TSTP Solution File: SWW193+1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWW193+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n017.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 300.01s 300.39s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWW193+1 : TPTP v8.1.0. Released v5.2.0.
% 0.11/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % DateTime : Sun Jun 5 09:04:45 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.97/1.55 *** allocated 10000 integers for termspace/termends
% 0.97/1.55 *** allocated 10000 integers for clauses
% 0.97/1.55 *** allocated 10000 integers for justifications
% 0.97/1.55 *** allocated 15000 integers for termspace/termends
% 0.97/1.55 *** allocated 22500 integers for termspace/termends
% 0.97/1.55 *** allocated 33750 integers for termspace/termends
% 0.97/1.55 Bliksem 1.12
% 0.97/1.55
% 0.97/1.55
% 0.97/1.55 Automatic Strategy Selection
% 0.97/1.55
% 0.97/1.55 *** allocated 50625 integers for termspace/termends
% 0.97/1.55 *** allocated 75937 integers for termspace/termends
% 0.97/1.55 *** allocated 113905 integers for termspace/termends
% 0.97/1.55
% 0.97/1.55 Clauses:
% 0.97/1.55
% 0.97/1.55 { ! hAPP( Y, skol1( X, Y ) ) = hAPP( X, skol1( X, Y ) ), Y = X }.
% 0.97/1.55 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( X, Y ) ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( c_Int_OPls )
% 0.97/1.55 , Y ) }.
% 0.97/1.55 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( c_Int_OPls )
% 0.97/1.55 , Y ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X
% 0.97/1.55 ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.97/1.55 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 0.97/1.55 , Y ), c_Groups_Oone__class_Oone( X ) ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, c_Int_OBit1(
% 0.97/1.55 c_Int_OPls ) ) }.
% 0.97/1.55 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, c_Int_OBit1(
% 0.97/1.55 c_Int_OPls ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( X, Y ), c_Groups_Oone__class_Oone( X )
% 0.97/1.55 ) }.
% 0.97/1.55 { ! class_Int_Onumber__ring( X ), c_Groups_Oone__class_Oone( X ) =
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( X, c_Int_OBit1( c_Int_OPls ) ) }.
% 0.97/1.55 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.97/1.55 c_Int_OBit1( c_Int_OPls ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.55 { ! class_Int_Onumber__ring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.55 ( X ), Y ), c_Int_Onumber__class_Onumber__of( X, c_Int_OBit1( c_Int_OPls
% 0.97/1.55 ) ) ) = Y }.
% 0.97/1.55 { ! class_Int_Onumber__ring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.55 ( X ), c_Int_Onumber__class_Onumber__of( X, c_Int_OBit1( c_Int_OPls ) ) )
% 0.97/1.55 , Y ) = Y }.
% 0.97/1.55 { ! class_Orderings_Opreorder( X ), c_Orderings_Oord__class_Oless__eq( X, Y
% 0.97/1.55 , Y ) }.
% 0.97/1.55 { v_z = c_Complex_Ocomplex_OComplex( v_x____, v_y____ ) }.
% 0.97/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.97/1.55 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) = X }.
% 0.97/1.55 { c_Int_OBit0( c_Int_OPls ) = c_Int_OPls }.
% 0.97/1.55 { ! c_Int_OPls = c_Int_OBit0( X ), c_Int_OPls = X }.
% 0.97/1.55 { ! c_Int_OPls = X, c_Int_OPls = c_Int_OBit0( X ) }.
% 0.97/1.55 { ! c_Int_OBit0( X ) = c_Int_OPls, X = c_Int_OPls }.
% 0.97/1.55 { ! X = c_Int_OPls, c_Int_OBit0( X ) = c_Int_OPls }.
% 0.97/1.55 { c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_z ) =
% 0.97/1.55 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.97/1.55 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, X ) }.
% 0.97/1.55 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, c_Int_OPls ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, c_Int_OPls ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Z ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, Z ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ), Y = X }.
% 0.97/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Int_OPls ), X
% 0.97/1.55 ) = c_Int_OPls }.
% 0.97/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Int_OBit0( Y
% 0.97/1.55 ) ), X ) = c_Int_OBit0( hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.55 tc_Int_Oint ), Y ), X ) ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( Y ),
% 0.97/1.55 c_Int_OBit1( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 0.97/1.55 ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( Y ),
% 0.97/1.55 c_Int_OBit1( X ) ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( Y ),
% 0.97/1.55 c_Int_OBit1( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 0.97/1.55 ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( Y ),
% 0.97/1.55 c_Int_OBit1( X ) ) }.
% 0.97/1.55 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, c_Int_OPls )
% 0.97/1.55 }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.97/1.55 c_Int_OBit0( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 0.97/1.55 ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.97/1.55 c_Int_OBit0( X ) ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.97/1.55 c_Int_OBit0( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 0.97/1.55 ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.97/1.55 c_Int_OBit0( X ) ) }.
% 0.97/1.55 { c_Groups_Oone__class_Oone( tc_Int_Oint ) =
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit1( c_Int_OPls )
% 0.97/1.55 ) }.
% 0.97/1.55 { c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit1( c_Int_OPls )
% 0.97/1.55 ) = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.97/1.55 { c_Groups_Oone__class_Oone( tc_Nat_Onat ) =
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit1( c_Int_OPls )
% 0.97/1.55 ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, c_Int_OBit1
% 0.97/1.55 ( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, X )
% 0.97/1.55 }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, X ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, c_Int_OBit1(
% 0.97/1.55 X ) ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.97/1.55 c_Int_OBit1( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 0.97/1.55 ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.97/1.55 c_Int_OBit1( X ) ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.97/1.55 c_Int_OBit1( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 0.97/1.55 ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.97/1.55 c_Int_OBit1( X ) ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( X ),
% 0.97/1.55 c_Int_OPls ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.97/1.55 c_Int_OPls ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, c_Int_OPls ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( X ),
% 0.97/1.55 c_Int_OPls ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, c_Int_OBit0
% 0.97/1.55 ( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, X )
% 0.97/1.55 }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, X ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, c_Int_OBit0(
% 0.97/1.55 X ) ) }.
% 0.97/1.55 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.55 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.97/1.55 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.97/1.55 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.97/1.55 hAPP( Y, U ) ) }.
% 0.97/1.55 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.55 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.97/1.55 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.55 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.97/1.55 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.55 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.97/1.55 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.55 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.97/1.55 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.55 , Y ), ! Z = T, c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.97/1.55 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y
% 0.97/1.55 ), ! Y = T, c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.97/1.55 { ! class_Orderings_Oorder( X ), ! Z = Y, !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.97/1.55 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.97/1.55 ( X, Y, T ), c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.97/1.55 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.55 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.97/1.55 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.55 , Y ), ! Y = Z, c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.97/1.55 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.97/1.55 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.97/1.55 hAPP( Y, U ) ) }.
% 0.97/1.55 { ! class_Orderings_Opreorder( X ), ! Z = Y,
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.55 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.97/1.55 ( X, Z, Y ) }.
% 0.97/1.55 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.97/1.55 ( X, Y, Z ) }.
% 0.97/1.55 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.55 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.97/1.55 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.55 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.97/1.55 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.97/1.55 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.97/1.55 hAPP( Y, U ) ) }.
% 0.97/1.55 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, hAPP
% 0.97/1.55 ( Z, skol2( X, Y, Z ) ), hAPP( Y, skol2( X, Y, Z ) ) ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }.
% 0.97/1.55 { ! class_Int_Onumber__ring( X ), ! class_Int_Oring__char__0( X ), !
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( X, Z ) =
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( X, Y ), Z = Y }.
% 0.97/1.55 { ! class_Int_Onumber__ring( X ), ! class_Int_Oring__char__0( X ), ! Z = Y
% 0.97/1.55 , c_Int_Onumber__class_Onumber__of( X, Z ) =
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( X, Y ) }.
% 0.97/1.55 { ! class_Int_Onumber( X ), ! c_Int_Onumber__class_Onumber__of( X, Z ) = Y
% 0.97/1.55 , Y = c_Int_Onumber__class_Onumber__of( X, Z ) }.
% 0.97/1.55 { ! class_Int_Onumber( X ), ! Y = c_Int_Onumber__class_Onumber__of( X, Z )
% 0.97/1.55 , c_Int_Onumber__class_Onumber__of( X, Z ) = Y }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ), Y = X }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Z ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, Z ) }.
% 0.97/1.55 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ) }.
% 0.97/1.55 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, X ) }.
% 0.97/1.55 { ! c_Int_OBit1( Y ) = c_Int_OBit1( X ), Y = X }.
% 0.97/1.55 { ! Y = X, c_Int_OBit1( Y ) = c_Int_OBit1( X ) }.
% 0.97/1.55 { ! c_Int_OBit0( Y ) = c_Int_OBit0( X ), Y = X }.
% 0.97/1.55 { ! Y = X, c_Int_OBit0( Y ) = c_Int_OBit0( X ) }.
% 0.97/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP
% 0.97/1.55 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), Y ) ), X ) =
% 0.97/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), hAPP
% 0.97/1.55 ( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.97/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) =
% 0.97/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y )
% 0.97/1.55 }.
% 0.97/1.55 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 0.97/1.55 , Z ), c_Int_Onumber__class_Onumber__of( X, Y ) ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z, Y ) }.
% 0.97/1.55 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z, Y ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 0.97/1.55 , Z ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.97/1.55 { ! class_Int_Onumber__ring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.55 ( X ), c_Int_Onumber__class_Onumber__of( X, T ) ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.97/1.55 Z ) ), Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( X, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), T ), Z ) ) ), Y ) }.
% 0.97/1.55 { ! class_Int_Onumber__ring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.55 ( X ), c_Int_Onumber__class_Onumber__of( X, Z ) ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( X, Y ) ) =
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( X, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ) }.
% 0.97/1.55 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X, hAPP
% 0.97/1.55 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ) = hAPP(
% 0.97/1.55 hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( X, Z ) ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.97/1.55 { ! c_Int_OBit1( X ) = c_Int_OPls }.
% 0.97/1.55 { ! c_Int_OPls = c_Int_OBit1( X ) }.
% 0.97/1.55 { ! c_Int_OBit1( Y ) = c_Int_OBit0( X ) }.
% 0.97/1.55 { ! c_Int_OBit0( Y ) = c_Int_OBit1( X ) }.
% 0.97/1.55 { c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), v_x____ ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.55 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.97/1.55 tc_RealDef_Oreal ), v_y____ ), c_Int_Onumber__class_Onumber__of(
% 0.97/1.55 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) =
% 0.97/1.55 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.97/1.55 { v_z = c_Complex_Ocomplex_OComplex( skol3, skol13 ) }.
% 0.97/1.55 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.55 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ),
% 0.97/1.55 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, v_z,
% 0.97/1.55 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) ) ) }.
% 0.97/1.55 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.55 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ),
% 0.97/1.55 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.97/1.55 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, v_z,
% 0.97/1.55 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) ) ) }.
% 0.97/1.55 { c_Groups_Oone__class_Oone( tc_Code__Numeral_Ocode__numeral ) =
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Code__Numeral_Ocode__numeral,
% 0.97/1.55 c_Int_OBit1( c_Int_OPls ) ) }.
% 0.97/1.55 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.97/1.55 = Y }.
% 0.97/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.97/1.55 = Y }.
% 0.97/1.55 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.97/1.55 = Y }.
% 0.97/1.55 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.97/1.55 = Y }.
% 0.97/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.97/1.55 = Y }.
% 0.97/1.55 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.97/1.55 = Y }.
% 0.97/1.55 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.55 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.97/1.55 c_Int_OBit1( c_Int_OPls ) ) ) ), X ) ) }.
% 0.97/1.55 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.55 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ),
% 0.97/1.55 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, v_z, c_Complex_Oii ) )
% 0.97/1.55 ) }.
% 0.97/1.55 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.55 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ),
% 0.97/1.55 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.97/1.55 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, v_z, c_Complex_Oii )
% 0.97/1.55 ) ) }.
% 0.97/1.55 { c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) = X }.
% 0.97/1.55 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.55 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y ),
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.97/1.55 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X ) ),
% 0.97/1.55 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) ) }.
% 0.97/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.97/1.55 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) = X }.
% 0.97/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.97/1.55 tc_Nat_Onat ) ) = Y }.
% 0.97/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 0.97/1.55 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = X }.
% 0.97/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) = hAPP
% 0.97/1.55 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) }.
% 0.97/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ) ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) =
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.97/1.55 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( X, T ), c_Groups_Ominus__class_Ominus(
% 0.97/1.55 X, c_Int_Onumber__class_Onumber__of( X, Z ), Y ) ) =
% 0.97/1.55 c_Groups_Ominus__class_Ominus( X, c_Int_Onumber__class_Onumber__of( X,
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_Int_Oint, T, Z ) ), Y ) }.
% 0.97/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) }.
% 0.97/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP(
% 0.97/1.55 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.97/1.55 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.97/1.55 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! U = T, Z = Y }.
% 0.97/1.55 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.97/1.55 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! Z = Y, U = T }.
% 0.97/1.55 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.97/1.55 c_Groups_Oplus__class_Oplus( X, Z, T ) = c_Groups_Oplus__class_Oplus( X,
% 0.97/1.55 Y, T ), Z = Y }.
% 0.97/1.55 { ! class_Groups_Ocancel__ab__semigroup__add( X ), !
% 0.97/1.55 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.97/1.55 T, Y ), Z = Y }.
% 0.97/1.55 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.97/1.55 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.97/1.55 T, Y ), Z = Y }.
% 0.97/1.55 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.55 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.97/1.55 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X
% 0.97/1.55 , U, Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.97/1.55 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.97/1.55 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.97/1.55 Y, Z ), T = Y }.
% 0.97/1.55 { ! class_Groups_Ocancel__semigroup__add( X ), ! T = Y,
% 0.97/1.55 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.97/1.55 Y, Z ) }.
% 0.97/1.55 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.97/1.55 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.97/1.55 T, Y ), Z = Y }.
% 0.97/1.55 { ! class_Groups_Ocancel__semigroup__add( X ), ! Z = Y,
% 0.97/1.55 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.97/1.55 T, Y ) }.
% 0.97/1.55 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.55 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.97/1.55 ( X, c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 0.97/1.55 { ! class_Groups_Oab__semigroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.55 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.97/1.55 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.97/1.55 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.55 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.97/1.55 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.97/1.55 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.97/1.55 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = Z }.
% 0.97/1.55 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.55 c_Groups_Ominus__class_Ominus( X, Z, Y ), Y ) = Z }.
% 0.97/1.55 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.97/1.55 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.97/1.55 ( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) }.
% 0.97/1.55 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.97/1.55 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.97/1.55 ( X, Z, c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.97/1.55 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.97/1.55 , Y ) = c_Groups_Oplus__class_Oplus( X, Y, Z ) }.
% 0.97/1.55 { ! class_Rings_Oring( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.97/1.55 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.55 ( X ), U ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 0.97/1.55 Z ) ), Y ) ) }.
% 0.97/1.55 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.97/1.55 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ) =
% 0.97/1.55 c_Groups_Ominus__class_Ominus( X, c_Int_Onumber__class_Onumber__of( X, Z
% 0.97/1.55 ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.97/1.55 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( X, T ), c_Groups_Oplus__class_Oplus( X
% 0.97/1.55 , c_Int_Onumber__class_Onumber__of( X, Z ), Y ) ) =
% 0.97/1.55 c_Groups_Oplus__class_Oplus( X, c_Int_Onumber__class_Onumber__of( X,
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_Int_Oint, T, Z ) ), Y ) }.
% 0.97/1.55 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( X, Z ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( X, Y ) ) =
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( X, c_Groups_Oplus__class_Oplus(
% 0.97/1.55 tc_Int_Oint, Z, Y ) ) }.
% 0.97/1.55 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ) =
% 0.97/1.55 c_Groups_Oplus__class_Oplus( X, c_Int_Onumber__class_Onumber__of( X, Z )
% 0.97/1.55 , c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.97/1.55 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.55 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.97/1.55 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.55 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.55 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.97/1.55 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, U, T ) }.
% 0.97/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.97/1.55 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.97/1.55 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.97/1.55 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.97/1.55 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.97/1.55 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.97/1.55 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.55 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.97/1.55 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.97/1.55 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.97/1.55 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.97/1.55 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.97/1.55 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.97/1.55 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.97/1.55 U ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.97/1.55 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.97/1.55 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.55 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.97/1.55 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.55 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.55 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.55 ( X ), U = T, Z = Y, ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.97/1.55 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.55 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.97/1.55 ) }.
% 0.97/1.55 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.55 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.97/1.55 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.55 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.97/1.55 ), ! U = T }.
% 0.97/1.55 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.55 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.97/1.55 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.55 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.97/1.55 ), ! Z = Y }.
% 0.97/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.97/1.55 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.55 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Y
% 0.97/1.55 ) ), Z ) }.
% 0.97/1.55 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.55 ( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.97/1.55 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.55 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.97/1.55 ), U = Z, T = Y }.
% 0.97/1.55 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.55 ( X ), ! U = Z, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.97/1.55 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.55 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.97/1.55 ) }.
% 0.97/1.55 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.55 ( X ), ! T = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.97/1.55 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.55 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.97/1.55 ) }.
% 0.97/1.55 { ! class_Rings_Oring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP
% 0.97/1.55 ( c_Groups_Otimes__class_Otimes( X ), Y ), Y ), c_Groups_Oone__class_Oone
% 0.97/1.55 ( X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.97/1.55 c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) ) ),
% 0.97/1.55 c_Groups_Ominus__class_Ominus( X, Y, c_Groups_Oone__class_Oone( X ) ) ) }
% 0.97/1.55 .
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ),
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, X ) ) }.
% 0.97/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ) ), X ) =
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.97/1.55 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.97/1.55 , Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.97/1.55 c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.97/1.55 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.97/1.55 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.97/1.55 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP
% 0.97/1.55 ( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.97/1.55 c_Groups_Oone__class_Oone( X ) ) ), Z ) }.
% 0.97/1.55 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = hAPP(
% 0.97/1.55 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X
% 0.97/1.55 , Z, c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.97/1.55 { ! class_Int_Onumber__ring( X ), hAPP( hAPP( c_Power_Opower__class_Opower
% 0.97/1.55 ( X ), c_Groups_Ominus__class_Ominus( X, Z, Y ) ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.55 c_Int_OPls ) ) ) ) = c_Groups_Ominus__class_Ominus( X,
% 0.97/1.55 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Power_Opower__class_Opower
% 0.97/1.55 ( X ), Z ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0(
% 0.97/1.55 c_Int_OBit1( c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower
% 0.97/1.55 ( X ), Y ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0(
% 0.97/1.55 c_Int_OBit1( c_Int_OPls ) ) ) ) ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.97/1.55 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ), Z ) ), Y ) ) }.
% 0.97/1.55 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.55 c_Groups_Oone__class_Oone( X ), c_Int_Onumber__class_Onumber__of( X, Y )
% 0.97/1.55 ) = c_Int_Onumber__class_Onumber__of( X, c_Groups_Oplus__class_Oplus(
% 0.97/1.55 tc_Int_Oint, c_Int_OBit1( c_Int_OPls ), Y ) ) }.
% 0.97/1.55 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( X, Y ), c_Groups_Oone__class_Oone( X )
% 0.97/1.55 ) = c_Int_Onumber__class_Onumber__of( X, c_Groups_Oplus__class_Oplus(
% 0.97/1.55 tc_Int_Oint, Y, c_Int_OBit1( c_Int_OPls ) ) ) }.
% 0.97/1.55 { ! class_Int_Onumber( X ), ! class_Rings_Oring( X ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.97/1.55 T ) ), c_Groups_Ominus__class_Ominus( X, Z, Y ) ) =
% 0.97/1.55 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.97/1.55 T ) ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( X, T ) ), Y ) ) }.
% 0.97/1.55 { ! class_Int_Onumber( X ), ! class_Rings_Oring( X ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 0.97/1.55 Z ) ), c_Int_Onumber__class_Onumber__of( X, Y ) ) =
% 0.97/1.55 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), T ), c_Int_Onumber__class_Onumber__of
% 0.97/1.55 ( X, Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( X, Y ) ) ) }.
% 0.97/1.55 { ! class_Int_Onumber( X ), ! class_Rings_Osemiring( X ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.97/1.55 T ) ), c_Groups_Oplus__class_Oplus( X, Z, Y ) ) =
% 0.97/1.55 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.55 ( X ), c_Int_Onumber__class_Onumber__of( X, T ) ), Z ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.97/1.55 T ) ), Y ) ) }.
% 0.97/1.55 { ! class_Int_Onumber( X ), ! class_Rings_Osemiring( X ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.97/1.55 ) ), c_Int_Onumber__class_Onumber__of( X, Y ) ) =
% 0.97/1.55 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.55 ( X ), T ), c_Int_Onumber__class_Onumber__of( X, Y ) ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), c_Int_Onumber__class_Onumber__of
% 0.97/1.55 ( X, Y ) ) ) }.
% 0.97/1.55 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( X, c_Int_OPls ) ) = Y }.
% 0.97/1.55 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( X, c_Int_OPls ), Y ) = Y }.
% 0.97/1.55 { ! class_Int_Onumber__ring( X ), hAPP( hAPP( c_Power_Opower__class_Opower
% 0.97/1.55 ( X ), c_Groups_Oplus__class_Oplus( X, Z, Y ) ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.55 c_Int_OPls ) ) ) ) = c_Groups_Oplus__class_Oplus( X,
% 0.97/1.55 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Power_Opower__class_Opower
% 0.97/1.55 ( X ), Z ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0(
% 0.97/1.55 c_Int_OBit1( c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower
% 0.97/1.55 ( X ), Y ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0(
% 0.97/1.55 c_Int_OBit1( c_Int_OPls ) ) ) ) ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.97/1.55 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ), Z ) ), Y ) ) }.
% 0.97/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( X ), Y ), c_Int_Onumber__class_Onumber__of
% 0.97/1.55 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) }.
% 0.97/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( X ), Z ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.55 c_Int_OPls ) ) ) ), Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.97/1.55 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ), hAPP( hAPP
% 0.97/1.55 ( c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.97/1.55 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( X ), Y ), c_Int_Onumber__class_Onumber__of
% 0.97/1.55 ( tc_Nat_Onat, c_Int_OBit1( c_Int_OBit1( c_Int_OPls ) ) ) ) = hAPP( hAPP
% 0.97/1.55 ( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ), Y ) }.
% 0.97/1.55 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( X ), Z ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.55 c_Int_OPls ) ) ) ), Y ) ) = hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.97/1.55 , hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.55 c_Int_OPls ) ) ) ) }.
% 0.97/1.55 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.97/1.55 c_Int_OBit1( Y ) ) = c_Groups_Oplus__class_Oplus( X,
% 0.97/1.55 c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( X, Y ) ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.97/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 0.97/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 0.97/1.55 { ! class_Groups_Oab__semigroup__mult( X ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Z ) }.
% 0.97/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 0.97/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), Y ) ) }.
% 0.97/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.55 { ! class_Groups_Oone( X ), ! c_Groups_Oone__class_Oone( X ) = Y, Y =
% 0.97/1.55 c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.55 { ! class_Groups_Oone( X ), ! Y = c_Groups_Oone__class_Oone( X ),
% 0.97/1.55 c_Groups_Oone__class_Oone( X ) = Y }.
% 0.97/1.55 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( X ), Y ), c_Int_Onumber__class_Onumber__of
% 0.97/1.55 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) = hAPP( hAPP
% 0.97/1.55 ( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.97/1.55 { ! class_Rings_Osemiring__1( X ), hAPP( hAPP( c_Power_Opower__class_Opower
% 0.97/1.55 ( X ), c_Groups_Oone__class_Oone( X ) ), c_Int_Onumber__class_Onumber__of
% 0.97/1.55 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) =
% 0.97/1.55 c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.55 { ! class_Int_Onumber__ring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.55 ( X ), c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.97/1.55 c_Groups_Oone__class_Oone( X ) ) ), c_Int_Onumber__class_Onumber__of( X,
% 0.97/1.55 Y ) ) = c_Int_Onumber__class_Onumber__of( X, c_Int_OBit0( Y ) ) }.
% 0.97/1.55 { ! class_Groups_Omonoid__mult( X ), ! class_Int_Onumber( X ), hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( X ), c_Int_Onumber__class_Onumber__of( X, Y
% 0.97/1.55 ) ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0(
% 0.97/1.55 c_Int_OBit1( c_Int_OPls ) ) ) ) = hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.97/1.55 Y ) ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.97/1.55 { ! class_Int_Onumber__ring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.55 ( X ), Y ), c_Int_Onumber__class_Onumber__of( X, c_Int_OBit0( c_Int_OBit1
% 0.97/1.55 ( c_Int_OPls ) ) ) ) = c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 0.97/1.55 { ! class_Int_Onumber__ring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.55 ( X ), c_Int_Onumber__class_Onumber__of( X, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.55 c_Int_OPls ) ) ) ), Y ) = c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 0.97/1.55 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.55 c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ) =
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( X, c_Int_OBit0( c_Int_OBit1( c_Int_OPls
% 0.97/1.55 ) ) ) }.
% 0.97/1.55 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.55 c_Int_OPls ) ) ) ) = c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Y ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.55 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.97/1.55 tc_RealDef_Oreal ), X ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 0.97/1.55 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.97/1.55 c_Int_OBit1( c_Int_OPls ) ) ) ), Y ) ), X ) ) }.
% 0.97/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.97/1.55 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ), hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), X ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.55 c_Int_OPls ) ) ) ) ) = hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.97/1.55 tc_RealDef_Oreal ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.55 tc_RealDef_Oreal ), c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal,
% 0.97/1.55 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ), X ) ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.55 c_Int_OPls ) ) ) ) }.
% 0.97/1.55 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.55 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X,
% 0.97/1.55 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.97/1.55 , Y ) ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.97/1.55 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, U,
% 0.97/1.55 Z ) ), c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus
% 0.97/1.55 ( X, T, Y ) ) ) ) }.
% 0.97/1.55 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.55 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( X ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.97/1.55 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) ) }.
% 0.97/1.55 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.55 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, Z,
% 0.97/1.55 Y ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.97/1.55 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.97/1.55 ( X, Y ) ) ) }.
% 0.97/1.55 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.55 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.97/1.55 ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.97/1.55 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.97/1.55 ( X, Y ) ) ) }.
% 0.97/1.55 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.55 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.97/1.55 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 0.97/1.55 c_RealVector_Onorm__class_Onorm( X, Y ) ) ) }.
% 0.97/1.55 { ! class_Rings_Olinordered__semidom( X ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), T )
% 0.97/1.55 , c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.97/1.55 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.55 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.97/1.55 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.55 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X, T,
% 0.97/1.55 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.55 ( X ), c_Groups_Ominus__class_Ominus( X, Z, W ) ), U ), Y ) ) }.
% 0.97/1.55 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.55 , T, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.97/1.55 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.55 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.55 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.97/1.55 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.55 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.97/1.55 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.55 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.55 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.55 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ) }.
% 0.97/1.55 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.55 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.97/1.55 Z ) ), U ), T ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.55 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.55 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.97/1.55 { ! c_Complex_Oii = c_Int_Onumber__class_Onumber__of( tc_Complex_Ocomplex,
% 0.97/1.55 X ) }.
% 0.97/1.55 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) =
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) }.
% 0.97/1.55 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus
% 0.97/1.55 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.97/1.55 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ),
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) = hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ) }.
% 0.97/1.55 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.97/1.55 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 0.97/1.55 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 0.97/1.55 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.55 { ! c_Complex_Oii = c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) }.
% 0.97/1.55 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Int_OPls ) = X }.
% 0.97/1.55 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, c_Int_OBit0( Y ), c_Int_OBit0
% 0.97/1.55 ( X ) ) = c_Int_OBit0( c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X )
% 0.97/1.55 ) }.
% 0.97/1.55 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Int_OPls ) = X }.
% 0.97/1.55 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Int_OPls, X ) = X }.
% 0.97/1.55 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Int_OBit0( Y ), c_Int_OBit0(
% 0.97/1.55 X ) ) = c_Int_OBit0( c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }
% 0.97/1.55 .
% 0.97/1.55 { c_Int_OBit0( X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, X ) }.
% 0.97/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.97/1.55 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ), X ) =
% 0.97/1.55 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.97/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.97/1.55 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ) =
% 0.97/1.55 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ),
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.97/1.55 { c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) =
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Int_Oint,
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 0.97/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ), X ) =
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.97/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) =
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.97/1.55 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.97/1.55 tc_Nat_Onat, Z, Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.97/1.55 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.97/1.55 { c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex,
% 0.97/1.55 c_Complex_Ocomplex_OComplex( T, Z ), c_Complex_Ocomplex_OComplex( Y, X )
% 0.97/1.55 ) = c_Complex_Ocomplex_OComplex( c_Groups_Ominus__class_Ominus(
% 0.97/1.55 tc_RealDef_Oreal, T, Y ), c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal
% 0.97/1.55 , Z, X ) ) }.
% 0.97/1.55 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.55 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.97/1.55 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.97/1.55 ( X, Y ) ), c_RealVector_Onorm__class_Onorm( X,
% 0.97/1.55 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) ) }.
% 0.97/1.55 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, c_Int_OBit1( Y ), c_Int_OBit1
% 0.97/1.55 ( X ) ) = c_Int_OBit0( c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X )
% 0.97/1.55 ) }.
% 0.97/1.55 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, c_Int_OBit1( Y ), c_Int_OBit0
% 0.97/1.55 ( X ) ) = c_Int_OBit1( c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X )
% 0.97/1.55 ) }.
% 0.97/1.55 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, c_Int_OPls, c_Int_OBit0( X )
% 0.97/1.55 ) = c_Int_OBit0( c_Groups_Ominus__class_Ominus( tc_Int_Oint, c_Int_OPls
% 0.97/1.55 , X ) ) }.
% 0.97/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( X ), T ), Y ) ) = hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.97/1.55 tc_Nat_Onat, Z, Y ) ) }.
% 0.97/1.55 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Int_OBit1( Y ), c_Int_OBit0(
% 0.97/1.55 X ) ) = c_Int_OBit1( c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }
% 0.97/1.55 .
% 0.97/1.55 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Int_OBit0( Y ), c_Int_OBit1(
% 0.97/1.55 X ) ) = c_Int_OBit1( c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }
% 0.97/1.55 .
% 0.97/1.55 { c_Int_OBit1( X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oone__class_Oone(
% 0.97/1.55 tc_Int_Oint ), X ), X ) }.
% 0.97/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.97/1.55 c_Complex_Ocomplex_OComplex( T, Z ) ), c_Complex_Ocomplex_OComplex( Y, X
% 0.97/1.55 ) ) = c_Complex_Ocomplex_OComplex( c_Groups_Ominus__class_Ominus(
% 0.97/1.55 tc_RealDef_Oreal, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.55 tc_RealDef_Oreal ), T ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.55 tc_RealDef_Oreal ), Z ), X ) ), c_Groups_Oplus__class_Oplus(
% 0.97/1.55 tc_RealDef_Oreal, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.55 tc_RealDef_Oreal ), T ), X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.55 tc_RealDef_Oreal ), Z ), Y ) ) ) }.
% 0.97/1.55 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.55 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.97/1.55 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X ) ),
% 0.97/1.55 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y ) ),
% 0.97/1.55 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) }.
% 0.97/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Int_OBit1( Y
% 0.97/1.55 ) ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Int_OBit0( hAPP(
% 0.97/1.55 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ), X ) }.
% 0.97/1.55 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) }.
% 0.97/1.55 { ! c_Complex_Ocomplex_OComplex( T, Z ) = c_Complex_Ocomplex_OComplex( Y, X
% 0.97/1.55 ), T = Y }.
% 0.97/1.55 { ! c_Complex_Ocomplex_OComplex( T, Z ) = c_Complex_Ocomplex_OComplex( Y, X
% 0.97/1.55 ), Z = X }.
% 0.97/1.55 { ! T = Y, ! Z = X, c_Complex_Ocomplex_OComplex( T, Z ) =
% 0.97/1.55 c_Complex_Ocomplex_OComplex( Y, X ) }.
% 0.97/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.55 c_Int_OPls ) ) ) ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, X
% 0.97/1.55 ) }.
% 0.97/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.55 c_Int_OPls ) ) ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, X ) }.
% 0.97/1.55 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.97/1.55 tc_Nat_Onat ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) =
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.55 c_Int_OPls ) ) ) }.
% 0.97/1.55 { ! class_Rings_Osemiring( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP
% 0.97/1.55 ( c_Groups_Otimes__class_Otimes( X ), U ), T ),
% 0.97/1.55 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.55 ( X ), Z ), T ), Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, U, Z
% 0.97/1.55 ) ), T ), Y ) }.
% 0.97/1.55 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.97/1.55 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.55 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.97/1.55 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.55 { ! class_Rings_Ocomm__semiring( X ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.97/1.55 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.55 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.55 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.55 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.55 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.55 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 0.97/1.55 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.55 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 0.97/1.55 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.55 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 0.97/1.55 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.55 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 0.97/1.55 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.55 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.97/1.55 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.97/1.55 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.97/1.55 = c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.55 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.97/1.55 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, Z,
% 0.97/1.55 Y ) ) = c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus
% 0.97/1.55 ( X, Y, Z ) ) }.
% 0.97/1.55 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.97/1.55 tc_Nat_Onat ) ) = Y }.
% 0.97/1.55 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.97/1.55 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.55 ( X ), Z ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.97/1.55 Z ) ), U ), T ) = Y }.
% 0.97/1.55 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.97/1.55 Z ) ), U ), T ) = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.97/1.55 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.55 ( X ), Z ), U ), Y ) }.
% 0.97/1.55 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.97/1.55 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.55 ( X ), Z ), U ), Y ), T = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.97/1.55 W ) ), U ), Y ) }.
% 0.97/1.55 { ! class_Rings_Oring( X ), ! T = c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.97/1.55 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.97/1.55 X, Z, W ) ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.97/1.55 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.55 ( X ), Z ), U ), Y ) }.
% 0.97/1.55 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.97/1.55 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.97/1.55 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.97/1.55 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.97/1.55 X, U, Z ) ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 0.97/1.55 Z ) ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 0.97/1.55 c_Groups_Ominus__class_Ominus( X, T, Y ) ) ) }.
% 0.97/1.55 { ! class_Rings_Olinordered__semidom( X ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 0.97/1.55 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.97/1.55 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.97/1.55 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.55 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.97/1.55 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.97/1.55 ( X, Y ) ), c_RealVector_Onorm__class_Onorm( X,
% 0.97/1.55 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) }.
% 0.97/1.55 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 0.97/1.55 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.97/1.55 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 0.97/1.55 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.97/1.55 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 0.97/1.55 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oone__class_Oone( X ) ) =
% 0.97/1.55 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.97/1.55 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 0.97/1.55 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.97/1.55 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) }.
% 0.97/1.55 { c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex,
% 0.97/1.55 c_Complex_Ocomplex_OComplex( T, Z ), c_Complex_Ocomplex_OComplex( Y, X )
% 0.97/1.55 ) = c_Complex_Ocomplex_OComplex( c_Groups_Oplus__class_Oplus(
% 0.97/1.55 tc_RealDef_Oreal, T, Y ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.97/1.55 Z, X ) ) }.
% 0.97/1.55 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ),
% 0.97/1.55 c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt( X ) ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.55 c_Int_OPls ) ) ) ) = X }.
% 0.97/1.55 { c_Complex_Ocomplex_Ocomplex__rec( T, Z, c_Complex_Ocomplex_OComplex( Y, X
% 0.97/1.55 ) ) = hAPP( hAPP( Z, Y ), X ) }.
% 0.97/1.55 { c_Complex_Ocomplex_Ocomplex__case( T, Z, c_Complex_Ocomplex_OComplex( Y,
% 0.97/1.55 X ) ) = hAPP( hAPP( Z, Y ), X ) }.
% 0.97/1.55 { ! class_Int_Onumber__ring( X ), hAPP( hAPP( c_Power_Opower__class_Opower
% 0.97/1.55 ( X ), c_Int_Onumber__class_Onumber__of( X, c_Int_OMin ) ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.55 c_Int_OPls ) ) ) ), Y ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.55 { ! class_Power_Opower( X ), c_Power_Opower__class_Opower( X ) =
% 0.97/1.55 c_Power_Opower_Opower( X, c_Groups_Oone__class_Oone( X ),
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ) ) }.
% 0.97/1.55 { c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.97/1.55 c_Complex_Ocomplex_OComplex( Y, X ) ) = c_NthRoot_Osqrt(
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Y ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.55 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.97/1.55 tc_RealDef_Oreal ), X ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 0.97/1.55 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) ) }.
% 0.97/1.55 { ! class_Rings_Olinordered__idom( X ), c_Orderings_Oord__class_Oless__eq(
% 0.97/1.55 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( X ), Z ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.55 c_Int_OPls ) ) ) ), Y ) ) ) }.
% 0.97/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.97/1.55 ( X, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( X ), Z ), c_Int_Onumber__class_Onumber__of
% 0.97/1.55 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ), hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( X ), Y ), c_Int_Onumber__class_Onumber__of
% 0.97/1.55 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ),
% 0.97/1.55 c_Groups_Ozero__class_Ozero( X ) ), Z = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.55 }.
% 0.97/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.97/1.55 ( X, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( X ), Z ), c_Int_Onumber__class_Onumber__of
% 0.97/1.55 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ), hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( X ), Y ), c_Int_Onumber__class_Onumber__of
% 0.97/1.55 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ),
% 0.97/1.55 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.55 }.
% 0.97/1.55 { ! class_Rings_Olinordered__idom( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.97/1.55 X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.97/1.55 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.55 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.55 c_Int_OPls ) ) ) ) ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ) }
% 0.97/1.55 .
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Osqrt( X
% 0.97/1.55 ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Osqrt( X )
% 0.97/1.55 , c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ) }
% 0.97/1.55 .
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), ! c_NthRoot_Osqrt(
% 0.97/1.55 X ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.55 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.97/1.55 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.97/1.55 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.97/1.55 .
% 0.97/1.55 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.97/1.55 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.97/1.55 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.55 tc_Nat_Onat ) }.
% 0.97/1.55 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.97/1.55 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.97/1.55 , ! Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 0.97/1.55 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y )
% 0.97/1.55 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.55 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.55 c_RealVector_Onorm__class_Onorm( X, Y ) = c_Groups_Ozero__class_Ozero(
% 0.97/1.55 tc_RealDef_Oreal ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.55 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X, Y )
% 0.97/1.55 = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.55 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.97/1.55 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.55 { c_NthRoot_Osqrt( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.55 { ! c_NthRoot_Osqrt( X ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal )
% 0.97/1.55 , X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.55 { ! X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X
% 0.97/1.55 ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.55 { ! c_NthRoot_Osqrt( Y ) = c_NthRoot_Osqrt( X ), Y = X }.
% 0.97/1.55 { ! Y = X, c_NthRoot_Osqrt( Y ) = c_NthRoot_Osqrt( X ) }.
% 0.97/1.55 { hAPP( hAPP( c_Power_Opower_Opower( T, Z, Y ), X ),
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = Z }.
% 0.97/1.55 { ! c_Complex_Ocomplex_OComplex( Y, X ) = c_Groups_Ozero__class_Ozero(
% 0.97/1.55 tc_Complex_Ocomplex ), Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal
% 0.97/1.55 ) }.
% 0.97/1.55 { ! c_Complex_Ocomplex_OComplex( Y, X ) = c_Groups_Ozero__class_Ozero(
% 0.97/1.55 tc_Complex_Ocomplex ), X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal
% 0.97/1.55 ) }.
% 0.97/1.55 { ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! X =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.97/1.55 c_Complex_Ocomplex_OComplex( Y, X ) = c_Groups_Ozero__class_Ozero(
% 0.97/1.55 tc_Complex_Ocomplex ) }.
% 0.97/1.55 { c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) =
% 0.97/1.55 c_Complex_Ocomplex_OComplex( c_Groups_Ozero__class_Ozero(
% 0.97/1.55 tc_RealDef_Oreal ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.97/1.55 { ! class_Groups_Ozero( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y, Y =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.55 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.55 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Osqrt( Y
% 0.97/1.55 ), c_NthRoot_Osqrt( X ) ), c_Orderings_Oord__class_Oless__eq(
% 0.97/1.55 tc_RealDef_Oreal, Y, X ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Osqrt( Y )
% 0.97/1.55 , c_NthRoot_Osqrt( X ) ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Osqrt( Y )
% 0.97/1.55 , c_NthRoot_Osqrt( X ) ) }.
% 0.97/1.55 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), ! Y =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.97/1.55 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.55 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), Y =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.97/1.55 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.55 { c_NthRoot_Osqrt( hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.55 tc_RealDef_Oreal ), Y ), X ) ) = hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_NthRoot_Osqrt( Y ) )
% 0.97/1.55 , c_NthRoot_Osqrt( X ) ) }.
% 0.97/1.55 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.55 c_RealVector_Onorm__class_Onorm( X, Y ), c_Groups_Ozero__class_Ozero(
% 0.97/1.55 tc_RealDef_Oreal ) ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.55 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq(
% 0.97/1.55 tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( X, Y ),
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.97/1.55 { c_NthRoot_Osqrt( hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.97/1.55 tc_RealDef_Oreal ), Y ), X ) ) = hAPP( hAPP( c_Power_Opower__class_Opower
% 0.97/1.55 ( tc_RealDef_Oreal ), c_NthRoot_Osqrt( Y ) ), X ) }.
% 0.97/1.55 { c_NthRoot_Osqrt( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) =
% 0.97/1.55 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.97/1.55 { ! c_NthRoot_Osqrt( X ) = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X
% 0.97/1.55 = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.97/1.55 { ! X = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X )
% 0.97/1.55 = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.97/1.55 { c_Int_OBit1( c_Int_OMin ) = c_Int_OMin }.
% 0.97/1.55 { ! c_Int_OMin = c_Int_OBit1( X ), c_Int_OMin = X }.
% 0.97/1.55 { ! c_Int_OMin = X, c_Int_OMin = c_Int_OBit1( X ) }.
% 0.97/1.55 { ! c_Int_OBit1( X ) = c_Int_OMin, X = c_Int_OMin }.
% 0.97/1.55 { ! X = c_Int_OMin, c_Int_OBit1( X ) = c_Int_OMin }.
% 0.97/1.55 { ! c_Int_OMin = c_Int_OPls }.
% 0.97/1.55 { ! c_Int_OPls = c_Int_OMin }.
% 0.97/1.55 { ! c_Int_OMin = c_Int_OBit0( X ) }.
% 0.97/1.55 { ! c_Int_OBit0( X ) = c_Int_OMin }.
% 0.97/1.55 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OMin, c_Int_OMin )
% 0.97/1.55 }.
% 0.97/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.97/1.55 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.97/1.55 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.55 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.55 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.55 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.97/1.55 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.55 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.97/1.55 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.55 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.55 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.55 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.97/1.55 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.55 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.97/1.55 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.55 { ! class_Rings_Oring__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.55 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.55 { ! class_Rings_Oring__no__zero__divisors( X ), ! Z =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.55 { ! class_Rings_Oring__no__zero__divisors( X ), ! Y =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.55 { ! class_Rings_Ono__zero__divisors( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.55 X ), Z = c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.55 { ! class_Rings_Ono__zero__divisors( X ), ! hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.55 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.55 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.55 c_Groups_Oplus__class_Oplus( X, Y, Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.55 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.55 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.97/1.55 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.55 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.55 ( X ), ! Z = c_Groups_Oplus__class_Oplus( X, Z, Y ), Y =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.55 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.55 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.97/1.55 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 0.97/1.55 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.97/1.55 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.97/1.55 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.97/1.55 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.97/1.55 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.97/1.55 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.97/1.55 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.55 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.97/1.55 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.55 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero( X ) =
% 0.97/1.55 c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 0.97/1.55 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.55 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.97/1.55 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.55 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.97/1.55 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.55 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.97/1.55 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.97/1.55 ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.97/1.55 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ominus__class_Ominus(
% 0.97/1.55 X, Z, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.55 { ! class_Groups_Oab__group__add( X ), ! Z = Y,
% 0.97/1.55 c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.97/1.55 ) }.
% 0.97/1.55 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.97/1.55 Z, Y ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.97/1.55 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y, Y )
% 0.97/1.55 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.55 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y,
% 0.97/1.55 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.97/1.55 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Oone__class_Oone( X ) =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.55 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.97/1.55 c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.55 { ! class_Rings_Oring__1__no__zero__divisors( X ), Y =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 0.97/1.55 ( X ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.55 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ),
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.55 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ),
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.97/1.55 { c_Int_OPls = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.97/1.55 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) = hAPP( hAPP
% 0.97/1.55 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ), Z = Y }.
% 0.97/1.55 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP
% 0.97/1.55 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) = hAPP(
% 0.97/1.55 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) }.
% 0.97/1.55 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) = hAPP( hAPP
% 0.97/1.55 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ), Z = Y }.
% 0.97/1.55 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP
% 0.97/1.55 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) = hAPP(
% 0.97/1.55 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) }.
% 0.97/1.55 { ! c_Groups_Ozero__class_Ozero( tc_Int_Oint ) = c_Groups_Oone__class_Oone
% 0.97/1.55 ( tc_Int_Oint ) }.
% 0.97/1.55 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero
% 0.97/1.55 ( tc_Int_Oint ) ) = X }.
% 0.97/1.55 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.55 tc_Int_Oint ), X ) = X }.
% 0.97/1.55 { ! c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) =
% 0.97/1.55 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.97/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.97/1.55 c_Complex_Oii ), c_Complex_Oii ) = c_Int_Onumber__class_Onumber__of(
% 0.97/1.55 tc_Complex_Ocomplex, c_Int_OMin ) }.
% 0.97/1.55 { ! c_Complex_Oii = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.97/1.55 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt(
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) ) ) }.
% 0.97/1.55 { c_Groups_Ominus__class_Ominus( tc_Code__Numeral_Ocode__numeral,
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_Code__Numeral_Ocode__numeral ),
% 0.97/1.55 c_Groups_Oone__class_Oone( tc_Code__Numeral_Ocode__numeral ) ) =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_Code__Numeral_Ocode__numeral ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.55 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.55 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.55 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.55 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Osqrt( X
% 0.97/1.55 ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.97/1.55 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.97/1.55 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Osqrt( X )
% 0.97/1.55 , c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.55 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.55 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( X ),
% 0.97/1.55 c_Int_OMin ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.97/1.55 c_Int_OMin ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, c_Int_OMin ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( X ),
% 0.97/1.55 c_Int_OMin ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OMin, c_Int_OBit1
% 0.97/1.55 ( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OMin, X )
% 0.97/1.55 }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OMin, X ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OMin, c_Int_OBit1(
% 0.97/1.55 X ) ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, c_Int_OMin
% 0.97/1.55 ) }.
% 0.97/1.55 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OMin, c_Int_OPls )
% 0.97/1.55 }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( X ),
% 0.97/1.55 c_Int_OMin ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.97/1.55 c_Int_OMin ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, c_Int_OMin ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( X ),
% 0.97/1.55 c_Int_OMin ) }.
% 0.97/1.55 { ! c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OPls ) =
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OMin ) }.
% 0.97/1.55 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.97/1.55 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) }.
% 0.97/1.55 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), alpha1( X, Y
% 0.97/1.55 , Z ), alpha15( X, Y, Z ) }.
% 0.97/1.55 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha1( X, Y, Z ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.55 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha15( X, Y, Z ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.55 { ! alpha15( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.97/1.55 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.55 { ! alpha15( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.97/1.55 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.97/1.55 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.97/1.55 c_Groups_Ozero__class_Ozero( X ) ), alpha15( X, Y, Z ) }.
% 0.97/1.55 { ! alpha1( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.55 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.97/1.55 { ! alpha1( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.55 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.55 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.55 c_Groups_Ozero__class_Ozero( X ), Y ), alpha1( X, Y, Z ) }.
% 0.97/1.55 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.97/1.55 ( X ) ), alpha2( X, Y, Z ), alpha16( X, Y, Z ) }.
% 0.97/1.55 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha2( X, Y, Z ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.97/1.55 ( X ) ) }.
% 0.97/1.55 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha16( X, Y, Z ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.97/1.55 ( X ) ) }.
% 0.97/1.55 { ! alpha16( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.97/1.55 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.55 { ! alpha16( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.55 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.97/1.55 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.97/1.55 ( X ), Y ), alpha16( X, Y, Z ) }.
% 0.97/1.55 { ! alpha2( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.55 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.97/1.55 { ! alpha2( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.97/1.55 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.55 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.97/1.55 c_Groups_Ozero__class_Ozero( X ) ), alpha2( X, Y, Z ) }.
% 0.97/1.55 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.55 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.55 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.55 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.55 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.55 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.97/1.55 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.55 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ),
% 0.97/1.55 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.55 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.55 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.97/1.55 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.55 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.97/1.55 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.55 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.55 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.55 X ), Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.97/1.55 ( X ) ) }.
% 0.97/1.55 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.55 , Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.55 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.97/1.55 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.55 { ! class_Rings_Oordered__semiring( X ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.97/1.55 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.97/1.55 { ! class_Rings_Oordered__semiring( X ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.97/1.55 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.55 { ! class_Rings_Oordered__comm__semiring( X ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.97/1.55 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.55 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.55 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.97/1.55 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.55 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.97/1.55 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.55 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.97/1.55 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.55 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.97/1.55 { ! class_Rings_Oordered__semiring( X ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.97/1.55 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.55 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.97/1.55 { ! class_Rings_Oordered__semiring( X ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.55 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.55 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.97/1.55 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.55 , c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.55 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.97/1.55 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.55 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.55 , Z, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.55 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.97/1.55 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.55 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.97/1.55 ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.97/1.55 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.55 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.97/1.55 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.55 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.55 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.55 X ), Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.97/1.55 ( X ) ) }.
% 0.97/1.55 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.55 c_Groups_Oplus__class_Oplus( X, Y, Y ) ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.55 ) }.
% 0.97/1.55 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.55 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.97/1.55 ), c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.97/1.55 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Y,
% 0.97/1.55 Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.55 ) }.
% 0.97/1.55 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.55 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X
% 0.97/1.55 , Y, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.55 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.55 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.55 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.55 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.97/1.55 ) }.
% 0.97/1.55 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.55 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.55 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 0.97/1.55 .
% 0.97/1.55 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.55 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.55 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.97/1.55 .
% 0.97/1.55 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.55 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.55 X ), Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), ! Z =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.97/1.55 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.55 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.55 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.97/1.55 Y, Z ) ) }.
% 0.97/1.55 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.55 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.97/1.55 Z, Y ) ) }.
% 0.97/1.55 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.55 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.97/1.55 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.55 , c_Groups_Oplus__class_Oplus( X, Y, Z ), c_Groups_Ozero__class_Ozero( X
% 0.97/1.55 ) ) }.
% 0.97/1.55 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 0.97/1.55 , Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.55 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 0.97/1.55 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.55 { ! class_Rings_Olinordered__semidom( X ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.97/1.55 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.55 { ! class_Rings_Olinordered__semidom( X ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.55 c_Groups_Oone__class_Oone( X ) ) }.
% 0.97/1.55 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.55 ( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! W = U, T = Z, !
% 0.97/1.55 c_Groups_Oplus__class_Oplus( X, W, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) =
% 0.97/1.55 c_Groups_Oplus__class_Oplus( X, U, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.55 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.55 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.55 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.97/1.55 ) = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X
% 0.97/1.55 ) }.
% 0.97/1.55 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.55 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.55 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.97/1.55 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.97/1.55 ) }.
% 0.97/1.55 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.55 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.55 { ! class_Rings_Olinordered__semidom( X ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.55 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.97/1.55 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.97/1.55 { ! class_Rings_Olinordered__semidom( X ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.97/1.55 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.97/1.55 { ! class_Int_Onumber__ring( X ), c_Groups_Ozero__class_Ozero( X ) =
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( X, c_Int_OPls ) }.
% 0.97/1.55 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.97/1.55 c_Int_OPls ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ozero__class_Ozero(
% 0.97/1.55 tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.55 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.97/1.55 , Y ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.97/1.55 c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.55 { c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OPls ) =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.55 { c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) =
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OPls ) }.
% 0.97/1.55 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.97/1.55 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.97/1.55 { c_Groups_Ozero__class_Ozero( tc_Int_Oint ) =
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OPls ) }.
% 0.97/1.55 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.97/1.55 tc_Int_Oint, c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ) =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.97/1.55 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.55 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.55 { ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! X =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.55 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.55 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 0.97/1.55 ( tc_Nat_Onat ) ) ), X ) ) }.
% 0.97/1.55 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) =
% 0.97/1.55 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.97/1.55 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) = hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ),
% 0.97/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 0.97/1.55 ( tc_Nat_Onat ) ) ) ) }.
% 0.97/1.55 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt(
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.97/1.55 c_Int_OBit1( c_Int_OPls ) ) ) ) ) }.
% 0.97/1.55 { ! c_Complex_Ocomplex_OComplex( Z, Y ) = c_Int_Onumber__class_Onumber__of
% 0.97/1.55 ( tc_Complex_Ocomplex, X ), Z = c_Int_Onumber__class_Onumber__of(
% 0.97/1.55 tc_RealDef_Oreal, X ) }.
% 0.97/1.55 { ! c_Complex_Ocomplex_OComplex( Z, Y ) = c_Int_Onumber__class_Onumber__of
% 0.97/1.55 ( tc_Complex_Ocomplex, X ), Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.55 tc_RealDef_Oreal ) }.
% 0.97/1.55 { ! Z = c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, X ), ! Y =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.97/1.55 c_Complex_Ocomplex_OComplex( Z, Y ) = c_Int_Onumber__class_Onumber__of(
% 0.97/1.55 tc_Complex_Ocomplex, X ) }.
% 0.97/1.55 { c_Groups_Ozero__class_Ozero( tc_Code__Numeral_Ocode__numeral ) =
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Code__Numeral_Ocode__numeral,
% 0.97/1.55 c_Int_OPls ) }.
% 0.97/1.55 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, c_NthRoot_Osqrt(
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) ) ) }.
% 0.97/1.55 { ! hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.97/1.55 c_NthRoot_Osqrt( X ) ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 0.97/1.55 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) = X,
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) )
% 0.97/1.55 , c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1
% 0.97/1.55 ( c_Int_OPls ) ) ) ) = X }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) )
% 0.97/1.55 , c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1
% 0.97/1.55 ( c_Int_OPls ) ) ) ) = X }.
% 0.97/1.55 { ! hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Y ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.55 c_Int_OPls ) ) ) ) = X, ! c_Orderings_Oord__class_Oless__eq(
% 0.97/1.55 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.97/1.55 c_NthRoot_Osqrt( X ) = Y }.
% 0.97/1.55 { ! c_NthRoot_Osqrt( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP(
% 0.97/1.55 hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ), X ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.55 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.97/1.55 tc_RealDef_Oreal ), Y ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 0.97/1.55 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) ) = Y, X =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.55 { ! c_NthRoot_Osqrt( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP(
% 0.97/1.55 hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Y ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.55 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.97/1.55 tc_RealDef_Oreal ), X ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 0.97/1.55 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) ) = Y, X =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.55 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, c_Int_OPls, c_Int_OBit1( X )
% 0.97/1.55 ) = c_Int_OBit1( c_Groups_Ominus__class_Ominus( tc_Int_Oint, c_Int_OMin
% 0.97/1.55 , X ) ) }.
% 0.97/1.55 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, c_Int_OMin, c_Int_OBit0( X )
% 0.97/1.55 ) = c_Int_OBit1( c_Groups_Ominus__class_Ominus( tc_Int_Oint, c_Int_OMin
% 0.97/1.55 , X ) ) }.
% 0.97/1.55 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, c_Int_OMin, c_Int_OBit1( X )
% 0.97/1.55 ) = c_Int_OBit0( c_Groups_Ominus__class_Ominus( tc_Int_Oint, c_Int_OMin
% 0.97/1.55 , X ) ) }.
% 0.97/1.55 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) =
% 0.97/1.55 c_Groups_Oone__class_Oone( tc_Int_Oint ), alpha3( X, Y ), alpha17( X, Y )
% 0.97/1.55 }.
% 0.97/1.55 { ! alpha3( X, Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint
% 0.97/1.55 ), Y ), X ) = c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.97/1.55 { ! alpha17( X, Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint
% 0.97/1.55 ), Y ), X ) = c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.97/1.55 { ! alpha17( X, Y ), Y = c_Int_Onumber__class_Onumber__of( tc_Int_Oint,
% 0.97/1.55 c_Int_OMin ) }.
% 0.97/1.55 { ! alpha17( X, Y ), X = c_Int_Onumber__class_Onumber__of( tc_Int_Oint,
% 0.97/1.55 c_Int_OMin ) }.
% 0.97/1.55 { ! Y = c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OMin ), ! X =
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OMin ), alpha17( X,
% 0.97/1.55 Y ) }.
% 0.97/1.55 { ! alpha3( X, Y ), Y = c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.97/1.55 { ! alpha3( X, Y ), X = c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.97/1.55 { ! Y = c_Groups_Oone__class_Oone( tc_Int_Oint ), ! X =
% 0.97/1.55 c_Groups_Oone__class_Oone( tc_Int_Oint ), alpha3( X, Y ) }.
% 0.97/1.55 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 0.97/1.55 c_Groups_Oone__class_Oone( tc_Int_Oint ), X = c_Groups_Oone__class_Oone(
% 0.97/1.55 tc_Int_Oint ), X = c_Int_Onumber__class_Onumber__of( tc_Int_Oint,
% 0.97/1.55 c_Int_OMin ) }.
% 0.97/1.55 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.97/1.55 X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 0.97/1.55 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.97/1.55 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.97/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.97/1.55 c_Groups_Ozero__class_Ozero( X ) ), Z = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.55 }.
% 0.97/1.55 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.97/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.97/1.55 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.55 }.
% 0.97/1.55 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.55 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.97/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.97/1.55 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.97/1.55 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.97/1.55 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.97/1.55 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) }.
% 0.97/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.97/1.55 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.97/1.55 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.97/1.55 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) }.
% 0.97/1.55 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.97/1.55 c_Int_OBit0( Y ) ) = c_Groups_Oplus__class_Oplus( X,
% 0.97/1.55 c_Groups_Oplus__class_Oplus( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( X, Y ) ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.97/1.55 { ! c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, c_Int_OPls ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, c_Int_OPls ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.55 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) =
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, c_Int_OPls ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, c_Int_OPls ),
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) =
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) }.
% 0.97/1.55 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt(
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Y ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.55 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.97/1.55 tc_RealDef_Oreal ), X ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 0.97/1.55 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) ) ) }.
% 0.97/1.55 { c_Complex_Oii = c_Complex_Ocomplex_OComplex( c_Groups_Ozero__class_Ozero
% 0.97/1.55 ( tc_RealDef_Oreal ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.97/1.55 { ! c_Complex_Ocomplex_OComplex( Y, X ) = c_Complex_Oii, Y =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.55 { ! c_Complex_Ocomplex_OComplex( Y, X ) = c_Complex_Oii, X =
% 0.97/1.55 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.97/1.55 { ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! X =
% 0.97/1.55 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ),
% 0.97/1.55 c_Complex_Ocomplex_OComplex( Y, X ) = c_Complex_Oii }.
% 0.97/1.55 { ! c_Complex_Ocomplex_OComplex( Y, X ) = c_Groups_Oone__class_Oone(
% 0.97/1.55 tc_Complex_Ocomplex ), Y = c_Groups_Oone__class_Oone( tc_RealDef_Oreal )
% 0.97/1.55 }.
% 0.97/1.55 { ! c_Complex_Ocomplex_OComplex( Y, X ) = c_Groups_Oone__class_Oone(
% 0.97/1.55 tc_Complex_Ocomplex ), X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal
% 0.97/1.55 ) }.
% 0.97/1.55 { ! Y = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), ! X =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.97/1.55 c_Complex_Ocomplex_OComplex( Y, X ) = c_Groups_Oone__class_Oone(
% 0.97/1.55 tc_Complex_Ocomplex ) }.
% 0.97/1.55 { c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) =
% 0.97/1.55 c_Complex_Ocomplex_OComplex( c_Groups_Oone__class_Oone( tc_RealDef_Oreal
% 0.97/1.55 ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.97/1.55 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt( hAPP(
% 0.97/1.55 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), T ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.55 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.97/1.55 tc_RealDef_Oreal ), Z ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 0.97/1.55 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) ),
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Y ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.55 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.97/1.55 tc_RealDef_Oreal ), X ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 0.97/1.55 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) ) ) ) }.
% 0.97/1.55 { ! class_Rings_Olinordered__semiring__1( X ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, T, Y ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.97/1.55 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.55 X ), W ), ! c_Groups_Oplus__class_Oplus( X, U, W ) =
% 0.97/1.55 c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.55 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.55 ( X ), U ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), T )
% 0.97/1.55 ), Y ) }.
% 0.97/1.55 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( X, Y ) ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, Y ) }.
% 0.97/1.55 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, Y ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.97/1.55 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 0.97/1.55 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, c_Int_OPls ) }.
% 0.97/1.55 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, c_Int_OPls ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 0.97/1.55 , Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.55 { ! class_Rings_Olinordered__semidom( X ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.97/1.55 ), ! c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oone__class_Oone
% 0.97/1.55 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 0.97/1.55 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ),
% 0.97/1.55 c_Complex_Oii ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 0.97/1.55 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) =
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Complex_Ocomplex, c_Int_OMin ) }.
% 0.97/1.55 { ! class_Rings_Osemiring__1( X ), hAPP( hAPP( c_Power_Opower__class_Opower
% 0.97/1.55 ( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.55 c_Int_OPls ) ) ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.55 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( X ), Y ), c_Int_Onumber__class_Onumber__of
% 0.97/1.55 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 0.97/1.55 .
% 0.97/1.55 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( X ), Y ), c_Int_Onumber__class_Onumber__of
% 0.97/1.55 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.55 { ! class_Rings_Olinordered__idom( X ), c_Orderings_Oord__class_Oless__eq(
% 0.97/1.55 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( X ), Y ), c_Int_Onumber__class_Onumber__of
% 0.97/1.55 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) }.
% 0.97/1.55 { ! class_Rings_Olinordered__semidom( X ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( X ), Z ), c_Int_Onumber__class_Onumber__of
% 0.97/1.55 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ), hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( X ), Y ), c_Int_Onumber__class_Onumber__of
% 0.97/1.55 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.55 ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.55 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( X ), Z ), c_Int_Onumber__class_Onumber__of
% 0.97/1.55 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) = hAPP( hAPP
% 0.97/1.55 ( c_Power_Opower__class_Opower( X ), Y ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.55 c_Int_OPls ) ) ) ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.55 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.55 ), Z = Y }.
% 0.97/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Oplus__class_Oplus( X,
% 0.97/1.55 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.55 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.55 c_Int_OPls ) ) ) ) ) = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Oplus__class_Oplus( X,
% 0.97/1.55 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.55 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.55 c_Int_OPls ) ) ) ) ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.55 { ! class_Rings_Olinordered__idom( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.97/1.55 X ), ! Y = c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus
% 0.97/1.55 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.55 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.55 c_Int_OPls ) ) ) ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.55 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, c_NthRoot_Osqrt(
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Y ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.55 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.97/1.55 tc_RealDef_Oreal ), X ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 0.97/1.55 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) ) ) }.
% 0.97/1.55 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, c_NthRoot_Osqrt(
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), X ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.55 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.97/1.55 tc_RealDef_Oreal ), Y ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 0.97/1.55 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) ) ) }.
% 0.97/1.55 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Osqrt(
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, T, Z ) ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.55 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.97/1.55 tc_RealDef_Oreal ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X )
% 0.97/1.55 ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0(
% 0.97/1.55 c_Int_OBit1( c_Int_OPls ) ) ) ) ) ), c_Groups_Oplus__class_Oplus(
% 0.97/1.55 tc_RealDef_Oreal, c_NthRoot_Osqrt( c_Groups_Oplus__class_Oplus(
% 0.97/1.55 tc_RealDef_Oreal, hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.97/1.55 tc_RealDef_Oreal ), T ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 0.97/1.55 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ), hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Y ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.55 c_Int_OPls ) ) ) ) ) ), c_NthRoot_Osqrt( c_Groups_Oplus__class_Oplus(
% 0.97/1.55 tc_RealDef_Oreal, hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.97/1.55 tc_RealDef_Oreal ), Z ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 0.97/1.55 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ), hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), X ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.55 c_Int_OPls ) ) ) ) ) ) ) ) }.
% 0.97/1.55 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.97/1.55 c_NthRoot_Osqrt( hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.55 tc_RealDef_Oreal ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP(
% 0.97/1.55 hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ), T ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.55 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.97/1.55 tc_RealDef_Oreal ), Z ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 0.97/1.55 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) ),
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Y ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.55 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.97/1.55 tc_RealDef_Oreal ), X ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 0.97/1.55 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) ) ) ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.55 c_Int_OPls ) ) ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.55 tc_RealDef_Oreal ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP(
% 0.97/1.55 hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ), T ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.55 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.97/1.55 tc_RealDef_Oreal ), Z ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 0.97/1.55 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) ),
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Y ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.55 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.97/1.55 tc_RealDef_Oreal ), X ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 0.97/1.55 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) ) }.
% 0.97/1.55 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Y ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.55 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.97/1.55 tc_RealDef_Oreal ), X ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 0.97/1.55 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.55 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Y ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.55 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.97/1.55 tc_RealDef_Oreal ), X ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 0.97/1.55 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.55 { ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! X =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Y ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.55 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.97/1.55 tc_RealDef_Oreal ), X ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 0.97/1.55 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.55 { ! class_Rings_Olinordered__idom( X ), c_Orderings_Oord__class_Oless__eq(
% 0.97/1.55 X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 0.97/1.55 ( hAPP( c_Power_Opower__class_Opower( X ), Z ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.55 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.55 c_Int_OPls ) ) ) ) ) ) }.
% 0.97/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.97/1.55 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.55 c_Int_OPls ) ) ) ), Z ) ), c_Groups_Ozero__class_Ozero( X ) ), Y =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.55 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.55 c_Int_OPls ) ) ) ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0( X ) ) ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit1( X ) ) ) }.
% 0.97/1.55 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit1( c_Int_OBit1(
% 0.97/1.55 c_Int_OPls ) ) ) ) }.
% 0.97/1.55 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y,
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.55 c_RealVector_Onorm__class_Onorm( X, Z ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ),
% 0.97/1.55 c_RealVector_Onorm__class_Onorm( X, T ) ) ), Z =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.55 { ! class_Power_Opower( X ), ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 0.97/1.55 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) =
% 0.97/1.55 c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.55 { ! class_Power_Opower( X ), Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.97/1.55 , hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) = hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ominus__class_Ominus(
% 0.97/1.55 tc_Nat_Onat, Z, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 0.97/1.55 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), !
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) ) =
% 0.97/1.55 c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.55 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) ) =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.55 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Ozero__class_Ozero(
% 0.97/1.55 tc_Int_Oint ) ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol4( X, Y ) ) }.
% 0.97/1.55 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.55 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 0.97/1.55 tc_Int_Oint ) ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.97/1.55 tc_Int_Oint, X, Y ) ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) }.
% 0.97/1.55 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.97/1.55 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.97/1.55 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) ) =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.97/1.55 .
% 0.97/1.55 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.97/1.55 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.97/1.55 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) ) =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( X ), ! c_Int_Onumber__class_Onumber__of(
% 0.97/1.55 tc_Nat_Onat, Y ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.55 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.97/1.55 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.97/1.55 , ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.55 c_Power_Opower__class_Opower( X ), Z ), c_Int_Onumber__class_Onumber__of
% 0.97/1.55 ( tc_Nat_Onat, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.55 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.97/1.55 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OPls ) ) }.
% 0.97/1.55 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.97/1.55 { c_Complex_Ocomplex_Ocomplex__size( c_Complex_Ocomplex_OComplex( Y, X ) )
% 0.97/1.55 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) =
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ), T =
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! T =
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ),
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) =
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.55 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 0.97/1.55 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) =
% 0.97/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, T,
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ),
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T,
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T,
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ),
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) }.
% 0.97/1.55 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ), Z = X }.
% 0.97/1.55 { ! Z = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.97/1.55 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ), Y = X }.
% 0.97/1.55 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) }.
% 0.97/1.55 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.55 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.97/1.55 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, c_Groups_Oplus__class_Oplus
% 0.97/1.55 ( tc_Nat_Onat, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.97/1.55 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.97/1.55 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, X ) }.
% 0.97/1.55 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ) }.
% 0.97/1.55 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ), Y = X }.
% 0.97/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 0.97/1.55 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP
% 0.97/1.55 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.97/1.55 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.55 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.97/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ), Y ) }.
% 0.97/1.55 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = Y, X =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.55 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.55 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.55 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.97/1.55 tc_Nat_Onat, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.55 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero
% 0.97/1.55 ( tc_Nat_Onat ) ) = X }.
% 0.97/1.55 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.55 tc_Nat_Onat ), X ) = X }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.55 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.55 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.97/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.55 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.55 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.55 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.55 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.97/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Z =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.97/1.55 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.97/1.55 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.97/1.55 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.97/1.55 .
% 0.97/1.55 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.97/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Y = X
% 0.97/1.55 , Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.55 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.97/1.55 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.97/1.55 .
% 0.97/1.55 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.97/1.55 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.97/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = X
% 0.97/1.55 , Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.55 { ! Z = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.97/1.55 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }
% 0.97/1.55 .
% 0.97/1.55 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.97/1.55 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.55 tc_Nat_Onat ), X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.55 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 0.97/1.55 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, X ) =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.55 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.97/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.97/1.55 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.97/1.55 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol5( X, Y ) ) }.
% 0.97/1.55 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, T ),
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ), X ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.55 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), T ), Z ),
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), X ) ) =
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus
% 0.97/1.55 ( tc_Nat_Onat, T, Y ) ), Z ), X ) }.
% 0.97/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.97/1.55 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) }.
% 0.97/1.55 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), T ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.97/1.55 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.55 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) =
% 0.97/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ) }.
% 0.97/1.55 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.55 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) =
% 0.97/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 0.97/1.55 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.55 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.97/1.55 Z, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.97/1.55 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.55 tc_Nat_Onat, Y, X ), Y ) = X }.
% 0.97/1.55 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.55 tc_Nat_Onat, Y, X ), X ) = Y }.
% 0.97/1.55 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ), Y ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ),
% 0.97/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, Z ),
% 0.97/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.97/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = Y }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.97/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.97/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X = Z }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), ! X = Z,
% 0.97/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.97/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ),
% 0.97/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.55 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.97/1.55 ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 0.97/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 0.97/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 0.97/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.97/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.97/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) =
% 0.97/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.97/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.55 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) = X }.
% 0.97/1.55 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), Y =
% 0.97/1.55 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.97/1.55 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X =
% 0.97/1.55 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.97/1.55 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.97/1.55 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Groups_Oone__class_Oone(
% 0.97/1.55 tc_Nat_Onat ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.97/1.55 , Y ), X ) }.
% 0.97/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.97/1.55 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.97/1.55 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.55 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Oone__class_Oone(
% 0.97/1.55 tc_Nat_Onat ) }.
% 0.97/1.55 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.55 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X = c_Groups_Oone__class_Oone(
% 0.97/1.55 tc_Nat_Onat ) }.
% 0.97/1.55 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.97/1.55 c_Groups_Oone__class_Oone( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.55 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.97/1.55 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y,
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.55 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.55 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X )
% 0.97/1.55 , X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y =
% 0.97/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.55 tc_Nat_Onat, X, Z ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.97/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), Z ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.97/1.55 tc_Nat_Onat, X, Y ), Z ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ), Y ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.55 tc_Nat_Onat, Z, X ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.97/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z, X =
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X =
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.97/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.97/1.55 tc_Nat_Onat, X, Y ), Y ) = X }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.97/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.97/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.97/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.97/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.97/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 0.97/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.56 tc_Nat_Onat, Z, X ), Y ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.97/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = X }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.97/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.56 tc_Nat_Onat, X, Z ), Y ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.97/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.97/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ),
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z,
% 0.97/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 0.97/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.56 tc_Nat_Onat, Z, Y ), X ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 0.97/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ),
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ),
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 0.97/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.56 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 0.97/1.56 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) =
% 0.97/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.56 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) =
% 0.97/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ),
% 0.97/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) = Z }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) = Z,
% 0.97/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) =
% 0.97/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) }.
% 0.97/1.56 { c_Nat_Osize__class_Osize( tc_Complex_Ocomplex,
% 0.97/1.56 c_Complex_Ocomplex_OComplex( Y, X ) ) = c_Groups_Ozero__class_Ozero(
% 0.97/1.56 tc_Nat_Onat ) }.
% 0.97/1.56 { ! class_Int_Onumber__ring( X ), hAPP( hAPP( c_Power_Opower__class_Opower
% 0.97/1.56 ( X ), c_Int_Onumber__class_Onumber__of( X, c_Int_OMin ) ), c_Nat_OSuc(
% 0.97/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.56 c_Int_OPls ) ) ) ), Y ) ) ) = c_Int_Onumber__class_Onumber__of( X,
% 0.97/1.56 c_Int_OMin ) }.
% 0.97/1.56 { c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, X ), X =
% 0.97/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.56 c_Int_OPls ) ) ) ), skol6( X ) ), c_Groups_Oone__class_Oone( tc_Int_Oint
% 0.97/1.56 ) ) }.
% 0.97/1.56 { ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.56 c_Int_OPls ) ) ) ), Y ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ), !
% 0.97/1.56 c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, X ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.97/1.56 ( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.97/1.56 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.56 c_Int_OPls ) ) ) ), Z ) ) ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.97/1.56 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.56 ( tc_Nat_Onat, c_Nat_OSuc( Z ), Y ), c_Nat_OSuc( X ) ) =
% 0.97/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.56 ( tc_Nat_Onat, Z, Y ), X ) }.
% 0.97/1.56 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.97/1.56 X ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 0.97/1.56 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.56 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.97/1.56 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.56 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.56 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.97/1.56 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 0.97/1.56 ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 0.97/1.56 c_Nat_OSuc( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X )
% 0.97/1.56 }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 0.97/1.56 c_Nat_OSuc( X ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 0.97/1.56 ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.97/1.56 { ! Y = c_Nat_OSuc( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.97/1.56 , c_Nat_OSuc( X ) ) }.
% 0.97/1.56 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), X ) }
% 0.97/1.56 .
% 0.97/1.56 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.97/1.56 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.97/1.56 { ! Y = X, c_Nat_OSuc( Y ) = c_Nat_OSuc( X ) }.
% 0.97/1.56 { ! c_Nat_OSuc( X ) = X }.
% 0.97/1.56 { ! X = c_Nat_OSuc( X ) }.
% 0.97/1.56 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 0.97/1.56 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.97/1.56 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.97/1.56 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.97/1.56 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.97/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.97/1.56 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z
% 0.97/1.56 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.56 c_Nat_OSuc( Z ) ), X ), Y = X }.
% 0.97/1.56 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.56 c_Nat_OSuc( Z ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.56 tc_Nat_Onat ), c_Nat_OSuc( Z ) ), X ) }.
% 0.97/1.56 { c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.56 { ! c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint,
% 0.97/1.56 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.97/1.56 { c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, X ),
% 0.97/1.56 c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, Y ),
% 0.97/1.56 c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint,
% 0.97/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) ) }.
% 0.97/1.56 { c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, X ), !
% 0.97/1.56 c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, Y ), !
% 0.97/1.56 c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint,
% 0.97/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) ) }.
% 0.97/1.56 { ! c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, X ),
% 0.97/1.56 c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, Y ), !
% 0.97/1.56 c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint,
% 0.97/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) ) }.
% 0.97/1.56 { ! c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, X ), !
% 0.97/1.56 c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, Y ),
% 0.97/1.56 c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint,
% 0.97/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) ) }.
% 0.97/1.56 { ! c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint,
% 0.97/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ), alpha4( X, Y ),
% 0.97/1.56 alpha18( X, Y ) }.
% 0.97/1.56 { ! alpha4( X, Y ), c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint,
% 0.97/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 0.97/1.56 { ! alpha18( X, Y ), c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint,
% 0.97/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 0.97/1.56 { ! alpha18( X, Y ), ! c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, Y ) }
% 0.97/1.56 .
% 0.97/1.56 { ! alpha18( X, Y ), ! c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, X ) }
% 0.97/1.56 .
% 0.97/1.56 { c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, Y ),
% 0.97/1.56 c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, X ), alpha18( X, Y ) }.
% 0.97/1.56 { ! alpha4( X, Y ), c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, Y ) }.
% 0.97/1.56 { ! alpha4( X, Y ), c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, X ) }.
% 0.97/1.56 { ! c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, Y ), !
% 0.97/1.56 c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, X ), alpha4( X, Y ) }.
% 0.97/1.56 { c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, X ),
% 0.97/1.56 c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, Y ), !
% 0.97/1.56 c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) }.
% 0.97/1.56 { ! c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, X ),
% 0.97/1.56 c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.97/1.56 { ! c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, X ),
% 0.97/1.56 c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) }.
% 0.97/1.56 { ! c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ),
% 0.97/1.56 c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, Y ),
% 0.97/1.56 c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, X ) }.
% 0.97/1.56 { ! c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, Y ),
% 0.97/1.56 c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.97/1.56 { ! c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, X ),
% 0.97/1.56 c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.97/1.56 { ! c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint,
% 0.97/1.56 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ), alpha5( X, Y ),
% 0.97/1.56 alpha19( X, Y ) }.
% 0.97/1.56 { ! alpha5( X, Y ), c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint,
% 0.97/1.56 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ) }.
% 0.97/1.56 { ! alpha19( X, Y ), c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint,
% 0.97/1.56 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ) }.
% 0.97/1.56 { ! alpha19( X, Y ), ! c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, Y ) }
% 0.97/1.56 .
% 0.97/1.56 { ! alpha19( X, Y ), ! c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, X ) }
% 0.97/1.56 .
% 0.97/1.56 { c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, Y ),
% 0.97/1.56 c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, X ), alpha19( X, Y ) }.
% 0.97/1.56 { ! alpha5( X, Y ), c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, Y ) }.
% 0.97/1.56 { ! alpha5( X, Y ), c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, X ) }.
% 0.97/1.56 { ! c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, Y ), !
% 0.97/1.56 c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, X ), alpha5( X, Y ) }.
% 0.97/1.56 { c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, X ), !
% 0.97/1.56 c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.56 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) }.
% 0.97/1.56 { hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), c_Nat_OSuc( X ) ) =
% 0.97/1.56 hAPP( hAPP( Z, Y ), hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), X
% 0.97/1.56 ) ) }.
% 0.97/1.56 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), hAPP( hAPP(
% 0.97/1.56 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.56 c_Nat_OSuc( Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.56 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.97/1.56 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.56 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) }.
% 0.97/1.56 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.97/1.56 , Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.97/1.56 , Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.97/1.56 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.56 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.97/1.56 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 0.97/1.56 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.97/1.56 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.56 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 0.97/1.56 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.56 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.97/1.56 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.97/1.56 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha6( X, Y ), alpha20( X
% 0.97/1.56 , Y ) }.
% 0.97/1.56 { ! alpha6( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.97/1.56 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.56 { ! alpha20( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.97/1.56 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.56 { ! alpha20( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.56 { ! alpha20( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.97/1.56 tc_Nat_Onat ) ) }.
% 0.97/1.56 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha20( X, Y ) }.
% 0.97/1.56 { ! alpha6( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.97/1.56 tc_Nat_Onat ) ) }.
% 0.97/1.56 { ! alpha6( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.56 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha6( X, Y ) }.
% 0.97/1.56 { ! c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.97/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ), alpha7( X, Y ), alpha21
% 0.97/1.56 ( X, Y ) }.
% 0.97/1.56 { ! alpha7( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.97/1.56 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.97/1.56 { ! alpha21( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.97/1.56 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.97/1.56 { ! alpha21( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.56 { ! alpha21( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.97/1.56 tc_Nat_Onat ) ) }.
% 0.97/1.56 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha21( X, Y ) }.
% 0.97/1.56 { ! alpha7( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.97/1.56 tc_Nat_Onat ) ) }.
% 0.97/1.56 { ! alpha7( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.56 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha7( X, Y ) }.
% 0.97/1.56 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.56 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y = c_Nat_OSuc
% 0.97/1.56 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.56 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.56 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X = c_Nat_OSuc
% 0.97/1.56 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.56 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.97/1.56 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.56 { c_Groups_Oone__class_Oone( tc_Nat_Onat ) = c_Nat_OSuc(
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Y )
% 0.97/1.56 ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), c_Nat_OSuc
% 0.97/1.56 ( X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.97/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.97/1.56 ), X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.97/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.97/1.56 ), X ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) =
% 0.97/1.56 c_Nat_OSuc( c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.97/1.56 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.97/1.56 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.97/1.56 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.97/1.56 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X ) }.
% 0.97/1.56 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 0.97/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.56 ( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) }.
% 0.97/1.56 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 0.97/1.56 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.97/1.56 { ! hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.56 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = c_Nat_OSuc(
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.56 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.56 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.56 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP(
% 0.97/1.56 hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc
% 0.97/1.56 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.56 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), c_Nat_OSuc(
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) = c_Nat_OSuc(
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.56 { ! c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.56 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ) ),
% 0.97/1.56 c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, Y ) }.
% 0.97/1.56 { ! c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.56 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ) ), ! X =
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.56 { ! c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, Y ), X =
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.56 c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.56 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ) ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 0.97/1.56 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ) = hAPP( hAPP(
% 0.97/1.56 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.97/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.56 X ), Y ), Z = Y }.
% 0.97/1.56 { ! class_Rings_Olinordered__semidom( X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.56 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ), hAPP( hAPP(
% 0.97/1.56 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ) ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.56 ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), Z ) =
% 0.97/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 0.97/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, c_Nat_OSuc(
% 0.97/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) ) =
% 0.97/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.56 tc_Nat_Onat, Z, Y ), c_Nat_OSuc( X ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.97/1.56 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__semidom( X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone
% 0.97/1.56 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.56 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ), Y ) }.
% 0.97/1.56 { c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit1( c_Int_OBit1(
% 0.97/1.56 c_Int_OPls ) ) ) = c_Nat_OSuc( c_Nat_OSuc( c_Nat_OSuc(
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.97/1.56 { c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit1( c_Int_OPls )
% 0.97/1.56 ) = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.56 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.97/1.56 tc_Nat_Onat, Z, Y ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ),
% 0.97/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) ) = hAPP
% 0.97/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.56 c_Power_Opower__class_Opower( X ), T ), c_Groups_Ominus__class_Ominus(
% 0.97/1.56 tc_Nat_Onat, Y, Z ) ) ), T ) }.
% 0.97/1.56 { c_Nat_OSuc( c_Nat_OSuc( c_Nat_OSuc( X ) ) ) = c_Groups_Oplus__class_Oplus
% 0.97/1.56 ( tc_Nat_Onat, c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit1
% 0.97/1.56 ( c_Int_OBit1( c_Int_OPls ) ) ), X ) }.
% 0.97/1.56 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = X }.
% 0.97/1.56 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.97/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.97/1.56 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) ) }.
% 0.97/1.56 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP
% 0.97/1.56 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), hAPP( hAPP(
% 0.97/1.56 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) ) = hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.97/1.56 Y ) ), c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.97/1.56 { c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.56 c_Int_OPls ) ) ) = c_Nat_OSuc( c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.97/1.56 tc_Nat_Onat ) ) ) }.
% 0.97/1.56 { c_Nat_OSuc( c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) =
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.56 c_Int_OPls ) ) ) }.
% 0.97/1.56 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.56 c_Int_OPls ) ) ), X ) = c_Nat_OSuc( c_Nat_OSuc( X ) ) }.
% 0.97/1.56 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.56 c_Int_OPls ) ) ) ) = c_Nat_OSuc( c_Nat_OSuc( X ) ) }.
% 0.97/1.56 { ! c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, X ), X = hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.56 c_Int_OPls ) ) ) ), skol7( X ) ) }.
% 0.97/1.56 { ! X = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.56 c_Int_OPls ) ) ) ), Y ), c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, X
% 0.97/1.56 ) }.
% 0.97/1.56 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.97/1.56 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.56 c_Int_OPls ) ) ) ), Y ) ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.56 X ), Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.97/1.56 c_Power_Opower__class_Opower( X ), Z ), Y ) ),
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.56 c_Int_OPls ) ) ) ) ) }.
% 0.97/1.56 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.56 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.56 c_Int_OPls ) ) ) ), Y ) ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.56 X ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.56 c_Power_Opower__class_Opower( X ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.56 c_Power_Opower__class_Opower( X ), Z ), Y ) ) ) }.
% 0.97/1.56 { ! Y = c_Groups_Ozero__class_Ozero( tc_Code__Numeral_Ocode__numeral ),
% 0.97/1.56 c_Code__Numeral_Onat__of__aux( Y, X ) = X }.
% 0.97/1.56 { Y = c_Groups_Ozero__class_Ozero( tc_Code__Numeral_Ocode__numeral ),
% 0.97/1.56 c_Code__Numeral_Onat__of__aux( Y, X ) = c_Code__Numeral_Onat__of__aux(
% 0.97/1.56 c_Groups_Ominus__class_Ominus( tc_Code__Numeral_Ocode__numeral, Y,
% 0.97/1.56 c_Groups_Oone__class_Oone( tc_Code__Numeral_Ocode__numeral ) ),
% 0.97/1.56 c_Nat_OSuc( X ) ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.56 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.97/1.56 , hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( hAPP(
% 0.97/1.56 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.56 c_Int_OPls ) ) ) ), Z ) ) ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.56 { c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, X ),
% 0.97/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.56 c_Int_OPls ) ) ) ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, X,
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.56 c_Int_OPls ) ) ) ) ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = X }.
% 0.97/1.56 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.56 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ), c_NthRoot_Osqrt(
% 0.97/1.56 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.56 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), X ),
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.56 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.97/1.56 tc_RealDef_Oreal ), Y ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 0.97/1.56 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.97/1.56 X ) ) }.
% 0.97/1.56 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( X ) ) }.
% 0.97/1.56 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.56 tc_Nat_Onat ), c_Nat_OSuc( X ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.97/1.56 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) = X
% 0.97/1.56 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.97/1.56 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), X = Y }
% 0.97/1.56 .
% 0.97/1.56 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y = X }
% 0.97/1.56 .
% 0.97/1.56 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X,
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.97/1.56 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.97/1.56 X ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.97/1.56 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) )
% 0.97/1.56 }.
% 0.97/1.56 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.56 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.97/1.56 ( tc_Int_Oint, c_Int_OPls, Y ) }.
% 0.97/1.56 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, Y ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.97/1.56 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Y
% 0.97/1.56 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless(
% 0.97/1.56 tc_Int_Oint, Y, c_Int_OPls ) }.
% 0.97/1.56 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, c_Int_OPls ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Y
% 0.97/1.56 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.56 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.56 , T, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.56 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.97/1.56 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.56 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.56 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 0.97/1.56 hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.97/1.56 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.97/1.56 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oone__class_Oone
% 0.97/1.56 ( tc_RealDef_Oreal ), c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) )
% 0.97/1.56 ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.56 ( tc_Nat_Onat ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, X ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.56 tc_Nat_Onat ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) }.
% 0.97/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X, Y ),
% 0.97/1.56 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.56 c_Groups_Oabs__class_Oabs( X, Y ) ), ! Y = c_Groups_Ozero__class_Ozero( X
% 0.97/1.56 ) }.
% 0.97/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ), Y =
% 0.97/1.56 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.97/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.56 c_Groups_Oabs__class_Oabs( X, Y ) = Y }.
% 0.97/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.56 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.97/1.56 c_Groups_Oone__class_Oone( X ), T ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.56 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.56 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.56 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.56 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.97/1.56 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.56 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.56 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.97/1.56 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.56 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.56 ( tc_Nat_Onat, T, Z ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.56 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.56 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.56 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs
% 0.97/1.56 ( tc_RealDef_Oreal, X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 0.97/1.56 , X ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ), alpha8( X, Y ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.97/1.56 { ! alpha8( X, Y ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) }.
% 0.97/1.56 { ! alpha8( X, Y ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, X ) }.
% 0.97/1.56 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), alpha8( X, Y ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, X ), alpha8( X
% 0.97/1.56 , Y ) }.
% 0.97/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.97/1.56 c_Groups_Oabs__class_Oabs( X, Y ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.97/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! Y =
% 0.97/1.56 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oabs__class_Oabs( X, Y ) =
% 0.97/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.97/1.56 c_Groups_Oabs__class_Oabs( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.97/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.97/1.56 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oabs__class_Oabs( X, Y
% 0.97/1.56 ) ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, hAPP
% 0.97/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 0.97/1.56 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__idom( X ), hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Y ) ),
% 0.97/1.56 c_Groups_Oabs__class_Oabs( X, Y ) ) = hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.97/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.97/1.56 c_Groups_Oabs__class_Oabs( X, c_Groups_Oplus__class_Oplus( X,
% 0.97/1.56 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ) )
% 0.97/1.56 = c_Groups_Oplus__class_Oplus( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.97/1.56 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.97/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.97/1.56 c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Z, Y ) )
% 0.97/1.56 = c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Y, Z )
% 0.97/1.56 ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X,
% 0.97/1.56 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, hAPP
% 0.97/1.56 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.56 c_Power_Opower__class_Opower( X ), c_Groups_Oabs__class_Oabs( X, Z ) ), Y
% 0.97/1.56 ) }.
% 0.97/1.56 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.97/1.56 X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }
% 0.97/1.56 .
% 0.97/1.56 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.97/1.56 X ), Z, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z )
% 0.97/1.56 }.
% 0.97/1.56 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.97/1.56 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z
% 0.97/1.56 ), c_Orderings_Oord__class_Oless( tc_fun( T, X ), Z, Y ) }.
% 0.97/1.56 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.56 , Y ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.97/1.56 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.56 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.97/1.56 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.56 , ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.97/1.56 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.56 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.97/1.56 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.56 , Y ), Y = Z, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.56 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.56 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.56 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.56 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.97/1.56 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.56 , Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.97/1.56 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.56 , Z, Y ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.56 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.56 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.56 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.56 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.56 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.97/1.56 ( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.56 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.97/1.56 ( X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.56 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.97/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ), Z = Y }.
% 0.97/1.56 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.97/1.56 ), ! Z = Y, c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.56 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.56 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.56 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.97/1.56 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.97/1.56 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.56 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.97/1.56 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.56 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.56 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.97/1.56 ( X, Z, Y ) }.
% 0.97/1.56 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.56 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.56 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.56 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.97/1.56 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.56 , Z, Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.56 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.56 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.56 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.56 , ! Z = Y }.
% 0.97/1.56 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.56 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.56 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.56 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.56 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.56 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.56 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.97/1.56 Z ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.56 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.97/1.56 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.97/1.56 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.56 , Y, Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.56 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Oabs__class_Oabs
% 0.97/1.56 ( tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( X, Y ) ) =
% 0.97/1.56 c_RealVector_Onorm__class_Onorm( X, Y ) }.
% 0.97/1.56 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.97/1.56 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ), c_Orderings_Oord__class_Oless
% 0.97/1.56 ( X, T, Y ) }.
% 0.97/1.56 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, T, Y ), c_Orderings_Oord__class_Oless(
% 0.97/1.56 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.97/1.56 , Y, Z ) ) }.
% 0.97/1.56 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.97/1.56 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.97/1.56 ( X, Z, Y ) }.
% 0.97/1.56 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.97/1.56 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.97/1.56 , T, Y ) ) }.
% 0.97/1.56 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.97/1.56 X, c_Groups_Oplus__class_Oplus( X, Z, T ), c_Groups_Oplus__class_Oplus( X
% 0.97/1.56 , Y, T ) ) }.
% 0.97/1.56 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.97/1.56 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.97/1.56 , T, Y ) ) }.
% 0.97/1.56 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.56 ( X, U, T ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.56 c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X, Y
% 0.97/1.56 , T ) ) }.
% 0.97/1.56 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, T )
% 0.97/1.56 , c_Groups_Oplus__class_Oplus( X, Y, T ) ), c_Orderings_Oord__class_Oless
% 0.97/1.56 ( X, Z, Y ) }.
% 0.97/1.56 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.97/1.56 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.97/1.56 ( X, Z, Y ) }.
% 0.97/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.56 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.97/1.56 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, U, T ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.56 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.97/1.56 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, U, T ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( Y ),
% 0.97/1.56 c_Int_OBit1( X ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.97/1.56 .
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( Y ), c_Int_OBit1
% 0.97/1.56 ( X ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( Y ),
% 0.97/1.56 c_Int_OBit1( X ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.97/1.56 .
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( Y ), c_Int_OBit1
% 0.97/1.56 ( X ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, c_Int_OPls ) }
% 0.97/1.56 .
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.97/1.56 c_Int_OBit0( X ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.97/1.56 .
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( Y ), c_Int_OBit0
% 0.97/1.56 ( X ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.97/1.56 c_Int_OBit0( X ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.97/1.56 .
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( Y ), c_Int_OBit0
% 0.97/1.56 ( X ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), Y = X }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.97/1.56 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), ! Y = X }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), Y = X,
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), ! Y = X }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), Y = X,
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.97/1.56 tc_Int_Oint, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.97/1.56 .
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OMin, c_Int_OMin ) }
% 0.97/1.56 .
% 0.97/1.56 { c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, X ) =
% 0.97/1.56 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__idom( X ), Z = Y,
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.97/1.56 X, Y, Z ) }.
% 0.97/1.56 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.97/1.56 Y ) }.
% 0.97/1.56 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.97/1.56 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.56 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.56 Y ), ! Z = Y }.
% 0.97/1.56 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.97/1.56 Z ), ! Z = Y }.
% 0.97/1.56 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.97/1.56 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Z = Y }.
% 0.97/1.56 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.97/1.56 Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.56 { ! class_Orderings_Olinorder( X ), ! Z = Y, !
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.56 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.97/1.56 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.56 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.97/1.56 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Y = Z }.
% 0.97/1.56 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.97/1.56 ), ! Y = Z, ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.56 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.97/1.56 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.56 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.56 , ! Z = Y }.
% 0.97/1.56 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.56 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.56 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.56 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.56 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.56 , ! Z = Y }.
% 0.97/1.56 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.56 , ! Y = Z }.
% 0.97/1.56 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.56 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.56 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.56 , ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.56 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X
% 0.97/1.56 , Y, T ), c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.97/1.56 { ! class_Orderings_Oorder( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless(
% 0.97/1.56 X, T, Y ), c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.97/1.56 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.97/1.56 ! Y = T, c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.97/1.56 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.56 , ! Z = T, c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.97/1.56 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.56 Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.97/1.56 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.56 , ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.97/1.56 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.56 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.56 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.97/1.56 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.97/1.56 c_Groups_Oabs__class_Oabs( X, c_Groups_Oabs__class_Oabs( X, Y ) ) =
% 0.97/1.56 c_Groups_Oabs__class_Oabs( X, Y ) }.
% 0.97/1.56 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Z
% 0.97/1.56 ), c_Int_Onumber__class_Onumber__of( X, Y ) ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, Y ) }.
% 0.97/1.56 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, Y ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Z
% 0.97/1.56 ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.56 , c_Groups_Oabs__class_Oabs( X, Z ), Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.56 ( X, c_Groups_Oabs__class_Oabs( X, U ), T ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 0.97/1.56 c_Groups_Oabs__class_Oabs( X, U ) ), hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Osqrt( Y ),
% 0.97/1.56 c_NthRoot_Osqrt( X ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Osqrt( Y ),
% 0.97/1.56 c_NthRoot_Osqrt( X ) ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.56 Y, X ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Osqrt( Y ),
% 0.97/1.56 c_NthRoot_Osqrt( X ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.97/1.56 ( tc_Nat_Onat, Y, Z ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y
% 0.97/1.56 , X ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.97/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, X ) =
% 0.97/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.56 tc_Nat_Onat, Y, T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.97/1.56 .
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.56 tc_Nat_Onat, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.97/1.56 .
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.97/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.97/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.97/1.56 ( tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) )
% 0.97/1.56 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.56 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }
% 0.97/1.56 .
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.97/1.56 ( tc_Nat_Onat, Y, X ), X ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.97/1.56 ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.56 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.56 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.56 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.56 tc_Nat_Onat ), X ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.56 ( tc_Nat_Onat ), X ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 0.97/1.56 .
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X =
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.56 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.56 tc_Nat_Onat ), X ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.56 ( tc_Nat_Onat, Y, Z ), X ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.56 ( tc_Nat_Onat, Z, X ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.97/1.56 ) }.
% 0.97/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.56 ), c_Groups_Oabs__class_Oabs( X, Y ) = Y }.
% 0.97/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Y ),
% 0.97/1.56 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.56 }.
% 0.97/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! Y =
% 0.97/1.56 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.56 c_Groups_Oabs__class_Oabs( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.56 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.97/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 0.97/1.56 c_Groups_Oplus__class_Oplus( X, Z, Y ) ), c_Groups_Oplus__class_Oplus( X
% 0.97/1.56 , c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) )
% 0.97/1.56 ) }.
% 0.97/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 0.97/1.56 c_Groups_Ominus__class_Ominus( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.97/1.56 c_Groups_Oabs__class_Oabs( X, Y ) ) ), c_Groups_Oabs__class_Oabs( X,
% 0.97/1.56 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) }.
% 0.97/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X,
% 0.97/1.56 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ),
% 0.97/1.56 c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Z, Y ) )
% 0.97/1.56 ) }.
% 0.97/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X,
% 0.97/1.56 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ),
% 0.97/1.56 c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Y, Z ) )
% 0.97/1.56 ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.56 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( X ), Z ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.56 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), T ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.56 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.97/1.56 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.97/1.56 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.97/1.56 ( tc_Int_Oint, c_Int_OBit1( c_Int_OPls ), Y ) }.
% 0.97/1.56 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( c_Int_OPls ), Y
% 0.97/1.56 ), c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.97/1.56 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Y
% 0.97/1.56 ), c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless(
% 0.97/1.56 tc_Int_Oint, Y, c_Int_OBit1( c_Int_OPls ) ) }.
% 0.97/1.56 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, c_Int_OBit1( c_Int_OPls )
% 0.97/1.56 ), c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X
% 0.97/1.56 , Y ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.56 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 0.97/1.56 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha9( X, Y, Z, T ),
% 0.97/1.56 alpha22( X, Y, Z, T ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha9( X, Y, Z, T ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha22( X, Y, Z, T ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.56 { ! alpha22( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.56 { ! alpha22( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, T ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.56 , ! c_Orderings_Oord__class_Oless( X, Y, T ), alpha22( X, Y, Z, T ) }.
% 0.97/1.56 { ! alpha9( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.97/1.56 { ! alpha9( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.97/1.56 , ! c_Orderings_Oord__class_Oless( X, T, Y ), alpha9( X, Y, Z, T ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha10( X, Y, Z, T ),
% 0.97/1.56 alpha23( X, Y, Z, T ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha10( X, Y, Z, T ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha23( X, Y, Z, T ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.56 { ! alpha23( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.56 { ! alpha23( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( X, T, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.56 , ! c_Orderings_Oord__class_Oless( X, Y, Z ), alpha23( X, Y, Z, T ) }.
% 0.97/1.56 { ! alpha10( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( X ), T ) }.
% 0.97/1.56 { ! alpha10( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T )
% 0.97/1.56 , ! c_Orderings_Oord__class_Oless( X, Z, Y ), alpha10( X, Y, Z, T ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.56 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.56 ! c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless
% 0.97/1.56 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.97/1.56 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.56 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.97/1.56 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.56 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.56 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.97/1.56 ( X ) ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.56 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.56 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.97/1.56 ( X ) ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.97/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.97/1.56 .
% 0.97/1.56 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.97/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ) }
% 0.97/1.56 .
% 0.97/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.56 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.56 ! c_Orderings_Oord__class_Oless( X, Z, T ), c_Orderings_Oord__class_Oless
% 0.97/1.56 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.97/1.56 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.56 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.97/1.56 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.97/1.56 ( X ) ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.56 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.56 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.56 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.97/1.56 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP
% 0.97/1.56 ( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.56 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.97/1.56 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.97/1.56 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__comm__semiring__strict( X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.56 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.97/1.56 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.97/1.56 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.56 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.97/1.56 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.97/1.56 ( c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.56 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.97/1.56 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP
% 0.97/1.56 ( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.56 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.97/1.56 ) ), c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 0.97/1.56 ) ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.56 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.97/1.56 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.97/1.56 ) ) }.
% 0.97/1.56 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.56 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.56 , c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.97/1.56 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.56 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless(
% 0.97/1.56 X, T, c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.97/1.56 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.56 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.97/1.56 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.56 c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.97/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.97/1.56 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Y
% 0.97/1.56 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.97/1.56 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.56 c_Groups_Oplus__class_Oplus( X, Y, Y ) ), c_Orderings_Oord__class_Oless(
% 0.97/1.56 X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.97/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.56 c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.97/1.56 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, U )
% 0.97/1.56 , c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.97/1.56 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, U, T ), c_Orderings_Oord__class_Oless(
% 0.97/1.56 X, c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X
% 0.97/1.56 , Y, T ) ) }.
% 0.97/1.56 { ! class_Int_Onumber( X ), ! class_Orderings_Olinorder( X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 0.97/1.56 , Z ), c_Int_Onumber__class_Onumber__of( X, Y ) ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Y
% 0.97/1.56 ), c_Int_Onumber__class_Onumber__of( X, Z ) ) }.
% 0.97/1.56 { ! class_Int_Onumber( X ), ! class_Orderings_Olinorder( X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Y
% 0.97/1.56 ), c_Int_Onumber__class_Onumber__of( X, Z ) ),
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 0.97/1.56 , Z ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.97/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.97/1.56 X, c_Groups_Ominus__class_Ominus( X, Z, Y ), c_Groups_Ozero__class_Ozero
% 0.97/1.56 ( X ) ) }.
% 0.97/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.97/1.56 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.97/1.56 , Z, Y ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.56 ( X, c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero( X ) ) }
% 0.97/1.56 .
% 0.97/1.56 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.97/1.56 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.56 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.56 ( X, c_Groups_Oone__class_Oone( X ), Z ), c_Orderings_Oord__class_Oless(
% 0.97/1.56 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.56 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless
% 0.97/1.56 ( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.97/1.56 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.97/1.56 , Y, c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) )
% 0.97/1.56 ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.56 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! hAPP( hAPP(
% 0.97/1.56 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.97/1.56 c_Power_Opower__class_Opower( X ), Y ), Z ), T = Z }.
% 0.97/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.56 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! T = Z, hAPP( hAPP(
% 0.97/1.56 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.97/1.56 c_Power_Opower__class_Opower( X ), Y ), Z ) }.
% 0.97/1.56 { c_NthRoot_Osqrt( hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.56 tc_RealDef_Oreal ), X ), X ) ) = c_Groups_Oabs__class_Oabs(
% 0.97/1.56 tc_RealDef_Oreal, X ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( X ),
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( X ),
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( X ),
% 0.97/1.56 c_Int_OPls ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Int_OPls )
% 0.97/1.56 }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Int_OPls ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( X ), c_Int_OPls
% 0.97/1.56 ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( c_Nat_OSuc(
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X =
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X = c_Nat_OSuc(
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.56 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( skol8( X ) ) }.
% 0.97/1.56 { ! X = c_Nat_OSuc( Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X =
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.56 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y =
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha11( X, Y ) }.
% 0.97/1.56 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.97/1.56 { ! alpha11( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.97/1.56 c_Nat_OSuc( X ) ) }.
% 0.97/1.56 { ! alpha11( X, Y ), Y = c_Nat_OSuc( skol9( Z, Y ) ) }.
% 0.97/1.56 { ! alpha11( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol9( X,
% 0.97/1.56 Y ), X ) }.
% 0.97/1.56 { ! Y = c_Nat_OSuc( Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.97/1.56 ), alpha11( X, Y ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( Y ),
% 0.97/1.56 c_Int_OBit0( X ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.97/1.56 .
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( Y ), c_Int_OBit0
% 0.97/1.56 ( X ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( Y ),
% 0.97/1.56 c_Int_OBit0( X ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.97/1.56 .
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( Y ), c_Int_OBit0
% 0.97/1.56 ( X ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( X ),
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( X ),
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, c_Int_OBit0( X
% 0.97/1.56 ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, X ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, c_Int_OBit0( X )
% 0.97/1.56 ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( X ),
% 0.97/1.56 c_Int_OPls ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Int_OPls )
% 0.97/1.56 }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Int_OPls ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( X ), c_Int_OPls
% 0.97/1.56 ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.56 ( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.56 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.56 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.97/1.56 tc_Nat_Onat, Y, X ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.56 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.97/1.56 tc_Nat_Onat, Y, X ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), X = c_Nat_OSuc(
% 0.97/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol10( X, Y ) ) ) }.
% 0.97/1.56 { ! X = c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.56 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 0.97/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ) }.
% 0.97/1.56 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 0.97/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X = Y }
% 0.97/1.56 .
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X = Y,
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.56 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.56 tc_Int_Oint ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.56 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.97/1.56 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP
% 0.97/1.56 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.56 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.97/1.56 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP
% 0.97/1.56 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.56 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.97/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP(
% 0.97/1.56 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.56 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 0.97/1.56 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.56 ( tc_Nat_Onat ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.56 tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.56 tc_Nat_Onat ), X ), Y ), Z = Y }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.56 ( tc_Nat_Onat ), X ), ! Z = Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.56 ( tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.56 tc_Nat_Onat ), X ), Y ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.56 tc_Nat_Onat ), Y ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.56 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.97/1.56 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.56 tc_Nat_Onat ), Z ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.56 ( tc_Nat_Onat ), Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 0.97/1.56 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.56 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.97/1.56 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.56 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.97/1.56 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.56 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.56 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.56 Y ), X ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.56 ( tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.56 tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.56 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.56 ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.56 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 0.97/1.56 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP
% 0.97/1.56 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.97/1.56 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ), X =
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.56 { ! X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.97/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.97/1.56 ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.97/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.97/1.56 ), X ) ) }.
% 0.97/1.56 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.56 c_RealVector_Onorm__class_Onorm( X, Y ), c_Groups_Ozero__class_Ozero(
% 0.97/1.56 tc_RealDef_Oreal ) ) }.
% 0.97/1.56 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.56 ( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Z ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.97/1.56 tc_Int_Oint, Y, T ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.97/1.56 .
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OMin, c_Int_OBit1( X
% 0.97/1.56 ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OMin, X ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OMin, X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OMin, c_Int_OBit1( X )
% 0.97/1.56 ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( X ),
% 0.97/1.56 c_Int_OMin ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Int_OMin )
% 0.97/1.56 }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Int_OMin ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( X ), c_Int_OMin
% 0.97/1.56 ) }.
% 0.97/1.56 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OMin,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.56 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OMin, c_Int_OPls ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, c_Int_OMin ) }
% 0.97/1.56 .
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OMin, c_Int_OBit0( X
% 0.97/1.56 ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OMin, X ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OMin, X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OMin, c_Int_OBit0( X )
% 0.97/1.56 ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z,
% 0.97/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.56 tc_Nat_Onat, Z, X ), Y ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.97/1.56 ( tc_Nat_Onat, Z, X ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z
% 0.97/1.56 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 0.97/1.56 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.97/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) = Y }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.97/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.97/1.56 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y
% 0.97/1.56 = X }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.97/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.97/1.56 tc_Int_Oint ) ) ) }.
% 0.97/1.56 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.97/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.97/1.56 tc_Int_Oint ) ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.56 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.97/1.56 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.56 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.97/1.56 ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.56 ( tc_Nat_Onat, Y, Z ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z )
% 0.97/1.56 ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ominus__class_Ominus
% 0.97/1.56 ( tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.56 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ),
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ) }
% 0.97/1.56 .
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Osqrt( X ),
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Osqrt( X ),
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), ! c_NthRoot_Osqrt(
% 0.97/1.56 X ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ) }
% 0.97/1.56 .
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.56 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.56 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.56 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.56 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Osqrt( X ),
% 0.97/1.56 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.97/1.56 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.97/1.56 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Osqrt( X ),
% 0.97/1.56 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.56 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.97/1.56 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), X =
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.56 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.56 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.56 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.56 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.97/1.56 ), X ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.56 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.97/1.56 , Y ), X ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.56 tc_Nat_Onat ), Y ) }.
% 0.97/1.56 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.56 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.97/1.56 ), X ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.56 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.56 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.56 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.97/1.56 ( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Z ), hAPP( hAPP
% 0.97/1.56 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.97/1.56 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 0.97/1.56 Y ) = c_Groups_Oabs__class_Oabs( X, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.56 { ! class_Rings_Oordered__ring__abs( X ), alpha28( X, Z ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.56 ), c_Groups_Oabs__class_Oabs( X, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 0.97/1.56 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.97/1.56 { ! class_Rings_Oordered__ring__abs( X ), alpha28( X, Z ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.56 ), c_Groups_Oabs__class_Oabs( X, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 0.97/1.56 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.97/1.56 { ! alpha28( X, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.97/1.56 { ! alpha28( X, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.56 { c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.56 ), c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero
% 0.97/1.56 ( X ) ), alpha28( X, Y ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__idom( X ), c_Orderings_Oord__class_Oless__eq(
% 0.97/1.56 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.97/1.56 c_Power_Opower__class_Opower( X ), c_Groups_Oabs__class_Oabs( X, Z ) ), Y
% 0.97/1.56 ) ) }.
% 0.97/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 0.97/1.56 c_Groups_Ominus__class_Ominus( X, Z, Y ) ), c_Groups_Oplus__class_Oplus(
% 0.97/1.56 X, c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) )
% 0.97/1.56 ) }.
% 0.97/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 0.97/1.56 c_Groups_Ominus__class_Ominus( X, c_Groups_Oplus__class_Oplus( X, U, T )
% 0.97/1.56 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) ), c_Groups_Oplus__class_Oplus
% 0.97/1.56 ( X, c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, U, Z
% 0.97/1.56 ) ), c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, T,
% 0.97/1.56 Y ) ) ) ) }.
% 0.97/1.56 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ),
% 0.97/1.56 c_Groups_Oabs__class_Oabs( X, c_Int_Onumber__class_Onumber__of( X,
% 0.97/1.56 c_Int_OMin ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.56 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ),
% 0.97/1.56 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.56 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), X ),
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.56 c_Int_OPls ) ) ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.56 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ), hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ),
% 0.97/1.56 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Z ) ) ), Y =
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.56 { ! class_Int_Onumber__ring( X ), !
% 0.97/1.56 class_RealVector_Oreal__normed__algebra__1( X ),
% 0.97/1.56 c_RealVector_Onorm__class_Onorm( X, c_Int_Onumber__class_Onumber__of( X,
% 0.97/1.56 Y ) ) = c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, Y ) ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.56 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.56 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.56 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.56 ! c_Orderings_Oord__class_Oless__eq( X, Z, T ),
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.56 ( X, U, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.97/1.56 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.56 ( X, U, T ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.97/1.56 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.97/1.56 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.56 , U ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, U, T ), ! c_Orderings_Oord__class_Oless
% 0.97/1.56 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.97/1.56 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.56 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.97/1.56 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.97/1.56 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.97/1.56 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.56 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.97/1.56 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.97/1.56 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.97/1.56 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.56 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.56 ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.56 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.56 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.97/1.56 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.56 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.56 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.56 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.97/1.56 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.56 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.97/1.56 ) ) }.
% 0.97/1.56 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.56 ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.97/1.56 ) ) }.
% 0.97/1.56 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.56 ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.97/1.56 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.97/1.56 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.56 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.56 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.97/1.56 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.97/1.56 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.56 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.97/1.56 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.56 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.97/1.56 ) ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 0.97/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__ring__strict( X ), Z =
% 0.97/1.56 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.97/1.56 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__ring__strict( X ), Y =
% 0.97/1.56 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.97/1.56 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.56 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP
% 0.97/1.56 ( c_Power_Opower__class_Opower( X ), Y ), T ) ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.56 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.97/1.56 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.56 c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ) ) }.
% 0.97/1.56 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.97/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.56 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, hAPP
% 0.97/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus
% 0.97/1.56 ( X, Z, W ) ), U ), Y ) ) }.
% 0.97/1.56 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X, T
% 0.97/1.56 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.97/1.56 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.56 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.97/1.56 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.97/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.56 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.97/1.56 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.97/1.56 X, W, Z ) ), U ), T ), Y ) }.
% 0.97/1.56 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.97/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.56 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.97/1.56 hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.97/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.56 ( X ), Z ), U ), Y ) ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.56 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.97/1.56 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.97/1.56 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.56 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.97/1.56 X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.97/1.56 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.56 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.97/1.56 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.97/1.56 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ) ) }.
% 0.97/1.56 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.97/1.56 c_RealVector_Onorm__class_Onorm( X, Y ) ), ! Y =
% 0.97/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.56 { ! class_RealVector_Oreal__normed__vector( X ), Y =
% 0.97/1.56 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless(
% 0.97/1.56 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.97/1.56 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, c_Int_OBit1( X
% 0.97/1.56 ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, X ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, c_Int_OBit1( X )
% 0.97/1.56 ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( X ),
% 0.97/1.56 c_Int_OPls ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Int_OPls )
% 0.97/1.56 }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Int_OPls ),
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( X ),
% 0.97/1.56 c_Int_OPls ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.97/1.56 c_Int_OBit1( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 0.97/1.56 ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( Y ), c_Int_OBit1
% 0.97/1.56 ( X ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.97/1.56 c_Int_OBit1( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 0.97/1.56 ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( Y ), c_Int_OBit1
% 0.97/1.56 ( X ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( Y ),
% 0.97/1.56 c_Int_OBit0( X ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.97/1.56 .
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( Y ),
% 0.97/1.56 c_Int_OBit0( X ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( Y ),
% 0.97/1.56 c_Int_OBit0( X ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.97/1.56 .
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( Y ),
% 0.97/1.56 c_Int_OBit0( X ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.56 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.97/1.56 tc_Nat_Onat, X, c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) )
% 0.97/1.56 ) ) = X }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.56 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ),
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ),
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ),
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ),
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 0.97/1.56 { ! class_RealVector_Oreal__normed__algebra( X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.56 c_RealVector_Onorm__class_Onorm( X, Z ), Y ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.56 c_RealVector_Onorm__class_Onorm( X, U ), T ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.56 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), T ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.56 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.56 tc_Int_Oint ), X ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.56 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.56 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.56 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP
% 0.97/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.56 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z
% 0.97/1.56 , Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.56 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X
% 0.97/1.56 ) }.
% 0.97/1.56 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.56 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 0.97/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 0.97/1.56 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.56 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 0.97/1.56 ) }.
% 0.97/1.56 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.56 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 0.97/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 0.97/1.56 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.97/1.56 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.97/1.56 , ! alpha12( X, Y, Z ) }.
% 0.97/1.56 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.97/1.56 , ! alpha24( X, Y, Z ) }.
% 0.97/1.56 { alpha12( X, Y, Z ), alpha24( X, Y, Z ), hBOOL( hAPP( Z,
% 0.97/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.97/1.56 { ! alpha24( X, Y, Z ), ! hBOOL( hAPP( Z, skol11( T, U, Z ) ) ) }.
% 0.97/1.56 { ! alpha24( X, Y, Z ), Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.97/1.56 skol11( X, Y, Z ) ) }.
% 0.97/1.56 { ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, T ), hBOOL( hAPP( Z, T
% 0.97/1.56 ) ), alpha24( X, Y, Z ) }.
% 0.97/1.56 { ! alpha12( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 0.97/1.56 }.
% 0.97/1.56 { ! alpha12( X, Y, Z ), ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero(
% 0.97/1.56 tc_Nat_Onat ) ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), hBOOL( hAPP( Z,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha12( X, Y, Z ) }.
% 0.97/1.56 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.97/1.56 , alpha13( X, Y, Z ) }.
% 0.97/1.56 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.97/1.56 , alpha25( X, Y, Z ) }.
% 0.97/1.56 { ! alpha13( X, Y, Z ), ! alpha25( X, Y, Z ), hBOOL( hAPP( Z,
% 0.97/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.97/1.56 { ! alpha25( X, Y, Z ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.97/1.56 T ), hBOOL( hAPP( Z, T ) ) }.
% 0.97/1.56 { ! hBOOL( hAPP( Z, skol12( T, U, Z ) ) ), alpha25( X, Y, Z ) }.
% 0.97/1.56 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, skol12( X, Y, Z ) ),
% 0.97/1.56 alpha25( X, Y, Z ) }.
% 0.97/1.56 { ! alpha13( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 0.97/1.56 ), hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.97/1.56 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), alpha13( X, Y, Z ) }
% 0.97/1.56 .
% 0.97/1.56 { ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha13
% 0.97/1.56 ( X, Y, Z ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.97/1.56 ( tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.97/1.56 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.97/1.56 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.97/1.56 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.56 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.56 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), X =
% 0.97/1.56 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.56 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.56 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), Y =
% 0.97/1.56 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.56 ( tc_Int_Oint ), X ), ! X = c_Groups_Oone__class_Oone( tc_Int_Oint ), ! Y
% 0.97/1.56 = c_Groups_Oone__class_Oone( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 0.97/1.56 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.97/1.56 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.56 c_RealVector_Onorm__class_Onorm( X, Z ), Y ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.56 c_RealVector_Onorm__class_Onorm( X, U ), T ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.56 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, Z, U
% 0.97/1.56 ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, T ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( X ),
% 0.97/1.56 c_Int_OMin ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.97/1.56 c_Int_OMin ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, c_Int_OMin ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( X ), c_Int_OMin
% 0.97/1.56 ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OMin, c_Int_OBit0
% 0.97/1.56 ( X ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OMin, X ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OMin, X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OMin, c_Int_OBit0(
% 0.97/1.56 X ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.97/1.56 tc_Int_Oint ) ), X ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.97/1.56 tc_Int_Oint ) ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X )
% 0.97/1.56 }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.97/1.56 tc_Int_Oint ) ), X ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.97/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.97/1.56 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X )
% 0.97/1.56 }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.97/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.97/1.56 tc_Int_Oint ) ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.97/1.56 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 0.97/1.56 ( tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.97/1.56 .
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.97/1.56 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 0.97/1.56 ( tc_Int_Oint ) ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.56 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.97/1.56 , Y ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) ),
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) =
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Orderings_Oord__class_Oless
% 0.97/1.56 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 0.97/1.56 { ! c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) =
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Orderings_Oord__class_Oless
% 0.97/1.56 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.56 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ),
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.56 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.56 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ),
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) ) }.
% 0.97/1.56 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ),
% 0.97/1.56 c_Groups_Oabs__class_Oabs( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.97/1.56 ), c_Int_Onumber__class_Onumber__of( X, c_Int_OMin ) ), Y ) ) =
% 0.97/1.56 c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.56 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.56 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 0.97/1.56 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.97/1.56 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.97/1.56 ( X, Y ) ) ), c_RealVector_Onorm__class_Onorm( X,
% 0.97/1.56 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.56 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.97/1.56 c_Power_Opower__class_Opower( X ), Y ), Z ) ), hAPP( hAPP(
% 0.97/1.56 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.56 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.56 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ),
% 0.97/1.56 c_Groups_Oone__class_Oone( X ) ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.56 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.56 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.56 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.56 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.56 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.56 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.56 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.56 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.56 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 0.97/1.56 c_Power_Opower__class_Opower( X ), T ), Z ) = hAPP( hAPP(
% 0.97/1.56 c_Power_Opower__class_Opower( X ), Y ), Z ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.97/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.56 X ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ), T = Y }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, c_Int_OPls ),
% 0.97/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) =
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) }.
% 0.97/1.56 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, c_Int_OPls ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Int_OPls ),
% 0.97/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) =
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) }.
% 0.97/1.56 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, c_Int_OPls ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Int_OPls ),
% 0.97/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) =
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 0.97/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.56 tc_Int_Oint ), c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.97/1.56 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.56 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.97/1.56 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) = X }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.56 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.97/1.56 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.56 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 0.97/1.56 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.56 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.56 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.56 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 0.97/1.56 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.56 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 0.97/1.56 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T,
% 0.97/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T,
% 0.97/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.56 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 0.97/1.56 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, hAPP
% 0.97/1.56 ( hAPP( c_Power_Opower__class_Opower( X ), Y ),
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.56 c_Int_OPls ) ) ) ) ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y )
% 0.97/1.56 , c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1
% 0.97/1.56 ( c_Int_OPls ) ) ) ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__idom( X ), hAPP( hAPP(
% 0.97/1.56 c_Power_Opower__class_Opower( X ), c_Groups_Oabs__class_Oabs( X, Y ) ),
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.56 c_Int_OPls ) ) ) ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ),
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.56 c_Int_OPls ) ) ) ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__semiring__1__strict( X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.56 ( X, T, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( X ), U ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), W
% 0.97/1.56 ), ! c_Groups_Oplus__class_Oplus( X, U, W ) = c_Groups_Oone__class_Oone
% 0.97/1.56 ( X ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X,
% 0.97/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), W ), T ) ), Y ) }.
% 0.97/1.56 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.56 tc_Nat_Onat ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0
% 0.97/1.56 ( c_Int_OBit1( c_Int_OPls ) ) ) ) }.
% 0.97/1.56 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.56 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), hAPP( hAPP
% 0.97/1.56 ( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.56 c_Power_Opower__class_Opower( X ), Z ), c_Groups_Ominus__class_Ominus(
% 0.97/1.56 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ), Z ) =
% 0.97/1.56 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, c_Int_OPls ), hAPP( hAPP
% 0.97/1.56 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Z ) ), hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) ), X ) ) =
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.56 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, c_Int_OPls ), hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Z ) ), hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) ), X ) ) = hAPP( hAPP
% 0.97/1.56 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ) ), X ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, c_Int_OPls ), hAPP( hAPP
% 0.97/1.56 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) ),
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) =
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.56 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, c_Int_OPls ), hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) ),
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) =
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OPls ), X ),
% 0.97/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.97/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y,
% 0.97/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit1( c_Int_OPls )
% 0.97/1.56 ) ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.56 ( tc_Nat_Onat ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ),
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) = c_Nat_OSuc(
% 0.97/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ),
% 0.97/1.56 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) }.
% 0.97/1.56 { c_NthRoot_Osqrt( hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.97/1.56 tc_RealDef_Oreal ), X ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 0.97/1.56 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) =
% 0.97/1.56 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) }.
% 0.97/1.56 { ! c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, X ), hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.56 c_Int_OPls ) ) ) ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, X,
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.56 c_Int_OPls ) ) ) ) ) = X }.
% 0.97/1.56 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.56 , hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ),
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.56 c_Int_OPls ) ) ) ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.56 , c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.97/1.56 c_Power_Opower__class_Opower( X ), Y ), c_Int_Onumber__class_Onumber__of
% 0.97/1.56 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ), ! Y =
% 0.97/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.97/1.56 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.56 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ),
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.56 c_Int_OPls ) ) ) ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.56 c_Int_OPls ) ) ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.97/1.56 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.56 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt(
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.97/1.56 c_Int_OBit1( c_Int_OPls ) ) ) ) ) }.
% 0.97/1.56 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.56 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_NthRoot_Osqrt(
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.97/1.56 c_Int_OBit1( c_Int_OPls ) ) ) ) ) }.
% 0.97/1.56 { ! c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, X ),
% 0.97/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.97/1.56 tc_Int_Oint, X, c_Groups_Oone__class_Oone( tc_Int_Oint ) ),
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.56 c_Int_OPls ) ) ) ) = c_Divides_Odiv__class_Odiv( tc_Int_Oint, X,
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.56 c_Int_OPls ) ) ) ) }.
% 0.97/1.56 { c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, X ),
% 0.97/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.97/1.56 tc_Int_Oint, X, c_Groups_Oone__class_Oone( tc_Int_Oint ) ),
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.56 c_Int_OPls ) ) ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.97/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X,
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.56 c_Int_OPls ) ) ) ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.56 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ),
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.56 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ),
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.56 c_Int_OPls ) ) ) ) ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.56 Z, Y ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.56 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.56 c_Power_Opower__class_Opower( X ), Z ), c_Int_Onumber__class_Onumber__of
% 0.97/1.56 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ), hAPP( hAPP(
% 0.97/1.56 c_Power_Opower__class_Opower( X ), Y ), c_Int_Onumber__class_Onumber__of
% 0.97/1.56 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ),
% 0.97/1.56 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.56 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 0.97/1.56 ( hAPP( c_Power_Opower__class_Opower( X ), Z ),
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.56 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ),
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.56 c_Int_OPls ) ) ) ) ) ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 0.97/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__idom( X ), Z = c_Groups_Ozero__class_Ozero( X
% 0.97/1.56 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Power_Opower__class_Opower
% 0.97/1.56 ( X ), Z ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0(
% 0.97/1.56 c_Int_OBit1( c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower
% 0.97/1.56 ( X ), Y ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0(
% 0.97/1.56 c_Int_OBit1( c_Int_OPls ) ) ) ) ) ) }.
% 0.97/1.56 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.97/1.56 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Power_Opower__class_Opower
% 0.97/1.56 ( X ), Z ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0(
% 0.97/1.56 c_Int_OBit1( c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower
% 0.97/1.56 ( X ), Y ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0(
% 0.97/1.56 c_Int_OBit1( c_Int_OPls ) ) ) ) ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.56 c_Int_OPls ) ) ) ), X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X =
% 0.97/1.56 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.97/1.56 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) )
% 0.97/1.56 , c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1
% 0.97/1.56 ( c_Int_OPls ) ) ) ) ) }.
% 0.97/1.56 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.56 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ), c_NthRoot_Osqrt(
% 0.97/1.56 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.56 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Y ),
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.56 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.97/1.56 tc_RealDef_Oreal ), X ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 0.97/1.56 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Divides_Odiv__class_Odiv
% 0.97/1.56 ( tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.97/1.56 c_Groups_Oone__class_Oone( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.56 c_Int_OPls ) ) ) ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.56 tc_Int_Oint ), c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0
% 0.97/1.56 ( c_Int_OBit1( c_Int_OPls ) ) ) ), X ) ) = c_Divides_Odiv__class_Odiv(
% 0.97/1.56 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.97/1.56 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.97/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.97/1.56 tc_Int_Oint, c_Groups_Oone__class_Oone( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0( c_Int_OBit1(
% 0.97/1.56 c_Int_OPls ) ) ) ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.56 tc_Int_Oint ), c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0
% 0.97/1.56 ( c_Int_OBit1( c_Int_OPls ) ) ) ), X ) ) = c_Divides_Odiv__class_Odiv(
% 0.97/1.56 tc_Int_Oint, Y, X ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ) ),
% 0.97/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Int_Onumber__class_Onumber__of
% 0.97/1.56 ( tc_Int_Oint, c_Int_OBit1( X ) ), c_Int_Onumber__class_Onumber__of(
% 0.97/1.56 tc_Int_Oint, c_Int_OBit0( Y ) ) ) = c_Divides_Odiv__class_Odiv(
% 0.97/1.56 tc_Int_Oint, c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ),
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ) ) }.
% 0.97/1.56 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ) ),
% 0.97/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Int_Onumber__class_Onumber__of
% 0.97/1.56 ( tc_Int_Oint, c_Int_OBit1( X ) ), c_Int_Onumber__class_Onumber__of(
% 0.97/1.56 tc_Int_Oint, c_Int_OBit0( Y ) ) ) = c_Divides_Odiv__class_Odiv(
% 0.97/1.56 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ),
% 0.97/1.56 c_Groups_Oone__class_Oone( tc_Int_Oint ) ),
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ) ) }.
% 0.97/1.56 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y = X,
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.97/1.56 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.97/1.56 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X = Y }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.97/1.56 { alpha29( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.97/1.56 hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.97/1.56 { alpha29( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP
% 0.97/1.56 ( X, Y ), Z ) ) }.
% 0.97/1.56 { ! alpha29( X, Y, Z ), alpha30( X, Y, Z ), Z = Y }.
% 0.97/1.56 { ! alpha29( X, Y, Z ), alpha30( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z
% 0.97/1.56 ) ) }.
% 0.97/1.56 { ! alpha30( X, Y, Z ), alpha29( X, Y, Z ) }.
% 0.97/1.56 { ! Z = Y, hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha29( X, Y, Z ) }.
% 0.97/1.56 { ! alpha30( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y )
% 0.97/1.56 }.
% 0.97/1.56 { ! alpha30( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP(
% 0.97/1.56 X, Y ), Z ) ), alpha30( X, Y, Z ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oabs__class_Oabs(
% 0.97/1.56 tc_Int_Oint, X ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X =
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.97/1.56 { ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oabs__class_Oabs(
% 0.97/1.56 tc_Int_Oint, X ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.97/1.56 { ! c_Groups_Oabs__class_Oabs( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) =
% 0.97/1.56 c_Groups_Oone__class_Oone( tc_Int_Oint ), c_Groups_Oabs__class_Oabs(
% 0.97/1.56 tc_Int_Oint, X ) = c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.56 ( tc_Int_Oint ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint )
% 0.97/1.56 , c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) ), X ) ), ! Y =
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X =
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.56 { Y = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.56 tc_Int_Oint ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ),
% 0.97/1.56 c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) ), X ) ) }.
% 0.97/1.56 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.56 tc_Int_Oint ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ),
% 0.97/1.56 c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) ), X ) ) }.
% 0.97/1.56 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.56 c_Power_Opower__class_Opower( tc_Int_Oint ), c_Groups_Oabs__class_Oabs(
% 0.97/1.56 tc_Int_Oint, Y ) ), X ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.56 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Z,
% 0.97/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Groups_Oplus__class_Oplus
% 0.97/1.56 ( tc_Int_Oint, c_Groups_Oabs__class_Oabs( tc_Int_Oint,
% 0.97/1.56 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, Z ) ),
% 0.97/1.56 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ), X ) ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.56 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.56 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Groups_Oplus__class_Oplus
% 0.97/1.56 ( tc_Int_Oint, c_Groups_Oabs__class_Oabs( tc_Int_Oint,
% 0.97/1.56 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ),
% 0.97/1.56 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ), X ) ), Y ) }.
% 0.97/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.56 }.
% 0.97/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X, Y,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X, Y,
% 0.97/1.56 c_Groups_Oone__class_Oone( X ) ) = Y }.
% 0.97/1.56 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.56 tc_Int_Oint ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.56 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ),
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.56 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.97/1.56 tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.97/1.56 tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.56 tc_Int_Oint ), Y ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.56 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ),
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.56 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.56 { ! class_Divides_Osemiring__div( X ), ! T = c_Groups_Ozero__class_Ozero( X
% 0.97/1.56 ), c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.97/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.56 { ! class_Divides_Osemiring__div( X ), T = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.56 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.97/1.56 c_Divides_Odiv__class_Odiv( X, Z, Y ) }.
% 0.97/1.56 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.56 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = Z }.
% 0.97/1.56 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.56 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) = Z }.
% 0.97/1.56 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.56 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.97/1.56 c_Divides_Odiv__class_Odiv( X, T, Z ) }.
% 0.97/1.56 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.56 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) =
% 0.97/1.56 c_Divides_Odiv__class_Odiv( X, T, Z ) }.
% 0.97/1.56 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.56 , c_Divides_Odiv__class_Odiv( X, Y, Y ) = c_Groups_Oone__class_Oone( X )
% 0.97/1.56 }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.97/1.56 tc_Int_Oint, X, Y ) ) }.
% 0.97/1.56 { ! c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X =
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), alpha14( X, Y ) }.
% 0.97/1.56 { ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.97/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.97/1.56 { ! alpha14( X, Y ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.97/1.56 { ! alpha14( X, Y ), alpha26( X, Y ), alpha27( X, Y ) }.
% 0.97/1.56 { ! alpha26( X, Y ), alpha14( X, Y ) }.
% 0.97/1.56 { ! alpha27( X, Y ), alpha14( X, Y ) }.
% 0.97/1.56 { ! alpha27( X, Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.56 { ! alpha27( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ), alpha27( X, Y ) }.
% 0.97/1.56 { ! alpha26( X, Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.97/1.56 { ! alpha26( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), alpha26( X, Y ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.56 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.97/1.56 tc_Int_Oint, Y, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.56 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.97/1.56 tc_Int_Oint, Y, X ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.56 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.97/1.56 tc_Int_Oint, Y, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X
% 0.97/1.56 , Y ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.56 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X
% 0.97/1.56 , Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.97/1.56 tc_Int_Oint, Y, X ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.56 tc_Int_Oint ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ),
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.56 tc_Int_Oint ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.56 tc_Int_Oint ), Y ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.56 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.97/1.56 tc_Int_Oint, X, Y ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.56 tc_Int_Oint ), Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.97/1.56 Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ),
% 0.97/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ),
% 0.97/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) =
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.97/1.56 tc_Int_Oint, Y, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y
% 0.97/1.56 , c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.97/1.56 tc_Int_Oint, Y, X ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.56 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.56 tc_Int_Oint ), Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.97/1.56 Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 0.97/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.97/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) =
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.56 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ),
% 0.97/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ),
% 0.97/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ) ) }.
% 0.97/1.56 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.97/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, X ) =
% 0.97/1.56 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.56 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.56 c_Groups_Oone__class_Oone( tc_Int_Oint ), Y ),
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.97/1.56 tc_Int_Oint, X, Y ), X ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.56 ( tc_Int_Oint ), X ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Z, hAPP(
% 0.97/1.56 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) =
% 0.97/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.97/1.56 tc_Int_Oint, Z, Y ), X ) }.
% 0.97/1.56 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Int_Onumber__class_Onumber__of
% 0.97/1.56 ( tc_Int_Oint, c_Int_OBit0( Y ) ), c_Int_Onumber__class_Onumber__of(
% 0.97/1.56 tc_Int_Oint, c_Int_OBit0( X ) ) ) = c_Divides_Odiv__class_Odiv(
% 0.97/1.56 tc_Int_Oint, c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 0.97/1.56 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) }.
% 0.97/1.56 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.56 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, T, hAPP
% 0.97/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) =
% 0.97/1.56 c_Groups_Oplus__class_Oplus( X, Z, c_Divides_Odiv__class_Odiv( X, T, Y )
% 0.97/1.56 ) }.
% 0.97/1.56 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.56 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, T, hAPP
% 0.97/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) =
% 0.97/1.56 c_Groups_Oplus__class_Oplus( X, Z, c_Divides_Odiv__class_Odiv( X, T, Y )
% 0.97/1.56 ) }.
% 0.97/1.56 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.56 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, Y, Z ),
% 0.97/1.56 Y ) = c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Z, Y
% 0.97/1.56 ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.97/1.56 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.56 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, Z, Y ),
% 0.97/1.56 Y ) = c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Z, Y
% 0.97/1.56 ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.97/1.56 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.97/1.56 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.56 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.97/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.97/1.56 ( tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.97/1.56 Z ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.97/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.56 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.97/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.56 { ! class_Orderings_Opreorder( X ), class_Orderings_Opreorder( tc_fun( Y, X
% 0.97/1.56 ) ) }.
% 0.97/1.56 { ! class_Orderings_Oorder( X ), class_Orderings_Oorder( tc_fun( Y, X ) ) }
% 0.97/1.56 .
% 0.97/1.56 { ! class_Orderings_Oord( X ), class_Orderings_Oord( tc_fun( Y, X ) ) }.
% 0.97/1.56 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.97/1.56 tc_Int_Oint ) }.
% 0.97/1.56 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.97/1.56 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Int_Oint ) }.
% 0.97/1.56 { class_Rings_Olinordered__comm__semiring__strict( tc_Int_Oint ) }.
% 0.97/1.56 { class_Rings_Olinordered__semiring__1__strict( tc_Int_Oint ) }.
% 0.97/1.56 { class_Rings_Olinordered__semiring__strict( tc_Int_Oint ) }.
% 0.97/1.56 { class_Groups_Oordered__ab__semigroup__add( tc_Int_Oint ) }.
% 0.97/1.56 { class_Groups_Oordered__ab__group__add__abs( tc_Int_Oint ) }.
% 0.97/1.56 { class_Groups_Oordered__comm__monoid__add( tc_Int_Oint ) }.
% 0.97/1.56 { class_Groups_Olinordered__ab__group__add( tc_Int_Oint ) }.
% 0.97/1.56 { class_Groups_Ocancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.97/1.56 { class_Rings_Oring__1__no__zero__divisors( tc_Int_Oint ) }.
% 0.97/1.56 { class_Rings_Oordered__cancel__semiring( tc_Int_Oint ) }.
% 0.97/1.56 { class_Rings_Olinordered__ring__strict( tc_Int_Oint ) }.
% 0.97/1.56 { class_Rings_Oring__no__zero__divisors( tc_Int_Oint ) }.
% 0.97/1.56 { class_Rings_Oordered__comm__semiring( tc_Int_Oint ) }.
% 0.97/1.56 { class_Rings_Olinordered__semiring__1( tc_Int_Oint ) }.
% 0.97/1.56 { class_Groups_Oordered__ab__group__add( tc_Int_Oint ) }.
% 0.97/1.56 { class_Groups_Ocancel__semigroup__add( tc_Int_Oint ) }.
% 0.97/1.56 { class_Rings_Olinordered__semiring( tc_Int_Oint ) }.
% 0.97/1.56 { class_Rings_Olinordered__semidom( tc_Int_Oint ) }.
% 0.97/1.56 { class_Groups_Oab__semigroup__mult( tc_Int_Oint ) }.
% 0.97/1.56 { class_Groups_Ocomm__monoid__mult( tc_Int_Oint ) }.
% 0.97/1.56 { class_Groups_Oab__semigroup__add( tc_Int_Oint ) }.
% 0.97/1.56 { class_Rings_Oordered__semiring( tc_Int_Oint ) }.
% 0.97/1.56 { class_Rings_Oordered__ring__abs( tc_Int_Oint ) }.
% 0.97/1.56 { class_Rings_Ono__zero__divisors( tc_Int_Oint ) }.
% 0.97/1.56 { class_Groups_Ocomm__monoid__add( tc_Int_Oint ) }.
% 0.97/1.56 { class_Rings_Olinordered__ring( tc_Int_Oint ) }.
% 0.97/1.56 { class_Rings_Olinordered__idom( tc_Int_Oint ) }.
% 0.97/1.56 { class_Rings_Ocomm__semiring__1( tc_Int_Oint ) }.
% 0.97/1.56 { class_Divides_Osemiring__div( tc_Int_Oint ) }.
% 0.97/1.56 { class_Rings_Ocomm__semiring( tc_Int_Oint ) }.
% 0.97/1.56 { class_Groups_Oab__group__add( tc_Int_Oint ) }.
% 0.97/1.56 { class_Rings_Ozero__neq__one( tc_Int_Oint ) }.
% 0.97/1.56 { class_Rings_Oordered__ring( tc_Int_Oint ) }.
% 0.97/1.56 { class_Orderings_Opreorder( tc_Int_Oint ) }.
% 0.97/1.56 { class_Orderings_Olinorder( tc_Int_Oint ) }.
% 0.97/1.56 { class_Groups_Omonoid__mult( tc_Int_Oint ) }.
% 0.97/1.56 { class_Rings_Ocomm__ring__1( tc_Int_Oint ) }.
% 0.97/1.56 { class_Groups_Omonoid__add( tc_Int_Oint ) }.
% 0.97/1.56 { class_Rings_Osemiring__1( tc_Int_Oint ) }.
% 0.97/1.56 { class_Rings_Osemiring__0( tc_Int_Oint ) }.
% 0.97/1.56 { class_Groups_Ogroup__add( tc_Int_Oint ) }.
% 0.97/1.56 { class_Rings_Omult__zero( tc_Int_Oint ) }.
% 0.97/1.56 { class_Orderings_Oorder( tc_Int_Oint ) }.
% 0.97/1.56 { class_Int_Oring__char__0( tc_Int_Oint ) }.
% 0.97/1.56 { class_Int_Onumber__ring( tc_Int_Oint ) }.
% 0.97/1.56 { class_Rings_Osemiring( tc_Int_Oint ) }.
% 0.97/1.56 { class_Orderings_Oord( tc_Int_Oint ) }.
% 0.97/1.56 { class_Rings_Oring__1( tc_Int_Oint ) }.
% 0.97/1.56 { class_Power_Opower( tc_Int_Oint ) }.
% 0.97/1.56 { class_Groups_Ozero( tc_Int_Oint ) }.
% 0.97/1.56 { class_Rings_Oring( tc_Int_Oint ) }.
% 0.97/1.56 { class_Int_Onumber( tc_Int_Oint ) }.
% 0.97/1.56 { class_Groups_Oone( tc_Int_Oint ) }.
% 0.97/1.56 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.97/1.56 tc_Nat_Onat ) }.
% 0.97/1.56 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.97/1.56 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Nat_Onat ) }.
% 0.97/1.56 { class_Rings_Olinordered__comm__semiring__strict( tc_Nat_Onat ) }.
% 0.97/1.56 { class_Rings_Olinordered__semiring__strict( tc_Nat_Onat ) }.
% 0.97/1.56 { class_Groups_Oordered__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.97/1.56 { class_Groups_Oordered__comm__monoid__add( tc_Nat_Onat ) }.
% 0.97/1.56 { class_Groups_Ocancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.97/1.56 { class_Rings_Oordered__cancel__semiring( tc_Nat_Onat ) }.
% 0.97/1.56 { class_Rings_Oordered__comm__semiring( tc_Nat_Onat ) }.
% 0.97/1.56 { class_Groups_Ocancel__semigroup__add( tc_Nat_Onat ) }.
% 0.97/1.56 { class_Rings_Olinordered__semiring( tc_Nat_Onat ) }.
% 0.97/1.56 { class_Rings_Olinordered__semidom( tc_Nat_Onat ) }.
% 0.97/1.56 { class_Groups_Oab__semigroup__mult( tc_Nat_Onat ) }.
% 0.97/1.56 { class_Groups_Ocomm__monoid__mult( tc_Nat_Onat ) }.
% 0.97/1.56 { class_Groups_Oab__semigroup__add( tc_Nat_Onat ) }.
% 0.97/1.56 { class_Rings_Oordered__semiring( tc_Nat_Onat ) }.
% 0.97/1.56 { class_Rings_Ono__zero__divisors( tc_Nat_Onat ) }.
% 0.97/1.56 { class_Groups_Ocomm__monoid__add( tc_Nat_Onat ) }.
% 0.97/1.56 { class_Rings_Ocomm__semiring__1( tc_Nat_Onat ) }.
% 0.97/1.56 { class_Divides_Osemiring__div( tc_Nat_Onat ) }.
% 0.97/1.56 { class_Rings_Ocomm__semiring( tc_Nat_Onat ) }.
% 0.97/1.56 { class_Rings_Ozero__neq__one( tc_Nat_Onat ) }.
% 0.97/1.56 { class_Orderings_Opreorder( tc_Nat_Onat ) }.
% 0.97/1.56 { class_Orderings_Olinorder( tc_Nat_Onat ) }.
% 0.97/1.56 { class_Groups_Omonoid__mult( tc_Nat_Onat ) }.
% 0.97/1.56 { class_Groups_Omonoid__add( tc_Nat_Onat ) }.
% 0.97/1.56 { class_Rings_Osemiring__1( tc_Nat_Onat ) }.
% 0.97/1.56 { class_Rings_Osemiring__0( tc_Nat_Onat ) }.
% 0.97/1.56 { class_Rings_Omult__zero( tc_Nat_Onat ) }.
% 0.97/1.56 { class_Orderings_Oorder( tc_Nat_Onat ) }.
% 0.97/1.56 { class_Rings_Osemiring( tc_Nat_Onat ) }.
% 0.97/1.56 { class_Orderings_Oord( tc_Nat_Onat ) }.
% 0.97/1.56 { class_Power_Opower( tc_Nat_Onat ) }.
% 0.97/1.56 { class_Groups_Ozero( tc_Nat_Onat ) }.
% 0.97/1.56 { class_Int_Onumber( tc_Nat_Onat ) }.
% 0.97/1.56 { class_Groups_Oone( tc_Nat_Onat ) }.
% 0.97/1.56 { class_Orderings_Opreorder( tc_HOL_Obool ) }.
% 0.97/1.56 { class_Orderings_Oorder( tc_HOL_Obool ) }.
% 0.97/1.56 { class_Orderings_Oord( tc_HOL_Obool ) }.
% 0.97/1.56 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.97/1.56 tc_RealDef_Oreal ) }.
% 0.97/1.56 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.97/1.56 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_RealDef_Oreal ) }
% 0.97/1.56 .
% 0.97/1.56 { class_Rings_Olinordered__comm__semiring__strict( tc_RealDef_Oreal ) }.
% 0.97/1.56 { class_Rings_Olinordered__semiring__1__strict( tc_RealDef_Oreal ) }.
% 0.97/1.56 { class_RealVector_Oreal__normed__div__algebra( tc_RealDef_Oreal ) }.
% 0.97/1.56 { class_Rings_Olinordered__semiring__strict( tc_RealDef_Oreal ) }.
% 0.97/1.56 { class_RealVector_Oreal__normed__algebra__1( tc_RealDef_Oreal ) }.
% 0.97/1.56 { class_Groups_Oordered__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.97/1.56 { class_Groups_Oordered__ab__group__add__abs( tc_RealDef_Oreal ) }.
% 0.97/1.56 { class_RealVector_Oreal__normed__algebra( tc_RealDef_Oreal ) }.
% 0.97/1.56 { class_Groups_Oordered__comm__monoid__add( tc_RealDef_Oreal ) }.
% 0.97/1.56 { class_Groups_Olinordered__ab__group__add( tc_RealDef_Oreal ) }.
% 0.97/1.56 { class_Groups_Ocancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.97/1.56 { class_Rings_Oring__1__no__zero__divisors( tc_RealDef_Oreal ) }.
% 0.97/1.56 { class_Rings_Oordered__cancel__semiring( tc_RealDef_Oreal ) }.
% 0.97/1.56 { class_RealVector_Oreal__normed__vector( tc_RealDef_Oreal ) }.
% 0.97/1.56 { class_Rings_Olinordered__ring__strict( tc_RealDef_Oreal ) }.
% 0.97/1.56 { class_Rings_Oring__no__zero__divisors( tc_RealDef_Oreal ) }.
% 0.97/1.56 { class_Rings_Oordered__comm__semiring( tc_RealDef_Oreal ) }.
% 0.97/1.56 { class_Rings_Olinordered__semiring__1( tc_RealDef_Oreal ) }.
% 0.97/1.56 { class_Groups_Oordered__ab__group__add( tc_RealDef_Oreal ) }.
% 0.97/1.56 { class_Groups_Ocancel__semigroup__add( tc_RealDef_Oreal ) }.
% 0.97/1.56 { class_Rings_Olinordered__semiring( tc_RealDef_Oreal ) }.
% 0.97/1.56 { class_Rings_Olinordered__semidom( tc_RealDef_Oreal ) }.
% 0.97/1.56 { class_Groups_Oab__semigroup__mult( tc_RealDef_Oreal ) }.
% 0.97/1.56 { class_Groups_Ocomm__monoid__mult( tc_RealDef_Oreal ) }.
% 0.97/1.56 { class_Groups_Oab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.97/1.56 { class_Rings_Oordered__semiring( tc_RealDef_Oreal ) }.
% 0.97/1.56 { class_Rings_Oordered__ring__abs( tc_RealDef_Oreal ) }.
% 0.97/1.56 { class_Rings_Ono__zero__divisors( tc_RealDef_Oreal ) }.
% 0.97/1.56 { class_Groups_Ocomm__monoid__add( tc_RealDef_Oreal ) }.
% 0.97/1.56 { class_Rings_Olinordered__ring( tc_RealDef_Oreal ) }.
% 0.97/1.56 { class_Rings_Olinordered__idom( tc_RealDef_Oreal ) }.
% 0.97/1.56 { class_Rings_Ocomm__semiring__1( tc_RealDef_Oreal ) }.
% 0.97/1.56 { class_Rings_Ocomm__semiring( tc_RealDef_Oreal ) }.
% 0.97/1.56 { class_Groups_Oab__group__add( tc_RealDef_Oreal ) }.
% 0.97/1.56 { class_Rings_Ozero__neq__one( tc_RealDef_Oreal ) }.
% 0.97/1.56 { class_Rings_Oordered__ring( tc_RealDef_Oreal ) }.
% 0.97/1.56 { class_Orderings_Opreorder( tc_RealDef_Oreal ) }.
% 0.97/1.56 { class_Orderings_Olinorder( tc_RealDef_Oreal ) }.
% 0.97/1.56 { class_Groups_Omonoid__mult( tc_RealDef_Oreal ) }.
% 0.97/1.56 { class_Rings_Ocomm__ring__1( tc_RealDef_Oreal ) }.
% 0.97/1.56 { class_Groups_Omonoid__add( tc_RealDef_Oreal ) }.
% 0.97/1.56 { class_Rings_Osemiring__1( tc_RealDef_Oreal ) }.
% 0.97/1.56 { class_Rings_Osemiring__0( tc_RealDef_Oreal ) }.
% 0.97/1.56 { class_Groups_Ogroup__add( tc_RealDef_Oreal ) }.
% 0.97/1.56 { class_Rings_Omult__zero( tc_RealDef_Oreal ) }.
% 0.97/1.56 { class_Orderings_Oorder( tc_RealDef_Oreal ) }.
% 0.97/1.56 { class_Int_Oring__char__0( tc_RealDef_Oreal ) }.
% 0.97/1.56 { class_Int_Onumber__ring( tc_RealDef_Oreal ) }.
% 0.97/1.56 { class_Rings_Osemiring( tc_RealDef_Oreal ) }.
% 0.97/1.56 { class_Orderings_Oord( tc_RealDef_Oreal ) }.
% 0.97/1.56 { class_Rings_Oring__1( tc_RealDef_Oreal ) }.
% 0.97/1.56 { class_Power_Opower( tc_RealDef_Oreal ) }.
% 0.97/1.56 { class_Groups_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.56 { class_Rings_Oring( tc_RealDef_Oreal ) }.
% 0.97/1.56 { class_Int_Onumber( tc_RealDef_Oreal ) }.
% 0.97/1.56 { class_Groups_Oone( tc_RealDef_Oreal ) }.
% 0.97/1.56 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.97/1.56 tc_Complex_Ocomplex ) }.
% 0.97/1.56 { class_RealVector_Oreal__normed__div__algebra( tc_Complex_Ocomplex ) }.
% 0.97/1.56 { class_RealVector_Oreal__normed__algebra__1( tc_Complex_Ocomplex ) }.
% 0.97/1.56 { class_RealVector_Oreal__normed__algebra( tc_Complex_Ocomplex ) }.
% 0.97/1.56 { class_Groups_Ocancel__ab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.97/1.56 { class_Rings_Oring__1__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.97/1.56 { class_RealVector_Oreal__normed__vector( tc_Complex_Ocomplex ) }.
% 0.97/1.56 { class_Rings_Oring__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.97/1.56 { class_Groups_Ocancel__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.97/1.56 { class_Groups_Oab__semigroup__mult( tc_Complex_Ocomplex ) }.
% 0.97/1.56 { class_Groups_Ocomm__monoid__mult( tc_Complex_Ocomplex ) }.
% 0.97/1.56 { class_Groups_Oab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.97/1.56 { class_Rings_Ono__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.97/1.56 { class_Groups_Ocomm__monoid__add( tc_Complex_Ocomplex ) }.
% 0.97/1.56 { class_Rings_Ocomm__semiring__1( tc_Complex_Ocomplex ) }.
% 0.97/1.56 { class_Rings_Ocomm__semiring( tc_Complex_Ocomplex ) }.
% 0.97/1.56 { class_Groups_Oab__group__add( tc_Complex_Ocomplex ) }.
% 0.97/1.56 { class_Rings_Ozero__neq__one( tc_Complex_Ocomplex ) }.
% 0.97/1.56 { class_Groups_Omonoid__mult( tc_Complex_Ocomplex ) }.
% 0.97/1.56 { class_Rings_Ocomm__ring__1( tc_Complex_Ocomplex ) }.
% 0.97/1.56 { class_Groups_Omonoid__add( tc_Complex_Ocomplex ) }.
% 0.97/1.56 { class_Rings_Osemiring__1( tc_Complex_Ocomplex ) }.
% 0.97/1.56 { class_Rings_Osemiring__0( tc_Complex_Ocomplex ) }.
% 0.97/1.56 { class_Groups_Ogroup__add( tc_Complex_Ocomplex ) }.
% 0.97/1.56 { class_Rings_Omult__zero( tc_Complex_Ocomplex ) }.
% 0.97/1.56 { class_Int_Oring__char__0( tc_Complex_Ocomplex ) }.
% 0.97/1.56 { class_Int_Onumber__ring( tc_Complex_Ocomplex ) }.
% 0.97/1.56 { class_Rings_Osemiring( tc_Complex_Ocomplex ) }.
% 0.97/1.56 { class_Rings_Oring__1( tc_Complex_Ocomplex ) }.
% 0.97/1.56 { class_Power_Opower( tc_Complex_Ocomplex ) }.
% 0.97/1.56 { class_Groups_Ozero( tc_Complex_Ocomplex ) }.
% 0.97/1.56 { class_Rings_Oring( tc_Complex_Ocomplex ) }.
% 0.97/1.56 { class_Int_Onumber( tc_Complex_Ocomplex ) }.
% 0.97/1.56 { class_Groups_Oone( tc_Complex_Ocomplex ) }.
% 0.97/1.56 { class_Groups_Oordered__cancel__ab__semigroup__add(
% 0.97/1.56 tc_Code__Numeral_Ocode__numeral ) }.
% 0.97/1.56 { class_Groups_Oordered__ab__semigroup__add__imp__le(
% 0.97/1.56 tc_Code__Numeral_Ocode__numeral ) }.
% 0.97/1.56 { class_Rings_Olinordered__comm__semiring__strict(
% 0.97/1.56 tc_Code__Numeral_Ocode__numeral ) }.
% 0.97/1.56 { class_Rings_Olinordered__semiring__strict(
% 0.97/1.57 tc_Code__Numeral_Ocode__numeral ) }.
% 0.97/1.57 { class_Groups_Oordered__ab__semigroup__add(
% 0.97/1.57 tc_Code__Numeral_Ocode__numeral ) }.
% 0.97/1.57 { class_Groups_Oordered__comm__monoid__add( tc_Code__Numeral_Ocode__numeral
% 0.97/1.57 ) }.
% 0.97/1.57 { class_Groups_Ocancel__ab__semigroup__add( tc_Code__Numeral_Ocode__numeral
% 0.97/1.57 ) }.
% 0.97/1.57 { class_Rings_Oordered__cancel__semiring( tc_Code__Numeral_Ocode__numeral )
% 0.97/1.57 }.
% 0.97/1.57 { class_Rings_Oordered__comm__semiring( tc_Code__Numeral_Ocode__numeral ) }
% 0.97/1.57 .
% 0.97/1.57 { class_Groups_Ocancel__semigroup__add( tc_Code__Numeral_Ocode__numeral ) }
% 0.97/1.57 .
% 0.97/1.57 { class_Rings_Olinordered__semiring( tc_Code__Numeral_Ocode__numeral ) }.
% 0.97/1.57 { class_Rings_Olinordered__semidom( tc_Code__Numeral_Ocode__numeral ) }.
% 0.97/1.57 { class_Groups_Oab__semigroup__mult( tc_Code__Numeral_Ocode__numeral ) }.
% 0.97/1.57 { class_Groups_Ocomm__monoid__mult( tc_Code__Numeral_Ocode__numeral ) }.
% 0.97/1.57 { class_Groups_Oab__semigroup__add( tc_Code__Numeral_Ocode__numeral ) }.
% 0.97/1.57 { class_Rings_Oordered__semiring( tc_Code__Numeral_Ocode__numeral ) }.
% 0.97/1.57 { class_Rings_Ono__zero__divisors( tc_Code__Numeral_Ocode__numeral ) }.
% 0.97/1.57 { class_Groups_Ocomm__monoid__add( tc_Code__Numeral_Ocode__numeral ) }.
% 0.97/1.57 { class_Rings_Ocomm__semiring__1( tc_Code__Numeral_Ocode__numeral ) }.
% 0.97/1.57 { class_Divides_Osemiring__div( tc_Code__Numeral_Ocode__numeral ) }.
% 0.97/1.57 { class_Rings_Ocomm__semiring( tc_Code__Numeral_Ocode__numeral ) }.
% 0.97/1.57 { class_Rings_Ozero__neq__one( tc_Code__Numeral_Ocode__numeral ) }.
% 0.97/1.57 { class_Orderings_Opreorder( tc_Code__Numeral_Ocode__numeral ) }.
% 0.97/1.57 { class_Orderings_Olinorder( tc_Code__Numeral_Ocode__numeral ) }.
% 0.97/1.57 { class_Groups_Omonoid__mult( tc_Code__Numeral_Ocode__numeral ) }.
% 0.97/1.57 { class_Groups_Omonoid__add( tc_Code__Numeral_Ocode__numeral ) }.
% 0.97/1.57 { class_Rings_Osemiring__1( tc_Code__Numeral_Ocode__numeral ) }.
% 0.97/1.57 { class_Rings_Osemiring__0( tc_Code__Numeral_Ocode__numeral ) }.
% 0.97/1.57 { class_Rings_Omult__zero( tc_Code__Numeral_Ocode__numeral ) }.
% 0.97/1.57 { class_Orderings_Oorder( tc_Code__Numeral_Ocode__numeral ) }.
% 0.97/1.57 { class_Rings_Osemiring( tc_Code__Numeral_Ocode__numeral ) }.
% 0.97/1.57 { class_Orderings_Oord( tc_Code__Numeral_Ocode__numeral ) }.
% 0.97/1.57 { class_Power_Opower( tc_Code__Numeral_Ocode__numeral ) }.
% 0.97/1.57 { class_Groups_Ozero( tc_Code__Numeral_Ocode__numeral ) }.
% 0.97/1.57 { class_Int_Onumber( tc_Code__Numeral_Ocode__numeral ) }.
% 0.97/1.57 { class_Groups_Oone( tc_Code__Numeral_Ocode__numeral ) }.
% 0.97/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.57 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.97/1.57 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.97/1.57 c_Int_OBit1( c_Int_OPls ) ) ) ), v_x____ ), c_Groups_Oone__class_Oone(
% 0.97/1.57 tc_RealDef_Oreal ) ) }.
% 0.97/1.57
% 0.97/1.57 *** allocated 15000 integers for clauses
% 0.97/1.57 *** allocated 22500 integers for clauses
% 0.97/1.57 *** allocated 33750 integers for clauses
% 0.97/1.57 *** allocated 50625 integers for clauses
% 0.97/1.57 *** allocated 75937 integers for clauses
% 0.97/1.57 percentage equality = 0.273588, percentage horn = 0.923797
% 0.97/1.57 This is a problem with some equality
% 0.97/1.57
% 0.97/1.57
% 0.97/1.57
% 0.97/1.57 Options Used:
% 0.97/1.57
% 0.97/1.57 useres = 1
% 0.97/1.57 useparamod = 1
% 0.97/1.57 useeqrefl = 1
% 0.97/1.57 useeqfact = 1
% 0.97/1.57 usefactor = 1
% 0.97/1.57 usesimpsplitting = 0
% 0.97/1.57 usesimpdemod = 5
% 0.97/1.57 usesimpres = 3
% 0.97/1.57
% 0.97/1.57 resimpinuse = 1000
% 0.97/1.57 resimpclauses = 20000
% 0.97/1.57 substype = eqrewr
% 0.97/1.57 backwardsubs = 1
% 0.97/1.57 selectoldest = 5
% 0.97/1.57
% 0.97/1.57 litorderings [0] = split
% 0.97/1.57 litorderings [1] = extend the termordering, first sorting on arguments
% 0.97/1.57
% 0.97/1.57 termordering = kbo
% 0.97/1.57
% 0.97/1.57 litapriori = 0
% 0.97/1.57 termapriori = 1
% 0.97/1.57 litaposteriori = 0
% 0.97/1.57 termaposteriori = 0
% 0.97/1.57 demodaposteriori = 0
% 0.97/1.57 ordereqreflfact = 0
% 0.97/1.57
% 0.97/1.57 litselect = negord
% 0.97/1.57
% 0.97/1.57 maxweight = 15
% 0.97/1.57 maxdepth = 30000
% 0.97/1.57 maxlength = 115
% 0.97/1.57 maxnrvars = 195
% 0.97/1.57 excuselevel = 1
% 0.97/1.57 increasemaxweight = 1
% 0.97/1.57
% 0.97/1.57 maxselected = 10000000
% 0.97/1.57 maxnrclauses = 10000000
% 0.97/1.57
% 0.97/1.57 showgenerated = 0
% 0.97/1.57 showkept = 0
% 0.97/1.57 showselected = 0
% 0.97/1.57 showdeleted = 0
% 0.97/1.57 showresimp = 1
% 0.97/1.57 showstatus = 2000
% 0.97/1.57
% 0.97/1.57 prologoutput = 0
% 0.97/1.57 nrgoals = 5000000
% 0.97/1.57 totalproof = 1
% 0.97/1.57
% 0.97/1.57 Symbols occurring in the translation:
% 0.97/1.57
% 0.97/1.57 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.97/1.57 . [1, 2] (w:1, o:185, a:1, s:1, b:0),
% 0.97/1.57 ! [4, 1] (w:0, o:106, a:1, s:1, b:0),
% 0.97/1.57 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.97/1.57 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.97/1.57 hAPP [38, 2] (w:1, o:209, a:1, s:1, b:0),
% 0.97/1.57 class_Int_Onumber__ring [41, 1] (w:1, o:111, a:1, s:1, b:0),
% 0.97/1.57 class_Rings_Olinordered__idom [42, 1] (w:1, o:112, a:1, s:1, b:0),
% 0.97/1.57 c_Groups_Oone__class_Oone [43, 1] (w:1, o:114, a:1, s:1, b:0),
% 0.97/1.57 c_Int_Onumber__class_Onumber__of [44, 2] (w:1, o:210, a:1, s:1, b:0)
% 0.97/1.57 ,
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq [45, 3] (w:1, o:239, a:1, s:1, b:0)
% 0.97/1.57 ,
% 0.97/1.57 tc_Int_Oint [46, 0] (w:1, o:30, a:1, s:1, b:0),
% 0.97/1.57 c_Int_OPls [47, 0] (w:1, o:31, a:1, s:1, b:0),
% 0.97/1.57 c_Int_OBit1 [48, 1] (w:1, o:116, a:1, s:1, b:0),
% 0.97/1.57 c_Groups_Otimes__class_Otimes [51, 1] (w:1, o:117, a:1, s:1, b:0),
% 0.97/1.57 class_Orderings_Opreorder [53, 1] (w:1, o:120, a:1, s:1, b:0),
% 0.97/1.57 v_z [54, 0] (w:1, o:34, a:1, s:1, b:0),
% 0.97/1.57 v_x____ [55, 0] (w:1, o:35, a:1, s:1, b:0),
% 0.97/1.57 v_y____ [56, 0] (w:1, o:33, a:1, s:1, b:0),
% 0.97/1.57 c_Complex_Ocomplex_OComplex [57, 2] (w:1, o:211, a:1, s:1, b:0),
% 0.97/1.57 tc_RealDef_Oreal [59, 0] (w:1, o:39, a:1, s:1, b:0),
% 0.97/1.57 c_Int_OBit0 [60, 1] (w:1, o:115, a:1, s:1, b:0),
% 0.97/1.57 tc_Complex_Ocomplex [63, 0] (w:1, o:48, a:1, s:1, b:0),
% 0.97/1.57 c_RealVector_Onorm__class_Onorm [64, 2] (w:1, o:212, a:1, s:1, b:0),
% 0.97/1.57
% 0.97/1.57 tc_Nat_Onat [68, 0] (w:1, o:49, a:1, s:1, b:0),
% 0.97/1.57 class_Orderings_Olinorder [76, 1] (w:1, o:121, a:1, s:1, b:0),
% 0.97/1.57 class_Orderings_Oord [78, 1] (w:1, o:118, a:1, s:1, b:0),
% 0.97/1.57 tc_fun [79, 2] (w:1, o:218, a:1, s:1, b:0),
% 0.97/1.57 class_Orderings_Oorder [80, 1] (w:1, o:119, a:1, s:1, b:0),
% 0.97/1.57 class_Int_Oring__char__0 [83, 1] (w:1, o:122, a:1, s:1, b:0),
% 0.97/1.57 class_Int_Onumber [85, 1] (w:1, o:123, a:1, s:1, b:0),
% 0.97/1.57 c_Power_Opower__class_Opower [90, 1] (w:1, o:124, a:1, s:1, b:0),
% 0.97/1.57 c_Groups_Oplus__class_Oplus [91, 3] (w:1, o:240, a:1, s:1, b:0),
% 0.97/1.57 c_Groups_Ominus__class_Ominus [93, 3] (w:1, o:241, a:1, s:1, b:0),
% 0.97/1.57 tc_Code__Numeral_Ocode__numeral [94, 0] (w:1, o:63, a:1, s:1, b:0),
% 0.97/1.57 class_Groups_Ocomm__monoid__mult [95, 1] (w:1, o:125, a:1, s:1, b:0)
% 0.97/1.68 ,
% 0.97/1.68 class_Rings_Ocomm__semiring__1 [96, 1] (w:1, o:127, a:1, s:1, b:0),
% 0.97/1.68 class_Groups_Omonoid__mult [97, 1] (w:1, o:129, a:1, s:1, b:0),
% 0.97/1.68 c_Complex_Oii [99, 0] (w:1, o:69, a:1, s:1, b:0),
% 0.97/1.68 class_Groups_Oab__group__add [106, 1] (w:1, o:130, a:1, s:1, b:0),
% 0.97/1.68 class_Groups_Ocancel__semigroup__add [107, 1] (w:1, o:131, a:1, s:1
% 0.97/1.68 , b:0),
% 0.97/1.68 class_Groups_Ocancel__ab__semigroup__add [108, 1] (w:1, o:132, a:1
% 0.97/1.68 , s:1, b:0),
% 0.97/1.68 class_Groups_Oab__semigroup__add [110, 1] (w:1, o:133, a:1, s:1, b:0)
% 0.97/1.68 ,
% 0.97/1.68 class_Groups_Ogroup__add [111, 1] (w:1, o:134, a:1, s:1, b:0),
% 0.97/1.68 class_Rings_Oring [112, 1] (w:1, o:135, a:1, s:1, b:0),
% 0.97/1.68 class_Groups_Oordered__ab__group__add [113, 1] (w:1, o:136, a:1, s:1
% 0.97/1.68 , b:0),
% 0.97/1.68 class_Groups_Oordered__ab__semigroup__add__imp__le [114, 1] (w:1, o:
% 0.97/1.68 137, a:1, s:1, b:0),
% 0.97/1.68 class_Groups_Oordered__ab__semigroup__add [115, 1] (w:1, o:138, a:1
% 0.97/1.68 , s:1, b:0),
% 0.97/1.68 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct [
% 0.97/1.68 116, 1] (w:1, o:166, a:1, s:1, b:0),
% 0.97/1.68 class_Rings_Oring__1 [119, 1] (w:1, o:139, a:1, s:1, b:0),
% 0.97/1.68 class_Rings_Osemiring [120, 1] (w:1, o:142, a:1, s:1, b:0),
% 0.97/1.68 class_Groups_Oab__semigroup__mult [124, 1] (w:1, o:167, a:1, s:1, b:0
% 0.97/1.68 ),
% 0.97/1.68 class_Groups_Oone [126, 1] (w:1, o:168, a:1, s:1, b:0),
% 0.97/1.68 class_Rings_Osemiring__1 [127, 1] (w:1, o:144, a:1, s:1, b:0),
% 0.97/1.68 class_RealVector_Oreal__normed__vector [128, 1] (w:1, o:145, a:1, s:1
% 0.97/1.68 , b:0),
% 0.97/1.68 class_RealVector_Oreal__normed__algebra__1 [129, 1] (w:1, o:146, a:1
% 0.97/1.68 , s:1, b:0),
% 0.97/1.68 class_RealVector_Oreal__normed__algebra [130, 1] (w:1, o:147, a:1, s:
% 0.97/1.68 1, b:0),
% 0.97/1.68 class_Rings_Olinordered__semidom [132, 1] (w:1, o:150, a:1, s:1, b:0)
% 0.97/1.68 ,
% 0.97/1.68 class_Rings_Oordered__ring [134, 1] (w:1, o:152, a:1, s:1, b:0),
% 0.97/1.68 class_Rings_Ocomm__semiring [142, 1] (w:1, o:153, a:1, s:1, b:0),
% 0.97/1.68 class_RealVector_Oreal__normed__div__algebra [145, 1] (w:1, o:154, a:
% 0.97/1.68 1, s:1, b:0),
% 0.97/1.68 c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt [146, 1] (w:1, o:
% 0.97/1.68 113, a:1, s:1, b:0),
% 0.97/1.68 c_Complex_Ocomplex_Ocomplex__rec [148, 3] (w:1, o:242, a:1, s:1, b:0)
% 0.97/1.68 ,
% 0.97/1.68 c_Complex_Ocomplex_Ocomplex__case [149, 3] (w:1, o:243, a:1, s:1, b:0
% 0.97/1.68 ),
% 0.97/1.68 c_Int_OMin [150, 0] (w:1, o:90, a:1, s:1, b:0),
% 0.97/1.68 class_Power_Opower [151, 1] (w:1, o:169, a:1, s:1, b:0),
% 0.97/1.68 c_Power_Opower_Opower [152, 3] (w:1, o:245, a:1, s:1, b:0),
% 0.97/1.68 c_NthRoot_Osqrt [153, 1] (w:1, o:170, a:1, s:1, b:0),
% 0.97/1.68 c_Groups_Ozero__class_Ozero [154, 1] (w:1, o:171, a:1, s:1, b:0),
% 0.97/1.68 class_Rings_Omult__zero [156, 1] (w:1, o:160, a:1, s:1, b:0),
% 0.97/1.68 class_Rings_Ono__zero__divisors [157, 1] (w:1, o:151, a:1, s:1, b:0)
% 0.97/1.68 ,
% 0.97/1.68 class_Rings_Ozero__neq__one [158, 1] (w:1, o:161, a:1, s:1, b:0),
% 0.97/1.68 class_Groups_Ozero [161, 1] (w:1, o:172, a:1, s:1, b:0),
% 0.97/1.68 class_Rings_Osemiring__0 [162, 1] (w:1, o:143, a:1, s:1, b:0),
% 0.97/1.68 class_Rings_Oring__no__zero__divisors [163, 1] (w:1, o:140, a:1, s:1
% 0.97/1.68 , b:0),
% 0.97/1.68 class_Groups_Olinordered__ab__group__add [164, 1] (w:1, o:128, a:1
% 0.97/1.68 , s:1, b:0),
% 0.97/1.68 class_Groups_Ocomm__monoid__add [165, 1] (w:1, o:173, a:1, s:1, b:0)
% 0.97/1.68 ,
% 0.97/1.68 class_Groups_Omonoid__add [166, 1] (w:1, o:174, a:1, s:1, b:0),
% 0.97/1.68 class_Rings_Oring__1__no__zero__divisors [167, 1] (w:1, o:141, a:1
% 0.97/1.68 , s:1, b:0),
% 0.97/1.68 class_Rings_Olinordered__ring [168, 1] (w:1, o:148, a:1, s:1, b:0),
% 0.97/1.68 class_Rings_Olinordered__ring__strict [169, 1] (w:1, o:149, a:1, s:1
% 0.97/1.68 , b:0),
% 0.97/1.68 class_Rings_Oordered__cancel__semiring [170, 1] (w:1, o:162, a:1, s:1
% 0.97/1.68 , b:0),
% 0.97/1.68 class_Rings_Oordered__semiring [171, 1] (w:1, o:164, a:1, s:1, b:0),
% 0.97/1.68
% 0.97/1.68 class_Rings_Oordered__comm__semiring [172, 1] (w:1, o:165, a:1, s:1
% 0.97/1.68 , b:0),
% 0.97/1.68 class_Groups_Oordered__comm__monoid__add [173, 1] (w:1, o:175, a:1
% 0.97/1.68 , s:1, b:0),
% 0.97/1.68 class_Rings_Olinordered__semiring__1 [177, 1] (w:1, o:155, a:1, s:1
% 0.97/1.68 , b:0),
% 0.97/1.68 c_Complex_Ocomplex_Ocomplex__size [181, 1] (w:1, o:176, a:1, s:1, b:0
% 0.97/1.68 ),
% 0.97/1.68 c_Nat_Osize__class_Osize [186, 2] (w:1, o:219, a:1, s:1, b:0),
% 14.18/14.57 c_Nat_OSuc [187, 1] (w:1, o:177, a:1, s:1, b:0),
% 14.18/14.57 c_Parity_Oeven__odd__class_Oeven [188, 2] (w:1, o:220, a:1, s:1, b:0)
% 14.18/14.57 ,
% 14.18/14.57 class_Rings_Ocomm__ring__1 [193, 1] (w:1, o:126, a:1, s:1, b:0),
% 14.18/14.57 c_Code__Numeral_Onat__of__aux [194, 2] (w:1, o:221, a:1, s:1, b:0),
% 14.18/14.57 c_Orderings_Oord__class_Oless [195, 3] (w:1, o:244, a:1, s:1, b:0),
% 14.18/14.57 c_Divides_Odiv__class_Odiv [196, 3] (w:1, o:246, a:1, s:1, b:0),
% 14.18/14.57 c_Groups_Oabs__class_Oabs [197, 2] (w:1, o:222, a:1, s:1, b:0),
% 14.18/14.57 class_Groups_Oordered__ab__group__add__abs [198, 1] (w:1, o:178, a:1
% 14.18/14.57 , s:1, b:0),
% 14.18/14.57 class_Groups_Oordered__cancel__ab__semigroup__add [199, 1] (w:1, o:
% 14.18/14.57 179, a:1, s:1, b:0),
% 14.18/14.57 class_Rings_Olinordered__semiring__strict [200, 1] (w:1, o:156, a:1
% 14.18/14.57 , s:1, b:0),
% 14.18/14.57 class_Rings_Olinordered__comm__semiring__strict [201, 1] (w:1, o:157
% 14.18/14.57 , a:1, s:1, b:0),
% 14.18/14.57 class_Rings_Oordered__ring__abs [206, 1] (w:1, o:163, a:1, s:1, b:0)
% 14.18/14.57 ,
% 14.18/14.57 class_Rings_Olinordered__semiring [207, 1] (w:1, o:158, a:1, s:1, b:0
% 14.18/14.57 ),
% 14.18/14.57 hBOOL [210, 1] (w:1, o:180, a:1, s:1, b:0),
% 14.18/14.57 class_Rings_Olinordered__semiring__1__strict [213, 1] (w:1, o:159, a:
% 14.18/14.57 1, s:1, b:0),
% 14.18/14.57 class_Divides_Osemiring__div [215, 1] (w:1, o:181, a:1, s:1, b:0),
% 14.18/14.57 tc_HOL_Obool [220, 0] (w:1, o:29, a:1, s:1, b:0),
% 14.18/14.57 alpha1 [221, 3] (w:1, o:247, a:1, s:1, b:1),
% 14.18/14.57 alpha2 [222, 3] (w:1, o:252, a:1, s:1, b:1),
% 14.18/14.57 alpha3 [223, 2] (w:1, o:228, a:1, s:1, b:1),
% 14.18/14.57 alpha4 [224, 2] (w:1, o:229, a:1, s:1, b:1),
% 14.18/14.57 alpha5 [225, 2] (w:1, o:230, a:1, s:1, b:1),
% 14.18/14.57 alpha6 [226, 2] (w:1, o:231, a:1, s:1, b:1),
% 14.18/14.57 alpha7 [227, 2] (w:1, o:232, a:1, s:1, b:1),
% 14.18/14.57 alpha8 [228, 2] (w:1, o:233, a:1, s:1, b:1),
% 14.18/14.57 alpha9 [229, 4] (w:1, o:260, a:1, s:1, b:1),
% 14.18/14.57 alpha10 [230, 4] (w:1, o:261, a:1, s:1, b:1),
% 14.18/14.57 alpha11 [231, 2] (w:1, o:234, a:1, s:1, b:1),
% 14.18/14.57 alpha12 [232, 3] (w:1, o:248, a:1, s:1, b:1),
% 14.18/14.57 alpha13 [233, 3] (w:1, o:249, a:1, s:1, b:1),
% 14.18/14.57 alpha14 [234, 2] (w:1, o:235, a:1, s:1, b:1),
% 14.18/14.57 alpha15 [235, 3] (w:1, o:250, a:1, s:1, b:1),
% 14.18/14.57 alpha16 [236, 3] (w:1, o:251, a:1, s:1, b:1),
% 14.18/14.57 alpha17 [237, 2] (w:1, o:236, a:1, s:1, b:1),
% 14.18/14.57 alpha18 [238, 2] (w:1, o:237, a:1, s:1, b:1),
% 14.18/14.57 alpha19 [239, 2] (w:1, o:238, a:1, s:1, b:1),
% 14.18/14.57 alpha20 [240, 2] (w:1, o:223, a:1, s:1, b:1),
% 14.18/14.57 alpha21 [241, 2] (w:1, o:224, a:1, s:1, b:1),
% 14.18/14.57 alpha22 [242, 4] (w:1, o:262, a:1, s:1, b:1),
% 14.18/14.57 alpha23 [243, 4] (w:1, o:263, a:1, s:1, b:1),
% 14.18/14.57 alpha24 [244, 3] (w:1, o:253, a:1, s:1, b:1),
% 14.18/14.57 alpha25 [245, 3] (w:1, o:254, a:1, s:1, b:1),
% 14.18/14.57 alpha26 [246, 2] (w:1, o:225, a:1, s:1, b:1),
% 14.18/14.57 alpha27 [247, 2] (w:1, o:226, a:1, s:1, b:1),
% 14.18/14.57 alpha28 [248, 2] (w:1, o:227, a:1, s:1, b:1),
% 14.18/14.57 alpha29 [249, 3] (w:1, o:255, a:1, s:1, b:1),
% 14.18/14.57 alpha30 [250, 3] (w:1, o:256, a:1, s:1, b:1),
% 14.18/14.57 skol1 [251, 2] (w:1, o:213, a:1, s:1, b:1),
% 14.18/14.57 skol2 [252, 3] (w:1, o:259, a:1, s:1, b:1),
% 14.18/14.57 skol3 [253, 0] (w:1, o:27, a:1, s:1, b:1),
% 14.18/14.57 skol4 [254, 2] (w:1, o:214, a:1, s:1, b:1),
% 14.18/14.57 skol5 [255, 2] (w:1, o:215, a:1, s:1, b:1),
% 14.18/14.57 skol6 [256, 1] (w:1, o:182, a:1, s:1, b:1),
% 14.18/14.57 skol7 [257, 1] (w:1, o:183, a:1, s:1, b:1),
% 14.18/14.57 skol8 [258, 1] (w:1, o:184, a:1, s:1, b:1),
% 14.18/14.57 skol9 [259, 2] (w:1, o:216, a:1, s:1, b:1),
% 14.18/14.57 skol10 [260, 2] (w:1, o:217, a:1, s:1, b:1),
% 14.18/14.57 skol11 [261, 3] (w:1, o:257, a:1, s:1, b:1),
% 14.18/14.57 skol12 [262, 3] (w:1, o:258, a:1, s:1, b:1),
% 14.18/14.57 skol13 [263, 0] (w:1, o:28, a:1, s:1, b:1).
% 14.18/14.57
% 14.18/14.57
% 14.18/14.57 Starting Search:
% 14.18/14.57
% 14.18/14.57 *** allocated 113905 integers for clauses
% 14.18/14.57 *** allocated 170857 integers for clauses
% 14.18/14.57 Resimplifying inuse:
% 14.18/14.57 Done
% 14.18/14.57
% 14.18/14.57
% 14.18/14.57 Intermediate Status:
% 14.18/14.57 Generated: 3033
% 14.18/14.57 Kept: 2001
% 14.18/14.57 Inuse: 95
% 14.18/14.57 Deleted: 2
% 14.18/14.57 Deletedinuse: 0
% 14.18/14.57
% 14.18/14.57 *** allocated 256285 integers for clauses
% 14.18/14.57 Resimplifying inuse:
% 14.18/14.57 Done
% 14.18/14.57
% 14.18/14.57 Resimplifying inuse:
% 14.18/14.57 Done
% 14.18/14.57
% 14.18/14.57 *** allocated 170857 integers for termspace/termends
% 14.18/14.57
% 14.18/14.57 Intermediate Status:
% 14.18/14.57 Generated: 8715
% 14.18/14.57 Kept: 4004
% 14.18/14.57 Inuse: 268
% 14.18/14.57 Deleted: 11
% 14.18/14.57 Deletedinuse: 5
% 14.18/14.57
% 14.18/14.57 *** allocated 384427 integers for clauses
% 70.64/71.05 Resimplifying inuse:
% 70.64/71.05 Done
% 70.64/71.05
% 70.64/71.05 Resimplifying inuse:
% 70.64/71.05 Done
% 70.64/71.05
% 70.64/71.05
% 70.64/71.05 Intermediate Status:
% 70.64/71.05 Generated: 14855
% 70.64/71.05 Kept: 6008
% 70.64/71.05 Inuse: 315
% 70.64/71.05 Deleted: 14
% 70.64/71.05 Deletedinuse: 6
% 70.64/71.05
% 70.64/71.05 Resimplifying inuse:
% 70.64/71.05 Done
% 70.64/71.05
% 70.64/71.05 *** allocated 576640 integers for clauses
% 70.64/71.05 *** allocated 256285 integers for termspace/termends
% 70.64/71.05
% 70.64/71.05 Intermediate Status:
% 70.64/71.05 Generated: 22850
% 70.64/71.05 Kept: 8009
% 70.64/71.05 Inuse: 410
% 70.64/71.05 Deleted: 17
% 70.64/71.05 Deletedinuse: 6
% 70.64/71.05
% 70.64/71.05 Resimplifying inuse:
% 70.64/71.05 Done
% 70.64/71.05
% 70.64/71.05 Resimplifying inuse:
% 70.64/71.05 Done
% 70.64/71.05
% 70.64/71.05
% 70.64/71.05 Intermediate Status:
% 70.64/71.05 Generated: 32433
% 70.64/71.05 Kept: 10262
% 70.64/71.05 Inuse: 459
% 70.64/71.05 Deleted: 18
% 70.64/71.05 Deletedinuse: 6
% 70.64/71.05
% 70.64/71.05 Resimplifying inuse:
% 70.64/71.05 Done
% 70.64/71.05
% 70.64/71.05 *** allocated 864960 integers for clauses
% 70.64/71.05 Resimplifying inuse:
% 70.64/71.05 Done
% 70.64/71.05
% 70.64/71.05 *** allocated 384427 integers for termspace/termends
% 70.64/71.05
% 70.64/71.05 Intermediate Status:
% 70.64/71.05 Generated: 41185
% 70.64/71.05 Kept: 12264
% 70.64/71.05 Inuse: 571
% 70.64/71.05 Deleted: 19
% 70.64/71.05 Deletedinuse: 6
% 70.64/71.05
% 70.64/71.05 Resimplifying inuse:
% 70.64/71.05 Done
% 70.64/71.05
% 70.64/71.05
% 70.64/71.05 Intermediate Status:
% 70.64/71.05 Generated: 53858
% 70.64/71.05 Kept: 14355
% 70.64/71.05 Inuse: 583
% 70.64/71.05 Deleted: 19
% 70.64/71.05 Deletedinuse: 6
% 70.64/71.05
% 70.64/71.05 Resimplifying inuse:
% 70.64/71.05 Done
% 70.64/71.05
% 70.64/71.05 *** allocated 576640 integers for termspace/termends
% 70.64/71.05 Resimplifying inuse:
% 70.64/71.05 Done
% 70.64/71.05
% 70.64/71.05 *** allocated 1297440 integers for clauses
% 70.64/71.05
% 70.64/71.05 Intermediate Status:
% 70.64/71.05 Generated: 63880
% 70.64/71.05 Kept: 16398
% 70.64/71.05 Inuse: 655
% 70.64/71.05 Deleted: 22
% 70.64/71.05 Deletedinuse: 6
% 70.64/71.05
% 70.64/71.05 Resimplifying inuse:
% 70.64/71.05 Done
% 70.64/71.05
% 70.64/71.05 Resimplifying inuse:
% 70.64/71.05 Done
% 70.64/71.05
% 70.64/71.05
% 70.64/71.05 Intermediate Status:
% 70.64/71.05 Generated: 73610
% 70.64/71.05 Kept: 18408
% 70.64/71.05 Inuse: 768
% 70.64/71.05 Deleted: 39
% 70.64/71.05 Deletedinuse: 6
% 70.64/71.05
% 70.64/71.05 Resimplifying inuse:
% 70.64/71.05 Done
% 70.64/71.05
% 70.64/71.05 Resimplifying inuse:
% 70.64/71.05 Done
% 70.64/71.05
% 70.64/71.05 Resimplifying clauses:
% 70.64/71.05 Done
% 70.64/71.05
% 70.64/71.05
% 70.64/71.05 Intermediate Status:
% 70.64/71.05 Generated: 79820
% 70.64/71.05 Kept: 20409
% 70.64/71.05 Inuse: 812
% 70.64/71.05 Deleted: 663
% 70.64/71.05 Deletedinuse: 6
% 70.64/71.05
% 70.64/71.05 *** allocated 864960 integers for termspace/termends
% 70.64/71.05 Resimplifying inuse:
% 70.64/71.05 Done
% 70.64/71.05
% 70.64/71.05 Resimplifying inuse:
% 70.64/71.05 Done
% 70.64/71.05
% 70.64/71.05
% 70.64/71.05 Intermediate Status:
% 70.64/71.05 Generated: 89494
% 70.64/71.05 Kept: 22479
% 70.64/71.05 Inuse: 893
% 70.64/71.05 Deleted: 663
% 70.64/71.05 Deletedinuse: 6
% 70.64/71.05
% 70.64/71.05 *** allocated 1946160 integers for clauses
% 70.64/71.05 Resimplifying inuse:
% 70.64/71.05 Done
% 70.64/71.05
% 70.64/71.05
% 70.64/71.05 Intermediate Status:
% 70.64/71.05 Generated: 97443
% 70.64/71.05 Kept: 24853
% 70.64/71.05 Inuse: 949
% 70.64/71.05 Deleted: 664
% 70.64/71.05 Deletedinuse: 6
% 70.64/71.05
% 70.64/71.05 Resimplifying inuse:
% 70.64/71.05 Done
% 70.64/71.05
% 70.64/71.05 Resimplifying inuse:
% 70.64/71.05 Done
% 70.64/71.05
% 70.64/71.05
% 70.64/71.05 Intermediate Status:
% 70.64/71.05 Generated: 110036
% 70.64/71.05 Kept: 28049
% 70.64/71.05 Inuse: 967
% 70.64/71.05 Deleted: 664
% 70.64/71.05 Deletedinuse: 6
% 70.64/71.05
% 70.64/71.05 Resimplifying inuse:
% 70.64/71.05 Done
% 70.64/71.05
% 70.64/71.05 Resimplifying inuse:
% 70.64/71.05 Done
% 70.64/71.05
% 70.64/71.05 *** allocated 1297440 integers for termspace/termends
% 70.64/71.05
% 70.64/71.05 Intermediate Status:
% 70.64/71.05 Generated: 120713
% 70.64/71.05 Kept: 30774
% 70.64/71.05 Inuse: 1027
% 70.64/71.05 Deleted: 664
% 70.64/71.05 Deletedinuse: 6
% 70.64/71.05
% 70.64/71.05 Resimplifying inuse:
% 70.64/71.05 Done
% 70.64/71.05
% 70.64/71.05 Resimplifying inuse:
% 70.64/71.05 Done
% 70.64/71.05
% 70.64/71.05
% 70.64/71.05 Intermediate Status:
% 70.64/71.05 Generated: 130258
% 70.64/71.05 Kept: 33565
% 70.64/71.05 Inuse: 1107
% 70.64/71.05 Deleted: 664
% 70.64/71.05 Deletedinuse: 6
% 70.64/71.05
% 70.64/71.05 Resimplifying inuse:
% 70.64/71.05 Done
% 70.64/71.05
% 70.64/71.05 *** allocated 2919240 integers for clauses
% 70.64/71.05 Resimplifying inuse:
% 70.64/71.05 Done
% 70.64/71.05
% 70.64/71.05
% 70.64/71.05 Intermediate Status:
% 70.64/71.05 Generated: 137512
% 70.64/71.05 Kept: 36311
% 70.64/71.05 Inuse: 1117
% 70.64/71.05 Deleted: 664
% 70.64/71.05 Deletedinuse: 6
% 70.64/71.05
% 70.64/71.05 Resimplifying inuse:
% 70.64/71.05 Done
% 70.64/71.05
% 70.64/71.05 Resimplifying inuse:
% 70.64/71.05 Done
% 70.64/71.05
% 70.64/71.05
% 70.64/71.05 Intermediate Status:
% 70.64/71.05 Generated: 147105
% 70.64/71.05 Kept: 39701
% 70.64/71.05 Inuse: 1146
% 70.64/71.05 Deleted: 665
% 70.64/71.05 Deletedinuse: 6
% 70.64/71.05
% 70.64/71.05 Resimplifying inuse:
% 70.64/71.05 Done
% 70.64/71.05
% 70.64/71.05 Resimplifying inuse:
% 70.64/71.05 Done
% 70.64/71.05
% 70.64/71.05 Resimplifying clauses:
% 70.64/71.05 Done
% 70.64/71.05
% 70.64/71.05
% 70.64/71.05 Intermediate Status:
% 70.64/71.05 Generated: 153444
% 70.64/71.05 Kept: 43286
% 70.64/71.05 Inuse: 1166
% 70.64/71.05 Deleted: 869
% 70.64/71.05 Deletedinuse: 6
% 70.64/71.05
% 70.64/71.05 Resimplifying inuse:
% 70.64/71.05 Done
% 70.64/71.05
% 70.64/71.05 Resimplifying inuse:
% 70.64/71.05 Done
% 70.64/71.05
% 70.64/71.05 *** allocated 1946160 integers for termspace/termends
% 70.64/71.05
% 70.64/71.05 Intermediate Status:
% 70.64/71.05 Generated: 161883
% 70.64/71.05 Kept: 46863
% 70.64/71.05 Inuse: 1201
% 70.64/71.05 Deleted: 869
% 70.64/71.05 Deletedinuse: 6
% 70.64/71.05
% 70.64/71.05 Resimplifying inuse:
% 70.64/71.05 Done
% 70.64/71.05
% 70.64/71.05 Resimplifying inuse:
% 70.64/71.05 Done
% 70.64/71.05
% 70.64/71.05
% 70.64/71.05 Intermediate Status:
% 70.64/71.05 Generated: 168475
% 70.64/71.05 Kept: 50031
% 70.64/71.05 Inuse: 1225
% 70.64/71.05 Deleted: 870
% 70.64/71.05 Deletedinuse: 6
% 70.64/71.05
% 70.64/71.05 Resimplifying inuse:
% 70.64/71.05 Done
% 70.64/71.05
% 70.64/71.05
% 70.64/71.05 Intermediate Status:
% 70.64/71.05 Generated: 183476
% 70.64/71.05 Kept: 53346
% 70.64/71.05 Inuse: 1265
% 70.64/71.05 Deleted: 870
% 70.64/71.05 Deletedinuse: 6
% 70.64/71.05
% 70.64/71.05 Resimplifying inuse:
% 70.64/71.05 Done
% 70.64/71.05
% 70.64/71.05 *** allocated 4378860 integers for clauses
% 70.64/71.05
% 70.64/71.05 Intermediate Status:
% 70.64/71.05 Generated: 197507
% 70.64/71.05 Kept: 56167
% 70.64/71.05 Inuse: 1280
% 70.64/71.05 Deleted: 870
% 70.64/71.05 Deletedinuse: 6
% 70.64/71.05
% 70.64/71.05 Resimplifying inuse:
% 70.64/71.05 Done
% 70.64/71.05
% 70.64/71.05 Resimplifying inuse:
% 70.64/71.05 Done
% 70.64/71.05
% 70.64/71.05
% 70.64/71.05 Intermediate Status:
% 70.64/71.05 Generated: 201438
% 70.64/71.05 Kept: 58179
% 70.64/71.05 Inuse: 1291
% 70.64/71.05 Deleted: 870
% 70.64/71.05 Deletedinuse: 6
% 70.64/71.05
% 70.64/71.05 Resimplifying inuse:
% 219.03/219.48 Done
% 219.03/219.48
% 219.03/219.48
% 219.03/219.48 Intermediate Status:
% 219.03/219.48 Generated: 205331
% 219.03/219.48 Kept: 60256
% 219.03/219.48 Inuse: 1300
% 219.03/219.48 Deleted: 870
% 219.03/219.48 Deletedinuse: 6
% 219.03/219.48
% 219.03/219.48
% 219.03/219.48 Intermediate Status:
% 219.03/219.48 Generated: 213745
% 219.03/219.48 Kept: 64391
% 219.03/219.48 Inuse: 1335
% 219.03/219.48 Deleted: 870
% 219.03/219.48 Deletedinuse: 6
% 219.03/219.48
% 219.03/219.48 Resimplifying inuse:
% 219.03/219.48 Done
% 219.03/219.48
% 219.03/219.48 Resimplifying clauses:
% 219.03/219.48 Done
% 219.03/219.48
% 219.03/219.48
% 219.03/219.48 Intermediate Status:
% 219.03/219.48 Generated: 220669
% 219.03/219.48 Kept: 68191
% 219.03/219.48 Inuse: 1350
% 219.03/219.48 Deleted: 1188
% 219.03/219.48 Deletedinuse: 6
% 219.03/219.48
% 219.03/219.48 Resimplifying inuse:
% 219.03/219.48 Done
% 219.03/219.48
% 219.03/219.48 Resimplifying inuse:
% 219.03/219.48 Done
% 219.03/219.48
% 219.03/219.48
% 219.03/219.48 Intermediate Status:
% 219.03/219.48 Generated: 226304
% 219.03/219.48 Kept: 70346
% 219.03/219.48 Inuse: 1380
% 219.03/219.48 Deleted: 1188
% 219.03/219.48 Deletedinuse: 6
% 219.03/219.48
% 219.03/219.48 *** allocated 2919240 integers for termspace/termends
% 219.03/219.48
% 219.03/219.48 Intermediate Status:
% 219.03/219.48 Generated: 246617
% 219.03/219.48 Kept: 72849
% 219.03/219.48 Inuse: 1385
% 219.03/219.48 Deleted: 1188
% 219.03/219.48 Deletedinuse: 6
% 219.03/219.48
% 219.03/219.48 Resimplifying inuse:
% 219.03/219.48 Done
% 219.03/219.48
% 219.03/219.48
% 219.03/219.48 Intermediate Status:
% 219.03/219.48 Generated: 267497
% 219.03/219.48 Kept: 75356
% 219.03/219.48 Inuse: 1390
% 219.03/219.48 Deleted: 1188
% 219.03/219.48 Deletedinuse: 6
% 219.03/219.48
% 219.03/219.48 Resimplifying inuse:
% 219.03/219.48 Done
% 219.03/219.48
% 219.03/219.48 Resimplifying inuse:
% 219.03/219.48 Done
% 219.03/219.48
% 219.03/219.48
% 219.03/219.48 Intermediate Status:
% 219.03/219.48 Generated: 274655
% 219.03/219.48 Kept: 77504
% 219.03/219.48 Inuse: 1435
% 219.03/219.48 Deleted: 1188
% 219.03/219.48 Deletedinuse: 6
% 219.03/219.48
% 219.03/219.48 Resimplifying inuse:
% 219.03/219.48 Done
% 219.03/219.48
% 219.03/219.48 Resimplifying inuse:
% 219.03/219.48 Done
% 219.03/219.48
% 219.03/219.48
% 219.03/219.48 Intermediate Status:
% 219.03/219.48 Generated: 279722
% 219.03/219.48 Kept: 79576
% 219.03/219.48 Inuse: 1475
% 219.03/219.48 Deleted: 1188
% 219.03/219.48 Deletedinuse: 6
% 219.03/219.48
% 219.03/219.48 Resimplifying inuse:
% 219.03/219.48 Done
% 219.03/219.48
% 219.03/219.48 Resimplifying inuse:
% 219.03/219.48 Done
% 219.03/219.48
% 219.03/219.48
% 219.03/219.48 Intermediate Status:
% 219.03/219.48 Generated: 284272
% 219.03/219.48 Kept: 81657
% 219.03/219.48 Inuse: 1525
% 219.03/219.48 Deleted: 1188
% 219.03/219.48 Deletedinuse: 6
% 219.03/219.48
% 219.03/219.48 Resimplifying inuse:
% 219.03/219.48 Done
% 219.03/219.48
% 219.03/219.48 Resimplifying inuse:
% 219.03/219.48 Done
% 219.03/219.48
% 219.03/219.48
% 219.03/219.48 Intermediate Status:
% 219.03/219.48 Generated: 290223
% 219.03/219.48 Kept: 83675
% 219.03/219.48 Inuse: 1569
% 219.03/219.48 Deleted: 1188
% 219.03/219.48 Deletedinuse: 6
% 219.03/219.48
% 219.03/219.48 Resimplifying inuse:
% 219.03/219.48 Done
% 219.03/219.48
% 219.03/219.48 Resimplifying clauses:
% 219.03/219.48 Done
% 219.03/219.48
% 219.03/219.48 Resimplifying inuse:
% 219.03/219.48 Done
% 219.03/219.48
% 219.03/219.48
% 219.03/219.48 Intermediate Status:
% 219.03/219.48 Generated: 296452
% 219.03/219.48 Kept: 85733
% 219.03/219.48 Inuse: 1588
% 219.03/219.48 Deleted: 1329
% 219.03/219.48 Deletedinuse: 6
% 219.03/219.48
% 219.03/219.48 Resimplifying inuse:
% 219.03/219.48 Done
% 219.03/219.48
% 219.03/219.48
% 219.03/219.48 Intermediate Status:
% 219.03/219.48 Generated: 309615
% 219.03/219.48 Kept: 88132
% 219.03/219.48 Inuse: 1605
% 219.03/219.48 Deleted: 1329
% 219.03/219.48 Deletedinuse: 6
% 219.03/219.48
% 219.03/219.48 Resimplifying inuse:
% 219.03/219.48 Done
% 219.03/219.48
% 219.03/219.48 Resimplifying inuse:
% 219.03/219.48 Done
% 219.03/219.48
% 219.03/219.48 *** allocated 6568290 integers for clauses
% 219.03/219.48
% 219.03/219.48 Intermediate Status:
% 219.03/219.48 Generated: 320084
% 219.03/219.48 Kept: 91112
% 219.03/219.48 Inuse: 1635
% 219.03/219.48 Deleted: 1329
% 219.03/219.48 Deletedinuse: 6
% 219.03/219.48
% 219.03/219.48 Resimplifying inuse:
% 219.03/219.48 Done
% 219.03/219.48
% 219.03/219.48 Resimplifying inuse:
% 219.03/219.48 Done
% 219.03/219.48
% 219.03/219.48
% 219.03/219.48 Intermediate Status:
% 219.03/219.48 Generated: 328976
% 219.03/219.48 Kept: 93127
% 219.03/219.48 Inuse: 1646
% 219.03/219.48 Deleted: 1329
% 219.03/219.48 Deletedinuse: 6
% 219.03/219.48
% 219.03/219.48 Resimplifying inuse:
% 219.03/219.48 Done
% 219.03/219.48
% 219.03/219.48 Resimplifying inuse:
% 219.03/219.48 Done
% 219.03/219.48
% 219.03/219.48
% 219.03/219.48 Intermediate Status:
% 219.03/219.48 Generated: 334822
% 219.03/219.48 Kept: 95301
% 219.03/219.48 Inuse: 1680
% 219.03/219.48 Deleted: 1329
% 219.03/219.48 Deletedinuse: 6
% 219.03/219.48
% 219.03/219.48
% 219.03/219.48 Intermediate Status:
% 219.03/219.48 Generated: 365213
% 219.03/219.48 Kept: 98485
% 219.03/219.48 Inuse: 1685
% 219.03/219.48 Deleted: 1329
% 219.03/219.48 Deletedinuse: 6
% 219.03/219.48
% 219.03/219.48 Resimplifying inuse:
% 219.03/219.48 Done
% 219.03/219.48
% 219.03/219.48 *** allocated 4378860 integers for termspace/termends
% 219.03/219.48 Resimplifying inuse:
% 219.03/219.48 Done
% 219.03/219.48
% 219.03/219.48
% 219.03/219.48 Intermediate Status:
% 219.03/219.48 Generated: 376272
% 219.03/219.48 Kept: 102253
% 219.03/219.48 Inuse: 1695
% 219.03/219.48 Deleted: 1329
% 219.03/219.48 Deletedinuse: 6
% 219.03/219.48
% 219.03/219.48 Resimplifying inuse:
% 219.03/219.48 Done
% 219.03/219.48
% 219.03/219.48 Resimplifying inuse:
% 219.03/219.48 Done
% 219.03/219.48
% 219.03/219.48
% 219.03/219.48 Intermediate Status:
% 219.03/219.48 Generated: 384647
% 219.03/219.48 Kept: 104482
% 219.03/219.48 Inuse: 1725
% 219.03/219.48 Deleted: 1329
% 219.03/219.48 Deletedinuse: 6
% 219.03/219.48
% 219.03/219.48 Resimplifying clauses:
% 219.03/219.48 Done
% 219.03/219.48
% 219.03/219.48 Resimplifying inuse:
% 219.03/219.48 Done
% 219.03/219.48
% 219.03/219.48
% 219.03/219.48 Intermediate Status:
% 219.03/219.48 Generated: 391759
% 219.03/219.48 Kept: 106684
% 219.03/219.48 Inuse: 1740
% 219.03/219.48 Deleted: 1562
% 219.03/219.48 Deletedinuse: 6
% 219.03/219.48
% 219.03/219.48 Resimplifying inuse:
% 219.03/219.48 Done
% 219.03/219.48
% 219.03/219.48 Resimplifying inuse:
% 219.03/219.48 Done
% 219.03/219.48
% 219.03/219.48
% 219.03/219.48 Intermediate Status:
% 219.03/219.48 Generated: 399123
% 219.03/219.48 Kept: 108837
% 219.03/219.48 Inuse: 1750
% 219.03/219.48 Deleted: 1562
% 219.03/219.48 Deletedinuse: 6
% 219.03/219.48
% 219.03/219.48 Resimplifying inuse:
% 219.03/219.48 Done
% 219.03/219.48
% 219.03/219.48
% 219.03/219.48 Intermediate Status:
% 219.03/219.48 Generated: 410822
% 219.03/219.48 Kept: 112088
% 219.03/219.48 Inuse: 1765
% 219.03/219.48 Deleted: 1563
% 219.03/219.48 Deletedinuse: 7
% 219.03/219.48
% 219.03/219.48 Resimplifying inuse:
% 219.03/219.48 Done
% 219.03/219.48
% 219.03/219.48
% 219.03/219.48 Intermediate Status:
% 219.03/219.48 Generated: 415986
% 219.03/219.48 Kept: 114584
% 219.03/219.48 Inuse: 1770
% 219.03/219.48 Deleted: 1563
% 219.03/219.48 Deletedinuse: 7
% 219.03/219.48
% 219.03/219.48 Resimplifying inuse:
% 219.03/219.48 Done
% 219.03/219.48
% 219.03/219.48 Resimplifying inuse:
% 219.03/219.48 Done
% 219.03/219.48
% 219.03/219.48
% 219.03/219.48 Intermediate Status:
% 219.03/219.48 Generated: 424452
% 219.03/219.48 Kept: 116967
% 219.03/219.48 Inuse: 1790
% 219.03/219.48 Deleted: 1563
% 219.03/219.48 Deletedinuse: 7
% 219.03/219.48
% 219.03/219.48 Resimplifying inuse:
% 219.03/219.48 Done
% 219.03/219.48
% 219.03/219.48 Resimplifying inuse:
% 219.03/219.48 Done
% 219.03/219.48
% 219.03/219.48
% 219.03/219.48 Intermediate Status:
% 219.03/219.48 Generated: 432132
% 219.03/219.48 Kept: 120030
% 219.03/219.48 Inuse: 1815
% 219.03/219.48 Deleted: 1563
% 219.03/219.48 Deletedinuse: 7
% 219.03/219.48
% 219.03/219.48 Resimplifying inuse:
% 219.03/219.48 Done
% 219.03/219.48
% 219.03/219.48
% 219.03/219.48 Intermediate Status:
% 219.03/219.48 Generated: 439565
% 219.03/219.48 Kept: Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------