TSTP Solution File: SCT165+1 by CSE---1.6
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SCT165+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% Computer : n023.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 : Thu Aug 31 14:10:20 EDT 2023
% Result : Theorem 1.50s 1.46s
% Output : CNFRefutation 1.50s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SCT165+1 : TPTP v8.1.2. Released v5.2.0.
% 0.12/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.13/0.34 % Computer : n023.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 24 15:22:57 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.58 start to proof:theBenchmark
% 1.32/1.41 %-------------------------------------------
% 1.32/1.41 % File :CSE---1.6
% 1.32/1.41 % Problem :theBenchmark
% 1.32/1.41 % Transform :cnf
% 1.32/1.41 % Format :tptp:raw
% 1.32/1.41 % Command :java -jar mcs_scs.jar %d %s
% 1.32/1.41
% 1.32/1.41 % Result :Theorem 0.250000s
% 1.32/1.41 % Output :CNFRefutation 0.250000s
% 1.32/1.41 %-------------------------------------------
% 1.32/1.42 %------------------------------------------------------------------------------
% 1.32/1.42 % File : SCT165+1 : TPTP v8.1.2. Released v5.2.0.
% 1.32/1.42 % Domain : Social Choice Theory
% 1.32/1.42 % Problem : Arrow's Impossibility Theorem 433653, 500 axioms selected
% 1.32/1.42 % Version : Especial.
% 1.32/1.42 % English :
% 1.32/1.42
% 1.32/1.42 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% 1.32/1.42 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% 1.32/1.42 % Source : [Bla11]
% 1.32/1.42 % Names : arrow_433653.500.p [Bla11]
% 1.32/1.42
% 1.32/1.42 % Status : ContradictoryAxioms
% 1.32/1.42 % Rating : 0.53 v8.1.0, 0.58 v7.5.0, 0.56 v7.4.0, 0.60 v7.3.0, 0.55 v7.1.0, 0.57 v7.0.0, 0.53 v6.4.0, 0.58 v6.3.0, 0.62 v6.2.0, 0.68 v6.1.0, 0.73 v6.0.0, 0.65 v5.5.0, 0.78 v5.4.0, 0.79 v5.3.0, 0.78 v5.2.0
% 1.32/1.42 % Syntax : Number of formulae : 533 ( 120 unt; 0 def)
% 1.32/1.42 % Number of atoms : 1422 ( 334 equ)
% 1.32/1.42 % Maximal formula atoms : 17 ( 2 avg)
% 1.32/1.42 % Number of connectives : 1048 ( 159 ~; 27 |; 55 &)
% 1.32/1.42 % ( 128 <=>; 679 =>; 0 <=; 0 <~>)
% 1.32/1.42 % Maximal formula depth : 16 ( 6 avg)
% 1.32/1.42 % Maximal term depth : 16 ( 2 avg)
% 1.32/1.42 % Number of predicates : 35 ( 34 usr; 0 prp; 1-6 aty)
% 1.32/1.42 % Number of functors : 61 ( 61 usr; 24 con; 0-6 aty)
% 1.32/1.42 % Number of variables : 1540 (1528 !; 12 ?)
% 1.32/1.42 % SPC : FOF_CAX_RFO_SEQ
% 1.32/1.42
% 1.32/1.42 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 1.32/1.42 % 2011-03-01 11:30:23
% 1.32/1.42 % : Renamed from SWW167+1
% 1.32/1.42 %------------------------------------------------------------------------------
% 1.32/1.42 %----Relevant facts (491)
% 1.32/1.42 fof(fact_ext,axiom,
% 1.32/1.42 ! [V_g_2,V_f_2] :
% 1.32/1.42 ( ! [B_x] : hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x)
% 1.32/1.42 => V_f_2 = V_g_2 ) ).
% 1.32/1.42
% 1.32/1.42 fof(fact_assms_I3_J,axiom,
% 1.32/1.42 c_Arrow__Order__Mirabelle_OIIA(v_F) ).
% 1.32/1.42
% 1.32/1.42 fof(fact_u,axiom,
% 1.32/1.42 c_Arrow__Order__Mirabelle_Ounanimity(v_F) ).
% 1.32/1.42
% 1.32/1.42 fof(fact__096a_A_126_061_Ab_096,axiom,
% 1.32/1.42 v_a____ != v_b____ ).
% 1.32/1.42
% 1.32/1.42 fof(fact__096c_A_126_061_Ad_096,axiom,
% 1.32/1.42 v_c____ != v_d____ ).
% 1.32/1.42
% 1.32/1.42 fof(fact__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096,axiom,
% 1.32/1.42 hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lab____)) ).
% 1.32/1.42
% 1.32/1.42 fof(fact__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096,axiom,
% 1.32/1.42 hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____)) ).
% 1.32/1.42
% 1.32/1.42 fof(fact__096_Ia_M_Ab_J_A_126_058_ALba_096,axiom,
% 1.32/1.42 ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lba____)) ).
% 1.32/1.42
% 1.32/1.42 fof(fact__096_Ib_M_Aa_J_A_126_058_ALab_096,axiom,
% 1.32/1.42 ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____)) ).
% 1.32/1.42
% 1.32/1.42 fof(fact__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_092_060_094esub_062_Ae_J_A_061_A_Ia_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_A_L_A1_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Ab_J_096,axiom,
% 1.32/1.42 ! [B_i] :
% 1.32/1.42 ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,B_i)),v_n____))
% 1.32/1.42 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,B_i)),v_e____))) )
% 1.32/1.42 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,B_i)),v_n____))
% 1.32/1.42 => ( ( hAPP(v_h____,B_i) = v_n____
% 1.32/1.42 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,B_i)),v_c____),v_e____))) )
% 1.32/1.42 & ( hAPP(v_h____,B_i) != v_n____
% 1.32/1.42 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,B_i)),v_e____))) ) ) ) )
% 1.32/1.42 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,B_i)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
% 1.32/1.42 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lab____)) )
% 1.32/1.42 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,B_i)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
% 1.32/1.42 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lba____)) ) ) ) ).
% 1.32/1.42
% 1.32/1.42 fof(fact_n_I3_J,axiom,
% 1.32/1.42 hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),v_Lab____)),v_Lba____)))) ).
% 1.32/1.42
% 1.32/1.42 fof(fact_n_I2_J,axiom,
% 1.32/1.42 ! [B_m] :
% 1.32/1.42 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m),v_n____))
% 1.32/1.42 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),B_m))),v_Lab____)),v_Lba____)))) ) ).
% 1.32/1.42
% 1.32/1.42 fof(fact_in__mkbot,axiom,
% 1.32/1.42 ! [V_z_2,V_L_2,V_y_2,V_x_2] :
% 1.32/1.42 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_y_2)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,V_L_2),V_z_2)))
% 1.32/1.42 <=> ( V_y_2 != V_z_2
% 1.32/1.42 & ( V_x_2 = V_z_2
% 1.32/1.42 => V_x_2 != V_y_2 )
% 1.32/1.42 & ( V_x_2 != V_z_2
% 1.32/1.42 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_y_2)),V_L_2)) ) ) ) ).
% 1.32/1.42
% 1.32/1.42 fof(fact_in__mktop,axiom,
% 1.32/1.42 ! [V_z_2,V_L_2,V_y_2,V_x_2] :
% 1.32/1.42 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_y_2)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,V_L_2),V_z_2)))
% 1.32/1.42 <=> ( V_x_2 != V_z_2
% 1.32/1.42 & ( V_y_2 = V_z_2
% 1.32/1.42 => V_x_2 != V_y_2 )
% 1.32/1.42 & ( V_y_2 != V_z_2
% 1.32/1.42 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_y_2)),V_L_2)) ) ) ) ).
% 1.32/1.42
% 1.32/1.42 fof(fact_PW,axiom,
% 1.32/1.42 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(v_F,v_P____)))
% 1.32/1.42 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____)))))) ) ).
% 1.32/1.42
% 1.32/1.42 fof(fact__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ad_J_A_061_A_Ic_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_092_060_094esub_062_Ad_J_096,axiom,
% 1.32/1.42 ! [B_i] :
% 1.32/1.42 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(v_P____,B_i)))
% 1.32/1.42 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,B_i)),v_n____))
% 1.32/1.42 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,B_i)),v_e____))) )
% 1.32/1.42 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,B_i)),v_n____))
% 1.32/1.42 => ( ( hAPP(v_h____,B_i) = v_n____
% 1.32/1.42 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,B_i)),v_c____),v_e____))) )
% 1.32/1.42 & ( hAPP(v_h____,B_i) != v_n____
% 1.32/1.42 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,B_i)),v_e____))) ) ) ) ) ) ).
% 1.32/1.42
% 1.32/1.42 fof(fact_PiProf,axiom,
% 1.32/1.43 ! [V_na_2] : hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),V_na_2))),v_Lab____)),v_Lba____)),c_Arrow__Order__Mirabelle_OProf)) ).
% 1.32/1.43
% 1.32/1.43 fof(fact__096_091_124_Ac_A_126_061_Ae_059_Aa_A_126_061_Ab_059_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_A_058_AProf_059_A_I_Fi_O_Aif_Ah_Ai_A_060_An_A_L_A1_Athen_ALab_Aelse_ALba_J_A_058_AProf_059_AALL_Ai_O_A_Ic_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_092_060_094esub_062_Ae_J_A_061_A_Ia_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_A_L_A1_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Ab_J_A_124_093_061_061_062_A_Ic_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_092_060_094esub_062_Ae_J_A_061_A_Ia_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_A_L_A1_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Ab_J_096,axiom,
% 1.32/1.43 ( v_c____ != v_e____
% 1.32/1.43 => ( v_a____ != v_b____
% 1.32/1.43 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____)))),c_Arrow__Order__Mirabelle_OProf))
% 1.32/1.43 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),v_Lab____)),v_Lba____)),c_Arrow__Order__Mirabelle_OProf))
% 1.32/1.43 => ( ! [B_i] :
% 1.32/1.43 ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,B_i)),v_n____))
% 1.32/1.43 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,B_i)),v_e____))) )
% 1.32/1.43 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,B_i)),v_n____))
% 1.32/1.43 => ( ( hAPP(v_h____,B_i) = v_n____
% 1.32/1.43 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,B_i)),v_c____),v_e____))) )
% 1.32/1.43 & ( hAPP(v_h____,B_i) != v_n____
% 1.32/1.43 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,B_i)),v_e____))) ) ) ) )
% 1.32/1.43 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,B_i)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
% 1.32/1.43 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lab____)) )
% 1.32/1.43 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,B_i)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
% 1.32/1.43 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lba____)) ) ) )
% 1.32/1.43 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
% 1.32/1.43 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),v_Lab____)),v_Lba____)))) ) ) ) ) ) ) ).
% 1.32/1.43
% 1.32/1.43 fof(fact__096_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_058_AProf_096,axiom,
% 1.32/1.43 hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____)))),c_Arrow__Order__Mirabelle_OProf)) ).
% 1.32/1.43
% 1.32/1.43 fof(fact_less__add__one,axiom,
% 1.32/1.43 ! [V_a,T_a] :
% 1.32/1.43 ( class_Rings_Olinordered__semidom(T_a)
% 1.32/1.43 => 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)))) ) ).
% 1.32/1.43
% 1.32/1.43 fof(fact_equalityCE,axiom,
% 1.32/1.43 ! [V_ca_2,T_a,V_B_2,V_A_2] :
% 1.32/1.43 ( V_A_2 = V_B_2
% 1.32/1.43 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
% 1.32/1.43 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) )
% 1.32/1.43 => ~ ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
% 1.32/1.43 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ) ).
% 1.32/1.43
% 1.32/1.43 fof(fact_pred__equals__eq2,axiom,
% 1.32/1.43 ! [V_S_2,V_R_2,T_b,T_a] :
% 1.32/1.43 ( 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(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(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,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(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(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,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)
% 1.32/1.43 <=> V_R_2 = V_S_2 ) ).
% 1.32/1.43
% 1.32/1.43 fof(fact_not__add__less1,axiom,
% 1.32/1.43 ! [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)) ).
% 1.32/1.43
% 1.32/1.43 fof(fact_not__add__less2,axiom,
% 1.32/1.43 ! [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)) ).
% 1.32/1.43
% 1.32/1.43 fof(fact_nat__add__left__cancel__less,axiom,
% 1.32/1.43 ! [V_na_2,V_m_2,V_k_2] :
% 1.32/1.43 ( 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_na_2)))
% 1.32/1.43 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) ) ).
% 1.32/1.43
% 1.32/1.43 fof(fact_trans__less__add1,axiom,
% 1.32/1.43 ! [V_m,V_j,V_i] :
% 1.32/1.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 1.32/1.43 => 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))) ) ).
% 1.32/1.43
% 1.32/1.43 fof(fact__096P_A_058_AProf_096,axiom,
% 1.32/1.43 hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_P____),c_Arrow__Order__Mirabelle_OProf)) ).
% 1.32/1.43
% 1.32/1.43 fof(fact__096Lba_A_058_ALin_096,axiom,
% 1.32/1.43 hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),v_Lba____),c_Arrow__Order__Mirabelle_OLin)) ).
% 1.32/1.43
% 1.32/1.43 fof(fact__096Lab_A_058_ALin_096,axiom,
% 1.32/1.43 hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),v_Lab____),c_Arrow__Order__Mirabelle_OLin)) ).
% 1.32/1.43
% 1.32/1.43 fof(fact_le__refl,axiom,
% 1.32/1.43 ! [V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_n)) ).
% 1.32/1.43
% 1.32/1.43 fof(fact_nat__le__linear,axiom,
% 1.32/1.43 ! [V_n,V_m] :
% 1.32/1.43 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n))
% 1.32/1.43 | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_m)) ) ).
% 1.32/1.43
% 1.32/1.43 fof(fact_eq__imp__le,axiom,
% 1.32/1.43 ! [V_n,V_m] :
% 1.32/1.43 ( V_m = V_n
% 1.32/1.43 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) ) ).
% 1.32/1.43
% 1.32/1.43 fof(fact_le__trans,axiom,
% 1.32/1.43 ! [V_k,V_j,V_i] :
% 1.32/1.43 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j))
% 1.32/1.43 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j),V_k))
% 1.32/1.43 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_k)) ) ) ).
% 1.32/1.43
% 1.32/1.43 fof(fact_le__antisym,axiom,
% 1.32/1.43 ! [V_n,V_m] :
% 1.32/1.43 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n))
% 1.32/1.43 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_m))
% 1.32/1.43 => V_m = V_n ) ) ).
% 1.32/1.43
% 1.32/1.43 fof(fact_psubsetD,axiom,
% 1.32/1.43 ! [V_ca_2,V_B_2,V_A_2,T_a] :
% 1.32/1.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 1.32/1.43 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
% 1.32/1.43 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ).
% 1.32/1.43
% 1.32/1.43 fof(fact_less__or__eq__imp__le,axiom,
% 1.32/1.43 ! [V_n,V_m] :
% 1.32/1.43 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 1.32/1.43 | V_m = V_n )
% 1.32/1.43 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) ) ).
% 1.32/1.43
% 1.32/1.43 fof(fact_le__neq__implies__less,axiom,
% 1.32/1.43 ! [V_n,V_m] :
% 1.32/1.43 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n))
% 1.32/1.43 => ( V_m != V_n
% 1.32/1.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 1.32/1.43
% 1.32/1.43 fof(fact_less__imp__le__nat,axiom,
% 1.32/1.43 ! [V_n,V_m] :
% 1.32/1.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 1.32/1.43 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) ) ).
% 1.32/1.43
% 1.32/1.43 fof(fact_le__eq__less__or__eq,axiom,
% 1.32/1.43 ! [V_na_2,V_m_2] :
% 1.32/1.43 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_na_2))
% 1.32/1.43 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2))
% 1.32/1.43 | V_m_2 = V_na_2 ) ) ).
% 1.32/1.43
% 1.32/1.43 fof(fact_nat__less__le,axiom,
% 1.32/1.43 ! [V_na_2,V_m_2] :
% 1.32/1.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2))
% 1.32/1.43 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_na_2))
% 1.32/1.43 & V_m_2 != V_na_2 ) ) ).
% 1.32/1.43
% 1.32/1.43 fof(fact_add__leE,axiom,
% 1.32/1.43 ! [V_n,V_k,V_m] :
% 1.32/1.43 ( hBOOL(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))
% 1.32/1.43 => ~ ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n))
% 1.32/1.43 => ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_n)) ) ) ).
% 1.32/1.43
% 1.32/1.43 fof(fact_add__leD1,axiom,
% 1.32/1.43 ! [V_n,V_k,V_m] :
% 1.32/1.43 ( hBOOL(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))
% 1.32/1.43 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) ) ).
% 1.32/1.43
% 1.32/1.43 fof(fact_add__leD2,axiom,
% 1.32/1.43 ! [V_n,V_k,V_m] :
% 1.32/1.43 ( hBOOL(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))
% 1.32/1.43 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_n)) ) ).
% 1.32/1.43
% 1.32/1.43 fof(fact_add__le__mono,axiom,
% 1.32/1.43 ! [V_l,V_k,V_j,V_i] :
% 1.32/1.43 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j))
% 1.32/1.43 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_l))
% 1.32/1.43 => hBOOL(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))) ) ) ).
% 1.32/1.43
% 1.32/1.43 fof(fact_add__le__mono1,axiom,
% 1.32/1.43 ! [V_k,V_j,V_i] :
% 1.32/1.43 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j))
% 1.32/1.43 => hBOOL(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))) ) ).
% 1.32/1.43
% 1.32/1.43 fof(fact_trans__le__add2,axiom,
% 1.32/1.43 ! [V_m,V_j,V_i] :
% 1.32/1.43 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j))
% 1.32/1.43 => hBOOL(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))) ) ).
% 1.32/1.43
% 1.32/1.43 fof(fact_trans__le__add1,axiom,
% 1.32/1.43 ! [V_m,V_j,V_i] :
% 1.32/1.43 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j))
% 1.32/1.43 => hBOOL(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))) ) ).
% 1.32/1.43
% 1.32/1.43 fof(fact_nat__add__left__cancel__le,axiom,
% 1.32/1.43 ! [V_na_2,V_m_2,V_k_2] :
% 1.32/1.43 ( hBOOL(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_na_2)))
% 1.32/1.43 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_na_2)) ) ).
% 1.32/1.43
% 1.32/1.43 fof(fact_le__iff__add,axiom,
% 1.32/1.43 ! [V_na_2,V_m_2] :
% 1.32/1.43 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_na_2))
% 1.32/1.43 <=> ? [B_k] : V_na_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k) ) ).
% 1.32/1.43
% 1.32/1.43 fof(fact_le__add1,axiom,
% 1.32/1.43 ! [V_m,V_n] : hBOOL(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))) ).
% 1.32/1.43
% 1.32/1.43 fof(fact_le__add2,axiom,
% 1.32/1.43 ! [V_m,V_n] : hBOOL(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))) ).
% 1.32/1.43
% 1.32/1.43 fof(fact_eq__mem__trans,axiom,
% 1.32/1.43 ! [V_A_2,T_a,V_ba_2,V_aa_2] :
% 1.32/1.43 ( V_aa_2 = V_ba_2
% 1.32/1.43 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_ba_2),V_A_2))
% 1.32/1.43 => hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2)) ) ) ).
% 1.32/1.43
% 1.32/1.43 fof(fact_eqelem__imp__iff,axiom,
% 1.32/1.43 ! [V_A_2,T_a,V_y_2,V_x_2] :
% 1.32/1.43 ( V_x_2 = V_y_2
% 1.32/1.43 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 1.32/1.43 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) ) ) ).
% 1.32/1.43
% 1.32/1.43 fof(fact_eqset__imp__iff,axiom,
% 1.32/1.43 ! [V_x_2,T_a,V_B_2,V_A_2] :
% 1.32/1.43 ( V_A_2 = V_B_2
% 1.32/1.43 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 1.32/1.43 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ).
% 1.32/1.43
% 1.32/1.43 fof(fact_eq__mem,axiom,
% 1.32/1.43 ! [V_y_2,V_x_2,T_a] :
% 1.32/1.43 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_fequal,V_y_2)))
% 1.32/1.43 <=> V_x_2 = V_y_2 ) ).
% 1.32/1.43
% 1.32/1.43 fof(fact_mem__def,axiom,
% 1.32/1.43 ! [V_A_2,V_x_2,T_a] :
% 1.32/1.43 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 1.32/1.43 <=> hBOOL(hAPP(V_A_2,V_x_2)) ) ).
% 1.32/1.43
% 1.32/1.43 fof(fact_linorder__neqE__linordered__idom,axiom,
% 1.32/1.43 ! [V_y,V_x,T_a] :
% 1.32/1.43 ( class_Rings_Olinordered__idom(T_a)
% 1.32/1.43 => ( V_x != V_y
% 1.32/1.43 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 1.32/1.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ).
% 1.32/1.43
% 1.32/1.43 fof(fact_nat__less__cases,axiom,
% 1.32/1.43 ! [V_Pa_2,V_na_2,V_m_2] :
% 1.32/1.43 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2))
% 1.32/1.43 => hBOOL(hAPP(hAPP(V_Pa_2,V_na_2),V_m_2)) )
% 1.32/1.43 => ( ( V_m_2 = V_na_2
% 1.32/1.43 => hBOOL(hAPP(hAPP(V_Pa_2,V_na_2),V_m_2)) )
% 1.32/1.43 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),V_m_2))
% 1.32/1.43 => hBOOL(hAPP(hAPP(V_Pa_2,V_na_2),V_m_2)) )
% 1.32/1.43 => hBOOL(hAPP(hAPP(V_Pa_2,V_na_2),V_m_2)) ) ) ) ).
% 1.32/1.43
% 1.32/1.43 fof(fact_less__not__refl3,axiom,
% 1.32/1.43 ! [V_t,V_s] :
% 1.32/1.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s),V_t))
% 1.32/1.43 => V_s != V_t ) ).
% 1.32/1.43
% 1.32/1.43 fof(fact_less__not__refl2,axiom,
% 1.32/1.43 ! [V_m,V_n] :
% 1.32/1.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m))
% 1.32/1.43 => V_m != V_n ) ).
% 1.32/1.43
% 1.32/1.44 fof(fact_less__irrefl__nat,axiom,
% 1.32/1.44 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ).
% 1.32/1.44
% 1.32/1.44 fof(fact_linorder__neqE__nat,axiom,
% 1.32/1.44 ! [V_y,V_x] :
% 1.32/1.44 ( V_x != V_y
% 1.32/1.44 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
% 1.32/1.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y),V_x)) ) ) ).
% 1.32/1.44
% 1.32/1.44 fof(fact_nat__neq__iff,axiom,
% 1.32/1.44 ! [V_na_2,V_m_2] :
% 1.32/1.44 ( V_m_2 != V_na_2
% 1.32/1.44 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2))
% 1.32/1.44 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),V_m_2)) ) ) ).
% 1.32/1.44
% 1.32/1.44 fof(fact_less__not__refl,axiom,
% 1.32/1.44 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ).
% 1.32/1.44
% 1.32/1.44 fof(fact_nat__add__right__cancel,axiom,
% 1.32/1.44 ! [V_na_2,V_k_2,V_m_2] :
% 1.32/1.44 ( 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_na_2),V_k_2)
% 1.32/1.44 <=> V_m_2 = V_na_2 ) ).
% 1.32/1.44
% 1.32/1.44 fof(fact_nat__add__left__cancel,axiom,
% 1.32/1.44 ! [V_na_2,V_m_2,V_k_2] :
% 1.32/1.44 ( 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_na_2)
% 1.32/1.44 <=> V_m_2 = V_na_2 ) ).
% 1.32/1.44
% 1.32/1.44 fof(fact_nat__add__assoc,axiom,
% 1.32/1.44 ! [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)) ).
% 1.32/1.44
% 1.32/1.44 fof(fact_nat__add__left__commute,axiom,
% 1.32/1.44 ! [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)) ).
% 1.32/1.44
% 1.32/1.44 fof(fact_nat__add__commute,axiom,
% 1.32/1.44 ! [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) ).
% 1.32/1.44
% 1.32/1.44 fof(fact_pred__equals__eq,axiom,
% 1.32/1.44 ! [V_S_2,V_R_2,T_a] :
% 1.32/1.44 ( 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)
% 1.32/1.44 <=> V_R_2 = V_S_2 ) ).
% 1.32/1.44
% 1.32/1.44 fof(fact_add__lessD1,axiom,
% 1.32/1.44 ! [V_k,V_j,V_i] :
% 1.32/1.44 ( 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))
% 1.32/1.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_k)) ) ).
% 1.32/1.44
% 1.32/1.44 fof(fact_less__add__eq__less,axiom,
% 1.32/1.44 ! [V_n,V_m,V_l,V_k] :
% 1.32/1.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l))
% 1.32/1.44 => ( 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)
% 1.32/1.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 1.32/1.44
% 1.32/1.44 fof(fact_add__less__mono,axiom,
% 1.32/1.44 ! [V_l,V_k,V_j,V_i] :
% 1.32/1.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 1.32/1.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l))
% 1.32/1.44 => 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))) ) ) ).
% 1.32/1.44
% 1.32/1.44 fof(fact_add__less__mono1,axiom,
% 1.32/1.44 ! [V_k,V_j,V_i] :
% 1.32/1.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 1.32/1.44 => 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))) ) ).
% 1.32/1.44
% 1.32/1.44 fof(fact_trans__less__add2,axiom,
% 1.32/1.44 ! [V_m,V_j,V_i] :
% 1.32/1.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 1.32/1.44 => 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))) ) ).
% 1.32/1.44
% 1.32/1.44 fof(fact__C3_C,axiom,
% 1.32/1.44 ! [V_P_H_2,V_Pa_2,V_ba_2,V_aa_2] :
% 1.32/1.44 ( V_aa_2 != V_ba_2
% 1.32/1.44 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),V_Pa_2),c_Arrow__Order__Mirabelle_OProf))
% 1.32/1.44 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),V_P_H_2),c_Arrow__Order__Mirabelle_OProf))
% 1.32/1.44 => ( ! [B_i] :
% 1.32/1.44 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_aa_2),V_ba_2)),hAPP(V_Pa_2,B_i)))
% 1.32/1.44 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_ba_2),V_aa_2)),hAPP(V_P_H_2,B_i))) )
% 1.32/1.44 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_aa_2),V_ba_2)),hAPP(v_F,V_Pa_2)))
% 1.32/1.44 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_ba_2),V_aa_2)),hAPP(v_F,V_P_H_2))) ) ) ) ) ) ).
% 1.32/1.44
% 1.32/1.44 fof(fact_pairwise__neutrality,axiom,
% 1.32/1.44 ! [V_P_H_2,V_Pa_2,V_b_H_2,V_a_H_2,V_ba_2,V_aa_2] :
% 1.32/1.44 ( V_aa_2 != V_ba_2
% 1.32/1.44 => ( V_a_H_2 != V_b_H_2
% 1.32/1.44 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),V_Pa_2),c_Arrow__Order__Mirabelle_OProf))
% 1.32/1.44 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),V_P_H_2),c_Arrow__Order__Mirabelle_OProf))
% 1.32/1.44 => ( ! [B_i] :
% 1.32/1.44 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_aa_2),V_ba_2)),hAPP(V_Pa_2,B_i)))
% 1.32/1.44 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_a_H_2),V_b_H_2)),hAPP(V_P_H_2,B_i))) )
% 1.32/1.44 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_aa_2),V_ba_2)),hAPP(v_F,V_Pa_2)))
% 1.32/1.44 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_a_H_2),V_b_H_2)),hAPP(v_F,V_P_H_2))) ) ) ) ) ) ) ).
% 1.32/1.44
% 1.32/1.44 fof(fact__C4_C,axiom,
% 1.32/1.44 ! [V_P_H_2,V_Pa_2,V_ca_2,V_ba_2,V_aa_2] :
% 1.32/1.44 ( V_aa_2 != V_ba_2
% 1.32/1.44 => ( V_ba_2 != V_ca_2
% 1.32/1.44 => ( V_aa_2 != V_ca_2
% 1.32/1.44 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),V_Pa_2),c_Arrow__Order__Mirabelle_OProf))
% 1.32/1.44 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),V_P_H_2),c_Arrow__Order__Mirabelle_OProf))
% 1.32/1.44 => ( ! [B_i] :
% 1.32/1.44 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_aa_2),V_ba_2)),hAPP(V_Pa_2,B_i)))
% 1.32/1.44 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_ba_2),V_ca_2)),hAPP(V_P_H_2,B_i))) )
% 1.32/1.44 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_aa_2),V_ba_2)),hAPP(v_F,V_Pa_2)))
% 1.32/1.44 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_ba_2),V_ca_2)),hAPP(v_F,V_P_H_2))) ) ) ) ) ) ) ) ).
% 1.32/1.44
% 1.32/1.44 fof(fact__C1_C,axiom,
% 1.32/1.44 ! [V_P_H_2,V_Pa_2,V_b_H_2,V_a_H_2,V_ba_2,V_aa_2] :
% 1.32/1.44 ( V_aa_2 != V_ba_2
% 1.32/1.44 => ( V_a_H_2 != V_b_H_2
% 1.32/1.44 => ( V_aa_2 != V_b_H_2
% 1.32/1.44 => ( V_ba_2 != V_a_H_2
% 1.32/1.44 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),V_Pa_2),c_Arrow__Order__Mirabelle_OProf))
% 1.32/1.44 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),V_P_H_2),c_Arrow__Order__Mirabelle_OProf))
% 1.32/1.44 => ( ! [B_i] :
% 1.32/1.44 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_aa_2),V_ba_2)),hAPP(V_Pa_2,B_i)))
% 1.32/1.44 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_a_H_2),V_b_H_2)),hAPP(V_P_H_2,B_i))) )
% 1.32/1.44 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_aa_2),V_ba_2)),hAPP(v_F,V_Pa_2)))
% 1.32/1.44 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_a_H_2),V_b_H_2)),hAPP(v_F,V_P_H_2))) ) ) ) ) ) ) ) ) ).
% 1.32/1.44
% 1.32/1.44 fof(fact__C2_C,axiom,
% 1.32/1.44 ! [V_P_H_2,V_Pa_2,V_b_H_2,V_a_H_2,V_ba_2,V_aa_2] :
% 1.32/1.44 ( V_aa_2 != V_ba_2
% 1.32/1.44 => ( V_a_H_2 != V_b_H_2
% 1.32/1.44 => ( V_aa_2 != V_b_H_2
% 1.32/1.44 => ( V_ba_2 != V_a_H_2
% 1.32/1.44 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),V_Pa_2),c_Arrow__Order__Mirabelle_OProf))
% 1.32/1.44 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),V_P_H_2),c_Arrow__Order__Mirabelle_OProf))
% 1.32/1.44 => ( ! [B_i] :
% 1.32/1.44 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_aa_2),V_ba_2)),hAPP(V_Pa_2,B_i)))
% 1.32/1.44 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_a_H_2),V_b_H_2)),hAPP(V_P_H_2,B_i))) )
% 1.32/1.44 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_aa_2),V_ba_2)),hAPP(v_F,V_Pa_2)))
% 1.32/1.44 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_a_H_2),V_b_H_2)),hAPP(v_F,V_P_H_2))) ) ) ) ) ) ) ) ) ).
% 1.32/1.44
% 1.32/1.44 fof(fact__096c_A_060_092_060_094bsub_062P_A_Iinv_Ah_An_J_092_060_094esub_062_Ad_096,axiom,
% 1.32/1.44 hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(v_P____,hAPP(c_Hilbert__Choice_Oinv__into(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)),v_h____),v_n____)))) ).
% 1.32/1.44
% 1.32/1.44 fof(fact_add__le__less__mono,axiom,
% 1.32/1.44 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.32/1.44 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 1.32/1.44 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
% 1.32/1.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 1.32/1.44 => 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))) ) ) ) ).
% 1.32/1.44
% 1.32/1.44 fof(fact_add__less__le__mono,axiom,
% 1.32/1.44 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.32/1.44 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 1.32/1.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 1.32/1.44 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_d))
% 1.32/1.44 => 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))) ) ) ) ).
% 1.32/1.44
% 1.32/1.44 fof(fact_order__refl,axiom,
% 1.32/1.44 ! [V_x,T_a] :
% 1.32/1.44 ( class_Orderings_Opreorder(T_a)
% 1.32/1.44 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_x)) ) ).
% 1.32/1.44
% 1.32/1.44 fof(fact__096EX_An_060N_O_A_IALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_Am_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Aa_J_A_G_Aa_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_A_L_A1_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Ab_096,axiom,
% 1.32/1.44 ? [B_n] :
% 1.32/1.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))))
% 1.32/1.44 & ! [B_m] :
% 1.32/1.44 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m),B_n))
% 1.32/1.44 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),B_m))),v_Lab____)),v_Lba____)))) )
% 1.32/1.44 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),v_Lab____)),v_Lba____)))) ) ).
% 1.32/1.44
% 1.32/1.44 fof(fact_termination__basic__simps_I4_J,axiom,
% 1.32/1.44 ! [V_y,V_z,V_x] :
% 1.32/1.44 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x),V_z))
% 1.32/1.44 => hBOOL(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))) ) ).
% 1.32/1.44
% 1.32/1.44 fof(fact_n_I1_J,axiom,
% 1.32/1.44 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),v_n____),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))))) ).
% 1.32/1.44
% 1.32/1.44 fof(fact_subsetD,axiom,
% 1.32/1.44 ! [V_ca_2,V_B_2,V_A_2,T_a] :
% 1.32/1.44 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2))
% 1.32/1.44 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
% 1.32/1.44 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ).
% 1.32/1.44
% 1.32/1.44 fof(fact_top1I,axiom,
% 1.32/1.44 ! [V_x_2,T_a] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_x_2)) ).
% 1.32/1.44
% 1.32/1.44 fof(fact_UNIV__I,axiom,
% 1.32/1.44 ! [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)))) ).
% 1.32/1.44
% 1.32/1.44 fof(fact_assms_I1_J,axiom,
% 1.32/1.44 hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_F),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,hAPP(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_Arrow__Order__Mirabelle_OLin)))) ).
% 1.32/1.44
% 1.32/1.44 fof(fact_injh,axiom,
% 1.32/1.44 c_Fun_Oinj__on(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,v_h____,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))) ).
% 1.32/1.44
% 1.32/1.44 fof(fact_subset__UNIV,axiom,
% 1.32/1.44 ! [V_A_2,T_a] : hBOOL(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)))) ).
% 1.32/1.44
% 1.32/1.44 fof(fact_psubset__eq,axiom,
% 1.32/1.44 ! [V_B_2,V_A_2,T_a] :
% 1.32/1.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 1.32/1.44 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2))
% 1.32/1.44 & V_A_2 != V_B_2 ) ) ).
% 1.32/1.44
% 1.32/1.44 fof(fact_less__fun__def,axiom,
% 1.32/1.44 ! [V_g_2,V_f_2,T_a,T_b] :
% 1.32/1.44 ( class_Orderings_Oord(T_b)
% 1.32/1.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b)),V_f_2),V_g_2))
% 1.32/1.44 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2),V_g_2))
% 1.32/1.44 & ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_g_2),V_f_2)) ) ) ) ).
% 1.32/1.44
% 1.32/1.44 fof(fact_subset__iff__psubset__eq,axiom,
% 1.32/1.44 ! [V_B_2,V_A_2,T_a] :
% 1.32/1.44 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2))
% 1.32/1.44 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 1.32/1.44 | V_A_2 = V_B_2 ) ) ).
% 1.32/1.44
% 1.32/1.44 fof(fact_psubset__imp__subset,axiom,
% 1.32/1.44 ! [V_B_2,V_A_2,T_a] :
% 1.32/1.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 1.32/1.44 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) ) ).
% 1.32/1.44
% 1.32/1.44 fof(fact_psubset__trans,axiom,
% 1.32/1.44 ! [V_C_2,V_B_2,V_A_2,T_a] :
% 1.32/1.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 1.32/1.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))
% 1.32/1.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 1.32/1.44
% 1.32/1.44 fof(fact_psubset__subset__trans,axiom,
% 1.32/1.44 ! [V_C_2,V_B_2,V_A_2,T_a] :
% 1.32/1.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 1.32/1.44 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2),V_C_2))
% 1.32/1.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 1.32/1.44
% 1.32/1.44 fof(fact_subset__psubset__trans,axiom,
% 1.32/1.44 ! [V_C_2,V_B_2,V_A_2,T_a] :
% 1.32/1.44 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2))
% 1.32/1.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))
% 1.32/1.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 1.32/1.44
% 1.32/1.44 fof(fact_top__apply,axiom,
% 1.32/1.44 ! [V_x_2,T_b,T_a] :
% 1.32/1.44 ( class_Orderings_Otop(T_a)
% 1.32/1.44 => hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_b,T_a)),V_x_2) = c_Orderings_Otop__class_Otop(T_a) ) ).
% 1.32/1.44
% 1.32/1.44 fof(fact_top__greatest,axiom,
% 1.32/1.44 ! [V_x,T_a] :
% 1.32/1.44 ( class_Orderings_Otop(T_a)
% 1.32/1.44 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),c_Orderings_Otop__class_Otop(T_a))) ) ).
% 1.32/1.44
% 1.32/1.44 fof(fact_pred__subset__eq2,axiom,
% 1.32/1.44 ! [V_S_2,V_R_2,T_b,T_a] :
% 1.32/1.44 ( hBOOL(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(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(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,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(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(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,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)))
% 1.32/1.44 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),V_R_2),V_S_2)) ) ).
% 1.32/1.44
% 1.32/1.44 fof(fact_in__mono,axiom,
% 1.32/1.44 ! [V_x_2,V_B_2,V_A_2,T_a] :
% 1.32/1.44 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2))
% 1.32/1.44 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 1.32/1.44 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ).
% 1.32/1.44
% 1.32/1.44 fof(fact_set__rev__mp,axiom,
% 1.32/1.44 ! [V_B_2,V_A_2,V_x_2,T_a] :
% 1.32/1.44 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 1.32/1.44 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2))
% 1.32/1.44 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ).
% 1.32/1.44
% 1.32/1.44 fof(fact_set__mp,axiom,
% 1.32/1.44 ! [V_x_2,V_B_2,V_A_2,T_a] :
% 1.32/1.44 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2))
% 1.32/1.44 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 1.32/1.44 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ).
% 1.32/1.44
% 1.32/1.44 fof(fact_pred__subset__eq,axiom,
% 1.32/1.44 ! [V_S_2,V_R_2,T_a] :
% 1.32/1.44 ( hBOOL(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)))
% 1.32/1.44 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_R_2),V_S_2)) ) ).
% 1.32/1.44
% 1.32/1.44 fof(fact_above__Lin,axiom,
% 1.32/1.44 ! [V_L_2,V_y_2,V_x_2] :
% 1.32/1.44 ( V_x_2 != V_y_2
% 1.32/1.44 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_L_2),c_Arrow__Order__Mirabelle_OLin))
% 1.32/1.44 => hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,V_L_2),V_x_2),V_y_2)),c_Arrow__Order__Mirabelle_OLin)) ) ) ).
% 1.32/1.44
% 1.32/1.44 fof(fact_mkbot__Lin,axiom,
% 1.32/1.44 ! [V_x_2,V_L_2] :
% 1.32/1.44 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_L_2),c_Arrow__Order__Mirabelle_OLin))
% 1.32/1.44 => hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,V_L_2),V_x_2)),c_Arrow__Order__Mirabelle_OLin)) ) ).
% 1.32/1.44
% 1.32/1.44 fof(fact_mktop__Lin,axiom,
% 1.32/1.44 ! [V_x_2,V_L_2] :
% 1.32/1.44 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_L_2),c_Arrow__Order__Mirabelle_OLin))
% 1.32/1.44 => hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,V_L_2),V_x_2)),c_Arrow__Order__Mirabelle_OLin)) ) ).
% 1.32/1.44
% 1.32/1.44 fof(fact_linorder__le__cases,axiom,
% 1.32/1.44 ! [V_y,V_x,T_a] :
% 1.32/1.44 ( class_Orderings_Olinorder(T_a)
% 1.32/1.44 => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y))
% 1.32/1.44 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) ) ) ).
% 1.32/1.44
% 1.32/1.44 fof(fact_le__funE,axiom,
% 1.32/1.44 ! [V_x_2,V_g_2,V_f_2,T_a,T_b] :
% 1.32/1.44 ( class_Orderings_Oord(T_b)
% 1.32/1.44 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2),V_g_2))
% 1.32/1.44 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2))) ) ) ).
% 1.32/1.44
% 1.32/1.44 fof(fact_xt1_I6_J,axiom,
% 1.32/1.44 ! [V_z,V_x,V_y,T_a] :
% 1.32/1.44 ( class_Orderings_Oorder(T_a)
% 1.32/1.44 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))
% 1.32/1.44 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_y))
% 1.32/1.44 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_x)) ) ) ) ).
% 1.32/1.44
% 1.32/1.44 fof(fact_xt1_I5_J,axiom,
% 1.32/1.44 ! [V_x,V_y,T_a] :
% 1.32/1.44 ( class_Orderings_Oorder(T_a)
% 1.32/1.44 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))
% 1.32/1.44 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y))
% 1.32/1.44 => V_x = V_y ) ) ) ).
% 1.32/1.44
% 1.32/1.44 fof(fact_order__trans,axiom,
% 1.32/1.44 ! [V_z,V_y,V_x,T_a] :
% 1.32/1.44 ( class_Orderings_Opreorder(T_a)
% 1.32/1.44 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y))
% 1.32/1.44 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_z))
% 1.32/1.44 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_z)) ) ) ) ).
% 1.32/1.44
% 1.32/1.44 fof(fact_order__antisym,axiom,
% 1.32/1.44 ! [V_y,V_x,T_a] :
% 1.32/1.44 ( class_Orderings_Oorder(T_a)
% 1.32/1.44 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y))
% 1.32/1.44 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))
% 1.32/1.44 => V_x = V_y ) ) ) ).
% 1.32/1.44
% 1.32/1.44 fof(fact_xt1_I4_J,axiom,
% 1.32/1.44 ! [V_c,V_a,V_b,T_a] :
% 1.32/1.44 ( class_Orderings_Oorder(T_a)
% 1.32/1.44 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a))
% 1.32/1.44 => ( V_b = V_c
% 1.32/1.44 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_a)) ) ) ) ).
% 1.32/1.44
% 1.32/1.44 fof(fact_ord__le__eq__trans,axiom,
% 1.32/1.44 ! [V_c,V_b,V_a,T_a] :
% 1.32/1.44 ( class_Orderings_Oord(T_a)
% 1.32/1.44 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
% 1.32/1.44 => ( V_b = V_c
% 1.32/1.44 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_c)) ) ) ) ).
% 1.32/1.44
% 1.32/1.44 fof(fact_xt1_I3_J,axiom,
% 1.32/1.44 ! [V_c,V_b,V_a,T_a] :
% 1.32/1.44 ( class_Orderings_Oorder(T_a)
% 1.32/1.44 => ( V_a = V_b
% 1.32/1.44 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_b))
% 1.32/1.44 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_a)) ) ) ) ).
% 1.32/1.44
% 1.32/1.44 fof(fact_ord__eq__le__trans,axiom,
% 1.32/1.44 ! [V_c,V_b,V_a,T_a] :
% 1.32/1.44 ( class_Orderings_Oord(T_a)
% 1.32/1.44 => ( V_a = V_b
% 1.32/1.44 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_c))
% 1.32/1.44 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_c)) ) ) ) ).
% 1.32/1.44
% 1.32/1.44 fof(fact_order__antisym__conv,axiom,
% 1.32/1.44 ! [V_x_2,V_y_2,T_a] :
% 1.32/1.44 ( class_Orderings_Oorder(T_a)
% 1.32/1.44 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y_2),V_x_2))
% 1.32/1.44 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2))
% 1.32/1.44 <=> V_x_2 = V_y_2 ) ) ) ).
% 1.32/1.44
% 1.32/1.44 fof(fact_le__funD,axiom,
% 1.32/1.44 ! [V_x_2,V_g_2,V_f_2,T_a,T_b] :
% 1.32/1.44 ( class_Orderings_Oord(T_b)
% 1.32/1.44 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2),V_g_2))
% 1.32/1.44 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2))) ) ) ).
% 1.32/1.44
% 1.32/1.44 fof(fact_order__eq__refl,axiom,
% 1.32/1.44 ! [V_y,V_x,T_a] :
% 1.32/1.44 ( class_Orderings_Opreorder(T_a)
% 1.32/1.44 => ( V_x = V_y
% 1.32/1.44 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) ) ) ).
% 1.32/1.44
% 1.32/1.44 fof(fact_order__eq__iff,axiom,
% 1.32/1.44 ! [V_y_2,V_x_2,T_a] :
% 1.32/1.44 ( class_Orderings_Oorder(T_a)
% 1.32/1.44 => ( V_x_2 = V_y_2
% 1.32/1.44 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2))
% 1.32/1.44 & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y_2),V_x_2)) ) ) ) ).
% 1.32/1.44
% 1.32/1.44 fof(fact_linorder__linear,axiom,
% 1.32/1.44 ! [V_y,V_x,T_a] :
% 1.32/1.44 ( class_Orderings_Olinorder(T_a)
% 1.32/1.44 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y))
% 1.32/1.44 | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) ) ) ).
% 1.32/1.44
% 1.32/1.44 fof(fact_le__fun__def,axiom,
% 1.32/1.44 ! [V_g_2,V_f_2,T_a,T_b] :
% 1.32/1.44 ( class_Orderings_Oord(T_b)
% 1.32/1.44 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2),V_g_2))
% 1.32/1.44 <=> ! [B_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) ) ).
% 1.32/1.44
% 1.32/1.44 fof(fact_notin__Lin__iff,axiom,
% 1.32/1.44 ! [V_y_2,V_x_2,V_L_2] :
% 1.32/1.44 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_L_2),c_Arrow__Order__Mirabelle_OLin))
% 1.32/1.44 => ( V_x_2 != V_y_2
% 1.32/1.44 => ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_y_2)),V_L_2))
% 1.32/1.44 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_y_2),V_x_2)),V_L_2)) ) ) ) ).
% 1.32/1.44
% 1.32/1.44 fof(fact_Lin__irrefl,axiom,
% 1.32/1.44 ! [V_ba_2,V_aa_2,V_L_2] :
% 1.32/1.44 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_L_2),c_Arrow__Order__Mirabelle_OLin))
% 1.32/1.44 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_aa_2),V_ba_2)),V_L_2))
% 1.32/1.44 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_ba_2),V_aa_2)),V_L_2)) ) ) ).
% 1.32/1.44
% 1.32/1.44 fof(fact_order__less__irrefl,axiom,
% 1.32/1.44 ! [V_x,T_a] :
% 1.32/1.44 ( class_Orderings_Opreorder(T_a)
% 1.32/1.44 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_x)) ) ).
% 1.32/1.44
% 1.32/1.44 fof(fact_linorder__neq__iff,axiom,
% 1.32/1.44 ! [V_y_2,V_x_2,T_a] :
% 1.32/1.44 ( class_Orderings_Olinorder(T_a)
% 1.32/1.44 => ( V_x_2 != V_y_2
% 1.32/1.44 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
% 1.32/1.44 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) ) ) ) ).
% 1.32/1.44
% 1.32/1.44 fof(fact_not__less__iff__gr__or__eq,axiom,
% 1.32/1.44 ! [V_y_2,V_x_2,T_a] :
% 1.32/1.44 ( class_Orderings_Olinorder(T_a)
% 1.32/1.44 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
% 1.32/1.44 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2))
% 1.32/1.44 | V_x_2 = V_y_2 ) ) ) ).
% 1.32/1.44
% 1.32/1.44 fof(fact_linorder__less__linear,axiom,
% 1.32/1.44 ! [V_y,V_x,T_a] :
% 1.32/1.44 ( class_Orderings_Olinorder(T_a)
% 1.32/1.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 1.32/1.44 | V_x = V_y
% 1.32/1.44 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 1.32/1.44
% 1.32/1.44 fof(fact_linorder__antisym__conv3,axiom,
% 1.32/1.44 ! [V_x_2,V_y_2,T_a] :
% 1.32/1.44 ( class_Orderings_Olinorder(T_a)
% 1.32/1.44 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2))
% 1.32/1.44 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
% 1.32/1.44 <=> V_x_2 = V_y_2 ) ) ) ).
% 1.32/1.44
% 1.32/1.44 fof(fact_linorder__neqE,axiom,
% 1.32/1.44 ! [V_y,V_x,T_a] :
% 1.32/1.44 ( class_Orderings_Olinorder(T_a)
% 1.32/1.44 => ( V_x != V_y
% 1.32/1.44 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 1.32/1.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ).
% 1.32/1.44
% 1.32/1.44 fof(fact_less__imp__neq,axiom,
% 1.32/1.44 ! [V_y,V_x,T_a] :
% 1.32/1.44 ( class_Orderings_Oorder(T_a)
% 1.32/1.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 1.32/1.44 => V_x != V_y ) ) ).
% 1.32/1.44
% 1.32/1.44 fof(fact_order__less__not__sym,axiom,
% 1.32/1.44 ! [V_y,V_x,T_a] :
% 1.32/1.44 ( class_Orderings_Opreorder(T_a)
% 1.32/1.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 1.32/1.44 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 1.32/1.44
% 1.32/1.44 fof(fact_order__less__imp__not__less,axiom,
% 1.32/1.44 ! [V_y,V_x,T_a] :
% 1.32/1.44 ( class_Orderings_Opreorder(T_a)
% 1.32/1.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 1.32/1.44 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 1.32/1.44
% 1.32/1.44 fof(fact_order__less__imp__not__eq,axiom,
% 1.32/1.44 ! [V_y,V_x,T_a] :
% 1.32/1.44 ( class_Orderings_Oorder(T_a)
% 1.32/1.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 1.32/1.44 => V_x != V_y ) ) ).
% 1.32/1.44
% 1.32/1.44 fof(fact_order__less__imp__not__eq2,axiom,
% 1.32/1.44 ! [V_y,V_x,T_a] :
% 1.32/1.44 ( class_Orderings_Oorder(T_a)
% 1.32/1.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 1.32/1.44 => V_y != V_x ) ) ).
% 1.32/1.44
% 1.32/1.45 fof(fact_order__less__asym_H,axiom,
% 1.32/1.45 ! [V_b,V_a,T_a] :
% 1.32/1.45 ( class_Orderings_Opreorder(T_a)
% 1.32/1.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 1.32/1.45 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_xt1_I9_J,axiom,
% 1.32/1.45 ! [V_a,V_b,T_a] :
% 1.32/1.45 ( class_Orderings_Oorder(T_a)
% 1.32/1.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 1.32/1.45 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_ord__eq__less__trans,axiom,
% 1.32/1.45 ! [V_c,V_b,V_a,T_a] :
% 1.32/1.45 ( class_Orderings_Oord(T_a)
% 1.32/1.45 => ( V_a = V_b
% 1.32/1.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
% 1.32/1.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_xt1_I1_J,axiom,
% 1.32/1.45 ! [V_c,V_b,V_a,T_a] :
% 1.32/1.45 ( class_Orderings_Oorder(T_a)
% 1.32/1.45 => ( V_a = V_b
% 1.32/1.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_b))
% 1.32/1.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_ord__less__eq__trans,axiom,
% 1.32/1.45 ! [V_c,V_b,V_a,T_a] :
% 1.32/1.45 ( class_Orderings_Oord(T_a)
% 1.32/1.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 1.32/1.45 => ( V_b = V_c
% 1.32/1.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_xt1_I2_J,axiom,
% 1.32/1.45 ! [V_c,V_a,V_b,T_a] :
% 1.32/1.45 ( class_Orderings_Oorder(T_a)
% 1.32/1.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 1.32/1.45 => ( V_b = V_c
% 1.32/1.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_order__less__trans,axiom,
% 1.32/1.45 ! [V_z,V_y,V_x,T_a] :
% 1.32/1.45 ( class_Orderings_Opreorder(T_a)
% 1.32/1.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 1.32/1.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z))
% 1.32/1.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_xt1_I10_J,axiom,
% 1.32/1.45 ! [V_z,V_x,V_y,T_a] :
% 1.32/1.45 ( class_Orderings_Oorder(T_a)
% 1.32/1.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
% 1.32/1.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y))
% 1.32/1.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_order__less__asym,axiom,
% 1.32/1.45 ! [V_y,V_x,T_a] :
% 1.32/1.45 ( class_Orderings_Opreorder(T_a)
% 1.32/1.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 1.32/1.45 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_linorder__cases,axiom,
% 1.32/1.45 ! [V_y,V_x,T_a] :
% 1.32/1.45 ( class_Orderings_Olinorder(T_a)
% 1.32/1.45 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 1.32/1.45 => ( V_x != V_y
% 1.32/1.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 1.32/1.45 ! [V_c,V_b,V_a,T_a] :
% 1.32/1.45 ( class_Groups_Oab__semigroup__add(T_a)
% 1.32/1.45 => 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)) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_add__left__cancel,axiom,
% 1.32/1.45 ! [V_ca_2,V_ba_2,V_aa_2,T_a] :
% 1.32/1.45 ( class_Groups_Ocancel__semigroup__add(T_a)
% 1.32/1.45 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_ba_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_ca_2)
% 1.32/1.45 <=> V_ba_2 = V_ca_2 ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_add__right__cancel,axiom,
% 1.32/1.45 ! [V_ca_2,V_aa_2,V_ba_2,T_a] :
% 1.32/1.45 ( class_Groups_Ocancel__semigroup__add(T_a)
% 1.32/1.45 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_ba_2),V_aa_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_ca_2),V_aa_2)
% 1.32/1.45 <=> V_ba_2 = V_ca_2 ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_add__left__imp__eq,axiom,
% 1.32/1.45 ! [V_c,V_b,V_a,T_a] :
% 1.32/1.45 ( class_Groups_Ocancel__semigroup__add(T_a)
% 1.32/1.45 => ( 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)
% 1.32/1.45 => V_b = V_c ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_add__imp__eq,axiom,
% 1.32/1.45 ! [V_c,V_b,V_a,T_a] :
% 1.32/1.45 ( class_Groups_Ocancel__ab__semigroup__add(T_a)
% 1.32/1.45 => ( 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)
% 1.32/1.45 => V_b = V_c ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_add__right__imp__eq,axiom,
% 1.32/1.45 ! [V_c,V_a,V_b,T_a] :
% 1.32/1.45 ( class_Groups_Ocancel__semigroup__add(T_a)
% 1.32/1.45 => ( 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)
% 1.32/1.45 => V_b = V_c ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_one__reorient,axiom,
% 1.32/1.45 ! [V_x_2,T_a] :
% 1.32/1.45 ( class_Groups_Oone(T_a)
% 1.32/1.45 => ( c_Groups_Oone__class_Oone(T_a) = V_x_2
% 1.32/1.45 <=> V_x_2 = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_const__Lin__Prof,axiom,
% 1.32/1.45 ! [V_L_2] :
% 1.32/1.45 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_L_2),c_Arrow__Order__Mirabelle_OLin))
% 1.32/1.45 => hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi),V_L_2)),c_Arrow__Order__Mirabelle_OProf)) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_in__above,axiom,
% 1.32/1.45 ! [V_y_2,V_x_2,V_L_2,V_ba_2,V_aa_2] :
% 1.32/1.45 ( V_aa_2 != V_ba_2
% 1.32/1.45 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_L_2),c_Arrow__Order__Mirabelle_OLin))
% 1.32/1.45 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_y_2)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,V_L_2),V_aa_2),V_ba_2)))
% 1.32/1.45 <=> ( V_x_2 != V_y_2
% 1.32/1.45 & ( V_x_2 = V_ba_2
% 1.32/1.45 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_aa_2),V_y_2)),V_L_2)) )
% 1.32/1.45 & ( V_x_2 != V_ba_2
% 1.32/1.45 => ( ( V_y_2 = V_ba_2
% 1.32/1.45 => ( V_x_2 = V_aa_2
% 1.32/1.45 | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_aa_2)),V_L_2)) ) )
% 1.32/1.45 & ( V_y_2 != V_ba_2
% 1.32/1.45 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_y_2)),V_L_2)) ) ) ) ) ) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_linorder__not__less,axiom,
% 1.32/1.45 ! [V_y_2,V_x_2,T_a] :
% 1.32/1.45 ( class_Orderings_Olinorder(T_a)
% 1.32/1.45 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
% 1.32/1.45 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y_2),V_x_2)) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_linorder__not__le,axiom,
% 1.32/1.45 ! [V_y_2,V_x_2,T_a] :
% 1.32/1.45 ( class_Orderings_Olinorder(T_a)
% 1.32/1.45 => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2))
% 1.32/1.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_linorder__le__less__linear,axiom,
% 1.32/1.45 ! [V_y,V_x,T_a] :
% 1.32/1.45 ( class_Orderings_Olinorder(T_a)
% 1.32/1.45 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y))
% 1.32/1.45 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_order__less__le,axiom,
% 1.32/1.45 ! [V_y_2,V_x_2,T_a] :
% 1.32/1.45 ( class_Orderings_Oorder(T_a)
% 1.32/1.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
% 1.32/1.45 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2))
% 1.32/1.45 & V_x_2 != V_y_2 ) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_less__le__not__le,axiom,
% 1.32/1.45 ! [V_y_2,V_x_2,T_a] :
% 1.32/1.45 ( class_Orderings_Opreorder(T_a)
% 1.32/1.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
% 1.32/1.45 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2))
% 1.32/1.45 & ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y_2),V_x_2)) ) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_order__le__less,axiom,
% 1.32/1.45 ! [V_y_2,V_x_2,T_a] :
% 1.32/1.45 ( class_Orderings_Oorder(T_a)
% 1.32/1.45 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2))
% 1.32/1.45 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
% 1.32/1.45 | V_x_2 = V_y_2 ) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_leI,axiom,
% 1.32/1.45 ! [V_y,V_x,T_a] :
% 1.32/1.45 ( class_Orderings_Olinorder(T_a)
% 1.32/1.45 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 1.32/1.45 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_not__leE,axiom,
% 1.32/1.45 ! [V_x,V_y,T_a] :
% 1.32/1.45 ( class_Orderings_Olinorder(T_a)
% 1.32/1.45 => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))
% 1.32/1.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_linorder__antisym__conv1,axiom,
% 1.32/1.45 ! [V_y_2,V_x_2,T_a] :
% 1.32/1.45 ( class_Orderings_Olinorder(T_a)
% 1.32/1.45 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
% 1.32/1.45 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2))
% 1.32/1.45 <=> V_x_2 = V_y_2 ) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_order__neq__le__trans,axiom,
% 1.32/1.45 ! [V_b,V_a,T_a] :
% 1.32/1.45 ( class_Orderings_Oorder(T_a)
% 1.32/1.45 => ( V_a != V_b
% 1.32/1.45 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
% 1.32/1.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_xt1_I12_J,axiom,
% 1.32/1.45 ! [V_b,V_a,T_a] :
% 1.32/1.45 ( class_Orderings_Oorder(T_a)
% 1.32/1.45 => ( V_a != V_b
% 1.32/1.45 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a))
% 1.32/1.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_leD,axiom,
% 1.32/1.45 ! [V_x,V_y,T_a] :
% 1.32/1.45 ( class_Orderings_Olinorder(T_a)
% 1.32/1.45 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))
% 1.32/1.45 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_order__less__imp__le,axiom,
% 1.32/1.45 ! [V_y,V_x,T_a] :
% 1.32/1.45 ( class_Orderings_Opreorder(T_a)
% 1.32/1.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 1.32/1.45 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_linorder__antisym__conv2,axiom,
% 1.32/1.45 ! [V_y_2,V_x_2,T_a] :
% 1.32/1.45 ( class_Orderings_Olinorder(T_a)
% 1.32/1.45 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2))
% 1.32/1.45 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
% 1.32/1.45 <=> V_x_2 = V_y_2 ) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_order__le__imp__less__or__eq,axiom,
% 1.32/1.45 ! [V_y,V_x,T_a] :
% 1.32/1.45 ( class_Orderings_Oorder(T_a)
% 1.32/1.45 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y))
% 1.32/1.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 1.32/1.45 | V_x = V_y ) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_order__le__neq__trans,axiom,
% 1.32/1.45 ! [V_b,V_a,T_a] :
% 1.32/1.45 ( class_Orderings_Oorder(T_a)
% 1.32/1.45 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
% 1.32/1.45 => ( V_a != V_b
% 1.32/1.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_xt1_I11_J,axiom,
% 1.32/1.45 ! [V_a,V_b,T_a] :
% 1.32/1.45 ( class_Orderings_Oorder(T_a)
% 1.32/1.45 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a))
% 1.32/1.45 => ( V_a != V_b
% 1.32/1.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_order__less__le__trans,axiom,
% 1.32/1.45 ! [V_z,V_y,V_x,T_a] :
% 1.32/1.45 ( class_Orderings_Opreorder(T_a)
% 1.32/1.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 1.32/1.45 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_z))
% 1.32/1.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_xt1_I7_J,axiom,
% 1.32/1.45 ! [V_z,V_x,V_y,T_a] :
% 1.32/1.45 ( class_Orderings_Oorder(T_a)
% 1.32/1.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
% 1.32/1.45 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_y))
% 1.32/1.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_order__le__less__trans,axiom,
% 1.32/1.45 ! [V_z,V_y,V_x,T_a] :
% 1.32/1.45 ( class_Orderings_Opreorder(T_a)
% 1.32/1.45 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y))
% 1.32/1.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z))
% 1.32/1.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_xt1_I8_J,axiom,
% 1.32/1.45 ! [V_z,V_x,V_y,T_a] :
% 1.32/1.45 ( class_Orderings_Oorder(T_a)
% 1.32/1.45 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))
% 1.32/1.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y))
% 1.32/1.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_add__le__cancel__right,axiom,
% 1.32/1.45 ! [V_ba_2,V_ca_2,V_aa_2,T_a] :
% 1.32/1.45 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 1.32/1.45 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_ba_2),V_ca_2)))
% 1.32/1.45 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2),V_ba_2)) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_add__le__cancel__left,axiom,
% 1.32/1.45 ! [V_ba_2,V_aa_2,V_ca_2,T_a] :
% 1.32/1.45 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 1.32/1.45 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_ca_2),V_aa_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_ca_2),V_ba_2)))
% 1.32/1.45 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2),V_ba_2)) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_add__right__mono,axiom,
% 1.32/1.45 ! [V_c,V_b,V_a,T_a] :
% 1.32/1.45 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 1.32/1.45 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
% 1.32/1.45 => hBOOL(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))) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_add__left__mono,axiom,
% 1.32/1.45 ! [V_c,V_b,V_a,T_a] :
% 1.32/1.45 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 1.32/1.45 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
% 1.32/1.45 => hBOOL(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))) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_add__mono,axiom,
% 1.32/1.45 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.32/1.45 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 1.32/1.45 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
% 1.32/1.45 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_d))
% 1.32/1.45 => hBOOL(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))) ) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_add__le__imp__le__right,axiom,
% 1.32/1.45 ! [V_b,V_c,V_a,T_a] :
% 1.32/1.45 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 1.32/1.45 => ( hBOOL(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)))
% 1.32/1.45 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_add__le__imp__le__left,axiom,
% 1.32/1.45 ! [V_b,V_a,V_c,T_a] :
% 1.32/1.45 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 1.32/1.45 => ( hBOOL(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)))
% 1.32/1.45 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_add__less__cancel__right,axiom,
% 1.32/1.45 ! [V_ba_2,V_ca_2,V_aa_2,T_a] :
% 1.32/1.45 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 1.32/1.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_ba_2),V_ca_2)))
% 1.32/1.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_aa_2),V_ba_2)) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_add__less__cancel__left,axiom,
% 1.32/1.45 ! [V_ba_2,V_aa_2,V_ca_2,T_a] :
% 1.32/1.45 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 1.32/1.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_ca_2),V_aa_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_ca_2),V_ba_2)))
% 1.32/1.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_aa_2),V_ba_2)) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_add__strict__right__mono,axiom,
% 1.32/1.45 ! [V_c,V_b,V_a,T_a] :
% 1.32/1.45 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 1.32/1.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 1.32/1.45 => 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))) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_add__strict__left__mono,axiom,
% 1.32/1.45 ! [V_c,V_b,V_a,T_a] :
% 1.32/1.45 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 1.32/1.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 1.32/1.45 => 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))) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_add__strict__mono,axiom,
% 1.32/1.45 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.32/1.45 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 1.32/1.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 1.32/1.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 1.32/1.45 => 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))) ) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_add__less__imp__less__right,axiom,
% 1.32/1.45 ! [V_b,V_c,V_a,T_a] :
% 1.32/1.45 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 1.32/1.45 => ( 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)))
% 1.32/1.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_add__less__imp__less__left,axiom,
% 1.32/1.45 ! [V_b,V_a,V_c,T_a] :
% 1.32/1.45 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 1.32/1.45 => ( 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)))
% 1.32/1.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_termination__basic__simps_I1_J,axiom,
% 1.32/1.45 ! [V_z,V_y,V_x] :
% 1.32/1.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
% 1.32/1.45 => 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))) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_termination__basic__simps_I2_J,axiom,
% 1.32/1.45 ! [V_y,V_z,V_x] :
% 1.32/1.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_z))
% 1.32/1.45 => 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))) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_termination__basic__simps_I5_J,axiom,
% 1.32/1.45 ! [V_y,V_x] :
% 1.32/1.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
% 1.32/1.45 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x),V_y)) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_termination__basic__simps_I3_J,axiom,
% 1.32/1.45 ! [V_z,V_y,V_x] :
% 1.32/1.45 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x),V_y))
% 1.32/1.45 => hBOOL(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))) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact__096_B_Bthesis_O_A_I_B_BLab_O_A_091_124_Aa_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_059_ALab_A_058_ALin_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096,axiom,
% 1.32/1.45 ~ ! [B_Lab] :
% 1.32/1.45 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),B_Lab))
% 1.32/1.45 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),B_Lab),c_Arrow__Order__Mirabelle_OLin)) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact__096_B_Bthesis_O_A_I_B_BLba_O_A_091_124_Ab_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_059_ALba_A_058_ALin_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096,axiom,
% 1.32/1.45 ~ ! [B_Lba] :
% 1.32/1.45 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),B_Lba))
% 1.32/1.45 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),B_Lba),c_Arrow__Order__Mirabelle_OLin)) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_in__rel__def,axiom,
% 1.32/1.45 ! [V_y_2,V_x_2,V_R_2,T_b,T_a] :
% 1.32/1.45 ( c_FunDef_Oin__rel(T_a,T_b,V_R_2,V_x_2,V_y_2)
% 1.32/1.45 <=> 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)) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact__096_B_Bthesis_O_A_I_B_Bn_O_A_091_124_An_A_060_AN_059_AALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_Am_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Aa_059_Aa_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_A_L_A1_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Ab_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096,axiom,
% 1.32/1.45 ~ ! [B_n] :
% 1.32/1.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))))
% 1.32/1.45 => ( ! [B_m] :
% 1.32/1.45 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m),B_n))
% 1.32/1.45 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),B_m))),v_Lab____)),v_Lba____)))) )
% 1.32/1.45 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),v_Lab____)),v_Lba____)))) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_in__below,axiom,
% 1.32/1.45 ! [V_y_2,V_x_2,V_L_2,V_ba_2,V_aa_2] :
% 1.32/1.45 ( V_aa_2 != V_ba_2
% 1.32/1.45 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_L_2),c_Arrow__Order__Mirabelle_OLin))
% 1.32/1.45 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_y_2)),c_Arrow__Order__Mirabelle_Obelow(V_L_2,V_aa_2,V_ba_2)))
% 1.32/1.45 <=> ( V_x_2 != V_y_2
% 1.32/1.45 & ( V_y_2 = V_aa_2
% 1.32/1.45 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_ba_2)),V_L_2)) )
% 1.32/1.45 & ( V_y_2 != V_aa_2
% 1.32/1.45 => ( ( V_x_2 = V_aa_2
% 1.32/1.45 => ( V_y_2 = V_ba_2
% 1.32/1.45 | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_ba_2),V_y_2)),V_L_2)) ) )
% 1.32/1.45 & ( V_x_2 != V_aa_2
% 1.32/1.45 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_y_2)),V_L_2)) ) ) ) ) ) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_below__Lin,axiom,
% 1.32/1.45 ! [V_L_2,V_y_2,V_x_2] :
% 1.32/1.45 ( V_x_2 != V_y_2
% 1.32/1.45 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_L_2),c_Arrow__Order__Mirabelle_OLin))
% 1.32/1.45 => hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Obelow(V_L_2,V_x_2,V_y_2)),c_Arrow__Order__Mirabelle_OLin)) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_unanimity__def,axiom,
% 1.32/1.45 ! [V_Fa_2] :
% 1.32/1.45 ( c_Arrow__Order__Mirabelle_Ounanimity(V_Fa_2)
% 1.32/1.45 <=> ! [B_x] :
% 1.32/1.45 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B_x),c_Arrow__Order__Mirabelle_OProf))
% 1.32/1.45 => ! [B_a,B_b] :
% 1.32/1.45 ( ! [B_i] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(B_x,B_i)))
% 1.32/1.45 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(V_Fa_2,B_x))) ) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_IIA__def,axiom,
% 1.32/1.45 ! [V_Fa_2] :
% 1.32/1.45 ( c_Arrow__Order__Mirabelle_OIIA(V_Fa_2)
% 1.32/1.45 <=> ! [B_x] :
% 1.32/1.45 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B_x),c_Arrow__Order__Mirabelle_OProf))
% 1.32/1.45 => ! [B_xa] :
% 1.32/1.45 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B_xa),c_Arrow__Order__Mirabelle_OProf))
% 1.32/1.45 => ! [B_a,B_b] :
% 1.32/1.45 ( ! [B_i] :
% 1.32/1.45 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(B_x,B_i)))
% 1.32/1.45 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(B_xa,B_i))) )
% 1.32/1.45 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(V_Fa_2,B_x)))
% 1.32/1.45 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(V_Fa_2,B_xa))) ) ) ) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_equalityI,axiom,
% 1.32/1.45 ! [V_B_2,V_A_2,T_a] :
% 1.32/1.45 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2))
% 1.32/1.45 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2),V_A_2))
% 1.32/1.45 => V_A_2 = V_B_2 ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_subset__refl,axiom,
% 1.32/1.45 ! [V_A_2,T_a] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_A_2)) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_set__eq__subset,axiom,
% 1.32/1.45 ! [T_a,V_B_2,V_A_2] :
% 1.32/1.45 ( V_A_2 = V_B_2
% 1.32/1.45 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2))
% 1.32/1.45 & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2),V_A_2)) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_rev__predicate1D,axiom,
% 1.32/1.45 ! [V_Q_2,T_a,V_x_2,V_Pa_2] :
% 1.32/1.45 ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 1.32/1.45 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_Pa_2),V_Q_2))
% 1.32/1.45 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_equalityD1,axiom,
% 1.32/1.45 ! [T_a,V_B_2,V_A_2] :
% 1.32/1.45 ( V_A_2 = V_B_2
% 1.32/1.45 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_equalityD2,axiom,
% 1.32/1.45 ! [T_a,V_B_2,V_A_2] :
% 1.32/1.45 ( V_A_2 = V_B_2
% 1.32/1.45 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2),V_A_2)) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_predicate1D,axiom,
% 1.32/1.45 ! [V_x_2,V_Q_2,V_Pa_2,T_a] :
% 1.32/1.45 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_Pa_2),V_Q_2))
% 1.32/1.45 => ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 1.32/1.45 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_subset__trans,axiom,
% 1.32/1.45 ! [V_C_2,V_B_2,V_A_2,T_a] :
% 1.32/1.45 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2))
% 1.32/1.45 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2),V_C_2))
% 1.32/1.45 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_C_2)) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_predicate2D,axiom,
% 1.32/1.45 ! [V_y_2,V_x_2,V_Q_2,V_Pa_2,T_b,T_a] :
% 1.32/1.45 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),V_Pa_2),V_Q_2))
% 1.32/1.45 => ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2))
% 1.32/1.45 => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_equalityE,axiom,
% 1.32/1.45 ! [T_a,V_B_2,V_A_2] :
% 1.32/1.45 ( V_A_2 = V_B_2
% 1.32/1.45 => ~ ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2))
% 1.32/1.45 => ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2),V_A_2)) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_rev__predicate2D,axiom,
% 1.32/1.45 ! [V_Q_2,T_b,T_a,V_y_2,V_x_2,V_Pa_2] :
% 1.32/1.45 ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2))
% 1.32/1.45 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),V_Pa_2),V_Q_2))
% 1.32/1.45 => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_PiE,axiom,
% 1.32/1.45 ! [V_x_2,V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 1.32/1.45 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_OPi(T_a,T_b,V_A_2,V_B_2)))
% 1.32/1.45 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_B_2,V_x_2)))
% 1.32/1.45 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_funcset__mem,axiom,
% 1.32/1.45 ! [V_x_2,V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 1.32/1.45 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_OPi(T_a,T_b,V_A_2,hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2))))
% 1.32/1.45 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 1.32/1.45 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),V_B_2)) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_inv__f__f,axiom,
% 1.32/1.45 ! [V_x_2,V_f_2,T_b,T_a] :
% 1.32/1.45 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 1.32/1.45 => hAPP(c_Hilbert__Choice_Oinv__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 ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_inv__f__eq,axiom,
% 1.32/1.45 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] :
% 1.32/1.45 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 1.32/1.45 => ( hAPP(V_f_2,V_x_2) = V_y_2
% 1.32/1.45 => hAPP(c_Hilbert__Choice_Oinv__into(T_a,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_f_2),V_y_2) = V_x_2 ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_inv__into__f__eq,axiom,
% 1.32/1.45 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] :
% 1.32/1.45 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 1.32/1.45 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 1.32/1.45 => ( hAPP(V_f_2,V_x_2) = V_y_2
% 1.32/1.45 => hAPP(c_Hilbert__Choice_Oinv__into(T_a,T_b,V_A_2,V_f_2),V_y_2) = V_x_2 ) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_inj__on__add__nat,axiom,
% 1.32/1.45 ! [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) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_Prof__def,axiom,
% 1.32/1.45 c_Arrow__Order__Mirabelle_OProf = c_FuncSet_OPi(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)),hAPP(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_OLin)) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_Pi__anti__mono,axiom,
% 1.32/1.45 ! [V_B_2,T_b,V_A_2,V_A_H_2,T_a] :
% 1.32/1.45 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_H_2),V_A_2))
% 1.32/1.45 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,T_b),tc_HOL_Obool),c_FuncSet_OPi(T_a,T_b,V_A_2,V_B_2)),c_FuncSet_OPi(T_a,T_b,V_A_H_2,V_B_2))) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_funcset__id,axiom,
% 1.32/1.45 ! [V_A_2,T_a] : hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_a)),c_COMBI(T_a)),c_FuncSet_OPi(T_a,T_a,V_A_2,hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2)))) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_Pi__UNIV,axiom,
% 1.32/1.45 ! [V_A_2,T_b,T_a] : c_FuncSet_OPi(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)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_a,T_b),tc_HOL_Obool)) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_Pi__mem,axiom,
% 1.32/1.45 ! [V_x_2,V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 1.32/1.45 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_OPi(T_a,T_b,V_A_2,V_B_2)))
% 1.32/1.45 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 1.32/1.45 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_B_2,V_x_2))) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_inv__into__f__f,axiom,
% 1.32/1.45 ! [V_x_2,V_A_2,V_f_2,T_b,T_a] :
% 1.32/1.45 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 1.32/1.45 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 1.32/1.45 => hAPP(c_Hilbert__Choice_Oinv__into(T_a,T_b,V_A_2,V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2 ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_inj__fun,axiom,
% 1.32/1.45 ! [T_c,V_f_2,T_b,T_a] :
% 1.32/1.45 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 1.32/1.45 => c_Fun_Oinj__on(T_a,tc_fun(T_c,T_b),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))) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_dictatorI,axiom,
% 1.32/1.45 ! [V_i_2,V_Fa_2] :
% 1.32/1.45 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),V_Fa_2),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,hAPP(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_Arrow__Order__Mirabelle_OLin))))
% 1.32/1.45 => ( ! [B_x] :
% 1.32/1.45 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B_x),c_Arrow__Order__Mirabelle_OProf))
% 1.32/1.45 => ! [B_a,B_b] :
% 1.32/1.45 ( B_a != B_b
% 1.32/1.45 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(B_x,V_i_2)))
% 1.32/1.45 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(V_Fa_2,B_x))) ) ) )
% 1.32/1.45 => c_Arrow__Order__Mirabelle_Odictator(V_Fa_2,V_i_2) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_inj__eq,axiom,
% 1.32/1.45 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] :
% 1.32/1.45 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 1.32/1.45 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 1.32/1.45 <=> V_x_2 = V_y_2 ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_injD,axiom,
% 1.32/1.45 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] :
% 1.32/1.45 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 1.32/1.45 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 1.32/1.45 => V_x_2 = V_y_2 ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_inj__on__def,axiom,
% 1.32/1.45 ! [V_A_2,V_f_2,T_b,T_a] :
% 1.32/1.45 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 1.32/1.45 <=> ! [B_x] :
% 1.32/1.45 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 1.32/1.45 => ! [B_xa] :
% 1.32/1.45 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2))
% 1.32/1.45 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_xa)
% 1.32/1.45 => B_x = B_xa ) ) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_inj__on__id2,axiom,
% 1.32/1.45 ! [V_A_2,T_a] : c_Fun_Oinj__on(T_a,T_a,c_COMBI(T_a),V_A_2) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_dictator__def,axiom,
% 1.32/1.45 ! [V_i_2,V_Fa_2] :
% 1.32/1.45 ( c_Arrow__Order__Mirabelle_Odictator(V_Fa_2,V_i_2)
% 1.32/1.45 <=> ! [B_x] :
% 1.32/1.45 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B_x),c_Arrow__Order__Mirabelle_OProf))
% 1.32/1.45 => hAPP(V_Fa_2,B_x) = hAPP(B_x,V_i_2) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_inj__on__contraD,axiom,
% 1.32/1.45 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] :
% 1.32/1.45 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 1.32/1.45 => ( V_x_2 != V_y_2
% 1.32/1.45 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 1.32/1.45 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2))
% 1.32/1.45 => hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) ) ) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_inj__on__iff,axiom,
% 1.32/1.45 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] :
% 1.32/1.45 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 1.32/1.45 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 1.32/1.45 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2))
% 1.32/1.45 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 1.32/1.45 <=> V_x_2 = V_y_2 ) ) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_inj__onD,axiom,
% 1.32/1.45 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] :
% 1.32/1.45 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 1.32/1.45 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 1.32/1.45 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 1.32/1.45 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2))
% 1.32/1.45 => V_x_2 = V_y_2 ) ) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_subset__inj__on,axiom,
% 1.32/1.45 ! [V_A_2,V_B_2,V_f_2,T_b,T_a] :
% 1.32/1.45 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2)
% 1.32/1.45 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2))
% 1.32/1.45 => c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_iso__tuple__UNIV__I,axiom,
% 1.32/1.45 ! [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)))) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_card__inj,axiom,
% 1.32/1.45 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 1.32/1.45 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_OPi(T_a,T_b,V_A_2,hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2))))
% 1.32/1.45 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 1.32/1.45 => ( c_Finite__Set_Ofinite(T_b,V_B_2)
% 1.32/1.45 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(T_a,V_A_2)),c_Finite__Set_Ocard(T_b,V_B_2))) ) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_Pi__mono,axiom,
% 1.32/1.45 ! [V_C_2,V_B_2,T_b,V_A_2,T_a] :
% 1.32/1.45 ( ! [B_x] :
% 1.32/1.45 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 1.32/1.45 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool),hAPP(V_B_2,B_x)),hAPP(V_C_2,B_x))) )
% 1.32/1.45 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,T_b),tc_HOL_Obool),c_FuncSet_OPi(T_a,T_b,V_A_2,V_B_2)),c_FuncSet_OPi(T_a,T_b,V_A_2,V_C_2))) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_Pi__I,axiom,
% 1.32/1.45 ! [V_B_2,V_f_2,T_b,V_A_2,T_a] :
% 1.32/1.45 ( ! [B_x] :
% 1.32/1.45 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 1.32/1.45 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,B_x)),hAPP(V_B_2,B_x))) )
% 1.32/1.45 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_OPi(T_a,T_b,V_A_2,V_B_2))) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_finite__indi,axiom,
% 1.32/1.45 c_Finite__Set_Ofinite(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_card__bij,axiom,
% 1.32/1.45 ! [V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 1.32/1.45 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_OPi(T_a,T_b,V_A_2,hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2))))
% 1.32/1.45 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 1.32/1.45 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,T_a)),V_g_2),c_FuncSet_OPi(T_b,T_a,V_B_2,hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_b),V_A_2))))
% 1.32/1.45 => ( c_Fun_Oinj__on(T_b,T_a,V_g_2,V_B_2)
% 1.32/1.45 => ( c_Finite__Set_Ofinite(T_a,V_A_2)
% 1.32/1.45 => ( c_Finite__Set_Ofinite(T_b,V_B_2)
% 1.32/1.45 => c_Finite__Set_Ocard(T_a,V_A_2) = c_Finite__Set_Ocard(T_b,V_B_2) ) ) ) ) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_card__psubset,axiom,
% 1.32/1.45 ! [V_A_2,V_B_2,T_a] :
% 1.32/1.45 ( c_Finite__Set_Ofinite(T_a,V_B_2)
% 1.32/1.45 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2))
% 1.32/1.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Finite__Set_Ocard(T_a,V_A_2)),c_Finite__Set_Ocard(T_a,V_B_2)))
% 1.32/1.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_psubset__card__mono,axiom,
% 1.32/1.45 ! [V_A_2,V_B_2,T_a] :
% 1.32/1.45 ( c_Finite__Set_Ofinite(T_a,V_B_2)
% 1.32/1.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 1.32/1.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Finite__Set_Ocard(T_a,V_A_2)),c_Finite__Set_Ocard(T_a,V_B_2))) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_card__mono,axiom,
% 1.32/1.45 ! [V_A_2,V_B_2,T_a] :
% 1.32/1.45 ( c_Finite__Set_Ofinite(T_a,V_B_2)
% 1.32/1.45 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2))
% 1.32/1.45 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(T_a,V_A_2)),c_Finite__Set_Ocard(T_a,V_B_2))) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_card__seteq,axiom,
% 1.32/1.45 ! [V_A_2,V_B_2,T_a] :
% 1.32/1.45 ( c_Finite__Set_Ofinite(T_a,V_B_2)
% 1.32/1.45 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2))
% 1.32/1.45 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(T_a,V_B_2)),c_Finite__Set_Ocard(T_a,V_A_2)))
% 1.32/1.45 => V_A_2 = V_B_2 ) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_finite,axiom,
% 1.32/1.45 ! [V_A_2,T_a] :
% 1.32/1.45 ( class_Finite__Set_Ofinite(T_a)
% 1.32/1.45 => c_Finite__Set_Ofinite(T_a,V_A_2) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_finite__code,axiom,
% 1.32/1.45 ! [V_A_2,T_a] :
% 1.32/1.45 ( class_Finite__Set_Ofinite(T_a)
% 1.32/1.45 => c_Finite__Set_Ofinite(T_a,V_A_2) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_card__UNIV__unit,axiom,
% 1.32/1.45 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) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_rev__finite__subset,axiom,
% 1.32/1.45 ! [V_A_2,V_B_2,T_a] :
% 1.32/1.45 ( c_Finite__Set_Ofinite(T_a,V_B_2)
% 1.32/1.45 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2))
% 1.32/1.45 => c_Finite__Set_Ofinite(T_a,V_A_2) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_finite__subset,axiom,
% 1.32/1.45 ! [V_B_2,V_A_2,T_a] :
% 1.32/1.45 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2))
% 1.32/1.45 => ( c_Finite__Set_Ofinite(T_a,V_B_2)
% 1.32/1.45 => c_Finite__Set_Ofinite(T_a,V_A_2) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_finite__Prod__UNIV,axiom,
% 1.32/1.45 ! [T_b,T_a] :
% 1.32/1.45 ( c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 1.32/1.45 => ( c_Finite__Set_Ofinite(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 1.32/1.45 => 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))) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_finite__Plus__UNIV__iff,axiom,
% 1.32/1.45 ! [T_b,T_a] :
% 1.32/1.45 ( 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)))
% 1.32/1.45 <=> ( c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 1.32/1.45 & c_Finite__Set_Ofinite(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_finite__option__UNIV,axiom,
% 1.32/1.45 ! [T_a] :
% 1.32/1.45 ( c_Finite__Set_Ofinite(tc_Option_Ooption(T_a),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(T_a),tc_HOL_Obool)))
% 1.32/1.45 <=> c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_finite__UNIV,axiom,
% 1.32/1.45 ! [T_a] :
% 1.32/1.45 ( class_Finite__Set_Ofinite(T_a)
% 1.32/1.45 => c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_card__eq__UNIV__imp__eq__UNIV,axiom,
% 1.32/1.45 ! [V_A_2,T_a] :
% 1.32/1.45 ( c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 1.32/1.45 => ( c_Finite__Set_Ocard(T_a,V_A_2) = c_Finite__Set_Ocard(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 1.32/1.45 => V_A_2 = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_finite__fun__UNIVD2,axiom,
% 1.32/1.45 ! [T_b,T_a] :
% 1.32/1.45 ( 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)))
% 1.32/1.45 => c_Finite__Set_Ofinite(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_card__Plus,axiom,
% 1.32/1.45 ! [V_B_2,T_b,V_A_2,T_a] :
% 1.32/1.45 ( c_Finite__Set_Ofinite(T_a,V_A_2)
% 1.32/1.45 => ( c_Finite__Set_Ofinite(T_b,V_B_2)
% 1.32/1.45 => 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),c_Finite__Set_Ocard(T_a,V_A_2)),c_Finite__Set_Ocard(T_b,V_B_2)) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_card_Oinsert,axiom,
% 1.32/1.45 ! [V_x_2,V_A_2,T_a] :
% 1.32/1.45 ( c_Finite__Set_Ofinite(T_a,V_A_2)
% 1.32/1.45 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 1.32/1.45 => c_Finite__Set_Ocard(T_a,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)),c_Finite__Set_Ocard(T_a,V_A_2)) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_folding__image__simple__idem_Osubset__idem,axiom,
% 1.32/1.45 ! [V_B_2,V_A_2,V_Fa_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 1.32/1.45 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_Fa_2)
% 1.32/1.45 => ( c_Finite__Set_Ofinite(T_b,V_A_2)
% 1.32/1.45 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool),V_B_2),V_A_2))
% 1.32/1.45 => 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) ) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_folding__image__simple__idem_Oin__idem,axiom,
% 1.32/1.45 ! [V_x_2,V_A_2,V_Fa_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 1.32/1.45 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_Fa_2)
% 1.32/1.45 => ( c_Finite__Set_Ofinite(T_b,V_A_2)
% 1.32/1.45 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 1.32/1.45 => 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) ) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_insertCI,axiom,
% 1.32/1.45 ! [V_ba_2,V_B_2,V_aa_2,T_a] :
% 1.32/1.45 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_B_2))
% 1.32/1.45 => V_aa_2 = V_ba_2 )
% 1.32/1.45 => hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Set_Oinsert(T_a,V_ba_2,V_B_2))) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_insertE,axiom,
% 1.32/1.45 ! [V_A_2,V_ba_2,V_aa_2,T_a] :
% 1.32/1.45 ( hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Set_Oinsert(T_a,V_ba_2,V_A_2)))
% 1.32/1.45 => ( V_aa_2 != V_ba_2
% 1.32/1.45 => hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2)) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_finite_OinsertI,axiom,
% 1.32/1.45 ! [V_aa_2,V_A_2,T_a] :
% 1.32/1.45 ( c_Finite__Set_Ofinite(T_a,V_A_2)
% 1.32/1.45 => c_Finite__Set_Ofinite(T_a,c_Set_Oinsert(T_a,V_aa_2,V_A_2)) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_folding__image__simple__idem_Oinsert__idem,axiom,
% 1.32/1.45 ! [V_x_2,V_A_2,V_Fa_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 1.32/1.45 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_Fa_2)
% 1.32/1.45 => ( c_Finite__Set_Ofinite(T_b,V_A_2)
% 1.32/1.45 => hAPP(V_Fa_2,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)) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_finite__insert,axiom,
% 1.32/1.45 ! [V_A_2,V_aa_2,T_a] :
% 1.32/1.45 ( c_Finite__Set_Ofinite(T_a,c_Set_Oinsert(T_a,V_aa_2,V_A_2))
% 1.32/1.45 <=> c_Finite__Set_Ofinite(T_a,V_A_2) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_folding__image__simple__idem_Oidem,axiom,
% 1.32/1.45 ! [V_x_2,V_Fa_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 1.32/1.45 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_Fa_2)
% 1.32/1.45 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_insert__mono,axiom,
% 1.32/1.45 ! [V_aa_2,V_D_2,V_C_2,T_a] :
% 1.32/1.45 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_C_2),V_D_2))
% 1.32/1.45 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_aa_2,V_C_2)),c_Set_Oinsert(T_a,V_aa_2,V_D_2))) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_subset__insertI2,axiom,
% 1.32/1.45 ! [V_ba_2,V_B_2,V_A_2,T_a] :
% 1.32/1.45 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2))
% 1.32/1.45 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),c_Set_Oinsert(T_a,V_ba_2,V_B_2))) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_subset__insertI,axiom,
% 1.32/1.45 ! [V_aa_2,V_B_2,T_a] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2),c_Set_Oinsert(T_a,V_aa_2,V_B_2))) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_insert__absorb2,axiom,
% 1.32/1.45 ! [V_A_2,V_x_2,T_a] : c_Set_Oinsert(T_a,V_x_2,c_Set_Oinsert(T_a,V_x_2,V_A_2)) = c_Set_Oinsert(T_a,V_x_2,V_A_2) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_insert__commute,axiom,
% 1.32/1.45 ! [V_A_2,V_y_2,V_x_2,T_a] : c_Set_Oinsert(T_a,V_x_2,c_Set_Oinsert(T_a,V_y_2,V_A_2)) = c_Set_Oinsert(T_a,V_y_2,c_Set_Oinsert(T_a,V_x_2,V_A_2)) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_insert__code,axiom,
% 1.32/1.45 ! [V_x_2,V_A_2,V_y_2,T_a] :
% 1.32/1.45 ( hBOOL(hAPP(c_Set_Oinsert(T_a,V_y_2,V_A_2),V_x_2))
% 1.32/1.45 <=> ( V_y_2 = V_x_2
% 1.32/1.45 | hBOOL(hAPP(V_A_2,V_x_2)) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_insertI1,axiom,
% 1.32/1.45 ! [V_B_2,V_aa_2,T_a] : hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Set_Oinsert(T_a,V_aa_2,V_B_2))) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_insert__iff,axiom,
% 1.32/1.45 ! [V_A_2,V_ba_2,V_aa_2,T_a] :
% 1.32/1.45 ( hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Set_Oinsert(T_a,V_ba_2,V_A_2)))
% 1.32/1.45 <=> ( V_aa_2 = V_ba_2
% 1.32/1.45 | hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2)) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_insert__ident,axiom,
% 1.32/1.45 ! [V_B_2,V_A_2,V_x_2,T_a] :
% 1.32/1.45 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 1.32/1.45 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2))
% 1.32/1.45 => ( c_Set_Oinsert(T_a,V_x_2,V_A_2) = c_Set_Oinsert(T_a,V_x_2,V_B_2)
% 1.32/1.45 <=> V_A_2 = V_B_2 ) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_insertI2,axiom,
% 1.32/1.45 ! [V_ba_2,V_B_2,V_aa_2,T_a] :
% 1.32/1.45 ( hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_B_2))
% 1.32/1.45 => hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Set_Oinsert(T_a,V_ba_2,V_B_2))) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_insert__absorb,axiom,
% 1.32/1.45 ! [V_A_2,V_aa_2,T_a] :
% 1.32/1.45 ( hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2))
% 1.32/1.45 => c_Set_Oinsert(T_a,V_aa_2,V_A_2) = V_A_2 ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_finite__Plus__iff,axiom,
% 1.32/1.45 ! [V_B_2,V_A_2,T_b,T_a] :
% 1.32/1.45 ( c_Finite__Set_Ofinite(tc_sum(T_a,T_b),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2))
% 1.32/1.45 <=> ( c_Finite__Set_Ofinite(T_a,V_A_2)
% 1.32/1.45 & c_Finite__Set_Ofinite(T_b,V_B_2) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_finite__Plus,axiom,
% 1.32/1.45 ! [V_B_2,T_b,V_A_2,T_a] :
% 1.32/1.45 ( c_Finite__Set_Ofinite(T_a,V_A_2)
% 1.32/1.45 => ( c_Finite__Set_Ofinite(T_b,V_B_2)
% 1.32/1.45 => c_Finite__Set_Ofinite(tc_sum(T_a,T_b),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2)) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_finite__PlusD_I1_J,axiom,
% 1.32/1.45 ! [V_B_2,V_A_2,T_b,T_a] :
% 1.32/1.45 ( c_Finite__Set_Ofinite(tc_sum(T_a,T_b),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2))
% 1.32/1.45 => c_Finite__Set_Ofinite(T_a,V_A_2) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_finite__PlusD_I2_J,axiom,
% 1.32/1.45 ! [V_B_2,V_A_2,T_b,T_a] :
% 1.32/1.45 ( c_Finite__Set_Ofinite(tc_sum(T_a,T_b),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2))
% 1.32/1.45 => c_Finite__Set_Ofinite(T_b,V_B_2) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_subset__insert,axiom,
% 1.32/1.45 ! [V_B_2,V_A_2,V_x_2,T_a] :
% 1.32/1.45 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 1.32/1.45 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),c_Set_Oinsert(T_a,V_x_2,V_B_2)))
% 1.32/1.45 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_insert__subset,axiom,
% 1.32/1.45 ! [V_B_2,V_A_2,V_x_2,T_a] :
% 1.32/1.45 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_x_2,V_A_2)),V_B_2))
% 1.32/1.45 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2))
% 1.32/1.45 & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_card__insert__le,axiom,
% 1.32/1.45 ! [V_x_2,V_A_2,T_a] :
% 1.32/1.45 ( c_Finite__Set_Ofinite(T_a,V_A_2)
% 1.32/1.45 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(T_a,V_A_2)),c_Finite__Set_Ocard(T_a,c_Set_Oinsert(T_a,V_x_2,V_A_2)))) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_UNIV__Plus__UNIV,axiom,
% 1.32/1.45 ! [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)) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_card__Plus__conv__if,axiom,
% 1.32/1.45 ! [V_B_2,T_b,V_A_2,T_a] :
% 1.32/1.45 ( ( ( c_Finite__Set_Ofinite(T_a,V_A_2)
% 1.32/1.45 & c_Finite__Set_Ofinite(T_b,V_B_2) )
% 1.32/1.45 => 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),c_Finite__Set_Ocard(T_a,V_A_2)),c_Finite__Set_Ocard(T_b,V_B_2)) )
% 1.32/1.45 & ( ~ ( c_Finite__Set_Ofinite(T_a,V_A_2)
% 1.32/1.45 & c_Finite__Set_Ofinite(T_b,V_B_2) )
% 1.32/1.45 => 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) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_folding__image__simple_Oinsert,axiom,
% 1.32/1.45 ! [V_x_2,V_A_2,V_Fa_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 1.32/1.45 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_Fa_2)
% 1.32/1.45 => ( c_Finite__Set_Ofinite(T_b,V_A_2)
% 1.32/1.45 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 1.32/1.45 => hAPP(V_Fa_2,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)) ) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_same__fstI,axiom,
% 1.32/1.45 ! [T_a,V_R_2,V_y_2,V_y_H_2,T_b,V_x_2,V_Pa_2] :
% 1.32/1.45 ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 1.32/1.45 => ( 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)))
% 1.32/1.45 => 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_Pa_2,V_R_2))) ) ) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_less__zeroE,axiom,
% 1.32/1.45 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_le0,axiom,
% 1.32/1.45 ! [V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ).
% 1.32/1.45
% 1.32/1.45 fof(fact_not__less0,axiom,
% 1.32/1.45 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 1.32/1.45
% 1.32/1.46 fof(fact_neq0__conv,axiom,
% 1.32/1.46 ! [V_na_2] :
% 1.32/1.46 ( V_na_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.32/1.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_na_2)) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_less__nat__zero__code,axiom,
% 1.32/1.46 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_gr__implies__not0,axiom,
% 1.32/1.46 ! [V_n,V_m] :
% 1.32/1.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 1.32/1.46 => V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_gr0I,axiom,
% 1.32/1.46 ! [V_n] :
% 1.32/1.46 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.32/1.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_plus__nat_Oadd__0,axiom,
% 1.32/1.46 ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ).
% 1.32/1.46
% 1.32/1.46 fof(fact_Nat_Oadd__0__right,axiom,
% 1.32/1.46 ! [V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 1.32/1.46
% 1.32/1.46 fof(fact_add__is__0,axiom,
% 1.32/1.46 ! [V_na_2,V_m_2] :
% 1.32/1.46 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_na_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.32/1.46 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.32/1.46 & V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_add__eq__self__zero,axiom,
% 1.32/1.46 ! [V_n,V_m] :
% 1.32/1.46 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_m
% 1.32/1.46 => V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_zero__reorient,axiom,
% 1.32/1.46 ! [V_x_2,T_a] :
% 1.32/1.46 ( class_Groups_Ozero(T_a)
% 1.32/1.46 => ( c_Groups_Ozero__class_Ozero(T_a) = V_x_2
% 1.32/1.46 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_one__neq__zero,axiom,
% 1.32/1.46 ! [T_a] :
% 1.32/1.46 ( class_Rings_Ozero__neq__one(T_a)
% 1.32/1.46 => c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_zero__neq__one,axiom,
% 1.32/1.46 ! [T_a] :
% 1.32/1.46 ( class_Rings_Ozero__neq__one(T_a)
% 1.32/1.46 => c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_add__0__left,axiom,
% 1.32/1.46 ! [V_a,T_a] :
% 1.32/1.46 ( class_Groups_Omonoid__add(T_a)
% 1.32/1.46 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_add__0,axiom,
% 1.32/1.46 ! [V_a,T_a] :
% 1.32/1.46 ( class_Groups_Ocomm__monoid__add(T_a)
% 1.32/1.46 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_double__zero__sym,axiom,
% 1.32/1.46 ! [V_aa_2,T_a] :
% 1.32/1.46 ( class_Groups_Olinordered__ab__group__add(T_a)
% 1.32/1.46 => ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_aa_2)
% 1.32/1.46 <=> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_add__0__right,axiom,
% 1.32/1.46 ! [V_a,T_a] :
% 1.32/1.46 ( class_Groups_Omonoid__add(T_a)
% 1.32/1.46 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_add_Ocomm__neutral,axiom,
% 1.32/1.46 ! [V_a,T_a] :
% 1.32/1.46 ( class_Groups_Ocomm__monoid__add(T_a)
% 1.32/1.46 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_less__eq__nat_Osimps_I1_J,axiom,
% 1.32/1.46 ! [V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_le__0__eq,axiom,
% 1.32/1.46 ! [V_na_2] :
% 1.32/1.46 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_na_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 1.32/1.46 <=> V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom,
% 1.32/1.46 ! [V_aa_2,T_a] :
% 1.32/1.46 ( class_Groups_Olinordered__ab__group__add(T_a)
% 1.32/1.46 => ( hBOOL(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_aa_2),V_aa_2)))
% 1.32/1.46 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_aa_2)) ) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom,
% 1.32/1.46 ! [V_aa_2,T_a] :
% 1.32/1.46 ( class_Groups_Olinordered__ab__group__add(T_a)
% 1.32/1.46 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_aa_2)),c_Groups_Ozero__class_Ozero(T_a)))
% 1.32/1.46 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_add__nonneg__nonneg,axiom,
% 1.32/1.46 ! [V_b,V_a,T_a] :
% 1.32/1.46 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.32/1.46 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 1.32/1.46 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 1.32/1.46 => hBOOL(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))) ) ) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_add__nonneg__eq__0__iff,axiom,
% 1.32/1.46 ! [V_y_2,V_x_2,T_a] :
% 1.32/1.46 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.32/1.46 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_x_2))
% 1.32/1.46 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_y_2))
% 1.32/1.46 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x_2),V_y_2) = c_Groups_Ozero__class_Ozero(T_a)
% 1.32/1.46 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 1.32/1.46 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_add__increasing,axiom,
% 1.32/1.46 ! [V_c,V_b,V_a,T_a] :
% 1.32/1.46 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.32/1.46 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 1.32/1.46 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_c))
% 1.32/1.46 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_add__increasing2,axiom,
% 1.32/1.46 ! [V_a,V_b,V_c,T_a] :
% 1.32/1.46 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.32/1.46 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 1.32/1.46 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a))
% 1.32/1.46 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_add__nonpos__nonpos,axiom,
% 1.32/1.46 ! [V_b,V_a,T_a] :
% 1.32/1.46 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.32/1.46 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 1.32/1.46 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 1.32/1.46 => hBOOL(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))) ) ) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_pos__add__strict,axiom,
% 1.32/1.46 ! [V_c,V_b,V_a,T_a] :
% 1.32/1.46 ( class_Rings_Olinordered__semidom(T_a)
% 1.32/1.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 1.32/1.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
% 1.32/1.46 => 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))) ) ) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_add__neg__neg,axiom,
% 1.32/1.46 ! [V_b,V_a,T_a] :
% 1.32/1.46 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.32/1.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 1.32/1.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 1.32/1.46 => 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))) ) ) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_add__pos__pos,axiom,
% 1.32/1.46 ! [V_b,V_a,T_a] :
% 1.32/1.46 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.32/1.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 1.32/1.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 1.32/1.46 => 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))) ) ) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom,
% 1.32/1.46 ! [V_aa_2,T_a] :
% 1.32/1.46 ( class_Groups_Olinordered__ab__group__add(T_a)
% 1.32/1.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_aa_2)),c_Groups_Ozero__class_Ozero(T_a)))
% 1.32/1.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_aa_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom,
% 1.32/1.46 ! [V_aa_2,T_a] :
% 1.32/1.46 ( class_Groups_Olinordered__ab__group__add(T_a)
% 1.32/1.46 => ( 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_aa_2),V_aa_2)))
% 1.32/1.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_aa_2)) ) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_not__one__le__zero,axiom,
% 1.32/1.46 ! [T_a] :
% 1.32/1.46 ( class_Rings_Olinordered__semidom(T_a)
% 1.32/1.46 => ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_zero__le__one,axiom,
% 1.32/1.46 ! [T_a] :
% 1.32/1.46 ( class_Rings_Olinordered__semidom(T_a)
% 1.32/1.46 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_zero__less__one,axiom,
% 1.32/1.46 ! [T_a] :
% 1.32/1.46 ( class_Rings_Olinordered__semidom(T_a)
% 1.32/1.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_not__one__less__zero,axiom,
% 1.32/1.46 ! [T_a] :
% 1.32/1.46 ( class_Rings_Olinordered__semidom(T_a)
% 1.32/1.46 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_add__gr__0,axiom,
% 1.32/1.46 ! [V_na_2,V_m_2] :
% 1.32/1.46 ( 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_na_2)))
% 1.32/1.46 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))
% 1.32/1.46 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_na_2)) ) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_card__infinite,axiom,
% 1.32/1.46 ! [V_A_2,T_a] :
% 1.32/1.46 ( ~ c_Finite__Set_Ofinite(T_a,V_A_2)
% 1.32/1.46 => c_Finite__Set_Ocard(T_a,V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_add__nonpos__neg,axiom,
% 1.32/1.46 ! [V_b,V_a,T_a] :
% 1.32/1.46 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.32/1.46 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 1.32/1.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 1.32/1.46 => 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))) ) ) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_add__neg__nonpos,axiom,
% 1.32/1.46 ! [V_b,V_a,T_a] :
% 1.32/1.46 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.32/1.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 1.32/1.46 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 1.32/1.46 => 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))) ) ) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_add__strict__increasing2,axiom,
% 1.32/1.46 ! [V_c,V_b,V_a,T_a] :
% 1.32/1.46 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.32/1.46 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 1.32/1.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
% 1.32/1.46 => 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))) ) ) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_add__strict__increasing,axiom,
% 1.32/1.46 ! [V_c,V_b,V_a,T_a] :
% 1.32/1.46 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.32/1.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 1.32/1.46 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_c))
% 1.32/1.46 => 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))) ) ) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_add__nonneg__pos,axiom,
% 1.32/1.46 ! [V_b,V_a,T_a] :
% 1.32/1.46 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.32/1.46 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 1.32/1.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 1.32/1.46 => 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))) ) ) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_add__pos__nonneg,axiom,
% 1.32/1.46 ! [V_b,V_a,T_a] :
% 1.32/1.46 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.32/1.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 1.32/1.46 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 1.32/1.46 => 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))) ) ) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_zero__less__two,axiom,
% 1.32/1.46 ! [T_a] :
% 1.32/1.46 ( class_Rings_Olinordered__semidom(T_a)
% 1.32/1.46 => 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)))) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_card__ge__0__finite,axiom,
% 1.32/1.46 ! [V_A_2,T_a] :
% 1.32/1.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Finite__Set_Ocard(T_a,V_A_2)))
% 1.32/1.46 => c_Finite__Set_Ofinite(T_a,V_A_2) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_finite__UNIV__card__ge__0,axiom,
% 1.32/1.46 ! [T_a] :
% 1.32/1.46 ( c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 1.32/1.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Finite__Set_Ocard(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_even__less__0__iff,axiom,
% 1.32/1.46 ! [V_aa_2,T_a] :
% 1.32/1.46 ( class_Rings_Olinordered__idom(T_a)
% 1.32/1.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_aa_2)),c_Groups_Ozero__class_Ozero(T_a)))
% 1.32/1.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_aa_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_in__lex__prod,axiom,
% 1.32/1.46 ! [V_s_2,V_r_2,V_b_H_2,V_a_H_2,V_ba_2,V_aa_2,T_b,T_a] :
% 1.32/1.46 ( 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_aa_2),V_ba_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)))
% 1.32/1.46 <=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_a_H_2)),V_r_2))
% 1.32/1.46 | ( V_aa_2 = V_a_H_2
% 1.32/1.46 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_ba_2),V_b_H_2)),V_s_2)) ) ) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_finite__fun__UNIVD1,axiom,
% 1.32/1.46 ! [T_b,T_a] :
% 1.32/1.46 ( 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)))
% 1.32/1.46 => ( 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))
% 1.32/1.46 => c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_Suc__mono,axiom,
% 1.32/1.46 ! [V_n,V_m] :
% 1.32/1.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 1.32/1.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_lessI,axiom,
% 1.32/1.46 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_n))) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_zero__less__Suc,axiom,
% 1.32/1.46 ! [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))) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_Suc__neq__Zero,axiom,
% 1.32/1.46 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_Zero__neq__Suc,axiom,
% 1.32/1.46 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_nat_Osimps_I3_J,axiom,
% 1.32/1.46 ! [V_nat_H_1] : hAPP(c_Nat_OSuc,V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_Suc__not__Zero,axiom,
% 1.32/1.46 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_nat_Osimps_I2_J,axiom,
% 1.32/1.46 ! [V_nat_H] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_nat_H) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_Zero__not__Suc,axiom,
% 1.32/1.46 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_Suc__leD,axiom,
% 1.32/1.46 ! [V_n,V_m] :
% 1.32/1.46 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m)),V_n))
% 1.32/1.46 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_le__SucE,axiom,
% 1.32/1.46 ! [V_n,V_m] :
% 1.32/1.46 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),hAPP(c_Nat_OSuc,V_n)))
% 1.32/1.46 => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n))
% 1.32/1.46 => V_m = hAPP(c_Nat_OSuc,V_n) ) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_le__SucI,axiom,
% 1.32/1.46 ! [V_n,V_m] :
% 1.32/1.46 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n))
% 1.32/1.46 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),hAPP(c_Nat_OSuc,V_n))) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_Suc__le__mono,axiom,
% 1.32/1.46 ! [V_m_2,V_na_2] :
% 1.32/1.46 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_na_2)),hAPP(c_Nat_OSuc,V_m_2)))
% 1.32/1.46 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_na_2),V_m_2)) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_le__Suc__eq,axiom,
% 1.32/1.46 ! [V_na_2,V_m_2] :
% 1.32/1.46 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_na_2)))
% 1.32/1.46 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_na_2))
% 1.32/1.46 | V_m_2 = hAPP(c_Nat_OSuc,V_na_2) ) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_not__less__eq__eq,axiom,
% 1.32/1.46 ! [V_na_2,V_m_2] :
% 1.32/1.46 ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_na_2))
% 1.32/1.46 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_na_2)),V_m_2)) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_Suc__n__not__le__n,axiom,
% 1.32/1.46 ! [V_n] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n)),V_n)) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_Suc__less__SucD,axiom,
% 1.32/1.46 ! [V_n,V_m] :
% 1.32/1.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)))
% 1.32/1.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_Suc__lessD,axiom,
% 1.32/1.46 ! [V_n,V_m] :
% 1.32/1.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
% 1.32/1.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_less__SucE,axiom,
% 1.32/1.46 ! [V_n,V_m] :
% 1.32/1.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)))
% 1.32/1.46 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 1.32/1.46 => V_m = V_n ) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_less__trans__Suc,axiom,
% 1.32/1.46 ! [V_k,V_j,V_i] :
% 1.32/1.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 1.32/1.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k))
% 1.32/1.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_i)),V_k)) ) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_Suc__lessI,axiom,
% 1.32/1.46 ! [V_n,V_m] :
% 1.32/1.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 1.32/1.46 => ( hAPP(c_Nat_OSuc,V_m) != V_n
% 1.32/1.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_less__SucI,axiom,
% 1.32/1.46 ! [V_n,V_m] :
% 1.32/1.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 1.32/1.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_less__antisym,axiom,
% 1.32/1.46 ! [V_m,V_n] :
% 1.32/1.46 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m))
% 1.32/1.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_m)))
% 1.32/1.46 => V_m = V_n ) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_not__less__less__Suc__eq,axiom,
% 1.32/1.46 ! [V_m_2,V_na_2] :
% 1.32/1.46 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),V_m_2))
% 1.32/1.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),hAPP(c_Nat_OSuc,V_m_2)))
% 1.32/1.46 <=> V_na_2 = V_m_2 ) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_Suc__less__eq,axiom,
% 1.32/1.46 ! [V_na_2,V_m_2] :
% 1.32/1.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),hAPP(c_Nat_OSuc,V_na_2)))
% 1.32/1.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_less__Suc__eq,axiom,
% 1.32/1.46 ! [V_na_2,V_m_2] :
% 1.32/1.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_na_2)))
% 1.32/1.46 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2))
% 1.32/1.46 | V_m_2 = V_na_2 ) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_not__less__eq,axiom,
% 1.32/1.46 ! [V_na_2,V_m_2] :
% 1.32/1.46 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2))
% 1.32/1.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),hAPP(c_Nat_OSuc,V_m_2))) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_add__Suc__shift,axiom,
% 1.32/1.46 ! [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)) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_add__Suc,axiom,
% 1.32/1.46 ! [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)) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_add__Suc__right,axiom,
% 1.32/1.46 ! [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)) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_n__not__Suc__n,axiom,
% 1.32/1.46 ! [V_n] : V_n != hAPP(c_Nat_OSuc,V_n) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_Suc__n__not__n,axiom,
% 1.32/1.46 ! [V_n] : hAPP(c_Nat_OSuc,V_n) != V_n ).
% 1.32/1.46
% 1.32/1.46 fof(fact_nat_Oinject,axiom,
% 1.32/1.46 ! [V_nat_H_2,V_nat_2] :
% 1.32/1.46 ( hAPP(c_Nat_OSuc,V_nat_2) = hAPP(c_Nat_OSuc,V_nat_H_2)
% 1.32/1.46 <=> V_nat_2 = V_nat_H_2 ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_Suc__inject,axiom,
% 1.32/1.46 ! [V_y,V_x] :
% 1.32/1.46 ( hAPP(c_Nat_OSuc,V_x) = hAPP(c_Nat_OSuc,V_y)
% 1.32/1.46 => V_x = V_y ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_inj__Suc,axiom,
% 1.32/1.46 ! [V_N_2] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,V_N_2) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_less__Suc__eq__0__disj,axiom,
% 1.32/1.46 ! [V_na_2,V_m_2] :
% 1.32/1.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_na_2)))
% 1.32/1.46 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.32/1.46 | ? [B_j] :
% 1.32/1.46 ( V_m_2 = hAPP(c_Nat_OSuc,B_j)
% 1.32/1.46 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_na_2)) ) ) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_less__Suc0,axiom,
% 1.32/1.46 ! [V_na_2] :
% 1.32/1.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
% 1.32/1.46 <=> V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_gr0__conv__Suc,axiom,
% 1.32/1.46 ! [V_na_2] :
% 1.32/1.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_na_2))
% 1.32/1.46 <=> ? [B_m] : V_na_2 = hAPP(c_Nat_OSuc,B_m) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_one__is__add,axiom,
% 1.32/1.46 ! [V_na_2,V_m_2] :
% 1.32/1.46 ( 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_na_2)
% 1.32/1.46 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 1.32/1.46 & V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 1.32/1.46 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.32/1.46 & V_na_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_add__is__1,axiom,
% 1.32/1.46 ! [V_na_2,V_m_2] :
% 1.32/1.46 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_na_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 1.32/1.46 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 1.32/1.46 & V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 1.32/1.46 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.32/1.46 & V_na_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_less__add__Suc1,axiom,
% 1.32/1.46 ! [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)))) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_less__add__Suc2,axiom,
% 1.32/1.46 ! [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)))) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_less__iff__Suc__add,axiom,
% 1.32/1.46 ! [V_na_2,V_m_2] :
% 1.32/1.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2))
% 1.32/1.46 <=> ? [B_k] : V_na_2 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k)) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_Suc__le__lessD,axiom,
% 1.32/1.46 ! [V_n,V_m] :
% 1.32/1.46 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m)),V_n))
% 1.32/1.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_le__less__Suc__eq,axiom,
% 1.32/1.46 ! [V_na_2,V_m_2] :
% 1.32/1.46 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_na_2))
% 1.32/1.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),hAPP(c_Nat_OSuc,V_m_2)))
% 1.32/1.46 <=> V_na_2 = V_m_2 ) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_Suc__leI,axiom,
% 1.32/1.46 ! [V_n,V_m] :
% 1.32/1.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 1.32/1.46 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m)),V_n)) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_le__imp__less__Suc,axiom,
% 1.32/1.46 ! [V_n,V_m] :
% 1.32/1.46 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n))
% 1.32/1.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_Suc__le__eq,axiom,
% 1.32/1.46 ! [V_na_2,V_m_2] :
% 1.32/1.46 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2)),V_na_2))
% 1.32/1.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_less__Suc__eq__le,axiom,
% 1.32/1.46 ! [V_na_2,V_m_2] :
% 1.32/1.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_na_2)))
% 1.32/1.46 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_na_2)) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_less__eq__Suc__le,axiom,
% 1.32/1.46 ! [V_m_2,V_na_2] :
% 1.32/1.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),V_m_2))
% 1.32/1.46 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_na_2)),V_m_2)) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_One__nat__def,axiom,
% 1.32/1.46 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_less__eq__Suc__le__raw,axiom,
% 1.32/1.46 ! [V_na_2] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2) = c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_na_2)) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_card__insert__disjoint,axiom,
% 1.32/1.46 ! [V_x_2,V_A_2,T_a] :
% 1.32/1.46 ( c_Finite__Set_Ofinite(T_a,V_A_2)
% 1.32/1.46 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 1.32/1.46 => c_Finite__Set_Ocard(T_a,c_Set_Oinsert(T_a,V_x_2,V_A_2)) = hAPP(c_Nat_OSuc,c_Finite__Set_Ocard(T_a,V_A_2)) ) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_card__insert__if,axiom,
% 1.32/1.46 ! [V_x_2,V_A_2,T_a] :
% 1.32/1.46 ( c_Finite__Set_Ofinite(T_a,V_A_2)
% 1.32/1.46 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 1.32/1.46 => c_Finite__Set_Ocard(T_a,c_Set_Oinsert(T_a,V_x_2,V_A_2)) = c_Finite__Set_Ocard(T_a,V_A_2) )
% 1.32/1.46 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 1.32/1.46 => c_Finite__Set_Ocard(T_a,c_Set_Oinsert(T_a,V_x_2,V_A_2)) = hAPP(c_Nat_OSuc,c_Finite__Set_Ocard(T_a,V_A_2)) ) ) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_double__eq__0__iff,axiom,
% 1.32/1.46 ! [V_aa_2,T_a] :
% 1.32/1.46 ( class_Groups_Olinordered__ab__group__add(T_a)
% 1.32/1.46 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_aa_2) = c_Groups_Ozero__class_Ozero(T_a)
% 1.32/1.46 <=> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_Suc__eq__plus1,axiom,
% 1.32/1.46 ! [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)) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_Suc__eq__plus1__left,axiom,
% 1.32/1.46 ! [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) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_nat_Osize_I2_J,axiom,
% 1.32/1.46 ! [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))) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_nat_Osize_I1_J,axiom,
% 1.32/1.46 c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_in__measure,axiom,
% 1.32/1.46 ! [V_f_2,V_y_2,V_x_2,T_a] :
% 1.32/1.46 ( 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_Omeasure(T_a,V_f_2)))
% 1.32/1.46 <=> 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))) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_mlex__leq,axiom,
% 1.32/1.46 ! [V_R_2,T_a,V_y_2,V_x_2,V_f_2] :
% 1.32/1.46 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
% 1.32/1.46 => ( 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))
% 1.32/1.46 => 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))) ) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_mlex__less,axiom,
% 1.32/1.46 ! [V_R_2,T_a,V_y_2,V_x_2,V_f_2] :
% 1.32/1.46 ( 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)))
% 1.32/1.46 => 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))) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_nat_Osize_I4_J,axiom,
% 1.32/1.46 ! [V_nat] : c_Nat_Osize__class_Osize(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_nat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_Nat_Onat,V_nat)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_Ints__odd__less__0,axiom,
% 1.32/1.46 ! [V_aa_2,T_a] :
% 1.32/1.46 ( class_Rings_Olinordered__idom(T_a)
% 1.32/1.46 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Int_Oring__1__class_OInts(T_a)))
% 1.32/1.46 => ( 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_aa_2)),V_aa_2)),c_Groups_Ozero__class_Ozero(T_a)))
% 1.32/1.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_aa_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_nat__size,axiom,
% 1.32/1.46 ! [V_n] : c_Nat_Osize__class_Osize(tc_Nat_Onat,V_n) = V_n ).
% 1.32/1.46
% 1.32/1.46 fof(fact_Ints__0,axiom,
% 1.32/1.46 ! [T_a] :
% 1.32/1.46 ( class_Rings_Oring__1(T_a)
% 1.32/1.46 => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Int_Oring__1__class_OInts(T_a))) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_Ints__add,axiom,
% 1.32/1.46 ! [V_ba_2,V_aa_2,T_a] :
% 1.32/1.46 ( class_Rings_Oring__1(T_a)
% 1.32/1.46 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Int_Oring__1__class_OInts(T_a)))
% 1.32/1.46 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_ba_2),c_Int_Oring__1__class_OInts(T_a)))
% 1.32/1.46 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_ba_2)),c_Int_Oring__1__class_OInts(T_a))) ) ) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_nat_Osize_I3_J,axiom,
% 1.32/1.46 c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_Ints__1,axiom,
% 1.32/1.46 ! [T_a] :
% 1.32/1.46 ( class_Rings_Oring__1(T_a)
% 1.32/1.46 => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Oone__class_Oone(T_a)),c_Int_Oring__1__class_OInts(T_a))) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_Ints__double__eq__0__iff,axiom,
% 1.32/1.46 ! [V_aa_2,T_a] :
% 1.32/1.46 ( class_Int_Oring__char__0(T_a)
% 1.32/1.46 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Int_Oring__1__class_OInts(T_a)))
% 1.32/1.46 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_aa_2) = c_Groups_Ozero__class_Ozero(T_a)
% 1.32/1.46 <=> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_Ints__odd__nonzero,axiom,
% 1.32/1.46 ! [V_aa_2,T_a] :
% 1.32/1.46 ( class_Int_Oring__char__0(T_a)
% 1.32/1.46 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Int_Oring__1__class_OInts(T_a)))
% 1.32/1.46 => 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_aa_2)),V_aa_2) != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
% 1.32/1.46 ! [V_a,T_a] :
% 1.32/1.46 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.32/1.46 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
% 1.32/1.46 ! [V_a,T_a] :
% 1.32/1.46 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.32/1.46 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
% 1.32/1.46 ! [V_c,V_a,T_a] :
% 1.32/1.46 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.32/1.46 => 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) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
% 1.32/1.46 ! [V_d,V_c,V_a,T_a] :
% 1.32/1.46 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.32/1.46 => 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)) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
% 1.32/1.46 ! [V_d,V_c,V_a,T_a] :
% 1.32/1.46 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.32/1.46 => 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) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
% 1.32/1.46 ! [V_c,V_b,V_a,T_a] :
% 1.32/1.46 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.32/1.46 => 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)) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
% 1.32/1.46 ! [V_c,V_b,V_a,T_a] :
% 1.32/1.46 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.32/1.46 => 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) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
% 1.32/1.46 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.32/1.46 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.32/1.46 => 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)) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_add__0__iff,axiom,
% 1.32/1.46 ! [V_aa_2,V_ba_2,T_a] :
% 1.32/1.46 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 1.32/1.46 => ( V_ba_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_ba_2),V_aa_2)
% 1.32/1.46 <=> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_in__finite__psubset,axiom,
% 1.32/1.46 ! [V_B_2,V_A_2,T_a] :
% 1.32/1.46 ( 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)))
% 1.32/1.46 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 1.32/1.46 & c_Finite__Set_Ofinite(T_a,V_B_2) ) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_ex__least__nat__less,axiom,
% 1.32/1.46 ! [V_na_2,V_Pa_2] :
% 1.32/1.46 ( ~ hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 1.32/1.46 => ( hBOOL(hAPP(V_Pa_2,V_na_2))
% 1.32/1.46 => ? [B_k] :
% 1.32/1.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_k),V_na_2))
% 1.32/1.46 & ! [B_i] :
% 1.32/1.46 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_i),B_k))
% 1.32/1.46 => ~ hBOOL(hAPP(V_Pa_2,B_i)) )
% 1.32/1.46 & hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_k),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_card_Oeq__fold__g,axiom,
% 1.32/1.46 ! [V_A_2,T_a] :
% 1.32/1.46 ( c_Finite__Set_Ofinite(T_a,V_A_2)
% 1.32/1.46 => c_Finite__Set_Ocard(T_a,V_A_2) = 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) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_card__def,axiom,
% 1.32/1.46 ! [V_A_2,T_a] :
% 1.32/1.46 ( ( c_Finite__Set_Ofinite(T_a,V_A_2)
% 1.32/1.46 => c_Finite__Set_Ocard(T_a,V_A_2) = 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) )
% 1.32/1.46 & ( ~ c_Finite__Set_Ofinite(T_a,V_A_2)
% 1.32/1.46 => c_Finite__Set_Ocard(T_a,V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_folding__image__simple_Oeq__fold__g,axiom,
% 1.32/1.46 ! [V_A_2,V_Fa_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 1.32/1.46 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_Fa_2)
% 1.32/1.46 => ( c_Finite__Set_Ofinite(T_b,V_A_2)
% 1.32/1.46 => hAPP(V_Fa_2,V_A_2) = c_Finite__Set_Ofold__image(T_a,T_b,V_f_2,V_g_2,V_z_2,V_A_2) ) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_surjh,axiom,
% 1.32/1.46 c_Set_Oimage(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,v_h____,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))) = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_less__eq__nat_Osimps_I2_J,axiom,
% 1.32/1.46 ! [V_na_2,V_m_2] :
% 1.32/1.46 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2)),V_na_2))
% 1.32/1.46 <=> hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_na_2)) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_image__eqI,axiom,
% 1.32/1.46 ! [T_a,V_A_2,T_b,V_x_2,V_f_2,V_ba_2] :
% 1.32/1.46 ( V_ba_2 = hAPP(V_f_2,V_x_2)
% 1.32/1.46 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 1.32/1.46 => hBOOL(hAPP(hAPP(c_member(T_a),V_ba_2),c_Set_Oimage(T_b,T_a,V_f_2,V_A_2))) ) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_finite__imageI,axiom,
% 1.32/1.46 ! [V_ha_2,T_b,V_Fa_2,T_a] :
% 1.32/1.46 ( c_Finite__Set_Ofinite(T_a,V_Fa_2)
% 1.32/1.46 => c_Finite__Set_Ofinite(T_b,c_Set_Oimage(T_a,T_b,V_ha_2,V_Fa_2)) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_pigeonhole,axiom,
% 1.32/1.46 ! [V_A_2,V_f_2,T_b,T_a] :
% 1.32/1.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Finite__Set_Ocard(T_a,c_Set_Oimage(T_b,T_a,V_f_2,V_A_2))),c_Finite__Set_Ocard(T_b,V_A_2)))
% 1.32/1.46 => ~ c_Fun_Oinj__on(T_b,T_a,V_f_2,V_A_2) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_finite__surj,axiom,
% 1.32/1.46 ! [V_f_2,V_B_2,T_b,V_A_2,T_a] :
% 1.32/1.46 ( c_Finite__Set_Ofinite(T_a,V_A_2)
% 1.32/1.46 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool),V_B_2),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2)))
% 1.32/1.46 => c_Finite__Set_Ofinite(T_b,V_B_2) ) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_finite__imageD,axiom,
% 1.32/1.46 ! [V_A_2,V_f_2,T_b,T_a] :
% 1.32/1.46 ( c_Finite__Set_Ofinite(T_a,c_Set_Oimage(T_b,T_a,V_f_2,V_A_2))
% 1.32/1.46 => ( c_Fun_Oinj__on(T_b,T_a,V_f_2,V_A_2)
% 1.32/1.46 => c_Finite__Set_Ofinite(T_b,V_A_2) ) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_inj__image__eq__iff,axiom,
% 1.32/1.46 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 1.32/1.46 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 1.32/1.46 => ( c_Set_Oimage(T_a,T_b,V_f_2,V_A_2) = c_Set_Oimage(T_a,T_b,V_f_2,V_B_2)
% 1.32/1.46 <=> V_A_2 = V_B_2 ) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_card__image,axiom,
% 1.32/1.46 ! [V_A_2,V_f_2,T_b,T_a] :
% 1.32/1.46 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 1.32/1.46 => c_Finite__Set_Ocard(T_b,c_Set_Oimage(T_a,T_b,V_f_2,V_A_2)) = c_Finite__Set_Ocard(T_a,V_A_2) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_image__inv__into__cancel,axiom,
% 1.32/1.46 ! [V_B_H_2,V_A_H_2,V_A_2,V_f_2,T_a,T_b] :
% 1.32/1.46 ( c_Set_Oimage(T_b,T_a,V_f_2,V_A_2) = V_A_H_2
% 1.32/1.46 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_H_2),V_A_H_2))
% 1.32/1.46 => c_Set_Oimage(T_b,T_a,V_f_2,c_Set_Oimage(T_a,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_a,V_A_2,V_f_2),V_B_H_2)) = V_B_H_2 ) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_image__surj__f__inv__f,axiom,
% 1.32/1.46 ! [V_A_2,V_f_2,T_a,T_b] :
% 1.32/1.46 ( 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))
% 1.32/1.46 => c_Set_Oimage(T_b,T_a,V_f_2,c_Set_Oimage(T_a,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_a,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),V_A_2)) = V_A_2 ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_surj__f__inv__f,axiom,
% 1.32/1.46 ! [V_y_2,V_f_2,T_a,T_b] :
% 1.32/1.46 ( 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))
% 1.32/1.46 => hAPP(V_f_2,hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_a,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),V_y_2)) = V_y_2 ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_surj__iff__all,axiom,
% 1.32/1.46 ! [V_f_2,T_a,T_b] :
% 1.32/1.46 ( 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))
% 1.32/1.46 <=> ! [B_x] : hAPP(V_f_2,hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_a,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),B_x)) = B_x ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_inj__on__strict__subset,axiom,
% 1.32/1.46 ! [V_A_2,V_B_2,V_f_2,T_b,T_a] :
% 1.32/1.46 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2)
% 1.32/1.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 1.32/1.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2)),c_Set_Oimage(T_a,T_b,V_f_2,V_B_2))) ) ) ).
% 1.32/1.46
% 1.32/1.46 fof(fact_range__composition,axiom,
% 1.50/1.46 ! [V_g_2,V_f_2,T_c,T_a,T_b] : c_Set_Oimage(T_b,T_a,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))) = c_Set_Oimage(T_c,T_a,V_f_2,c_Set_Oimage(T_b,T_c,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ).
% 1.50/1.46
% 1.50/1.46 fof(fact_image__insert,axiom,
% 1.50/1.46 ! [V_B_2,V_aa_2,V_f_2,T_a,T_b] : c_Set_Oimage(T_b,T_a,V_f_2,c_Set_Oinsert(T_b,V_aa_2,V_B_2)) = c_Set_Oinsert(T_a,hAPP(V_f_2,V_aa_2),c_Set_Oimage(T_b,T_a,V_f_2,V_B_2)) ).
% 1.50/1.46
% 1.50/1.46 fof(fact_image__image,axiom,
% 1.50/1.46 ! [V_A_2,V_g_2,T_c,V_f_2,T_a,T_b] : c_Set_Oimage(T_b,T_a,V_f_2,c_Set_Oimage(T_c,T_b,V_g_2,V_A_2)) = c_Set_Oimage(T_c,T_a,hAPP(c_COMBB(T_b,T_a,T_c,V_f_2),V_g_2),V_A_2) ).
% 1.50/1.46
% 1.50/1.46 fof(fact_subset__image__iff,axiom,
% 1.50/1.46 ! [V_A_2,V_f_2,T_b,V_B_2,T_a] :
% 1.50/1.46 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2),c_Set_Oimage(T_b,T_a,V_f_2,V_A_2)))
% 1.50/1.46 <=> ? [B_AA] :
% 1.50/1.46 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool),B_AA),V_A_2))
% 1.50/1.46 & V_B_2 = c_Set_Oimage(T_b,T_a,V_f_2,B_AA) ) ) ).
% 1.50/1.46
% 1.50/1.46 fof(fact_image__mono,axiom,
% 1.50/1.46 ! [V_f_2,T_b,V_B_2,V_A_2,T_a] :
% 1.50/1.46 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2))
% 1.50/1.46 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2)),c_Set_Oimage(T_a,T_b,V_f_2,V_B_2))) ) ).
% 1.50/1.46
% 1.50/1.46 fof(fact_image__ident,axiom,
% 1.50/1.46 ! [V_Y_2,T_a] : c_Set_Oimage(T_a,T_a,c_COMBI(T_a),V_Y_2) = V_Y_2 ).
% 1.50/1.46
% 1.50/1.46 fof(fact_nat__case__Suc,axiom,
% 1.50/1.46 ! [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) ).
% 1.50/1.46
% 1.50/1.46 fof(fact_nat__case__0,axiom,
% 1.50/1.46 ! [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 ).
% 1.50/1.46
% 1.50/1.46 fof(fact_finite__range__imageI,axiom,
% 1.50/1.46 ! [V_f_2,T_c,V_g_2,T_b,T_a] :
% 1.50/1.46 ( c_Finite__Set_Ofinite(T_a,c_Set_Oimage(T_b,T_a,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 1.50/1.46 => c_Finite__Set_Ofinite(T_c,c_Set_Oimage(T_b,T_c,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)))) ) ).
% 1.50/1.46
% 1.50/1.46 fof(fact_eq__card__imp__inj__on,axiom,
% 1.50/1.46 ! [V_f_2,T_b,V_A_2,T_a] :
% 1.50/1.46 ( c_Finite__Set_Ofinite(T_a,V_A_2)
% 1.50/1.46 => ( c_Finite__Set_Ocard(T_b,c_Set_Oimage(T_a,T_b,V_f_2,V_A_2)) = c_Finite__Set_Ocard(T_a,V_A_2)
% 1.50/1.46 => c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) ) ) ).
% 1.50/1.46
% 1.50/1.46 fof(fact_inj__on__iff__eq__card,axiom,
% 1.50/1.46 ! [V_f_2,T_b,V_A_2,T_a] :
% 1.50/1.46 ( c_Finite__Set_Ofinite(T_a,V_A_2)
% 1.50/1.46 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 1.50/1.46 <=> c_Finite__Set_Ocard(T_b,c_Set_Oimage(T_a,T_b,V_f_2,V_A_2)) = c_Finite__Set_Ocard(T_a,V_A_2) ) ) ).
% 1.50/1.46
% 1.50/1.46 fof(fact_card__image__le,axiom,
% 1.50/1.46 ! [V_f_2,T_b,V_A_2,T_a] :
% 1.50/1.46 ( c_Finite__Set_Ofinite(T_a,V_A_2)
% 1.50/1.46 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(T_b,c_Set_Oimage(T_a,T_b,V_f_2,V_A_2))),c_Finite__Set_Ocard(T_a,V_A_2))) ) ).
% 1.50/1.46
% 1.50/1.46 fof(fact_inj__image__subset__iff,axiom,
% 1.50/1.46 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 1.50/1.46 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 1.50/1.46 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2)),c_Set_Oimage(T_a,T_b,V_f_2,V_B_2)))
% 1.50/1.46 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) ) ) ).
% 1.50/1.46
% 1.50/1.46 fof(fact_finite__UNIV__surj__inj,axiom,
% 1.50/1.46 ! [V_f_2,T_a] :
% 1.50/1.46 ( c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 1.50/1.46 => ( 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))
% 1.50/1.46 => c_Fun_Oinj__on(T_a,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ) ).
% 1.50/1.46
% 1.50/1.46 fof(fact_finite__UNIV__inj__surj,axiom,
% 1.50/1.46 ! [V_f_2,T_a] :
% 1.50/1.46 ( c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 1.50/1.46 => ( c_Fun_Oinj__on(T_a,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 1.50/1.46 => 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)) ) ) ).
% 1.50/1.46
% 1.50/1.46 fof(fact_finite__surj__inj,axiom,
% 1.50/1.46 ! [V_f_2,V_A_2,T_a] :
% 1.50/1.46 ( c_Finite__Set_Ofinite(T_a,V_A_2)
% 1.50/1.46 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),c_Set_Oimage(T_a,T_a,V_f_2,V_A_2)))
% 1.50/1.46 => c_Fun_Oinj__on(T_a,T_a,V_f_2,V_A_2) ) ) ).
% 1.50/1.46
% 1.50/1.46 fof(fact_endo__inj__surj,axiom,
% 1.50/1.46 ! [V_f_2,V_A_2,T_a] :
% 1.50/1.46 ( c_Finite__Set_Ofinite(T_a,V_A_2)
% 1.50/1.46 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Set_Oimage(T_a,T_a,V_f_2,V_A_2)),V_A_2))
% 1.50/1.46 => ( c_Fun_Oinj__on(T_a,T_a,V_f_2,V_A_2)
% 1.50/1.46 => c_Set_Oimage(T_a,T_a,V_f_2,V_A_2) = V_A_2 ) ) ) ).
% 1.50/1.46
% 1.50/1.46 fof(fact_inj__image__mem__iff,axiom,
% 1.50/1.46 ! [V_A_2,V_aa_2,V_f_2,T_b,T_a] :
% 1.50/1.46 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 1.50/1.46 => ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_aa_2)),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2)))
% 1.50/1.46 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2)) ) ) ).
% 1.50/1.46
% 1.50/1.46 fof(fact_range__ex1__eq,axiom,
% 1.50/1.46 ! [V_ba_2,V_f_2,T_b,T_a] :
% 1.50/1.46 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 1.50/1.46 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),c_Set_Oimage(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))))
% 1.50/1.46 <=> ? [B_x] :
% 1.50/1.46 ( V_ba_2 = hAPP(V_f_2,B_x)
% 1.50/1.46 & ! [B_y] :
% 1.50/1.46 ( V_ba_2 = hAPP(V_f_2,B_y)
% 1.50/1.46 => B_y = B_x ) ) ) ) ).
% 1.50/1.46
% 1.50/1.46 fof(fact_rev__image__eqI,axiom,
% 1.50/1.46 ! [T_b,V_f_2,V_ba_2,V_A_2,V_x_2,T_a] :
% 1.50/1.46 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 1.50/1.46 => ( V_ba_2 = hAPP(V_f_2,V_x_2)
% 1.50/1.46 => hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2))) ) ) ).
% 1.50/1.46
% 1.50/1.46 fof(fact_imageI,axiom,
% 1.50/1.46 ! [V_f_2,T_b,V_A_2,V_x_2,T_a] :
% 1.50/1.46 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 1.50/1.46 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2))) ) ).
% 1.50/1.46
% 1.50/1.46 fof(fact_image__iff,axiom,
% 1.50/1.46 ! [V_A_2,V_f_2,T_b,V_z_2,T_a] :
% 1.50/1.46 ( hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),c_Set_Oimage(T_b,T_a,V_f_2,V_A_2)))
% 1.50/1.46 <=> ? [B_x] :
% 1.50/1.46 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 1.50/1.46 & V_z_2 = hAPP(V_f_2,B_x) ) ) ).
% 1.50/1.46
% 1.50/1.46 fof(fact_inv__into__injective,axiom,
% 1.50/1.46 ! [V_y_2,V_x_2,V_f_2,V_A_2,T_b,T_a] :
% 1.50/1.46 ( hAPP(c_Hilbert__Choice_Oinv__into(T_a,T_b,V_A_2,V_f_2),V_x_2) = hAPP(c_Hilbert__Choice_Oinv__into(T_a,T_b,V_A_2,V_f_2),V_y_2)
% 1.50/1.46 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2)))
% 1.50/1.46 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2)))
% 1.50/1.46 => V_x_2 = V_y_2 ) ) ) ).
% 1.50/1.46
% 1.50/1.46 fof(fact_inv__into__into,axiom,
% 1.50/1.46 ! [V_A_2,V_f_2,T_b,V_x_2,T_a] :
% 1.50/1.46 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Set_Oimage(T_b,T_a,V_f_2,V_A_2)))
% 1.50/1.46 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_a,V_A_2,V_f_2),V_x_2)),V_A_2)) ) ).
% 1.50/1.46
% 1.50/1.46 fof(fact_f__inv__into__f,axiom,
% 1.50/1.46 ! [V_A_2,V_f_2,T_b,V_y_2,T_a] :
% 1.50/1.46 ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),c_Set_Oimage(T_b,T_a,V_f_2,V_A_2)))
% 1.50/1.46 => hAPP(V_f_2,hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_a,V_A_2,V_f_2),V_y_2)) = V_y_2 ) ).
% 1.50/1.46
% 1.50/1.46 fof(fact_range__eqI,axiom,
% 1.50/1.46 ! [T_b,T_a,V_x_2,V_f_2,V_ba_2] :
% 1.50/1.46 ( V_ba_2 = hAPP(V_f_2,V_x_2)
% 1.50/1.46 => hBOOL(hAPP(hAPP(c_member(T_a),V_ba_2),c_Set_Oimage(T_b,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) ) ).
% 1.50/1.46
% 1.50/1.46 fof(fact_rangeI,axiom,
% 1.50/1.46 ! [T_b,V_x_2,V_f_2,T_a] : hBOOL(hAPP(hAPP(c_member(T_a),hAPP(V_f_2,V_x_2)),c_Set_Oimage(T_b,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) ).
% 1.50/1.46
% 1.50/1.46 fof(fact_insert__image,axiom,
% 1.50/1.46 ! [V_f_2,T_b,V_A_2,V_x_2,T_a] :
% 1.50/1.46 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 1.50/1.46 => c_Set_Oinsert(T_b,hAPP(V_f_2,V_x_2),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2)) = c_Set_Oimage(T_a,T_b,V_f_2,V_A_2) ) ).
% 1.50/1.46
% 1.50/1.46 fof(fact_inv__into__image__cancel,axiom,
% 1.50/1.46 ! [V_S_2,V_A_2,V_f_2,T_b,T_a] :
% 1.50/1.46 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 1.50/1.46 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_S_2),V_A_2))
% 1.50/1.46 => c_Set_Oimage(T_b,T_a,c_Hilbert__Choice_Oinv__into(T_a,T_b,V_A_2,V_f_2),c_Set_Oimage(T_a,T_b,V_f_2,V_S_2)) = V_S_2 ) ) ).
% 1.50/1.46
% 1.50/1.46 fof(fact_inj__on__inv__into,axiom,
% 1.50/1.46 ! [V_A_2,V_f_2,T_b,V_B_2,T_a] :
% 1.50/1.46 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2),c_Set_Oimage(T_b,T_a,V_f_2,V_A_2)))
% 1.50/1.46 => c_Fun_Oinj__on(T_a,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_a,V_A_2,V_f_2),V_B_2) ) ).
% 1.50/1.46
% 1.50/1.46 fof(fact_surj__imp__inj__inv,axiom,
% 1.50/1.46 ! [V_f_2,T_a,T_b] :
% 1.50/1.46 ( 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))
% 1.50/1.46 => c_Fun_Oinj__on(T_a,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_a,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ).
% 1.50/1.46
% 1.50/1.46 fof(fact_inv__image__comp,axiom,
% 1.50/1.46 ! [V_X_2,V_f_2,T_b,T_a] :
% 1.50/1.46 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 1.50/1.46 => c_Set_Oimage(T_b,T_a,c_Hilbert__Choice_Oinv__into(T_a,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_f_2),c_Set_Oimage(T_a,T_b,V_f_2,V_X_2)) = V_X_2 ) ).
% 1.50/1.46
% 1.50/1.46 fof(fact_image__inv__f__f,axiom,
% 1.50/1.46 ! [V_A_2,V_f_2,T_b,T_a] :
% 1.50/1.46 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 1.50/1.46 => c_Set_Oimage(T_b,T_a,c_Hilbert__Choice_Oinv__into(T_a,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_f_2),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2)) = V_A_2 ) ).
% 1.50/1.46
% 1.50/1.46 fof(fact_inj__imp__surj__inv,axiom,
% 1.50/1.46 ! [V_f_2,T_b,T_a] :
% 1.50/1.46 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 1.50/1.46 => c_Set_Oimage(T_b,T_a,c_Hilbert__Choice_Oinv__into(T_a,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),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)) ) ).
% 1.50/1.46
% 1.50/1.46 fof(fact_funcset__image,axiom,
% 1.50/1.46 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 1.50/1.46 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_OPi(T_a,T_b,V_A_2,hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2))))
% 1.50/1.46 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2)),V_B_2)) ) ).
% 1.50/1.46
% 1.50/1.46 fof(fact_card__bij__eq,axiom,
% 1.50/1.46 ! [V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 1.50/1.46 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 1.50/1.46 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2)),V_B_2))
% 1.50/1.46 => ( c_Fun_Oinj__on(T_b,T_a,V_g_2,V_B_2)
% 1.50/1.46 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Set_Oimage(T_b,T_a,V_g_2,V_B_2)),V_A_2))
% 1.50/1.46 => ( c_Finite__Set_Ofinite(T_a,V_A_2)
% 1.50/1.46 => ( c_Finite__Set_Ofinite(T_b,V_B_2)
% 1.50/1.46 => c_Finite__Set_Ocard(T_a,V_A_2) = c_Finite__Set_Ocard(T_b,V_B_2) ) ) ) ) ) ) ).
% 1.50/1.46
% 1.50/1.46 fof(fact_card__inj__on__le,axiom,
% 1.50/1.46 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 1.50/1.46 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 1.50/1.46 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2)),V_B_2))
% 1.50/1.46 => ( c_Finite__Set_Ofinite(T_b,V_B_2)
% 1.50/1.46 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(T_a,V_A_2)),c_Finite__Set_Ocard(T_b,V_B_2))) ) ) ) ).
% 1.50/1.46
% 1.50/1.46 fof(fact__096_B_Bthesis_O_A_I_B_Bh_O_A_091_124_Ainj_Ah_059_Arange_Ah_A_061_A_1230_O_O_060N_125_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096,axiom,
% 1.50/1.46 ~ ! [B_h] :
% 1.50/1.46 ( c_Fun_Oinj__on(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,B_h,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))
% 1.50/1.46 => c_Set_Oimage(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,B_h,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))) != c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))) ) ).
% 1.50/1.46
% 1.50/1.46 fof(fact_inj__on__iff__card__le,axiom,
% 1.50/1.46 ! [V_B_2,T_b,V_A_2,T_a] :
% 1.50/1.46 ( c_Finite__Set_Ofinite(T_a,V_A_2)
% 1.50/1.46 => ( c_Finite__Set_Ofinite(T_b,V_B_2)
% 1.50/1.46 => ( ? [B_f] :
% 1.50/1.46 ( c_Fun_Oinj__on(T_a,T_b,B_f,V_A_2)
% 1.50/1.46 & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool),c_Set_Oimage(T_a,T_b,B_f,V_A_2)),V_B_2)) )
% 1.50/1.46 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(T_a,V_A_2)),c_Finite__Set_Ocard(T_b,V_B_2))) ) ) ) ).
% 1.50/1.46
% 1.50/1.46 fof(fact_finite__atLeastLessThan,axiom,
% 1.50/1.46 ! [V_u_2,V_l_2] : c_Finite__Set_Ofinite(tc_Nat_Onat,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_l_2,V_u_2)) ).
% 1.50/1.46
% 1.50/1.46 fof(fact_image__Suc__atLeastLessThan,axiom,
% 1.50/1.46 ! [V_j_2,V_i_2] : c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2,V_j_2)) = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_i_2),hAPP(c_Nat_OSuc,V_j_2)) ).
% 1.50/1.46
% 1.50/1.46 fof(fact_image__add__atLeastLessThan,axiom,
% 1.50/1.46 ! [V_j_2,V_i_2,V_k_2] : 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_OatLeastLessThan(tc_Nat_Onat,V_i_2,V_j_2)) = 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)) ).
% 1.50/1.46
% 1.50/1.46 fof(fact_finite__nat__set__iff__bounded,axiom,
% 1.50/1.46 ! [V_N_2] :
% 1.50/1.46 ( c_Finite__Set_Ofinite(tc_Nat_Onat,V_N_2)
% 1.50/1.46 <=> ? [B_m] :
% 1.50/1.46 ! [B_x] :
% 1.50/1.46 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
% 1.50/1.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_x),B_m)) ) ) ).
% 1.50/1.46
% 1.50/1.46 fof(fact_finite__nat__set__iff__bounded__le,axiom,
% 1.50/1.46 ! [V_N_2] :
% 1.50/1.46 ( c_Finite__Set_Ofinite(tc_Nat_Onat,V_N_2)
% 1.50/1.46 <=> ? [B_m] :
% 1.50/1.46 ! [B_x] :
% 1.50/1.46 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
% 1.50/1.46 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_x),B_m)) ) ) ).
% 1.50/1.46
% 1.50/1.46 fof(fact_atLeastLessThan__eq__iff,axiom,
% 1.50/1.46 ! [V_da_2,V_ca_2,V_ba_2,V_aa_2,T_a] :
% 1.50/1.46 ( class_Orderings_Olinorder(T_a)
% 1.50/1.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_aa_2),V_ba_2))
% 1.50/1.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),V_da_2))
% 1.50/1.46 => ( c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_aa_2,V_ba_2) = c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_ca_2,V_da_2)
% 1.50/1.46 <=> ( V_aa_2 = V_ca_2
% 1.50/1.46 & V_ba_2 = V_da_2 ) ) ) ) ) ).
% 1.50/1.46
% 1.50/1.46 fof(fact_atLeastLessThan__inj_I1_J,axiom,
% 1.50/1.46 ! [V_da_2,V_ca_2,V_ba_2,V_aa_2,T_a] :
% 1.50/1.46 ( class_Orderings_Olinorder(T_a)
% 1.50/1.46 => ( c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_aa_2,V_ba_2) = c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_ca_2,V_da_2)
% 1.50/1.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_aa_2),V_ba_2))
% 1.50/1.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),V_da_2))
% 1.50/1.46 => V_aa_2 = V_ca_2 ) ) ) ) ).
% 1.50/1.46
% 1.50/1.46 fof(fact_atLeastLessThan__inj_I2_J,axiom,
% 1.50/1.46 ! [V_da_2,V_ca_2,V_ba_2,V_aa_2,T_a] :
% 1.50/1.46 ( class_Orderings_Olinorder(T_a)
% 1.50/1.46 => ( c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_aa_2,V_ba_2) = c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_ca_2,V_da_2)
% 1.50/1.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_aa_2),V_ba_2))
% 1.50/1.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),V_da_2))
% 1.50/1.46 => V_ba_2 = V_da_2 ) ) ) ) ).
% 1.50/1.46
% 1.50/1.46 fof(fact_subset__card__intvl__is__intvl,axiom,
% 1.50/1.46 ! [V_k_2,V_A_2] :
% 1.50/1.46 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool),V_A_2),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_k_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),c_Finite__Set_Ocard(tc_Nat_Onat,V_A_2)))))
% 1.50/1.46 => V_A_2 = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_k_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),c_Finite__Set_Ocard(tc_Nat_Onat,V_A_2))) ) ).
% 1.50/1.46
% 1.50/1.46 fof(fact_atLeastLessThan__subset__iff,axiom,
% 1.50/1.46 ! [V_da_2,V_ca_2,V_ba_2,V_aa_2,T_a] :
% 1.50/1.46 ( class_Orderings_Olinorder(T_a)
% 1.50/1.46 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_aa_2,V_ba_2)),c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_ca_2,V_da_2)))
% 1.50/1.46 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_ba_2),V_aa_2))
% 1.50/1.46 | ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_ca_2),V_aa_2))
% 1.50/1.46 & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_ba_2),V_da_2)) ) ) ) ) ).
% 1.50/1.46
% 1.50/1.46 %----Arity declarations (33)
% 1.50/1.46 fof(arity_fun__Orderings_Opreorder,axiom,
% 1.50/1.46 ! [T_2,T_1] :
% 1.50/1.46 ( class_Orderings_Opreorder(T_1)
% 1.50/1.46 => class_Orderings_Opreorder(tc_fun(T_2,T_1)) ) ).
% 1.50/1.46
% 1.50/1.46 fof(arity_fun__Finite__Set_Ofinite,axiom,
% 1.50/1.46 ! [T_1,T_2] :
% 1.50/1.46 ( ( class_Finite__Set_Ofinite(T_2)
% 1.50/1.46 & class_Finite__Set_Ofinite(T_1) )
% 1.50/1.46 => class_Finite__Set_Ofinite(tc_fun(T_2,T_1)) ) ).
% 1.50/1.46
% 1.50/1.46 fof(arity_fun__Orderings_Oorder,axiom,
% 1.50/1.46 ! [T_2,T_1] :
% 1.50/1.46 ( class_Orderings_Oorder(T_1)
% 1.50/1.46 => class_Orderings_Oorder(tc_fun(T_2,T_1)) ) ).
% 1.50/1.46
% 1.50/1.46 fof(arity_fun__Orderings_Otop,axiom,
% 1.50/1.46 ! [T_2,T_1] :
% 1.50/1.46 ( class_Orderings_Otop(T_1)
% 1.50/1.46 => class_Orderings_Otop(tc_fun(T_2,T_1)) ) ).
% 1.50/1.46
% 1.50/1.46 fof(arity_fun__Orderings_Oord,axiom,
% 1.50/1.46 ! [T_2,T_1] :
% 1.50/1.46 ( class_Orderings_Oord(T_1)
% 1.50/1.46 => class_Orderings_Oord(tc_fun(T_2,T_1)) ) ).
% 1.50/1.46
% 1.50/1.46 fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 1.50/1.46 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ).
% 1.50/1.46
% 1.50/1.46 fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 1.50/1.46 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ).
% 1.50/1.46
% 1.50/1.46 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 1.50/1.46 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ).
% 1.50/1.46
% 1.50/1.46 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom,
% 1.50/1.46 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ).
% 1.50/1.46
% 1.50/1.46 fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom,
% 1.50/1.46 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ).
% 1.50/1.46
% 1.50/1.46 fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom,
% 1.50/1.46 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ).
% 1.50/1.46
% 1.50/1.46 fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom,
% 1.50/1.46 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ).
% 1.50/1.46
% 1.50/1.46 fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom,
% 1.50/1.46 class_Rings_Olinordered__semidom(tc_Nat_Onat) ).
% 1.50/1.46
% 1.50/1.46 fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom,
% 1.50/1.46 class_Groups_Oab__semigroup__add(tc_Nat_Onat) ).
% 1.50/1.46
% 1.50/1.46 fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom,
% 1.50/1.46 class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ).
% 1.50/1.46
% 1.50/1.46 fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom,
% 1.50/1.46 class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ).
% 1.50/1.46
% 1.50/1.46 fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom,
% 1.50/1.46 class_Rings_Ozero__neq__one(tc_Nat_Onat) ).
% 1.50/1.46
% 1.50/1.46 fof(arity_Nat__Onat__Orderings_Opreorder,axiom,
% 1.50/1.46 class_Orderings_Opreorder(tc_Nat_Onat) ).
% 1.50/1.46
% 1.50/1.46 fof(arity_Nat__Onat__Orderings_Olinorder,axiom,
% 1.50/1.46 class_Orderings_Olinorder(tc_Nat_Onat) ).
% 1.50/1.46
% 1.50/1.46 fof(arity_Nat__Onat__Groups_Omonoid__add,axiom,
% 1.50/1.46 class_Groups_Omonoid__add(tc_Nat_Onat) ).
% 1.50/1.46
% 1.50/1.46 fof(arity_Nat__Onat__Orderings_Oorder,axiom,
% 1.50/1.46 class_Orderings_Oorder(tc_Nat_Onat) ).
% 1.50/1.46
% 1.50/1.46 fof(arity_Nat__Onat__Orderings_Oord,axiom,
% 1.50/1.46 class_Orderings_Oord(tc_Nat_Onat) ).
% 1.50/1.46
% 1.50/1.46 fof(arity_Nat__Onat__Groups_Ozero,axiom,
% 1.50/1.46 class_Groups_Ozero(tc_Nat_Onat) ).
% 1.50/1.46
% 1.50/1.46 fof(arity_Nat__Onat__Groups_Oone,axiom,
% 1.50/1.46 class_Groups_Oone(tc_Nat_Onat) ).
% 1.50/1.46
% 1.50/1.46 fof(arity_HOL__Obool__Orderings_Opreorder,axiom,
% 1.50/1.46 class_Orderings_Opreorder(tc_HOL_Obool) ).
% 1.50/1.46
% 1.50/1.46 fof(arity_HOL__Obool__Finite__Set_Ofinite,axiom,
% 1.50/1.46 class_Finite__Set_Ofinite(tc_HOL_Obool) ).
% 1.50/1.46
% 1.50/1.46 fof(arity_HOL__Obool__Orderings_Oorder,axiom,
% 1.50/1.46 class_Orderings_Oorder(tc_HOL_Obool) ).
% 1.50/1.46
% 1.50/1.46 fof(arity_HOL__Obool__Orderings_Otop,axiom,
% 1.50/1.46 class_Orderings_Otop(tc_HOL_Obool) ).
% 1.50/1.46
% 1.50/1.46 fof(arity_HOL__Obool__Orderings_Oord,axiom,
% 1.50/1.46 class_Orderings_Oord(tc_HOL_Obool) ).
% 1.50/1.46
% 1.50/1.46 fof(arity_sum__Finite__Set_Ofinite,axiom,
% 1.50/1.46 ! [T_1,T_2] :
% 1.50/1.46 ( ( class_Finite__Set_Ofinite(T_2)
% 1.50/1.46 & class_Finite__Set_Ofinite(T_1) )
% 1.50/1.46 => class_Finite__Set_Ofinite(tc_sum(T_2,T_1)) ) ).
% 1.50/1.46
% 1.50/1.46 fof(arity_Option__Ooption__Finite__Set_Ofinite,axiom,
% 1.50/1.46 ! [T_1] :
% 1.50/1.46 ( class_Finite__Set_Ofinite(T_1)
% 1.50/1.46 => class_Finite__Set_Ofinite(tc_Option_Ooption(T_1)) ) ).
% 1.50/1.46
% 1.50/1.46 fof(arity_prod__Finite__Set_Ofinite,axiom,
% 1.50/1.46 ! [T_1,T_2] :
% 1.50/1.46 ( ( class_Finite__Set_Ofinite(T_2)
% 1.50/1.46 & class_Finite__Set_Ofinite(T_1) )
% 1.50/1.46 => class_Finite__Set_Ofinite(tc_prod(T_2,T_1)) ) ).
% 1.50/1.46
% 1.50/1.46 fof(arity_Product____Type__Ounit__Finite__Set_Ofinite,axiom,
% 1.50/1.46 class_Finite__Set_Ofinite(tc_Product__Type_Ounit) ).
% 1.50/1.46
% 1.50/1.46 %----Helper facts (8)
% 1.50/1.46 fof(help_c__COMBI__1,axiom,
% 1.50/1.46 ! [V_P,T_a] : hAPP(c_COMBI(T_a),V_P) = V_P ).
% 1.50/1.46
% 1.50/1.46 fof(help_c__COMBK__1,axiom,
% 1.50/1.46 ! [V_Q,V_P,T_b,T_a] : hAPP(hAPP(c_COMBK(T_a,T_b),V_P),V_Q) = V_P ).
% 1.50/1.46
% 1.50/1.46 fof(help_c__COMBB__1,axiom,
% 1.50/1.46 ! [V_R_2,V_Q_2,V_Pa_2,T_c,T_a,T_b] : hAPP(hAPP(c_COMBB(T_b,T_a,T_c,V_Pa_2),V_Q_2),V_R_2) = hAPP(V_Pa_2,hAPP(V_Q_2,V_R_2)) ).
% 1.50/1.46
% 1.50/1.46 fof(help_c__COMBC__1,axiom,
% 1.50/1.46 ! [V_R_2,V_Q_2,V_Pa_2,T_a,T_c,T_b] : hAPP(hAPP(hAPP(c_COMBC(T_b,T_c,T_a),V_Pa_2),V_Q_2),V_R_2) = hAPP(hAPP(V_Pa_2,V_R_2),V_Q_2) ).
% 1.50/1.46
% 1.50/1.46 fof(help_c__COMBS__1,axiom,
% 1.50/1.46 ! [V_R_2,V_Q_2,V_Pa_2,T_a,T_c,T_b] : hAPP(c_COMBS(T_b,T_c,T_a,V_Pa_2,V_Q_2),V_R_2) = hAPP(hAPP(V_Pa_2,V_R_2),hAPP(V_Q_2,V_R_2)) ).
% 1.50/1.46
% 1.50/1.46 fof(help_c__fequal__1,axiom,
% 1.50/1.46 ! [V_y_2,V_x_2] :
% 1.50/1.46 ( ~ hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2))
% 1.50/1.46 | V_x_2 = V_y_2 ) ).
% 1.50/1.46
% 1.50/1.46 fof(help_c__fequal__2,axiom,
% 1.50/1.46 ! [V_y_2,V_x_2] :
% 1.50/1.46 ( V_x_2 != V_y_2
% 1.50/1.46 | hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) ) ).
% 1.50/1.46
% 1.50/1.46 fof(help_c__fFalse__1,axiom,
% 1.50/1.46 ~ hBOOL(c_fFalse) ).
% 1.50/1.46
% 1.50/1.46 %----Conjectures (1)
% 1.50/1.46 fof(conj_0,conjecture,
% 1.50/1.46 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
% 1.50/1.46 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),v_Lab____)),v_Lba____)))) ) ).
% 1.50/1.46
% 1.50/1.46 %------------------------------------------------------------------------------
% 1.50/1.46 %-------------------------------------------
% 1.50/1.46 % Proof found
% 1.50/1.46 % SZS status Theorem for theBenchmark
% 1.50/1.46 % SZS output start Proof
% 1.50/1.46 %ClaNum:1089(EqnAxiom:262)
% 1.50/1.46 %VarNum:5295(SingletonVarNum:1745)
% 1.50/1.46 %MaxLitNum:10
% 1.50/1.46 %MaxfuncDepth:12
% 1.50/1.46 %SharedTerms:291
% 1.50/1.46 %goalClause: 1088
% 1.50/1.46 [263]P1(a1)
% 1.50/1.46 [264]P2(a1)
% 1.50/1.46 [265]P4(a2)
% 1.50/1.46 [266]P5(a2)
% 1.50/1.46 [267]P21(a2)
% 1.50/1.46 [268]P21(a3)
% 1.50/1.46 [269]P22(a2)
% 1.50/1.46 [270]P22(a3)
% 1.50/1.46 [271]P28(a3)
% 1.50/1.46 [272]P23(a2)
% 1.50/1.46 [273]P27(a2)
% 1.50/1.46 [274]P27(a3)
% 1.50/1.46 [275]P6(a2)
% 1.50/1.46 [276]P13(a2)
% 1.50/1.46 [277]P14(a2)
% 1.50/1.46 [278]P15(a2)
% 1.50/1.46 [279]P19(a2)
% 1.50/1.46 [280]P20(a2)
% 1.50/1.46 [281]P7(a3)
% 1.50/1.46 [282]P7(a92)
% 1.50/1.46 [283]P24(a2)
% 1.50/1.46 [284]P31(a2)
% 1.50/1.46 [285]P16(a2)
% 1.50/1.46 [286]P17(a2)
% 1.50/1.46 [287]P25(a2)
% 1.50/1.46 [288]P29(a2)
% 1.50/1.46 [289]P33(a2)
% 1.50/1.46 [372]~E(a102,a100)
% 1.50/1.46 [373]~E(a104,a103)
% 1.50/1.46 [374]~P34(a40)
% 1.50/1.46 [290]E(f21(f4(a2)),f4(a2))
% 1.50/1.46 [292]E(f28(a22,f4(a2)),f5(a2))
% 1.50/1.46 [298]P8(a90,f31(f94(a90,a3)))
% 1.50/1.46 [329]P9(a90,a2,a97,f31(f94(a90,a3)))
% 1.50/1.46 [330]P9(a90,a2,a45,f31(f94(a90,a3)))
% 1.50/1.46 [299]E(f15(a92,f31(f94(a92,a3))),f5(a2))
% 1.50/1.46 [331]P34(f28(f28(f30(a2),a106),f15(a90,f31(f94(a90,a3)))))
% 1.50/1.46 [332]P34(f28(f28(f30(a2),a77),f15(a90,f31(f94(a90,a3)))))
% 1.50/1.46 [333]P34(f28(f28(f30(a2),a46),f15(a90,f31(f94(a90,a3)))))
% 1.50/1.46 [340]E(f32(a2,f4(a2),f15(a90,f31(f94(a90,a3)))),f37(a90,a2,a97,f31(f94(a90,a3))))
% 1.50/1.46 [341]E(f32(a2,f4(a2),f15(a90,f31(f94(a90,a3)))),f37(a90,a2,a45,f31(f94(a90,a3))))
% 1.50/1.46 [345]P34(f28(f28(f35(f94(f96(a91,a91),a3)),a98),a8))
% 1.50/1.46 [346]P34(f28(f28(f35(f94(f96(a91,a91),a3)),a99),a8))
% 1.50/1.46 [347]P34(f28(f28(f35(f94(f96(a91,a91),a3)),a47),a8))
% 1.50/1.46 [348]P34(f28(f28(f35(f94(f96(a91,a91),a3)),a48),a8))
% 1.50/1.46 [351]P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a100),a102)),a98))
% 1.50/1.46 [352]P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a100),a102)),a47))
% 1.50/1.46 [353]P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a102),a100)),a99))
% 1.50/1.46 [354]P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a102),a100)),a48))
% 1.50/1.46 [391]~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a100),a102)),a99))
% 1.50/1.46 [392]~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a102),a100)),a98))
% 1.50/1.46 [356]E(f18(a90,f94(f96(a91,a91),a3),f31(f94(a90,a3)),f28(f16(f94(f94(f96(a91,a91),a3),a3),a90),a8)),a9)
% 1.50/1.46 [359]P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),a101),a9))
% 1.50/1.46 [365]P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a104)),f28(a101,f28(f23(a90,a2,f31(f94(a90,a3)),a97),a106))))
% 1.50/1.46 [366]P34(f28(f28(f35(f94(f94(a90,f94(f96(a91,a91),a3)),f94(f96(a91,a91),a3))),a1),f18(f94(a90,f94(f96(a91,a91),a3)),f94(f96(a91,a91),a3),a9,f28(f16(f94(f94(f96(a91,a91),a3),a3),f94(a90,f94(f96(a91,a91),a3))),a8))))
% 1.50/1.46 [368]P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a100),a102)),f28(a1,f28(f28(f7(a90,f94(f96(a91,a91),a3),f94(f96(a91,a91),a3)),f28(f28(f7(a90,f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),f28(f10(a3,f94(f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),a90,f24(f94(f96(a91,a91),a3))),f28(f28(f7(a90,a2,a3),f28(f10(a2,f94(a2,a3),a90,f30(a2)),a97)),f28(f28(f20(a2),a106),f5(a2))))),a98)),a99))))
% 1.50/1.46 [369]P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a100),a102)),f28(a1,f28(f28(f7(a90,f94(f96(a91,a91),a3),f94(f96(a91,a91),a3)),f28(f28(f7(a90,f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),f28(f10(a3,f94(f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),a90,f24(f94(f96(a91,a91),a3))),f28(f28(f7(a90,a2,a3),f28(f10(a2,f94(a2,a3),a90,f30(a2)),a97)),f28(f28(f20(a2),a77),f5(a2))))),a98)),a99))))
% 1.50/1.46 [370]P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a100),a102)),f28(a1,f28(f28(f7(a90,f94(f96(a91,a91),a3),f94(f96(a91,a91),a3)),f28(f28(f7(a90,f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),f28(f10(a3,f94(f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),a90,f24(f94(f96(a91,a91),a3))),f28(f28(f7(a90,a2,a3),f28(f10(a2,f94(a2,a3),a90,f30(a2)),a97)),f28(f28(f20(a2),a46),f5(a2))))),a98)),a99))))
% 1.50/1.46 [371]P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),f17(a90,f94(f96(a91,a91),a3),f94(f96(a91,a91),a3),f17(a90,f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3)),f28(f10(a3,f94(f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),a90,f24(f94(f96(a91,a91),a3))),f28(f28(f7(a90,a2,a3),f28(f10(a2,f94(a2,a3),a90,f30(a2)),a97)),a106)),f28(f28(f7(a90,a91,f94(f96(a91,a91),a3)),f28(f10(f94(f96(a91,a91),a3),f94(a91,f94(f96(a91,a91),a3)),a90,a11),a101)),a105)),f17(a90,f94(f96(a91,a91),a3),f94(f96(a91,a91),a3),f17(a90,f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3)),f28(f10(a3,f94(f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),a90,f24(f94(f96(a91,a91),a3))),f28(f28(f7(a90,a2,a3),f28(f10(a2,f94(a2,a3),a90,a39),a97)),a106)),f28(f28(f7(a90,a91,f94(f96(a91,a91),a3)),f28(f28(f7(a90,a91,f94(a91,f94(f96(a91,a91),a3))),f28(f10(f94(f96(a91,a91),a3),f94(a91,f94(a91,f94(f96(a91,a91),a3))),a90,a12),a101)),a103)),a105)),f28(f28(f7(a90,a91,f94(f96(a91,a91),a3)),f28(f10(f94(f96(a91,a91),a3),f94(a91,f94(f96(a91,a91),a3)),a90,a13),a101)),a105)))),a9))
% 1.50/1.46 [320]P9(a2,a2,a22,x3201)
% 1.50/1.46 [291]E(f27(a2,x2911),x2911)
% 1.50/1.46 [376]~E(f28(a22,x3761),x3761)
% 1.50/1.46 [382]~E(f28(a22,x3821),f4(a2))
% 1.50/1.46 [295]E(f28(f28(f20(a2),x2951),f4(a2)),x2951)
% 1.50/1.46 [296]E(f29(a2,f28(a22,x2961)),f28(f30(a2),x2961))
% 1.50/1.46 [300]E(f28(f28(f20(a2),x3001),f5(a2)),f28(a22,x3001))
% 1.50/1.46 [302]P34(f28(f29(a2,x3021),x3021))
% 1.50/1.46 [310]P34(f28(f28(f30(a2),x3101),f28(a22,x3101)))
% 1.50/1.46 [311]P34(f28(f28(f30(a2),f4(a2)),f28(a22,x3111)))
% 1.50/1.46 [387]~P34(f28(f28(f30(a2),x3871),f4(a2)))
% 1.50/1.46 [297]E(f28(f28(f20(a2),f4(a2)),x2971),x2971)
% 1.50/1.46 [301]E(f28(f28(f20(a2),f5(a2)),x3011),f28(a22,x3011))
% 1.50/1.46 [304]P34(f28(f29(a2,f4(a2)),x3041))
% 1.50/1.46 [307]E(f28(f28(f20(a2),f21(x3071)),f28(a22,f4(a2))),f21(f28(a22,x3071)))
% 1.50/1.46 [312]E(f28(f28(f20(a2),f27(a2,x3121)),f28(a22,f4(a2))),f27(a2,f28(a22,x3121)))
% 1.50/1.47 [384]~P34(f28(f28(f30(a2),x3841),x3841))
% 1.50/1.47 [388]~P34(f28(f29(a2,f28(a22,x3881)),x3881))
% 1.50/1.47 [367]P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),f28(f28(f7(a90,f94(f96(a91,a91),a3),f94(f96(a91,a91),a3)),f28(f28(f7(a90,f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),f28(f10(a3,f94(f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),a90,f24(f94(f96(a91,a91),a3))),f28(f28(f7(a90,a2,a3),f28(f10(a2,f94(a2,a3),a90,f30(a2)),a97)),x3671))),a98)),a99)),a9))
% 1.50/1.47 [308]P8(a2,f32(a2,x3081,x3082))
% 1.50/1.47 [322]P9(x3221,x3221,f6(x3221),x3222)
% 1.50/1.47 [294]E(f28(f6(x2941),x2942),x2942)
% 1.50/1.47 [323]E(f37(x3231,x3231,f6(x3231),x3232),x3232)
% 1.50/1.47 [339]E(f37(a2,a2,a22,f32(a2,x3391,x3392)),f32(a2,f28(a22,x3391),f28(a22,x3392)))
% 1.50/1.47 [305]E(f28(f28(f20(a2),x3051),x3052),f28(f28(f20(a2),x3052),x3051))
% 1.50/1.47 [309]P34(f28(f31(f94(x3091,a3)),x3092))
% 1.50/1.47 [313]E(f28(f28(f20(a2),f28(a22,x3131)),x3132),f28(f28(f20(a2),x3131),f28(a22,x3132)))
% 1.50/1.47 [315]P34(f28(f29(f94(x3151,a3),x3152),x3152))
% 1.50/1.47 [318]P34(f28(f28(f35(x3181),x3182),f31(f94(x3181,a3))))
% 1.50/1.47 [327]P34(f28(f29(f94(x3271,a3),x3272),f31(f94(x3271,a3))))
% 1.50/1.47 [338]E(f38(x3381,x3382,f31(f94(x3381,a3)),f31(f94(x3382,a3))),f31(f94(f95(x3381,x3382),a3)))
% 1.50/1.47 [350]P9(a2,a2,f28(f28(f7(a2,a2,a2),f20(a2)),x3501),x3502)
% 1.50/1.47 [314]E(f28(f28(f20(a2),x3141),f28(a22,x3142)),f28(a22,f28(f28(f20(a2),x3141),x3142)))
% 1.50/1.47 [316]E(f28(f28(f20(a2),f28(a22,x3161)),x3162),f28(a22,f28(f28(f20(a2),x3161),x3162)))
% 1.50/1.47 [324]P34(f28(f29(a2,x3241),f28(f28(f20(a2),x3242),x3241)))
% 1.50/1.47 [325]P34(f28(f29(a2,x3251),f28(f28(f20(a2),x3251),x3252)))
% 1.50/1.47 [342]P34(f28(f28(f30(a2),x3421),f28(a22,f28(f28(f20(a2),x3422),x3421))))
% 1.50/1.47 [343]P34(f28(f28(f30(a2),x3431),f28(a22,f28(f28(f20(a2),x3431),x3432))))
% 1.50/1.47 [362]P34(f28(f28(f35(f94(x3621,x3621)),f6(x3621)),f18(x3621,x3621,x3622,f28(f16(f94(x3621,a3),x3621),x3622))))
% 1.50/1.47 [389]~P34(f28(f28(f30(a2),f28(f28(f20(a2),x3891),x3892)),x3892))
% 1.50/1.47 [390]~P34(f28(f28(f30(a2),f28(f28(f20(a2),x3901),x3902)),x3901))
% 1.50/1.47 [319]E(f36(x3191,x3192,f36(x3191,x3192,x3193)),f36(x3191,x3192,x3193))
% 1.50/1.47 [321]E(f26(x3211,x3212,x3213,f4(a2)),x3212)
% 1.50/1.47 [334]P34(f28(f28(f35(x3341),x3342),f36(x3341,x3342,x3343)))
% 1.50/1.47 [337]P34(f28(f29(f94(x3371,a3),x3372),f36(x3371,x3373,x3372)))
% 1.50/1.47 [326]E(f28(f28(f20(a2),x3261),f28(f28(f20(a2),x3262),x3263)),f28(f28(f20(a2),x3262),f28(f28(f20(a2),x3261),x3263)))
% 1.50/1.47 [349]E(f18(x3491,x3492,x3493,f28(f16(f94(x3492,a3),x3491),f31(f94(x3492,a3)))),f31(f94(f94(x3491,x3492),a3)))
% 1.50/1.47 [357]E(f37(a2,a2,f28(f28(f7(a2,a2,a2),f20(a2)),x3571),f32(a2,x3572,x3573)),f32(a2,f28(f28(f20(a2),x3572),x3571),f28(f28(f20(a2),x3573),x3571)))
% 1.50/1.47 [336]E(f28(f28(f20(a2),f28(f28(f20(a2),x3361),x3362)),x3363),f28(f28(f20(a2),x3361),f28(f28(f20(a2),x3362),x3363)))
% 1.50/1.47 [328]E(f26(x3281,x3282,x3283,f28(a22,x3284)),f28(x3283,x3284))
% 1.50/1.47 [335]E(f36(x3351,x3352,f36(x3351,x3353,x3354)),f36(x3351,x3353,f36(x3351,x3352,x3354)))
% 1.50/1.47 [306]E(f28(f28(f16(x3061,x3062),x3063),x3064),x3063)
% 1.50/1.47 [360]P34(f28(f28(f35(x3601),f28(x3602,x3603)),f37(x3604,x3601,x3602,f31(f94(x3604,a3)))))
% 1.50/1.47 [355]E(f37(x3551,x3552,x3553,f36(x3551,x3554,x3555)),f36(x3552,f28(x3553,x3554),f37(x3551,x3552,x3553,x3555)))
% 1.50/1.47 [363]E(f37(x3631,x3632,f28(f10(x3633,x3632,x3631,x3634),x3635),f31(f94(x3631,a3))),f37(x3633,x3632,x3634,f37(x3631,x3633,x3635,f31(f94(x3631,a3)))))
% 1.50/1.47 [364]E(f28(f17(x3641,x3642,x3643,x3644,x3645),x3646),f28(f28(x3644,x3646),f28(x3645,x3646)))
% 1.50/1.47 [358]E(f28(f28(f10(x3581,x3582,x3583,x3584),x3585),x3586),f28(x3584,f28(x3585,x3586)))
% 1.50/1.47 [361]E(f37(x3611,x3612,x3613,f37(x3614,x3611,x3615,x3616)),f37(x3614,x3612,f28(f10(x3611,x3612,x3614,x3613),x3615),x3616))
% 1.50/1.47 [344]E(f28(f28(f28(f7(x3441,x3442,x3443),x3444),x3445),x3446),f28(f28(x3444,x3446),x3445))
% 1.50/1.47 [1031]~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a104)),f28(a1,a101)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a104)),f28(a1,f17(a90,f94(f96(a91,a91),a3),f94(f96(a91,a91),a3),f17(a90,f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3)),f28(f10(a3,f94(f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),a90,f24(f94(f96(a91,a91),a3))),f28(f28(f7(a90,a2,a3),f28(f10(a2,f94(a2,a3),a90,f30(a2)),a97)),a106)),f28(f28(f7(a90,a91,f94(f96(a91,a91),a3)),f28(f10(f94(f96(a91,a91),a3),f94(a91,f94(f96(a91,a91),a3)),a90,a11),a101)),a105)),f17(a90,f94(f96(a91,a91),a3),f94(f96(a91,a91),a3),f17(a90,f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3)),f28(f10(a3,f94(f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),a90,f24(f94(f96(a91,a91),a3))),f28(f28(f7(a90,a2,a3),f28(f10(a2,f94(a2,a3),a90,a39),a97)),a106)),f28(f28(f7(a90,a91,f94(f96(a91,a91),a3)),f28(f28(f7(a90,a91,f94(a91,f94(f96(a91,a91),a3))),f28(f10(f94(f96(a91,a91),a3),f94(a91,f94(a91,f94(f96(a91,a91),a3))),a90,a12),a101)),a103)),a105)),f28(f28(f7(a90,a91,f94(f96(a91,a91),a3)),f28(f10(f94(f96(a91,a91),a3),f94(a91,f94(f96(a91,a91),a3)),a90,a13),a101)),a105))))))
% 1.50/1.47 [1033]P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a104)),f28(a1,a101)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a104)),f28(a1,f17(a90,f94(f96(a91,a91),a3),f94(f96(a91,a91),a3),f17(a90,f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3)),f28(f10(a3,f94(f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),a90,f24(f94(f96(a91,a91),a3))),f28(f28(f7(a90,a2,a3),f28(f10(a2,f94(a2,a3),a90,f30(a2)),a97)),a106)),f28(f28(f7(a90,a91,f94(f96(a91,a91),a3)),f28(f10(f94(f96(a91,a91),a3),f94(a91,f94(f96(a91,a91),a3)),a90,a11),a101)),a105)),f17(a90,f94(f96(a91,a91),a3),f94(f96(a91,a91),a3),f17(a90,f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3)),f28(f10(a3,f94(f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),a90,f24(f94(f96(a91,a91),a3))),f28(f28(f7(a90,a2,a3),f28(f10(a2,f94(a2,a3),a90,a39),a97)),a106)),f28(f28(f7(a90,a91,f94(f96(a91,a91),a3)),f28(f28(f7(a90,a91,f94(a91,f94(f96(a91,a91),a3))),f28(f10(f94(f96(a91,a91),a3),f94(a91,f94(a91,f94(f96(a91,a91),a3))),a90,a12),a101)),a103)),a105)),f28(f28(f7(a90,a91,f94(f96(a91,a91),a3)),f28(f10(f94(f96(a91,a91),a3),f94(a91,f94(f96(a91,a91),a3)),a90,a13),a101)),a105))))))
% 1.50/1.47 [1088]~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a100),a102)),f28(a1,f28(f28(f7(a90,f94(f96(a91,a91),a3),f94(f96(a91,a91),a3)),f28(f28(f7(a90,f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),f28(f10(a3,f94(f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),a90,f24(f94(f96(a91,a91),a3))),f28(f28(f7(a90,a2,a3),f28(f10(a2,f94(a2,a3),a90,f30(a2)),a97)),f28(f28(f20(a2),a106),f5(a2))))),a98)),a99))))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a105)),f28(a1,f17(a90,f94(f96(a91,a91),a3),f94(f96(a91,a91),a3),f17(a90,f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3)),f28(f10(a3,f94(f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),a90,f24(f94(f96(a91,a91),a3))),f28(f28(f7(a90,a2,a3),f28(f10(a2,f94(a2,a3),a90,f30(a2)),a97)),a106)),f28(f28(f7(a90,a91,f94(f96(a91,a91),a3)),f28(f10(f94(f96(a91,a91),a3),f94(a91,f94(f96(a91,a91),a3)),a90,a11),a101)),a105)),f17(a90,f94(f96(a91,a91),a3),f94(f96(a91,a91),a3),f17(a90,f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3)),f28(f10(a3,f94(f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),a90,f24(f94(f96(a91,a91),a3))),f28(f28(f7(a90,a2,a3),f28(f10(a2,f94(a2,a3),a90,a39),a97)),a106)),f28(f28(f7(a90,a91,f94(f96(a91,a91),a3)),f28(f28(f7(a90,a91,f94(a91,f94(f96(a91,a91),a3))),f28(f10(f94(f96(a91,a91),a3),f94(a91,f94(a91,f94(f96(a91,a91),a3))),a90,a12),a101)),a103)),a105)),f28(f28(f7(a90,a91,f94(f96(a91,a91),a3)),f28(f10(f94(f96(a91,a91),a3),f94(a91,f94(f96(a91,a91),a3)),a90,a13),a101)),a105))))))
% 1.50/1.47 [393]~P7(x3931)+P7(f93(x3931))
% 1.50/1.47 [395]~P31(x3951)+~E(f5(x3951),f4(x3951))
% 1.50/1.47 [452]~P4(x4521)+P34(f28(f29(x4521,f4(x4521)),f5(x4521)))
% 1.50/1.47 [457]E(x4571,f4(a2))+~P34(f28(f29(a2,x4571),f4(a2)))
% 1.50/1.47 [466]~P32(x4661)+P34(f28(f28(f35(x4661),f5(x4661)),f25(x4661)))
% 1.50/1.47 [467]~P32(x4671)+P34(f28(f28(f35(x4671),f4(x4671)),f25(x4671)))
% 1.50/1.47 [468]~P4(x4681)+P34(f28(f28(f30(x4681),f4(x4681)),f5(x4681)))
% 1.50/1.47 [507]~P4(x5071)+~P34(f28(f29(x5071,f5(x5071)),f4(x5071)))
% 1.50/1.47 [536]~P4(x5361)+~P34(f28(f28(f30(x5361),f5(x5361)),f4(x5361)))
% 1.50/1.47 [445]E(x4451,f4(a2))+P34(f28(f28(f30(a2),f4(a2)),x4451))
% 1.50/1.47 [503]E(f28(a22,f65(x5031)),x5031)+~P34(f28(f28(f30(a2),f4(a2)),x5031))
% 1.50/1.47 [515]~P8(x5151,f31(f94(x5151,a3)))+P8(f93(x5151),f31(f94(f93(x5151),a3)))
% 1.50/1.47 [522]P8(x5221,f31(f94(x5221,a3)))+~P8(f93(x5221),f31(f94(f93(x5221),a3)))
% 1.50/1.47 [543]E(x5431,f4(a2))+~P34(f28(f28(f30(a2),x5431),f28(a22,f4(a2))))
% 1.50/1.47 [649]~P4(x6491)+P34(f28(f28(f30(x6491),f4(x6491)),f28(f28(f20(x6491),f5(x6491)),f5(x6491))))
% 1.50/1.47 [822]P1(x8221)+P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),f54(x8221)),a9))
% 1.50/1.47 [823]P1(x8231)+P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),f56(x8231)),a9))
% 1.50/1.47 [824]P2(x8241)+P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),f51(x8241)),a9))
% 1.50/1.47 [841]P2(x8411)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),f50(x8411)),f53(x8411))),f28(x8411,f51(x8411))))
% 1.50/1.47 [670]~P8(x6701,f31(f94(x6701,a3)))+P34(f28(f28(f30(a2),f4(a2)),f15(x6701,f31(f94(x6701,a3)))))
% 1.50/1.47 [908]~P34(f28(f28(f35(f94(f96(a91,a91),a3)),x9081),a8))+P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),f28(f16(f94(f96(a91,a91),a3),a90),x9081)),a9))
% 1.50/1.47 [1028]~P34(f28(f29(a2,x10281),a106))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a102),a100)),f28(a1,f28(f28(f7(a90,f94(f96(a91,a91),a3),f94(f96(a91,a91),a3)),f28(f28(f7(a90,f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),f28(f10(a3,f94(f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),a90,f24(f94(f96(a91,a91),a3))),f28(f28(f7(a90,a2,a3),f28(f10(a2,f94(a2,a3),a90,f30(a2)),a97)),x10281))),a98)),a99))))
% 1.50/1.47 [1029]~P34(f28(f29(a2,x10291),a77))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a102),a100)),f28(a1,f28(f28(f7(a90,f94(f96(a91,a91),a3),f94(f96(a91,a91),a3)),f28(f28(f7(a90,f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),f28(f10(a3,f94(f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),a90,f24(f94(f96(a91,a91),a3))),f28(f28(f7(a90,a2,a3),f28(f10(a2,f94(a2,a3),a90,f30(a2)),a97)),x10291))),a98)),a99))))
% 1.50/1.47 [1030]~P34(f28(f29(a2,x10301),a46))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a102),a100)),f28(a1,f28(f28(f7(a90,f94(f96(a91,a91),a3),f94(f96(a91,a91),a3)),f28(f28(f7(a90,f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),f28(f10(a3,f94(f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),a90,f24(f94(f96(a91,a91),a3))),f28(f28(f7(a90,a2,a3),f28(f10(a2,f94(a2,a3),a90,f30(a2)),a97)),x10301))),a98)),a99))))
% 1.50/1.47 [397]~P7(x3971)+P8(x3971,x3972)
% 1.50/1.47 [399]P8(x3991,x3992)+E(f15(x3991,x3992),f4(a2))
% 1.50/1.47 [400]~P21(x4002)+P21(f94(x4001,x4002))
% 1.50/1.47 [401]~P22(x4012)+P22(f94(x4011,x4012))
% 1.50/1.47 [402]~P28(x4022)+P28(f94(x4021,x4022))
% 1.50/1.47 [403]~P27(x4032)+P27(f94(x4031,x4032))
% 1.50/1.47 [405]E(x4051,x4052)+~E(f28(a22,x4051),f28(a22,x4052))
% 1.50/1.47 [410]~P16(x4101)+E(f28(f28(f20(x4101),x4102),f4(x4101)),x4102)
% 1.50/1.47 [411]~P17(x4111)+E(f28(f28(f20(x4111),x4112),f4(x4111)),x4112)
% 1.50/1.47 [412]~P29(x4121)+E(f28(f28(f20(x4121),x4122),f4(x4121)),x4122)
% 1.50/1.47 [421]~E(x4211,x4212)+P34(f28(f28(a39,x4211),x4212))
% 1.50/1.47 [424]~E(x4241,x4242)+P34(f28(f29(a2,x4241),x4242))
% 1.50/1.47 [429]~P21(x4291)+P34(f28(f29(x4291,x4292),x4292))
% 1.50/1.47 [441]~P28(x4411)+P34(f28(f29(x4411,x4412),f31(x4411)))
% 1.50/1.47 [451]E(x4511,x4512)+~P34(f28(f28(a39,x4511),x4512))
% 1.50/1.47 [453]E(x4531,x4532)+~E(f28(x4531,f49(x4532,x4531)),f28(x4532,f49(x4532,x4531)))
% 1.50/1.47 [458]P3(x4581,x4582)+~E(f28(x4581,f57(x4582,x4581)),f28(f57(x4582,x4581),x4582))
% 1.50/1.47 [460]~E(x4601,x4602)+P34(f28(f28(f30(a2),x4601),f28(a22,x4602)))
% 1.50/1.47 [463]~E(x4631,f4(a2))+P34(f28(f28(f30(a2),x4631),f28(a22,x4632)))
% 1.50/1.47 [475]P34(f28(f29(a2,x4752),x4751))+P34(f28(f29(a2,x4751),x4752))
% 1.50/1.47 [506]E(f28(f28(f20(a2),x5061),f66(x5062,x5061)),x5062)+~P34(f28(f29(a2,x5061),x5062))
% 1.50/1.47 [540]~P34(f28(f29(a2,x5401),x5402))+P34(f28(f29(a2,x5401),f28(a22,x5402)))
% 1.50/1.47 [564]~P34(f28(f29(a2,x5641),x5642))+P34(f28(f28(f30(a2),x5641),f28(a22,x5642)))
% 1.50/1.47 [565]P8(x5651,x5652)+~P34(f28(f28(f30(a2),f4(a2)),f15(x5651,x5652)))
% 1.50/1.47 [584]P34(f28(f29(a2,x5841),x5842))+~P34(f28(f28(f30(a2),x5841),f28(a22,x5842)))
% 1.50/1.47 [609]~P34(f28(f29(a2,x6091),x6092))+P34(f28(f29(a2,f28(a22,x6091)),f28(a22,x6092)))
% 1.50/1.47 [648]P34(f28(f29(a2,x6481),x6482))+~P34(f28(f29(a2,f28(a22,x6481)),f28(a22,x6482)))
% 1.50/1.47 [970]~P8(x9701,x9702)+E(f19(a2,x9701,f20(a2),f28(f16(a2,x9701),f5(a2)),f4(a2),x9702),f15(x9701,x9702))
% 1.50/1.47 [416]~P16(x4161)+E(f28(f28(f20(x4161),f4(x4161)),x4162),x4162)
% 1.50/1.47 [417]~P17(x4171)+E(f28(f28(f20(x4171),f4(x4171)),x4172),x4172)
% 1.50/1.47 [418]~P29(x4181)+E(f28(f28(f20(x4181),f4(x4181)),x4182),x4182)
% 1.50/1.47 [420]E(x4201,f4(a2))+~E(f28(f28(f20(a2),x4202),x4201),x4202)
% 1.50/1.47 [425]E(x4251,f4(a2))+~E(f28(f28(f20(a2),x4252),x4251),f4(a2))
% 1.50/1.47 [426]E(x4261,f4(a2))+~E(f28(f28(f20(a2),x4261),x4262),f4(a2))
% 1.50/1.47 [454]~E(x4541,f28(a22,x4542))+P34(f28(f28(f30(a2),f4(a2)),x4541))
% 1.50/1.47 [474]~E(x4741,x4742)+~P34(f28(f28(f30(a2),x4741),x4742))
% 1.50/1.47 [476]~E(x4761,f4(a2))+~P34(f28(f28(f30(a2),x4762),x4761))
% 1.50/1.47 [488]~P21(x4881)+~P34(f28(f28(f30(x4881),x4882),x4882))
% 1.50/1.47 [517]P8(a2,x5171)+P34(f28(f28(f35(a2),f78(x5171,x5172)),x5171))
% 1.50/1.47 [518]P8(a2,x5181)+P34(f28(f28(f35(a2),f82(x5181,x5182)),x5181))
% 1.50/1.47 [535]P34(f28(f29(a2,x5351),x5352))+~P34(f28(f28(f30(a2),x5351),x5352))
% 1.50/1.47 [537]P34(f28(f28(f30(a2),x5372),f28(a22,x5371)))+P34(f28(f28(f30(a2),x5371),x5372))
% 1.50/1.47 [544]P34(f28(f29(a2,x5441),x5442))+P34(f28(f29(a2,f28(a22,x5442)),x5441))
% 1.50/1.47 [579]P34(f28(f28(f30(a2),x5791),f28(a22,x5792)))+~P34(f28(f28(f30(a2),x5791),x5792))
% 1.50/1.47 [583]P8(a2,x5831)+~P34(f28(f29(a2,f82(x5831,x5832)),x5832))
% 1.50/1.47 [585]E(f28(a22,f28(f28(f20(a2),x5851),f71(x5852,x5851))),x5852)+~P34(f28(f28(f30(a2),x5851),x5852))
% 1.50/1.47 [598]~P34(f28(f28(f30(a2),x5981),x5982))+P34(f28(f29(a2,f28(a22,x5981)),x5982))
% 1.50/1.47 [605]P8(a2,x6051)+~P34(f28(f28(f30(a2),f78(x6051,x6052)),x6052))
% 1.50/1.47 [611]P34(f28(f29(a2,x6111),x6112))+~P34(f28(f29(a2,f28(a22,x6111)),x6112))
% 1.50/1.47 [613]~P4(x6131)+P34(f28(f28(f30(x6131),x6132),f28(f28(f20(x6131),x6132),f5(x6131))))
% 1.50/1.47 [627]P34(f28(f28(f30(a2),x6271),x6272))+~P34(f28(f29(a2,f28(a22,x6271)),x6272))
% 1.50/1.47 [628]~P34(f28(f28(f30(a2),x6282),f28(a22,x6281)))+~P34(f28(f28(f30(a2),x6281),x6282))
% 1.50/1.47 [629]P8(x6291,f31(f94(x6291,a3)))+~P8(f94(x6292,x6291),f31(f94(f94(x6292,x6291),a3)))
% 1.50/1.47 [630]P8(x6301,f31(f94(x6301,a3)))+~P8(f95(x6302,x6301),f31(f94(f95(x6302,x6301),a3)))
% 1.50/1.47 [631]P8(x6311,f31(f94(x6311,a3)))+~P8(f95(x6311,x6312),f31(f94(f95(x6311,x6312),a3)))
% 1.50/1.47 [637]P34(f28(f28(f30(a2),f28(a22,x6371)),f28(a22,x6372)))+~P34(f28(f28(f30(a2),x6371),x6372))
% 1.50/1.47 [638]~P34(f28(f29(a2,x6381),x6382))+~P34(f28(f29(a2,f28(a22,x6382)),x6381))
% 1.50/1.47 [639]P34(f28(f28(f30(a2),x6391),x6392))+~P34(f28(f28(f30(a2),f28(a22,x6391)),x6392))
% 1.50/1.47 [668]~P34(f28(f28(f30(a2),f28(a22,x6681)),f28(a22,x6682)))+P34(f28(f28(f30(a2),x6681),x6682))
% 1.50/1.47 [750]P34(f26(a3,a40,f29(a2,x7501),x7502))+~P34(f28(f29(a2,f28(a22,x7501)),x7502))
% 1.50/1.47 [783]~P34(f26(a3,a40,f29(a2,x7831),x7832))+P34(f28(f29(a2,f28(a22,x7831)),x7832))
% 1.50/1.47 [805]P2(x8051)+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),f50(x8051)),f53(x8051))),f28(f51(x8051),x8052)))
% 1.50/1.47 [828]P3(x8281,x8282)+P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),f57(x8282,x8281)),a9))
% 1.50/1.47 [833]E(f32(a2,x8331,f28(f28(f20(a2),x8331),f15(a2,x8332))),x8332)+~P34(f28(f29(f94(a2,a3),x8332),f32(a2,x8331,f28(f28(f20(a2),x8331),f15(a2,x8332)))))
% 1.50/1.47 [846]P34(f28(f28(f35(f94(f96(a91,a91),a3)),f28(f28(a11,x8461),x8462)),a8))+~P34(f28(f28(f35(f94(f96(a91,a91),a3)),x8461),a8))
% 1.50/1.47 [847]P34(f28(f28(f35(f94(f96(a91,a91),a3)),f28(f28(a13,x8471),x8472)),a8))+~P34(f28(f28(f35(f94(f96(a91,a91),a3)),x8471),a8))
% 1.50/1.47 [462]~P8(x4621,x4623)+P8(x4621,f36(x4621,x4622,x4623))
% 1.50/1.47 [516]P8(x5161,x5162)+~P8(x5161,f36(x5161,x5163,x5162))
% 1.50/1.47 [478]~E(x4782,x4783)+P34(f28(f28(f35(x4781),x4782),f28(a39,x4783)))
% 1.50/1.47 [541]E(x5411,x5412)+~P34(f28(f28(f35(x5413),x5411),f28(a39,x5412)))
% 1.50/1.47 [957]P8(x9571,x9572)+~P34(f28(f28(f35(f96(f94(x9571,a3),f94(x9571,a3))),f28(f28(f33(f94(x9571,a3),f94(x9571,a3)),x9573),x9572)),f42(x9571)))
% 1.50/1.47 [427]~P28(x4272)+E(f28(f31(f94(x4271,x4272)),x4273),f31(x4272))
% 1.50/1.47 [446]~P29(x4461)+E(f28(f28(f20(x4461),x4462),x4463),f28(f28(f20(x4461),x4463),x4462))
% 1.50/1.47 [464]E(x4641,x4642)+~E(f28(f28(f20(a2),x4643),x4641),f28(f28(f20(a2),x4643),x4642))
% 1.50/1.47 [465]E(x4651,x4652)+~E(f28(f28(f20(a2),x4651),x4653),f28(f28(f20(a2),x4652),x4653))
% 1.50/1.47 [469]~E(x4692,f28(f28(f20(a2),x4691),x4693))+P34(f28(f29(a2,x4691),x4692))
% 1.50/1.47 [477]~P34(f28(x4773,x4772))+P34(f28(f28(f35(x4771),x4772),x4773))
% 1.50/1.47 [489]~E(x4893,x4892)+P34(f28(f29(f94(x4891,a3),x4892),x4893))
% 1.50/1.47 [495]~E(x4952,x4953)+P34(f28(f29(f94(x4951,a3),x4952),x4953))
% 1.50/1.47 [513]P34(f28(x5131,x5132))+~P34(f28(f28(f35(x5133),x5132),x5131))
% 1.50/1.47 [530]E(f36(x5301,x5302,x5303),x5303)+~P34(f28(f28(f35(x5301),x5302),x5303))
% 1.50/1.47 [719]~P8(x7191,x7192)+P34(f28(f29(a2,f15(x7191,x7192)),f15(x7191,f36(x7191,x7193,x7192))))
% 1.50/1.47 [801]E(x8011,x8012)+~E(f28(f28(f7(x8013,f94(x8013,a3),a3),f35(x8013)),x8011),f28(f28(f7(x8013,f94(x8013,a3),a3),f35(x8013)),x8012))
% 1.50/1.47 [827]~P9(x8272,x8271,x8273,f31(f94(x8272,a3)))+E(f37(x8271,x8272,f23(x8272,x8271,f31(f94(x8272,a3)),x8273),f31(f94(x8271,a3))),f31(f94(x8272,a3)))
% 1.50/1.47 [829]P9(x8291,x8292,f23(x8292,x8291,f31(f94(x8292,a3)),x8293),f31(f94(x8291,a3)))+~E(f37(x8292,x8291,x8293,f31(f94(x8292,a3))),f31(f94(x8291,a3)))
% 1.50/1.47 [874]~E(f28(x8743,f28(f23(x8741,x8742,f31(f94(x8741,a3)),x8743),f73(x8743,x8742,x8741))),f73(x8743,x8742,x8741))+E(f37(x8741,x8742,x8743,f31(f94(x8741,a3))),f31(f94(x8742,a3)))
% 1.50/1.47 [560]~E(x5602,f28(a22,f28(f28(f20(a2),x5601),x5603)))+P34(f28(f28(f30(a2),x5601),x5602))
% 1.50/1.47 [633]~P34(f28(f29(a2,x6331),x6333))+P34(f28(f29(a2,x6331),f28(f28(f20(a2),x6332),x6333)))
% 1.50/1.47 [635]~P34(f28(f29(a2,x6351),x6352))+P34(f28(f29(a2,x6351),f28(f28(f20(a2),x6352),x6353)))
% 1.50/1.47 [657]~P34(f28(f28(f30(a2),x6571),x6573))+P34(f28(f28(f30(a2),x6571),f28(f28(f20(a2),x6572),x6573)))
% 1.50/1.47 [659]~P34(f28(f28(f30(a2),x6591),x6592))+P34(f28(f28(f30(a2),x6591),f28(f28(f20(a2),x6592),x6593)))
% 1.50/1.47 [669]~E(x6691,x6692)+~P34(f28(f28(f30(f94(x6693,a3)),x6691),x6692))
% 1.50/1.47 [709]P34(f28(f29(f94(x7091,a3),x7092),x7093))+~P34(f28(f28(f30(f94(x7091,a3)),x7092),x7093))
% 1.50/1.47 [732]~P34(f28(f29(a2,x7322),x7323))+P34(f28(f29(a2,f28(f28(f20(a2),x7321),x7322)),f28(f28(f20(a2),x7321),x7323)))
% 1.50/1.47 [733]~P34(f28(f29(a2,x7331),x7333))+P34(f28(f29(a2,f28(f28(f20(a2),x7331),x7332)),f28(f28(f20(a2),x7333),x7332)))
% 1.50/1.47 [744]~P34(f28(f28(f30(a2),x7442),x7443))+P34(f28(f28(f30(a2),f28(f28(f20(a2),x7441),x7442)),f28(f28(f20(a2),x7441),x7443)))
% 1.50/1.47 [745]~P34(f28(f28(f30(a2),x7451),x7453))+P34(f28(f28(f30(a2),f28(f28(f20(a2),x7451),x7452)),f28(f28(f20(a2),x7453),x7452)))
% 1.50/1.47 [790]P34(f28(f29(a2,x7901),x7902))+~P34(f28(f29(a2,f28(f28(f20(a2),x7903),x7901)),f28(f28(f20(a2),x7903),x7902)))
% 1.50/1.47 [800]P34(f28(f28(f30(a2),x8001),x8002))+~P34(f28(f28(f30(a2),f28(f28(f20(a2),x8003),x8001)),f28(f28(f20(a2),x8003),x8002)))
% 1.50/1.47 [946]~P34(f28(f29(f94(x9461,a3),x9462),x9463))+P34(f28(f29(f94(x9461,a3),f28(f28(f7(x9461,f94(x9461,a3),a3),f35(x9461)),x9462)),f28(f28(f7(x9461,f94(x9461,a3),a3),f35(x9461)),x9463)))
% 1.50/1.47 [962]~P34(f28(f28(f35(f96(f94(x9621,a3),f94(x9621,a3))),f28(f28(f33(f94(x9621,a3),f94(x9621,a3)),x9622),x9623)),f42(x9621)))+P34(f28(f28(f30(f94(x9621,a3)),x9622),x9623))
% 1.50/1.47 [976]P34(f28(f29(f94(x9761,a3),x9762),x9763))+~P34(f28(f29(f94(x9761,a3),f28(f28(f7(x9761,f94(x9761,a3),a3),f35(x9761)),x9762)),f28(f28(f7(x9761,f94(x9761,a3),a3),f35(x9761)),x9763)))
% 1.50/1.47 [737]P34(f28(f29(a2,x7371),x7372))+~P34(f28(f29(a2,f28(f28(f20(a2),x7373),x7371)),x7372))
% 1.50/1.47 [738]P34(f28(f29(a2,x7381),x7382))+~P34(f28(f29(a2,f28(f28(f20(a2),x7381),x7383)),x7382))
% 1.50/1.47 [752]P34(f28(f28(f30(a2),x7521),x7522))+~P34(f28(f28(f30(a2),f28(f28(f20(a2),x7521),x7523)),x7522))
% 1.50/1.47 [685]~P8(x6852,x6854)+P8(x6851,f37(x6852,x6851,x6853,x6854))
% 1.50/1.47 [759]P8(x7591,x7592)+~P8(f95(x7593,x7591),f38(x7593,x7591,x7594,x7592))
% 1.50/1.47 [760]P8(x7601,x7602)+~P8(f95(x7601,x7603),f38(x7601,x7603,x7602,x7604))
% 1.50/1.47 [788]P9(x7881,x7882,x7883,x7884)+~E(f58(x7884,x7883,x7882,x7881),f64(x7884,x7883,x7882,x7881))
% 1.50/1.47 [554]~E(x5542,x5544)+P34(f28(f36(x5541,x5542,x5543),x5544))
% 1.50/1.47 [582]~P34(f28(x5823,x5824))+P34(f28(f36(x5821,x5822,x5823),x5824))
% 1.50/1.47 [604]~E(x6042,x6043)+P34(f28(f28(f35(x6041),x6042),f36(x6041,x6043,x6044)))
% 1.50/1.47 [696]P8(x6962,x6964)+E(f15(f95(x6961,x6962),f38(x6961,x6962,x6963,x6964)),f4(a2))
% 1.50/1.47 [697]P8(x6971,x6973)+E(f15(f95(x6971,x6972),f38(x6971,x6972,x6973,x6974)),f4(a2))
% 1.50/1.47 [773]~P9(x7732,x7731,x7733,x7734)+E(f15(x7731,f37(x7732,x7731,x7733,x7734)),f15(x7732,x7734))
% 1.50/1.47 [803]~P9(x8031,x8032,x8033,f31(f94(x8031,a3)))+E(f28(f23(x8031,x8032,f31(f94(x8031,a3)),x8033),f28(x8033,x8034)),x8034)
% 1.50/1.47 [818]P9(x8184,x8183,x8181,x8182)+E(f28(x8181,f58(x8182,x8181,x8183,x8184)),f28(x8181,f64(x8182,x8181,x8183,x8184)))
% 1.50/1.47 [832]P34(f28(f28(f35(f96(x8321,x8321)),f28(f28(f33(x8321,x8321),x8322),x8323)),f41(x8321,x8324)))+~P34(f28(f28(f30(a2),f28(x8324,x8322)),f28(x8324,x8323)))
% 1.50/1.47 [843]~P9(x8432,x8431,x8433,f31(f94(x8432,a3)))+E(f37(x8431,x8432,f23(x8432,x8431,f31(f94(x8432,a3)),x8433),f37(x8432,x8431,x8433,x8434)),x8434)
% 1.50/1.47 [850]~P34(f28(f28(f35(f96(x8504,x8504)),f28(f28(f33(x8504,x8504),x8502),x8503)),f41(x8504,x8501)))+P34(f28(f28(f30(a2),f28(x8501,x8502)),f28(x8501,x8503)))
% 1.50/1.47 [940]~P8(x9402,x9404)+P34(f28(f29(a2,f15(x9401,f37(x9402,x9401,x9403,x9404))),f15(x9402,x9404)))
% 1.50/1.47 [974]~P9(x9741,x9742,x9743,x9744)+~P34(f28(f28(f30(a2),f15(x9742,f37(x9741,x9742,x9743,x9744))),f15(x9741,x9744)))
% 1.50/1.47 [675]P34(f28(f28(f35(x6751),x6752),f36(x6751,x6753,x6754)))+~P34(f28(f28(f35(x6751),x6752),x6754))
% 1.50/1.47 [714]P34(f28(f29(f94(x7141,a3),x7142),f36(x7141,x7143,x7144)))+~P34(f28(f29(f94(x7141,a3),x7142),x7144))
% 1.50/1.47 [793]P34(f28(f28(f35(x7931),x7932),x7933))+~P34(f28(f29(f94(x7931,a3),f36(x7931,x7932,x7934)),x7933))
% 1.50/1.47 [795]P34(f28(f29(f94(x7951,a3),f36(x7951,x7952,x7953)),f36(x7951,x7952,x7954)))+~P34(f28(f29(f94(x7951,a3),x7953),x7954))
% 1.50/1.47 [804]~P34(f28(f29(f94(x8041,a3),f36(x8041,x8044,x8042)),x8043))+P34(f28(f29(f94(x8041,a3),x8042),x8043))
% 1.50/1.47 [834]~E(x8341,x8342)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x8343),x8341)),f28(f28(a13,x8344),x8342)))
% 1.50/1.47 [835]~E(x8351,x8352)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x8351),x8353)),f28(f28(a11,x8354),x8352)))
% 1.50/1.47 [852]~P9(x8521,x8523,x8524,f31(f94(x8521,a3)))+P9(x8521,f94(x8522,x8523),f28(f10(x8523,f94(x8522,x8523),x8521,f16(x8523,x8522)),x8524),f31(f94(x8521,a3)))
% 1.50/1.47 [860]P9(x8601,x8602,x8603,x8604)+P34(f28(f28(f35(x8601),f58(x8604,x8603,x8602,x8601)),x8604))
% 1.50/1.47 [861]P9(x8611,x8612,x8613,x8614)+P34(f28(f28(f35(x8611),f64(x8614,x8613,x8612,x8611)),x8614))
% 1.50/1.47 [595]~P29(x5951)+E(f28(f28(f20(x5951),x5952),f28(f28(f20(x5951),x5953),x5954)),f28(f28(f20(x5951),x5953),f28(f28(f20(x5951),x5952),x5954)))
% 1.50/1.47 [653]~P6(x6531)+E(f28(f28(f20(x6531),f28(f28(f20(x6531),x6532),x6533)),x6534),f28(f28(f20(x6531),x6532),f28(f28(f20(x6531),x6533),x6534)))
% 1.50/1.47 [654]~P29(x6541)+E(f28(f28(f20(x6541),f28(f28(f20(x6541),x6542),x6543)),x6544),f28(f28(f20(x6541),x6542),f28(f28(f20(x6541),x6543),x6544)))
% 1.50/1.47 [683]~P29(x6831)+E(f28(f28(f20(x6831),f28(f28(f20(x6831),x6832),x6833)),x6834),f28(f28(f20(x6831),f28(f28(f20(x6831),x6832),x6834)),x6833))
% 1.50/1.47 [840]~E(f37(x8402,x8403,x8401,f31(f94(x8402,a3))),f31(f94(x8403,a3)))+E(f28(x8401,f28(f23(x8402,x8403,f31(f94(x8402,a3)),x8401),x8404)),x8404)
% 1.50/1.47 [867]~E(f37(x8671,x8672,x8673,f31(f94(x8671,a3))),f31(f94(x8672,a3)))+E(f37(x8671,x8672,x8673,f37(x8672,x8671,f23(x8671,x8672,f31(f94(x8671,a3)),x8673),x8674)),x8674)
% 1.50/1.47 [1020]E(x10201,x10202)+~E(f28(f28(f7(x10203,f94(f96(x10203,x10204),a3),f94(x10204,a3)),f28(f10(f94(x10204,f94(f94(f96(x10203,x10204),a3),a3)),f94(f94(f96(x10203,x10204),a3),f94(x10204,a3)),x10203,f7(x10204,f94(f96(x10203,x10204),a3),a3)),f28(f10(f94(x10204,f96(x10203,x10204)),f94(x10204,f94(f94(f96(x10203,x10204),a3),a3)),x10203,f10(f96(x10203,x10204),f94(f94(f96(x10203,x10204),a3),a3),x10204,f35(f96(x10203,x10204)))),f33(x10203,x10204)))),x10201),f28(f28(f7(x10203,f94(f96(x10203,x10204),a3),f94(x10204,a3)),f28(f10(f94(x10204,f94(f94(f96(x10203,x10204),a3),a3)),f94(f94(f96(x10203,x10204),a3),f94(x10204,a3)),x10203,f7(x10204,f94(f96(x10203,x10204),a3),a3)),f28(f10(f94(x10204,f96(x10203,x10204)),f94(x10204,f94(f94(f96(x10203,x10204),a3),a3)),x10203,f10(f96(x10203,x10204),f94(f94(f96(x10203,x10204),a3),a3),x10204,f35(f96(x10203,x10204)))),f33(x10203,x10204)))),x10202))
% 1.50/1.47 [1026]~P34(f28(f29(f94(f96(x10261,x10262),a3),x10263),x10264))+P34(f28(f29(f94(x10261,f94(x10262,a3)),f28(f28(f7(x10261,f94(f96(x10261,x10262),a3),f94(x10262,a3)),f28(f10(f94(x10262,f94(f94(f96(x10261,x10262),a3),a3)),f94(f94(f96(x10261,x10262),a3),f94(x10262,a3)),x10261,f7(x10262,f94(f96(x10261,x10262),a3),a3)),f28(f10(f94(x10262,f96(x10261,x10262)),f94(x10262,f94(f94(f96(x10261,x10262),a3),a3)),x10261,f10(f96(x10261,x10262),f94(f94(f96(x10261,x10262),a3),a3),x10262,f35(f96(x10261,x10262)))),f33(x10261,x10262)))),x10263)),f28(f28(f7(x10261,f94(f96(x10261,x10262),a3),f94(x10262,a3)),f28(f10(f94(x10262,f94(f94(f96(x10261,x10262),a3),a3)),f94(f94(f96(x10261,x10262),a3),f94(x10262,a3)),x10261,f7(x10262,f94(f96(x10261,x10262),a3),a3)),f28(f10(f94(x10262,f96(x10261,x10262)),f94(x10262,f94(f94(f96(x10261,x10262),a3),a3)),x10261,f10(f96(x10261,x10262),f94(f94(f96(x10261,x10262),a3),a3),x10262,f35(f96(x10261,x10262)))),f33(x10261,x10262)))),x10264)))
% 1.50/1.47 [1027]P34(f28(f29(f94(f96(x10271,x10272),a3),x10273),x10274))+~P34(f28(f29(f94(x10271,f94(x10272,a3)),f28(f28(f7(x10271,f94(f96(x10271,x10272),a3),f94(x10272,a3)),f28(f10(f94(x10272,f94(f94(f96(x10271,x10272),a3),a3)),f94(f94(f96(x10271,x10272),a3),f94(x10272,a3)),x10271,f7(x10272,f94(f96(x10271,x10272),a3),a3)),f28(f10(f94(x10272,f96(x10271,x10272)),f94(x10272,f94(f94(f96(x10271,x10272),a3),a3)),x10271,f10(f96(x10271,x10272),f94(f94(f96(x10271,x10272),a3),a3),x10272,f35(f96(x10271,x10272)))),f33(x10271,x10272)))),x10273)),f28(f28(f7(x10271,f94(f96(x10271,x10272),a3),f94(x10272,a3)),f28(f10(f94(x10272,f94(f94(f96(x10271,x10272),a3),a3)),f94(f94(f96(x10271,x10272),a3),f94(x10272,a3)),x10271,f7(x10272,f94(f96(x10271,x10272),a3),a3)),f28(f10(f94(x10272,f96(x10271,x10272)),f94(x10272,f94(f94(f96(x10271,x10272),a3),a3)),x10271,f10(f96(x10271,x10272),f94(f94(f96(x10271,x10272),a3),a3),x10272,f35(f96(x10271,x10272)))),f33(x10271,x10272)))),x10274)))
% 1.50/1.47 [838]P34(f28(f28(f35(f96(x8381,x8381)),f28(f28(f33(x8381,x8381),x8382),x8383)),f44(x8381,x8384,x8385)))+~P34(f28(f28(f30(a2),f28(x8384,x8382)),f28(x8384,x8383)))
% 1.50/1.47 [857]E(f28(x8571,f72(x8572,x8571,x8573,x8574)),x8574)+~P34(f28(f28(f35(x8575),x8574),f37(x8573,x8575,x8571,x8572)))
% 1.50/1.47 [873]P9(x8731,x8732,f23(x8732,x8731,x8733,x8734),x8735)+~P34(f28(f29(f94(x8731,a3),x8735),f37(x8732,x8731,x8734,x8733)))
% 1.50/1.47 [944]E(f37(x9441,x9442,x9443,f75(x9444,x9443,x9441,x9445,x9442)),x9445)+~P34(f28(f29(f94(x9442,a3),x9445),f37(x9441,x9442,x9443,x9444)))
% 1.50/1.47 [782]E(f36(x7821,f28(x7822,x7823),f37(x7824,x7821,x7822,x7825)),f37(x7824,x7821,x7822,x7825))+~P34(f28(f28(f35(x7824),x7823),x7825))
% 1.50/1.47 [826]P34(f28(f28(f35(x8261),f28(x8262,x8263)),f37(x8264,x8261,x8262,x8265)))+~P34(f28(f28(f35(x8264),x8263),x8265))
% 1.50/1.47 [877]E(f28(x8771,f28(f23(x8772,x8773,x8774,x8771),x8775)),x8775)+~P34(f28(f28(f35(x8773),x8775),f37(x8772,x8773,x8771,x8774)))
% 1.50/1.47 [898]P34(f28(f29(f94(x8981,a3),f37(x8982,x8981,x8983,x8984)),f37(x8982,x8981,x8983,x8985)))+~P34(f28(f29(f94(x8982,a3),x8984),x8985))
% 1.50/1.47 [913]~P8(x9133,f37(x9132,x9133,x9135,f31(f94(x9132,a3))))+P8(x9131,f37(x9132,x9131,f28(f10(x9133,x9131,x9132,x9134),x9135),f31(f94(x9132,a3))))
% 1.50/1.47 [920]P34(f28(f29(f94(f94(x9201,x9202),a3),f18(x9201,x9202,x9203,x9204)),f18(x9201,x9202,x9205,x9204)))+~P34(f28(f29(f94(x9201,a3),x9205),x9203))
% 1.50/1.47 [930]~P34(f28(f28(f35(x9305),x9304),f37(x9301,x9305,x9303,x9302)))+P34(f28(f28(f35(x9301),f72(x9302,x9303,x9301,x9304)),x9302))
% 1.50/1.47 [991]P34(f28(f28(f35(f94(x9911,x9914)),x9913),f18(x9911,x9914,x9915,x9912)))+P34(f28(f28(f35(x9911),f67(x9912,x9913,x9914,x9915,x9911)),x9915))
% 1.50/1.47 [992]~P34(f28(f29(f94(x9925,a3),x9924),f37(x9921,x9925,x9923,x9922)))+P34(f28(f29(f94(x9921,a3),f75(x9922,x9923,x9921,x9924,x9925)),x9922))
% 1.50/1.47 [995]P34(f28(f29(f94(f94(x9951,x9954),a3),f18(x9951,x9954,x9955,x9953)),f18(x9951,x9954,x9955,x9952)))+P34(f28(f28(f35(x9951),f68(x9952,x9953,x9954,x9955,x9951)),x9955))
% 1.50/1.47 [1013]P34(f28(f28(f35(f94(x10131,x10132)),x10133),f18(x10131,x10132,x10134,x10135)))+~P34(f28(f28(f35(x10132),f28(x10133,f67(x10135,x10133,x10132,x10134,x10131))),f28(x10135,f67(x10135,x10133,x10132,x10134,x10131))))
% 1.50/1.47 [1014]P34(f28(f29(f94(f94(x10141,x10142),a3),f18(x10141,x10142,x10143,x10144)),f18(x10141,x10142,x10143,x10145)))+~P34(f28(f29(f94(x10142,a3),f28(x10144,f68(x10145,x10144,x10142,x10143,x10141))),f28(x10145,f68(x10145,x10144,x10142,x10143,x10141))))
% 1.50/1.47 [729]~P29(x7291)+E(f28(f28(f20(x7291),f28(f28(f20(x7291),x7292),x7293)),f28(f28(f20(x7291),x7294),x7295)),f28(f28(f20(x7291),f28(f28(f20(x7291),x7292),x7294)),f28(f28(f20(x7291),x7293),x7295)))
% 1.50/1.47 [825]~E(x8252,f28(x8254,x8255))+P34(f28(f28(f35(x8251),x8252),f37(x8253,x8251,x8254,f31(f94(x8253,a3)))))
% 1.50/1.47 [967]~P34(f28(f28(f35(x9672),x9675),f37(x9671,x9672,x9674,x9673)))+P34(f28(f28(f35(x9671),f28(f23(x9671,x9672,x9673,x9674),x9675)),x9673))
% 1.50/1.47 [880]P10(x8801,x8802,x8803,x8804,x8805)+~P34(f28(f28(f35(f96(x8801,x8802)),f28(f28(f33(x8801,x8802),x8804),x8805)),x8803))
% 1.50/1.47 [885]~P10(x8851,x8852,x8855,x8853,x8854)+P34(f28(f28(f35(f96(x8851,x8852)),f28(f28(f33(x8851,x8852),x8853),x8854)),x8855))
% 1.50/1.47 [960]P34(f28(f29(f94(x9601,a3),f37(x9602,x9601,x9603,x9604)),x9605))+~P34(f28(f28(f35(f94(x9602,x9601)),x9603),f18(x9602,x9601,x9604,f28(f16(f94(x9601,a3),x9602),x9605))))
% 1.50/1.47 [982]~P11(x9823,x9824,x9821,x9825,x9826,x9827)+E(f28(f28(x9821,x9822),x9822),x9822)
% 1.50/1.47 [988]P34(f28(f28(f35(f96(f96(x9881,x9882),f96(x9881,x9882))),f28(f28(f33(f96(x9881,x9882),f96(x9881,x9882)),f28(f28(f33(x9881,x9882),x9883),x9884)),f28(f28(f33(x9881,x9882),x9885),x9886))),f43(x9881,x9882,x9887,x9888)))+~P34(f28(f28(f35(f96(x9881,x9881)),f28(f28(f33(x9881,x9881),x9883),x9885)),x9887))
% 1.50/1.47 [859]P1(x8591)+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),f59(x8591)),f60(x8591))),f28(x8591,f56(x8591))))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),f59(x8591)),f60(x8591))),f28(x8591,f54(x8591))))
% 1.50/1.47 [907]P1(x9071)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),f59(x9071)),f60(x9071))),f28(x9071,f56(x9071))))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),f59(x9071)),f60(x9071))),f28(x9071,f54(x9071))))
% 1.50/1.47 [883]~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a104)),f28(a101,x8831)))+~P34(f28(f28(f30(a2),f28(a97,x8831)),a106))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a104)),f28(f28(a11,f28(a101,x8831)),a105)))
% 1.50/1.47 [889]P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a104)),f28(a101,x8891)))+~P34(f28(f28(f30(a2),f28(a97,x8891)),a106))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a104)),f28(f28(a11,f28(a101,x8891)),a105)))
% 1.50/1.47 [406]~P7(x4062)+~P7(x4061)+P7(f96(x4061,x4062))
% 1.50/1.47 [407]~P7(x4072)+~P7(x4071)+P7(f94(x4071,x4072))
% 1.50/1.47 [408]~P7(x4082)+~P7(x4081)+P7(f95(x4081,x4082))
% 1.50/1.47 [542]E(x5421,x5422)+~P34(f28(f29(a2,x5422),x5421))+~P34(f28(f29(a2,x5421),x5422))
% 1.50/1.47 [567]E(x5671,f4(a2))+E(f28(a22,f69(x5672,x5671)),x5671)+~P34(f28(f28(f30(a2),x5671),f28(a22,x5672)))
% 1.50/1.47 [575]E(x5751,f28(a22,x5752))+P34(f28(f29(a2,x5751),x5752))+~P34(f28(f29(a2,x5751),f28(a22,x5752)))
% 1.50/1.47 [612]E(x6121,x6122)+~P34(f28(f29(a2,x6122),x6121))+~P34(f28(f28(f30(a2),x6121),f28(a22,x6122)))
% 1.50/1.47 [713]~P18(x7131)+~P34(f28(f29(x7131,x7132),f4(x7131)))+P34(f28(f29(x7131,f28(f28(f20(x7131),x7132),x7132)),f4(x7131)))
% 1.50/1.47 [727]~P30(x7271)+~P34(f28(f28(f30(x7271),x7272),f4(x7271)))+P34(f28(f28(f30(x7271),f28(f28(f20(x7271),x7272),x7272)),f4(x7271)))
% 1.50/1.47 [728]~P18(x7281)+~P34(f28(f28(f30(x7281),x7282),f4(x7281)))+P34(f28(f28(f30(x7281),f28(f28(f20(x7281),x7282),x7282)),f4(x7281)))
% 1.50/1.47 [765]~P18(x7651)+~P34(f28(f29(x7651,f28(f28(f20(x7651),x7652),x7652)),f4(x7651)))+P34(f28(f29(x7651,x7652),f4(x7651)))
% 1.50/1.47 [778]~P30(x7781)+~P34(f28(f28(f30(x7781),f28(f28(f20(x7781),x7782),x7782)),f4(x7781)))+P34(f28(f28(f30(x7781),x7782),f4(x7781)))
% 1.50/1.47 [779]~P18(x7791)+~P34(f28(f28(f30(x7791),f28(f28(f20(x7791),x7792),x7792)),f4(x7791)))+P34(f28(f28(f30(x7791),x7792),f4(x7791)))
% 1.50/1.47 [409]~E(x4092,f4(a2))+~E(x4091,f4(a2))+E(f28(f28(f20(a2),x4091),x4092),f4(a2))
% 1.50/1.47 [415]~P18(x4151)+~E(x4152,f4(x4151))+E(f28(f28(f20(x4151),x4152),x4152),f4(x4151))
% 1.50/1.47 [436]~E(x4362,f4(a2))+~E(x4361,f28(a22,f4(a2)))+E(f28(f28(f20(a2),x4361),x4362),f28(a22,f4(a2)))
% 1.50/1.47 [437]~E(x4371,f4(a2))+~E(x4372,f28(a22,f4(a2)))+E(f28(f28(f20(a2),x4371),x4372),f28(a22,f4(a2)))
% 1.50/1.47 [440]~P18(x4402)+E(x4401,f4(x4402))+~E(f28(f28(f20(x4402),x4401),x4401),f4(x4402))
% 1.50/1.47 [443]E(x4431,f4(a2))+E(x4432,f4(a2))+~E(f28(f28(f20(a2),x4432),x4431),f28(a22,f4(a2)))
% 1.50/1.47 [449]E(x4491,f4(a2))+E(x4491,f28(a22,f4(a2)))+~E(f28(f28(f20(a2),x4492),x4491),f28(a22,f4(a2)))
% 1.50/1.47 [450]E(x4501,f4(a2))+E(x4501,f28(a22,f4(a2)))+~E(f28(f28(f20(a2),x4501),x4502),f28(a22,f4(a2)))
% 1.50/1.47 [456]E(x4561,f28(a22,f4(a2)))+E(x4562,f28(a22,f4(a2)))+~E(f28(f28(f20(a2),x4561),x4562),f28(a22,f4(a2)))
% 1.50/1.47 [505]E(x5051,x5052)+P34(f28(f28(f30(a2),x5052),x5051))+P34(f28(f28(f30(a2),x5051),x5052))
% 1.50/1.47 [521]E(x5211,x5212)+~P34(f28(f29(a2,x5211),x5212))+P34(f28(f28(f30(a2),x5211),x5212))
% 1.50/1.47 [559]~P8(a2,x5592)+P34(f28(f29(a2,x5591),f83(x5592)))+~P34(f28(f28(f35(a2),x5591),x5592))
% 1.50/1.47 [561]E(x5611,f31(f94(x5612,a3)))+~P8(x5612,f31(f94(x5612,a3)))+~E(f15(x5612,x5611),f15(x5612,f31(f94(x5612,a3))))
% 1.50/1.47 [573]~P8(a2,x5732)+P34(f28(f28(f30(a2),x5731),f79(x5732)))+~P34(f28(f28(f35(a2),x5731),x5732))
% 1.50/1.47 [576]~P34(f28(x5761,x5762))+P34(f28(x5761,f4(a2)))+P34(f28(f28(f30(a2),f70(x5762,x5761)),x5762))
% 1.50/1.47 [602]E(x6021,x6022)+~P34(f28(f28(f30(a2),x6021),f28(a22,x6022)))+P34(f28(f28(f30(a2),x6021),x6022))
% 1.50/1.47 [620]E(f28(a22,x6201),x6202)+~P34(f28(f28(f30(a2),x6201),x6202))+P34(f28(f28(f30(a2),f28(a22,x6201)),x6202))
% 1.50/1.47 [642]~P8(x6422,f31(f94(x6422,a3)))+~P8(x6421,f31(f94(x6421,a3)))+P8(f96(x6421,x6422),f31(f94(f96(x6421,x6422),a3)))
% 1.50/1.47 [643]~P8(x6432,f31(f94(x6432,a3)))+~P8(x6431,f31(f94(x6431,a3)))+P8(f95(x6431,x6432),f31(f94(f95(x6431,x6432),a3)))
% 1.50/1.47 [655]E(x6551,f4(a2))+~P34(f28(f28(f30(a2),x6551),f28(a22,x6552)))+P34(f28(f28(f30(a2),f69(x6552,x6551)),x6552))
% 1.50/1.47 [666]P8(x6662,f31(f94(x6662,a3)))+E(f15(x6661,f31(f94(x6661,a3))),f28(a22,f4(a2)))+~P8(f94(x6662,x6661),f31(f94(f94(x6662,x6661),a3)))
% 1.50/1.47 [676]~P34(f28(x6761,x6762))+P34(f28(x6761,f4(a2)))+P34(f28(x6761,f28(f28(f20(a2),f70(x6762,x6761)),f5(a2))))
% 1.50/1.47 [770]~P9(x7701,x7701,x7702,f31(f94(x7701,a3)))+~P8(x7701,f31(f94(x7701,a3)))+E(f37(x7701,x7701,x7702,f31(f94(x7701,a3))),f31(f94(x7701,a3)))
% 1.50/1.47 [775]P9(x7751,x7751,x7752,f31(f94(x7751,a3)))+~P8(x7751,f31(f94(x7751,a3)))+~E(f37(x7751,x7751,x7752,f31(f94(x7751,a3))),f31(f94(x7751,a3)))
% 1.50/1.47 [881]P1(x8811)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),f59(x8811)),f60(x8811))),f28(f56(x8811),x8812)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),f59(x8811)),f60(x8811))),f28(f54(x8811),x8812)))
% 1.50/1.47 [882]P1(x8821)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),f59(x8821)),f60(x8821))),f28(f54(x8821),x8822)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),f59(x8821)),f60(x8821))),f28(f56(x8821),x8822)))
% 1.50/1.47 [672]~P18(x6721)+~P34(f28(f29(x6721,f4(x6721)),x6722))+P34(f28(f29(x6721,f4(x6721)),f28(f28(f20(x6721),x6722),x6722)))
% 1.50/1.47 [695]~P18(x6951)+~P34(f28(f28(f30(x6951),f4(x6951)),x6952))+P34(f28(f28(f30(x6951),f4(x6951)),f28(f28(f20(x6951),x6952),x6952)))
% 1.50/1.47 [704]~P18(x7041)+P34(f28(f29(x7041,f4(x7041)),x7042))+~P34(f28(f29(x7041,f4(x7041)),f28(f28(f20(x7041),x7042),x7042)))
% 1.50/1.47 [716]P34(f28(f28(f30(a2),f4(a2)),x7162))+P34(f28(f28(f30(a2),f4(a2)),x7161))+~P34(f28(f28(f30(a2),f4(a2)),f28(f28(f20(a2),x7162),x7161)))
% 1.50/1.47 [717]~P18(x7171)+P34(f28(f28(f30(x7171),f4(x7171)),x7172))+~P34(f28(f28(f30(x7171),f4(x7171)),f28(f28(f20(x7171),x7172),x7172)))
% 1.50/1.47 [718]~P26(x7181)+~P34(f28(f28(f35(x7181),x7182),f25(x7181)))+~E(f28(f28(f20(x7181),f28(f28(f20(x7181),f5(x7181)),x7182)),x7182),f4(x7181))
% 1.50/1.47 [1001]P3(x10011,x10012)+~E(f61(x10012,x10011),f62(x10012,x10011))+~P34(f28(f28(f35(f94(f94(a90,f94(f96(a91,a91),a3)),f94(f96(a91,a91),a3))),x10011),f18(f94(a90,f94(f96(a91,a91),a3)),f94(f96(a91,a91),a3),a9,f28(f16(f94(f94(f96(a91,a91),a3),a3),f94(a90,f94(f96(a91,a91),a3))),a8))))
% 1.50/1.47 [1002]P3(x10021,x10022)+P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),f63(x10022,x10021)),a9))+~P34(f28(f28(f35(f94(f94(a90,f94(f96(a91,a91),a3)),f94(f96(a91,a91),a3))),x10021),f18(f94(a90,f94(f96(a91,a91),a3)),f94(f96(a91,a91),a3),a9,f28(f16(f94(f94(f96(a91,a91),a3),a3),f94(a90,f94(f96(a91,a91),a3))),a8))))
% 1.50/1.47 [1003]P3(x10031,x10032)+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),f62(x10032,x10031)),f61(x10032,x10031))),f28(f63(x10032,x10031),x10032)))+~P34(f28(f28(f35(f94(f94(a90,f94(f96(a91,a91),a3)),f94(f96(a91,a91),a3))),x10031),f18(f94(a90,f94(f96(a91,a91),a3)),f94(f96(a91,a91),a3),a9,f28(f16(f94(f94(f96(a91,a91),a3),a3),f94(a90,f94(f96(a91,a91),a3))),a8))))
% 1.50/1.47 [1004]P3(x10041,x10042)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),f62(x10042,x10041)),f61(x10042,x10041))),f28(x10041,f63(x10042,x10041))))+~P34(f28(f28(f35(f94(f94(a90,f94(f96(a91,a91),a3)),f94(f96(a91,a91),a3))),x10041),f18(f94(a90,f94(f96(a91,a91),a3)),f94(f96(a91,a91),a3),a9,f28(f16(f94(f94(f96(a91,a91),a3),a3),f94(a90,f94(f96(a91,a91),a3))),a8))))
% 1.50/1.47 [431]~E(x4312,x4313)+~P21(x4311)+P34(f28(f29(x4311,x4312),x4313))
% 1.50/1.47 [433]~E(x4332,x4333)+~P27(x4331)+P34(f28(f29(x4331,x4332),x4333))
% 1.50/1.47 [481]~P23(x4811)+P34(f28(f29(x4811,x4813),x4812))+P34(f28(f29(x4811,x4812),x4813))
% 1.50/1.47 [594]~P34(f28(f29(a2,x5941),x5943))+P34(f28(f29(a2,x5941),x5942))+~P34(f28(f29(a2,x5943),x5942))
% 1.50/1.47 [855]~P8(x8551,x8553)+P9(x8551,x8551,x8552,x8553)+~P34(f28(f29(f94(x8551,a3),x8553),f37(x8551,x8551,x8552,x8553)))
% 1.50/1.47 [413]~P33(x4131)+~E(x4133,f4(x4131))+E(f28(f28(f20(x4131),x4132),x4133),x4132)
% 1.50/1.47 [438]~P33(x4382)+E(x4381,f4(x4382))+~E(f28(f28(f20(x4382),x4383),x4381),x4383)
% 1.50/1.47 [501]~E(x5011,x5012)+~P23(x5013)+~P34(f28(f28(f30(x5013),x5011),x5012))
% 1.50/1.47 [502]~E(x5021,x5022)+~P27(x5023)+~P34(f28(f28(f30(x5023),x5021),x5022))
% 1.50/1.47 [512]~P23(x5121)+P34(f28(f29(x5121,x5122),x5123))+P34(f28(f28(f30(x5121),x5123),x5122))
% 1.50/1.47 [556]~P21(x5561)+P34(f28(f29(x5561,x5562),x5563))+~P34(f28(f28(f30(x5561),x5562),x5563))
% 1.50/1.47 [558]~P27(x5581)+P34(f28(f29(x5581,x5582),x5583))+~P34(f28(f28(f30(x5581),x5582),x5583))
% 1.50/1.47 [581]~P8(x5811,x5813)+E(f15(x5811,f36(x5811,x5812,x5813)),f28(a22,f15(x5811,x5813)))+P34(f28(f28(f35(x5811),x5812),x5813))
% 1.50/1.47 [586]~P21(x5861)+~P34(f28(f29(x5861,x5862),x5863))+~P34(f28(f28(f30(x5861),x5863),x5862))
% 1.50/1.47 [589]~P23(x5891)+~P34(f28(f29(x5891,x5892),x5893))+~P34(f28(f28(f30(x5891),x5893),x5892))
% 1.50/1.47 [592]P8(x5921,x5922)+~P8(x5921,x5923)+~P34(f28(f29(f94(x5921,a3),x5922),x5923))
% 1.50/1.47 [593]~E(x5931,f28(a22,x5933))+P34(f28(f28(f30(a2),x5931),f28(a22,x5932)))+~P34(f28(f28(f30(a2),x5933),x5932))
% 1.50/1.47 [606]~P8(x6061,x6063)+E(f15(x6061,f36(x6061,x6062,x6063)),f15(x6061,x6063))+~P34(f28(f28(f35(x6061),x6062),x6063))
% 1.50/1.47 [608]~P8(x6081,x6083)+E(f15(x6081,f36(x6081,x6082,x6083)),f28(f28(f20(a2),f5(a2)),f15(x6081,x6083)))+P34(f28(f28(f35(x6081),x6082),x6083))
% 1.50/1.47 [617]~P21(x6171)+~P34(f28(f28(f30(x6171),x6173),x6172))+~P34(f28(f28(f30(x6171),x6172),x6173))
% 1.50/1.47 [618]~P23(x6181)+~P34(f28(f28(f30(x6181),x6183),x6182))+~P34(f28(f28(f30(x6181),x6182),x6183))
% 1.50/1.47 [619]~P27(x6191)+~P34(f28(f28(f30(x6191),x6193),x6192))+~P34(f28(f28(f30(x6191),x6192),x6193))
% 1.50/1.47 [671]~P34(f28(f28(f30(a2),x6711),x6713))+~P34(f28(f28(f30(a2),x6713),x6712))+P34(f28(f28(f30(a2),f28(a22,x6711)),x6712))
% 1.50/1.47 [684]~P8(x6841,x6843)+P34(f28(f29(a2,f15(x6841,x6842)),f15(x6841,x6843)))+~P34(f28(f29(f94(x6841,a3),x6842),x6843))
% 1.50/1.47 [694]E(x6941,x6942)+~P34(f28(f29(f94(x6943,a3),x6941),x6942))+~P34(f28(f29(f94(x6943,a3),x6942),x6941))
% 1.50/1.47 [699]E(x6991,x6992)+~P34(f28(f29(f94(x6993,a3),x6991),x6992))+P34(f28(f28(f30(f94(x6993,a3)),x6991),x6992))
% 1.50/1.47 [730]~P8(x7301,x7303)+P34(f28(f28(f30(a2),f15(x7301,x7302)),f15(x7301,x7303)))+~P34(f28(f28(f30(f94(x7301,a3)),x7302),x7303))
% 1.50/1.47 [923]~P8(x9231,x9233)+P34(f28(f28(f35(f96(f94(x9231,a3),f94(x9231,a3))),f28(f28(f33(f94(x9231,a3),f94(x9231,a3)),x9232),x9233)),f42(x9231)))+~P34(f28(f28(f30(f94(x9231,a3)),x9232),x9233))
% 1.50/1.47 [851]E(x8511,x8512)+P34(f28(f28(f35(f94(f96(a91,a91),a3)),f14(x8513,x8511,x8512)),a8))+~P34(f28(f28(f35(f94(f96(a91,a91),a3)),x8513),a8))
% 1.50/1.47 [858]E(x8581,x8582)+~P34(f28(f28(f35(f94(f96(a91,a91),a3)),x8583),a8))+P34(f28(f28(f35(f94(f96(a91,a91),a3)),f28(f28(f28(a12,x8583),x8581),x8582)),a8))
% 1.50/1.47 [925]~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9253),x9252)),x9251))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9252),x9253)),x9251))+~P34(f28(f28(f35(f94(f96(a91,a91),a3)),x9251),a8))
% 1.50/1.47 [854]~P3(x8541,x8543)+E(f28(x8541,x8542),f28(x8542,x8543))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x8542),a9))
% 1.50/1.47 [701]~P8(x7012,x7014)+~P8(x7011,x7013)+P8(f95(x7011,x7012),f38(x7011,x7012,x7013,x7014))
% 1.50/1.47 [812]P8(x8121,x8122)+~P9(x8121,x8123,x8124,x8122)+~P8(x8123,f37(x8121,x8123,x8124,x8122))
% 1.50/1.47 [651]E(x6511,x6512)+P34(f28(x6513,x6512))+~P34(f28(f36(x6514,x6511,x6513),x6512))
% 1.50/1.47 [723]~P8(x7232,x7234)+~P8(x7231,x7233)+E(f15(f95(x7231,x7232),f38(x7231,x7232,x7233,x7234)),f28(f28(f20(a2),f15(x7231,x7233)),f15(x7232,x7234)))
% 1.50/1.47 [797]~P8(x7971,x7974)+P9(x7971,x7972,x7973,x7974)+~E(f15(x7972,f37(x7971,x7972,x7973,x7974)),f15(x7971,x7974))
% 1.50/1.47 [483]~P13(x4833)+E(x4831,x4832)+~E(f28(f28(f20(x4833),x4834),x4831),f28(f28(f20(x4833),x4834),x4832))
% 1.50/1.47 [484]~P14(x4843)+E(x4841,x4842)+~E(f28(f28(f20(x4843),x4844),x4841),f28(f28(f20(x4843),x4844),x4842))
% 1.50/1.47 [486]~P13(x4863)+E(x4861,x4862)+~E(f28(f28(f20(x4863),x4861),x4864),f28(f28(f20(x4863),x4862),x4864))
% 1.50/1.47 [624]P34(f28(x6241,x6242))+~P34(f28(x6243,x6242))+~P34(f28(f29(f94(x6244,a3),x6243),x6241))
% 1.50/1.47 [641]~E(f28(f28(f20(a2),x6413),x6412),f28(f28(f20(a2),x6411),x6414))+~P34(f28(f28(f30(a2),x6413),x6414))+P34(f28(f28(f30(a2),x6411),x6412))
% 1.50/1.47 [692]P34(f28(f28(f35(x6921),x6922),x6923))+~P34(f28(f28(f35(x6921),x6922),x6924))+~P34(f28(f29(f94(x6921,a3),x6924),x6923))
% 1.50/1.47 [706]E(x7061,x7062)+~P34(f28(f28(f35(x7063),x7061),f36(x7063,x7062,x7064)))+P34(f28(f28(f35(x7063),x7061),x7064))
% 1.50/1.47 [726]~P34(f28(f29(f94(x7261,a3),x7262),x7264))+~P34(f28(f29(f94(x7261,a3),x7264),x7263))+P34(f28(f29(f94(x7261,a3),x7262),x7263))
% 1.50/1.47 [764]~P34(f28(f29(f94(x7641,a3),x7643),f36(x7641,x7642,x7644)))+P34(f28(f28(f35(x7641),x7642),x7643))+P34(f28(f29(f94(x7641,a3),x7643),x7644))
% 1.50/1.47 [789]~P34(f28(f28(f35(x7891),x7892),x7894))+~P34(f28(f29(f94(x7891,a3),x7893),x7894))+P34(f28(f29(f94(x7891,a3),f36(x7891,x7892,x7893)),x7894))
% 1.50/1.47 [836]~E(x8361,x8362)+~E(x8361,x8363)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x8362),x8361)),f28(f28(a11,x8364),x8363)))
% 1.50/1.47 [837]~E(x8371,x8372)+~E(x8371,x8373)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x8371),x8372)),f28(f28(a13,x8374),x8373)))
% 1.50/1.47 [987]~P22(x9872)+~P34(f28(f29(x9872,f28(x9873,f89(x9874,x9873,x9871,x9872))),f28(x9874,f89(x9874,x9873,x9871,x9872))))+P34(f28(f29(f94(x9871,x9872),x9873),x9874))
% 1.50/1.47 [720]~P22(x7202)+P34(f28(f29(f94(x7201,x7202),x7203),x7204))+~P34(f28(f28(f30(f94(x7201,x7202)),x7203),x7204))
% 1.50/1.47 [731]P34(f28(f28(f35(x7311),x7312),x7313))+~P34(f28(f28(f35(x7311),x7312),x7314))+~P34(f28(f28(f30(f94(x7311,a3)),x7314),x7313))
% 1.50/1.47 [748]~P22(x7481)+~P34(f28(f29(f94(x7482,x7481),x7483),x7484))+~P34(f28(f28(f30(f94(x7482,x7481)),x7484),x7483))
% 1.50/1.47 [753]~P19(x7531)+~P34(f28(f29(x7531,x7533),x7534))+P34(f28(f29(x7531,f28(f28(f20(x7531),x7532),x7533)),f28(f28(f20(x7531),x7532),x7534)))
% 1.50/1.47 [754]~P20(x7541)+~P34(f28(f29(x7541,x7543),x7544))+P34(f28(f29(x7541,f28(f28(f20(x7541),x7542),x7543)),f28(f28(f20(x7541),x7542),x7544)))
% 1.50/1.47 [755]~P19(x7551)+~P34(f28(f29(x7551,x7552),x7554))+P34(f28(f29(x7551,f28(f28(f20(x7551),x7552),x7553)),f28(f28(f20(x7551),x7554),x7553)))
% 1.50/1.47 [756]~P20(x7561)+~P34(f28(f29(x7561,x7562),x7564))+P34(f28(f29(x7561,f28(f28(f20(x7561),x7562),x7563)),f28(f28(f20(x7561),x7564),x7563)))
% 1.50/1.47 [761]~P34(f28(f29(a2,x7612),x7614))+~P34(f28(f29(a2,x7611),x7613))+P34(f28(f29(a2,f28(f28(f20(a2),x7611),x7612)),f28(f28(f20(a2),x7613),x7614)))
% 1.50/1.47 [766]~P5(x7661)+~P34(f28(f28(f30(x7661),x7663),x7664))+P34(f28(f28(f30(x7661),f28(f28(f20(x7661),x7662),x7663)),f28(f28(f20(x7661),x7662),x7664)))
% 1.50/1.47 [767]~P19(x7671)+~P34(f28(f28(f30(x7671),x7673),x7674))+P34(f28(f28(f30(x7671),f28(f28(f20(x7671),x7672),x7673)),f28(f28(f20(x7671),x7672),x7674)))
% 1.50/1.47 [768]~P5(x7681)+~P34(f28(f28(f30(x7681),x7682),x7684))+P34(f28(f28(f30(x7681),f28(f28(f20(x7681),x7682),x7683)),f28(f28(f20(x7681),x7684),x7683)))
% 1.50/1.47 [769]~P19(x7691)+~P34(f28(f28(f30(x7691),x7692),x7694))+P34(f28(f28(f30(x7691),f28(f28(f20(x7691),x7692),x7693)),f28(f28(f20(x7691),x7694),x7693)))
% 1.50/1.47 [776]~P34(f28(f28(f30(a2),x7762),x7764))+~P34(f28(f28(f30(a2),x7761),x7763))+P34(f28(f28(f30(a2),f28(f28(f20(a2),x7761),x7762)),f28(f28(f20(a2),x7763),x7764)))
% 1.50/1.47 [784]~P34(f28(f29(f94(x7841,a3),x7844),x7843))+~P34(f28(f28(f30(f94(x7841,a3)),x7842),x7844))+P34(f28(f28(f30(f94(x7841,a3)),x7842),x7843))
% 1.50/1.47 [785]~P34(f28(f29(f94(x7851,a3),x7852),x7854))+~P34(f28(f28(f30(f94(x7851,a3)),x7854),x7853))+P34(f28(f28(f30(f94(x7851,a3)),x7852),x7853))
% 1.50/1.47 [808]~P19(x8081)+P34(f28(f29(x8081,x8082),x8083))+~P34(f28(f29(x8081,f28(f28(f20(x8081),x8084),x8082)),f28(f28(f20(x8081),x8084),x8083)))
% 1.50/1.47 [810]~P19(x8101)+P34(f28(f29(x8101,x8102),x8103))+~P34(f28(f29(x8101,f28(f28(f20(x8101),x8102),x8104)),f28(f28(f20(x8101),x8103),x8104)))
% 1.50/1.47 [811]~P34(f28(f28(f30(f94(x8111,a3)),x8112),x8114))+P34(f28(f28(f30(f94(x8111,a3)),x8112),x8113))+~P34(f28(f28(f30(f94(x8111,a3)),x8114),x8113))
% 1.50/1.47 [814]~P19(x8141)+P34(f28(f28(f30(x8141),x8142),x8143))+~P34(f28(f28(f30(x8141),f28(f28(f20(x8141),x8144),x8142)),f28(f28(f20(x8141),x8144),x8143)))
% 1.50/1.47 [816]~P19(x8161)+P34(f28(f28(f30(x8161),x8162),x8163))+~P34(f28(f28(f30(x8161),f28(f28(f20(x8161),x8162),x8164)),f28(f28(f20(x8161),x8163),x8164)))
% 1.50/1.47 [888]~P9(x8884,x8883,x8881,f31(f94(x8884,a3)))+E(f28(x8881,f74(x8882,x8881,x8883,x8884)),x8882)+~P34(f28(f28(f35(x8883),x8882),f37(x8884,x8883,x8881,f31(f94(x8884,a3)))))
% 1.50/1.47 [871]E(x8711,x8712)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x8713),x8711)),f28(f28(a11,x8714),x8712)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x8713),x8711)),x8714))
% 1.50/1.47 [872]E(x8721,x8722)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x8721),x8723)),f28(f28(a13,x8724),x8722)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x8721),x8723)),x8724))
% 1.50/1.47 [682]E(x6821,x6822)+~E(f28(x6823,x6821),f28(x6823,x6822))+~P9(x6824,x6825,x6823,f31(f94(x6824,a3)))
% 1.50/1.47 [817]E(x8171,x8172)+~E(f37(x8173,x8174,x8175,x8171),f37(x8173,x8174,x8175,x8172))+~P9(x8173,x8174,x8175,f31(f94(x8173,a3)))
% 1.50/1.47 [848]P8(x8481,x8482)+~P8(x8483,x8484)+~P34(f28(f29(f94(x8481,a3),x8482),f37(x8483,x8481,x8485,x8484)))
% 1.50/1.47 [688]~P22(x6881)+P34(f28(f29(x6881,f28(x6882,x6883)),f28(x6884,x6883)))+~P34(f28(f29(f94(x6885,x6881),x6882),x6884))
% 1.50/1.47 [774]P9(x7741,x7742,x7743,x7744)+~P9(x7741,x7742,x7743,x7745)+~P34(f28(f29(f94(x7741,a3),x7744),x7745))
% 1.50/1.47 [799]~P9(x7991,x7992,x7994,x7993)+E(f28(f23(x7991,x7992,x7993,x7994),f28(x7994,x7995)),x7995)+~P34(f28(f28(f35(x7991),x7995),x7993))
% 1.50/1.47 [849]~P9(x8492,x8491,x8494,x8493)+E(f37(x8491,x8492,f23(x8492,x8491,x8493,x8494),f37(x8492,x8491,x8494,x8495)),x8495)+~P34(f28(f29(f94(x8492,a3),x8495),x8493))
% 1.50/1.47 [868]~P9(x8681,x8684,x8685,f31(f94(x8681,a3)))+~P34(f28(f28(f35(x8684),f28(x8685,x8682)),f37(x8681,x8684,x8685,x8683)))+P34(f28(f28(f35(x8681),x8682),x8683))
% 1.50/1.47 [964]~P9(x9641,x9644,x9645,f31(f94(x9641,a3)))+~P34(f28(f29(f94(x9644,a3),f37(x9641,x9644,x9645,x9642)),f37(x9641,x9644,x9645,x9643)))+P34(f28(f29(f94(x9641,a3),x9642),x9643))
% 1.50/1.47 [802]~E(f28(x8023,x8025),x8024)+~P9(x8021,x8022,x8023,f31(f94(x8021,a3)))+E(f28(f23(x8021,x8022,f31(f94(x8021,a3)),x8023),x8024),x8025)
% 1.50/1.47 [938]~P9(x9382,x9381,x9383,x9385)+P34(f28(f28(f30(f94(x9381,a3)),f37(x9382,x9381,x9383,x9384)),f37(x9382,x9381,x9383,x9385)))+~P34(f28(f28(f30(f94(x9382,a3)),x9384),x9385))
% 1.50/1.47 [893]P34(f28(f28(f35(f96(x8931,x8931)),f28(f28(f33(x8931,x8931),x8932),x8933)),f44(x8931,x8934,x8935)))+~P34(f28(f29(a2,f28(x8934,x8932)),f28(x8934,x8933)))+~P34(f28(f28(f35(f96(x8931,x8931)),f28(f28(f33(x8931,x8931),x8932),x8933)),x8935))
% 1.50/1.47 [821]~E(x8212,f28(x8214,x8216))+P34(f28(f28(f35(x8211),x8212),f37(x8213,x8211,x8214,x8215)))+~P34(f28(f28(f35(x8213),x8216),x8215))
% 1.50/1.47 [844]~E(x8442,f37(x8443,x8441,x8444,x8446))+P34(f28(f29(f94(x8441,a3),x8442),f37(x8443,x8441,x8444,x8445)))+~P34(f28(f29(f94(x8443,a3),x8446),x8445))
% 1.50/1.47 [862]~E(f37(x8621,x8622,x8623,x8624),x8626)+E(f37(x8621,x8622,x8623,f37(x8622,x8621,f23(x8621,x8622,x8624,x8623),x8625)),x8625)+~P34(f28(f29(f94(x8622,a3),x8625),x8626))
% 1.50/1.47 [870]~P34(f28(f28(f35(f94(x8705,x8701)),x8702),f18(x8705,x8701,x8706,x8704)))+P34(f28(f28(f35(x8701),f28(x8702,x8703)),f28(x8704,x8703)))+~P34(f28(f28(f35(x8705),x8703),x8706))
% 1.50/1.47 [747]P34(f28(f28(x7471,x7472),x7473))+~P34(f28(f28(x7474,x7472),x7473))+~P34(f28(f29(f94(x7475,f94(x7476,a3)),x7474),x7471))
% 1.50/1.47 [906]P34(f28(f28(f35(x9061),f28(x9062,x9063)),x9064))+~P34(f28(f28(f35(x9065),x9063),x9066))+~P34(f28(f28(f35(f94(x9065,x9061)),x9062),f18(x9065,x9061,x9066,f28(f16(f94(x9061,a3),x9065),x9064))))
% 1.50/1.47 [997]~P8(x9974,x9972)+~P12(x9973,x9974,x9975,x9977,x9976,x9971)+E(f28(x9971,x9972),f19(x9973,x9974,x9975,x9976,x9977,x9972))
% 1.50/1.47 [990]~P34(f28(x9906,x9903))+~P34(f28(f28(f35(f96(x9902,x9902)),f28(f28(f33(x9902,x9902),x9904),x9905)),f28(x9907,x9903)))+P34(f28(f28(f35(f96(f96(x9901,x9902),f96(x9901,x9902))),f28(f28(f33(f96(x9901,x9902),f96(x9901,x9902)),f28(f28(f33(x9901,x9902),x9903),x9904)),f28(f28(f33(x9901,x9902),x9903),x9905))),f34(x9901,x9902,x9906,x9907)))
% 1.50/1.47 [983]~P8(x9832,x9834)+~P11(x9837,x9832,x9835,x9838,x9836,x9831)+E(f28(x9831,f36(x9832,x9833,x9834)),f28(f28(x9835,f28(x9836,x9833)),f28(x9831,x9834)))
% 1.50/1.47 [989]~E(x9893,x9895)+P34(f28(f28(f35(f96(f96(x9891,x9892),f96(x9891,x9892))),f28(f28(f33(f96(x9891,x9892),f96(x9891,x9892)),f28(f28(f33(x9891,x9892),x9893),x9894)),f28(f28(f33(x9891,x9892),x9895),x9896))),f43(x9891,x9892,x9897,x9898)))+~P34(f28(f28(f35(f96(x9892,x9892)),f28(f28(f33(x9892,x9892),x9894),x9896)),x9898))
% 1.50/1.47 [996]E(x9961,x9962)+~P34(f28(f28(f35(f96(f96(x9963,x9965),f96(x9963,x9965))),f28(f28(f33(f96(x9963,x9965),f96(x9963,x9965)),f28(f28(f33(x9963,x9965),x9961),x9966)),f28(f28(f33(x9963,x9965),x9962),x9967))),f43(x9963,x9965,x9964,x9968)))+P34(f28(f28(f35(f96(x9963,x9963)),f28(f28(f33(x9963,x9963),x9961),x9962)),x9964))
% 1.50/1.47 [1000]~P34(f28(f28(f35(f96(f96(x10001,x10005),f96(x10001,x10005))),f28(f28(f33(f96(x10001,x10005),f96(x10001,x10005)),f28(f28(f33(x10001,x10005),x10002),x10006)),f28(f28(f33(x10001,x10005),x10003),x10007))),f43(x10001,x10005,x10004,x10008)))+P34(f28(f28(f35(f96(x10001,x10001)),f28(f28(f33(x10001,x10001),x10002),x10003)),x10004))+P34(f28(f28(f35(f96(x10005,x10005)),f28(f28(f33(x10005,x10005),x10006),x10007)),x10008))
% 1.50/1.47 [879]E(f28(a97,x8791),a106)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a104)),f28(a101,x8791)))+P34(f28(f28(f30(a2),f28(a97,x8791)),a106))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a104)),f28(f28(a13,f28(a101,x8791)),a105)))
% 1.50/1.47 [887]E(f28(a97,x8871),a106)+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a104)),f28(a101,x8871)))+P34(f28(f28(f30(a2),f28(a97,x8871)),a106))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a104)),f28(f28(a13,f28(a101,x8871)),a105)))
% 1.50/1.47 [945]E(f28(a97,x9451),a106)+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a104)),f28(a101,x9451)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a104)),f28(f28(a13,f28(a101,x9451)),a105)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a104)),f28(f28(a11,f28(a101,x9451)),a105)))
% 1.50/1.47 [891]~E(f28(a97,x8911),a106)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a104)),f28(a101,x8911)))+P34(f28(f28(f30(a2),f28(a97,x8911)),a106))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a104)),f28(f28(f28(a12,f28(a101,x8911)),a103),a105)))
% 1.50/1.47 [897]~P34(f28(f28(f30(a2),f28(a97,x8971)),f28(f28(f20(a2),a106),f5(a2))))+~P34(f28(f28(f30(a2),f28(a97,x8971)),a106))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a105)),f28(f28(a11,f28(a101,x8971)),a105)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a100),a102)),a98))
% 1.50/1.47 [909]~E(f28(a97,x9091),a106)+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a104)),f28(a101,x9091)))+P34(f28(f28(f30(a2),f28(a97,x9091)),a106))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a104)),f28(f28(f28(a12,f28(a101,x9091)),a103),a105)))
% 1.50/1.47 [959]~E(f28(a97,x9591),a106)+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a104)),f28(a101,x9591)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a104)),f28(f28(a11,f28(a101,x9591)),a105)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a104)),f28(f28(f28(a12,f28(a101,x9591)),a103),a105)))
% 1.50/1.47 [961]P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a104)),f28(a101,x9611)))+P34(f28(f28(f30(a2),f28(a97,x9611)),a106))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a104)),f28(f28(a13,f28(a101,x9611)),a105)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a104)),f28(f28(f28(a12,f28(a101,x9611)),a103),a105)))
% 1.50/1.47 [975]P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a104)),f28(a101,x9751)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a104)),f28(f28(a13,f28(a101,x9751)),a105)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a104)),f28(f28(a11,f28(a101,x9751)),a105)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a104)),f28(f28(f28(a12,f28(a101,x9751)),a103),a105)))
% 1.50/1.47 [886]~P30(x8861)+~P34(f28(f28(f35(x8861),x8862),f25(x8861)))+P34(f28(f28(f30(x8861),f28(f28(f20(x8861),f28(f28(f20(x8861),f5(x8861)),x8862)),x8862)),f4(x8861)))+~P34(f28(f28(f30(x8861),x8862),f4(x8861)))
% 1.50/1.47 [942]~P30(x9421)+~P34(f28(f28(f35(x9421),x9422),f25(x9421)))+~P34(f28(f28(f30(x9421),f28(f28(f20(x9421),f28(f28(f20(x9421),f5(x9421)),x9422)),x9422)),f4(x9421)))+P34(f28(f28(f30(x9421),x9422),f4(x9421)))
% 1.50/1.47 [562]~P26(x5621)+~E(x5622,f4(x5621))+E(f28(f28(f20(x5621),x5622),x5622),f4(x5621))+~P34(f28(f28(f35(x5621),x5622),f25(x5621)))
% 1.50/1.47 [577]~P26(x5772)+E(x5771,f4(x5772))+~E(f28(f28(f20(x5772),x5771),x5771),f4(x5772))+~P34(f28(f28(f35(x5772),x5771),f25(x5772)))
% 1.50/1.47 [571]E(x5711,x5712)+~P27(x5713)+~P34(f28(f29(x5713,x5712),x5711))+~P34(f28(f29(x5713,x5711),x5712))
% 1.50/1.47 [610]~P34(f28(x6101,x6102))+~P34(f28(x6101,x6103))+~P34(f28(f29(a2,x6103),f70(x6102,x6101)))+P34(f28(x6101,f4(a2)))
% 1.50/1.47 [751]~P25(x7511)+~P34(f28(f29(x7511,x7513),f4(x7511)))+~P34(f28(f29(x7511,x7512),f4(x7511)))+P34(f28(f29(x7511,f28(f28(f20(x7511),x7512),x7513)),f4(x7511)))
% 1.50/1.47 [762]~P25(x7621)+~P34(f28(f29(x7621,x7623),f4(x7621)))+~P34(f28(f28(f30(x7621),x7622),f4(x7621)))+P34(f28(f28(f30(x7621),f28(f28(f20(x7621),x7622),x7623)),f4(x7621)))
% 1.50/1.47 [763]~P25(x7631)+~P34(f28(f29(x7631,x7632),f4(x7631)))+~P34(f28(f28(f30(x7631),x7633),f4(x7631)))+P34(f28(f28(f30(x7631),f28(f28(f20(x7631),x7632),x7633)),f4(x7631)))
% 1.50/1.47 [771]~P32(x7711)+~P34(f28(f28(f35(x7711),x7713),f25(x7711)))+~P34(f28(f28(f35(x7711),x7712),f25(x7711)))+P34(f28(f28(f35(x7711),f28(f28(f20(x7711),x7712),x7713)),f25(x7711)))
% 1.50/1.47 [772]~P25(x7721)+~P34(f28(f28(f30(x7721),x7723),f4(x7721)))+~P34(f28(f28(f30(x7721),x7722),f4(x7721)))+P34(f28(f28(f30(x7721),f28(f28(f20(x7721),x7722),x7723)),f4(x7721)))
% 1.50/1.47 [514]~E(x5142,x5143)+~P23(x5141)+P34(f28(f29(x5141,x5142),x5143))+P34(f28(f28(f30(x5141),x5142),x5143))
% 1.50/1.47 [523]~P30(x5233)+E(x5231,x5232)+P34(f28(f28(f30(x5233),x5232),x5231))+P34(f28(f28(f30(x5233),x5231),x5232))
% 1.50/1.47 [529]~P23(x5293)+E(x5291,x5292)+P34(f28(f28(f30(x5293),x5292),x5291))+P34(f28(f28(f30(x5293),x5291),x5292))
% 1.50/1.47 [545]~P27(x5453)+E(x5451,x5452)+~P34(f28(f29(x5453,x5452),x5451))+P34(f28(f28(f30(x5453),x5452),x5451))
% 1.50/1.47 [547]~P23(x5473)+E(x5471,x5472)+~P34(f28(f29(x5473,x5471),x5472))+P34(f28(f28(f30(x5473),x5471),x5472))
% 1.50/1.47 [553]~P27(x5533)+E(x5531,x5532)+~P34(f28(f29(x5533,x5531),x5532))+P34(f28(f28(f30(x5533),x5531),x5532))
% 1.50/1.47 [607]~P21(x6071)+~P34(f28(f29(x6071,x6073),x6072))+P34(f28(f29(x6071,x6072),x6073))+P34(f28(f28(f30(x6071),x6073),x6072))
% 1.50/1.47 [715]E(x7151,x7152)+~P8(x7153,x7151)+~P34(f28(f29(a2,f15(x7153,x7151)),f15(x7153,x7152)))+~P34(f28(f29(f94(x7153,a3),x7152),x7151))
% 1.50/1.47 [934]~P8(x9341,x9343)+~P9(x9341,x9341,x9342,x9343)+E(f37(x9341,x9341,x9342,x9343),x9343)+~P34(f28(f29(f94(x9341,a3),f37(x9341,x9341,x9342,x9343)),x9343))
% 1.50/1.47 [734]~P25(x7341)+~P34(f28(f28(f30(x7341),f4(x7341)),x7343))+~P34(f28(f28(f30(x7341),f4(x7341)),x7342))+P34(f28(f28(f30(x7341),f4(x7341)),f28(f28(f20(x7341),x7342),x7343)))
% 1.50/1.47 [781]~P8(x7811,x7813)+~P34(f28(f28(f30(a2),f15(x7811,x7812)),f15(x7811,x7813)))+~P34(f28(f29(f94(x7811,a3),x7812),x7813))+P34(f28(f28(f30(f94(x7811,a3)),x7812),x7813))
% 1.50/1.47 [876]E(x8761,x8762)+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x8761),x8762)),x8763))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x8762),x8761)),x8763))+~P34(f28(f28(f35(f94(f96(a91,a91),a3)),x8763),a8))
% 1.50/1.47 [621]~P27(x6211)+~P34(f28(f29(x6211,x6214),x6213))+P34(f28(f29(x6211,x6212),x6213))+~P34(f28(f29(x6211,x6212),x6214))
% 1.50/1.47 [622]~P21(x6221)+~P34(f28(f29(x6221,x6222),x6224))+P34(f28(f29(x6221,x6222),x6223))+~P34(f28(f29(x6221,x6224),x6223))
% 1.50/1.47 [806]~P8(x8062,x8063)+~P8(x8061,x8064)+P9(x8061,x8062,f80(x8063,x8062,x8064,x8061),x8064)+~P34(f28(f29(a2,f15(x8061,x8064)),f15(x8062,x8063)))
% 1.50/1.47 [640]E(x6401,x6402)+~E(f36(x6403,x6404,x6401),f36(x6403,x6404,x6402))+P34(f28(f28(f35(x6403),x6404),x6402))+P34(f28(f28(f35(x6403),x6404),x6401))
% 1.50/1.47 [644]~P27(x6441)+~P34(f28(f29(x6441,x6442),x6444))+~P34(f28(f28(f30(x6441),x6444),x6443))+P34(f28(f28(f30(x6441),x6442),x6443))
% 1.50/1.47 [645]~P27(x6451)+~P34(f28(f29(x6451,x6454),x6453))+~P34(f28(f28(f30(x6451),x6452),x6454))+P34(f28(f28(f30(x6451),x6452),x6453))
% 1.50/1.47 [646]~P21(x6461)+~P34(f28(f29(x6461,x6464),x6463))+~P34(f28(f28(f30(x6461),x6462),x6464))+P34(f28(f28(f30(x6461),x6462),x6463))
% 1.50/1.47 [647]~P21(x6471)+~P34(f28(f29(x6471,x6472),x6474))+~P34(f28(f28(f30(x6471),x6474),x6473))+P34(f28(f28(f30(x6471),x6472),x6473))
% 1.50/1.47 [662]~P27(x6621)+~P34(f28(f28(f30(x6621),x6624),x6623))+P34(f28(f28(f30(x6621),x6622),x6623))+~P34(f28(f28(f30(x6621),x6622),x6624))
% 1.50/1.47 [663]~P21(x6631)+~P34(f28(f28(f30(x6631),x6632),x6634))+P34(f28(f28(f30(x6631),x6632),x6633))+~P34(f28(f28(f30(x6631),x6634),x6633))
% 1.50/1.47 [791]~E(x7913,x7911)+E(x7911,x7912)+E(x7913,x7912)+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x7912),x7913)),f28(f28(a11,x7914),x7911)))
% 1.50/1.47 [792]~E(x7923,x7921)+E(x7921,x7922)+E(x7923,x7922)+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x7923),x7922)),f28(f28(a13,x7924),x7921)))
% 1.50/1.47 [702]~P25(x7021)+~P34(f28(f29(x7021,x7022),x7023))+~P34(f28(f29(x7021,f4(x7021)),x7024))+P34(f28(f29(x7021,x7022),f28(f28(f20(x7021),x7023),x7024)))
% 1.50/1.47 [703]~P25(x7031)+~P34(f28(f29(x7031,x7032),x7034))+~P34(f28(f29(x7031,f4(x7031)),x7033))+P34(f28(f29(x7031,x7032),f28(f28(f20(x7031),x7033),x7034)))
% 1.50/1.47 [711]~P25(x7111)+~P34(f28(f29(x7111,x7112),x7114))+~P34(f28(f28(f30(x7111),f4(x7111)),x7113))+P34(f28(f28(f30(x7111),x7112),f28(f28(f20(x7111),x7113),x7114)))
% 1.50/1.47 [712]~P25(x7121)+~P34(f28(f29(x7121,f4(x7121)),x7123))+~P34(f28(f28(f30(x7121),x7122),x7124))+P34(f28(f28(f30(x7121),x7122),f28(f28(f20(x7121),x7123),x7124)))
% 1.50/1.47 [721]~P4(x7211)+~P34(f28(f28(f30(x7211),f4(x7211)),x7213))+~P34(f28(f28(f30(x7211),x7212),x7214))+P34(f28(f28(f30(x7211),x7212),f28(f28(f20(x7211),x7213),x7214)))
% 1.50/1.47 [749]~P22(x7492)+~P34(f28(f29(f94(x7491,x7492),x7494),x7493))+P34(f28(f29(f94(x7491,x7492),x7493),x7494))+P34(f28(f28(f30(f94(x7491,x7492)),x7494),x7493))
% 1.50/1.47 [973]~P8(x9732,x9734)+~P8(x9731,x9733)+~P34(f28(f29(a2,f15(x9732,x9734)),f15(x9731,x9733)))+P34(f28(f29(f94(x9731,a3),f37(x9732,x9731,f80(x9733,x9731,x9734,x9732),x9734)),x9733))
% 1.50/1.47 [863]E(x8631,x8632)+E(x8633,x8632)+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x8633),x8631)),f28(f28(a11,x8634),x8632)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x8633),x8631)),x8634))
% 1.50/1.47 [864]E(x8641,x8642)+E(x8643,x8642)+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x8643),x8641)),f28(f28(a13,x8644),x8642)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x8643),x8641)),x8644))
% 1.50/1.47 [865]E(x8651,x8652)+E(x8653,x8651)+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x8653),x8651)),f28(f28(a13,x8654),x8652)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x8653),x8651)),x8654))
% 1.50/1.47 [866]E(x8661,x8662)+E(x8661,x8663)+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x8661),x8663)),f28(f28(a11,x8664),x8662)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x8661),x8663)),x8664))
% 1.50/1.47 [980]~P2(x9803)+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9801),x9802)),f28(x9803,x9804)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9801),x9802)),f28(x9804,f52(x9803,x9804,x9801,x9802))))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x9804),a9))
% 1.50/1.47 [830]~P23(x8301)+P34(f28(f29(x8301,x8302),x8303))+P34(f28(f29(x8301,x8304),x8303))+~P34(f28(f29(f94(x8301,a3),f32(x8301,x8303,x8302)),f32(x8301,x8304,x8305)))
% 1.50/1.47 [831]~P23(x8311)+P34(f28(f29(x8311,x8312),x8313))+P34(f28(f29(x8311,x8312),x8314))+~P34(f28(f29(f94(x8311,a3),f32(x8311,x8313,x8312)),f32(x8311,x8315,x8314)))
% 1.50/1.47 [933]~P8(x9333,x9334)+~P9(x9331,x9333,x9335,x9332)+P34(f28(f29(a2,f15(x9331,x9332)),f15(x9333,x9334)))+~P34(f28(f29(f94(x9333,a3),f37(x9331,x9333,x9335,x9332)),x9334))
% 1.50/1.47 [780]~P20(x7801)+~P34(f28(f29(x7801,x7803),x7805))+~P34(f28(f29(x7801,x7802),x7804))+P34(f28(f29(x7801,f28(f28(f20(x7801),x7802),x7803)),f28(f28(f20(x7801),x7804),x7805)))
% 1.50/1.47 [786]~P5(x7861)+~P34(f28(f29(x7861,x7863),x7865))+~P34(f28(f28(f30(x7861),x7862),x7864))+P34(f28(f28(f30(x7861),f28(f28(f20(x7861),x7862),x7863)),f28(f28(f20(x7861),x7864),x7865)))
% 1.50/1.47 [787]~P5(x7871)+~P34(f28(f29(x7871,x7872),x7874))+~P34(f28(f28(f30(x7871),x7873),x7875))+P34(f28(f28(f30(x7871),f28(f28(f20(x7871),x7872),x7873)),f28(f28(f20(x7871),x7874),x7875)))
% 1.50/1.47 [794]~P5(x7941)+~P34(f28(f28(f30(x7941),x7943),x7945))+~P34(f28(f28(f30(x7941),x7942),x7944))+P34(f28(f28(f30(x7941),f28(f28(f20(x7941),x7942),x7943)),f28(f28(f20(x7941),x7944),x7945)))
% 1.50/1.47 [878]~E(x8782,f28(x8783,x8781))+E(x8781,f74(x8782,x8783,x8784,x8785))+~P9(x8785,x8784,x8783,f31(f94(x8785,a3)))+~P34(f28(f28(f35(x8784),x8782),f37(x8785,x8784,x8783,f31(f94(x8785,a3)))))
% 1.50/1.47 [875]E(x8751,x8752)+~E(x8753,x8754)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x8753),x8754)),f14(x8755,x8751,x8752)))+~P34(f28(f28(f35(f94(f96(a91,a91),a3)),x8755),a8))
% 1.50/1.47 [884]E(x8841,x8842)+~E(x8843,x8844)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x8843),x8844)),f28(f28(f28(a12,x8845),x8841),x8842)))+~P34(f28(f28(f35(f94(f96(a91,a91),a3)),x8845),a8))
% 1.50/1.47 [924]~P8(x9243,x9244)+~P9(x9241,x9243,x9245,x9242)+P34(f28(f29(a2,f15(x9241,x9242)),f15(x9243,x9244)))+~P34(f28(f28(f35(f94(x9241,x9243)),x9245),f18(x9241,x9243,x9242,f28(f16(f94(x9243,a3),x9241),x9244))))
% 1.50/1.47 [956]E(x9561,x9562)+~E(f28(f23(x9563,x9564,x9565,x9566),x9561),f28(f23(x9563,x9564,x9565,x9566),x9562))+~P34(f28(f28(f35(x9564),x9562),f37(x9563,x9564,x9566,x9565)))+~P34(f28(f28(f35(x9564),x9561),f37(x9563,x9564,x9566,x9565)))
% 1.50/1.47 [798]~P9(x7981,x7982,x7984,x7983)+~E(f28(x7984,x7986),x7985)+E(f28(f23(x7981,x7982,x7983,x7984),x7985),x7986)+~P34(f28(f28(f35(x7981),x7986),x7983))
% 1.50/1.47 [984]~P11(x9847,x9846,x9841,x9848,x9842,x9844)+~P8(x9846,x9845)+E(f28(f28(x9841,f28(x9842,x9843)),f28(x9844,x9845)),f28(x9844,x9845))+~P34(f28(f28(f35(x9846),x9843),x9845))
% 1.50/1.47 [985]~P8(x9852,x9854)+~P12(x9857,x9852,x9855,x9858,x9856,x9851)+E(f28(x9851,f36(x9852,x9853,x9854)),f28(f28(x9855,f28(x9856,x9853)),f28(x9851,x9854)))+P34(f28(f28(f35(x9852),x9853),x9854))
% 1.50/1.47 [986]~P11(x9866,x9865,x9861,x9867,x9868,x9862)+~P8(x9865,x9864)+E(f28(f28(x9861,f28(x9862,x9863)),f28(x9862,x9864)),f28(x9862,x9864))+~P34(f28(f29(f94(x9865,a3),x9863),x9864))
% 1.50/1.47 [1089]E(a102,a100)+E(a105,a103)+P35(a500)+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),f28(f28(f7(a90,f94(f96(a91,a91),a3),f94(f96(a91,a91),a3)),f28(f28(f7(a90,f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),f28(f10(a3,f94(f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),a90,f24(f94(f96(a91,a91),a3))),f28(f28(f7(a90,a2,a3),f28(f10(a2,f94(a2,a3),a90,f30(a2)),a97)),f28(f28(f20(a2),a106),f5(a2))))),a98)),a99)),a9))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),f17(a90,f94(f96(a91,a91),a3),f94(f96(a91,a91),a3),f17(a90,f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3)),f28(f10(a3,f94(f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),a90,f24(f94(f96(a91,a91),a3))),f28(f28(f7(a90,a2,a3),f28(f10(a2,f94(a2,a3),a90,f30(a2)),a97)),a106)),f28(f28(f7(a90,a91,f94(f96(a91,a91),a3)),f28(f10(f94(f96(a91,a91),a3),f94(a91,f94(f96(a91,a91),a3)),a90,a11),a101)),a105)),f17(a90,f94(f96(a91,a91),a3),f94(f96(a91,a91),a3),f17(a90,f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3)),f28(f10(a3,f94(f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),a90,f24(f94(f96(a91,a91),a3))),f28(f28(f7(a90,a2,a3),f28(f10(a2,f94(a2,a3),a90,a39),a97)),a106)),f28(f28(f7(a90,a91,f94(f96(a91,a91),a3)),f28(f28(f7(a90,a91,f94(a91,f94(f96(a91,a91),a3))),f28(f10(f94(f96(a91,a91),a3),f94(a91,f94(a91,f94(f96(a91,a91),a3))),a90,a12),a101)),a103)),a105)),f28(f28(f7(a90,a91,f94(f96(a91,a91),a3)),f28(f10(f94(f96(a91,a91),a3),f94(a91,f94(f96(a91,a91),a3)),a90,a13),a101)),a105)))),a9))
% 1.50/1.47 [894]E(f28(a97,x8941),a106)+P34(f28(f28(f30(a2),f28(a97,x8941)),f28(f28(f20(a2),a106),f5(a2))))+P34(f28(f28(f30(a2),f28(a97,x8941)),a106))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a105)),f28(f28(a13,f28(a101,x8941)),a105)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a100),a102)),a99))
% 1.50/1.47 [895]E(f28(a97,x8951),a106)+~P34(f28(f28(f30(a2),f28(a97,x8951)),f28(f28(f20(a2),a106),f5(a2))))+P34(f28(f28(f30(a2),f28(a97,x8951)),a106))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a105)),f28(f28(a13,f28(a101,x8951)),a105)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a100),a102)),a98))
% 1.50/1.47 [921]~E(f28(a97,x9211),a106)+~P34(f28(f28(f30(a2),f28(a97,x9211)),f28(f28(f20(a2),a106),f5(a2))))+P34(f28(f28(f30(a2),f28(a97,x9211)),a106))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a105)),f28(f28(f28(a12,f28(a101,x9211)),a103),a105)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a100),a102)),a98))
% 1.50/1.47 [931]~E(f28(a97,x9311),a106)+P34(f28(f28(f30(a2),f28(a97,x9311)),f28(f28(f20(a2),a106),f5(a2))))+P34(f28(f28(f30(a2),f28(a97,x9311)),a106))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a105)),f28(f28(f28(a12,f28(a101,x9311)),a103),a105)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a100),a102)),a99))
% 1.50/1.47 [951]E(f28(a97,x9511),a106)+P34(f28(f28(f30(a2),f28(a97,x9511)),f28(f28(f20(a2),a106),f5(a2))))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a105)),f28(f28(a13,f28(a101,x9511)),a105)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a105)),f28(f28(a11,f28(a101,x9511)),a105)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a100),a102)),a99))
% 1.50/1.47 [963]~E(f28(a97,x9631),a106)+P34(f28(f28(f30(a2),f28(a97,x9631)),f28(f28(f20(a2),a106),f5(a2))))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a105)),f28(f28(a11,f28(a101,x9631)),a105)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a105)),f28(f28(f28(a12,f28(a101,x9631)),a103),a105)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a100),a102)),a99))
% 1.50/1.47 [965]P34(f28(f28(f30(a2),f28(a97,x9651)),f28(f28(f20(a2),a106),f5(a2))))+P34(f28(f28(f30(a2),f28(a97,x9651)),a106))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a105)),f28(f28(a13,f28(a101,x9651)),a105)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a105)),f28(f28(f28(a12,f28(a101,x9651)),a103),a105)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a100),a102)),a99))
% 1.50/1.47 [978]P34(f28(f28(f30(a2),f28(a97,x9781)),f28(f28(f20(a2),a106),f5(a2))))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a105)),f28(f28(a13,f28(a101,x9781)),a105)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a105)),f28(f28(a11,f28(a101,x9781)),a105)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a105)),f28(f28(f28(a12,f28(a101,x9781)),a103),a105)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a100),a102)),a99))
% 1.50/1.47 [660]~P25(x6602)+E(x6601,f4(x6602))+~E(f28(f28(f20(x6602),x6603),x6601),f4(x6602))+~P34(f28(f29(x6602,f4(x6602)),x6603))+~P34(f28(f29(x6602,f4(x6602)),x6601))
% 1.50/1.47 [661]~P25(x6612)+E(x6611,f4(x6612))+~E(f28(f28(f20(x6612),x6611),x6613),f4(x6612))+~P34(f28(f29(x6612,f4(x6612)),x6613))+~P34(f28(f29(x6612,f4(x6612)),x6611))
% 1.50/1.47 [679]~P23(x6793)+E(x6791,x6792)+~E(f32(x6793,x6794,x6791),f32(x6793,x6795,x6792))+~P34(f28(f28(f30(x6793),x6795),x6792))+~P34(f28(f28(f30(x6793),x6794),x6791))
% 1.50/1.47 [680]~P23(x6803)+E(x6801,x6802)+~E(f32(x6803,x6801,x6804),f32(x6803,x6802,x6805))+~P34(f28(f28(f30(x6803),x6802),x6805))+~P34(f28(f28(f30(x6803),x6801),x6804))
% 1.50/1.47 [911]E(x9111,x9112)+~E(x9115,x9111)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9113),x9115)),f14(x9114,x9111,x9112)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9113),x9112)),x9114))+~P34(f28(f28(f35(f94(f96(a91,a91),a3)),x9114),a8))
% 1.50/1.47 [927]E(x9271,x9272)+~E(x9275,x9271)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9275),x9273)),f28(f28(f28(a12,x9274),x9272),x9271)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9272),x9273)),x9274))+~P34(f28(f28(f35(f94(f96(a91,a91),a3)),x9274),a8))
% 1.50/1.47 [743]E(x7431,x7432)+~P9(x7434,x7435,x7433,x7436)+~E(f28(x7433,x7431),f28(x7433,x7432))+~P34(f28(f28(f35(x7434),x7432),x7436))+~P34(f28(f28(f35(x7434),x7431),x7436))
% 1.50/1.47 [650]~P25(x6501)+~E(x6503,f4(x6501))+~E(x6502,f4(x6501))+E(f28(f28(f20(x6501),x6502),x6503),f4(x6501))+~P34(f28(f29(x6501,f4(x6501)),x6503))+~P34(f28(f29(x6501,f4(x6501)),x6502))
% 1.50/1.47 [900]~E(x9003,x9001)+E(x9001,x9002)+E(x9003,x9004)+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9004),x9003)),f14(x9005,x9001,x9002)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9004),x9002)),x9005))+~P34(f28(f28(f35(f94(f96(a91,a91),a3)),x9005),a8))
% 1.50/1.47 [912]E(x9121,x9122)+E(x9121,x9123)+E(x9124,x9121)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9124),x9123)),f14(x9125,x9121,x9122)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9124),x9123)),x9125))+~P34(f28(f28(f35(f94(f96(a91,a91),a3)),x9125),a8))
% 1.50/1.47 [915]~E(x9153,x9151)+E(x9151,x9152)+E(x9153,x9154)+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9153),x9154)),f28(f28(f28(a12,x9155),x9152),x9151)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9152),x9154)),x9155))+~P34(f28(f28(f35(f94(f96(a91,a91),a3)),x9155),a8))
% 1.50/1.47 [928]E(x9281,x9282)+E(x9281,x9283)+E(x9284,x9281)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9283),x9284)),f28(f28(f28(a12,x9285),x9282),x9281)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9283),x9284)),x9285))+~P34(f28(f28(f35(f94(f96(a91,a91),a3)),x9285),a8))
% 1.50/1.47 [1043]~P35(a500)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a105)),f28(f28(a11,f28(a101,a86)),a105)))+~P34(f28(f28(f30(a2),f28(a97,a86)),a106))+~P34(f28(f28(f30(a2),f28(a97,a86)),f28(f28(f20(a2),a106),f5(a2))))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a100),a102)),a98))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a100),a102)),f28(a1,f28(f28(f7(a90,f94(f96(a91,a91),a3),f94(f96(a91,a91),a3)),f28(f28(f7(a90,f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),f28(f10(a3,f94(f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),a90,f24(f94(f96(a91,a91),a3))),f28(f28(f7(a90,a2,a3),f28(f10(a2,f94(a2,a3),a90,f30(a2)),a97)),f28(f28(f20(a2),a106),f5(a2))))),a98)),a99))))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a105)),f28(a1,f17(a90,f94(f96(a91,a91),a3),f94(f96(a91,a91),a3),f17(a90,f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3)),f28(f10(a3,f94(f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),a90,f24(f94(f96(a91,a91),a3))),f28(f28(f7(a90,a2,a3),f28(f10(a2,f94(a2,a3),a90,f30(a2)),a97)),a106)),f28(f28(f7(a90,a91,f94(f96(a91,a91),a3)),f28(f10(f94(f96(a91,a91),a3),f94(a91,f94(f96(a91,a91),a3)),a90,a11),a101)),a105)),f17(a90,f94(f96(a91,a91),a3),f94(f96(a91,a91),a3),f17(a90,f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3)),f28(f10(a3,f94(f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),a90,f24(f94(f96(a91,a91),a3))),f28(f28(f7(a90,a2,a3),f28(f10(a2,f94(a2,a3),a90,a39),a97)),a106)),f28(f28(f7(a90,a91,f94(f96(a91,a91),a3)),f28(f28(f7(a90,a91,f94(a91,f94(f96(a91,a91),a3))),f28(f10(f94(f96(a91,a91),a3),f94(a91,f94(a91,f94(f96(a91,a91),a3))),a90,a12),a101)),a103)),a105)),f28(f28(f7(a90,a91,f94(f96(a91,a91),a3)),f28(f10(f94(f96(a91,a91),a3),f94(a91,f94(f96(a91,a91),a3)),a90,a13),a101)),a105))))))
% 1.50/1.47 [993]E(x9931,x9932)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9931),x9932)),f28(a1,x9934)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9932),x9931)),f28(a1,x9933)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9932),x9931)),f28(x9933,f81(x9933,x9934,x9932,x9931))))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9931),x9932)),f28(x9934,f81(x9933,x9934,x9932,x9931))))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x9933),a9))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x9934),a9))
% 1.50/1.47 [994]E(x9941,x9942)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9941),x9942)),f28(a1,x9944)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9942),x9941)),f28(a1,x9943)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9942),x9941)),f28(x9943,f81(x9944,x9943,x9941,x9942))))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9941),x9942)),f28(x9944,f81(x9944,x9943,x9941,x9942))))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x9943),a9))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x9944),a9))
% 1.50/1.47 [998]E(x9981,x9982)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9981),x9982)),f28(a1,x9984)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9982),x9981)),f28(a1,x9983)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9982),x9981)),f28(x9983,f81(x9983,x9984,x9982,x9981))))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9981),x9982)),f28(x9984,f81(x9983,x9984,x9982,x9981))))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x9983),a9))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x9984),a9))
% 1.50/1.47 [999]E(x9991,x9992)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9991),x9992)),f28(a1,x9994)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9992),x9991)),f28(a1,x9993)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9992),x9991)),f28(x9993,f81(x9994,x9993,x9991,x9992))))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9991),x9992)),f28(x9994,f81(x9994,x9993,x9991,x9992))))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x9993),a9))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x9994),a9))
% 1.50/1.47 [853]~E(x8533,x8532)+~E(x8534,x8531)+E(x8531,x8532)+E(x8531,x8533)+E(x8534,x8533)+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x8534),x8533)),f14(x8535,x8531,x8532)))+~P34(f28(f28(f35(f94(f96(a91,a91),a3)),x8535),a8))
% 1.50/1.47 [856]~E(x8563,x8562)+~E(x8564,x8561)+E(x8561,x8562)+E(x8561,x8563)+E(x8564,x8563)+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x8563),x8564)),f28(f28(f28(a12,x8565),x8562),x8561)))+~P34(f28(f28(f35(f94(f96(a91,a91),a3)),x8565),a8))
% 1.50/1.47 [901]E(x9014,x9013)+E(x9011,x9012)+E(x9013,x9011)+E(x9014,x9011)+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9014),x9013)),f14(x9015,x9011,x9012)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9014),x9013)),x9015))+~P34(f28(f28(f35(f94(f96(a91,a91),a3)),x9015),a8))
% 1.50/1.47 [902]~E(x9023,x9021)+E(x9021,x9022)+E(x9023,x9022)+E(x9024,x9023)+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9024),x9023)),f14(x9025,x9022,x9021)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9024),x9023)),x9025))+~P34(f28(f28(f35(f94(f96(a91,a91),a3)),x9025),a8))
% 1.50/1.47 [903]~E(x9034,x9031)+E(x9031,x9032)+E(x9031,x9033)+E(x9034,x9032)+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9034),x9032)),f14(x9035,x9031,x9033)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9033),x9032)),x9035))+~P34(f28(f28(f35(f94(f96(a91,a91),a3)),x9035),a8))
% 1.50/1.47 [904]~E(x9044,x9042)+~E(x9043,x9041)+E(x9041,x9042)+E(x9043,x9044)+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9043),x9044)),f14(x9045,x9041,x9042)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9043),x9042)),x9045))+~P34(f28(f28(f35(f94(f96(a91,a91),a3)),x9045),a8))
% 1.50/1.47 [914]E(x9143,x9141)+E(x9141,x9142)+E(x9143,x9142)+~E(x9145,x9143)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9145),x9141)),f14(x9144,x9143,x9142)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9142),x9141)),x9144))+~P34(f28(f28(f35(f94(f96(a91,a91),a3)),x9144),a8))
% 1.50/1.47 [916]E(x9164,x9163)+E(x9161,x9162)+E(x9163,x9161)+E(x9164,x9161)+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9164),x9163)),f28(f28(f28(a12,x9165),x9162),x9161)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9164),x9163)),x9165))+~P34(f28(f28(f35(f94(f96(a91,a91),a3)),x9165),a8))
% 1.50/1.47 [917]~E(x9173,x9171)+E(x9171,x9172)+E(x9173,x9172)+E(x9173,x9174)+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9173),x9174)),f28(f28(f28(a12,x9175),x9171),x9172)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9173),x9174)),x9175))+~P34(f28(f28(f35(f94(f96(a91,a91),a3)),x9175),a8))
% 1.50/1.47 [918]~E(x9184,x9181)+E(x9181,x9182)+E(x9181,x9183)+E(x9184,x9183)+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9183),x9184)),f28(f28(f28(a12,x9185),x9182),x9181)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9183),x9182)),x9185))+~P34(f28(f28(f35(f94(f96(a91,a91),a3)),x9185),a8))
% 1.50/1.47 [919]~E(x9194,x9192)+~E(x9193,x9191)+E(x9191,x9192)+E(x9193,x9194)+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9194),x9193)),f28(f28(f28(a12,x9195),x9192),x9191)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9192),x9193)),x9195))+~P34(f28(f28(f35(f94(f96(a91,a91),a3)),x9195),a8))
% 1.50/1.47 [929]E(x9293,x9291)+E(x9291,x9292)+E(x9293,x9292)+~E(x9295,x9293)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9291),x9295)),f28(f28(f28(a12,x9294),x9292),x9293)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9291),x9292)),x9294))+~P34(f28(f28(f35(f94(f96(a91,a91),a3)),x9294),a8))
% 1.50/1.47 [947]E(x9471,x9472)+E(x9473,x9472)+E(x9474,x9473)+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9474),x9473)),f14(x9475,x9472,x9471)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9474),x9473)),x9475))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9471),x9473)),x9475))+~P34(f28(f28(f35(f94(f96(a91,a91),a3)),x9475),a8))
% 1.50/1.47 [948]E(x9481,x9482)+E(x9483,x9481)+E(x9483,x9484)+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9483),x9484)),f14(x9485,x9481,x9482)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9483),x9484)),x9485))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9483),x9482)),x9485))+~P34(f28(f28(f35(f94(f96(a91,a91),a3)),x9485),a8))
% 1.50/1.47 [949]~E(x9494,x9491)+E(x9491,x9492)+E(x9493,x9494)+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9493),x9494)),f14(x9495,x9492,x9491)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9493),x9494)),x9495))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9493),x9491)),x9495))+~P34(f28(f28(f35(f94(f96(a91,a91),a3)),x9495),a8))
% 1.50/1.47 [950]~E(x9503,x9501)+E(x9501,x9502)+E(x9503,x9504)+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9503),x9504)),f14(x9505,x9501,x9502)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9502),x9504)),x9505))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9503),x9502)),x9505))+~P34(f28(f28(f35(f94(f96(a91,a91),a3)),x9505),a8))
% 1.50/1.47 [952]E(x9521,x9522)+E(x9523,x9521)+E(x9524,x9523)+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9524),x9523)),f28(f28(f28(a12,x9525),x9522),x9521)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9524),x9523)),x9525))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9522),x9523)),x9525))+~P34(f28(f28(f35(f94(f96(a91,a91),a3)),x9525),a8))
% 1.50/1.47 [953]E(x9531,x9532)+E(x9533,x9532)+E(x9533,x9534)+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9533),x9534)),f28(f28(f28(a12,x9535),x9531),x9532)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9533),x9534)),x9535))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9533),x9531)),x9535))+~P34(f28(f28(f35(f94(f96(a91,a91),a3)),x9535),a8))
% 1.50/1.47 [954]~E(x9543,x9541)+E(x9541,x9542)+E(x9543,x9544)+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9543),x9544)),f28(f28(f28(a12,x9545),x9541),x9542)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9543),x9544)),x9545))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9541),x9544)),x9545))+~P34(f28(f28(f35(f94(f96(a91,a91),a3)),x9545),a8))
% 1.50/1.47 [955]~E(x9553,x9551)+E(x9551,x9552)+E(x9553,x9554)+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9554),x9553)),f28(f28(f28(a12,x9555),x9552),x9551)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9552),x9553)),x9555))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9554),x9552)),x9555))+~P34(f28(f28(f35(f94(f96(a91,a91),a3)),x9555),a8))
% 1.50/1.47 [971]E(x9711,x9712)+E(x9713,x9714)+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9713),x9714)),f14(x9715,x9712,x9711)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9713),x9714)),x9715))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9711),x9714)),x9715))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9713),x9711)),x9715))+~P34(f28(f28(f35(f94(f96(a91,a91),a3)),x9715),a8))
% 1.50/1.47 [972]E(x9721,x9722)+E(x9723,x9724)+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9723),x9724)),f28(f28(f28(a12,x9725),x9721),x9722)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9723),x9724)),x9725))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9721),x9724)),x9725))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9723),x9721)),x9725))+~P34(f28(f28(f35(f94(f96(a91,a91),a3)),x9725),a8))
% 1.50/1.47 [1007]~P1(x10073)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10071),x10072)),f28(x10073,x10075)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10071),x10072)),f28(x10073,x10074)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10071),x10072)),f28(x10075,f55(x10073,x10074,x10075,x10071,x10072))))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10071),x10072)),f28(x10074,f55(x10073,x10074,x10075,x10071,x10072))))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x10074),a9))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x10075),a9))
% 1.50/1.47 [1008]~P1(x10083)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10081),x10082)),f28(x10083,x10085)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10081),x10082)),f28(x10083,x10084)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10081),x10082)),f28(x10085,f55(x10083,x10085,x10084,x10081,x10082))))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10081),x10082)),f28(x10084,f55(x10083,x10085,x10084,x10081,x10082))))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x10084),a9))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x10085),a9))
% 1.50/1.47 [1011]~P1(x10113)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10111),x10112)),f28(x10113,x10115)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10111),x10112)),f28(x10113,x10114)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10111),x10112)),f28(x10115,f55(x10113,x10114,x10115,x10111,x10112))))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10111),x10112)),f28(x10114,f55(x10113,x10114,x10115,x10111,x10112))))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x10114),a9))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x10115),a9))
% 1.50/1.47 [1012]~P1(x10123)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10121),x10122)),f28(x10123,x10125)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10121),x10122)),f28(x10123,x10124)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10121),x10122)),f28(x10125,f55(x10123,x10125,x10124,x10121,x10122))))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10121),x10122)),f28(x10124,f55(x10123,x10125,x10124,x10121,x10122))))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x10124),a9))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x10125),a9))
% 1.50/1.47 [981]~P8(x9813,x9814)+~P8(x9811,x9812)+~P9(x9813,x9811,x9815,x9814)+~P9(x9811,x9813,x9816,x9812)+E(f15(x9811,x9812),f15(x9813,x9814))+~P34(f28(f29(f94(x9813,a3),f37(x9811,x9813,x9816,x9812)),x9814))+~P34(f28(f29(f94(x9811,a3),f37(x9813,x9811,x9815,x9814)),x9812))
% 1.50/1.47 [977]~P8(x9773,x9774)+~P8(x9771,x9772)+~P9(x9773,x9771,x9775,x9774)+~P9(x9771,x9773,x9776,x9772)+E(f15(x9771,x9772),f15(x9773,x9774))+~P34(f28(f28(f35(f94(x9773,x9771)),x9775),f18(x9773,x9771,x9774,f28(f16(f94(x9771,a3),x9773),x9772))))+~P34(f28(f28(f35(f94(x9771,x9773)),x9776),f18(x9771,x9773,x9772,f28(f16(f94(x9773,a3),x9771),x9774))))
% 1.50/1.47 [1034]~P35(a500)+E(f28(a97,a86),a106)+P34(f28(f28(f30(a2),f28(a97,a86)),f28(f28(f20(a2),a106),f5(a2))))+P34(f28(f28(f30(a2),f28(a97,a86)),a106))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a105)),f28(f28(a13,f28(a101,a86)),a105)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a100),a102)),f28(a1,f28(f28(f7(a90,f94(f96(a91,a91),a3),f94(f96(a91,a91),a3)),f28(f28(f7(a90,f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),f28(f10(a3,f94(f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),a90,f24(f94(f96(a91,a91),a3))),f28(f28(f7(a90,a2,a3),f28(f10(a2,f94(a2,a3),a90,f30(a2)),a97)),f28(f28(f20(a2),a106),f5(a2))))),a98)),a99))))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a105)),f28(a1,f17(a90,f94(f96(a91,a91),a3),f94(f96(a91,a91),a3),f17(a90,f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3)),f28(f10(a3,f94(f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),a90,f24(f94(f96(a91,a91),a3))),f28(f28(f7(a90,a2,a3),f28(f10(a2,f94(a2,a3),a90,f30(a2)),a97)),a106)),f28(f28(f7(a90,a91,f94(f96(a91,a91),a3)),f28(f10(f94(f96(a91,a91),a3),f94(a91,f94(f96(a91,a91),a3)),a90,a11),a101)),a105)),f17(a90,f94(f96(a91,a91),a3),f94(f96(a91,a91),a3),f17(a90,f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3)),f28(f10(a3,f94(f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),a90,f24(f94(f96(a91,a91),a3))),f28(f28(f7(a90,a2,a3),f28(f10(a2,f94(a2,a3),a90,a39),a97)),a106)),f28(f28(f7(a90,a91,f94(f96(a91,a91),a3)),f28(f28(f7(a90,a91,f94(a91,f94(f96(a91,a91),a3))),f28(f10(f94(f96(a91,a91),a3),f94(a91,f94(a91,f94(f96(a91,a91),a3))),a90,a12),a101)),a103)),a105)),f28(f28(f7(a90,a91,f94(f96(a91,a91),a3)),f28(f10(f94(f96(a91,a91),a3),f94(a91,f94(f96(a91,a91),a3)),a90,a13),a101)),a105))))))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a100),a102)),a99))
% 1.50/1.47 [1038]~P35(a500)+~E(f28(a97,a86),a106)+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a105)),f28(f28(f28(a12,f28(a101,a86)),a103),a105)))+P34(f28(f28(f30(a2),f28(a97,a86)),f28(f28(f20(a2),a106),f5(a2))))+P34(f28(f28(f30(a2),f28(a97,a86)),a106))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a100),a102)),f28(a1,f28(f28(f7(a90,f94(f96(a91,a91),a3),f94(f96(a91,a91),a3)),f28(f28(f7(a90,f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),f28(f10(a3,f94(f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),a90,f24(f94(f96(a91,a91),a3))),f28(f28(f7(a90,a2,a3),f28(f10(a2,f94(a2,a3),a90,f30(a2)),a97)),f28(f28(f20(a2),a106),f5(a2))))),a98)),a99))))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a100),a102)),a99))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a105)),f28(a1,f17(a90,f94(f96(a91,a91),a3),f94(f96(a91,a91),a3),f17(a90,f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3)),f28(f10(a3,f94(f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),a90,f24(f94(f96(a91,a91),a3))),f28(f28(f7(a90,a2,a3),f28(f10(a2,f94(a2,a3),a90,f30(a2)),a97)),a106)),f28(f28(f7(a90,a91,f94(f96(a91,a91),a3)),f28(f10(f94(f96(a91,a91),a3),f94(a91,f94(f96(a91,a91),a3)),a90,a11),a101)),a105)),f17(a90,f94(f96(a91,a91),a3),f94(f96(a91,a91),a3),f17(a90,f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3)),f28(f10(a3,f94(f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),a90,f24(f94(f96(a91,a91),a3))),f28(f28(f7(a90,a2,a3),f28(f10(a2,f94(a2,a3),a90,a39),a97)),a106)),f28(f28(f7(a90,a91,f94(f96(a91,a91),a3)),f28(f28(f7(a90,a91,f94(a91,f94(f96(a91,a91),a3))),f28(f10(f94(f96(a91,a91),a3),f94(a91,f94(a91,f94(f96(a91,a91),a3))),a90,a12),a101)),a103)),a105)),f28(f28(f7(a90,a91,f94(f96(a91,a91),a3)),f28(f10(f94(f96(a91,a91),a3),f94(a91,f94(f96(a91,a91),a3)),a90,a13),a101)),a105))))))
% 1.50/1.47 [1042]~P35(a500)+E(f28(a97,a86),a106)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a105)),f28(f28(a13,f28(a101,a86)),a105)))+~P34(f28(f28(f30(a2),f28(a97,a86)),f28(f28(f20(a2),a106),f5(a2))))+P34(f28(f28(f30(a2),f28(a97,a86)),a106))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a100),a102)),a98))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a100),a102)),f28(a1,f28(f28(f7(a90,f94(f96(a91,a91),a3),f94(f96(a91,a91),a3)),f28(f28(f7(a90,f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),f28(f10(a3,f94(f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),a90,f24(f94(f96(a91,a91),a3))),f28(f28(f7(a90,a2,a3),f28(f10(a2,f94(a2,a3),a90,f30(a2)),a97)),f28(f28(f20(a2),a106),f5(a2))))),a98)),a99))))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a105)),f28(a1,f17(a90,f94(f96(a91,a91),a3),f94(f96(a91,a91),a3),f17(a90,f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3)),f28(f10(a3,f94(f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),a90,f24(f94(f96(a91,a91),a3))),f28(f28(f7(a90,a2,a3),f28(f10(a2,f94(a2,a3),a90,f30(a2)),a97)),a106)),f28(f28(f7(a90,a91,f94(f96(a91,a91),a3)),f28(f10(f94(f96(a91,a91),a3),f94(a91,f94(f96(a91,a91),a3)),a90,a11),a101)),a105)),f17(a90,f94(f96(a91,a91),a3),f94(f96(a91,a91),a3),f17(a90,f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3)),f28(f10(a3,f94(f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),a90,f24(f94(f96(a91,a91),a3))),f28(f28(f7(a90,a2,a3),f28(f10(a2,f94(a2,a3),a90,a39),a97)),a106)),f28(f28(f7(a90,a91,f94(f96(a91,a91),a3)),f28(f28(f7(a90,a91,f94(a91,f94(f96(a91,a91),a3))),f28(f10(f94(f96(a91,a91),a3),f94(a91,f94(a91,f94(f96(a91,a91),a3))),a90,a12),a101)),a103)),a105)),f28(f28(f7(a90,a91,f94(f96(a91,a91),a3)),f28(f10(f94(f96(a91,a91),a3),f94(a91,f94(f96(a91,a91),a3)),a90,a13),a101)),a105))))))
% 1.50/1.47 [1045]~P35(a500)+~E(f28(a97,a86),a106)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a105)),f28(f28(f28(a12,f28(a101,a86)),a103),a105)))+~P34(f28(f28(f30(a2),f28(a97,a86)),f28(f28(f20(a2),a106),f5(a2))))+P34(f28(f28(f30(a2),f28(a97,a86)),a106))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a100),a102)),a98))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a100),a102)),f28(a1,f28(f28(f7(a90,f94(f96(a91,a91),a3),f94(f96(a91,a91),a3)),f28(f28(f7(a90,f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),f28(f10(a3,f94(f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),a90,f24(f94(f96(a91,a91),a3))),f28(f28(f7(a90,a2,a3),f28(f10(a2,f94(a2,a3),a90,f30(a2)),a97)),f28(f28(f20(a2),a106),f5(a2))))),a98)),a99))))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a105)),f28(a1,f17(a90,f94(f96(a91,a91),a3),f94(f96(a91,a91),a3),f17(a90,f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3)),f28(f10(a3,f94(f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),a90,f24(f94(f96(a91,a91),a3))),f28(f28(f7(a90,a2,a3),f28(f10(a2,f94(a2,a3),a90,f30(a2)),a97)),a106)),f28(f28(f7(a90,a91,f94(f96(a91,a91),a3)),f28(f10(f94(f96(a91,a91),a3),f94(a91,f94(f96(a91,a91),a3)),a90,a11),a101)),a105)),f17(a90,f94(f96(a91,a91),a3),f94(f96(a91,a91),a3),f17(a90,f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3)),f28(f10(a3,f94(f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),a90,f24(f94(f96(a91,a91),a3))),f28(f28(f7(a90,a2,a3),f28(f10(a2,f94(a2,a3),a90,a39),a97)),a106)),f28(f28(f7(a90,a91,f94(f96(a91,a91),a3)),f28(f28(f7(a90,a91,f94(a91,f94(f96(a91,a91),a3))),f28(f10(f94(f96(a91,a91),a3),f94(a91,f94(a91,f94(f96(a91,a91),a3))),a90,a12),a101)),a103)),a105)),f28(f28(f7(a90,a91,f94(f96(a91,a91),a3)),f28(f10(f94(f96(a91,a91),a3),f94(a91,f94(f96(a91,a91),a3)),a90,a13),a101)),a105))))))
% 1.50/1.47 [1050]~P35(a500)+E(f28(a97,a86),a106)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a105)),f28(f28(a11,f28(a101,a86)),a105)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a105)),f28(f28(a13,f28(a101,a86)),a105)))+~P34(f28(f28(f30(a2),f28(a97,a86)),f28(f28(f20(a2),a106),f5(a2))))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a100),a102)),a98))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a100),a102)),f28(a1,f28(f28(f7(a90,f94(f96(a91,a91),a3),f94(f96(a91,a91),a3)),f28(f28(f7(a90,f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),f28(f10(a3,f94(f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),a90,f24(f94(f96(a91,a91),a3))),f28(f28(f7(a90,a2,a3),f28(f10(a2,f94(a2,a3),a90,f30(a2)),a97)),f28(f28(f20(a2),a106),f5(a2))))),a98)),a99))))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a105)),f28(a1,f17(a90,f94(f96(a91,a91),a3),f94(f96(a91,a91),a3),f17(a90,f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3)),f28(f10(a3,f94(f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),a90,f24(f94(f96(a91,a91),a3))),f28(f28(f7(a90,a2,a3),f28(f10(a2,f94(a2,a3),a90,f30(a2)),a97)),a106)),f28(f28(f7(a90,a91,f94(f96(a91,a91),a3)),f28(f10(f94(f96(a91,a91),a3),f94(a91,f94(f96(a91,a91),a3)),a90,a11),a101)),a105)),f17(a90,f94(f96(a91,a91),a3),f94(f96(a91,a91),a3),f17(a90,f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3)),f28(f10(a3,f94(f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),a90,f24(f94(f96(a91,a91),a3))),f28(f28(f7(a90,a2,a3),f28(f10(a2,f94(a2,a3),a90,a39),a97)),a106)),f28(f28(f7(a90,a91,f94(f96(a91,a91),a3)),f28(f28(f7(a90,a91,f94(a91,f94(f96(a91,a91),a3))),f28(f10(f94(f96(a91,a91),a3),f94(a91,f94(a91,f94(f96(a91,a91),a3))),a90,a12),a101)),a103)),a105)),f28(f28(f7(a90,a91,f94(f96(a91,a91),a3)),f28(f10(f94(f96(a91,a91),a3),f94(a91,f94(f96(a91,a91),a3)),a90,a13),a101)),a105))))))
% 1.50/1.47 [1053]~P35(a500)+~E(f28(a97,a86),a106)+~P34(f28(f28(f30(a2),f28(a97,a86)),f28(f28(f20(a2),a106),f5(a2))))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a105)),f28(f28(a11,f28(a101,a86)),a105)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a105)),f28(f28(f28(a12,f28(a101,a86)),a103),a105)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a100),a102)),a98))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a100),a102)),f28(a1,f28(f28(f7(a90,f94(f96(a91,a91),a3),f94(f96(a91,a91),a3)),f28(f28(f7(a90,f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),f28(f10(a3,f94(f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),a90,f24(f94(f96(a91,a91),a3))),f28(f28(f7(a90,a2,a3),f28(f10(a2,f94(a2,a3),a90,f30(a2)),a97)),f28(f28(f20(a2),a106),f5(a2))))),a98)),a99))))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a105)),f28(a1,f17(a90,f94(f96(a91,a91),a3),f94(f96(a91,a91),a3),f17(a90,f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3)),f28(f10(a3,f94(f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),a90,f24(f94(f96(a91,a91),a3))),f28(f28(f7(a90,a2,a3),f28(f10(a2,f94(a2,a3),a90,f30(a2)),a97)),a106)),f28(f28(f7(a90,a91,f94(f96(a91,a91),a3)),f28(f10(f94(f96(a91,a91),a3),f94(a91,f94(f96(a91,a91),a3)),a90,a11),a101)),a105)),f17(a90,f94(f96(a91,a91),a3),f94(f96(a91,a91),a3),f17(a90,f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3)),f28(f10(a3,f94(f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),a90,f24(f94(f96(a91,a91),a3))),f28(f28(f7(a90,a2,a3),f28(f10(a2,f94(a2,a3),a90,a39),a97)),a106)),f28(f28(f7(a90,a91,f94(f96(a91,a91),a3)),f28(f28(f7(a90,a91,f94(a91,f94(f96(a91,a91),a3))),f28(f10(f94(f96(a91,a91),a3),f94(a91,f94(a91,f94(f96(a91,a91),a3))),a90,a12),a101)),a103)),a105)),f28(f28(f7(a90,a91,f94(f96(a91,a91),a3)),f28(f10(f94(f96(a91,a91),a3),f94(a91,f94(f96(a91,a91),a3)),a90,a13),a101)),a105))))))
% 1.50/1.47 [1054]~P35(a500)+~P34(f28(f28(f30(a2),f28(a97,a86)),f28(f28(f20(a2),a106),f5(a2))))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a105)),f28(f28(a13,f28(a101,a86)),a105)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a105)),f28(f28(f28(a12,f28(a101,a86)),a103),a105)))+P34(f28(f28(f30(a2),f28(a97,a86)),a106))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a100),a102)),a98))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a100),a102)),f28(a1,f28(f28(f7(a90,f94(f96(a91,a91),a3),f94(f96(a91,a91),a3)),f28(f28(f7(a90,f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),f28(f10(a3,f94(f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),a90,f24(f94(f96(a91,a91),a3))),f28(f28(f7(a90,a2,a3),f28(f10(a2,f94(a2,a3),a90,f30(a2)),a97)),f28(f28(f20(a2),a106),f5(a2))))),a98)),a99))))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a105)),f28(a1,f17(a90,f94(f96(a91,a91),a3),f94(f96(a91,a91),a3),f17(a90,f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3)),f28(f10(a3,f94(f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),a90,f24(f94(f96(a91,a91),a3))),f28(f28(f7(a90,a2,a3),f28(f10(a2,f94(a2,a3),a90,f30(a2)),a97)),a106)),f28(f28(f7(a90,a91,f94(f96(a91,a91),a3)),f28(f10(f94(f96(a91,a91),a3),f94(a91,f94(f96(a91,a91),a3)),a90,a11),a101)),a105)),f17(a90,f94(f96(a91,a91),a3),f94(f96(a91,a91),a3),f17(a90,f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3)),f28(f10(a3,f94(f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),a90,f24(f94(f96(a91,a91),a3))),f28(f28(f7(a90,a2,a3),f28(f10(a2,f94(a2,a3),a90,a39),a97)),a106)),f28(f28(f7(a90,a91,f94(f96(a91,a91),a3)),f28(f28(f7(a90,a91,f94(a91,f94(f96(a91,a91),a3))),f28(f10(f94(f96(a91,a91),a3),f94(a91,f94(a91,f94(f96(a91,a91),a3))),a90,a12),a101)),a103)),a105)),f28(f28(f7(a90,a91,f94(f96(a91,a91),a3)),f28(f10(f94(f96(a91,a91),a3),f94(a91,f94(f96(a91,a91),a3)),a90,a13),a101)),a105))))))
% 1.50/1.47 [1059]~P35(a500)+~P34(f28(f28(f30(a2),f28(a97,a86)),f28(f28(f20(a2),a106),f5(a2))))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a105)),f28(f28(a11,f28(a101,a86)),a105)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a105)),f28(f28(a13,f28(a101,a86)),a105)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a105)),f28(f28(f28(a12,f28(a101,a86)),a103),a105)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a100),a102)),a98))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a100),a102)),f28(a1,f28(f28(f7(a90,f94(f96(a91,a91),a3),f94(f96(a91,a91),a3)),f28(f28(f7(a90,f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),f28(f10(a3,f94(f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),a90,f24(f94(f96(a91,a91),a3))),f28(f28(f7(a90,a2,a3),f28(f10(a2,f94(a2,a3),a90,f30(a2)),a97)),f28(f28(f20(a2),a106),f5(a2))))),a98)),a99))))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a105)),f28(a1,f17(a90,f94(f96(a91,a91),a3),f94(f96(a91,a91),a3),f17(a90,f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3)),f28(f10(a3,f94(f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),a90,f24(f94(f96(a91,a91),a3))),f28(f28(f7(a90,a2,a3),f28(f10(a2,f94(a2,a3),a90,f30(a2)),a97)),a106)),f28(f28(f7(a90,a91,f94(f96(a91,a91),a3)),f28(f10(f94(f96(a91,a91),a3),f94(a91,f94(f96(a91,a91),a3)),a90,a11),a101)),a105)),f17(a90,f94(f96(a91,a91),a3),f94(f96(a91,a91),a3),f17(a90,f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3)),f28(f10(a3,f94(f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),a90,f24(f94(f96(a91,a91),a3))),f28(f28(f7(a90,a2,a3),f28(f10(a2,f94(a2,a3),a90,a39),a97)),a106)),f28(f28(f7(a90,a91,f94(f96(a91,a91),a3)),f28(f28(f7(a90,a91,f94(a91,f94(f96(a91,a91),a3))),f28(f10(f94(f96(a91,a91),a3),f94(a91,f94(a91,f94(f96(a91,a91),a3))),a90,a12),a101)),a103)),a105)),f28(f28(f7(a90,a91,f94(f96(a91,a91),a3)),f28(f10(f94(f96(a91,a91),a3),f94(a91,f94(f96(a91,a91),a3)),a90,a13),a101)),a105))))))
% 1.50/1.47 [1015]E(x10151,x10152)+E(x10153,x10154)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10153),x10154)),f28(a1,x10156)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10151),x10152)),f28(a1,x10155)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10151),x10152)),f28(x10155,f85(x10155,x10156,x10152,x10151,x10154,x10153))))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10153),x10154)),f28(x10156,f85(x10155,x10156,x10152,x10151,x10154,x10153))))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x10155),a9))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x10156),a9))
% 1.50/1.47 [1016]E(x10161,x10162)+E(x10163,x10164)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10163),x10164)),f28(a1,x10166)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10161),x10162)),f28(a1,x10165)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10161),x10162)),f28(x10165,f85(x10166,x10165,x10164,x10163,x10162,x10161))))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10163),x10164)),f28(x10166,f85(x10166,x10165,x10164,x10163,x10162,x10161))))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x10165),a9))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x10166),a9))
% 1.50/1.47 [1021]E(x10211,x10212)+E(x10213,x10214)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10213),x10214)),f28(a1,x10216)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10211),x10212)),f28(a1,x10215)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10211),x10212)),f28(x10215,f85(x10215,x10216,x10212,x10211,x10214,x10213))))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10213),x10214)),f28(x10216,f85(x10215,x10216,x10212,x10211,x10214,x10213))))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x10215),a9))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x10216),a9))
% 1.50/1.47 [1022]E(x10221,x10222)+E(x10223,x10224)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10223),x10224)),f28(a1,x10226)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10221),x10222)),f28(a1,x10225)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10221),x10222)),f28(x10225,f85(x10226,x10225,x10224,x10223,x10222,x10221))))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10223),x10224)),f28(x10226,f85(x10226,x10225,x10224,x10223,x10222,x10221))))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x10225),a9))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x10226),a9))
% 1.50/1.47 [1005]E(x10053,x10051)+E(x10051,x10052)+E(x10053,x10052)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10053),x10051)),f28(a1,x10055)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10052),x10053)),f28(a1,x10054)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10052),x10053)),f28(x10054,f84(x10055,x10054,x10051,x10053,x10052))))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10053),x10051)),f28(x10055,f84(x10055,x10054,x10051,x10053,x10052))))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x10054),a9))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x10055),a9))
% 1.50/1.47 [1006]E(x10063,x10061)+E(x10061,x10062)+E(x10063,x10062)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10063),x10061)),f28(a1,x10065)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10061),x10062)),f28(a1,x10064)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10061),x10062)),f28(x10064,f84(x10064,x10065,x10062,x10061,x10063))))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10063),x10061)),f28(x10065,f84(x10064,x10065,x10062,x10061,x10063))))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x10064),a9))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x10065),a9))
% 1.50/1.47 [1009]E(x10093,x10091)+E(x10091,x10092)+E(x10093,x10092)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10093),x10091)),f28(a1,x10095)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10092),x10093)),f28(a1,x10094)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10092),x10093)),f28(x10094,f84(x10095,x10094,x10091,x10093,x10092))))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10093),x10091)),f28(x10095,f84(x10095,x10094,x10091,x10093,x10092))))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x10094),a9))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x10095),a9))
% 1.50/1.47 [1010]E(x10103,x10101)+E(x10101,x10102)+E(x10103,x10102)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10103),x10101)),f28(a1,x10105)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10101),x10102)),f28(a1,x10104)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10101),x10102)),f28(x10104,f84(x10104,x10105,x10102,x10101,x10103))))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10103),x10101)),f28(x10105,f84(x10104,x10105,x10102,x10101,x10103))))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x10104),a9))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x10105),a9))
% 1.50/1.47 [1017]E(x10174,x10173)+E(x10171,x10172)+E(x10173,x10172)+E(x10174,x10171)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10174),x10173)),f28(a1,x10176)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10172),x10171)),f28(a1,x10175)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10172),x10171)),f28(x10175,f87(x10175,x10176,x10171,x10172,x10173,x10174))))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10174),x10173)),f28(x10176,f87(x10175,x10176,x10171,x10172,x10173,x10174))))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x10175),a9))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x10176),a9))
% 1.50/1.47 [1018]E(x10184,x10183)+E(x10181,x10182)+E(x10183,x10181)+E(x10184,x10182)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10184),x10183)),f28(a1,x10186)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10181),x10182)),f28(a1,x10185)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10181),x10182)),f28(x10185,f88(x10185,x10186,x10182,x10181,x10183,x10184))))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10184),x10183)),f28(x10186,f88(x10185,x10186,x10182,x10181,x10183,x10184))))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x10185),a9))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x10186),a9))
% 1.50/1.47 [1019]E(x10194,x10193)+E(x10191,x10192)+E(x10193,x10191)+E(x10194,x10192)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10194),x10193)),f28(a1,x10196)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10191),x10192)),f28(a1,x10195)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10191),x10192)),f28(x10195,f88(x10196,x10195,x10193,x10194,x10192,x10191))))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10194),x10193)),f28(x10196,f88(x10196,x10195,x10193,x10194,x10192,x10191))))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x10195),a9))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x10196),a9))
% 1.50/1.47 [1023]E(x10234,x10233)+E(x10231,x10232)+E(x10233,x10232)+E(x10234,x10231)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10234),x10233)),f28(a1,x10236)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10232),x10231)),f28(a1,x10235)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10232),x10231)),f28(x10235,f87(x10235,x10236,x10231,x10232,x10233,x10234))))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10234),x10233)),f28(x10236,f87(x10235,x10236,x10231,x10232,x10233,x10234))))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x10235),a9))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x10236),a9))
% 1.50/1.47 [1024]E(x10244,x10243)+E(x10241,x10242)+E(x10243,x10241)+E(x10244,x10242)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10244),x10243)),f28(a1,x10246)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10241),x10242)),f28(a1,x10245)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10241),x10242)),f28(x10245,f88(x10245,x10246,x10242,x10241,x10243,x10244))))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10244),x10243)),f28(x10246,f88(x10245,x10246,x10242,x10241,x10243,x10244))))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x10245),a9))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x10246),a9))
% 1.50/1.47 [1025]E(x10254,x10253)+E(x10251,x10252)+E(x10253,x10251)+E(x10254,x10252)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10254),x10253)),f28(a1,x10256)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10251),x10252)),f28(a1,x10255)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10251),x10252)),f28(x10255,f88(x10256,x10255,x10253,x10254,x10252,x10251))))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10254),x10253)),f28(x10256,f88(x10256,x10255,x10253,x10254,x10252,x10251))))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x10255),a9))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x10256),a9))
% 1.50/1.47 %EqnAxiom
% 1.50/1.47 [1]E(x11,x11)
% 1.50/1.47 [2]E(x22,x21)+~E(x21,x22)
% 1.50/1.47 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 1.50/1.47 [4]~E(x41,x42)+E(f4(x41),f4(x42))
% 1.50/1.47 [5]~E(x51,x52)+E(f21(x51),f21(x52))
% 1.50/1.47 [6]~E(x61,x62)+E(f28(x61,x63),f28(x62,x63))
% 1.50/1.47 [7]~E(x71,x72)+E(f28(x73,x71),f28(x73,x72))
% 1.50/1.47 [8]~E(x81,x82)+E(f27(x81,x83),f27(x82,x83))
% 1.50/1.47 [9]~E(x91,x92)+E(f27(x93,x91),f27(x93,x92))
% 1.50/1.47 [10]~E(x101,x102)+E(f7(x101,x103,x104),f7(x102,x103,x104))
% 1.50/1.47 [11]~E(x111,x112)+E(f7(x113,x111,x114),f7(x113,x112,x114))
% 1.50/1.47 [12]~E(x121,x122)+E(f7(x123,x124,x121),f7(x123,x124,x122))
% 1.50/1.47 [13]~E(x131,x132)+E(f10(x131,x133,x134,x135),f10(x132,x133,x134,x135))
% 1.50/1.47 [14]~E(x141,x142)+E(f10(x143,x141,x144,x145),f10(x143,x142,x144,x145))
% 1.50/1.47 [15]~E(x151,x152)+E(f10(x153,x154,x151,x155),f10(x153,x154,x152,x155))
% 1.50/1.47 [16]~E(x161,x162)+E(f10(x163,x164,x165,x161),f10(x163,x164,x165,x162))
% 1.50/1.47 [17]~E(x171,x172)+E(f5(x171),f5(x172))
% 1.50/1.47 [18]~E(x181,x182)+E(f17(x181,x183,x184,x185,x186),f17(x182,x183,x184,x185,x186))
% 1.50/1.47 [19]~E(x191,x192)+E(f17(x193,x191,x194,x195,x196),f17(x193,x192,x194,x195,x196))
% 1.50/1.47 [20]~E(x201,x202)+E(f17(x203,x204,x201,x205,x206),f17(x203,x204,x202,x205,x206))
% 1.50/1.47 [21]~E(x211,x212)+E(f17(x213,x214,x215,x211,x216),f17(x213,x214,x215,x212,x216))
% 1.50/1.47 [22]~E(x221,x222)+E(f17(x223,x224,x225,x226,x221),f17(x223,x224,x225,x226,x222))
% 1.50/1.47 [23]~E(x231,x232)+E(f96(x231,x233),f96(x232,x233))
% 1.50/1.47 [24]~E(x241,x242)+E(f96(x243,x241),f96(x243,x242))
% 1.50/1.47 [25]~E(x251,x252)+E(f94(x251,x253),f94(x252,x253))
% 1.50/1.47 [26]~E(x261,x262)+E(f94(x263,x261),f94(x263,x262))
% 1.50/1.47 [27]~E(x271,x272)+E(f6(x271),f6(x272))
% 1.50/1.47 [28]~E(x281,x282)+E(f24(x281),f24(x282))
% 1.50/1.47 [29]~E(x291,x292)+E(f20(x291),f20(x292))
% 1.50/1.47 [30]~E(x301,x302)+E(f68(x301,x303,x304,x305,x306),f68(x302,x303,x304,x305,x306))
% 1.50/1.47 [31]~E(x311,x312)+E(f68(x313,x311,x314,x315,x316),f68(x313,x312,x314,x315,x316))
% 1.50/1.47 [32]~E(x321,x322)+E(f68(x323,x324,x321,x325,x326),f68(x323,x324,x322,x325,x326))
% 1.50/1.47 [33]~E(x331,x332)+E(f68(x333,x334,x335,x331,x336),f68(x333,x334,x335,x332,x336))
% 1.50/1.47 [34]~E(x341,x342)+E(f68(x343,x344,x345,x346,x341),f68(x343,x344,x345,x346,x342))
% 1.50/1.47 [35]~E(x351,x352)+E(f18(x351,x353,x354,x355),f18(x352,x353,x354,x355))
% 1.50/1.47 [36]~E(x361,x362)+E(f18(x363,x361,x364,x365),f18(x363,x362,x364,x365))
% 1.50/1.47 [37]~E(x371,x372)+E(f18(x373,x374,x371,x375),f18(x373,x374,x372,x375))
% 1.50/1.47 [38]~E(x381,x382)+E(f18(x383,x384,x385,x381),f18(x383,x384,x385,x382))
% 1.50/1.47 [39]~E(x391,x392)+E(f29(x391,x393),f29(x392,x393))
% 1.50/1.47 [40]~E(x401,x402)+E(f29(x403,x401),f29(x403,x402))
% 1.50/1.47 [41]~E(x411,x412)+E(f35(x411),f35(x412))
% 1.50/1.47 [42]~E(x421,x422)+E(f60(x421),f60(x422))
% 1.50/1.47 [43]~E(x431,x432)+E(f30(x431),f30(x432))
% 1.50/1.47 [44]~E(x441,x442)+E(f67(x441,x443,x444,x445,x446),f67(x442,x443,x444,x445,x446))
% 1.50/1.47 [45]~E(x451,x452)+E(f67(x453,x451,x454,x455,x456),f67(x453,x452,x454,x455,x456))
% 1.50/1.47 [46]~E(x461,x462)+E(f67(x463,x464,x461,x465,x466),f67(x463,x464,x462,x465,x466))
% 1.50/1.47 [47]~E(x471,x472)+E(f67(x473,x474,x475,x471,x476),f67(x473,x474,x475,x472,x476))
% 1.50/1.47 [48]~E(x481,x482)+E(f67(x483,x484,x485,x486,x481),f67(x483,x484,x485,x486,x482))
% 1.50/1.47 [49]~E(x491,x492)+E(f33(x491,x493),f33(x492,x493))
% 1.50/1.47 [50]~E(x501,x502)+E(f33(x503,x501),f33(x503,x502))
% 1.50/1.47 [51]~E(x511,x512)+E(f15(x511,x513),f15(x512,x513))
% 1.50/1.47 [52]~E(x521,x522)+E(f15(x523,x521),f15(x523,x522))
% 1.50/1.47 [53]~E(x531,x532)+E(f42(x531),f42(x532))
% 1.50/1.47 [54]~E(x541,x542)+E(f54(x541),f54(x542))
% 1.50/1.47 [55]~E(x551,x552)+E(f37(x551,x553,x554,x555),f37(x552,x553,x554,x555))
% 1.50/1.47 [56]~E(x561,x562)+E(f37(x563,x561,x564,x565),f37(x563,x562,x564,x565))
% 1.50/1.47 [57]~E(x571,x572)+E(f37(x573,x574,x571,x575),f37(x573,x574,x572,x575))
% 1.50/1.47 [58]~E(x581,x582)+E(f37(x583,x584,x585,x581),f37(x583,x584,x585,x582))
% 1.50/1.47 [59]~E(x591,x592)+E(f31(x591),f31(x592))
% 1.50/1.47 [60]~E(x601,x602)+E(f36(x601,x603,x604),f36(x602,x603,x604))
% 1.50/1.47 [61]~E(x611,x612)+E(f36(x613,x611,x614),f36(x613,x612,x614))
% 1.50/1.47 [62]~E(x621,x622)+E(f36(x623,x624,x621),f36(x623,x624,x622))
% 1.50/1.47 [63]~E(x631,x632)+E(f32(x631,x633,x634),f32(x632,x633,x634))
% 1.50/1.47 [64]~E(x641,x642)+E(f32(x643,x641,x644),f32(x643,x642,x644))
% 1.50/1.47 [65]~E(x651,x652)+E(f32(x653,x654,x651),f32(x653,x654,x652))
% 1.50/1.47 [66]~E(x661,x662)+E(f85(x661,x663,x664,x665,x666,x667),f85(x662,x663,x664,x665,x666,x667))
% 1.50/1.47 [67]~E(x671,x672)+E(f85(x673,x671,x674,x675,x676,x677),f85(x673,x672,x674,x675,x676,x677))
% 1.50/1.47 [68]~E(x681,x682)+E(f85(x683,x684,x681,x685,x686,x687),f85(x683,x684,x682,x685,x686,x687))
% 1.50/1.47 [69]~E(x691,x692)+E(f85(x693,x694,x695,x691,x696,x697),f85(x693,x694,x695,x692,x696,x697))
% 1.50/1.47 [70]~E(x701,x702)+E(f85(x703,x704,x705,x706,x701,x707),f85(x703,x704,x705,x706,x702,x707))
% 1.50/1.47 [71]~E(x711,x712)+E(f85(x713,x714,x715,x716,x717,x711),f85(x713,x714,x715,x716,x717,x712))
% 1.50/1.47 [72]~E(x721,x722)+E(f95(x721,x723),f95(x722,x723))
% 1.50/1.47 [73]~E(x731,x732)+E(f95(x733,x731),f95(x733,x732))
% 1.50/1.47 [74]~E(x741,x742)+E(f16(x741,x743),f16(x742,x743))
% 1.50/1.47 [75]~E(x751,x752)+E(f16(x753,x751),f16(x753,x752))
% 1.50/1.47 [76]~E(x761,x762)+E(f55(x761,x763,x764,x765,x766),f55(x762,x763,x764,x765,x766))
% 1.50/1.47 [77]~E(x771,x772)+E(f55(x773,x771,x774,x775,x776),f55(x773,x772,x774,x775,x776))
% 1.50/1.47 [78]~E(x781,x782)+E(f55(x783,x784,x781,x785,x786),f55(x783,x784,x782,x785,x786))
% 1.50/1.47 [79]~E(x791,x792)+E(f55(x793,x794,x795,x791,x796),f55(x793,x794,x795,x792,x796))
% 1.50/1.47 [80]~E(x801,x802)+E(f55(x803,x804,x805,x806,x801),f55(x803,x804,x805,x806,x802))
% 1.50/1.47 [81]~E(x811,x812)+E(f58(x811,x813,x814,x815),f58(x812,x813,x814,x815))
% 1.50/1.47 [82]~E(x821,x822)+E(f58(x823,x821,x824,x825),f58(x823,x822,x824,x825))
% 1.50/1.47 [83]~E(x831,x832)+E(f58(x833,x834,x831,x835),f58(x833,x834,x832,x835))
% 1.50/1.47 [84]~E(x841,x842)+E(f58(x843,x844,x845,x841),f58(x843,x844,x845,x842))
% 1.50/1.47 [85]~E(x851,x852)+E(f51(x851),f51(x852))
% 1.50/1.47 [86]~E(x861,x862)+E(f87(x861,x863,x864,x865,x866,x867),f87(x862,x863,x864,x865,x866,x867))
% 1.50/1.47 [87]~E(x871,x872)+E(f87(x873,x871,x874,x875,x876,x877),f87(x873,x872,x874,x875,x876,x877))
% 1.50/1.47 [88]~E(x881,x882)+E(f87(x883,x884,x881,x885,x886,x887),f87(x883,x884,x882,x885,x886,x887))
% 1.50/1.47 [89]~E(x891,x892)+E(f87(x893,x894,x895,x891,x896,x897),f87(x893,x894,x895,x892,x896,x897))
% 1.50/1.47 [90]~E(x901,x902)+E(f87(x903,x904,x905,x906,x901,x907),f87(x903,x904,x905,x906,x902,x907))
% 1.50/1.47 [91]~E(x911,x912)+E(f87(x913,x914,x915,x916,x917,x911),f87(x913,x914,x915,x916,x917,x912))
% 1.50/1.47 [92]~E(x921,x922)+E(f50(x921),f50(x922))
% 1.50/1.47 [93]~E(x931,x932)+E(f43(x931,x933,x934,x935),f43(x932,x933,x934,x935))
% 1.50/1.47 [94]~E(x941,x942)+E(f43(x943,x941,x944,x945),f43(x943,x942,x944,x945))
% 1.50/1.47 [95]~E(x951,x952)+E(f43(x953,x954,x951,x955),f43(x953,x954,x952,x955))
% 1.50/1.47 [96]~E(x961,x962)+E(f43(x963,x964,x965,x961),f43(x963,x964,x965,x962))
% 1.50/1.47 [97]~E(x971,x972)+E(f23(x971,x973,x974,x975),f23(x972,x973,x974,x975))
% 1.50/1.47 [98]~E(x981,x982)+E(f23(x983,x981,x984,x985),f23(x983,x982,x984,x985))
% 1.50/1.47 [99]~E(x991,x992)+E(f23(x993,x994,x991,x995),f23(x993,x994,x992,x995))
% 1.50/1.47 [100]~E(x1001,x1002)+E(f23(x1003,x1004,x1005,x1001),f23(x1003,x1004,x1005,x1002))
% 1.50/1.47 [101]~E(x1011,x1012)+E(f62(x1011,x1013),f62(x1012,x1013))
% 1.50/1.47 [102]~E(x1021,x1022)+E(f62(x1023,x1021),f62(x1023,x1022))
% 1.50/1.47 [103]~E(x1031,x1032)+E(f25(x1031),f25(x1032))
% 1.50/1.47 [104]~E(x1041,x1042)+E(f19(x1041,x1043,x1044,x1045,x1046,x1047),f19(x1042,x1043,x1044,x1045,x1046,x1047))
% 1.50/1.47 [105]~E(x1051,x1052)+E(f19(x1053,x1051,x1054,x1055,x1056,x1057),f19(x1053,x1052,x1054,x1055,x1056,x1057))
% 1.50/1.47 [106]~E(x1061,x1062)+E(f19(x1063,x1064,x1061,x1065,x1066,x1067),f19(x1063,x1064,x1062,x1065,x1066,x1067))
% 1.50/1.47 [107]~E(x1071,x1072)+E(f19(x1073,x1074,x1075,x1071,x1076,x1077),f19(x1073,x1074,x1075,x1072,x1076,x1077))
% 1.50/1.47 [108]~E(x1081,x1082)+E(f19(x1083,x1084,x1085,x1086,x1081,x1087),f19(x1083,x1084,x1085,x1086,x1082,x1087))
% 1.50/1.47 [109]~E(x1091,x1092)+E(f19(x1093,x1094,x1095,x1096,x1097,x1091),f19(x1093,x1094,x1095,x1096,x1097,x1092))
% 1.50/1.47 [110]~E(x1101,x1102)+E(f88(x1101,x1103,x1104,x1105,x1106,x1107),f88(x1102,x1103,x1104,x1105,x1106,x1107))
% 1.50/1.47 [111]~E(x1111,x1112)+E(f88(x1113,x1111,x1114,x1115,x1116,x1117),f88(x1113,x1112,x1114,x1115,x1116,x1117))
% 1.50/1.47 [112]~E(x1121,x1122)+E(f88(x1123,x1124,x1121,x1125,x1126,x1127),f88(x1123,x1124,x1122,x1125,x1126,x1127))
% 1.50/1.47 [113]~E(x1131,x1132)+E(f88(x1133,x1134,x1135,x1131,x1136,x1137),f88(x1133,x1134,x1135,x1132,x1136,x1137))
% 1.50/1.47 [114]~E(x1141,x1142)+E(f88(x1143,x1144,x1145,x1146,x1141,x1147),f88(x1143,x1144,x1145,x1146,x1142,x1147))
% 1.50/1.47 [115]~E(x1151,x1152)+E(f88(x1153,x1154,x1155,x1156,x1157,x1151),f88(x1153,x1154,x1155,x1156,x1157,x1152))
% 1.50/1.47 [116]~E(x1161,x1162)+E(f81(x1161,x1163,x1164,x1165),f81(x1162,x1163,x1164,x1165))
% 1.50/1.47 [117]~E(x1171,x1172)+E(f81(x1173,x1171,x1174,x1175),f81(x1173,x1172,x1174,x1175))
% 1.50/1.47 [118]~E(x1181,x1182)+E(f81(x1183,x1184,x1181,x1185),f81(x1183,x1184,x1182,x1185))
% 1.50/1.47 [119]~E(x1191,x1192)+E(f81(x1193,x1194,x1195,x1191),f81(x1193,x1194,x1195,x1192))
% 1.50/1.47 [120]~E(x1201,x1202)+E(f84(x1201,x1203,x1204,x1205,x1206),f84(x1202,x1203,x1204,x1205,x1206))
% 1.50/1.47 [121]~E(x1211,x1212)+E(f84(x1213,x1211,x1214,x1215,x1216),f84(x1213,x1212,x1214,x1215,x1216))
% 1.50/1.47 [122]~E(x1221,x1222)+E(f84(x1223,x1224,x1221,x1225,x1226),f84(x1223,x1224,x1222,x1225,x1226))
% 1.50/1.47 [123]~E(x1231,x1232)+E(f84(x1233,x1234,x1235,x1231,x1236),f84(x1233,x1234,x1235,x1232,x1236))
% 1.50/1.47 [124]~E(x1241,x1242)+E(f84(x1243,x1244,x1245,x1246,x1241),f84(x1243,x1244,x1245,x1246,x1242))
% 1.50/1.47 [125]~E(x1251,x1252)+E(f14(x1251,x1253,x1254),f14(x1252,x1253,x1254))
% 1.50/1.47 [126]~E(x1261,x1262)+E(f14(x1263,x1261,x1264),f14(x1263,x1262,x1264))
% 1.50/1.47 [127]~E(x1271,x1272)+E(f14(x1273,x1274,x1271),f14(x1273,x1274,x1272))
% 1.50/1.47 [128]~E(x1281,x1282)+E(f44(x1281,x1283,x1284),f44(x1282,x1283,x1284))
% 1.50/1.47 [129]~E(x1291,x1292)+E(f44(x1293,x1291,x1294),f44(x1293,x1292,x1294))
% 1.50/1.47 [130]~E(x1301,x1302)+E(f44(x1303,x1304,x1301),f44(x1303,x1304,x1302))
% 1.50/1.47 [131]~E(x1311,x1312)+E(f74(x1311,x1313,x1314,x1315),f74(x1312,x1313,x1314,x1315))
% 1.50/1.47 [132]~E(x1321,x1322)+E(f74(x1323,x1321,x1324,x1325),f74(x1323,x1322,x1324,x1325))
% 1.50/1.47 [133]~E(x1331,x1332)+E(f74(x1333,x1334,x1331,x1335),f74(x1333,x1334,x1332,x1335))
% 1.50/1.47 [134]~E(x1341,x1342)+E(f74(x1343,x1344,x1345,x1341),f74(x1343,x1344,x1345,x1342))
% 1.50/1.47 [135]~E(x1351,x1352)+E(f93(x1351),f93(x1352))
% 1.50/1.47 [136]~E(x1361,x1362)+E(f63(x1361,x1363),f63(x1362,x1363))
% 1.50/1.47 [137]~E(x1371,x1372)+E(f63(x1373,x1371),f63(x1373,x1372))
% 1.50/1.47 [138]~E(x1381,x1382)+E(f59(x1381),f59(x1382))
% 1.50/1.47 [139]~E(x1391,x1392)+E(f76(x1391,x1393,x1394,x1395,x1396),f76(x1392,x1393,x1394,x1395,x1396))
% 1.50/1.47 [140]~E(x1401,x1402)+E(f76(x1403,x1401,x1404,x1405,x1406),f76(x1403,x1402,x1404,x1405,x1406))
% 1.50/1.47 [141]~E(x1411,x1412)+E(f76(x1413,x1414,x1411,x1415,x1416),f76(x1413,x1414,x1412,x1415,x1416))
% 1.50/1.47 [142]~E(x1421,x1422)+E(f76(x1423,x1424,x1425,x1421,x1426),f76(x1423,x1424,x1425,x1422,x1426))
% 1.50/1.47 [143]~E(x1431,x1432)+E(f76(x1433,x1434,x1435,x1436,x1431),f76(x1433,x1434,x1435,x1436,x1432))
% 1.50/1.47 [144]~E(x1441,x1442)+E(f26(x1441,x1443,x1444,x1445),f26(x1442,x1443,x1444,x1445))
% 1.50/1.47 [145]~E(x1451,x1452)+E(f26(x1453,x1451,x1454,x1455),f26(x1453,x1452,x1454,x1455))
% 1.50/1.47 [146]~E(x1461,x1462)+E(f26(x1463,x1464,x1461,x1465),f26(x1463,x1464,x1462,x1465))
% 1.50/1.47 [147]~E(x1471,x1472)+E(f26(x1473,x1474,x1475,x1471),f26(x1473,x1474,x1475,x1472))
% 1.50/1.47 [148]~E(x1481,x1482)+E(f89(x1481,x1483,x1484,x1485),f89(x1482,x1483,x1484,x1485))
% 1.50/1.47 [149]~E(x1491,x1492)+E(f89(x1493,x1491,x1494,x1495),f89(x1493,x1492,x1494,x1495))
% 1.50/1.47 [150]~E(x1501,x1502)+E(f89(x1503,x1504,x1501,x1505),f89(x1503,x1504,x1502,x1505))
% 1.50/1.47 [151]~E(x1511,x1512)+E(f89(x1513,x1514,x1515,x1511),f89(x1513,x1514,x1515,x1512))
% 1.50/1.47 [152]~E(x1521,x1522)+E(f56(x1521),f56(x1522))
% 1.50/1.47 [153]~E(x1531,x1532)+E(f34(x1531,x1533,x1534,x1535),f34(x1532,x1533,x1534,x1535))
% 1.50/1.47 [154]~E(x1541,x1542)+E(f34(x1543,x1541,x1544,x1545),f34(x1543,x1542,x1544,x1545))
% 1.50/1.47 [155]~E(x1551,x1552)+E(f34(x1553,x1554,x1551,x1555),f34(x1553,x1554,x1552,x1555))
% 1.50/1.47 [156]~E(x1561,x1562)+E(f34(x1563,x1564,x1565,x1561),f34(x1563,x1564,x1565,x1562))
% 1.50/1.47 [157]~E(x1571,x1572)+E(f69(x1571,x1573),f69(x1572,x1573))
% 1.50/1.47 [158]~E(x1581,x1582)+E(f69(x1583,x1581),f69(x1583,x1582))
% 1.50/1.47 [159]~E(x1591,x1592)+E(f83(x1591),f83(x1592))
% 1.50/1.47 [160]~E(x1601,x1602)+E(f41(x1601,x1603),f41(x1602,x1603))
% 1.50/1.47 [161]~E(x1611,x1612)+E(f41(x1613,x1611),f41(x1613,x1612))
% 1.50/1.47 [162]~E(x1621,x1622)+E(f49(x1621,x1623),f49(x1622,x1623))
% 1.50/1.47 [163]~E(x1631,x1632)+E(f49(x1633,x1631),f49(x1633,x1632))
% 1.50/1.47 [164]~E(x1641,x1642)+E(f38(x1641,x1643,x1644,x1645),f38(x1642,x1643,x1644,x1645))
% 1.50/1.47 [165]~E(x1651,x1652)+E(f38(x1653,x1651,x1654,x1655),f38(x1653,x1652,x1654,x1655))
% 1.50/1.47 [166]~E(x1661,x1662)+E(f38(x1663,x1664,x1661,x1665),f38(x1663,x1664,x1662,x1665))
% 1.50/1.47 [167]~E(x1671,x1672)+E(f38(x1673,x1674,x1675,x1671),f38(x1673,x1674,x1675,x1672))
% 1.50/1.47 [168]~E(x1681,x1682)+E(f82(x1681,x1683),f82(x1682,x1683))
% 1.50/1.47 [169]~E(x1691,x1692)+E(f82(x1693,x1691),f82(x1693,x1692))
% 1.50/1.47 [170]~E(x1701,x1702)+E(f72(x1701,x1703,x1704,x1705),f72(x1702,x1703,x1704,x1705))
% 1.50/1.47 [171]~E(x1711,x1712)+E(f72(x1713,x1711,x1714,x1715),f72(x1713,x1712,x1714,x1715))
% 1.50/1.47 [172]~E(x1721,x1722)+E(f72(x1723,x1724,x1721,x1725),f72(x1723,x1724,x1722,x1725))
% 1.50/1.47 [173]~E(x1731,x1732)+E(f72(x1733,x1734,x1735,x1731),f72(x1733,x1734,x1735,x1732))
% 1.50/1.47 [174]~E(x1741,x1742)+E(f61(x1741,x1743),f61(x1742,x1743))
% 1.50/1.47 [175]~E(x1751,x1752)+E(f61(x1753,x1751),f61(x1753,x1752))
% 1.50/1.47 [176]~E(x1761,x1762)+E(f53(x1761),f53(x1762))
% 1.50/1.47 [177]~E(x1771,x1772)+E(f73(x1771,x1773,x1774),f73(x1772,x1773,x1774))
% 1.50/1.47 [178]~E(x1781,x1782)+E(f73(x1783,x1781,x1784),f73(x1783,x1782,x1784))
% 1.50/1.47 [179]~E(x1791,x1792)+E(f73(x1793,x1794,x1791),f73(x1793,x1794,x1792))
% 1.50/1.47 [180]~E(x1801,x1802)+E(f78(x1801,x1803),f78(x1802,x1803))
% 1.50/1.47 [181]~E(x1811,x1812)+E(f78(x1813,x1811),f78(x1813,x1812))
% 1.50/1.47 [182]~E(x1821,x1822)+E(f52(x1821,x1823,x1824,x1825),f52(x1822,x1823,x1824,x1825))
% 1.50/1.47 [183]~E(x1831,x1832)+E(f52(x1833,x1831,x1834,x1835),f52(x1833,x1832,x1834,x1835))
% 1.50/1.47 [184]~E(x1841,x1842)+E(f52(x1843,x1844,x1841,x1845),f52(x1843,x1844,x1842,x1845))
% 1.50/1.47 [185]~E(x1851,x1852)+E(f52(x1853,x1854,x1855,x1851),f52(x1853,x1854,x1855,x1852))
% 1.50/1.47 [186]~E(x1861,x1862)+E(f64(x1861,x1863,x1864,x1865),f64(x1862,x1863,x1864,x1865))
% 1.50/1.47 [187]~E(x1871,x1872)+E(f64(x1873,x1871,x1874,x1875),f64(x1873,x1872,x1874,x1875))
% 1.50/1.47 [188]~E(x1881,x1882)+E(f64(x1883,x1884,x1881,x1885),f64(x1883,x1884,x1882,x1885))
% 1.50/1.47 [189]~E(x1891,x1892)+E(f64(x1893,x1894,x1895,x1891),f64(x1893,x1894,x1895,x1892))
% 1.50/1.47 [190]~E(x1901,x1902)+E(f80(x1901,x1903,x1904,x1905),f80(x1902,x1903,x1904,x1905))
% 1.50/1.47 [191]~E(x1911,x1912)+E(f80(x1913,x1911,x1914,x1915),f80(x1913,x1912,x1914,x1915))
% 1.50/1.47 [192]~E(x1921,x1922)+E(f80(x1923,x1924,x1921,x1925),f80(x1923,x1924,x1922,x1925))
% 1.50/1.47 [193]~E(x1931,x1932)+E(f80(x1933,x1934,x1935,x1931),f80(x1933,x1934,x1935,x1932))
% 1.50/1.47 [194]~E(x1941,x1942)+E(f65(x1941),f65(x1942))
% 1.50/1.47 [195]~E(x1951,x1952)+E(f70(x1951,x1953),f70(x1952,x1953))
% 1.50/1.47 [196]~E(x1961,x1962)+E(f70(x1963,x1961),f70(x1963,x1962))
% 1.50/1.47 [197]~E(x1971,x1972)+E(f57(x1971,x1973),f57(x1972,x1973))
% 1.50/1.47 [198]~E(x1981,x1982)+E(f57(x1983,x1981),f57(x1983,x1982))
% 1.50/1.47 [199]~E(x1991,x1992)+E(f75(x1991,x1993,x1994,x1995,x1996),f75(x1992,x1993,x1994,x1995,x1996))
% 1.50/1.47 [200]~E(x2001,x2002)+E(f75(x2003,x2001,x2004,x2005,x2006),f75(x2003,x2002,x2004,x2005,x2006))
% 1.50/1.47 [201]~E(x2011,x2012)+E(f75(x2013,x2014,x2011,x2015,x2016),f75(x2013,x2014,x2012,x2015,x2016))
% 1.50/1.47 [202]~E(x2021,x2022)+E(f75(x2023,x2024,x2025,x2021,x2026),f75(x2023,x2024,x2025,x2022,x2026))
% 1.50/1.47 [203]~E(x2031,x2032)+E(f75(x2033,x2034,x2035,x2036,x2031),f75(x2033,x2034,x2035,x2036,x2032))
% 1.50/1.47 [204]~E(x2041,x2042)+E(f71(x2041,x2043),f71(x2042,x2043))
% 1.50/1.47 [205]~E(x2051,x2052)+E(f71(x2053,x2051),f71(x2053,x2052))
% 1.50/1.47 [206]~E(x2061,x2062)+E(f79(x2061),f79(x2062))
% 1.50/1.47 [207]~E(x2071,x2072)+E(f66(x2071,x2073),f66(x2072,x2073))
% 1.50/1.47 [208]~E(x2081,x2082)+E(f66(x2083,x2081),f66(x2083,x2082))
% 1.50/1.47 [209]~P1(x2091)+P1(x2092)+~E(x2091,x2092)
% 1.50/1.47 [210]~P2(x2101)+P2(x2102)+~E(x2101,x2102)
% 1.50/1.47 [211]~P4(x2111)+P4(x2112)+~E(x2111,x2112)
% 1.50/1.47 [212]~P5(x2121)+P5(x2122)+~E(x2121,x2122)
% 1.50/1.47 [213]~P21(x2131)+P21(x2132)+~E(x2131,x2132)
% 1.50/1.47 [214]~P35(x2141)+P35(x2142)+~E(x2141,x2142)
% 1.50/1.47 [215]~P22(x2151)+P22(x2152)+~E(x2151,x2152)
% 1.50/1.47 [216]~P34(x2161)+P34(x2162)+~E(x2161,x2162)
% 1.50/1.47 [217]~P28(x2171)+P28(x2172)+~E(x2171,x2172)
% 1.50/1.47 [218]~P23(x2181)+P23(x2182)+~E(x2181,x2182)
% 1.50/1.47 [219]~P27(x2191)+P27(x2192)+~E(x2191,x2192)
% 1.50/1.47 [220]P8(x2202,x2203)+~E(x2201,x2202)+~P8(x2201,x2203)
% 1.50/1.47 [221]P8(x2213,x2212)+~E(x2211,x2212)+~P8(x2213,x2211)
% 1.50/1.47 [222]~P6(x2221)+P6(x2222)+~E(x2221,x2222)
% 1.50/1.47 [223]~P13(x2231)+P13(x2232)+~E(x2231,x2232)
% 1.50/1.47 [224]~P14(x2241)+P14(x2242)+~E(x2241,x2242)
% 1.50/1.47 [225]~P15(x2251)+P15(x2252)+~E(x2251,x2252)
% 1.50/1.47 [226]~P19(x2261)+P19(x2262)+~E(x2261,x2262)
% 1.50/1.47 [227]~P20(x2271)+P20(x2272)+~E(x2271,x2272)
% 1.50/1.47 [228]~P7(x2281)+P7(x2282)+~E(x2281,x2282)
% 1.50/1.47 [229]P9(x2292,x2293,x2294,x2295)+~E(x2291,x2292)+~P9(x2291,x2293,x2294,x2295)
% 1.50/1.47 [230]P9(x2303,x2302,x2304,x2305)+~E(x2301,x2302)+~P9(x2303,x2301,x2304,x2305)
% 1.50/1.47 [231]P9(x2313,x2314,x2312,x2315)+~E(x2311,x2312)+~P9(x2313,x2314,x2311,x2315)
% 1.50/1.47 [232]P9(x2323,x2324,x2325,x2322)+~E(x2321,x2322)+~P9(x2323,x2324,x2325,x2321)
% 1.50/1.47 [233]~P24(x2331)+P24(x2332)+~E(x2331,x2332)
% 1.50/1.47 [234]~P31(x2341)+P31(x2342)+~E(x2341,x2342)
% 1.50/1.47 [235]~P16(x2351)+P16(x2352)+~E(x2351,x2352)
% 1.50/1.47 [236]~P17(x2361)+P17(x2362)+~E(x2361,x2362)
% 1.50/1.47 [237]~P25(x2371)+P25(x2372)+~E(x2371,x2372)
% 1.50/1.47 [238]~P29(x2381)+P29(x2382)+~E(x2381,x2382)
% 1.50/1.47 [239]~P33(x2391)+P33(x2392)+~E(x2391,x2392)
% 1.50/1.47 [240]~P18(x2401)+P18(x2402)+~E(x2401,x2402)
% 1.50/1.47 [241]P3(x2412,x2413)+~E(x2411,x2412)+~P3(x2411,x2413)
% 1.50/1.47 [242]P3(x2423,x2422)+~E(x2421,x2422)+~P3(x2423,x2421)
% 1.50/1.47 [243]~P26(x2431)+P26(x2432)+~E(x2431,x2432)
% 1.50/1.47 [244]~P30(x2441)+P30(x2442)+~E(x2441,x2442)
% 1.50/1.47 [245]~P32(x2451)+P32(x2452)+~E(x2451,x2452)
% 1.50/1.47 [246]P10(x2462,x2463,x2464,x2465,x2466)+~E(x2461,x2462)+~P10(x2461,x2463,x2464,x2465,x2466)
% 1.50/1.47 [247]P10(x2473,x2472,x2474,x2475,x2476)+~E(x2471,x2472)+~P10(x2473,x2471,x2474,x2475,x2476)
% 1.50/1.47 [248]P10(x2483,x2484,x2482,x2485,x2486)+~E(x2481,x2482)+~P10(x2483,x2484,x2481,x2485,x2486)
% 1.50/1.47 [249]P10(x2493,x2494,x2495,x2492,x2496)+~E(x2491,x2492)+~P10(x2493,x2494,x2495,x2491,x2496)
% 1.50/1.47 [250]P10(x2503,x2504,x2505,x2506,x2502)+~E(x2501,x2502)+~P10(x2503,x2504,x2505,x2506,x2501)
% 1.50/1.47 [251]P12(x2512,x2513,x2514,x2515,x2516,x2517)+~E(x2511,x2512)+~P12(x2511,x2513,x2514,x2515,x2516,x2517)
% 1.50/1.47 [252]P12(x2523,x2522,x2524,x2525,x2526,x2527)+~E(x2521,x2522)+~P12(x2523,x2521,x2524,x2525,x2526,x2527)
% 1.50/1.47 [253]P12(x2533,x2534,x2532,x2535,x2536,x2537)+~E(x2531,x2532)+~P12(x2533,x2534,x2531,x2535,x2536,x2537)
% 1.50/1.47 [254]P12(x2543,x2544,x2545,x2542,x2546,x2547)+~E(x2541,x2542)+~P12(x2543,x2544,x2545,x2541,x2546,x2547)
% 1.50/1.47 [255]P12(x2553,x2554,x2555,x2556,x2552,x2557)+~E(x2551,x2552)+~P12(x2553,x2554,x2555,x2556,x2551,x2557)
% 1.50/1.47 [256]P12(x2563,x2564,x2565,x2566,x2567,x2562)+~E(x2561,x2562)+~P12(x2563,x2564,x2565,x2566,x2567,x2561)
% 1.50/1.47 [257]P11(x2572,x2573,x2574,x2575,x2576,x2577)+~E(x2571,x2572)+~P11(x2571,x2573,x2574,x2575,x2576,x2577)
% 1.50/1.47 [258]P11(x2583,x2582,x2584,x2585,x2586,x2587)+~E(x2581,x2582)+~P11(x2583,x2581,x2584,x2585,x2586,x2587)
% 1.50/1.47 [259]P11(x2593,x2594,x2592,x2595,x2596,x2597)+~E(x2591,x2592)+~P11(x2593,x2594,x2591,x2595,x2596,x2597)
% 1.50/1.47 [260]P11(x2603,x2604,x2605,x2602,x2606,x2607)+~E(x2601,x2602)+~P11(x2603,x2604,x2605,x2601,x2606,x2607)
% 1.50/1.47 [261]P11(x2613,x2614,x2615,x2616,x2612,x2617)+~E(x2611,x2612)+~P11(x2613,x2614,x2615,x2616,x2611,x2617)
% 1.50/1.47 [262]P11(x2623,x2624,x2625,x2626,x2627,x2622)+~E(x2621,x2622)+~P11(x2623,x2624,x2625,x2626,x2627,x2621)
% 1.50/1.47
% 1.50/1.47 %-------------------------------------------
% 1.50/1.48 cnf(1097,plain,
% 1.50/1.48 (~P34(f28(f28(f30(a2),f28(f28(f20(a2),x10971),x10972)),x10972))),
% 1.50/1.48 inference(rename_variables,[],[389])).
% 1.50/1.48 cnf(1100,plain,
% 1.50/1.48 (~P34(f28(f28(f30(a2),x11001),x11001))),
% 1.50/1.48 inference(rename_variables,[],[384])).
% 1.50/1.48 cnf(1107,plain,
% 1.50/1.48 (P34(f28(f28(f30(a2),x11071),f28(a22,x11071)))),
% 1.50/1.48 inference(rename_variables,[],[310])).
% 1.50/1.48 cnf(1112,plain,
% 1.50/1.48 (~P34(f28(f28(f30(a2),f28(f28(f20(a2),x11121),x11122)),x11122))),
% 1.50/1.48 inference(rename_variables,[],[389])).
% 1.50/1.48 cnf(1115,plain,
% 1.50/1.48 (~P34(f28(f29(a2,f28(a22,x11151)),x11151))),
% 1.50/1.48 inference(rename_variables,[],[388])).
% 1.50/1.48 cnf(1129,plain,
% 1.50/1.48 (P34(f28(f29(a2,x11291),x11291))),
% 1.50/1.48 inference(rename_variables,[],[302])).
% 1.50/1.48 cnf(1132,plain,
% 1.50/1.48 (P34(f28(f29(a2,x11321),f28(f28(f20(a2),x11322),x11321)))),
% 1.50/1.48 inference(rename_variables,[],[324])).
% 1.50/1.48 cnf(1135,plain,
% 1.50/1.48 (P34(f28(f29(a2,x11351),f28(f28(f20(a2),x11352),x11351)))),
% 1.50/1.48 inference(rename_variables,[],[324])).
% 1.50/1.48 cnf(1140,plain,
% 1.50/1.48 (~P34(f28(f28(f30(a2),f28(f28(f20(a2),x11401),x11402)),x11402))),
% 1.50/1.48 inference(rename_variables,[],[389])).
% 1.50/1.48 cnf(1146,plain,
% 1.50/1.48 (P34(f28(f28(f30(a2),x11461),f28(a22,x11461)))),
% 1.50/1.48 inference(rename_variables,[],[310])).
% 1.50/1.48 cnf(1149,plain,
% 1.50/1.48 (P34(f28(f29(a2,x11491),f28(f28(f20(a2),x11492),x11491)))),
% 1.50/1.48 inference(rename_variables,[],[324])).
% 1.50/1.48 cnf(1154,plain,
% 1.50/1.48 (~P34(f28(f29(a2,f28(a22,x11541)),x11541))),
% 1.50/1.48 inference(rename_variables,[],[388])).
% 1.50/1.48 cnf(1157,plain,
% 1.50/1.48 (~P34(f28(f29(a2,f28(a22,x11571)),x11571))),
% 1.50/1.48 inference(rename_variables,[],[388])).
% 1.50/1.48 cnf(1165,plain,
% 1.50/1.48 (P34(f28(f29(a2,x11651),x11651))),
% 1.50/1.48 inference(rename_variables,[],[302])).
% 1.50/1.48 cnf(1206,plain,
% 1.50/1.48 (~P34(f28(f28(f30(a2),x12061),x12061))),
% 1.50/1.48 inference(rename_variables,[],[384])).
% 1.50/1.48 cnf(1209,plain,
% 1.50/1.48 (P34(f28(f28(f30(a2),x12091),f28(a22,x12091)))),
% 1.50/1.48 inference(rename_variables,[],[310])).
% 1.50/1.48 cnf(1215,plain,
% 1.50/1.48 (P34(f28(f29(f94(x12151,a3),x12152),f36(x12151,x12153,x12152)))),
% 1.50/1.48 inference(rename_variables,[],[337])).
% 1.50/1.48 cnf(1218,plain,
% 1.50/1.48 (P34(f28(f29(f94(x12181,a3),x12182),f36(x12181,x12183,x12182)))),
% 1.50/1.48 inference(rename_variables,[],[337])).
% 1.50/1.48 cnf(1233,plain,
% 1.50/1.48 (P34(f28(f29(f94(x12331,a3),x12332),x12332))),
% 1.50/1.48 inference(rename_variables,[],[315])).
% 1.50/1.48 cnf(1239,plain,
% 1.50/1.48 (E(f37(x12391,x12391,f6(x12391),x12392),x12392)),
% 1.50/1.48 inference(rename_variables,[],[323])).
% 1.50/1.48 cnf(1244,plain,
% 1.50/1.48 (P34(f28(f29(f94(x12441,a3),x12442),x12442))),
% 1.50/1.48 inference(rename_variables,[],[315])).
% 1.50/1.48 cnf(1258,plain,
% 1.50/1.48 (E(f27(a2,x12581),x12581)),
% 1.50/1.48 inference(rename_variables,[],[291])).
% 1.50/1.48 cnf(1262,plain,
% 1.50/1.48 (~E(f28(a22,x12621),x12621)),
% 1.50/1.48 inference(rename_variables,[],[376])).
% 1.50/1.48 cnf(1294,plain,
% 1.50/1.48 (~P34(f28(f28(f30(a2),x12941),x12941))),
% 1.50/1.48 inference(rename_variables,[],[384])).
% 1.50/1.48 cnf(1305,plain,
% 1.50/1.48 ($false),
% 1.50/1.48 inference(scs_inference,[],[267,272,273,276,277,281,372,374,329,298,290,345,333,332,331,392,354,341,366,368,322,291,1258,376,1262,308,382,323,1239,302,1129,1165,315,1233,1244,384,1100,1206,1294,388,1115,1154,1157,337,1215,1218,310,1107,1146,1209,387,300,301,318,327,324,1132,1135,1149,389,1097,1112,1140,360,342,2,397,1088,476,463,454,847,846,503,474,460,441,405,560,469,783,752,750,738,737,668,659,657,639,638,637,635,633,628,627,611,609,584,579,564,540,537,535,513,477,475,585,506,826,530,453,898,885,880,850,838,832,804,793,714,675,920,795,782,857,873,840,829,877,944,960,874,988,248,232,230,229,221,217,216,3,443,502,501,456,433,431,851,774,592,484,483,682,848,593,671,624,573,559]),
% 1.50/1.48 ['proof']).
% 1.50/1.48 % SZS output end Proof
% 1.50/1.48 % Total time :0.250000s
%------------------------------------------------------------------------------