f243(f881(x111351,a869)),x111352),f329(f329(f115(f881(x111351,a869)),x111353),f252(f881(x111351,a869)))))),
% 187.33/188.09 inference(scs_inference,[],[4323,3521,4459,10208,10218,10229,10240,10341,10344,10347,10450,10563,10866,11030,4474,10434,10527,3065,3118,3234,10211,10275,10278,10368,10371,3212,3740,3108,3169,3136,3115,3337,3205,3229,10475,3383,4541,3919,4484,10266,4530,10980,3384,3166,10333,4066,3921,10986,4553,10918,11117,4554,11019,4555,3188,3482,3644,3583,3796,3347,10352,10470,10541,10602,10605,10643,10737,10970,3733,3260,4524,10243,10246,10272,10745,10758,10876,4536,3720,3491,3869,3306,3308,3281,4521,4479,4030,3982,3645,4019,3663,10992,11055,4542,10761,3276,10361,10457,10588,10650,10719,10764,10767,10800,10823,10860,10898,3277,10390,10445,10655,10740,3280,4520,10309,10399,10512,10536,10782,10826,3437,10608,10871,10915,4532,10791,10803,10907,10925,10928,10983,11069,11077,11093,3341,10637,10667,3373,3800,3738,10312,4529,10263,10625,10628,11072,3300,10670,10820,4110,4527,3808,4510,4513,3251,3255,4512,4511,4515,4544,10234,10237,10493,10544,10547,10552,4551,3886,3727,10931,10937,3729,10673,3547,10591,10594,10679,10847,4548,4549,10730,4170,3760,4546,10285,10288,10631,3731,10597,4003,4568,4594,4643,4645,4675,4692,4699,4700,4739,4769,4775,4860,4885,4886,4921,4946,4947,4969,4970,4983,4987,5010,5017,5035,5038,5039,5040,5045,5046,5068,5093,5094,5104,5109,5115,5160,5161,5169,5178,5183,5185,5195,5197,5203,5207,5222,5229,5232,5233,5234,5238,5274,5287,5295,5297,5298,5302,5303,5304,5312,5315,5319,5320,5321,5328,5332,5333,5334,5342,5346,5347,5348,5353,5366,5375,5387,5389,5397,5398,5402,5406,5431,5437,5447,5448,5463,5475,5497,5503,5519,5520,5523,5542,5550,5551,5556,5557,5567,5569,5581,5585,5594,5595,5597,5612,5617,5627,5628,5640,5647,5661,5665,5668,5674,5675,5676,5679,5684,5722,5723,5726,5728,5731,5732,5733,5735,5737,5739,5744,5751,5766,5780,5785,5786,5799,5800,5805,5809,5811,5816,5857,5869,5878,5882,5893,5897,5898,5906,5920,5926,5944,5947,5959,5985,5999,6024,6044,6045,6048,6062,6064,6066,6068,6081,6082,6085,6087,6090,6091,6103,6109,6110,6111,6113,6115,6158,6159,6166,6172,6176,6212,6214,6216,6218,6227,6229,6231,6237,6239,6245,6248,6256,6263,6264,6265,6270,6292,6293,6294,6296,6302,6307,6341,6342,6344,6345,6346,6348,6349,6350,6351,6358,6391,6392,6401,6422,6423,6443,6446,6457,6458,6464,6495,6497,6511,6549,6551,6552,6606,6630,6672,6692,6701,6702,6703,6704,6723,6724,6730,6743,6746,6748,6750,6751,6752,6754,6768,6779,6781,6782,6795,6799,6850,6861,6863,6867,6884,6885,6921,6933,6964,6998,7052,7080,7135,7156,7165,7168,7223,7231,7289,7291,7306,7316,7317,7318,7337,7343,7345,7395,7405,7408,7424,7476,7478,7481,7524,7525,7543,7610,7629,7652,7676,7691,7706,7717,7726,7727,7756,7759,7761,7771,7809,7820,7845,7903,7937,7969,8016,8032,8048,8049,8124,8177,8196,8220,8240,8264,8362,8364,8370,8386,8390,8406,8429,8440,8442,8457,8463,8467,8490,8504,8505,8521,8522,8527,8528,8529,8530,8531,8549,8550,8551,8559,8573,8575,8587,8591,8593,8594,8595,8603,8608,8635,8636,8668,8681,8685,8703,8725,8726,8727,8728,8740,8741,8763,8773,8783,8784,8785,8786,8788,8809,8810,8821,8865,8871,8877,8889,8894,8896,8899,8900,8904,8914,8997,9028,9029,9030,9045,9063,9068,9096,9097])).
% 187.33/188.09 cnf(11136,plain,
% 187.33/188.09 (P24(f329(f329(f243(f881(x111361,a869)),x111362),f252(f881(x111361,a869))))),
% 187.33/188.09 inference(rename_variables,[],[3663])).
% 187.33/188.09 cnf(11139,plain,
% 187.33/188.09 (~P24(f329(f329(f193(f881(x111391,f881(x111392,a869))),x111393),x111394))),
% 187.33/188.09 inference(rename_variables,[],[4549])).
% 187.33/188.09 cnf(11148,plain,
% 187.33/188.09 (~P24(f329(f329(f331(x111481),x111482),f193(f881(x111481,a869))))),
% 187.33/188.09 inference(rename_variables,[],[4532])).
% 187.33/188.09 cnf(11151,plain,
% 187.33/188.09 (~P24(f329(f329(f331(f880(x111511,x111511)),f329(f329(f264(x111511,x111511),x111512),x111513)),f151(x111511,f118(f881(x111511,a874)))))),
% 187.33/188.09 inference(rename_variables,[],[4551])).
% 187.33/188.09 cnf(11156,plain,
% 187.33/188.09 (~P24(f329(f329(f331(x111561),x111562),f193(f881(x111561,a869))))),
% 187.33/188.09 inference(rename_variables,[],[4532])).
% 187.33/188.09 cnf(11158,plain,
% 187.33/188.09 (P24(f329(f329(f243(f881(x111581,a869)),f329(f283(x111582,x111581,f193(f881(f880(x111582,x111581),a869))),x111583)),x111584))),
% 187.33/188.09 inference(scs_inference,[],[4323,3521,4459,10208,10218,10229,10240,10341,10344,10347,10450,10563,10866,11030,4474,10434,10527,3065,3118,3234,10211,10275,10278,10368,10371,3212,3740,3108,3169,3136,3115,3337,3205,3229,10475,3383,4541,3919,4484,10266,4530,10980,3384,3166,10333,4066,3921,10986,4553,10918,11117,4554,11019,4555,3188,3482,3644,3583,3796,3347,10352,10470,10541,10602,10605,10643,10737,10970,3733,3260,4524,10243,10246,10272,10745,10758,10876,4536,3720,3491,3869,3306,3308,3281,4521,4479,4030,3982,3645,4019,3663,10992,11055,4542,10761,3276,10361,10457,10588,10650,10719,10764,10767,10800,10823,10860,10898,3277,10390,10445,10655,10740,3280,4520,10309,10399,10512,10536,10782,10826,3437,10608,10871,10915,4532,10791,10803,10907,10925,10928,10983,11069,11077,11093,11131,11148,3341,10637,10667,3373,3800,3738,10312,4529,10263,10625,10628,11072,3300,10670,10820,4110,4527,3808,4510,4513,3251,3255,4512,4511,4515,4544,10234,10237,10493,10544,10547,10552,4551,3886,3727,10931,10937,3729,10673,11008,3547,10591,10594,10679,10847,4548,4549,10730,10829,4170,3760,4546,10285,10288,10631,3731,10597,4003,4568,4594,4643,4645,4675,4692,4699,4700,4739,4769,4775,4860,4885,4886,4921,4946,4947,4969,4970,4983,4987,5010,5017,5035,5038,5039,5040,5045,5046,5068,5093,5094,5104,5109,5115,5160,5161,5169,5178,5183,5185,5195,5197,5203,5207,5222,5229,5232,5233,5234,5238,5274,5287,5295,5297,5298,5302,5303,5304,5312,5315,5319,5320,5321,5328,5332,5333,5334,5342,5346,5347,5348,5353,5366,5375,5387,5389,5397,5398,5402,5406,5431,5437,5447,5448,5463,5475,5497,5503,5519,5520,5523,5542,5550,5551,5556,5557,5567,5569,5581,5585,5594,5595,5597,5612,5617,5627,5628,5640,5647,5661,5665,5668,5674,5675,5676,5679,5684,5722,5723,5726,5728,5731,5732,5733,5735,5737,5739,5744,5751,5766,5780,5785,5786,5799,5800,5805,5809,5811,5816,5857,5869,5878,5882,5893,5897,5898,5906,5920,5926,5944,5947,5959,5985,5999,6024,6044,6045,6048,6062,6064,6066,6068,6081,6082,6085,6087,6090,6091,6103,6109,6110,6111,6113,6115,6158,6159,6166,6172,6176,6212,6214,6216,6218,6227,6229,6231,6237,6239,6245,6248,6256,6263,6264,6265,6270,6292,6293,6294,6296,6302,6307,6341,6342,6344,6345,6346,6348,6349,6350,6351,6358,6391,6392,6401,6422,6423,6443,6446,6457,6458,6464,6495,6497,6511,6549,6551,6552,6606,6630,6672,6692,6701,6702,6703,6704,6723,6724,6730,6743,6746,6748,6750,6751,6752,6754,6768,6779,6781,6782,6795,6799,6850,6861,6863,6867,6884,6885,6921,6933,6964,6998,7052,7080,7135,7156,7165,7168,7223,7231,7289,7291,7306,7316,7317,7318,7337,7343,7345,7395,7405,7408,7424,7476,7478,7481,7524,7525,7543,7610,7629,7652,7676,7691,7706,7717,7726,7727,7756,7759,7761,7771,7809,7820,7845,7903,7937,7969,8016,8032,8048,8049,8124,8177,8196,8220,8240,8264,8362,8364,8370,8386,8390,8406,8429,8440,8442,8457,8463,8467,8490,8504,8505,8521,8522,8527,8528,8529,8530,8531,8549,8550,8551,8559,8573,8575,8587,8591,8593,8594,8595,8603,8608,8635,8636,8668,8681,8685,8703,8725,8726,8727,8728,8740,8741,8763,8773,8783,8784,8785,8786,8788,8809,8810,8821,8865,8871,8877,8889,8894,8896,8899,8900,8904,8914,8997,9028,9029,9030,9045,9063,9068,9096,9097,9138,9141,9167,9212,9213,9214,9229,9256,9270])).
% 187.33/188.09 cnf(11159,plain,
% 187.33/188.09 (P24(f329(f329(f243(f881(x111591,a869)),f193(f881(x111591,a869))),x111592))),
% 187.33/188.09 inference(rename_variables,[],[3729])).
% 187.33/188.09 cnf(11162,plain,
% 187.33/188.09 (P24(f329(f329(f331(f880(x111621,x111621)),f329(f329(f264(x111621,x111621),x111622),x111622)),f305(x111621,x111623)))),
% 187.33/188.09 inference(rename_variables,[],[3921])).
% 187.33/188.09 cnf(11164,plain,
% 187.33/188.09 (~P39(x111641,x111642,x111643,f329(f329(f152(x111644,x111641),x111645),f329(a117,f118(x111644))),f118(x111642))),
% 187.33/188.09 inference(scs_inference,[],[4323,3521,4459,10208,10218,10229,10240,10341,10344,10347,10450,10563,10866,11030,4474,10434,10527,3065,3118,3234,10211,10275,10278,10368,10371,3212,3740,3108,3169,3136,3115,3337,3205,3229,10475,3383,4541,3919,4484,10266,4530,10980,3384,3166,10333,4066,3921,10986,11112,4553,10918,11117,4554,11019,4555,3188,3482,3644,3583,3796,3347,10352,10470,10541,10602,10605,10643,10737,10970,3733,3260,4524,10243,10246,10272,10745,10758,10876,4536,3720,3491,3869,3306,3308,3281,4521,4479,4030,3982,3645,4019,3663,10992,11055,4542,10761,3276,10361,10457,10588,10650,10719,10764,10767,10800,10823,10860,10898,3277,10390,10445,10655,10740,3280,4520,10309,10399,10512,10536,10782,10826,3437,10608,10871,10915,4532,10791,10803,10907,10925,10928,10983,11069,11077,11093,11131,11148,3341,10637,10667,3373,3800,3738,10312,4529,10263,10625,10628,11072,3300,10670,10820,4110,4527,3808,4510,4513,3251,3255,4512,4511,4515,4544,10234,10237,10493,10544,10547,10552,4551,3886,3727,10931,10937,3729,10673,11008,3547,10591,10594,10679,10847,4548,4549,10730,10829,4170,3760,4546,10285,10288,10631,3731,10597,4003,4568,4594,4643,4645,4675,4692,4699,4700,4739,4769,4775,4860,4885,4886,4921,4946,4947,4969,4970,4983,4987,5010,5017,5035,5038,5039,5040,5045,5046,5068,5093,5094,5104,5109,5115,5160,5161,5169,5178,5183,5185,5195,5197,5203,5207,5222,5229,5232,5233,5234,5238,5274,5287,5295,5297,5298,5302,5303,5304,5312,5315,5319,5320,5321,5328,5332,5333,5334,5342,5346,5347,5348,5353,5366,5375,5387,5389,5397,5398,5402,5406,5431,5437,5447,5448,5463,5475,5497,5503,5519,5520,5523,5542,5550,5551,5556,5557,5567,5569,5581,5585,5594,5595,5597,5612,5617,5627,5628,5640,5647,5661,5665,5668,5674,5675,5676,5679,5684,5722,5723,5726,5728,5731,5732,5733,5735,5737,5739,5744,5751,5766,5780,5785,5786,5799,5800,5805,5809,5811,5816,5857,5869,5878,5882,5893,5897,5898,5906,5920,5926,5944,5947,5959,5985,5999,6024,6044,6045,6048,6062,6064,6066,6068,6081,6082,6085,6087,6090,6091,6103,6109,6110,6111,6113,6115,6158,6159,6166,6172,6176,6212,6214,6216,6218,6227,6229,6231,6237,6239,6245,6248,6256,6263,6264,6265,6270,6292,6293,6294,6296,6302,6307,6341,6342,6344,6345,6346,6348,6349,6350,6351,6358,6391,6392,6401,6422,6423,6443,6446,6457,6458,6464,6495,6497,6511,6549,6551,6552,6606,6630,6672,6692,6701,6702,6703,6704,6723,6724,6730,6743,6746,6748,6750,6751,6752,6754,6768,6779,6781,6782,6795,6799,6850,6861,6863,6867,6884,6885,6921,6933,6964,6998,7052,7080,7135,7156,7165,7168,7223,7231,7289,7291,7306,7316,7317,7318,7337,7343,7345,7395,7405,7408,7424,7476,7478,7481,7524,7525,7543,7610,7629,7652,7676,7691,7706,7717,7726,7727,7756,7759,7761,7771,7809,7820,7845,7903,7937,7969,8016,8032,8048,8049,8124,8177,8196,8220,8240,8264,8362,8364,8370,8386,8390,8406,8429,8440,8442,8457,8463,8467,8490,8504,8505,8521,8522,8527,8528,8529,8530,8531,8549,8550,8551,8559,8573,8575,8587,8591,8593,8594,8595,8603,8608,8635,8636,8668,8681,8685,8703,8725,8726,8727,8728,8740,8741,8763,8773,8783,8784,8785,8786,8788,8809,8810,8821,8865,8871,8877,8889,8894,8896,8899,8900,8904,8914,8997,9028,9029,9030,9045,9063,9068,9096,9097,9138,9141,9167,9212,9213,9214,9229,9256,9270,9276,9279])).
% 187.33/188.09 cnf(11168,plain,
% 187.33/188.09 (P39(x111681,x111682,x111683,f329(f329(f152(x111684,x111681),x111685),f119(x111684,f118(x111684))),f118(x111682))),
% 187.33/188.09 inference(scs_inference,[],[4323,3521,4459,10208,10218,10229,10240,10341,10344,10347,10450,10563,10866,11030,4474,10434,10527,3065,3118,3234,10211,10275,10278,10368,10371,3212,3740,3108,3169,3136,3115,3337,3205,3229,10475,3383,4541,3919,4484,10266,4530,10980,3384,3166,10333,4066,3921,10986,11112,4553,10918,11117,4554,11019,4555,3188,3482,3644,3583,3796,3347,10352,10470,10541,10602,10605,10643,10737,10970,3733,3260,4524,10243,10246,10272,10745,10758,10876,4536,3720,3491,3869,3306,3308,3281,4521,4479,4030,3982,3645,4019,3663,10992,11055,4542,10761,3276,10361,10457,10588,10650,10719,10764,10767,10800,10823,10860,10898,3277,10390,10445,10655,10740,3280,4520,10309,10399,10512,10536,10782,10826,3437,10608,10871,10915,4532,10791,10803,10907,10925,10928,10983,11069,11077,11093,11131,11148,3341,10637,10667,3373,3800,3738,10312,4529,10263,10625,10628,11072,3300,10670,10820,4110,4527,3808,4510,4513,3251,3255,4512,4511,4515,4544,10234,10237,10493,10544,10547,10552,4551,3886,3727,10931,10937,3729,10673,11008,3547,10591,10594,10679,10847,4548,4549,10730,10829,4170,3760,4546,10285,10288,10631,3731,10597,4003,4568,4594,4643,4645,4675,4692,4699,4700,4739,4769,4775,4860,4885,4886,4921,4946,4947,4969,4970,4983,4987,5010,5017,5035,5038,5039,5040,5045,5046,5068,5093,5094,5104,5109,5115,5160,5161,5169,5178,5183,5185,5195,5197,5203,5207,5222,5229,5232,5233,5234,5238,5274,5287,5295,5297,5298,5302,5303,5304,5312,5315,5319,5320,5321,5328,5332,5333,5334,5342,5346,5347,5348,5353,5366,5375,5387,5389,5397,5398,5402,5406,5431,5437,5447,5448,5463,5475,5497,5503,5519,5520,5523,5542,5550,5551,5556,5557,5567,5569,5581,5585,5594,5595,5597,5612,5617,5627,5628,5640,5647,5661,5665,5668,5674,5675,5676,5679,5684,5722,5723,5726,5728,5731,5732,5733,5735,5737,5739,5744,5751,5766,5780,5785,5786,5799,5800,5805,5809,5811,5816,5857,5869,5878,5882,5893,5897,5898,5906,5920,5926,5944,5947,5959,5985,5999,6024,6044,6045,6048,6062,6064,6066,6068,6081,6082,6085,6087,6090,6091,6103,6109,6110,6111,6113,6115,6158,6159,6166,6172,6176,6212,6214,6216,6218,6227,6229,6231,6237,6239,6245,6248,6256,6263,6264,6265,6270,6292,6293,6294,6296,6302,6307,6341,6342,6344,6345,6346,6348,6349,6350,6351,6358,6391,6392,6401,6422,6423,6443,6446,6457,6458,6464,6495,6497,6511,6549,6551,6552,6606,6630,6672,6692,6701,6702,6703,6704,6723,6724,6730,6743,6746,6748,6750,6751,6752,6754,6768,6779,6781,6782,6795,6799,6850,6861,6863,6867,6884,6885,6921,6933,6964,6998,7052,7080,7135,7156,7165,7168,7223,7231,7289,7291,7306,7316,7317,7318,7337,7343,7345,7395,7405,7408,7424,7476,7478,7481,7524,7525,7543,7610,7629,7652,7676,7691,7706,7717,7726,7727,7756,7759,7761,7771,7809,7820,7845,7903,7937,7969,8016,8032,8048,8049,8124,8177,8196,8220,8240,8264,8362,8364,8370,8386,8390,8406,8429,8440,8442,8457,8463,8467,8490,8504,8505,8521,8522,8527,8528,8529,8530,8531,8549,8550,8551,8559,8573,8575,8587,8591,8593,8594,8595,8603,8608,8635,8636,8668,8681,8685,8703,8725,8726,8727,8728,8740,8741,8763,8773,8783,8784,8785,8786,8788,8809,8810,8821,8865,8871,8877,8889,8894,8896,8899,8900,8904,8914,8997,9028,9029,9030,9045,9063,9068,9096,9097,9138,9141,9167,9212,9213,9214,9229,9256,9270,9276,9279,9301,9302])).
% 187.33/188.09 cnf(11173,plain,
% 187.33/188.09 (~P24(f329(f329(f331(f880(f875(x111731),f875(x111731))),f329(f329(f264(f875(x111731),f875(x111731)),x111732),f118(x111731))),f155(x111731,x111733)))),
% 187.33/188.09 inference(rename_variables,[],[4555])).
% 187.33/188.09 cnf(11176,plain,
% 187.33/188.09 (~P24(f329(f329(f331(f880(f875(x111761),f875(x111761))),f329(f329(f264(f875(x111761),f875(x111761)),f118(x111761)),x111762)),f143(x111761,x111763)))),
% 187.33/188.09 inference(rename_variables,[],[4556])).
% 187.33/188.09 cnf(11181,plain,
% 187.33/188.09 (~P24(f329(f329(f331(f880(f881(x111811,a869),f881(x111811,a869))),f329(f329(f264(f881(x111811,a869),f881(x111811,a869)),x111812),f193(f881(x111811,a869)))),f304(x111811)))),
% 187.33/188.09 inference(scs_inference,[],[4323,3521,4459,10208,10218,10229,10240,10341,10344,10347,10450,10563,10866,11030,4474,10434,10527,3065,3118,3234,10211,10275,10278,10368,10371,3212,3740,3108,3169,3136,3115,3337,3205,3229,10475,3383,4541,3919,4484,10266,4530,10980,3384,3166,10333,4066,3921,10986,11112,4553,10918,11117,4554,11019,4555,11123,4556,4557,3188,3482,3644,3583,3796,3347,10352,10470,10541,10602,10605,10643,10737,10970,3733,3260,4524,10243,10246,10272,10745,10758,10876,4536,3720,3491,3869,3306,3308,3281,4521,4479,4030,3982,3645,4019,3663,10992,11055,4542,10761,11128,3276,10361,10457,10588,10650,10719,10764,10767,10800,10823,10860,10898,3277,10390,10445,10655,10740,3280,4520,10309,10399,10512,10536,10782,10826,3437,10608,10871,10915,4532,10791,10803,10907,10925,10928,10983,11069,11077,11093,11131,11148,3341,10637,10667,3373,3800,3738,10312,4529,10263,10625,10628,11072,3300,10670,10820,4110,4527,3808,4510,4513,3251,3255,4512,4511,4515,4544,10234,10237,10493,10544,10547,10552,4551,3886,3727,10931,10937,3729,10673,11008,3547,10591,10594,10679,10847,4548,4549,10730,10829,4170,3760,4546,10285,10288,10631,3731,10597,4003,4568,4594,4643,4645,4675,4692,4699,4700,4739,4769,4775,4860,4885,4886,4921,4946,4947,4969,4970,4983,4987,5010,5017,5035,5038,5039,5040,5045,5046,5068,5093,5094,5104,5109,5115,5160,5161,5169,5178,5183,5185,5195,5197,5203,5207,5222,5229,5232,5233,5234,5238,5274,5287,5295,5297,5298,5302,5303,5304,5312,5315,5319,5320,5321,5328,5332,5333,5334,5342,5346,5347,5348,5353,5366,5375,5387,5389,5397,5398,5402,5406,5431,5437,5447,5448,5463,5475,5497,5503,5519,5520,5523,5542,5550,5551,5556,5557,5567,5569,5581,5585,5594,5595,5597,5612,5617,5627,5628,5640,5647,5661,5665,5668,5674,5675,5676,5679,5684,5722,5723,5726,5728,5731,5732,5733,5735,5737,5739,5744,5751,5766,5780,5785,5786,5799,5800,5805,5809,5811,5816,5857,5869,5878,5882,5893,5897,5898,5906,5920,5926,5944,5947,5959,5985,5999,6024,6044,6045,6048,6062,6064,6066,6068,6081,6082,6085,6087,6090,6091,6103,6109,6110,6111,6113,6115,6158,6159,6166,6172,6176,6212,6214,6216,6218,6227,6229,6231,6237,6239,6245,6248,6256,6263,6264,6265,6270,6292,6293,6294,6296,6302,6307,6341,6342,6344,6345,6346,6348,6349,6350,6351,6358,6391,6392,6401,6422,6423,6443,6446,6457,6458,6464,6495,6497,6511,6549,6551,6552,6606,6630,6672,6692,6701,6702,6703,6704,6723,6724,6730,6743,6746,6748,6750,6751,6752,6754,6768,6779,6781,6782,6795,6799,6850,6861,6863,6867,6884,6885,6921,6933,6964,6998,7052,7080,7135,7156,7165,7168,7223,7231,7289,7291,7306,7316,7317,7318,7337,7343,7345,7395,7405,7408,7424,7476,7478,7481,7524,7525,7543,7610,7629,7652,7676,7691,7706,7717,7726,7727,7756,7759,7761,7771,7809,7820,7845,7903,7937,7969,8016,8032,8048,8049,8124,8177,8196,8220,8240,8264,8362,8364,8370,8386,8390,8406,8429,8440,8442,8457,8463,8467,8490,8504,8505,8521,8522,8527,8528,8529,8530,8531,8549,8550,8551,8559,8573,8575,8587,8591,8593,8594,8595,8603,8608,8635,8636,8668,8681,8685,8703,8725,8726,8727,8728,8740,8741,8763,8773,8783,8784,8785,8786,8788,8809,8810,8821,8865,8871,8877,8889,8894,8896,8899,8900,8904,8914,8997,9028,9029,9030,9045,9063,9068,9096,9097,9138,9141,9167,9212,9213,9214,9229,9256,9270,9276,9279,9301,9302,9330,9391,9426,9427,9428])).
% 187.33/188.09 cnf(11184,plain,
% 187.33/188.09 (P24(f329(f329(f331(x111841),x111842),f252(f881(x111841,a869))))),
% 187.33/188.09 inference(rename_variables,[],[3437])).
% 187.33/188.09 cnf(11189,plain,
% 187.33/188.09 (P24(f329(f329(f243(f881(x111891,a869)),f193(f881(x111891,a869))),x111892))),
% 187.33/188.09 inference(rename_variables,[],[3729])).
% 187.33/188.09 cnf(11192,plain,
% 187.33/188.09 (~P24(f329(f329(f331(x111921),x111922),f193(f881(x111921,a869))))),
% 187.33/188.09 inference(rename_variables,[],[4532])).
% 187.33/188.09 cnf(11195,plain,
% 187.33/188.09 (P24(f329(f329(f243(f881(x111951,a869)),x111952),f252(f881(x111951,a869))))),
% 187.33/188.09 inference(rename_variables,[],[3663])).
% 187.33/188.09 cnf(11199,plain,
% 187.33/188.09 (P24(f329(f329(f243(f881(x111991,a869)),f329(f283(x111992,x111991,x111993),f193(f881(x111992,a869)))),x111994))),
% 187.33/188.09 inference(scs_inference,[],[4323,3521,4459,10208,10218,10229,10240,10341,10344,10347,10450,10563,10866,11030,4474,10434,10527,3065,3118,3234,10211,10275,10278,10368,10371,3212,3740,3108,3169,3136,3115,3337,3205,3229,10475,3383,4541,3919,4484,10266,4530,10980,3384,3166,10333,4066,3921,10986,11112,4553,10918,11117,4554,11019,4555,11123,4556,4557,3188,3482,3644,3583,3796,3347,10352,10470,10541,10602,10605,10643,10737,10970,3733,3260,4524,10243,10246,10272,10745,10758,10876,4536,3720,3491,3869,3306,3308,3281,4521,4479,4030,3982,3645,4019,3663,10992,11055,11136,4542,10761,11128,3276,10361,10457,10588,10650,10719,10764,10767,10800,10823,10860,10898,3277,10390,10445,10655,10740,3280,4520,10309,10399,10512,10536,10782,10826,3437,10608,10871,10915,4532,10791,10803,10907,10925,10928,10983,11069,11077,11093,11131,11148,11156,3341,10637,10667,3373,3800,3738,10312,4529,10263,10625,10628,11072,3300,10670,10820,4110,4527,3808,4510,4513,3251,3255,4512,4511,4515,4544,10234,10237,10493,10544,10547,10552,4551,3886,3727,10931,10937,3729,10673,11008,11159,11189,3547,10591,10594,10679,10847,4548,4549,10730,10829,4170,4071,3760,4546,10285,10288,10631,3731,10597,4003,4568,4594,4643,4645,4675,4692,4699,4700,4739,4769,4775,4860,4885,4886,4921,4946,4947,4969,4970,4983,4987,5010,5017,5035,5038,5039,5040,5045,5046,5068,5093,5094,5104,5109,5115,5160,5161,5169,5178,5183,5185,5195,5197,5203,5207,5222,5229,5232,5233,5234,5238,5274,5287,5295,5297,5298,5302,5303,5304,5312,5315,5319,5320,5321,5328,5332,5333,5334,5342,5346,5347,5348,5353,5366,5375,5387,5389,5397,5398,5402,5406,5431,5437,5447,5448,5463,5475,5497,5503,5519,5520,5523,5542,5550,5551,5556,5557,5567,5569,5581,5585,5594,5595,5597,5612,5617,5627,5628,5640,5647,5661,5665,5668,5674,5675,5676,5679,5684,5722,5723,5726,5728,5731,5732,5733,5735,5737,5739,5744,5751,5766,5780,5785,5786,5799,5800,5805,5809,5811,5816,5857,5869,5878,5882,5893,5897,5898,5906,5920,5926,5944,5947,5959,5985,5999,6024,6044,6045,6048,6062,6064,6066,6068,6081,6082,6085,6087,6090,6091,6103,6109,6110,6111,6113,6115,6158,6159,6166,6172,6176,6212,6214,6216,6218,6227,6229,6231,6237,6239,6245,6248,6256,6263,6264,6265,6270,6292,6293,6294,6296,6302,6307,6341,6342,6344,6345,6346,6348,6349,6350,6351,6358,6391,6392,6401,6422,6423,6443,6446,6457,6458,6464,6495,6497,6511,6549,6551,6552,6606,6630,6672,6692,6701,6702,6703,6704,6723,6724,6730,6743,6746,6748,6750,6751,6752,6754,6768,6779,6781,6782,6795,6799,6850,6861,6863,6867,6884,6885,6921,6933,6964,6998,7052,7080,7135,7156,7165,7168,7223,7231,7289,7291,7306,7316,7317,7318,7337,7343,7345,7395,7405,7408,7424,7476,7478,7481,7524,7525,7543,7610,7629,7652,7676,7691,7706,7717,7726,7727,7756,7759,7761,7771,7809,7820,7845,7903,7937,7969,8016,8032,8048,8049,8124,8177,8196,8220,8240,8264,8362,8364,8370,8386,8390,8406,8429,8440,8442,8457,8463,8467,8490,8504,8505,8521,8522,8527,8528,8529,8530,8531,8549,8550,8551,8559,8573,8575,8587,8591,8593,8594,8595,8603,8608,8635,8636,8668,8681,8685,8703,8725,8726,8727,8728,8740,8741,8763,8773,8783,8784,8785,8786,8788,8809,8810,8821,8865,8871,8877,8889,8894,8896,8899,8900,8904,8914,8997,9028,9029,9030,9045,9063,9068,9096,9097,9138,9141,9167,9212,9213,9214,9229,9256,9270,9276,9279,9301,9302,9330,9391,9426,9427,9428,9453,9454,9472,9491,9497,9511,9534])).
% 187.33/188.09 cnf(11200,plain,
% 187.33/188.09 (P24(f329(f329(f243(f881(x112001,a869)),f193(f881(x112001,a869))),x112002))),
% 187.33/188.09 inference(rename_variables,[],[3729])).
% 187.33/188.09 cnf(11213,plain,
% 187.33/188.09 (P24(f329(f252(f881(x112131,a869)),x112132))),
% 187.33/188.09 inference(rename_variables,[],[3341])).
% 187.33/188.09 cnf(11221,plain,
% 187.33/188.09 (~P24(f329(f329(f331(f880(f875(x112211),f875(x112211))),f329(f329(f264(f875(x112211),f875(x112211)),x112212),f118(x112211))),f143(x112211,x112213)))),
% 187.33/188.09 inference(rename_variables,[],[4553])).
% 187.33/188.09 cnf(11224,plain,
% 187.33/188.09 (~P24(f329(f329(f331(f880(f875(x112241),f875(x112241))),f329(f329(f264(f875(x112241),f875(x112241)),x112242),f118(x112241))),f145(x112241,x112243)))),
% 187.33/188.09 inference(rename_variables,[],[4554])).
% 187.33/188.09 cnf(11227,plain,
% 187.33/188.09 (~E(f329(f329(f149(x112271),x112272),x112273),x112273)),
% 187.33/188.09 inference(rename_variables,[],[4484])).
% 187.33/188.09 cnf(11230,plain,
% 187.33/188.09 (~E(f329(a117,x112301),x112301)),
% 187.33/188.09 inference(rename_variables,[],[4459])).
% 187.33/188.09 cnf(11233,plain,
% 187.33/188.09 (~P24(f329(f329(f331(x112331),x112332),f193(f881(x112331,a869))))),
% 187.33/188.09 inference(rename_variables,[],[4532])).
% 187.33/188.09 cnf(11238,plain,
% 187.33/188.09 (P24(f329(f329(f331(f880(f875(x112381),f875(x112381))),f329(f329(f264(f875(x112381),f875(x112381)),x112382),x112382)),f156(x112381,f305(x112381,x112383))))),
% 187.33/188.09 inference(rename_variables,[],[4060])).
% 187.33/188.09 cnf(11243,plain,
% 187.33/188.09 (~P24(f329(f329(f331(f880(f875(x112431),f875(x112431))),f329(f329(f264(f875(x112431),f875(x112431)),x112432),f118(x112431))),f143(x112431,x112433)))),
% 187.33/188.09 inference(rename_variables,[],[4553])).
% 187.33/188.09 cnf(11247,plain,
% 187.33/188.09 (E(f329(f329(f149(x112471),f671(f305(x112471,x112472),f329(f329(f149(x112471),x112473),x112474),x112474,x112473,x112471)),f672(f305(x112471,x112472),f329(f329(f149(x112471),x112473),x112474),x112474,x112473,x112471)),f329(f329(f149(x112471),x112473),x112474))),
% 187.33/188.09 inference(scs_inference,[],[4323,3521,4459,10208,10218,10229,10240,10341,10344,10347,10450,10563,10866,11030,11033,4474,10434,10527,3065,3118,3234,10211,10275,10278,10368,10371,3212,3740,3108,3169,3136,3115,3337,3205,3229,10475,3383,4541,3919,4484,10266,10431,4530,10980,3384,3166,10333,4066,3921,10986,11112,4553,10918,11117,11221,4554,11019,11120,4555,11123,4556,11176,4557,3188,3482,3644,3583,3796,3347,10352,10470,10541,10602,10605,10643,10737,10970,3733,3260,4524,10243,10246,10272,10745,10758,10876,4536,3720,3491,3869,3306,3308,3281,4521,4479,4060,11238,4030,3982,3645,4019,3663,10992,11055,11136,4542,10761,11128,3276,10361,10457,10588,10650,10719,10764,10767,10800,10823,10860,10898,3277,10390,10445,10655,10740,3280,4520,10309,10399,10512,10536,10782,10826,3437,10608,10871,10915,4532,10791,10803,10907,10925,10928,10983,11069,11077,11093,11131,11148,11156,11192,3341,10637,10667,10676,3373,3800,3738,10312,4529,10263,10625,10628,11072,3300,10670,10820,4110,4527,3808,4510,4513,3251,3255,4512,4511,4515,4544,10234,10237,10493,10544,10547,10552,4551,3886,3727,10931,10937,3729,10673,11008,11159,11189,3547,10591,10594,10679,10847,4548,4549,10730,10829,4170,4071,3760,4546,10285,10288,10631,3731,10597,4003,4568,4594,4643,4645,4675,4692,4699,4700,4739,4769,4775,4860,4885,4886,4921,4946,4947,4969,4970,4983,4987,5010,5017,5035,5038,5039,5040,5045,5046,5068,5093,5094,5104,5109,5115,5160,5161,5169,5178,5183,5185,5195,5197,5203,5207,5222,5229,5232,5233,5234,5238,5274,5287,5295,5297,5298,5302,5303,5304,5312,5315,5319,5320,5321,5328,5332,5333,5334,5342,5346,5347,5348,5353,5366,5375,5387,5389,5397,5398,5402,5406,5431,5437,5447,5448,5463,5475,5497,5503,5519,5520,5523,5542,5550,5551,5556,5557,5567,5569,5581,5585,5594,5595,5597,5612,5617,5627,5628,5640,5647,5661,5665,5668,5674,5675,5676,5679,5684,5722,5723,5726,5728,5731,5732,5733,5735,5737,5739,5744,5751,5766,5780,5785,5786,5799,5800,5805,5809,5811,5816,5857,5869,5878,5882,5893,5897,5898,5906,5920,5926,5944,5947,5959,5985,5999,6024,6044,6045,6048,6062,6064,6066,6068,6081,6082,6085,6087,6090,6091,6103,6109,6110,6111,6113,6115,6158,6159,6166,6172,6176,6212,6214,6216,6218,6227,6229,6231,6237,6239,6245,6248,6256,6263,6264,6265,6270,6292,6293,6294,6296,6302,6307,6341,6342,6344,6345,6346,6348,6349,6350,6351,6358,6391,6392,6401,6422,6423,6443,6446,6457,6458,6464,6495,6497,6511,6549,6551,6552,6606,6630,6672,6692,6701,6702,6703,6704,6723,6724,6730,6743,6746,6748,6750,6751,6752,6754,6768,6779,6781,6782,6795,6799,6850,6861,6863,6867,6884,6885,6921,6933,6964,6998,7052,7080,7135,7156,7165,7168,7223,7231,7289,7291,7306,7316,7317,7318,7337,7343,7345,7395,7405,7408,7424,7476,7478,7481,7524,7525,7543,7610,7629,7652,7676,7691,7706,7717,7726,7727,7756,7759,7761,7771,7809,7820,7845,7903,7937,7969,8016,8032,8048,8049,8124,8177,8196,8220,8240,8264,8362,8364,8370,8386,8390,8406,8429,8440,8442,8457,8463,8467,8490,8504,8505,8521,8522,8527,8528,8529,8530,8531,8549,8550,8551,8559,8573,8575,8587,8591,8593,8594,8595,8603,8608,8635,8636,8668,8681,8685,8703,8725,8726,8727,8728,8740,8741,8763,8773,8783,8784,8785,8786,8788,8809,8810,8821,8865,8871,8877,8889,8894,8896,8899,8900,8904,8914,8997,9028,9029,9030,9045,9063,9068,9096,9097,9138,9141,9167,9212,9213,9214,9229,9256,9270,9276,9279,9301,9302,9330,9391,9426,9427,9428,9453,9454,9472,9491,9497,9511,9534,9556,9564,9565,9566,9567,9582,9584,9589,9620,9621,9627,9628,9672,9673,9705,9714,9724,9726,9727])).
% 187.33/188.09 cnf(11253,plain,
% 187.33/188.09 (~P24(f329(f329(f331(x112531),x112532),f193(f881(x112531,a869))))),
% 187.33/188.09 inference(rename_variables,[],[4532])).
% 187.33/188.09 cnf(11256,plain,
% 187.33/188.09 (~P24(f329(f329(f331(x112561),x112562),f193(f881(x112561,a869))))),
% 187.33/188.09 inference(rename_variables,[],[4532])).
% 187.33/188.09 cnf(11259,plain,
% 187.33/188.09 (~P24(f329(f329(f331(x112591),x112592),f193(f881(x112591,a869))))),
% 187.33/188.09 inference(rename_variables,[],[4532])).
% 187.33/188.09 cnf(11262,plain,
% 187.33/188.09 (P24(f329(f329(f331(x112621),x112622),f252(f881(x112621,a869))))),
% 187.33/188.09 inference(rename_variables,[],[3437])).
% 187.33/188.09 cnf(11265,plain,
% 187.33/188.09 (~P24(f329(f329(f244(a874),x112651),f2(a874)))),
% 187.33/188.09 inference(rename_variables,[],[4524])).
% 187.33/188.09 cnf(11270,plain,
% 187.33/188.09 (~P24(f329(f329(f331(f880(x112701,x112701)),f329(f329(f264(x112701,x112701),x112702),x112703)),f151(x112701,f118(f881(x112701,a874)))))),
% 187.33/188.09 inference(rename_variables,[],[4551])).
% 187.33/188.09 cnf(11273,plain,
% 187.33/188.09 (~E(f329(f308(x112731,f881(x112731,a869),x112732),x112733),f329(f306(x112731),x112733))),
% 187.33/188.09 inference(rename_variables,[],[4530])).
% 187.33/188.09 cnf(11276,plain,
% 187.33/188.09 (~E(f329(f308(x112761,f881(x112761,a869),x112762),x112763),f329(f306(x112761),x112763))),
% 187.33/188.09 inference(rename_variables,[],[4530])).
% 187.33/188.09 cnf(11278,plain,
% 187.33/188.09 (E(f329(f329(f264(a874,a874),f659(f305(a874,a319),a319,a874,f329(f329(f264(a874,a874),x112781),f329(a117,x112781)),a874,a874)),f660(f305(a874,a319),a319,a874,f329(f329(f264(a874,a874),x112781),f329(a117,x112781)),a874,a874)),f329(f329(f264(a874,a874),x112781),f329(a117,x112781)))),
% 187.33/188.09 inference(scs_inference,[],[4323,3521,4459,10208,10218,10229,10240,10341,10344,10347,10450,10563,10866,11030,11033,4474,10434,10527,3065,3118,3234,10211,10275,10278,10368,10371,3212,3740,3108,3169,3136,3115,3337,3205,3229,10475,3383,4541,3919,4484,10266,10431,4530,10980,11050,11273,3384,3166,10333,4066,3921,10986,11112,4553,10918,11117,11221,4554,11019,11120,4555,11123,4556,11176,4557,3188,3482,3644,3583,3796,3347,10352,10470,10541,10602,10605,10643,10737,10970,3733,3260,4524,10243,10246,10272,10745,10758,10876,4536,3720,3491,3869,3306,3308,3281,4521,4479,4060,11238,4030,3982,3645,4019,3663,10992,11055,11136,4542,10761,11128,3276,10361,10457,10588,10650,10719,10764,10767,10800,10823,10860,10898,3277,10390,10445,10655,10740,3280,4520,10309,10399,10512,10536,10782,10826,3437,10608,10871,10915,11184,4532,10791,10803,10907,10925,10928,10983,11069,11077,11093,11131,11148,11156,11192,11233,11253,11256,3341,10637,10667,10676,3373,3800,3738,10312,4529,10263,10625,10628,11072,3300,10670,10820,4110,4527,3808,4510,4513,3251,3255,4512,4511,4515,4544,10234,10237,10493,10544,10547,10552,4551,11151,3886,3727,10931,10937,3729,10673,11008,11159,11189,3547,10591,10594,10679,10847,4548,4549,10730,10829,4170,4071,3760,4546,10285,10288,10631,3731,10597,4003,4568,4594,4643,4645,4675,4692,4699,4700,4739,4769,4775,4860,4885,4886,4921,4946,4947,4969,4970,4983,4987,5010,5017,5035,5038,5039,5040,5045,5046,5068,5093,5094,5104,5109,5115,5160,5161,5169,5178,5183,5185,5195,5197,5203,5207,5222,5229,5232,5233,5234,5238,5274,5287,5295,5297,5298,5302,5303,5304,5312,5315,5319,5320,5321,5328,5332,5333,5334,5342,5346,5347,5348,5353,5366,5375,5387,5389,5397,5398,5402,5406,5431,5437,5447,5448,5463,5475,5497,5503,5519,5520,5523,5542,5550,5551,5556,5557,5567,5569,5581,5585,5594,5595,5597,5612,5617,5627,5628,5640,5647,5661,5665,5668,5674,5675,5676,5679,5684,5722,5723,5726,5728,5731,5732,5733,5735,5737,5739,5744,5751,5766,5780,5785,5786,5799,5800,5805,5809,5811,5816,5857,5869,5878,5882,5893,5897,5898,5906,5920,5926,5944,5947,5959,5985,5999,6024,6044,6045,6048,6062,6064,6066,6068,6081,6082,6085,6087,6090,6091,6103,6109,6110,6111,6113,6115,6158,6159,6166,6172,6176,6212,6214,6216,6218,6227,6229,6231,6237,6239,6245,6248,6256,6263,6264,6265,6270,6292,6293,6294,6296,6302,6307,6341,6342,6344,6345,6346,6348,6349,6350,6351,6358,6391,6392,6401,6422,6423,6443,6446,6457,6458,6464,6495,6497,6511,6549,6551,6552,6606,6630,6672,6692,6701,6702,6703,6704,6723,6724,6730,6743,6746,6748,6750,6751,6752,6754,6768,6779,6781,6782,6795,6799,6850,6861,6863,6867,6884,6885,6921,6933,6964,6998,7052,7080,7135,7156,7165,7168,7223,7231,7289,7291,7306,7316,7317,7318,7337,7343,7345,7395,7405,7408,7424,7476,7478,7481,7524,7525,7543,7610,7629,7652,7676,7691,7706,7717,7726,7727,7756,7759,7761,7771,7809,7820,7845,7903,7937,7969,8016,8032,8048,8049,8124,8177,8196,8220,8240,8264,8362,8364,8370,8386,8390,8406,8429,8440,8442,8457,8463,8467,8490,8504,8505,8521,8522,8527,8528,8529,8530,8531,8549,8550,8551,8559,8573,8575,8587,8591,8593,8594,8595,8603,8608,8635,8636,8668,8681,8685,8703,8725,8726,8727,8728,8740,8741,8763,8773,8783,8784,8785,8786,8788,8809,8810,8821,8865,8871,8877,8889,8894,8896,8899,8900,8904,8914,8997,9028,9029,9030,9045,9063,9068,9096,9097,9138,9141,9167,9212,9213,9214,9229,9256,9270,9276,9279,9301,9302,9330,9391,9426,9427,9428,9453,9454,9472,9491,9497,9511,9534,9556,9564,9565,9566,9567,9582,9584,9589,9620,9621,9627,9628,9672,9673,9705,9714,9724,9726,9727,9736,9750,9753,9781,9814,9816,9820,9878,9919,9920,9922])).
% 187.33/188.09 cnf(11281,plain,
% 187.33/188.09 (~P24(f329(f329(f331(f880(f875(x112811),f875(x112811))),f329(f329(f264(f875(x112811),f875(x112811)),x112812),f118(x112811))),f143(x112811,x112813)))),
% 187.33/188.09 inference(rename_variables,[],[4553])).
% 187.33/188.09 cnf(11287,plain,
% 187.33/188.09 (~P24(f329(f329(f331(f880(f875(x112871),f875(x112871))),f329(f329(f264(f875(x112871),f875(x112871)),x112872),f118(x112871))),f143(x112871,x112873)))),
% 187.33/188.09 inference(rename_variables,[],[4553])).
% 187.33/188.09 cnf(11290,plain,
% 187.33/188.09 (~P24(f329(f329(f331(x112901),x112902),f193(f881(x112901,a869))))),
% 187.33/188.09 inference(rename_variables,[],[4532])).
% 187.33/188.09 cnf(11294,plain,
% 187.33/188.09 (P24(f329(f329(f331(f880(x112941,x112942)),f329(f329(f264(x112941,x112942),f329(x112943,x112944)),f329(x112945,x112944))),f329(f308(f880(x112946,x112946),f880(x112941,x112942),f269(x112946,x112941,x112946,x112942,x112943,x112945)),f305(x112946,x112947))))),
% 187.33/188.09 inference(scs_inference,[],[4323,3521,4459,10208,10218,10229,10240,10341,10344,10347,10450,10563,10866,11030,11033,4474,10434,10527,3065,3118,3234,10211,10275,10278,10368,10371,3212,3740,3108,3169,3136,3115,3337,3205,3229,10475,3383,4541,3919,4484,10266,10431,4530,10980,11050,11273,3384,3166,10333,4066,3921,10986,11112,11162,4553,10918,11117,11221,11243,11281,4554,11019,11120,11224,4555,11123,4556,11176,4557,3188,3482,3644,3583,3796,3347,10352,10470,10541,10602,10605,10643,10737,10970,3733,3260,4524,10243,10246,10272,10745,10758,10876,4536,3720,3491,3869,3306,3308,3281,4521,4479,4060,11238,4030,3982,3645,4019,3663,10992,11055,11136,4542,10761,11128,3276,10361,10457,10588,10650,10719,10764,10767,10800,10823,10860,10898,3277,10390,10445,10655,10740,3280,4520,10309,10399,10512,10536,10782,10826,3437,10608,10871,10915,11184,4532,10791,10803,10907,10925,10928,10983,11069,11077,11093,11131,11148,11156,11192,11233,11253,11256,11259,3341,10637,10667,10676,3373,3800,3738,10312,4529,10263,10625,10628,11072,3300,10670,10820,4110,4527,3808,4510,4513,3251,3255,4512,4511,4515,4544,10234,10237,10493,10544,10547,10552,4551,11151,3886,3727,10931,10937,3729,10673,11008,11159,11189,3547,10591,10594,10679,10847,4548,4549,10730,10829,4170,4071,3760,4546,10285,10288,10631,3731,10597,4003,4568,4594,4643,4645,4675,4692,4699,4700,4739,4769,4775,4860,4885,4886,4921,4946,4947,4969,4970,4983,4987,5010,5017,5035,5038,5039,5040,5045,5046,5068,5093,5094,5104,5109,5115,5160,5161,5169,5178,5183,5185,5195,5197,5203,5207,5222,5229,5232,5233,5234,5238,5274,5287,5295,5297,5298,5302,5303,5304,5312,5315,5319,5320,5321,5328,5332,5333,5334,5342,5346,5347,5348,5353,5366,5375,5387,5389,5397,5398,5402,5406,5431,5437,5447,5448,5463,5475,5497,5503,5519,5520,5523,5542,5550,5551,5556,5557,5567,5569,5581,5585,5594,5595,5597,5612,5617,5627,5628,5640,5647,5661,5665,5668,5674,5675,5676,5679,5684,5722,5723,5726,5728,5731,5732,5733,5735,5737,5739,5744,5751,5766,5780,5785,5786,5799,5800,5805,5809,5811,5816,5857,5869,5878,5882,5893,5897,5898,5906,5920,5926,5944,5947,5959,5985,5999,6024,6044,6045,6048,6062,6064,6066,6068,6081,6082,6085,6087,6090,6091,6103,6109,6110,6111,6113,6115,6158,6159,6166,6172,6176,6212,6214,6216,6218,6227,6229,6231,6237,6239,6245,6248,6256,6263,6264,6265,6270,6292,6293,6294,6296,6302,6307,6341,6342,6344,6345,6346,6348,6349,6350,6351,6358,6391,6392,6401,6422,6423,6443,6446,6457,6458,6464,6495,6497,6511,6549,6551,6552,6606,6630,6672,6692,6701,6702,6703,6704,6723,6724,6730,6743,6746,6748,6750,6751,6752,6754,6768,6779,6781,6782,6795,6799,6850,6861,6863,6867,6884,6885,6921,6933,6964,6998,7052,7080,7135,7156,7165,7168,7223,7231,7289,7291,7306,7316,7317,7318,7337,7343,7345,7395,7405,7408,7424,7476,7478,7481,7524,7525,7543,7610,7629,7652,7676,7691,7706,7717,7726,7727,7756,7759,7761,7771,7809,7820,7845,7903,7937,7969,8016,8032,8048,8049,8124,8177,8196,8220,8240,8264,8362,8364,8370,8386,8390,8406,8429,8440,8442,8457,8463,8467,8490,8504,8505,8521,8522,8527,8528,8529,8530,8531,8549,8550,8551,8559,8573,8575,8587,8591,8593,8594,8595,8603,8608,8635,8636,8668,8681,8685,8703,8725,8726,8727,8728,8740,8741,8763,8773,8783,8784,8785,8786,8788,8809,8810,8821,8865,8871,8877,8889,8894,8896,8899,8900,8904,8914,8997,9028,9029,9030,9045,9063,9068,9096,9097,9138,9141,9167,9212,9213,9214,9229,9256,9270,9276,9279,9301,9302,9330,9391,9426,9427,9428,9453,9454,9472,9491,9497,9511,9534,9556,9564,9565,9566,9567,9582,9584,9589,9620,9621,9627,9628,9672,9673,9705,9714,9724,9726,9727,9736,9750,9753,9781,9814,9816,9820,9878,9919,9920,9922,9932,9933,9953,9958,9999,10050])).
% 187.33/188.09 cnf(11297,plain,
% 187.33/188.09 (~P24(f329(f329(f331(x112971),x112972),f193(f881(x112971,a869))))),
% 187.33/188.09 inference(rename_variables,[],[4532])).
% 187.33/188.09 cnf(11300,plain,
% 187.33/188.09 (~P24(f329(f329(f331(x113001),x113002),f193(f881(x113001,a869))))),
% 187.33/188.09 inference(rename_variables,[],[4532])).
% 187.33/188.09 cnf(11303,plain,
% 187.33/188.09 (P24(f329(f329(f331(x113031),f329(x113032,x113033)),f329(f308(x113034,x113031,x113032),f252(f881(x113034,a869)))))),
% 187.33/188.09 inference(rename_variables,[],[3886])).
% 187.33/188.09 cnf(11306,plain,
% 187.33/188.09 (~P24(f329(f329(f331(f880(x113061,x113061)),f329(f329(f264(x113061,x113061),x113062),x113063)),f151(x113061,f118(f881(x113061,a874)))))),
% 187.33/188.09 inference(rename_variables,[],[4551])).
% 187.33/188.09 cnf(11314,plain,
% 187.33/188.09 (E(f119(x113141,f118(x113141)),f118(x113141))),
% 187.33/188.09 inference(rename_variables,[],[3118])).
% 187.33/188.09 cnf(11317,plain,
% 187.33/188.09 (~E(f329(a117,x113171),x113171)),
% 187.33/188.09 inference(rename_variables,[],[4459])).
% 187.33/188.09 cnf(11324,plain,
% 187.33/188.09 (~E(f329(a117,x113241),x113241)),
% 187.33/188.09 inference(rename_variables,[],[4459])).
% 187.33/188.09 cnf(11329,plain,
% 187.33/188.09 (E(f329(f260(x113291,x113291),f261(x113291,x113292)),x113292)),
% 187.33/188.09 inference(rename_variables,[],[3234])).
% 187.33/188.09 cnf(11332,plain,
% 187.33/188.09 (E(f329(f260(x113321,x113321),f261(x113321,x113322)),x113322)),
% 187.33/188.09 inference(rename_variables,[],[3234])).
% 187.33/188.09 cnf(11338,plain,
% 187.33/188.09 (~E(f329(a117,x113381),x113381)),
% 187.33/188.09 inference(rename_variables,[],[4459])).
% 187.33/188.09 cnf(11345,plain,
% 187.33/188.09 (~E(f329(f329(f80(a1),x113451),x113451),a102)),
% 187.33/188.09 inference(rename_variables,[],[4482])).
% 187.33/188.09 cnf(11354,plain,
% 187.33/188.09 (E(f329(f329(f22(a874),f2(a874)),x113541),f2(a874))),
% 187.33/188.09 inference(rename_variables,[],[3189])).
% 187.33/188.09 cnf(11357,plain,
% 187.33/188.09 (~P24(f329(f329(f244(a874),x113571),f2(a874)))),
% 187.33/188.09 inference(rename_variables,[],[4524])).
% 187.33/188.09 cnf(11364,plain,
% 187.33/188.09 (E(f329(f329(f80(a1),f329(f329(f81(a1),x113641),f329(f329(f39(a1),x113642),x113641))),f45(a1,x113642,x113641)),x113642)),
% 187.33/188.09 inference(rename_variables,[],[3832])).
% 187.33/188.09 cnf(11390,plain,
% 187.33/188.09 (~E(f329(a117,x113901),x113901)),
% 187.33/188.09 inference(rename_variables,[],[4459])).
% 187.33/188.09 cnf(11393,plain,
% 187.33/188.09 (~E(f329(a117,x113931),x113931)),
% 187.33/188.09 inference(rename_variables,[],[4459])).
% 187.33/188.09 cnf(11419,plain,
% 187.33/188.09 (~P24(f329(f63(x114191,x114192,f193(f881(x114191,a869))),x114193))),
% 187.33/188.09 inference(rename_variables,[],[4544])).
% 187.33/188.09 cnf(11422,plain,
% 187.33/188.09 (~P24(f329(f329(f193(f881(x114221,f881(x114222,a869))),x114223),x114224))),
% 187.33/188.09 inference(rename_variables,[],[4549])).
% 187.33/188.09 cnf(11425,plain,
% 187.33/188.09 (P24(f329(f329(f331(x114251),x114252),f252(f881(x114251,a869))))),
% 187.33/188.09 inference(rename_variables,[],[3437])).
% 187.33/188.09 cnf(11437,plain,
% 187.33/188.09 (~E(f329(a117,x114371),x114371)),
% 187.33/188.09 inference(rename_variables,[],[4459])).
% 187.33/188.09 cnf(11440,plain,
% 187.33/188.09 (P24(f329(f329(f243(a1),x114401),x114401))),
% 187.33/188.09 inference(rename_variables,[],[3277])).
% 187.33/188.09 cnf(11447,plain,
% 187.33/188.09 (P24(f329(f67(x114471,x114472,x114473,x114474,f193(f881(x114471,a869))),x114474))),
% 187.33/188.09 inference(rename_variables,[],[4209])).
% 187.33/188.09 cnf(11448,plain,
% 187.33/188.09 (E(f329(f260(x114481,x114481),f261(x114481,x114482)),x114482)),
% 187.33/188.09 inference(rename_variables,[],[3234])).
% 187.33/188.09 cnf(11453,plain,
% 187.33/188.09 (~P24(f329(f329(f193(f881(x114531,f881(x114532,a869))),x114533),x114534))),
% 187.33/188.09 inference(rename_variables,[],[4549])).
% 187.33/188.09 cnf(11464,plain,
% 187.33/188.09 (~P24(f329(f329(f244(a874),f329(f329(f80(a874),x114641),x114642)),x114642))),
% 187.33/188.09 inference(rename_variables,[],[4546])).
% 187.33/188.09 cnf(11467,plain,
% 187.33/188.09 (~P24(f329(f329(f244(a1),f329(f105(a1),x114671)),f2(a1)))),
% 187.33/188.09 inference(rename_variables,[],[4536])).
% 187.33/188.09 cnf(11483,plain,
% 187.33/188.09 (~E(f329(f329(f106(a874),f329(a117,x114831)),x114831),f329(a117,x114831))),
% 187.33/188.09 inference(scs_inference,[],[4323,3521,4459,10208,10218,10229,10240,10341,10344,10347,10450,10563,10866,11030,11033,11230,11317,11324,11338,11390,11393,4474,10434,10527,3193,2874,2880,2884,2885,2892,2895,2903,2909,2917,2920,2932,2944,2952,2953,2954,2974,3010,3019,3020,3035,3047,3053,3065,4455,3118,11314,3234,10211,10275,10278,10368,10371,10664,11329,11332,3212,3740,3108,3832,11364,3169,3136,3115,3337,3205,3229,10475,3383,4541,3919,4484,10266,10431,4530,10980,11050,11273,11276,3384,3166,10333,10640,3167,3087,3189,11354,4066,3921,10986,11112,11162,4553,10918,11117,11221,11243,11281,11287,4554,11019,11120,11224,4555,11123,4556,11176,4557,3188,3482,3644,4482,3583,3796,3347,10352,10470,10541,10602,10605,10643,10737,10970,3733,3260,4524,10243,10246,10272,10745,10758,10876,11265,11357,4536,3720,3491,3869,3306,3308,3281,4521,4479,3474,4537,4060,11238,3604,4030,3982,3645,4019,3663,10992,11055,11136,4542,10761,11128,3276,10361,10457,10588,10650,10719,10764,10767,10800,10823,10860,10898,3277,10390,10445,10655,10740,10863,3280,4520,10309,10399,10512,10536,10782,10826,3437,10608,10871,10915,11184,11262,4532,10791,10803,10907,10925,10928,10983,11069,11077,11093,11131,11148,11156,11192,11233,11253,11256,11259,11290,11297,3341,10637,10667,10676,3373,3800,3738,10312,4529,10263,10625,10628,11072,11090,3300,10670,10820,4110,4527,3808,4510,4513,3251,3255,4512,4511,4515,4209,4544,10234,10237,10493,10544,10547,10552,10957,4551,11151,11270,3886,3727,10931,10937,3729,10673,11008,11159,11189,3547,10591,10594,10679,10847,4548,4538,4549,10730,10829,11139,11422,4170,4071,3760,4546,10285,10288,10631,10634,3731,10597,4003,4568,4594,4643,4645,4675,4692,4699,4700,4739,4769,4775,4860,4885,4886,4921,4946,4947,4969,4970,4983,4987,5010,5017,5035,5038,5039,5040,5045,5046,5068,5093,5094,5104,5109,5115,5160,5161,5169,5178,5183,5185,5195,5197,5203,5207,5222,5229,5232,5233,5234,5238,5274,5287,5295,5297,5298,5302,5303,5304,5312,5315,5319,5320,5321,5328,5332,5333,5334,5342,5346,5347,5348,5353,5366,5375,5387,5389,5397,5398,5402,5406,5431,5437,5447,5448,5463,5475,5497,5503,5519,5520,5523,5542,5550,5551,5556,5557,5567,5569,5581,5585,5594,5595,5597,5612,5617,5627,5628,5640,5647,5661,5665,5668,5674,5675,5676,5679,5684,5722,5723,5726,5728,5731,5732,5733,5735,5737,5739,5744,5751,5766,5780,5785,5786,5799,5800,5805,5809,5811,5816,5857,5869,5878,5882,5893,5897,5898,5906,5920,5926,5944,5947,5959,5985,5999,6024,6044,6045,6048,6062,6064,6066,6068,6081,6082,6085,6087,6090,6091,6103,6109,6110,6111,6113,6115,6158,6159,6166,6172,6176,6212,6214,6216,6218,6227,6229,6231,6237,6239,6245,6248,6256,6263,6264,6265,6270,6292,6293,6294,6296,6302,6307,6341,6342,6344,6345,6346,6348,6349,6350,6351,6358,6391,6392,6401,6422,6423,6443,6446,6457,6458,6464,6495,6497,6511,6549,6551,6552,6606,6630,6672,6692,6701,6702,6703,6704,6723,6724,6730,6743,6746,6748,6750,6751,6752,6754,6768,6779,6781,6782,6795,6799,6850,6861,6863,6867,6884,6885,6921,6933,6964,6998,7052,7080,7135,7156,7165,7168,7223,7231,7289,7291,7306,7316,7317,7318,7337,7343,7345,7395,7405,7408,7424,7476,7478,7481,7524,7525,7543,7610,7629,7652,7676,7691,7706,7717,7726,7727,7756,7759,7761,7771,7809,7820,7845,7903,7937,7969,8016,8032,8048,8049,8124,8177,8196,8220,8240,8264,8362,8364,8370,8386,8390,8406,8429,8440,8442,8457,8463,8467,8490,8504,8505,8521,8522,8527,8528,8529,8530,8531,8549,8550,8551,8559,8573,8575,8587,8591,8593,8594,8595,8603,8608,8635,8636,8668,8681,8685,8703,8725,8726,8727,8728,8740,8741,8763,8773,8783,8784,8785,8786,8788,8809,8810,8821,8865,8871,8877,8889,8894,8896,8899,8900,8904,8914,8997,9028,9029,9030,9045,9063,9068,9096,9097,9138,9141,9167,9212,9213,9214,9229,9256,9270,9276,9279,9301,9302,9330,9391,9426,9427,9428,9453,9454,9472,9491,9497,9511,9534,9556,9564,9565,9566,9567,9582,9584,9589,9620,9621,9627,9628,9672,9673,9705,9714,9724,9726,9727,9736,9750,9753,9781,9814,9816,9820,9878,9919,9920,9922,9932,9933,9953,9958,9999,10050,10122,10123,10176,10192,2,8,9,4581,4582,4600,4631,4633,4634,4661,4667,4668,4679,4728,4730,4760,4774,4804,4900,4901,4914,4934,4990,4991,4994,4995,4997,4999,5000,5009,5013,5014,5024,5036,5037,5043,5063,5064,5081,5086,5087,5088,5089,5092,5100,5103,5110,5175,5181,5182,5189,5219,5230,5236,5252,5272,5273,5280,5281,5282,5291,5301,5308,5310,5311,5317,5324,5325,5338,5339,5340,5341,5343,5344,5349,5350])).
% 187.33/188.09 cnf(11490,plain,
% 187.33/188.09 (E(f329(f260(x114901,x114901),f261(x114901,x114902)),x114902)),
% 187.33/188.09 inference(rename_variables,[],[3234])).
% 187.33/188.09 cnf(11495,plain,
% 187.33/188.09 (E(f329(f260(x114951,x114951),f261(x114951,x114952)),x114952)),
% 187.33/188.09 inference(rename_variables,[],[3234])).
% 187.33/188.09 cnf(11498,plain,
% 187.33/188.09 (~P24(f329(f329(f244(a1),f329(f105(a1),x114981)),f2(a1)))),
% 187.33/188.09 inference(rename_variables,[],[4536])).
% 187.33/188.09 cnf(11503,plain,
% 187.33/188.09 (~E(f329(a117,x115031),x115031)),
% 187.33/188.09 inference(rename_variables,[],[4459])).
% 187.33/188.09 cnf(11512,plain,
% 187.33/188.09 (~P24(f329(f329(f244(a874),x115121),x115121))),
% 187.33/188.09 inference(rename_variables,[],[4520])).
% 187.33/188.09 cnf(11533,plain,
% 187.33/188.09 (~P24(f329(f329(f244(a1),f329(f105(a1),x115331)),f2(a1)))),
% 187.33/188.09 inference(rename_variables,[],[4536])).
% 187.33/188.09 cnf(11548,plain,
% 187.33/188.09 (~P24(f329(f329(f243(a874),f329(a117,x115481)),x115481))),
% 187.33/188.09 inference(rename_variables,[],[4529])).
% 187.33/188.09 cnf(11549,plain,
% 187.33/188.09 (~E(f329(a117,x115491),x115491)),
% 187.33/188.09 inference(rename_variables,[],[4459])).
% 187.33/188.09 cnf(11559,plain,
% 187.33/188.09 (~P24(f329(f329(f244(a874),f329(f329(f80(a874),x115591),x115592)),x115591))),
% 187.33/188.09 inference(rename_variables,[],[4547])).
% 187.33/188.09 cnf(11562,plain,
% 187.33/188.09 (~P24(f329(f329(f244(a1),f329(f105(a1),x115621)),f2(a1)))),
% 187.33/188.09 inference(rename_variables,[],[4536])).
% 187.33/188.09 cnf(11565,plain,
% 187.33/188.09 (~E(f329(a117,x115651),x115651)),
% 187.33/188.09 inference(rename_variables,[],[4459])).
% 187.33/188.09 cnf(11578,plain,
% 187.33/188.09 (P24(f329(f329(f331(x115781),x115782),f329(f329(f307(x115781),x115782),x115783)))),
% 187.33/188.09 inference(rename_variables,[],[3594])).
% 187.33/188.09 cnf(11579,plain,
% 187.33/188.09 (~P24(f329(f329(f243(a1),f2(a1)),f329(f79(a1),f329(f105(a1),f329(a117,x115791)))))),
% 187.33/188.09 inference(rename_variables,[],[4548])).
% 187.33/188.09 cnf(11582,plain,
% 187.33/188.09 (P24(f329(f329(f244(a874),f329(f329(f22(a874),x115821),x115822)),f329(a117,x115821)))),
% 187.33/188.09 inference(rename_variables,[],[3733])).
% 187.33/188.09 cnf(11585,plain,
% 187.33/188.09 (P24(f329(f329(f243(a874),f45(a874,x115851,x115852)),x115851))),
% 187.33/188.09 inference(rename_variables,[],[3738])).
% 187.33/188.09 cnf(11591,plain,
% 187.33/188.09 (E(f329(f260(x115911,x115911),f261(x115911,x115912)),x115912)),
% 187.33/188.09 inference(rename_variables,[],[3234])).
% 187.33/188.09 cnf(11596,plain,
% 187.33/188.09 (E(f329(f329(f126(x115961),f169(x115961,x115962,x115963)),f169(x115961,x115964,x115963)),f329(f329(f126(x115961),f169(x115961,x115964,x115963)),f169(x115961,x115962,x115963)))),
% 187.33/188.09 inference(rename_variables,[],[3847])).
% 187.33/188.09 cnf(11601,plain,
% 187.33/188.09 (~P24(f329(f329(f243(a874),f329(a117,x116011)),x116011))),
% 187.33/188.09 inference(rename_variables,[],[4529])).
% 187.33/188.09 cnf(11610,plain,
% 187.33/188.09 (~P24(f329(f329(f244(a874),x116101),x116101))),
% 187.33/188.09 inference(rename_variables,[],[4520])).
% 187.33/188.09 cnf(11613,plain,
% 187.33/188.09 (P24(f329(f329(f243(a874),f45(a874,x116131,x116132)),x116131))),
% 187.33/188.09 inference(rename_variables,[],[3738])).
% 187.33/188.09 cnf(11614,plain,
% 187.33/188.09 (P24(f329(f329(f243(a874),f2(a874)),x116141))),
% 187.33/188.09 inference(rename_variables,[],[3300])).
% 187.33/188.09 cnf(11616,plain,
% 187.33/188.09 (~P24(f329(f329(f243(a1),f78(a1)),f2(a1)))),
% 187.33/188.09 inference(scs_inference,[],[4323,3521,4459,10208,10218,10229,10240,10341,10344,10347,10450,10563,10866,11030,11033,11230,11317,11324,11338,11390,11393,11437,11503,11549,4474,10434,10527,3193,2873,2874,2880,2881,2884,2885,2892,2895,2896,2903,2904,2909,2917,2920,2932,2944,2952,2953,2954,2974,3010,3019,3020,3022,3035,3047,3053,3065,4455,3847,11596,3118,11314,3234,10211,10275,10278,10368,10371,10664,11329,11332,11448,11490,11495,3212,3740,3108,3484,3832,11364,3169,3136,3131,3115,3116,3337,3205,3229,10475,3383,4541,3919,4484,10266,10431,4530,10980,11050,11273,11276,3384,3166,10333,10640,3167,3442,3087,3189,11354,4066,3921,10986,11112,11162,4553,10918,11117,11221,11243,11281,11287,4554,11019,11120,11224,4555,11123,4556,11176,4557,3188,3482,3644,4350,4351,4482,3583,3796,3347,10352,10470,10541,10602,10605,10643,10737,10970,3733,3260,4524,10243,10246,10272,10745,10758,10876,11265,11357,4536,11467,11498,11533,3720,3491,3869,3306,3308,3281,4521,4479,3474,4537,4060,11238,3604,4030,3982,3645,4019,3663,10992,11055,11136,4542,10761,11128,3276,10361,10457,10588,10650,10719,10764,10767,10800,10823,10860,10898,3277,10390,10445,10655,10740,10863,3280,4520,10309,10399,10512,10536,10782,10826,10836,11512,3437,10608,10871,10915,11184,11262,4532,10791,10803,10907,10925,10928,10983,11069,11077,11093,11131,11148,11156,11192,11233,11253,11256,11259,11290,11297,3341,10637,10667,10676,3379,3373,3800,3738,10312,11585,4529,10263,10625,10628,11072,11090,11548,3300,10670,10820,10891,4110,4527,3808,4510,4513,3251,3255,4512,4511,4515,3594,4209,4544,10234,10237,10493,10544,10547,10552,10957,4551,11151,11270,3886,3727,10931,10937,3729,10673,11008,11159,11189,3547,10591,10594,10679,10847,4548,4538,4549,10730,10829,11139,11422,4170,4071,3760,4546,10285,10288,10631,10634,4547,3731,10597,4003,4568,4594,4643,4645,4675,4692,4699,4700,4739,4769,4775,4860,4885,4886,4921,4946,4947,4969,4970,4983,4987,5010,5017,5035,5038,5039,5040,5045,5046,5068,5093,5094,5104,5109,5115,5160,5161,5169,5178,5183,5185,5195,5197,5203,5207,5222,5229,5232,5233,5234,5238,5274,5287,5295,5297,5298,5302,5303,5304,5312,5315,5319,5320,5321,5328,5332,5333,5334,5342,5346,5347,5348,5353,5366,5375,5387,5389,5397,5398,5402,5406,5431,5437,5447,5448,5463,5475,5497,5503,5519,5520,5523,5542,5550,5551,5556,5557,5567,5569,5581,5585,5594,5595,5597,5612,5617,5627,5628,5640,5647,5661,5665,5668,5674,5675,5676,5679,5684,5722,5723,5726,5728,5731,5732,5733,5735,5737,5739,5744,5751,5766,5780,5785,5786,5799,5800,5805,5809,5811,5816,5857,5869,5878,5882,5893,5897,5898,5906,5920,5926,5944,5947,5959,5985,5999,6024,6044,6045,6048,6062,6064,6066,6068,6081,6082,6085,6087,6090,6091,6103,6109,6110,6111,6113,6115,6158,6159,6166,6172,6176,6212,6214,6216,6218,6227,6229,6231,6237,6239,6245,6248,6256,6263,6264,6265,6270,6292,6293,6294,6296,6302,6307,6341,6342,6344,6345,6346,6348,6349,6350,6351,6358,6391,6392,6401,6422,6423,6443,6446,6457,6458,6464,6495,6497,6511,6549,6551,6552,6606,6630,6672,6692,6701,6702,6703,6704,6723,6724,6730,6743,6746,6748,6750,6751,6752,6754,6768,6779,6781,6782,6795,6799,6850,6861,6863,6867,6884,6885,6921,6933,6964,6998,7052,7080,7135,7156,7165,7168,7223,7231,7289,7291,7306,7316,7317,7318,7337,7343,7345,7395,7405,7408,7424,7476,7478,7481,7524,7525,7543,7610,7629,7652,7676,7691,7706,7717,7726,7727,7756,7759,7761,7771,7809,7820,7845,7903,7937,7969,8016,8032,8048,8049,8124,8177,8196,8220,8240,8264,8362,8364,8370,8386,8390,8406,8429,8440,8442,8457,8463,8467,8490,8504,8505,8521,8522,8527,8528,8529,8530,8531,8549,8550,8551,8559,8573,8575,8587,8591,8593,8594,8595,8603,8608,8635,8636,8668,8681,8685,8703,8725,8726,8727,8728,8740,8741,8763,8773,8783,8784,8785,8786,8788,8809,8810,8821,8865,8871,8877,8889,8894,8896,8899,8900,8904,8914,8997,9028,9029,9030,9045,9063,9068,9096,9097,9138,9141,9167,9212,9213,9214,9229,9256,9270,9276,9279,9301,9302,9330,9391,9426,9427,9428,9453,9454,9472,9491,9497,9511,9534,9556,9564,9565,9566,9567,9582,9584,9589,9620,9621,9627,9628,9672,9673,9705,9714,9724,9726,9727,9736,9750,9753,9781,9814,9816,9820,9878,9919,9920,9922,9932,9933,9953,9958,9999,10050,10122,10123,10176,10192,2,8,9,4581,4582,4600,4631,4633,4634,4661,4667,4668,4679,4728,4730,4760,4774,4804,4900,4901,4914,4934,4990,4991,4994,4995,4997,4999,5000,5009,5013,5014,5024,5036,5037,5043,5063,5064,5081,5086,5087,5088,5089,5092,5100,5103,5110,5175,5181,5182,5189,5219,5230,5236,5252,5272,5273,5280,5281,5282,5291,5301,5308,5310,5311,5317,5324,5325,5338,5339,5340,5341,5343,5344,5349,5350,5351,5352,5383,5384,5385,5393,5394,5395,5396,5439,5444,5446,5482,5484,5485,5487,5488,5490,5491,5493,5502,5507,5509,5510,5511,5512,5513,5514,5521,5531,5534,5545,5561,5562,5565,5575,5577,5578,5579,5604,5614,5630,5631,5641,5642,5644,5646,5651,5686,5691,5693,5753,5787,5788])).
% 187.33/188.09 cnf(11631,plain,
% 187.33/188.09 (~P24(f329(f329(f244(a874),x116311),x116311))),
% 187.33/188.09 inference(rename_variables,[],[4520])).
% 187.33/188.09 cnf(11634,plain,
% 187.33/188.09 (~P24(f329(f329(f244(a874),x116341),x116341))),
% 187.33/188.09 inference(rename_variables,[],[4520])).
% 187.33/188.09 cnf(11637,plain,
% 187.33/188.09 (~P24(f329(f329(f244(a874),x116371),x116371))),
% 187.33/188.09 inference(rename_variables,[],[4520])).
% 187.33/188.09 cnf(11640,plain,
% 187.33/188.09 (P24(f329(f329(f331(x116401),f329(x116402,x116403)),f329(f308(x116404,x116401,x116402),f252(f881(x116404,a869)))))),
% 187.33/188.09 inference(rename_variables,[],[3886])).
% 187.33/188.09 cnf(11641,plain,
% 187.33/188.09 (~P24(f329(f329(f243(a874),f329(a117,x116411)),x116411))),
% 187.33/188.09 inference(rename_variables,[],[4529])).
% 187.33/188.09 cnf(11644,plain,
% 187.33/188.09 (P24(f329(f329(f331(x116441),f329(x116442,x116443)),f329(f308(x116444,x116441,x116442),f252(f881(x116444,a869)))))),
% 187.33/188.09 inference(rename_variables,[],[3886])).
% 187.33/188.09 cnf(11645,plain,
% 187.33/188.09 (~P24(f329(f329(f244(a874),f329(f329(f80(a874),x116451),x116452)),x116452))),
% 187.33/188.09 inference(rename_variables,[],[4546])).
% 187.33/188.09 cnf(11650,plain,
% 187.33/188.09 (~P24(f329(f329(f244(a874),f329(f329(f80(a874),x116501),x116502)),x116501))),
% 187.33/188.09 inference(rename_variables,[],[4547])).
% 187.33/188.09 cnf(11653,plain,
% 187.33/188.09 (~P24(f329(f329(f244(a874),x116531),x116531))),
% 187.33/188.09 inference(rename_variables,[],[4520])).
% 187.33/188.09 cnf(11656,plain,
% 187.33/188.09 (P24(f329(f329(f243(a874),x116561),x116561))),
% 187.33/188.09 inference(rename_variables,[],[3276])).
% 187.33/188.09 cnf(11662,plain,
% 187.33/188.09 (~P40(x116621,x116622,f118(x116621))),
% 187.33/188.09 inference(rename_variables,[],[4493])).
% 187.33/188.09 cnf(11665,plain,
% 187.33/188.09 (P24(f329(f329(f331(x116651),x116652),f252(f881(x116651,a869))))),
% 187.33/188.09 inference(rename_variables,[],[3437])).
% 187.33/188.09 cnf(11666,plain,
% 187.33/188.09 (~P24(f329(f329(f243(a874),f329(a117,x116661)),x116661))),
% 187.33/188.09 inference(rename_variables,[],[4529])).
% 187.33/188.09 cnf(11669,plain,
% 187.33/188.09 (~P24(f329(f63(x116691,x116692,f193(f881(x116691,a869))),x116693))),
% 187.33/188.09 inference(rename_variables,[],[4544])).
% 187.33/188.09 cnf(11682,plain,
% 187.33/188.09 (~P24(f329(f329(f331(x116821),x116822),f193(f881(x116821,a869))))),
% 187.33/188.09 inference(rename_variables,[],[4532])).
% 187.33/188.09 cnf(11685,plain,
% 187.33/188.09 (E(f329(f329(f16(x116851,x116852),x116853),x116854),x116853)),
% 187.33/188.09 inference(rename_variables,[],[3267])).
% 187.33/188.09 cnf(11688,plain,
% 187.33/188.09 (E(f329(f329(f16(x116881,x116882),x116883),x116884),x116883)),
% 187.33/188.09 inference(rename_variables,[],[3267])).
% 187.33/188.09 cnf(11700,plain,
% 187.33/188.09 (P24(f329(f329(f244(a874),f2(a874)),f329(a117,x117001)))),
% 187.33/188.09 inference(rename_variables,[],[3359])).
% 187.33/188.09 cnf(11703,plain,
% 187.33/188.09 (P24(f329(f329(f243(a874),x117031),x117031))),
% 187.33/188.09 inference(rename_variables,[],[3276])).
% 187.33/188.09 cnf(11706,plain,
% 187.33/188.09 (P24(f329(f329(f331(x117061),f329(x117062,x117063)),f329(f308(x117064,x117061,x117062),f252(f881(x117064,a869)))))),
% 187.33/188.09 inference(rename_variables,[],[3886])).
% 187.33/188.09 cnf(11709,plain,
% 187.33/188.09 (P24(f329(f62(x117091),f329(f171(x117091),x117092)))),
% 187.33/188.09 inference(rename_variables,[],[3320])).
% 187.33/188.09 cnf(11712,plain,
% 187.33/188.09 (P24(f329(f62(x117121),f329(f171(x117121),x117122)))),
% 187.33/188.09 inference(rename_variables,[],[3320])).
% 187.33/188.09 cnf(11715,plain,
% 187.33/188.09 (P24(f329(f329(f243(a1),f329(f79(a1),f329(f105(a1),x117151))),f329(f105(a1),x117152)))),
% 187.33/188.09 inference(rename_variables,[],[3761])).
% 187.33/188.09 cnf(11718,plain,
% 187.33/188.09 (~P24(f329(f329(f331(x117181),x117182),f193(f881(x117181,a869))))),
% 187.33/188.09 inference(rename_variables,[],[4532])).
% 187.33/188.09 cnf(11734,plain,
% 187.33/188.09 (~P24(f329(f329(f331(a874),x117341),f329(f250(a874),f2(a874))))),
% 187.33/188.09 inference(scs_inference,[],[4323,3521,4492,4493,4459,10208,10218,10229,10240,10341,10344,10347,10450,10563,10866,11030,11033,11230,11317,11324,11338,11390,11393,11437,11503,11549,4474,10434,10527,3193,2873,2874,2877,2880,2881,2884,2885,2892,2895,2896,2903,2904,2909,2917,2920,2932,2944,2952,2953,2954,2974,3010,3019,3020,3022,3029,3035,3047,3053,3065,4455,3847,11596,3118,11314,3234,10211,10275,10278,10368,10371,10664,11329,11332,11448,11490,11495,3212,3740,3108,3484,3832,11364,3169,3136,3131,3115,3116,3337,3205,3229,10475,3383,4541,3919,4484,10266,10431,3267,11685,4530,10980,11050,11273,11276,3384,3166,10333,10640,3167,3442,3087,3189,11354,4066,3921,10986,11112,11162,4553,10918,11117,11221,11243,11281,11287,4554,11019,11120,11224,4555,11123,4556,11176,4557,3188,3482,3644,4350,4351,4482,3583,3796,3347,10352,10470,10541,10602,10605,10643,10737,10970,3733,11582,3260,3359,4524,10243,10246,10272,10745,10758,10876,11265,11357,4536,11467,11498,11533,3720,3491,3869,3306,3308,3281,4521,4479,3474,4537,4060,11238,3604,3320,11709,4030,3982,3645,4019,3663,10992,11055,11136,4542,10761,11128,3276,10361,10457,10588,10650,10719,10764,10767,10800,10823,10860,10898,10934,11656,3277,10390,10445,10655,10740,10863,3280,3355,4520,10309,10399,10512,10536,10782,10826,10836,11512,11610,11631,11634,11637,3437,10608,10871,10915,11184,11262,11425,4532,10791,10803,10907,10925,10928,10983,11069,11077,11093,11131,11148,11156,11192,11233,11253,11256,11259,11290,11297,11300,11682,3341,10637,10667,10676,3379,3373,3800,3738,10312,11585,4529,10263,10625,10628,11072,11090,11548,11601,11641,11666,3300,10670,10820,10891,3761,4110,4527,3808,4510,4513,3251,3255,4512,4511,4515,3594,4209,4544,10234,10237,10493,10544,10547,10552,10957,11419,4551,11151,11270,3996,3886,11303,11640,11644,3727,10931,10937,3729,10673,11008,11159,11189,3547,10591,10594,10679,10847,4548,11579,4538,4549,10730,10829,11139,11422,4170,4071,3760,3707,4546,10285,10288,10631,10634,11464,4547,11559,3731,10597,4003,4568,4594,4643,4645,4675,4692,4699,4700,4739,4769,4775,4860,4885,4886,4921,4946,4947,4969,4970,4983,4987,5010,5017,5035,5038,5039,5040,5045,5046,5068,5093,5094,5104,5109,5115,5160,5161,5169,5178,5183,5185,5195,5197,5203,5207,5222,5229,5232,5233,5234,5238,5274,5287,5295,5297,5298,5302,5303,5304,5312,5315,5319,5320,5321,5328,5332,5333,5334,5342,5346,5347,5348,5353,5366,5375,5387,5389,5397,5398,5402,5406,5431,5437,5447,5448,5463,5475,5497,5503,5519,5520,5523,5542,5550,5551,5556,5557,5567,5569,5581,5585,5594,5595,5597,5612,5617,5627,5628,5640,5647,5661,5665,5668,5674,5675,5676,5679,5684,5722,5723,5726,5728,5731,5732,5733,5735,5737,5739,5744,5751,5766,5780,5785,5786,5799,5800,5805,5809,5811,5816,5857,5869,5878,5882,5893,5897,5898,5906,5920,5926,5944,5947,5959,5985,5999,6024,6044,6045,6048,6062,6064,6066,6068,6081,6082,6085,6087,6090,6091,6103,6109,6110,6111,6113,6115,6158,6159,6166,6172,6176,6212,6214,6216,6218,6227,6229,6231,6237,6239,6245,6248,6256,6263,6264,6265,6270,6292,6293,6294,6296,6302,6307,6341,6342,6344,6345,6346,6348,6349,6350,6351,6358,6391,6392,6401,6422,6423,6443,6446,6457,6458,6464,6495,6497,6511,6549,6551,6552,6606,6630,6672,6692,6701,6702,6703,6704,6723,6724,6730,6743,6746,6748,6750,6751,6752,6754,6768,6779,6781,6782,6795,6799,6850,6861,6863,6867,6884,6885,6921,6933,6964,6998,7052,7080,7135,7156,7165,7168,7223,7231,7289,7291,7306,7316,7317,7318,7337,7343,7345,7395,7405,7408,7424,7476,7478,7481,7524,7525,7543,7610,7629,7652,7676,7691,7706,7717,7726,7727,7756,7759,7761,7771,7809,7820,7845,7903,7937,7969,8016,8032,8048,8049,8124,8177,8196,8220,8240,8264,8362,8364,8370,8386,8390,8406,8429,8440,8442,8457,8463,8467,8490,8504,8505,8521,8522,8527,8528,8529,8530,8531,8549,8550,8551,8559,8573,8575,8587,8591,8593,8594,8595,8603,8608,8635,8636,8668,8681,8685,8703,8725,8726,8727,8728,8740,8741,8763,8773,8783,8784,8785,8786,8788,8809,8810,8821,8865,8871,8877,8889,8894,8896,8899,8900,8904,8914,8997,9028,9029,9030,9045,9063,9068,9096,9097,9138,9141,9167,9212,9213,9214,9229,9256,9270,9276,9279,9301,9302,9330,9391,9426,9427,9428,9453,9454,9472,9491,9497,9511,9534,9556,9564,9565,9566,9567,9582,9584,9589,9620,9621,9627,9628,9672,9673,9705,9714,9724,9726,9727,9736,9750,9753,9781,9814,9816,9820,9878,9919,9920,9922,9932,9933,9953,9958,9999,10050,10122,10123,10176,10192,2,8,9,4581,4582,4600,4631,4633,4634,4661,4667,4668,4679,4728,4730,4760,4774,4804,4900,4901,4914,4934,4990,4991,4994,4995,4997,4999,5000,5009,5013,5014,5024,5036,5037,5043,5063,5064,5081,5086,5087,5088,5089,5092,5100,5103,5110,5175,5181,5182,5189,5219,5230,5236,5252,5272,5273,5280,5281,5282,5291,5301,5308,5310,5311,5317,5324,5325,5338,5339,5340,5341,5343,5344,5349,5350,5351,5352,5383,5384,5385,5393,5394,5395,5396,5439,5444,5446,5482,5484,5485,5487,5488,5490,5491,5493,5502,5507,5509,5510,5511,5512,5513,5514,5521,5531,5534,5545,5561,5562,5565,5575,5577,5578,5579,5604,5614,5630,5631,5641,5642,5644,5646,5651,5686,5691,5693,5753,5787,5788,5792,5798,5801,5802,5803,5804,5810,5821,5822,5824,5825,5833,5854,5885,5901,5904,5905,5907,5916,5934,5938,5941,5942,5943,5961,5972,5973,6001,6002,6006,6026,6029,6033,6052,6057,6058,6083,6086,6094,6102,6108,6112,6119,6120,6121,6122])).
% 187.33/188.09 cnf(11736,plain,
% 187.33/188.09 (P24(f329(f329(f243(a1),f45(a874,x117361,f193(a874))),x117361))),
% 187.33/188.09 inference(scs_inference,[],[4323,3521,4492,4493,4459,10208,10218,10229,10240,10341,10344,10347,10450,10563,10866,11030,11033,11230,11317,11324,11338,11390,11393,11437,11503,11549,4474,10434,10527,3193,2873,2874,2877,2880,2881,2884,2885,2892,2895,2896,2903,2904,2909,2917,2920,2932,2944,2952,2953,2954,2974,3010,3019,3020,3022,3029,3035,3047,3053,3065,4455,3847,11596,3118,11314,3234,10211,10275,10278,10368,10371,10664,11329,11332,11448,11490,11495,3212,3740,3108,3484,3832,11364,3169,3136,3131,3115,3116,3337,3205,3229,10475,3383,4541,3919,4484,10266,10431,3267,11685,4530,10980,11050,11273,11276,3384,3166,10333,10640,3167,3442,3087,3189,11354,4066,3921,10986,11112,11162,4553,10918,11117,11221,11243,11281,11287,4554,11019,11120,11224,4555,11123,4556,11176,4557,3188,3482,3644,4350,4351,4482,3583,3796,3347,10352,10470,10541,10602,10605,10643,10737,10970,3733,11582,3260,3359,4524,10243,10246,10272,10745,10758,10876,11265,11357,4536,11467,11498,11533,3720,3491,3869,3306,3308,3281,4521,4479,3474,4537,4060,11238,3604,3320,11709,4030,3982,3645,4019,3663,10992,11055,11136,4542,10761,11128,3276,10361,10457,10588,10650,10719,10764,10767,10800,10823,10860,10898,10934,11656,3277,10390,10445,10655,10740,10863,11440,3280,3355,4520,10309,10399,10512,10536,10782,10826,10836,11512,11610,11631,11634,11637,3437,10608,10871,10915,11184,11262,11425,4532,10791,10803,10907,10925,10928,10983,11069,11077,11093,11131,11148,11156,11192,11233,11253,11256,11259,11290,11297,11300,11682,3341,10637,10667,10676,3379,3373,3800,3738,10312,11585,4529,10263,10625,10628,11072,11090,11548,11601,11641,11666,3300,10670,10820,10891,3761,4110,4527,3808,4510,4513,3251,3255,4512,4511,4515,3594,4209,4544,10234,10237,10493,10544,10547,10552,10957,11419,4551,11151,11270,3996,3886,11303,11640,11644,3727,10931,10937,3729,10673,11008,11159,11189,3547,10591,10594,10679,10847,4548,11579,4538,4549,10730,10829,11139,11422,4170,4071,3760,3707,4546,10285,10288,10631,10634,11464,4547,11559,3731,10597,4003,4568,4594,4643,4645,4675,4692,4699,4700,4739,4769,4775,4860,4885,4886,4921,4946,4947,4969,4970,4983,4987,5010,5017,5035,5038,5039,5040,5045,5046,5068,5093,5094,5104,5109,5115,5160,5161,5169,5178,5183,5185,5195,5197,5203,5207,5222,5229,5232,5233,5234,5238,5274,5287,5295,5297,5298,5302,5303,5304,5312,5315,5319,5320,5321,5328,5332,5333,5334,5342,5346,5347,5348,5353,5366,5375,5387,5389,5397,5398,5402,5406,5431,5437,5447,5448,5463,5475,5497,5503,5519,5520,5523,5542,5550,5551,5556,5557,5567,5569,5581,5585,5594,5595,5597,5612,5617,5627,5628,5640,5647,5661,5665,5668,5674,5675,5676,5679,5684,5722,5723,5726,5728,5731,5732,5733,5735,5737,5739,5744,5751,5766,5780,5785,5786,5799,5800,5805,5809,5811,5816,5857,5869,5878,5882,5893,5897,5898,5906,5920,5926,5944,5947,5959,5985,5999,6024,6044,6045,6048,6062,6064,6066,6068,6081,6082,6085,6087,6090,6091,6103,6109,6110,6111,6113,6115,6158,6159,6166,6172,6176,6212,6214,6216,6218,6227,6229,6231,6237,6239,6245,6248,6256,6263,6264,6265,6270,6292,6293,6294,6296,6302,6307,6341,6342,6344,6345,6346,6348,6349,6350,6351,6358,6391,6392,6401,6422,6423,6443,6446,6457,6458,6464,6495,6497,6511,6549,6551,6552,6606,6630,6672,6692,6701,6702,6703,6704,6723,6724,6730,6743,6746,6748,6750,6751,6752,6754,6768,6779,6781,6782,6795,6799,6850,6861,6863,6867,6884,6885,6921,6933,6964,6998,7052,7080,7135,7156,7165,7168,7223,7231,7289,7291,7306,7316,7317,7318,7337,7343,7345,7395,7405,7408,7424,7476,7478,7481,7524,7525,7543,7610,7629,7652,7676,7691,7706,7717,7726,7727,7756,7759,7761,7771,7809,7820,7845,7903,7937,7969,8016,8032,8048,8049,8124,8177,8196,8220,8240,8264,8362,8364,8370,8386,8390,8406,8429,8440,8442,8457,8463,8467,8490,8504,8505,8521,8522,8527,8528,8529,8530,8531,8549,8550,8551,8559,8573,8575,8587,8591,8593,8594,8595,8603,8608,8635,8636,8668,8681,8685,8703,8725,8726,8727,8728,8740,8741,8763,8773,8783,8784,8785,8786,8788,8809,8810,8821,8865,8871,8877,8889,8894,8896,8899,8900,8904,8914,8997,9028,9029,9030,9045,9063,9068,9096,9097,9138,9141,9167,9212,9213,9214,9229,9256,9270,9276,9279,9301,9302,9330,9391,9426,9427,9428,9453,9454,9472,9491,9497,9511,9534,9556,9564,9565,9566,9567,9582,9584,9589,9620,9621,9627,9628,9672,9673,9705,9714,9724,9726,9727,9736,9750,9753,9781,9814,9816,9820,9878,9919,9920,9922,9932,9933,9953,9958,9999,10050,10122,10123,10176,10192,2,8,9,4581,4582,4600,4631,4633,4634,4661,4667,4668,4679,4728,4730,4760,4774,4804,4900,4901,4914,4934,4990,4991,4994,4995,4997,4999,5000,5009,5013,5014,5024,5036,5037,5043,5063,5064,5081,5086,5087,5088,5089,5092,5100,5103,5110,5175,5181,5182,5189,5219,5230,5236,5252,5272,5273,5280,5281,5282,5291,5301,5308,5310,5311,5317,5324,5325,5338,5339,5340,5341,5343,5344,5349,5350,5351,5352,5383,5384,5385,5393,5394,5395,5396,5439,5444,5446,5482,5484,5485,5487,5488,5490,5491,5493,5502,5507,5509,5510,5511,5512,5513,5514,5521,5531,5534,5545,5561,5562,5565,5575,5577,5578,5579,5604,5614,5630,5631,5641,5642,5644,5646,5651,5686,5691,5693,5753,5787,5788,5792,5798,5801,5802,5803,5804,5810,5821,5822,5824,5825,5833,5854,5885,5901,5904,5905,5907,5916,5934,5938,5941,5942,5943,5961,5972,5973,6001,6002,6006,6026,6029,6033,6052,6057,6058,6083,6086,6094,6102,6108,6112,6119,6120,6121,6122,6161])).
% 187.33/188.09 cnf(11737,plain,
% 187.33/188.09 (P24(f329(f329(f243(a1),x117371),x117371))),
% 187.33/188.09 inference(rename_variables,[],[3277])).
% 187.33/188.09 cnf(11740,plain,
% 187.33/188.09 (P24(f329(f329(f243(a1),x117401),x117401))),
% 187.33/188.09 inference(rename_variables,[],[3277])).
% 187.33/188.09 cnf(11749,plain,
% 187.33/188.09 (P24(f329(f329(f243(a1),x117491),x117491))),
% 187.33/188.09 inference(rename_variables,[],[3277])).
% 187.33/188.09 cnf(11752,plain,
% 187.33/188.09 (~P24(f329(f329(f244(a874),x117521),f2(a874)))),
% 187.33/188.09 inference(rename_variables,[],[4524])).
% 187.33/188.09 cnf(11757,plain,
% 187.33/188.09 (~P24(f329(f329(f244(a874),x117571),f2(a874)))),
% 187.33/188.09 inference(rename_variables,[],[4524])).
% 187.33/188.09 cnf(11764,plain,
% 187.33/188.09 (P24(f329(f252(f881(x117641,a869)),x117642))),
% 187.33/188.09 inference(rename_variables,[],[3341])).
% 187.33/188.09 cnf(11769,plain,
% 187.33/188.09 (P24(f329(f329(f243(a874),f2(a874)),x117691))),
% 187.33/188.09 inference(rename_variables,[],[3300])).
% 187.33/188.09 cnf(11770,plain,
% 187.33/188.09 (~P24(f329(f329(f243(a874),f329(a117,x117701)),x117701))),
% 187.33/188.09 inference(rename_variables,[],[4529])).
% 187.33/188.09 cnf(11773,plain,
% 187.33/188.09 (~P24(f329(f63(x117731,x117732,f193(f881(x117731,a869))),x117733))),
% 187.33/188.09 inference(rename_variables,[],[4544])).
% 187.33/188.09 cnf(11792,plain,
% 187.33/188.09 (P24(f329(f329(f244(a1),f329(f79(a1),f78(a1))),f2(a1)))),
% 187.33/188.09 inference(scs_inference,[],[4323,3521,4492,4493,4459,10208,10218,10229,10240,10341,10344,10347,10450,10563,10866,11030,11033,11230,11317,11324,11338,11390,11393,11437,11503,11549,4474,10434,10527,3193,2873,2874,2877,2880,2881,2884,2885,2892,2895,2896,2903,2904,2908,2909,2917,2920,2932,2944,2952,2953,2954,2961,2974,3010,3019,3020,3022,3029,3035,3037,3047,3053,3065,4455,3847,11596,3118,11314,3234,10211,10275,10278,10368,10371,10664,11329,11332,11448,11490,11495,3212,3740,3108,3484,3832,11364,3169,3136,3131,3115,3116,3337,3205,3229,10475,3383,4541,3919,4484,10266,10431,3267,11685,4530,10980,11050,11273,11276,3384,3166,10333,10640,3167,3442,3087,3189,11354,4066,3921,10986,11112,11162,4553,10918,11117,11221,11243,11281,11287,4554,11019,11120,11224,4555,11123,4556,11176,4557,3188,3482,3644,4350,4351,4482,3583,3796,3347,10352,10470,10541,10602,10605,10643,10737,10970,3733,11582,3260,3359,4524,10243,10246,10272,10745,10758,10876,11265,11357,11752,11757,4536,11467,11498,11533,11562,3720,3491,3869,3306,3308,3281,4521,4479,3474,4537,4060,11238,3604,3320,11709,4030,3982,3645,4019,3663,10992,11055,11136,4542,10761,11128,3276,10361,10457,10588,10650,10719,10764,10767,10800,10823,10860,10898,10934,11656,3277,10390,10445,10655,10740,10863,11440,11737,11740,3280,3355,4520,10309,10399,10512,10536,10782,10826,10836,11512,11610,11631,11634,11637,3437,10608,10871,10915,11184,11262,11425,4532,10791,10803,10907,10925,10928,10983,11069,11077,11093,11131,11148,11156,11192,11233,11253,11256,11259,11290,11297,11300,11682,3341,10637,10667,10676,11213,3379,3373,3800,3738,10312,11585,11613,4529,10263,10625,10628,11072,11090,11548,11601,11641,11666,3300,10670,10820,10891,11614,3761,4110,4527,3808,4510,4513,3251,3255,4512,4511,4515,3594,4209,4544,10234,10237,10493,10544,10547,10552,10957,11419,11669,11773,4551,11151,11270,3996,3886,11303,11640,11644,3727,10931,10937,3729,10673,11008,11159,11189,3547,10591,10594,10679,10847,4548,11579,4538,4549,10730,10829,11139,11422,4170,4071,3760,3707,4546,10285,10288,10631,10634,11464,4547,11559,3731,10597,4003,4568,4594,4643,4645,4675,4692,4699,4700,4739,4769,4775,4860,4885,4886,4921,4946,4947,4969,4970,4983,4987,5010,5017,5035,5038,5039,5040,5045,5046,5068,5093,5094,5104,5109,5115,5160,5161,5169,5178,5183,5185,5195,5197,5203,5207,5222,5229,5232,5233,5234,5238,5274,5287,5295,5297,5298,5302,5303,5304,5312,5315,5319,5320,5321,5328,5332,5333,5334,5342,5346,5347,5348,5353,5366,5375,5387,5389,5397,5398,5402,5406,5431,5437,5447,5448,5463,5475,5497,5503,5519,5520,5523,5542,5550,5551,5556,5557,5567,5569,5581,5585,5594,5595,5597,5612,5617,5627,5628,5640,5647,5661,5665,5668,5674,5675,5676,5679,5684,5722,5723,5726,5728,5731,5732,5733,5735,5737,5739,5744,5751,5766,5780,5785,5786,5799,5800,5805,5809,5811,5816,5857,5869,5878,5882,5893,5897,5898,5906,5920,5926,5944,5947,5959,5985,5999,6024,6044,6045,6048,6062,6064,6066,6068,6081,6082,6085,6087,6090,6091,6103,6109,6110,6111,6113,6115,6158,6159,6166,6172,6176,6212,6214,6216,6218,6227,6229,6231,6237,6239,6245,6248,6256,6263,6264,6265,6270,6292,6293,6294,6296,6302,6307,6341,6342,6344,6345,6346,6348,6349,6350,6351,6358,6391,6392,6401,6422,6423,6443,6446,6457,6458,6464,6495,6497,6511,6549,6551,6552,6606,6630,6672,6692,6701,6702,6703,6704,6723,6724,6730,6743,6746,6748,6750,6751,6752,6754,6768,6779,6781,6782,6795,6799,6850,6861,6863,6867,6884,6885,6921,6933,6964,6998,7052,7080,7135,7156,7165,7168,7223,7231,7289,7291,7306,7316,7317,7318,7337,7343,7345,7395,7405,7408,7424,7476,7478,7481,7524,7525,7543,7610,7629,7652,7676,7691,7706,7717,7726,7727,7756,7759,7761,7771,7809,7820,7845,7903,7937,7969,8016,8032,8048,8049,8124,8177,8196,8220,8240,8264,8362,8364,8370,8386,8390,8406,8429,8440,8442,8457,8463,8467,8490,8504,8505,8521,8522,8527,8528,8529,8530,8531,8549,8550,8551,8559,8573,8575,8587,8591,8593,8594,8595,8603,8608,8635,8636,8668,8681,8685,8703,8725,8726,8727,8728,8740,8741,8763,8773,8783,8784,8785,8786,8788,8809,8810,8821,8865,8871,8877,8889,8894,8896,8899,8900,8904,8914,8997,9028,9029,9030,9045,9063,9068,9096,9097,9138,9141,9167,9212,9213,9214,9229,9256,9270,9276,9279,9301,9302,9330,9391,9426,9427,9428,9453,9454,9472,9491,9497,9511,9534,9556,9564,9565,9566,9567,9582,9584,9589,9620,9621,9627,9628,9672,9673,9705,9714,9724,9726,9727,9736,9750,9753,9781,9814,9816,9820,9878,9919,9920,9922,9932,9933,9953,9958,9999,10050,10122,10123,10176,10192,2,8,9,4581,4582,4600,4631,4633,4634,4661,4667,4668,4679,4728,4730,4760,4774,4804,4900,4901,4914,4934,4990,4991,4994,4995,4997,4999,5000,5009,5013,5014,5024,5036,5037,5043,5063,5064,5081,5086,5087,5088,5089,5092,5100,5103,5110,5175,5181,5182,5189,5219,5230,5236,5252,5272,5273,5280,5281,5282,5291,5301,5308,5310,5311,5317,5324,5325,5338,5339,5340,5341,5343,5344,5349,5350,5351,5352,5383,5384,5385,5393,5394,5395,5396,5439,5444,5446,5482,5484,5485,5487,5488,5490,5491,5493,5502,5507,5509,5510,5511,5512,5513,5514,5521,5531,5534,5545,5561,5562,5565,5575,5577,5578,5579,5604,5614,5630,5631,5641,5642,5644,5646,5651,5686,5691,5693,5753,5787,5788,5792,5798,5801,5802,5803,5804,5810,5821,5822,5824,5825,5833,5854,5885,5901,5904,5905,5907,5916,5934,5938,5941,5942,5943,5961,5972,5973,6001,6002,6006,6026,6029,6033,6052,6057,6058,6083,6086,6094,6102,6108,6112,6119,6120,6121,6122,6161,6177,6230,6266,6268,6289,6290,6295,6299,6300,6303,6309,6318,6333,6353,6354,6359,6369,6384,6404,6410,6412,6427,6428])).
% 187.33/188.09 cnf(11795,plain,
% 187.33/188.09 (~P24(f329(f329(f243(a874),f329(a117,x117951)),x117951))),
% 187.33/188.09 inference(rename_variables,[],[4529])).
% 187.33/188.09 cnf(11798,plain,
% 187.33/188.09 (~P24(f329(f329(f243(a874),f329(a117,x117981)),x117981))),
% 187.33/188.09 inference(rename_variables,[],[4529])).
% 187.33/188.09 cnf(11801,plain,
% 187.33/188.09 (~P24(f329(f329(f243(a874),f329(a117,x118011)),x118011))),
% 187.33/188.09 inference(rename_variables,[],[4529])).
% 187.33/188.09 cnf(11804,plain,
% 187.33/188.09 (~P24(f329(f329(f243(a874),f329(a117,x118041)),x118041))),
% 187.33/188.09 inference(rename_variables,[],[4529])).
% 187.33/188.09 cnf(11807,plain,
% 187.33/188.09 (~P24(f329(f329(f244(a874),x118071),x118071))),
% 187.33/188.09 inference(rename_variables,[],[4520])).
% 187.33/188.09 cnf(11810,plain,
% 187.33/188.09 (~P24(f329(f329(f244(a874),x118101),x118101))),
% 187.33/188.09 inference(rename_variables,[],[4520])).
% 187.33/188.09 cnf(11813,plain,
% 187.33/188.09 (~P24(f329(f329(f244(a874),x118131),x118131))),
% 187.33/188.09 inference(rename_variables,[],[4520])).
% 187.33/188.09 cnf(11816,plain,
% 187.33/188.09 (~P24(f329(f329(f244(a874),x118161),x118161))),
% 187.33/188.09 inference(rename_variables,[],[4520])).
% 187.33/188.09 cnf(11832,plain,
% 187.33/188.09 (P24(f329(f329(f243(a874),f329(f329(f22(a874),x118321),f329(a117,x118321))),f2(a874)))),
% 187.33/188.09 inference(scs_inference,[],[4323,3521,4492,4493,4459,10208,10218,10229,10240,10341,10344,10347,10450,10563,10866,11030,11033,11230,11317,11324,11338,11390,11393,11437,11503,11549,4474,10434,10527,3193,2873,2874,2877,2880,2881,2884,2885,2892,2895,2896,2903,2904,2908,2909,2917,2920,2932,2944,2952,2953,2954,2961,2974,3010,3019,3020,3022,3029,3035,3037,3047,3053,3065,4455,3847,11596,3118,11314,3234,10211,10275,10278,10368,10371,10664,11329,11332,11448,11490,11495,3212,3740,3108,3484,3832,11364,3169,3136,3131,3115,3116,3337,3205,3229,10475,3383,4541,3919,4484,10266,10431,3267,11685,4530,10980,11050,11273,11276,3384,3166,10333,10640,3167,3442,3087,3189,11354,4066,3921,10986,11112,11162,4553,10918,11117,11221,11243,11281,11287,4554,11019,11120,11224,4555,11123,4556,11176,4557,3188,3482,3644,4350,4351,4482,3583,3796,3347,10352,10470,10541,10602,10605,10643,10737,10970,3733,11582,3260,3359,4524,10243,10246,10272,10745,10758,10876,11265,11357,11752,11757,4536,11467,11498,11533,11562,3720,3491,3869,3306,3308,3281,4521,4479,3474,4537,4060,11238,3604,3320,11709,4030,3982,3645,4019,3663,10992,11055,11136,4542,10761,11128,3276,10361,10457,10588,10650,10719,10764,10767,10800,10823,10860,10898,10934,11656,11703,3277,10390,10445,10655,10740,10863,11440,11737,11740,3280,3355,4520,10309,10399,10512,10536,10782,10826,10836,11512,11610,11631,11634,11637,11653,11807,11810,11813,3437,10608,10871,10915,11184,11262,11425,4532,10791,10803,10907,10925,10928,10983,11069,11077,11093,11131,11148,11156,11192,11233,11253,11256,11259,11290,11297,11300,11682,3341,10637,10667,10676,11213,3379,3373,3800,3738,10312,11585,11613,4529,10263,10625,10628,11072,11090,11548,11601,11641,11666,11770,11795,11798,11801,3300,10670,10820,10891,11614,3761,4110,4527,3808,4510,4513,3251,3255,4512,4511,4515,3594,4209,4544,10234,10237,10493,10544,10547,10552,10957,11419,11669,11773,4551,11151,11270,3996,3886,11303,11640,11644,3727,10931,10937,3729,10673,11008,11159,11189,3547,10591,10594,10679,10847,4548,11579,4538,4549,10730,10829,11139,11422,4170,4071,3760,3707,4546,10285,10288,10631,10634,11464,4547,11559,3731,10597,4003,4568,4594,4643,4645,4675,4692,4699,4700,4739,4769,4775,4860,4885,4886,4921,4946,4947,4969,4970,4983,4987,5010,5017,5035,5038,5039,5040,5045,5046,5068,5093,5094,5104,5109,5115,5160,5161,5169,5178,5183,5185,5195,5197,5203,5207,5222,5229,5232,5233,5234,5238,5274,5287,5295,5297,5298,5302,5303,5304,5312,5315,5319,5320,5321,5328,5332,5333,5334,5342,5346,5347,5348,5353,5366,5375,5387,5389,5397,5398,5402,5406,5431,5437,5447,5448,5463,5475,5497,5503,5519,5520,5523,5542,5550,5551,5556,5557,5567,5569,5581,5585,5594,5595,5597,5612,5617,5627,5628,5640,5647,5661,5665,5668,5674,5675,5676,5679,5684,5722,5723,5726,5728,5731,5732,5733,5735,5737,5739,5744,5751,5766,5780,5785,5786,5799,5800,5805,5809,5811,5816,5857,5869,5878,5882,5893,5897,5898,5906,5920,5926,5944,5947,5959,5985,5999,6024,6044,6045,6048,6062,6064,6066,6068,6081,6082,6085,6087,6090,6091,6103,6109,6110,6111,6113,6115,6158,6159,6166,6172,6176,6212,6214,6216,6218,6227,6229,6231,6237,6239,6245,6248,6256,6263,6264,6265,6270,6292,6293,6294,6296,6302,6307,6341,6342,6344,6345,6346,6348,6349,6350,6351,6358,6391,6392,6401,6422,6423,6443,6446,6457,6458,6464,6495,6497,6511,6549,6551,6552,6606,6630,6672,6692,6701,6702,6703,6704,6723,6724,6730,6743,6746,6748,6750,6751,6752,6754,6768,6779,6781,6782,6795,6799,6850,6861,6863,6867,6884,6885,6921,6933,6964,6998,7052,7080,7135,7156,7165,7168,7223,7231,7289,7291,7306,7316,7317,7318,7337,7343,7345,7395,7405,7408,7424,7476,7478,7481,7524,7525,7543,7610,7629,7652,7676,7691,7706,7717,7726,7727,7756,7759,7761,7771,7809,7820,7845,7903,7937,7969,8016,8032,8048,8049,8124,8177,8196,8220,8240,8264,8362,8364,8370,8386,8390,8406,8429,8440,8442,8457,8463,8467,8490,8504,8505,8521,8522,8527,8528,8529,8530,8531,8549,8550,8551,8559,8573,8575,8587,8591,8593,8594,8595,8603,8608,8635,8636,8668,8681,8685,8703,8725,8726,8727,8728,8740,8741,8763,8773,8783,8784,8785,8786,8788,8809,8810,8821,8865,8871,8877,8889,8894,8896,8899,8900,8904,8914,8997,9028,9029,9030,9045,9063,9068,9096,9097,9138,9141,9167,9212,9213,9214,9229,9256,9270,9276,9279,9301,9302,9330,9391,9426,9427,9428,9453,9454,9472,9491,9497,9511,9534,9556,9564,9565,9566,9567,9582,9584,9589,9620,9621,9627,9628,9672,9673,9705,9714,9724,9726,9727,9736,9750,9753,9781,9814,9816,9820,9878,9919,9920,9922,9932,9933,9953,9958,9999,10050,10122,10123,10176,10192,2,8,9,4581,4582,4600,4631,4633,4634,4661,4667,4668,4679,4728,4730,4760,4774,4804,4900,4901,4914,4934,4990,4991,4994,4995,4997,4999,5000,5009,5013,5014,5024,5036,5037,5043,5063,5064,5081,5086,5087,5088,5089,5092,5100,5103,5110,5175,5181,5182,5189,5219,5230,5236,5252,5272,5273,5280,5281,5282,5291,5301,5308,5310,5311,5317,5324,5325,5338,5339,5340,5341,5343,5344,5349,5350,5351,5352,5383,5384,5385,5393,5394,5395,5396,5439,5444,5446,5482,5484,5485,5487,5488,5490,5491,5493,5502,5507,5509,5510,5511,5512,5513,5514,5521,5531,5534,5545,5561,5562,5565,5575,5577,5578,5579,5604,5614,5630,5631,5641,5642,5644,5646,5651,5686,5691,5693,5753,5787,5788,5792,5798,5801,5802,5803,5804,5810,5821,5822,5824,5825,5833,5854,5885,5901,5904,5905,5907,5916,5934,5938,5941,5942,5943,5961,5972,5973,6001,6002,6006,6026,6029,6033,6052,6057,6058,6083,6086,6094,6102,6108,6112,6119,6120,6121,6122,6161,6177,6230,6266,6268,6289,6290,6295,6299,6300,6303,6309,6318,6333,6353,6354,6359,6369,6384,6404,6410,6412,6427,6428,6431,6432,6434,6436,6437,6438,6440,6442,6445,6450,6451,6453,6454,6460,6462,6505])).
% 187.33/188.09 cnf(11833,plain,
% 187.33/188.09 (P24(f329(f329(f243(a874),x118331),x118331))),
% 187.33/188.09 inference(rename_variables,[],[3276])).
% 187.33/188.09 cnf(11838,plain,
% 187.33/188.09 (P24(f329(f329(f243(a1),x118381),f329(f75(a1),x118381)))),
% 187.33/188.09 inference(scs_inference,[],[4323,3521,4492,4493,4459,10208,10218,10229,10240,10341,10344,10347,10450,10563,10866,11030,11033,11230,11317,11324,11338,11390,11393,11437,11503,11549,4474,10434,10527,3490,3193,2873,2874,2877,2880,2881,2884,2885,2892,2895,2896,2903,2904,2908,2909,2917,2920,2932,2944,2952,2953,2954,2961,2974,3010,3019,3020,3022,3029,3035,3037,3047,3053,3065,4455,3847,11596,3118,11314,3234,10211,10275,10278,10368,10371,10664,11329,11332,11448,11490,11495,3212,3740,3108,3484,3832,11364,3169,3136,3131,3115,3116,3337,3205,3229,10475,3383,4541,3919,4484,10266,10431,3267,11685,4530,10980,11050,11273,11276,3384,3166,10333,10640,3167,3442,3087,3189,11354,4066,3921,10986,11112,11162,4553,10918,11117,11221,11243,11281,11287,4554,11019,11120,11224,4555,11123,4556,11176,4557,3188,3482,3644,4350,4351,4482,3583,3796,3347,10352,10470,10541,10602,10605,10643,10737,10970,3733,11582,3260,3359,4524,10243,10246,10272,10745,10758,10876,11265,11357,11752,11757,4536,11467,11498,11533,11562,3720,3491,3869,3306,3308,3281,4521,4479,3474,4537,4060,11238,3604,3320,11709,4030,3982,3645,4019,3663,10992,11055,11136,4542,10761,11128,3276,10361,10457,10588,10650,10719,10764,10767,10800,10823,10860,10898,10934,11656,11703,3277,10390,10445,10655,10740,10863,11440,11737,11740,11749,3280,3355,4520,10309,10399,10512,10536,10782,10826,10836,11512,11610,11631,11634,11637,11653,11807,11810,11813,3437,10608,10871,10915,11184,11262,11425,4532,10791,10803,10907,10925,10928,10983,11069,11077,11093,11131,11148,11156,11192,11233,11253,11256,11259,11290,11297,11300,11682,3341,10637,10667,10676,11213,3379,3373,3800,3738,10312,11585,11613,4529,10263,10625,10628,11072,11090,11548,11601,11641,11666,11770,11795,11798,11801,3300,10670,10820,10891,11614,3761,4110,4527,3808,4510,4513,3251,3255,4512,4511,4515,3594,4209,4544,10234,10237,10493,10544,10547,10552,10957,11419,11669,11773,4551,11151,11270,3996,3886,11303,11640,11644,3727,10931,10937,3729,10673,11008,11159,11189,3547,10591,10594,10679,10847,4548,11579,4538,4549,10730,10829,11139,11422,4170,4071,3760,3707,4546,10285,10288,10631,10634,11464,4547,11559,3731,10597,4003,4568,4594,4643,4645,4675,4692,4699,4700,4739,4769,4775,4860,4885,4886,4921,4946,4947,4969,4970,4983,4987,5010,5017,5035,5038,5039,5040,5045,5046,5068,5093,5094,5104,5109,5115,5160,5161,5169,5178,5183,5185,5195,5197,5203,5207,5222,5229,5232,5233,5234,5238,5274,5287,5295,5297,5298,5302,5303,5304,5312,5315,5319,5320,5321,5328,5332,5333,5334,5342,5346,5347,5348,5353,5366,5375,5387,5389,5397,5398,5402,5406,5431,5437,5447,5448,5463,5475,5497,5503,5519,5520,5523,5542,5550,5551,5556,5557,5567,5569,5581,5585,5594,5595,5597,5612,5617,5627,5628,5640,5647,5661,5665,5668,5674,5675,5676,5679,5684,5722,5723,5726,5728,5731,5732,5733,5735,5737,5739,5744,5751,5766,5780,5785,5786,5799,5800,5805,5809,5811,5816,5857,5869,5878,5882,5893,5897,5898,5906,5920,5926,5944,5947,5959,5985,5999,6024,6044,6045,6048,6062,6064,6066,6068,6081,6082,6085,6087,6090,6091,6103,6109,6110,6111,6113,6115,6158,6159,6166,6172,6176,6212,6214,6216,6218,6227,6229,6231,6237,6239,6245,6248,6256,6263,6264,6265,6270,6292,6293,6294,6296,6302,6307,6341,6342,6344,6345,6346,6348,6349,6350,6351,6358,6391,6392,6401,6422,6423,6443,6446,6457,6458,6464,6495,6497,6511,6549,6551,6552,6606,6630,6672,6692,6701,6702,6703,6704,6723,6724,6730,6743,6746,6748,6750,6751,6752,6754,6768,6779,6781,6782,6795,6799,6850,6861,6863,6867,6884,6885,6921,6933,6964,6998,7052,7080,7135,7156,7165,7168,7223,7231,7289,7291,7306,7316,7317,7318,7337,7343,7345,7395,7405,7408,7424,7476,7478,7481,7524,7525,7543,7610,7629,7652,7676,7691,7706,7717,7726,7727,7756,7759,7761,7771,7809,7820,7845,7903,7937,7969,8016,8032,8048,8049,8124,8177,8196,8220,8240,8264,8362,8364,8370,8386,8390,8406,8429,8440,8442,8457,8463,8467,8490,8504,8505,8521,8522,8527,8528,8529,8530,8531,8549,8550,8551,8559,8573,8575,8587,8591,8593,8594,8595,8603,8608,8635,8636,8668,8681,8685,8703,8725,8726,8727,8728,8740,8741,8763,8773,8783,8784,8785,8786,8788,8809,8810,8821,8865,8871,8877,8889,8894,8896,8899,8900,8904,8914,8997,9028,9029,9030,9045,9063,9068,9096,9097,9138,9141,9167,9212,9213,9214,9229,9256,9270,9276,9279,9301,9302,9330,9391,9426,9427,9428,9453,9454,9472,9491,9497,9511,9534,9556,9564,9565,9566,9567,9582,9584,9589,9620,9621,9627,9628,9672,9673,9705,9714,9724,9726,9727,9736,9750,9753,9781,9814,9816,9820,9878,9919,9920,9922,9932,9933,9953,9958,9999,10050,10122,10123,10176,10192,2,8,9,4581,4582,4600,4631,4633,4634,4661,4667,4668,4679,4728,4730,4760,4774,4804,4900,4901,4914,4934,4990,4991,4994,4995,4997,4999,5000,5009,5013,5014,5024,5036,5037,5043,5063,5064,5081,5086,5087,5088,5089,5092,5100,5103,5110,5175,5181,5182,5189,5219,5230,5236,5252,5272,5273,5280,5281,5282,5291,5301,5308,5310,5311,5317,5324,5325,5338,5339,5340,5341,5343,5344,5349,5350,5351,5352,5383,5384,5385,5393,5394,5395,5396,5439,5444,5446,5482,5484,5485,5487,5488,5490,5491,5493,5502,5507,5509,5510,5511,5512,5513,5514,5521,5531,5534,5545,5561,5562,5565,5575,5577,5578,5579,5604,5614,5630,5631,5641,5642,5644,5646,5651,5686,5691,5693,5753,5787,5788,5792,5798,5801,5802,5803,5804,5810,5821,5822,5824,5825,5833,5854,5885,5901,5904,5905,5907,5916,5934,5938,5941,5942,5943,5961,5972,5973,6001,6002,6006,6026,6029,6033,6052,6057,6058,6083,6086,6094,6102,6108,6112,6119,6120,6121,6122,6161,6177,6230,6266,6268,6289,6290,6295,6299,6300,6303,6309,6318,6333,6353,6354,6359,6369,6384,6404,6410,6412,6427,6428,6431,6432,6434,6436,6437,6438,6440,6442,6445,6450,6451,6453,6454,6460,6462,6505,6510,6524])).
% 187.33/188.09 cnf(11839,plain,
% 187.33/188.09 (P24(f329(f329(f243(a1),x118391),x118391))),
% 187.33/188.09 inference(rename_variables,[],[3277])).
% 187.33/188.09 cnf(11850,plain,
% 187.33/188.09 (P24(f329(f329(f243(a1),x118501),x118501))),
% 187.33/188.09 inference(rename_variables,[],[3277])).
% 187.33/188.09 cnf(11853,plain,
% 187.33/188.09 (P24(f329(f329(f243(f881(f880(f875(x118531),f875(x118531)),a869)),f156(x118531,x118532)),f305(f875(x118531),f155(x118531,x118532))))),
% 187.33/188.09 inference(rename_variables,[],[3987])).
% 187.33/188.09 cnf(11860,plain,
% 187.33/188.09 (P24(f329(f329(f244(a874),x118601),f329(a117,x118601)))),
% 187.33/188.09 inference(rename_variables,[],[3347])).
% 187.33/188.09 cnf(11863,plain,
% 187.33/188.09 (P24(f329(f329(f331(f881(x118631,a869)),x118632),f329(f306(x118631),x118632)))),
% 187.33/188.09 inference(rename_variables,[],[3645])).
% 187.33/188.09 cnf(11864,plain,
% 187.33/188.09 (~E(f329(a117,x118641),x118641)),
% 187.33/188.09 inference(rename_variables,[],[4459])).
% 187.33/188.09 cnf(11869,plain,
% 187.33/188.09 (P24(f329(f329(f243(a1),x118691),x118691))),
% 187.33/188.09 inference(rename_variables,[],[3277])).
% 187.33/188.09 cnf(11874,plain,
% 187.33/188.09 (P24(f329(f329(f243(a1),x118741),x118741))),
% 187.33/188.09 inference(rename_variables,[],[3277])).
% 187.33/188.09 cnf(11885,plain,
% 187.33/188.09 (P24(f329(f329(f243(f881(x118851,a869)),x118852),f329(f329(f307(x118851),x118853),x118852)))),
% 187.33/188.09 inference(rename_variables,[],[3727])).
% 187.33/188.09 cnf(11888,plain,
% 187.33/188.09 (P24(f329(f329(f243(a874),x118881),x118881))),
% 187.33/188.09 inference(rename_variables,[],[3276])).
% 187.33/188.09 cnf(11889,plain,
% 187.33/188.09 (~E(f329(a117,x118891),x118891)),
% 187.33/188.09 inference(rename_variables,[],[4459])).
% 187.33/188.09 cnf(11900,plain,
% 187.33/188.09 (~P24(f329(f329(f244(a874),x119001),x119001))),
% 187.33/188.09 inference(rename_variables,[],[4520])).
% 187.33/188.09 cnf(11901,plain,
% 187.33/188.09 (~E(f329(a117,x119011),x119011)),
% 187.33/188.09 inference(rename_variables,[],[4459])).
% 187.33/188.09 cnf(11904,plain,
% 187.33/188.09 (P24(f329(f329(f243(a874),x119041),x119041))),
% 187.33/188.09 inference(rename_variables,[],[3276])).
% 187.33/188.09 cnf(11907,plain,
% 187.33/188.09 (P24(f329(f329(f243(a874),x119071),x119071))),
% 187.33/188.09 inference(rename_variables,[],[3276])).
% 187.33/188.09 cnf(11910,plain,
% 187.33/188.09 (P24(f329(f329(f243(a874),x119101),x119101))),
% 187.33/188.09 inference(rename_variables,[],[3276])).
% 187.33/188.09 cnf(11913,plain,
% 187.33/188.09 (P24(f329(f329(f243(a874),x119131),x119131))),
% 187.33/188.09 inference(rename_variables,[],[3276])).
% 187.33/188.09 cnf(11916,plain,
% 187.33/188.09 (P24(f329(f329(f243(a1),x119161),x119161))),
% 187.33/188.09 inference(rename_variables,[],[3277])).
% 187.33/188.09 cnf(11919,plain,
% 187.33/188.09 (~P24(f329(f329(f244(a874),x119191),x119191))),
% 187.33/188.09 inference(rename_variables,[],[4520])).
% 187.33/188.09 cnf(11922,plain,
% 187.33/188.09 (~P24(f329(f329(f244(a874),x119221),x119221))),
% 187.33/188.09 inference(rename_variables,[],[4520])).
% 187.33/188.09 cnf(11923,plain,
% 187.33/188.09 (P24(f329(f329(f244(a874),x119231),f329(a117,x119231)))),
% 187.33/188.09 inference(rename_variables,[],[3347])).
% 187.33/188.09 cnf(11930,plain,
% 187.33/188.09 (~E(f329(a117,x119301),x119301)),
% 187.33/188.09 inference(rename_variables,[],[4459])).
% 187.33/188.09 cnf(11935,plain,
% 187.33/188.09 (~P24(f329(f329(f244(a874),x119351),x119351))),
% 187.33/188.09 inference(rename_variables,[],[4520])).
% 187.33/188.09 cnf(11936,plain,
% 187.33/188.09 (~E(f329(a117,x119361),x119361)),
% 187.33/188.09 inference(rename_variables,[],[4459])).
% 187.33/188.09 cnf(11939,plain,
% 187.33/188.09 (P24(f329(f329(f243(a1),x119391),x119391))),
% 187.33/188.09 inference(rename_variables,[],[3277])).
% 187.33/188.09 cnf(11956,plain,
% 187.33/188.09 (P24(f329(f329(f243(a1),x119561),x119561))),
% 187.33/188.09 inference(rename_variables,[],[3277])).
% 187.33/188.09 cnf(11961,plain,
% 187.33/188.09 (P24(f329(f329(f243(a874),f2(a874)),x119611))),
% 187.33/188.09 inference(rename_variables,[],[3300])).
% 187.33/188.09 cnf(11978,plain,
% 187.33/188.09 (~P24(f329(f329(f244(a874),x119781),f2(a874)))),
% 187.33/188.09 inference(rename_variables,[],[4524])).
% 187.33/188.09 cnf(11981,plain,
% 187.33/188.09 (~P24(f329(f329(f244(a874),x119811),f2(a874)))),
% 187.33/188.09 inference(rename_variables,[],[4524])).
% 187.33/188.09 cnf(11984,plain,
% 187.33/188.09 (~P24(f329(f329(f331(x119841),x119842),f193(f881(x119841,a869))))),
% 187.33/188.09 inference(rename_variables,[],[4532])).
% 187.33/188.09 cnf(11987,plain,
% 187.33/188.09 (~P24(f329(f329(f331(x119871),x119872),f193(f881(x119871,a869))))),
% 187.33/188.09 inference(rename_variables,[],[4532])).
% 187.33/188.09 cnf(11989,plain,
% 187.33/188.09 (~P24(f329(f329(f244(a874),x119891),f329(f329(f106(a874),x119892),x119891)))),
% 187.33/188.09 inference(scs_inference,[],[4323,3521,4492,4493,4459,10208,10218,10229,10240,10341,10344,10347,10450,10563,10866,11030,11033,11230,11317,11324,11338,11390,11393,11437,11503,11549,11565,11864,11889,11901,11930,4474,10434,10527,3490,3193,2873,2874,2877,2880,2881,2884,2885,2892,2895,2896,2903,2904,2908,2909,2917,2920,2932,2944,2952,2953,2954,2961,2974,3010,3019,3020,3022,3029,3035,3037,3047,3053,3065,4455,3847,11596,3118,11314,3234,10211,10275,10278,10368,10371,10664,11329,11332,11448,11490,11495,3212,3219,3740,3979,3108,3484,3832,11364,3169,3136,3131,3115,3116,3337,3205,3229,10475,3383,4541,3919,4484,10266,10431,3267,11685,4530,10980,11050,11273,11276,3384,3166,10333,10640,3167,3442,3087,3189,11354,4066,3921,10986,11112,11162,4553,10918,11117,11221,11243,11281,11287,4554,11019,11120,11224,4555,11123,4556,11176,4557,3188,3482,3644,4350,4351,4482,3583,3796,3347,10352,10470,10541,10602,10605,10643,10737,10970,11860,3733,11582,3260,3359,4524,10243,10246,10272,10745,10758,10876,11265,11357,11752,11757,11978,4536,11467,11498,11533,11562,3720,3491,3869,3306,3308,3281,4521,4479,3474,4537,4060,11238,3604,3320,11709,4030,3987,3982,3645,4019,3663,10992,11055,11136,4542,10761,11128,3276,10361,10457,10588,10650,10719,10764,10767,10800,10823,10860,10898,10934,11656,11703,11833,11888,11904,11907,11910,11913,3277,10390,10445,10655,10740,10863,11440,11737,11740,11749,11839,11850,11869,11874,11916,11939,3280,3355,4520,10309,10399,10512,10536,10782,10826,10836,11512,11610,11631,11634,11637,11653,11807,11810,11813,11816,11900,11919,11922,11935,3437,10608,10871,10915,11184,11262,11425,4532,10791,10803,10907,10925,10928,10983,11069,11077,11093,11131,11148,11156,11192,11233,11253,11256,11259,11290,11297,11300,11682,11718,11984,3341,10637,10667,10676,11213,3379,3373,3800,3738,10312,11585,11613,4529,10263,10625,10628,11072,11090,11548,11601,11641,11666,11770,11795,11798,11801,11804,3300,10670,10820,10891,11614,11769,3761,4110,4527,3772,3808,4510,4513,3251,3255,4512,4511,4515,3779,3594,4209,4544,10234,10237,10493,10544,10547,10552,10957,11419,11669,11773,4551,11151,11270,3996,3886,11303,11640,11644,3727,10931,10937,10952,3729,10673,11008,11159,11189,3547,10591,10594,10679,10847,4548,11579,4538,4549,10730,10829,11139,11422,4170,4071,3760,3707,4546,10285,10288,10631,10634,11464,4547,11559,3731,10597,4003,4568,4594,4643,4645,4675,4692,4699,4700,4739,4769,4775,4860,4885,4886,4921,4946,4947,4969,4970,4983,4987,5010,5017,5035,5038,5039,5040,5045,5046,5068,5093,5094,5104,5109,5115,5160,5161,5169,5178,5183,5185,5195,5197,5203,5207,5222,5229,5232,5233,5234,5238,5274,5287,5295,5297,5298,5302,5303,5304,5312,5315,5319,5320,5321,5328,5332,5333,5334,5342,5346,5347,5348,5353,5366,5375,5387,5389,5397,5398,5402,5406,5431,5437,5447,5448,5463,5475,5497,5503,5519,5520,5523,5542,5550,5551,5556,5557,5567,5569,5581,5585,5594,5595,5597,5612,5617,5627,5628,5640,5647,5661,5665,5668,5674,5675,5676,5679,5684,5722,5723,5726,5728,5731,5732,5733,5735,5737,5739,5744,5751,5766,5780,5785,5786,5799,5800,5805,5809,5811,5816,5857,5869,5878,5882,5893,5897,5898,5906,5920,5926,5944,5947,5959,5985,5999,6024,6044,6045,6048,6062,6064,6066,6068,6081,6082,6085,6087,6090,6091,6103,6109,6110,6111,6113,6115,6158,6159,6166,6172,6176,6212,6214,6216,6218,6227,6229,6231,6237,6239,6245,6248,6256,6263,6264,6265,6270,6292,6293,6294,6296,6302,6307,6341,6342,6344,6345,6346,6348,6349,6350,6351,6358,6391,6392,6401,6422,6423,6443,6446,6457,6458,6464,6495,6497,6511,6549,6551,6552,6606,6630,6672,6692,6701,6702,6703,6704,6723,6724,6730,6743,6746,6748,6750,6751,6752,6754,6768,6779,6781,6782,6795,6799,6850,6861,6863,6867,6884,6885,6921,6933,6964,6998,7052,7080,7135,7156,7165,7168,7223,7231,7289,7291,7306,7316,7317,7318,7337,7343,7345,7395,7405,7408,7424,7476,7478,7481,7524,7525,7543,7610,7629,7652,7676,7691,7706,7717,7726,7727,7756,7759,7761,7771,7809,7820,7845,7903,7937,7969,8016,8032,8048,8049,8124,8177,8196,8220,8240,8264,8362,8364,8370,8386,8390,8406,8429,8440,8442,8457,8463,8467,8490,8504,8505,8521,8522,8527,8528,8529,8530,8531,8549,8550,8551,8559,8573,8575,8587,8591,8593,8594,8595,8603,8608,8635,8636,8668,8681,8685,8703,8725,8726,8727,8728,8740,8741,8763,8773,8783,8784,8785,8786,8788,8809,8810,8821,8865,8871,8877,8889,8894,8896,8899,8900,8904,8914,8997,9028,9029,9030,9045,9063,9068,9096,9097,9138,9141,9167,9212,9213,9214,9229,9256,9270,9276,9279,9301,9302,9330,9391,9426,9427,9428,9453,9454,9472,9491,9497,9511,9534,9556,9564,9565,9566,9567,9582,9584,9589,9620,9621,9627,9628,9672,9673,9705,9714,9724,9726,9727,9736,9750,9753,9781,9814,9816,9820,9878,9919,9920,9922,9932,9933,9953,9958,9999,10050,10122,10123,10176,10192,2,8,9,4581,4582,4600,4631,4633,4634,4661,4667,4668,4679,4728,4730,4760,4774,4804,4900,4901,4914,4934,4990,4991,4994,4995,4997,4999,5000,5009,5013,5014,5024,5036,5037,5043,5063,5064,5081,5086,5087,5088,5089,5092,5100,5103,5110,5175,5181,5182,5189,5219,5230,5236,5252,5272,5273,5280,5281,5282,5291,5301,5308,5310,5311,5317,5324,5325,5338,5339,5340,5341,5343,5344,5349,5350,5351,5352,5383,5384,5385,5393,5394,5395,5396,5439,5444,5446,5482,5484,5485,5487,5488,5490,5491,5493,5502,5507,5509,5510,5511,5512,5513,5514,5521,5531,5534,5545,5561,5562,5565,5575,5577,5578,5579,5604,5614,5630,5631,5641,5642,5644,5646,5651,5686,5691,5693,5753,5787,5788,5792,5798,5801,5802,5803,5804,5810,5821,5822,5824,5825,5833,5854,5885,5901,5904,5905,5907,5916,5934,5938,5941,5942,5943,5961,5972,5973,6001,6002,6006,6026,6029,6033,6052,6057,6058,6083,6086,6094,6102,6108,6112,6119,6120,6121,6122,6161,6177,6230,6266,6268,6289,6290,6295,6299,6300,6303,6309,6318,6333,6353,6354,6359,6369,6384,6404,6410,6412,6427,6428,6431,6432,6434,6436,6437,6438,6440,6442,6445,6450,6451,6453,6454,6460,6462,6505,6510,6524,6526,6527,6528,6563,6568,6570,6575,6576,6584,6588,6601,6625,6626,6628,6629,6640,6646,6663,6666,6685,6718,6719,6720,6725,6739,6758,6760,6762,6764,6769,6775,6777,6792,6797,6800,6836,6837,6838,6852,6853,6855,6856,6875,6877,6893,6919,6941,6952,6954,6956,6958,6959,6960,6995,6996,7001,7002,7009])).
% 187.33/188.09 cnf(11990,plain,
% 187.33/188.09 (~P24(f329(f329(f244(a874),x119901),x119901))),
% 187.33/188.09 inference(rename_variables,[],[4520])).
% 187.33/188.09 cnf(11992,plain,
% 187.33/188.09 (~P24(f329(f329(f244(a874),x119921),f329(f329(f106(a874),x119921),x119922)))),
% 187.33/188.09 inference(scs_inference,[],[4323,3521,4492,4493,4459,10208,10218,10229,10240,10341,10344,10347,10450,10563,10866,11030,11033,11230,11317,11324,11338,11390,11393,11437,11503,11549,11565,11864,11889,11901,11930,4474,10434,10527,3490,3193,2873,2874,2877,2880,2881,2884,2885,2892,2895,2896,2903,2904,2908,2909,2917,2920,2932,2944,2952,2953,2954,2961,2974,3010,3019,3020,3022,3029,3035,3037,3047,3053,3065,4455,3847,11596,3118,11314,3234,10211,10275,10278,10368,10371,10664,11329,11332,11448,11490,11495,3212,3219,3740,3979,3108,3484,3832,11364,3169,3136,3131,3115,3116,3337,3205,3229,10475,3383,4541,3919,4484,10266,10431,3267,11685,4530,10980,11050,11273,11276,3384,3166,10333,10640,3167,3442,3087,3189,11354,4066,3921,10986,11112,11162,4553,10918,11117,11221,11243,11281,11287,4554,11019,11120,11224,4555,11123,4556,11176,4557,3188,3482,3644,4350,4351,4482,3583,3796,3347,10352,10470,10541,10602,10605,10643,10737,10970,11860,3733,11582,3260,3359,4524,10243,10246,10272,10745,10758,10876,11265,11357,11752,11757,11978,4536,11467,11498,11533,11562,3720,3491,3869,3306,3308,3281,4521,4479,3474,4537,4060,11238,3604,3320,11709,4030,3987,3982,3645,4019,3663,10992,11055,11136,4542,10761,11128,3276,10361,10457,10588,10650,10719,10764,10767,10800,10823,10860,10898,10934,11656,11703,11833,11888,11904,11907,11910,11913,3277,10390,10445,10655,10740,10863,11440,11737,11740,11749,11839,11850,11869,11874,11916,11939,3280,3355,4520,10309,10399,10512,10536,10782,10826,10836,11512,11610,11631,11634,11637,11653,11807,11810,11813,11816,11900,11919,11922,11935,11990,3437,10608,10871,10915,11184,11262,11425,4532,10791,10803,10907,10925,10928,10983,11069,11077,11093,11131,11148,11156,11192,11233,11253,11256,11259,11290,11297,11300,11682,11718,11984,3341,10637,10667,10676,11213,3379,3373,3800,3738,10312,11585,11613,4529,10263,10625,10628,11072,11090,11548,11601,11641,11666,11770,11795,11798,11801,11804,3300,10670,10820,10891,11614,11769,3761,4110,4527,3772,3808,4510,4513,3251,3255,4512,4511,4515,3779,3594,4209,4544,10234,10237,10493,10544,10547,10552,10957,11419,11669,11773,4551,11151,11270,3996,3886,11303,11640,11644,3727,10931,10937,10952,3729,10673,11008,11159,11189,3547,10591,10594,10679,10847,4548,11579,4538,4549,10730,10829,11139,11422,4170,4071,3760,3707,4546,10285,10288,10631,10634,11464,4547,11559,3731,10597,4003,4568,4594,4643,4645,4675,4692,4699,4700,4739,4769,4775,4860,4885,4886,4921,4946,4947,4969,4970,4983,4987,5010,5017,5035,5038,5039,5040,5045,5046,5068,5093,5094,5104,5109,5115,5160,5161,5169,5178,5183,5185,5195,5197,5203,5207,5222,5229,5232,5233,5234,5238,5274,5287,5295,5297,5298,5302,5303,5304,5312,5315,5319,5320,5321,5328,5332,5333,5334,5342,5346,5347,5348,5353,5366,5375,5387,5389,5397,5398,5402,5406,5431,5437,5447,5448,5463,5475,5497,5503,5519,5520,5523,5542,5550,5551,5556,5557,5567,5569,5581,5585,5594,5595,5597,5612,5617,5627,5628,5640,5647,5661,5665,5668,5674,5675,5676,5679,5684,5722,5723,5726,5728,5731,5732,5733,5735,5737,5739,5744,5751,5766,5780,5785,5786,5799,5800,5805,5809,5811,5816,5857,5869,5878,5882,5893,5897,5898,5906,5920,5926,5944,5947,5959,5985,5999,6024,6044,6045,6048,6062,6064,6066,6068,6081,6082,6085,6087,6090,6091,6103,6109,6110,6111,6113,6115,6158,6159,6166,6172,6176,6212,6214,6216,6218,6227,6229,6231,6237,6239,6245,6248,6256,6263,6264,6265,6270,6292,6293,6294,6296,6302,6307,6341,6342,6344,6345,6346,6348,6349,6350,6351,6358,6391,6392,6401,6422,6423,6443,6446,6457,6458,6464,6495,6497,6511,6549,6551,6552,6606,6630,6672,6692,6701,6702,6703,6704,6723,6724,6730,6743,6746,6748,6750,6751,6752,6754,6768,6779,6781,6782,6795,6799,6850,6861,6863,6867,6884,6885,6921,6933,6964,6998,7052,7080,7135,7156,7165,7168,7223,7231,7289,7291,7306,7316,7317,7318,7337,7343,7345,7395,7405,7408,7424,7476,7478,7481,7524,7525,7543,7610,7629,7652,7676,7691,7706,7717,7726,7727,7756,7759,7761,7771,7809,7820,7845,7903,7937,7969,8016,8032,8048,8049,8124,8177,8196,8220,8240,8264,8362,8364,8370,8386,8390,8406,8429,8440,8442,8457,8463,8467,8490,8504,8505,8521,8522,8527,8528,8529,8530,8531,8549,8550,8551,8559,8573,8575,8587,8591,8593,8594,8595,8603,8608,8635,8636,8668,8681,8685,8703,8725,8726,8727,8728,8740,8741,8763,8773,8783,8784,8785,8786,8788,8809,8810,8821,8865,8871,8877,8889,8894,8896,8899,8900,8904,8914,8997,9028,9029,9030,9045,9063,9068,9096,9097,9138,9141,9167,9212,9213,9214,9229,9256,9270,9276,9279,9301,9302,9330,9391,9426,9427,9428,9453,9454,9472,9491,9497,9511,9534,9556,9564,9565,9566,9567,9582,9584,9589,9620,9621,9627,9628,9672,9673,9705,9714,9724,9726,9727,9736,9750,9753,9781,9814,9816,9820,9878,9919,9920,9922,9932,9933,9953,9958,9999,10050,10122,10123,10176,10192,2,8,9,4581,4582,4600,4631,4633,4634,4661,4667,4668,4679,4728,4730,4760,4774,4804,4900,4901,4914,4934,4990,4991,4994,4995,4997,4999,5000,5009,5013,5014,5024,5036,5037,5043,5063,5064,5081,5086,5087,5088,5089,5092,5100,5103,5110,5175,5181,5182,5189,5219,5230,5236,5252,5272,5273,5280,5281,5282,5291,5301,5308,5310,5311,5317,5324,5325,5338,5339,5340,5341,5343,5344,5349,5350,5351,5352,5383,5384,5385,5393,5394,5395,5396,5439,5444,5446,5482,5484,5485,5487,5488,5490,5491,5493,5502,5507,5509,5510,5511,5512,5513,5514,5521,5531,5534,5545,5561,5562,5565,5575,5577,5578,5579,5604,5614,5630,5631,5641,5642,5644,5646,5651,5686,5691,5693,5753,5787,5788,5792,5798,5801,5802,5803,5804,5810,5821,5822,5824,5825,5833,5854,5885,5901,5904,5905,5907,5916,5934,5938,5941,5942,5943,5961,5972,5973,6001,6002,6006,6026,6029,6033,6052,6057,6058,6083,6086,6094,6102,6108,6112,6119,6120,6121,6122,6161,6177,6230,6266,6268,6289,6290,6295,6299,6300,6303,6309,6318,6333,6353,6354,6359,6369,6384,6404,6410,6412,6427,6428,6431,6432,6434,6436,6437,6438,6440,6442,6445,6450,6451,6453,6454,6460,6462,6505,6510,6524,6526,6527,6528,6563,6568,6570,6575,6576,6584,6588,6601,6625,6626,6628,6629,6640,6646,6663,6666,6685,6718,6719,6720,6725,6739,6758,6760,6762,6764,6769,6775,6777,6792,6797,6800,6836,6837,6838,6852,6853,6855,6856,6875,6877,6893,6919,6941,6952,6954,6956,6958,6959,6960,6995,6996,7001,7002,7009,7010])).
% 187.33/188.09 cnf(11993,plain,
% 187.33/188.09 (~P24(f329(f329(f244(a874),x119931),x119931))),
% 187.33/188.09 inference(rename_variables,[],[4520])).
% 187.33/188.09 cnf(11996,plain,
% 187.33/188.09 (~P24(f329(f329(f244(a874),x119961),x119961))),
% 187.33/188.09 inference(rename_variables,[],[4520])).
% 187.33/188.09 cnf(11999,plain,
% 187.33/188.09 (~P24(f329(f329(f244(a874),x119991),x119991))),
% 187.33/188.09 inference(rename_variables,[],[4520])).
% 187.33/188.09 cnf(12002,plain,
% 187.33/188.09 (P24(f329(f329(f244(a874),x120021),f329(a117,x120021)))),
% 187.33/188.09 inference(rename_variables,[],[3347])).
% 187.33/188.09 cnf(12009,plain,
% 187.33/188.09 (P24(f329(f329(f331(f881(x120091,a869)),x120092),f329(f306(x120091),x120092)))),
% 187.33/188.09 inference(rename_variables,[],[3645])).
% 187.33/188.09 cnf(12014,plain,
% 187.33/188.09 (P24(f329(f329(f243(f881(x120141,a869)),x120142),f329(f329(f307(x120141),x120143),x120142)))),
% 187.33/188.09 inference(rename_variables,[],[3727])).
% 187.33/188.09 cnf(12021,plain,
% 187.33/188.09 (~P24(f329(f329(f331(x120211),x120212),f193(f881(x120211,a869))))),
% 187.33/188.09 inference(rename_variables,[],[4532])).
% 187.33/188.09 cnf(12030,plain,
% 187.33/188.09 (P24(f329(f329(f243(f881(x120301,a869)),x120302),f252(f881(x120301,a869))))),
% 187.33/188.09 inference(rename_variables,[],[3663])).
% 187.33/188.09 cnf(12031,plain,
% 187.33/188.09 (~E(f329(a117,x120311),x120311)),
% 187.33/188.09 inference(rename_variables,[],[4459])).
% 187.33/188.09 cnf(12034,plain,
% 187.33/188.09 (P24(f329(f329(f243(f881(x120341,a869)),f193(f881(x120341,a869))),x120342))),
% 187.33/188.09 inference(rename_variables,[],[3729])).
% 187.33/188.09 cnf(12042,plain,
% 187.33/188.09 (P24(f329(f329(f244(a874),x120421),f329(a117,x120421)))),
% 187.33/188.09 inference(rename_variables,[],[3347])).
% 187.33/188.09 cnf(12050,plain,
% 187.33/188.09 (~P24(f329(f329(f331(f880(x120501,x120501)),x120502),f151(x120501,f118(f881(x120501,a874)))))),
% 187.33/188.09 inference(scs_inference,[],[4323,3521,4492,4493,4459,10208,10218,10229,10240,10341,10344,10347,10450,10563,10866,11030,11033,11230,11317,11324,11338,11390,11393,11437,11503,11549,11565,11864,11889,11901,11930,11936,4474,10434,10527,3490,3193,2873,2874,2876,2877,2880,2881,2884,2885,2892,2895,2896,2903,2904,2908,2909,2917,2920,2932,2944,2952,2953,2954,2961,2974,3010,3019,3020,3022,3029,3035,3037,3047,3053,3065,4455,3847,11596,3118,11314,3234,10211,10275,10278,10368,10371,10664,11329,11332,11448,11490,11495,11591,3212,3219,3740,3979,3108,3484,3832,11364,3169,3136,3131,4560,3115,3116,3337,3205,3229,10475,3383,4541,3919,4484,10266,10431,3267,11685,4530,10980,11050,11273,11276,3384,3166,10333,10640,3167,3442,3087,3189,11354,4066,3921,10986,11112,11162,4553,10918,11117,11221,11243,11281,11287,4554,11019,11120,11224,4555,11123,4556,11176,4557,3188,3482,3644,4350,4351,4482,3583,3796,3468,3722,3347,10352,10470,10541,10602,10605,10643,10737,10970,11860,11923,12002,3733,11582,3260,3359,3546,4524,10243,10246,10272,10745,10758,10876,11265,11357,11752,11757,11978,4536,11467,11498,11533,11562,3720,3491,3869,3306,3308,3281,4521,4479,3474,4537,4060,11238,3604,3320,11709,4030,3987,3982,3645,11863,4019,3663,10992,11055,11136,11195,4542,10761,11128,3276,10361,10457,10588,10650,10719,10764,10767,10800,10823,10860,10898,10934,11656,11703,11833,11888,11904,11907,11910,11913,3277,10390,10445,10655,10740,10863,11440,11737,11740,11749,11839,11850,11869,11874,11916,11939,3280,3355,4520,10309,10399,10512,10536,10782,10826,10836,11512,11610,11631,11634,11637,11653,11807,11810,11813,11816,11900,11919,11922,11935,11990,11993,11996,3437,10608,10871,10915,11184,11262,11425,4532,10791,10803,10907,10925,10928,10983,11069,11077,11093,11131,11148,11156,11192,11233,11253,11256,11259,11290,11297,11300,11682,11718,11984,11987,3341,10637,10667,10676,11213,3379,3373,3800,3738,10312,11585,11613,4529,10263,10625,10628,11072,11090,11548,11601,11641,11666,11770,11795,11798,11801,11804,3300,10670,10820,10891,11614,11769,3761,4110,4527,3772,3808,4510,4513,3251,3255,4512,4511,4515,3779,3594,4209,4544,10234,10237,10493,10544,10547,10552,10957,11419,11669,11773,4551,11151,11270,3996,3886,11303,11640,11644,3727,10931,10937,10952,11885,3729,10673,11008,11159,11189,11200,3547,10591,10594,10679,10847,4548,11579,4538,4549,10730,10829,11139,11422,4170,4071,3760,3707,4546,10285,10288,10631,10634,11464,4547,11559,3731,10597,4003,4568,4594,4643,4645,4675,4692,4699,4700,4739,4769,4775,4860,4885,4886,4921,4946,4947,4969,4970,4983,4987,5010,5017,5035,5038,5039,5040,5045,5046,5068,5093,5094,5104,5109,5115,5160,5161,5169,5178,5183,5185,5195,5197,5203,5207,5222,5229,5232,5233,5234,5238,5274,5287,5295,5297,5298,5302,5303,5304,5312,5315,5319,5320,5321,5328,5332,5333,5334,5342,5346,5347,5348,5353,5366,5375,5387,5389,5397,5398,5402,5406,5431,5437,5447,5448,5463,5475,5497,5503,5519,5520,5523,5542,5550,5551,5556,5557,5567,5569,5581,5585,5594,5595,5597,5612,5617,5627,5628,5640,5647,5661,5665,5668,5674,5675,5676,5679,5684,5722,5723,5726,5728,5731,5732,5733,5735,5737,5739,5744,5751,5766,5780,5785,5786,5799,5800,5805,5809,5811,5816,5857,5869,5878,5882,5893,5897,5898,5906,5920,5926,5944,5947,5959,5985,5999,6024,6044,6045,6048,6062,6064,6066,6068,6081,6082,6085,6087,6090,6091,6103,6109,6110,6111,6113,6115,6158,6159,6166,6172,6176,6212,6214,6216,6218,6227,6229,6231,6237,6239,6245,6248,6256,6263,6264,6265,6270,6292,6293,6294,6296,6302,6307,6341,6342,6344,6345,6346,6348,6349,6350,6351,6358,6391,6392,6401,6422,6423,6443,6446,6457,6458,6464,6495,6497,6511,6549,6551,6552,6606,6630,6672,6692,6701,6702,6703,6704,6723,6724,6730,6743,6746,6748,6750,6751,6752,6754,6768,6779,6781,6782,6795,6799,6850,6861,6863,6867,6884,6885,6921,6933,6964,6998,7052,7080,7135,7156,7165,7168,7223,7231,7289,7291,7306,7316,7317,7318,7337,7343,7345,7395,7405,7408,7424,7476,7478,7481,7524,7525,7543,7610,7629,7652,7676,7691,7706,7717,7726,7727,7756,7759,7761,7771,7809,7820,7845,7903,7937,7969,8016,8032,8048,8049,8124,8177,8196,8220,8240,8264,8362,8364,8370,8386,8390,8406,8429,8440,8442,8457,8463,8467,8490,8504,8505,8521,8522,8527,8528,8529,8530,8531,8549,8550,8551,8559,8573,8575,8587,8591,8593,8594,8595,8603,8608,8635,8636,8668,8681,8685,8703,8725,8726,8727,8728,8740,8741,8763,8773,8783,8784,8785,8786,8788,8809,8810,8821,8865,8871,8877,8889,8894,8896,8899,8900,8904,8914,8997,9028,9029,9030,9045,9063,9068,9096,9097,9138,9141,9167,9212,9213,9214,9229,9256,9270,9276,9279,9301,9302,9330,9391,9426,9427,9428,9453,9454,9472,9491,9497,9511,9534,9556,9564,9565,9566,9567,9582,9584,9589,9620,9621,9627,9628,9672,9673,9705,9714,9724,9726,9727,9736,9750,9753,9781,9814,9816,9820,9878,9919,9920,9922,9932,9933,9953,9958,9999,10050,10122,10123,10176,10192,2,8,9,4581,4582,4600,4631,4633,4634,4661,4667,4668,4679,4728,4730,4760,4774,4804,4900,4901,4914,4934,4990,4991,4994,4995,4997,4999,5000,5009,5013,5014,5024,5036,5037,5043,5063,5064,5081,5086,5087,5088,5089,5092,5100,5103,5110,5175,5181,5182,5189,5219,5230,5236,5252,5272,5273,5280,5281,5282,5291,5301,5308,5310,5311,5317,5324,5325,5338,5339,5340,5341,5343,5344,5349,5350,5351,5352,5383,5384,5385,5393,5394,5395,5396,5439,5444,5446,5482,5484,5485,5487,5488,5490,5491,5493,5502,5507,5509,5510,5511,5512,5513,5514,5521,5531,5534,5545,5561,5562,5565,5575,5577,5578,5579,5604,5614,5630,5631,5641,5642,5644,5646,5651,5686,5691,5693,5753,5787,5788,5792,5798,5801,5802,5803,5804,5810,5821,5822,5824,5825,5833,5854,5885,5901,5904,5905,5907,5916,5934,5938,5941,5942,5943,5961,5972,5973,6001,6002,6006,6026,6029,6033,6052,6057,6058,6083,6086,6094,6102,6108,6112,6119,6120,6121,6122,6161,6177,6230,6266,6268,6289,6290,6295,6299,6300,6303,6309,6318,6333,6353,6354,6359,6369,6384,6404,6410,6412,6427,6428,6431,6432,6434,6436,6437,6438,6440,6442,6445,6450,6451,6453,6454,6460,6462,6505,6510,6524,6526,6527,6528,6563,6568,6570,6575,6576,6584,6588,6601,6625,6626,6628,6629,6640,6646,6663,6666,6685,6718,6719,6720,6725,6739,6758,6760,6762,6764,6769,6775,6777,6792,6797,6800,6836,6837,6838,6852,6853,6855,6856,6875,6877,6893,6919,6941,6952,6954,6956,6958,6959,6960,6995,6996,7001,7002,7009,7010,7012,7014,7033,7042,7043,7055,7065,7104,7114,7118,7125,7136,7142,7144,7150,7158,7159,7172,7189,7207,7209,7226])).
% 187.33/188.09 cnf(12051,plain,
% 187.33/188.09 (E(f329(f260(x120511,x120511),f261(x120511,x120512)),x120512)),
% 187.33/188.09 inference(rename_variables,[],[3234])).
% 187.33/188.09 cnf(12062,plain,
% 187.33/188.09 (~P24(f329(f329(f243(a874),f329(a117,x120621)),x120621))),
% 187.33/188.09 inference(rename_variables,[],[4529])).
% 187.33/188.09 cnf(12063,plain,
% 187.33/188.09 (~P24(f329(f329(f244(a874),x120631),f2(a874)))),
% 187.33/188.09 inference(rename_variables,[],[4524])).
% 187.33/188.09 cnf(12066,plain,
% 187.33/188.09 (P24(f329(f62(x120661),f193(f881(x120661,a869))))),
% 187.33/188.09 inference(rename_variables,[],[3355])).
% 187.33/188.09 cnf(12067,plain,
% 187.33/188.09 (~P24(f329(f329(f331(x120671),x120672),f193(f881(x120671,a869))))),
% 187.33/188.09 inference(rename_variables,[],[4532])).
% 187.33/188.09 cnf(12072,plain,
% 187.33/188.09 (~P24(f329(f329(f244(a874),x120721),f2(a874)))),
% 187.33/188.09 inference(rename_variables,[],[4524])).
% 187.33/188.09 cnf(12073,plain,
% 187.33/188.09 (~P24(f329(f329(f244(a874),x120731),x120731))),
% 187.33/188.09 inference(rename_variables,[],[4520])).
% 187.33/188.09 cnf(12078,plain,
% 187.33/188.09 (P24(f329(f329(f243(f881(x120781,a869)),f329(f171(x120781),f175(x120781,x120782,x120783))),f329(f171(x120781),x120782)))),
% 187.33/188.09 inference(rename_variables,[],[3982])).
% 187.33/188.09 cnf(12081,plain,
% 187.33/188.09 (P21(x120811,x120811,f5(x120811),x120812)),
% 187.33/188.09 inference(rename_variables,[],[3521])).
% 187.33/188.09 cnf(12086,plain,
% 187.33/188.09 (P24(f329(f329(f331(f881(x120861,a869)),x120862),f329(f306(x120861),x120862)))),
% 187.33/188.09 inference(rename_variables,[],[3645])).
% 187.33/188.09 cnf(12093,plain,
% 187.33/188.09 (P24(f329(f329(f243(a874),x120931),x120931))),
% 187.33/188.09 inference(rename_variables,[],[3276])).
% 187.33/188.09 cnf(12096,plain,
% 187.33/188.09 (~P24(f329(f329(f331(x120961),x120962),f193(f881(x120961,a869))))),
% 187.33/188.09 inference(rename_variables,[],[4532])).
% 187.33/188.09 cnf(12099,plain,
% 187.33/188.09 (P24(f329(f329(f243(f881(x120991,a869)),x120992),f329(f329(f307(x120991),x120993),x120992)))),
% 187.33/188.09 inference(rename_variables,[],[3727])).
% 187.33/188.09 cnf(12100,plain,
% 187.33/188.09 (P24(f329(f329(f243(f881(x121001,a869)),x121002),f252(f881(x121001,a869))))),
% 187.33/188.09 inference(rename_variables,[],[3663])).
% 187.33/188.09 cnf(12107,plain,
% 187.33/188.09 (P24(f329(f329(f243(a874),x121071),x121071))),
% 187.33/188.09 inference(rename_variables,[],[3276])).
% 187.33/188.09 cnf(12110,plain,
% 187.33/188.09 (P24(f329(f329(f243(a874),x121101),x121101))),
% 187.33/188.09 inference(rename_variables,[],[3276])).
% 187.33/188.09 cnf(12113,plain,
% 187.33/188.09 (P24(f329(f329(f243(a874),x121131),x121131))),
% 187.33/188.09 inference(rename_variables,[],[3276])).
% 187.33/188.09 cnf(12116,plain,
% 187.33/188.09 (P24(f329(f329(f243(a874),x121161),x121161))),
% 187.33/188.09 inference(rename_variables,[],[3276])).
% 187.33/188.09 cnf(12119,plain,
% 187.33/188.09 (P24(f329(f329(f244(a874),x121191),f329(a117,x121191)))),
% 187.33/188.09 inference(rename_variables,[],[3347])).
% 187.33/188.09 cnf(12122,plain,
% 187.33/188.09 (P24(f329(f329(f244(a874),x121221),f329(a117,x121221)))),
% 187.33/188.09 inference(rename_variables,[],[3347])).
% 187.33/188.09 cnf(12125,plain,
% 187.33/188.09 (P24(f329(f329(f243(f881(x121251,a869)),x121252),x121252))),
% 187.33/188.09 inference(rename_variables,[],[3579])).
% 187.33/188.09 cnf(12127,plain,
% 187.33/188.09 (~P24(f329(f329(f243(a1),f329(f329(f22(a1),a83),a102)),f2(a1)))),
% 187.33/188.09 inference(scs_inference,[],[4323,3521,11045,4492,4493,4459,10208,10218,10229,10240,10341,10344,10347,10450,10563,10866,11030,11033,11230,11317,11324,11338,11390,11393,11437,11503,11549,11565,11864,11889,11901,11930,11936,4474,10434,10527,3490,3193,2873,2874,2876,2877,2880,2881,2883,2884,2885,2892,2895,2896,2903,2904,2908,2909,2917,2920,2932,2944,2952,2953,2954,2961,2974,3010,3019,3020,3022,3029,3035,3037,3047,3053,3065,4455,3847,11596,3118,11314,3234,10211,10275,10278,10368,10371,10664,11329,11332,11448,11490,11495,11591,3212,3219,3740,3979,3108,3484,3832,11364,3169,3136,3131,4560,3115,3116,3337,3205,3229,10475,3383,4541,3919,4484,10266,10431,3267,11685,4530,10980,11050,11273,11276,3384,3166,10333,10640,3167,3442,3087,3189,11354,4066,3921,10986,11112,11162,4553,10918,11117,11221,11243,11281,11287,4554,11019,11120,11224,4555,11123,4556,11176,4557,3188,3482,3644,4350,4351,4482,3583,3796,3468,3722,3347,10352,10470,10541,10602,10605,10643,10737,10970,11860,11923,12002,12042,12119,3733,11582,3260,3359,3546,4524,10243,10246,10272,10745,10758,10876,11265,11357,11752,11757,11978,11981,12063,4536,11467,11498,11533,11562,3720,3491,3869,3306,3308,3281,4521,4479,3474,4537,4060,11238,3604,3320,11709,11712,4030,3987,3982,10989,3645,11863,12009,4019,3663,10992,11055,11136,11195,12030,4542,10761,11128,3276,10361,10457,10588,10650,10719,10764,10767,10800,10823,10860,10898,10934,11656,11703,11833,11888,11904,11907,11910,11913,12093,12107,12110,12113,3277,10390,10445,10655,10740,10863,11440,11737,11740,11749,11839,11850,11869,11874,11916,11939,3280,3355,12066,4520,10309,10399,10512,10536,10782,10826,10836,11512,11610,11631,11634,11637,11653,11807,11810,11813,11816,11900,11919,11922,11935,11990,11993,11996,11999,3437,10608,10871,10915,11184,11262,11425,4532,10791,10803,10907,10925,10928,10983,11069,11077,11093,11131,11148,11156,11192,11233,11253,11256,11259,11290,11297,11300,11682,11718,11984,11987,12021,12067,3341,10637,10667,10676,11213,3379,3373,3800,3738,10312,11585,11613,4529,10263,10625,10628,11072,11090,11548,11601,11641,11666,11770,11795,11798,11801,11804,3300,10670,10820,10891,11614,11769,3761,4110,4527,3772,3808,4510,4513,3251,3255,4512,4511,4515,3779,3594,4209,4544,10234,10237,10493,10544,10547,10552,10957,11419,11669,11773,4551,11151,11270,3996,3886,11303,11640,11644,3727,10931,10937,10952,11885,12014,3579,3729,10673,11008,11159,11189,11200,3547,10591,10594,10679,10847,4548,11579,4538,4549,10730,10829,11139,11422,4170,4071,3760,3707,4546,10285,10288,10631,10634,11464,4547,11559,3731,10597,4003,4568,4594,4643,4645,4675,4692,4699,4700,4739,4769,4775,4860,4885,4886,4921,4946,4947,4969,4970,4983,4987,5010,5017,5035,5038,5039,5040,5045,5046,5068,5093,5094,5104,5109,5115,5160,5161,5169,5178,5183,5185,5195,5197,5203,5207,5222,5229,5232,5233,5234,5238,5274,5287,5295,5297,5298,5302,5303,5304,5312,5315,5319,5320,5321,5328,5332,5333,5334,5342,5346,5347,5348,5353,5366,5375,5387,5389,5397,5398,5402,5406,5431,5437,5447,5448,5463,5475,5497,5503,5519,5520,5523,5542,5550,5551,5556,5557,5567,5569,5581,5585,5594,5595,5597,5612,5617,5627,5628,5640,5647,5661,5665,5668,5674,5675,5676,5679,5684,5722,5723,5726,5728,5731,5732,5733,5735,5737,5739,5744,5751,5766,5780,5785,5786,5799,5800,5805,5809,5811,5816,5857,5869,5878,5882,5893,5897,5898,5906,5920,5926,5944,5947,5959,5985,5999,6024,6044,6045,6048,6062,6064,6066,6068,6081,6082,6085,6087,6090,6091,6103,6109,6110,6111,6113,6115,6158,6159,6166,6172,6176,6212,6214,6216,6218,6227,6229,6231,6237,6239,6245,6248,6256,6263,6264,6265,6270,6292,6293,6294,6296,6302,6307,6341,6342,6344,6345,6346,6348,6349,6350,6351,6358,6391,6392,6401,6422,6423,6443,6446,6457,6458,6464,6495,6497,6511,6549,6551,6552,6606,6630,6672,6692,6701,6702,6703,6704,6723,6724,6730,6743,6746,6748,6750,6751,6752,6754,6768,6779,6781,6782,6795,6799,6850,6861,6863,6867,6884,6885,6921,6933,6964,6998,7052,7080,7135,7156,7165,7168,7223,7231,7289,7291,7306,7316,7317,7318,7337,7343,7345,7395,7405,7408,7424,7476,7478,7481,7524,7525,7543,7610,7629,7652,7676,7691,7706,7717,7726,7727,7756,7759,7761,7771,7809,7820,7845,7903,7937,7969,8016,8032,8048,8049,8124,8177,8196,8220,8240,8264,8362,8364,8370,8386,8390,8406,8429,8440,8442,8457,8463,8467,8490,8504,8505,8521,8522,8527,8528,8529,8530,8531,8549,8550,8551,8559,8573,8575,8587,8591,8593,8594,8595,8603,8608,8635,8636,8668,8681,8685,8703,8725,8726,8727,8728,8740,8741,8763,8773,8783,8784,8785,8786,8788,8809,8810,8821,8865,8871,8877,8889,8894,8896,8899,8900,8904,8914,8997,9028,9029,9030,9045,9063,9068,9096,9097,9138,9141,9167,9212,9213,9214,9229,9256,9270,9276,9279,9301,9302,9330,9391,9426,9427,9428,9453,9454,9472,9491,9497,9511,9534,9556,9564,9565,9566,9567,9582,9584,9589,9620,9621,9627,9628,9672,9673,9705,9714,9724,9726,9727,9736,9750,9753,9781,9814,9816,9820,9878,9919,9920,9922,9932,9933,9953,9958,9999,10050,10122,10123,10176,10192,2,8,9,4581,4582,4600,4631,4633,4634,4661,4667,4668,4679,4728,4730,4760,4774,4804,4900,4901,4914,4934,4990,4991,4994,4995,4997,4999,5000,5009,5013,5014,5024,5036,5037,5043,5063,5064,5081,5086,5087,5088,5089,5092,5100,5103,5110,5175,5181,5182,5189,5219,5230,5236,5252,5272,5273,5280,5281,5282,5291,5301,5308,5310,5311,5317,5324,5325,5338,5339,5340,5341,5343,5344,5349,5350,5351,5352,5383,5384,5385,5393,5394,5395,5396,5439,5444,5446,5482,5484,5485,5487,5488,5490,5491,5493,5502,5507,5509,5510,5511,5512,5513,5514,5521,5531,5534,5545,5561,5562,5565,5575,5577,5578,5579,5604,5614,5630,5631,5641,5642,5644,5646,5651,5686,5691,5693,5753,5787,5788,5792,5798,5801,5802,5803,5804,5810,5821,5822,5824,5825,5833,5854,5885,5901,5904,5905,5907,5916,5934,5938,5941,5942,5943,5961,5972,5973,6001,6002,6006,6026,6029,6033,6052,6057,6058,6083,6086,6094,6102,6108,6112,6119,6120,6121,6122,6161,6177,6230,6266,6268,6289,6290,6295,6299,6300,6303,6309,6318,6333,6353,6354,6359,6369,6384,6404,6410,6412,6427,6428,6431,6432,6434,6436,6437,6438,6440,6442,6445,6450,6451,6453,6454,6460,6462,6505,6510,6524,6526,6527,6528,6563,6568,6570,6575,6576,6584,6588,6601,6625,6626,6628,6629,6640,6646,6663,6666,6685,6718,6719,6720,6725,6739,6758,6760,6762,6764,6769,6775,6777,6792,6797,6800,6836,6837,6838,6852,6853,6855,6856,6875,6877,6893,6919,6941,6952,6954,6956,6958,6959,6960,6995,6996,7001,7002,7009,7010,7012,7014,7033,7042,7043,7055,7065,7104,7114,7118,7125,7136,7142,7144,7150,7158,7159,7172,7189,7207,7209,7226,7275,7276,7277,7279,7281,7285,7290,7313,7358,7391,7406,7423,7456,7459,7485,7509,7526,7529,7530,7540,7559,7561,7563,7565,7566,7567,7592,7618])).
% 187.33/188.09 cnf(12132,plain,
% 187.33/188.09 (P24(f329(f329(f331(f881(x121321,a869)),x121322),f329(f306(x121321),x121322)))),
% 187.33/188.09 inference(rename_variables,[],[3645])).
% 187.33/188.09 cnf(12138,plain,
% 187.33/188.09 (~P24(f329(f329(f244(a1),f329(f329(f80(a1),a83),a83)),f2(a1)))),
% 187.33/188.09 inference(scs_inference,[],[4323,3521,11045,4492,4493,4459,10208,10218,10229,10240,10341,10344,10347,10450,10563,10866,11030,11033,11230,11317,11324,11338,11390,11393,11437,11503,11549,11565,11864,11889,11901,11930,11936,4474,10434,10527,3490,3193,2873,2874,2876,2877,2880,2881,2883,2884,2885,2892,2895,2896,2903,2904,2908,2909,2917,2920,2932,2944,2952,2953,2954,2961,2974,3010,3019,3020,3022,3029,3035,3037,3047,3053,3065,4455,3847,11596,3118,11314,3234,10211,10275,10278,10368,10371,10664,11329,11332,11448,11490,11495,11591,3212,3219,3740,3979,3108,3484,3832,11364,3169,3136,3131,4560,3115,3116,3337,3205,3229,10475,3383,4541,3919,4484,10266,10431,3267,11685,4530,10980,11050,11273,11276,3384,3166,10333,10640,3167,3442,3087,3189,11354,4066,3921,10986,11112,11162,4553,10918,11117,11221,11243,11281,11287,4554,11019,11120,11224,4555,11123,4556,11176,4557,3188,3482,3644,4350,4351,4482,3583,3796,3468,3722,3347,10352,10470,10541,10602,10605,10643,10737,10970,11860,11923,12002,12042,12119,3733,11582,3260,3359,3546,4524,10243,10246,10272,10745,10758,10876,11265,11357,11752,11757,11978,11981,12063,4536,11467,11498,11533,11562,3720,3491,3869,3306,3308,3281,4521,4479,3474,4537,4060,11238,3604,3320,11709,11712,4030,3987,3982,10989,3645,11863,12009,12086,4019,3663,10992,11055,11136,11195,12030,4542,10761,11128,3276,10361,10457,10588,10650,10719,10764,10767,10800,10823,10860,10898,10934,11656,11703,11833,11888,11904,11907,11910,11913,12093,12107,12110,12113,3277,10390,10445,10655,10740,10863,11440,11737,11740,11749,11839,11850,11869,11874,11916,11939,3280,3355,12066,4520,10309,10399,10512,10536,10782,10826,10836,11512,11610,11631,11634,11637,11653,11807,11810,11813,11816,11900,11919,11922,11935,11990,11993,11996,11999,3437,10608,10871,10915,11184,11262,11425,4532,10791,10803,10907,10925,10928,10983,11069,11077,11093,11131,11148,11156,11192,11233,11253,11256,11259,11290,11297,11300,11682,11718,11984,11987,12021,12067,3341,10637,10667,10676,11213,3379,3373,3800,3738,10312,11585,11613,4529,10263,10625,10628,11072,11090,11548,11601,11641,11666,11770,11795,11798,11801,11804,3300,10670,10820,10891,11614,11769,3761,4110,4527,3772,3808,4510,4513,3251,3255,4512,4511,4515,3779,3594,4209,4544,10234,10237,10493,10544,10547,10552,10957,11419,11669,11773,4551,11151,11270,3996,3886,11303,11640,11644,3727,10931,10937,10952,11885,12014,3579,3729,10673,11008,11159,11189,11200,3547,10591,10594,10679,10847,4548,11579,4538,4549,10730,10829,11139,11422,4170,4071,3760,3707,4546,10285,10288,10631,10634,11464,4547,11559,3731,10597,4003,4568,4594,4643,4645,4675,4692,4699,4700,4739,4769,4775,4860,4885,4886,4921,4946,4947,4969,4970,4983,4987,5010,5017,5035,5038,5039,5040,5045,5046,5068,5093,5094,5104,5109,5115,5160,5161,5169,5178,5183,5185,5195,5197,5203,5207,5222,5229,5232,5233,5234,5238,5274,5287,5295,5297,5298,5302,5303,5304,5312,5315,5319,5320,5321,5328,5332,5333,5334,5342,5346,5347,5348,5353,5366,5375,5387,5389,5397,5398,5402,5406,5431,5437,5447,5448,5463,5475,5497,5503,5519,5520,5523,5542,5550,5551,5556,5557,5567,5569,5581,5585,5594,5595,5597,5612,5617,5627,5628,5640,5647,5661,5665,5668,5674,5675,5676,5679,5684,5722,5723,5726,5728,5731,5732,5733,5735,5737,5739,5744,5751,5766,5780,5785,5786,5799,5800,5805,5809,5811,5816,5857,5869,5878,5882,5893,5897,5898,5906,5920,5926,5944,5947,5959,5985,5999,6024,6044,6045,6048,6062,6064,6066,6068,6081,6082,6085,6087,6090,6091,6103,6109,6110,6111,6113,6115,6158,6159,6166,6172,6176,6212,6214,6216,6218,6227,6229,6231,6237,6239,6245,6248,6256,6263,6264,6265,6270,6292,6293,6294,6296,6302,6307,6341,6342,6344,6345,6346,6348,6349,6350,6351,6358,6391,6392,6401,6422,6423,6443,6446,6457,6458,6464,6495,6497,6511,6549,6551,6552,6606,6630,6672,6692,6701,6702,6703,6704,6723,6724,6730,6743,6746,6748,6750,6751,6752,6754,6768,6779,6781,6782,6795,6799,6850,6861,6863,6867,6884,6885,6921,6933,6964,6998,7052,7080,7135,7156,7165,7168,7223,7231,7289,7291,7306,7316,7317,7318,7337,7343,7345,7395,7405,7408,7424,7476,7478,7481,7524,7525,7543,7610,7629,7652,7676,7691,7706,7717,7726,7727,7756,7759,7761,7771,7809,7820,7845,7903,7937,7969,8016,8032,8048,8049,8124,8177,8196,8220,8240,8264,8362,8364,8370,8386,8390,8406,8429,8440,8442,8457,8463,8467,8490,8504,8505,8521,8522,8527,8528,8529,8530,8531,8549,8550,8551,8559,8573,8575,8587,8591,8593,8594,8595,8603,8608,8635,8636,8668,8681,8685,8703,8725,8726,8727,8728,8740,8741,8763,8773,8783,8784,8785,8786,8788,8809,8810,8821,8865,8871,8877,8889,8894,8896,8899,8900,8904,8914,8997,9028,9029,9030,9045,9063,9068,9096,9097,9138,9141,9167,9212,9213,9214,9229,9256,9270,9276,9279,9301,9302,9330,9391,9426,9427,9428,9453,9454,9472,9491,9497,9511,9534,9556,9564,9565,9566,9567,9582,9584,9589,9620,9621,9627,9628,9672,9673,9705,9714,9724,9726,9727,9736,9750,9753,9781,9814,9816,9820,9878,9919,9920,9922,9932,9933,9953,9958,9999,10050,10122,10123,10176,10192,2,8,9,4581,4582,4600,4631,4633,4634,4661,4667,4668,4679,4728,4730,4760,4774,4804,4900,4901,4914,4934,4990,4991,4994,4995,4997,4999,5000,5009,5013,5014,5024,5036,5037,5043,5063,5064,5081,5086,5087,5088,5089,5092,5100,5103,5110,5175,5181,5182,5189,5219,5230,5236,5252,5272,5273,5280,5281,5282,5291,5301,5308,5310,5311,5317,5324,5325,5338,5339,5340,5341,5343,5344,5349,5350,5351,5352,5383,5384,5385,5393,5394,5395,5396,5439,5444,5446,5482,5484,5485,5487,5488,5490,5491,5493,5502,5507,5509,5510,5511,5512,5513,5514,5521,5531,5534,5545,5561,5562,5565,5575,5577,5578,5579,5604,5614,5630,5631,5641,5642,5644,5646,5651,5686,5691,5693,5753,5787,5788,5792,5798,5801,5802,5803,5804,5810,5821,5822,5824,5825,5833,5854,5885,5901,5904,5905,5907,5916,5934,5938,5941,5942,5943,5961,5972,5973,6001,6002,6006,6026,6029,6033,6052,6057,6058,6083,6086,6094,6102,6108,6112,6119,6120,6121,6122,6161,6177,6230,6266,6268,6289,6290,6295,6299,6300,6303,6309,6318,6333,6353,6354,6359,6369,6384,6404,6410,6412,6427,6428,6431,6432,6434,6436,6437,6438,6440,6442,6445,6450,6451,6453,6454,6460,6462,6505,6510,6524,6526,6527,6528,6563,6568,6570,6575,6576,6584,6588,6601,6625,6626,6628,6629,6640,6646,6663,6666,6685,6718,6719,6720,6725,6739,6758,6760,6762,6764,6769,6775,6777,6792,6797,6800,6836,6837,6838,6852,6853,6855,6856,6875,6877,6893,6919,6941,6952,6954,6956,6958,6959,6960,6995,6996,7001,7002,7009,7010,7012,7014,7033,7042,7043,7055,7065,7104,7114,7118,7125,7136,7142,7144,7150,7158,7159,7172,7189,7207,7209,7226,7275,7276,7277,7279,7281,7285,7290,7313,7358,7391,7406,7423,7456,7459,7485,7509,7526,7529,7530,7540,7559,7561,7563,7565,7566,7567,7592,7618,7619,7651,7653,7654,7655])).
% 187.33/188.09 cnf(12141,plain,
% 187.33/188.09 (~E(f329(a117,x121411),x121411)),
% 187.33/188.09 inference(rename_variables,[],[4459])).
% 187.33/188.09 cnf(12142,plain,
% 187.33/188.09 (E(f329(f308(x121421,x121421,f5(x121421)),x121422),x121422)),
% 187.33/188.09 inference(rename_variables,[],[3337])).
% 187.33/188.09 cnf(12145,plain,
% 187.33/188.09 (P37(x121451,x121452,f118(x121451),f118(x121451))),
% 187.33/188.09 inference(rename_variables,[],[3530])).
% 187.33/188.09 cnf(12148,plain,
% 187.33/188.09 (~E(f329(a117,x121481),x121481)),
% 187.33/188.09 inference(rename_variables,[],[4459])).
% 187.33/188.09 cnf(12161,plain,
% 187.33/188.09 (~P24(f329(f329(f244(a874),x121611),x121611))),
% 187.33/188.09 inference(rename_variables,[],[4520])).
% 187.33/188.09 cnf(12164,plain,
% 187.33/188.09 (~P24(f329(f329(f244(a874),x121641),x121641))),
% 187.33/188.09 inference(rename_variables,[],[4520])).
% 187.33/188.09 cnf(12169,plain,
% 187.33/188.09 (P24(f329(f329(f243(a874),f2(a874)),x121691))),
% 187.33/188.09 inference(rename_variables,[],[3300])).
% 187.33/188.09 cnf(12176,plain,
% 187.33/188.09 (P33(a874,f329(f167(a874),f329(f329(f152(f875(x121761),a874),f194(f875(x121761))),f179(x121761,x121762))))),
% 187.33/188.09 inference(rename_variables,[],[3842])).
% 187.33/188.09 cnf(12179,plain,
% 187.33/188.09 (P21(x121791,x121791,f5(x121791),x121792)),
% 187.33/188.09 inference(rename_variables,[],[3521])).
% 187.33/188.09 cnf(12182,plain,
% 187.33/188.09 (P24(f329(f329(f331(f875(x121821)),f118(x121821)),f159(x121821,x121822)))),
% 187.33/188.09 inference(rename_variables,[],[3482])).
% 187.33/188.09 cnf(12185,plain,
% 187.33/188.09 (~P24(f329(f329(f193(f881(x121851,f881(x121852,a869))),x121853),x121854))),
% 187.33/188.09 inference(rename_variables,[],[4549])).
% 187.33/188.09 cnf(12190,plain,
% 187.33/188.09 (P24(f329(f329(f243(a874),x121901),x121901))),
% 187.33/188.09 inference(rename_variables,[],[3276])).
% 187.33/188.09 cnf(12191,plain,
% 187.33/188.09 (P24(f329(f329(f243(a874),f2(a874)),x121911))),
% 187.33/188.09 inference(rename_variables,[],[3300])).
% 187.33/188.09 cnf(12193,plain,
% 187.33/188.09 (P24(f329(f329(f243(a1),f2(a1)),f864(x121931,f193(f881(x121932,f881(x121933,a869))),f78(a1))))),
% 187.33/188.09 inference(scs_inference,[],[4323,3521,11045,12081,3530,4492,4493,4477,4459,10208,10218,10229,10240,10341,10344,10347,10450,10563,10866,11030,11033,11230,11317,11324,11338,11390,11393,11437,11503,11549,11565,11864,11889,11901,11930,11936,12031,12141,4474,10434,10527,3490,3193,2873,2874,2876,2877,2880,2881,2883,2884,2885,2892,2895,2896,2903,2904,2908,2909,2917,2920,2932,2944,2952,2953,2954,2961,2974,3010,3019,3020,3022,3029,3035,3037,3047,3053,3065,4455,3847,11596,3118,11314,3234,10211,10275,10278,10368,10371,10664,11329,11332,11448,11490,11495,11591,3212,3219,3740,3979,3108,3484,3832,11364,3169,3136,3131,4560,3115,3116,3151,3337,10815,3205,3229,10475,3383,4541,3919,4484,10266,10431,3267,11685,4530,10980,11050,11273,11276,3384,3166,10333,10640,3167,3442,3087,3189,11354,4066,3921,10986,11112,11162,4553,10918,11117,11221,11243,11281,11287,4554,11019,11120,11224,4555,11123,4556,11176,4557,3188,3482,3644,4350,4351,4482,3583,3796,3842,3468,3722,3347,10352,10470,10541,10602,10605,10643,10737,10970,11860,11923,12002,12042,12119,3733,11582,3260,3359,3546,4524,10243,10246,10272,10745,10758,10876,11265,11357,11752,11757,11978,11981,12063,12072,4536,11467,11498,11533,11562,3720,3491,3869,3306,3308,3281,4521,4479,3474,4537,4060,11238,3604,3320,11709,11712,4030,3987,3982,10989,3645,11863,12009,12086,12132,4019,3663,10992,11055,11136,11195,12030,4542,10761,11128,3276,10361,10457,10588,10650,10719,10764,10767,10800,10823,10860,10898,10934,11656,11703,11833,11888,11904,11907,11910,11913,12093,12107,12110,12113,12116,3277,10390,10445,10655,10740,10863,11440,11737,11740,11749,11839,11850,11869,11874,11916,11939,3280,3355,12066,4520,10309,10399,10512,10536,10782,10826,10836,11512,11610,11631,11634,11637,11653,11807,11810,11813,11816,11900,11919,11922,11935,11990,11993,11996,11999,12073,12161,3437,10608,10871,10915,11184,11262,11425,11665,4532,10791,10803,10907,10925,10928,10983,11069,11077,11093,11131,11148,11156,11192,11233,11253,11256,11259,11290,11297,11300,11682,11718,11984,11987,12021,12067,3341,10637,10667,10676,11213,3379,3373,3800,3738,10312,11585,11613,4529,10263,10625,10628,11072,11090,11548,11601,11641,11666,11770,11795,11798,11801,11804,12062,3300,10670,10820,10891,11614,11769,11961,12169,3761,4110,4527,3772,3808,4510,4513,3251,3255,4512,3174,4511,4515,3779,3594,4209,4544,10234,10237,10493,10544,10547,10552,10957,11419,11669,11773,4551,11151,11270,3996,3886,11303,11640,11644,3727,10931,10937,10952,11885,12014,3579,3729,10673,11008,11159,11189,11200,3547,10591,10594,10679,10847,4548,11579,4538,4549,10730,10829,11139,11422,11453,12185,4170,4071,3760,3707,4546,10285,10288,10631,10634,11464,4547,11559,3731,10597,4003,4568,4594,4643,4645,4675,4692,4699,4700,4739,4769,4775,4860,4885,4886,4921,4946,4947,4969,4970,4983,4987,5010,5017,5035,5038,5039,5040,5045,5046,5068,5093,5094,5104,5109,5115,5160,5161,5169,5178,5183,5185,5195,5197,5203,5207,5222,5229,5232,5233,5234,5238,5274,5287,5295,5297,5298,5302,5303,5304,5312,5315,5319,5320,5321,5328,5332,5333,5334,5342,5346,5347,5348,5353,5366,5375,5387,5389,5397,5398,5402,5406,5431,5437,5447,5448,5463,5475,5497,5503,5519,5520,5523,5542,5550,5551,5556,5557,5567,5569,5581,5585,5594,5595,5597,5612,5617,5627,5628,5640,5647,5661,5665,5668,5674,5675,5676,5679,5684,5722,5723,5726,5728,5731,5732,5733,5735,5737,5739,5744,5751,5766,5780,5785,5786,5799,5800,5805,5809,5811,5816,5857,5869,5878,5882,5893,5897,5898,5906,5920,5926,5944,5947,5959,5985,5999,6024,6044,6045,6048,6062,6064,6066,6068,6081,6082,6085,6087,6090,6091,6103,6109,6110,6111,6113,6115,6158,6159,6166,6172,6176,6212,6214,6216,6218,6227,6229,6231,6237,6239,6245,6248,6256,6263,6264,6265,6270,6292,6293,6294,6296,6302,6307,6341,6342,6344,6345,6346,6348,6349,6350,6351,6358,6391,6392,6401,6422,6423,6443,6446,6457,6458,6464,6495,6497,6511,6549,6551,6552,6606,6630,6672,6692,6701,6702,6703,6704,6723,6724,6730,6743,6746,6748,6750,6751,6752,6754,6768,6779,6781,6782,6795,6799,6850,6861,6863,6867,6884,6885,6921,6933,6964,6998,7052,7080,7135,7156,7165,7168,7223,7231,7289,7291,7306,7316,7317,7318,7337,7343,7345,7395,7405,7408,7424,7476,7478,7481,7524,7525,7543,7610,7629,7652,7676,7691,7706,7717,7726,7727,7756,7759,7761,7771,7809,7820,7845,7903,7937,7969,8016,8032,8048,8049,8124,8177,8196,8220,8240,8264,8362,8364,8370,8386,8390,8406,8429,8440,8442,8457,8463,8467,8490,8504,8505,8521,8522,8527,8528,8529,8530,8531,8549,8550,8551,8559,8573,8575,8587,8591,8593,8594,8595,8603,8608,8635,8636,8668,8681,8685,8703,8725,8726,8727,8728,8740,8741,8763,8773,8783,8784,8785,8786,8788,8809,8810,8821,8865,8871,8877,8889,8894,8896,8899,8900,8904,8914,8997,9028,9029,9030,9045,9063,9068,9096,9097,9138,9141,9167,9212,9213,9214,9229,9256,9270,9276,9279,9301,9302,9330,9391,9426,9427,9428,9453,9454,9472,9491,9497,9511,9534,9556,9564,9565,9566,9567,9582,9584,9589,9620,9621,9627,9628,9672,9673,9705,9714,9724,9726,9727,9736,9750,9753,9781,9814,9816,9820,9878,9919,9920,9922,9932,9933,9953,9958,9999,10050,10122,10123,10176,10192,2,8,9,4581,4582,4600,4631,4633,4634,4661,4667,46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% 187.33/188.09 cnf(12194,plain,
% 187.33/188.09 (~P24(f329(f329(f193(f881(x121941,f881(x121942,a869))),x121943),x121944))),
% 187.33/188.09 inference(rename_variables,[],[4549])).
% 187.33/188.09 cnf(12197,plain,
% 187.33/188.09 (P24(f329(f329(f243(f881(f880(f875(x121971),f875(x121971)),a869)),f156(x121971,x121972)),f305(f875(x121971),f155(x121971,x121972))))),
% 187.33/188.09 inference(rename_variables,[],[3987])).
% 187.33/188.09 cnf(12203,plain,
% 187.33/188.09 (P24(f329(f329(f243(f881(x122031,a869)),f329(f171(x122031),f175(x122031,x122032,x122033))),f329(f171(x122031),x122032)))),
% 187.33/188.09 inference(rename_variables,[],[3982])).
% 187.33/188.09 cnf(12204,plain,
% 187.33/188.09 (P24(f329(f329(f243(f881(x122041,a869)),f329(f171(x122041),f329(f134(x122041,x122042),x122043))),f329(f171(x122041),x122043)))),
% 187.33/188.09 inference(rename_variables,[],[3931])).
% 187.33/188.09 cnf(12207,plain,
% 187.33/188.09 (~P24(f329(f329(f244(f881(x122071,a869)),x122072),f193(f881(x122071,a869))))),
% 187.33/188.09 inference(rename_variables,[],[4542])).
% 187.33/188.09 cnf(12210,plain,
% 187.33/188.09 (P21(x122101,f878(x122101),f236(x122101),x122102)),
% 187.33/188.09 inference(rename_variables,[],[3531])).
% 187.33/188.09 cnf(12215,plain,
% 187.33/188.09 (P24(f329(f329(f243(f881(x122151,a869)),f329(f308(x122152,x122151,x122153),f329(f309(x122152,x122151,x122153),x122154))),x122154))),
% 187.33/188.09 inference(rename_variables,[],[4170])).
% 187.33/188.09 cnf(12218,plain,
% 187.33/188.09 (P24(f329(f62(f878(x122181)),f329(f308(x122182,f878(x122181),f329(f177(x122182,x122181),x122183)),f252(f881(x122182,a869)))))),
% 187.33/188.09 inference(rename_variables,[],[3996])).
% 187.33/188.09 cnf(12223,plain,
% 187.33/188.09 (P24(f329(f329(f331(f875(x122231)),f118(x122231)),f159(x122231,x122232)))),
% 187.33/188.09 inference(rename_variables,[],[3482])).
% 187.33/188.09 cnf(12226,plain,
% 187.33/188.09 (~P24(f329(f329(f331(f880(f875(x122261),f875(x122261))),f329(f329(f264(f875(x122261),f875(x122261)),x122262),f118(x122261))),f143(x122261,x122263)))),
% 187.33/188.09 inference(rename_variables,[],[4553])).
% 187.33/188.09 cnf(12229,plain,
% 187.33/188.09 (~P24(f329(f329(f244(a874),x122291),f2(a874)))),
% 187.33/188.09 inference(rename_variables,[],[4524])).
% 187.33/188.09 cnf(12231,plain,
% 187.33/188.09 (~P24(f329(f62(x122311),f252(f881(x122311,a869))))),
% 187.33/188.09 inference(scs_inference,[],[4323,3521,11045,12081,3530,3531,3245,4492,4493,3145,4477,4459,10208,10218,10229,10240,10341,10344,10347,10450,10563,10866,11030,11033,11230,11317,11324,11338,11390,11393,11437,11503,11549,11565,11864,11889,11901,11930,11936,12031,12141,4474,10434,10527,3490,3193,2873,2874,2876,2877,2880,2881,2883,2884,2885,2892,2895,2896,2903,2904,2908,2909,2917,2920,2932,2938,2944,2952,2953,2954,2961,2974,3010,3019,3020,3022,3029,3035,3037,3047,3053,3065,4455,3847,11596,3118,11314,3234,10211,10275,10278,10368,10371,10664,11329,11332,11448,11490,11495,11591,3212,3219,3740,3979,3108,3484,3832,11364,3169,3136,3131,4560,3115,3116,3151,3337,10815,3205,3229,10475,3383,4541,3919,4484,10266,10431,3267,11685,4530,10980,11050,11273,11276,3384,3166,10333,10640,3167,3442,3087,3189,11354,4066,3921,10986,11112,11162,4553,10918,11117,11221,11243,11281,11287,4554,11019,11120,11224,4555,11123,4556,11176,4557,3188,3482,12182,12223,3644,4350,4351,4482,3583,3796,3842,3468,3722,3347,10352,10470,10541,10602,10605,10643,10737,10970,11860,11923,12002,12042,12119,3733,11582,3260,3359,3546,4524,10243,10246,10272,10745,10758,10876,11265,11357,11752,11757,11978,11981,12063,12072,4536,11467,11498,11533,11562,3720,3491,3869,3306,3308,3281,4521,4479,3474,4537,4060,11238,3604,3320,11709,11712,4030,3987,11853,12197,3931,3982,10989,12078,3645,11863,12009,12086,12132,4019,3663,10992,11055,11136,11195,12030,4542,10761,11128,3276,10361,10457,10588,10650,10719,10764,10767,10800,10823,10860,10898,10934,11656,11703,11833,11888,11904,11907,11910,11913,12093,12107,12110,12113,12116,3277,10390,10445,10655,10740,10863,11440,11737,11740,11749,11839,11850,11869,11874,11916,11939,3280,3355,12066,4520,10309,10399,10512,10536,10782,10826,10836,11512,11610,11631,11634,11637,11653,11807,11810,11813,11816,11900,11919,11922,11935,11990,11993,11996,11999,12073,12161,3437,10608,10871,10915,11184,11262,11425,11665,4532,10791,10803,10907,10925,10928,10983,11069,11077,11093,11131,11148,11156,11192,11233,11253,11256,11259,11290,11297,11300,11682,11718,11984,11987,12021,12067,3341,10637,10667,10676,11213,3379,3373,3800,3738,10312,11585,11613,4529,10263,10625,10628,11072,11090,11548,11601,11641,11666,11770,11795,11798,11801,11804,12062,3300,10670,10820,10891,11614,11769,11961,12169,3761,4110,4527,3772,3808,4510,4513,3251,3255,4512,3174,4511,4515,3779,3594,4209,4544,10234,10237,10493,10544,10547,10552,10957,11419,11669,11773,4551,11151,11270,3996,3886,11303,11640,11644,3727,10931,10937,10952,11885,12014,3579,12125,3729,10673,11008,11159,11189,11200,3547,10591,10594,10679,10847,4548,11579,4538,4549,10730,10829,11139,11422,11453,12185,4170,10806,4071,3760,3707,4546,10285,10288,10631,10634,11464,4547,11559,3731,10597,4003,4568,4594,4643,4645,4675,4692,4699,4700,4739,4769,4775,4860,4885,4886,4921,4946,4947,4969,4970,4983,4987,5010,5017,5035,5038,5039,5040,5045,5046,5068,5093,5094,5104,5109,5115,5160,5161,5169,5178,5183,5185,5195,5197,5203,5207,5222,5229,5232,5233,5234,5238,5274,5287,5295,5297,5298,5302,5303,5304,5312,5315,5319,5320,5321,5328,5332,5333,5334,5342,5346,5347,5348,5353,5366,5375,5387,5389,5397,5398,5402,5406,5431,5437,5447,5448,5463,5475,5497,5503,5519,5520,5523,5542,5550,5551,5556,5557,5567,5569,5581,5585,5594,5595,5597,5612,5617,5627,5628,5640,5647,5661,5665,5668,5674,5675,5676,5679,5684,5722,5723,5726,5728,5731,5732,5733,5735,5737,5739,5744,5751,5766,5780,5785,5786,5799,5800,5805,5809,5811,5816,5857,5869,5878,5882,5893,5897,5898,5906,5920,5926,5944,5947,5959,5985,5999,6024,6044,6045,6048,6062,6064,6066,6068,6081,6082,6085,6087,6090,6091,6103,6109,6110,6111,6113,6115,6158,6159,6166,6172,6176,6212,6214,6216,6218,6227,6229,6231,6237,6239,6245,6248,6256,6263,6264,6265,6270,6292,6293,6294,6296,6302,6307,6341,6342,6344,6345,6346,6348,6349,6350,6351,6358,6391,6392,6401,6422,6423,6443,6446,6457,6458,6464,6495,6497,6511,6549,6551,6552,6606,6630,6672,6692,6701,6702,6703,6704,6723,6724,6730,6743,6746,6748,6750,6751,6752,6754,6768,6779,6781,6782,6795,6799,6850,6861,6863,6867,6884,6885,6921,6933,6964,6998,7052,7080,7135,7156,7165,7168,7223,7231,7289,7291,7306,7316,7317,7318,7337,7343,7345,7395,7405,7408,7424,7476,7478,7481,7524,7525,7543,7610,7629,7652,7676,7691,7706,7717,7726,7727,7756,7759,7761,7771,7809,7820,7845,7903,7937,7969,8016,8032,8048,8049,8124,8177,8196,8220,8240,8264,8362,8364,8370,8386,8390,8406,8429,8440,8442,8457,8463,8467,8490,8504,8505,8521,8522,8527,8528,8529,8530,8531,8549,8550,8551,8559,8573,8575,8587,8591,8593,8594,8595,8603,8608,8635,8636,8668,8681,8685,8703,8725,8726,8727,8728,8740,8741,8763,8773,8783,8784,8785,8786,8788,8809,8810,8821,8865,8871,8877,8889,8894,8896,8899,8900,8904,8914,8997,9028,9029,9030,9045,9063,9068,9096,9097,9138,9141,9167,9212,9213,9214,9229,9256,9270,9276,9279,9301,9302,9330,9391,9426,9427,9428,9453,9454,9472,9491,9497,9511,9534,9556,9564,9565,9566,9567,9582,9584,9589,9620,9621,9627,9628,9672,9673,9705,9714,9724,9726,9727,9736,9750,9753,9781,9814,9816,9820,9878,9919,9920,9922,9932,9933,9953,9958,9999,10050,10122,10123,10176,10192,2,8,9,4581,4582,4600,4631,4633,4634,4661,4667,4668,4679,4728,4730,4760,4774,4804,4900,4901,4914,4934,4990,4991,4994,4995,4997,4999,5000,5009,5013,5014,5024,5036,5037,5043,5063,5064,5081,5086,5087,5088,5089,5092,5100,5103,5110,5175,5181,5182,5189,5219,5230,5236,5252,5272,5273,5280,5281,5282,5291,5301,5308,5310,5311,5317,5324,5325,5338,5339,5340,5341,5343,5344,5349,5350,5351,5352,5383,5384,5385,5393,5394,5395,5396,5439,5444,5446,5482,5484,5485,5487,5488,5490,5491,5493,5502,5507,5509,5510,5511,5512,5513,5514,5521,5531,5534,5545,5561,5562,5565,5575,5577,5578,5579,5604,5614,5630,5631,5641,5642,5644,5646,5651,5686,5691,5693,5753,5787,5788,5792,5798,5801,5802,5803,5804,5810,5821,5822,5824,5825,5833,5854,5885,5901,5904,5905,5907,5916,5934,5938,5941,5942,5943,5961,5972,5973,6001,6002,6006,6026,6029,6033,6052,6057,6058,6083,6086,6094,6102,6108,6112,6119,6120,6121,6122,6161,6177,6230,6266,6268,6289,6290,6295,6299,6300,6303,6309,6318,6333,6353,6354,6359,6369,6384,6404,6410,6412,6427,6428,6431,6432,6434,6436,6437,6438,6440,6442,6445,6450,6451,6453,6454,6460,6462,6505,6510,6524,6526,6527,6528,6563,6568,6570,6575,6576,6584,6588,6601,6625,6626,6628,6629,6640,6646,6663,6666,6685,6718,6719,6720,6725,6739,6758,6760,6762,6764,6769,6775,6777,6792,6797,6800,6836,6837,6838,6852,6853,6855,6856,6875,6877,6893,6919,6941,6952,6954,6956,6958,6959,6960,6995,6996,7001,7002,7009,7010,7012,7014,7033,7042,7043,7055,7065,7104,7114,7118,7125,7136,7142,7144,7150,7158,7159,7172,7189,7207,7209,7226,7275,7276,7277,7279,7281,7285,7290,7313,7358,7391,7406,7423,7456,7459,7485,7509,7526,7529,7530,7540,7559,7561,7563,7565,7566,7567,7592,7618,7619,7651,7653,7654,7655,7660,7683,7692,7703,7708,7714,7716,7722,7734,7735,7737,7762,7769,7792,7858,7859,7906,7914,7915,7939,7940,7957,7958,8023,8024,8051,8080,8091,8093,8102,8114,8146,8152,8159])).
% 187.33/188.09 cnf(12232,plain,
% 187.33/188.09 (P24(f329(f329(f243(f881(x122321,a869)),x122322),x122322))),
% 187.33/188.09 inference(rename_variables,[],[3579])).
% 187.33/188.09 cnf(12235,plain,
% 187.33/188.09 (~P24(f329(f329(f331(x122351),x122352),f193(f881(x122351,a869))))),
% 187.33/188.09 inference(rename_variables,[],[4532])).
% 187.33/188.09 cnf(12238,plain,
% 187.33/188.09 (~P24(f329(f329(f193(f881(x122381,f881(x122382,a869))),x122383),x122384))),
% 187.33/188.09 inference(rename_variables,[],[4549])).
% 187.33/188.09 cnf(12241,plain,
% 187.33/188.09 (P24(f329(f329(f243(f881(x122411,a869)),x122412),x122412))),
% 187.33/188.09 inference(rename_variables,[],[3579])).
% 187.33/188.09 cnf(12246,plain,
% 187.33/188.09 (E(f329(f260(x122461,x122461),f261(x122461,x122462)),x122462)),
% 187.33/188.09 inference(rename_variables,[],[3234])).
% 187.33/188.09 cnf(12251,plain,
% 187.33/188.09 (P24(f329(f329(f243(a874),x122511),x122511))),
% 187.33/188.09 inference(rename_variables,[],[3276])).
% 187.33/188.09 cnf(12254,plain,
% 187.33/188.09 (~P24(f329(f329(f244(a874),x122541),x122541))),
% 187.33/188.09 inference(rename_variables,[],[4520])).
% 187.33/188.09 cnf(12257,plain,
% 187.33/188.09 (~P24(f329(f329(f244(a874),x122571),x122571))),
% 187.33/188.09 inference(rename_variables,[],[4520])).
% 187.33/188.09 cnf(12268,plain,
% 187.33/188.09 (P21(x122681,x122681,f5(x122681),x122682)),
% 187.33/188.09 inference(rename_variables,[],[3521])).
% 187.33/188.09 cnf(12273,plain,
% 187.33/188.09 (~P24(f329(f329(f331(x122731),x122732),f193(f881(x122731,a869))))),
% 187.33/188.09 inference(rename_variables,[],[4532])).
% 187.33/188.09 cnf(12276,plain,
% 187.33/188.09 (P24(f329(f329(f331(f880(x122761,x122761)),f329(f329(f264(x122761,x122761),x122762),x122762)),f305(x122761,x122763)))),
% 187.33/188.09 inference(rename_variables,[],[3921])).
% 187.33/188.09 cnf(12279,plain,
% 187.33/188.09 (~P24(f329(f329(f331(x122791),x122792),f193(f881(x122791,a869))))),
% 187.33/188.09 inference(rename_variables,[],[4532])).
% 187.33/188.09 cnf(12282,plain,
% 187.33/188.09 (P24(f329(f329(f331(f880(x122821,x122821)),f329(f329(f264(x122821,x122821),x122822),x122822)),f305(x122821,x122823)))),
% 187.33/188.09 inference(rename_variables,[],[3921])).
% 187.33/188.09 cnf(12292,plain,
% 187.33/188.09 (~E(f329(f329(f149(x122921),x122922),x122923),x122923)),
% 187.33/188.09 inference(rename_variables,[],[4484])).
% 187.33/188.09 cnf(12295,plain,
% 187.33/188.09 (P24(f329(f329(f331(x122951),x122952),f252(f881(x122951,a869))))),
% 187.33/188.09 inference(rename_variables,[],[3437])).
% 187.33/188.09 cnf(12296,plain,
% 187.33/188.09 (~E(f329(a117,x122961),x122961)),
% 187.33/188.09 inference(rename_variables,[],[4459])).
% 187.33/188.09 cnf(12299,plain,
% 187.33/188.09 (P24(f329(f329(f331(f875(x122991)),f118(x122991)),f159(x122991,x122992)))),
% 187.33/188.09 inference(rename_variables,[],[3482])).
% 187.33/188.09 cnf(12300,plain,
% 187.33/188.09 (~E(f329(f329(f149(x123001),x123002),x123003),f118(x123001))),
% 187.33/188.09 inference(rename_variables,[],[4491])).
% 187.33/188.09 cnf(12303,plain,
% 187.33/188.09 (P24(f329(f329(f331(x123031),f329(x123032,x123033)),f329(f308(x123034,x123031,x123032),f252(f881(x123034,a869)))))),
% 187.33/188.09 inference(rename_variables,[],[3886])).
% 187.33/188.09 cnf(12304,plain,
% 187.33/188.09 (P21(x123041,x123041,f5(x123041),x123042)),
% 187.33/188.09 inference(rename_variables,[],[3521])).
% 187.33/188.09 cnf(12307,plain,
% 187.33/188.09 (P24(f329(f329(f243(f881(x123071,a869)),f193(f881(x123071,a869))),x123072))),
% 187.33/188.09 inference(rename_variables,[],[3729])).
% 187.33/188.09 cnf(12308,plain,
% 187.33/188.09 (P24(f329(f329(f243(f881(x123081,a869)),x123082),x123082))),
% 187.33/188.09 inference(rename_variables,[],[3579])).
% 187.33/188.09 cnf(12311,plain,
% 187.33/188.09 (P24(f329(f329(f331(x123111),f329(x123112,x123113)),f329(f308(x123114,x123111,x123112),f252(f881(x123114,a869)))))),
% 187.33/188.09 inference(rename_variables,[],[3886])).
% 187.33/188.09 cnf(12312,plain,
% 187.33/188.09 (P21(x123121,x123121,f5(x123121),x123122)),
% 187.33/188.09 inference(rename_variables,[],[3521])).
% 187.33/188.09 cnf(12315,plain,
% 187.33/188.09 (P24(f329(f329(f331(f880(f875(x123151),f875(x123151))),f329(f329(f264(f875(x123151),f875(x123151)),f118(x123151)),f118(x123151))),f156(x123151,x123152)))),
% 187.33/188.09 inference(rename_variables,[],[4066])).
% 187.33/188.09 cnf(12318,plain,
% 187.33/188.09 (~P24(f329(f329(f244(a874),x123181),x123181))),
% 187.33/188.09 inference(rename_variables,[],[4520])).
% 187.33/188.09 cnf(12319,plain,
% 187.33/188.09 (~P24(f329(f329(f244(a874),x123191),f2(a874)))),
% 187.33/188.09 inference(rename_variables,[],[4524])).
% 187.33/188.09 cnf(12325,plain,
% 187.33/188.09 (E(f329(f329(f126(x123251),x123252),f118(x123251)),x123252)),
% 187.33/188.09 inference(rename_variables,[],[3206])).
% 187.33/188.09 cnf(12326,plain,
% 187.33/188.09 (~E(f329(f329(f149(x123261),x123262),x123263),x123263)),
% 187.33/188.09 inference(rename_variables,[],[4484])).
% 187.33/188.09 cnf(12329,plain,
% 187.33/188.09 (E(f329(f329(f126(x123291),x123292),f118(x123291)),x123292)),
% 187.33/188.09 inference(rename_variables,[],[3206])).
% 187.33/188.09 cnf(12330,plain,
% 187.33/188.09 (~E(f329(f329(f149(x123301),x123302),x123303),x123303)),
% 187.33/188.09 inference(rename_variables,[],[4484])).
% 187.33/188.09 cnf(12333,plain,
% 187.33/188.09 (E(f329(f329(f126(x123331),x123332),f118(x123331)),x123332)),
% 187.33/188.09 inference(rename_variables,[],[3206])).
% 187.33/188.09 cnf(12342,plain,
% 187.33/188.09 (P24(f329(f329(f243(f881(x123421,a869)),x123422),f252(f881(x123421,a869))))),
% 187.33/188.09 inference(rename_variables,[],[3663])).
% 187.33/188.09 cnf(12346,plain,
% 187.33/188.09 (~P24(f329(f329(f244(a874),x123461),x123461))),
% 187.33/188.09 inference(rename_variables,[],[4520])).
% 187.33/188.09 cnf(12347,plain,
% 187.33/188.09 (~E(f329(a117,x123471),x123471)),
% 187.33/188.09 inference(rename_variables,[],[4459])).
% 187.33/188.09 cnf(12350,plain,
% 187.33/188.09 (P24(f329(f329(f243(f881(x123501,a869)),f193(f881(x123501,a869))),x123502))),
% 187.33/188.09 inference(rename_variables,[],[3729])).
% 187.33/188.09 cnf(12353,plain,
% 187.33/188.09 (P24(f329(f329(f243(a874),x123531),x123531))),
% 187.33/188.09 inference(rename_variables,[],[3276])).
% 187.33/188.09 cnf(12356,plain,
% 187.33/188.09 (P24(f329(f329(f243(f881(x123561,a869)),x123562),x123562))),
% 187.33/188.09 inference(rename_variables,[],[3579])).
% 187.33/188.09 cnf(12361,plain,
% 187.33/188.09 (P24(f329(f329(f243(f881(x123611,a869)),x123612),f329(f329(f307(x123611),x123613),x123612)))),
% 187.33/188.09 inference(rename_variables,[],[3727])).
% 187.33/188.09 cnf(12364,plain,
% 187.33/188.09 (P24(f329(f329(f243(f881(x123641,a869)),x123642),x123642))),
% 187.33/188.09 inference(rename_variables,[],[3579])).
% 187.33/188.09 cnf(12365,plain,
% 187.33/188.09 (~P24(f329(f329(f331(x123651),x123652),f193(f881(x123651,a869))))),
% 187.33/188.09 inference(rename_variables,[],[4532])).
% 187.33/188.09 cnf(12368,plain,
% 187.33/188.09 (~P24(f329(f329(f331(x123681),x123682),f193(f881(x123681,a869))))),
% 187.33/188.09 inference(rename_variables,[],[4532])).
% 187.33/188.09 cnf(12376,plain,
% 187.33/188.09 (~P24(f329(f329(f243(f881(f880(x123761,x123761),a869)),f329(f308(f880(x123761,x123761),f880(x123761,x123761),f5(f880(x123761,x123761))),f252(f881(f880(x123761,x123761),a869)))),f329(f308(f880(x123761,x123761),f880(x123761,x123761),f5(f880(x123761,x123761))),f193(f881(f880(x123761,x123761),a869)))))),
% 187.33/188.09 inference(scs_inference,[],[4323,3521,11045,12081,12179,12268,12304,12312,3530,3531,3245,4492,4493,3145,4477,4459,10208,10218,10229,10240,10341,10344,10347,10450,10563,10866,11030,11033,11230,11317,11324,11338,11390,11393,11437,11503,11549,11565,11864,11889,11901,11930,11936,12031,12141,12148,12296,4474,10434,10527,3336,3490,3193,2873,2874,2876,2877,2880,2881,2883,2884,2885,2892,2895,2896,2903,2904,2908,2909,2910,2917,2920,2932,2938,2944,2952,2953,2954,2961,2974,3010,3019,3020,3022,3029,3035,3037,3047,3053,3065,4455,3847,11596,3118,11314,3234,10211,10275,10278,10368,10371,10664,11329,11332,11448,11490,11495,11591,12051,3206,12325,12329,3212,3219,3740,3979,3108,4471,3484,3832,11364,3169,3136,3131,4560,3115,3116,3151,3337,10815,12142,3204,3205,3229,10475,3383,4541,3919,4484,10266,10431,11227,12292,12326,4491,12300,3267,11685,4530,10980,11050,11273,11276,3384,3166,10333,10640,3167,3442,3087,3189,11354,4066,12315,3921,10986,11112,11162,12276,12282,4553,10918,11117,11221,11243,11281,11287,12226,4554,11019,11120,11224,4555,11123,4556,11176,4557,3188,3482,12182,12223,12299,3644,4350,4351,4482,11345,3583,3796,3842,3468,3722,3347,10352,10470,10541,10602,10605,10643,10737,10970,11860,11923,12002,12042,12119,12122,3733,11582,3260,3359,3546,4524,10243,10246,10272,10745,10758,10876,11265,11357,11752,11757,11978,11981,12063,12072,12229,4536,11467,11498,11533,11562,3720,3491,3869,3306,3308,3281,4521,4479,3672,3474,4537,4060,11238,3604,3320,11709,11712,4030,3987,11853,12197,3931,3982,10989,12078,3645,11863,12009,12086,12132,4019,3663,10992,11055,11136,11195,12030,12100,4542,10761,11128,3276,10361,10457,10588,10650,10719,10764,10767,10800,10823,10860,10898,10934,11656,11703,11833,11888,11904,11907,11910,11913,12093,12107,12110,12113,12116,12190,12251,3277,10390,10445,10655,10740,10863,11440,11737,11740,11749,11839,11850,11869,11874,11916,11939,3280,3355,12066,4520,10309,10399,10512,10536,10782,10826,10836,11512,11610,11631,11634,11637,11653,11807,11810,11813,11816,11900,11919,11922,11935,11990,11993,11996,11999,12073,12161,12164,12254,12257,12318,3437,10608,10871,10915,11184,11262,11425,11665,4532,10791,10803,10907,10925,10928,10983,11069,11077,11093,11131,11148,11156,11192,11233,11253,11256,11259,11290,11297,11300,11682,11718,11984,11987,12021,12067,12096,12235,12273,12279,12365,3341,10637,10667,10676,11213,3379,3373,3800,3738,10312,11585,11613,4529,10263,10625,10628,11072,11090,11548,11601,11641,11666,11770,11795,11798,11801,11804,12062,3300,10670,10820,10891,11614,11769,11961,12169,3761,4110,4527,3772,3808,4510,4513,3251,3255,4512,3174,4511,4515,3779,3594,4209,4544,10234,10237,10493,10544,10547,10552,10957,11419,11669,11773,4551,11151,11270,11306,3996,3886,11303,11640,11644,11706,12303,3727,10931,10937,10952,11885,12014,12099,3579,12125,12232,12241,12308,12356,3729,10673,11008,11159,11189,11200,12034,12307,3547,10591,10594,10679,10847,4548,11579,4538,4549,10730,10829,11139,11422,11453,12185,12194,4170,10806,4071,3760,3707,4546,10285,10288,10631,10634,11464,4547,11559,3731,10597,4003,4568,4594,4643,4645,4675,4692,4699,4700,4739,4769,4775,4860,4885,4886,4921,4946,4947,4969,4970,4983,4987,5010,5017,5035,5038,5039,5040,5045,5046,5068,5093,5094,5104,5109,5115,5160,5161,5169,5178,5183,5185,5195,5197,5203,5207,5222,5229,5232,5233,5234,5238,5274,5287,5295,5297,5298,5302,5303,5304,5312,5315,5319,5320,5321,5328,5332,5333,5334,5342,5346,5347,5348,5353,5366,5375,5387,5389,5397,5398,5402,5406,5431,5437,5447,5448,5463,5475,5497,5503,5519,5520,5523,5542,5550,5551,5556,5557,5567,5569,5581,5585,5594,5595,5597,5612,5617,5627,5628,5640,5647,5661,5665,5668,5674,5675,5676,5679,5684,5722,5723,5726,5728,5731,5732,5733,5735,5737,5739,5744,5751,5766,5780,5785,5786,5799,5800,5805,5809,5811,5816,5857,5869,5878,5882,5893,5897,5898,5906,5920,5926,5944,5947,5959,5985,5999,6024,6044,6045,6048,6062,6064,6066,6068,6081,6082,6085,6087,6090,6091,6103,6109,6110,6111,6113,6115,6158,6159,6166,6172,6176,6212,6214,6216,6218,6227,6229,6231,6237,6239,6245,6248,6256,6263,6264,6265,6270,6292,6293,6294,6296,6302,6307,6341,6342,6344,6345,6346,6348,6349,6350,6351,6358,6391,6392,6401,6422,6423,6443,6446,6457,6458,6464,6495,6497,6511,6549,6551,6552,6606,6630,6672,6692,6701,6702,6703,6704,6723,6724,6730,6743,6746,6748,6750,6751,6752,6754,6768,6779,6781,6782,6795,6799,6850,6861,6863,6867,6884,6885,6921,6933,6964,6998,7052,7080,7135,7156,7165,7168,7223,7231,7289,7291,7306,7316,7317,7318,7337,7343,7345,7395,7405,7408,7424,7476,7478,7481,7524,7525,7543,7610,7629,7652,7676,7691,7706,7717,7726,7727,7756,7759,7761,7771,7809,7820,7845,7903,7937,7969,8016,8032,8048,8049,8124,8177,8196,8220,8240,8264,8362,8364,8370,8386,8390,8406,8429,8440,8442,8457,8463,8467,8490,8504,8505,8521,8522,8527,8528,8529,8530,8531,8549,8550,8551,8559,8573,8575,8587,8591,8593,8594,8595,8603,8608,8635,8636,8668,8681,8685,8703,8725,8726,8727,8728,8740,8741,8763,8773,8783,8784,8785,8786,8788,8809,8810,8821,8865,8871,8877,8889,8894,8896,8899,8900,8904,8914,8997,9028,9029,9030,9045,9063,9068,9096,9097,9138,9141,9167,9212,9213,9214,9229,9256,9270,9276,9279,9301,9302,9330,9391,9426,9427,9428,9453,9454,9472,9491,9497,9511,9534,9556,9564,9565,9566,9567,9582,9584,9589,9620,9621,9627,9628,9672,9673,9705,9714,9724,9726,9727,9736,9750,9753,9781,9814,9816,9820,9878,9919,9920,9922,9932,9933,9953,9958,9999,10050,10122,10123,10176,10192,2,8,9,4581,4582,4600,4631,4633,4634,4661,4667,4668,4679,4728,4730,4760,4774,4804,4900,4901,4914,4934,4990,4991,4994,4995,4997,4999,5000,5009,5013,5014,5024,5036,5037,5043,5063,5064,5081,5086,5087,5088,5089,5092,5100,5103,5110,5175,5181,5182,5189,5219,5230,5236,5252,5272,5273,5280,5281,5282,5291,5301,5308,5310,5311,5317,5324,5325,5338,5339,5340,5341,5343,5344,5349,5350,5351,5352,5383,5384,5385,5393,5394,5395,5396,5439,5444,5446,5482,5484,5485,5487,5488,5490,5491,5493,5502,5507,5509,5510,5511,5512,5513,5514,5521,5531,5534,5545,5561,5562,5565,5575,5577,5578,5579,5604,5614,5630,5631,5641,5642,5644,5646,5651,5686,5691,5693,5753,5787,5788,5792,5798,5801,5802,5803,5804,5810,5821,5822,5824,5825,5833,5854,5885,5901,5904,5905,5907,5916,5934,5938,5941,5942,5943,5961,5972,5973,6001,6002,6006,6026,6029,6033,6052,6057,6058,6083,6086,6094,6102,6108,6112,6119,6120,6121,6122,6161,6177,6230,6266,6268,6289,6290,6295,6299,6300,6303,6309,6318,6333,6353,6354,6359,6369,6384,6404,6410,6412,6427,6428,6431,6432,6434,6436,6437,6438,6440,6442,6445,6450,6451,6453,6454,6460,6462,6505,6510,6524,6526,6527,6528,6563,6568,6570,6575,6576,6584,6588,6601,6625,6626,6628,6629,6640,6646,6663,6666,6685,6718,6719,6720,6725,6739,6758,6760,6762,6764,6769,6775,6777,6792,6797,6800,6836,6837,6838,6852,6853,6855,6856,6875,6877,6893,6919,6941,6952,6954,6956,6958,6959,6960,6995,6996,7001,7002,7009,7010,7012,7014,7033,7042,7043,7055,7065,7104,7114,7118,7125,7136,7142,7144,7150,7158,7159,7172,7189,7207,7209,7226,7275,7276,7277,7279,7281,7285,7290,7313,7358,7391,7406,7423,7456,7459,7485,7509,7526,7529,7530,7540,7559,7561,7563,7565,7566,7567,7592,7618,7619,7651,7653,7654,7655,7660,7683,7692,7703,7708,7714,7716,7722,7734,7735,7737,7762,7769,7792,7858,7859,7906,7914,7915,7939,7940,7957,7958,8023,8024,8051,8080,8091,8093,8102,8114,8146,8152,8159,8172,8191,8197,8219,8262,8292,8304,8322,8325,8355,8378,8443,8444,8447,8449,8553,8554,8555,8556,8582,8611,8639,8684,8702,8757,8802,8805,8818,8825,8862,8910,8911,8929,8930,9070,9074,9094,9104,9127,9129,9132,9136,9139,9140,9153,9154,9174,9180])).
% 187.33/188.09 cnf(12377,plain,
% 187.33/188.09 (P21(x123771,x123771,f5(x123771),x123772)),
% 187.33/188.09 inference(rename_variables,[],[3521])).
% 187.33/188.09 cnf(12380,plain,
% 187.33/188.09 (E(f329(f194(f875(x123801)),f329(f166(x123801),x123802)),f329(f194(f875(x123801)),x123802))),
% 187.33/188.09 inference(rename_variables,[],[3291])).
% 187.33/188.09 cnf(12383,plain,
% 187.33/188.09 (~P24(f329(f329(f244(a874),x123831),x123831))),
% 187.33/188.09 inference(rename_variables,[],[4520])).
% 187.33/188.09 cnf(12384,plain,
% 187.33/188.09 (P24(f329(f252(f881(x123841,a869)),x123842))),
% 187.33/188.09 inference(rename_variables,[],[3341])).
% 187.33/188.09 cnf(12389,plain,
% 187.33/188.09 (~P24(f329(f329(f331(x123891),x123892),f193(f881(x123891,a869))))),
% 187.33/188.09 inference(rename_variables,[],[4532])).
% 187.33/188.09 cnf(12392,plain,
% 187.33/188.09 (P24(f329(f329(f331(x123921),f329(x123922,x123923)),f329(f308(x123924,x123921,x123922),f252(f881(x123924,a869)))))),
% 187.33/188.09 inference(rename_variables,[],[3886])).
% 187.33/188.09 cnf(12393,plain,
% 187.33/188.09 (P24(f329(f329(f331(f880(x123931,x123931)),f329(f329(f264(x123931,x123931),x123932),x123932)),f305(x123931,x123933)))),
% 187.33/188.09 inference(rename_variables,[],[3921])).
% 187.33/188.09 cnf(12396,plain,
% 187.33/188.09 (P24(f329(f329(f331(f880(x123961,x123961)),f329(f329(f264(x123961,x123961),x123962),x123962)),f305(x123961,x123963)))),
% 187.33/188.09 inference(rename_variables,[],[3921])).
% 187.33/188.09 cnf(12399,plain,
% 187.33/188.09 (P24(f329(f329(f243(a874),x123991),x123991))),
% 187.33/188.09 inference(rename_variables,[],[3276])).
% 187.33/188.09 cnf(12400,plain,
% 187.33/188.09 (P24(f329(f252(f881(x124001,a869)),x124002))),
% 187.33/188.09 inference(rename_variables,[],[3341])).
% 187.33/188.09 cnf(12403,plain,
% 187.33/188.09 (P24(f329(f62(x124031),f329(f171(x124031),x124032)))),
% 187.33/188.09 inference(rename_variables,[],[3320])).
% 187.33/188.09 cnf(12408,plain,
% 187.33/188.09 (P24(f329(f329(f331(f880(f875(x124081),f875(x124081))),f329(f329(f264(f875(x124081),f875(x124081)),f118(x124081)),f118(x124081))),f329(f329(f286(f875(x124081),f875(x124081),f875(x124081)),f156(x124081,x124082)),f156(x124081,x124082))))),
% 187.33/188.09 inference(scs_inference,[],[4323,3521,11045,12081,12179,12268,12304,12312,3530,3531,3245,4492,4493,3145,4477,4459,10208,10218,10229,10240,10341,10344,10347,10450,10563,10866,11030,11033,11230,11317,11324,11338,11390,11393,11437,11503,11549,11565,11864,11889,11901,11930,11936,12031,12141,12148,12296,4474,10434,10527,3336,3490,3193,2873,2874,2876,2877,2880,2881,2883,2884,2885,2892,2895,2896,2903,2904,2908,2909,2910,2917,2920,2932,2938,2944,2952,2953,2954,2961,2974,3010,3019,3020,3022,3029,3035,3037,3047,3053,3065,4455,3847,11596,3118,11314,3234,10211,10275,10278,10368,10371,10664,11329,11332,11448,11490,11495,11591,12051,3206,12325,12329,12333,3212,3219,3740,3979,3108,4471,3484,3832,11364,3169,3136,3131,4560,3115,3116,3151,3291,3337,10815,12142,3204,3205,3229,10475,3383,4541,3919,4484,10266,10431,11227,12292,12326,4491,12300,3267,11685,4530,10980,11050,11273,11276,3384,3166,10333,10640,3167,3442,3087,3189,11354,4066,12315,3921,10986,11112,11162,12276,12282,12393,4553,10918,11117,11221,11243,11281,11287,12226,4554,11019,11120,11224,4555,11123,4556,11176,4557,3188,3482,12182,12223,12299,3644,4350,4351,4482,11345,3583,3796,3842,3468,3722,3347,10352,10470,10541,10602,10605,10643,10737,10970,11860,11923,12002,12042,12119,12122,3733,11582,3260,3359,3546,4524,10243,10246,10272,10745,10758,10876,11265,11357,11752,11757,11978,11981,12063,12072,12229,4536,11467,11498,11533,11562,3720,3491,3869,3306,3308,3281,4521,4479,3672,3474,4537,4060,11238,3604,3320,11709,11712,4030,3987,11853,12197,3931,3982,10989,12078,3645,11863,12009,12086,12132,4019,3663,10992,11055,11136,11195,12030,12100,4542,10761,11128,3276,10361,10457,10588,10650,10719,10764,10767,10800,10823,10860,10898,10934,11656,11703,11833,11888,11904,11907,11910,11913,12093,12107,12110,12113,12116,12190,12251,12353,3277,10390,10445,10655,10740,10863,11440,11737,11740,11749,11839,11850,11869,11874,11916,11939,3280,3355,12066,4520,10309,10399,10512,10536,10782,10826,10836,11512,11610,11631,11634,11637,11653,11807,11810,11813,11816,11900,11919,11922,11935,11990,11993,11996,11999,12073,12161,12164,12254,12257,12318,12346,3437,10608,10871,10915,11184,11262,11425,11665,4532,10791,10803,10907,10925,10928,10983,11069,11077,11093,11131,11148,11156,11192,11233,11253,11256,11259,11290,11297,11300,11682,11718,11984,11987,12021,12067,12096,12235,12273,12279,12365,12368,3341,10637,10667,10676,11213,11764,12384,3379,3373,3800,3738,10312,11585,11613,4529,10263,10625,10628,11072,11090,11548,11601,11641,11666,11770,11795,11798,11801,11804,12062,3300,10670,10820,10891,11614,11769,11961,12169,3761,4110,4527,3772,3808,4510,4513,3251,3255,4512,3174,4511,4515,3779,3594,4209,4544,10234,10237,10493,10544,10547,10552,10957,11419,11669,11773,4551,11151,11270,11306,3996,3886,11303,11640,11644,11706,12303,12311,3727,10931,10937,10952,11885,12014,12099,3579,12125,12232,12241,12308,12356,3729,10673,11008,11159,11189,11200,12034,12307,3547,10591,10594,10679,10847,4548,11579,4538,4549,10730,10829,11139,11422,11453,12185,12194,4170,10806,4071,3760,3707,4546,10285,10288,10631,10634,11464,4547,11559,3731,10597,4003,4568,4594,4643,4645,4675,4692,4699,4700,4739,4769,4775,4860,4885,4886,4921,4946,4947,4969,4970,4983,4987,5010,5017,5035,5038,5039,5040,5045,5046,5068,5093,5094,5104,5109,5115,5160,5161,5169,5178,5183,5185,5195,5197,5203,5207,5222,5229,5232,5233,5234,5238,5274,5287,5295,5297,5298,5302,5303,5304,5312,5315,5319,5320,5321,5328,5332,5333,5334,5342,5346,5347,5348,5353,5366,5375,5387,5389,5397,5398,5402,5406,5431,5437,5447,5448,5463,5475,5497,5503,5519,5520,5523,5542,5550,5551,5556,5557,5567,5569,5581,5585,5594,5595,5597,5612,5617,5627,5628,5640,5647,5661,5665,5668,5674,5675,5676,5679,5684,5722,5723,5726,5728,5731,5732,5733,5735,5737,5739,5744,5751,5766,5780,5785,5786,5799,5800,5805,5809,5811,5816,5857,5869,5878,5882,5893,5897,5898,5906,5920,5926,5944,5947,5959,5985,5999,6024,6044,6045,6048,6062,6064,6066,6068,6081,6082,6085,6087,6090,6091,6103,6109,6110,6111,6113,6115,6158,6159,6166,6172,6176,6212,6214,6216,6218,6227,6229,6231,6237,6239,6245,6248,6256,6263,6264,6265,6270,6292,6293,6294,6296,6302,6307,6341,6342,6344,6345,6346,6348,6349,6350,6351,6358,6391,6392,6401,6422,6423,6443,6446,6457,6458,6464,6495,6497,6511,6549,6551,6552,6606,6630,6672,6692,6701,6702,6703,6704,6723,6724,6730,6743,6746,6748,6750,6751,6752,6754,6768,6779,6781,6782,6795,6799,6850,6861,6863,6867,6884,6885,6921,6933,6964,6998,7052,7080,7135,7156,7165,7168,7223,7231,7289,7291,7306,7316,7317,7318,7337,7343,7345,7395,7405,7408,7424,7476,7478,7481,7524,7525,7543,7610,7629,7652,7676,7691,7706,7717,7726,7727,7756,7759,7761,7771,7809,7820,7845,7903,7937,7969,8016,8032,8048,8049,8124,8177,8196,8220,8240,8264,8362,8364,8370,8386,8390,8406,8429,8440,8442,8457,8463,8467,8490,8504,8505,8521,8522,8527,8528,8529,8530,8531,8549,8550,8551,8559,8573,8575,8587,8591,8593,8594,8595,8603,8608,8635,8636,8668,8681,8685,8703,8725,8726,8727,8728,8740,8741,8763,8773,8783,8784,8785,8786,8788,8809,8810,8821,8865,8871,8877,8889,8894,8896,8899,8900,8904,8914,8997,9028,9029,9030,9045,9063,9068,9096,9097,9138,9141,9167,9212,9213,9214,9229,9256,9270,9276,9279,9301,9302,9330,9391,9426,9427,9428,9453,9454,9472,9491,9497,9511,9534,9556,9564,9565,9566,9567,9582,9584,9589,9620,9621,9627,9628,9672,9673,9705,9714,9724,9726,9727,9736,9750,9753,9781,9814,9816,9820,9878,9919,9920,9922,9932,9933,9953,9958,9999,10050,10122,10123,10176,10192,2,8,9,4581,4582,4600,4631,4633,4634,4661,4667,4668,4679,4728,4730,4760,4774,4804,4900,4901,4914,4934,4990,4991,4994,4995,4997,4999,5000,5009,5013,5014,5024,5036,5037,5043,5063,5064,5081,5086,5087,5088,5089,5092,5100,5103,5110,5175,5181,5182,5189,5219,5230,5236,5252,5272,5273,5280,5281,5282,5291,5301,5308,5310,5311,5317,5324,5325,5338,5339,5340,5341,5343,5344,5349,5350,5351,5352,5383,5384,5385,5393,5394,5395,5396,5439,5444,5446,5482,5484,5485,5487,5488,5490,5491,5493,5502,5507,5509,5510,5511,5512,5513,5514,5521,5531,5534,5545,5561,5562,5565,5575,5577,5578,5579,5604,5614,5630,5631,5641,5642,5644,5646,5651,5686,5691,5693,5753,5787,5788,5792,5798,5801,5802,5803,5804,5810,5821,5822,5824,5825,5833,5854,5885,5901,5904,5905,5907,5916,5934,5938,5941,5942,5943,5961,5972,5973,6001,6002,6006,6026,6029,6033,6052,6057,6058,6083,6086,6094,6102,6108,6112,6119,6120,6121,6122,6161,6177,6230,6266,6268,6289,6290,6295,6299,6300,6303,6309,6318,6333,6353,6354,6359,6369,6384,6404,6410,6412,6427,6428,6431,6432,6434,6436,6437,6438,6440,6442,6445,6450,6451,6453,6454,6460,6462,6505,6510,6524,6526,6527,6528,6563,6568,6570,6575,6576,6584,6588,6601,6625,6626,6628,6629,6640,6646,6663,6666,6685,6718,6719,6720,6725,6739,6758,6760,6762,6764,6769,6775,6777,6792,6797,6800,6836,6837,6838,6852,6853,6855,6856,6875,6877,6893,6919,6941,6952,6954,6956,6958,6959,6960,6995,6996,7001,7002,7009,7010,7012,7014,7033,7042,7043,7055,7065,7104,7114,7118,7125,7136,7142,7144,7150,7158,7159,7172,7189,7207,7209,7226,7275,7276,7277,7279,7281,7285,7290,7313,7358,7391,7406,7423,7456,7459,7485,7509,7526,7529,7530,7540,7559,7561,7563,7565,7566,7567,7592,7618,7619,7651,7653,7654,7655,7660,7683,7692,7703,7708,7714,7716,7722,7734,7735,7737,7762,7769,7792,7858,7859,7906,7914,7915,7939,7940,7957,7958,8023,8024,8051,8080,8091,8093,8102,8114,8146,8152,8159,8172,8191,8197,8219,8262,8292,8304,8322,8325,8355,8378,8443,8444,8447,8449,8553,8554,8555,8556,8582,8611,8639,8684,8702,8757,8802,8805,8818,8825,8862,8910,8911,8929,8930,9070,9074,9094,9104,9127,9129,9132,9136,9139,9140,9153,9154,9174,9180,9192,9240,9241,9260,9314,9315,9322,9383,9388,9423])).
% 187.33/188.09 cnf(12410,plain,
% 187.33/188.09 (P24(f329(f329(f331(f880(x124101,x124101)),f329(f329(f264(x124101,x124101),x124102),x124102)),f329(f329(f286(x124101,x124101,x124101),f305(x124101,x124103)),f305(x124101,f305(x124101,x124103)))))),
% 187.33/188.09 inference(scs_inference,[],[4323,3521,11045,12081,12179,12268,12304,12312,3530,3531,3245,4492,4493,3145,4477,4459,10208,10218,10229,10240,10341,10344,10347,10450,10563,10866,11030,11033,11230,11317,11324,11338,11390,11393,11437,11503,11549,11565,11864,11889,11901,11930,11936,12031,12141,12148,12296,4474,10434,10527,3336,3490,3193,2873,2874,2876,2877,2880,2881,2883,2884,2885,2892,2895,2896,2903,2904,2908,2909,2910,2917,2920,2932,2938,2944,2952,2953,2954,2961,2974,3010,3019,3020,3022,3029,3035,3037,3047,3053,3065,4455,3847,11596,3118,11314,3234,10211,10275,10278,10368,10371,10664,11329,11332,11448,11490,11495,11591,12051,3206,12325,12329,12333,3212,3219,3740,3979,3108,4471,3484,3832,11364,3169,3136,3131,4560,3115,3116,3151,3291,3337,10815,12142,3204,3205,3229,10475,3383,4541,3919,4484,10266,10431,11227,12292,12326,4491,12300,3267,11685,4530,10980,11050,11273,11276,3384,3166,10333,10640,3167,3442,3087,3189,11354,4066,12315,3921,10986,11112,11162,12276,12282,12393,12396,4553,10918,11117,11221,11243,11281,11287,12226,4554,11019,11120,11224,4555,11123,4556,11176,4557,3188,3482,12182,12223,12299,3644,4350,4351,4482,11345,3583,3796,3842,3468,3722,3347,10352,10470,10541,10602,10605,10643,10737,10970,11860,11923,12002,12042,12119,12122,3733,11582,3260,3359,3546,4524,10243,10246,10272,10745,10758,10876,11265,11357,11752,11757,11978,11981,12063,12072,12229,4536,11467,11498,11533,11562,3720,3491,3869,3306,3308,3281,4521,4479,3672,3474,4537,4060,11238,3604,3320,11709,11712,4030,3987,11853,12197,3931,3982,10989,12078,3645,11863,12009,12086,12132,4019,3663,10992,11055,11136,11195,12030,12100,4542,10761,11128,3276,10361,10457,10588,10650,10719,10764,10767,10800,10823,10860,10898,10934,11656,11703,11833,11888,11904,11907,11910,11913,12093,12107,12110,12113,12116,12190,12251,12353,3277,10390,10445,10655,10740,10863,11440,11737,11740,11749,11839,11850,11869,11874,11916,11939,3280,3355,12066,4520,10309,10399,10512,10536,10782,10826,10836,11512,11610,11631,11634,11637,11653,11807,11810,11813,11816,11900,11919,11922,11935,11990,11993,11996,11999,12073,12161,12164,12254,12257,12318,12346,3437,10608,10871,10915,11184,11262,11425,11665,4532,10791,10803,10907,10925,10928,10983,11069,11077,11093,11131,11148,11156,11192,11233,11253,11256,11259,11290,11297,11300,11682,11718,11984,11987,12021,12067,12096,12235,12273,12279,12365,12368,3341,10637,10667,10676,11213,11764,12384,3379,3373,3800,3738,10312,11585,11613,4529,10263,10625,10628,11072,11090,11548,11601,11641,11666,11770,11795,11798,11801,11804,12062,3300,10670,10820,10891,11614,11769,11961,12169,3761,4110,4527,3772,3808,4510,4513,3251,3255,4512,3174,4511,4515,3779,3594,4209,4544,10234,10237,10493,10544,10547,10552,10957,11419,11669,11773,4551,11151,11270,11306,3996,3886,11303,11640,11644,11706,12303,12311,3727,10931,10937,10952,11885,12014,12099,3579,12125,12232,12241,12308,12356,3729,10673,11008,11159,11189,11200,12034,12307,3547,10591,10594,10679,10847,4548,11579,4538,4549,10730,10829,11139,11422,11453,12185,12194,4170,10806,4071,3760,3707,4546,10285,10288,10631,10634,11464,4547,11559,3731,10597,4003,4568,4594,4643,4645,4675,4692,4699,4700,4739,4769,4775,4860,4885,4886,4921,4946,4947,4969,4970,4983,4987,5010,5017,5035,5038,5039,5040,5045,5046,5068,5093,5094,5104,5109,5115,5160,5161,5169,5178,5183,5185,5195,5197,5203,5207,5222,5229,5232,5233,5234,5238,5274,5287,5295,5297,5298,5302,5303,5304,5312,5315,5319,5320,5321,5328,5332,5333,5334,5342,5346,5347,5348,5353,5366,5375,5387,5389,5397,5398,5402,5406,5431,5437,5447,5448,5463,5475,5497,5503,5519,5520,5523,5542,5550,5551,5556,5557,5567,5569,5581,5585,5594,5595,5597,5612,5617,5627,5628,5640,5647,5661,5665,5668,5674,5675,5676,5679,5684,5722,5723,5726,5728,5731,5732,5733,5735,5737,5739,5744,5751,5766,5780,5785,5786,5799,5800,5805,5809,5811,5816,5857,5869,5878,5882,5893,5897,5898,5906,5920,5926,5944,5947,5959,5985,5999,6024,6044,6045,6048,6062,6064,6066,6068,6081,6082,6085,6087,6090,6091,6103,6109,6110,6111,6113,6115,6158,6159,6166,6172,6176,6212,6214,6216,6218,6227,6229,6231,6237,6239,6245,6248,6256,6263,6264,6265,6270,6292,6293,6294,6296,6302,6307,6341,6342,6344,6345,6346,6348,6349,6350,6351,6358,6391,6392,6401,6422,6423,6443,6446,6457,6458,6464,6495,6497,6511,6549,6551,6552,6606,6630,6672,6692,6701,6702,6703,6704,6723,6724,6730,6743,6746,6748,6750,6751,6752,6754,6768,6779,6781,6782,6795,6799,6850,6861,6863,6867,6884,6885,6921,6933,6964,6998,7052,7080,7135,7156,7165,7168,7223,7231,7289,7291,7306,7316,7317,7318,7337,7343,7345,7395,7405,7408,7424,7476,7478,7481,7524,7525,7543,7610,7629,7652,7676,7691,7706,7717,7726,7727,7756,7759,7761,7771,7809,7820,7845,7903,7937,7969,8016,8032,8048,8049,8124,8177,8196,8220,8240,8264,8362,8364,8370,8386,8390,8406,8429,8440,8442,8457,8463,8467,8490,8504,8505,8521,8522,8527,8528,8529,8530,8531,8549,8550,8551,8559,8573,8575,8587,8591,8593,8594,8595,8603,8608,8635,8636,8668,8681,8685,8703,8725,8726,8727,8728,8740,8741,8763,8773,8783,8784,8785,8786,8788,8809,8810,8821,8865,8871,8877,8889,8894,8896,8899,8900,89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% 187.33/188.09 cnf(12413,plain,
% 187.33/188.09 (~P24(f329(f329(f193(f881(x124131,f881(x124132,a869))),x124133),x124134))),
% 187.33/188.09 inference(rename_variables,[],[4549])).
% 187.33/188.09 cnf(12416,plain,
% 187.33/188.09 (P24(f329(f329(f243(f881(x124161,a869)),x124162),f252(f881(x124161,a869))))),
% 187.33/188.09 inference(rename_variables,[],[3663])).
% 187.33/188.09 cnf(12419,plain,
% 187.33/188.09 (P24(f329(f329(f331(f880(x124191,x124191)),f329(f329(f264(x124191,x124191),x124192),x124192)),f305(x124191,x124193)))),
% 187.33/188.09 inference(rename_variables,[],[3921])).
% 187.33/188.09 cnf(12422,plain,
% 187.33/188.09 (~P24(f329(f329(f244(a874),f329(f329(f80(a874),x124221),x124222)),x124222))),
% 187.33/188.09 inference(rename_variables,[],[4546])).
% 187.33/188.09 cnf(12423,plain,
% 187.33/188.09 (P24(f329(f329(f244(a874),x124231),f329(a117,x124231)))),
% 187.33/188.09 inference(rename_variables,[],[3347])).
% 187.33/188.09 cnf(12426,plain,
% 187.33/188.09 (P24(f329(f329(f243(f881(x124261,a869)),f329(f171(x124261),f329(f134(x124261,x124262),x124263))),f329(f171(x124261),x124263)))),
% 187.33/188.09 inference(rename_variables,[],[3931])).
% 187.33/188.09 cnf(12429,plain,
% 187.33/188.09 (P24(f329(f329(f243(f881(x124291,a869)),x124292),f252(f881(x124291,a869))))),
% 187.33/188.09 inference(rename_variables,[],[3663])).
% 187.33/188.09 cnf(12434,plain,
% 187.33/188.09 (E(f329(f260(x124341,x124341),f261(x124341,x124342)),x124342)),
% 187.33/188.09 inference(rename_variables,[],[3234])).
% 187.33/188.09 cnf(12441,plain,
% 187.33/188.09 (P24(f329(f329(f331(f880(f880(f875(x124411),f875(x124411)),f880(f875(x124411),f875(x124411)))),f549(f305(f880(f875(x124411),f875(x124411)),x124412),f143(x124411,x124413),f880(f875(x124411),f875(x124411)))),f305(f880(f875(x124411),f875(x124411)),x124412)))),
% 187.33/188.09 inference(scs_inference,[],[4323,3521,11045,12081,12179,12268,12304,12312,3530,3531,3245,4492,4493,3145,4477,4459,10208,10218,10229,10240,10341,10344,10347,10450,10563,10866,11030,11033,11230,11317,11324,11338,11390,11393,11437,11503,11549,11565,11864,11889,11901,11930,11936,12031,12141,12148,12296,4474,10434,10527,3336,3490,3193,2873,2874,2876,2877,2880,2881,2883,2884,2885,2892,2895,2896,2903,2904,2908,2909,2910,2917,2920,2932,2938,2944,2952,2953,2954,2961,2974,3010,3019,3020,3022,3029,3035,3037,3047,3053,3065,4455,3619,3847,11596,3118,11314,3234,10211,10275,10278,10368,10371,10664,11329,11332,11448,11490,11495,11591,12051,12246,3206,12325,12329,12333,3212,3219,3740,3979,3108,4471,3484,3832,11364,3169,3136,3131,4560,3115,3116,3151,3291,3337,10815,12142,3204,3205,3229,10475,3383,4541,3919,4484,10266,10431,11227,12292,12326,4491,12300,3267,11685,4530,10980,11050,11273,11276,3384,3166,10333,10640,3167,3442,3087,3189,11354,4066,12315,3921,10986,11112,11162,12276,12282,12393,12396,12419,4553,10918,11117,11221,11243,11281,11287,12226,4554,11019,11120,11224,4555,11123,4556,11176,4557,3188,3482,12182,12223,12299,3644,4350,4351,4482,11345,3583,3796,3842,3468,3722,3347,10352,10470,10541,10602,10605,10643,10737,10970,11860,11923,12002,12042,12119,12122,3733,11582,3260,3359,3546,4524,10243,10246,10272,10745,10758,10876,11265,11357,11752,11757,11978,11981,12063,12072,12229,4536,11467,11498,11533,11562,3720,3491,3869,3306,3308,3281,4521,4479,3672,4203,3474,4537,4060,11238,3604,3320,11709,11712,4030,3987,11853,12197,3931,12204,3982,10989,12078,3645,11863,12009,12086,12132,4019,3663,10992,11055,11136,11195,12030,12100,12342,12416,4542,10761,11128,3276,10361,10457,10588,10650,10719,10764,10767,10800,10823,10860,10898,10934,11656,11703,11833,11888,11904,11907,11910,11913,12093,12107,12110,12113,12116,12190,12251,12353,3277,10390,10445,10655,10740,10863,11440,11737,11740,11749,11839,11850,11869,11874,11916,11939,3280,3355,12066,4520,10309,10399,10512,10536,10782,10826,10836,11512,11610,11631,11634,11637,11653,11807,11810,11813,11816,11900,11919,11922,11935,11990,11993,11996,11999,12073,12161,12164,12254,12257,12318,12346,3437,10608,10871,10915,11184,11262,11425,11665,4532,10791,10803,10907,10925,10928,10983,11069,11077,11093,11131,11148,11156,11192,11233,11253,11256,11259,11290,11297,11300,11682,11718,11984,11987,12021,12067,12096,12235,12273,12279,12365,12368,3341,10637,10667,10676,11213,11764,12384,3379,3373,3800,3738,10312,11585,11613,4529,10263,10625,10628,11072,11090,11548,11601,11641,11666,11770,11795,11798,11801,11804,12062,3300,10670,10820,10891,11614,11769,11961,12169,3761,4110,4527,3772,3808,4510,4513,3251,3255,4512,3174,4511,4515,3779,3594,4209,4544,10234,10237,10493,10544,10547,10552,10957,11419,11669,11773,4551,11151,11270,11306,3996,3886,11303,11640,11644,11706,12303,12311,3727,10931,10937,10952,11885,12014,12099,3579,12125,12232,12241,12308,12356,4064,3729,10673,11008,11159,11189,11200,12034,12307,3547,10591,10594,10679,10847,4548,11579,4538,4549,10730,10829,11139,11422,11453,12185,12194,12238,4170,10806,4071,3760,3707,4546,10285,10288,10631,10634,11464,11645,4547,11559,3731,10597,4003,4568,4594,4643,4645,4675,4692,4699,4700,4739,4769,4775,4860,4885,4886,4921,4946,4947,4969,4970,4983,4987,5010,5017,5035,5038,5039,5040,5045,5046,5068,5093,5094,5104,5109,5115,5160,5161,5169,5178,5183,5185,5195,5197,5203,5207,5222,5229,5232,5233,5234,5238,5274,5287,5295,5297,5298,5302,5303,5304,5312,5315,5319,5320,5321,5328,5332,5333,5334,5342,5346,5347,5348,5353,5366,5375,5387,5389,5397,5398,5402,5406,5431,5437,5447,5448,5463,5475,5497,5503,5519,5520,5523,5542,5550,5551,5556,5557,5567,5569,5581,5585,5594,5595,5597,5612,5617,5627,5628,5640,5647,5661,5665,5668,5674,5675,5676,5679,5684,5722,5723,5726,5728,5731,5732,5733,5735,5737,5739,5744,5751,5766,5780,5785,5786,5799,5800,5805,5809,5811,5816,5857,5869,5878,5882,5893,5897,5898,5906,5920,5926,5944,5947,5959,5985,5999,6024,6044,6045,6048,6062,6064,6066,6068,6081,6082,6085,6087,6090,6091,6103,6109,6110,6111,6113,6115,6158,6159,6166,6172,6176,6212,6214,6216,6218,6227,6229,6231,6237,6239,6245,6248,6256,6263,6264,6265,6270,6292,6293,6294,6296,6302,6307,6341,6342,6344,6345,6346,6348,6349,6350,6351,6358,6391,6392,6401,6422,6423,6443,6446,6457,6458,6464,6495,6497,6511,6549,6551,6552,6606,6630,6672,6692,6701,6702,6703,6704,6723,6724,6730,6743,6746,6748,6750,6751,6752,6754,6768,6779,6781,6782,6795,6799,6850,6861,6863,6867,6884,6885,6921,6933,6964,6998,7052,7080,7135,7156,7165,7168,7223,7231,7289,7291,7306,7316,7317,7318,7337,7343,7345,7395,7405,7408,7424,7476,7478,7481,7524,7525,7543,7610,7629,7652,7676,7691,7706,7717,7726,7727,7756,7759,7761,7771,7809,7820,7845,7903,7937,7969,8016,8032,8048,8049,8124,8177,8196,8220,8240,8264,8362,8364,8370,8386,8390,8406,8429,8440,8442,8457,8463,8467,8490,8504,8505,8521,8522,8527,8528,8529,8530,8531,8549,8550,8551,8559,8573,8575,8587,8591,8593,8594,8595,8603,8608,8635,8636,8668,8681,8685,8703,8725,8726,8727,8728,8740,8741,8763,8773,8783,8784,8785,8786,8788,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% 187.33/188.09 cnf(12445,plain,
% 187.33/188.09 (~P24(f329(f329(f331(x124451),x124452),f193(f881(x124451,a869))))),
% 187.33/188.09 inference(rename_variables,[],[4532])).
% 187.33/188.09 cnf(12446,plain,
% 187.33/188.09 (P24(f329(f329(f331(f880(f875(x124461),f875(x124461))),f329(f329(f264(f875(x124461),f875(x124461)),f118(x124461)),f118(x124461))),f156(x124461,x124462)))),
% 187.33/188.09 inference(rename_variables,[],[4066])).
% 187.33/188.09 cnf(12448,plain,
% 187.33/188.09 (P24(f329(f329(f331(f880(a874,a874)),f329(f329(f264(a874,a874),f329(a117,x124481)),f329(a117,f329(a117,x124481)))),f329(f329(f286(a874,a874,a874),f305(a874,a319)),f305(a874,f305(a874,a319)))))),
% 187.33/188.09 inference(scs_inference,[],[4323,3521,11045,12081,12179,12268,12304,12312,3530,3531,3245,4492,4493,3145,4477,4459,10208,10218,10229,10240,10341,10344,10347,10450,10563,10866,11030,11033,11230,11317,11324,11338,11390,11393,11437,11503,11549,11565,11864,11889,11901,11930,11936,12031,12141,12148,12296,4474,10434,10527,3336,3490,3193,2873,2874,2876,2877,2880,2881,2883,2884,2885,2892,2895,2896,2903,2904,2908,2909,2910,2917,2920,2932,2938,2944,2952,2953,2954,2961,2974,3010,3019,3020,3022,3029,3035,3037,3047,3053,3065,4455,3619,3847,11596,3118,11314,3234,10211,10275,10278,10368,10371,10664,11329,11332,11448,11490,11495,11591,12051,12246,3206,12325,12329,12333,3212,3219,3740,3979,3108,4471,3484,3832,11364,3169,3136,3131,4560,3115,3116,3151,3291,3337,10815,12142,3204,3205,3229,10475,3383,4541,3919,4484,10266,10431,11227,12292,12326,4491,12300,3267,11685,4530,10980,11050,11273,11276,3384,3166,10333,10640,3167,3442,3087,3189,11354,4066,12315,3921,10986,11112,11162,12276,12282,12393,12396,12419,4553,10918,11117,11221,11243,11281,11287,12226,4554,11019,11120,11224,4555,11123,4556,11176,4557,3188,3482,12182,12223,12299,3644,4350,4351,4482,11345,3583,3796,3842,3468,3722,3347,10352,10470,10541,10602,10605,10643,10737,10970,11860,11923,12002,12042,12119,12122,3733,11582,3260,3359,3546,4524,10243,10246,10272,10745,10758,10876,11265,11357,11752,11757,11978,11981,12063,12072,12229,4536,11467,11498,11533,11562,3720,3491,3869,3306,3308,3281,4521,4479,3672,4203,3474,4537,4060,11238,3604,3320,11709,11712,4030,3987,11853,12197,3931,12204,3982,10989,12078,3645,11863,12009,12086,12132,4019,3663,10992,11055,11136,11195,12030,12100,12342,12416,4542,10761,11128,3276,10361,10457,10588,10650,10719,10764,10767,10800,10823,10860,10898,10934,11656,11703,11833,11888,11904,11907,11910,11913,12093,12107,12110,12113,12116,12190,12251,12353,3277,10390,10445,10655,10740,10863,11440,11737,11740,11749,11839,11850,11869,11874,11916,11939,3280,3355,12066,4520,10309,10399,10512,10536,10782,10826,10836,11512,11610,11631,11634,11637,11653,11807,11810,11813,11816,11900,11919,11922,11935,11990,11993,11996,11999,12073,12161,12164,12254,12257,12318,12346,3437,10608,10871,10915,11184,11262,11425,11665,4532,10791,10803,10907,10925,10928,10983,11069,11077,11093,11131,11148,11156,11192,11233,11253,11256,11259,11290,11297,11300,11682,11718,11984,11987,12021,12067,12096,12235,12273,12279,12365,12368,12389,3341,10637,10667,10676,11213,11764,12384,3379,3373,3800,3738,10312,11585,11613,4529,10263,10625,10628,11072,11090,11548,11601,11641,11666,11770,11795,11798,11801,11804,12062,3300,10670,10820,10891,11614,11769,11961,12169,3761,4110,4527,3772,3808,4510,4513,3251,3255,4512,3174,4511,4515,3779,3594,4209,4544,10234,10237,10493,10544,10547,10552,10957,11419,11669,11773,4551,11151,11270,11306,3996,3886,11303,11640,11644,11706,12303,12311,3727,10931,10937,10952,11885,12014,12099,3579,12125,12232,12241,12308,12356,4064,3729,10673,11008,11159,11189,11200,12034,12307,3547,10591,10594,10679,10847,4548,11579,4538,4549,10730,10829,11139,11422,11453,12185,12194,12238,4170,10806,4071,3760,3707,4546,10285,10288,10631,10634,11464,11645,4547,11559,3731,10597,4003,4568,4594,4643,4645,4675,4692,4699,4700,4739,4769,4775,4860,4885,4886,4921,4946,4947,4969,4970,4983,4987,5010,5017,5035,5038,5039,5040,5045,5046,5068,5093,5094,5104,5109,5115,5160,5161,5169,5178,5183,5185,5195,5197,5203,5207,5222,5229,5232,5233,5234,5238,5274,5287,5295,5297,5298,5302,5303,5304,5312,5315,5319,5320,5321,5328,5332,5333,5334,5342,5346,5347,5348,5353,5366,5375,5387,5389,5397,5398,5402,5406,5431,5437,5447,5448,5463,5475,5497,5503,5519,5520,5523,5542,5550,5551,5556,5557,5567,5569,5581,5585,5594,5595,5597,5612,5617,5627,5628,5640,5647,5661,5665,5668,5674,5675,5676,5679,5684,5722,5723,5726,5728,5731,5732,5733,5735,5737,5739,5744,5751,5766,5780,5785,5786,5799,5800,5805,5809,5811,5816,5857,5869,5878,5882,5893,5897,5898,5906,5920,5926,5944,5947,5959,5985,5999,6024,6044,6045,6048,6062,6064,6066,6068,6081,6082,6085,6087,6090,6091,6103,6109,6110,6111,6113,6115,6158,6159,6166,6172,6176,6212,6214,6216,6218,6227,6229,6231,6237,6239,6245,6248,6256,6263,6264,6265,6270,6292,6293,6294,6296,6302,6307,6341,6342,6344,6345,6346,6348,6349,6350,6351,6358,6391,6392,6401,6422,6423,6443,6446,6457,6458,6464,6495,6497,6511,6549,6551,6552,6606,6630,6672,6692,6701,6702,6703,6704,6723,6724,6730,6743,6746,6748,6750,6751,6752,6754,6768,6779,6781,6782,6795,6799,6850,6861,6863,6867,6884,6885,6921,6933,6964,6998,7052,7080,7135,7156,7165,7168,7223,7231,7289,7291,7306,7316,7317,7318,7337,7343,7345,7395,7405,7408,7424,7476,7478,7481,7524,7525,7543,7610,7629,7652,7676,7691,7706,7717,7726,7727,7756,7759,7761,7771,7809,7820,7845,7903,7937,7969,8016,8032,8048,8049,8124,8177,8196,8220,8240,8264,8362,8364,8370,8386,8390,8406,8429,8440,8442,8457,8463,8467,8490,8504,8505,8521,8522,8527,8528,8529,8530,8531,8549,8550,8551,8559,8573,8575,8587,8591,8593,8594,8595,8603,8608,8635,8636,8668,8681,8685,8703,8725,8726,8727,8728,8740,8741,8763,8773,8783,8784,8785,8786,8788,8809,8810,8821,8865,8871,8877,8889,8894,8896,8899,8900,8904,8914,8997,9028,9029,9030,9045,9063,9068,9096,9097,9138,9141,9167,9212,9213,9214,9229,9256,9270,9276,9279,9301,9302,9330,9391,9426,9427,9428,9453,9454,9472,9491,9497,9511,9534,9556,9564,9565,9566,9567,9582,9584,9589,9620,9621,9627,9628,9672,9673,9705,9714,9724,9726,9727,9736,9750,9753,9781,9814,9816,9820,9878,9919,9920,9922,9932,9933,9953,9958,9999,10050,10122,10123,10176,10192,2,8,9,4581,4582,4600,4631,4633,4634,4661,4667,4668,4679,4728,4730,4760,4774,4804,4900,4901,4914,4934,4990,4991,4994,4995,4997,4999,5000,5009,5013,5014,5024,5036,5037,5043,5063,5064,5081,5086,5087,5088,5089,5092,5100,5103,5110,5175,5181,5182,5189,5219,5230,5236,5252,5272,5273,5280,5281,5282,5291,5301,5308,5310,5311,5317,5324,5325,5338,5339,5340,5341,5343,5344,5349,5350,5351,5352,5383,5384,5385,5393,5394,5395,5396,5439,5444,5446,5482,5484,5485,5487,5488,5490,5491,5493,5502,5507,5509,5510,5511,5512,5513,5514,5521,5531,5534,5545,5561,5562,5565,5575,5577,5578,5579,5604,5614,5630,5631,5641,5642,5644,5646,5651,5686,5691,5693,5753,5787,5788,5792,5798,5801,5802,5803,5804,5810,5821,5822,5824,5825,5833,5854,5885,5901,5904,5905,5907,5916,5934,5938,5941,5942,5943,5961,5972,5973,6001,6002,6006,6026,6029,6033,6052,6057,6058,6083,6086,6094,6102,6108,6112,6119,6120,6121,6122,6161,6177,6230,6266,6268,6289,6290,6295,6299,6300,6303,6309,6318,6333,6353,6354,6359,6369,6384,6404,6410,6412,6427,6428,6431,6432,6434,6436,6437,6438,6440,6442,6445,6450,6451,6453,6454,6460,6462,6505,6510,6524,6526,6527,6528,6563,6568,6570,6575,6576,6584,6588,6601,6625,6626,6628,6629,6640,6646,6663,6666,6685,6718,6719,6720,6725,6739,6758,6760,6762,6764,6769,6775,6777,6792,6797,6800,6836,6837,6838,6852,6853,6855,6856,6875,6877,6893,6919,6941,6952,6954,6956,6958,6959,6960,6995,6996,7001,7002,7009,7010,7012,7014,7033,7042,7043,7055,7065,7104,7114,7118,7125,7136,7142,7144,7150,7158,7159,7172,7189,7207,7209,7226,7275,7276,7277,7279,7281,7285,7290,7313,7358,7391,7406,7423,7456,7459,7485,7509,7526,7529,7530,7540,7559,7561,7563,7565,7566,7567,7592,7618,7619,7651,7653,7654,7655,7660,7683,7692,7703,7708,7714,7716,7722,7734,7735,7737,7762,7769,7792,7858,7859,7906,7914,7915,7939,7940,7957,7958,8023,8024,8051,8080,8091,8093,8102,8114,8146,8152,8159,8172,8191,8197,8219,8262,8292,8304,8322,8325,8355,8378,8443,8444,8447,8449,8553,8554,8555,8556,8582,8611,8639,8684,8702,8757,8802,8805,8818,8825,8862,8910,8911,8929,8930,9070,9074,9094,9104,9127,9129,9132,9136,9139,9140,9153,9154,9174,9180,9192,9240,9241,9260,9314,9315,9322,9383,9388,9423,9430,9433,9436,9437,9452,9468,9477,9487,9490,9500,9501,9504,9506,9532])).
% 187.33/188.09 cnf(12451,plain,
% 187.33/188.09 (~P24(f329(f329(f331(x124511),x124512),f193(f881(x124511,a869))))),
% 187.33/188.09 inference(rename_variables,[],[4532])).
% 187.33/188.09 cnf(12454,plain,
% 187.33/188.09 (P36(x124541,x124542,f118(x124541))),
% 187.33/188.09 inference(rename_variables,[],[3211])).
% 187.33/188.09 cnf(12457,plain,
% 187.33/188.09 (E(f329(f194(f875(x124571)),f329(f166(x124571),x124572)),f329(f194(f875(x124571)),x124572))),
% 187.33/188.09 inference(rename_variables,[],[3291])).
% 187.33/188.09 cnf(12460,plain,
% 187.33/188.09 (~P24(f329(f329(f331(x124601),x124602),f193(f881(x124601,a869))))),
% 187.33/188.09 inference(rename_variables,[],[4532])).
% 187.33/188.09 cnf(12464,plain,
% 187.33/188.09 (~P24(f329(f329(f331(f880(f875(x124641),f875(x124641))),f329(f329(f264(f875(x124641),f875(x124641)),x124642),x124642)),f145(x124641,f151(x124641,f118(f881(x124641,a874))))))),
% 187.33/188.09 inference(scs_inference,[],[4323,3521,11045,12081,12179,12268,12304,12312,3530,3531,3245,3211,4492,4493,3145,4477,4459,10208,10218,10229,10240,10341,10344,10347,10450,10563,10866,11030,11033,11230,11317,11324,11338,11390,11393,11437,11503,11549,11565,11864,11889,11901,11930,11936,12031,12141,12148,12296,4474,10434,10527,3336,3490,3193,2873,2874,2876,2877,2880,2881,2883,2884,2885,2892,2895,2896,2903,2904,2908,2909,2910,2917,2920,2932,2938,2944,2952,2953,2954,2961,2974,3010,3019,3020,3022,3029,3035,3037,3047,3053,3065,4455,3619,3847,11596,3118,11314,3234,10211,10275,10278,10368,10371,10664,11329,11332,11448,11490,11495,11591,12051,12246,3206,12325,12329,12333,3212,3219,3740,3979,3108,4471,3484,3832,11364,3169,3136,3131,4560,3115,3116,3151,3291,12380,3337,10815,12142,3204,3205,3229,10475,3383,4541,3919,4484,10266,10431,11227,12292,12326,4491,12300,3267,11685,4530,10980,11050,11273,11276,3384,3166,10333,10640,3167,3442,3087,3189,11354,4066,12315,12446,3921,10986,11112,11162,12276,12282,12393,12396,12419,4553,10918,11117,11221,11243,11281,11287,12226,4554,11019,11120,11224,4555,11123,4556,11176,4557,3188,3482,12182,12223,12299,3644,4350,4351,4482,11345,3583,3796,3842,3468,3722,3347,10352,10470,10541,10602,10605,10643,10737,10970,11860,11923,12002,12042,12119,12122,3733,11582,3260,3359,3546,4524,10243,10246,10272,10745,10758,10876,11265,11357,11752,11757,11978,11981,12063,12072,12229,4536,11467,11498,11533,11562,3720,3491,3869,3306,3308,3281,4521,4479,3672,4203,3474,4537,4060,11238,3604,3320,11709,11712,4030,3987,11853,12197,3931,12204,3982,10989,12078,3645,11863,12009,12086,12132,4019,3663,10992,11055,11136,11195,12030,12100,12342,12416,4542,10761,11128,3276,10361,10457,10588,10650,10719,10764,10767,10800,10823,10860,10898,10934,11656,11703,11833,11888,11904,11907,11910,11913,12093,12107,12110,12113,12116,12190,12251,12353,3277,10390,10445,10655,10740,10863,11440,11737,11740,11749,11839,11850,11869,11874,11916,11939,3280,3355,12066,4520,10309,10399,10512,10536,10782,10826,10836,11512,11610,11631,11634,11637,11653,11807,11810,11813,11816,11900,11919,11922,11935,11990,11993,11996,11999,12073,12161,12164,12254,12257,12318,12346,12383,3437,10608,10871,10915,11184,11262,11425,11665,4532,10791,10803,10907,10925,10928,10983,11069,11077,11093,11131,11148,11156,11192,11233,11253,11256,11259,11290,11297,11300,11682,11718,11984,11987,12021,12067,12096,12235,12273,12279,12365,12368,12389,12445,12451,3341,10637,10667,10676,11213,11764,12384,3379,3373,3800,3738,10312,11585,11613,4529,10263,10625,10628,11072,11090,11548,11601,11641,11666,11770,11795,11798,11801,11804,12062,3300,10670,10820,10891,11614,11769,11961,12169,3761,4110,4527,3772,3808,4510,4513,3251,3255,4512,3174,4511,4515,3779,3594,4209,11447,4544,10234,10237,10493,10544,10547,10552,10957,11419,11669,11773,4551,11151,11270,11306,3996,3886,11303,11640,11644,11706,12303,12311,3727,10931,10937,10952,11885,12014,12099,3579,12125,12232,12241,12308,12356,4064,3729,10673,11008,11159,11189,11200,12034,12307,3547,10591,10594,10679,10847,4548,11579,4538,4549,10730,10829,11139,11422,11453,12185,12194,12238,4170,10806,4071,3760,3707,4546,10285,10288,10631,10634,11464,11645,4547,11559,3731,10597,4003,4568,4594,4643,4645,4675,4692,4699,4700,4739,4769,4775,4860,4885,4886,4921,4946,4947,4969,4970,4983,4987,5010,5017,5035,5038,5039,5040,5045,5046,5068,5093,5094,5104,5109,5115,5160,5161,5169,5178,5183,5185,5195,5197,5203,5207,5222,5229,5232,5233,5234,5238,5274,5287,5295,5297,5298,5302,5303,5304,5312,5315,5319,5320,5321,5328,5332,5333,5334,5342,5346,5347,5348,5353,5366,5375,5387,5389,5397,5398,5402,5406,5431,5437,5447,5448,5463,5475,5497,5503,5519,5520,5523,5542,5550,5551,5556,5557,5567,5569,5581,5585,5594,5595,5597,5612,5617,5627,5628,5640,5647,5661,5665,5668,5674,5675,5676,5679,5684,5722,5723,5726,5728,5731,5732,5733,5735,5737,5739,5744,5751,5766,5780,5785,5786,5799,5800,5805,5809,5811,5816,5857,5869,5878,5882,5893,5897,5898,5906,5920,5926,5944,5947,5959,5985,5999,6024,6044,6045,6048,6062,6064,6066,6068,6081,6082,6085,6087,6090,6091,6103,6109,6110,6111,6113,6115,6158,6159,6166,6172,6176,6212,6214,6216,6218,6227,6229,6231,6237,6239,6245,6248,6256,6263,6264,6265,6270,6292,6293,6294,6296,6302,6307,6341,6342,6344,6345,6346,6348,6349,6350,6351,6358,6391,6392,6401,6422,6423,6443,6446,6457,6458,6464,6495,6497,6511,6549,6551,6552,6606,6630,6672,6692,6701,6702,6703,6704,6723,6724,6730,6743,6746,6748,6750,6751,6752,6754,6768,6779,6781,6782,6795,6799,6850,6861,6863,6867,6884,6885,6921,6933,6964,6998,7052,7080,7135,7156,7165,7168,7223,7231,7289,7291,7306,7316,7317,7318,7337,7343,7345,7395,7405,7408,7424,7476,7478,7481,7524,7525,7543,7610,7629,7652,7676,7691,7706,7717,7726,7727,7756,7759,7761,7771,7809,7820,7845,7903,7937,7969,8016,8032,8048,8049,8124,8177,8196,8220,8240,8264,8362,8364,8370,8386,8390,8406,8429,8440,8442,8457,8463,8467,8490,8504,8505,8521,8522,8527,8528,8529,8530,8531,8549,8550,8551,8559,8573,8575,8587,8591,8593,8594,8595,8603,8608,8635,8636,8668,8681,8685,8703,8725,8726,8727,872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% 187.33/188.09 cnf(12466,plain,
% 187.33/188.09 (~P24(f329(f329(f244(a874),x124661),x124661))),
% 187.33/188.09 inference(rename_variables,[],[4520])).
% 187.33/188.09 cnf(12469,plain,
% 187.33/188.09 (P24(f329(f329(f331(x124691),x124692),f252(f881(x124691,a869))))),
% 187.33/188.09 inference(rename_variables,[],[3437])).
% 187.33/188.09 cnf(12476,plain,
% 187.33/188.09 (P24(f329(f329(f243(f881(x124761,a869)),x124762),x124762))),
% 187.33/188.09 inference(rename_variables,[],[3579])).
% 187.33/188.09 cnf(12479,plain,
% 187.33/188.09 (~P24(f329(f329(f331(x124791),x124792),f193(f881(x124791,a869))))),
% 187.33/188.09 inference(rename_variables,[],[4532])).
% 187.33/188.09 cnf(12482,plain,
% 187.33/188.09 (P24(f329(f329(f243(a1),f2(a1)),f329(f329(f254(a1),f329(f75(a1),x124821)),x124822)))),
% 187.33/188.09 inference(rename_variables,[],[3760])).
% 187.33/188.09 cnf(12485,plain,
% 187.33/188.09 (~E(f329(a117,x124851),x124851)),
% 187.33/188.09 inference(rename_variables,[],[4459])).
% 187.33/188.09 cnf(12487,plain,
% 187.33/188.09 (E(f329(f260(x124871,x124871),f261(x124871,x124872)),x124872)),
% 187.33/188.09 inference(rename_variables,[],[3234])).
% 187.33/188.09 cnf(12489,plain,
% 187.33/188.09 (P42(x124891,f151(x124891,x124892))),
% 187.33/188.09 inference(rename_variables,[],[3145])).
% 187.33/188.09 cnf(12493,plain,
% 187.33/188.09 (E(f329(f260(x124931,x124931),f261(x124931,x124932)),x124932)),
% 187.33/188.09 inference(rename_variables,[],[3234])).
% 187.33/188.09 cnf(12498,plain,
% 187.33/188.09 (P21(x124981,x124981,f5(x124981),x124982)),
% 187.33/188.09 inference(rename_variables,[],[3521])).
% 187.33/188.09 cnf(12500,plain,
% 187.33/188.09 (P21(x125001,x125001,f5(x125001),x125002)),
% 187.33/188.09 inference(rename_variables,[],[3521])).
% 187.33/188.09 cnf(12508,plain,
% 187.33/188.09 (E(f193(f881(f880(x125081,x125081),a869)),f261(x125081,f193(f881(x125081,a869))))),
% 187.33/188.09 inference(rename_variables,[],[3350])).
% 187.33/188.09 cnf(12510,plain,
% 187.33/188.09 (E(f329(f260(x125101,x125101),f261(x125101,x125102)),x125102)),
% 187.33/188.09 inference(rename_variables,[],[3234])).
% 187.33/188.09 cnf(12512,plain,
% 187.33/188.09 (E(f329(f260(x125121,x125121),f261(x125121,x125122)),x125122)),
% 187.33/188.09 inference(rename_variables,[],[3234])).
% 187.33/188.09 cnf(12517,plain,
% 187.33/188.09 (P44(x125171,x125172,f261(x125171,x125172))),
% 187.33/188.09 inference(rename_variables,[],[3244])).
% 187.33/188.09 cnf(12519,plain,
% 187.33/188.09 (P44(x125191,x125192,f261(x125191,x125192))),
% 187.33/188.09 inference(rename_variables,[],[3244])).
% 187.33/188.09 cnf(12523,plain,
% 187.33/188.09 (P34(x125231,f2(a874),f329(f329(f329(f92(x125231),x125232),f329(a26,x125233)),x125234))),
% 187.33/188.09 inference(rename_variables,[],[3656])).
% 187.33/188.09 cnf(12529,plain,
% 187.33/188.09 (P54(x125291,x125291,f261(x125291,x125292))),
% 187.33/188.09 inference(rename_variables,[],[3245])).
% 187.33/188.09 cnf(12535,plain,
% 187.33/188.09 (E(f329(f260(x125351,x125351),f261(x125351,x125352)),x125352)),
% 187.33/188.09 inference(rename_variables,[],[3234])).
% 187.33/188.09 cnf(12537,plain,
% 187.33/188.09 (E(f329(f260(x125371,x125371),f261(x125371,x125372)),x125372)),
% 187.33/188.09 inference(rename_variables,[],[3234])).
% 187.33/188.09 cnf(12543,plain,
% 187.33/188.09 (P55(x125431,f193(f881(x125431,a869)),x125432)),
% 187.33/188.09 inference(rename_variables,[],[3298])).
% 187.33/188.09 cnf(12558,plain,
% 187.33/188.09 (P37(x125581,x125582,f118(x125581),f118(x125581))),
% 187.33/188.09 inference(rename_variables,[],[3530])).
% 187.33/188.09 cnf(12560,plain,
% 187.33/188.09 (P37(x125601,x125602,f118(x125601),f118(x125601))),
% 187.33/188.09 inference(rename_variables,[],[3530])).
% 187.33/188.09 cnf(12566,plain,
% 187.33/188.09 (E(f329(f260(x125661,x125661),f261(x125661,x125662)),x125662)),
% 187.33/188.09 inference(rename_variables,[],[3234])).
% 187.33/188.09 cnf(12568,plain,
% 187.33/188.09 (E(f329(f260(x125681,x125681),f261(x125681,x125682)),x125682)),
% 187.33/188.09 inference(rename_variables,[],[3234])).
% 187.33/188.09 cnf(12573,plain,
% 187.33/188.09 (E(f329(f260(x125731,x125731),f261(x125731,x125732)),x125732)),
% 187.33/188.09 inference(rename_variables,[],[3234])).
% 187.33/188.09 cnf(12575,plain,
% 187.33/188.09 (P20(x125751,x125752,f193(f881(f873(x125751),a869)))),
% 187.33/188.09 inference(rename_variables,[],[3335])).
% 187.33/188.09 cnf(12583,plain,
% 187.33/188.09 (P47(x125831,x125832,x125833,x125834,f193(f881(x125831,a869)),x125834)),
% 187.33/188.09 inference(rename_variables,[],[4233])).
% 187.33/188.09 cnf(12586,plain,
% 187.33/188.09 (P47(x125861,x125862,x125863,x125864,f193(f881(x125861,a869)),x125864)),
% 187.33/188.09 inference(rename_variables,[],[4233])).
% 187.33/188.09 cnf(12590,plain,
% 187.33/188.09 (P11(x125901,f881(x125901,a869),f307(x125901))),
% 187.33/188.09 inference(rename_variables,[],[3248])).
% 187.33/188.09 cnf(12599,plain,
% 187.33/188.09 (E(f329(f260(x125991,x125991),f261(x125991,x125992)),x125992)),
% 187.33/188.09 inference(rename_variables,[],[3234])).
% 187.33/188.09 cnf(12601,plain,
% 187.33/188.09 (P24(f329(f329(f244(a874),f2(a874)),f329(a117,x126011)))),
% 187.33/188.09 inference(rename_variables,[],[3359])).
% 187.33/188.09 cnf(12602,plain,
% 187.33/188.09 (~E(f329(a117,x126021),x126021)),
% 187.33/188.09 inference(rename_variables,[],[4459])).
% 187.33/188.09 cnf(12608,plain,
% 187.33/188.09 (P24(f329(f329(f244(a874),x126081),f329(a117,x126081)))),
% 187.33/188.09 inference(rename_variables,[],[3347])).
% 187.33/188.09 cnf(12613,plain,
% 187.33/188.09 (~P24(f329(f329(f244(a874),x126131),f2(a874)))),
% 187.33/188.09 inference(rename_variables,[],[4524])).
% 187.33/188.09 cnf(12615,plain,
% 187.33/188.09 (P24(f329(f329(f243(a1),a83),f2(a1)))),
% 187.33/188.09 inference(scs_inference,[],[4323,3521,11045,12081,12179,12268,12304,12312,12377,12498,3530,12145,12558,12560,3531,12210,3244,12517,12519,3245,12529,3211,12454,4492,4493,11662,4233,12583,12586,3248,12590,3086,3145,12489,4477,3581,4459,10208,10218,10229,10240,10341,10344,10347,10450,10563,10866,11030,11033,11230,11317,11324,11338,11390,11393,11437,11503,11549,11565,11864,11889,11901,11930,11936,12031,12141,12148,12296,12347,12485,4474,10434,10527,3336,3298,12543,3490,3193,2873,2874,2876,2877,2880,2881,2883,2884,2885,2892,2895,2896,2903,2904,2908,2909,2910,2917,2920,2932,2938,2944,2952,2953,2954,2961,2974,3010,3019,3020,3022,3029,3035,3037,3047,3053,4454,3065,3144,4455,3619,3847,11596,3118,11314,3258,3234,10211,10275,10278,10368,10371,10664,11329,11332,11448,11490,11495,11591,12051,12246,12434,12487,12493,12510,12512,12535,12537,12566,12568,12573,3206,12325,12329,12333,3212,3219,3740,3979,3108,4471,3484,3832,11364,3335,12575,3169,3136,3313,3656,12523,3131,3953,3661,4438,4560,3115,3116,3151,3291,12380,12457,3337,10815,12142,3204,3205,3229,10475,3383,4541,10404,3919,4484,10266,10431,11227,12292,12326,4491,12300,3267,11685,4530,10980,11050,11273,11276,3384,3605,3350,12508,3166,10333,10640,3167,3442,3159,3087,3189,11354,4066,12315,12446,3921,10986,11112,11162,12276,12282,12393,12396,12419,4553,10918,11117,11221,11243,11281,11287,12226,4554,11019,11120,11224,4555,11123,4556,11176,4557,3188,3482,12182,12223,12299,3644,4350,4351,4482,11345,3583,3796,3842,3468,3722,3347,10352,10470,10541,10602,10605,10643,10737,10970,11860,11923,12002,12042,12119,12122,12423,3733,11582,3260,3359,11700,3546,4524,10243,10246,10272,10745,10758,10876,11265,11357,11752,11757,11978,11981,12063,12072,12229,12319,4536,11467,11498,11533,11562,3720,3491,3869,3306,3308,3281,4521,4479,3672,4203,3988,3474,4537,4060,11238,3604,3320,11709,11712,4030,3987,11853,12197,3931,12204,3982,10989,12078,3645,11863,12009,12086,12132,4019,3663,10992,11055,11136,11195,12030,12100,12342,12416,4542,10761,11128,3276,10361,10457,10588,10650,10719,10764,10767,10800,10823,10860,10898,10934,11656,11703,11833,11888,11904,11907,11910,11913,12093,12107,12110,12113,12116,12190,12251,12353,3277,10390,10445,10655,10740,10863,11440,11737,11740,11749,11839,11850,11869,11874,11916,11939,3280,3355,12066,4520,10309,10399,10512,10536,10782,10826,10836,11512,11610,11631,11634,11637,11653,11807,11810,11813,11816,11900,11919,11922,11935,11990,11993,11996,11999,12073,12161,12164,12254,12257,12318,12346,12383,3437,10608,10871,10915,11184,11262,11425,11665,12295,4532,10791,10803,10907,10925,10928,10983,11069,11077,11093,11131,11148,11156,11192,11233,11253,11256,11259,11290,11297,11300,11682,11718,11984,11987,12021,12067,12096,12235,12273,12279,12365,12368,12389,12445,12451,12460,3341,10637,10667,10676,11213,11764,12384,3379,3373,3800,3738,10312,11585,11613,4529,10263,10625,10628,11072,11090,11548,11601,11641,11666,11770,11795,11798,11801,11804,12062,3300,10670,10820,10891,11614,11769,11961,12169,3761,4110,4527,3772,3808,4510,4513,3251,3255,4512,3174,4511,4515,3779,3594,4209,11447,4544,10234,10237,10493,10544,10547,10552,10957,11419,11669,11773,4551,11151,11270,11306,3996,3886,11303,11640,11644,11706,12303,12311,3727,10931,10937,10952,11885,12014,12099,3579,12125,12232,12241,12308,12356,12364,4064,3729,10673,11008,11159,11189,11200,12034,12307,3547,10591,10594,10679,10847,4548,11579,4538,4549,10730,10829,11139,11422,11453,12185,12194,12238,12413,4170,10806,4071,3760,3707,4546,10285,10288,10631,10634,11464,11645,4547,11559,3731,10597,4003,4568,4594,4643,4645,4675,4692,4699,4700,4739,4769,4775,4860,4885,4886,4921,4946,4947,4969,4970,4983,4987,5010,5017,5035,5038,5039,5040,5045,5046,5068,5093,5094,5104,5109,5115,5160,5161,5169,5178,5183,5185,5195,5197,5203,5207,5222,5229,5232,5233,5234,5238,5274,5287,5295,5297,5298,5302,5303,5304,5312,5315,5319,5320,5321,5328,5332,5333,5334,5342,5346,5347,5348,5353,5366,5375,5387,5389,5397,5398,5402,5406,5431,5437,5447,5448,5463,5475,5497,5503,5519,5520,5523,5542,5550,5551,5556,5557,5567,5569,5581,5585,5594,5595,5597,5612,5617,5627,5628,5640,5647,5661,5665,5668,5674,5675,5676,5679,5684,5722,5723,5726,5728,5731,5732,5733,5735,5737,5739,5744,5751,5766,5780,5785,5786,5799,5800,5805,5809,5811,5816,5857,5869,5878,5882,5893,5897,5898,5906,5920,5926,5944,5947,5959,5985,5999,6024,6044,6045,6048,6062,6064,6066,6068,6081,6082,6085,6087,6090,6091,6103,6109,6110,6111,6113,6115,6158,6159,6166,6172,6176,6212,6214,6216,6218,6227,6229,6231,6237,6239,6245,6248,6256,6263,6264,6265,6270,6292,6293,6294,6296,6302,6307,6341,6342,6344,6345,6346,6348,6349,6350,6351,6358,6391,6392,6401,6422,6423,6443,6446,6457,6458,6464,6495,6497,6511,6549,6551,6552,6606,6630,6672,6692,6701,6702,6703,6704,6723,6724,6730,6743,6746,6748,6750,6751,6752,6754,6768,6779,6781,6782,6795,6799,6850,6861,6863,6867,6884,6885,6921,6933,6964,6998,7052,7080,7135,7156,7165,7168,7223,7231,7289,7291,7306,7316,7317,7318,7337,7343,7345,7395,7405,7408,7424,7476,7478,7481,7524,7525,7543,7610,7629,7652,7676,7691,7706,771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% 187.33/188.09 cnf(12622,plain,
% 187.33/188.09 (~P24(f329(f329(f244(a1),f329(f105(a1),x126221)),f329(f79(a1),f329(f105(a1),x126222))))),
% 187.33/188.09 inference(rename_variables,[],[4543])).
% 187.33/188.09 cnf(12632,plain,
% 187.33/188.09 (~P24(f329(f329(f244(a874),x126321),f2(a874)))),
% 187.33/188.09 inference(rename_variables,[],[4524])).
% 187.33/188.09 cnf(12635,plain,
% 187.33/188.09 (~P24(f329(f329(f244(a874),x126351),f2(a874)))),
% 187.33/188.09 inference(rename_variables,[],[4524])).
% 187.33/188.09 cnf(12638,plain,
% 187.33/188.09 (P24(f329(f62(a874),f302(a874,x126381,x126382)))),
% 187.33/188.09 inference(rename_variables,[],[3493])).
% 187.33/188.09 cnf(12641,plain,
% 187.33/188.09 (P24(f329(f62(a874),f302(a874,x126411,x126412)))),
% 187.33/188.09 inference(rename_variables,[],[3493])).
% 187.33/188.09 cnf(12644,plain,
% 187.33/188.09 (P24(f329(f62(a874),f302(a874,x126441,x126442)))),
% 187.33/188.09 inference(rename_variables,[],[3493])).
% 187.33/188.09 cnf(12647,plain,
% 187.33/188.09 (P24(f329(f62(a874),f302(a874,x126471,x126472)))),
% 187.33/188.09 inference(rename_variables,[],[3493])).
% 187.33/188.09 cnf(12654,plain,
% 187.33/188.09 (P24(f329(f329(f243(a1),f329(f79(a1),f329(f105(a1),x126541))),f329(f105(a1),x126542)))),
% 187.33/188.09 inference(rename_variables,[],[3761])).
% 187.33/188.09 cnf(12656,plain,
% 187.33/188.09 (P24(f329(f329(f243(a1),f2(a1)),f329(f108(a1),f2(a1))))),
% 187.33/188.09 inference(scs_inference,[],[4323,3521,11045,12081,12179,12268,12304,12312,12377,12498,3530,12145,12558,12560,3531,12210,3244,12517,12519,3245,12529,3211,12454,4492,4493,11662,4233,12583,12586,3248,12590,3086,3145,12489,4477,3581,4459,10208,10218,10229,10240,10341,10344,10347,10450,10563,10866,11030,11033,11230,11317,11324,11338,11390,11393,11437,11503,11549,11565,11864,11889,11901,11930,11936,12031,12141,12148,12296,12347,12485,4474,10434,10527,3336,3298,12543,3490,3193,2873,2874,2876,2877,2880,2881,2883,2884,2885,2892,2895,2896,2903,2904,2908,2909,2910,2917,2920,2932,2938,2944,2952,2953,2954,2961,2974,3010,3019,3020,3022,3029,3035,3036,3037,3047,3053,4454,3065,3144,4455,3619,3847,11596,3118,11314,3258,3234,10211,10275,10278,10368,10371,10664,11329,11332,11448,11490,11495,11591,12051,12246,12434,12487,12493,12510,12512,12535,12537,12566,12568,12573,3206,12325,12329,12333,3212,3219,3740,3979,3108,4471,3484,3832,11364,3335,12575,3169,3136,3313,3656,12523,3131,3953,3661,4438,4560,3115,3116,3096,3151,3291,12380,12457,3337,10815,12142,3204,3205,3229,10475,3383,4541,10404,3919,4484,10266,10431,11227,12292,12326,4491,12300,3267,11685,4530,10980,11050,11273,11276,3384,3605,3350,12508,3166,10333,10640,3167,3442,3159,3087,3189,11354,4066,12315,12446,3921,10986,11112,11162,12276,12282,12393,12396,12419,4553,10918,11117,11221,11243,11281,11287,12226,4554,11019,11120,11224,4555,11123,4556,11176,4557,3188,3482,12182,12223,12299,3644,4350,4351,4482,11345,3583,3796,3842,3468,3722,3347,10352,10470,10541,10602,10605,10643,10737,10970,11860,11923,12002,12042,12119,12122,12423,3733,11582,3260,3359,11700,3546,4524,10243,10246,10272,10745,10758,10876,11265,11357,11752,11757,11978,11981,12063,12072,12229,12319,12613,12632,4536,11467,11498,11533,11562,3720,3491,3493,12638,12641,12644,3869,3306,3308,3281,4521,4479,3672,4203,3988,3474,4537,4060,11238,3604,3320,11709,11712,4030,3987,11853,12197,3931,12204,3982,10989,12078,3645,11863,12009,12086,12132,4019,3663,10992,11055,11136,11195,12030,12100,12342,12416,4542,10761,11128,3276,10361,10457,10588,10650,10719,10764,10767,10800,10823,10860,10898,10934,11656,11703,11833,11888,11904,11907,11910,11913,12093,12107,12110,12113,12116,12190,12251,12353,3277,10390,10445,10655,10740,10863,11440,11737,11740,11749,11839,11850,11869,11874,11916,11939,3280,3355,12066,4520,10309,10399,10512,10536,10782,10826,10836,11512,11610,11631,11634,11637,11653,11807,11810,11813,11816,11900,11919,11922,11935,11990,11993,11996,11999,12073,12161,12164,12254,12257,12318,12346,12383,3437,10608,10871,10915,11184,11262,11425,11665,12295,4532,10791,10803,10907,10925,10928,10983,11069,11077,11093,11131,11148,11156,11192,11233,11253,11256,11259,11290,11297,11300,11682,11718,11984,11987,12021,12067,12096,12235,12273,12279,12365,12368,12389,12445,12451,12460,3341,10637,10667,10676,11213,11764,12384,3379,3373,3800,3738,10312,11585,11613,4529,10263,10625,10628,11072,11090,11548,11601,11641,11666,11770,11795,11798,11801,11804,12062,3300,10670,10820,10891,11614,11769,11961,12169,3761,11715,4110,4527,3772,3808,4510,4513,4514,3251,3255,4512,3174,4511,4515,3779,3594,4209,11447,4544,10234,10237,10493,10544,10547,10552,10957,11419,11669,11773,4551,11151,11270,11306,3996,3886,11303,11640,11644,11706,12303,12311,3727,10931,10937,10952,11885,12014,12099,3579,12125,12232,12241,12308,12356,12364,4064,3729,10673,11008,11159,11189,11200,12034,12307,3547,10591,10594,10679,10847,3549,4548,11579,4538,4543,12622,4549,10730,10829,11139,11422,11453,12185,12194,12238,12413,4170,10806,4071,3760,3707,3708,4546,10285,10288,10631,10634,11464,11645,4547,11559,3731,10597,4003,4568,4594,4643,4645,4675,4692,4699,4700,4739,4769,4775,4860,4885,4886,4921,4946,4947,4969,4970,4983,4987,5010,5017,5035,5038,5039,5040,5045,5046,5068,5093,5094,5104,5109,5115,5160,5161,5169,5178,5183,5185,5195,5197,5203,5207,5222,5229,5232,5233,5234,5238,5274,5287,5295,5297,5298,5302,5303,5304,5312,5315,5319,5320,5321,5328,5332,5333,5334,5342,5346,5347,5348,5353,5366,5375,5387,5389,5397,5398,5402,5406,5431,5437,5447,5448,5463,5475,5497,5503,5519,5520,5523,5542,5550,5551,5556,5557,5567,5569,5581,5585,5594,5595,5597,5612,5617,5627,5628,5640,5647,5661,5665,5668,5674,5675,5676,5679,5684,5722,5723,5726,5728,5731,5732,5733,5735,5737,5739,5744,5751,5766,5780,5785,5786,5799,5800,5805,5809,5811,5816,5857,5869,5878,5882,5893,5897,5898,5906,5920,5926,5944,5947,5959,5985,5999,6024,6044,6045,6048,6062,6064,6066,6068,6081,6082,6085,6087,6090,6091,6103,6109,6110,6111,6113,6115,6158,6159,6166,6172,6176,6212,6214,6216,6218,6227,6229,6231,6237,6239,6245,6248,6256,6263,6264,6265,6270,6292,6293,6294,6296,6302,6307,6341,6342,6344,6345,6346,6348,6349,6350,6351,6358,6391,6392,6401,6422,6423,6443,6446,6457,6458,6464,6495,6497,6511,6549,6551,6552,6606,6630,6672,6692,6701,6702,6703,6704,6723,6724,6730,6743,6746,6748,6750,6751,6752,6754,6768,6779,6781,6782,6795,6799,6850,6861,6863,6867,6884,6885,6921,6933,6964,6998,7052,7080,7135,7156,7165,7168,7223,7231,7289,7291,7306,7316,7317,7318,7337,7343,7345,7395,7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% 187.33/188.09 cnf(12659,plain,
% 187.33/188.09 (~P24(f329(f329(f244(a874),x126591),f2(a874)))),
% 187.33/188.09 inference(rename_variables,[],[4524])).
% 187.33/188.09 cnf(12660,plain,
% 187.33/188.09 (P24(f329(f329(f243(a874),x126601),x126601))),
% 187.33/188.09 inference(rename_variables,[],[3276])).
% 187.33/188.09 cnf(12667,plain,
% 187.33/188.09 (P24(f329(f329(f244(a874),x126671),f329(a117,x126671)))),
% 187.33/188.09 inference(rename_variables,[],[3347])).
% 187.33/188.09 cnf(12669,plain,
% 187.33/188.09 (P24(f329(f329(f243(a1),f2(a1)),a83))),
% 187.33/188.09 inference(scs_inference,[],[4323,3521,11045,12081,12179,12268,12304,12312,12377,12498,3530,12145,12558,12560,3531,12210,3244,12517,12519,3245,12529,3211,12454,4492,4493,11662,4233,12583,12586,3248,12590,3086,3145,12489,4477,3581,4459,10208,10218,10229,10240,10341,10344,10347,10450,10563,10866,11030,11033,11230,11317,11324,11338,11390,11393,11437,11503,11549,11565,11864,11889,11901,11930,11936,12031,12141,12148,12296,12347,12485,4474,10434,10527,3336,3298,12543,3490,3193,2873,2874,2876,2877,2880,2881,2883,2884,2885,2892,2895,2896,2903,2904,2908,2909,2910,2917,2920,2932,2938,2944,2952,2953,2954,2961,2974,3010,3019,3020,3022,3029,3035,3036,3037,3047,3053,4454,3065,3144,4455,3619,3847,11596,3118,11314,3258,3234,10211,10275,10278,10368,10371,10664,11329,11332,11448,11490,11495,11591,12051,12246,12434,12487,12493,12510,12512,12535,12537,12566,12568,12573,3206,12325,12329,12333,3212,3219,3740,3979,3108,4471,3484,3832,11364,3335,12575,3169,3136,3313,3656,12523,3131,3953,3661,4438,4560,3115,3116,3096,3151,3291,12380,12457,3337,10815,12142,3204,3205,3229,10475,3383,4541,10404,3919,4484,10266,10431,11227,12292,12326,4491,12300,3267,11685,4530,10980,11050,11273,11276,3384,3605,3350,12508,3166,10333,10640,3167,3442,3159,3087,3189,11354,4066,12315,12446,3921,10986,11112,11162,12276,12282,12393,12396,12419,4553,10918,11117,11221,11243,11281,11287,12226,4554,11019,11120,11224,4555,11123,4556,11176,4557,3188,3482,12182,12223,12299,3644,4350,4351,4482,11345,3583,3622,3796,3842,3468,3722,3347,10352,10470,10541,10602,10605,10643,10737,10970,11860,11923,12002,12042,12119,12122,12423,12608,3733,11582,3260,3359,11700,3546,4524,10243,10246,10272,10745,10758,10876,11265,11357,11752,11757,11978,11981,12063,12072,12229,12319,12613,12632,12635,4536,11467,11498,11533,11562,3720,3491,3493,12638,12641,12644,3869,3306,3308,3281,4521,3165,4479,3672,4203,3988,3474,4537,4060,11238,3604,3320,11709,11712,4030,3987,11853,12197,3931,12204,3982,10989,12078,3645,11863,12009,12086,12132,4019,3663,10992,11055,11136,11195,12030,12100,12342,12416,4542,10761,11128,3276,10361,10457,10588,10650,10719,10764,10767,10800,10823,10860,10898,10934,11656,11703,11833,11888,11904,11907,11910,11913,12093,12107,12110,12113,12116,12190,12251,12353,12399,3277,10390,10445,10655,10740,10863,11440,11737,11740,11749,11839,11850,11869,11874,11916,11939,3280,3355,12066,4520,10309,10399,10512,10536,10782,10826,10836,11512,11610,11631,11634,11637,11653,11807,11810,11813,11816,11900,11919,11922,11935,11990,11993,11996,11999,12073,12161,12164,12254,12257,12318,12346,12383,3437,10608,10871,10915,11184,11262,11425,11665,12295,4532,10791,10803,10907,10925,10928,10983,11069,11077,11093,11131,11148,11156,11192,11233,11253,11256,11259,11290,11297,11300,11682,11718,11984,11987,12021,12067,12096,12235,12273,12279,12365,12368,12389,12445,12451,12460,3341,10637,10667,10676,11213,11764,12384,3379,3373,3800,3738,10312,11585,11613,4529,10263,10625,10628,11072,11090,11548,11601,11641,11666,11770,11795,11798,11801,11804,12062,3300,10670,10820,10891,11614,11769,11961,12169,3761,11715,4110,3497,4527,3772,3808,4510,4513,4514,3251,3255,4512,3174,4511,4515,3779,3594,4209,11447,4544,10234,10237,10493,10544,10547,10552,10957,11419,11669,11773,4551,11151,11270,11306,3996,3886,11303,11640,11644,11706,12303,12311,3727,10931,10937,10952,11885,12014,12099,3579,12125,12232,12241,12308,12356,12364,4064,3729,10673,11008,11159,11189,11200,12034,12307,3547,10591,10594,10679,10847,3549,4548,11579,4538,4543,12622,4549,10730,10829,11139,11422,11453,12185,12194,12238,12413,4170,10806,4071,3760,3707,3708,4546,10285,10288,10631,10634,11464,11645,4547,11559,3731,10597,4003,4568,4594,4643,4645,4675,4692,4699,4700,4739,4769,4775,4860,4885,4886,4921,4946,4947,4969,4970,4983,4987,5010,5017,5035,5038,5039,5040,5045,5046,5068,5093,5094,5104,5109,5115,5160,5161,5169,5178,5183,5185,5195,5197,5203,5207,5222,5229,5232,5233,5234,5238,5274,5287,5295,5297,5298,5302,5303,5304,5312,5315,5319,5320,5321,5328,5332,5333,5334,5342,5346,5347,5348,5353,5366,5375,5387,5389,5397,5398,5402,5406,5431,5437,5447,5448,5463,5475,5497,5503,5519,5520,5523,5542,5550,5551,5556,5557,5567,5569,5581,5585,5594,5595,5597,5612,5617,5627,5628,5640,5647,5661,5665,5668,5674,5675,5676,5679,5684,5722,5723,5726,5728,5731,5732,5733,5735,5737,5739,5744,5751,5766,5780,5785,5786,5799,5800,5805,5809,5811,5816,5857,5869,5878,5882,5893,5897,5898,5906,5920,5926,5944,5947,5959,5985,5999,6024,6044,6045,6048,6062,6064,6066,6068,6081,6082,6085,6087,6090,6091,6103,6109,6110,6111,6113,6115,6158,6159,6166,6172,6176,6212,6214,6216,6218,6227,6229,6231,6237,6239,6245,6248,6256,6263,6264,6265,6270,6292,6293,6294,6296,6302,6307,6341,6342,6344,6345,6346,6348,6349,6350,6351,6358,6391,6392,6401,6422,6423,6443,6446,6457,6458,6464,6495,6497,6511,6549,6551,6552,6606,6630,6672,6692,6701,6702,6703,6704,6723,6724,6730,6743,6746,6748,6750,6751,6752,6754,6768,6779,6781,6782,6795,6799,6850,6861,6863,6867,6884,6885,6921,6933,6964,6998,7052,7080,7135,7156,7165,7168,7223,7231,7289,7291,7306,731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% 187.33/188.09 cnf(12672,plain,
% 187.33/188.09 (P24(f329(f329(f331(x126721),f329(x126722,x126723)),f329(f308(x126724,x126721,x126722),f252(f881(x126724,a869)))))),
% 187.33/188.09 inference(rename_variables,[],[3886])).
% 187.33/188.09 cnf(12673,plain,
% 187.33/188.09 (~E(f329(a117,x126731),f2(a874))),
% 187.33/188.09 inference(rename_variables,[],[4469])).
% 187.33/188.09 cnf(12675,plain,
% 187.33/188.09 (~P24(f329(f329(f244(a1),f2(a1)),f329(f108(a1),f2(a1))))),
% 187.33/188.09 inference(scs_inference,[],[4323,3521,11045,12081,12179,12268,12304,12312,12377,12498,3530,12145,12558,12560,3531,12210,3244,12517,12519,3245,12529,3211,12454,4492,4493,11662,4233,12583,12586,3248,12590,3086,3145,12489,4477,3581,4459,10208,10218,10229,10240,10341,10344,10347,10450,10563,10866,11030,11033,11230,11317,11324,11338,11390,11393,11437,11503,11549,11565,11864,11889,11901,11930,11936,12031,12141,12148,12296,12347,12485,4474,10434,10527,3336,3298,12543,3490,3193,4469,2873,2874,2876,2877,2880,2881,2883,2884,2885,2892,2895,2896,2903,2904,2908,2909,2910,2917,2920,2932,2938,2944,2952,2953,2954,2961,2974,3010,3019,3020,3022,3029,3035,3036,3037,3047,3053,4454,3065,3144,4455,3619,3847,11596,3118,11314,3258,3234,10211,10275,10278,10368,10371,10664,11329,11332,11448,11490,11495,11591,12051,12246,12434,12487,12493,12510,12512,12535,12537,12566,12568,12573,3206,12325,12329,12333,3212,3219,3740,3979,3108,4471,3484,3832,11364,3335,12575,3169,3136,3313,3656,12523,3131,3953,3661,4438,4560,3115,3116,3096,3151,3291,12380,12457,3337,10815,12142,3204,3205,3229,10475,3383,4541,10404,3919,4484,10266,10431,11227,12292,12326,4491,12300,3267,11685,4530,10980,11050,11273,11276,3384,3605,3350,12508,3166,10333,10640,3167,3442,3159,3087,3189,11354,4066,12315,12446,3921,10986,11112,11162,12276,12282,12393,12396,12419,4553,10918,11117,11221,11243,11281,11287,12226,4554,11019,11120,11224,4555,11123,4556,11176,4557,3188,3482,12182,12223,12299,3644,4350,4351,4482,11345,3583,3622,3796,3842,3468,3722,3347,10352,10470,10541,10602,10605,10643,10737,10970,11860,11923,12002,12042,12119,12122,12423,12608,3733,11582,3260,3359,11700,3546,4524,10243,10246,10272,10745,10758,10876,11265,11357,11752,11757,11978,11981,12063,12072,12229,12319,12613,12632,12635,4536,11467,11498,11533,11562,3720,3491,3493,12638,12641,12644,3869,3306,3308,3281,4521,3165,4479,3672,4203,3988,3474,4537,4060,11238,3604,3320,11709,11712,4030,3987,11853,12197,3931,12204,3982,10989,12078,3645,11863,12009,12086,12132,4019,3663,10992,11055,11136,11195,12030,12100,12342,12416,4542,10761,11128,3276,10361,10457,10588,10650,10719,10764,10767,10800,10823,10860,10898,10934,11656,11703,11833,11888,11904,11907,11910,11913,12093,12107,12110,12113,12116,12190,12251,12353,12399,3277,10390,10445,10655,10740,10863,11440,11737,11740,11749,11839,11850,11869,11874,11916,11939,3280,3355,12066,4520,10309,10399,10512,10536,10782,10826,10836,11512,11610,11631,11634,11637,11653,11807,11810,11813,11816,11900,11919,11922,11935,11990,11993,11996,11999,12073,12161,12164,12254,12257,12318,12346,12383,3437,10608,10871,10915,11184,11262,11425,11665,12295,4532,10791,10803,10907,10925,10928,10983,11069,11077,11093,11131,11148,11156,11192,11233,11253,11256,11259,11290,11297,11300,11682,11718,11984,11987,12021,12067,12096,12235,12273,12279,12365,12368,12389,12445,12451,12460,3341,10637,10667,10676,11213,11764,12384,3379,3373,3800,3738,10312,11585,11613,4529,10263,10625,10628,11072,11090,11548,11601,11641,11666,11770,11795,11798,11801,11804,12062,3300,10670,10820,10891,11614,11769,11961,12169,3761,11715,4110,3497,4527,3772,3808,4510,4513,4514,3251,3255,4512,3174,4511,4515,3779,3594,4209,11447,4544,10234,10237,10493,10544,10547,10552,10957,11419,11669,11773,4551,11151,11270,11306,3996,12218,3886,11303,11640,11644,11706,12303,12311,12392,3727,10931,10937,10952,11885,12014,12099,3579,12125,12232,12241,12308,12356,12364,4064,3729,10673,11008,11159,11189,11200,12034,12307,3547,10591,10594,10679,10847,3549,4548,11579,4538,4543,12622,4549,10730,10829,11139,11422,11453,12185,12194,12238,12413,4170,10806,4071,3760,3707,3708,4546,10285,10288,10631,10634,11464,11645,4547,11559,3731,10597,4003,4568,4594,4643,4645,4675,4692,4699,4700,4739,4769,4775,4860,4885,4886,4921,4946,4947,4969,4970,4983,4987,5010,5017,5035,5038,5039,5040,5045,5046,5068,5093,5094,5104,5109,5115,5160,5161,5169,5178,5183,5185,5195,5197,5203,5207,5222,5229,5232,5233,5234,5238,5274,5287,5295,5297,5298,5302,5303,5304,5312,5315,5319,5320,5321,5328,5332,5333,5334,5342,5346,5347,5348,5353,5366,5375,5387,5389,5397,5398,5402,5406,5431,5437,5447,5448,5463,5475,5497,5503,5519,5520,5523,5542,5550,5551,5556,5557,5567,5569,5581,5585,5594,5595,5597,5612,5617,5627,5628,5640,5647,5661,5665,5668,5674,5675,5676,5679,5684,5722,5723,5726,5728,5731,5732,5733,5735,5737,5739,5744,5751,5766,5780,5785,5786,5799,5800,5805,5809,5811,5816,5857,5869,5878,5882,5893,5897,5898,5906,5920,5926,5944,5947,5959,5985,5999,6024,6044,6045,6048,6062,6064,6066,6068,6081,6082,6085,6087,6090,6091,6103,6109,6110,6111,6113,6115,6158,6159,6166,6172,6176,6212,6214,6216,6218,6227,6229,6231,6237,6239,6245,6248,6256,6263,6264,6265,6270,6292,6293,6294,6296,6302,6307,6341,6342,6344,6345,6346,6348,6349,6350,6351,6358,6391,6392,6401,6422,6423,6443,6446,6457,6458,6464,6495,6497,6511,6549,6551,6552,6606,6630,6672,6692,6701,6702,6703,6704,6723,6724,6730,6743,6746,6748,6750,6751,6752,6754,6768,6779,6781,6782,6795,6799,6850,6861,6863,6867,6884,6885,6921,6933,6964,6998,7052,7080,7135,7156,7165,7168,7223,7231,7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% 187.33/188.09 cnf(12678,plain,
% 187.33/188.09 (P24(f329(f329(f243(a1),x126781),x126781))),
% 187.33/188.09 inference(rename_variables,[],[3277])).
% 187.33/188.09 cnf(12681,plain,
% 187.33/188.09 (P24(f329(f62(a874),f302(a874,x126811,x126812)))),
% 187.33/188.09 inference(rename_variables,[],[3493])).
% 187.33/188.09 cnf(12684,plain,
% 187.33/188.09 (P24(f329(f62(a874),f302(a874,x126841,x126842)))),
% 187.33/188.09 inference(rename_variables,[],[3493])).
% 187.33/188.09 cnf(12687,plain,
% 187.33/188.09 (P24(f329(f329(f243(a874),x126871),x126871))),
% 187.33/188.09 inference(rename_variables,[],[3276])).
% 187.33/188.09 cnf(12688,plain,
% 187.33/188.09 (~E(f329(a117,x126881),f2(a874))),
% 187.33/188.09 inference(rename_variables,[],[4469])).
% 187.33/188.09 cnf(12705,plain,
% 187.33/188.09 (P24(f329(f329(f243(a874),f45(a874,x127051,x127052)),x127051))),
% 187.33/188.09 inference(rename_variables,[],[3738])).
% 187.33/188.09 cnf(12710,plain,
% 187.33/188.09 (P24(f329(f329(f244(a874),x127101),f329(a117,x127101)))),
% 187.33/188.09 inference(rename_variables,[],[3347])).
% 187.33/188.09 cnf(12713,plain,
% 187.33/188.09 (P24(f329(f329(f244(a874),x127131),f329(a117,x127131)))),
% 187.33/188.09 inference(rename_variables,[],[3347])).
% 187.33/188.09 cnf(12714,plain,
% 187.33/188.09 (~P24(f329(f329(f244(a874),x127141),f2(a874)))),
% 187.33/188.09 inference(rename_variables,[],[4524])).
% 187.33/188.09 cnf(12723,plain,
% 187.33/188.09 (~P24(f329(f329(f244(a1),f329(f105(a1),x127231)),f2(a1)))),
% 187.33/188.09 inference(rename_variables,[],[4536])).
% 187.33/188.09 cnf(12724,plain,
% 187.33/188.09 (P24(f329(f252(f881(x127241,a869)),x127242))),
% 187.33/188.09 inference(rename_variables,[],[3341])).
% 187.33/188.09 cnf(12727,plain,
% 187.33/188.09 (~P24(f329(f329(f244(a1),f329(f105(a1),x127271)),f2(a1)))),
% 187.33/188.09 inference(rename_variables,[],[4536])).
% 187.33/188.09 cnf(12728,plain,
% 187.33/188.09 (P24(f329(f252(f881(x127281,a869)),x127282))),
% 187.33/188.09 inference(rename_variables,[],[3341])).
% 187.33/188.09 cnf(12731,plain,
% 187.33/188.09 (P24(f329(f252(f881(x127311,a869)),x127312))),
% 187.33/188.09 inference(rename_variables,[],[3341])).
% 187.33/188.09 cnf(12742,plain,
% 187.33/188.09 (~P24(f329(f329(f331(x127421),x127422),f193(f881(x127421,a869))))),
% 187.33/188.09 inference(rename_variables,[],[4532])).
% 187.33/188.09 cnf(12743,plain,
% 187.33/188.09 (P24(f329(f62(x127431),f193(f881(x127431,a869))))),
% 187.33/188.09 inference(rename_variables,[],[3355])).
% 187.33/188.09 cnf(12752,plain,
% 187.33/188.09 (P24(f329(f329(f243(a874),f2(a874)),x127521))),
% 187.33/188.09 inference(rename_variables,[],[3300])).
% 187.33/188.09 cnf(12755,plain,
% 187.33/188.09 (P24(f329(f329(f244(a874),x127551),f329(a117,x127551)))),
% 187.33/188.09 inference(rename_variables,[],[3347])).
% 187.33/188.09 cnf(12756,plain,
% 187.33/188.09 (~E(f329(a117,x127561),x127561)),
% 187.33/188.09 inference(rename_variables,[],[4459])).
% 187.33/188.09 cnf(12759,plain,
% 187.33/188.10 (~P24(f329(f329(f331(x127591),x127592),f193(f881(x127591,a869))))),
% 187.33/188.10 inference(rename_variables,[],[4532])).
% 187.33/188.10 cnf(12762,plain,
% 187.33/188.10 (~P24(f329(f329(f331(x127621),x127622),f193(f881(x127621,a869))))),
% 187.33/188.10 inference(rename_variables,[],[4532])).
% 187.33/188.10 cnf(12765,plain,
% 187.33/188.10 (P24(f329(f329(f243(a874),x127651),x127651))),
% 187.33/188.10 inference(rename_variables,[],[3276])).
% 187.33/188.10 cnf(12773,plain,
% 187.33/188.10 (P24(f329(f329(f244(a874),x127731),f329(a117,x127731)))),
% 187.33/188.10 inference(rename_variables,[],[3347])).
% 187.33/188.10 cnf(12776,plain,
% 187.33/188.10 (P24(f329(f329(f243(a874),x127761),x127761))),
% 187.39/188.10 inference(rename_variables,[],[3276])).
% 187.39/188.10 cnf(12781,plain,
% 187.39/188.10 (P24(f329(f329(f243(a874),x127811),x127811))),
% 187.39/188.10 inference(rename_variables,[],[3276])).
% 187.39/188.10 cnf(12784,plain,
% 187.39/188.10 (P24(f329(f329(f243(a874),x127841),x127841))),
% 187.39/188.10 inference(rename_variables,[],[3276])).
% 187.39/188.10 cnf(12787,plain,
% 187.39/188.10 (P24(f329(f329(f243(a874),x127871),x127871))),
% 187.39/188.10 inference(rename_variables,[],[3276])).
% 187.39/188.10 cnf(12790,plain,
% 187.39/188.10 (E(f329(f329(f22(f881(x127901,a869)),f193(f881(x127901,a869))),x127902),f193(f881(x127901,a869)))),
% 187.39/188.10 inference(rename_variables,[],[3552])).
% 187.39/188.10 cnf(12791,plain,
% 187.39/188.10 (P24(f329(f62(x127911),f193(f881(x127911,a869))))),
% 187.39/188.10 inference(rename_variables,[],[3355])).
% 187.39/188.10 cnf(12794,plain,
% 187.39/188.10 (E(f329(f329(f22(f881(x127941,a869)),f193(f881(x127941,a869))),x127942),f193(f881(x127941,a869)))),
% 187.39/188.10 inference(rename_variables,[],[3552])).
% 187.39/188.10 cnf(12795,plain,
% 187.39/188.10 (P24(f329(f62(x127951),f193(f881(x127951,a869))))),
% 187.39/188.10 inference(rename_variables,[],[3355])).
% 187.39/188.10 cnf(12798,plain,
% 187.39/188.10 (E(f329(f329(f22(f881(x127981,a869)),f193(f881(x127981,a869))),x127982),f193(f881(x127981,a869)))),
% 187.39/188.10 inference(rename_variables,[],[3552])).
% 187.39/188.10 cnf(12799,plain,
% 187.39/188.10 (P24(f329(f62(x127991),f193(f881(x127991,a869))))),
% 187.39/188.10 inference(rename_variables,[],[3355])).
% 187.39/188.10 cnf(12802,plain,
% 187.39/188.10 (E(f329(f329(f22(f881(x128021,a869)),f193(f881(x128021,a869))),x128022),f193(f881(x128021,a869)))),
% 187.39/188.10 inference(rename_variables,[],[3552])).
% 187.39/188.10 cnf(12803,plain,
% 187.39/188.10 (P24(f329(f62(x128031),f193(f881(x128031,a869))))),
% 187.39/188.10 inference(rename_variables,[],[3355])).
% 187.39/188.10 cnf(12807,plain,
% 187.39/188.10 (E(f329(f260(x128071,x128071),f261(x128071,x128072)),x128072)),
% 187.39/188.10 inference(rename_variables,[],[3234])).
% 187.39/188.10 cnf(12812,plain,
% 187.39/188.10 (E(f329(f329(f22(f881(x128121,a869)),f193(f881(x128121,a869))),x128122),f193(f881(x128121,a869)))),
% 187.39/188.10 inference(rename_variables,[],[3552])).
% 187.39/188.10 cnf(12813,plain,
% 187.39/188.10 (P24(f329(f62(x128131),f193(f881(x128131,a869))))),
% 187.39/188.10 inference(rename_variables,[],[3355])).
% 187.39/188.10 cnf(12817,plain,
% 187.39/188.10 (P24(f329(f62(x128171),f193(f881(x128171,a869))))),
% 187.39/188.10 inference(rename_variables,[],[3355])).
% 187.39/188.10 cnf(12820,plain,
% 187.39/188.10 (P24(f329(f329(f243(a874),x128201),x128201))),
% 187.39/188.10 inference(rename_variables,[],[3276])).
% 187.39/188.10 cnf(12824,plain,
% 187.39/188.10 (P24(f329(f329(f243(a1),x128241),x128241))),
% 187.39/188.10 inference(rename_variables,[],[3277])).
% 187.39/188.10 cnf(12833,plain,
% 187.39/188.10 (P24(f329(f329(f243(a874),x128331),x128331))),
% 187.39/188.10 inference(rename_variables,[],[3276])).
% 187.39/188.10 cnf(12844,plain,
% 187.39/188.10 (P24(f329(f329(f243(a874),x128441),x128441))),
% 187.39/188.10 inference(rename_variables,[],[3276])).
% 187.39/188.10 cnf(12847,plain,
% 187.39/188.10 (P24(f329(f329(f243(a1),x128471),x128471))),
% 187.39/188.10 inference(rename_variables,[],[3277])).
% 187.39/188.10 cnf(12854,plain,
% 187.39/188.10 (~P24(f329(f329(f331(x128541),x128542),f193(f881(x128541,a869))))),
% 187.39/188.10 inference(rename_variables,[],[4532])).
% 187.39/188.10 cnf(12865,plain,
% 187.39/188.10 (P24(f329(f329(f331(x128651),x128652),f252(f881(x128651,a869))))),
% 187.39/188.10 inference(rename_variables,[],[3437])).
% 187.39/188.10 cnf(12869,plain,
% 187.39/188.10 (P24(f329(f329(f243(f881(x128691,a869)),x128692),f252(f881(x128691,a869))))),
% 187.39/188.10 inference(rename_variables,[],[3663])).
% 187.39/188.10 cnf(12872,plain,
% 187.39/188.10 (P24(f329(f329(f243(f881(x128721,a869)),x128722),x128722))),
% 187.39/188.10 inference(rename_variables,[],[3579])).
% 187.39/188.10 cnf(12878,plain,
% 187.39/188.10 (~P24(f329(f329(f244(a874),x128781),f2(a874)))),
% 187.39/188.10 inference(rename_variables,[],[4524])).
% 187.39/188.10 cnf(12879,plain,
% 187.39/188.10 (P24(f329(f329(f243(a1),x128791),x128791))),
% 187.39/188.10 inference(rename_variables,[],[3277])).
% 187.39/188.10 cnf(12883,plain,
% 187.39/188.10 (~P24(f329(f329(f244(a874),x128831),f2(a874)))),
% 187.39/188.10 inference(rename_variables,[],[4524])).
% 187.39/188.10 cnf(12884,plain,
% 187.39/188.10 (P24(f329(f329(f243(a1),x128841),x128841))),
% 187.39/188.10 inference(rename_variables,[],[3277])).
% 187.39/188.10 cnf(12893,plain,
% 187.39/188.10 (P24(f329(f329(f243(a874),x128931),x128931))),
% 187.39/188.10 inference(rename_variables,[],[3276])).
% 187.39/188.10 cnf(12900,plain,
% 187.39/188.10 (E(f329(f329(f16(x129001,x129002),x129003),x129004),x129003)),
% 187.39/188.10 inference(rename_variables,[],[3267])).
% 187.39/188.10 cnf(12903,plain,
% 187.39/188.10 (P24(f329(f329(f243(f881(x129031,a869)),f329(f171(x129031),f175(x129031,x129032,x129033))),f329(f171(x129031),x129032)))),
% 187.39/188.10 inference(rename_variables,[],[3982])).
% 187.39/188.10 cnf(12907,plain,
% 187.39/188.10 (~P24(f329(f329(f244(a874),x129071),f2(a874)))),
% 187.39/188.10 inference(rename_variables,[],[4524])).
% 187.39/188.10 cnf(12908,plain,
% 187.39/188.10 (P24(f329(f329(f243(a1),x129081),x129081))),
% 187.39/188.10 inference(rename_variables,[],[3277])).
% 187.39/188.10 cnf(12912,plain,
% 187.39/188.10 (~P24(f329(f329(f244(a874),x129121),f2(a874)))),
% 187.39/188.10 inference(rename_variables,[],[4524])).
% 187.39/188.10 cnf(12913,plain,
% 187.39/188.10 (P24(f329(f329(f243(a1),x129131),x129131))),
% 187.39/188.10 inference(rename_variables,[],[3277])).
% 187.39/188.10 cnf(12917,plain,
% 187.39/188.10 (~P24(f329(f329(f243(f881(a874,a869)),f300(a874,f329(a117,x129171),f329(a117,x129171))),f300(a874,x129172,x129171)))),
% 187.39/188.10 inference(scs_inference,[],[4323,3521,11045,12081,12179,12268,12304,12312,12377,12498,3530,12145,12558,12560,3531,12210,3244,12517,12519,3245,12529,3211,12454,4492,4493,11662,4233,12583,12586,3248,12590,3086,3145,12489,4477,3581,4459,10208,10218,10229,10240,10341,10344,10347,10450,10563,10866,11030,11033,11230,11317,11324,11338,11390,11393,11437,11503,11549,11565,11864,11889,11901,11930,11936,12031,12141,12148,12296,12347,12485,12602,4474,10434,10527,3336,3298,12543,3490,3193,4469,12673,2873,2874,2876,2877,2880,2881,2883,2884,2885,2891,2892,2895,2896,2903,2904,2908,2909,2910,2911,2917,2920,2923,2932,2938,2944,2952,2953,2954,2961,2974,2982,2986,2987,2988,2997,3010,3019,3020,3022,3023,3029,3035,3036,3037,3038,3047,3053,4454,3065,3144,4455,3619,3847,11596,3118,11314,3258,3234,10211,10275,10278,10368,10371,10664,11329,11332,11448,11490,11495,11591,12051,12246,12434,12487,12493,12510,12512,12535,12537,12566,12568,12573,12599,3860,3206,12325,12329,12333,3212,3219,3740,3979,3108,4471,3484,3832,11364,3335,12575,3169,3136,3313,3656,12523,3131,3953,3661,4438,4560,3115,3116,3096,3151,3291,12380,12457,3337,10815,12142,3204,3205,3229,10475,3383,4541,10404,3919,4484,10266,10431,11227,12292,12326,4491,12300,3267,11685,11688,4530,10980,11050,11273,11276,3384,3605,3350,12508,3166,10333,10640,3167,3442,3159,3087,3189,11354,4066,12315,12446,3921,10986,11112,11162,12276,12282,12393,12396,12419,4553,10918,11117,11221,11243,11281,11287,12226,4554,11019,11120,11224,4555,11123,4556,11176,4557,3188,3482,12182,12223,12299,3644,4350,4351,4482,11345,3583,3622,3796,3552,12790,12794,12798,12802,12812,3842,12176,3468,3722,3347,10352,10470,10541,10602,10605,10643,10737,10970,11860,11923,12002,12042,12119,12122,12423,12608,12667,12710,12713,12755,12773,3733,11582,3260,3359,11700,3546,4524,10243,10246,10272,10745,10758,10876,11265,11357,11752,11757,11978,11981,12063,12072,12229,12319,12613,12632,12635,12659,12714,12878,12883,12907,4536,11467,11498,11533,11562,12723,12727,3720,3491,3493,12638,12641,12644,12647,12681,3869,3306,3308,3281,4521,3165,4479,3672,4203,3988,3474,4537,4060,11238,3604,3320,11709,11712,12403,4030,3987,11853,12197,3931,12204,3982,10989,12078,12203,3645,11863,12009,12086,12132,4019,3663,10992,11055,11136,11195,12030,12100,12342,12416,12429,4542,10761,11128,3276,10361,10457,10588,10650,10719,10764,10767,10800,10823,10860,10898,10934,11656,11703,11833,11888,11904,11907,11910,11913,12093,12107,12110,12113,12116,12190,12251,12353,12399,12660,12687,12765,12776,12781,12784,12787,12820,12833,12844,12893,3277,10390,10445,10655,10740,10863,11440,11737,11740,11749,11839,11850,11869,11874,11916,11939,11956,12678,12824,12847,12879,12884,12908,3280,3355,12066,12743,12791,12795,12799,12803,12813,12817,4520,10309,10399,10512,10536,10782,10826,10836,11512,11610,11631,11634,11637,11653,11807,11810,11813,11816,11900,11919,11922,11935,11990,11993,11996,11999,12073,12161,12164,12254,12257,12318,12346,12383,12466,3437,10608,10871,10915,11184,11262,11425,11665,12295,12469,4532,10791,10803,10907,10925,10928,10983,11069,11077,11093,11131,11148,11156,11192,11233,11253,11256,11259,11290,11297,11300,11682,11718,11984,11987,12021,12067,12096,12235,12273,12279,12365,12368,12389,12445,12451,12460,12479,12742,12759,12762,3341,10637,10667,10676,11213,11764,12384,12400,12724,12728,12731,3379,3373,3800,3738,10312,11585,11613,12705,4529,10263,10625,10628,11072,11090,11548,11601,11641,11666,11770,11795,11798,11801,11804,12062,3300,10670,10820,10891,11614,11769,11961,12169,12191,3761,11715,12654,4110,3497,4527,3772,3808,4510,4513,4514,3251,3255,4512,3174,4511,4515,3779,3594,4209,11447,4544,10234,10237,10493,10544,10547,10552,10957,11419,11669,11773,4551,11151,11270,11306,3996,12218,3886,11303,11640,11644,11706,12303,12311,12392,3727,10931,10937,10952,11885,12014,12099,3579,12125,12232,12241,12308,12356,12364,12476,3617,4064,3729,10673,11008,11159,11189,11200,12034,12307,3547,10591,10594,10679,10847,3549,4548,11579,4538,4543,12622,4549,10730,10829,11139,11422,11453,12185,12194,12238,12413,4170,10806,4071,3760,12482,3707,3708,4546,10285,10288,10631,10634,11464,11645,12422,4547,11559,11650,3731,10597,4003,4568,4594,4643,4645,4675,4692,4699,4700,4739,4769,4775,4860,4885,4886,4921,4946,4947,4969,4970,4983,4987,5010,5017,5035,5038,5039,5040,5045,5046,5068,5093,5094,5104,5109,5115,5160,5161,5169,5178,5183,5185,5195,5197,5203,5207,5222,5229,5232,5233,5234,5238,5274,5287,5295,5297,5298,5302,5303,5304,5312,5315,5319,5320,5321,5328,5332,5333,5334,5342,5346,5347,5348,5353,5366,5375,5387,5389,5397,5398,5402,5406,5431,5437,5447,5448,5463,5475,5497,5503,5519,5520,5523,5542,5550,5551,5556,5557,5567,5569,5581,5585,5594,5595,5597,5612,5617,5627,5628,5640,5647,5661,5665,5668,5674,5675,5676,5679,5684,5722,5723,5726,5728,5731,5732,5733,5735,5737,5739,5744,5751,5766,5780,5785,5786,5799,5800,5805,5809,5811,5816,5857,5869,5878,5882,5893,5897,5898,5906,5920,5926,5944,5947,5959,5985,5999,6024,6044,6045,6048,6062,6064,6066,6068,6081,6082,6085,6087,6090,6091,6103,6109,6110,6111,6113,61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% 187.39/188.10 cnf(12918,plain,
% 187.39/188.10 (P24(f329(f329(f243(a874),x129181),x129181))),
% 187.39/188.10 inference(rename_variables,[],[3276])).
% 187.39/188.10 cnf(12920,plain,
% 187.39/188.10 (~P24(f329(f329(f244(f881(a874,a869)),f300(a874,f329(a117,x129201),f329(a117,x129201))),f300(a874,x129202,x129201)))),
% 187.39/188.10 inference(scs_inference,[],[4323,3521,11045,12081,12179,12268,12304,12312,12377,12498,3530,12145,12558,12560,3531,12210,3244,12517,12519,3245,12529,3211,12454,4492,4493,11662,4233,12583,12586,3248,12590,3086,3145,12489,4477,3581,4459,10208,10218,10229,10240,10341,10344,10347,10450,10563,10866,11030,11033,11230,11317,11324,11338,11390,11393,11437,11503,11549,11565,11864,11889,11901,11930,11936,12031,12141,12148,12296,12347,12485,12602,4474,10434,10527,3336,3298,12543,3490,3193,4469,12673,2873,2874,2876,2877,2880,2881,2883,2884,2885,2891,2892,2895,2896,2903,2904,2908,2909,2910,2911,2917,2920,2923,2932,2938,2944,2952,2953,2954,2961,2974,2982,2986,2987,2988,2997,3010,3019,3020,3022,3023,3029,3035,3036,3037,3038,3047,3053,4454,3065,3144,4455,3619,3847,11596,3118,11314,3258,3234,10211,10275,10278,10368,10371,10664,11329,11332,11448,11490,11495,11591,12051,12246,12434,12487,12493,12510,12512,12535,12537,12566,12568,12573,12599,3860,3206,12325,12329,12333,3212,3219,3740,3979,3108,4471,3484,3832,11364,3335,12575,3169,3136,3313,3656,12523,3131,3953,3661,4438,4560,3115,3116,3096,3151,3291,12380,12457,3337,10815,12142,3204,3205,3229,10475,3383,4541,10404,3919,4484,10266,10431,11227,12292,12326,4491,12300,3267,11685,11688,4530,10980,11050,11273,11276,3384,3605,3350,12508,3166,10333,10640,3167,3442,3159,3087,3189,11354,4066,12315,12446,3921,10986,11112,11162,12276,12282,12393,12396,12419,4553,10918,11117,11221,11243,11281,11287,12226,4554,11019,11120,11224,4555,11123,4556,11176,4557,3188,3482,12182,12223,12299,3644,4350,4351,4482,11345,3583,3622,3796,3552,12790,12794,12798,12802,12812,3842,12176,3468,3722,3347,10352,10470,10541,10602,10605,10643,10737,10970,11860,11923,12002,12042,12119,12122,12423,12608,12667,12710,12713,12755,12773,3733,11582,3260,3359,11700,3546,4524,10243,10246,10272,10745,10758,10876,11265,11357,11752,11757,11978,11981,12063,12072,12229,12319,12613,12632,12635,12659,12714,12878,12883,12907,4536,11467,11498,11533,11562,12723,12727,3720,3491,3493,12638,12641,12644,12647,12681,3869,3306,3308,3281,4521,3165,4479,3672,4203,3988,3474,4537,4060,11238,3604,3320,11709,11712,12403,4030,3987,11853,12197,3931,12204,3982,10989,12078,12203,3645,11863,12009,12086,12132,4019,3663,10992,11055,11136,11195,12030,12100,12342,12416,12429,4542,10761,11128,3276,10361,10457,10588,10650,10719,10764,10767,10800,10823,10860,10898,10934,11656,11703,11833,11888,11904,11907,11910,11913,12093,12107,12110,12113,12116,12190,12251,12353,12399,12660,12687,12765,12776,12781,12784,12787,12820,12833,12844,12893,12918,3277,10390,10445,10655,10740,10863,11440,11737,11740,11749,11839,11850,11869,11874,11916,11939,11956,12678,12824,12847,12879,12884,12908,3280,3355,12066,12743,12791,12795,12799,12803,12813,12817,4520,10309,10399,10512,10536,10782,10826,10836,11512,11610,11631,11634,11637,11653,11807,11810,11813,11816,11900,11919,11922,11935,11990,11993,11996,11999,12073,12161,12164,12254,12257,12318,12346,12383,12466,3437,10608,10871,10915,11184,11262,11425,11665,12295,12469,4532,10791,10803,10907,10925,10928,10983,11069,11077,11093,11131,11148,11156,11192,11233,11253,11256,11259,11290,11297,11300,11682,11718,11984,11987,12021,12067,12096,12235,12273,12279,12365,12368,12389,12445,12451,12460,12479,12742,12759,12762,3341,10637,10667,10676,11213,11764,12384,12400,12724,12728,12731,3379,3373,3800,3738,10312,11585,11613,12705,4529,10263,10625,10628,11072,11090,11548,11601,11641,11666,11770,11795,11798,11801,11804,12062,3300,10670,10820,10891,11614,11769,11961,12169,12191,3761,11715,12654,4110,3497,4527,3772,3808,4510,4513,4514,3251,3255,4512,3174,4511,4515,3779,3594,4209,11447,4544,10234,10237,10493,10544,10547,10552,10957,11419,11669,11773,4551,11151,11270,11306,3996,12218,3886,11303,11640,11644,11706,12303,12311,12392,3727,10931,10937,10952,11885,12014,12099,3579,12125,12232,12241,12308,12356,12364,12476,3617,4064,3729,10673,11008,11159,11189,11200,12034,12307,3547,10591,10594,10679,10847,3549,4548,11579,4538,4543,12622,4549,10730,10829,11139,11422,11453,12185,12194,12238,12413,4170,10806,4071,3760,12482,3707,3708,4546,10285,10288,10631,10634,11464,11645,12422,4547,11559,11650,3731,10597,4003,4568,4594,4643,4645,4675,4692,4699,4700,4739,4769,4775,4860,4885,4886,4921,4946,4947,4969,4970,4983,4987,5010,5017,5035,5038,5039,5040,5045,5046,5068,5093,5094,5104,5109,5115,5160,5161,5169,5178,5183,5185,5195,5197,5203,5207,5222,5229,5232,5233,5234,5238,5274,5287,5295,5297,5298,5302,5303,5304,5312,5315,5319,5320,5321,5328,5332,5333,5334,5342,5346,5347,5348,5353,5366,5375,5387,5389,5397,5398,5402,5406,5431,5437,5447,5448,5463,5475,5497,5503,5519,5520,5523,5542,5550,5551,5556,5557,5567,5569,5581,5585,5594,5595,5597,5612,5617,5627,5628,5640,5647,5661,5665,5668,5674,5675,5676,5679,5684,5722,5723,5726,5728,5731,5732,5733,5735,5737,5739,5744,5751,5766,5780,5785,5786,5799,5800,5805,5809,5811,5816,5857,5869,5878,5882,5893,5897,5898,5906,5920,5926,5944,5947,5959,5985,5999,6024,6044,6045,6048,6062,6064,6066,6068,6081,6082,6085,6087,6090,6091,6103,6109,6110,6111,6113,6115,6158,6159,6166,6172,6176,6212,6214,6216,6218,6227,6229,6231,6237,6239,6245,6248,6256,6263,6264,6265,6270,6292,6293,6294,6296,6302,6307,6341,6342,6344,6345,6346,6348,6349,6350,6351,6358,6391,6392,6401,6422,6423,6443,6446,6457,6458,6464,6495,6497,6511,6549,6551,6552,6606,6630,6672,6692,6701,6702,6703,6704,6723,6724,6730,6743,6746,6748,6750,6751,6752,6754,6768,6779,6781,6782,6795,6799,6850,6861,6863,6867,6884,6885,6921,6933,6964,6998,7052,7080,7135,7156,7165,7168,7223,7231,7289,7291,7306,7316,7317,7318,7337,7343,7345,7395,7405,7408,7424,7476,7478,7481,7524,7525,7543,7610,7629,7652,7676,7691,7706,7717,7726,7727,7756,7759,7761,7771,7809,7820,7845,7903,7937,7969,8016,8032,8048,8049,8124,8177,8196,8220,8240,8264,8362,8364,8370,8386,8390,8406,8429,8440,8442,8457,8463,8467,8490,8504,8505,8521,8522,8527,8528,8529,8530,8531,8549,8550,8551,8559,8573,8575,8587,8591,8593,8594,8595,8603,8608,8635,8636,8668,8681,8685,8703,8725,8726,8727,8728,8740,8741,8763,8773,8783,8784,8785,8786,8788,8809,8810,8821,8865,8871,8877,8889,8894,8896,8899,8900,8904,8914,8997,9028,9029,9030,9045,9063,9068,9096,9097,9138,9141,9167,9212,9213,9214,9229,9256,9270,9276,9279,9301,9302,9330,9391,9426,9427,9428,9453,9454,9472,9491,9497,9511,9534,9556,9564,9565,9566,9567,9582,9584,9589,9620,9621,9627,9628,9672,9673,9705,9714,9724,9726,9727,9736,9750,9753,9781,9814,9816,9820,9878,9919,9920,9922,9932,9933,9953,9958,9999,10050,10122,10123,10176,10192,2,8,9,4581,4582,4600,4631,4633,4634,4661,4667,4668,4679,4728,4730,4760,4774,4804,4900,4901,4914,4934,4990,4991,4994,4995,4997,4999,5000,5009,5013,5014,5024,5036,5037,5043,5063,5064,5081,5086,5087,5088,5089,5092,5100,5103,5110,5175,5181,5182,5189,5219,5230,5236,5252,5272,5273,5280,5281,5282,5291,5301,5308,5310,5311,5317,5324,5325,5338,5339,5340,5341,5343,5344,5349,5350,5351,5352,5383,5384,5385,5393,5394,5395,5396,5439,5444,5446,5482,5484,5485,5487,5488,5490,5491,5493,5502,5507,5509,5510,5511,5512,5513,5514,5521,5531,5534,5545,5561,5562,5565,5575,5577,5578,5579,5604,5614,5630,5631,5641,5642,5644,5646,5651,5686,5691,5693,5753,5787,5788,5792,5798,5801,5802,5803,5804,5810,5821,5822,5824,5825,5833,5854,5885,5901,5904,5905,5907,5916,5934,5938,5941,5942,5943,5961,5972,5973,6001,6002,6006,6026,6029,6033,6052,6057,6058,6083,6086,6094,6102,6108,6112,6119,6120,6121,6122,6161,6177,6230,6266,6268,6289,6290,6295,6299,6300,6303,6309,6318,6333,6353,6354,6359,6369,6384,6404,6410,6412,6427,6428,6431,6432,6434,6436,6437,6438,6440,6442,6445,6450,6451,6453,6454,6460,6462,6505,6510,6524,6526,6527,6528,6563,6568,6570,6575,6576,6584,6588,6601,6625,6626,6628,6629,6640,6646,6663,6666,6685,6718,6719,6720,6725,6739,6758,6760,6762,6764,6769,6775,6777,6792,6797,6800,6836,6837,6838,6852,6853,6855,6856,6875,6877,6893,6919,6941,6952,6954,6956,6958,6959,6960,6995,6996,7001,7002,7009,7010,7012,7014,7033,7042,7043,7055,7065,7104,7114,7118,7125,7136,7142,7144,7150,7158,7159,7172,7189,7207,7209,7226,7275,7276,7277,7279,7281,7285,7290,7313,7358,7391,7406,7423,7456,7459,7485,7509,7526,7529,7530,7540,7559,7561,7563,7565,7566,7567,7592,7618,7619,7651,7653,7654,7655,7660,7683,7692,7703,7708,7714,7716,7722,7734,7735,7737,7762,7769,7792,7858,7859,7906,7914,7915,7939,7940,7957,7958,8023,8024,8051,8080,8091,8093,8102,8114,8146,8152,8159,8172,8191,8197,8219,8262,8292,8304,8322,8325,8355,8378,8443,8444,8447,8449,8553,8554,8555,8556,8582,8611,8639,8684,8702,8757,8802,8805,8818,8825,8862,8910,8911,8929,8930,9070,9074,9094,9104,9127,9129,9132,9136,9139,9140,9153,9154,9174,9180,9192,9240,9241,9260,9314,9315,9322,9383,9388,9423,9430,9433,9436,9437,9452,9468,9477,9487,9490,9500,9501,9504,9506,9532,9655,9699,9700,9743,9788,9905,9962,10027,10101,10114,10119,3,2614,2616,2617,2618,2619,2620,2621,2628,2629,2630,2631,2636,2637,2638,2639,2644,2651,2652,2657,2658,2659,2661,2662,2663,2666,2667,2668,2670,2671,2674,2675,2676,2681,2682,2687,2688,2689,2695,2696,2697,2702,2703,2705,2706,2710,2712,2713,2716,2718,2719,2721,2723,2726,2735,2736,2737,2764,2767,2789,2792,2793,2794,2801,2803,2805,2807,2819,2820,2822,2829,5211,5271,5369,5455,5456,5457,5532,5629,5660,5694,5710,5712,5718,5781,5782,5783,5784,5790,5823,5956,5991,6000,6023,6060,6095,6100,6247,6252,6287,6288,6308,6311,6313,6320,6321,6322,6323,6324,6325,6326,6327,6406,6474,6475,6562,6595,6596,6637,6638,6776,6791,6864,6865,6872,6894,6917,6925,6927,6974,6999,7000,7018,7019,7054,7098,7099,7196,7257,7258,7259,7260,7274,7307,7363,7364,7373,7381,7382,7394,7426,7427,7428,7429,7573,7574,7576,7578,7584,7585,7800,7806,7807,7817,7856,7935,7977,8035,8056,8057,8072,8131,8233,8302,8303,8305,8340,8402,8403,8476,8497,8498])).
% 187.39/188.10 cnf(12921,plain,
% 187.39/188.10 (P24(f329(f329(f243(a874),x129211),x129211))),
% 187.39/188.10 inference(rename_variables,[],[3276])).
% 187.39/188.10 cnf(12924,plain,
% 187.39/188.10 (~P24(f329(f329(f243(a874),f329(a117,x129241)),x129241))),
% 187.39/188.10 inference(rename_variables,[],[4529])).
% 187.39/188.10 cnf(12929,plain,
% 187.39/188.10 (E(x129291,f511(f329(f5(x129292),f329(f5(x129292),x129291)),f5(x129292),x129292,x129292))),
% 187.39/188.10 inference(scs_inference,[],[4323,3521,11045,12081,12179,12268,12304,12312,12377,12498,12500,3530,12145,12558,12560,3531,12210,3244,12517,12519,3245,12529,3211,12454,4492,4493,11662,4233,12583,12586,3248,12590,3086,3145,12489,4477,3581,4459,10208,10218,10229,10240,10341,10344,10347,10450,10563,10866,11030,11033,11230,11317,11324,11338,11390,11393,11437,11503,11549,11565,11864,11889,11901,11930,11936,12031,12141,12148,12296,12347,12485,12602,4474,10434,10527,3336,3298,12543,3490,3193,4469,12673,2873,2874,2876,2877,2880,2881,2883,2884,2885,2891,2892,2895,2896,2903,2904,2908,2909,2910,2911,2917,2920,2923,2932,2938,2944,2952,2953,2954,2961,2974,2982,2986,2987,2988,2997,3010,3019,3020,3022,3023,3029,3035,3036,3037,3038,3047,3053,4454,3065,3144,4455,3619,3847,11596,3118,11314,3258,3234,10211,10275,10278,10368,10371,10664,11329,11332,11448,11490,11495,11591,12051,12246,12434,12487,12493,12510,12512,12535,12537,12566,12568,12573,12599,3860,3206,12325,12329,12333,3212,3219,3740,3979,3107,3108,4471,3484,3832,11364,3335,12575,3169,3136,3313,3656,12523,3131,3953,3661,4438,4560,3115,3116,3096,3151,3291,12380,12457,3337,10815,12142,3204,3205,3229,10475,3383,4541,10404,3919,4484,10266,10431,11227,12292,12326,4491,12300,3267,11685,11688,4530,10980,11050,11273,11276,3384,3605,3350,12508,3166,10333,10640,3167,3442,3159,3087,3189,11354,4066,12315,12446,3921,10986,11112,11162,12276,12282,12393,12396,12419,4553,10918,11117,11221,11243,11281,11287,12226,4554,11019,11120,11224,4555,11123,4556,11176,4557,3188,3482,12182,12223,12299,3644,4350,4351,4482,11345,3583,3622,3796,3552,12790,12794,12798,12802,12812,3842,12176,3468,3722,3347,10352,10470,10541,10602,10605,10643,10737,10970,11860,11923,12002,12042,12119,12122,12423,12608,12667,12710,12713,12755,12773,3733,11582,3260,3359,11700,3546,4524,10243,10246,10272,10745,10758,10876,11265,11357,11752,11757,11978,11981,12063,12072,12229,12319,12613,12632,12635,12659,12714,12878,12883,12907,4536,11467,11498,11533,11562,12723,12727,3720,3491,3493,12638,12641,12644,12647,12681,3869,3306,3308,3281,4521,3165,4479,3672,4203,3988,3474,4537,4060,11238,3604,3320,11709,11712,12403,4030,3987,11853,12197,3931,12204,3982,10989,12078,12203,3645,11863,12009,12086,12132,4019,3663,10992,11055,11136,11195,12030,12100,12342,12416,12429,4542,10761,11128,3276,10361,10457,10588,10650,10719,10764,10767,10800,10823,10860,10898,10934,11656,11703,11833,11888,11904,11907,11910,11913,12093,12107,12110,12113,12116,12190,12251,12353,12399,12660,12687,12765,12776,12781,12784,12787,12820,12833,12844,12893,12918,12921,3277,10390,10445,10655,10740,10863,11440,11737,11740,11749,11839,11850,11869,11874,11916,11939,11956,12678,12824,12847,12879,12884,12908,3280,3355,12066,12743,12791,12795,12799,12803,12813,12817,4520,10309,10399,10512,10536,10782,10826,10836,11512,11610,11631,11634,11637,11653,11807,11810,11813,11816,11900,11919,11922,11935,11990,11993,11996,11999,12073,12161,12164,12254,12257,12318,12346,12383,12466,3437,10608,10871,10915,11184,11262,11425,11665,12295,12469,4532,10791,10803,10907,10925,10928,10983,11069,11077,11093,11131,11148,11156,11192,11233,11253,11256,11259,11290,11297,11300,11682,11718,11984,11987,12021,12067,12096,12235,12273,12279,12365,12368,12389,12445,12451,12460,12479,12742,12759,12762,3341,10637,10667,10676,11213,11764,12384,12400,12724,12728,12731,3379,3373,3800,3738,10312,11585,11613,12705,4529,10263,10625,10628,11072,11090,11548,11601,11641,11666,11770,11795,11798,11801,11804,12062,12924,3300,10670,10820,10891,11614,11769,11961,12169,12191,3761,11715,12654,4110,3497,4527,3772,3808,4510,4513,4514,3251,3255,4512,3174,4511,4515,3779,3594,4209,11447,4544,10234,10237,10493,10544,10547,10552,10957,11419,11669,11773,4551,11151,11270,11306,3996,12218,3886,11303,11640,11644,11706,12303,12311,12392,12672,3727,10931,10937,10952,11885,12014,12099,3579,12125,12232,12241,12308,12356,12364,12476,3617,4064,3729,10673,11008,11159,11189,11200,12034,12307,3547,10591,10594,10679,10847,3549,4548,11579,4538,4543,12622,4549,10730,10829,11139,11422,11453,12185,12194,12238,12413,4170,10806,4071,3760,12482,3707,3708,4546,10285,10288,10631,10634,11464,11645,12422,4547,11559,11650,3731,10597,4003,4568,4594,4643,4645,4675,4692,4699,4700,4739,4769,4775,4860,4885,4886,4921,4946,4947,4969,4970,4983,4987,5010,5017,5035,5038,5039,5040,5045,5046,5068,5093,5094,5104,5109,5115,5160,5161,5169,5178,5183,5185,5195,5197,5203,5207,5222,5229,5232,5233,5234,5238,5274,5287,5295,5297,5298,5302,5303,5304,5312,5315,5319,5320,5321,5328,5332,5333,5334,5342,5346,5347,5348,5353,5366,5375,5387,5389,5397,5398,5402,5406,5431,5437,5447,5448,5463,5475,5497,5503,5519,5520,5523,5542,5550,5551,5556,5557,5567,5569,5581,5585,5594,5595,5597,5612,5617,5627,5628,5640,5647,5661,5665,5668,5674,5675,5676,5679,5684,5722,5723,5726,5728,5731,5732,5733,5735,5737,5739,5744,5751,5766,5780,5785,5786,5799,5800,5805,5809,5811,5816,5857,5869,5878,5882,5893,5897,5898,5906,5920,5926,5944,5947,5959,5985,5999,6024,6044,6045,6048,6062,6064,6066,6068,6081,6082,6085,6087,60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% 187.39/188.10 cnf(12930,plain,
% 187.39/188.10 (P24(f329(f329(f331(x129301),f329(x129302,x129303)),f329(f308(x129304,x129301,x129302),f252(f881(x129304,a869)))))),
% 187.39/188.10 inference(rename_variables,[],[3886])).
% 187.39/188.10 cnf(12931,plain,
% 187.39/188.10 (P21(x129311,x129311,f5(x129311),x129312)),
% 187.39/188.10 inference(rename_variables,[],[3521])).
% 187.39/188.10 cnf(12935,plain,
% 187.39/188.10 (P24(f329(f329(f331(x129351),x129352),f252(f881(x129351,a869))))),
% 187.39/188.10 inference(rename_variables,[],[3437])).
% 187.39/188.10 cnf(12936,plain,
% 187.39/188.10 (~P24(f329(f329(f331(x129361),x129362),f193(f881(x129361,a869))))),
% 187.39/188.10 inference(rename_variables,[],[4532])).
% 187.39/188.10 cnf(12939,plain,
% 187.39/188.10 (P21(x129391,x129391,f5(x129391),x129392)),
% 187.39/188.10 inference(rename_variables,[],[3521])).
% 187.39/188.10 cnf(12942,plain,
% 187.39/188.10 (P21(x129421,x129421,f5(x129421),x129422)),
% 187.39/188.10 inference(rename_variables,[],[3521])).
% 187.39/188.10 cnf(12946,plain,
% 187.39/188.10 (P21(x129461,x129461,f5(x129461),x129462)),
% 187.39/188.10 inference(rename_variables,[],[3521])).
% 187.39/188.10 cnf(12949,plain,
% 187.39/188.10 (~P24(f329(f329(f244(f881(x129491,a869)),x129492),f193(f881(x129491,a869))))),
% 187.39/188.10 inference(rename_variables,[],[4542])).
% 187.39/188.10 cnf(12952,plain,
% 187.39/188.10 (P21(x129521,x129521,f5(x129521),x129522)),
% 187.39/188.10 inference(rename_variables,[],[3521])).
% 187.39/188.10 cnf(12955,plain,
% 187.39/188.10 (P21(x129551,x129551,f5(x129551),x129552)),
% 187.39/188.10 inference(rename_variables,[],[3521])).
% 187.39/188.10 cnf(12966,plain,
% 187.39/188.10 (P24(f329(f329(f243(f881(x129661,a869)),f193(f881(x129661,a869))),x129662))),
% 187.39/188.10 inference(rename_variables,[],[3729])).
% 187.39/188.10 cnf(12970,plain,
% 187.39/188.10 (E(f329(f260(x129701,x129701),f261(x129701,x129702)),x129702)),
% 187.39/188.10 inference(rename_variables,[],[3234])).
% 187.39/188.10 cnf(12974,plain,
% 187.39/188.10 (~P24(f329(f329(f331(x129741),x129742),f193(f881(x129741,a869))))),
% 187.39/188.10 inference(rename_variables,[],[4532])).
% 187.39/188.10 cnf(12978,plain,
% 187.39/188.10 (P24(f329(f329(f331(x129781),f329(x129782,x129783)),f329(f308(x129784,x129781,x129782),f252(f881(x129784,a869)))))),
% 187.39/188.10 inference(rename_variables,[],[3886])).
% 187.39/188.10 cnf(12979,plain,
% 187.39/188.10 (P21(x129791,x129791,f5(x129791),x129792)),
% 187.39/188.10 inference(rename_variables,[],[3521])).
% 187.39/188.10 cnf(12982,plain,
% 187.39/188.10 (P24(f329(f329(f331(x129821),x129822),f252(f881(x129821,a869))))),
% 187.39/188.10 inference(rename_variables,[],[3437])).
% 187.39/188.10 cnf(12989,plain,
% 187.39/188.10 (~P24(f329(f329(f331(x129891),x129892),f193(f881(x129891,a869))))),
% 187.39/188.10 inference(rename_variables,[],[4532])).
% 187.39/188.10 cnf(12992,plain,
% 187.39/188.10 (~P24(f329(f329(f331(x129921),x129922),f193(f881(x129921,a869))))),
% 187.39/188.10 inference(rename_variables,[],[4532])).
% 187.39/188.10 cnf(12996,plain,
% 187.39/188.10 (E(f329(f329(f16(x129961,x129962),x129963),x129964),x129963)),
% 187.39/188.10 inference(rename_variables,[],[3267])).
% 187.39/188.10 cnf(12999,plain,
% 187.39/188.10 (P24(f329(f329(f244(a874),x129991),f329(a117,x129991)))),
% 187.39/188.10 inference(rename_variables,[],[3347])).
% 187.39/188.10 cnf(13000,plain,
% 187.39/188.10 (~E(f329(a117,x130001),x130001)),
% 187.39/188.10 inference(rename_variables,[],[4459])).
% 187.39/188.10 cnf(13003,plain,
% 187.39/188.10 (P24(f329(f329(f244(a874),x130031),f329(a117,f329(f329(f80(a874),x130032),x130031))))),
% 187.39/188.10 inference(rename_variables,[],[3731])).
% 187.39/188.10 cnf(13004,plain,
% 187.39/188.10 (P24(f329(f329(f244(a874),x130041),f329(a117,x130041)))),
% 187.39/188.10 inference(rename_variables,[],[3347])).
% 187.39/188.10 cnf(13006,plain,
% 187.39/188.10 (~E(f329(f329(f81(a874),f329(a117,f2(a874))),f33(x130061,x130062)),f329(f329(f81(a874),f329(a117,f2(a874))),f32(x130063,x130064)))),
% 187.39/188.10 inference(scs_inference,[],[4323,3521,11045,12081,12179,12268,12304,12312,12377,12498,12500,12931,12939,12942,12946,12952,12955,3530,12145,12558,12560,3531,12210,3244,12517,12519,3245,12529,3211,12454,4492,4493,11662,4233,12583,12586,3248,12590,3086,3145,12489,4477,3581,4459,10208,10218,10229,10240,10341,10344,10347,10450,10563,10866,11030,11033,11230,11317,11324,11338,11390,11393,11437,11503,11549,11565,11864,11889,11901,11930,11936,12031,12141,12148,12296,12347,12485,12602,12756,13000,4474,10434,10527,3336,3298,12543,3490,3193,4469,12673,2873,2874,2876,2877,2880,2881,2883,2884,2885,2891,2892,2895,2896,2903,2904,2908,2909,2910,2911,2917,2920,2923,2932,2938,2944,2949,2952,2953,2954,2961,2974,2982,2986,2987,2988,2997,3010,3019,3020,3022,3023,3029,3035,3036,3037,3038,3047,3053,4454,3065,3144,4455,3619,3847,11596,3118,11314,3258,3234,10211,10275,10278,10368,10371,10664,11329,11332,11448,11490,11495,11591,12051,12246,12434,12487,12493,12510,12512,12535,12537,12566,12568,12573,12599,12807,3860,3206,12325,12329,12333,3212,3219,3740,3979,3107,3108,4471,3484,3832,11364,3335,12575,3169,3136,3313,3656,12523,3131,3953,3152,3661,4438,4560,3115,3116,3096,3151,3291,12380,12457,3337,10815,12142,3204,3205,3229,10475,3383,4541,10404,3919,4484,10266,10431,11227,12292,12326,12330,4491,12300,3267,11685,11688,12900,4530,10980,11050,11273,11276,3264,3384,3605,3350,12508,3166,10333,10640,3167,4518,3442,3159,3087,3189,11354,4066,12315,12446,3921,10986,11112,11162,12276,12282,12393,12396,12419,4553,10918,11117,11221,11243,11281,11287,12226,4554,11019,11120,11224,4555,11123,11173,4556,11176,4557,3188,3482,12182,12223,12299,3644,4350,4351,4482,11345,3583,3622,3796,3552,12790,12794,12798,12802,12812,3842,12176,3468,3722,3347,10352,10470,10541,10602,10605,10643,10737,10970,11860,11923,12002,12042,12119,12122,12423,12608,12667,12710,12713,12755,12773,12999,3733,11582,3260,3359,11700,3546,4524,10243,10246,10272,10745,10758,10876,11265,11357,11752,11757,11978,11981,12063,12072,12229,12319,12613,12632,12635,12659,12714,12878,12883,12907,4536,11467,11498,11533,11562,12723,12727,3720,3491,3493,12638,12641,12644,12647,12681,3869,3306,3308,3281,4521,3165,4479,3672,4203,3988,3474,4537,4060,11238,3604,3320,11709,11712,12403,4030,3987,11853,12197,3931,12204,3982,10989,12078,12203,3645,11863,12009,12086,12132,4019,3663,10992,11055,11136,11195,12030,12100,12342,12416,12429,12869,4542,10761,11128,12207,12949,3276,10361,10457,10588,10650,10719,10764,10767,10800,10823,10860,10898,10934,11656,11703,11833,11888,11904,11907,11910,11913,12093,12107,12110,12113,12116,12190,12251,12353,12399,12660,12687,12765,12776,12781,12784,12787,12820,12833,12844,12893,12918,12921,3277,10390,10445,10655,10740,10863,11440,11737,11740,11749,11839,11850,11869,11874,11916,11939,11956,12678,12824,12847,12879,12884,12908,3280,3355,12066,12743,12791,12795,12799,12803,12813,12817,4520,10309,10399,10512,10536,10782,10826,10836,11512,11610,11631,11634,11637,11653,11807,11810,11813,11816,11900,11919,11922,11935,11990,11993,11996,11999,12073,12161,12164,12254,12257,12318,12346,12383,12466,3437,10608,10871,10915,11184,11262,11425,11665,12295,12469,12865,12935,4532,10791,10803,10907,10925,10928,10983,11069,11077,11093,11131,11148,11156,11192,11233,11253,11256,11259,11290,11297,11300,11682,11718,11984,11987,12021,12067,12096,12235,12273,12279,12365,12368,12389,12445,12451,12460,12479,12742,12759,12762,12854,12936,12974,12989,3341,10637,10667,10676,11213,11764,12384,12400,12724,12728,12731,3379,3373,3800,3738,10312,11585,11613,12705,4529,10263,10625,10628,11072,11090,11548,11601,11641,11666,11770,11795,11798,11801,11804,12062,12924,3300,10670,10820,10891,11614,11769,11961,12169,12191,3761,11715,12654,4110,3497,4527,3772,3808,4510,4513,4514,3251,3255,4512,3174,4511,4515,3779,3594,11578,4209,11447,4544,10234,10237,10493,10544,10547,10552,10957,11419,11669,11773,4551,11151,11270,11306,3996,12218,3886,11303,11640,11644,11706,12303,12311,12392,12672,12930,12978,3727,10931,10937,10952,11885,12014,12099,12361,3579,12125,12232,12241,12308,12356,12364,12476,3617,4064,3729,10673,11008,11159,11189,11200,12034,12307,12350,3547,10591,10594,10679,10847,3549,4548,11579,4538,4543,12622,4549,10730,10829,11139,11422,11453,12185,12194,12238,12413,4170,10806,12215,4071,3760,12482,3707,3708,4546,10285,10288,10631,10634,11464,11645,12422,4547,11559,11650,3731,10597,10853,4003,4568,4594,4643,4645,4675,4692,4699,4700,4739,4769,4775,4860,4885,4886,4921,4946,4947,4969,4970,4983,4987,5010,5017,5035,5038,5039,5040,5045,5046,5068,5093,5094,5104,5109,5115,5160,5161,5169,5178,5183,5185,5195,5197,5203,5207,5222,5229,5232,5233,5234,5238,5274,5287,5295,5297,5298,5302,5303,5304,5312,5315,5319,5320,5321,5328,5332,5333,5334,5342,5346,5347,5348,5353,5366,5375,5387,5389,5397,5398,5402,5406,5431,5437,5447,5448,5463,5475,5497,5503,5519,5520,5523,5542,5550,5551,5556,5557,5567,5569,5581,5585,5594,5595,5597,5612,5617,5627,5628,5640,5647,5661,5665,5668,5674,5675,5676,5679,5684,5722,5723,5726,5728,5731,5732,5733,5735,5737,5739,574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% 187.39/188.10 cnf(13008,plain,
% 187.39/188.10 (~E(f329(a117,x130081),x130081)),
% 187.39/188.10 inference(rename_variables,[],[4459])).
% 187.39/188.10 cnf(13013,plain,
% 187.39/188.10 (P24(f329(f329(f243(a1),f2(a1)),f329(f105(a1),x130131)))),
% 187.39/188.10 inference(rename_variables,[],[3379])).
% 187.39/188.10 cnf(13016,plain,
% 187.39/188.10 (P24(f329(f329(f243(a874),f2(a874)),x130161))),
% 187.39/188.10 inference(rename_variables,[],[3300])).
% 187.39/188.10 cnf(13020,plain,
% 187.39/188.10 (~E(f329(a117,x130201),f2(a874))),
% 187.39/188.10 inference(rename_variables,[],[4469])).
% 187.39/188.10 cnf(13023,plain,
% 187.39/188.10 (P24(f329(f329(f243(a1),x130231),x130231))),
% 187.39/188.10 inference(rename_variables,[],[3277])).
% 187.39/188.10 cnf(13033,plain,
% 187.39/188.10 (~P24(f329(f329(f331(x130331),x130332),f193(f881(x130331,a869))))),
% 187.39/188.10 inference(rename_variables,[],[4532])).
% 187.39/188.10 cnf(13036,plain,
% 187.39/188.10 (P24(f329(f62(a874),f302(a874,x130361,x130362)))),
% 187.39/188.10 inference(rename_variables,[],[3493])).
% 187.39/188.10 cnf(13037,plain,
% 187.39/188.10 (E(f329(f329(f241(a874),f329(a117,x130371)),f329(a117,x130372)),f329(a117,f329(f329(f241(a874),x130371),x130372)))),
% 187.39/188.10 inference(rename_variables,[],[3454])).
% 187.39/188.10 cnf(13040,plain,
% 187.39/188.10 (P24(f329(f62(a874),f302(a874,x130401,x130402)))),
% 187.39/188.10 inference(rename_variables,[],[3493])).
% 187.39/188.10 cnf(13041,plain,
% 187.39/188.10 (E(f329(f329(f242(a874),f329(a117,x130411)),f329(a117,x130412)),f329(a117,f329(f329(f242(a874),x130411),x130412)))),
% 187.39/188.10 inference(rename_variables,[],[3455])).
% 187.39/188.10 cnf(13044,plain,
% 187.39/188.10 (P24(f329(f62(a874),f302(a874,x130441,x130442)))),
% 187.39/188.10 inference(rename_variables,[],[3493])).
% 187.39/188.10 cnf(13048,plain,
% 187.39/188.10 (P24(f329(f62(a874),f302(a874,x130481,x130482)))),
% 187.39/188.10 inference(rename_variables,[],[3493])).
% 187.39/188.10 cnf(13052,plain,
% 187.39/188.10 (P24(f329(f329(f243(f881(x130521,a869)),f329(f171(x130521),f329(f134(x130521,x130522),x130523))),f329(f171(x130521),x130523)))),
% 187.39/188.10 inference(rename_variables,[],[3931])).
% 187.39/188.10 cnf(13053,plain,
% 187.39/188.10 (E(f329(f329(f16(x130531,x130532),x130533),x130534),x130533)),
% 187.39/188.10 inference(rename_variables,[],[3267])).
% 187.39/188.10 cnf(13056,plain,
% 187.39/188.10 (P24(f329(f329(f243(f881(x130561,a869)),f329(f171(x130561),f329(f329(f174(x130561),x130562),x130563))),f329(f171(x130561),x130563)))),
% 187.39/188.10 inference(rename_variables,[],[3976])).
% 187.39/188.10 cnf(13057,plain,
% 187.39/188.10 (E(f329(f329(f16(x130571,x130572),x130573),x130574),x130573)),
% 187.39/188.10 inference(rename_variables,[],[3267])).
% 187.39/188.10 cnf(13061,plain,
% 187.39/188.10 (E(f329(f329(f16(x130611,x130612),x130613),x130614),x130613)),
% 187.39/188.10 inference(rename_variables,[],[3267])).
% 187.39/188.10 cnf(13074,plain,
% 187.39/188.10 (P24(f329(f329(f243(a1),f2(a1)),f329(f105(a1),x130741)))),
% 187.39/188.10 inference(rename_variables,[],[3379])).
% 187.39/188.10 cnf(13077,plain,
% 187.39/188.10 (~P24(f329(f329(f331(x130771),x130772),f193(f881(x130771,a869))))),
% 187.39/188.10 inference(rename_variables,[],[4532])).
% 187.39/188.10 cnf(13080,plain,
% 187.39/188.10 (~P24(f329(f329(f331(x130801),x130802),f193(f881(x130801,a869))))),
% 187.39/188.10 inference(rename_variables,[],[4532])).
% 187.39/188.10 cnf(13081,plain,
% 187.39/188.10 (E(f329(f260(x130811,x130811),f261(x130811,x130812)),x130812)),
% 187.39/188.10 inference(rename_variables,[],[3234])).
% 187.39/188.10 cnf(13082,plain,
% 187.39/188.10 (P21(x130821,x130821,f5(x130821),x130822)),
% 187.39/188.10 inference(rename_variables,[],[3521])).
% 187.39/188.10 cnf(13086,plain,
% 187.39/188.10 (E(f329(f260(x130861,x130861),f261(x130861,x130862)),x130862)),
% 187.39/188.10 inference(rename_variables,[],[3234])).
% 187.39/188.10 cnf(13091,plain,
% 187.39/188.10 (P24(f329(f329(f244(f881(a1,a869)),f300(a1,f78(a1),f2(a1))),f300(a1,f2(a1),f78(a1))))),
% 187.39/188.10 inference(scs_inference,[],[4323,3521,11045,12081,12179,12268,12304,12312,12377,12498,12500,12931,12939,12942,12946,12952,12955,12979,13082,3530,12145,12558,12560,3531,12210,3244,12517,12519,3245,12529,3211,12454,4492,4493,11662,4233,12583,12586,3248,12590,3086,3145,12489,4477,3581,4459,10208,10218,10229,10240,10341,10344,10347,10450,10563,10866,11030,11033,11230,11317,11324,11338,11390,11393,11437,11503,11549,11565,11864,11889,11901,11930,11936,12031,12141,12148,12296,12347,12485,12602,12756,13000,4474,10434,10527,3336,3298,12543,3490,3193,4469,12673,12688,2873,2874,2876,2877,2880,2881,2883,2884,2885,2891,2892,2895,2896,2903,2904,2908,2909,2910,2911,2917,2920,2923,2932,2938,2944,2949,2952,2953,2954,2961,2965,2974,2982,2983,2986,2987,2988,2997,3010,3019,3020,3022,3023,3029,3035,3036,3037,3038,3047,3053,4454,3065,3144,4455,3619,3847,11596,3118,11314,3258,3234,10211,10275,10278,10368,10371,10664,11329,11332,11448,11490,11495,11591,12051,12246,12434,12487,12493,12510,12512,12535,12537,12566,12568,12573,12599,12807,12970,13081,3860,3206,12325,12329,12333,3212,3219,3740,3979,3107,3108,4471,3484,3832,11364,3335,12575,3169,3136,3313,3656,12523,3131,3953,3152,3661,4438,4560,3115,3116,3096,3151,3291,12380,12457,3337,10815,12142,3204,3205,3229,10475,3383,4541,10404,3919,4484,10266,10431,11227,12292,12326,12330,4491,12300,3267,11685,11688,12900,12996,13053,13057,13061,4530,10980,11050,11273,11276,3264,3384,3605,3376,3350,12508,3166,10333,10640,3167,4518,3442,3159,3087,3272,3189,11354,4066,12315,12446,3921,10986,11112,11162,12276,12282,12393,12396,12419,4553,10918,11117,11221,11243,11281,11287,12226,4554,11019,11120,11224,4555,11123,11173,4556,11176,4557,3188,3482,12182,12223,12299,3644,4350,4351,4482,11345,3583,3622,3796,3552,12790,12794,12798,12802,12812,3842,12176,3468,3722,3347,10352,10470,10541,10602,10605,10643,10737,10970,11860,11923,12002,12042,12119,12122,12423,12608,12667,12710,12713,12755,12773,12999,3733,11582,3260,3359,11700,3546,4524,10243,10246,10272,10745,10758,10876,11265,11357,11752,11757,11978,11981,12063,12072,12229,12319,12613,12632,12635,12659,12714,12878,12883,12907,4536,11467,11498,11533,11562,12723,12727,3720,3491,3493,12638,12641,12644,12647,12681,12684,13036,13040,13044,3494,3869,3454,13037,3455,13041,3306,3308,3281,4521,3165,4479,3672,4203,3988,3474,4537,4060,11238,3604,3320,11709,11712,12403,4030,3987,11853,12197,3931,12204,12426,13052,3976,13056,3982,10989,12078,12203,12903,3645,11863,12009,12086,12132,4019,3663,10992,11055,11136,11195,12030,12100,12342,12416,12429,12869,4542,10761,11128,12207,12949,3276,10361,10457,10588,10650,10719,10764,10767,10800,10823,10860,10898,10934,11656,11703,11833,11888,11904,11907,11910,11913,12093,12107,12110,12113,12116,12190,12251,12353,12399,12660,12687,12765,12776,12781,12784,12787,12820,12833,12844,12893,12918,12921,3277,10390,10445,10655,10740,10863,11440,11737,11740,11749,11839,11850,11869,11874,11916,11939,11956,12678,12824,12847,12879,12884,12908,12913,3280,3355,12066,12743,12791,12795,12799,12803,12813,12817,4520,10309,10399,10512,10536,10782,10826,10836,11512,11610,11631,11634,11637,11653,11807,11810,11813,11816,11900,11919,11922,11935,11990,11993,11996,11999,12073,12161,12164,12254,12257,12318,12346,12383,12466,3437,10608,10871,10915,11184,11262,11425,11665,12295,12469,12865,12935,12982,4532,10791,10803,10907,10925,10928,10983,11069,11077,11093,11131,11148,11156,11192,11233,11253,11256,11259,11290,11297,11300,11682,11718,11984,11987,12021,12067,12096,12235,12273,12279,12365,12368,12389,12445,12451,12460,12479,12742,12759,12762,12854,12936,12974,12989,12992,13033,13077,13080,3341,10637,10667,10676,11213,11764,12384,12400,12724,12728,12731,3379,13013,3373,3800,3738,10312,11585,11613,12705,4529,10263,10625,10628,11072,11090,11548,11601,11641,11666,11770,11795,11798,11801,11804,12062,12924,3300,10670,10820,10891,11614,11769,11961,12169,12191,12752,3761,11715,12654,4110,3497,4527,3772,3808,4510,4513,4514,3251,3255,4512,3174,4511,4515,4286,3779,3594,11578,4209,11447,4544,10234,10237,10493,10544,10547,10552,10957,11419,11669,11773,4551,11151,11270,11306,3996,12218,3886,11303,11640,11644,11706,12303,12311,12392,12672,12930,12978,3727,10931,10937,10952,11885,12014,12099,12361,3579,12125,12232,12241,12308,12356,12364,12476,12872,3617,4064,3729,10673,11008,11159,11189,11200,12034,12307,12350,12966,3547,10591,10594,10679,10847,3549,4548,11579,4538,4543,12622,4549,10730,10829,11139,11422,11453,12185,12194,12238,12413,4170,10806,12215,4071,3760,12482,3707,3708,4546,10285,10288,10631,10634,11464,11645,12422,4547,11559,11650,3731,10597,10853,4003,4568,4594,4643,4645,4675,4692,4699,4700,4739,4769,4775,4860,4885,4886,4921,4946,4947,4969,4970,4983,4987,5010,5017,5035,5038,5039,5040,5045,5046,5068,5093,5094,5104,5109,5115,5160,5161,5169,5178,5183,5185,5195,5197,5203,5207,5222,5229,5232,5233,5234,5238,5274,5287,5295,5297,5298,5302,5303,5304,5312,5315,5319,5320,5321,5328,5332,5333,5334,5342,5346,5347,5348,5353,5366,5375,5387,5389,5397,5398,5402,5406,5431,5437,5447,5448,5463,5475,5497,5503,5519,5520,5523,5542,5550,5551,5556,5557,5567,5569,5581,5585,5594,5595,5597,5612,5617,5627,5628,5640,5647,5661,5665,5668,5674,5675,5676,5679,5684,5722,5723,5726,5728,5731,5732,5733,5735,5737,5739,5744,5751,5766,5780,5785,5786,5799,5800,5805,5809,5811,5816,5857,5869,5878,5882,5893,5897,5898,5906,5920,5926,5944,5947,5959,5985,5999,6024,6044,6045,6048,6062,6064,6066,6068,6081,6082,6085,6087,6090,6091,6103,6109,6110,6111,6113,6115,6158,6159,6166,6172,6176,6212,6214,6216,6218,6227,6229,6231,6237,6239,6245,6248,6256,6263,6264,6265,6270,6292,6293,6294,6296,6302,6307,6341,6342,6344,6345,6346,6348,6349,6350,6351,6358,6391,6392,6401,6422,6423,6443,6446,6457,6458,6464,6495,6497,6511,6549,6551,6552,6606,6630,6672,6692,6701,6702,6703,6704,6723,6724,6730,6743,6746,6748,6750,6751,6752,6754,6768,6779,6781,6782,6795,6799,6850,6861,6863,6867,6884,6885,6921,6933,6964,6998,7052,7080,7135,7156,7165,7168,7223,7231,7289,7291,7306,7316,7317,7318,7337,7343,7345,7395,7405,7408,7424,7476,7478,7481,7524,7525,7543,7610,7629,7652,7676,7691,7706,7717,7726,7727,7756,7759,7761,7771,7809,7820,7845,7903,7937,7969,8016,8032,8048,8049,8124,8177,8196,8220,8240,8264,8362,8364,8370,8386,8390,8406,8429,8440,8442,8457,8463,8467,8490,8504,8505,8521,8522,8527,8528,8529,8530,8531,8549,8550,8551,8559,8573,8575,8587,8591,8593,8594,8595,8603,8608,8635,8636,8668,8681,8685,8703,8725,8726,8727,8728,8740,8741,8763,8773,8783,8784,8785,8786,8788,8809,8810,8821,8865,8871,8877,8889,8894,8896,8899,8900,8904,8914,8997,9028,9029,9030,9045,9063,9068,9096,9097,9138,9141,9167,9212,9213,9214,9229,9256,9270,9276,9279,9301,9302,9330,9391,9426,9427,9428,9453,9454,9472,9491,9497,9511,9534,9556,9564,9565,9566,9567,9582,9584,9589,9620,9621,9627,9628,9672,9673,9705,9714,9724,9726,9727,9736,9750,9753,9781,9814,9816,9820,9878,9919,9920,9922,9932,9933,9953,9958,9999,10050,10122,10123,10176,10192,2,8,9,4581,4582,4600,4631,4633,4634,4661,4667,4668,4679,4728,4730,4760,4774,4804,4900,4901,4914,4934,4990,4991,4994,4995,4997,4999,5000,5009,5013,5014,5024,5036,5037,5043,5063,5064,5081,5086,5087,5088,5089,5092,5100,5103,5110,5175,5181,5182,5189,5219,5230,5236,5252,5272,5273,5280,5281,5282,5291,5301,5308,5310,5311,5317,5324,5325,5338,5339,5340,5341,5343,5344,5349,5350,5351,5352,5383,5384,5385,5393,5394,5395,5396,5439,5444,5446,5482,5484,5485,5487,5488,5490,5491,5493,5502,5507,5509,5510,5511,5512,5513,5514,5521,5531,5534,5545,5561,5562,5565,5575,5577,5578,5579,5604,5614,5630,5631,5641,5642,5644,5646,5651,5686,5691,5693,5753,5787,5788,5792,5798,5801,5802,5803,5804,5810,5821,5822,5824,5825,5833,5854,5885,5901,5904,5905,5907,5916,5934,5938,5941,5942,5943,5961,5972,5973,6001,6002,6006,6026,6029,6033,6052,6057,6058,6083,6086,6094,6102,6108,6112,6119,6120,6121,6122,6161,6177,6230,6266,6268,6289,6290,6295,6299,6300,6303,6309,6318,6333,6353,6354,6359,6369,6384,6404,6410,6412,6427,6428,6431,6432,6434,6436,6437,6438,6440,6442,6445,6450,6451,6453,6454,6460,6462,6505,6510,6524,6526,6527,6528,6563,6568,6570,6575,6576,6584,6588,6601,6625,6626,6628,6629,6640,6646,6663,6666,6685,6718,6719,6720,6725,6739,6758,6760,6762,6764,6769,6775,6777,6792,6797,6800,6836,6837,6838,6852,6853,6855,6856,6875,6877,6893,6919,6941,6952,6954,6956,6958,6959,6960,6995,6996,7001,7002,7009,7010,7012,7014,7033,7042,7043,7055,7065,7104,7114,7118,7125,7136,7142,7144,7150,7158,7159,7172,7189,7207,7209,7226,7275,7276,7277,7279,7281,7285,7290,7313,7358,7391,7406,7423,7456,7459,7485,7509,7526,7529,7530,7540,7559,7561,7563,7565,7566,7567,7592,7618,7619,7651,7653,7654,7655,7660,7683,7692,7703,7708,7714,7716,7722,7734,7735,7737,7762,7769,7792,7858,7859,7906,7914,7915,7939,7940,7957,7958,8023,8024,8051,8080,8091,8093,8102,8114,8146,8152,8159,8172,8191,8197,8219,8262,8292,8304,8322,8325,8355,8378,8443,8444,8447,8449,8553,8554,8555,8556,8582,8611,8639,8684,8702,8757,8802,8805,8818,8825,8862,8910,8911,8929,8930,9070,9074,9094,9104,9127,9129,9132,9136,9139,9140,9153,9154,9174,9180,9192,9240,9241,9260,9314,9315,9322,9383,9388,9423,9430,9433,9436,9437,9452,9468,9477,9487,9490,9500,9501,9504,9506,9532,9655,9699,9700,9743,9788,9905,9962,10027,10101,10114,10119,3,2614,2616,2617,2618,2619,2620,2621,2628,2629,2630,2631,2636,2637,2638,2639,2644,2651,2652,2657,2658,2659,2661,2662,2663,2666,2667,2668,2670,2671,2674,2675,2676,2681,2682,2687,2688,2689,2695,2696,2697,2702,2703,2705,2706,2710,2712,2713,2716,2718,2719,2721,2723,2726,2735,2736,2737,2764,2767,2789,2792,2793,2794,2801,2803,2805,2807,2819,2820,2822,2829,5211,5271,5369,5455,5456,5457,5532,5629,5660,5694,5710,5712,5718,5781,5782,5783,5784,5790,5823,5956,5991,6000,6023,6060,6095,6100,6247,6252,6287,6288,6308,6311,6313,6320,6321,6322,6323,6324,6325,6326,6327,6406,6474,6475,6562,6595,6596,6637,6638,6776,6791,6864,6865,6872,6894,6917,6925,6927,6974,6999,7000,7018,7019,7054,7098,7099,7196,7257,7258,7259,7260,7274,7307,7363,7364,7373,7381,7382,7394,7426,7427,7428,7429,7573,7574,7576,7578,7584,7585,7800,7806,7807,7817,7856,7935,7977,8035,8056,8057,8072,8131,8233,8302,8303,8305,8340,8402,8403,8476,8497,8498,8499,8500,8643,8855,8879,8880,8961,8976,9031,9032,9148,9184,9207,9242,9284,9475,9737,9931,9987,9989,6018,6389,6390,6477,6498,6499,6916,7134,8287,8568,8601,8796,8987,8988,9059,9060,9332,9333,9334,9335,9535,9808,10110,10161,10162,6459,8393])).
% 187.39/188.10 cnf(13093,plain,
% 187.39/188.10 (P24(f329(f329(f244(f881(a1,a869)),f300(a1,f2(a1),f2(a1))),f300(a1,f329(f79(a1),f329(f105(a1),f329(a117,x130931))),f2(a1))))),
% 187.39/188.10 inference(scs_inference,[],[4323,3521,11045,12081,12179,12268,12304,12312,12377,12498,12500,12931,12939,12942,12946,12952,12955,12979,13082,3530,12145,12558,12560,3531,12210,3244,12517,12519,3245,12529,3211,12454,4492,4493,11662,4233,12583,12586,3248,12590,3086,3145,12489,4477,3581,4459,10208,10218,10229,10240,10341,10344,10347,10450,10563,10866,11030,11033,11230,11317,11324,11338,11390,11393,11437,11503,11549,11565,11864,11889,11901,11930,11936,12031,12141,12148,12296,12347,12485,12602,12756,13000,4474,10434,10527,3336,3298,12543,3490,3193,4469,12673,12688,2873,2874,2876,2877,2880,2881,2883,2884,2885,2891,2892,2895,2896,2903,2904,2908,2909,2910,2911,2917,2920,2923,2932,2938,2944,2949,2952,2953,2954,2961,2965,2974,2982,2983,2986,2987,2988,2997,3010,3019,3020,3022,3023,3029,3035,3036,3037,3038,3047,3053,4454,3065,3144,4455,3619,3847,11596,3118,11314,3258,3234,10211,10275,10278,10368,10371,10664,11329,11332,11448,11490,11495,11591,12051,12246,12434,12487,12493,12510,12512,12535,12537,12566,12568,12573,12599,12807,12970,13081,3860,3206,12325,12329,12333,3212,3219,3740,3979,3107,3108,4471,3484,3832,11364,3335,12575,3169,3136,3313,3656,12523,3131,3953,3152,3661,4438,4560,3115,3116,3096,3151,3291,12380,12457,3337,10815,12142,3204,3205,3229,10475,3383,4541,10404,3919,4484,10266,10431,11227,12292,12326,12330,4491,12300,3267,11685,11688,12900,12996,13053,13057,13061,4530,10980,11050,11273,11276,3264,3384,3605,3376,3350,12508,3166,10333,10640,3167,4518,3442,3159,3087,3272,3189,11354,4066,12315,12446,3921,10986,11112,11162,12276,12282,12393,12396,12419,4553,10918,11117,11221,11243,11281,11287,12226,4554,11019,11120,11224,4555,11123,11173,4556,11176,4557,3188,3482,12182,12223,12299,3644,4350,4351,4482,11345,3583,3622,3796,3552,12790,12794,12798,12802,12812,3842,12176,3468,3722,3347,10352,10470,10541,10602,10605,10643,10737,10970,11860,11923,12002,12042,12119,12122,12423,12608,12667,12710,12713,12755,12773,12999,3733,11582,3260,3359,11700,3546,4524,10243,10246,10272,10745,10758,10876,11265,11357,11752,11757,11978,11981,12063,12072,12229,12319,12613,12632,12635,12659,12714,12878,12883,12907,4536,11467,11498,11533,11562,12723,12727,3720,3491,3493,12638,12641,12644,12647,12681,12684,13036,13040,13044,3494,3869,3454,13037,3455,13041,3306,3308,3281,4521,3165,4479,3672,4203,3988,3474,4537,4060,11238,3604,3320,11709,11712,12403,4030,3987,11853,12197,3931,12204,12426,13052,3976,13056,3982,10989,12078,12203,12903,3645,11863,12009,12086,12132,4019,3663,10992,11055,11136,11195,12030,12100,12342,12416,12429,12869,4542,10761,11128,12207,12949,3276,10361,10457,10588,10650,10719,10764,10767,10800,10823,10860,10898,10934,11656,11703,11833,11888,11904,11907,11910,11913,12093,12107,12110,12113,12116,12190,12251,12353,12399,12660,12687,12765,12776,12781,12784,12787,12820,12833,12844,12893,12918,12921,3277,10390,10445,10655,10740,10863,11440,11737,11740,11749,11839,11850,11869,11874,11916,11939,11956,12678,12824,12847,12879,12884,12908,12913,13023,3280,3355,12066,12743,12791,12795,12799,12803,12813,12817,4520,10309,10399,10512,10536,10782,10826,10836,11512,11610,11631,11634,11637,11653,11807,11810,11813,11816,11900,11919,11922,11935,11990,11993,11996,11999,12073,12161,12164,12254,12257,12318,12346,12383,12466,3437,10608,10871,10915,11184,11262,11425,11665,12295,12469,12865,12935,12982,4532,10791,10803,10907,10925,10928,10983,11069,11077,11093,11131,11148,11156,11192,11233,11253,11256,11259,11290,11297,11300,11682,11718,11984,11987,12021,12067,12096,12235,12273,12279,12365,12368,12389,12445,12451,12460,12479,12742,12759,12762,12854,12936,12974,12989,12992,13033,13077,13080,3341,10637,10667,10676,11213,11764,12384,12400,12724,12728,12731,3379,13013,3373,3800,3738,10312,11585,11613,12705,4529,10263,10625,10628,11072,11090,11548,11601,11641,11666,11770,11795,11798,11801,11804,12062,12924,3300,10670,10820,10891,11614,11769,11961,12169,12191,12752,3761,11715,12654,4110,3497,4527,3772,3808,4510,4513,4514,3251,3255,4512,3174,4511,4515,4286,3779,3594,11578,4209,11447,4544,10234,10237,10493,10544,10547,10552,10957,11419,11669,11773,4551,11151,11270,11306,3996,12218,3886,11303,11640,11644,11706,12303,12311,12392,12672,12930,12978,3727,10931,10937,10952,11885,12014,12099,12361,3579,12125,12232,12241,12308,12356,12364,12476,12872,3617,4064,3729,10673,11008,11159,11189,11200,12034,12307,12350,12966,3547,10591,10594,10679,10847,3549,4548,11579,4538,4543,12622,4549,10730,10829,11139,11422,11453,12185,12194,12238,12413,4170,10806,12215,4071,3760,12482,3707,3708,4546,10285,10288,10631,10634,11464,11645,12422,4547,11559,11650,3731,10597,10853,4003,4568,4594,4643,4645,4675,4692,4699,4700,4739,4769,4775,4860,4885,4886,4921,4946,4947,4969,4970,4983,4987,5010,5017,5035,5038,5039,5040,5045,5046,5068,5093,5094,5104,5109,5115,5160,5161,5169,5178,5183,5185,5195,5197,5203,5207,5222,5229,5232,5233,5234,5238,5274,5287,5295,5297,5298,5302,5303,5304,5312,5315,5319,5320,5321,5328,5332,5333,5334,5342,5346,5347,5348,5353,5366,5375,5387,5389,5397,5398,5402,5406,5431,5437,5447,5448,5463,5475,5497,5503,5519,5520,5523,5542,5550,5551,5556,5557,5567,5569,5581,5585,5594,5595,5597,5612,5617,5627,5628,5640,5647,5661,5665,5668,5674,5675,5676,5679,5684,5722,5723,5726,5728,5731,5732,5733,5735,5737,5739,5744,5751,5766,5780,5785,5786,5799,5800,5805,5809,5811,5816,5857,5869,5878,5882,5893,5897,5898,5906,5920,5926,5944,5947,5959,5985,5999,6024,6044,6045,6048,6062,6064,6066,6068,6081,6082,6085,6087,6090,6091,6103,6109,6110,6111,6113,6115,6158,6159,6166,6172,6176,6212,6214,6216,6218,6227,6229,6231,6237,6239,6245,6248,6256,6263,6264,6265,6270,6292,6293,6294,6296,6302,6307,6341,6342,6344,6345,6346,6348,6349,6350,6351,6358,6391,6392,6401,6422,6423,6443,6446,6457,6458,6464,6495,6497,6511,6549,6551,6552,6606,6630,6672,6692,6701,6702,6703,6704,6723,6724,6730,6743,6746,6748,6750,6751,6752,6754,6768,6779,6781,6782,6795,6799,6850,6861,6863,6867,6884,6885,6921,6933,6964,6998,7052,7080,7135,7156,7165,7168,7223,7231,7289,7291,7306,7316,7317,7318,7337,7343,7345,7395,7405,7408,7424,7476,7478,7481,7524,7525,7543,7610,7629,7652,7676,7691,7706,7717,7726,7727,7756,7759,7761,7771,7809,7820,7845,7903,7937,7969,8016,8032,8048,8049,8124,8177,8196,8220,8240,8264,8362,8364,8370,8386,8390,8406,8429,8440,8442,8457,8463,8467,8490,8504,8505,8521,8522,8527,8528,8529,8530,8531,8549,8550,8551,8559,8573,8575,8587,8591,8593,8594,8595,8603,8608,8635,8636,8668,8681,8685,8703,8725,8726,8727,8728,8740,8741,8763,8773,8783,8784,8785,8786,8788,8809,8810,8821,8865,8871,8877,8889,8894,8896,8899,8900,8904,8914,8997,9028,9029,9030,9045,9063,9068,9096,9097,9138,9141,9167,9212,9213,9214,9229,9256,9270,9276,9279,9301,9302,9330,9391,9426,9427,9428,9453,9454,9472,9491,9497,9511,9534,9556,9564,9565,9566,9567,9582,9584,9589,9620,9621,9627,9628,9672,9673,9705,9714,9724,9726,9727,9736,9750,9753,9781,9814,9816,9820,9878,9919,9920,9922,9932,9933,9953,9958,9999,10050,10122,10123,10176,10192,2,8,9,4581,4582,4600,4631,4633,4634,4661,4667,4668,4679,4728,4730,4760,4774,4804,4900,4901,4914,4934,4990,4991,4994,4995,4997,4999,5000,5009,5013,5014,5024,5036,5037,5043,5063,5064,5081,5086,5087,5088,5089,5092,5100,5103,5110,5175,5181,5182,5189,5219,5230,5236,5252,5272,5273,5280,5281,5282,5291,5301,5308,5310,5311,5317,5324,5325,5338,5339,5340,5341,5343,5344,5349,5350,5351,5352,5383,5384,5385,5393,5394,5395,5396,5439,5444,5446,5482,5484,5485,5487,5488,5490,5491,5493,5502,5507,5509,5510,5511,5512,5513,5514,5521,5531,5534,5545,5561,5562,5565,5575,5577,5578,5579,5604,5614,5630,5631,5641,5642,5644,5646,5651,5686,5691,5693,5753,5787,5788,5792,5798,5801,5802,5803,5804,5810,5821,5822,5824,5825,5833,5854,5885,5901,5904,5905,5907,5916,5934,5938,5941,5942,5943,5961,5972,5973,6001,6002,6006,6026,6029,6033,6052,6057,6058,6083,6086,6094,6102,6108,6112,6119,6120,6121,6122,6161,6177,6230,6266,6268,6289,6290,6295,6299,6300,6303,6309,6318,6333,6353,6354,6359,6369,6384,6404,6410,6412,6427,6428,6431,6432,6434,6436,6437,6438,6440,6442,6445,6450,6451,6453,6454,6460,6462,6505,6510,6524,6526,6527,6528,6563,6568,6570,6575,6576,6584,6588,6601,6625,6626,6628,6629,6640,6646,6663,6666,6685,6718,6719,6720,6725,6739,6758,6760,6762,6764,6769,6775,6777,6792,6797,6800,6836,6837,6838,6852,6853,6855,6856,6875,6877,6893,6919,6941,6952,6954,6956,6958,6959,6960,6995,6996,7001,7002,7009,7010,7012,7014,7033,7042,7043,7055,7065,7104,7114,7118,7125,7136,7142,7144,7150,7158,7159,7172,7189,7207,7209,7226,7275,7276,7277,7279,7281,7285,7290,7313,7358,7391,7406,7423,7456,7459,7485,7509,7526,7529,7530,7540,7559,7561,7563,7565,7566,7567,7592,7618,7619,7651,7653,7654,7655,7660,7683,7692,7703,7708,7714,7716,7722,7734,7735,7737,7762,7769,7792,7858,7859,7906,7914,7915,7939,7940,7957,7958,8023,8024,8051,8080,8091,8093,8102,8114,8146,8152,8159,8172,8191,8197,8219,8262,8292,8304,8322,8325,8355,8378,8443,8444,8447,8449,8553,8554,8555,8556,8582,8611,8639,8684,8702,8757,8802,8805,8818,8825,8862,8910,8911,8929,8930,9070,9074,9094,9104,9127,9129,9132,9136,9139,9140,9153,9154,9174,9180,9192,9240,9241,9260,9314,9315,9322,9383,9388,9423,9430,9433,9436,9437,9452,9468,9477,9487,9490,9500,9501,9504,9506,9532,9655,9699,9700,9743,9788,9905,9962,10027,10101,10114,10119,3,2614,2616,2617,2618,2619,2620,2621,2628,2629,2630,2631,2636,2637,2638,2639,2644,2651,2652,2657,2658,2659,2661,2662,2663,2666,2667,2668,2670,2671,2674,2675,2676,2681,2682,2687,2688,2689,2695,2696,2697,2702,2703,2705,2706,2710,2712,2713,2716,2718,2719,2721,2723,2726,2735,2736,2737,2764,2767,2789,2792,2793,2794,2801,2803,2805,2807,2819,2820,2822,2829,5211,5271,5369,5455,5456,5457,5532,5629,5660,5694,5710,5712,5718,5781,5782,5783,5784,5790,5823,5956,5991,6000,6023,6060,6095,6100,6247,6252,6287,6288,6308,6311,6313,6320,6321,6322,6323,6324,6325,6326,6327,6406,6474,6475,6562,6595,6596,6637,6638,6776,6791,6864,6865,6872,6894,6917,6925,6927,6974,6999,7000,7018,7019,7054,7098,7099,7196,7257,7258,7259,7260,7274,7307,7363,7364,7373,7381,7382,7394,7426,7427,7428,7429,7573,7574,7576,7578,7584,7585,7800,7806,7807,7817,7856,7935,7977,8035,8056,8057,8072,8131,8233,8302,8303,8305,8340,8402,8403,8476,8497,8498,8499,8500,8643,8855,8879,8880,8961,8976,9031,9032,9148,9184,9207,9242,9284,9475,9737,9931,9987,9989,6018,6389,6390,6477,6498,6499,6916,7134,8287,8568,8601,8796,8987,8988,9059,9060,9332,9333,9334,9335,9535,9808,10110,10161,10162,6459,8393,8394])).
% 187.39/188.10 cnf(13100,plain,
% 187.39/188.10 (P24(f329(f329(f243(a874),f2(a874)),x131001))),
% 187.39/188.10 inference(rename_variables,[],[3300])).
% 187.39/188.10 cnf(13101,plain,
% 187.39/188.10 (P24(f329(f329(f244(a874),f2(a874)),f329(a117,x131011)))),
% 187.39/188.10 inference(rename_variables,[],[3359])).
% 187.39/188.10 cnf(13102,plain,
% 187.39/188.10 (E(f329(f260(x131021,x131021),f261(x131021,x131022)),x131022)),
% 187.39/188.10 inference(rename_variables,[],[3234])).
% 187.39/188.10 cnf(13121,plain,
% 187.39/188.10 (E(f329(f329(f80(a874),f2(a874)),f855(f329(a117,f2(a874)),f2(a874))),f2(a874))),
% 187.39/188.10 inference(scs_inference,[],[4323,3521,11045,12081,12179,12268,12304,12312,12377,12498,12500,12931,12939,12942,12946,12952,12955,12979,13082,3530,12145,12558,12560,3531,12210,3244,12517,12519,3245,12529,3211,12454,4492,4493,11662,4233,12583,12586,3248,12590,3086,3145,12489,4477,3581,4459,10208,10218,10229,10240,10341,10344,10347,10450,10563,10866,11030,11033,11230,11317,11324,11338,11390,11393,11437,11503,11549,11565,11864,11889,11901,11930,11936,12031,12141,12148,12296,12347,12485,12602,12756,13000,4474,10434,10527,3336,3298,12543,3490,3193,4469,12673,12688,13020,2873,2874,2876,2877,2880,2881,2883,2884,2885,2891,2892,2895,2896,2903,2904,2908,2909,2910,2911,2917,2918,2920,2923,2932,2938,2942,2944,2949,2952,2953,2954,2961,2965,2974,2982,2983,2986,2987,2988,2997,3010,3019,3020,3022,3023,3029,3035,3036,3037,3038,3047,3053,4454,3065,3144,4455,3619,3847,11596,3118,11314,3258,3234,10211,10275,10278,10368,10371,10664,11329,11332,11448,11490,11495,11591,12051,12246,12434,12487,12493,12510,12512,12535,12537,12566,12568,12573,12599,12807,12970,13081,13086,13102,3860,3206,12325,12329,12333,3212,3219,3740,3979,3107,3108,4471,3484,3832,11364,3335,12575,3169,3136,3313,3656,12523,3131,3953,3152,3661,4438,4560,3115,3116,3096,3151,3291,12380,12457,3337,10815,12142,3204,3205,3229,10475,3383,4541,10404,3919,4484,10266,10431,11227,12292,12326,12330,4491,12300,3267,11685,11688,12900,12996,13053,13057,13061,4530,10980,11050,11273,11276,3264,3384,3605,3376,3350,12508,3166,10333,10640,3167,4518,3442,3159,3087,3272,3189,11354,4066,12315,12446,3921,10986,11112,11162,12276,12282,12393,12396,12419,4553,10918,11117,11221,11243,11281,11287,12226,4554,11019,11120,11224,4555,11123,11173,4556,11176,4557,3188,3482,12182,12223,12299,3644,4350,4351,3465,4482,11345,3583,3622,3796,3552,12790,12794,12798,12802,12812,3842,12176,3468,3722,3347,10352,10470,10541,10602,10605,10643,10737,10970,11860,11923,12002,12042,12119,12122,12423,12608,12667,12710,12713,12755,12773,12999,13004,3733,11582,3260,3359,11700,12601,13101,3546,4524,10243,10246,10272,10745,10758,10876,11265,11357,11752,11757,11978,11981,12063,12072,12229,12319,12613,12632,12635,12659,12714,12878,12883,12907,12912,4536,11467,11498,11533,11562,12723,12727,3720,3491,3493,12638,12641,12644,12647,12681,12684,13036,13040,13044,3494,3869,3454,13037,3455,13041,3306,3308,3281,4521,3165,4479,3672,4203,3988,3474,4537,4060,11238,3604,3320,11709,11712,12403,4030,3987,11853,12197,3931,12204,12426,13052,3976,13056,3982,10989,12078,12203,12903,3983,3645,11863,12009,12086,12132,4019,3663,10992,11055,11136,11195,12030,12100,12342,12416,12429,12869,4542,10761,11128,12207,12949,3276,10361,10457,10588,10650,10719,10764,10767,10800,10823,10860,10898,10934,11656,11703,11833,11888,11904,11907,11910,11913,12093,12107,12110,12113,12116,12190,12251,12353,12399,12660,12687,12765,12776,12781,12784,12787,12820,12833,12844,12893,12918,12921,3277,10390,10445,10655,10740,10863,11440,11737,11740,11749,11839,11850,11869,11874,11916,11939,11956,12678,12824,12847,12879,12884,12908,12913,13023,3280,3355,12066,12743,12791,12795,12799,12803,12813,12817,4520,10309,10399,10512,10536,10782,10826,10836,11512,11610,11631,11634,11637,11653,11807,11810,11813,11816,11900,11919,11922,11935,11990,11993,11996,11999,12073,12161,12164,12254,12257,12318,12346,12383,12466,3437,10608,10871,10915,11184,11262,11425,11665,12295,12469,12865,12935,12982,4532,10791,10803,10907,10925,10928,10983,11069,11077,11093,11131,11148,11156,11192,11233,11253,11256,11259,11290,11297,11300,11682,11718,11984,11987,12021,12067,12096,12235,12273,12279,12365,12368,12389,12445,12451,12460,12479,12742,12759,12762,12854,12936,12974,12989,12992,13033,13077,13080,3341,10637,10667,10676,11213,11764,12384,12400,12724,12728,12731,3379,13013,13074,3373,3800,3738,10312,11585,11613,12705,4529,10263,10625,10628,11072,11090,11548,11601,11641,11666,11770,11795,11798,11801,11804,12062,12924,3300,10670,10820,10891,11614,11769,11961,12169,12191,12752,13016,13100,3761,11715,12654,4110,3497,4527,3772,3808,4510,4513,4514,3251,3255,4512,3174,4511,4515,4286,3779,3594,11578,4209,11447,4544,10234,10237,10493,10544,10547,10552,10957,11419,11669,11773,4551,11151,11270,11306,3996,12218,3886,11303,11640,11644,11706,12303,12311,12392,12672,12930,12978,3727,10931,10937,10952,11885,12014,12099,12361,3579,12125,12232,12241,12308,12356,12364,12476,12872,3617,4064,3729,10673,11008,11159,11189,11200,12034,12307,12350,12966,3547,10591,10594,10679,10847,3549,4548,11579,4538,4543,12622,4549,10730,10829,11139,11422,11453,12185,12194,12238,12413,4170,10806,12215,4071,3760,12482,3707,3708,4546,10285,10288,10631,10634,11464,11645,12422,4547,11559,11650,3731,10597,10853,13003,4003,4568,4594,4643,4645,4675,4692,4699,4700,4739,4769,4775,4860,4885,4886,4921,4946,4947,4969,4970,4983,4987,5010,5017,5035,5038,5039,5040,5045,5046,5068,5093,5094,5104,5109,5115,5160,5161,5169,5178,5183,5185,5195,5197,5203,5207,5222,5229,5232,5233,5234,5238,5274,5287,5295,5297,5298,5302,5303,5304,5312,5315,5319,5320,5321,5328,5332,5333,5334,5342,5346,5347,5348,5353,5366,5375,5387,5389,5397,5398,5402,5406,5431,5437,5447,5448,5463,5475,5497,5503,5519,5520,5523,5542,5550,5551,5556,5557,5567,5569,5581,5585,5594,5595,5597,5612,5617,5627,5628,5640,5647,5661,5665,5668,5674,5675,5676,5679,5684,5722,5723,5726,5728,5731,5732,5733,5735,5737,5739,5744,5751,5766,5780,5785,5786,5799,5800,5805,5809,5811,5816,5857,5869,5878,5882,5893,5897,5898,5906,5920,5926,5944,5947,5959,5985,5999,6024,6044,6045,6048,6062,6064,6066,6068,6081,6082,6085,6087,6090,6091,6103,6109,6110,6111,6113,6115,6158,6159,6166,6172,6176,6212,6214,6216,6218,6227,6229,6231,6237,6239,6245,6248,6256,6263,6264,6265,6270,6292,6293,6294,6296,6302,6307,6341,6342,6344,6345,6346,6348,6349,6350,6351,6358,6391,6392,6401,6422,6423,6443,6446,6457,6458,6464,6495,6497,6511,6549,6551,6552,6606,6630,6672,6692,6701,6702,6703,6704,6723,6724,6730,6743,6746,6748,6750,6751,6752,6754,6768,6779,6781,6782,6795,6799,6850,6861,6863,6867,6884,6885,6921,6933,6964,6998,7052,7080,7135,7156,7165,7168,7223,7231,7289,7291,7306,7316,7317,7318,7337,7343,7345,7395,7405,7408,7424,7476,7478,7481,7524,7525,7543,7610,7629,7652,7676,7691,7706,7717,7726,7727,7756,7759,7761,7771,7809,7820,7845,7903,7937,7969,8016,8032,8048,8049,8124,8177,8196,8220,8240,8264,8362,8364,8370,8386,8390,8406,8429,8440,8442,8457,8463,8467,8490,8504,8505,8521,8522,8527,8528,8529,8530,8531,8549,8550,8551,8559,8573,8575,8587,8591,8593,8594,8595,8603,8608,8635,8636,8668,8681,8685,8703,8725,8726,8727,8728,8740,8741,8763,8773,8783,8784,8785,8786,8788,8809,8810,8821,8865,8871,8877,8889,8894,8896,8899,8900,8904,8914,8997,9028,9029,9030,9045,9063,9068,9096,9097,9138,9141,9167,9212,9213,9214,9229,9256,9270,9276,9279,9301,9302,9330,9391,9426,9427,9428,9453,9454,9472,9491,9497,9511,9534,9556,9564,9565,9566,9567,9582,9584,9589,9620,9621,9627,9628,9672,9673,9705,9714,9724,9726,9727,9736,9750,9753,9781,9814,9816,9820,9878,9919,9920,9922,9932,9933,9953,9958,9999,10050,10122,10123,10176,10192,2,8,9,4581,4582,4600,4631,4633,4634,4661,4667,4668,4679,4728,4730,4760,4774,4804,4900,4901,4914,4934,4990,4991,4994,4995,4997,4999,5000,5009,5013,5014,5024,5036,5037,5043,5063,5064,5081,5086,5087,5088,5089,5092,5100,5103,5110,5175,5181,5182,5189,5219,5230,5236,5252,5272,5273,5280,5281,5282,5291,5301,5308,5310,5311,5317,5324,5325,5338,5339,5340,5341,5343,5344,5349,5350,5351,5352,5383,5384,5385,5393,5394,5395,5396,5439,5444,5446,5482,5484,5485,5487,5488,5490,5491,5493,5502,5507,5509,5510,5511,5512,5513,5514,5521,5531,5534,5545,5561,5562,5565,5575,5577,5578,5579,5604,5614,5630,5631,5641,5642,5644,5646,5651,5686,5691,5693,5753,5787,5788,5792,5798,5801,5802,5803,5804,5810,5821,5822,5824,5825,5833,5854,5885,5901,5904,5905,5907,5916,5934,5938,5941,5942,5943,5961,5972,5973,6001,6002,6006,6026,6029,6033,6052,6057,6058,6083,6086,6094,6102,6108,6112,6119,6120,6121,6122,6161,6177,6230,6266,6268,6289,6290,6295,6299,6300,6303,6309,6318,6333,6353,6354,6359,6369,6384,6404,6410,6412,6427,6428,6431,6432,6434,6436,6437,6438,6440,6442,6445,6450,6451,6453,6454,6460,6462,6505,6510,6524,6526,6527,6528,6563,6568,6570,6575,6576,6584,6588,6601,6625,6626,6628,6629,6640,6646,6663,6666,6685,6718,6719,6720,6725,6739,6758,6760,6762,6764,6769,6775,6777,6792,6797,6800,6836,6837,6838,6852,6853,6855,6856,6875,6877,6893,6919,6941,6952,6954,6956,6958,6959,6960,6995,6996,7001,7002,7009,7010,7012,7014,7033,7042,7043,7055,7065,7104,7114,7118,7125,7136,7142,7144,7150,7158,7159,7172,7189,7207,7209,7226,7275,7276,7277,7279,7281,7285,7290,7313,7358,7391,7406,7423,7456,7459,7485,7509,7526,7529,7530,7540,7559,7561,7563,7565,7566,7567,7592,7618,7619,7651,7653,7654,7655,7660,7683,7692,7703,7708,7714,7716,7722,7734,7735,7737,7762,7769,7792,7858,7859,7906,7914,7915,7939,7940,7957,7958,8023,8024,8051,8080,8091,8093,8102,8114,8146,8152,8159,8172,8191,8197,8219,8262,8292,8304,8322,8325,8355,8378,8443,8444,8447,8449,8553,8554,8555,8556,8582,8611,8639,8684,8702,8757,8802,8805,8818,8825,8862,8910,8911,8929,8930,9070,9074,9094,9104,9127,9129,9132,9136,9139,9140,9153,9154,9174,9180,9192,9240,9241,9260,9314,9315,9322,9383,9388,9423,9430,9433,9436,9437,9452,9468,9477,9487,9490,9500,9501,9504,9506,9532,9655,9699,9700,9743,9788,9905,9962,10027,10101,10114,10119,3,2614,2616,2617,2618,2619,2620,2621,2628,2629,2630,2631,2636,2637,2638,2639,2644,2651,2652,2657,2658,2659,2661,2662,2663,2666,2667,2668,2670,2671,2674,2675,2676,2681,2682,2687,2688,2689,2695,2696,2697,2702,2703,2705,2706,2710,2712,2713,2716,2718,2719,2721,2723,2726,2735,2736,2737,2764,2767,2789,2792,2793,2794,2801,2803,2805,2807,2819,2820,2822,2829,5211,5271,5369,5455,5456,5457,5532,5629,5660,5694,5710,5712,5718,5781,5782,5783,5784,5790,5823,5956,5991,6000,6023,6060,6095,6100,6247,6252,6287,6288,6308,6311,6313,6320,6321,6322,6323,6324,6325,6326,6327,6406,6474,6475,6562,6595,6596,6637,6638,6776,6791,6864,6865,6872,6894,6917,6925,6927,6974,6999,7000,7018,7019,7054,7098,7099,7196,7257,7258,7259,7260,7274,7307,7363,7364,7373,7381,7382,7394,7426,7427,7428,7429,7573,7574,7576,7578,7584,7585,7800,7806,7807,7817,7856,7935,7977,8035,8056,8057,8072,8131,8233,8302,8303,8305,8340,8402,8403,8476,8497,8498,8499,8500,8643,8855,8879,8880,8961,8976,9031,9032,9148,9184,9207,9242,9284,9475,9737,9931,9987,9989,6018,6389,6390,6477,6498,6499,6916,7134,8287,8568,8601,8796,8987,8988,9059,9060,9332,9333,9334,9335,9535,9808,10110,10161,10162,6459,8393,8394,8845,8863,9809,10160,4635,4637])).
% 187.39/188.10 cnf(13171,plain,
% 187.39/188.10 (~P24(f329(f329(f244(a1),f2(a1)),f2(a1)))),
% 187.39/188.10 inference(scs_inference,[],[4323,3521,11045,12081,12179,12268,12304,12312,12377,12498,12500,12931,12939,12942,12946,12952,12955,12979,13082,3530,12145,12558,12560,3531,12210,3244,12517,12519,3245,12529,3211,12454,4492,4493,11662,4233,12583,12586,3248,12590,3086,3145,12489,4477,3581,4459,10208,10218,10229,10240,10341,10344,10347,10450,10563,10866,11030,11033,11230,11317,11324,11338,11390,11393,11437,11503,11549,11565,11864,11889,11901,11930,11936,12031,12141,12148,12296,12347,12485,12602,12756,13000,4474,10434,10527,3336,3298,12543,3490,3193,4469,12673,12688,13020,2873,2874,2876,2877,2880,2881,2883,2884,2885,2891,2892,2895,2896,2903,2904,2908,2909,2910,2911,2917,2918,2920,2923,2932,2938,2942,2944,2949,2952,2953,2954,2961,2965,2974,2982,2983,2986,2987,2988,2997,3010,3019,3020,3022,3023,3029,3035,3036,3037,3038,3047,3053,4454,3065,3144,4455,3619,3847,11596,3118,11314,3258,3234,10211,10275,10278,10368,10371,10664,11329,11332,11448,11490,11495,11591,12051,12246,12434,12487,12493,12510,12512,12535,12537,12566,12568,12573,12599,12807,12970,13081,13086,13102,3860,3206,12325,12329,12333,3212,3219,3740,3979,3107,3108,4471,3484,3832,11364,3335,12575,3169,3136,3313,3656,12523,3131,3953,3152,3661,4438,4560,3115,3116,3096,3151,3291,12380,12457,3337,10815,12142,3204,3205,3229,10475,3383,4541,10404,3919,4484,10266,10431,11227,12292,12326,12330,4491,12300,3267,11685,11688,12900,12996,13053,13057,13061,4530,10980,11050,11273,11276,3264,3384,3605,3376,3350,12508,3166,10333,10640,3167,4518,3442,3159,3087,3272,3189,11354,4066,12315,12446,3921,10986,11112,11162,12276,12282,12393,12396,12419,4553,10918,11117,11221,11243,11281,11287,12226,4554,11019,11120,11224,4555,11123,11173,4556,11176,4557,3188,3482,12182,12223,12299,3644,4350,4351,3465,4482,11345,3583,3622,3796,3552,12790,12794,12798,12802,12812,3842,12176,3468,3722,3347,10352,10470,10541,10602,10605,10643,10737,10970,11860,11923,12002,12042,12119,12122,12423,12608,12667,12710,12713,12755,12773,12999,13004,3733,11582,3260,3359,11700,12601,13101,3546,4524,10243,10246,10272,10745,10758,10876,11265,11357,11752,11757,11978,11981,12063,12072,12229,12319,12613,12632,12635,12659,12714,12878,12883,12907,12912,4536,11467,11498,11533,11562,12723,12727,3720,3491,3493,12638,12641,12644,12647,12681,12684,13036,13040,13044,3494,3869,3454,13037,3455,13041,3306,3308,3281,4521,3165,4479,3672,4203,3988,3474,4537,4060,11238,3604,3320,11709,11712,12403,4030,3987,11853,12197,3931,12204,12426,13052,3976,13056,3982,10989,12078,12203,12903,3983,3645,11863,12009,12086,12132,4019,3663,10992,11055,11136,11195,12030,12100,12342,12416,12429,12869,4542,10761,11128,12207,12949,3276,10361,10457,10588,10650,10719,10764,10767,10800,10823,10860,10898,10934,11656,11703,11833,11888,11904,11907,11910,11913,12093,12107,12110,12113,12116,12190,12251,12353,12399,12660,12687,12765,12776,12781,12784,12787,12820,12833,12844,12893,12918,12921,3277,10390,10445,10655,10740,10863,11440,11737,11740,11749,11839,11850,11869,11874,11916,11939,11956,12678,12824,12847,12879,12884,12908,12913,13023,3280,3355,12066,12743,12791,12795,12799,12803,12813,12817,4520,10309,10399,10512,10536,10782,10826,10836,11512,11610,11631,11634,11637,11653,11807,11810,11813,11816,11900,11919,11922,11935,11990,11993,11996,11999,12073,12161,12164,12254,12257,12318,12346,12383,12466,3437,10608,10871,10915,11184,11262,11425,11665,12295,12469,12865,12935,12982,4532,10791,10803,10907,10925,10928,10983,11069,11077,11093,11131,11148,11156,11192,11233,11253,11256,11259,11290,11297,11300,11682,11718,11984,11987,12021,12067,12096,12235,12273,12279,12365,12368,12389,12445,12451,12460,12479,12742,12759,12762,12854,12936,12974,12989,12992,13033,13077,13080,3341,10637,10667,10676,11213,11764,12384,12400,12724,12728,12731,3379,13013,13074,3373,3800,3738,10312,11585,11613,12705,4529,10263,10625,10628,11072,11090,11548,11601,11641,11666,11770,11795,11798,11801,11804,12062,12924,3300,10670,10820,10891,11614,11769,11961,12169,12191,12752,13016,13100,3761,11715,12654,4110,3497,4527,3772,3808,4510,4513,4514,3251,3255,4512,3174,4511,4515,4286,3779,3594,11578,4209,11447,4544,10234,10237,10493,10544,10547,10552,10957,11419,11669,11773,4551,11151,11270,11306,3996,12218,3886,11303,11640,11644,11706,12303,12311,12392,12672,12930,12978,3727,10931,10937,10952,11885,12014,12099,12361,3579,12125,12232,12241,12308,12356,12364,12476,12872,3617,4064,3729,10673,11008,11159,11189,11200,12034,12307,12350,12966,3547,10591,10594,10679,10847,3549,4548,11579,4538,4543,12622,4549,10730,10829,11139,11422,11453,12185,12194,12238,12413,4170,10806,12215,4071,3760,12482,3707,3708,4546,10285,10288,10631,10634,11464,11645,12422,4547,11559,11650,3731,10597,10853,13003,4003,4568,4594,4643,4645,4675,4692,4699,4700,4739,4769,4775,4860,4885,4886,4921,4946,4947,4969,4970,4983,4987,5010,5017,5035,5038,5039,5040,5045,5046,5068,5093,5094,5104,5109,5115,5160,5161,5169,5178,5183,5185,5195,5197,5203,5207,5222,5229,5232,5233,5234,5238,5274,5287,5295,5297,5298,5302,5303,5304,5312,5315,5319,5320,5321,5328,5332,5333,5334,5342,5346,5347,5348,5353,5366,5375,5387,5389,5397,5398,5402,5406,5431,5437,5447,5448,5463,5475,5497,5503,5519,5520,5523,5542,5550,5551,5556,5557,5567,5569,5581,5585,5594,5595,5597,5612,5617,5627,5628,5640,5647,5661,5665,5668,5674,5675,5676,5679,5684,5722,5723,5726,5728,5731,5732,5733,5735,5737,5739,5744,5751,5766,5780,5785,5786,5799,5800,5805,5809,5811,5816,5857,5869,5878,5882,5893,5897,5898,5906,5920,5926,5944,5947,5959,5985,5999,6024,6044,6045,6048,6062,6064,6066,6068,6081,6082,6085,6087,6090,6091,6103,6109,6110,6111,6113,6115,6158,6159,6166,6172,6176,6212,6214,6216,6218,6227,6229,6231,6237,6239,6245,6248,6256,6263,6264,6265,6270,6292,6293,6294,6296,6302,6307,6341,6342,6344,6345,6346,6348,6349,6350,6351,6358,6391,6392,6401,6422,6423,6443,6446,6457,6458,6464,6495,6497,6511,6549,6551,6552,6606,6630,6672,6692,6701,6702,6703,6704,6723,6724,6730,6743,6746,6748,6750,6751,6752,6754,6768,6779,6781,6782,6795,6799,6850,6861,6863,6867,6884,6885,6921,6933,6964,6998,7052,7080,7135,7156,7165,7168,7223,7231,7289,7291,7306,7316,7317,7318,7337,7343,7345,7395,7405,7408,7424,7476,7478,7481,7524,7525,7543,7610,7629,7652,7676,7691,7706,7717,7726,7727,7756,7759,7761,7771,7809,7820,7845,7903,7937,7969,8016,8032,8048,8049,8124,8177,8196,8220,8240,8264,8362,8364,8370,8386,8390,8406,8429,8440,8442,8457,8463,8467,8490,8504,8505,8521,8522,8527,8528,8529,8530,8531,8549,8550,8551,8559,8573,8575,8587,8591,8593,8594,8595,8603,8608,8635,8636,8668,8681,8685,8703,8725,8726,8727,8728,8740,8741,8763,8773,8783,8784,8785,8786,8788,8809,8810,8821,8865,8871,8877,8889,8894,8896,8899,8900,8904,8914,8997,9028,9029,9030,9045,9063,9068,9096,9097,9138,9141,9167,9212,9213,9214,9229,9256,9270,9276,9279,9301,9302,9330,9391,9426,9427,9428,9453,9454,9472,9491,9497,9511,9534,9556,9564,9565,9566,9567,9582,9584,9589,9620,9621,9627,9628,9672,9673,9705,9714,9724,9726,9727,9736,9750,9753,9781,9814,9816,9820,9878,9919,9920,9922,9932,9933,9953,9958,9999,10050,10122,10123,10176,10192,2,8,9,4581,4582,4600,4631,4633,4634,4661,4667,4668,4679,4728,4730,4760,4774,4804,4900,4901,4914,4934,4990,4991,4994,4995,4997,4999,5000,5009,5013,5014,5024,5036,5037,5043,5063,5064,5081,5086,5087,5088,5089,5092,5100,5103,5110,5175,5181,5182,5189,5219,5230,5236,5252,5272,5273,5280,5281,5282,5291,5301,5308,5310,5311,5317,5324,5325,5338,5339,5340,5341,5343,5344,5349,5350,5351,5352,5383,5384,5385,5393,5394,5395,5396,5439,5444,5446,5482,5484,5485,5487,5488,5490,5491,5493,5502,5507,5509,5510,5511,5512,5513,5514,5521,5531,5534,5545,5561,5562,5565,5575,5577,5578,5579,5604,5614,5630,5631,5641,5642,5644,5646,5651,5686,5691,5693,5753,5787,5788,5792,5798,5801,5802,5803,5804,5810,5821,5822,5824,5825,5833,5854,5885,5901,5904,5905,5907,5916,5934,5938,5941,5942,5943,5961,5972,5973,6001,6002,6006,6026,6029,6033,6052,6057,6058,6083,6086,6094,6102,6108,6112,6119,6120,6121,6122,6161,6177,6230,6266,6268,6289,6290,6295,6299,6300,6303,6309,6318,6333,6353,6354,6359,6369,6384,6404,6410,6412,6427,6428,6431,6432,6434,6436,6437,6438,6440,6442,6445,6450,6451,6453,6454,6460,6462,6505,6510,6524,6526,6527,6528,6563,6568,6570,6575,6576,6584,6588,6601,6625,6626,6628,6629,6640,6646,6663,6666,6685,6718,6719,6720,6725,6739,6758,6760,6762,6764,6769,6775,6777,6792,6797,6800,6836,6837,6838,6852,6853,6855,6856,6875,6877,6893,6919,6941,6952,6954,6956,6958,6959,6960,6995,6996,7001,7002,7009,7010,7012,7014,7033,7042,7043,7055,7065,7104,7114,7118,7125,7136,7142,7144,7150,7158,7159,7172,7189,7207,7209,7226,7275,7276,7277,7279,7281,7285,7290,7313,7358,7391,7406,7423,7456,7459,7485,7509,7526,7529,7530,7540,7559,7561,7563,7565,7566,7567,7592,7618,7619,7651,7653,7654,7655,7660,7683,7692,7703,7708,7714,7716,7722,7734,7735,7737,7762,7769,7792,7858,7859,7906,7914,7915,7939,7940,7957,7958,8023,8024,8051,8080,8091,8093,8102,8114,8146,8152,8159,8172,8191,8197,8219,8262,8292,8304,8322,8325,8355,8378,8443,8444,8447,8449,8553,8554,8555,8556,8582,8611,8639,8684,8702,8757,8802,8805,8818,8825,8862,8910,8911,8929,8930,9070,9074,9094,9104,9127,9129,9132,9136,9139,9140,9153,9154,9174,9180,9192,9240,9241,9260,9314,9315,9322,9383,9388,9423,9430,9433,9436,9437,9452,9468,9477,9487,9490,9500,9501,9504,9506,9532,9655,9699,9700,9743,9788,9905,9962,10027,10101,10114,10119,3,2614,2616,2617,2618,2619,2620,2621,2628,2629,2630,2631,2636,2637,2638,2639,2644,2651,2652,2657,2658,2659,2661,2662,2663,2666,2667,2668,2670,2671,2674,2675,2676,2681,2682,2687,2688,2689,2695,2696,2697,2702,2703,2705,2706,2710,2712,2713,2716,2718,2719,2721,2723,2726,2735,2736,2737,2764,2767,2789,2792,2793,2794,2801,2803,2805,2807,2819,2820,2822,2829,5211,5271,5369,5455,5456,5457,5532,5629,5660,5694,5710,5712,5718,5781,5782,5783,5784,5790,5823,5956,5991,6000,6023,6060,6095,6100,6247,6252,6287,6288,6308,6311,6313,6320,6321,6322,6323,6324,6325,6326,6327,6406,6474,6475,6562,6595,6596,6637,6638,6776,6791,6864,6865,6872,6894,6917,6925,6927,6974,6999,7000,7018,7019,7054,7098,7099,7196,7257,7258,7259,7260,7274,7307,7363,7364,7373,7381,7382,7394,7426,7427,7428,7429,7573,7574,7576,7578,7584,7585,7800,7806,7807,7817,7856,7935,7977,8035,8056,8057,8072,8131,8233,8302,8303,8305,8340,8402,8403,8476,8497,8498,8499,8500,8643,8855,8879,8880,8961,8976,9031,9032,9148,9184,9207,9242,9284,9475,9737,9931,9987,9989,6018,6389,6390,6477,6498,6499,6916,7134,8287,8568,8601,8796,8987,8988,9059,9060,9332,9333,9334,9335,9535,9808,10110,10161,10162,6459,8393,8394,8845,8863,9809,10160,4635,4637,4638,4693,4701,4838,4854,4855,4883,4884,4913,4968,5031,5090,5168,5204,5206,5214,5215,5241,5316,5337,5471,5537,5538,5539,5656])).
% 187.39/188.10 cnf(13173,plain,
% 187.39/188.10 (P24(f329(f329(f244(a1),f2(a1)),f329(f75(a1),f78(a1))))),
% 187.39/188.10 inference(scs_inference,[],[4323,3521,11045,12081,12179,12268,12304,12312,12377,12498,12500,12931,12939,12942,12946,12952,12955,12979,13082,3530,12145,12558,12560,3531,12210,3244,12517,12519,3245,12529,3211,12454,4492,4493,11662,4233,12583,12586,3248,12590,3086,3145,12489,4477,3581,4459,10208,10218,10229,10240,10341,10344,10347,10450,10563,10866,11030,11033,11230,11317,11324,11338,11390,11393,11437,11503,11549,11565,11864,11889,11901,11930,11936,12031,12141,12148,12296,12347,12485,12602,12756,13000,4474,10434,10527,3336,3298,12543,3490,3193,4469,12673,12688,13020,2873,2874,2876,2877,2880,2881,2883,2884,2885,2891,2892,2895,2896,2903,2904,2908,2909,2910,2911,2917,2918,2920,2923,2932,2938,2942,2944,2949,2952,2953,2954,2961,2965,2974,2982,2983,2986,2987,2988,2997,3010,3019,3020,3022,3023,3029,3035,3036,3037,3038,3047,3053,4454,3065,3144,4455,3619,3847,11596,3118,11314,3258,3234,10211,10275,10278,10368,10371,10664,11329,11332,11448,11490,11495,11591,12051,12246,12434,12487,12493,12510,12512,12535,12537,12566,12568,12573,12599,12807,12970,13081,13086,13102,3860,3206,12325,12329,12333,3212,3219,3740,3979,3107,3108,4471,3484,3832,11364,3335,12575,3169,3136,3313,3656,12523,3131,3953,3152,3661,4438,4560,3115,3116,3096,3151,3291,12380,12457,3337,10815,12142,3204,3205,3229,10475,3383,4541,10404,3919,4484,10266,10431,11227,12292,12326,12330,4491,12300,3267,11685,11688,12900,12996,13053,13057,13061,4530,10980,11050,11273,11276,3264,3384,3605,3376,3350,12508,3166,10333,10640,3167,4518,3442,3159,3087,3272,3189,11354,4066,12315,12446,3921,10986,11112,11162,12276,12282,12393,12396,12419,4553,10918,11117,11221,11243,11281,11287,12226,4554,11019,11120,11224,4555,11123,11173,4556,11176,4557,3188,3482,12182,12223,12299,3644,4350,4351,3465,4482,11345,3583,3622,3796,3552,12790,12794,12798,12802,12812,3842,12176,3468,3722,3347,10352,10470,10541,10602,10605,10643,10737,10970,11860,11923,12002,12042,12119,12122,12423,12608,12667,12710,12713,12755,12773,12999,13004,3733,11582,3260,3359,11700,12601,13101,3546,4524,10243,10246,10272,10745,10758,10876,11265,11357,11752,11757,11978,11981,12063,12072,12229,12319,12613,12632,12635,12659,12714,12878,12883,12907,12912,4536,11467,11498,11533,11562,12723,12727,3720,3491,3493,12638,12641,12644,12647,12681,12684,13036,13040,13044,3494,3869,3454,13037,3455,13041,3306,3308,3281,4521,3165,4479,3672,4203,3988,3474,4537,4060,11238,3604,3320,11709,11712,12403,4030,3987,11853,12197,3931,12204,12426,13052,3976,13056,3982,10989,12078,12203,12903,3983,3645,11863,12009,12086,12132,4019,3663,10992,11055,11136,11195,12030,12100,12342,12416,12429,12869,4542,10761,11128,12207,12949,3276,10361,10457,10588,10650,10719,10764,10767,10800,10823,10860,10898,10934,11656,11703,11833,11888,11904,11907,11910,11913,12093,12107,12110,12113,12116,12190,12251,12353,12399,12660,12687,12765,12776,12781,12784,12787,12820,12833,12844,12893,12918,12921,3277,10390,10445,10655,10740,10863,11440,11737,11740,11749,11839,11850,11869,11874,11916,11939,11956,12678,12824,12847,12879,12884,12908,12913,13023,3280,3355,12066,12743,12791,12795,12799,12803,12813,12817,4520,10309,10399,10512,10536,10782,10826,10836,11512,11610,11631,11634,11637,11653,11807,11810,11813,11816,11900,11919,11922,11935,11990,11993,11996,11999,12073,12161,12164,12254,12257,12318,12346,12383,12466,3437,10608,10871,10915,11184,11262,11425,11665,12295,12469,12865,12935,12982,4532,10791,10803,10907,10925,10928,10983,11069,11077,11093,11131,11148,11156,11192,11233,11253,11256,11259,11290,11297,11300,11682,11718,11984,11987,12021,12067,12096,12235,12273,12279,12365,12368,12389,12445,12451,12460,12479,12742,12759,12762,12854,12936,12974,12989,12992,13033,13077,13080,3341,10637,10667,10676,11213,11764,12384,12400,12724,12728,12731,3379,13013,13074,3373,3800,3738,10312,11585,11613,12705,4529,10263,10625,10628,11072,11090,11548,11601,11641,11666,11770,11795,11798,11801,11804,12062,12924,3300,10670,10820,10891,11614,11769,11961,12169,12191,12752,13016,13100,3761,11715,12654,4110,3497,4527,3772,3808,4510,4513,4514,3251,3255,4512,3174,4511,4515,4286,3779,3594,11578,4209,11447,4544,10234,10237,10493,10544,10547,10552,10957,11419,11669,11773,4551,11151,11270,11306,3996,12218,3886,11303,11640,11644,11706,12303,12311,12392,12672,12930,12978,3727,10931,10937,10952,11885,12014,12099,12361,3579,12125,12232,12241,12308,12356,12364,12476,12872,3617,4064,3729,10673,11008,11159,11189,11200,12034,12307,12350,12966,3547,10591,10594,10679,10847,3549,4548,11579,4538,4543,12622,4549,10730,10829,11139,11422,11453,12185,12194,12238,12413,4170,10806,12215,4071,3760,12482,3707,3708,4546,10285,10288,10631,10634,11464,11645,12422,4547,11559,11650,3731,10597,10853,13003,4003,4568,4594,4643,4645,4675,4692,4699,4700,4739,4769,4775,4860,4885,4886,4921,4946,4947,4969,4970,4983,4987,5010,5017,5035,5038,5039,5040,5045,5046,5068,5093,5094,5104,5109,5115,5160,5161,5169,5178,5183,5185,5195,5197,5203,5207,5222,5229,5232,5233,5234,5238,5274,5287,5295,5297,5298,5302,5303,5304,5312,5315,5319,5320,5321,5328,5332,5333,5334,5342,5346,5347,5348,5353,5366,5375,5387,5389,5397,5398,5402,5406,5431,5437,5447,5448,5463,5475,5497,5503,5519,5520,5523,5542,5550,5551,5556,5557,5567,5569,5581,5585,5594,5595,5597,5612,5617,5627,5628,5640,5647,5661,5665,5668,5674,5675,5676,5679,5684,5722,5723,5726,5728,5731,5732,5733,5735,5737,5739,5744,5751,5766,5780,5785,5786,5799,5800,5805,5809,5811,5816,5857,5869,5878,5882,5893,5897,5898,5906,5920,5926,5944,5947,5959,5985,5999,6024,6044,6045,6048,6062,6064,6066,6068,6081,6082,6085,6087,6090,6091,6103,6109,6110,6111,6113,6115,6158,6159,6166,6172,6176,6212,6214,6216,6218,6227,6229,6231,6237,6239,6245,6248,6256,6263,6264,6265,6270,6292,6293,6294,6296,6302,6307,6341,6342,6344,6345,6346,6348,6349,6350,6351,6358,6391,6392,6401,6422,6423,6443,6446,6457,6458,6464,6495,6497,6511,6549,6551,6552,6606,6630,6672,6692,6701,6702,6703,6704,6723,6724,6730,6743,6746,6748,6750,6751,6752,6754,6768,6779,6781,6782,6795,6799,6850,6861,6863,6867,6884,6885,6921,6933,6964,6998,7052,7080,7135,7156,7165,7168,7223,7231,7289,7291,7306,7316,7317,7318,7337,7343,7345,7395,7405,7408,7424,7476,7478,7481,7524,7525,7543,7610,7629,7652,7676,7691,7706,7717,7726,7727,7756,7759,7761,7771,7809,7820,7845,7903,7937,7969,8016,8032,8048,8049,8124,8177,8196,8220,8240,8264,8362,8364,8370,8386,8390,8406,8429,8440,8442,8457,8463,8467,8490,8504,8505,8521,8522,8527,8528,8529,8530,8531,8549,8550,8551,8559,8573,8575,8587,8591,8593,8594,8595,8603,8608,8635,8636,8668,8681,8685,8703,8725,8726,8727,8728,8740,8741,8763,8773,8783,8784,8785,8786,8788,8809,8810,8821,8865,8871,8877,8889,8894,8896,8899,8900,8904,8914,8997,9028,9029,9030,9045,9063,9068,9096,9097,9138,9141,9167,9212,9213,9214,9229,9256,9270,9276,9279,9301,9302,9330,9391,9426,9427,9428,9453,9454,9472,9491,9497,9511,9534,9556,9564,9565,9566,9567,9582,9584,9589,9620,9621,9627,9628,9672,9673,9705,9714,9724,9726,9727,9736,9750,9753,9781,9814,9816,9820,9878,9919,9920,9922,9932,9933,9953,9958,9999,10050,10122,10123,10176,10192,2,8,9,4581,4582,4600,4631,4633,4634,4661,4667,4668,4679,4728,4730,4760,4774,4804,4900,4901,4914,4934,4990,4991,4994,4995,4997,4999,5000,5009,5013,5014,5024,5036,5037,5043,5063,5064,5081,5086,5087,5088,5089,5092,5100,5103,5110,5175,5181,5182,5189,5219,5230,5236,5252,5272,5273,5280,5281,5282,5291,5301,5308,5310,5311,5317,5324,5325,5338,5339,5340,5341,5343,5344,5349,5350,5351,5352,5383,5384,5385,5393,5394,5395,5396,5439,5444,5446,5482,5484,5485,5487,5488,5490,5491,5493,5502,5507,5509,5510,5511,5512,5513,5514,5521,5531,5534,5545,5561,5562,5565,5575,5577,5578,5579,5604,5614,5630,5631,5641,5642,5644,5646,5651,5686,5691,5693,5753,5787,5788,5792,5798,5801,5802,5803,5804,5810,5821,5822,5824,5825,5833,5854,5885,5901,5904,5905,5907,5916,5934,5938,5941,5942,5943,5961,5972,5973,6001,6002,6006,6026,6029,6033,6052,6057,6058,6083,6086,6094,6102,6108,6112,6119,6120,6121,6122,6161,6177,6230,6266,6268,6289,6290,6295,6299,6300,6303,6309,6318,6333,6353,6354,6359,6369,6384,6404,6410,6412,6427,6428,6431,6432,6434,6436,6437,6438,6440,6442,6445,6450,6451,6453,6454,6460,6462,6505,6510,6524,6526,6527,6528,6563,6568,6570,6575,6576,6584,6588,6601,6625,6626,6628,6629,6640,6646,6663,6666,6685,6718,6719,6720,6725,6739,6758,6760,6762,6764,6769,6775,6777,6792,6797,6800,6836,6837,6838,6852,6853,6855,6856,6875,6877,6893,6919,6941,6952,6954,6956,6958,6959,6960,6995,6996,7001,7002,7009,7010,7012,7014,7033,7042,7043,7055,7065,7104,7114,7118,7125,7136,7142,7144,7150,7158,7159,7172,7189,7207,7209,7226,7275,7276,7277,7279,7281,7285,7290,7313,7358,7391,7406,7423,7456,7459,7485,7509,7526,7529,7530,7540,7559,7561,7563,7565,7566,7567,7592,7618,7619,7651,7653,7654,7655,7660,7683,7692,7703,7708,7714,7716,7722,7734,7735,7737,7762,7769,7792,7858,7859,7906,7914,7915,7939,7940,7957,7958,8023,8024,8051,8080,8091,8093,8102,8114,8146,8152,8159,8172,8191,8197,8219,8262,8292,8304,8322,8325,8355,8378,8443,8444,8447,8449,8553,8554,8555,8556,8582,8611,8639,8684,8702,8757,8802,8805,8818,8825,8862,8910,8911,8929,8930,9070,9074,9094,9104,9127,9129,9132,9136,9139,9140,9153,9154,9174,9180,9192,9240,9241,9260,9314,9315,9322,9383,9388,9423,9430,9433,9436,9437,9452,9468,9477,9487,9490,9500,9501,9504,9506,9532,9655,9699,9700,9743,9788,9905,9962,10027,10101,10114,10119,3,2614,2616,2617,2618,2619,2620,2621,2628,2629,2630,2631,2636,2637,2638,2639,2644,2651,2652,2657,2658,2659,2661,2662,2663,2666,2667,2668,2670,2671,2674,2675,2676,2681,2682,2687,2688,2689,2695,2696,2697,2702,2703,2705,2706,2710,2712,2713,2716,2718,2719,2721,2723,2726,2735,2736,2737,2764,2767,2789,2792,2793,2794,2801,2803,2805,2807,2819,2820,2822,2829,5211,5271,5369,5455,5456,5457,5532,5629,5660,5694,5710,5712,5718,5781,5782,5783,5784,5790,5823,5956,5991,6000,6023,6060,6095,6100,6247,6252,6287,6288,6308,6311,6313,6320,6321,6322,6323,6324,6325,6326,6327,6406,6474,6475,6562,6595,6596,6637,6638,6776,6791,6864,6865,6872,6894,6917,6925,6927,6974,6999,7000,7018,7019,7054,7098,7099,7196,7257,7258,7259,7260,7274,7307,7363,7364,7373,7381,7382,7394,7426,7427,7428,7429,7573,7574,7576,7578,7584,7585,7800,7806,7807,7817,7856,7935,7977,8035,8056,8057,8072,8131,8233,8302,8303,8305,8340,8402,8403,8476,8497,8498,8499,8500,8643,8855,8879,8880,8961,8976,9031,9032,9148,9184,9207,9242,9284,9475,9737,9931,9987,9989,6018,6389,6390,6477,6498,6499,6916,7134,8287,8568,8601,8796,8987,8988,9059,9060,9332,9333,9334,9335,9535,9808,10110,10161,10162,6459,8393,8394,8845,8863,9809,10160,4635,4637,4638,4693,4701,4838,4854,4855,4883,4884,4913,4968,5031,5090,5168,5204,5206,5214,5215,5241,5316,5337,5471,5537,5538,5539,5656,5657])).
% 187.39/188.10 cnf(13187,plain,
% 187.39/188.10 (~P24(f329(f329(f244(a874),f329(a117,f329(f329(f80(a874),x131871),x131872))),f329(a117,x131871)))),
% 187.39/188.10 inference(scs_inference,[],[4323,3521,11045,12081,12179,12268,12304,12312,12377,12498,12500,12931,12939,12942,12946,12952,12955,12979,13082,3530,12145,12558,12560,3531,12210,3244,12517,12519,3245,12529,3211,12454,4492,4493,11662,4233,12583,12586,3248,12590,3086,3145,12489,4477,3581,4459,10208,10218,10229,10240,10341,10344,10347,10450,10563,10866,11030,11033,11230,11317,11324,11338,11390,11393,11437,11503,11549,11565,11864,11889,11901,11930,11936,12031,12141,12148,12296,12347,12485,12602,12756,13000,4474,10434,10527,3336,3298,12543,3490,3193,4469,12673,12688,13020,2873,2874,2876,2877,2880,2881,2883,2884,2885,2891,2892,2895,2896,2903,2904,2908,2909,2910,2911,2917,2918,2920,2923,2932,2938,2942,2944,2949,2952,2953,2954,2961,2965,2974,2982,2983,2986,2987,2988,2997,3010,3019,3020,3022,3023,3029,3035,3036,3037,3038,3047,3053,4454,3065,3144,4455,3619,3847,11596,3118,11314,3258,3234,10211,10275,10278,10368,10371,10664,11329,11332,11448,11490,11495,11591,12051,12246,12434,12487,12493,12510,12512,12535,12537,12566,12568,12573,12599,12807,12970,13081,13086,13102,3860,3206,12325,12329,12333,3212,3219,3740,3979,3107,3108,4471,3484,3832,11364,3335,12575,3169,3136,3313,3656,12523,3131,3953,3152,3661,4438,4560,3115,3116,3096,3151,3291,12380,12457,3337,10815,12142,3204,3205,3229,10475,3383,4541,10404,3919,4484,10266,10431,11227,12292,12326,12330,4491,12300,3267,11685,11688,12900,12996,13053,13057,13061,4530,10980,11050,11273,11276,3264,3384,3605,3376,3350,12508,3166,10333,10640,3167,4518,3442,3159,3087,3272,3189,11354,4066,12315,12446,3921,10986,11112,11162,12276,12282,12393,12396,12419,4553,10918,11117,11221,11243,11281,11287,12226,4554,11019,11120,11224,4555,11123,11173,4556,11176,4557,3188,3482,12182,12223,12299,3644,4350,4351,3465,4482,11345,3583,3622,3796,3552,12790,12794,12798,12802,12812,3842,12176,3468,3722,3347,10352,10470,10541,10602,10605,10643,10737,10970,11860,11923,12002,12042,12119,12122,12423,12608,12667,12710,12713,12755,12773,12999,13004,3733,11582,3260,3359,11700,12601,13101,3546,4524,10243,10246,10272,10745,10758,10876,11265,11357,11752,11757,11978,11981,12063,12072,12229,12319,12613,12632,12635,12659,12714,12878,12883,12907,12912,4536,11467,11498,11533,11562,12723,12727,3720,3491,3493,12638,12641,12644,12647,12681,12684,13036,13040,13044,3494,3869,3454,13037,3455,13041,3306,3308,3281,4521,3165,4479,3672,4203,3988,3474,4537,4060,11238,3604,3320,11709,11712,12403,4030,3987,11853,12197,3931,12204,12426,13052,3976,13056,3982,10989,12078,12203,12903,3983,3645,11863,12009,12086,12132,4019,3663,10992,11055,11136,11195,12030,12100,12342,12416,12429,12869,4542,10761,11128,12207,12949,3276,10361,10457,10588,10650,10719,10764,10767,10800,10823,10860,10898,10934,11656,11703,11833,11888,11904,11907,11910,11913,12093,12107,12110,12113,12116,12190,12251,12353,12399,12660,12687,12765,12776,12781,12784,12787,12820,12833,12844,12893,12918,12921,3277,10390,10445,10655,10740,10863,11440,11737,11740,11749,11839,11850,11869,11874,11916,11939,11956,12678,12824,12847,12879,12884,12908,12913,13023,3280,3355,12066,12743,12791,12795,12799,12803,12813,12817,4520,10309,10399,10512,10536,10782,10826,10836,11512,11610,11631,11634,11637,11653,11807,11810,11813,11816,11900,11919,11922,11935,11990,11993,11996,11999,12073,12161,12164,12254,12257,12318,12346,12383,12466,3437,10608,10871,10915,11184,11262,11425,11665,12295,12469,12865,12935,12982,4532,10791,10803,10907,10925,10928,10983,11069,11077,11093,11131,11148,11156,11192,11233,11253,11256,11259,11290,11297,11300,11682,11718,11984,11987,12021,12067,12096,12235,12273,12279,12365,12368,12389,12445,12451,12460,12479,12742,12759,12762,12854,12936,12974,12989,12992,13033,13077,13080,3341,10637,10667,10676,11213,11764,12384,12400,12724,12728,12731,3379,13013,13074,3373,3800,3738,10312,11585,11613,12705,4529,10263,10625,10628,11072,11090,11548,11601,11641,11666,11770,11795,11798,11801,11804,12062,12924,3300,10670,10820,10891,11614,11769,11961,12169,12191,12752,13016,13100,3761,11715,12654,4110,3497,4527,3772,3808,4510,4513,4514,3251,3255,4512,3174,4511,4515,4286,3779,3594,11578,4209,11447,4544,10234,10237,10493,10544,10547,10552,10957,11419,11669,11773,4551,11151,11270,11306,3996,12218,3886,11303,11640,11644,11706,12303,12311,12392,12672,12930,12978,3727,10931,10937,10952,11885,12014,12099,12361,3579,12125,12232,12241,12308,12356,12364,12476,12872,3617,4064,3729,10673,11008,11159,11189,11200,12034,12307,12350,12966,3547,10591,10594,10679,10847,3549,4548,11579,4538,4543,12622,4549,10730,10829,11139,11422,11453,12185,12194,12238,12413,4170,10806,12215,4071,3760,12482,3707,3708,4546,10285,10288,10631,10634,11464,11645,12422,4547,11559,11650,3731,10597,10853,13003,4003,4568,4594,4643,4645,4675,4692,4699,4700,4739,4769,4775,4860,4885,4886,4921,4946,4947,4969,4970,4983,4987,5010,5017,5035,5038,5039,5040,5045,5046,5068,5093,5094,5104,5109,5115,5160,5161,5169,5178,5183,5185,5195,5197,5203,5207,5222,5229,5232,5233,5234,5238,5274,5287,5295,5297,5298,5302,5303,5304,5312,5315,5319,5320,5321,5328,5332,5333,5334,5342,5346,5347,5348,5353,5366,5375,5387,5389,5397,5398,5402,5406,5431,5437,5447,5448,5463,5475,5497,5503,5519,5520,5523,5542,5550,5551,5556,5557,5567,5569,5581,5585,5594,5595,5597,5612,5617,5627,5628,5640,5647,5661,5665,5668,5674,5675,5676,5679,5684,5722,5723,5726,5728,5731,5732,5733,5735,5737,5739,5744,5751,5766,5780,5785,5786,5799,5800,5805,5809,5811,5816,5857,5869,5878,5882,5893,5897,5898,5906,5920,5926,5944,5947,5959,5985,5999,6024,6044,6045,6048,6062,6064,6066,6068,6081,6082,6085,6087,6090,6091,6103,6109,6110,6111,6113,6115,6158,6159,6166,6172,6176,6212,6214,6216,6218,6227,6229,6231,6237,6239,6245,6248,6256,6263,6264,6265,6270,6292,6293,6294,6296,6302,6307,6341,6342,6344,6345,6346,6348,6349,6350,6351,6358,6391,6392,6401,6422,6423,6443,6446,6457,6458,6464,6495,6497,6511,6549,6551,6552,6606,6630,6672,6692,6701,6702,6703,6704,6723,6724,6730,6743,6746,6748,6750,6751,6752,6754,6768,6779,6781,6782,6795,6799,6850,6861,6863,6867,6884,6885,6921,6933,6964,6998,7052,7080,7135,7156,7165,7168,7223,7231,7289,7291,7306,7316,7317,7318,7337,7343,7345,7395,7405,7408,7424,7476,7478,7481,7524,7525,7543,7610,7629,7652,7676,7691,7706,7717,7726,7727,7756,7759,7761,7771,7809,7820,7845,7903,7937,7969,8016,8032,8048,8049,8124,8177,8196,8220,8240,8264,8362,8364,8370,8386,8390,8406,8429,8440,8442,8457,8463,8467,8490,8504,8505,8521,8522,8527,8528,8529,8530,8531,8549,8550,8551,8559,8573,8575,8587,8591,8593,8594,8595,8603,8608,8635,8636,8668,8681,8685,8703,8725,8726,8727,8728,8740,8741,8763,8773,8783,8784,8785,8786,8788,8809,8810,8821,8865,8871,8877,8889,8894,8896,8899,8900,8904,8914,8997,9028,9029,9030,9045,9063,9068,9096,9097,9138,9141,9167,9212,9213,9214,9229,9256,9270,9276,9279,9301,9302,9330,9391,9426,9427,9428,9453,9454,9472,9491,9497,9511,9534,9556,9564,9565,9566,9567,9582,9584,9589,9620,9621,9627,9628,9672,9673,9705,9714,9724,9726,9727,9736,9750,9753,9781,9814,9816,9820,9878,9919,9920,9922,9932,9933,9953,9958,9999,10050,10122,10123,10176,10192,2,8,9,4581,4582,4600,4631,4633,4634,4661,4667,4668,4679,4728,4730,4760,4774,4804,4900,4901,4914,4934,4990,4991,4994,4995,4997,4999,5000,5009,5013,5014,5024,5036,5037,5043,5063,5064,5081,5086,5087,5088,5089,5092,5100,5103,5110,5175,5181,5182,5189,5219,5230,5236,5252,5272,5273,5280,5281,5282,5291,5301,5308,5310,5311,5317,5324,5325,5338,5339,5340,5341,5343,5344,5349,5350,5351,5352,5383,5384,5385,5393,5394,5395,5396,5439,5444,5446,5482,5484,5485,5487,5488,5490,5491,5493,5502,5507,5509,5510,5511,5512,5513,5514,5521,5531,5534,5545,5561,5562,5565,5575,5577,5578,5579,5604,5614,5630,5631,5641,5642,5644,5646,5651,5686,5691,5693,5753,5787,5788,5792,5798,5801,5802,5803,5804,5810,5821,5822,5824,5825,5833,5854,5885,5901,5904,5905,5907,5916,5934,5938,5941,5942,5943,5961,5972,5973,6001,6002,6006,6026,6029,6033,6052,6057,6058,6083,6086,6094,6102,6108,6112,6119,6120,6121,6122,6161,6177,6230,6266,6268,6289,6290,6295,6299,6300,6303,6309,6318,6333,6353,6354,6359,6369,6384,6404,6410,6412,6427,6428,6431,6432,6434,6436,6437,6438,6440,6442,6445,6450,6451,6453,6454,6460,6462,6505,6510,6524,6526,6527,6528,6563,6568,6570,6575,6576,6584,6588,6601,6625,6626,6628,6629,6640,6646,6663,6666,6685,6718,6719,6720,6725,6739,6758,6760,6762,6764,6769,6775,6777,6792,6797,6800,6836,6837,6838,6852,6853,6855,6856,6875,6877,6893,6919,6941,6952,6954,6956,6958,6959,6960,6995,6996,7001,7002,7009,7010,7012,7014,7033,7042,7043,7055,7065,7104,7114,7118,7125,7136,7142,7144,7150,7158,7159,7172,7189,7207,7209,7226,7275,7276,7277,7279,7281,7285,7290,7313,7358,7391,7406,7423,7456,7459,7485,7509,7526,7529,7530,7540,7559,7561,7563,7565,7566,7567,7592,7618,7619,7651,7653,7654,7655,7660,7683,7692,7703,7708,7714,7716,7722,7734,7735,7737,7762,7769,7792,7858,7859,7906,7914,7915,7939,7940,7957,7958,8023,8024,8051,8080,8091,8093,8102,8114,8146,8152,8159,8172,8191,8197,8219,8262,8292,8304,8322,8325,8355,8378,8443,8444,8447,8449,8553,8554,8555,8556,8582,8611,8639,8684,8702,8757,8802,8805,8818,8825,8862,8910,8911,8929,8930,9070,9074,9094,9104,9127,9129,9132,9136,9139,9140,9153,9154,9174,9180,9192,9240,9241,9260,9314,9315,9322,9383,9388,9423,9430,9433,9436,9437,9452,9468,9477,9487,9490,9500,9501,9504,9506,9532,9655,9699,9700,9743,9788,9905,9962,10027,10101,10114,10119,3,2614,2616,2617,2618,2619,2620,2621,2628,2629,2630,2631,2636,2637,2638,2639,2644,2651,2652,2657,2658,2659,2661,2662,2663,2666,2667,2668,2670,2671,2674,2675,2676,2681,2682,2687,2688,2689,2695,2696,2697,2702,2703,2705,2706,2710,2712,2713,2716,2718,2719,2721,2723,2726,2735,2736,2737,2764,2767,2789,2792,2793,2794,2801,2803,2805,2807,2819,2820,2822,2829,5211,5271,5369,5455,5456,5457,5532,5629,5660,5694,5710,5712,5718,5781,5782,5783,5784,5790,5823,5956,5991,6000,6023,6060,6095,6100,6247,6252,6287,6288,6308,6311,6313,6320,6321,6322,6323,6324,6325,6326,6327,6406,6474,6475,6562,6595,6596,6637,6638,6776,6791,6864,6865,6872,6894,6917,6925,6927,6974,6999,7000,7018,7019,7054,7098,7099,7196,7257,7258,7259,7260,7274,7307,7363,7364,7373,7381,7382,7394,7426,7427,7428,7429,7573,7574,7576,7578,7584,7585,7800,7806,7807,7817,7856,7935,7977,8035,8056,8057,8072,8131,8233,8302,8303,8305,8340,8402,8403,8476,8497,8498,8499,8500,8643,8855,8879,8880,8961,8976,9031,9032,9148,9184,9207,9242,9284,9475,9737,9931,9987,9989,6018,6389,6390,6477,6498,6499,6916,7134,8287,8568,8601,8796,8987,8988,9059,9060,9332,9333,9334,9335,9535,9808,10110,10161,10162,6459,8393,8394,8845,8863,9809,10160,4635,4637,4638,4693,4701,4838,4854,4855,4883,4884,4913,4968,5031,5090,5168,5204,5206,5214,5215,5241,5316,5337,5471,5537,5538,5539,5656,5657,5683,5687,5747,5749,5758,5764,5836])).
% 187.39/188.10 cnf(13191,plain,
% 187.39/188.10 (~E(f329(f187(x131911,f881(x131912,a869),x131913,f193(f881(x131911,a869))),x131914),f329(f236(f881(x131912,a869)),f329(f329(f42(f45(a1,x131915,x131915),f881(x131912,a869)),x131916),a117)))),
% 187.39/188.10 inference(scs_inference,[],[4323,3521,11045,12081,12179,12268,12304,12312,12377,12498,12500,12931,12939,12942,12946,12952,12955,12979,13082,3530,12145,12558,12560,3531,12210,3244,12517,12519,3245,12529,3211,12454,4492,4493,11662,4233,12583,12586,3248,12590,3086,3145,12489,4477,3581,4459,10208,10218,10229,10240,10341,10344,10347,10450,10563,10866,11030,11033,11230,11317,11324,11338,11390,11393,11437,11503,11549,11565,11864,11889,11901,11930,11936,12031,12141,12148,12296,12347,12485,12602,12756,13000,4474,10434,10527,3336,3298,12543,3490,3193,4469,12673,12688,13020,2873,2874,2876,2877,2880,2881,2883,2884,2885,2891,2892,2895,2896,2903,2904,2908,2909,2910,2911,2917,2918,2920,2923,2932,2938,2942,2944,2949,2952,2953,2954,2961,2965,2974,2982,2983,2986,2987,2988,2997,3010,3019,3020,3022,3023,3029,3035,3036,3037,3038,3047,3053,4454,3065,3144,4455,3619,3847,11596,3118,11314,3258,3234,10211,10275,10278,10368,10371,10664,11329,11332,11448,11490,11495,11591,12051,12246,12434,12487,12493,12510,12512,12535,12537,12566,12568,12573,12599,12807,12970,13081,13086,13102,3860,3206,12325,12329,12333,3212,3219,3740,3979,3107,3108,4471,3484,3832,11364,3335,12575,3169,3136,3313,3656,12523,3131,3953,3152,3661,4438,4560,3115,3116,3096,3151,3291,12380,12457,3337,10815,12142,3204,3205,3229,10475,3383,4541,10404,3919,4484,10266,10431,11227,12292,12326,12330,4491,12300,3267,11685,11688,12900,12996,13053,13057,13061,4530,10980,11050,11273,11276,3264,3384,3605,3376,3350,12508,3166,10333,10640,3167,4518,3442,3159,3087,3272,3189,11354,4066,12315,12446,3921,10986,11112,11162,12276,12282,12393,12396,12419,4553,10918,11117,11221,11243,11281,11287,12226,4554,11019,11120,11224,4555,11123,11173,4556,11176,4557,3188,3482,12182,12223,12299,3644,4350,4351,3465,4482,11345,3583,3622,3796,3552,12790,12794,12798,12802,12812,3842,12176,3468,3722,3347,10352,10470,10541,10602,10605,10643,10737,10970,11860,11923,12002,12042,12119,12122,12423,12608,12667,12710,12713,12755,12773,12999,13004,3733,11582,3260,3359,11700,12601,13101,3546,4524,10243,10246,10272,10745,10758,10876,11265,11357,11752,11757,11978,11981,12063,12072,12229,12319,12613,12632,12635,12659,12714,12878,12883,12907,12912,4536,11467,11498,11533,11562,12723,12727,3720,3491,3493,12638,12641,12644,12647,12681,12684,13036,13040,13044,3494,3869,3454,13037,3455,13041,3306,3308,3281,4521,3165,4479,3672,4203,3988,3474,4537,4060,11238,3604,3320,11709,11712,12403,4030,3987,11853,12197,3931,12204,12426,13052,3976,13056,3982,10989,12078,12203,12903,3983,3645,11863,12009,12086,12132,4019,3663,10992,11055,11136,11195,12030,12100,12342,12416,12429,12869,4542,10761,11128,12207,12949,3276,10361,10457,10588,10650,10719,10764,10767,10800,10823,10860,10898,10934,11656,11703,11833,11888,11904,11907,11910,11913,12093,12107,12110,12113,12116,12190,12251,12353,12399,12660,12687,12765,12776,12781,12784,12787,12820,12833,12844,12893,12918,12921,3277,10390,10445,10655,10740,10863,11440,11737,11740,11749,11839,11850,11869,11874,11916,11939,11956,12678,12824,12847,12879,12884,12908,12913,13023,3280,3355,12066,12743,12791,12795,12799,12803,12813,12817,4520,10309,10399,10512,10536,10782,10826,10836,11512,11610,11631,11634,11637,11653,11807,11810,11813,11816,11900,11919,11922,11935,11990,11993,11996,11999,12073,12161,12164,12254,12257,12318,12346,12383,12466,3437,10608,10871,10915,11184,11262,11425,11665,12295,12469,12865,12935,12982,4532,10791,10803,10907,10925,10928,10983,11069,11077,11093,11131,11148,11156,11192,11233,11253,11256,11259,11290,11297,11300,11682,11718,11984,11987,12021,12067,12096,12235,12273,12279,12365,12368,12389,12445,12451,12460,12479,12742,12759,12762,12854,12936,12974,12989,12992,13033,13077,13080,3341,10637,10667,10676,11213,11764,12384,12400,12724,12728,12731,3379,13013,13074,3373,3800,3738,10312,11585,11613,12705,4529,10263,10625,10628,11072,11090,11548,11601,11641,11666,11770,11795,11798,11801,11804,12062,12924,3300,10670,10820,10891,11614,11769,11961,12169,12191,12752,13016,13100,3761,11715,12654,4110,3497,4527,3772,3808,4510,4513,4514,3251,3255,4512,3174,4511,4515,4286,3779,3594,11578,4209,11447,4544,10234,10237,10493,10544,10547,10552,10957,11419,11669,11773,4551,11151,11270,11306,3996,12218,3886,11303,11640,11644,11706,12303,12311,12392,12672,12930,12978,3727,10931,10937,10952,11885,12014,12099,12361,3579,12125,12232,12241,12308,12356,12364,12476,12872,3617,4064,3729,10673,11008,11159,11189,11200,12034,12307,12350,12966,3547,10591,10594,10679,10847,3549,4548,11579,4538,4543,12622,4549,10730,10829,11139,11422,11453,12185,12194,12238,12413,4170,10806,12215,4071,3760,12482,3707,3708,4546,10285,10288,10631,10634,11464,11645,12422,4547,11559,11650,3731,10597,10853,13003,4003,4568,4594,4643,4645,4675,4692,4699,4700,4739,4769,4775,4860,4885,4886,4921,4946,4947,4969,4970,4983,4987,5010,5017,5035,5038,5039,5040,5045,5046,5068,5093,5094,5104,5109,5115,5160,5161,5169,5178,5183,5185,5195,5197,5203,5207,5222,5229,5232,5233,5234,5238,5274,5287,5295,5297,5298,5302,5303,5304,5312,5315,5319,5320,5321,5328,5332,5333,5334,5342,5346,5347,5348,5353,5366,5375,5387,5389,5397,5398,5402,5406,5431,5437,5447,5448,5463,5475,5497,5503,5519,5520,5523,5542,5550,5551,5556,5557,5567,5569,5581,5585,5594,5595,5597,5612,5617,5627,5628,5640,5647,5661,5665,5668,5674,5675,5676,5679,5684,5722,5723,5726,5728,5731,5732,5733,5735,5737,5739,5744,5751,5766,5780,5785,5786,5799,5800,5805,5809,5811,5816,5857,5869,5878,5882,5893,5897,5898,5906,5920,5926,5944,5947,5959,5985,5999,6024,6044,6045,6048,6062,6064,6066,6068,6081,6082,6085,6087,6090,6091,6103,6109,6110,6111,6113,6115,6158,6159,6166,6172,6176,6212,6214,6216,6218,6227,6229,6231,6237,6239,6245,6248,6256,6263,6264,6265,6270,6292,6293,6294,6296,6302,6307,6341,6342,6344,6345,6346,6348,6349,6350,6351,6358,6391,6392,6401,6422,6423,6443,6446,6457,6458,6464,6495,6497,6511,6549,6551,6552,6606,6630,6672,6692,6701,6702,6703,6704,6723,6724,6730,6743,6746,6748,6750,6751,6752,6754,6768,6779,6781,6782,6795,6799,6850,6861,6863,6867,6884,6885,6921,6933,6964,6998,7052,7080,7135,7156,7165,7168,7223,7231,7289,7291,7306,7316,7317,7318,7337,7343,7345,7395,7405,7408,7424,7476,7478,7481,7524,7525,7543,7610,7629,7652,7676,7691,7706,7717,7726,7727,7756,7759,7761,7771,7809,7820,7845,7903,7937,7969,8016,8032,8048,8049,8124,8177,8196,8220,8240,8264,8362,8364,8370,8386,8390,8406,8429,8440,8442,8457,8463,8467,8490,8504,8505,8521,8522,8527,8528,8529,8530,8531,8549,8550,8551,8559,8573,8575,8587,8591,8593,8594,8595,8603,8608,8635,8636,8668,8681,8685,8703,8725,8726,8727,8728,8740,8741,8763,8773,8783,8784,8785,8786,8788,8809,8810,8821,8865,8871,8877,8889,8894,8896,8899,8900,8904,8914,8997,9028,9029,9030,9045,9063,9068,9096,9097,9138,9141,9167,9212,9213,9214,9229,9256,9270,9276,9279,9301,9302,9330,9391,9426,9427,9428,9453,9454,9472,9491,9497,9511,9534,9556,9564,9565,9566,9567,9582,9584,9589,9620,9621,9627,9628,9672,9673,9705,9714,9724,9726,9727,9736,9750,9753,9781,9814,9816,9820,9878,9919,9920,9922,9932,9933,9953,9958,9999,10050,10122,10123,10176,10192,2,8,9,4581,4582,4600,4631,4633,4634,4661,4667,4668,4679,4728,4730,4760,4774,4804,4900,4901,4914,4934,4990,4991,4994,4995,4997,4999,5000,5009,5013,5014,5024,5036,5037,5043,5063,5064,5081,5086,5087,5088,5089,5092,5100,5103,5110,5175,5181,5182,5189,5219,5230,5236,5252,5272,5273,5280,5281,5282,5291,5301,5308,5310,5311,5317,5324,5325,5338,5339,5340,5341,5343,5344,5349,5350,5351,5352,5383,5384,5385,5393,5394,5395,5396,5439,5444,5446,5482,5484,5485,5487,5488,5490,5491,5493,5502,5507,5509,5510,5511,5512,5513,5514,5521,5531,5534,5545,5561,5562,5565,5575,5577,5578,5579,5604,5614,5630,5631,5641,5642,5644,5646,5651,5686,5691,5693,5753,5787,5788,5792,5798,5801,5802,5803,5804,5810,5821,5822,5824,5825,5833,5854,5885,5901,5904,5905,5907,5916,5934,5938,5941,5942,5943,5961,5972,5973,6001,6002,6006,6026,6029,6033,6052,6057,6058,6083,6086,6094,6102,6108,6112,6119,6120,6121,6122,6161,6177,6230,6266,6268,6289,6290,6295,6299,6300,6303,6309,6318,6333,6353,6354,6359,6369,6384,6404,6410,6412,6427,6428,6431,6432,6434,6436,6437,6438,6440,6442,6445,6450,6451,6453,6454,6460,6462,6505,6510,6524,6526,6527,6528,6563,6568,6570,6575,6576,6584,6588,6601,6625,6626,6628,6629,6640,6646,6663,6666,6685,6718,6719,6720,6725,6739,6758,6760,6762,6764,6769,6775,6777,6792,6797,6800,6836,6837,6838,6852,6853,6855,6856,6875,6877,6893,6919,6941,6952,6954,6956,6958,6959,6960,6995,6996,7001,7002,7009,7010,7012,7014,7033,7042,7043,7055,7065,7104,7114,7118,7125,7136,7142,7144,7150,7158,7159,7172,7189,7207,7209,7226,7275,7276,7277,7279,7281,7285,7290,7313,7358,7391,7406,7423,7456,7459,7485,7509,7526,7529,7530,7540,7559,7561,7563,7565,7566,7567,7592,7618,7619,7651,7653,7654,7655,7660,7683,7692,7703,7708,7714,7716,7722,7734,7735,7737,7762,7769,7792,7858,7859,7906,7914,7915,7939,7940,7957,7958,8023,8024,8051,8080,8091,8093,8102,8114,8146,8152,8159,8172,8191,8197,8219,8262,8292,8304,8322,8325,8355,8378,8443,8444,8447,8449,8553,8554,8555,8556,8582,8611,8639,8684,8702,8757,8802,8805,8818,8825,8862,8910,8911,8929,8930,9070,9074,9094,9104,9127,9129,9132,9136,9139,9140,9153,9154,9174,9180,9192,9240,9241,9260,9314,9315,9322,9383,9388,9423,9430,9433,9436,9437,9452,9468,9477,9487,9490,9500,9501,9504,9506,9532,9655,9699,9700,9743,9788,9905,9962,10027,10101,10114,10119,3,2614,2616,2617,2618,2619,2620,2621,2628,2629,2630,2631,2636,2637,2638,2639,2644,2651,2652,2657,2658,2659,2661,2662,2663,2666,2667,2668,2670,2671,2674,2675,2676,2681,2682,2687,2688,2689,2695,2696,2697,2702,2703,2705,2706,2710,2712,2713,2716,2718,2719,2721,2723,2726,2735,2736,2737,2764,2767,2789,2792,2793,2794,2801,2803,2805,2807,2819,2820,2822,2829,5211,5271,5369,5455,5456,5457,5532,5629,5660,5694,5710,5712,5718,5781,5782,5783,5784,5790,5823,5956,5991,6000,6023,6060,6095,6100,6247,6252,6287,6288,6308,6311,6313,6320,6321,6322,6323,6324,6325,6326,6327,6406,6474,6475,6562,6595,6596,6637,6638,6776,6791,6864,6865,6872,6894,6917,6925,6927,6974,6999,7000,7018,7019,7054,7098,7099,7196,7257,7258,7259,7260,7274,7307,7363,7364,7373,7381,7382,7394,7426,7427,7428,7429,7573,7574,7576,7578,7584,7585,7800,7806,7807,7817,7856,7935,7977,8035,8056,8057,8072,8131,8233,8302,8303,8305,8340,8402,8403,8476,8497,8498,8499,8500,8643,8855,8879,8880,8961,8976,9031,9032,9148,9184,9207,9242,9284,9475,9737,9931,9987,9989,6018,6389,6390,6477,6498,6499,6916,7134,8287,8568,8601,8796,8987,8988,9059,9060,9332,9333,9334,9335,9535,9808,10110,10161,10162,6459,8393,8394,8845,8863,9809,10160,4635,4637,4638,4693,4701,4838,4854,4855,4883,4884,4913,4968,5031,5090,5168,5204,5206,5214,5215,5241,5316,5337,5471,5537,5538,5539,5656,5657,5683,5687,5747,5749,5758,5764,5836,5914,6041])).
% 187.39/188.10 cnf(13195,plain,
% 187.39/188.10 (~P24(f329(f62(x131951),f40(f881(x131951,a869),f252(f881(f881(x131951,a869),a869)))))),
% 187.39/188.10 inference(scs_inference,[],[4323,3521,11045,12081,12179,12268,12304,12312,12377,12498,12500,12931,12939,12942,12946,12952,12955,12979,13082,3530,12145,12558,12560,3531,12210,3244,12517,12519,3245,12529,3211,12454,4492,4493,11662,4233,12583,12586,3248,12590,3086,3145,12489,4477,3581,4459,10208,10218,10229,10240,10341,10344,10347,10450,10563,10866,11030,11033,11230,11317,11324,11338,11390,11393,11437,11503,11549,11565,11864,11889,11901,11930,11936,12031,12141,12148,12296,12347,12485,12602,12756,13000,4474,10434,10527,3336,3298,12543,3490,3193,4469,12673,12688,13020,2873,2874,2876,2877,2880,2881,2883,2884,2885,2891,2892,2895,2896,2903,2904,2908,2909,2910,2911,2917,2918,2920,2923,2932,2938,2942,2944,2949,2952,2953,2954,2961,2965,2974,2982,2983,2986,2987,2988,2997,3010,3019,3020,3022,3023,3029,3035,3036,3037,3038,3047,3053,4454,3065,3144,4455,3619,3847,11596,3118,11314,3258,3234,10211,10275,10278,10368,10371,10664,11329,11332,11448,11490,11495,11591,12051,12246,12434,12487,12493,12510,12512,12535,12537,12566,12568,12573,12599,12807,12970,13081,13086,13102,3860,3206,12325,12329,12333,3212,3219,3740,3979,3107,3108,4471,3484,3832,11364,3335,12575,3169,3136,3313,3656,12523,3131,3953,3152,3661,4438,4560,3115,3116,3096,3151,3291,12380,12457,3337,10815,12142,3204,3205,3229,10475,3383,4541,10404,3919,4484,10266,10431,11227,12292,12326,12330,4491,12300,3267,11685,11688,12900,12996,13053,13057,13061,4530,10980,11050,11273,11276,3264,3384,3605,3376,3350,12508,3166,10333,10640,3167,4518,3442,3159,3087,3272,3189,11354,4066,12315,12446,3921,10986,11112,11162,12276,12282,12393,12396,12419,4553,10918,11117,11221,11243,11281,11287,12226,4554,11019,11120,11224,4555,11123,11173,4556,11176,4557,3188,3482,12182,12223,12299,3644,4350,4351,3465,4482,11345,3583,3622,3796,3552,12790,12794,12798,12802,12812,3842,12176,3468,3722,3347,10352,10470,10541,10602,10605,10643,10737,10970,11860,11923,12002,12042,12119,12122,12423,12608,12667,12710,12713,12755,12773,12999,13004,3733,11582,3260,3359,11700,12601,13101,3546,4524,10243,10246,10272,10745,10758,10876,11265,11357,11752,11757,11978,11981,12063,12072,12229,12319,12613,12632,12635,12659,12714,12878,12883,12907,12912,4536,11467,11498,11533,11562,12723,12727,3720,3491,3493,12638,12641,12644,12647,12681,12684,13036,13040,13044,3494,3869,3454,13037,3455,13041,3306,3308,3281,4521,3165,4479,3672,4203,3988,3474,4537,4060,11238,3604,3320,11709,11712,12403,4030,3987,11853,12197,3931,12204,12426,13052,3976,13056,3982,10989,12078,12203,12903,3983,3645,11863,12009,12086,12132,4019,3663,10992,11055,11136,11195,12030,12100,12342,12416,12429,12869,4542,10761,11128,12207,12949,3276,10361,10457,10588,10650,10719,10764,10767,10800,10823,10860,10898,10934,11656,11703,11833,11888,11904,11907,11910,11913,12093,12107,12110,12113,12116,12190,12251,12353,12399,12660,12687,12765,12776,12781,12784,12787,12820,12833,12844,12893,12918,12921,3277,10390,10445,10655,10740,10863,11440,11737,11740,11749,11839,11850,11869,11874,11916,11939,11956,12678,12824,12847,12879,12884,12908,12913,13023,3280,3355,12066,12743,12791,12795,12799,12803,12813,12817,4520,10309,10399,10512,10536,10782,10826,10836,11512,11610,11631,11634,11637,11653,11807,11810,11813,11816,11900,11919,11922,11935,11990,11993,11996,11999,12073,12161,12164,12254,12257,12318,12346,12383,12466,3437,10608,10871,10915,11184,11262,11425,11665,12295,12469,12865,12935,12982,4532,10791,10803,10907,10925,10928,10983,11069,11077,11093,11131,11148,11156,11192,11233,11253,11256,11259,11290,11297,11300,11682,11718,11984,11987,12021,12067,12096,12235,12273,12279,12365,12368,12389,12445,12451,12460,12479,12742,12759,12762,12854,12936,12974,12989,12992,13033,13077,13080,3341,10637,10667,10676,11213,11764,12384,12400,12724,12728,12731,3379,13013,13074,3373,3800,3738,10312,11585,11613,12705,4529,10263,10625,10628,11072,11090,11548,11601,11641,11666,11770,11795,11798,11801,11804,12062,12924,3300,10670,10820,10891,11614,11769,11961,12169,12191,12752,13016,13100,3761,11715,12654,4110,3497,4527,3772,3808,4510,4513,4514,3251,3255,4512,3174,4511,4515,4286,3779,3594,11578,4209,11447,4544,10234,10237,10493,10544,10547,10552,10957,11419,11669,11773,4551,11151,11270,11306,3996,12218,3886,11303,11640,11644,11706,12303,12311,12392,12672,12930,12978,3727,10931,10937,10952,11885,12014,12099,12361,3579,12125,12232,12241,12308,12356,12364,12476,12872,3617,4064,3729,10673,11008,11159,11189,11200,12034,12307,12350,12966,3547,10591,10594,10679,10847,3549,4548,11579,4538,4543,12622,4549,10730,10829,11139,11422,11453,12185,12194,12238,12413,4170,10806,12215,4071,3760,12482,3707,3708,4546,10285,10288,10631,10634,11464,11645,12422,4547,11559,11650,3731,10597,10853,13003,4003,4568,4594,4643,4645,4675,4692,4699,4700,4739,4769,4775,4860,4885,4886,4921,4946,4947,4969,4970,4983,4987,5010,5017,5035,5038,5039,5040,5045,5046,5068,5093,5094,5104,5109,5115,5160,5161,5169,5178,5183,5185,5195,5197,5203,5207,5222,5229,5232,5233,5234,5238,5274,5287,5295,5297,5298,5302,5303,5304,5312,5315,5319,5320,5321,5328,5332,5333,5334,5342,5346,5347,5348,5353,5366,5375,5387,5389,5397,5398,5402,5406,5431,5437,5447,5448,5463,5475,5497,5503,5519,5520,5523,5542,5550,5551,5556,5557,5567,5569,5581,5585,5594,5595,5597,5612,5617,5627,5628,5640,5647,5661,5665,5668,5674,5675,5676,5679,5684,5722,5723,5726,5728,5731,5732,5733,5735,5737,5739,5744,5751,5766,5780,5785,5786,5799,5800,5805,5809,5811,5816,5857,5869,5878,5882,5893,5897,5898,5906,5920,5926,5944,5947,5959,5985,5999,6024,6044,6045,6048,6062,6064,6066,6068,6081,6082,6085,6087,6090,6091,6103,6109,6110,6111,6113,6115,6158,6159,6166,6172,6176,6212,6214,6216,6218,6227,6229,6231,6237,6239,6245,6248,6256,6263,6264,6265,6270,6292,6293,6294,6296,6302,6307,6341,6342,6344,6345,6346,6348,6349,6350,6351,6358,6391,6392,6401,6422,6423,6443,6446,6457,6458,6464,6495,6497,6511,6549,6551,6552,6606,6630,6672,6692,6701,6702,6703,6704,6723,6724,6730,6743,6746,6748,6750,6751,6752,6754,6768,6779,6781,6782,6795,6799,6850,6861,6863,6867,6884,6885,6921,6933,6964,6998,7052,7080,7135,7156,7165,7168,7223,7231,7289,7291,7306,7316,7317,7318,7337,7343,7345,7395,7405,7408,7424,7476,7478,7481,7524,7525,7543,7610,7629,7652,7676,7691,7706,7717,7726,7727,7756,7759,7761,7771,7809,7820,7845,7903,7937,7969,8016,8032,8048,8049,8124,8177,8196,8220,8240,8264,8362,8364,8370,8386,8390,8406,8429,8440,8442,8457,8463,8467,8490,8504,8505,8521,8522,8527,8528,8529,8530,8531,8549,8550,8551,8559,8573,8575,8587,8591,8593,8594,8595,8603,8608,8635,8636,8668,8681,8685,8703,8725,8726,8727,8728,8740,8741,8763,8773,8783,8784,8785,8786,8788,8809,8810,8821,8865,8871,8877,8889,8894,8896,8899,8900,8904,8914,8997,9028,9029,9030,9045,9063,9068,9096,9097,9138,9141,9167,9212,9213,9214,9229,9256,9270,9276,9279,9301,9302,9330,9391,9426,9427,9428,9453,9454,9472,9491,9497,9511,9534,9556,9564,9565,9566,9567,9582,9584,9589,9620,9621,9627,9628,9672,9673,9705,9714,9724,9726,9727,9736,9750,9753,9781,9814,9816,9820,9878,9919,9920,9922,9932,9933,9953,9958,9999,10050,10122,10123,10176,10192,2,8,9,4581,4582,4600,4631,4633,4634,4661,4667,4668,4679,4728,4730,4760,4774,4804,4900,4901,4914,4934,4990,4991,4994,4995,4997,4999,5000,5009,5013,5014,5024,5036,5037,5043,5063,5064,5081,5086,5087,5088,5089,5092,5100,5103,5110,5175,5181,5182,5189,5219,5230,5236,5252,5272,5273,5280,5281,5282,5291,5301,5308,5310,5311,5317,5324,5325,5338,5339,5340,5341,5343,5344,5349,5350,5351,5352,5383,5384,5385,5393,5394,5395,5396,5439,5444,5446,5482,5484,5485,5487,5488,5490,5491,5493,5502,5507,5509,5510,5511,5512,5513,5514,5521,5531,5534,5545,5561,5562,5565,5575,5577,5578,5579,5604,5614,5630,5631,5641,5642,5644,5646,5651,5686,5691,5693,5753,5787,5788,5792,5798,5801,5802,5803,5804,5810,5821,5822,5824,5825,5833,5854,5885,5901,5904,5905,5907,5916,5934,5938,5941,5942,5943,5961,5972,5973,6001,6002,6006,6026,6029,6033,6052,6057,6058,6083,6086,6094,6102,6108,6112,6119,6120,6121,6122,6161,6177,6230,6266,6268,6289,6290,6295,6299,6300,6303,6309,6318,6333,6353,6354,6359,6369,6384,6404,6410,6412,6427,6428,6431,6432,6434,6436,6437,6438,6440,6442,6445,6450,6451,6453,6454,6460,6462,6505,6510,6524,6526,6527,6528,6563,6568,6570,6575,6576,6584,6588,6601,6625,6626,6628,6629,6640,6646,6663,6666,6685,6718,6719,6720,6725,6739,6758,6760,6762,6764,6769,6775,6777,6792,6797,6800,6836,6837,6838,6852,6853,6855,6856,6875,6877,6893,6919,6941,6952,6954,6956,6958,6959,6960,6995,6996,7001,7002,7009,7010,7012,7014,7033,7042,7043,7055,7065,7104,7114,7118,7125,7136,7142,7144,7150,7158,7159,7172,7189,7207,7209,7226,7275,7276,7277,7279,7281,7285,7290,7313,7358,7391,7406,7423,7456,7459,7485,7509,7526,7529,7530,7540,7559,7561,7563,7565,7566,7567,7592,7618,7619,7651,7653,7654,7655,7660,7683,7692,7703,7708,7714,7716,7722,7734,7735,7737,7762,7769,7792,7858,7859,7906,7914,7915,7939,7940,7957,7958,8023,8024,8051,8080,8091,8093,8102,8114,8146,8152,8159,8172,8191,8197,8219,8262,8292,8304,8322,8325,8355,8378,8443,8444,8447,8449,8553,8554,8555,8556,8582,8611,8639,8684,8702,8757,8802,8805,8818,8825,8862,8910,8911,8929,8930,9070,9074,9094,9104,9127,9129,9132,9136,9139,9140,9153,9154,9174,9180,9192,9240,9241,9260,9314,9315,9322,9383,9388,9423,9430,9433,9436,9437,9452,9468,9477,9487,9490,9500,9501,9504,9506,9532,9655,9699,9700,9743,9788,9905,9962,10027,10101,10114,10119,3,2614,2616,2617,2618,2619,2620,2621,2628,2629,2630,2631,2636,2637,2638,2639,2644,2651,2652,2657,2658,2659,2661,2662,2663,2666,2667,2668,2670,2671,2674,2675,2676,2681,2682,2687,2688,2689,2695,2696,2697,2702,2703,2705,2706,2710,2712,2713,2716,2718,2719,2721,2723,2726,2735,2736,2737,2764,2767,2789,2792,2793,2794,2801,2803,2805,2807,2819,2820,2822,2829,5211,5271,5369,5455,5456,5457,5532,5629,5660,5694,5710,5712,5718,5781,5782,5783,5784,5790,5823,5956,5991,6000,6023,6060,6095,6100,6247,6252,6287,6288,6308,6311,6313,6320,6321,6322,6323,6324,6325,6326,6327,6406,6474,6475,6562,6595,6596,6637,6638,6776,6791,6864,6865,6872,6894,6917,6925,6927,6974,6999,7000,7018,7019,7054,7098,7099,7196,7257,7258,7259,7260,7274,7307,7363,7364,7373,7381,7382,7394,7426,7427,7428,7429,7573,7574,7576,7578,7584,7585,7800,7806,7807,7817,7856,7935,7977,8035,8056,8057,8072,8131,8233,8302,8303,8305,8340,8402,8403,8476,8497,8498,8499,8500,8643,8855,8879,8880,8961,8976,9031,9032,9148,9184,9207,9242,9284,9475,9737,9931,9987,9989,6018,6389,6390,6477,6498,6499,6916,7134,8287,8568,8601,8796,8987,8988,9059,9060,9332,9333,9334,9335,9535,9808,10110,10161,10162,6459,8393,8394,8845,8863,9809,10160,4635,4637,4638,4693,4701,4838,4854,4855,4883,4884,4913,4968,5031,5090,5168,5204,5206,5214,5215,5241,5316,5337,5471,5537,5538,5539,5656,5657,5683,5687,5747,5749,5758,5764,5836,5914,6041,6067,6233])).
% 187.39/188.10 cnf(13207,plain,
% 187.39/188.10 (~P24(f329(f329(f244(a874),f2(a874)),f193(a874)))),
% 187.39/188.10 inference(scs_inference,[],[4323,3521,11045,12081,12179,12268,12304,12312,12377,12498,12500,12931,12939,12942,12946,12952,12955,12979,13082,3530,12145,12558,12560,3531,12210,3244,12517,12519,3245,12529,3211,12454,4492,4493,11662,4233,12583,12586,3248,12590,3086,3145,12489,4477,3581,4459,10208,10218,10229,10240,10341,10344,10347,10450,10563,10866,11030,11033,11230,11317,11324,11338,11390,11393,11437,11503,11549,11565,11864,11889,11901,11930,11936,12031,12141,12148,12296,12347,12485,12602,12756,13000,4474,10434,10527,3336,3298,12543,3490,3193,4469,12673,12688,13020,2873,2874,2876,2877,2880,2881,2883,2884,2885,2891,2892,2895,2896,2903,2904,2908,2909,2910,2911,2917,2918,2920,2923,2932,2938,2942,2944,2949,2952,2953,2954,2961,2965,2974,2982,2983,2986,2987,2988,2997,3010,3019,3020,3022,3023,3029,3035,3036,3037,3038,3047,3053,4454,3065,3144,4455,3619,3847,11596,3118,11314,3258,3234,10211,10275,10278,10368,10371,10664,11329,11332,11448,11490,11495,11591,12051,12246,12434,12487,12493,12510,12512,12535,12537,12566,12568,12573,12599,12807,12970,13081,13086,13102,3860,3206,12325,12329,12333,3212,3219,3740,3979,3107,3108,4471,3484,3832,11364,3335,12575,3169,3136,3313,3656,12523,3131,3953,3152,3661,4438,4560,3115,3116,3096,3151,3291,12380,12457,3337,10815,12142,3204,3205,3229,10475,3383,4541,10404,3919,4484,10266,10431,11227,12292,12326,12330,4491,12300,3267,11685,11688,12900,12996,13053,13057,13061,4530,10980,11050,11273,11276,3264,3384,3605,3376,3350,12508,3166,10333,10640,3167,4518,3442,3159,3087,3272,3189,11354,4066,12315,12446,3921,10986,11112,11162,12276,12282,12393,12396,12419,4553,10918,11117,11221,11243,11281,11287,12226,4554,11019,11120,11224,4555,11123,11173,4556,11176,4557,3188,3482,12182,12223,12299,3644,4350,4351,3465,4482,11345,3583,3622,3796,3552,12790,12794,12798,12802,12812,3842,12176,3468,3722,3347,10352,10470,10541,10602,10605,10643,10737,10970,11860,11923,12002,12042,12119,12122,12423,12608,12667,12710,12713,12755,12773,12999,13004,3733,11582,3260,3359,11700,12601,13101,3546,4524,10243,10246,10272,10745,10758,10876,11265,11357,11752,11757,11978,11981,12063,12072,12229,12319,12613,12632,12635,12659,12714,12878,12883,12907,12912,4536,11467,11498,11533,11562,12723,12727,3720,3491,3493,12638,12641,12644,12647,12681,12684,13036,13040,13044,3494,3869,3454,13037,3455,13041,3306,3308,3281,4521,3165,4479,3672,4203,3988,3474,4537,4060,11238,3604,3320,11709,11712,12403,4030,3987,11853,12197,3931,12204,12426,13052,3976,13056,3982,10989,12078,12203,12903,3983,3645,11863,12009,12086,12132,4019,3663,10992,11055,11136,11195,12030,12100,12342,12416,12429,12869,4542,10761,11128,12207,12949,3276,10361,10457,10588,10650,10719,10764,10767,10800,10823,10860,10898,10934,11656,11703,11833,11888,11904,11907,11910,11913,12093,12107,12110,12113,12116,12190,12251,12353,12399,12660,12687,12765,12776,12781,12784,12787,12820,12833,12844,12893,12918,12921,3277,10390,10445,10655,10740,10863,11440,11737,11740,11749,11839,11850,11869,11874,11916,11939,11956,12678,12824,12847,12879,12884,12908,12913,13023,3280,3355,12066,12743,12791,12795,12799,12803,12813,12817,4520,10309,10399,10512,10536,10782,10826,10836,11512,11610,11631,11634,11637,11653,11807,11810,11813,11816,11900,11919,11922,11935,11990,11993,11996,11999,12073,12161,12164,12254,12257,12318,12346,12383,12466,3437,10608,10871,10915,11184,11262,11425,11665,12295,12469,12865,12935,12982,4532,10791,10803,10907,10925,10928,10983,11069,11077,11093,11131,11148,11156,11192,11233,11253,11256,11259,11290,11297,11300,11682,11718,11984,11987,12021,12067,12096,12235,12273,12279,12365,12368,12389,12445,12451,12460,12479,12742,12759,12762,12854,12936,12974,12989,12992,13033,13077,13080,3341,10637,10667,10676,11213,11764,12384,12400,12724,12728,12731,3379,13013,13074,3373,3800,3738,10312,11585,11613,12705,4529,10263,10625,10628,11072,11090,11548,11601,11641,11666,11770,11795,11798,11801,11804,12062,12924,3300,10670,10820,10891,11614,11769,11961,12169,12191,12752,13016,13100,3761,11715,12654,4110,3497,4527,3772,3808,4510,4513,4514,3251,3255,4512,3174,4511,4515,4286,3779,3594,11578,4209,11447,4544,10234,10237,10493,10544,10547,10552,10957,11419,11669,11773,4551,11151,11270,11306,3996,12218,3886,11303,11640,11644,11706,12303,12311,12392,12672,12930,12978,3727,10931,10937,10952,11885,12014,12099,12361,3579,12125,12232,12241,12308,12356,12364,12476,12872,3617,4064,3729,10673,11008,11159,11189,11200,12034,12307,12350,12966,3547,10591,10594,10679,10847,3549,4548,11579,4538,4543,12622,4549,10730,10829,11139,11422,11453,12185,12194,12238,12413,4170,10806,12215,4071,3760,12482,3707,3708,4546,10285,10288,10631,10634,11464,11645,12422,4547,11559,11650,3731,10597,10853,13003,4003,4568,4594,4643,4645,4675,4692,4699,4700,4739,4769,4775,4860,4885,4886,4921,4946,4947,4969,4970,4983,4987,5010,5017,5035,5038,5039,5040,5045,5046,5068,5093,5094,5104,5109,5115,5160,5161,5169,5178,5183,5185,5195,5197,5203,5207,5222,5229,5232,5233,5234,5238,5274,5287,5295,5297,5298,5302,5303,5304,5312,5315,5319,5320,5321,5328,5332,5333,5334,5342,5346,5347,5348,5353,5366,5375,5387,5389,5397,5398,5402,5406,5431,5437,5447,5448,5463,5475,5497,5503,5519,5520,5523,5542,5550,5551,5556,5557,5567,5569,5581,5585,5594,5595,5597,5612,5617,5627,5628,5640,5647,5661,5665,5668,5674,5675,5676,5679,5684,5722,5723,5726,5728,5731,5732,5733,5735,5737,5739,5744,5751,5766,5780,5785,5786,5799,5800,5805,5809,5811,5816,5857,5869,5878,5882,5893,5897,5898,5906,5920,5926,5944,5947,5959,5985,5999,6024,6044,6045,6048,6062,6064,6066,6068,6081,6082,6085,6087,6090,6091,6103,6109,6110,6111,6113,6115,6158,6159,6166,6172,6176,6212,6214,6216,6218,6227,6229,6231,6237,6239,6245,6248,6256,6263,6264,6265,6270,6292,6293,6294,6296,6302,6307,6341,6342,6344,6345,6346,6348,6349,6350,6351,6358,6391,6392,6401,6422,6423,6443,6446,6457,6458,6464,6495,6497,6511,6549,6551,6552,6606,6630,6672,6692,6701,6702,6703,6704,6723,6724,6730,6743,6746,6748,6750,6751,6752,6754,6768,6779,6781,6782,6795,6799,6850,6861,6863,6867,6884,6885,6921,6933,6964,6998,7052,7080,7135,7156,7165,7168,7223,7231,7289,7291,7306,7316,7317,7318,7337,7343,7345,7395,7405,7408,7424,7476,7478,7481,7524,7525,7543,7610,7629,7652,7676,7691,7706,7717,7726,7727,7756,7759,7761,7771,7809,7820,7845,7903,7937,7969,8016,8032,8048,8049,8124,8177,8196,8220,8240,8264,8362,8364,8370,8386,8390,8406,8429,8440,8442,8457,8463,8467,8490,8504,8505,8521,8522,8527,8528,8529,8530,8531,8549,8550,8551,8559,8573,8575,8587,8591,8593,8594,8595,8603,8608,8635,8636,8668,8681,8685,8703,8725,8726,8727,8728,8740,8741,8763,8773,8783,8784,8785,8786,8788,8809,8810,8821,8865,8871,8877,8889,8894,8896,8899,8900,8904,8914,8997,9028,9029,9030,9045,9063,9068,9096,9097,9138,9141,9167,9212,9213,9214,9229,9256,9270,9276,9279,9301,9302,9330,9391,9426,9427,9428,9453,9454,9472,9491,9497,9511,9534,9556,9564,9565,9566,9567,9582,9584,9589,9620,9621,9627,9628,9672,9673,9705,9714,9724,9726,9727,9736,9750,9753,9781,9814,9816,9820,9878,9919,9920,9922,9932,9933,9953,9958,9999,10050,10122,10123,10176,10192,2,8,9,4581,4582,4600,4631,4633,4634,4661,4667,4668,4679,4728,4730,4760,4774,4804,4900,4901,4914,4934,4990,4991,4994,4995,4997,4999,5000,5009,5013,5014,5024,5036,5037,5043,5063,5064,5081,5086,5087,5088,5089,5092,5100,5103,5110,5175,5181,5182,5189,5219,5230,5236,5252,5272,5273,5280,5281,5282,5291,5301,5308,5310,5311,5317,5324,5325,5338,5339,5340,5341,5343,5344,5349,5350,5351,5352,5383,5384,5385,5393,5394,5395,5396,5439,5444,5446,5482,5484,5485,5487,5488,5490,5491,5493,5502,5507,5509,5510,5511,5512,5513,5514,5521,5531,5534,5545,5561,5562,5565,5575,5577,5578,5579,5604,5614,5630,5631,5641,5642,5644,5646,5651,5686,5691,5693,5753,5787,5788,5792,5798,5801,5802,5803,5804,5810,5821,5822,5824,5825,5833,5854,5885,5901,5904,5905,5907,5916,5934,5938,5941,5942,5943,5961,5972,5973,6001,6002,6006,6026,6029,6033,6052,6057,6058,6083,6086,6094,6102,6108,6112,6119,6120,6121,6122,6161,6177,6230,6266,6268,6289,6290,6295,6299,6300,6303,6309,6318,6333,6353,6354,6359,6369,6384,6404,6410,6412,6427,6428,6431,6432,6434,6436,6437,6438,6440,6442,6445,6450,6451,6453,6454,6460,6462,6505,6510,6524,6526,6527,6528,6563,6568,6570,6575,6576,6584,6588,6601,6625,6626,6628,6629,6640,6646,6663,6666,6685,6718,6719,6720,6725,6739,6758,6760,6762,6764,6769,6775,6777,6792,6797,6800,6836,6837,6838,6852,6853,6855,6856,6875,6877,6893,6919,6941,6952,6954,6956,6958,6959,6960,6995,6996,7001,7002,7009,7010,7012,7014,7033,7042,7043,7055,7065,7104,7114,7118,7125,7136,7142,7144,7150,7158,7159,7172,7189,7207,7209,7226,7275,7276,7277,7279,7281,7285,7290,7313,7358,7391,7406,7423,7456,7459,7485,7509,7526,7529,7530,7540,7559,7561,7563,7565,7566,7567,7592,7618,7619,7651,7653,7654,7655,7660,7683,7692,7703,7708,7714,7716,7722,7734,7735,7737,7762,7769,7792,7858,7859,7906,7914,7915,7939,7940,7957,7958,8023,8024,8051,8080,8091,8093,8102,8114,8146,8152,8159,8172,8191,8197,8219,8262,8292,8304,8322,8325,8355,8378,8443,8444,8447,8449,8553,8554,8555,8556,8582,8611,8639,8684,8702,8757,8802,8805,8818,8825,8862,8910,8911,8929,8930,9070,9074,9094,9104,9127,9129,9132,9136,9139,9140,9153,9154,9174,9180,9192,9240,9241,9260,9314,9315,9322,9383,9388,9423,9430,9433,9436,9437,9452,9468,9477,9487,9490,9500,9501,9504,9506,9532,9655,9699,9700,9743,9788,9905,9962,10027,10101,10114,10119,3,2614,2616,2617,2618,2619,2620,2621,2628,2629,2630,2631,2636,2637,2638,2639,2644,2651,2652,2657,2658,2659,2661,2662,2663,2666,2667,2668,2670,2671,2674,2675,2676,2681,2682,2687,2688,2689,2695,2696,2697,2702,2703,2705,2706,2710,2712,2713,2716,2718,2719,2721,2723,2726,2735,2736,2737,2764,2767,2789,2792,2793,2794,2801,2803,2805,2807,2819,2820,2822,2829,5211,5271,5369,5455,5456,5457,5532,5629,5660,5694,5710,5712,5718,5781,5782,5783,5784,5790,5823,5956,5991,6000,6023,6060,6095,6100,6247,6252,6287,6288,6308,6311,6313,6320,6321,6322,6323,6324,6325,6326,6327,6406,6474,6475,6562,6595,6596,6637,6638,6776,6791,6864,6865,6872,6894,6917,6925,6927,6974,6999,7000,7018,7019,7054,7098,7099,7196,7257,7258,7259,7260,7274,7307,7363,7364,7373,7381,7382,7394,7426,7427,7428,7429,7573,7574,7576,7578,7584,7585,7800,7806,7807,7817,7856,7935,7977,8035,8056,8057,8072,8131,8233,8302,8303,8305,8340,8402,8403,8476,8497,8498,8499,8500,8643,8855,8879,8880,8961,8976,9031,9032,9148,9184,9207,9242,9284,9475,9737,9931,9987,9989,6018,6389,6390,6477,6498,6499,6916,7134,8287,8568,8601,8796,8987,8988,9059,9060,9332,9333,9334,9335,9535,9808,10110,10161,10162,6459,8393,8394,8845,8863,9809,10160,4635,4637,4638,4693,4701,4838,4854,4855,4883,4884,4913,4968,5031,5090,5168,5204,5206,5214,5215,5241,5316,5337,5471,5537,5538,5539,5656,5657,5683,5687,5747,5749,5758,5764,5836,5914,6041,6067,6233,6352,6508,6710,6711,6928,6969])).
% 187.39/188.10 cnf(13240,plain,
% 187.39/188.10 (~P24(f329(f329(f243(a874),f329(a117,f329(f140(a874,a874,f80(a874),f2(a874)),f169(a874,f329(a117,f2(a874)),f329(a117,f2(a874)))))),f329(a117,f2(a874))))),
% 187.39/188.10 inference(scs_inference,[],[4323,3521,11045,12081,12179,12268,12304,12312,12377,12498,12500,12931,12939,12942,12946,12952,12955,12979,13082,3530,12145,12558,12560,3531,12210,3244,12517,12519,3245,12529,3211,12454,4492,4493,11662,4233,12583,12586,3248,12590,3086,3145,12489,4477,3581,4459,10208,10218,10229,10240,10341,10344,10347,10450,10563,10866,11030,11033,11230,11317,11324,11338,11390,11393,11437,11503,11549,11565,11864,11889,11901,11930,11936,12031,12141,12148,12296,12347,12485,12602,12756,13000,13008,4474,10434,10527,3336,3298,12543,3490,3193,4469,12673,12688,13020,2873,2874,2876,2877,2880,2881,2883,2884,2885,2891,2892,2895,2896,2903,2904,2908,2909,2910,2911,2917,2918,2920,2923,2932,2938,2942,2944,2949,2952,2953,2954,2961,2965,2974,2982,2983,2986,2987,2988,2997,3010,3019,3020,3022,3023,3029,3035,3036,3037,3038,3047,3053,4454,3065,3144,4455,3619,3847,11596,3118,11314,3258,3234,10211,10275,10278,10368,10371,10664,11329,11332,11448,11490,11495,11591,12051,12246,12434,12487,12493,12510,12512,12535,12537,12566,12568,12573,12599,12807,12970,13081,13086,13102,3860,3206,12325,12329,12333,3212,3219,3740,3979,3107,3108,4471,3484,3832,11364,3335,12575,3169,3648,3136,3313,3656,12523,3131,3953,3152,3661,4438,4560,3115,3116,3096,3151,3291,12380,12457,3337,10815,12142,3204,3205,3229,10475,3383,4541,10404,3919,4484,10266,10431,11227,12292,12326,12330,4491,12300,3267,11685,11688,12900,12996,13053,13057,13061,4530,10980,11050,11273,11276,3264,3384,3605,3376,3350,12508,3166,10333,10640,3167,4518,3442,3159,3087,3272,3189,11354,4066,12315,12446,3921,10986,11112,11162,12276,12282,12393,12396,12419,4553,10918,11117,11221,11243,11281,11287,12226,4554,11019,11120,11224,4555,11123,11173,4556,11176,4557,3188,3482,12182,12223,12299,3644,4350,4351,3465,4482,11345,3583,3622,3796,3552,12790,12794,12798,12802,12812,3842,12176,3468,3722,3347,10352,10470,10541,10602,10605,10643,10737,10970,11860,11923,12002,12042,12119,12122,12423,12608,12667,12710,12713,12755,12773,12999,13004,3733,11582,3260,3359,11700,12601,13101,3546,4524,10243,10246,10272,10745,10758,10876,11265,11357,11752,11757,11978,11981,12063,12072,12229,12319,12613,12632,12635,12659,12714,12878,12883,12907,12912,4536,11467,11498,11533,11562,12723,12727,3720,3491,3493,12638,12641,12644,12647,12681,12684,13036,13040,13044,13048,3494,3869,3454,13037,3455,13041,3306,3308,3281,4521,3165,4479,3672,4203,3988,3474,4537,4060,11238,3604,3320,11709,11712,12403,4030,3987,11853,12197,3931,12204,12426,13052,3976,13056,3982,10989,12078,12203,12903,3983,3645,11863,12009,12086,12132,4019,3663,10992,11055,11136,11195,12030,12100,12342,12416,12429,12869,4542,10761,11128,12207,12949,3276,10361,10457,10588,10650,10719,10764,10767,10800,10823,10860,10898,10934,11656,11703,11833,11888,11904,11907,11910,11913,12093,12107,12110,12113,12116,12190,12251,12353,12399,12660,12687,12765,12776,12781,12784,12787,12820,12833,12844,12893,12918,12921,3277,10390,10445,10655,10740,10863,11440,11737,11740,11749,11839,11850,11869,11874,11916,11939,11956,12678,12824,12847,12879,12884,12908,12913,13023,3280,3355,12066,12743,12791,12795,12799,12803,12813,12817,4520,10309,10399,10512,10536,10782,10826,10836,11512,11610,11631,11634,11637,11653,11807,11810,11813,11816,11900,11919,11922,11935,11990,11993,11996,11999,12073,12161,12164,12254,12257,12318,12346,12383,12466,3437,10608,10871,10915,11184,11262,11425,11665,12295,12469,12865,12935,12982,4532,10791,10803,10907,10925,10928,10983,11069,11077,11093,11131,11148,11156,11192,11233,11253,11256,11259,11290,11297,11300,11682,11718,11984,11987,12021,12067,12096,12235,12273,12279,12365,12368,12389,12445,12451,12460,12479,12742,12759,12762,12854,12936,12974,12989,12992,13033,13077,13080,3341,10637,10667,10676,11213,11764,12384,12400,12724,12728,12731,3379,13013,13074,3373,3800,3738,10312,11585,11613,12705,4529,10263,10625,10628,11072,11090,11548,11601,11641,11666,11770,11795,11798,11801,11804,12062,12924,3300,10670,10820,10891,11614,11769,11961,12169,12191,12752,13016,13100,3761,11715,12654,4110,3497,4527,3772,3808,4510,4513,4514,3251,3255,4512,3174,4511,4515,4286,3779,3594,11578,4209,11447,4544,10234,10237,10493,10544,10547,10552,10957,11419,11669,11773,4551,11151,11270,11306,3996,12218,3886,11303,11640,11644,11706,12303,12311,12392,12672,12930,12978,3727,10931,10937,10952,11885,12014,12099,12361,3579,12125,12232,12241,12308,12356,12364,12476,12872,3617,4064,3729,10673,11008,11159,11189,11200,12034,12307,12350,12966,3547,10591,10594,10679,10847,3549,4548,11579,4538,4543,12622,4549,10730,10829,11139,11422,11453,12185,12194,12238,12413,4170,10806,12215,4071,3760,12482,3707,3708,4546,10285,10288,10631,10634,11464,11645,12422,4547,11559,11650,3731,10597,10853,13003,4003,4568,4594,4643,4645,4675,4692,4699,4700,4739,4769,4775,4860,4885,4886,4921,4946,4947,4969,4970,4983,4987,5010,5017,5035,5038,5039,5040,5045,5046,5068,5093,5094,5104,5109,5115,5160,5161,5169,5178,5183,5185,5195,5197,5203,5207,5222,5229,5232,5233,5234,5238,5274,5287,5295,5297,5298,5302,5303,5304,5312,5315,5319,5320,5321,5328,5332,5333,5334,5342,5346,5347,5348,5353,5366,5375,5387,5389,5397,5398,5402,5406,5431,5437,5447,5448,5463,5475,5497,5503,5519,5520,5523,5542,5550,5551,5556,5557,5567,5569,5581,5585,5594,5595,5597,5612,5617,5627,5628,5640,5647,5661,5665,5668,5674,5675,5676,5679,5684,5722,5723,5726,5728,5731,5732,5733,5735,5737,5739,5744,5751,5766,5780,5785,5786,5799,5800,5805,5809,5811,5816,5857,5869,5878,5882,5893,5897,5898,5906,5920,5926,5944,5947,5959,5985,5999,6024,6044,6045,6048,6062,6064,6066,6068,6081,6082,6085,6087,6090,6091,6103,6109,6110,6111,6113,6115,6158,6159,6166,6172,6176,6212,6214,6216,6218,6227,6229,6231,6237,6239,6245,6248,6256,6263,6264,6265,6270,6292,6293,6294,6296,6302,6307,6341,6342,6344,6345,6346,6348,6349,6350,6351,6358,6391,6392,6401,6422,6423,6443,6446,6457,6458,6464,6495,6497,6511,6549,6551,6552,6606,6630,6672,6692,6701,6702,6703,6704,6723,6724,6730,6743,6746,6748,6750,6751,6752,6754,6768,6779,6781,6782,6795,6799,6850,6861,6863,6867,6884,6885,6921,6933,6964,6998,7052,7080,7135,7156,7165,7168,7223,7231,7289,7291,7306,7316,7317,7318,7337,7343,7345,7395,7405,7408,7424,7476,7478,7481,7524,7525,7543,7610,7629,7652,7676,7691,7706,7717,7726,7727,7756,7759,7761,7771,7809,7820,7845,7903,7937,7969,8016,8032,8048,8049,8124,8177,8196,8220,8240,8264,8362,8364,8370,8386,8390,8406,8429,8440,8442,8457,8463,8467,8490,8504,8505,8521,8522,8527,8528,8529,8530,8531,8549,8550,8551,8559,8573,8575,8587,8591,8593,8594,8595,8603,8608,8635,8636,8668,8681,8685,8703,8725,8726,8727,8728,8740,8741,8763,8773,8783,8784,8785,8786,8788,8809,8810,8821,8865,8871,8877,8889,8894,8896,8899,8900,8904,8914,8997,9028,9029,9030,9045,9063,9068,9096,9097,9138,9141,9167,9212,9213,9214,9229,9256,9270,9276,9279,9301,9302,9330,9391,9426,9427,9428,9453,9454,9472,9491,9497,9511,9534,9556,9564,9565,9566,9567,9582,9584,9589,9620,9621,9627,9628,9672,9673,9705,9714,9724,9726,9727,9736,9750,9753,9781,9814,9816,9820,9878,9919,9920,9922,9932,9933,9953,9958,9999,10050,10122,10123,10176,10192,2,8,9,4581,4582,4600,4631,4633,4634,4661,4667,4668,4679,4728,4730,4760,4774,4804,4900,4901,4914,4934,4990,4991,4994,4995,4997,4999,5000,5009,5013,5014,5024,5036,5037,5043,5063,5064,5081,5086,5087,5088,5089,5092,5100,5103,5110,5175,5181,5182,5189,5219,5230,5236,5252,5272,5273,5280,5281,5282,5291,5301,5308,5310,5311,5317,5324,5325,5338,5339,5340,5341,5343,5344,5349,5350,5351,5352,5383,5384,5385,5393,5394,5395,5396,5439,5444,5446,5482,5484,5485,5487,5488,5490,5491,5493,5502,5507,5509,5510,5511,5512,5513,5514,5521,5531,5534,5545,5561,5562,5565,5575,5577,5578,5579,5604,5614,5630,5631,5641,5642,5644,5646,5651,5686,5691,5693,5753,5787,5788,5792,5798,5801,5802,5803,5804,5810,5821,5822,5824,5825,5833,5854,5885,5901,5904,5905,5907,5916,5934,5938,5941,5942,5943,5961,5972,5973,6001,6002,6006,6026,6029,6033,6052,6057,6058,6083,6086,6094,6102,6108,6112,6119,6120,6121,6122,6161,6177,6230,6266,6268,6289,6290,6295,6299,6300,6303,6309,6318,6333,6353,6354,6359,6369,6384,6404,6410,6412,6427,6428,6431,6432,6434,6436,6437,6438,6440,6442,6445,6450,6451,6453,6454,6460,6462,6505,6510,6524,6526,6527,6528,6563,6568,6570,6575,6576,6584,6588,6601,6625,6626,6628,6629,6640,6646,6663,6666,6685,6718,6719,6720,6725,6739,6758,6760,6762,6764,6769,6775,6777,6792,6797,6800,6836,6837,6838,6852,6853,6855,6856,6875,6877,6893,6919,6941,6952,6954,6956,6958,6959,6960,6995,6996,7001,7002,7009,7010,7012,7014,7033,7042,7043,7055,7065,7104,7114,7118,7125,7136,7142,7144,7150,7158,7159,7172,7189,7207,7209,7226,7275,7276,7277,7279,7281,7285,7290,7313,7358,7391,7406,7423,7456,7459,7485,7509,7526,7529,7530,7540,7559,7561,7563,7565,7566,7567,7592,7618,7619,7651,7653,7654,7655,7660,7683,7692,7703,7708,7714,7716,7722,7734,7735,7737,7762,7769,7792,7858,7859,7906,7914,7915,7939,7940,7957,7958,8023,8024,8051,8080,8091,8093,8102,8114,8146,8152,8159,8172,8191,8197,8219,8262,8292,8304,8322,8325,8355,8378,8443,8444,8447,8449,8553,8554,8555,8556,8582,8611,8639,8684,8702,8757,8802,8805,8818,8825,8862,8910,8911,8929,8930,9070,9074,9094,9104,9127,9129,9132,9136,9139,9140,9153,9154,9174,9180,9192,9240,9241,9260,9314,9315,9322,9383,9388,9423,9430,9433,9436,9437,9452,9468,9477,9487,9490,9500,9501,9504,9506,9532,9655,9699,9700,9743,9788,9905,9962,10027,10101,10114,10119,3,2614,2616,2617,2618,2619,2620,2621,2628,2629,2630,2631,2636,2637,2638,2639,2644,2651,2652,2657,2658,2659,2661,2662,2663,2666,2667,2668,2670,2671,2674,2675,2676,2681,2682,2687,2688,2689,2695,2696,2697,2702,2703,2705,2706,2710,2712,2713,2716,2718,2719,2721,2723,2726,2735,2736,2737,2764,2767,2789,2792,2793,2794,2801,2803,2805,2807,2819,2820,2822,2829,5211,5271,5369,5455,5456,5457,5532,5629,5660,5694,5710,5712,5718,5781,5782,5783,5784,5790,5823,5956,5991,6000,6023,6060,6095,6100,6247,6252,6287,6288,6308,6311,6313,6320,6321,6322,6323,6324,6325,6326,6327,6406,6474,6475,6562,6595,6596,6637,6638,6776,6791,6864,6865,6872,6894,6917,6925,6927,6974,6999,7000,7018,7019,7054,7098,7099,7196,7257,7258,7259,7260,7274,7307,7363,7364,7373,7381,7382,7394,7426,7427,7428,7429,7573,7574,7576,7578,7584,7585,7800,7806,7807,7817,7856,7935,7977,8035,8056,8057,8072,8131,8233,8302,8303,8305,8340,8402,8403,8476,8497,8498,8499,8500,8643,8855,8879,8880,8961,8976,9031,9032,9148,9184,9207,9242,9284,9475,9737,9931,9987,9989,6018,6389,6390,6477,6498,6499,6916,7134,8287,8568,8601,8796,8987,8988,9059,9060,9332,9333,9334,9335,9535,9808,10110,10161,10162,6459,8393,8394,8845,8863,9809,10160,4635,4637,4638,4693,4701,4838,4854,4855,4883,4884,4913,4968,5031,5090,5168,5204,5206,5214,5215,5241,5316,5337,5471,5537,5538,5539,5656,5657,5683,5687,5747,5749,5758,5764,5836,5914,6041,6067,6233,6352,6508,6710,6711,6928,6969,7140,7365,7435,7776,7778,7872,8033,8803,9062,9298,9570,4868,4915,5056,5888])).
% 187.39/188.10 cnf(13317,plain,
% 187.39/188.10 (~P24(f329(f329(f193(f881(x133171,f881(x133172,a869))),x133173),x133174))),
% 187.39/188.10 inference(rename_variables,[],[4549])).
% 187.39/188.10 cnf(13322,plain,
% 187.39/188.10 (~E(f329(f329(f149(x133221),x133222),x133223),x133223)),
% 187.39/188.10 inference(rename_variables,[],[4484])).
% 187.39/188.10 cnf(13334,plain,
% 187.39/188.10 (P24(f329(f329(f243(f881(x133341,a869)),f329(f171(x133341),f329(f134(x133341,x133342),x133343))),f329(f171(x133341),x133343)))),
% 187.39/188.10 inference(rename_variables,[],[3931])).
% 187.39/188.10 cnf(13341,plain,
% 187.39/188.10 (~P24(f329(f329(f331(a874),x133411),f329(f250(a874),f2(a874))))),
% 187.39/188.10 inference(rename_variables,[],[11734])).
% 187.39/188.10 cnf(13346,plain,
% 187.39/188.10 (~P24(f329(f329(f331(x133461),x133462),f193(f881(x133461,a869))))),
% 187.39/188.10 inference(rename_variables,[],[4532])).
% 187.39/188.10 cnf(13353,plain,
% 187.39/188.10 (P24(f329(f329(f243(f881(x133531,a869)),x133532),x133532))),
% 187.39/188.10 inference(rename_variables,[],[3579])).
% 187.39/188.10 cnf(13363,plain,
% 187.39/188.10 (~E(f329(f329(f149(x133631),x133632),x133633),x133633)),
% 187.39/188.10 inference(rename_variables,[],[4484])).
% 187.39/188.10 cnf(13386,plain,
% 187.39/188.10 (~P39(x133861,x133862,x133863,f329(f329(f152(x133864,x133861),x133865),f329(a117,f118(x133864))),f118(x133862))),
% 187.39/188.10 inference(rename_variables,[],[11164])).
% 187.39/188.10 cnf(13389,plain,
% 187.39/188.10 (~E(f329(f329(f149(x133891),x133892),x133893),x133893)),
% 187.39/188.10 inference(rename_variables,[],[4484])).
% 187.39/188.10 cnf(13394,plain,
% 187.39/188.10 (~P24(f329(f329(f331(x133941),x133942),f193(f881(x133941,a869))))),
% 187.39/188.10 inference(rename_variables,[],[4532])).
% 187.39/188.10 cnf(13415,plain,
% 187.39/188.10 (~E(f329(a117,x134151),f2(a874))),
% 187.39/188.10 inference(rename_variables,[],[4469])).
% 187.39/188.10 cnf(13418,plain,
% 187.39/188.10 (P24(f329(f329(f243(a874),f2(a874)),x134181))),
% 187.39/188.10 inference(rename_variables,[],[3300])).
% 187.39/188.10 cnf(13421,plain,
% 187.39/188.10 (~P24(f329(f329(f243(a874),f329(f329(f81(a874),f329(a117,x134211)),f329(a117,x134211))),x134211))),
% 187.39/188.10 inference(rename_variables,[],[10678])).
% 187.39/188.10 cnf(13428,plain,
% 187.39/188.10 (P24(f329(f329(f244(a1),f329(f329(f22(a1),x134281),f78(a1))),x134281))),
% 187.39/188.10 inference(rename_variables,[],[10739])).
% 187.39/188.10 cnf(13433,plain,
% 187.39/188.10 (P24(f329(f329(f243(f881(x134331,a869)),x134332),x134332))),
% 187.39/188.10 inference(rename_variables,[],[3579])).
% 187.39/188.10 cnf(13436,plain,
% 187.39/188.10 (~P24(f329(f329(f331(x134361),x134362),f193(f881(x134361,a869))))),
% 187.39/188.10 inference(rename_variables,[],[4532])).
% 187.39/188.10 cnf(13458,plain,
% 187.39/188.10 (P24(f329(f329(f244(a874),x134581),f329(a117,f329(f329(f80(a874),x134582),x134581))))),
% 187.39/188.10 inference(rename_variables,[],[3731])).
% 187.39/188.10 cnf(13463,plain,
% 187.39/188.10 (E(f329(f260(x134631,x134631),f261(x134631,x134632)),x134632)),
% 187.39/188.10 inference(rename_variables,[],[3234])).
% 187.39/188.10 cnf(13470,plain,
% 187.39/188.10 (~P24(f329(f329(f243(a874),f329(f329(f81(a874),f329(a117,x134701)),f329(a117,x134701))),x134701))),
% 187.39/188.10 inference(rename_variables,[],[10678])).
% 187.39/188.10 cnf(13481,plain,
% 187.39/188.10 (P24(f329(f329(f243(a874),x134811),f329(f329(f81(a874),x134811),x134811)))),
% 187.39/188.10 inference(rename_variables,[],[3547])).
% 187.39/188.10 cnf(13484,plain,
% 187.39/188.10 (~P24(f329(f329(f244(a874),f329(f329(f80(a874),x134841),x134842)),x134841))),
% 187.39/188.10 inference(rename_variables,[],[4547])).
% 187.39/188.10 cnf(13487,plain,
% 187.39/188.10 (~P24(f329(f329(f331(f880(x134871,x134871)),x134872),f261(x134871,f193(f881(x134871,a869)))))),
% 187.39/188.10 inference(rename_variables,[],[10924])).
% 187.39/188.10 cnf(13492,plain,
% 187.39/188.10 (~P24(f329(f329(f331(f880(x134921,x134921)),x134922),f261(x134921,f193(f881(x134921,a869)))))),
% 187.39/188.10 inference(rename_variables,[],[10924])).
% 187.39/188.10 cnf(13497,plain,
% 187.39/188.10 (E(f329(x134971,f711(f329(x134971,x134972),f329(f236(x134973),x134972),x134971,x134974,x134973)),f329(x134971,x134972))),
% 187.39/188.10 inference(rename_variables,[],[11103])).
% 187.39/188.10 cnf(13508,plain,
% 187.39/188.10 (~P24(f329(f329(f243(a874),f329(a117,x135081)),x135081))),
% 187.39/188.10 inference(rename_variables,[],[4529])).
% 187.39/188.10 cnf(13511,plain,
% 187.39/188.10 (~P24(f329(f329(f243(a874),f329(a117,x135111)),x135111))),
% 187.39/188.10 inference(rename_variables,[],[4529])).
% 187.39/188.10 cnf(13514,plain,
% 187.39/188.10 (~P24(f329(f329(f331(a874),x135141),f329(f250(a874),f2(a874))))),
% 187.39/188.10 inference(rename_variables,[],[11734])).
% 187.39/188.10 cnf(13517,plain,
% 187.39/188.10 (P24(f329(f329(f243(a874),x135171),f329(f329(f80(a874),x135171),x135172)))),
% 187.39/188.10 inference(rename_variables,[],[3549])).
% 187.39/188.10 cnf(13540,plain,
% 187.39/188.10 (P24(f329(f329(f329(f329(a201,a24),x135401),x135402),x135401))),
% 187.39/188.10 inference(rename_variables,[],[3617])).
% 187.39/188.10 cnf(13543,plain,
% 187.39/188.10 (~P24(f329(f329(f331(f880(x135431,x135431)),x135432),f261(x135431,f193(f881(x135431,a869)))))),
% 187.39/188.10 inference(rename_variables,[],[10924])).
% 187.39/188.10 cnf(13546,plain,
% 187.39/188.10 (~P24(f329(f329(f243(a874),f329(f329(f81(a874),f329(a117,x135461)),f329(a117,x135461))),x135461))),
% 187.39/188.10 inference(rename_variables,[],[10678])).
% 187.39/188.10 cnf(13549,plain,
% 187.39/188.10 (~P24(f329(f329(f193(f881(x135491,f881(x135492,a869))),x135493),x135494))),
% 187.39/188.10 inference(rename_variables,[],[4549])).
% 187.39/188.10 cnf(13570,plain,
% 187.39/188.10 (~P24(f329(f329(f331(x135701),x135702),f193(f881(x135701,a869))))),
% 187.39/188.10 inference(rename_variables,[],[4532])).
% 187.39/188.10 cnf(13575,plain,
% 187.39/188.10 (~P24(f329(f329(f331(f880(x135751,x135751)),x135752),f261(x135751,f193(f881(x135751,a869)))))),
% 187.39/188.10 inference(rename_variables,[],[10924])).
% 187.39/188.10 cnf(13578,plain,
% 187.39/188.10 (E(f329(x135781,f711(f329(x135781,x135782),f329(f236(x135783),x135782),x135781,x135784,x135783)),f329(x135781,x135782))),
% 187.39/188.10 inference(rename_variables,[],[11103])).
% 187.39/188.10 cnf(13583,plain,
% 187.39/188.10 (~E(f329(f329(f106(a874),f329(a117,x135831)),x135831),f329(a117,x135831))),
% 187.39/188.10 inference(rename_variables,[],[11483])).
% 187.39/188.10 cnf(13586,plain,
% 187.39/188.10 (~P24(f329(f329(f331(x135861),x135862),f193(f881(x135861,a869))))),
% 187.39/188.10 inference(rename_variables,[],[4532])).
% 187.39/188.10 cnf(13595,plain,
% 187.39/188.10 (~P24(f329(f329(f243(a874),f329(a117,x135951)),x135951))),
% 187.39/188.10 inference(rename_variables,[],[4529])).
% 187.39/188.10 cnf(13600,plain,
% 187.39/188.10 (~P24(f329(f329(f331(a874),x136001),f329(f250(a874),f2(a874))))),
% 187.39/188.10 inference(rename_variables,[],[11734])).
% 187.39/188.10 cnf(13608,plain,
% 187.39/188.10 (~P24(f329(f329(f331(x136081),x136082),f193(f881(x136081,a869))))),
% 187.39/188.10 inference(rename_variables,[],[4532])).
% 187.39/188.10 cnf(13613,plain,
% 187.39/188.10 (P24(f329(f329(f331(x136131),f329(x136132,x136133)),f329(f308(x136134,x136131,x136132),f252(f881(x136134,a869)))))),
% 187.39/188.10 inference(rename_variables,[],[3886])).
% 187.39/188.10 cnf(13618,plain,
% 187.39/188.10 (~P24(f329(f329(f331(a874),x136181),f329(f250(a874),f2(a874))))),
% 187.39/188.10 inference(rename_variables,[],[11734])).
% 187.39/188.10 cnf(13625,plain,
% 187.39/188.10 (~E(f329(f329(f149(x136251),x136252),x136253),x136253)),
% 187.39/188.10 inference(rename_variables,[],[4484])).
% 187.39/188.10 cnf(13630,plain,
% 187.39/188.10 (E(f329(x136301,f711(f329(x136301,x136302),f329(f236(x136303),x136302),x136301,x136304,x136303)),f329(x136301,x136302))),
% 187.39/188.10 inference(rename_variables,[],[11103])).
% 187.39/188.10 cnf(13647,plain,
% 187.39/188.10 (E(f329(f260(x136471,x136471),f261(x136471,x136472)),x136472)),
% 187.39/188.10 inference(rename_variables,[],[3234])).
% 187.39/188.10 cnf(13662,plain,
% 187.39/188.10 (~E(f329(f329(f149(x136621),x136622),x136623),x136623)),
% 187.39/188.10 inference(rename_variables,[],[4484])).
% 187.39/188.10 cnf(13673,plain,
% 187.39/188.10 (~P24(f329(f329(f193(f881(x136731,f881(x136732,a869))),x136733),x136734))),
% 187.39/188.10 inference(rename_variables,[],[4549])).
% 187.39/188.10 cnf(13678,plain,
% 187.39/188.10 (P24(f329(f329(f244(a1),f329(f329(f22(a1),x136781),f78(a1))),x136781))),
% 187.39/188.10 inference(rename_variables,[],[10739])).
% 187.39/188.10 cnf(13681,plain,
% 187.39/188.10 (~P24(f329(f329(f331(x136811),x136812),f193(f881(x136811,a869))))),
% 187.39/188.10 inference(rename_variables,[],[4532])).
% 187.39/188.10 cnf(13684,plain,
% 187.39/188.10 (~E(f329(f329(f149(x136841),x136842),x136843),x136843)),
% 187.39/188.10 inference(rename_variables,[],[4484])).
% 187.39/188.10 cnf(13689,plain,
% 187.39/188.10 (~P24(f329(f329(f331(x136891),x136892),f329(f309(x136891,x136893,x136894),f193(f881(x136893,a869)))))),
% 187.39/188.10 inference(rename_variables,[],[10927])).
% 187.39/188.10 cnf(13697,plain,
% 187.39/188.10 (~P24(f329(f329(f331(x136971),x136972),f329(f309(x136971,x136973,x136974),f193(f881(x136973,a869)))))),
% 187.39/188.10 inference(rename_variables,[],[10927])).
% 187.39/188.10 cnf(13707,plain,
% 187.39/188.10 (P24(f329(f329(f329(f329(a201,a24),x137071),x137072),x137071))),
% 187.39/188.10 inference(rename_variables,[],[3617])).
% 187.39/188.10 cnf(13720,plain,
% 187.39/188.10 (~P24(f329(f329(f331(f880(x137201,x137201)),x137202),f261(x137201,f193(f881(x137201,a869)))))),
% 187.39/188.10 inference(rename_variables,[],[10924])).
% 187.39/188.10 cnf(13725,plain,
% 187.39/188.10 (~P24(f329(f329(f331(x137251),x137252),f193(f881(x137251,a869))))),
% 187.39/188.10 inference(rename_variables,[],[4532])).
% 187.39/188.10 cnf(13730,plain,
% 187.39/188.10 (~P24(f329(f329(f331(a874),x137301),f329(f250(a874),f2(a874))))),
% 187.39/188.10 inference(rename_variables,[],[11734])).
% 187.39/188.10 cnf(13740,plain,
% 187.39/188.10 (P24(f329(f329(f243(a874),x137401),f329(f329(f81(a874),x137401),x137401)))),
% 187.39/188.10 inference(rename_variables,[],[3547])).
% 187.39/188.10 cnf(13763,plain,
% 187.39/188.10 (P24(f329(f329(f331(f880(x137631,x137631)),f329(f329(f264(x137631,x137631),x137632),x137632)),f305(x137631,x137633)))),
% 187.39/188.10 inference(rename_variables,[],[3921])).
% 187.39/188.10 cnf(13771,plain,
% 187.39/188.10 (P24(f329(f329(f243(f881(x137711,a869)),x137712),x137712))),
% 187.39/188.10 inference(rename_variables,[],[3579])).
% 187.39/188.10 cnf(13776,plain,
% 187.39/188.10 (~P24(f329(f329(f331(x137761),x137762),f193(f881(x137761,a869))))),
% 187.39/188.10 inference(rename_variables,[],[4532])).
% 187.39/188.10 cnf(13781,plain,
% 187.39/188.10 (P24(f329(f329(f243(a874),x137811),f329(f329(f81(a874),x137811),x137811)))),
% 187.39/188.10 inference(rename_variables,[],[3547])).
% 187.39/188.10 cnf(13813,plain,
% 187.39/188.10 (~P24(f329(f329(f331(a874),x138131),f329(f250(a874),f2(a874))))),
% 187.39/188.10 inference(rename_variables,[],[11734])).
% 187.39/188.10 cnf(13816,plain,
% 187.39/188.10 (~P24(f329(f329(f331(f880(x138161,x138161)),x138162),f261(x138161,f193(f881(x138161,a869)))))),
% 187.39/188.10 inference(rename_variables,[],[10924])).
% 187.39/188.10 cnf(13819,plain,
% 187.39/188.10 (~P24(f329(f329(f331(x138191),x138192),f193(f881(x138191,a869))))),
% 187.39/188.10 inference(rename_variables,[],[4532])).
% 187.39/188.10 cnf(13827,plain,
% 187.39/188.10 (~E(x138271,f329(a117,x138271))),
% 187.39/188.10 inference(rename_variables,[],[10295])).
% 187.39/188.10 cnf(13834,plain,
% 187.39/188.10 (E(f329(f329(f126(x138341),x138342),f118(x138341)),x138342)),
% 187.39/188.10 inference(rename_variables,[],[3206])).
% 187.39/188.10 cnf(13844,plain,
% 187.39/188.10 (E(f329(f329(f126(x138441),x138442),f118(x138441)),x138442)),
% 187.39/188.10 inference(rename_variables,[],[3206])).
% 187.39/188.10 cnf(13859,plain,
% 187.39/188.10 (~P24(f329(f329(f331(f880(f875(x138591),f875(x138591))),f329(f329(f264(f875(x138591),f875(x138591)),x138592),f118(x138591))),f143(x138591,x138593)))),
% 187.39/188.10 inference(rename_variables,[],[4553])).
% 187.39/188.10 cnf(13877,plain,
% 187.39/188.10 (~P24(f329(f329(f331(f880(f875(x138771),f875(x138771))),f329(f329(f264(f875(x138771),f875(x138771)),x138772),f118(x138771))),f145(x138771,x138773)))),
% 187.39/188.10 inference(rename_variables,[],[4554])).
% 187.39/188.10 cnf(13880,plain,
% 187.39/188.10 (~P24(f329(f329(f244(a874),f329(f329(f80(a874),x138801),x138802)),x138801))),
% 187.39/188.10 inference(rename_variables,[],[4547])).
% 187.39/188.10 cnf(13885,plain,
% 187.39/188.10 (~E(f329(f329(f149(x138851),x138852),x138853),x138853)),
% 187.39/188.10 inference(rename_variables,[],[4484])).
% 187.39/188.10 cnf(13898,plain,
% 187.39/188.10 (P39(x138981,x138982,x138983,f329(f329(f152(x138984,x138981),x138985),f119(x138984,f118(x138984))),f118(x138982))),
% 187.39/188.10 inference(rename_variables,[],[11168])).
% 187.39/188.10 cnf(13916,plain,
% 187.39/188.10 (P24(f329(f329(f243(f881(x139161,a869)),x139162),x139162))),
% 187.39/188.10 inference(rename_variables,[],[3579])).
% 187.39/188.10 cnf(13919,plain,
% 187.39/188.10 (~P24(f329(f329(f331(x139191),x139192),f193(f881(x139191,a869))))),
% 187.39/188.10 inference(rename_variables,[],[4532])).
% 187.39/188.10 cnf(13934,plain,
% 187.39/188.10 (~E(f329(f329(f149(x139341),x139342),x139343),x139343)),
% 187.39/188.10 inference(rename_variables,[],[4484])).
% 187.39/188.10 cnf(13966,plain,
% 187.39/188.10 (E(f329(f260(x139661,x139661),f261(x139661,x139662)),x139662)),
% 187.39/188.10 inference(rename_variables,[],[3234])).
% 187.39/188.10 cnf(13971,plain,
% 187.39/188.10 (E(f329(f260(x139711,x139711),f261(x139711,x139712)),x139712)),
% 187.39/188.10 inference(rename_variables,[],[3234])).
% 187.39/188.10 cnf(13974,plain,
% 187.39/188.10 (~P24(f329(f329(f193(f881(x139741,f881(x139742,a869))),x139743),x139744))),
% 187.39/188.10 inference(rename_variables,[],[4549])).
% 187.39/188.10 cnf(13979,plain,
% 187.39/188.10 (P24(f329(f329(f331(x139791),f329(x139792,x139793)),f329(f308(x139794,x139791,x139792),f252(f881(x139794,a869)))))),
% 187.39/188.10 inference(rename_variables,[],[3886])).
% 187.39/188.10 cnf(13989,plain,
% 187.39/188.10 (P24(f329(f329(f243(f881(x139891,a869)),x139892),x139892))),
% 187.39/188.10 inference(rename_variables,[],[3579])).
% 187.39/188.10 cnf(13994,plain,
% 187.39/188.10 (P24(f329(f329(f243(a874),x139941),f329(f329(f81(a874),x139941),x139941)))),
% 187.39/188.10 inference(rename_variables,[],[3547])).
% 187.39/188.10 cnf(14014,plain,
% 187.39/188.10 (~P24(f329(f329(f331(f880(x140141,x140141)),x140142),f261(x140141,f193(f881(x140141,a869)))))),
% 187.39/188.10 inference(rename_variables,[],[10924])).
% 187.39/188.10 cnf(14017,plain,
% 187.39/188.10 (~P24(f329(f329(f331(f880(x140171,x140171)),x140172),f261(x140171,f193(f881(x140171,a869)))))),
% 187.39/188.10 inference(rename_variables,[],[10924])).
% 187.39/188.10 cnf(14025,plain,
% 187.39/188.10 (~P24(f329(f329(f331(a874),x140251),f329(f250(a874),f2(a874))))),
% 187.39/188.10 inference(rename_variables,[],[11734])).
% 187.39/188.10 cnf(14138,plain,
% 187.39/188.10 ($false),
% 187.39/188.10 inference(scs_inference,[],[3306,3720,3308,3869,4066,3065,4548,3281,4510,4536,4030,3921,13763,3355,4553,13859,4512,3373,3733,4532,13346,13394,13436,13570,13586,13608,13681,13725,13776,13819,13919,3379,3886,13613,13979,3617,13540,13707,3383,4474,4469,13415,4541,4484,13322,13363,13389,13625,13662,13684,13885,13934,3260,3359,4060,3987,3931,13334,3276,3277,3738,3300,13418,3594,3727,3579,13353,13433,13771,13916,13989,3547,13481,13740,13781,13994,3549,13517,4170,3731,13458,3234,13463,13647,13966,13971,3206,13834,13844,3116,3644,4554,13877,4555,4557,4520,4529,13508,13511,13595,4538,4543,4549,13317,13549,13673,13974,4546,4547,13484,13880,3490,11483,13583,10295,13827,13006,10562,13191,10349,12615,11792,11832,12408,11294,13173,13091,12193,10593,11838,12656,13093,10581,12669,11035,12410,12441,12448,10914,11135,10878,10739,13428,13678,11736,3647,10909,11199,11158,11103,13497,13578,13630,13121,10274,12929,10408,11278,11247,10683,10524,3338,3311,3218,11101,11181,12917,12920,13187,10688,13171,13207,11616,12138,12127,11125,12231,10259,12675,11734,13341,13514,13600,13618,13730,13813,14025,13240,10696,11089,10924,13487,13492,13543,13575,13720,13816,14014,14017,12050,10927,13689,13697,11130,10678,13421,13470,13546,10781,11989,11992,12464,12376,13195,11164,13386,11168,13898,2887,2,5731,5959,5298,6779,8406,6293,5328,6933,5287,6044,8763,5346,6724,4838,5169,9534,8370,8551,7761,4775,5628,5786,6349,6998,8725,9428,5321,6081,7052,9736,4594,8591,6672,7405,5749,5398,7343,6263,8783,5471,5785,5811,6296,6214,5229,6348,5595,5679,9472,9427,6067,8264,8,6768,8914,5594,5722,9063,5402,6231,8997,8048,5758,5295,6212,5676,6748,7435,5523,7706,6218,9781,5675,10123,9565,5214,5431,9922,6704,5744,5780,5878,9750,6302,5017,6115,6358,7165,4769,5337,9999,5551,5735,6245,8467,8821,4886,9298,5687,8899,9141,6159,5537,9814,6352,5185,9816,8364,9212,4635,4739,8463,8703,5348,8809,5241,5406,6172,6710,5316,8531,8559,8741,7424,5519,8785,4970,6158,8595,6701,4638,7316,5448,6109,6751,6884,8220,8521,5093,6307,7140,6754,7289,8196,4692,5661,8529,5204,5040,5920,8549,6401,9621,4921,5161,7756,9628,8575,9214,9919,6062,5197,5627,5674,7478,9567,4854,9753,5315,9932,9330,7903,5389,5869,6085,6730,9279,6511,4947,8504,5039,5366,9564,8668,5447,5475,9213,9270,6248,7809,5947,8016,8522,6928,5232,9566,9878,5160,5206,6464,6850,7727,7395,5897,4699,8784,8786,9028,4968,8390,8685,5640,9,5334,6068,7168,5234,5333,9391,8810,6176,7291,9426,9958,9138,9726,5031,8177,8608,5010,6350,9724,5104,5914,5302,6110,6111,5045,6746,8587,5195,5297,8530,8240,9589,5520,9511,9953,6443,6861,8894,9454,5747,5597,4643,5215,6233,7337,9062,9933,8593,5312,6113,5463,6964,5168,9301,4568,5387,6341,6723,6885,8603,6091,5503,5882,9229,10176,6863,8049,8594,4860,7771,6495,6799,7525,10122,10192,7543,7969,8803,4946,6422,6743,7476,4913,8528,4693,5094,6702,6711,5944,5304,8773,9045,9097,5668,6342,8442,9068,5353,5723,6606,5893,7135,8490,8865,6256,4645,5397,5233,5665,9302,5836,9556,5799,6391,6703,7365,8877,9030,8440,5274,6457,6458,5898,8636,4675]),
% 187.39/188.10 ['proof']).
% 187.39/188.10 % SZS output end Proof
% 187.39/188.10 % Total time :173.110000s
%------------------------------------------------------------------------------