TSTP Solution File: SWW194+1 by Bliksem---1.12

%------------------------------------------------------------------------------
% File     : Bliksem---1.12
% Problem  : SWW194+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : bliksem %s

% Computer : n025.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 0s
% DateTime : Wed Jul 20 23:21:10 EDT 2022

% Result   : Timeout 300.04s 300.50s
% Output   : None 
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SWW194+1 : TPTP v8.1.0. Released v5.2.0.
% 0.03/0.13  % Command  : bliksem %s
% 0.12/0.34  % Computer : n025.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % DateTime : Sat Jun  4 07:35:46 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.97/1.59  *** allocated 10000 integers for termspace/termends
% 0.97/1.59  *** allocated 10000 integers for clauses
% 0.97/1.59  *** allocated 10000 integers for justifications
% 0.97/1.59  *** allocated 15000 integers for termspace/termends
% 0.97/1.59  *** allocated 22500 integers for termspace/termends
% 0.97/1.59  *** allocated 33750 integers for termspace/termends
% 0.97/1.59  Bliksem 1.12
% 0.97/1.59  
% 0.97/1.59  
% 0.97/1.59  Automatic Strategy Selection
% 0.97/1.59  
% 0.97/1.59  *** allocated 50625 integers for termspace/termends
% 0.97/1.59  *** allocated 75937 integers for termspace/termends
% 0.97/1.59  *** allocated 113905 integers for termspace/termends
% 0.97/1.59  
% 0.97/1.59  Clauses:
% 0.97/1.59  
% 0.97/1.59  { ! hAPP( Y, skol1( X, Y ) ) = hAPP( X, skol1( X, Y ) ), Y = X }.
% 0.97/1.59  { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, 
% 0.97/1.59    c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0( 
% 0.97/1.59    c_Int_OBit1( c_Int_OPls ) ) ) ), v_x____ ) ), c_Groups_Oone__class_Oone( 
% 0.97/1.59    tc_RealDef_Oreal ) ) }.
% 0.97/1.59  { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, 
% 0.97/1.59    c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0( 
% 0.97/1.59    c_Int_OBit1( c_Int_OPls ) ) ) ), v_y____ ) ), c_Groups_Oone__class_Oone( 
% 0.97/1.59    tc_RealDef_Oreal ) ) }.
% 0.97/1.59  { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0( 
% 0.97/1.59    c_Int_OBit1( c_Int_OPls ) ) ) ), v_x____ ), c_Groups_Oone__class_Oone( 
% 0.97/1.59    tc_RealDef_Oreal ) ) }.
% 0.97/1.59  { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0( 
% 0.97/1.59    c_Int_OBit1( c_Int_OPls ) ) ) ), v_y____ ), c_Groups_Oone__class_Oone( 
% 0.97/1.59    tc_RealDef_Oreal ) ) }.
% 0.97/1.59  { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, 
% 0.97/1.59    c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( tc_RealDef_Oreal ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0( 
% 0.97/1.59    c_Int_OBit1( c_Int_OPls ) ) ) ), X ) ) }.
% 0.97/1.59  { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0( 
% 0.97/1.59    c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ), hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( tc_RealDef_Oreal ), X ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( 
% 0.97/1.59    c_Int_OPls ) ) ) ) ) = hAPP( hAPP( c_Power_Opower__class_Opower( 
% 0.97/1.59    tc_RealDef_Oreal ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( 
% 0.97/1.59    tc_RealDef_Oreal ), c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, 
% 0.97/1.59    c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ), X ) ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( 
% 0.97/1.59    c_Int_OPls ) ) ) ) }.
% 0.97/1.59  { ! class_Groups_Omonoid__mult( X ), ! class_Int_Onumber( X ), hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( X ), c_Int_Onumber__class_Onumber__of( X, Y
% 0.97/1.59     ) ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( 
% 0.97/1.59    c_Int_OBit1( c_Int_OPls ) ) ) ) = hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X, 
% 0.97/1.59    Y ) ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.97/1.59  { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, hAPP
% 0.97/1.59    ( hAPP( c_Power_Opower__class_Opower( X ), Y ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( 
% 0.97/1.59    c_Int_OPls ) ) ) ) ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y )
% 0.97/1.59    , c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1
% 0.97/1.59    ( c_Int_OPls ) ) ) ) }.
% 0.97/1.59  { ! class_Rings_Olinordered__idom( X ), hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( X ), c_Groups_Oabs__class_Oabs( X, Y ) ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( 
% 0.97/1.59    c_Int_OPls ) ) ) ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( 
% 0.97/1.59    c_Int_OPls ) ) ) ) }.
% 0.97/1.59  { ! class_Rings_Osemiring__1( X ), hAPP( hAPP( c_Power_Opower__class_Opower
% 0.97/1.59    ( X ), c_Groups_Oone__class_Oone( X ) ), c_Int_Onumber__class_Onumber__of
% 0.97/1.59    ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) = 
% 0.97/1.59    c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.59  { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( X ), Y ), c_Int_Onumber__class_Onumber__of
% 0.97/1.59    ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) }.
% 0.97/1.59  { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( X ), Y ), c_Int_Onumber__class_Onumber__of
% 0.97/1.59    ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) = hAPP( hAPP
% 0.97/1.59    ( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.97/1.59  { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( X ), Z ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( 
% 0.97/1.59    c_Int_OPls ) ) ) ), Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.97/1.59     ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ), hAPP( hAPP
% 0.97/1.59    ( c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.97/1.59  { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OMin ), hAPP( 
% 0.97/1.59    hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0( 
% 0.97/1.59    c_Int_OBit1( c_Int_OPls ) ) ) ), v_x____ ) ) }.
% 0.97/1.59  { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( X ), Y ), c_Int_Onumber__class_Onumber__of
% 0.97/1.59    ( tc_Nat_Onat, c_Int_OBit1( c_Int_OBit1( c_Int_OPls ) ) ) ) = hAPP( hAPP
% 0.97/1.59    ( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ), Y ) }.
% 0.97/1.59  { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OMin ), hAPP( 
% 0.97/1.59    hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0( 
% 0.97/1.59    c_Int_OBit1( c_Int_OPls ) ) ) ), v_y____ ) ) }.
% 0.97/1.59  { ! c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OPls ) = 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OMin ) }.
% 0.97/1.59  { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( X ), hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) = hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) }.
% 0.97/1.59  { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone( 
% 0.97/1.59    tc_Nat_Onat ) ) = Y }.
% 0.97/1.59  { c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit1( c_Int_OPls )
% 0.97/1.59     ) = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.97/1.59  { c_Groups_Oone__class_Oone( tc_Nat_Onat ) = 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit1( c_Int_OPls )
% 0.97/1.59     ) }.
% 0.97/1.59  { ! class_Int_Onumber__ring( X ), hAPP( hAPP( c_Power_Opower__class_Opower
% 0.97/1.59    ( X ), c_Int_Onumber__class_Onumber__of( X, c_Int_OMin ) ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( 
% 0.97/1.59    c_Int_OPls ) ) ) ), Y ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.59  { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.59  { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), U ), T ) ), Y ) ) }.
% 0.97/1.59  { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), U ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 0.97/1.59  { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Z ) }.
% 0.97/1.59  { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.59  { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 0.97/1.59  { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.59  { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 0.97/1.59  { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ), Y = X }.
% 0.97/1.59  { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Z ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, Z ) }.
% 0.97/1.59  { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ) }.
% 0.97/1.59  { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, X ) }.
% 0.97/1.59  { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP
% 0.97/1.59    ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), Y ) ), X ) = 
% 0.97/1.59    hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), hAPP
% 0.97/1.59    ( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.97/1.59  { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) =
% 0.97/1.59     hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y )
% 0.97/1.59     }.
% 0.97/1.59  { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( X ), Z ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( 
% 0.97/1.59    c_Int_OPls ) ) ) ), Y ) ) = hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.97/1.59    , hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( 
% 0.97/1.59    c_Int_OPls ) ) ) ) }.
% 0.97/1.59  { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.97/1.59     = Y }.
% 0.97/1.59  { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.97/1.59     = Y }.
% 0.97/1.59  { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( X ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.97/1.59  { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), 
% 0.97/1.59    c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) = X }.
% 0.97/1.59  { ! class_Int_Onumber__ring( X ), c_Groups_Oone__class_Oone( X ) = 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( X, c_Int_OBit1( c_Int_OPls ) ) }.
% 0.97/1.59  { c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( tc_RealDef_Oreal ), v_x____ ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( 
% 0.97/1.59    c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower( 
% 0.97/1.59    tc_RealDef_Oreal ), v_y____ ), c_Int_Onumber__class_Onumber__of( 
% 0.97/1.59    tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) = 
% 0.97/1.59    c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.97/1.59  { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), 
% 0.97/1.59    c_Groups_Oabs__class_Oabs( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.97/1.59     ), c_Int_Onumber__class_Onumber__of( X, c_Int_OMin ) ), Y ) ) = 
% 0.97/1.59    c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.59  { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 0.97/1.59    , Y ), c_Groups_Oone__class_Oone( X ) ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, c_Int_OBit1( 
% 0.97/1.59    c_Int_OPls ) ) }.
% 0.97/1.59  { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, c_Int_OBit1( 
% 0.97/1.59    c_Int_OPls ) ), c_Orderings_Oord__class_Oless__eq( X, 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( X, Y ), c_Groups_Oone__class_Oone( X )
% 0.97/1.59     ) }.
% 0.97/1.59  { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( X, Y ) ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( c_Int_OPls )
% 0.97/1.59    , Y ) }.
% 0.97/1.59  { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( c_Int_OPls )
% 0.97/1.59    , Y ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X
% 0.97/1.59     ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.97/1.59  { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), 
% 0.97/1.59    c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt( X ) ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( 
% 0.97/1.59    c_Int_OPls ) ) ) ) = X }.
% 0.97/1.59  { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), 
% 0.97/1.59    c_Groups_Oabs__class_Oabs( X, c_Int_Onumber__class_Onumber__of( X, 
% 0.97/1.59    c_Int_OMin ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.59  { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X, 
% 0.97/1.59    c_Int_OBit1( c_Int_OPls ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.59  { ! class_Int_Onumber__ring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.59    ( X ), c_Int_Onumber__class_Onumber__of( X, c_Int_OBit1( c_Int_OPls ) ) )
% 0.97/1.59    , Y ) = Y }.
% 0.97/1.59  { ! class_Int_Onumber__ring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.59    ( X ), Y ), c_Int_Onumber__class_Onumber__of( X, c_Int_OBit1( c_Int_OPls
% 0.97/1.59     ) ) ) = Y }.
% 0.97/1.59  { ! class_Rings_Olinordered__semidom( X ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), T )
% 0.97/1.59    , c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.97/1.59  { ! class_Rings_Olinordered__semidom( X ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 0.97/1.59    , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), 
% 0.97/1.59    hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.97/1.59  { v_z = c_Complex_Ocomplex_OComplex( v_x____, v_y____ ) }.
% 0.97/1.59  { c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_z ) = 
% 0.97/1.59    c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.97/1.59  { c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) = X }.
% 0.97/1.59  { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X, 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ) = 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( X, c_Int_Onumber__class_Onumber__of( X, Z )
% 0.97/1.59    , c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.97/1.59  { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.97/1.59    , Y ) = c_Groups_Oplus__class_Oplus( X, Y, Z ) }.
% 0.97/1.59  { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.97/1.59    , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.97/1.59    ( X, Z, c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.97/1.59  { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.97/1.59    , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.97/1.59    ( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) }.
% 0.97/1.59  { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X, 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( X, Z ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( X, Y ) ) = 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( X, c_Groups_Oplus__class_Oplus( 
% 0.97/1.59    tc_Int_Oint, Z, Y ) ) }.
% 0.97/1.59  { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ) ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) = 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Int_Oint, hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.97/1.59  { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 0.97/1.59  { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) }.
% 0.97/1.59  { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X, 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( X, T ), c_Groups_Oplus__class_Oplus( X
% 0.97/1.59    , c_Int_Onumber__class_Onumber__of( X, Z ), Y ) ) = 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( X, c_Int_Onumber__class_Onumber__of( X, 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( tc_Int_Oint, T, Z ) ), Y ) }.
% 0.97/1.59  { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.97/1.59    ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.97/1.59  { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.97/1.59    ( X, c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 0.97/1.59  { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.97/1.59    , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X
% 0.97/1.59    , U, Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.97/1.59  { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ), Y = X }.
% 0.97/1.59  { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Z ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, Z ) }.
% 0.97/1.59  { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ) }.
% 0.97/1.59  { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, X ) }.
% 0.97/1.59  { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( Y ), 
% 0.97/1.59    c_Int_OBit1( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 0.97/1.59     ) }.
% 0.97/1.59  { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( Y ), 
% 0.97/1.59    c_Int_OBit1( X ) ) }.
% 0.97/1.59  { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( Y ), 
% 0.97/1.59    c_Int_OBit1( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 0.97/1.59     ) }.
% 0.97/1.59  { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( Y ), 
% 0.97/1.59    c_Int_OBit1( X ) ) }.
% 0.97/1.59  { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, c_Int_OPls )
% 0.97/1.59     }.
% 0.97/1.59  { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( Y ), 
% 0.97/1.59    c_Int_OBit0( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 0.97/1.59     ) }.
% 0.97/1.59  { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( Y ), 
% 0.97/1.59    c_Int_OBit0( X ) ) }.
% 0.97/1.59  { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( Y ), 
% 0.97/1.59    c_Int_OBit0( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 0.97/1.59     ) }.
% 0.97/1.59  { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( Y ), 
% 0.97/1.59    c_Int_OBit0( X ) ) }.
% 0.97/1.59  { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OMin, c_Int_OMin )
% 0.97/1.59     }.
% 0.97/1.59  { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, c_Int_OPls ) }.
% 0.97/1.59  { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) }.
% 0.97/1.59  { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, c_Int_OPls ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) }.
% 0.97/1.59  { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X, 
% 0.97/1.59    Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.59  { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.59    ( X ), U = T, Z = Y, ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) = 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.59    ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.97/1.59     ) }.
% 0.97/1.59  { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.59    ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) = 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.59    ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.97/1.59     ), ! U = T }.
% 0.97/1.59  { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.59    ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) = 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.59    ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.97/1.59     ), ! Z = Y }.
% 0.97/1.59  { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.97/1.59     ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.59  { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, 
% 0.97/1.59    hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Y
% 0.97/1.59     ) ), Z ) }.
% 0.97/1.59  { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.59    ( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.59    ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.97/1.59     ), U = Z, T = Y }.
% 0.97/1.59  { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.59    ( X ), ! U = Z, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.59    ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.97/1.59     ) }.
% 0.97/1.59  { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.59    ( X ), ! T = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.59    ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.97/1.59     ) }.
% 0.97/1.59  { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ), 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, X ) ) }.
% 0.97/1.59  { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ) ), X ) = 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.97/1.59  { ! class_Int_Onumber( X ), ! class_Rings_Osemiring( X ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X, 
% 0.97/1.59    T ) ), c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.59    ( X ), c_Int_Onumber__class_Onumber__of( X, T ) ), Z ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X, 
% 0.97/1.59    T ) ), Y ) ) }.
% 0.97/1.59  { ! class_Int_Onumber( X ), ! class_Rings_Osemiring( X ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.97/1.59     ) ), c_Int_Onumber__class_Onumber__of( X, Y ) ) = 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.59    ( X ), T ), c_Int_Onumber__class_Onumber__of( X, Y ) ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), Z ), c_Int_Onumber__class_Onumber__of
% 0.97/1.59    ( X, Y ) ) ) }.
% 0.97/1.59  { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X, Y, 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( X, c_Int_OPls ) ) = Y }.
% 0.97/1.59  { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X, 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( X, c_Int_OPls ), Y ) = Y }.
% 0.97/1.59  { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, c_Int_OBit1
% 0.97/1.59    ( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, X )
% 0.97/1.59     }.
% 0.97/1.59  { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, X ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, c_Int_OBit1( 
% 0.97/1.59    X ) ) }.
% 0.97/1.59  { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( Y ), 
% 0.97/1.59    c_Int_OBit1( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 0.97/1.59     ) }.
% 0.97/1.59  { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( Y ), 
% 0.97/1.59    c_Int_OBit1( X ) ) }.
% 0.97/1.59  { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( Y ), 
% 0.97/1.59    c_Int_OBit1( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 0.97/1.59     ) }.
% 0.97/1.59  { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( Y ), 
% 0.97/1.59    c_Int_OBit1( X ) ) }.
% 0.97/1.59  { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, c_Int_OBit0
% 0.97/1.59    ( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, X )
% 0.97/1.59     }.
% 0.97/1.59  { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, X ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, c_Int_OBit0( 
% 0.97/1.59    X ) ) }.
% 0.97/1.59  { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( X ), 
% 0.97/1.59    c_Int_OPls ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, 
% 0.97/1.59    c_Int_OPls ) }.
% 0.97/1.59  { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, c_Int_OPls ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( X ), 
% 0.97/1.59    c_Int_OPls ) }.
% 0.97/1.59  { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( X ), 
% 0.97/1.59    c_Int_OMin ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, 
% 0.97/1.59    c_Int_OMin ) }.
% 0.97/1.59  { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, c_Int_OMin ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( X ), 
% 0.97/1.59    c_Int_OMin ) }.
% 0.97/1.59  { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OMin, c_Int_OBit1
% 0.97/1.59    ( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OMin, X )
% 0.97/1.59     }.
% 0.97/1.59  { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OMin, X ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OMin, c_Int_OBit1( 
% 0.97/1.59    X ) ) }.
% 0.97/1.59  { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, c_Int_OMin
% 0.97/1.59     ) }.
% 0.97/1.59  { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OMin, c_Int_OPls )
% 0.97/1.59     }.
% 0.97/1.59  { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( X ), 
% 0.97/1.59    c_Int_OMin ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, 
% 0.97/1.59    c_Int_OMin ) }.
% 0.97/1.59  { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, c_Int_OMin ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( X ), 
% 0.97/1.59    c_Int_OMin ) }.
% 0.97/1.59  { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X, 
% 0.97/1.59    c_Groups_Oone__class_Oone( X ), c_Int_Onumber__class_Onumber__of( X, Y )
% 0.97/1.59     ) = c_Int_Onumber__class_Onumber__of( X, c_Groups_Oplus__class_Oplus( 
% 0.97/1.59    tc_Int_Oint, c_Int_OBit1( c_Int_OPls ), Y ) ) }.
% 0.97/1.59  { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X, 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( X, Y ), c_Groups_Oone__class_Oone( X )
% 0.97/1.59     ) = c_Int_Onumber__class_Onumber__of( X, c_Groups_Oplus__class_Oplus( 
% 0.97/1.59    tc_Int_Oint, Y, c_Int_OBit1( c_Int_OPls ) ) ) }.
% 0.97/1.59  { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X, 
% 0.97/1.59    c_Int_OBit1( Y ) ) = c_Groups_Oplus__class_Oplus( X, 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( X, Y ) ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.97/1.59  { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.97/1.59    , Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ), 
% 0.97/1.59    c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.97/1.59  { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.97/1.59    , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP
% 0.97/1.59    ( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y, 
% 0.97/1.59    c_Groups_Oone__class_Oone( X ) ) ), Z ) }.
% 0.97/1.59  { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, 
% 0.97/1.59    hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = hAPP( 
% 0.97/1.59    hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X
% 0.97/1.59    , Z, c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.97/1.59  { ! class_Int_Onumber__ring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.59    ( X ), c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ), 
% 0.97/1.59    c_Groups_Oone__class_Oone( X ) ) ), c_Int_Onumber__class_Onumber__of( X, 
% 0.97/1.59    Y ) ) = c_Int_Onumber__class_Onumber__of( X, c_Int_OBit0( Y ) ) }.
% 0.97/1.59  { ! class_Int_Onumber( X ), ! c_Int_Onumber__class_Onumber__of( X, Z ) = Y
% 0.97/1.59    , Y = c_Int_Onumber__class_Onumber__of( X, Z ) }.
% 0.97/1.59  { ! class_Int_Onumber( X ), ! Y = c_Int_Onumber__class_Onumber__of( X, Z )
% 0.97/1.59    , c_Int_Onumber__class_Onumber__of( X, Z ) = Y }.
% 0.97/1.59  { ! class_Int_Onumber__ring( X ), ! class_Int_Oring__char__0( X ), ! 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( X, Z ) = 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( X, Y ), Z = Y }.
% 0.97/1.59  { ! class_Int_Onumber__ring( X ), ! class_Int_Oring__char__0( X ), ! Z = Y
% 0.97/1.59    , c_Int_Onumber__class_Onumber__of( X, Z ) = 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( X, Y ) }.
% 0.97/1.59  { ! c_Int_OBit1( Y ) = c_Int_OBit1( X ), Y = X }.
% 0.97/1.59  { ! Y = X, c_Int_OBit1( Y ) = c_Int_OBit1( X ) }.
% 0.97/1.59  { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone( 
% 0.97/1.59    tc_Nat_Onat ) ) = Y }.
% 0.97/1.59  { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Int_OPls ), X
% 0.97/1.59     ) = c_Int_OPls }.
% 0.97/1.59  { ! c_Int_OBit0( Y ) = c_Int_OBit0( X ), Y = X }.
% 0.97/1.59  { ! Y = X, c_Int_OBit0( Y ) = c_Int_OBit0( X ) }.
% 0.97/1.59  { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Int_OBit0( Y
% 0.97/1.59     ) ), X ) = c_Int_OBit0( hAPP( hAPP( c_Groups_Otimes__class_Otimes( 
% 0.97/1.59    tc_Int_Oint ), Y ), X ) ) }.
% 0.97/1.59  { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 0.97/1.59    ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.59  { ! class_Int_Onumber__ring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.59    ( X ), Y ), c_Int_Onumber__class_Onumber__of( X, c_Int_OBit0( c_Int_OBit1
% 0.97/1.59    ( c_Int_OPls ) ) ) ) = c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 0.97/1.59  { ! class_Int_Onumber__ring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.59    ( X ), c_Int_Onumber__class_Onumber__of( X, c_Int_OBit0( c_Int_OBit1( 
% 0.97/1.59    c_Int_OPls ) ) ) ), Y ) = c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 0.97/1.59  { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X, 
% 0.97/1.59    c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ) = 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( X, c_Int_OBit0( c_Int_OBit1( c_Int_OPls
% 0.97/1.59     ) ) ) }.
% 0.97/1.59  { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) = 
% 0.97/1.59    c_Groups_Oone__class_Oone( tc_Int_Oint ), X = c_Groups_Oone__class_Oone( 
% 0.97/1.59    tc_Int_Oint ), X = c_Int_Onumber__class_Onumber__of( tc_Int_Oint, 
% 0.97/1.59    c_Int_OMin ) }.
% 0.97/1.59  { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) = 
% 0.97/1.59    c_Groups_Oone__class_Oone( tc_Int_Oint ), alpha1( X, Y ), alpha33( X, Y )
% 0.97/1.59     }.
% 0.97/1.59  { ! alpha1( X, Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint
% 0.97/1.59     ), Y ), X ) = c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.97/1.59  { ! alpha33( X, Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint
% 0.97/1.59     ), Y ), X ) = c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.97/1.59  { ! alpha33( X, Y ), Y = c_Int_Onumber__class_Onumber__of( tc_Int_Oint, 
% 0.97/1.59    c_Int_OMin ) }.
% 0.97/1.59  { ! alpha33( X, Y ), X = c_Int_Onumber__class_Onumber__of( tc_Int_Oint, 
% 0.97/1.59    c_Int_OMin ) }.
% 0.97/1.59  { ! Y = c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OMin ), ! X = 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OMin ), alpha33( X, 
% 0.97/1.59    Y ) }.
% 0.97/1.59  { ! alpha1( X, Y ), Y = c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.97/1.59  { ! alpha1( X, Y ), X = c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.97/1.59  { ! Y = c_Groups_Oone__class_Oone( tc_Int_Oint ), ! X = 
% 0.97/1.59    c_Groups_Oone__class_Oone( tc_Int_Oint ), alpha1( X, Y ) }.
% 0.97/1.59  { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 0.97/1.59    , Z ), c_Int_Onumber__class_Onumber__of( X, Y ) ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z, Y ) }.
% 0.97/1.59  { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z, Y ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 0.97/1.59    , Z ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.97/1.59  { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X, hAPP
% 0.97/1.59    ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ) = hAPP( 
% 0.97/1.59    hAPP( c_Groups_Otimes__class_Otimes( X ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( X, Z ) ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.97/1.59  { ! class_Int_Onumber__ring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.59    ( X ), c_Int_Onumber__class_Onumber__of( X, Z ) ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( X, Y ) ) = 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( X, hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ) }.
% 0.97/1.59  { ! class_Int_Onumber__ring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.59    ( X ), c_Int_Onumber__class_Onumber__of( X, T ) ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X, 
% 0.97/1.59    Z ) ), Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( X, hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( tc_Int_Oint ), T ), Z ) ) ), Y ) }.
% 0.97/1.59  { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.97/1.59  { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( X ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.97/1.59  { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( X ), c_Groups_Oone__class_Oone( X ) ), Y ) 
% 0.97/1.59    = c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.59  { ! class_Int_Onumber__ring( X ), hAPP( hAPP( c_Power_Opower__class_Opower
% 0.97/1.59    ( X ), c_Groups_Oplus__class_Oplus( X, Z, Y ) ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( 
% 0.97/1.59    c_Int_OPls ) ) ) ) = c_Groups_Oplus__class_Oplus( X, 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Power_Opower__class_Opower
% 0.97/1.59    ( X ), Z ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( 
% 0.97/1.59    c_Int_OBit1( c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower
% 0.97/1.59    ( X ), Y ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( 
% 0.97/1.59    c_Int_OBit1( c_Int_OPls ) ) ) ) ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X, 
% 0.97/1.59    c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ), Z ) ), Y ) ) }.
% 0.97/1.59  { ! c_Int_OPls = c_Int_OBit1( X ) }.
% 0.97/1.59  { ! c_Int_OBit1( X ) = c_Int_OPls }.
% 0.97/1.59  { c_Groups_Oone__class_Oone( tc_Int_Oint ) = 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit1( c_Int_OPls )
% 0.97/1.59     ) }.
% 0.97/1.59  { ! c_Int_OBit0( Y ) = c_Int_OBit1( X ) }.
% 0.97/1.59  { ! c_Int_OBit1( Y ) = c_Int_OBit0( X ) }.
% 0.97/1.59  { c_Int_OBit0( c_Int_OPls ) = c_Int_OPls }.
% 0.97/1.59  { ! c_Int_OPls = c_Int_OBit0( X ), c_Int_OPls = X }.
% 0.97/1.59  { ! c_Int_OPls = X, c_Int_OPls = c_Int_OBit0( X ) }.
% 0.97/1.59  { ! c_Int_OBit0( X ) = c_Int_OPls, X = c_Int_OPls }.
% 0.97/1.59  { ! X = c_Int_OPls, c_Int_OBit0( X ) = c_Int_OPls }.
% 0.97/1.59  { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( X ), hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) }.
% 0.97/1.59  { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, hAPP
% 0.97/1.59    ( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( X ), c_Groups_Oabs__class_Oabs( X, Z ) ), Y
% 0.97/1.59     ) }.
% 0.97/1.59  { c_Int_OBit1( c_Int_OMin ) = c_Int_OMin }.
% 0.97/1.59  { ! c_Int_OMin = c_Int_OBit1( X ), c_Int_OMin = X }.
% 0.97/1.59  { ! c_Int_OMin = X, c_Int_OMin = c_Int_OBit1( X ) }.
% 0.97/1.59  { ! c_Int_OBit1( X ) = c_Int_OMin, X = c_Int_OMin }.
% 0.97/1.59  { ! X = c_Int_OMin, c_Int_OBit1( X ) = c_Int_OMin }.
% 0.97/1.59  { ! c_Int_OMin = c_Int_OPls }.
% 0.97/1.59  { ! c_Int_OPls = c_Int_OMin }.
% 0.97/1.59  { ! c_Int_OMin = c_Int_OBit0( X ) }.
% 0.97/1.59  { ! c_Int_OBit0( X ) = c_Int_OMin }.
% 0.97/1.59  { hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ), 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( 
% 0.97/1.59    c_Int_OPls ) ) ) ) = c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Y ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( 
% 0.97/1.59    c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower( 
% 0.97/1.59    tc_RealDef_Oreal ), X ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, 
% 0.97/1.59    c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0( 
% 0.97/1.59    c_Int_OBit1( c_Int_OPls ) ) ) ), Y ) ), X ) ) }.
% 0.97/1.59  { v_z = c_Complex_Ocomplex_OComplex( skol2, skol9 ) }.
% 0.97/1.59  { ! class_Groups_Oordered__ab__group__add__abs( X ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( X, Z, Y ) ), c_Groups_Oplus__class_Oplus( X
% 0.97/1.59    , c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) )
% 0.97/1.59     ) }.
% 0.97/1.59  { ! class_Orderings_Opreorder( X ), c_Orderings_Oord__class_Oless__eq( X, Y
% 0.97/1.59    , Y ) }.
% 0.97/1.59  { ! class_Int_Onumber__ring( X ), hAPP( hAPP( c_Power_Opower__class_Opower
% 0.97/1.59    ( X ), c_Int_Onumber__class_Onumber__of( X, c_Int_OMin ) ), c_Nat_OSuc( 
% 0.97/1.59    hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( 
% 0.97/1.59    c_Int_OPls ) ) ) ), Y ) ) ) = c_Int_Onumber__class_Onumber__of( X, 
% 0.97/1.59    c_Int_OMin ) }.
% 0.97/1.59  { ! class_Power_Opower( X ), c_Power_Opower__class_Opower( X ) = 
% 0.97/1.59    c_Power_Opower_Opower( X, c_Groups_Oone__class_Oone( X ), 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ) ) }.
% 0.97/1.59  { ! class_Int_Onumber__ring( X ), hAPP( hAPP( c_Power_Opower__class_Opower
% 0.97/1.59    ( X ), c_Groups_Ominus__class_Ominus( X, Z, Y ) ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( 
% 0.97/1.59    c_Int_OPls ) ) ) ) = c_Groups_Ominus__class_Ominus( X, 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Power_Opower__class_Opower
% 0.97/1.59    ( X ), Z ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( 
% 0.97/1.59    c_Int_OBit1( c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower
% 0.97/1.59    ( X ), Y ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( 
% 0.97/1.59    c_Int_OBit1( c_Int_OPls ) ) ) ) ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X, 
% 0.97/1.59    c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ), Z ) ), Y ) ) }.
% 0.97/1.59  { ! class_Rings_Olinordered__idom( X ), c_Orderings_Oord__class_Oless__eq( 
% 0.97/1.59    X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( X ), Z ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( 
% 0.97/1.59    c_Int_OPls ) ) ) ), Y ) ) ) }.
% 0.97/1.59  { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, 
% 0.97/1.59    c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ), c_NthRoot_Osqrt( 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Y ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( 
% 0.97/1.59    c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower( 
% 0.97/1.59    tc_RealDef_Oreal ), X ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, 
% 0.97/1.59    c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) ) ) }.
% 0.97/1.59  { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, 
% 0.97/1.59    c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ), c_NthRoot_Osqrt( 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( tc_RealDef_Oreal ), X ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( 
% 0.97/1.59    c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower( 
% 0.97/1.59    tc_RealDef_Oreal ), Y ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, 
% 0.97/1.59    c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) ) ) }.
% 0.97/1.59  { ! class_Rings_Olinordered__idom( X ), c_Orderings_Oord__class_Oless__eq( 
% 0.97/1.59    X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 0.97/1.59    ( hAPP( c_Power_Opower__class_Opower( X ), Z ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( 
% 0.97/1.59    c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( 
% 0.97/1.59    c_Int_OPls ) ) ) ) ) ) }.
% 0.97/1.59  { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, 
% 0.97/1.59    c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), 
% 0.97/1.59    c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, 
% 0.97/1.59    c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, v_z, 
% 0.97/1.59    c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) ) ) }.
% 0.97/1.59  { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, 
% 0.97/1.59    c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), 
% 0.97/1.59    c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, v_z, 
% 0.97/1.59    c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) ) ) }.
% 0.97/1.59  { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, 
% 0.97/1.59    c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), 
% 0.97/1.59    c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, 
% 0.97/1.59    c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, v_z, c_Complex_Oii )
% 0.97/1.59     ) ) }.
% 0.97/1.59  { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, 
% 0.97/1.59    c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), 
% 0.97/1.59    c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, v_z, c_Complex_Oii ) )
% 0.97/1.59     ) }.
% 0.97/1.59  { ! c_Groups_Ozero__class_Ozero( tc_Int_Oint ) = c_Groups_Oone__class_Oone
% 0.97/1.59    ( tc_Int_Oint ) }.
% 0.97/1.59  { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus( 
% 0.97/1.59    tc_Int_Oint, c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ) = 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.97/1.59  { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X, 
% 0.97/1.59    c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ) = 
% 0.97/1.59    c_Groups_Ominus__class_Ominus( X, c_Int_Onumber__class_Onumber__of( X, Z
% 0.97/1.59     ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.97/1.59  { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), 
% 0.97/1.59    c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) = X }.
% 0.97/1.59  { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), 
% 0.97/1.59    c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = X }.
% 0.97/1.59  { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) = hAPP
% 0.97/1.59    ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) }.
% 0.97/1.59  { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = X }.
% 0.97/1.59  { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc( 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus( 
% 0.97/1.59    tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) ) }.
% 0.97/1.59  { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) = hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ) }.
% 0.97/1.59  { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) = 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.97/1.59  { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), 
% 0.97/1.59    c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ) = 
% 0.97/1.59    c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.97/1.59  { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), c_Nat_OSuc( 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) = c_Nat_OSuc( 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.59  { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( 
% 0.97/1.59    hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.97/1.59  { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ), X ) = 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.97/1.59  { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), 
% 0.97/1.59    c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ), X ) = 
% 0.97/1.59    c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.97/1.59  { ! hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = 
% 0.97/1.59    c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X = 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = c_Nat_OSuc( 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.59  { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc( 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.59  { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( 
% 0.97/1.59    hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc
% 0.97/1.59    ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.59  { ! c_Groups_Oabs__class_Oabs( tc_Int_Oint, hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) = 
% 0.97/1.59    c_Groups_Oone__class_Oone( tc_Int_Oint ), c_Groups_Oabs__class_Oabs( 
% 0.97/1.59    tc_Int_Oint, X ) = c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.97/1.59  { hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), c_Nat_OSuc( X ) ) = 
% 0.97/1.59    hAPP( hAPP( Z, Y ), hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), X
% 0.97/1.59     ) ) }.
% 0.97/1.59  { hAPP( hAPP( c_Power_Opower_Opower( T, Z, Y ), X ), 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = Z }.
% 0.97/1.59  { c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, 
% 0.97/1.59    c_Complex_Ocomplex_OComplex( T, Z ), c_Complex_Ocomplex_OComplex( Y, X )
% 0.97/1.59     ) = c_Complex_Ocomplex_OComplex( c_Groups_Ominus__class_Ominus( 
% 0.97/1.59    tc_RealDef_Oreal, T, Y ), c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal
% 0.97/1.59    , Z, X ) ) }.
% 0.97/1.59  { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus( 
% 0.97/1.59    tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 0.97/1.59  { ! c_Complex_Ocomplex_OComplex( Y, X ) = c_Groups_Ozero__class_Ozero( 
% 0.97/1.59    tc_Complex_Ocomplex ), Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal
% 0.97/1.59     ) }.
% 0.97/1.59  { ! c_Complex_Ocomplex_OComplex( Y, X ) = c_Groups_Ozero__class_Ozero( 
% 0.97/1.59    tc_Complex_Ocomplex ), X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal
% 0.97/1.59     ) }.
% 0.97/1.59  { ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! X = 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), 
% 0.97/1.59    c_Complex_Ocomplex_OComplex( Y, X ) = c_Groups_Ozero__class_Ozero( 
% 0.97/1.59    tc_Complex_Ocomplex ) }.
% 0.97/1.59  { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, 
% 0.97/1.59    c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, 
% 0.97/1.59    c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X ) ), 
% 0.97/1.59    c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y ) ), 
% 0.97/1.59    c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) }.
% 0.97/1.59  { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus
% 0.97/1.59    ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.97/1.59  { ! class_Groups_Oordered__ab__group__add( X ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, Z, Y ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 0.97/1.59    , Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.59  { ! class_Groups_Oordered__ab__group__add( X ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 0.97/1.59    , Y ), c_Groups_Ozero__class_Ozero( X ) ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.59  { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) = 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) }.
% 0.97/1.59  { c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero
% 0.97/1.59    ( tc_Int_Oint ) ) = X }.
% 0.97/1.59  { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ozero__class_Ozero( 
% 0.97/1.59    tc_Int_Oint ), X ) = X }.
% 0.97/1.59  { c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) = 
% 0.97/1.59    c_Complex_Ocomplex_OComplex( c_Groups_Ozero__class_Ozero( 
% 0.97/1.59    tc_RealDef_Oreal ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.97/1.59  { ! class_Groups_Ozero( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y, Y = 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59  { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X ), 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( X ) = Y }.
% 0.97/1.59  { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y, 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.97/1.59  { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y, Y )
% 0.97/1.59     = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59  { ! class_Groups_Oab__group__add( X ), ! Z = Y, 
% 0.97/1.59    c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.97/1.59     ) }.
% 0.97/1.59  { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X, 
% 0.97/1.59    Z, Y ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.97/1.59  { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.97/1.59     ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.97/1.59  { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ominus__class_Ominus( 
% 0.97/1.59    X, Z, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59  { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X, 
% 0.97/1.59    U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! U = T, Z = Y }.
% 0.97/1.59  { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X, 
% 0.97/1.59    U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! Z = Y, U = T }.
% 0.97/1.59  { ! c_NthRoot_Osqrt( Y ) = c_NthRoot_Osqrt( X ), Y = X }.
% 0.97/1.59  { ! Y = X, c_NthRoot_Osqrt( Y ) = c_NthRoot_Osqrt( X ) }.
% 0.97/1.59  { ! c_NthRoot_Osqrt( X ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal )
% 0.97/1.59    , X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.59  { ! X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X
% 0.97/1.59     ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.59  { c_NthRoot_Osqrt( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) = 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.59  { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ) }.
% 0.97/1.59  { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ) }
% 0.97/1.59    .
% 0.97/1.59  { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Osqrt( X
% 0.97/1.59     ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.97/1.59  { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Osqrt( X )
% 0.97/1.59    , c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.97/1.59  { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ) }
% 0.97/1.59    .
% 0.97/1.59  { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), ! c_NthRoot_Osqrt( 
% 0.97/1.59    X ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X = 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.59  { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, 
% 0.97/1.59    c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ), 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.97/1.59  { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, 
% 0.97/1.59    c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ), 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.97/1.59  { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) = 
% 0.97/1.59    c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.59    ( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) }.
% 0.97/1.59  { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), 
% 0.97/1.59    c_Nat_OSuc( Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59  { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, 
% 0.97/1.59    c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.97/1.59  { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, 
% 0.97/1.59    c_Groups_Oone__class_Oone( tc_Nat_Onat ), X ) }.
% 0.97/1.59  { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ) }.
% 0.97/1.59  { ! class_Groups_Oordered__ab__group__add( X ), ! 
% 0.97/1.59    c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.97/1.59    ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, U, T ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.59  { ! class_Groups_Oordered__ab__group__add( X ), ! 
% 0.97/1.59    c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.97/1.59    ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, U, T ) }.
% 0.97/1.59  { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), ! 
% 0.97/1.59    class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.97/1.59    , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) = 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.97/1.59    .
% 0.97/1.59  { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), ! 
% 0.97/1.59    class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.97/1.59    , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) = 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( 
% 0.97/1.59    tc_Nat_Onat ) }.
% 0.97/1.59  { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), ! 
% 0.97/1.59    class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.97/1.59    , ! Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 0.97/1.59    ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) 
% 0.97/1.59    = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59  { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, 
% 0.97/1.59    c_Groups_Ominus__class_Ominus( X, Z, Y ), Y ) = Z }.
% 0.97/1.59  { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = Z }.
% 0.97/1.59  { ! class_Groups_Oordered__ab__group__add__abs( X ), 
% 0.97/1.59    c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Z, Y ) ) 
% 0.97/1.59    = c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Y, Z )
% 0.97/1.59     ) }.
% 0.97/1.59  { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X, 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.97/1.59  { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X, 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.97/1.59  { ! class_Groups_Olinordered__ab__group__add( X ), ! 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( X ) = c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.97/1.59    , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59  { ! class_Groups_Olinordered__ab__group__add( X ), ! Y = 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero( X ) = 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 0.97/1.59  { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y, 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.97/1.59  { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.97/1.59    , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.97/1.59  { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.59  { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), 
% 0.97/1.59    c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 0.97/1.59    ( tc_Nat_Onat ) ) ), X ) ) }.
% 0.97/1.59  { ! class_Groups_Oordered__ab__group__add__abs( X ), ! 
% 0.97/1.59    c_Groups_Oabs__class_Oabs( X, Y ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.97/1.59     c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59  { ! class_Groups_Oordered__ab__group__add__abs( X ), ! Y = 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( X ), c_Groups_Oabs__class_Oabs( X, Y ) = 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59  { ! class_Groups_Oordered__ab__group__add__abs( X ), 
% 0.97/1.59    c_Groups_Oabs__class_Oabs( X, c_Groups_Ozero__class_Ozero( X ) ) = 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59  { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP
% 0.97/1.59    ( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc( 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc( 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) ) = hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z, 
% 0.97/1.59    Y ) ), c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.97/1.59  { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, 
% 0.97/1.59    c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y ), 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, 
% 0.97/1.59    c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X ) ), 
% 0.97/1.59    c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) ) }.
% 0.97/1.59  { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ) = hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.97/1.59     ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( 
% 0.97/1.59    X ), Y ), Z = Y }.
% 0.97/1.59  { ! class_Rings_Olinordered__semidom( X ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ), hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ) ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.59     ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.59  { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Osqrt( Y )
% 0.97/1.59    , c_NthRoot_Osqrt( X ) ) }.
% 0.97/1.59  { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Osqrt( Y
% 0.97/1.59     ), c_NthRoot_Osqrt( X ) ), c_Orderings_Oord__class_Oless__eq( 
% 0.97/1.59    tc_RealDef_Oreal, Y, X ) }.
% 0.97/1.59  { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Osqrt( Y )
% 0.97/1.59    , c_NthRoot_Osqrt( X ) ) }.
% 0.97/1.59  { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), ! Y = 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.97/1.59     ) = c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.59  { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), Y = 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.97/1.59     ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59  { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) = 
% 0.97/1.59    c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.97/1.59  { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) = hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), 
% 0.97/1.59    c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 0.97/1.59    ( tc_Nat_Onat ) ) ) ) }.
% 0.97/1.59  { c_NthRoot_Osqrt( hAPP( hAPP( c_Groups_Otimes__class_Otimes( 
% 0.97/1.59    tc_RealDef_Oreal ), Y ), X ) ) = hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_NthRoot_Osqrt( Y ) )
% 0.97/1.59    , c_NthRoot_Osqrt( X ) ) }.
% 0.97/1.59  { c_NthRoot_Osqrt( hAPP( hAPP( c_Power_Opower__class_Opower( 
% 0.97/1.59    tc_RealDef_Oreal ), Y ), X ) ) = hAPP( hAPP( c_Power_Opower__class_Opower
% 0.97/1.59    ( tc_RealDef_Oreal ), c_NthRoot_Osqrt( Y ) ), X ) }.
% 0.97/1.59  { ! c_NthRoot_Osqrt( X ) = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X
% 0.97/1.59     = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.97/1.59  { ! X = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X )
% 0.97/1.59     = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.97/1.59  { c_NthRoot_Osqrt( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) = 
% 0.97/1.59    c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.97/1.59  { c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Int_OPls ) = X }.
% 0.97/1.59  { c_Groups_Ominus__class_Ominus( tc_Int_Oint, c_Int_OBit0( Y ), c_Int_OBit0
% 0.97/1.59    ( X ) ) = c_Int_OBit0( c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X )
% 0.97/1.59     ) }.
% 0.97/1.59  { c_Int_OBit1( X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oone__class_Oone( 
% 0.97/1.59    tc_Int_Oint ), X ), X ) }.
% 0.97/1.59  { c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Int_OPls ) = X }.
% 0.97/1.59  { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Int_OPls, X ) = X }.
% 0.97/1.59  { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Int_OBit0( Y ), c_Int_OBit0( 
% 0.97/1.59    X ) ) = c_Int_OBit0( c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }
% 0.97/1.59    .
% 0.97/1.59  { c_Int_OBit0( X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, X ) }.
% 0.97/1.59  { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ), 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.97/1.59  { c_Groups_Oplus__class_Oplus( tc_Int_Oint, 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) = 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Int_Oint, 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 0.97/1.59  { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.97/1.59     ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59  { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.97/1.59     ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59  { ! class_Groups_Olinordered__ab__group__add( X ), ! 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( X, Y, Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.59    , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59  { ! class_Groups_Olinordered__ab__group__add( X ), ! Y = 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Y ) 
% 0.97/1.59    = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59  { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.59    ( X ), ! Z = c_Groups_Oplus__class_Oplus( X, Z, Y ), Y = 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59  { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.59    ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z = 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 0.97/1.59  { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.97/1.59    , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.97/1.59  { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.97/1.59  { ! class_Rings_Oring__1__no__zero__divisors( X ), Y = 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 0.97/1.59    ( X ) }.
% 0.97/1.59  { c_Int_OPls = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.97/1.59  { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( tc_Int_Oint ), c_Groups_Oabs__class_Oabs( 
% 0.97/1.59    tc_Int_Oint, Y ) ), X ) ) }.
% 0.97/1.59  { ! class_Groups_Oordered__ab__group__add__abs( X ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, 
% 0.97/1.59    c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ), 
% 0.97/1.59    c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Y, Z ) )
% 0.97/1.59     ) }.
% 0.97/1.59  { ! class_Groups_Oordered__ab__group__add__abs( X ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, 
% 0.97/1.59    c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ), 
% 0.97/1.59    c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Z, Y ) )
% 0.97/1.59     ) }.
% 0.97/1.59  { ! class_Groups_Oordered__ab__group__add__abs( X ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, 
% 0.97/1.59    c_Groups_Ominus__class_Ominus( X, c_Groups_Oabs__class_Oabs( X, Z ), 
% 0.97/1.59    c_Groups_Oabs__class_Oabs( X, Y ) ) ), c_Groups_Oabs__class_Oabs( X, 
% 0.97/1.59    c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) }.
% 0.97/1.59  { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) = hAPP( hAPP
% 0.97/1.59    ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ), Z = Y }.
% 0.97/1.59  { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP
% 0.97/1.59    ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) = hAPP( 
% 0.97/1.59    hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) }.
% 0.97/1.59  { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) = hAPP( hAPP
% 0.97/1.59    ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ), Z = Y }.
% 0.97/1.59  { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP
% 0.97/1.59    ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) = hAPP( 
% 0.97/1.59    hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) }.
% 0.97/1.59  { ! c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) = 
% 0.97/1.59    c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.97/1.59  { ! class_Groups_Olinordered__ab__group__add( X ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( X, Y, Y ) ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.59     ) }.
% 0.97/1.59  { ! class_Groups_Olinordered__ab__group__add( X ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.59     ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.97/1.59     ), c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.97/1.59  { ! class_Groups_Olinordered__ab__group__add( X ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Y, 
% 0.97/1.59    Y ), c_Groups_Ozero__class_Ozero( X ) ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.59     ) }.
% 0.97/1.59  { ! class_Groups_Olinordered__ab__group__add( X ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.59     ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X
% 0.97/1.59    , Y, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.59  { ! class_Groups_Oordered__comm__monoid__add( X ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.59     ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( 
% 0.97/1.59    X ), Z ), c_Orderings_Oord__class_Oless__eq( X, 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.97/1.59     ) }.
% 0.97/1.59  { ! class_Groups_Oordered__comm__monoid__add( X ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.59     ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( 
% 0.97/1.59    X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) = 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 0.97/1.59    .
% 0.97/1.59  { ! class_Groups_Oordered__comm__monoid__add( X ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.59     ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( 
% 0.97/1.59    X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) = 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.97/1.59    .
% 0.97/1.59  { ! class_Groups_Oordered__comm__monoid__add( X ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.59     ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( 
% 0.97/1.59    X ), Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), ! Z = 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z ) 
% 0.97/1.59    = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59  { ! class_Groups_Oordered__comm__monoid__add( X ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.59     ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X, 
% 0.97/1.59    Y, Z ) ) }.
% 0.97/1.59  { ! class_Groups_Oordered__comm__monoid__add( X ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.59     ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X, 
% 0.97/1.59    Z, Y ) ) }.
% 0.97/1.59  { ! class_Groups_Oordered__comm__monoid__add( X ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.59     ), ! c_Orderings_Oord__class_Oless__eq( X, Z, 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.59    , c_Groups_Oplus__class_Oplus( X, Y, Z ), c_Groups_Ozero__class_Ozero( X
% 0.97/1.59     ) ) }.
% 0.97/1.59  { ! class_Groups_Oordered__ab__group__add__abs( X ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.59     ), c_Groups_Oabs__class_Oabs( X, Y ) = Y }.
% 0.97/1.59  { ! class_Groups_Oordered__ab__group__add__abs( X ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Y ), 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.59     }.
% 0.97/1.59  { ! class_Groups_Oordered__ab__group__add__abs( X ), ! Y = 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq( X, 
% 0.97/1.59    c_Groups_Oabs__class_Oabs( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.59  { ! class_Groups_Oordered__ab__group__add__abs( X ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), 
% 0.97/1.59    c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.97/1.59  { c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, 
% 0.97/1.59    c_Complex_Ocomplex_OComplex( T, Z ), c_Complex_Ocomplex_OComplex( Y, X )
% 0.97/1.59     ) = c_Complex_Ocomplex_OComplex( c_Groups_Oplus__class_Oplus( 
% 0.97/1.59    tc_RealDef_Oreal, T, Y ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, 
% 0.97/1.59    Z, X ) ) }.
% 0.97/1.59  { c_Nat_OSuc( c_Nat_OSuc( c_Nat_OSuc( X ) ) ) = c_Groups_Oplus__class_Oplus
% 0.97/1.59    ( tc_Nat_Onat, c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit1
% 0.97/1.59    ( c_Int_OBit1( c_Int_OPls ) ) ), X ) }.
% 0.97/1.59  { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt( 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) ) ) }.
% 0.97/1.59  { ! class_Rings_Olinordered__semidom( X ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.59     ), ! c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone
% 0.97/1.59    ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ), Y ) }.
% 0.97/1.59  { c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit1( c_Int_OBit1( 
% 0.97/1.59    c_Int_OPls ) ) ) = c_Nat_OSuc( c_Nat_OSuc( c_Nat_OSuc( 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.97/1.59  { c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit1( c_Int_OPls )
% 0.97/1.59     ) = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.59  { ! c_Complex_Ocomplex_OComplex( Z, Y ) = c_Int_Onumber__class_Onumber__of
% 0.97/1.59    ( tc_Complex_Ocomplex, X ), Z = c_Int_Onumber__class_Onumber__of( 
% 0.97/1.59    tc_RealDef_Oreal, X ) }.
% 0.97/1.59  { ! c_Complex_Ocomplex_OComplex( Z, Y ) = c_Int_Onumber__class_Onumber__of
% 0.97/1.59    ( tc_Complex_Ocomplex, X ), Y = c_Groups_Ozero__class_Ozero( 
% 0.97/1.59    tc_RealDef_Oreal ) }.
% 0.97/1.59  { ! Z = c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, X ), ! Y = 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), 
% 0.97/1.59    c_Complex_Ocomplex_OComplex( Z, Y ) = c_Int_Onumber__class_Onumber__of( 
% 0.97/1.59    tc_Complex_Ocomplex, X ) }.
% 0.97/1.59  { ! c_Complex_Ocomplex_OComplex( Y, X ) = c_Groups_Oone__class_Oone( 
% 0.97/1.59    tc_Complex_Ocomplex ), Y = c_Groups_Oone__class_Oone( tc_RealDef_Oreal )
% 0.97/1.59     }.
% 0.97/1.59  { ! c_Complex_Ocomplex_OComplex( Y, X ) = c_Groups_Oone__class_Oone( 
% 0.97/1.59    tc_Complex_Ocomplex ), X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal
% 0.97/1.59     ) }.
% 0.97/1.59  { ! Y = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), ! X = 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), 
% 0.97/1.59    c_Complex_Ocomplex_OComplex( Y, X ) = c_Groups_Oone__class_Oone( 
% 0.97/1.59    tc_Complex_Ocomplex ) }.
% 0.97/1.59  { c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) = 
% 0.97/1.59    c_Complex_Ocomplex_OComplex( c_Groups_Oone__class_Oone( tc_RealDef_Oreal
% 0.97/1.59     ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.97/1.59  { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( 
% 0.97/1.59    c_Int_OPls ) ) ), X ) = c_Nat_OSuc( c_Nat_OSuc( X ) ) }.
% 0.97/1.59  { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( 
% 0.97/1.59    c_Int_OPls ) ) ) ) = c_Nat_OSuc( c_Nat_OSuc( X ) ) }.
% 0.97/1.59  { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, 
% 0.97/1.59    c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, 
% 0.97/1.59    c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ) }.
% 0.97/1.59  { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Osqrt( X
% 0.97/1.59     ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, 
% 0.97/1.59    c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.97/1.59  { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, 
% 0.97/1.59    c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Osqrt( X )
% 0.97/1.59    , c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.97/1.59  { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, 
% 0.97/1.59    c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, 
% 0.97/1.59    c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 0.97/1.59  { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, 
% 0.97/1.59    c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, 
% 0.97/1.59    c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ) }.
% 0.97/1.59  { ! class_Rings_Oring( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.59    ( X ), U ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U, 
% 0.97/1.59    Z ) ), Y ) ) }.
% 0.97/1.59  { ! class_Int_Onumber( X ), ! class_Rings_Oring( X ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T, 
% 0.97/1.59    Z ) ), c_Int_Onumber__class_Onumber__of( X, Y ) ) = 
% 0.97/1.59    c_Groups_Ominus__class_Ominus( X, hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), T ), c_Int_Onumber__class_Onumber__of
% 0.97/1.59    ( X, Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( X, Y ) ) ) }.
% 0.97/1.59  { ! class_Int_Onumber( X ), ! class_Rings_Oring( X ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X, 
% 0.97/1.59    T ) ), c_Groups_Ominus__class_Ominus( X, Z, Y ) ) = 
% 0.97/1.59    c_Groups_Ominus__class_Ominus( X, hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X, 
% 0.97/1.59    T ) ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( X, T ) ), Y ) ) }.
% 0.97/1.59  { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X, 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( X, T ), c_Groups_Ominus__class_Ominus( 
% 0.97/1.59    X, c_Int_Onumber__class_Onumber__of( X, Z ), Y ) ) = 
% 0.97/1.59    c_Groups_Ominus__class_Ominus( X, c_Int_Onumber__class_Onumber__of( X, 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( tc_Int_Oint, T, Z ) ), Y ) }.
% 0.97/1.59  { ! class_Groups_Oordered__ab__group__add__abs( X ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, 
% 0.97/1.59    c_Groups_Ominus__class_Ominus( X, c_Groups_Oplus__class_Oplus( X, U, T )
% 0.97/1.59    , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) ), c_Groups_Oplus__class_Oplus
% 0.97/1.59    ( X, c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, U, Z
% 0.97/1.59     ) ), c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, T, 
% 0.97/1.59    Y ) ) ) ) }.
% 0.97/1.59  { ! class_Groups_Oordered__ab__group__add__abs( X ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, 
% 0.97/1.59    c_Groups_Ominus__class_Ominus( X, Z, Y ) ), c_Groups_Oplus__class_Oplus( 
% 0.97/1.59    X, c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) )
% 0.97/1.59     ) }.
% 0.97/1.59  { c_NthRoot_Osqrt( hAPP( hAPP( c_Groups_Otimes__class_Otimes( 
% 0.97/1.59    tc_RealDef_Oreal ), X ), X ) ) = c_Groups_Oabs__class_Oabs( 
% 0.97/1.59    tc_RealDef_Oreal, X ) }.
% 0.97/1.59  { c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( 
% 0.97/1.59    c_Int_OPls ) ) ) = c_Nat_OSuc( c_Nat_OSuc( c_Groups_Ozero__class_Ozero( 
% 0.97/1.59    tc_Nat_Onat ) ) ) }.
% 0.97/1.59  { c_Nat_OSuc( c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) = 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( 
% 0.97/1.59    c_Int_OPls ) ) ) }.
% 0.97/1.59  { c_Groups_Ominus__class_Ominus( tc_Int_Oint, c_Int_OBit1( Y ), c_Int_OBit1
% 0.97/1.59    ( X ) ) = c_Int_OBit0( c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X )
% 0.97/1.59     ) }.
% 0.97/1.59  { c_Groups_Ominus__class_Ominus( tc_Int_Oint, c_Int_OBit1( Y ), c_Int_OBit0
% 0.97/1.59    ( X ) ) = c_Int_OBit1( c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X )
% 0.97/1.59     ) }.
% 0.97/1.59  { c_Groups_Ominus__class_Ominus( tc_Int_Oint, c_Int_OPls, c_Int_OBit0( X )
% 0.97/1.59     ) = c_Int_OBit0( c_Groups_Ominus__class_Ominus( tc_Int_Oint, c_Int_OPls
% 0.97/1.59    , X ) ) }.
% 0.97/1.59  { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 0.97/1.59  { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 0.97/1.59  { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.97/1.59  { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) }.
% 0.97/1.59  { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.97/1.59    , Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.97/1.59    , Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.97/1.59  { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( X ), T ), Y ) ) = hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus( 
% 0.97/1.59    tc_Nat_Onat, Z, Y ) ) }.
% 0.97/1.59  { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus( 
% 0.97/1.59    tc_Nat_Onat, Z, Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), 
% 0.97/1.59    hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.97/1.59  { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Int_OBit1( Y
% 0.97/1.59     ) ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Int_OBit0( hAPP( 
% 0.97/1.59    hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ), X ) }.
% 0.97/1.59  { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Int_OBit1( Y ), c_Int_OBit0( 
% 0.97/1.59    X ) ) = c_Int_OBit1( c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }
% 0.97/1.59    .
% 0.97/1.59  { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Int_OBit0( Y ), c_Int_OBit1( 
% 0.97/1.59    X ) ) = c_Int_OBit1( c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }
% 0.97/1.59    .
% 0.97/1.59  { ! class_Rings_Olinordered__ring__strict( X ), ! 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.59    ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.97/1.59     ) = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X
% 0.97/1.59     ) }.
% 0.97/1.59  { ! class_Rings_Olinordered__ring__strict( X ), ! 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.59    ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.97/1.59     ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.97/1.59     ) }.
% 0.97/1.59  { ! class_Rings_Olinordered__ring__strict( X ), ! Z = 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.59    , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) = 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59  { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.59    ( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! W = U, T = Z, ! 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( X, W, hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) = 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( X, U, hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.59  { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), 
% 0.97/1.59    c_Complex_Ocomplex_OComplex( T, Z ) ), c_Complex_Ocomplex_OComplex( Y, X
% 0.97/1.59     ) ) = c_Complex_Ocomplex_OComplex( c_Groups_Ominus__class_Ominus( 
% 0.97/1.59    tc_RealDef_Oreal, hAPP( hAPP( c_Groups_Otimes__class_Otimes( 
% 0.97/1.59    tc_RealDef_Oreal ), T ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( 
% 0.97/1.59    tc_RealDef_Oreal ), Z ), X ) ), c_Groups_Oplus__class_Oplus( 
% 0.97/1.59    tc_RealDef_Oreal, hAPP( hAPP( c_Groups_Otimes__class_Otimes( 
% 0.97/1.59    tc_RealDef_Oreal ), T ), X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( 
% 0.97/1.59    tc_RealDef_Oreal ), Z ), Y ) ) ) }.
% 0.97/1.59  { ! class_Rings_Olinordered__semidom( X ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, Z, Y ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.97/1.59     ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.97/1.59  { ! class_Rings_Olinordered__semidom( X ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.59     ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.97/1.59     ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.97/1.59  { ! class_Int_Onumber__ring( X ), c_Groups_Ozero__class_Ozero( X ) = 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( X, c_Int_OPls ) }.
% 0.97/1.59  { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X, 
% 0.97/1.59    c_Int_OPls ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59  { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ozero__class_Ozero( 
% 0.97/1.59    tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.59  { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.97/1.59    , Y ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = 
% 0.97/1.59    c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.59  { c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OPls ) = 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.59  { c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OPls ) }.
% 0.97/1.59  { c_Groups_Ozero__class_Ozero( tc_Int_Oint ) = 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OPls ) }.
% 0.97/1.59  { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) = 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y = 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.59  { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) = 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X = 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.59  { ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! X = 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) = 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.59  { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt( 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0( 
% 0.97/1.59    c_Int_OBit1( c_Int_OPls ) ) ) ) ) }.
% 0.97/1.59  { c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, 
% 0.97/1.59    c_Complex_Ocomplex_OComplex( Y, X ) ) = c_NthRoot_Osqrt( 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Y ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( 
% 0.97/1.59    c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower( 
% 0.97/1.59    tc_RealDef_Oreal ), X ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, 
% 0.97/1.59    c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) ) }.
% 0.97/1.59  { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, c_NthRoot_Osqrt( 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) ) ) }.
% 0.97/1.59  { ! hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Y ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( 
% 0.97/1.59    c_Int_OPls ) ) ) ) = X, ! c_Orderings_Oord__class_Oless__eq( 
% 0.97/1.59    tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), 
% 0.97/1.59    c_NthRoot_Osqrt( X ) = Y }.
% 0.97/1.59  { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) )
% 0.97/1.59    , c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1
% 0.97/1.59    ( c_Int_OPls ) ) ) ) = X }.
% 0.97/1.59  { ! hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ), 
% 0.97/1.59    c_NthRoot_Osqrt( X ) ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, 
% 0.97/1.59    c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) = X, 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ) }.
% 0.97/1.59  { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) )
% 0.97/1.59    , c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1
% 0.97/1.59    ( c_Int_OPls ) ) ) ) = X }.
% 0.97/1.59  { ! class_Rings_Oring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP
% 0.97/1.59    ( c_Groups_Otimes__class_Otimes( X ), Y ), Y ), c_Groups_Oone__class_Oone
% 0.97/1.59    ( X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) ) ), 
% 0.97/1.59    c_Groups_Ominus__class_Ominus( X, Y, c_Groups_Oone__class_Oone( X ) ) ) }
% 0.97/1.59    .
% 0.97/1.59  { ! c_NthRoot_Osqrt( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( 
% 0.97/1.59    hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ), X ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( 
% 0.97/1.59    c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower( 
% 0.97/1.59    tc_RealDef_Oreal ), Y ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, 
% 0.97/1.59    c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) ) = Y, X = 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.59  { ! c_NthRoot_Osqrt( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( 
% 0.97/1.59    hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Y ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( 
% 0.97/1.59    c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower( 
% 0.97/1.59    tc_RealDef_Oreal ), X ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, 
% 0.97/1.59    c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) ) = Y, X = 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.59  { c_Groups_Ominus__class_Ominus( tc_Int_Oint, c_Int_OPls, c_Int_OBit1( X )
% 0.97/1.59     ) = c_Int_OBit1( c_Groups_Ominus__class_Ominus( tc_Int_Oint, c_Int_OMin
% 0.97/1.59    , X ) ) }.
% 0.97/1.59  { c_Groups_Ominus__class_Ominus( tc_Int_Oint, c_Int_OMin, c_Int_OBit1( X )
% 0.97/1.59     ) = c_Int_OBit0( c_Groups_Ominus__class_Ominus( tc_Int_Oint, c_Int_OMin
% 0.97/1.59    , X ) ) }.
% 0.97/1.59  { c_Groups_Ominus__class_Ominus( tc_Int_Oint, c_Int_OMin, c_Int_OBit0( X )
% 0.97/1.59     ) = c_Int_OBit1( c_Groups_Ominus__class_Ominus( tc_Int_Oint, c_Int_OMin
% 0.97/1.59    , X ) ) }.
% 0.97/1.59  { ! class_Rings_Olinordered__ring__strict( X ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, 
% 0.97/1.59    hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ), 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( X ) ), Z = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.59     }.
% 0.97/1.59  { ! class_Rings_Olinordered__ring__strict( X ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, 
% 0.97/1.59    hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ), 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.59     }.
% 0.97/1.59  { ! class_Rings_Olinordered__ring__strict( X ), ! Z = 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.59    , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, 
% 0.97/1.59    hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ), 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.59  { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq( 
% 0.97/1.59    X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 0.97/1.59    ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.97/1.59  { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.59    , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.97/1.59  { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.97/1.59    ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ), 
% 0.97/1.59    hAPP( Y, U ) ) }.
% 0.97/1.59  { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.59    , Y ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.97/1.59  { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.59    , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.97/1.59  { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.59    , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.97/1.59  { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.59    , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.97/1.59  { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.59    , Y ), ! Z = T, c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.97/1.59  { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y
% 0.97/1.59     ), ! Y = T, c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.97/1.59  { ! class_Orderings_Oorder( X ), ! Z = Y, ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, T, Y ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.97/1.59  { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.97/1.59    ( X, Y, T ), c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.97/1.59  { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.59    , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.97/1.59  { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.59    , Y ), ! Y = Z, c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.97/1.59  { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.97/1.59    ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ), 
% 0.97/1.59    hAPP( Y, U ) ) }.
% 0.97/1.59  { ! class_Orderings_Opreorder( X ), ! Z = Y, 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.59  { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.97/1.59    ( X, Z, Y ) }.
% 0.97/1.59  { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.97/1.59    ( X, Y, Z ) }.
% 0.97/1.59  { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.59    , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.97/1.59  { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.59    , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.97/1.59  { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.97/1.59    ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ), 
% 0.97/1.59    hAPP( Y, U ) ) }.
% 0.97/1.59  { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, hAPP
% 0.97/1.59    ( Z, skol3( X, Y, Z ) ), hAPP( Y, skol3( X, Y, Z ) ) ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }.
% 0.97/1.59  { ! class_Groups_Oab__semigroup__mult( X ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.59  { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X, 
% 0.97/1.59    c_Int_OBit0( Y ) ) = c_Groups_Oplus__class_Oplus( X, 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( X, c_Groups_Ozero__class_Ozero( X ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( X, Y ) ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.97/1.59  { ! class_Groups_Oab__semigroup__add( X ), c_Groups_Oplus__class_Oplus( X, 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.97/1.59    ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.97/1.59  { ! class_Groups_Ocancel__semigroup__add( X ), ! 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X, 
% 0.97/1.59    T, Y ), Z = Y }.
% 0.97/1.59  { ! class_Groups_Ocancel__semigroup__add( X ), ! Z = Y, 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X, 
% 0.97/1.59    T, Y ) }.
% 0.97/1.59  { ! class_Groups_Ocancel__semigroup__add( X ), ! 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X, 
% 0.97/1.59    Y, Z ), T = Y }.
% 0.97/1.59  { ! class_Groups_Ocancel__semigroup__add( X ), ! T = Y, 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X, 
% 0.97/1.59    Y, Z ) }.
% 0.97/1.59  { ! class_Groups_Ocancel__semigroup__add( X ), ! 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X, 
% 0.97/1.59    T, Y ), Z = Y }.
% 0.97/1.59  { ! class_Groups_Ocancel__ab__semigroup__add( X ), ! 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X, 
% 0.97/1.59    T, Y ), Z = Y }.
% 0.97/1.59  { ! class_Groups_Ocancel__semigroup__add( X ), ! 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( X, Z, T ) = c_Groups_Oplus__class_Oplus( X, 
% 0.97/1.59    Y, T ), Z = Y }.
% 0.97/1.59  { ! class_Rings_Olinordered__idom( X ), c_Orderings_Oord__class_Oless__eq( 
% 0.97/1.59    X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( X ), c_Groups_Oabs__class_Oabs( X, Z ) ), Y
% 0.97/1.59     ) ) }.
% 0.97/1.59  { ! class_Groups_Oone( X ), ! c_Groups_Oone__class_Oone( X ) = Y, Y = 
% 0.97/1.59    c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.59  { ! class_Groups_Oone( X ), ! Y = c_Groups_Oone__class_Oone( X ), 
% 0.97/1.59    c_Groups_Oone__class_Oone( X ) = Y }.
% 0.97/1.59  { ! c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) = 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, c_Int_OPls ) }.
% 0.97/1.59  { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, c_Int_OPls ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) = 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.59  { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, c_Int_OPls ) }.
% 0.97/1.59  { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, c_Int_OPls ), 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) }.
% 0.97/1.59  { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt( 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Y ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( 
% 0.97/1.59    c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower( 
% 0.97/1.59    tc_RealDef_Oreal ), X ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, 
% 0.97/1.59    c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) ) ) }.
% 0.97/1.59  { ! class_Groups_Oordered__ab__group__add__abs( X ), 
% 0.97/1.59    c_Groups_Oabs__class_Oabs( X, c_Groups_Oabs__class_Oabs( X, Y ) ) = 
% 0.97/1.59    c_Groups_Oabs__class_Oabs( X, Y ) }.
% 0.97/1.59  { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.97/1.59    ( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( 
% 0.97/1.59    c_Int_OPls ) ) ) ), Z ) ) ) ), c_Orderings_Oord__class_Oless__eq( X, 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.97/1.59  { ! c_Complex_Ocomplex_OComplex( T, Z ) = c_Complex_Ocomplex_OComplex( Y, X
% 0.97/1.59     ), T = Y }.
% 0.97/1.59  { ! c_Complex_Ocomplex_OComplex( T, Z ) = c_Complex_Ocomplex_OComplex( Y, X
% 0.97/1.59     ), Z = X }.
% 0.97/1.59  { ! T = Y, ! Z = X, c_Complex_Ocomplex_OComplex( T, Z ) = 
% 0.97/1.59    c_Complex_Ocomplex_OComplex( Y, X ) }.
% 0.97/1.59  { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt( hAPP( 
% 0.97/1.59    hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( tc_RealDef_Oreal ), T ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( 
% 0.97/1.59    c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower( 
% 0.97/1.59    tc_RealDef_Oreal ), Z ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, 
% 0.97/1.59    c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) ), 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Y ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( 
% 0.97/1.59    c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower( 
% 0.97/1.59    tc_RealDef_Oreal ), X ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, 
% 0.97/1.59    c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) ) ) ) }.
% 0.97/1.59  { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 0.97/1.59    , Y ), c_Groups_Ozero__class_Ozero( X ) ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, c_Int_OPls ) }.
% 0.97/1.59  { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, c_Int_OPls ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 0.97/1.59    , Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.59  { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( X, Y ) ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, Y ) }.
% 0.97/1.59  { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, Y ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.97/1.59  { ! class_Rings_Olinordered__semidom( X ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.97/1.59     ), ! c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oone__class_Oone
% 0.97/1.59    ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 0.97/1.59  { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( 
% 0.97/1.59    c_Int_OPls ) ) ) ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, X
% 0.97/1.59     ) }.
% 0.97/1.59  { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( 
% 0.97/1.59    c_Int_OPls ) ) ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, X ) }.
% 0.97/1.59  { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oone__class_Oone( 
% 0.97/1.59    tc_Nat_Onat ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( 
% 0.97/1.59    c_Int_OPls ) ) ) }.
% 0.97/1.59  { ! class_Rings_Oring__1__no__zero__divisors( X ), ! hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( X ), Y ), c_Int_Onumber__class_Onumber__of
% 0.97/1.59    ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) = 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 0.97/1.59    .
% 0.97/1.59  { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y = 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( X ), Y ), c_Int_Onumber__class_Onumber__of
% 0.97/1.59    ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) = 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59  { ! class_Rings_Osemiring__1( X ), hAPP( hAPP( c_Power_Opower__class_Opower
% 0.97/1.59    ( X ), c_Groups_Ozero__class_Ozero( X ) ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( 
% 0.97/1.59    c_Int_OPls ) ) ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59  { c_NthRoot_Osqrt( hAPP( hAPP( c_Power_Opower__class_Opower( 
% 0.97/1.59    tc_RealDef_Oreal ), X ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, 
% 0.97/1.59    c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) = 
% 0.97/1.59    c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) }.
% 0.97/1.59  { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( X ), Z ), c_Int_Onumber__class_Onumber__of
% 0.97/1.59    ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) = hAPP( hAPP
% 0.97/1.59    ( c_Power_Opower__class_Opower( X ), Y ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( 
% 0.97/1.59    c_Int_OPls ) ) ) ), ! c_Orderings_Oord__class_Oless__eq( X, 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( X ), Z ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.59     ), Z = Y }.
% 0.97/1.59  { ! class_Rings_Olinordered__semidom( X ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( X ), Z ), c_Int_Onumber__class_Onumber__of
% 0.97/1.59    ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ), hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( X ), Y ), c_Int_Onumber__class_Onumber__of
% 0.97/1.59    ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.59     ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.59  { ! class_Rings_Olinordered__idom( X ), c_Orderings_Oord__class_Oless__eq( 
% 0.97/1.59    X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( X ), Y ), c_Int_Onumber__class_Onumber__of
% 0.97/1.59    ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) }.
% 0.97/1.59  { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Oplus__class_Oplus( X, 
% 0.97/1.59    hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( 
% 0.97/1.59    c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( 
% 0.97/1.59    c_Int_OPls ) ) ) ) ) = c_Groups_Ozero__class_Ozero( X ), Z = 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59  { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Oplus__class_Oplus( X, 
% 0.97/1.59    hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( 
% 0.97/1.59    c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( 
% 0.97/1.59    c_Int_OPls ) ) ) ) ) = c_Groups_Ozero__class_Ozero( X ), Y = 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59  { ! class_Rings_Olinordered__idom( X ), ! Z = c_Groups_Ozero__class_Ozero( 
% 0.97/1.59    X ), ! Y = c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus
% 0.97/1.59    ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( 
% 0.97/1.59    c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( 
% 0.97/1.59    c_Int_OPls ) ) ) ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59  { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Osqrt( 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( tc_RealDef_Oreal ), 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, T, Z ) ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( 
% 0.97/1.59    c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower( 
% 0.97/1.59    tc_RealDef_Oreal ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X )
% 0.97/1.59     ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( 
% 0.97/1.59    c_Int_OBit1( c_Int_OPls ) ) ) ) ) ), c_Groups_Oplus__class_Oplus( 
% 0.97/1.59    tc_RealDef_Oreal, c_NthRoot_Osqrt( c_Groups_Oplus__class_Oplus( 
% 0.97/1.59    tc_RealDef_Oreal, hAPP( hAPP( c_Power_Opower__class_Opower( 
% 0.97/1.59    tc_RealDef_Oreal ), T ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, 
% 0.97/1.59    c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ), hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Y ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( 
% 0.97/1.59    c_Int_OPls ) ) ) ) ) ), c_NthRoot_Osqrt( c_Groups_Oplus__class_Oplus( 
% 0.97/1.59    tc_RealDef_Oreal, hAPP( hAPP( c_Power_Opower__class_Opower( 
% 0.97/1.59    tc_RealDef_Oreal ), Z ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, 
% 0.97/1.59    c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ), hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( tc_RealDef_Oreal ), X ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( 
% 0.97/1.59    c_Int_OPls ) ) ) ) ) ) ) ) }.
% 0.97/1.59  { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, c_NthRoot_Osqrt( 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( tc_RealDef_Oreal ), X ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( 
% 0.97/1.59    c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower( 
% 0.97/1.59    tc_RealDef_Oreal ), Y ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, 
% 0.97/1.59    c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) ) ) }.
% 0.97/1.59  { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, c_NthRoot_Osqrt( 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Y ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( 
% 0.97/1.59    c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower( 
% 0.97/1.59    tc_RealDef_Oreal ), X ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, 
% 0.97/1.59    c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) ) ) }.
% 0.97/1.59  { hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ), 
% 0.97/1.59    c_NthRoot_Osqrt( hAPP( hAPP( c_Groups_Otimes__class_Otimes( 
% 0.97/1.59    tc_RealDef_Oreal ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( 
% 0.97/1.59    hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ), T ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( 
% 0.97/1.59    c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower( 
% 0.97/1.59    tc_RealDef_Oreal ), Z ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, 
% 0.97/1.59    c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) ), 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Y ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( 
% 0.97/1.59    c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower( 
% 0.97/1.59    tc_RealDef_Oreal ), X ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, 
% 0.97/1.59    c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) ) ) ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( 
% 0.97/1.59    c_Int_OPls ) ) ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( 
% 0.97/1.59    tc_RealDef_Oreal ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( 
% 0.97/1.59    hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ), T ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( 
% 0.97/1.59    c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower( 
% 0.97/1.59    tc_RealDef_Oreal ), Z ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, 
% 0.97/1.59    c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) ), 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Y ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( 
% 0.97/1.59    c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower( 
% 0.97/1.59    tc_RealDef_Oreal ), X ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, 
% 0.97/1.59    c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) ) }.
% 0.97/1.59  { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Y ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( 
% 0.97/1.59    c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower( 
% 0.97/1.59    tc_RealDef_Oreal ), X ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, 
% 0.97/1.59    c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) = 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y = 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.59  { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Y ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( 
% 0.97/1.59    c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower( 
% 0.97/1.59    tc_RealDef_Oreal ), X ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, 
% 0.97/1.59    c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) = 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X = 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.59  { ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! X = 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Y ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( 
% 0.97/1.59    c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower( 
% 0.97/1.59    tc_RealDef_Oreal ), X ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, 
% 0.97/1.59    c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) = 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.59  { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T, 
% 0.97/1.59    Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.59  { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z, 
% 0.97/1.59    T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.59  { ! class_Groups_Oordered__ab__semigroup__add( X ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, Z, Y ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, U, T ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z, 
% 0.97/1.59    U ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.97/1.59  { ! class_Groups_Oordered__ab__semigroup__add( X ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, Z, Y ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T, 
% 0.97/1.59    Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.97/1.59  { ! class_Groups_Oordered__ab__semigroup__add( X ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, Z, Y ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z, 
% 0.97/1.59    T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.97/1.59  { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T, 
% 0.97/1.59    Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.59  { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, Z, Y ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T, 
% 0.97/1.59    Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.97/1.59  { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T, 
% 0.97/1.59    Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.97/1.59  { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, T, Y ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T, 
% 0.97/1.59    Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.97/1.59  { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.97/1.59     = Y }.
% 0.97/1.59  { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.97/1.59     = Y }.
% 0.97/1.59  { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.97/1.59     = Y }.
% 0.97/1.59  { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.97/1.59     = Y }.
% 0.97/1.59  { ! class_Groups_Oordered__ab__group__add__abs( X ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Z ), 
% 0.97/1.59    Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.59  { ! class_Groups_Oordered__ab__group__add__abs( X ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oabs__class_Oabs( X, Y
% 0.97/1.59     ) ) }.
% 0.97/1.59  { ! class_Groups_Oordered__ab__group__add__abs( X ), 
% 0.97/1.59    c_Groups_Oabs__class_Oabs( X, c_Groups_Oplus__class_Oplus( X, 
% 0.97/1.59    c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ) ) 
% 0.97/1.59    = c_Groups_Oplus__class_Oplus( X, c_Groups_Oabs__class_Oabs( X, Z ), 
% 0.97/1.59    c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.97/1.59  { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( 
% 0.97/1.59    c_Int_OPls ) ) ) ), Y ) ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( 
% 0.97/1.59    X ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( X ), Z ), Y ) ), hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( X ), Z ), Y ) ) ) }.
% 0.97/1.59  { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( 
% 0.97/1.59    c_Int_OPls ) ) ) ), Y ) ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( 
% 0.97/1.59    X ), Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( X ), Z ), Y ) ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( 
% 0.97/1.59    c_Int_OPls ) ) ) ) ) }.
% 0.97/1.59  { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.97/1.59    ( X, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( X ), Z ), c_Int_Onumber__class_Onumber__of
% 0.97/1.59    ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ), hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( X ), Y ), c_Int_Onumber__class_Onumber__of
% 0.97/1.59    ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ), 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( X ) ), Z = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.59     }.
% 0.97/1.59  { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.97/1.59    ( X, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( X ), Z ), c_Int_Onumber__class_Onumber__of
% 0.97/1.59    ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ), hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( X ), Y ), c_Int_Onumber__class_Onumber__of
% 0.97/1.59    ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ), 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.59     }.
% 0.97/1.59  { ! class_Rings_Olinordered__idom( X ), ! Z = c_Groups_Ozero__class_Ozero( 
% 0.97/1.59    X ), ! Y = c_Groups_Ozero__class_Ozero( X ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, 
% 0.97/1.59    hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( 
% 0.97/1.59    c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( 
% 0.97/1.59    c_Int_OPls ) ) ) ) ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.59  { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.97/1.59    ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( 
% 0.97/1.59    c_Int_OPls ) ) ) ), Z ) ), c_Groups_Ozero__class_Ozero( X ) ), Y = 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59  { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_Int_Oint ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0( c_Int_OBit1( 
% 0.97/1.59    c_Int_OPls ) ) ) ) }.
% 0.97/1.59  { ! class_RealVector_Oreal__normed__vector( X ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, 
% 0.97/1.59    c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.97/1.59    , Y ) ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, 
% 0.97/1.59    c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, U, 
% 0.97/1.59    Z ) ), c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus
% 0.97/1.59    ( X, T, Y ) ) ) ) }.
% 0.97/1.59  { ! class_Rings_Olinordered__semiring__1( X ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, Z, Y ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, T, Y ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.97/1.59     ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( 
% 0.97/1.59    X ), W ), ! c_Groups_Oplus__class_Oplus( X, U, W ) = 
% 0.97/1.59    c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless__eq( X, 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.59    ( X ), U ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), T )
% 0.97/1.59     ), Y ) }.
% 0.97/1.59  { ! class_Int_Onumber__ring( X ), ! 
% 0.97/1.59    class_RealVector_Oreal__normed__algebra__1( X ), 
% 0.97/1.59    c_RealVector_Onorm__class_Onorm( X, c_Int_Onumber__class_Onumber__of( X, 
% 0.97/1.59    Y ) ) = c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, Y ) ) }.
% 0.97/1.59  { ! class_RealVector_Oreal__normed__vector( X ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, 
% 0.97/1.59    c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, 
% 0.97/1.59    c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, 
% 0.97/1.59    c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.97/1.59    ( X, Y ) ) ), c_RealVector_Onorm__class_Onorm( X, 
% 0.97/1.59    c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) }.
% 0.97/1.59  { ! class_RealVector_Oreal__normed__algebra__1( X ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, 
% 0.97/1.59    c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( X ), Z ), Y ) ), hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( tc_RealDef_Oreal ), 
% 0.97/1.59    c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) ) }.
% 0.97/1.59  { ! class_RealVector_Oreal__normed__vector( X ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, 
% 0.97/1.59    c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, Z, 
% 0.97/1.59    Y ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, 
% 0.97/1.59    c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.97/1.59    ( X, Y ) ) ) }.
% 0.97/1.59  { ! c_Complex_Oii = c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) }.
% 0.97/1.59  { ! c_Complex_Oii = c_Int_Onumber__class_Onumber__of( tc_Complex_Ocomplex, 
% 0.97/1.59    X ) }.
% 0.97/1.59  { ! c_Complex_Oii = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.97/1.59  { c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, X ) = 
% 0.97/1.59    c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) }.
% 0.97/1.59  { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), 
% 0.97/1.59    c_Complex_Oii ), c_Complex_Oii ) = c_Int_Onumber__class_Onumber__of( 
% 0.97/1.59    tc_Complex_Ocomplex, c_Int_OMin ) }.
% 0.97/1.59  { ! c_Complex_Ocomplex_OComplex( Y, X ) = c_Complex_Oii, Y = 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.59  { ! c_Complex_Ocomplex_OComplex( Y, X ) = c_Complex_Oii, X = 
% 0.97/1.59    c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.97/1.59  { ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! X = 
% 0.97/1.59    c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), 
% 0.97/1.59    c_Complex_Ocomplex_OComplex( Y, X ) = c_Complex_Oii }.
% 0.97/1.59  { c_Complex_Oii = c_Complex_Ocomplex_OComplex( c_Groups_Ozero__class_Ozero
% 0.97/1.59    ( tc_RealDef_Oreal ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.97/1.59  { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Ozero__class_Ozero( 
% 0.97/1.59    tc_Int_Oint ) ) }.
% 0.97/1.59  { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.59    ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) = 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59  { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.97/1.59     ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59  { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.97/1.59     ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59  { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.59    ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) = 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59  { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.97/1.59     ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59  { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.97/1.59     ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59  { ! class_Rings_Oring__no__zero__divisors( X ), ! hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.59     = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59  { ! class_Rings_Oring__no__zero__divisors( X ), ! Z = 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59  { ! class_Rings_Oring__no__zero__divisors( X ), ! Y = 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59  { ! class_Rings_Ono__zero__divisors( X ), Y = c_Groups_Ozero__class_Ozero( 
% 0.97/1.59    X ), Z = c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), Y ), Z ) = 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59  { ! class_Rings_Ono__zero__divisors( X ), ! hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.59     = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59  { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Oone__class_Oone( X ) = 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59  { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Ozero__class_Ozero( X ) = 
% 0.97/1.59    c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.59  { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X, 
% 0.97/1.59    Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.59  { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X, 
% 0.97/1.59    Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.59  { ! class_Rings_Ocomm__semiring( X ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.97/1.59     ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.59  { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.97/1.59     ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.59  { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.97/1.59     ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.59  { ! class_Rings_Osemiring( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP
% 0.97/1.59    ( c_Groups_Otimes__class_Otimes( X ), U ), T ), 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.59    ( X ), Z ), T ), Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, U, Z
% 0.97/1.59     ) ), T ), Y ) }.
% 0.97/1.59  { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 0.97/1.59    , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.59  { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 0.97/1.59    , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.59  { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T, 
% 0.97/1.59    Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.59  { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T, 
% 0.97/1.59    Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.59  { ! class_RealVector_Oreal__normed__vector( X ), ! 
% 0.97/1.59    c_RealVector_Onorm__class_Onorm( X, Y ) = c_Groups_Ozero__class_Ozero( 
% 0.97/1.59    tc_RealDef_Oreal ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59  { ! class_RealVector_Oreal__normed__vector( X ), ! Y = 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X, Y )
% 0.97/1.59     = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.59  { ! class_RealVector_Oreal__normed__vector( X ), 
% 0.97/1.59    c_RealVector_Onorm__class_Onorm( X, c_Groups_Ozero__class_Ozero( X ) ) = 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.59  { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, hAPP
% 0.97/1.59    ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ), 
% 0.97/1.59    c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.97/1.59  { ! class_Rings_Olinordered__idom( X ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Y ) ), 
% 0.97/1.59    c_Groups_Oabs__class_Oabs( X, Y ) ) = hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.97/1.59  { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, 
% 0.97/1.59    c_Groups_Oone__class_Oone( X ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.59  { ! class_RealVector_Oreal__normed__vector( X ), 
% 0.97/1.59    c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, Z, 
% 0.97/1.59    Y ) ) = c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus
% 0.97/1.59    ( X, Y, Z ) ) }.
% 0.97/1.59  { ! class_RealVector_Oreal__normed__vector( X ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), 
% 0.97/1.59    c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.97/1.59  { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oone__class_Oone( 
% 0.97/1.59    tc_Int_Oint ) ) }.
% 0.97/1.59  { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus( 
% 0.97/1.59    tc_Int_Oint, X, Y ) ) }.
% 0.97/1.59  { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) }.
% 0.97/1.59  { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Oabs__class_Oabs
% 0.97/1.59    ( tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( X, Y ) ) = 
% 0.97/1.59    c_RealVector_Onorm__class_Onorm( X, Y ) }.
% 0.97/1.59  { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) }.
% 0.97/1.59  { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), 
% 0.97/1.59    c_Complex_Oii ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, 
% 0.97/1.59    c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) = 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Complex_Ocomplex, c_Int_OMin ) }.
% 0.97/1.59  { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq( 
% 0.97/1.59    X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) }.
% 0.97/1.59  { ! class_Rings_Olinordered__ring__strict( X ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), 
% 0.97/1.59    hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), alpha2( X, Y
% 0.97/1.59    , Z ), alpha34( X, Y, Z ) }.
% 0.97/1.59  { ! class_Rings_Olinordered__ring__strict( X ), ! alpha2( X, Y, Z ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), 
% 0.97/1.59    hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.59  { ! class_Rings_Olinordered__ring__strict( X ), ! alpha34( X, Y, Z ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), 
% 0.97/1.59    hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.59  { ! alpha34( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z, 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.59  { ! alpha34( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y, 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.59  { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.97/1.59     ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y, 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( X ) ), alpha34( X, Y, Z ) }.
% 0.97/1.59  { ! alpha2( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.97/1.59  { ! alpha2( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.97/1.59  { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.59    , Z ), ! c_Orderings_Oord__class_Oless__eq( X, 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( X ), Y ), alpha2( X, Y, Z ) }.
% 0.97/1.59  { ! class_Rings_Olinordered__ring__strict( X ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.97/1.59    ( X ) ), alpha3( X, Y, Z ), alpha35( X, Y, Z ) }.
% 0.97/1.59  { ! class_Rings_Olinordered__ring__strict( X ), ! alpha3( X, Y, Z ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.97/1.59    ( X ) ) }.
% 0.97/1.59  { ! class_Rings_Olinordered__ring__strict( X ), ! alpha35( X, Y, Z ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.97/1.59    ( X ) ) }.
% 0.97/1.59  { ! alpha35( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z, 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.59  { ! alpha35( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.97/1.59  { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.97/1.59     ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.97/1.59    ( X ), Y ), alpha35( X, Y, Z ) }.
% 0.97/1.59  { ! alpha3( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.97/1.59  { ! alpha3( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y, 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.59  { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.59    , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y, 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( X ) ), alpha3( X, Y, Z ) }.
% 0.97/1.59  { ! class_Rings_Oordered__cancel__semiring( X ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.59     ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( 
% 0.97/1.59    X ), Z ), c_Orderings_Oord__class_Oless__eq( X, 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.59  { ! class_Rings_Oordered__cancel__semiring( X ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.59     ), ! c_Orderings_Oord__class_Oless__eq( X, Z, 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.59    , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.59  { ! class_Rings_Oordered__cancel__semiring( X ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.59     ), ! c_Orderings_Oord__class_Oless__eq( X, Z, 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.59    , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.59  { ! class_Rings_Oordered__cancel__semiring( X ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.59     ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( 
% 0.97/1.59    X ), Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.97/1.59    ( X ) ) }.
% 0.97/1.59  { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.59    , Y, c_Groups_Ozero__class_Ozero( X ) ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.59     ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.97/1.59     ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.59  { ! class_Rings_Oordered__semiring( X ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, Z, Y ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.97/1.59     ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.97/1.59  { ! class_Rings_Oordered__semiring( X ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, Z, Y ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.97/1.59     ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.59  { ! class_Rings_Oordered__comm__semiring( X ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, Z, Y ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.97/1.59     ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.59  { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.59    , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T, 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.59    , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.97/1.59  { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.59    , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T, 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.59    , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.97/1.59  { ! class_Rings_Oordered__semiring( X ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, Z, Y ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, U, T ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.97/1.59     ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( 
% 0.97/1.59    X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.97/1.59  { ! class_Rings_Oordered__semiring( X ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, Z, Y ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, U, T ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.59     ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( 
% 0.97/1.59    X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.97/1.59  { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.59    , c_Groups_Ozero__class_Ozero( X ), Z ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.59     ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.97/1.59     ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.59  { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.59    , Z, c_Groups_Ozero__class_Ozero( X ) ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.59     ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.97/1.59     ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.59  { ! class_Rings_Oordered__cancel__semiring( X ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.97/1.59     ), ! c_Orderings_Oord__class_Oless__eq( X, Y, 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.59    , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.59  { ! class_Rings_Oordered__cancel__semiring( X ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.59     ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( 
% 0.97/1.59    X ), Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.97/1.59    ( X ) ) }.
% 0.97/1.59  { ! class_Rings_Olinordered__semidom( X ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.59  { ! class_Rings_Olinordered__semidom( X ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), 
% 0.97/1.59    c_Groups_Oone__class_Oone( X ) ) }.
% 0.97/1.59  { ! class_RealVector_Oreal__normed__algebra( X ), 
% 0.97/1.59    c_Groups_Ominus__class_Ominus( X, hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X, hAPP( 
% 0.97/1.59    hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( 
% 0.97/1.59    X, U, Z ) ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U, 
% 0.97/1.59    Z ) ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), 
% 0.97/1.59    c_Groups_Ominus__class_Ominus( X, T, Y ) ) ) }.
% 0.97/1.59  { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) = 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.59    ( X ), Z ), U ), Y ), T = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z, 
% 0.97/1.59    W ) ), U ), Y ) }.
% 0.97/1.59  { ! class_Rings_Oring( X ), ! T = c_Groups_Oplus__class_Oplus( X, hAPP( 
% 0.97/1.59    hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( 
% 0.97/1.59    X, Z, W ) ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) = 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.59    ( X ), Z ), U ), Y ) }.
% 0.97/1.59  { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) = 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.59    ( X ), Z ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W, 
% 0.97/1.59    Z ) ), U ), T ) = Y }.
% 0.97/1.59  { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W, 
% 0.97/1.59    Z ) ), U ), T ) = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) = 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.59    ( X ), Z ), U ), Y ) }.
% 0.97/1.59  { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), ! 
% 0.97/1.59    class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.97/1.59    , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) ) = 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.97/1.59    .
% 0.97/1.59  { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), ! 
% 0.97/1.59    class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.97/1.59    , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) ) = 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( X ), ! c_Int_Onumber__class_Onumber__of( 
% 0.97/1.59    tc_Nat_Onat, Y ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.59  { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), ! 
% 0.97/1.59    class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.97/1.59    , ! Z = c_Groups_Ozero__class_Ozero( X ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) = 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( X ), Z ), c_Int_Onumber__class_Onumber__of
% 0.97/1.59    ( tc_Nat_Onat, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59  { ! class_RealVector_Oreal__normed__vector( X ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, 
% 0.97/1.59    c_RealVector_Onorm__class_Onorm( X, Y ), c_Groups_Ozero__class_Ozero( 
% 0.97/1.59    tc_RealDef_Oreal ) ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59  { ! class_RealVector_Oreal__normed__vector( X ), ! Y = 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq( 
% 0.97/1.59    tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( X, Y ), 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.97/1.59  { ! class_RealVector_Oreal__normed__vector( X ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, 
% 0.97/1.59    c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, 
% 0.97/1.59    c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.97/1.59    ( X, Y ) ), c_RealVector_Onorm__class_Onorm( X, 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( X, Z, Y ) ) ) }.
% 0.97/1.59  { ! class_RealVector_Oreal__normed__vector( X ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, 
% 0.97/1.59    c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, 
% 0.97/1.59    c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.97/1.59    ( X, Y ) ), c_RealVector_Onorm__class_Onorm( X, 
% 0.97/1.59    c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) }.
% 0.97/1.59  { ! class_RealVector_Oreal__normed__div__algebra( X ), 
% 0.97/1.59    c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), 
% 0.97/1.59    c_RealVector_Onorm__class_Onorm( X, Z ) ), 
% 0.97/1.59    c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.97/1.59  { ! class_RealVector_Oreal__normed__algebra__1( X ), 
% 0.97/1.59    c_RealVector_Onorm__class_Onorm( X, c_Groups_Oone__class_Oone( X ) ) = 
% 0.97/1.59    c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.97/1.59  { ! class_RealVector_Oreal__normed__div__algebra( X ), 
% 0.97/1.59    c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( tc_RealDef_Oreal ), 
% 0.97/1.59    c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) }.
% 0.97/1.59  { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.97/1.59    ( X, c_Groups_Ozero__class_Ozero( X ), Y ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.97/1.59     ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.97/1.59    ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) }.
% 0.97/1.59  { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.97/1.59    ( X, c_Groups_Ozero__class_Ozero( X ), Y ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.97/1.59     ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.97/1.59    ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) }.
% 0.97/1.59  { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.59    , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), W ), U ), T ), 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.59    ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X, T, 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.59    ( X ), c_Groups_Ominus__class_Ominus( X, Z, W ) ), U ), Y ) ) }.
% 0.97/1.59  { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.59    , T, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z, 
% 0.97/1.59    W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X, 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.59    ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.97/1.59  { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.59    , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), W ), U ), T ), 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.59    ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X, 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.59    ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ) }.
% 0.97/1.59  { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.59    , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W, 
% 0.97/1.59    Z ) ), U ), T ), Y ), c_Orderings_Oord__class_Oless__eq( X, 
% 0.97/1.59    c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.59    ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.97/1.59  { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.97/1.59    ( X, c_Groups_Ozero__class_Ozero( X ), Y ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ), 
% 0.97/1.59    Y ) = c_Groups_Oabs__class_Oabs( X, hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.59  { ! class_Rings_Oordered__ring__abs( X ), alpha99( X, Z ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.59     ), c_Groups_Oabs__class_Oabs( X, hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ), 
% 0.97/1.59    c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.97/1.59  { ! class_Rings_Oordered__ring__abs( X ), alpha99( X, Z ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.59     ), c_Groups_Oabs__class_Oabs( X, hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ), 
% 0.97/1.59    c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.97/1.59  { ! alpha99( X, Y ), ! c_Orderings_Oord__class_Oless__eq( X, 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.97/1.59  { ! alpha99( X, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.59  { c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.59     ), c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero
% 0.97/1.59    ( X ) ), alpha99( X, Y ) }.
% 0.97/1.59  { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), ! 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) = 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) ) = 
% 0.97/1.59    c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.59  { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) = 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) ) = 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59  { ! class_RealVector_Oreal__normed__algebra( X ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, 
% 0.97/1.59    c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), 
% 0.97/1.59    c_RealVector_Onorm__class_Onorm( X, Z ) ), 
% 0.97/1.59    c_RealVector_Onorm__class_Onorm( X, Y ) ) ) }.
% 0.97/1.59  { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_Int_Oint ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit1( c_Int_OBit1( 
% 0.97/1.59    c_Int_OPls ) ) ) ) }.
% 0.97/1.59  { ! class_RealVector_Oreal__normed__vector( X ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, 
% 0.97/1.59    c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.97/1.59     ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, 
% 0.97/1.59    c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.97/1.59    ( X, Y ) ) ) }.
% 0.97/1.59  { ! class_Power_Opower( X ), ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 0.97/1.59     ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) = 
% 0.97/1.59    c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.59  { ! class_Power_Opower( X ), Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.97/1.59    , hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) = hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ominus__class_Ominus( 
% 0.97/1.59    tc_Nat_Onat, Z, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 0.97/1.59  { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_Int_Oint ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_Int_Oint ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0( X ) ) ) }.
% 0.97/1.59  { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_Int_Oint ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ), 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_Int_Oint ), 
% 0.97/1.59    c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit1( X ) ) ) }.
% 0.97/1.59  { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless__eq( 
% 0.97/1.59    tc_Nat_Onat, Z, Y ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), 
% 0.97/1.59    c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) ) = hAPP
% 0.97/1.59    ( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP( 
% 0.97/1.59    c_Power_Opower__class_Opower( X ), T ), c_Groups_Ominus__class_Ominus( 
% 0.97/1.59    tc_Nat_Onat, Y, Z ) ) ), T ) }.
% 0.97/1.59  { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.97/1.59  { ! class_RealVector_Oreal__normed__vector( X ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), ! 
% 0.97/1.59    c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, 
% 0.97/1.59    c_RealVector_Onorm__class_Onorm( X, Z ), hAPP( hAPP( 
% 0.97/1.59    c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), 
% 0.97/1.59    c_RealVector_Onorm__class_Onorm( X, T ) ) ), Z = 
% 0.97/1.59    c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59  { ! X = c_Nat_OSuc( X ) }.
% 0.97/1.59  { ! c_Nat_OSuc( X ) = X }.
% 0.97/1.59  { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.97/1.60  { ! Y = X, c_Nat_OSuc( Y ) = c_Nat_OSuc( X ) }.
% 0.97/1.60  { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.97/1.60  { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.97/1.60  { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, c_Groups_Oplus__class_Oplus
% 0.97/1.60    ( tc_Nat_Onat, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.97/1.60  { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus( 
% 0.97/1.60    tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.97/1.60  { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) = 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ), Y = X }.
% 0.97/1.60  { ! Y = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) = 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) }.
% 0.97/1.60  { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) = 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ), Z = X }.
% 0.97/1.60  { ! Z = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) = 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.97/1.60  { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, X ) }.
% 0.97/1.60  { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ) }.
% 0.97/1.60  { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ), Y = X }.
% 0.97/1.60  { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP
% 0.97/1.60    ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.97/1.60  { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP( 
% 0.97/1.60    hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.60  { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.60    ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, 
% 0.97/1.60    c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ), Y ) }.
% 0.97/1.60  { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.97/1.60  { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.97/1.60  { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.60  { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.60  { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.97/1.60  { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.60  { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( 
% 0.97/1.60    tc_Nat_Onat ), X ) = X }.
% 0.97/1.60  { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero
% 0.97/1.60    ( tc_Nat_Onat ) ) = X }.
% 0.97/1.60  { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.60  { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X = 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.60  { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus( 
% 0.97/1.60    tc_Nat_Onat, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.60  { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = Y, X = 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.60  { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X = 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.60  { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.60  { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) = 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.97/1.60  { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) = 
% 0.97/1.60    c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.97/1.60  { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) = 
% 0.97/1.60    c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), X ) }
% 0.97/1.60    .
% 0.97/1.60  { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ), !
% 0.97/1.60     c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 0.97/1.60     ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.97/1.60  { ! Y = c_Nat_OSuc( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.97/1.60    , c_Nat_OSuc( X ) ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), 
% 0.97/1.60    c_Nat_OSuc( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X )
% 0.97/1.60     }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), 
% 0.97/1.60    c_Nat_OSuc( X ) ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 0.97/1.60     ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.60  { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) = 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.60  { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.60  { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X = 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.60  { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.60  { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.60  { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = 
% 0.97/1.60    hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Y = X
% 0.97/1.60    , Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.60  { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.97/1.60     ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.97/1.60    .
% 0.97/1.60  { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.97/1.60  { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = 
% 0.97/1.60    hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = X
% 0.97/1.60    , Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.60  { ! Z = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.97/1.60     ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }
% 0.97/1.60    .
% 0.97/1.60  { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.97/1.60  { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) = 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! 
% 0.97/1.60    c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.97/1.60  { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, X ) = 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.60  { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 0.97/1.60  { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( 
% 0.97/1.60    tc_Nat_Onat ), X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.60  { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z
% 0.97/1.60     ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), 
% 0.97/1.60    c_Nat_OSuc( Z ) ), X ), Y = X }.
% 0.97/1.60  { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), 
% 0.97/1.60    c_Nat_OSuc( Z ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( 
% 0.97/1.60    tc_Nat_Onat ), c_Nat_OSuc( Z ) ), X ) }.
% 0.97/1.60  { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.97/1.60  { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X = 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol4( X, Y ) ) }.
% 0.97/1.60  { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X = 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol5( X, Y ) ) }.
% 0.97/1.60  { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ), 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, T ), 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ), X ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.60  { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc( 
% 0.97/1.60    X ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 0.97/1.60  { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.60    ( tc_Nat_Onat, c_Nat_OSuc( Z ), Y ), c_Nat_OSuc( X ) ) = 
% 0.97/1.60    c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.60    ( tc_Nat_Onat, Z, Y ), X ) }.
% 0.97/1.60  { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) = 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.97/1.60  { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ), X ) = 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.60  { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) }.
% 0.97/1.60  { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), T ), hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.97/1.60  { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus( 
% 0.97/1.60    tc_Nat_Onat, Y, X ), X ) = Y }.
% 0.97/1.60  { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus( 
% 0.97/1.60    tc_Nat_Onat, Y, X ), Y ) = X }.
% 0.97/1.60  { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.60    ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, 
% 0.97/1.60    Z, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.97/1.60  { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus( 
% 0.97/1.60    tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) =
% 0.97/1.60     c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 0.97/1.60  { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus( 
% 0.97/1.60    tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) =
% 0.97/1.60     c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ) }.
% 0.97/1.60  { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, 
% 0.97/1.60    c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ), Y ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, 
% 0.97/1.60    c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ), 
% 0.97/1.60    c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, 
% 0.97/1.60    c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, Z ), 
% 0.97/1.60    c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), 
% 0.97/1.60    c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, 
% 0.97/1.60    c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = Y }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), ! 
% 0.97/1.60    c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = 
% 0.97/1.60    c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X = Z }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), ! X = Z, 
% 0.97/1.60    c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = 
% 0.97/1.60    c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), 
% 0.97/1.60    c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.60    ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.97/1.60     ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, 
% 0.97/1.60    c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), 
% 0.97/1.60    c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, 
% 0.97/1.60    c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), 
% 0.97/1.60    c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 0.97/1.60  { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), 
% 0.97/1.60    c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) = 
% 0.97/1.60    c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.97/1.60  { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), 
% 0.97/1.60    c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ), X ) = 
% 0.97/1.60    c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.60  { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), 
% 0.97/1.60    c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) = X }.
% 0.97/1.60  { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), Y = 
% 0.97/1.60    c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.97/1.60  { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X = 
% 0.97/1.60    c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.97/1.60  { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X = 
% 0.97/1.60    c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Groups_Oone__class_Oone( 
% 0.97/1.60    tc_Nat_Onat ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.97/1.60    , Y ), X ) }.
% 0.97/1.60  { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), 
% 0.97/1.60    c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.97/1.60  { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = 
% 0.97/1.60    c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Oone__class_Oone( 
% 0.97/1.60    tc_Nat_Onat ) }.
% 0.97/1.60  { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = 
% 0.97/1.60    c_Groups_Oone__class_Oone( tc_Nat_Onat ), X = c_Groups_Oone__class_Oone( 
% 0.97/1.60    tc_Nat_Onat ) }.
% 0.97/1.60  { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X = 
% 0.97/1.60    c_Groups_Oone__class_Oone( tc_Nat_Onat ), hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = 
% 0.97/1.60    c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.97/1.60  { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc( 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha4( X, Y ), alpha36( X
% 0.97/1.60    , Y ) }.
% 0.97/1.60  { ! alpha4( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = 
% 0.97/1.60    c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.60  { ! alpha36( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = 
% 0.97/1.60    c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.60  { ! alpha36( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.60  { ! alpha36( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( 
% 0.97/1.60    tc_Nat_Onat ) ) }.
% 0.97/1.60  { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc( 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha36( X, Y ) }.
% 0.97/1.60  { ! alpha4( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( 
% 0.97/1.60    tc_Nat_Onat ) ) }.
% 0.97/1.60  { ! alpha4( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.60  { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X = 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha4( X, Y ) }.
% 0.97/1.60  { ! c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ), alpha5( X, Y ), alpha37
% 0.97/1.60    ( X, Y ) }.
% 0.97/1.60  { ! alpha5( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.97/1.60     ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.97/1.60  { ! alpha37( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.97/1.60     ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.97/1.60  { ! alpha37( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.60  { ! alpha37( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( 
% 0.97/1.60    tc_Nat_Onat ) ) }.
% 0.97/1.60  { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc( 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha37( X, Y ) }.
% 0.97/1.60  { ! alpha5( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( 
% 0.97/1.60    tc_Nat_Onat ) ) }.
% 0.97/1.60  { ! alpha5( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.60  { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X = 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha5( X, Y ) }.
% 0.97/1.60  { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = 
% 0.97/1.60    c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y = c_Nat_OSuc
% 0.97/1.60    ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.60  { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = 
% 0.97/1.60    c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X = c_Nat_OSuc
% 0.97/1.60    ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.60  { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X = 
% 0.97/1.60    c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc( 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.60  { c_Groups_Oone__class_Oone( tc_Nat_Onat ) = c_Nat_OSuc( 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.60  { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) = 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), 
% 0.97/1.60    c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) = 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.60  { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) = 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), 
% 0.97/1.60    c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) = 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.60  { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), c_Nat_OSuc
% 0.97/1.60    ( X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.60  { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Y )
% 0.97/1.60     ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ), 
% 0.97/1.60    hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.97/1.60     ), X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ), 
% 0.97/1.60    hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.97/1.60     ), X ) ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), 
% 0.97/1.60    c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) = 
% 0.97/1.60    c_Nat_OSuc( c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.97/1.60  { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X )
% 0.97/1.60    , X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), 
% 0.97/1.60    c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus( 
% 0.97/1.60    tc_Nat_Onat, X, Z ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, 
% 0.97/1.60    c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), Z ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus( 
% 0.97/1.60    tc_Nat_Onat, X, Y ), Z ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ), Y ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), 
% 0.97/1.60    c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus( 
% 0.97/1.60    tc_Nat_Onat, Z, X ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, 
% 0.97/1.60    c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! 
% 0.97/1.60    c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z, X = 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X = 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), 
% 0.97/1.60    c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus( 
% 0.97/1.60    tc_Nat_Onat, X, Y ), Y ) = X }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, 
% 0.97/1.60    c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, 
% 0.97/1.60    c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, 
% 0.97/1.60    c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = 
% 0.97/1.60    c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus( 
% 0.97/1.60    tc_Nat_Onat, Z, X ), Y ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, 
% 0.97/1.60    c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = X }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, 
% 0.97/1.60    c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus( 
% 0.97/1.60    tc_Nat_Onat, X, Z ), Y ) ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, 
% 0.97/1.60    c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, 
% 0.97/1.60    c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), 
% 0.97/1.60    c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, 
% 0.97/1.60    c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = 
% 0.97/1.60    c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus( 
% 0.97/1.60    tc_Nat_Onat, Z, Y ), X ) }.
% 0.97/1.60  { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ), 
% 0.97/1.60    c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.60  { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_Int_Oint ), 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OPls ) ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), 
% 0.97/1.60    c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( 
% 0.97/1.60    c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), Z ) = 
% 0.97/1.60    c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ), 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), 
% 0.97/1.60    c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, c_Nat_OSuc( 
% 0.97/1.60    c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) ) = 
% 0.97/1.60    c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus( 
% 0.97/1.60    tc_Nat_Onat, Z, Y ), c_Nat_OSuc( X ) ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, 
% 0.97/1.60    c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ), hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), 
% 0.97/1.60    c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Z ) ) ), Y = 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.60  { c_Complex_Ocomplex_Ocomplex__size( c_Complex_Ocomplex_OComplex( Y, X ) ) 
% 0.97/1.60    = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ), 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), 
% 0.97/1.60    c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), 
% 0.97/1.60    c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ), 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), 
% 0.97/1.60    c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus( 
% 0.97/1.60    tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 0.97/1.60     ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) = 
% 0.97/1.60    c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus( 
% 0.97/1.60    tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), 
% 0.97/1.60    c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) = 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ), 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), 
% 0.97/1.60    c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) = Z }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), 
% 0.97/1.60    c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) = Z, 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) = 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) }.
% 0.97/1.60  { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = 
% 0.97/1.60    hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Z = 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.97/1.60  { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.97/1.60  { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.97/1.60     ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.97/1.60    .
% 0.97/1.60  { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), T ), Z ), 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), X ) ) = 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus
% 0.97/1.60    ( tc_Nat_Onat, T, Y ) ), Z ), X ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) = 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ), T = 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), 
% 0.97/1.60    c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! T = 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), 
% 0.97/1.60    c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ), 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) = 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), 
% 0.97/1.60    c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus( 
% 0.97/1.60    tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 0.97/1.60     ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) = 
% 0.97/1.60    c_Groups_Ominus__class_Ominus( tc_Nat_Onat, T, 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), 
% 0.97/1.60    c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ), 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), 
% 0.97/1.60    c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), 
% 0.97/1.60    c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ), 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) }.
% 0.97/1.60  { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, 
% 0.97/1.60    c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, Y, c_NthRoot_Osqrt( 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP( 
% 0.97/1.60    c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Y ), 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( 
% 0.97/1.60    c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower( 
% 0.97/1.60    tc_RealDef_Oreal ), X ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, 
% 0.97/1.60    c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) ) ) ), 
% 0.97/1.60    c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.97/1.60  { c_Nat_Osize__class_Osize( tc_Complex_Ocomplex, 
% 0.97/1.60    c_Complex_Ocomplex_OComplex( Y, X ) ) = c_Groups_Ozero__class_Ozero( 
% 0.97/1.60    tc_Nat_Onat ) }.
% 0.97/1.60  { c_Complex_Ocomplex_Ocomplex__case( T, Z, c_Complex_Ocomplex_OComplex( Y, 
% 0.97/1.60    X ) ) = hAPP( hAPP( Z, Y ), X ) }.
% 0.97/1.60  { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.60     }.
% 0.97/1.60  { ! class_RealVector_Oreal__normed__field( X ), 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.97/1.60     = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.60  { ! class_Rings_Odivision__ring__inverse__zero( X ), 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.60     = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.60  { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X, 
% 0.97/1.60    c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) = 
% 0.97/1.60    c_Groups_Ominus__class_Ominus( X, c_Rings_Oinverse__class_Odivide( X, T, 
% 0.97/1.60    Y ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.97/1.60  { ! class_RealVector_Oreal__normed__field( X ), 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus( X, T, 
% 0.97/1.60    Z ), Y ) = c_Groups_Ominus__class_Ominus( X, 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( X, T, Y ), 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.97/1.60  { ! class_Rings_Odivision__ring( X ), hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), T ), c_Rings_Oinverse__class_Odivide
% 0.97/1.60    ( X, Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 0.97/1.60  { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X, 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.97/1.60    ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ), 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.97/1.60  { ! class_RealVector_Oreal__normed__field( X ), 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, T, Z
% 0.97/1.60     ), Y ) = c_Groups_Oplus__class_Oplus( X, c_Rings_Oinverse__class_Odivide
% 0.97/1.60    ( X, T, Y ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.97/1.60  { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X, Y
% 0.97/1.60    , c_Groups_Oone__class_Oone( X ) ) = Y }.
% 0.97/1.60  { ! class_Fields_Ofield__inverse__zero( X ), hAPP( hAPP( 
% 0.97/1.60    c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide( X, T
% 0.97/1.60    , Z ) ), Y ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP( 
% 0.97/1.60    c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP( 
% 0.97/1.60    c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.97/1.60  { c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ), hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ) ) = 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, X, Y ) }.
% 0.97/1.60  { c_NthRoot_Osqrt( c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, Y, X
% 0.97/1.60     ) ) = c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, c_NthRoot_Osqrt
% 0.97/1.60    ( Y ), c_NthRoot_Osqrt( X ) ) }.
% 0.97/1.60  { ! class_RealVector_Oreal__normed__field( X ), Y = 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X, 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) = 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, 
% 0.97/1.60    c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.97/1.60    ( X, Y ) ) }.
% 0.97/1.60  { ! class_Fields_Ofield__inverse__zero( X ), ! 
% 0.97/1.60    class_RealVector_Oreal__normed__field( X ), 
% 0.97/1.60    c_RealVector_Onorm__class_Onorm( X, c_Rings_Oinverse__class_Odivide( X, Z
% 0.97/1.60    , Y ) ) = c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, 
% 0.97/1.60    c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.97/1.60    ( X, Y ) ) }.
% 0.97/1.60  { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.60    , ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, T = 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.97/1.60  { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.60    , ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z }.
% 0.97/1.60  { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.60    , ! c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z, T = hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.97/1.60  { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.60    , ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z }.
% 0.97/1.60  { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.60    , ! T = c_Rings_Oinverse__class_Odivide( X, Z, Y ), hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z }.
% 0.97/1.60  { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.60    , ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, T = 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.97/1.60  { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Y = 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X, Y, 
% 0.97/1.60    Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.60  { ! class_Rings_Odivision__ring__inverse__zero( X ), Y = 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X, Y, 
% 0.97/1.60    Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.60  { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.60    , c_Rings_Oinverse__class_Odivide( X, Y, Y ) = c_Groups_Oone__class_Oone
% 0.97/1.60    ( X ) }.
% 0.97/1.60  { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.60    , ! c_Rings_Oinverse__class_Odivide( X, Z, Y ) = 
% 0.97/1.60    c_Groups_Oone__class_Oone( X ), Z = Y }.
% 0.97/1.60  { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.60    , ! Z = Y, c_Rings_Oinverse__class_Odivide( X, Z, Y ) = 
% 0.97/1.60    c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.60  { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP( 
% 0.97/1.60    hAPP( c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide
% 0.97/1.60    ( X, T, Y ) ), Z ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP( 
% 0.97/1.60    c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP( 
% 0.97/1.60    c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.97/1.60  { ! class_Fields_Ofield__inverse__zero( X ), 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( X, c_Groups_Oone__class_Oone( X ), hAPP
% 0.97/1.60    ( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP( 
% 0.97/1.60    c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide( X, 
% 0.97/1.60    c_Groups_Oone__class_Oone( X ), Z ) ), Y ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, Y, X ) ), alpha6( X, Y
% 0.97/1.60     ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, Y, X ) ), alpha38( X, 
% 0.97/1.60    Y ) }.
% 0.97/1.60  { ! alpha6( X, Y ), ! alpha38( X, Y ), c_Orderings_Oord__class_Oless__eq( 
% 0.97/1.60    tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, Y, X ) ) }.
% 0.97/1.60  { ! alpha38( X, Y ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), alpha38( X, Y ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), alpha38( X, Y ) }.
% 0.97/1.60  { ! alpha6( X, Y ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y
% 0.97/1.60    , c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), alpha6( X, Y ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), alpha6( X, Y ) }.
% 0.97/1.60  { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), ! 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( X, T, c_Int_Onumber__class_Onumber__of( 
% 0.97/1.60    X, Z ) ) = Y, alpha39( X, Y, Z, T ) }.
% 0.97/1.60  { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), ! 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( X, T, c_Int_Onumber__class_Onumber__of( 
% 0.97/1.60    X, Z ) ) = Y, alpha7( X, Y, Z ) }.
% 0.97/1.60  { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), ! 
% 0.97/1.60    alpha39( X, Y, Z, T ), ! alpha7( X, Y, Z ), 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( X, T, c_Int_Onumber__class_Onumber__of( 
% 0.97/1.60    X, Z ) ) = Y }.
% 0.97/1.60  { ! alpha39( X, Y, Z, T ), c_Int_Onumber__class_Onumber__of( X, Z ) = 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ), T = hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), Y ), c_Int_Onumber__class_Onumber__of
% 0.97/1.60    ( X, Z ) ) }.
% 0.97/1.60  { ! c_Int_Onumber__class_Onumber__of( X, Z ) = c_Groups_Ozero__class_Ozero
% 0.97/1.60    ( X ), alpha39( X, Y, Z, T ) }.
% 0.97/1.60  { ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( X, Z ) ), alpha39( X, Y, Z, T ) }.
% 0.97/1.60  { ! alpha7( X, Y, Z ), ! c_Int_Onumber__class_Onumber__of( X, Z ) = 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 0.97/1.60    .
% 0.97/1.60  { c_Int_Onumber__class_Onumber__of( X, Z ) = c_Groups_Ozero__class_Ozero( X
% 0.97/1.60     ), alpha7( X, Y, Z ) }.
% 0.97/1.60  { ! Y = c_Groups_Ozero__class_Ozero( X ), alpha7( X, Y, Z ) }.
% 0.97/1.60  { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), ! 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( X, T, Z ) = 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( X, Y ), alpha40( X, Y, Z, T ) }.
% 0.97/1.60  { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), ! 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( X, T, Z ) = 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( X, Y ), alpha8( X, Y, Z ) }.
% 0.97/1.60  { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), ! 
% 0.97/1.60    alpha40( X, Y, Z, T ), ! alpha8( X, Y, Z ), 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( X, T, Z ) = 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( X, Y ) }.
% 0.97/1.60  { ! alpha40( X, Y, Z, T ), Z = c_Groups_Ozero__class_Ozero( X ), T = hAPP( 
% 0.97/1.60    hAPP( c_Groups_Otimes__class_Otimes( X ), 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( X, Y ) ), Z ) }.
% 0.97/1.60  { ! Z = c_Groups_Ozero__class_Ozero( X ), alpha40( X, Y, Z, T ) }.
% 0.97/1.60  { ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( X, Y ) ), Z ), alpha40( X, Y, Z, T ) }
% 0.97/1.60    .
% 0.97/1.60  { ! alpha8( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero( X ), 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.97/1.60     ) }.
% 0.97/1.60  { Z = c_Groups_Ozero__class_Ozero( X ), alpha8( X, Y, Z ) }.
% 0.97/1.60  { ! c_Int_Onumber__class_Onumber__of( X, Y ) = c_Groups_Ozero__class_Ozero
% 0.97/1.60    ( X ), alpha8( X, Y, Z ) }.
% 0.97/1.60  { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), ! 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( X, T ) = 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( X, Z, Y ), alpha41( X, Y, Z, T ) }.
% 0.97/1.60  { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), ! 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( X, T ) = 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( X, Z, Y ), alpha9( X, Y, T ) }.
% 0.97/1.60  { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), ! 
% 0.97/1.60    alpha41( X, Y, Z, T ), ! alpha9( X, Y, T ), 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( X, T ) = 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.97/1.60  { ! alpha41( X, Y, Z, T ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP
% 0.97/1.60    ( c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X
% 0.97/1.60    , T ) ), Y ) = Z }.
% 0.97/1.60  { ! Y = c_Groups_Ozero__class_Ozero( X ), alpha41( X, Y, Z, T ) }.
% 0.97/1.60  { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( X, T ) ), Y ) = Z, alpha41( X, Y, Z, T
% 0.97/1.60     ) }.
% 0.97/1.60  { ! alpha9( X, Y, Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( X, Z ) = c_Groups_Ozero__class_Ozero( X
% 0.97/1.60     ) }.
% 0.97/1.60  { Y = c_Groups_Ozero__class_Ozero( X ), alpha9( X, Y, Z ) }.
% 0.97/1.60  { ! c_Int_Onumber__class_Onumber__of( X, Z ) = c_Groups_Ozero__class_Ozero
% 0.97/1.60    ( X ), alpha9( X, Y, Z ) }.
% 0.97/1.60  { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), ! T 
% 0.97/1.60    = c_Rings_Oinverse__class_Odivide( X, Z, c_Int_Onumber__class_Onumber__of
% 0.97/1.60    ( X, Y ) ), alpha42( X, Y, Z, T ) }.
% 0.97/1.60  { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), ! T 
% 0.97/1.60    = c_Rings_Oinverse__class_Odivide( X, Z, c_Int_Onumber__class_Onumber__of
% 0.97/1.60    ( X, Y ) ), alpha10( X, Y, T ) }.
% 0.97/1.60  { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), ! 
% 0.97/1.60    alpha42( X, Y, Z, T ), ! alpha10( X, Y, T ), T = 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( X, Z, c_Int_Onumber__class_Onumber__of( 
% 0.97/1.60    X, Y ) ) }.
% 0.97/1.60  { ! alpha42( X, Y, Z, T ), c_Int_Onumber__class_Onumber__of( X, Y ) = 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), T ), c_Int_Onumber__class_Onumber__of
% 0.97/1.60    ( X, Y ) ) = Z }.
% 0.97/1.60  { ! c_Int_Onumber__class_Onumber__of( X, Y ) = c_Groups_Ozero__class_Ozero
% 0.97/1.60    ( X ), alpha42( X, Y, Z, T ) }.
% 0.97/1.60  { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( X, Y ) ) = Z, alpha42( X, Y, Z, T ) }.
% 0.97/1.60  { ! alpha10( X, Y, Z ), ! c_Int_Onumber__class_Onumber__of( X, Y ) = 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.97/1.60    .
% 0.97/1.60  { c_Int_Onumber__class_Onumber__of( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.97/1.60     ), alpha10( X, Y, Z ) }.
% 0.97/1.60  { ! Z = c_Groups_Ozero__class_Ozero( X ), alpha10( X, Y, Z ) }.
% 0.97/1.60  { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber__ring( X )
% 0.97/1.60    , c_Rings_Oinverse__class_Odivide( X, Y, c_Int_Onumber__class_Onumber__of
% 0.97/1.60    ( X, c_Int_OPls ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.60  { ! class_Fields_Ofield( X ), ! class_Int_Onumber__ring( X ), 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( X, Y, c_Int_Onumber__class_Onumber__of( 
% 0.97/1.60    X, c_Int_OBit1( c_Int_OPls ) ) ) = Y }.
% 0.97/1.60  { ! class_Fields_Ofield( X ), ! class_Int_Onumber__ring( X ), 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( X, Y, c_Int_Onumber__class_Onumber__of( 
% 0.97/1.60    X, c_Int_OBit1( c_Int_OPls ) ) ) = Y }.
% 0.97/1.60  { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ), hAPP( hAPP( 
% 0.97/1.60    c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ominus__class_Ominus( 
% 0.97/1.60    tc_Nat_Onat, Z, T ) ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP( 
% 0.97/1.60    c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP( 
% 0.97/1.60    c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.97/1.60  { c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ), 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0( 
% 0.97/1.60    c_Int_OBit1( c_Int_OPls ) ) ) ), X ) = c_Rings_Oinverse__class_Odivide( 
% 0.97/1.60    tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X )
% 0.97/1.60    , c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0( 
% 0.97/1.60    c_Int_OBit1( c_Int_OPls ) ) ) ) }.
% 0.97/1.60  { c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ), 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0( 
% 0.97/1.60    c_Int_OBit1( c_Int_OPls ) ) ) ), Y ) = c_Rings_Oinverse__class_Odivide( 
% 0.97/1.60    tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, Y )
% 0.97/1.60    , c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0( 
% 0.97/1.60    c_Int_OBit1( c_Int_OPls ) ) ) ) }.
% 0.97/1.60  { c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, X, 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0( 
% 0.97/1.60    c_Int_OBit1( c_Int_OPls ) ) ) ), c_Rings_Oinverse__class_Odivide( 
% 0.97/1.60    tc_RealDef_Oreal, X, c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, 
% 0.97/1.60    c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) = X }.
% 0.97/1.60  { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X, 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.97/1.60    , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( 
% 0.97/1.60    X, U, Z ), c_Groups_Ominus__class_Ominus( X, T, Y ) ) }.
% 0.97/1.60  { c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, hAPP( Z, Y ), hAPP( hAPP
% 0.97/1.60    ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, 
% 0.97/1.60    c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, hAPP( Z, X ), hAPP( Z, Y
% 0.97/1.60     ) ), c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, Y ) ) ), Y ) ) 
% 0.97/1.60    = c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, hAPP( Z, X ), hAPP( 
% 0.97/1.60    hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, 
% 0.97/1.60    c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, hAPP( Z, X ), hAPP( Z, Y
% 0.97/1.60     ) ), c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, Y ) ) ), X ) )
% 0.97/1.60     }.
% 0.97/1.60  { ! class_RealVector_Oreal__field( X ), c_Rings_Oinverse__class_Odivide( X
% 0.97/1.60    , c_Groups_Ominus__class_Ominus( X, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), W ), U ), hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.60    ( X ), W ), c_Rings_Oinverse__class_Odivide( X, 
% 0.97/1.60    c_Groups_Ominus__class_Ominus( X, U, Z ), Y ) ), hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Odivide( X, 
% 0.97/1.60    c_Groups_Ominus__class_Ominus( X, W, T ), Y ) ), Z ) ) }.
% 0.97/1.60  { ! Z = c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, Y, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0( 
% 0.97/1.60    c_Int_OBit1( c_Int_OPls ) ) ) ), X ) ), hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0( 
% 0.97/1.60    c_Int_OBit1( c_Int_OPls ) ) ) ), Z ) = c_Rings_Oinverse__class_Odivide( 
% 0.97/1.60    tc_RealDef_Oreal, Y, X ) }.
% 0.97/1.60  { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0( 
% 0.97/1.60    c_Int_OBit1( c_Int_OPls ) ) ) ), Z ) = c_Rings_Oinverse__class_Odivide( 
% 0.97/1.60    tc_RealDef_Oreal, Y, X ), Z = c_Rings_Oinverse__class_Odivide( 
% 0.97/1.60    tc_RealDef_Oreal, Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes( 
% 0.97/1.60    tc_RealDef_Oreal ), c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, 
% 0.97/1.60    c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ), X ) ) }.
% 0.97/1.60  { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), 
% 0.97/1.60    c_Groups_Ominus__class_Ominus( X, T, c_Rings_Oinverse__class_Odivide( X, 
% 0.97/1.60    Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X, 
% 0.97/1.60    c_Groups_Ominus__class_Ominus( X, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), Y ), T ), Z ), Y ) }.
% 0.97/1.60  { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), 
% 0.97/1.60    c_Groups_Ominus__class_Ominus( X, c_Rings_Oinverse__class_Odivide( X, T, 
% 0.97/1.60    Y ), Z ) = c_Rings_Oinverse__class_Odivide( X, 
% 0.97/1.60    c_Groups_Ominus__class_Ominus( X, T, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) }.
% 0.97/1.60  { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z = 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ), c_Groups_Ominus__class_Ominus( X, 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( X, U, Y ), 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( X, T, Z ) ) = 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus( X, 
% 0.97/1.60    hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.60  { ! class_Fields_Ofield__inverse__zero( X ), hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Odivide( X, U
% 0.97/1.60    , T ) ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) = 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field__inverse__zero( X ), 
% 0.97/1.60    c_Groups_Oabs__class_Oabs( X, c_Rings_Oinverse__class_Odivide( X, Z, Y )
% 0.97/1.60     ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oabs__class_Oabs( X, Z
% 0.97/1.60     ), c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field__inverse__zero( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( X, Z, Y ) ), alpha11( X, Y, Z ), alpha43
% 0.97/1.60    ( X, Y, Z ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha11( X, Y, Z
% 0.97/1.60     ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.97/1.60     ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha43( X, Y, Z
% 0.97/1.60     ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.97/1.60     ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.97/1.60  { ! alpha43( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.60  { ! alpha43( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.97/1.60     ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ) ), alpha43( X, Y, Z ) }.
% 0.97/1.60  { ! alpha11( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.97/1.60  { ! alpha11( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.60    , Z ), ! c_Orderings_Oord__class_Oless__eq( X, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ), Y ), alpha11( X, Y, Z ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field__inverse__zero( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.97/1.60    , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ), alpha12( X, Y, Z ), alpha44
% 0.97/1.60    ( X, Y, Z ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha12( X, Y, Z
% 0.97/1.60     ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 0.97/1.60    ( X, Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha44( X, Y, Z
% 0.97/1.60     ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 0.97/1.60    ( X, Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.60  { ! alpha44( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.60  { ! alpha44( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.97/1.60     ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.97/1.60    ( X ), Y ), alpha44( X, Y, Z ) }.
% 0.97/1.60  { ! alpha12( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.97/1.60  { ! alpha12( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.60    , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ) ), alpha12( X, Y, Z ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field__inverse__zero( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( X, Z, Y ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.97/1.60     ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 0.97/1.60    ( X, Z, T ), c_Rings_Oinverse__class_Odivide( X, Y, T ) ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field__inverse__zero( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( X, Z, Y ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.60     ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 0.97/1.60    ( X, Y, T ), c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 0.97/1.60  { ! class_Fields_Ofield__inverse__zero( X ), ! T = 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( X, Z, Y ), alpha45( X, Y, Z, T ) }.
% 0.97/1.60  { ! class_Fields_Ofield__inverse__zero( X ), ! T = 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( X, Z, Y ), alpha13( X, Y, T ) }.
% 0.97/1.60  { ! class_Fields_Ofield__inverse__zero( X ), ! alpha45( X, Y, Z, T ), ! 
% 0.97/1.60    alpha13( X, Y, T ), T = c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.97/1.60  { ! alpha45( X, Y, Z, T ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP
% 0.97/1.60    ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z }.
% 0.97/1.60  { ! Y = c_Groups_Ozero__class_Ozero( X ), alpha45( X, Y, Z, T ) }.
% 0.97/1.60  { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, alpha45( 
% 0.97/1.60    X, Y, Z, T ) }.
% 0.97/1.60  { ! alpha13( X, Y, Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z = 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.60  { Y = c_Groups_Ozero__class_Ozero( X ), alpha13( X, Y, Z ) }.
% 0.97/1.60  { ! Z = c_Groups_Ozero__class_Ozero( X ), alpha13( X, Y, Z ) }.
% 0.97/1.60  { ! class_Fields_Ofield__inverse__zero( X ), ! 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y, alpha46( X, Y, Z, T ) }.
% 0.97/1.60  { ! class_Fields_Ofield__inverse__zero( X ), ! 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y, alpha14( X, Y, Z ) }.
% 0.97/1.60  { ! class_Fields_Ofield__inverse__zero( X ), ! alpha46( X, Y, Z, T ), ! 
% 0.97/1.60    alpha14( X, Y, Z ), c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y }.
% 0.97/1.60  { ! alpha46( X, Y, Z, T ), Z = c_Groups_Ozero__class_Ozero( X ), T = hAPP( 
% 0.97/1.60    hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 0.97/1.60  { ! Z = c_Groups_Ozero__class_Ozero( X ), alpha46( X, Y, Z, T ) }.
% 0.97/1.60  { ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), alpha46( 
% 0.97/1.60    X, Y, Z, T ) }.
% 0.97/1.60  { ! alpha14( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero( X ), Y = 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.60  { Z = c_Groups_Ozero__class_Ozero( X ), alpha14( X, Y, Z ) }.
% 0.97/1.60  { ! Y = c_Groups_Ozero__class_Ozero( X ), alpha14( X, Y, Z ) }.
% 0.97/1.60  { ! class_Fields_Ofield__inverse__zero( X ), Y = 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X, 
% 0.97/1.60    hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 0.97/1.60  { ! class_Fields_Ofield__inverse__zero( X ), Y = 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X, 
% 0.97/1.60    hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 0.97/1.60  { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z = 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ), ! c_Rings_Oinverse__class_Odivide( X, U
% 0.97/1.60    , Y ) = c_Rings_Oinverse__class_Odivide( X, T, Z ), hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), U ), Z ) = hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), T ), Y ) }.
% 0.97/1.60  { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z = 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), U ), Z ) = hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), T ), Y ), 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( X, U, Y ) = 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field( X ), Y = c_Groups_Ozero__class_Ozero( 
% 0.97/1.60    X ), c_Groups_Oabs__class_Oabs( X, c_Rings_Oinverse__class_Odivide( X, Z
% 0.97/1.60    , Y ) ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oabs__class_Oabs( 
% 0.97/1.60    X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.97/1.60  { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z = 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( X, U, Y ), 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( X, T, Z ) ) = 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, hAPP
% 0.97/1.60    ( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.60  { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( X, c_Rings_Oinverse__class_Odivide( X, T, Y
% 0.97/1.60     ), Z ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus
% 0.97/1.60    ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) }
% 0.97/1.60    .
% 0.97/1.60  { ! class_Fields_Ofield__inverse__zero( X ), Y = 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ) = 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, T, 
% 0.97/1.60    hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) }.
% 0.97/1.60  { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( X, T, c_Rings_Oinverse__class_Odivide( X, Z
% 0.97/1.60    , Y ) ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus
% 0.97/1.60    ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), Z ), Y ) }
% 0.97/1.60    .
% 0.97/1.60  { ! class_Fields_Ofield__inverse__zero( X ), Y = 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, T, 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) = 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z, 
% 0.97/1.60    hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Y ) }.
% 0.97/1.60  { c_Transcendental_Oarctan( X ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.60    ( tc_RealDef_Oreal ), c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal
% 0.97/1.60    , c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ), c_Transcendental_Oarctan
% 0.97/1.60    ( c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, X, 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oone__class_Oone
% 0.97/1.60    ( tc_RealDef_Oreal ), c_NthRoot_Osqrt( c_Groups_Oplus__class_Oplus( 
% 0.97/1.60    tc_RealDef_Oreal, c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), hAPP( 
% 0.97/1.60    hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ), X ), 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( 
% 0.97/1.60    c_Int_OPls ) ) ) ) ) ) ) ) ) ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, X, 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0( 
% 0.97/1.60    c_Int_OBit1( c_Int_OPls ) ) ) ) ), ! c_Orderings_Oord__class_Oless( 
% 0.97/1.60    tc_RealDef_Oreal, Z, c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, X
% 0.97/1.60    , c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0( 
% 0.97/1.60    c_Int_OBit1( c_Int_OPls ) ) ) ) ), ! c_Orderings_Oord__class_Oless__eq( 
% 0.97/1.60    tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.97/1.60     c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Osqrt( 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP( 
% 0.97/1.60    c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Y ), 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( 
% 0.97/1.60    c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower( 
% 0.97/1.60    tc_RealDef_Oreal ), Z ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, 
% 0.97/1.60    c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) ), X ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, 
% 0.97/1.60    c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ), 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, X, c_NthRoot_Osqrt( 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0( 
% 0.97/1.60    c_Int_OBit1( c_Int_OPls ) ) ) ) ) ), ! c_Orderings_Oord__class_Oless( 
% 0.97/1.60    tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Z ), 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, X, c_NthRoot_Osqrt( 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0( 
% 0.97/1.60    c_Int_OBit1( c_Int_OPls ) ) ) ) ) ), c_Orderings_Oord__class_Oless( 
% 0.97/1.60    tc_RealDef_Oreal, c_NthRoot_Osqrt( c_Groups_Oplus__class_Oplus( 
% 0.97/1.60    tc_RealDef_Oreal, hAPP( hAPP( c_Power_Opower__class_Opower( 
% 0.97/1.60    tc_RealDef_Oreal ), Y ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, 
% 0.97/1.60    c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ), hAPP( hAPP( 
% 0.97/1.60    c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Z ), 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( 
% 0.97/1.60    c_Int_OPls ) ) ) ) ) ), X ) }.
% 0.97/1.60  { ! class_Rings_Olinordered__ring__strict( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60    ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.97/1.60    ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP
% 0.97/1.60    ( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.97/1.60  { ! class_Rings_Olinordered__ring__strict( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60    ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.97/1.60    ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.97/1.60    ( c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.97/1.60  { ! class_Rings_Olinordered__comm__semiring__strict( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60    ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.97/1.60    ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.97/1.60    ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.60  { ! class_Rings_Olinordered__semiring__strict( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60    ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.97/1.60    ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.97/1.60    ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.60  { ! class_Rings_Olinordered__semiring__strict( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60    ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.97/1.60    ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP
% 0.97/1.60    ( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.97/1.60  { ! class_Rings_Olinordered__ring__strict( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ), 
% 0.97/1.60    ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.60    , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), 
% 0.97/1.60    hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.60  { ! class_Rings_Olinordered__semiring__strict( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ), 
% 0.97/1.60    ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.97/1.60    , c_Orderings_Oord__class_Oless( X, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.97/1.60    ( X ) ) }.
% 0.97/1.60  { ! class_Rings_Olinordered__ring__strict( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ), 
% 0.97/1.60    ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.97/1.60  { ! class_Rings_Olinordered__ring__strict( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ), 
% 0.97/1.60    ! c_Orderings_Oord__class_Oless( X, Z, T ), c_Orderings_Oord__class_Oless
% 0.97/1.60    ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.97/1.60    ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.60  { ! class_Rings_Olinordered__semiring__strict( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.97/1.60    ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ) }
% 0.97/1.60    .
% 0.97/1.60  { ! class_Rings_Olinordered__semiring__strict( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.97/1.60    ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.97/1.60    .
% 0.97/1.60  { ! class_Rings_Olinordered__semiring__strict( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ), 
% 0.97/1.60    ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.60    , c_Orderings_Oord__class_Oless( X, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.97/1.60    ( X ) ) }.
% 0.97/1.60  { ! class_Rings_Olinordered__semiring__strict( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ), 
% 0.97/1.60    ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.60    , c_Orderings_Oord__class_Oless( X, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.97/1.60    ( X ) ) }.
% 0.97/1.60  { ! class_Rings_Olinordered__semiring__strict( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ), 
% 0.97/1.60    ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.97/1.60    , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), 
% 0.97/1.60    hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.60  { ! class_Rings_Olinordered__ring__strict( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ), 
% 0.97/1.60    ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.97/1.60  { ! class_Rings_Olinordered__ring__strict( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ), 
% 0.97/1.60    ! c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless
% 0.97/1.60    ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.97/1.60    ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.60  { ! class_Rings_Olinordered__ring__strict( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha15( X, Y, Z, T ), 
% 0.97/1.60    alpha47( X, Y, Z, T ) }.
% 0.97/1.60  { ! class_Rings_Olinordered__ring__strict( X ), ! alpha15( X, Y, Z, T ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.60  { ! class_Rings_Olinordered__ring__strict( X ), ! alpha47( X, Y, Z, T ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.60  { ! alpha47( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.60  { ! alpha47( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( X, T, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.60    , ! c_Orderings_Oord__class_Oless( X, Y, Z ), alpha47( X, Y, Z, T ) }.
% 0.97/1.60  { ! alpha15( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ), T ) }.
% 0.97/1.60  { ! alpha15( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T )
% 0.97/1.60    , ! c_Orderings_Oord__class_Oless( X, Z, Y ), alpha15( X, Y, Z, T ) }.
% 0.97/1.60  { ! class_Rings_Olinordered__ring__strict( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha16( X, Y, Z, T ), 
% 0.97/1.60    alpha48( X, Y, Z, T ) }.
% 0.97/1.60  { ! class_Rings_Olinordered__ring__strict( X ), ! alpha16( X, Y, Z, T ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.60  { ! class_Rings_Olinordered__ring__strict( X ), ! alpha48( X, Y, Z, T ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.60  { ! alpha48( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.60  { ! alpha48( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, T ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.60    , ! c_Orderings_Oord__class_Oless( X, Y, T ), alpha48( X, Y, Z, T ) }.
% 0.97/1.60  { ! alpha16( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.97/1.60  { ! alpha16( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.97/1.60    , ! c_Orderings_Oord__class_Oless( X, T, Y ), alpha16( X, Y, Z, T ) }.
% 0.97/1.60  { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.60    , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ), 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.60  { ! class_Groups_Oordered__comm__monoid__add( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ), 
% 0.97/1.60    ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.60    , c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.97/1.60     ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.60  { ! class_Groups_Oordered__comm__monoid__add( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ), 
% 0.97/1.60    ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.97/1.60    , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.97/1.60  { ! class_Groups_Olinordered__ab__group__add( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.97/1.60    , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Y
% 0.97/1.60    , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.60  { ! class_Groups_Olinordered__ab__group__add( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.97/1.60    , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.60  { ! class_Groups_Olinordered__ab__group__add( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( X, Y, Y ) ), c_Orderings_Oord__class_Oless( 
% 0.97/1.60    X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.97/1.60  { ! class_Groups_Olinordered__ab__group__add( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.97/1.60  { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.60    , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.97/1.60     ) ), c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 0.97/1.60     ) ) }.
% 0.97/1.60  { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.60    , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.97/1.60    , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.97/1.60     ) ) }.
% 0.97/1.60  { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60    ( X, c_Groups_Ozero__class_Ozero( X ), Y ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless( 
% 0.97/1.60    X, T, c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.97/1.60  { c_Transcendental_Oarctan( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal )
% 0.97/1.60     ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, 
% 0.97/1.60    c_Transcendental_Oarctan( Y ), c_Transcendental_Oarctan( X ) ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oarctan
% 0.97/1.60    ( Y ), c_Transcendental_Oarctan( X ) ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Osqrt( Y ), 
% 0.97/1.60    c_NthRoot_Osqrt( X ) ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Osqrt( Y ), 
% 0.97/1.60    c_NthRoot_Osqrt( X ) ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, 
% 0.97/1.60    Y, X ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Osqrt( Y ), 
% 0.97/1.60    c_NthRoot_Osqrt( X ) ) }.
% 0.97/1.60  { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Y
% 0.97/1.60     ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( 
% 0.97/1.60    tc_Int_Oint, Y, c_Int_OPls ) }.
% 0.97/1.60  { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, c_Int_OPls ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Y
% 0.97/1.60     ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.60  { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.97/1.60    ( tc_Int_Oint, c_Int_OPls, Y ) }.
% 0.97/1.60  { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, Y ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.97/1.60  { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60    ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.60    , T, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless( X, 
% 0.97/1.60    hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP( 
% 0.97/1.60    c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 0.97/1.60  { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60    ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60    ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP( 
% 0.97/1.60    hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.97/1.60  { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Y, 
% 0.97/1.60    Y ) }.
% 0.97/1.60  { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.97/1.60    , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.60  { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, 
% 0.97/1.60    Y ), ! Z = Y }.
% 0.97/1.60  { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y, 
% 0.97/1.60    Z ), ! Z = Y }.
% 0.97/1.60  { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.97/1.60     ), c_Orderings_Oord__class_Oless( X, Y, Z ), Z = Y }.
% 0.97/1.60  { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y, 
% 0.97/1.60    Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.60  { ! class_Orderings_Olinorder( X ), ! Z = Y, ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.60  { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.97/1.60     ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.60  { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.97/1.60     ), c_Orderings_Oord__class_Oless( X, Y, Z ), Y = Z }.
% 0.97/1.60  { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.97/1.60     ), ! Y = Z, ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.60  { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.97/1.60    , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.60  { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.60    , ! Z = Y }.
% 0.97/1.60  { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, 
% 0.97/1.60    Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.60  { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, 
% 0.97/1.60    Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.60  { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.60    , ! Z = Y }.
% 0.97/1.60  { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.60    , ! Y = Z }.
% 0.97/1.60  { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, 
% 0.97/1.60    Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.60  { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.60    , ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.60  { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X
% 0.97/1.60    , Y, T ), c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.97/1.60  { ! class_Orderings_Oorder( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless( 
% 0.97/1.60    X, T, Y ), c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.97/1.60  { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y ), 
% 0.97/1.60    ! Y = T, c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.97/1.60  { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.60    , ! Z = T, c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.97/1.60  { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, 
% 0.97/1.60    Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.97/1.60  { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.60    , ! c_Orderings_Oord__class_Oless( X, T, Z ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.97/1.60  { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, 
% 0.97/1.60    Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.60  { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.97/1.60     ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), Y = X }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.97/1.60  { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), ! Y = X }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), Y = X, 
% 0.97/1.60    c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ) }.
% 0.97/1.60  { ! class_Groups_Oordered__ab__group__add( X ), ! 
% 0.97/1.60    c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.97/1.60    ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, U, T ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.60  { ! class_Groups_Oordered__ab__group__add( X ), ! 
% 0.97/1.60    c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.97/1.60    ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Z, Y ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, U, T ) }.
% 0.97/1.60  { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.97/1.60    , c_Groups_Oplus__class_Oplus( X, Y, Z ) ), c_Orderings_Oord__class_Oless
% 0.97/1.60    ( X, T, Y ) }.
% 0.97/1.60  { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, T, Y ), c_Orderings_Oord__class_Oless( 
% 0.97/1.60    X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.97/1.60    , Y, Z ) ) }.
% 0.97/1.60  { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.97/1.60    , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.97/1.60    ( X, Z, Y ) }.
% 0.97/1.60  { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless( 
% 0.97/1.60    X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.97/1.60    , T, Y ) ) }.
% 0.97/1.60  { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless( 
% 0.97/1.60    X, c_Groups_Oplus__class_Oplus( X, Z, T ), c_Groups_Oplus__class_Oplus( X
% 0.97/1.60    , Y, T ) ) }.
% 0.97/1.60  { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless( 
% 0.97/1.60    X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.97/1.60    , T, Y ) ) }.
% 0.97/1.60  { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60    ( X, U, T ), c_Orderings_Oord__class_Oless( X, 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X, Y
% 0.97/1.60    , T ) ) }.
% 0.97/1.60  { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, T )
% 0.97/1.60    , c_Groups_Oplus__class_Oplus( X, Y, T ) ), c_Orderings_Oord__class_Oless
% 0.97/1.60    ( X, Z, Y ) }.
% 0.97/1.60  { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.97/1.60    , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.97/1.60    ( X, Z, Y ) }.
% 0.97/1.60  { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.60    , Y ), ! c_Orderings_Oord__class_Oless( X, T, Z ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.97/1.60  { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.60    , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.97/1.60  { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.60    , ! c_Orderings_Oord__class_Oless__eq( X, T, Z ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.97/1.60  { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, 
% 0.97/1.60    Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.97/1.60  { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.60    , Y ), Y = Z, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.60  { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.60    , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.60  { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.60    , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.97/1.60  { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.60    , Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.97/1.60  { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.60    , Z, Y ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.60  { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, 
% 0.97/1.60    Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.60  { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.60    , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.60  { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.97/1.60    ( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.60  { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.97/1.60    ( X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.60  { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.97/1.60     ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ), Z = Y }.
% 0.97/1.60  { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.97/1.60     ), ! Z = Y, c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.60  { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.60    , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.60  { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.97/1.60     ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.97/1.60  { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.60    , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.97/1.60  { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.60    , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.60  { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.97/1.60    ( X, Z, Y ) }.
% 0.97/1.60  { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, 
% 0.97/1.60    Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.60  { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, 
% 0.97/1.60    Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.97/1.60  { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.60    , Z, Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.60  { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.60    , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.60  { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.60    , ! Z = Y }.
% 0.97/1.60  { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.60    , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.60  { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.60    , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.60  { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.60    , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.60  { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y, 
% 0.97/1.60    Z ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.60  { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.97/1.60     ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.97/1.60  { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.60    , Y, Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.60  { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60    ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X, 
% 0.97/1.60    c_Groups_Oone__class_Oone( X ), T ), c_Orderings_Oord__class_Oless( X, 
% 0.97/1.60    hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP( 
% 0.97/1.60    c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.97/1.60  { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60    ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60    ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.97/1.60    ( c_Power_Opower__class_Opower( X ), Y ), Z ) ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.97/1.60  { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60    ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60    ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.97/1.60    ( c_Power_Opower__class_Opower( X ), Y ), Z ) ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.97/1.60  { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60    ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60    ( tc_Nat_Onat, T, Z ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP( 
% 0.97/1.60    c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP( 
% 0.97/1.60    c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.97/1.60  { ! class_Rings_Olinordered__idom( X ), Z = Y, 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless( 
% 0.97/1.60    X, Y, Z ) }.
% 0.97/1.60  { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Z
% 0.97/1.60     ), c_Int_Onumber__class_Onumber__of( X, Y ) ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, Y ) }.
% 0.97/1.60  { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, Y ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Z
% 0.97/1.60     ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.97/1.60  { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Y
% 0.97/1.60     ), c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless( 
% 0.97/1.60    tc_Int_Oint, Y, c_Int_OBit1( c_Int_OPls ) ) }.
% 0.97/1.60  { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, c_Int_OBit1( c_Int_OPls )
% 0.97/1.60     ), c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X
% 0.97/1.60    , Y ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.97/1.60  { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.97/1.60    ( tc_Int_Oint, c_Int_OBit1( c_Int_OPls ), Y ) }.
% 0.97/1.60  { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( c_Int_OPls ), Y
% 0.97/1.60     ), c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.97/1.60  { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60    ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ), Z ), ! c_Orderings_Oord__class_Oless( 
% 0.97/1.60    tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), T ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, hAPP( hAPP( 
% 0.97/1.60    c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP( 
% 0.97/1.60    c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.97/1.60  { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( X, Z, Y ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, U, T ), c_Orderings_Oord__class_Oless( 
% 0.97/1.60    X, c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X
% 0.97/1.60    , Y, T ) ) }.
% 0.97/1.60  { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, Z, Y ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( X, U, T ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, U )
% 0.97/1.60    , c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.97/1.60  { ! class_Int_Onumber( X ), ! class_Orderings_Olinorder( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 0.97/1.60    , Z ), c_Int_Onumber__class_Onumber__of( X, Y ) ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Y
% 0.97/1.60     ), c_Int_Onumber__class_Onumber__of( X, Z ) ) }.
% 0.97/1.60  { ! class_Int_Onumber( X ), ! class_Orderings_Olinorder( X ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Y
% 0.97/1.60     ), c_Int_Onumber__class_Onumber__of( X, Z ) ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 0.97/1.60    , Z ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.97/1.60  { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.97/1.60    , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.97/1.60  { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60    ( X, c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero( X ) ) }
% 0.97/1.60    .
% 0.97/1.60  { ! class_Groups_Oordered__ab__group__add( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless( 
% 0.97/1.60    X, c_Groups_Ominus__class_Ominus( X, Z, Y ), c_Groups_Ozero__class_Ozero
% 0.97/1.60    ( X ) ) }.
% 0.97/1.60  { ! class_Groups_Oordered__ab__group__add( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.97/1.60     ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.97/1.60    , Z, Y ) }.
% 0.97/1.60  { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60    ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60    ( X, c_Groups_Oone__class_Oone( X ), Z ), c_Orderings_Oord__class_Oless( 
% 0.97/1.60    X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.60  { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60    ( X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless
% 0.97/1.60    ( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP( 
% 0.97/1.60    c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.97/1.60  { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.97/1.60    , Y, c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) )
% 0.97/1.60     ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless( 
% 0.97/1.60    X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, T, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( X, Y, T ), 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless( 
% 0.97/1.60    X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless( X, 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( X, Z, T ), 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( X, Y, T ) ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless( 
% 0.97/1.60    X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60    ( X, Z, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.97/1.60    ( X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X
% 0.97/1.60    , Y, Z ) ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless( 
% 0.97/1.60    X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60    ( X, c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless
% 0.97/1.60    ( X, c_Rings_Oinverse__class_Odivide( X, Y, Z ), 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless( 
% 0.97/1.60    X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60    ( X, Z, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.97/1.60    ( X, c_Rings_Oinverse__class_Odivide( X, Y, Z ), 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless( 
% 0.97/1.60    X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60    ( X, c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless
% 0.97/1.60    ( X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X
% 0.97/1.60    , Y, Z ) ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field__inverse__zero( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, Z, 
% 0.97/1.60    Y ), c_Groups_Ozero__class_Ozero( X ) ), alpha17( X, Y, Z ), alpha49( X, 
% 0.97/1.60    Y, Z ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha17( X, Y, Z
% 0.97/1.60     ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X
% 0.97/1.60    , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha49( X, Y, Z
% 0.97/1.60     ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X
% 0.97/1.60    , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.60  { ! alpha49( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.60  { ! alpha49( X, Y, Z ), c_Orderings_Oord__class_Oless( X, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.60    , ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.60     ), alpha49( X, Y, Z ) }.
% 0.97/1.60  { ! alpha17( X, Y, Z ), c_Orderings_Oord__class_Oless( X, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.97/1.60  { ! alpha17( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.97/1.60    , ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.60     ), alpha17( X, Y, Z ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field__inverse__zero( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( X, Z, Y ) ), alpha18( X, Y, Z ), alpha50
% 0.97/1.60    ( X, Y, Z ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha18( X, Y, Z
% 0.97/1.60     ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha50( X, Y, Z
% 0.97/1.60     ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.97/1.60  { ! alpha50( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.60  { ! alpha50( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.60    , ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.60     ), alpha50( X, Y, Z ) }.
% 0.97/1.60  { ! alpha18( X, Y, Z ), c_Orderings_Oord__class_Oless( X, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.97/1.60  { ! alpha18( X, Y, Z ), c_Orderings_Oord__class_Oless( X, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.97/1.60    , ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.60     ), alpha18( X, Y, Z ) }.
% 0.97/1.60  { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60    ( X, c_Groups_Oone__class_Oone( X ), Y ), ! hAPP( hAPP( 
% 0.97/1.60    c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP( 
% 0.97/1.60    c_Power_Opower__class_Opower( X ), Y ), Z ), T = Z }.
% 0.97/1.60  { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60    ( X, c_Groups_Oone__class_Oone( X ), Y ), ! T = Z, hAPP( hAPP( 
% 0.97/1.60    c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP( 
% 0.97/1.60    c_Power_Opower__class_Opower( X ), Y ), Z ) }.
% 0.97/1.60  { ! class_Groups_Oordered__ab__group__add__abs( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X, Y ), 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.60  { ! class_Groups_Oordered__ab__group__add__abs( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), 
% 0.97/1.60    c_Groups_Oabs__class_Oabs( X, Y ) ), ! Y = c_Groups_Ozero__class_Ozero( X
% 0.97/1.60     ) }.
% 0.97/1.60  { ! class_Groups_Oordered__ab__group__add__abs( X ), Y = 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ), c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.97/1.60  { ! class_Groups_Oordered__ab__group__add__abs( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ), 
% 0.97/1.60    c_Groups_Oabs__class_Oabs( X, Y ) = Y }.
% 0.97/1.60  { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.60    , c_Groups_Oabs__class_Oabs( X, Z ), Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60    ( X, c_Groups_Oabs__class_Oabs( X, U ), T ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ), 
% 0.97/1.60    c_Groups_Oabs__class_Oabs( X, U ) ), hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.97/1.60  { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ), X = 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.60  { ! X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) }.
% 0.97/1.60  { ! class_RealVector_Oreal__normed__vector( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, 
% 0.97/1.60    c_RealVector_Onorm__class_Onorm( X, Y ), c_Groups_Ozero__class_Ozero( 
% 0.97/1.60    tc_RealDef_Oreal ) ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ) }
% 0.97/1.60    .
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Osqrt( X ), 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Osqrt( X ), 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), ! c_NthRoot_Osqrt( 
% 0.97/1.60    X ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ) }
% 0.97/1.60    .
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Osqrt( X ), 
% 0.97/1.60    c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, 
% 0.97/1.60    c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, 
% 0.97/1.60    c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Osqrt( X ), 
% 0.97/1.60    c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, 
% 0.97/1.60    c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, 
% 0.97/1.60    c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, 
% 0.97/1.60    c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, 
% 0.97/1.60    c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ) }.
% 0.97/1.60  { ! class_Rings_Olinordered__ring__strict( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ), 
% 0.97/1.60    ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.97/1.60  { ! class_Rings_Olinordered__ring__strict( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ), 
% 0.97/1.60    ! c_Orderings_Oord__class_Oless__eq( X, T, Z ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.60  { ! class_Rings_Olinordered__ring__strict( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ), 
% 0.97/1.60    ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.97/1.60  { ! class_Rings_Olinordered__ring__strict( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ), 
% 0.97/1.60    ! c_Orderings_Oord__class_Oless__eq( X, Z, T ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.60  { ! class_Rings_Olinordered__semiring__strict( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60    ( X, U, T ), ! c_Orderings_Oord__class_Oless( X, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ), Y ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.97/1.60     ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.97/1.60  { ! class_Rings_Olinordered__semiring__strict( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60    ( X, U, T ), ! c_Orderings_Oord__class_Oless__eq( X, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ), Z ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.97/1.60     ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.97/1.60  { ! class_Rings_Olinordered__semiring__strict( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, Z, Y ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( X, U, T ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.97/1.60     ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.60    , U ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.97/1.60  { ! class_Rings_Olinordered__semiring__strict( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( X, Z, Y ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, U, T ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60    ( X, c_Groups_Ozero__class_Ozero( X ), Z ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.97/1.60     ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.97/1.60  { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60    ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.97/1.60    ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.97/1.60     ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.97/1.60  { ! class_Rings_Olinordered__semiring__strict( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.97/1.60     ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.97/1.60  { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60    ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.97/1.60    ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.97/1.60     ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.60  { ! class_Rings_Olinordered__semiring__strict( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.97/1.60     ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.60  { ! class_Rings_Olinordered__semiring__strict( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.97/1.60  { ! class_Rings_Olinordered__semiring__strict( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.60  { ! class_Groups_Oordered__comm__monoid__add( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.60     ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.97/1.60     ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.97/1.60    , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.60  { ! class_Groups_Oordered__comm__monoid__add( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ), 
% 0.97/1.60    ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.97/1.60     ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.97/1.60    , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.60  { ! class_Groups_Oordered__comm__monoid__add( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.60     ), ! c_Orderings_Oord__class_Oless( X, T, Z ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.97/1.60     ) ) }.
% 0.97/1.60  { ! class_Groups_Oordered__comm__monoid__add( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ), 
% 0.97/1.60    ! c_Orderings_Oord__class_Oless__eq( X, T, Z ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.97/1.60     ) ) }.
% 0.97/1.60  { ! class_Groups_Oordered__comm__monoid__add( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.60     ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.60    , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.60    , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.97/1.60  { ! class_Groups_Oordered__comm__monoid__add( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ), 
% 0.97/1.60    ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.60    , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.60    , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.97/1.60  { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.60    , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ), 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.60  { ! class_Rings_Olinordered__ring__strict( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.60    ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.97/1.60     ) ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y = 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.60  { ! class_Rings_Olinordered__ring__strict( X ), Z = 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP( 
% 0.97/1.60    hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.97/1.60  { ! class_Rings_Olinordered__ring__strict( X ), Y = 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP( 
% 0.97/1.60    hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.97/1.60  { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60    ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP
% 0.97/1.60    ( c_Power_Opower__class_Opower( X ), Y ), T ) ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.60     ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.60  { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.97/1.60    , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, 
% 0.97/1.60    c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ) ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.60     ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.60    , Z ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.97/1.60    ( X ), c_Rings_Oinverse__class_Odivide( X, Y, Z ) ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.60     ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.97/1.60     ) ), c_Orderings_Oord__class_Oless__eq( X, 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( X, Y, Z ), c_Groups_Ozero__class_Ozero( 
% 0.97/1.60    X ) ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless( 
% 0.97/1.60    X, c_Groups_Ozero__class_Ozero( X ), Y ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( X, Y, Z ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ), 
% 0.97/1.60    ! c_Orderings_Oord__class_Oless( X, T, U ), c_Orderings_Oord__class_Oless
% 0.97/1.60    ( X, c_Rings_Oinverse__class_Odivide( X, Y, U ), 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.60     ), ! c_Orderings_Oord__class_Oless( X, Y, Z ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ), 
% 0.97/1.60    ! c_Orderings_Oord__class_Oless__eq( X, T, U ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, Y, 
% 0.97/1.60    U ), c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.60     ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ), 
% 0.97/1.60    ! c_Orderings_Oord__class_Oless__eq( X, T, U ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.97/1.60    , Y, U ), c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.60     ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.60    , Z ), c_Orderings_Oord__class_Oless__eq( X, 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( X, Y, Z ), c_Groups_Ozero__class_Ozero( 
% 0.97/1.60    X ) ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.60     ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.97/1.60     ) ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( 
% 0.97/1.60    X ), c_Rings_Oinverse__class_Odivide( X, Y, Z ) ) }.
% 0.97/1.60  { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X, 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.60    ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, hAPP
% 0.97/1.60    ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus
% 0.97/1.60    ( X, Z, W ) ), U ), Y ) ) }.
% 0.97/1.60  { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X, T
% 0.97/1.60    , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z, 
% 0.97/1.60    W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless( X, 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.60    ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.97/1.60  { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X, 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.60    ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP( 
% 0.97/1.60    hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( 
% 0.97/1.60    X, W, Z ) ), U ), T ), Y ) }.
% 0.97/1.60  { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X, 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.60    ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP( 
% 0.97/1.60    hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ), T ), 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.60    ( X ), Z ), U ), Y ) ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field__inverse__zero( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X, 
% 0.97/1.60    Z, Y ) ), alpha51( X, Y, Z, T ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field__inverse__zero( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X, 
% 0.97/1.60    Z, Y ) ), alpha63( X, Y, Z, T ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha51( X, Y, Z
% 0.97/1.60    , T ), ! alpha63( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T, 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.97/1.60  { ! alpha63( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ), Y ), alpha75( X, Y, Z, T ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.97/1.60    , alpha63( X, Y, Z, T ) }.
% 0.97/1.60  { ! alpha75( X, Y, Z, T ), alpha63( X, Y, Z, T ) }.
% 0.97/1.60  { ! alpha75( X, Y, Z, T ), alpha87( X, Y, Z, T ) }.
% 0.97/1.60  { ! alpha75( X, Y, Z, T ), alpha19( X, Y, T ) }.
% 0.97/1.60  { ! alpha87( X, Y, Z, T ), ! alpha19( X, Y, T ), alpha75( X, Y, Z, T ) }.
% 0.97/1.60  { ! alpha87( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Y, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Z, 
% 0.97/1.60    hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.60  { c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ), 
% 0.97/1.60    alpha87( X, Y, Z, T ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha87( X, Y, Z, T ) }.
% 0.97/1.60  { ! alpha51( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X, 
% 0.97/1.60    hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.97/1.60  { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ), 
% 0.97/1.60    alpha51( X, Y, Z, T ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ), alpha51( X, Y, Z, T )
% 0.97/1.60     }.
% 0.97/1.60  { ! alpha19( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Z, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.60    , alpha19( X, Y, Z ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.60    , alpha19( X, Y, Z ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field__inverse__zero( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T, 
% 0.97/1.60    Z ), Y ), alpha52( X, Y, Z, T ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field__inverse__zero( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T, 
% 0.97/1.60    Z ), Y ), alpha64( X, Y, Z, T ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha52( X, Y, Z
% 0.97/1.60    , T ), ! alpha64( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( X, T, Z ), Y ) }.
% 0.97/1.60  { ! alpha64( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ), Z ), alpha76( X, Y, Z, T ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.97/1.60    , alpha64( X, Y, Z, T ) }.
% 0.97/1.60  { ! alpha76( X, Y, Z, T ), alpha64( X, Y, Z, T ) }.
% 0.97/1.60  { ! alpha76( X, Y, Z, T ), alpha88( X, Y, Z, T ) }.
% 0.97/1.60  { ! alpha76( X, Y, Z, T ), alpha20( X, Y, Z ) }.
% 0.97/1.60  { ! alpha88( X, Y, Z, T ), ! alpha20( X, Y, Z ), alpha76( X, Y, Z, T ) }.
% 0.97/1.60  { ! alpha88( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Z, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, 
% 0.97/1.60    hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ) }.
% 0.97/1.60  { c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) ), 
% 0.97/1.60    alpha88( X, Y, Z, T ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ), alpha88( X, Y, Z, T )
% 0.97/1.60     }.
% 0.97/1.60  { ! alpha52( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless( X, 
% 0.97/1.60    T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.60  { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ), 
% 0.97/1.60    alpha52( X, Y, Z, T ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha52( X, Y, Z, T ) }.
% 0.97/1.60  { ! alpha20( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.60    , alpha20( X, Y, Z ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.97/1.60    , alpha20( X, Y, Z ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless( 
% 0.97/1.60    X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60    ( X, T, c_Rings_Oinverse__class_Odivide( X, Z, Y ) ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless( 
% 0.97/1.60    X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60    ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X, 
% 0.97/1.60    Z, Y ) ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless( 
% 0.97/1.60    X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60    ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless( 
% 0.97/1.60    X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60    ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T, 
% 0.97/1.60    Y ), Z ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless( 
% 0.97/1.60    X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60    ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T, 
% 0.97/1.60    Y ), Z ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless( 
% 0.97/1.60    X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60    ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X, 
% 0.97/1.60    Z, Y ) ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless( 
% 0.97/1.60    X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60    ( X, T, c_Rings_Oinverse__class_Odivide( X, Z, Y ) ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless( 
% 0.97/1.60    X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60    ( X, Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X, 
% 0.97/1.60    Z, Y ) ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless( 
% 0.97/1.60    X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60    ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless( 
% 0.97/1.60    X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60    ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T, 
% 0.97/1.60    Y ), Z ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless( 
% 0.97/1.60    X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.60    , c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T, 
% 0.97/1.60    Y ), c_Rings_Oinverse__class_Odivide( X, T, Z ) ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless( 
% 0.97/1.60    X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, T, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless( X, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T, 
% 0.97/1.60    Z ), c_Rings_Oinverse__class_Odivide( X, T, Y ) ) }.
% 0.97/1.60  { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60    ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless( 
% 0.97/1.60    X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP( 
% 0.97/1.60    c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.97/1.60  { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60    ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless( 
% 0.97/1.60    X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP( 
% 0.97/1.60    c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless( 
% 0.97/1.60    X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z, 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.97/1.60     ), c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ), 
% 0.97/1.60    c_Groups_Oone__class_Oone( X ) ) ) ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless( 
% 0.97/1.60    X, Z, Y ), c_Orderings_Oord__class_Oless( X, 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.97/1.60     ), c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ), 
% 0.97/1.60    c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.97/1.60  { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60    ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless( 
% 0.97/1.60    X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP( 
% 0.97/1.60    c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ) ) }.
% 0.97/1.60  { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.60    , c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, T, Z )
% 0.97/1.60     ), Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus
% 0.97/1.60    ( X, Z, Y ), T ) }.
% 0.97/1.60  { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.60    , c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, T, Z )
% 0.97/1.60     ), Y ), c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus
% 0.97/1.60    ( X, Z, Y ) ) }.
% 0.97/1.60  { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.60    , c_Groups_Ominus__class_Ominus( X, Z, Y ), T ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.97/1.60     ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X, 
% 0.97/1.60    c_Groups_Ominus__class_Ominus( X, T, Z ) ), Y ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field__inverse__zero( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ), 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( X, c_Groups_Oabs__class_Oabs( X, Z ), Y
% 0.97/1.60     ) = c_Groups_Oabs__class_Oabs( X, c_Rings_Oinverse__class_Odivide( X, Z
% 0.97/1.60    , Y ) ) }.
% 0.97/1.60  { ! class_RealVector_Oreal__normed__vector( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), 
% 0.97/1.60    c_RealVector_Onorm__class_Onorm( X, Y ) ), ! Y = 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.60  { ! class_RealVector_Oreal__normed__vector( X ), Y = 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( 
% 0.97/1.60    tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), 
% 0.97/1.60    c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 0.97/1.60  { ! class_RealVector_Oreal__normed__algebra( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, 
% 0.97/1.60    c_RealVector_Onorm__class_Onorm( X, Z ), Y ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, 
% 0.97/1.60    c_RealVector_Onorm__class_Onorm( X, U ), T ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, 
% 0.97/1.60    c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), T ) ) }.
% 0.97/1.60  { ! class_RealVector_Oreal__normed__vector( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, 
% 0.97/1.60    c_RealVector_Onorm__class_Onorm( X, Z ), Y ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, 
% 0.97/1.60    c_RealVector_Onorm__class_Onorm( X, U ), T ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, 
% 0.97/1.60    c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, Z, U
% 0.97/1.60     ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, T ) ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs
% 0.97/1.60    ( tc_RealDef_Oreal, X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 0.97/1.60    , X ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, 
% 0.97/1.60    c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ), 
% 0.97/1.60    c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, 
% 0.97/1.60    c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ), 
% 0.97/1.60    c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Transcendental_Oarctan( 
% 0.97/1.60    X ), c_Transcendental_Oarctan( Y ) ) = c_Transcendental_Oarctan( 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X, Y ), 
% 0.97/1.60    c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, 
% 0.97/1.60    c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) ) ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field__inverse__zero( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( X, Z, Y ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.60     ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.60    , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.97/1.60    , T, Z ), c_Rings_Oinverse__class_Odivide( X, T, Y ) ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( X, Z, Y ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.97/1.60     ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.60    , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.97/1.60    , T, Y ), c_Rings_Oinverse__class_Odivide( X, T, Z ) ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless( 
% 0.97/1.60    X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.97/1.60    , T, Y ), Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless( 
% 0.97/1.60    X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.97/1.60    , T, Y ), Z ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless( 
% 0.97/1.60    X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.97/1.60    ( X, Z, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Z, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless( 
% 0.97/1.60    X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( X, Z, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.97/1.60    ( X, Z, Y ) ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless( 
% 0.97/1.60    X, c_Groups_Ozero__class_Ozero( X ), Y ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.97/1.60    ( X, Z, Y ) ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless( 
% 0.97/1.60    X, c_Groups_Ozero__class_Ozero( X ), Y ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.97/1.60    , T, Y ), Z ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless( 
% 0.97/1.60    X, c_Groups_Ozero__class_Ozero( X ), Y ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.97/1.60    , T, Y ), Z ), c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless( 
% 0.97/1.60    X, c_Groups_Ozero__class_Ozero( X ), Y ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.97/1.60    , T, Y ), Z ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless( 
% 0.97/1.60    X, c_Groups_Ozero__class_Ozero( X ), Y ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.97/1.60    ( X, Z, Y ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless( 
% 0.97/1.60    X, c_Groups_Ozero__class_Ozero( X ), Y ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.97/1.60    ( X, Z, Y ) ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field__inverse__zero( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.97/1.60    , T, Z ), Y ), alpha53( X, Y, Z, T ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field__inverse__zero( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.97/1.60    , T, Z ), Y ), alpha65( X, Y, Z, T ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha53( X, Y, Z
% 0.97/1.60    , T ), ! alpha65( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( X, 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( X, T, Z ), Y ) }.
% 0.97/1.60  { ! alpha65( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ), Z ), alpha77( X, Y, Z, T ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.97/1.60    , alpha65( X, Y, Z, T ) }.
% 0.97/1.60  { ! alpha77( X, Y, Z, T ), alpha65( X, Y, Z, T ) }.
% 0.97/1.60  { ! alpha77( X, Y, Z, T ), alpha89( X, Y, Z, T ) }.
% 0.97/1.60  { ! alpha77( X, Y, Z, T ), alpha21( X, Y, Z ) }.
% 0.97/1.60  { ! alpha89( X, Y, Z, T ), ! alpha21( X, Y, Z ), alpha77( X, Y, Z, T ) }.
% 0.97/1.60  { ! alpha89( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Z, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.60    , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ) }.
% 0.97/1.60  { c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) ), 
% 0.97/1.60    alpha89( X, Y, Z, T ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ), alpha89( X, Y, Z, T )
% 0.97/1.60     }.
% 0.97/1.60  { ! alpha53( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless__eq
% 0.97/1.60    ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.60  { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ), 
% 0.97/1.60    alpha53( X, Y, Z, T ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha53( X, Y, Z, T ) }.
% 0.97/1.60  { ! alpha21( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.60    , c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.60    , alpha21( X, Y, Z ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.60    , Y ), alpha21( X, Y, Z ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field__inverse__zero( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.97/1.60    ( X, Z, Y ) ), alpha54( X, Y, Z, T ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field__inverse__zero( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.97/1.60    ( X, Z, Y ) ), alpha66( X, Y, Z, T ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha54( X, Y, Z
% 0.97/1.60    , T ), ! alpha66( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( X, T, 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.97/1.60  { ! alpha66( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ), Y ), alpha78( X, Y, Z, T ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.97/1.60    , alpha66( X, Y, Z, T ) }.
% 0.97/1.60  { ! alpha78( X, Y, Z, T ), alpha66( X, Y, Z, T ) }.
% 0.97/1.60  { ! alpha78( X, Y, Z, T ), alpha90( X, Y, Z, T ) }.
% 0.97/1.60  { ! alpha78( X, Y, Z, T ), alpha22( X, Y, T ) }.
% 0.97/1.60  { ! alpha90( X, Y, Z, T ), ! alpha22( X, Y, T ), alpha78( X, Y, Z, T ) }.
% 0.97/1.60  { ! alpha90( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Y, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.60    , Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.60  { c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ), 
% 0.97/1.60    alpha90( X, Y, Z, T ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( X, Z, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha90( X, Y, Z, T ) }.
% 0.97/1.60  { ! alpha54( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless__eq
% 0.97/1.60    ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.97/1.60  { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ), 
% 0.97/1.60    alpha54( X, Y, Z, T ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ), alpha54( X, Y, Z, T )
% 0.97/1.60     }.
% 0.97/1.60  { ! alpha22( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.60    , Z, c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.60    , alpha22( X, Y, Z ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.97/1.60     ) ), alpha22( X, Y, Z ) }.
% 0.97/1.60  { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60    ( X, c_Groups_Ozero__class_Ozero( X ), Y ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP( 
% 0.97/1.60    c_Power_Opower__class_Opower( X ), Y ), Z ) ), hAPP( hAPP( 
% 0.97/1.60    c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field__inverse__zero( X ), ! 
% 0.97/1.60    class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless( X, 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( X, T, c_Int_Onumber__class_Onumber__of( 
% 0.97/1.60    X, Z ) ), Y ), alpha55( X, Y, Z, T ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field__inverse__zero( X ), ! 
% 0.97/1.60    class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless( X, 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( X, T, c_Int_Onumber__class_Onumber__of( 
% 0.97/1.60    X, Z ) ), Y ), alpha67( X, Y, Z, T ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field__inverse__zero( X ), ! 
% 0.97/1.60    class_Int_Onumber( X ), ! alpha55( X, Y, Z, T ), ! alpha67( X, Y, Z, T )
% 0.97/1.60    , c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T
% 0.97/1.60    , c_Int_Onumber__class_Onumber__of( X, Z ) ), Y ) }.
% 0.97/1.60  { ! alpha67( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ), c_Int_Onumber__class_Onumber__of( X, Z
% 0.97/1.60     ) ), alpha79( X, Y, Z, T ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( X, Z ) ), alpha67( X, Y, Z, T ) }.
% 0.97/1.60  { ! alpha79( X, Y, Z, T ), alpha67( X, Y, Z, T ) }.
% 0.97/1.60  { ! alpha79( X, Y, Z, T ), alpha91( X, Y, Z, T ) }.
% 0.97/1.60  { ! alpha79( X, Y, Z, T ), alpha23( X, Y, Z ) }.
% 0.97/1.60  { ! alpha91( X, Y, Z, T ), ! alpha23( X, Y, Z ), alpha79( X, Y, Z, T ) }.
% 0.97/1.60  { ! alpha91( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( X, Z ), c_Groups_Ozero__class_Ozero( X
% 0.97/1.60     ) ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), Y ), c_Int_Onumber__class_Onumber__of
% 0.97/1.60    ( X, Z ) ), T ) }.
% 0.97/1.60  { c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Z
% 0.97/1.60     ), c_Groups_Ozero__class_Ozero( X ) ), alpha91( X, Y, Z, T ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), Y ), c_Int_Onumber__class_Onumber__of
% 0.97/1.60    ( X, Z ) ), T ), alpha91( X, Y, Z, T ) }.
% 0.97/1.60  { ! alpha55( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ), c_Int_Onumber__class_Onumber__of( X, Z
% 0.97/1.60     ) ), c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), Y ), c_Int_Onumber__class_Onumber__of
% 0.97/1.60    ( X, Z ) ) ) }.
% 0.97/1.60  { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( X, Z ) ), alpha55( X, Y, Z, T ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), Y ), c_Int_Onumber__class_Onumber__of
% 0.97/1.60    ( X, Z ) ) ), alpha55( X, Y, Z, T ) }.
% 0.97/1.60  { ! alpha23( X, Y, Z ), c_Orderings_Oord__class_Oless( X, 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( X, Z ), c_Groups_Ozero__class_Ozero( X
% 0.97/1.60     ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.60    , Y ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, 
% 0.97/1.60    Z ), c_Groups_Ozero__class_Ozero( X ) ), alpha23( X, Y, Z ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.97/1.60    , alpha23( X, Y, Z ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field__inverse__zero( X ), ! 
% 0.97/1.60    class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless( X, 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( X, T, Z ), 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( X, Y ) ), alpha56( X, Y, Z, T ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field__inverse__zero( X ), ! 
% 0.97/1.60    class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless( X, 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( X, T, Z ), 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( X, Y ) ), alpha68( X, Y, Z, T ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field__inverse__zero( X ), ! 
% 0.97/1.60    class_Int_Onumber( X ), ! alpha56( X, Y, Z, T ), ! alpha68( X, Y, Z, T )
% 0.97/1.60    , c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T
% 0.97/1.60    , Z ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.97/1.60  { ! alpha68( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ), Z ), alpha80( X, Y, Z, T ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.97/1.60    , alpha68( X, Y, Z, T ) }.
% 0.97/1.60  { ! alpha80( X, Y, Z, T ), alpha68( X, Y, Z, T ) }.
% 0.97/1.60  { ! alpha80( X, Y, Z, T ), alpha92( X, Y, Z, T ) }.
% 0.97/1.60  { ! alpha80( X, Y, Z, T ), alpha24( X, Y, Z ) }.
% 0.97/1.60  { ! alpha92( X, Y, Z, T ), ! alpha24( X, Y, Z ), alpha80( X, Y, Z, T ) }.
% 0.97/1.60  { ! alpha92( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Z, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, 
% 0.97/1.60    hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( X, Y ) ), Z ), T ) }.
% 0.97/1.60  { c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) ), 
% 0.97/1.60    alpha92( X, Y, Z, T ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X, 
% 0.97/1.60    Y ) ), Z ), T ), alpha92( X, Y, Z, T ) }.
% 0.97/1.60  { ! alpha56( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless( X, 
% 0.97/1.60    T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( X, Y ) ), Z ) ) }.
% 0.97/1.60  { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ), 
% 0.97/1.60    alpha56( X, Y, Z, T ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X, 
% 0.97/1.60    Y ) ), Z ) ), alpha56( X, Y, Z, T ) }.
% 0.97/1.60  { ! alpha24( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ), c_Int_Onumber__class_Onumber__of( X, Y
% 0.97/1.60     ) ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.60    , alpha24( X, Y, Z ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( X, Y ) ), alpha24( X, Y, Z ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field__inverse__zero( X ), ! 
% 0.97/1.60    class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless( X, 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( X, T ), c_Rings_Oinverse__class_Odivide
% 0.97/1.60    ( X, Z, Y ) ), alpha57( X, Y, Z, T ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field__inverse__zero( X ), ! 
% 0.97/1.60    class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless( X, 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( X, T ), c_Rings_Oinverse__class_Odivide
% 0.97/1.60    ( X, Z, Y ) ), alpha69( X, Y, Z, T ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field__inverse__zero( X ), ! 
% 0.97/1.60    class_Int_Onumber( X ), ! alpha57( X, Y, Z, T ), ! alpha69( X, Y, Z, T )
% 0.97/1.60    , c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, 
% 0.97/1.60    T ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.97/1.60  { ! alpha69( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ), Y ), alpha81( X, Y, Z, T ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.97/1.60    , alpha69( X, Y, Z, T ) }.
% 0.97/1.60  { ! alpha81( X, Y, Z, T ), alpha69( X, Y, Z, T ) }.
% 0.97/1.60  { ! alpha81( X, Y, Z, T ), alpha93( X, Y, Z, T ) }.
% 0.97/1.60  { ! alpha81( X, Y, Z, T ), alpha25( X, Y, T ) }.
% 0.97/1.60  { ! alpha93( X, Y, Z, T ), ! alpha25( X, Y, T ), alpha81( X, Y, Z, T ) }.
% 0.97/1.60  { ! alpha93( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Y, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Z, 
% 0.97/1.60    hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( X, T ) ), Y ) ) }.
% 0.97/1.60  { c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ), 
% 0.97/1.60    alpha93( X, Y, Z, T ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X, 
% 0.97/1.60    T ) ), Y ) ), alpha93( X, Y, Z, T ) }.
% 0.97/1.60  { ! alpha57( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X, 
% 0.97/1.60    hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( X, T ) ), Y ), Z ) }.
% 0.97/1.60  { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ), 
% 0.97/1.60    alpha57( X, Y, Z, T ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X, 
% 0.97/1.60    T ) ), Y ), Z ), alpha57( X, Y, Z, T ) }.
% 0.97/1.60  { ! alpha25( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( X, Z ), c_Groups_Ozero__class_Ozero( X
% 0.97/1.60     ) ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.60    , alpha25( X, Y, Z ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, 
% 0.97/1.60    Z ), c_Groups_Ozero__class_Ozero( X ) ), alpha25( X, Y, Z ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field__inverse__zero( X ), ! 
% 0.97/1.60    class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless( X, T, 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( X, Z, c_Int_Onumber__class_Onumber__of( 
% 0.97/1.60    X, Y ) ) ), alpha58( X, Y, Z, T ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field__inverse__zero( X ), ! 
% 0.97/1.60    class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless( X, T, 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( X, Z, c_Int_Onumber__class_Onumber__of( 
% 0.97/1.60    X, Y ) ) ), alpha70( X, Y, Z, T ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field__inverse__zero( X ), ! 
% 0.97/1.60    class_Int_Onumber( X ), ! alpha58( X, Y, Z, T ), ! alpha70( X, Y, Z, T )
% 0.97/1.60    , c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X
% 0.97/1.60    , Z, c_Int_Onumber__class_Onumber__of( X, Y ) ) ) }.
% 0.97/1.60  { ! alpha70( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ), c_Int_Onumber__class_Onumber__of( X, Y
% 0.97/1.60     ) ), alpha82( X, Y, Z, T ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( X, Y ) ), alpha70( X, Y, Z, T ) }.
% 0.97/1.60  { ! alpha82( X, Y, Z, T ), alpha70( X, Y, Z, T ) }.
% 0.97/1.60  { ! alpha82( X, Y, Z, T ), alpha94( X, Y, Z, T ) }.
% 0.97/1.60  { ! alpha82( X, Y, Z, T ), alpha26( X, Y, T ) }.
% 0.97/1.60  { ! alpha94( X, Y, Z, T ), ! alpha26( X, Y, T ), alpha82( X, Y, Z, T ) }.
% 0.97/1.60  { ! alpha94( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.97/1.60     ) ), c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), T ), c_Int_Onumber__class_Onumber__of
% 0.97/1.60    ( X, Y ) ) ) }.
% 0.97/1.60  { c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Y
% 0.97/1.60     ), c_Groups_Ozero__class_Ozero( X ) ), alpha94( X, Y, Z, T ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), T ), c_Int_Onumber__class_Onumber__of
% 0.97/1.60    ( X, Y ) ) ), alpha94( X, Y, Z, T ) }.
% 0.97/1.60  { ! alpha58( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ), c_Int_Onumber__class_Onumber__of( X, Y
% 0.97/1.60     ) ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), T ), c_Int_Onumber__class_Onumber__of
% 0.97/1.60    ( X, Y ) ), Z ) }.
% 0.97/1.60  { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( X, Y ) ), alpha58( X, Y, Z, T ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), T ), c_Int_Onumber__class_Onumber__of
% 0.97/1.60    ( X, Y ) ), Z ), alpha58( X, Y, Z, T ) }.
% 0.97/1.60  { ! alpha26( X, Y, Z ), c_Orderings_Oord__class_Oless( X, 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.97/1.60     ) ), c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.97/1.60     ) ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, 
% 0.97/1.60    Y ), c_Groups_Ozero__class_Ozero( X ) ), alpha26( X, Y, Z ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.60    , alpha26( X, Y, Z ) }.
% 0.97/1.60  { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60    ( X, c_Groups_Ozero__class_Ozero( X ), Y ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, hAPP( hAPP( 
% 0.97/1.60    c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ), 
% 0.97/1.60    c_Groups_Oone__class_Oone( X ) ) }.
% 0.97/1.60  { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60    ( X, c_Groups_Oone__class_Oone( X ), Y ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP( 
% 0.97/1.60    c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP( 
% 0.97/1.60    c_Power_Opower__class_Opower( X ), Y ), Z ) ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.97/1.60  { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60    ( X, c_Groups_Oone__class_Oone( X ), Y ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP( 
% 0.97/1.60    c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP( 
% 0.97/1.60    c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.97/1.60  { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60    ( X, c_Groups_Oone__class_Oone( X ), Y ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP( 
% 0.97/1.60    c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP( 
% 0.97/1.60    c_Power_Opower__class_Opower( X ), Y ), Z ) ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.97/1.60  { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oone__class_Oone
% 0.97/1.60    ( tc_RealDef_Oreal ), c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) )
% 0.97/1.60     ) }.
% 0.97/1.60  { ! class_Rings_Olinordered__semiring__1__strict( X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60    ( X, T, Y ), ! c_Orderings_Oord__class_Oless__eq( X, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ), U ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), W
% 0.97/1.60     ), ! c_Groups_Oplus__class_Oplus( X, U, W ) = c_Groups_Oone__class_Oone
% 0.97/1.60    ( X ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, 
% 0.97/1.60    hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), W ), T ) ), Y ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field__inverse__zero( X ), ! 
% 0.97/1.60    class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless__eq( X, 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( X, T, c_Int_Onumber__class_Onumber__of( 
% 0.97/1.60    X, Z ) ), Y ), alpha59( X, Y, Z, T ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field__inverse__zero( X ), ! 
% 0.97/1.60    class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless__eq( X, 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( X, T, c_Int_Onumber__class_Onumber__of( 
% 0.97/1.60    X, Z ) ), Y ), alpha71( X, Y, Z, T ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field__inverse__zero( X ), ! 
% 0.97/1.60    class_Int_Onumber( X ), ! alpha59( X, Y, Z, T ), ! alpha71( X, Y, Z, T )
% 0.97/1.60    , c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( 
% 0.97/1.60    X, T, c_Int_Onumber__class_Onumber__of( X, Z ) ), Y ) }.
% 0.97/1.60  { ! alpha71( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ), c_Int_Onumber__class_Onumber__of( X, Z
% 0.97/1.60     ) ), alpha83( X, Y, Z, T ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( X, Z ) ), alpha71( X, Y, Z, T ) }.
% 0.97/1.60  { ! alpha83( X, Y, Z, T ), alpha71( X, Y, Z, T ) }.
% 0.97/1.60  { ! alpha83( X, Y, Z, T ), alpha95( X, Y, Z, T ) }.
% 0.97/1.60  { ! alpha83( X, Y, Z, T ), alpha27( X, Y, Z ) }.
% 0.97/1.60  { ! alpha95( X, Y, Z, T ), ! alpha27( X, Y, Z ), alpha83( X, Y, Z, T ) }.
% 0.97/1.60  { ! alpha95( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( X, Z ), c_Groups_Ozero__class_Ozero( X
% 0.97/1.60     ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), Y ), c_Int_Onumber__class_Onumber__of
% 0.97/1.60    ( X, Z ) ), T ) }.
% 0.97/1.60  { c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Z
% 0.97/1.60     ), c_Groups_Ozero__class_Ozero( X ) ), alpha95( X, Y, Z, T ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), Y ), c_Int_Onumber__class_Onumber__of
% 0.97/1.60    ( X, Z ) ), T ), alpha95( X, Y, Z, T ) }.
% 0.97/1.60  { ! alpha59( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ), c_Int_Onumber__class_Onumber__of( X, Z
% 0.97/1.60     ) ), c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), Y ), c_Int_Onumber__class_Onumber__of
% 0.97/1.60    ( X, Z ) ) ) }.
% 0.97/1.60  { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( X, Z ) ), alpha59( X, Y, Z, T ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), Y ), c_Int_Onumber__class_Onumber__of
% 0.97/1.60    ( X, Z ) ) ), alpha59( X, Y, Z, T ) }.
% 0.97/1.60  { ! alpha27( X, Y, Z ), c_Orderings_Oord__class_Oless( X, 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( X, Z ), c_Groups_Ozero__class_Ozero( X
% 0.97/1.60     ) ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( 
% 0.97/1.60    X ), Y ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, 
% 0.97/1.60    Z ), c_Groups_Ozero__class_Ozero( X ) ), alpha27( X, Y, Z ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.60    , Y ), alpha27( X, Y, Z ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field__inverse__zero( X ), ! 
% 0.97/1.60    class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless__eq( X, 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( X, T, Z ), 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( X, Y ) ), alpha60( X, Y, Z, T ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field__inverse__zero( X ), ! 
% 0.97/1.60    class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless__eq( X, 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( X, T, Z ), 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( X, Y ) ), alpha72( X, Y, Z, T ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field__inverse__zero( X ), ! 
% 0.97/1.60    class_Int_Onumber( X ), ! alpha60( X, Y, Z, T ), ! alpha72( X, Y, Z, T )
% 0.97/1.60    , c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( 
% 0.97/1.60    X, T, Z ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.97/1.60  { ! alpha72( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ), Z ), alpha84( X, Y, Z, T ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.97/1.60    , alpha72( X, Y, Z, T ) }.
% 0.97/1.60  { ! alpha84( X, Y, Z, T ), alpha72( X, Y, Z, T ) }.
% 0.97/1.60  { ! alpha84( X, Y, Z, T ), alpha96( X, Y, Z, T ) }.
% 0.97/1.60  { ! alpha84( X, Y, Z, T ), alpha28( X, Y, Z ) }.
% 0.97/1.60  { ! alpha96( X, Y, Z, T ), ! alpha28( X, Y, Z ), alpha84( X, Y, Z, T ) }.
% 0.97/1.60  { ! alpha96( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Z, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.60    , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( X, Y ) ), Z ), T ) }.
% 0.97/1.60  { c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) ), 
% 0.97/1.60    alpha96( X, Y, Z, T ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X, 
% 0.97/1.60    Y ) ), Z ), T ), alpha96( X, Y, Z, T ) }.
% 0.97/1.60  { ! alpha60( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless__eq
% 0.97/1.60    ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( X, Y ) ), Z ) ) }.
% 0.97/1.60  { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ), 
% 0.97/1.60    alpha60( X, Y, Z, T ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X, 
% 0.97/1.60    Y ) ), Z ) ), alpha60( X, Y, Z, T ) }.
% 0.97/1.60  { ! alpha28( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.60    , c_Groups_Ozero__class_Ozero( X ), c_Int_Onumber__class_Onumber__of( X, 
% 0.97/1.60    Y ) ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.60    , alpha28( X, Y, Z ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.60    , c_Int_Onumber__class_Onumber__of( X, Y ) ), alpha28( X, Y, Z ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field__inverse__zero( X ), ! 
% 0.97/1.60    class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless__eq( X, 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( X, T ), c_Rings_Oinverse__class_Odivide
% 0.97/1.60    ( X, Z, Y ) ), alpha61( X, Y, Z, T ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field__inverse__zero( X ), ! 
% 0.97/1.60    class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless__eq( X, 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( X, T ), c_Rings_Oinverse__class_Odivide
% 0.97/1.60    ( X, Z, Y ) ), alpha73( X, Y, Z, T ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field__inverse__zero( X ), ! 
% 0.97/1.60    class_Int_Onumber( X ), ! alpha61( X, Y, Z, T ), ! alpha73( X, Y, Z, T )
% 0.97/1.60    , c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of
% 0.97/1.60    ( X, T ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.97/1.60  { ! alpha73( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ), Y ), alpha85( X, Y, Z, T ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.97/1.60    , alpha73( X, Y, Z, T ) }.
% 0.97/1.60  { ! alpha85( X, Y, Z, T ), alpha73( X, Y, Z, T ) }.
% 0.97/1.60  { ! alpha85( X, Y, Z, T ), alpha97( X, Y, Z, T ) }.
% 0.97/1.60  { ! alpha85( X, Y, Z, T ), alpha29( X, Y, T ) }.
% 0.97/1.60  { ! alpha97( X, Y, Z, T ), ! alpha29( X, Y, T ), alpha85( X, Y, Z, T ) }.
% 0.97/1.60  { ! alpha97( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Y, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.60    , Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( X, T ) ), Y ) ) }.
% 0.97/1.60  { c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ), 
% 0.97/1.60    alpha97( X, Y, Z, T ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( X, Z, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X, 
% 0.97/1.60    T ) ), Y ) ), alpha97( X, Y, Z, T ) }.
% 0.97/1.60  { ! alpha61( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless__eq
% 0.97/1.60    ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( X, T ) ), Y ), Z ) }.
% 0.97/1.60  { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ), 
% 0.97/1.60    alpha61( X, Y, Z, T ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X, 
% 0.97/1.60    T ) ), Y ), Z ), alpha61( X, Y, Z, T ) }.
% 0.97/1.60  { ! alpha29( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.60    , c_Int_Onumber__class_Onumber__of( X, Z ), c_Groups_Ozero__class_Ozero( 
% 0.97/1.60    X ) ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.60    , alpha29( X, Y, Z ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of
% 0.97/1.60    ( X, Z ), c_Groups_Ozero__class_Ozero( X ) ), alpha29( X, Y, Z ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field__inverse__zero( X ), ! 
% 0.97/1.60    class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless__eq( X, T, 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( X, Z, c_Int_Onumber__class_Onumber__of( 
% 0.97/1.60    X, Y ) ) ), alpha62( X, Y, Z, T ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field__inverse__zero( X ), ! 
% 0.97/1.60    class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless__eq( X, T, 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( X, Z, c_Int_Onumber__class_Onumber__of( 
% 0.97/1.60    X, Y ) ) ), alpha74( X, Y, Z, T ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field__inverse__zero( X ), ! 
% 0.97/1.60    class_Int_Onumber( X ), ! alpha62( X, Y, Z, T ), ! alpha74( X, Y, Z, T )
% 0.97/1.60    , c_Orderings_Oord__class_Oless__eq( X, T, 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( X, Z, c_Int_Onumber__class_Onumber__of( 
% 0.97/1.60    X, Y ) ) ) }.
% 0.97/1.60  { ! alpha74( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ), c_Int_Onumber__class_Onumber__of( X, Y
% 0.97/1.60     ) ), alpha86( X, Y, Z, T ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( X, Y ) ), alpha74( X, Y, Z, T ) }.
% 0.97/1.60  { ! alpha86( X, Y, Z, T ), alpha74( X, Y, Z, T ) }.
% 0.97/1.60  { ! alpha86( X, Y, Z, T ), alpha98( X, Y, Z, T ) }.
% 0.97/1.60  { ! alpha86( X, Y, Z, T ), alpha30( X, Y, T ) }.
% 0.97/1.60  { ! alpha98( X, Y, Z, T ), ! alpha30( X, Y, T ), alpha86( X, Y, Z, T ) }.
% 0.97/1.60  { ! alpha98( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.97/1.60     ) ), c_Orderings_Oord__class_Oless__eq( X, Z, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), T ), c_Int_Onumber__class_Onumber__of
% 0.97/1.60    ( X, Y ) ) ) }.
% 0.97/1.60  { c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Y
% 0.97/1.60     ), c_Groups_Ozero__class_Ozero( X ) ), alpha98( X, Y, Z, T ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( X, Z, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), T ), c_Int_Onumber__class_Onumber__of
% 0.97/1.60    ( X, Y ) ) ), alpha98( X, Y, Z, T ) }.
% 0.97/1.60  { ! alpha62( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ), c_Int_Onumber__class_Onumber__of( X, Y
% 0.97/1.60     ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), T ), c_Int_Onumber__class_Onumber__of
% 0.97/1.60    ( X, Y ) ), Z ) }.
% 0.97/1.60  { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( X, Y ) ), alpha62( X, Y, Z, T ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( X ), T ), c_Int_Onumber__class_Onumber__of
% 0.97/1.60    ( X, Y ) ), Z ), alpha62( X, Y, Z, T ) }.
% 0.97/1.60  { ! alpha30( X, Y, Z ), c_Orderings_Oord__class_Oless( X, 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.97/1.60     ) ), c_Orderings_Oord__class_Oless__eq( X, Z, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, 
% 0.97/1.60    Y ), c_Groups_Ozero__class_Ozero( X ) ), alpha30( X, Y, Z ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.97/1.60     ) ), alpha30( X, Y, Z ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field__inverse__zero( X ), ! 
% 0.97/1.60    class_Int_Onumber__ring( X ), ! c_Orderings_Oord__class_Oless( X, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X, Y, 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( X, c_Int_OBit0( c_Int_OBit1( c_Int_OPls
% 0.97/1.60     ) ) ) ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero
% 0.97/1.60    ( X ), Y ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field__inverse__zero( X ), ! 
% 0.97/1.60    class_Int_Onumber__ring( X ), ! c_Orderings_Oord__class_Oless( X, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X, Y, 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( X, c_Int_OBit0( c_Int_OBit1( c_Int_OPls
% 0.97/1.60     ) ) ) ) ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field__inverse__zero( X ), ! 
% 0.97/1.60    class_Int_Onumber__ring( X ), ! c_Orderings_Oord__class_Oless( X, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X, Y, 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( X, c_Int_OBit0( c_Int_OBit1( c_Int_OPls
% 0.97/1.60     ) ) ) ) ) }.
% 0.97/1.60  { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.60    , hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( 
% 0.97/1.60    c_Int_OPls ) ) ) ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.60  { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.60    , c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP( 
% 0.97/1.60    c_Power_Opower__class_Opower( X ), Y ), c_Int_Onumber__class_Onumber__of
% 0.97/1.60    ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ), ! Y = 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.60  { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.97/1.60     ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), 
% 0.97/1.60    hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( 
% 0.97/1.60    c_Int_OPls ) ) ) ) ) }.
% 0.97/1.60  { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt( 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0( 
% 0.97/1.60    c_Int_OBit1( c_Int_OPls ) ) ) ) ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ), 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0( 
% 0.97/1.60    c_Int_OBit1( c_Int_OPls ) ) ) ) ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ), 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0( 
% 0.97/1.60    c_Int_OBit1( c_Int_OPls ) ) ) ), X ) }.
% 0.97/1.60  { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, 
% 0.97/1.60    c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_NthRoot_Osqrt( 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0( 
% 0.97/1.60    c_Int_OBit1( c_Int_OPls ) ) ) ) ) }.
% 0.97/1.60  { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60    ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( 
% 0.97/1.60    c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( 
% 0.97/1.60    c_Int_OPls ) ) ) ) ), ! c_Orderings_Oord__class_Oless__eq( X, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X, 
% 0.97/1.60    Z, Y ) }.
% 0.97/1.60  { ! class_Fields_Olinordered__field__inverse__zero( X ), ! 
% 0.97/1.60    class_Int_Onumber__ring( X ), c_Orderings_Oord__class_Oless( X, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X, 
% 0.97/1.60    c_Groups_Oone__class_Oone( X ), c_Int_Onumber__class_Onumber__of( X, 
% 0.97/1.60    c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) }.
% 0.97/1.60  { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.60    , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( 
% 0.97/1.60    c_Power_Opower__class_Opower( X ), Z ), c_Int_Onumber__class_Onumber__of
% 0.97/1.60    ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ), hAPP( hAPP( 
% 0.97/1.60    c_Power_Opower__class_Opower( X ), Y ), c_Int_Onumber__class_Onumber__of
% 0.97/1.60    ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ), 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.60  { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.60    , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 0.97/1.60    ( hAPP( c_Power_Opower__class_Opower( X ), Z ), 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( 
% 0.97/1.60    c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( 
% 0.97/1.60    c_Int_OPls ) ) ) ) ) ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y = 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.60  { ! class_Rings_Olinordered__idom( X ), Z = c_Groups_Ozero__class_Ozero( X
% 0.97/1.60     ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Power_Opower__class_Opower
% 0.97/1.60    ( X ), Z ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( 
% 0.97/1.60    c_Int_OBit1( c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower
% 0.97/1.60    ( X ), Y ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( 
% 0.97/1.60    c_Int_OBit1( c_Int_OPls ) ) ) ) ) ) }.
% 0.97/1.60  { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.97/1.60     ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Power_Opower__class_Opower
% 0.97/1.60    ( X ), Z ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( 
% 0.97/1.60    c_Int_OBit1( c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower
% 0.97/1.60    ( X ), Y ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( 
% 0.97/1.60    c_Int_OBit1( c_Int_OPls ) ) ) ) ) ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP( 
% 0.97/1.60    c_Power_Opower__class_Opower( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) )
% 0.97/1.60    , c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1
% 0.97/1.60    ( c_Int_OPls ) ) ) ) ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, 
% 0.97/1.60    c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, X, c_NthRoot_Osqrt( 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0( 
% 0.97/1.60    c_Int_OBit1( c_Int_OPls ) ) ) ) ), X ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, 
% 0.97/1.60    c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ), 
% 0.97/1.60    c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP( 
% 0.97/1.60    c_Power_Opower__class_Opower( tc_RealDef_Oreal ), X ), 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( 
% 0.97/1.60    c_Int_OPls ) ) ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.97/1.60  { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.60    , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.97/1.60    , hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( hAPP( 
% 0.97/1.60    hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( 
% 0.97/1.60    c_Int_OPls ) ) ) ), Z ) ) ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.60  { c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, c_Transcendental_Opi, 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0( 
% 0.97/1.60    c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) = 
% 0.97/1.60    c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, hAPP( hAPP( 
% 0.97/1.60    c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0( 
% 0.97/1.60    c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ), c_Transcendental_Oarctan
% 0.97/1.60    ( c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, 
% 0.97/1.60    c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit1( 
% 0.97/1.60    c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) ) ), 
% 0.97/1.60    c_Transcendental_Oarctan( c_Rings_Oinverse__class_Odivide( 
% 0.97/1.60    tc_RealDef_Oreal, c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), 
% 0.97/1.60    c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit1( 
% 0.97/1.60    c_Int_OBit1( c_Int_OBit1( c_Int_OBit1( c_Int_OBit0( c_Int_OBit1( 
% 0.97/1.60    c_Int_OBit1( c_Int_OBit1( c_Int_OPls ) ) ) ) ) ) ) ) ) ) ) ) }.
% 0.97/1.60  { c_Complex_Ocomplex_Ocomplex__rec( T, Z, c_Complex_Ocomplex_OComplex( Y, X
% 0.97/1.60     ) ) = hAPP( hAPP( Z, Y ), X ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), 
% 0.97/1.60    c_RComplete_Onatceiling( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X
% 0.97/1.60    , c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) = 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatceiling( X ), 
% 0.97/1.60    c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc( 
% 0.97/1.60    X ) ) }.
% 0.97/1.60  { c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( X ) ) }.
% 0.97/1.60  { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( 
% 0.97/1.60    tc_Nat_Onat ), c_Nat_OSuc( X ) ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.97/1.60    ( tc_Nat_Onat, Y, Z ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y
% 0.97/1.60    , X ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, X ) = 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus( 
% 0.97/1.60    tc_Nat_Onat, Y, T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.97/1.60    .
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus( 
% 0.97/1.60    tc_Nat_Onat, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.97/1.60    .
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, 
% 0.97/1.60    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.97/1.60    ( tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) )
% 0.97/1.60    , c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus( 
% 0.97/1.60    tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }
% 0.97/1.60    .
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.97/1.60    ( tc_Nat_Onat, Y, X ), X ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.97/1.60    ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Opi, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.60  { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Opi ) }
% 0.97/1.60    .
% 0.97/1.60  { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( 
% 0.97/1.60    tc_Nat_Onat ), X ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.60    ( tc_Nat_Onat ), X ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 0.97/1.60    .
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X = 
% 0.97/1.60    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.60    ( tc_Nat_Onat, Y, Z ), X ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! 
% 0.97/1.60    c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.60    ( tc_Nat_Onat, Z, X ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.97/1.60     ) }.
% 0.97/1.60  { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( 
% 0.97/1.60    tc_Nat_Onat ), X ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X, 
% 0.97/1.60    c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.60  { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.60  { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), 
% 0.97/1.60    c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X, 
% 0.97/1.61    c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), 
% 0.97/1.61    c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.61  { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.97/1.61  { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), 
% 0.97/1.61    c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.97/1.61  { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), 
% 0.97/1.61    c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X = Y }.
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.97/1.61  { alpha100( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ), 
% 0.97/1.61    hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.97/1.61  { alpha100( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( 
% 0.97/1.61    hAPP( X, Y ), Z ) ) }.
% 0.97/1.61  { ! alpha100( X, Y, Z ), alpha101( X, Y, Z ), Z = Y }.
% 0.97/1.61  { ! alpha100( X, Y, Z ), alpha101( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), 
% 0.97/1.61    Z ) ) }.
% 0.97/1.61  { ! alpha101( X, Y, Z ), alpha100( X, Y, Z ) }.
% 0.97/1.61  { ! Z = Y, hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha100( X, Y, Z ) }.
% 0.97/1.61  { ! alpha101( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y )
% 0.97/1.61     }.
% 0.97/1.61  { ! alpha101( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP( 
% 0.97/1.61    X, Y ), Z ) ), alpha101( X, Y, Z ) }.
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.97/1.61    ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ), 
% 0.97/1.61    c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), 
% 0.97/1.61    c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! 
% 0.97/1.61    c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ), 
% 0.97/1.61    c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) }.
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) = X
% 0.97/1.61    , c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), 
% 0.97/1.61    c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.97/1.61  { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! 
% 0.97/1.61    c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), X = Y }
% 0.97/1.61    .
% 0.97/1.61  { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! 
% 0.97/1.61    c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y = X }
% 0.97/1.61    .
% 0.97/1.61  { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X, 
% 0.97/1.61    c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.97/1.61    ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), 
% 0.97/1.61    c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc( 
% 0.97/1.61    X ) ) }.
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), 
% 0.97/1.61    c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), 
% 0.97/1.61    c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.97/1.61  { ! Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) )
% 0.97/1.61     }.
% 0.97/1.61  { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), 
% 0.97/1.61    c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), ! 
% 0.97/1.61    c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OMin, c_Int_OMin ) }
% 0.97/1.61    .
% 0.97/1.61  { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y = X, 
% 0.97/1.61    c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, 
% 0.97/1.61    c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ), 
% 0.97/1.61    c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ), 
% 0.97/1.61    c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), 
% 0.97/1.61    c_Orderings_Oord__class_Oless( tc_Int_Oint, 
% 0.97/1.61    c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ), 
% 0.97/1.61    c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) }.
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), 
% 0.97/1.61    c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus( 
% 0.97/1.61    tc_Int_Oint, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.97/1.61    .
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), 
% 0.97/1.61    c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), ! Y = X }.
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), Y = X, 
% 0.97/1.61    c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( Y ), 
% 0.97/1.61    c_Int_OBit0( X ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.97/1.61    .
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), 
% 0.97/1.61    c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( Y ), c_Int_OBit0
% 0.97/1.61    ( X ) ) }.
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( Y ), 
% 0.97/1.61    c_Int_OBit0( X ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.97/1.61    .
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), 
% 0.97/1.61    c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( Y ), c_Int_OBit0
% 0.97/1.61    ( X ) ) }.
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, c_Int_OPls ) }
% 0.97/1.61    .
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( Y ), 
% 0.97/1.61    c_Int_OBit1( X ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.97/1.61    .
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), 
% 0.97/1.61    c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( Y ), c_Int_OBit1
% 0.97/1.61    ( X ) ) }.
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( Y ), 
% 0.97/1.61    c_Int_OBit1( X ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.97/1.61    .
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), 
% 0.97/1.61    c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( Y ), c_Int_OBit1
% 0.97/1.61    ( X ) ) }.
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, 
% 0.97/1.61    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ), 
% 0.97/1.61    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ), alpha31( X, Y ) }.
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, 
% 0.97/1.61    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ), 
% 0.97/1.61    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ), 
% 0.97/1.61    c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.97/1.61  { ! alpha31( X, Y ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), 
% 0.97/1.61    c_Orderings_Oord__class_Oless( tc_Nat_Onat, 
% 0.97/1.61    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ), 
% 0.97/1.61    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) }.
% 0.97/1.61  { ! alpha31( X, Y ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), 
% 0.97/1.61    c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, X ) }.
% 0.97/1.61  { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), alpha31( X, Y ) }.
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, X ), alpha31( X
% 0.97/1.61    , Y ) }.
% 0.97/1.61  { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T, 
% 0.97/1.61    X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }
% 0.97/1.61    .
% 0.97/1.61  { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T, 
% 0.97/1.61    X ), Z, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z )
% 0.97/1.61     }.
% 0.97/1.61  { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.97/1.61    ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z
% 0.97/1.61     ), c_Orderings_Oord__class_Oless( tc_fun( T, X ), Z, Y ) }.
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.61    ( tc_Nat_Onat ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ), 
% 0.97/1.61    c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, X ) }.
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, X ), 
% 0.97/1.61    c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( 
% 0.97/1.61    tc_Nat_Onat ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) }.
% 0.97/1.61  { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, 
% 0.97/1.61    c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Opi ) }
% 0.97/1.61    .
% 0.97/1.61  { ! c_Transcendental_Opi = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal )
% 0.97/1.61     }.
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( X ), 
% 0.97/1.61    c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), 
% 0.97/1.61    c_Orderings_Oord__class_Oless( tc_Int_Oint, X, 
% 0.97/1.61    c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, 
% 0.97/1.61    c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), 
% 0.97/1.61    c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( X ), 
% 0.97/1.61    c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( X ), 
% 0.97/1.61    c_Int_OPls ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Int_OPls )
% 0.97/1.61     }.
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Int_OPls ), 
% 0.97/1.61    c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( X ), c_Int_OPls
% 0.97/1.61     ) }.
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, 
% 0.97/1.61    c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( Y ), 
% 0.97/1.61    c_Int_OBit0( X ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.97/1.61    .
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), 
% 0.97/1.61    c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( Y ), c_Int_OBit0
% 0.97/1.61    ( X ) ) }.
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( Y ), 
% 0.97/1.61    c_Int_OBit0( X ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.97/1.61    .
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), 
% 0.97/1.61    c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( Y ), c_Int_OBit0
% 0.97/1.61    ( X ) ) }.
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( X ), 
% 0.97/1.61    c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), 
% 0.97/1.61    c_Orderings_Oord__class_Oless( tc_Int_Oint, X, 
% 0.97/1.61    c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, 
% 0.97/1.61    c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), 
% 0.97/1.61    c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( X ), 
% 0.97/1.61    c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y = 
% 0.97/1.61    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha32( X, Y ) }.
% 0.97/1.61  { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), 
% 0.97/1.61    c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.97/1.61  { ! alpha32( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, 
% 0.97/1.61    c_Nat_OSuc( X ) ) }.
% 0.97/1.61  { ! alpha32( X, Y ), Y = c_Nat_OSuc( skol6( Z, Y ) ) }.
% 0.97/1.61  { ! alpha32( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol6( X, 
% 0.97/1.61    Y ), X ) }.
% 0.97/1.61  { ! Y = c_Nat_OSuc( Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.97/1.61     ), alpha32( X, Y ) }.
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( 
% 0.97/1.61    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X = 
% 0.97/1.61    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.61  { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), 
% 0.97/1.61    c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( 
% 0.97/1.61    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.61    ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( skol7( X ) ) }.
% 0.97/1.61  { ! X = c_Nat_OSuc( Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, 
% 0.97/1.61    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( c_Nat_OSuc( 
% 0.97/1.61    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X = 
% 0.97/1.61    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X = c_Nat_OSuc( 
% 0.97/1.61    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( X ), 
% 0.97/1.61    c_Int_OPls ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Int_OPls )
% 0.97/1.61     }.
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Int_OPls ), 
% 0.97/1.61    c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( X ), c_Int_OPls
% 0.97/1.61     ) }.
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, c_Int_OBit0( X
% 0.97/1.61     ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, X ) }.
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, X ), 
% 0.97/1.61    c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, c_Int_OBit0( X )
% 0.97/1.61     ) }.
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.61    ( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ), 
% 0.97/1.61    c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( 
% 0.97/1.61    tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, 
% 0.97/1.61    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.61    ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, 
% 0.97/1.61    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus( 
% 0.97/1.61    tc_Nat_Onat, Y, X ) ) }.
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.61    ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, 
% 0.97/1.61    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus( 
% 0.97/1.61    tc_Nat_Onat, Y, X ) ) }.
% 0.97/1.61  { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( 
% 0.97/1.61    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.97/1.61  { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( 
% 0.97/1.61    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ) }.
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), X = c_Nat_OSuc( 
% 0.97/1.61    c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol8( X, Y ) ) ) }.
% 0.97/1.61  { ! X = c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ), 
% 0.97/1.61    c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ), 
% 0.97/1.61    c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! 
% 0.97/1.61    c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X = Y }
% 0.97/1.61    .
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X = Y, 
% 0.97/1.61    c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), 
% 0.97/1.61    c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), 
% 0.97/1.61    c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ), 
% 0.97/1.61    c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), 
% 0.97/1.61    c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), 
% 0.97/1.61    c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), 
% 0.97/1.61    c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), 
% 0.97/1.61    c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ), 
% 0.97/1.61    c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.61  { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero( 
% 0.97/1.61    tc_Int_Oint ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.61    ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.97/1.61    , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, 
% 0.97/1.61    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.61    ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.97/1.61    , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, 
% 0.97/1.61    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.61    ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, 
% 0.97/1.61    c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), 
% 0.97/1.61    c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( 
% 0.97/1.61    tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), 
% 0.97/1.61    Y ), X ) ) }.
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP( 
% 0.97/1.61    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP( 
% 0.97/1.61    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), 
% 0.97/1.61    c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( 
% 0.97/1.61    tc_Nat_Onat ), Z ) }.
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP( 
% 0.97/1.61    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP( 
% 0.97/1.61    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), 
% 0.97/1.61    c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.61    ( tc_Nat_Onat ), Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 0.97/1.61     ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP( 
% 0.97/1.61    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP( 
% 0.97/1.61    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP( 
% 0.97/1.61    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP( 
% 0.97/1.61    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), 
% 0.97/1.61    c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( 
% 0.97/1.61    tc_Nat_Onat ), Y ) }.
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP( 
% 0.97/1.61    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP( 
% 0.97/1.61    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), 
% 0.97/1.61    c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X ) }.
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.61    ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.97/1.61     ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP( 
% 0.97/1.61    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP( 
% 0.97/1.61    c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! 
% 0.97/1.61    c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( 
% 0.97/1.61    tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( 
% 0.97/1.61    hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP
% 0.97/1.61    ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! 
% 0.97/1.61    c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( 
% 0.97/1.61    tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( 
% 0.97/1.61    hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP
% 0.97/1.61    ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.97/1.61  { ! class_Orderings_Opreorder( X ), class_Orderings_Opreorder( tc_fun( Y, X
% 0.97/1.61     ) ) }.
% 0.97/1.61  { ! class_Orderings_Oorder( X ), class_Orderings_Oorder( tc_fun( Y, X ) ) }
% 0.97/1.61    .
% 0.97/1.61  { ! class_Orderings_Oord( X ), class_Orderings_Oord( tc_fun( Y, X ) ) }.
% 0.97/1.61  { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct( 
% 0.97/1.61    tc_Int_Oint ) }.
% 0.97/1.61  { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.97/1.61  { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Int_Oint ) }.
% 0.97/1.61  { class_Rings_Olinordered__comm__semiring__strict( tc_Int_Oint ) }.
% 0.97/1.61  { class_Rings_Olinordered__semiring__1__strict( tc_Int_Oint ) }.
% 0.97/1.61  { class_Rings_Olinordered__semiring__strict( tc_Int_Oint ) }.
% 0.97/1.61  { class_Groups_Oordered__ab__semigroup__add( tc_Int_Oint ) }.
% 0.97/1.61  { class_Groups_Oordered__ab__group__add__abs( tc_Int_Oint ) }.
% 0.97/1.61  { class_Groups_Oordered__comm__monoid__add( tc_Int_Oint ) }.
% 0.97/1.61  { class_Groups_Olinordered__ab__group__add( tc_Int_Oint ) }.
% 0.97/1.61  { class_Groups_Ocancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.97/1.61  { class_Rings_Oring__1__no__zero__divisors( tc_Int_Oint ) }.
% 0.97/1.61  { class_Rings_Oordered__cancel__semiring( tc_Int_Oint ) }.
% 0.97/1.61  { class_Rings_Olinordered__ring__strict( tc_Int_Oint ) }.
% 0.97/1.61  { class_Rings_Oring__no__zero__divisors( tc_Int_Oint ) }.
% 0.97/1.61  { class_Rings_Oordered__comm__semiring( tc_Int_Oint ) }.
% 0.97/1.61  { class_Rings_Olinordered__semiring__1( tc_Int_Oint ) }.
% 0.97/1.61  { class_Groups_Oordered__ab__group__add( tc_Int_Oint ) }.
% 0.97/1.61  { class_Groups_Ocancel__semigroup__add( tc_Int_Oint ) }.
% 0.97/1.61  { class_Rings_Olinordered__semiring( tc_Int_Oint ) }.
% 0.97/1.61  { class_Rings_Olinordered__semidom( tc_Int_Oint ) }.
% 0.97/1.61  { class_Groups_Oab__semigroup__mult( tc_Int_Oint ) }.
% 0.97/1.61  { class_Groups_Ocomm__monoid__mult( tc_Int_Oint ) }.
% 0.97/1.61  { class_Groups_Oab__semigroup__add( tc_Int_Oint ) }.
% 0.97/1.61  { class_Rings_Oordered__semiring( tc_Int_Oint ) }.
% 0.97/1.61  { class_Rings_Oordered__ring__abs( tc_Int_Oint ) }.
% 0.97/1.61  { class_Rings_Ono__zero__divisors( tc_Int_Oint ) }.
% 0.97/1.61  { class_Groups_Ocomm__monoid__add( tc_Int_Oint ) }.
% 0.97/1.61  { class_Rings_Olinordered__ring( tc_Int_Oint ) }.
% 0.97/1.61  { class_Rings_Olinordered__idom( tc_Int_Oint ) }.
% 0.97/1.61  { class_Rings_Ocomm__semiring__1( tc_Int_Oint ) }.
% 0.97/1.61  { class_Rings_Ocomm__semiring( tc_Int_Oint ) }.
% 0.97/1.61  { class_Groups_Oab__group__add( tc_Int_Oint ) }.
% 0.97/1.61  { class_Rings_Ozero__neq__one( tc_Int_Oint ) }.
% 0.97/1.61  { class_Rings_Oordered__ring( tc_Int_Oint ) }.
% 0.97/1.61  { class_Orderings_Opreorder( tc_Int_Oint ) }.
% 0.97/1.61  { class_Orderings_Olinorder( tc_Int_Oint ) }.
% 0.97/1.61  { class_Groups_Omonoid__mult( tc_Int_Oint ) }.
% 0.97/1.61  { class_Rings_Ocomm__ring__1( tc_Int_Oint ) }.
% 0.97/1.61  { class_Groups_Omonoid__add( tc_Int_Oint ) }.
% 0.97/1.61  { class_Rings_Osemiring__1( tc_Int_Oint ) }.
% 0.97/1.61  { class_Rings_Osemiring__0( tc_Int_Oint ) }.
% 0.97/1.61  { class_Groups_Ogroup__add( tc_Int_Oint ) }.
% 0.97/1.61  { class_Rings_Omult__zero( tc_Int_Oint ) }.
% 0.97/1.61  { class_Orderings_Oorder( tc_Int_Oint ) }.
% 0.97/1.61  { class_Int_Oring__char__0( tc_Int_Oint ) }.
% 0.97/1.61  { class_Int_Onumber__ring( tc_Int_Oint ) }.
% 0.97/1.61  { class_Rings_Osemiring( tc_Int_Oint ) }.
% 0.97/1.61  { class_Orderings_Oord( tc_Int_Oint ) }.
% 0.97/1.61  { class_Rings_Oring__1( tc_Int_Oint ) }.
% 0.97/1.61  { class_Power_Opower( tc_Int_Oint ) }.
% 0.97/1.61  { class_Groups_Ozero( tc_Int_Oint ) }.
% 0.97/1.61  { class_Rings_Oring( tc_Int_Oint ) }.
% 0.97/1.61  { class_Int_Onumber( tc_Int_Oint ) }.
% 0.97/1.61  { class_Groups_Oone( tc_Int_Oint ) }.
% 0.97/1.61  { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct( 
% 0.97/1.61    tc_Nat_Onat ) }.
% 0.97/1.61  { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.97/1.61  { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Nat_Onat ) }.
% 0.97/1.61  { class_Rings_Olinordered__comm__semiring__strict( tc_Nat_Onat ) }.
% 0.97/1.61  { class_Rings_Olinordered__semiring__strict( tc_Nat_Onat ) }.
% 0.97/1.61  { class_Groups_Oordered__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.97/1.61  { class_Groups_Oordered__comm__monoid__add( tc_Nat_Onat ) }.
% 0.97/1.61  { class_Groups_Ocancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.97/1.61  { class_Rings_Oordered__cancel__semiring( tc_Nat_Onat ) }.
% 0.97/1.61  { class_Rings_Oordered__comm__semiring( tc_Nat_Onat ) }.
% 0.97/1.61  { class_Groups_Ocancel__semigroup__add( tc_Nat_Onat ) }.
% 0.97/1.61  { class_Rings_Olinordered__semiring( tc_Nat_Onat ) }.
% 0.97/1.61  { class_Rings_Olinordered__semidom( tc_Nat_Onat ) }.
% 0.97/1.61  { class_Groups_Oab__semigroup__mult( tc_Nat_Onat ) }.
% 0.97/1.61  { class_Groups_Ocomm__monoid__mult( tc_Nat_Onat ) }.
% 0.97/1.61  { class_Groups_Oab__semigroup__add( tc_Nat_Onat ) }.
% 0.97/1.61  { class_Rings_Oordered__semiring( tc_Nat_Onat ) }.
% 0.97/1.61  { class_Rings_Ono__zero__divisors( tc_Nat_Onat ) }.
% 0.97/1.61  { class_Groups_Ocomm__monoid__add( tc_Nat_Onat ) }.
% 0.97/1.61  { class_Rings_Ocomm__semiring__1( tc_Nat_Onat ) }.
% 0.97/1.61  { class_Rings_Ocomm__semiring( tc_Nat_Onat ) }.
% 0.97/1.61  { class_Rings_Ozero__neq__one( tc_Nat_Onat ) }.
% 0.97/1.61  { class_Orderings_Opreorder( tc_Nat_Onat ) }.
% 0.97/1.61  { class_Orderings_Olinorder( tc_Nat_Onat ) }.
% 0.97/1.61  { class_Groups_Omonoid__mult( tc_Nat_Onat ) }.
% 0.97/1.61  { class_Groups_Omonoid__add( tc_Nat_Onat ) }.
% 0.97/1.61  { class_Rings_Osemiring__1( tc_Nat_Onat ) }.
% 0.97/1.61  { class_Rings_Osemiring__0( tc_Nat_Onat ) }.
% 0.97/1.61  { class_Rings_Omult__zero( tc_Nat_Onat ) }.
% 0.97/1.61  { class_Orderings_Oorder( tc_Nat_Onat ) }.
% 0.97/1.61  { class_Rings_Osemiring( tc_Nat_Onat ) }.
% 0.97/1.61  { class_Orderings_Oord( tc_Nat_Onat ) }.
% 0.97/1.61  { class_Power_Opower( tc_Nat_Onat ) }.
% 0.97/1.61  { class_Groups_Ozero( tc_Nat_Onat ) }.
% 0.97/1.61  { class_Int_Onumber( tc_Nat_Onat ) }.
% 0.97/1.61  { class_Groups_Oone( tc_Nat_Onat ) }.
% 0.97/1.61  { class_Orderings_Opreorder( tc_HOL_Obool ) }.
% 0.97/1.61  { class_Orderings_Oorder( tc_HOL_Obool ) }.
% 0.97/1.61  { class_Orderings_Oord( tc_HOL_Obool ) }.
% 0.97/1.61  { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct( 
% 0.97/1.61    tc_RealDef_Oreal ) }.
% 0.97/1.61  { class_Groups_Oordered__cancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.97/1.61  { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_RealDef_Oreal ) }
% 0.97/1.61    .
% 0.97/1.61  { class_Rings_Olinordered__comm__semiring__strict( tc_RealDef_Oreal ) }.
% 0.97/1.61  { class_Fields_Olinordered__field__inverse__zero( tc_RealDef_Oreal ) }.
% 0.97/1.61  { class_Rings_Olinordered__semiring__1__strict( tc_RealDef_Oreal ) }.
% 0.97/1.61  { class_RealVector_Oreal__normed__div__algebra( tc_RealDef_Oreal ) }.
% 0.97/1.61  { class_Rings_Olinordered__semiring__strict( tc_RealDef_Oreal ) }.
% 0.97/1.61  { class_Rings_Odivision__ring__inverse__zero( tc_RealDef_Oreal ) }.
% 0.97/1.61  { class_RealVector_Oreal__normed__algebra__1( tc_RealDef_Oreal ) }.
% 0.97/1.61  { class_Groups_Oordered__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.97/1.61  { class_Groups_Oordered__ab__group__add__abs( tc_RealDef_Oreal ) }.
% 0.97/1.61  { class_RealVector_Oreal__normed__algebra( tc_RealDef_Oreal ) }.
% 0.97/1.61  { class_Groups_Oordered__comm__monoid__add( tc_RealDef_Oreal ) }.
% 0.97/1.61  { class_Groups_Olinordered__ab__group__add( tc_RealDef_Oreal ) }.
% 0.97/1.61  { class_Groups_Ocancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.97/1.61  { class_Rings_Oring__1__no__zero__divisors( tc_RealDef_Oreal ) }.
% 0.97/1.61  { class_Rings_Oordered__cancel__semiring( tc_RealDef_Oreal ) }.
% 0.97/1.61  { class_RealVector_Oreal__normed__vector( tc_RealDef_Oreal ) }.
% 0.97/1.61  { class_Rings_Olinordered__ring__strict( tc_RealDef_Oreal ) }.
% 0.97/1.61  { class_RealVector_Oreal__normed__field( tc_RealDef_Oreal ) }.
% 0.97/1.61  { class_Rings_Oring__no__zero__divisors( tc_RealDef_Oreal ) }.
% 0.97/1.61  { class_Rings_Oordered__comm__semiring( tc_RealDef_Oreal ) }.
% 0.97/1.61  { class_Rings_Olinordered__semiring__1( tc_RealDef_Oreal ) }.
% 0.97/1.61  { class_Groups_Oordered__ab__group__add( tc_RealDef_Oreal ) }.
% 0.97/1.61  { class_Groups_Ocancel__semigroup__add( tc_RealDef_Oreal ) }.
% 0.97/1.61  { class_Rings_Olinordered__semiring( tc_RealDef_Oreal ) }.
% 0.97/1.61  { class_Fields_Ofield__inverse__zero( tc_RealDef_Oreal ) }.
% 0.97/1.61  { class_Rings_Olinordered__semidom( tc_RealDef_Oreal ) }.
% 0.97/1.61  { class_Groups_Oab__semigroup__mult( tc_RealDef_Oreal ) }.
% 0.97/1.61  { class_Groups_Ocomm__monoid__mult( tc_RealDef_Oreal ) }.
% 0.97/1.61  { class_Groups_Oab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.97/1.61  { class_Fields_Olinordered__field( tc_RealDef_Oreal ) }.
% 0.97/1.61  { class_Rings_Oordered__semiring( tc_RealDef_Oreal ) }.
% 0.97/1.61  { class_Rings_Oordered__ring__abs( tc_RealDef_Oreal ) }.
% 0.97/1.61  { class_Rings_Ono__zero__divisors( tc_RealDef_Oreal ) }.
% 0.97/1.61  { class_Groups_Ocomm__monoid__add( tc_RealDef_Oreal ) }.
% 0.97/1.61  { class_Rings_Olinordered__ring( tc_RealDef_Oreal ) }.
% 0.97/1.61  { class_Rings_Olinordered__idom( tc_RealDef_Oreal ) }.
% 0.97/1.61  { class_Rings_Ocomm__semiring__1( tc_RealDef_Oreal ) }.
% 0.97/1.61  { class_RealVector_Oreal__field( tc_RealDef_Oreal ) }.
% 0.97/1.61  { class_Rings_Odivision__ring( tc_RealDef_Oreal ) }.
% 0.97/1.61  { class_Rings_Ocomm__semiring( tc_RealDef_Oreal ) }.
% 0.97/1.61  { class_Groups_Oab__group__add( tc_RealDef_Oreal ) }.
% 0.97/1.61  { class_Rings_Ozero__neq__one( tc_RealDef_Oreal ) }.
% 0.97/1.61  { class_Rings_Oordered__ring( tc_RealDef_Oreal ) }.
% 0.97/1.61  { class_Orderings_Opreorder( tc_RealDef_Oreal ) }.
% 0.97/1.61  { class_Orderings_Olinorder( tc_RealDef_Oreal ) }.
% 0.97/1.61  { class_Groups_Omonoid__mult( tc_RealDef_Oreal ) }.
% 0.97/1.61  { class_Rings_Ocomm__ring__1( tc_RealDef_Oreal ) }.
% 0.97/1.61  { class_Groups_Omonoid__add( tc_RealDef_Oreal ) }.
% 0.97/1.61  { class_Rings_Osemiring__1( tc_RealDef_Oreal ) }.
% 0.97/1.61  { class_Rings_Osemiring__0( tc_RealDef_Oreal ) }.
% 0.97/1.61  { class_Groups_Ogroup__add( tc_RealDef_Oreal ) }.
% 0.97/1.61  { class_Rings_Omult__zero( tc_RealDef_Oreal ) }.
% 0.97/1.61  { class_Orderings_Oorder( tc_RealDef_Oreal ) }.
% 0.97/1.61  { class_Int_Oring__char__0( tc_RealDef_Oreal ) }.
% 0.97/1.61  { class_Int_Onumber__ring( tc_RealDef_Oreal ) }.
% 0.97/1.61  { class_Rings_Osemiring( tc_RealDef_Oreal ) }.
% 0.97/1.61  { class_Orderings_Oord( tc_RealDef_Oreal ) }.
% 0.97/1.61  { class_Rings_Oring__1( tc_RealDef_Oreal ) }.
% 0.97/1.61  { class_Fields_Ofield( tc_RealDef_Oreal ) }.
% 0.97/1.61  { class_Power_Opower( tc_RealDef_Oreal ) }.
% 0.97/1.61  { class_Groups_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.61  { class_Rings_Oring( tc_RealDef_Oreal ) }.
% 0.97/1.61  { class_Int_Onumber( tc_RealDef_Oreal ) }.
% 0.97/1.61  { class_Groups_Oone( tc_RealDef_Oreal ) }.
% 0.97/1.61  { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct( 
% 0.97/1.61    tc_Complex_Ocomplex ) }.
% 0.97/1.61  { class_RealVector_Oreal__normed__div__algebra( tc_Complex_Ocomplex ) }.
% 0.97/1.61  { class_Rings_Odivision__ring__inverse__zero( tc_Complex_Ocomplex ) }.
% 0.97/1.61  { class_RealVector_Oreal__normed__algebra__1( tc_Complex_Ocomplex ) }.
% 0.97/1.61  { class_RealVector_Oreal__normed__algebra( tc_Complex_Ocomplex ) }.
% 0.97/1.61  { class_Groups_Ocancel__ab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.97/1.61  { class_Rings_Oring__1__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.97/1.61  { class_RealVector_Oreal__normed__vector( tc_Complex_Ocomplex ) }.
% 0.97/1.61  { class_RealVector_Oreal__normed__field( tc_Complex_Ocomplex ) }.
% 0.97/1.61  { class_Rings_Oring__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.97/1.61  { class_Groups_Ocancel__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.97/1.61  { class_Fields_Ofield__inverse__zero( tc_Complex_Ocomplex ) }.
% 0.97/1.61  { class_Groups_Oab__semigroup__mult( tc_Complex_Ocomplex ) }.
% 0.97/1.61  { class_Groups_Ocomm__monoid__mult( tc_Complex_Ocomplex ) }.
% 0.97/1.61  { class_Groups_Oab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.97/1.61  { class_Rings_Ono__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.97/1.61  { class_Groups_Ocomm__monoid__add( tc_Complex_Ocomplex ) }.
% 0.97/1.61  { class_Rings_Ocomm__semiring__1( tc_Complex_Ocomplex ) }.
% 0.97/1.61  { class_RealVector_Oreal__field( tc_Complex_Ocomplex ) }.
% 0.97/1.61  { class_Rings_Odivision__ring( tc_Complex_Ocomplex ) }.
% 0.97/1.61  { class_Rings_Ocomm__semiring( tc_Complex_Ocomplex ) }.
% 0.97/1.61  { class_Groups_Oab__group__add( tc_Complex_Ocomplex ) }.
% 0.97/1.61  { class_Rings_Ozero__neq__one( tc_Complex_Ocomplex ) }.
% 0.97/1.61  { class_Groups_Omonoid__mult( tc_Complex_Ocomplex ) }.
% 0.97/1.61  { class_Rings_Ocomm__ring__1( tc_Complex_Ocomplex ) }.
% 0.97/1.61  { class_Groups_Omonoid__add( tc_Complex_Ocomplex ) }.
% 0.97/1.61  { class_Rings_Osemiring__1( tc_Complex_Ocomplex ) }.
% 0.97/1.61  { class_Rings_Osemiring__0( tc_Complex_Ocomplex ) }.
% 0.97/1.61  { class_Groups_Ogroup__add( tc_Complex_Ocomplex ) }.
% 0.97/1.61  { class_Rings_Omult__zero( tc_Complex_Ocomplex ) }.
% 0.97/1.61  { class_Int_Oring__char__0( tc_Complex_Ocomplex ) }.
% 0.97/1.61  { class_Int_Onumber__ring( tc_Complex_Ocomplex ) }.
% 0.97/1.61  { class_Rings_Osemiring( tc_Complex_Ocomplex ) }.
% 0.97/1.61  { class_Rings_Oring__1( tc_Complex_Ocomplex ) }.
% 0.97/1.61  { class_Fields_Ofield( tc_Complex_Ocomplex ) }.
% 0.97/1.61  { class_Power_Opower( tc_Complex_Ocomplex ) }.
% 0.97/1.61  { class_Groups_Ozero( tc_Complex_Ocomplex ) }.
% 0.97/1.61  { class_Rings_Oring( tc_Complex_Ocomplex ) }.
% 0.97/1.61  { class_Int_Onumber( tc_Complex_Ocomplex ) }.
% 0.97/1.61  { class_Groups_Oone( tc_Complex_Ocomplex ) }.
% 0.97/1.61  { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP( 
% 0.97/1.61    c_Power_Opower__class_Opower( tc_RealDef_Oreal ), 
% 0.97/1.61    c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, hAPP( hAPP( 
% 0.97/1.61    c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), 
% 0.97/1.61    c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0( 
% 0.97/1.61    c_Int_OBit1( c_Int_OPls ) ) ) ), v_x____ ) ) ), 
% 0.97/1.61    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( 
% 0.97/1.61    c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower( 
% 0.97/1.61    tc_RealDef_Oreal ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), 
% 0.97/1.61    c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( 
% 0.97/1.61    c_Int_OPls ) ) ) ) ) }.
% 0.97/1.61  
% 0.97/1.61  *** allocated 15000 integers for clauses
% 0.97/1.61  *** allocated 22500 integers for clauses
% 0.97/1.61  *** allocated 33750 integers for clauses
% 0.97/1.61  *** allocated 50625 integers for clauses
% 0.97/1.61  *** allocated 75937 integers for clauses
% 0.97/1.61  *** allocated 113905 integers for clauses
% 0.97/1.61  percentage equality = 0.244778, percentage horn = 0.903664
% 0.97/1.61  This is a problem with some equality
% 0.97/1.61  
% 0.97/1.61  
% 0.97/1.61  
% 0.97/1.61  Options Used:
% 0.97/1.61  
% 0.97/1.61  useres =            1
% 0.97/1.61  useparamod =        1
% 0.97/1.61  useeqrefl =         1
% 0.97/1.61  useeqfact =         1
% 0.97/1.61  usefactor =         1
% 0.97/1.61  usesimpsplitting =  0
% 0.97/1.61  usesimpdemod =      5
% 0.97/1.61  usesimpres =        3
% 0.97/1.61  
% 0.97/1.61  resimpinuse      =  1000
% 0.97/1.61  resimpclauses =     20000
% 0.97/1.61  substype =          eqrewr
% 0.97/1.61  backwardsubs =      1
% 0.97/1.61  selectoldest =      5
% 0.97/1.61  
% 0.97/1.61  litorderings [0] =  split
% 0.97/1.61  litorderings [1] =  extend the termordering, first sorting on arguments
% 0.97/1.61  
% 0.97/1.61  termordering =      kbo
% 0.97/1.61  
% 0.97/1.61  litapriori =        0
% 0.97/1.61  termapriori =       1
% 0.97/1.61  litaposteriori =    0
% 0.97/1.61  termaposteriori =   0
% 0.97/1.61  demodaposteriori =  0
% 0.97/1.61  ordereqreflfact =   0
% 0.97/1.61  
% 0.97/1.61  litselect =         negord
% 0.97/1.61  
% 0.97/1.61  maxweight =         15
% 0.97/1.61  maxdepth =          30000
% 0.97/1.61  maxlength =         115
% 0.97/1.61  maxnrvars =         195
% 0.97/1.61  excuselevel =       1
% 0.97/1.61  increasemaxweight = 1
% 0.97/1.61  
% 0.97/1.61  maxselected =       10000000
% 0.97/1.61  maxnrclauses =      10000000
% 0.97/1.61  
% 0.97/1.61  showgenerated =    0
% 0.97/1.61  showkept =         0
% 0.97/1.61  showselected =     0
% 0.97/1.61  showdeleted =      0
% 0.97/1.61  showresimp =       1
% 0.97/1.61  showstatus =       2000
% 0.97/1.61  
% 0.97/1.61  prologoutput =     0
% 0.97/1.61  nrgoals =          5000000
% 0.97/1.61  totalproof =       1
% 0.97/1.61  
% 0.97/1.61  Symbols occurring in the translation:
% 0.97/1.61  
% 0.97/1.61  {}  [0, 0]      (w:1, o:2, a:1, s:1, b:0), 
% 0.97/1.61  .  [1, 2]      (w:1, o:188, a:1, s:1, b:0), 
% 0.97/1.61  !  [4, 1]      (w:0, o:102, a:1, s:1, b:0), 
% 0.97/1.61  =  [13, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 0.97/1.61  ==>  [14, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 0.97/1.61  hAPP  [38, 2]      (w:1, o:212, a:1, s:1, b:0), 
% 0.97/1.61  tc_RealDef_Oreal  [39, 0]      (w:1, o:14, a:1, s:1, b:0), 
% 0.97/1.61  c_Groups_Otimes__class_Otimes  [40, 1]      (w:1, o:108, a:1, s:1, b:0), 
% 0.97/1.61  c_Int_OPls  [41, 0]      (w:1, o:15, a:1, s:1, b:0), 
% 0.97/1.61  c_Int_OBit1  [42, 1]      (w:1, o:110, a:1, s:1, b:0), 
% 0.97/1.61  c_Int_OBit0  [43, 1]      (w:1, o:109, a:1, s:1, b:0), 
% 0.97/1.61  c_Int_Onumber__class_Onumber__of  [44, 2]      (w:1, o:213, a:1, s:1, b:0)
% 0.97/1.61    , 
% 0.97/1.61  v_x____  [45, 0]      (w:1, o:16, a:1, s:1, b:0), 
% 0.97/1.61  c_Groups_Oabs__class_Oabs  [46, 2]      (w:1, o:214, a:1, s:1, b:0), 
% 0.97/1.61  c_Groups_Oone__class_Oone  [47, 1]      (w:1, o:111, a:1, s:1, b:0), 
% 0.97/1.61  c_Orderings_Oord__class_Oless__eq  [48, 3]      (w:1, o:235, a:1, s:1, b:0)
% 0.97/1.61    , 
% 0.97/1.61  v_y____  [49, 0]      (w:1, o:17, a:1, s:1, b:0), 
% 0.97/1.61  c_Power_Opower__class_Opower  [51, 1]      (w:1, o:112, a:1, s:1, b:0), 
% 0.97/1.61  tc_Nat_Onat  [53, 0]      (w:1, o:31, a:1, s:1, b:0), 
% 0.97/1.61  class_Groups_Omonoid__mult  [56, 1]      (w:1, o:118, a:1, s:1, b:0), 
% 0.97/1.61  class_Int_Onumber  [57, 1]      (w:1, o:119, a:1, s:1, b:0), 
% 0.97/1.61  class_Rings_Olinordered__idom  [60, 1]      (w:1, o:120, a:1, s:1, b:0), 
% 0.97/1.61  class_Rings_Osemiring__1  [61, 1]      (w:1, o:126, a:1, s:1, b:0), 
% 0.97/1.61  class_Rings_Ocomm__semiring__1  [62, 1]      (w:1, o:128, a:1, s:1, b:0), 
% 0.97/1.61  c_Int_OMin  [63, 0]      (w:1, o:35, a:1, s:1, b:0), 
% 0.97/1.61  tc_Int_Oint  [64, 0]      (w:1, o:37, a:1, s:1, b:0), 
% 0.97/1.61  class_Int_Onumber__ring  [67, 1]      (w:1, o:129, a:1, s:1, b:0), 
% 0.97/1.61  c_Groups_Oplus__class_Oplus  [81, 3]      (w:1, o:236, a:1, s:1, b:0), 
% 0.97/1.61  tc_Complex_Ocomplex  [84, 0]      (w:1, o:70, a:1, s:1, b:0), 
% 0.97/1.61  c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt  [85, 1]      (w:1, o:107
% 0.97/1.61    , a:1, s:1, b:0), 
% 0.97/1.61  class_Rings_Olinordered__semidom  [87, 1]      (w:1, o:132, a:1, s:1, b:0)
% 0.97/1.61    , 
% 0.97/1.61  v_z  [88, 0]      (w:1, o:72, a:1, s:1, b:0), 
% 0.97/1.61  c_Complex_Ocomplex_OComplex  [89, 2]      (w:1, o:215, a:1, s:1, b:0), 
% 0.97/1.61  c_RealVector_Onorm__class_Onorm  [90, 2]      (w:1, o:216, a:1, s:1, b:0), 
% 0.97/1.61    
% 0.97/1.61  class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct  [
% 0.97/1.61    104, 1]      (w:1, o:156, a:1, s:1, b:0), 
% 0.97/1.61  class_Rings_Osemiring  [108, 1]      (w:1, o:133, a:1, s:1, b:0), 
% 0.97/1.61  class_Int_Oring__char__0  [109, 1]      (w:1, o:157, a:1, s:1, b:0), 
% 0.97/1.61  class_Groups_Ocomm__monoid__mult  [113, 1]      (w:1, o:158, a:1, s:1, b:0)
% 0.97/1.61    , 
% 0.97/1.61  class_Groups_Oordered__ab__group__add__abs  [115, 1]      (w:1, o:159, a:1
% 0.97/1.61    , s:1, b:0), 
% 0.97/1.61  class_Orderings_Opreorder  [116, 1]      (w:1, o:162, a:1, s:1, b:0), 
% 0.97/1.61  c_Nat_OSuc  [117, 1]      (w:1, o:163, a:1, s:1, b:0), 
% 0.97/1.61  class_Power_Opower  [118, 1]      (w:1, o:165, a:1, s:1, b:0), 
% 0.97/1.61  c_Power_Opower_Opower  [119, 3]      (w:1, o:238, a:1, s:1, b:0), 
% 0.97/1.61  c_Groups_Ominus__class_Ominus  [120, 3]      (w:1, o:239, a:1, s:1, b:0), 
% 0.97/1.61  c_Groups_Ozero__class_Ozero  [121, 1]      (w:1, o:166, a:1, s:1, b:0), 
% 0.97/1.61  c_NthRoot_Osqrt  [122, 1]      (w:1, o:167, a:1, s:1, b:0), 
% 0.97/1.61  c_Complex_Oii  [123, 0]      (w:1, o:83, a:1, s:1, b:0), 
% 0.97/1.61  class_Groups_Oordered__ab__group__add  [126, 1]      (w:1, o:168, a:1, s:1
% 0.97/1.61    , b:0), 
% 0.97/1.61  class_Groups_Ozero  [127, 1]      (w:1, o:169, a:1, s:1, b:0), 
% 0.97/1.61  class_Groups_Ogroup__add  [128, 1]      (w:1, o:170, a:1, s:1, b:0), 
% 0.97/1.61  class_Groups_Oab__group__add  [129, 1]      (w:1, o:171, a:1, s:1, b:0), 
% 0.97/1.61  class_Rings_Osemiring__0  [130, 1]      (w:1, o:125, a:1, s:1, b:0), 
% 0.97/1.61  class_Rings_Omult__zero  [131, 1]      (w:1, o:139, a:1, s:1, b:0), 
% 0.97/1.61  class_Rings_Ono__zero__divisors  [132, 1]      (w:1, o:140, a:1, s:1, b:0)
% 0.97/1.61    , 
% 0.97/1.61  class_Rings_Ozero__neq__one  [133, 1]      (w:1, o:141, a:1, s:1, b:0), 
% 0.97/1.61  class_Groups_Omonoid__add  [134, 1]      (w:1, o:172, a:1, s:1, b:0), 
% 0.97/1.61  class_Groups_Ocomm__monoid__add  [135, 1]      (w:1, o:173, a:1, s:1, b:0)
% 0.97/1.61    , 
% 0.97/1.61  class_Groups_Olinordered__ab__group__add  [136, 1]      (w:1, o:117, a:1
% 0.97/1.61    , s:1, b:0), 
% 0.97/1.61  class_Rings_Ocomm__ring__1  [137, 1]      (w:1, o:127, a:1, s:1, b:0), 
% 0.97/1.61  class_Rings_Oring__1__no__zero__divisors  [138, 1]      (w:1, o:121, a:1
% 0.97/1.61    , s:1, b:0), 
% 0.97/1.61  class_Groups_Oordered__comm__monoid__add  [139, 1]      (w:1, o:174, a:1
% 0.97/1.61    , s:1, b:0), 
% 0.97/1.61  class_Rings_Oring  [141, 1]      (w:1, o:122, a:1, s:1, b:0), 
% 0.97/1.61  class_Rings_Olinordered__ring__strict  [142, 1]      (w:1, o:130, a:1, s:1
% 0.97/1.61    , b:0), 
% 0.97/1.61  class_Rings_Oring__1  [143, 1]      (w:1, o:123, a:1, s:1, b:0), 
% 0.97/1.61  class_Rings_Olinordered__ring  [144, 1]      (w:1, o:131, a:1, s:1, b:0), 
% 0.97/1.61  class_Orderings_Olinorder  [145, 1]      (w:1, o:164, a:1, s:1, b:0), 
% 0.97/1.61  class_Orderings_Oord  [146, 1]      (w:1, o:160, a:1, s:1, b:0), 
% 0.97/1.61  tc_fun  [147, 2]      (w:1, o:222, a:1, s:1, b:0), 
% 0.97/1.61  class_Orderings_Oorder  [148, 1]      (w:1, o:161, a:1, s:1, b:0), 
% 0.97/1.61  class_Groups_Oab__semigroup__mult  [149, 1]      (w:1, o:175, a:1, s:1, b:0
% 0.97/1.61    ), 
% 0.97/1.61  class_Groups_Oab__semigroup__add  [150, 1]      (w:1, o:176, a:1, s:1, b:0)
% 0.97/1.61    , 
% 0.97/1.61  class_Groups_Ocancel__semigroup__add  [151, 1]      (w:1, o:177, a:1, s:1
% 0.97/1.61    , b:0), 
% 0.97/1.61  class_Groups_Ocancel__ab__semigroup__add  [152, 1]      (w:1, o:178, a:1
% 0.97/1.61    , s:1, b:0), 
% 0.97/1.61  class_Groups_Oone  [153, 1]      (w:1, o:179, a:1, s:1, b:0), 
% 0.97/1.61  class_Groups_Oordered__ab__semigroup__add__imp__le  [160, 1]      (w:1, o:
% 0.97/1.61    180, a:1, s:1, b:0), 
% 0.97/1.61  class_Groups_Oordered__ab__semigroup__add  [161, 1]      (w:1, o:181, a:1
% 0.97/1.61    , s:1, b:0), 
% 0.97/1.61  class_RealVector_Oreal__normed__vector  [162, 1]      (w:1, o:142, a:1, s:1
% 0.97/1.61    , b:0), 
% 0.97/1.61  class_Rings_Olinordered__semiring__1  [164, 1]      (w:1, o:134, a:1, s:1
% 0.97/1.61    , b:0), 
% 0.97/1.61  class_RealVector_Oreal__normed__algebra__1  [165, 1]      (w:1, o:143, a:1
% 0.97/1.61    , s:1, b:0), 
% 0.97/1.61  class_RealVector_Oreal__normed__algebra  [166, 1]      (w:1, o:144, a:1, s:
% 0.97/1.61    1, b:0), 
% 0.97/1.61  class_Rings_Oring__no__zero__divisors  [167, 1]      (w:1, o:124, a:1, s:1
% 0.97/1.61    , b:0), 
% 0.97/1.61  class_Rings_Ocomm__semiring  [169, 1]      (w:1, o:145, a:1, s:1, b:0), 
% 0.97/1.61  class_Rings_Oordered__cancel__semiring  [172, 1]      (w:1, o:146, a:1, s:1
% 0.97/1.62    , b:0), 
% 0.97/1.62  class_Rings_Oordered__ring  [173, 1]      (w:1, o:147, a:1, s:1, b:0), 
% 0.97/1.62  class_Rings_Oordered__semiring  [174, 1]      (w:1, o:149, a:1, s:1, b:0), 
% 0.97/1.62    
% 0.97/1.62  class_Rings_Oordered__comm__semiring  [175, 1]      (w:1, o:150, a:1, s:1
% 0.97/1.62    , b:0), 
% 0.97/1.62  class_RealVector_Oreal__normed__div__algebra  [177, 1]      (w:1, o:151, a:
% 0.97/1.62    1, s:1, b:0), 
% 0.97/1.62  class_Rings_Oordered__ring__abs  [178, 1]      (w:1, o:148, a:1, s:1, b:0)
% 0.97/1.62    , 
% 0.97/1.62  c_Complex_Ocomplex_Ocomplex__size  [189, 1]      (w:1, o:182, a:1, s:1, b:0
% 0.97/1.62    ), 
% 0.97/1.62  c_Rings_Oinverse__class_Odivide  [191, 3]      (w:1, o:240, a:1, s:1, b:0)
% 0.97/1.62    , 
% 0.97/1.62  c_Nat_Osize__class_Osize  [192, 2]      (w:1, o:223, a:1, s:1, b:0), 
% 0.97/1.62  c_Complex_Ocomplex_Ocomplex__case  [194, 3]      (w:1, o:241, a:1, s:1, b:0
% 0.97/1.62    ), 
% 0.97/1.62  class_Rings_Odivision__ring  [195, 1]      (w:1, o:152, a:1, s:1, b:0), 
% 0.97/1.62  class_RealVector_Oreal__normed__field  [196, 1]      (w:1, o:153, a:1, s:1
% 0.97/1.62    , b:0), 
% 0.97/1.62  class_Rings_Odivision__ring__inverse__zero  [197, 1]      (w:1, o:154, a:1
% 0.97/1.62    , s:1, b:0), 
% 0.97/1.62  class_Fields_Ofield__inverse__zero  [198, 1]      (w:1, o:113, a:1, s:1, b:
% 0.97/1.62    0), 
% 0.97/1.62  class_Fields_Ofield  [199, 1]      (w:1, o:114, a:1, s:1, b:0), 
% 0.97/1.62  class_RealVector_Oreal__field  [201, 1]      (w:1, o:155, a:1, s:1, b:0), 
% 0.97/1.62  class_Fields_Olinordered__field__inverse__zero  [202, 1]      (w:1, o:115
% 0.97/1.62    , a:1, s:1, b:0), 
% 0.97/1.62  class_Fields_Olinordered__field  [203, 1]      (w:1, o:116, a:1, s:1, b:0)
% 0.97/1.62    , 
% 0.97/1.62  c_Transcendental_Oarctan  [204, 1]      (w:1, o:183, a:1, s:1, b:0), 
% 0.97/1.62  c_Orderings_Oord__class_Oless  [205, 3]      (w:1, o:237, a:1, s:1, b:0), 
% 0.97/1.62  class_Rings_Olinordered__comm__semiring__strict  [206, 1]      (w:1, o:135
% 0.97/1.62    , a:1, s:1, b:0), 
% 0.97/1.62  class_Rings_Olinordered__semiring__strict  [207, 1]      (w:1, o:136, a:1
% 0.97/1.62    , s:1, b:0), 
% 0.97/1.62  class_Groups_Oordered__cancel__ab__semigroup__add  [208, 1]      (w:1, o:
% 0.97/1.62    184, a:1, s:1, b:0), 
% 0.97/1.62  class_Rings_Olinordered__semiring  [209, 1]      (w:1, o:137, a:1, s:1, b:0
% 0.97/1.62    ), 
% 0.97/1.62  class_Rings_Olinordered__semiring__1__strict  [212, 1]      (w:1, o:138, a:
% 0.97/1.62    1, s:1, b:0), 
% 0.97/1.62  c_Transcendental_Opi  [213, 0]      (w:1, o:98, a:1, s:1, b:0), 
% 0.97/1.62  c_Complex_Ocomplex_Ocomplex__rec  [214, 3]      (w:1, o:242, a:1, s:1, b:0)
% 0.97/1.62    , 
% 0.97/1.62  c_RComplete_Onatceiling  [215, 1]      (w:1, o:185, a:1, s:1, b:0), 
% 0.97/1.62  hBOOL  [218, 1]      (w:1, o:186, a:1, s:1, b:0), 
% 0.97/1.62  tc_HOL_Obool  [223, 0]      (w:1, o:36, a:1, s:1, b:0), 
% 0.97/1.62  alpha1  [224, 2]      (w:1, o:224, a:1, s:1, b:1), 
% 0.97/1.62  alpha2  [225, 3]      (w:1, o:253, a:1, s:1, b:1), 
% 0.97/1.62  alpha3  [226, 3]      (w:1, o:264, a:1, s:1, b:1), 
% 0.97/1.62  alpha4  [227, 2]      (w:1, o:231, a:1, s:1, b:1), 
% 0.97/1.62  alpha5  [228, 2]      (w:1, o:232, a:1, s:1, b:1), 
% 0.97/1.62  alpha6  [229, 2]      (w:1, o:233, a:1, s:1, b:1), 
% 0.97/1.62  alpha7  [230, 3]      (w:1, o:265, a:1, s:1, b:1), 
% 0.97/1.62  alpha8  [231, 3]      (w:1, o:266, a:1, s:1, b:1), 
% 0.97/1.62  alpha9  [232, 3]      (w:1, o:267, a:1, s:1, b:1), 
% 0.97/1.62  alpha10  [233, 3]      (w:1, o:243, a:1, s:1, b:1), 
% 0.97/1.62  alpha11  [234, 3]      (w:1, o:246, a:1, s:1, b:1), 
% 0.97/1.62  alpha12  [235, 3]      (w:1, o:247, a:1, s:1, b:1), 
% 0.97/1.62  alpha13  [236, 3]      (w:1, o:248, a:1, s:1, b:1), 
% 0.97/1.62  alpha14  [237, 3]      (w:1, o:249, a:1, s:1, b:1), 
% 0.97/1.62  alpha15  [238, 4]      (w:1, o:276, a:1, s:1, b:1), 
% 0.97/1.62  alpha16  [239, 4]      (w:1, o:277, a:1, s:1, b:1), 
% 0.97/1.62  alpha17  [240, 3]      (w:1, o:250, a:1, s:1, b:1), 
% 0.97/1.62  alpha18  [241, 3]      (w:1, o:251, a:1, s:1, b:1), 
% 0.97/1.62  alpha19  [242, 3]      (w:1, o:252, a:1, s:1, b:1), 
% 0.97/1.62  alpha20  [243, 3]      (w:1, o:254, a:1, s:1, b:1), 
% 0.97/1.62  alpha21  [244, 3]      (w:1, o:255, a:1, s:1, b:1), 
% 0.97/1.62  alpha22  [245, 3]      (w:1, o:256, a:1, s:1, b:1), 
% 0.97/1.62  alpha23  [246, 3]      (w:1, o:257, a:1, s:1, b:1), 
% 0.97/1.62  alpha24  [247, 3]      (w:1, o:258, a:1, s:1, b:1), 
% 0.97/1.62  alpha25  [248, 3]      (w:1, o:259, a:1, s:1, b:1), 
% 0.97/1.62  alpha26  [249, 3]      (w:1, o:260, a:1, s:1, b:1), 
% 0.97/1.62  alpha27  [250, 3]      (w:1, o:261, a:1, s:1, b:1), 
% 0.97/1.62  alpha28  [251, 3]      (w:1, o:262, a:1, s:1, b:1), 
% 0.97/1.62  alpha29  [252, 3]      (w:1, o:263, a:1, s:1, b:1), 
% 0.97/1.62  alpha30  [253, 3]      (w:1, o:268, a:1, s:1, b:1), 
% 0.97/1.62  alpha31  [254, 2]      (w:1, o:225, a:1, s:1, b:1), 
% 0.97/1.62  alpha32  [255, 2]      (w:1, o:226, a:1, s:1, b:1), 
% 0.97/1.62  alpha33  [256, 2]      (w:1, o:227, a:1, s:1, b:1), 
% 0.97/1.62  alpha34  [257, 3]      (w:1, o:269, a:1, s:1, b:1), 
% 13.09/13.50  alpha35  [258, 3]      (w:1, o:270, a:1, s:1, b:1), 
% 13.09/13.50  alpha36  [259, 2]      (w:1, o:228, a:1, s:1, b:1), 
% 13.09/13.50  alpha37  [260, 2]      (w:1, o:229, a:1, s:1, b:1), 
% 13.09/13.50  alpha38  [261, 2]      (w:1, o:230, a:1, s:1, b:1), 
% 13.09/13.50  alpha39  [262, 4]      (w:1, o:278, a:1, s:1, b:1), 
% 13.09/13.50  alpha40  [263, 4]      (w:1, o:279, a:1, s:1, b:1), 
% 13.09/13.50  alpha41  [264, 4]      (w:1, o:280, a:1, s:1, b:1), 
% 13.09/13.50  alpha42  [265, 4]      (w:1, o:281, a:1, s:1, b:1), 
% 13.09/13.50  alpha43  [266, 3]      (w:1, o:271, a:1, s:1, b:1), 
% 13.09/13.50  alpha44  [267, 3]      (w:1, o:272, a:1, s:1, b:1), 
% 13.09/13.50  alpha45  [268, 4]      (w:1, o:282, a:1, s:1, b:1), 
% 13.09/13.50  alpha46  [269, 4]      (w:1, o:283, a:1, s:1, b:1), 
% 13.09/13.50  alpha47  [270, 4]      (w:1, o:284, a:1, s:1, b:1), 
% 13.09/13.50  alpha48  [271, 4]      (w:1, o:285, a:1, s:1, b:1), 
% 13.09/13.50  alpha49  [272, 3]      (w:1, o:273, a:1, s:1, b:1), 
% 13.09/13.50  alpha50  [273, 3]      (w:1, o:274, a:1, s:1, b:1), 
% 13.09/13.50  alpha51  [274, 4]      (w:1, o:286, a:1, s:1, b:1), 
% 13.09/13.50  alpha52  [275, 4]      (w:1, o:287, a:1, s:1, b:1), 
% 13.09/13.50  alpha53  [276, 4]      (w:1, o:288, a:1, s:1, b:1), 
% 13.09/13.50  alpha54  [277, 4]      (w:1, o:289, a:1, s:1, b:1), 
% 13.09/13.50  alpha55  [278, 4]      (w:1, o:290, a:1, s:1, b:1), 
% 13.09/13.50  alpha56  [279, 4]      (w:1, o:291, a:1, s:1, b:1), 
% 13.09/13.50  alpha57  [280, 4]      (w:1, o:292, a:1, s:1, b:1), 
% 13.09/13.50  alpha58  [281, 4]      (w:1, o:293, a:1, s:1, b:1), 
% 13.09/13.50  alpha59  [282, 4]      (w:1, o:294, a:1, s:1, b:1), 
% 13.09/13.50  alpha60  [283, 4]      (w:1, o:295, a:1, s:1, b:1), 
% 13.09/13.50  alpha61  [284, 4]      (w:1, o:296, a:1, s:1, b:1), 
% 13.09/13.50  alpha62  [285, 4]      (w:1, o:297, a:1, s:1, b:1), 
% 13.09/13.50  alpha63  [286, 4]      (w:1, o:298, a:1, s:1, b:1), 
% 13.09/13.50  alpha64  [287, 4]      (w:1, o:299, a:1, s:1, b:1), 
% 13.09/13.50  alpha65  [288, 4]      (w:1, o:300, a:1, s:1, b:1), 
% 13.09/13.50  alpha66  [289, 4]      (w:1, o:301, a:1, s:1, b:1), 
% 13.09/13.50  alpha67  [290, 4]      (w:1, o:302, a:1, s:1, b:1), 
% 13.09/13.50  alpha68  [291, 4]      (w:1, o:303, a:1, s:1, b:1), 
% 13.09/13.50  alpha69  [292, 4]      (w:1, o:304, a:1, s:1, b:1), 
% 13.09/13.50  alpha70  [293, 4]      (w:1, o:305, a:1, s:1, b:1), 
% 13.09/13.50  alpha71  [294, 4]      (w:1, o:306, a:1, s:1, b:1), 
% 13.09/13.50  alpha72  [295, 4]      (w:1, o:307, a:1, s:1, b:1), 
% 13.09/13.50  alpha73  [296, 4]      (w:1, o:308, a:1, s:1, b:1), 
% 13.09/13.50  alpha74  [297, 4]      (w:1, o:309, a:1, s:1, b:1), 
% 13.09/13.50  alpha75  [298, 4]      (w:1, o:310, a:1, s:1, b:1), 
% 13.09/13.50  alpha76  [299, 4]      (w:1, o:311, a:1, s:1, b:1), 
% 13.09/13.50  alpha77  [300, 4]      (w:1, o:312, a:1, s:1, b:1), 
% 13.09/13.50  alpha78  [301, 4]      (w:1, o:313, a:1, s:1, b:1), 
% 13.09/13.50  alpha79  [302, 4]      (w:1, o:314, a:1, s:1, b:1), 
% 13.09/13.50  alpha80  [303, 4]      (w:1, o:315, a:1, s:1, b:1), 
% 13.09/13.50  alpha81  [304, 4]      (w:1, o:316, a:1, s:1, b:1), 
% 13.09/13.50  alpha82  [305, 4]      (w:1, o:317, a:1, s:1, b:1), 
% 13.09/13.50  alpha83  [306, 4]      (w:1, o:318, a:1, s:1, b:1), 
% 13.09/13.50  alpha84  [307, 4]      (w:1, o:319, a:1, s:1, b:1), 
% 13.09/13.50  alpha85  [308, 4]      (w:1, o:320, a:1, s:1, b:1), 
% 13.09/13.50  alpha86  [309, 4]      (w:1, o:321, a:1, s:1, b:1), 
% 13.09/13.50  alpha87  [310, 4]      (w:1, o:322, a:1, s:1, b:1), 
% 13.09/13.50  alpha88  [311, 4]      (w:1, o:323, a:1, s:1, b:1), 
% 13.09/13.50  alpha89  [312, 4]      (w:1, o:324, a:1, s:1, b:1), 
% 13.09/13.50  alpha90  [313, 4]      (w:1, o:325, a:1, s:1, b:1), 
% 13.09/13.50  alpha91  [314, 4]      (w:1, o:326, a:1, s:1, b:1), 
% 13.09/13.50  alpha92  [315, 4]      (w:1, o:327, a:1, s:1, b:1), 
% 13.09/13.50  alpha93  [316, 4]      (w:1, o:328, a:1, s:1, b:1), 
% 13.09/13.50  alpha94  [317, 4]      (w:1, o:329, a:1, s:1, b:1), 
% 13.09/13.50  alpha95  [318, 4]      (w:1, o:330, a:1, s:1, b:1), 
% 13.09/13.50  alpha96  [319, 4]      (w:1, o:331, a:1, s:1, b:1), 
% 13.09/13.50  alpha97  [320, 4]      (w:1, o:332, a:1, s:1, b:1), 
% 13.09/13.50  alpha98  [321, 4]      (w:1, o:333, a:1, s:1, b:1), 
% 13.09/13.50  alpha99  [322, 2]      (w:1, o:234, a:1, s:1, b:1), 
% 13.09/13.50  alpha100  [323, 3]      (w:1, o:244, a:1, s:1, b:1), 
% 13.09/13.50  alpha101  [324, 3]      (w:1, o:245, a:1, s:1, b:1), 
% 13.09/13.50  skol1  [325, 2]      (w:1, o:217, a:1, s:1, b:1), 
% 13.09/13.50  skol2  [326, 0]      (w:1, o:12, a:1, s:1, b:1), 
% 13.09/13.50  skol3  [327, 3]      (w:1, o:275, a:1, s:1, b:1), 
% 13.09/13.50  skol4  [328, 2]      (w:1, o:218, a:1, s:1, b:1), 
% 13.09/13.50  skol5  [329, 2]      (w:1, o:219, a:1, s:1, b:1), 
% 13.09/13.50  skol6  [330, 2]      (w:1, o:220, a:1, s:1, b:1), 
% 13.09/13.50  skol7  [331, 1]      (w:1, o:187, a:1, s:1, b:1), 
% 13.09/13.50  skol8  [332, 2]      (w:1, o:221, a:1, s:1, b:1), 
% 13.09/13.50  skol9  [333, 0]      (w:1, o:13, a:1, s:1, b:1).
% 13.09/13.50  
% 13.09/13.50  
% 13.09/13.50  Starting Search:
% 13.09/13.50  
% 13.09/13.50  *** allocated 170857 integers for clauses
% 68.68/69.12  Resimplifying inuse:
% 68.68/69.12  Done
% 68.68/69.12  
% 68.68/69.12  
% 68.68/69.12  Intermediate Status:
% 68.68/69.12  Generated:    2900
% 68.68/69.12  Kept:         2014
% 68.68/69.12  Inuse:        26
% 68.68/69.12  Deleted:      0
% 68.68/69.12  Deletedinuse: 0
% 68.68/69.12  
% 68.68/69.12  *** allocated 256285 integers for clauses
% 68.68/69.12  Resimplifying inuse:
% 68.68/69.12  Done
% 68.68/69.12  
% 68.68/69.12  *** allocated 170857 integers for termspace/termends
% 68.68/69.12  *** allocated 384427 integers for clauses
% 68.68/69.12  
% 68.68/69.12  Intermediate Status:
% 68.68/69.12  Generated:    9470
% 68.68/69.12  Kept:         4176
% 68.68/69.12  Inuse:        299
% 68.68/69.12  Deleted:      22
% 68.68/69.12  Deletedinuse: 0
% 68.68/69.12  
% 68.68/69.12  Resimplifying inuse:
% 68.68/69.12  Done
% 68.68/69.12  
% 68.68/69.12  *** allocated 256285 integers for termspace/termends
% 68.68/69.12  Resimplifying inuse:
% 68.68/69.12  Done
% 68.68/69.12  
% 68.68/69.12  *** allocated 576640 integers for clauses
% 68.68/69.12  
% 68.68/69.12  Intermediate Status:
% 68.68/69.12  Generated:    19292
% 68.68/69.12  Kept:         6186
% 68.68/69.12  Inuse:        363
% 68.68/69.12  Deleted:      23
% 68.68/69.12  Deletedinuse: 0
% 68.68/69.12  
% 68.68/69.12  Resimplifying inuse:
% 68.68/69.12  Done
% 68.68/69.12  
% 68.68/69.12  *** allocated 384427 integers for termspace/termends
% 68.68/69.12  
% 68.68/69.12  Intermediate Status:
% 68.68/69.12  Generated:    27503
% 68.68/69.12  Kept:         8475
% 68.68/69.12  Inuse:        504
% 68.68/69.12  Deleted:      27
% 68.68/69.12  Deletedinuse: 0
% 68.68/69.12  
% 68.68/69.12  Resimplifying inuse:
% 68.68/69.12  Done
% 68.68/69.12  
% 68.68/69.12  *** allocated 864960 integers for clauses
% 68.68/69.12  Resimplifying inuse:
% 68.68/69.12  Done
% 68.68/69.12  
% 68.68/69.12  
% 68.68/69.12  Intermediate Status:
% 68.68/69.12  Generated:    37620
% 68.68/69.12  Kept:         11103
% 68.68/69.12  Inuse:        539
% 68.68/69.12  Deleted:      28
% 68.68/69.12  Deletedinuse: 1
% 68.68/69.12  
% 68.68/69.12  Resimplifying inuse:
% 68.68/69.12  Done
% 68.68/69.12  
% 68.68/69.12  Resimplifying inuse:
% 68.68/69.12  Done
% 68.68/69.12  
% 68.68/69.12  
% 68.68/69.12  Intermediate Status:
% 68.68/69.12  Generated:    46130
% 68.68/69.12  Kept:         13293
% 68.68/69.12  Inuse:        590
% 68.68/69.12  Deleted:      32
% 68.68/69.12  Deletedinuse: 1
% 68.68/69.12  
% 68.68/69.12  Resimplifying inuse:
% 68.68/69.12  Done
% 68.68/69.12  
% 68.68/69.12  *** allocated 576640 integers for termspace/termends
% 68.68/69.12  Resimplifying inuse:
% 68.68/69.12  Done
% 68.68/69.12  
% 68.68/69.12  *** allocated 1297440 integers for clauses
% 68.68/69.12  
% 68.68/69.12  Intermediate Status:
% 68.68/69.12  Generated:    52813
% 68.68/69.12  Kept:         15343
% 68.68/69.12  Inuse:        670
% 68.68/69.12  Deleted:      37
% 68.68/69.12  Deletedinuse: 1
% 68.68/69.12  
% 68.68/69.12  Resimplifying inuse:
% 68.68/69.12  Done
% 68.68/69.12  
% 68.68/69.12  Resimplifying inuse:
% 68.68/69.12  Done
% 68.68/69.12  
% 68.68/69.12  
% 68.68/69.12  Intermediate Status:
% 68.68/69.12  Generated:    59597
% 68.68/69.12  Kept:         17343
% 68.68/69.12  Inuse:        782
% 68.68/69.12  Deleted:      45
% 68.68/69.12  Deletedinuse: 1
% 68.68/69.12  
% 68.68/69.12  Resimplifying inuse:
% 68.68/69.12  Done
% 68.68/69.12  
% 68.68/69.12  
% 68.68/69.12  Intermediate Status:
% 68.68/69.12  Generated:    65766
% 68.68/69.12  Kept:         20152
% 68.68/69.12  Inuse:        843
% 68.68/69.12  Deleted:      49
% 68.68/69.12  Deletedinuse: 1
% 68.68/69.12  
% 68.68/69.12  Resimplifying inuse:
% 68.68/69.12  Done
% 68.68/69.12  
% 68.68/69.12  Resimplifying clauses:
% 68.68/69.12  Done
% 68.68/69.12  
% 68.68/69.12  *** allocated 864960 integers for termspace/termends
% 68.68/69.12  *** allocated 1946160 integers for clauses
% 68.68/69.12  
% 68.68/69.12  Intermediate Status:
% 68.68/69.12  Generated:    72201
% 68.68/69.12  Kept:         23254
% 68.68/69.12  Inuse:        898
% 68.68/69.12  Deleted:      820
% 68.68/69.12  Deletedinuse: 1
% 68.68/69.12  
% 68.68/69.12  Resimplifying inuse:
% 68.68/69.12  Done
% 68.68/69.12  
% 68.68/69.12  
% 68.68/69.12  Intermediate Status:
% 68.68/69.12  Generated:    75586
% 68.68/69.12  Kept:         25554
% 68.68/69.12  Inuse:        903
% 68.68/69.12  Deleted:      820
% 68.68/69.12  Deletedinuse: 1
% 68.68/69.12  
% 68.68/69.12  Resimplifying inuse:
% 68.68/69.12  Done
% 68.68/69.12  
% 68.68/69.12  Resimplifying inuse:
% 68.68/69.12  Done
% 68.68/69.12  
% 68.68/69.12  
% 68.68/69.12  Intermediate Status:
% 68.68/69.12  Generated:    82630
% 68.68/69.12  Kept:         28200
% 68.68/69.12  Inuse:        923
% 68.68/69.12  Deleted:      820
% 68.68/69.12  Deletedinuse: 1
% 68.68/69.12  
% 68.68/69.12  Resimplifying inuse:
% 68.68/69.12  Done
% 68.68/69.12  
% 68.68/69.12  Resimplifying inuse:
% 68.68/69.12  Done
% 68.68/69.12  
% 68.68/69.12  
% 68.68/69.12  Intermediate Status:
% 68.68/69.12  Generated:    89866
% 68.68/69.12  Kept:         30721
% 68.68/69.12  Inuse:        993
% 68.68/69.12  Deleted:      821
% 68.68/69.12  Deletedinuse: 2
% 68.68/69.12  
% 68.68/69.12  Resimplifying inuse:
% 68.68/69.12  Done
% 68.68/69.12  
% 68.68/69.12  Resimplifying inuse:
% 68.68/69.12  Done
% 68.68/69.12  
% 68.68/69.12  
% 68.68/69.12  Intermediate Status:
% 68.68/69.12  Generated:    97746
% 68.68/69.12  Kept:         33578
% 68.68/69.12  Inuse:        1028
% 68.68/69.12  Deleted:      821
% 68.68/69.12  Deletedinuse: 2
% 68.68/69.12  
% 68.68/69.12  Resimplifying inuse:
% 68.68/69.12  Done
% 68.68/69.12  
% 68.68/69.12  *** allocated 1297440 integers for termspace/termends
% 68.68/69.12  Resimplifying inuse:
% 68.68/69.12  Done
% 68.68/69.12  
% 68.68/69.12  
% 68.68/69.12  Intermediate Status:
% 68.68/69.12  Generated:    101981
% 68.68/69.12  Kept:         35584
% 68.68/69.12  Inuse:        1060
% 68.68/69.12  Deleted:      821
% 68.68/69.12  Deletedinuse: 2
% 68.68/69.12  
% 68.68/69.12  Resimplifying inuse:
% 68.68/69.12  Done
% 68.68/69.12  
% 68.68/69.12  *** allocated 2919240 integers for clauses
% 68.68/69.12  
% 68.68/69.12  Intermediate Status:
% 68.68/69.12  Generated:    110968
% 68.68/69.12  Kept:         37590
% 68.68/69.12  Inuse:        1092
% 68.68/69.12  Deleted:      821
% 68.68/69.12  Deletedinuse: 2
% 68.68/69.12  
% 68.68/69.12  Resimplifying inuse:
% 68.68/69.12  Done
% 68.68/69.12  
% 68.68/69.12  
% 68.68/69.12  Intermediate Status:
% 68.68/69.12  Generated:    117857
% 68.68/69.12  Kept:         39647
% 68.68/69.12  Inuse:        1103
% 68.68/69.12  Deleted:      821
% 68.68/69.12  Deletedinuse: 2
% 68.68/69.12  
% 68.68/69.12  Resimplifying inuse:
% 68.68/69.12  Done
% 68.68/69.12  
% 68.68/69.12  Resimplifying inuse:
% 68.68/69.12  Done
% 68.68/69.12  
% 68.68/69.12  Resimplifying clauses:
% 68.68/69.12  Done
% 68.68/69.12  
% 68.68/69.12  
% 68.68/69.12  Intermediate Status:
% 68.68/69.12  Generated:    122805
% 68.68/69.12  Kept:         41653
% 68.68/69.12  Inuse:        1128
% 68.68/69.12  Deleted:      1655
% 68.68/69.12  Deletedinuse: 3
% 68.68/69.12  
% 68.68/69.12  Resimplifying inuse:
% 68.68/69.12  Done
% 68.68/69.12  
% 68.68/69.12  
% 68.68/69.12  Intermediate Status:
% 68.68/69.12  Generated:    128597
% 68.68/69.12  Kept:         44293
% 68.68/69.12  Inuse:        1173
% 68.68/69.12  Deleted:      1656
% 68.68/69.12  Deletedinuse: 4
% 68.68/69.12  
% 68.68/69.12  Resimplifying inuse:
% 68.68/69.12  Done
% 68.68/69.12  
% 68.68/69.12  Resimplifying inuse:
% 68.68/69.12  Done
% 68.68/69.12  
% 68.68/69.12  
% 68.68/69.12  Intermediate Status:
% 68.68/69.12  Generated:    133791
% 68.68/69.12  Kept:         46323
% 68.68/69.12  Inuse:        1208
% 68.68/69.12  Deleted:      1656
% 68.68/69.12  Deletedinuse: 4
% 68.68/69.12  
% 68.68/69.12  
% 68.68/69.12  Intermediate Status:
% 68.68/69.12  Generated:    150161
% 68.68/69.12  Kept:         48729
% 68.68/69.12  Inuse:        1218
% 68.68/69.12  Deleted:      1656
% 68.68/69.12  Deletedinuse: 4
% 68.68/69.12  
% 68.68/69.12  Resimplifying inuse:
% 68.68/69.12  Done
% 68.68/69.12  
% 68.68/69.12  *** allocated 1946160 integers for termspace/termends
% 68.68/69.12  Resimplifying inuse:
% 68.68/69.12  Done
% 68.68/69.12  
% 68.68/69.12  
% 68.68/69.12  Intermediate Status:
% 68.68/69.12  Generated:    172554
% 168.36/168.81  Kept:         52131
% 168.36/168.81  Inuse:        1228
% 168.36/168.81  Deleted:      1656
% 168.36/168.81  Deletedinuse: 4
% 168.36/168.81  
% 168.36/168.81  Resimplifying inuse:
% 168.36/168.81  Done
% 168.36/168.81  
% 168.36/168.81  Resimplifying inuse:
% 168.36/168.81  Done
% 168.36/168.81  
% 168.36/168.81  
% 168.36/168.81  Intermediate Status:
% 168.36/168.81  Generated:    184988
% 168.36/168.81  Kept:         55295
% 168.36/168.81  Inuse:        1258
% 168.36/168.81  Deleted:      1656
% 168.36/168.81  Deletedinuse: 4
% 168.36/168.81  
% 168.36/168.81  Resimplifying inuse:
% 168.36/168.81  Done
% 168.36/168.81  
% 168.36/168.81  Resimplifying inuse:
% 168.36/168.81  Done
% 168.36/168.81  
% 168.36/168.81  
% 168.36/168.81  Intermediate Status:
% 168.36/168.81  Generated:    192799
% 168.36/168.81  Kept:         57328
% 168.36/168.81  Inuse:        1278
% 168.36/168.81  Deleted:      1656
% 168.36/168.81  Deletedinuse: 4
% 168.36/168.81  
% 168.36/168.81  Resimplifying inuse:
% 168.36/168.81  Done
% 168.36/168.81  
% 168.36/168.81  *** allocated 4378860 integers for clauses
% 168.36/168.81  
% 168.36/168.81  Intermediate Status:
% 168.36/168.81  Generated:    197113
% 168.36/168.81  Kept:         59404
% 168.36/168.81  Inuse:        1293
% 168.36/168.81  Deleted:      1656
% 168.36/168.81  Deletedinuse: 4
% 168.36/168.81  
% 168.36/168.81  Resimplifying inuse:
% 168.36/168.81  Done
% 168.36/168.81  
% 168.36/168.81  Resimplifying inuse:
% 168.36/168.81  Done
% 168.36/168.81  
% 168.36/168.81  
% 168.36/168.81  Intermediate Status:
% 168.36/168.81  Generated:    203939
% 168.36/168.81  Kept:         62444
% 168.36/168.81  Inuse:        1323
% 168.36/168.81  Deleted:      1656
% 168.36/168.81  Deletedinuse: 4
% 168.36/168.81  
% 168.36/168.81  Resimplifying inuse:
% 168.36/168.81  Done
% 168.36/168.81  
% 168.36/168.81  Resimplifying clauses:
% 168.36/168.81  Done
% 168.36/168.81  
% 168.36/168.81  Resimplifying inuse:
% 168.36/168.81  Done
% 168.36/168.81  
% 168.36/168.81  
% 168.36/168.81  Intermediate Status:
% 168.36/168.81  Generated:    209611
% 168.36/168.81  Kept:         64692
% 168.36/168.81  Inuse:        1333
% 168.36/168.81  Deleted:      2002
% 168.36/168.81  Deletedinuse: 4
% 168.36/168.81  
% 168.36/168.81  Resimplifying inuse:
% 168.36/168.81  Done
% 168.36/168.81  
% 168.36/168.81  
% 168.36/168.81  Intermediate Status:
% 168.36/168.81  Generated:    216142
% 168.36/168.81  Kept:         68217
% 168.36/168.81  Inuse:        1343
% 168.36/168.81  Deleted:      2002
% 168.36/168.81  Deletedinuse: 4
% 168.36/168.81  
% 168.36/168.81  Resimplifying inuse:
% 168.36/168.81  Done
% 168.36/168.81  
% 168.36/168.81  Resimplifying inuse:
% 168.36/168.81  Done
% 168.36/168.81  
% 168.36/168.81  
% 168.36/168.81  Intermediate Status:
% 168.36/168.81  Generated:    224020
% 168.36/168.81  Kept:         70228
% 168.36/168.81  Inuse:        1381
% 168.36/168.81  Deleted:      2002
% 168.36/168.81  Deletedinuse: 4
% 168.36/168.81  
% 168.36/168.81  Resimplifying inuse:
% 168.36/168.81  Done
% 168.36/168.81  
% 168.36/168.81  Resimplifying inuse:
% 168.36/168.81  Done
% 168.36/168.81  
% 168.36/168.81  
% 168.36/168.81  Intermediate Status:
% 168.36/168.81  Generated:    230234
% 168.36/168.81  Kept:         72233
% 168.36/168.81  Inuse:        1407
% 168.36/168.81  Deleted:      2002
% 168.36/168.81  Deletedinuse: 4
% 168.36/168.81  
% 168.36/168.81  Resimplifying inuse:
% 168.36/168.81  Done
% 168.36/168.81  
% 168.36/168.81  *** allocated 2919240 integers for termspace/termends
% 168.36/168.81  Resimplifying inuse:
% 168.36/168.81  Done
% 168.36/168.81  
% 168.36/168.81  
% 168.36/168.81  Intermediate Status:
% 168.36/168.81  Generated:    237797
% 168.36/168.81  Kept:         74355
% 168.36/168.81  Inuse:        1443
% 168.36/168.81  Deleted:      2002
% 168.36/168.81  Deletedinuse: 4
% 168.36/168.81  
% 168.36/168.81  Resimplifying inuse:
% 168.36/168.81  Done
% 168.36/168.81  
% 168.36/168.81  Resimplifying inuse:
% 168.36/168.81  Done
% 168.36/168.81  
% 168.36/168.81  
% 168.36/168.81  Intermediate Status:
% 168.36/168.81  Generated:    245292
% 168.36/168.81  Kept:         76369
% 168.36/168.81  Inuse:        1476
% 168.36/168.81  Deleted:      2002
% 168.36/168.81  Deletedinuse: 4
% 168.36/168.81  
% 168.36/168.81  Resimplifying inuse:
% 168.36/168.81  Done
% 168.36/168.81  
% 168.36/168.81  
% 168.36/168.81  Intermediate Status:
% 168.36/168.81  Generated:    254246
% 168.36/168.81  Kept:         79747
% 168.36/168.81  Inuse:        1483
% 168.36/168.81  Deleted:      2002
% 168.36/168.81  Deletedinuse: 4
% 168.36/168.81  
% 168.36/168.81  Resimplifying inuse:
% 168.36/168.81  Done
% 168.36/168.81  
% 168.36/168.81  
% 168.36/168.81  Intermediate Status:
% 168.36/168.81  Generated:    285752
% 168.36/168.81  Kept:         83187
% 168.36/168.81  Inuse:        1493
% 168.36/168.81  Deleted:      2002
% 168.36/168.81  Deletedinuse: 4
% 168.36/168.81  
% 168.36/168.81  Resimplifying inuse:
% 168.36/168.81  Done
% 168.36/168.81  
% 168.36/168.81  Resimplifying clauses:
% 168.36/168.81  Done
% 168.36/168.81  
% 168.36/168.81  Resimplifying inuse:
% 168.36/168.81  Done
% 168.36/168.81  
% 168.36/168.81  
% 168.36/168.81  Intermediate Status:
% 168.36/168.81  Generated:    293195
% 168.36/168.81  Kept:         85246
% 168.36/168.81  Inuse:        1518
% 168.36/168.81  Deleted:      2319
% 168.36/168.81  Deletedinuse: 4
% 168.36/168.81  
% 168.36/168.81  Resimplifying inuse:
% 168.36/168.81  Done
% 168.36/168.81  
% 168.36/168.81  
% 168.36/168.81  Intermediate Status:
% 168.36/168.81  Generated:    300295
% 168.36/168.81  Kept:         87375
% 168.36/168.81  Inuse:        1533
% 168.36/168.81  Deleted:      2319
% 168.36/168.81  Deletedinuse: 4
% 168.36/168.81  
% 168.36/168.81  Resimplifying inuse:
% 168.36/168.81  Done
% 168.36/168.81  
% 168.36/168.81  Resimplifying inuse:
% 168.36/168.81  Done
% 168.36/168.81  
% 168.36/168.81  *** allocated 6568290 integers for clauses
% 168.36/168.81  
% 168.36/168.81  Intermediate Status:
% 168.36/168.81  Generated:    306725
% 168.36/168.81  Kept:         89448
% 168.36/168.81  Inuse:        1543
% 168.36/168.81  Deleted:      2319
% 168.36/168.81  Deletedinuse: 4
% 168.36/168.81  
% 168.36/168.81  Resimplifying inuse:
% 168.36/168.81  Done
% 168.36/168.81  
% 168.36/168.81  Resimplifying inuse:
% 168.36/168.81  Done
% 168.36/168.81  
% 168.36/168.81  
% 168.36/168.81  Intermediate Status:
% 168.36/168.81  Generated:    313614
% 168.36/168.81  Kept:         91502
% 168.36/168.81  Inuse:        1572
% 168.36/168.81  Deleted:      2319
% 168.36/168.81  Deletedinuse: 4
% 168.36/168.81  
% 168.36/168.81  Resimplifying inuse:
% 168.36/168.81  Done
% 168.36/168.81  
% 168.36/168.81  
% 168.36/168.81  Intermediate Status:
% 168.36/168.81  Generated:    325104
% 168.36/168.81  Kept:         95107
% 168.36/168.81  Inuse:        1578
% 168.36/168.81  Deleted:      2319
% 168.36/168.81  Deletedinuse: 4
% 168.36/168.81  
% 168.36/168.81  Resimplifying inuse:
% 168.36/168.81  Done
% 168.36/168.81  
% 168.36/168.81  Resimplifying inuse:
% 168.36/168.81  Done
% 168.36/168.81  
% 168.36/168.81  
% 168.36/168.81  Intermediate Status:
% 168.36/168.81  Generated:    334363
% 168.36/168.81  Kept:         97128
% 168.36/168.81  Inuse:        1593
% 168.36/168.81  Deleted:      2319
% 168.36/168.81  Deletedinuse: 4
% 168.36/168.81  
% 168.36/168.81  
% 168.36/168.81  Intermediate Status:
% 168.36/168.81  Generated:    343265
% 168.36/168.81  Kept:         99262
% 168.36/168.81  Inuse:        1603
% 168.36/168.81  Deleted:      2319
% 168.36/168.81  Deletedinuse: 4
% 168.36/168.81  
% 168.36/168.81  Resimplifying inuse:
% 168.36/168.81  Done
% 168.36/168.81  
% 168.36/168.81  Resimplifying inuse:
% 168.36/168.81  Done
% 168.36/168.81  
% 168.36/168.81  
% 168.36/168.81  Intermediate Status:
% 168.36/168.81  Generated:    351156
% 168.36/168.81  Kept:         101320
% 168.36/168.81  Inuse:        1643
% 168.36/168.81  Deleted:      2319
% 168.36/168.81  Deletedinuse: 4
% 168.36/168.81  
% 168.36/168.81  Resimplifying inuse:
% 168.36/168.81  Done
% 168.36/168.81  
% 168.36/168.81  *** allocated 4378860 integers for termspace/termends
% 168.36/168.81  
% 168.36/168.81  Intermediate Status:
% 168.36/168.81  Generated:    361696
% 168.36/168.81  Kept:         103544
% 168.36/168.81  Inuse:        1658
% 168.36/168.81  Deleted:      2319
% 168.36/168.81  Deletedinuse: 4
% 168.36/168.81  
% 168.36/168.81  Resimplifying inuse:
% 168.36/168.81  Done
% 168.36/168.81  
% 168.36/168.81  Resimplifying clauses:
% 168.36/168.81  Done
% 168.36/168.81  
% 168.36/168.81  Resimplifying inuse:
% 168.36/168.81  Done
% 168.36/168.81  
% 168.36/168.81  
% 168.36/168.81  Intermediate Status:
% 168.36/168.81  Generated:    371412
% 168.36/168.81  Kept:         105550
% 168.36/168.81  Inuse:        1670
% 168.36/168.81  Deleted:      2722
% 168.36/168.81  Deletedinuse: 4
% 168.36/168.81  
% 168.36/168.81  Resimplifying inuse:
% 168.36/168.81  Done
% 168.36/168.81  
% 168.36/168.81  
% 168.36/168.81  Intermediate Status:
% 168.36/168.81  Generated:    381642
% 168.36/168.81  Kept:         107756
% 168.36/168.81  Inuse:        1683
% 168.36/168.81  Deleted:      2722
% 168.36/168.81  Deletedinuse: 4
% 168.36/168.81  
% 168.36/168.81  Resimplifying inuse:
% 168.36/168.81  Done
% 168.36/168.81  
% 168.36/168.81  Resimplifying inuse:
% 300.04/300.50  Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------