TSTP Solution File: SWW224+1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWW224+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n026.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 23:21:22 EDT 2022
% Result : Timeout 300.03s 300.45s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW224+1 : TPTP v8.1.0. Released v5.2.0.
% 0.07/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n026.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
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % DateTime : Sat Jun 4 10:34:14 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.97/1.57 *** allocated 10000 integers for termspace/termends
% 0.97/1.57 *** allocated 10000 integers for clauses
% 0.97/1.57 *** allocated 10000 integers for justifications
% 0.97/1.57 *** allocated 15000 integers for termspace/termends
% 0.97/1.57 *** allocated 22500 integers for termspace/termends
% 0.97/1.57 *** allocated 33750 integers for termspace/termends
% 0.97/1.57 Bliksem 1.12
% 0.97/1.57
% 0.97/1.57
% 0.97/1.57 Automatic Strategy Selection
% 0.97/1.57
% 0.97/1.57 *** allocated 50625 integers for termspace/termends
% 0.97/1.57 *** allocated 75937 integers for termspace/termends
% 0.97/1.57 *** allocated 113905 integers for termspace/termends
% 0.97/1.57
% 0.97/1.57 Clauses:
% 0.97/1.57
% 0.97/1.57 { ! hAPP( Y, skol1( X, Y ) ) = hAPP( X, skol1( X, Y ) ), Y = X }.
% 0.97/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.57 , c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, T, Z )
% 0.97/1.57 ), Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus
% 0.97/1.57 ( X, Z, Y ), T ) }.
% 0.97/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.57 , c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, T, Z )
% 0.97/1.57 ), Y ), c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus
% 0.97/1.57 ( X, Z, Y ) ) }.
% 0.97/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.57 , c_Groups_Ominus__class_Ominus( X, Z, Y ), T ), !
% 0.97/1.57 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.97/1.57 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X,
% 0.97/1.57 c_Groups_Ominus__class_Ominus( X, T, Z ) ), Y ) }.
% 0.97/1.57 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 0.97/1.57 c_Groups_Ominus__class_Ominus( X, Z, Y ) ), c_Groups_Oplus__class_Oplus(
% 0.97/1.57 X, c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) )
% 0.97/1.57 ) }.
% 0.97/1.57 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 0.97/1.57 c_Groups_Ominus__class_Ominus( X, c_Groups_Oplus__class_Oplus( X, U, T )
% 0.97/1.57 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) ), c_Groups_Oplus__class_Oplus
% 0.97/1.57 ( X, c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, U, Z
% 0.97/1.57 ) ), c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, T,
% 0.97/1.57 Y ) ) ) ) }.
% 0.97/1.57 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 0.97/1.57 c_Groups_Ominus__class_Ominus( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.97/1.57 c_Groups_Oabs__class_Oabs( X, Y ) ) ), c_Groups_Oabs__class_Oabs( X,
% 0.97/1.57 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) }.
% 0.97/1.57 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X,
% 0.97/1.57 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ),
% 0.97/1.57 c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Z, Y ) )
% 0.97/1.57 ) }.
% 0.97/1.57 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X,
% 0.97/1.57 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ),
% 0.97/1.57 c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Y, Z ) )
% 0.97/1.57 ) }.
% 0.97/1.57 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 0.97/1.57 c_Groups_Oplus__class_Oplus( X, Z, Y ) ), c_Groups_Oplus__class_Oplus( X
% 0.97/1.57 , c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) )
% 0.97/1.57 ) }.
% 0.97/1.57 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.97/1.57 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.97/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, U )
% 0.97/1.57 , c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.97/1.57 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.57 c_Orderings_Oord__class_Oless( X, U, T ), c_Orderings_Oord__class_Oless(
% 0.97/1.57 X, c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X
% 0.97/1.57 , Y, T ) ) }.
% 0.97/1.57 { ! class_Orderings_Opreorder( X ), c_Orderings_Oord__class_Oless__eq( X, Y
% 0.97/1.57 , Y ) }.
% 0.97/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.57 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ),
% 0.97/1.57 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, X ) ) }.
% 0.97/1.57 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.97/1.57 c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Z, Y ) )
% 0.97/1.57 = c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Y, Z )
% 0.97/1.57 ) }.
% 0.97/1.57 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.57 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.97/1.57 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.97/1.57 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.97/1.57 hAPP( Y, U ) ) }.
% 0.97/1.57 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.57 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.97/1.57 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.57 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.97/1.57 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.57 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.97/1.57 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.57 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.97/1.57 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.57 , Y ), ! Z = T, c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.97/1.57 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y
% 0.97/1.57 ), ! Y = T, c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.97/1.57 { ! class_Orderings_Oorder( X ), ! Z = Y, !
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.97/1.57 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.97/1.57 ( X, Y, T ), c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.97/1.57 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.57 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.97/1.57 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.57 , Y ), ! Y = Z, c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.97/1.57 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.97/1.57 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.97/1.57 hAPP( Y, U ) ) }.
% 0.97/1.57 { ! class_Orderings_Opreorder( X ), ! Z = Y,
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.57 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.97/1.57 ( X, Z, Y ) }.
% 0.97/1.57 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.97/1.57 ( X, Y, Z ) }.
% 0.97/1.57 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.57 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.97/1.57 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.57 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.97/1.57 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.97/1.57 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.97/1.57 hAPP( Y, U ) ) }.
% 0.97/1.57 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, hAPP
% 0.97/1.57 ( Z, skol2( X, Y, Z ) ), hAPP( Y, skol2( X, Y, Z ) ) ),
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }.
% 0.97/1.57 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.97/1.57 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.57 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.57 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.57 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.57 , ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.97/1.57 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.97/1.57 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.57 Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 0.97/1.57 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.97/1.57 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.57 , ! Z = T, c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.97/1.57 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.97/1.57 ! Y = T, c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.97/1.57 { ! class_Orderings_Oorder( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless(
% 0.97/1.57 X, T, Y ), c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.97/1.57 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X
% 0.97/1.57 , Y, T ), c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.97/1.57 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.57 , ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.57 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.57 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.57 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.57 , ! Y = Z }.
% 0.97/1.57 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.57 , ! Z = Y }.
% 0.97/1.57 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.57 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.57 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.57 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.57 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.57 , ! Z = Y }.
% 0.97/1.57 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.97/1.57 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.57 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.97/1.57 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Y = Z }.
% 0.97/1.57 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.97/1.57 ), ! Y = Z, ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.57 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.97/1.57 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.57 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.97/1.57 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Z = Y }.
% 0.97/1.57 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.97/1.57 Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.57 { ! class_Orderings_Olinorder( X ), ! Z = Y, !
% 0.97/1.57 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.57 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.97/1.57 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.57 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.57 Y ), ! Z = Y }.
% 0.97/1.57 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.97/1.57 Z ), ! Z = Y }.
% 0.97/1.57 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.97/1.57 Y ) }.
% 0.97/1.57 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.97/1.57 c_Groups_Oplus__class_Oplus( X, Z, T ) = c_Groups_Oplus__class_Oplus( X,
% 0.97/1.57 Y, T ), Z = Y }.
% 0.97/1.57 { ! class_Groups_Ocancel__ab__semigroup__add( X ), !
% 0.97/1.57 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.97/1.57 T, Y ), Z = Y }.
% 0.97/1.57 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.97/1.57 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.97/1.57 T, Y ), Z = Y }.
% 0.97/1.57 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.97/1.57 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.97/1.57 Y, Z ), T = Y }.
% 0.97/1.57 { ! class_Groups_Ocancel__semigroup__add( X ), ! T = Y,
% 0.97/1.57 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.97/1.57 Y, Z ) }.
% 0.97/1.57 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.97/1.57 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.97/1.57 T, Y ), Z = Y }.
% 0.97/1.57 { ! class_Groups_Ocancel__semigroup__add( X ), ! Z = Y,
% 0.97/1.57 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.97/1.57 T, Y ) }.
% 0.97/1.57 { ! class_Groups_Oab__semigroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.57 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.97/1.57 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.97/1.57 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.97/1.57 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! U = T, Z = Y }.
% 0.97/1.57 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.97/1.57 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! Z = Y, U = T }.
% 0.97/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), !
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ), Y = X }.
% 0.97/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), !
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Z ),
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, Z ) }.
% 0.97/1.57 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ) }.
% 0.97/1.57 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, X ) }.
% 0.97/1.57 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.97/1.57 c_Groups_Oabs__class_Oabs( X, c_Groups_Oabs__class_Oabs( X, Y ) ) =
% 0.97/1.57 c_Groups_Oabs__class_Oabs( X, Y ) }.
% 0.97/1.57 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.57 , Y ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.97/1.57 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.97/1.57 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.57 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 0.97/1.57 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.97/1.57 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.57 , ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.97/1.57 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.97/1.57 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.57 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 0.97/1.57 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.97/1.57 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.57 , Y ), Y = Z, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.57 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.57 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.57 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.57 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.97/1.57 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.57 , Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.97/1.57 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.57 , Z, Y ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.57 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.57 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.57 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.57 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.57 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.97/1.57 ( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.57 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.97/1.57 ( X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.57 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.97/1.57 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ), Z = Y }.
% 0.97/1.57 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.97/1.57 ), ! Z = Y, c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.57 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.57 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.57 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.97/1.57 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.97/1.57 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.57 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.97/1.57 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.57 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.57 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.97/1.57 ( X, Z, Y ) }.
% 0.97/1.57 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.57 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.57 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.57 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.97/1.57 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.57 , Z, Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.97/1.57 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.57 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.57 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.57 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.57 , ! Z = Y }.
% 0.97/1.57 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.57 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.57 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.57 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.57 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.57 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.57 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.97/1.57 Z ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.57 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.97/1.57 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.97/1.57 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.57 , Y, Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.57 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.97/1.57 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.57 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.97/1.57 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ),
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.57 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.97/1.57 U ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.97/1.57 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.97/1.57 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.97/1.57 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.97/1.57 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.97/1.57 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.97/1.57 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.57 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.97/1.57 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.97/1.57 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.97/1.57 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ),
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.97/1.57 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.97/1.57 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.97/1.57 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.97/1.57 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.97/1.57 ( X, Z, Y ) }.
% 0.97/1.57 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, T )
% 0.97/1.57 , c_Groups_Oplus__class_Oplus( X, Y, T ) ), c_Orderings_Oord__class_Oless
% 0.97/1.57 ( X, Z, Y ) }.
% 0.97/1.57 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.97/1.57 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.57 ( X, U, T ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.57 c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X, Y
% 0.97/1.57 , T ) ) }.
% 0.97/1.57 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.97/1.57 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.97/1.57 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.97/1.57 , T, Y ) ) }.
% 0.97/1.57 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.97/1.57 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.97/1.57 X, c_Groups_Oplus__class_Oplus( X, Z, T ), c_Groups_Oplus__class_Oplus( X
% 0.97/1.57 , Y, T ) ) }.
% 0.97/1.57 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.97/1.57 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.97/1.57 ( X, Z, Y ) }.
% 0.97/1.57 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.57 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.97/1.57 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.97/1.57 , T, Y ) ) }.
% 0.97/1.57 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.97/1.57 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ), c_Orderings_Oord__class_Oless
% 0.97/1.57 ( X, T, Y ) }.
% 0.97/1.57 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.57 c_Orderings_Oord__class_Oless( X, T, Y ), c_Orderings_Oord__class_Oless(
% 0.97/1.57 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.97/1.57 , Y, Z ) ) }.
% 0.97/1.57 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.57 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.97/1.57 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.57 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.57 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.97/1.57 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( X, U, T ) }.
% 0.97/1.57 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.57 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.97/1.57 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, U, T ),
% 0.97/1.57 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.57 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.57 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.97/1.57 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.97/1.57 c_Orderings_Oord__class_Oless( X, U, T ) }.
% 0.97/1.57 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.97/1.57 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = Z }.
% 0.97/1.57 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.57 c_Groups_Ominus__class_Ominus( X, Z, Y ), Y ) = Z }.
% 0.97/1.57 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.97/1.57 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.57 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oabs__class_Oabs( X, Y
% 0.97/1.57 ) ) }.
% 0.97/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.97/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), Y = X }.
% 0.97/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.97/1.57 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.97/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.97/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), ! Y = X }.
% 0.97/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), Y = X,
% 0.97/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ) }.
% 0.97/1.57 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.97/1.57 c_Groups_Oabs__class_Oabs( X, c_Groups_Oplus__class_Oplus( X,
% 0.97/1.57 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ) )
% 0.97/1.57 = c_Groups_Oplus__class_Oplus( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.97/1.57 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.97/1.57 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.97/1.57 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.97/1.57 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus(
% 0.97/1.57 X, U, Z ), c_Groups_Ominus__class_Ominus( X, T, Y ) ) }.
% 0.97/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.97/1.57 c_RealDef_Opositive( c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X,
% 0.97/1.57 Y ) ) }.
% 0.97/1.57 { ! c_RealDef_Opositive( c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X
% 0.97/1.57 , Y ) ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ) }.
% 0.97/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.57 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs
% 0.97/1.57 ( tc_RealDef_Oreal, X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 0.97/1.57 , X ) }.
% 0.97/1.57 { ! class_Groups_Ominus( X ), hAPP( c_Groups_Ominus__class_Ominus( tc_fun(
% 0.97/1.57 U, X ), T, Z ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( T, Y ),
% 0.97/1.57 hAPP( Z, Y ) ) }.
% 0.97/1.57 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.57 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.97/1.57 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X
% 0.97/1.57 , U, Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.97/1.57 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.57 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.97/1.57 ( X, c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 0.97/1.57 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.57 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.97/1.57 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.97/1.57 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.97/1.57 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.97/1.57 ( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) }.
% 0.97/1.57 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.97/1.57 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.97/1.57 ( X, Z, c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.97/1.57 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.97/1.57 , Y ) = c_Groups_Oplus__class_Oplus( X, Y, Z ) }.
% 0.97/1.57 { ! class_Rings_Olinordered__idom( X ), Z = Y,
% 0.97/1.57 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.97/1.57 X, Y, Z ) }.
% 0.97/1.57 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.57 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.97/1.57 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.97/1.57 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.57 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), v_d____ ) }.
% 0.97/1.57 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), v_r ) }.
% 0.97/1.57 { ! c_RealDef_Opositive( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) )
% 0.97/1.57 }.
% 0.97/1.57 { ! c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) =
% 0.97/1.57 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.97/1.57 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.57 ( X, c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero( X ) ) }
% 0.97/1.57 .
% 0.97/1.57 { ! class_Rings_Olinordered__semidom( X ), !
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.97/1.57 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.57 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.97/1.57 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.97/1.57 { ! class_Rings_Olinordered__semidom( X ),
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.57 c_Groups_Oone__class_Oone( X ) ) }.
% 0.97/1.57 { ! class_Groups_Oone( X ), ! c_Groups_Oone__class_Oone( X ) = Y, Y =
% 0.97/1.57 c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.57 { ! class_Groups_Oone( X ), ! Y = c_Groups_Oone__class_Oone( X ),
% 0.97/1.57 c_Groups_Oone__class_Oone( X ) = Y }.
% 0.97/1.57 { ! class_Groups_Ozero( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y, Y =
% 0.97/1.57 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.57 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.57 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 0.97/1.57 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.97/1.57 X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }
% 0.97/1.57 .
% 0.97/1.57 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.97/1.57 X ), Z, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z )
% 0.97/1.57 }.
% 0.97/1.57 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.97/1.57 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z
% 0.97/1.57 ), c_Orderings_Oord__class_Oless( tc_fun( T, X ), Z, Y ) }.
% 0.97/1.57 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.97/1.57 c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.57 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Oone__class_Oone( X ) =
% 0.97/1.57 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.57 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.57 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.97/1.57 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.97/1.57 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.97/1.57 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.57 ( X ), ! Z = c_Groups_Oplus__class_Oplus( X, Z, Y ), Y =
% 0.97/1.57 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.57 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.57 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.97/1.57 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 0.97/1.57 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X,
% 0.97/1.57 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.57 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.97/1.57 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.57 c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ) ) }.
% 0.97/1.57 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.57 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.97/1.57 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.57 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.97/1.57 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.57 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.97/1.57 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.57 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.97/1.57 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero( X ) =
% 0.97/1.57 c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 0.97/1.57 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.97/1.57 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.97/1.57 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.97/1.57 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.97/1.57 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y,
% 0.97/1.57 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.97/1.57 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y, Y )
% 0.97/1.57 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.57 { ! class_Groups_Oab__group__add( X ), ! Z = Y,
% 0.97/1.57 c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.97/1.57 ) }.
% 0.97/1.57 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.97/1.57 Z, Y ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.97/1.57 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.97/1.57 ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.97/1.57 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ominus__class_Ominus(
% 0.97/1.57 X, Z, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.57 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.97/1.57 c_Groups_Oabs__class_Oabs( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.97/1.57 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.57 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.97/1.57 c_Groups_Oabs__class_Oabs( X, Y ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.97/1.57 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.57 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! Y =
% 0.97/1.57 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oabs__class_Oabs( X, Y ) =
% 0.97/1.57 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.57 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.97/1.57 , Y, c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) )
% 0.97/1.57 ) }.
% 0.97/1.57 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.57 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.97/1.57 c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless(
% 0.97/1.57 X, T, c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.97/1.57 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.97/1.57 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oone__class_Oone
% 0.97/1.57 ( tc_RealDef_Oreal ), c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) )
% 0.97/1.57 ) }.
% 0.97/1.57 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.57 c_Groups_Oplus__class_Oplus( X, Y, Y ) ),
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.57 ) }.
% 0.97/1.57 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.57 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.97/1.57 ), c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.97/1.57 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Y,
% 0.97/1.57 Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.57 ) }.
% 0.97/1.57 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.57 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X
% 0.97/1.57 , Y, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.57 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.57 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.57 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.57 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.97/1.57 ) }.
% 0.97/1.57 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.57 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.57 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.97/1.57 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 0.97/1.57 .
% 0.97/1.57 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.57 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.57 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.97/1.57 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.97/1.57 .
% 0.97/1.57 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.57 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.57 X ), Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), ! Z =
% 0.97/1.57 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.97/1.57 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.57 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.57 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.97/1.57 Y, Z ) ) }.
% 0.97/1.57 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.57 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.97/1.57 Z, Y ) ) }.
% 0.97/1.57 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.57 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.97/1.57 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.57 , c_Groups_Oplus__class_Oplus( X, Y, Z ), c_Groups_Ozero__class_Ozero( X
% 0.97/1.57 ) ) }.
% 0.97/1.57 { ! c_RealDef_Opositive( X ), ! c_RealDef_Opositive( Y ),
% 0.97/1.57 c_RealDef_Opositive( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X, Y
% 0.97/1.57 ) ) }.
% 0.97/1.57 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.57 c_Groups_Oplus__class_Oplus( X, Y, Y ) ), c_Orderings_Oord__class_Oless(
% 0.97/1.57 X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.97/1.57 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.57 c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.97/1.57 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.97/1.57 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Y
% 0.97/1.57 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.57 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.57 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.97/1.57 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.57 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.57 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.97/1.57 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.57 c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.97/1.57 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.57 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.57 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.57 , c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.97/1.57 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.57 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 0.97/1.57 , Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.57 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 0.97/1.57 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.57 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.57 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.97/1.57 X, c_Groups_Ominus__class_Ominus( X, Z, Y ), c_Groups_Ozero__class_Ozero
% 0.97/1.57 ( X ) ) }.
% 0.97/1.57 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.97/1.57 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.97/1.57 , Z, Y ) }.
% 0.97/1.57 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.57 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.97/1.57 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Y ),
% 0.97/1.57 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.57 }.
% 0.97/1.57 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! Y =
% 0.97/1.57 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.57 c_Groups_Oabs__class_Oabs( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.57 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.57 ), c_Groups_Oabs__class_Oabs( X, Y ) = Y }.
% 0.97/1.57 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.97/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X, Y ),
% 0.97/1.57 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.57 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.97/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.57 c_Groups_Oabs__class_Oabs( X, Y ) ), ! Y = c_Groups_Ozero__class_Ozero( X
% 0.97/1.57 ) }.
% 0.97/1.57 { ! class_Groups_Oordered__ab__group__add__abs( X ), Y =
% 0.97/1.57 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.57 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.97/1.57 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.97/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.57 c_Groups_Oabs__class_Oabs( X, Y ) = Y }.
% 0.97/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.57 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ),
% 0.97/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.97/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.57 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ),
% 0.97/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.97/1.57 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.57 ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.57 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.57 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.97/1.57 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.57 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.57 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.57 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.97/1.57 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.57 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.97/1.57 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.97/1.57 ) ) }.
% 0.97/1.57 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.57 ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.97/1.57 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.97/1.57 ) ) }.
% 0.97/1.57 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.57 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.57 ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.97/1.57 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.97/1.57 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.57 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.97/1.57 ) ), c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 0.97/1.57 ) ) }.
% 0.97/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.57 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.97/1.57 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.97/1.57 ) ) }.
% 0.97/1.57 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.57 c_Groups_Oplus__class_Oplus( X, Y, Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.57 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.57 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.97/1.57 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.97/1.57 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), !
% 0.97/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, Z ),
% 0.97/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol3( T, U, W ) ) }.
% 0.97/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), !
% 0.97/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, Z ), !
% 0.97/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.57 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 0.97/1.57 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, T ) ), skol3( X, Y, Z
% 0.97/1.57 ) ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, T ) }.
% 0.97/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), !
% 0.97/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, Z ), !
% 0.97/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.57 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 0.97/1.57 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, T ) ), skol3( X, Y, Z
% 0.97/1.57 ) ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, T, Z ) }.
% 0.97/1.57 { ! class_Rings_Olinordered__semiring__1__strict( X ), !
% 0.97/1.57 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.57 ( X, T, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.57 c_Groups_Ozero__class_Ozero( X ), U ), !
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), W
% 0.97/1.57 ), ! c_Groups_Oplus__class_Oplus( X, U, W ) = c_Groups_Oone__class_Oone
% 0.97/1.57 ( X ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X,
% 0.97/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.97/1.57 c_Groups_Otimes__class_Otimes( X ), W ), T ) ), Y ) }.
% 0.97/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), !
% 0.97/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, Z ),
% 0.97/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol4( T, U, W ) ) }.
% 0.97/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), !
% 0.97/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, Z ), !
% 0.97/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.57 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 0.97/1.57 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, T ) ), skol4( X, Y, Z
% 0.97/1.57 ) ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, T ) }.
% 0.97/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), !
% 0.97/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, Z ), !
% 0.97/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.57 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 0.97/1.57 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, T ) ), skol4( X, Y, Z
% 0.97/1.57 ) ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, T, Z ) }.
% 0.97/1.57 { ! class_Rings_Olinordered__semiring__1( X ), !
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( X, T, Y ), !
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.97/1.57 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.57 X ), W ), ! c_Groups_Oplus__class_Oplus( X, U, W ) =
% 0.97/1.57 c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.57 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.57 ( X ), U ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), T )
% 0.97/1.57 ), Y ) }.
% 0.97/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.57 tc_Int_Oint, Y ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal
% 0.97/1.57 , X, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.57 tc_Int_Oint, Z ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ),
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, Z ) }.
% 0.97/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 0.97/1.57 = c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.57 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.97/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.57 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Groups_Osgn__class_Osgn( X, Y
% 0.97/1.57 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.57 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Groups_Osgn__class_Osgn( X, Y
% 0.97/1.57 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.57 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, X ) }.
% 0.97/1.57 { c_RealDef_Oreal( tc_Int_Oint, c_Groups_Oone__class_Oone( tc_Int_Oint ) )
% 0.97/1.57 = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.97/1.57 { c_RealDef_Oreal( tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint )
% 0.97/1.57 ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.57 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, Y ) =
% 0.97/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ),
% 0.97/1.57 c_Groups_Osgn__class_Osgn( X, Y ) ) }.
% 0.97/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.57 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ),
% 0.97/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.57 tc_Int_Oint ), X ) }.
% 0.97/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.57 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.57 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) }.
% 0.97/1.57 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ) }.
% 0.97/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 0.97/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), ! Y = X }.
% 0.97/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), Y = X,
% 0.97/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.97/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.97/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.97/1.57 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X )
% 0.97/1.57 }.
% 0.97/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.97/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.97/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.97/1.57 tc_Int_Oint ) ) ) }.
% 0.97/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.97/1.57 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 0.97/1.57 ( tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.97/1.57 .
% 0.97/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.97/1.57 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 0.97/1.57 ( tc_Int_Oint ) ) ) }.
% 0.97/1.57 { ! c_RealDef_Oreal( tc_Int_Oint, X ) = c_Groups_Ozero__class_Ozero(
% 0.97/1.57 tc_RealDef_Oreal ), X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.97/1.57 { ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_RealDef_Oreal(
% 0.97/1.57 tc_Int_Oint, X ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.57 { ! class_Rings_Olinordered__idom( X ), hAPP( hAPP(
% 0.97/1.57 c_Groups_Otimes__class_Otimes( X ), c_Groups_Osgn__class_Osgn( X, Y ) ),
% 0.97/1.57 c_Groups_Oabs__class_Oabs( X, Y ) ) = Y }.
% 0.97/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.97/1.57 tc_Int_Oint ) ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X )
% 0.97/1.57 }.
% 0.97/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.97/1.57 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.97/1.57 tc_Int_Oint ) ), X ) }.
% 0.97/1.57 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hAPP( hAPP(
% 0.97/1.57 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) = hAPP( hAPP
% 0.97/1.57 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ), Z = Y }.
% 0.97/1.57 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP
% 0.97/1.57 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) = hAPP(
% 0.97/1.58 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) }.
% 0.97/1.58 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) = hAPP( hAPP
% 0.97/1.58 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ), Z = Y }.
% 0.97/1.58 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP
% 0.97/1.58 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) = hAPP(
% 0.97/1.58 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.58 tc_Int_Oint ), c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.97/1.58 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.97/1.58 tc_Int_Oint ) ), X ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ),
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Z ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, Z ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ), Y = X }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Z ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.97/1.58 tc_Int_Oint, Y, T ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.97/1.58 .
% 0.97/1.58 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.58 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), Y ) ) }.
% 0.97/1.58 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 0.97/1.58 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Z ) }.
% 0.97/1.58 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.58 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 0.97/1.58 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.58 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.97/1.58 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 0.97/1.58 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 0.97/1.58 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 0.97/1.58 { ! class_Rings_Olinordered__idom( X ), c_Groups_Osgn__class_Osgn( X, hAPP
% 0.97/1.58 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Osgn__class_Osgn( X, Z ) ),
% 0.97/1.58 c_Groups_Osgn__class_Osgn( X, Y ) ) }.
% 0.97/1.58 { ! class_Rings_Olinordered__idom( X ), c_Groups_Osgn__class_Osgn( X,
% 0.97/1.58 c_Groups_Osgn__class_Osgn( X, Y ) ) = c_Groups_Osgn__class_Osgn( X, Y ) }
% 0.97/1.58 .
% 0.97/1.58 { ! class_Groups_Oab__semigroup__mult( X ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.58 { ! c_RealDef_Oreal( tc_Int_Oint, Y ) = c_RealDef_Oreal( tc_Int_Oint, X ),
% 0.97/1.58 Y = X }.
% 0.97/1.58 { ! Y = X, c_RealDef_Oreal( tc_Int_Oint, Y ) = c_RealDef_Oreal( tc_Int_Oint
% 0.97/1.58 , X ) }.
% 0.97/1.58 { c_RealDef_Oreal( tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.58 tc_Int_Oint ), Y ), X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.58 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Int_Oint, Y ) ), c_RealDef_Oreal
% 0.97/1.58 ( tc_Int_Oint, X ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.58 tc_Int_Oint, Y ), c_RealDef_Oreal( tc_Int_Oint, X ) ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.58 tc_Int_Oint, Y ), c_RealDef_Oreal( tc_Int_Oint, X ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.58 tc_Int_Oint, X ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.58 tc_Int_Oint, X ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.97/1.58 tc_Int_Oint, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.97/1.58 tc_Int_Oint, X ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.58 tc_Int_Oint, Y ), c_RealDef_Oreal( tc_Int_Oint, X ) ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.58 tc_Int_Oint, Y ), c_RealDef_Oreal( tc_Int_Oint, X ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.58 tc_Int_Oint, X ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.58 tc_Int_Oint, X ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.97/1.58 tc_Int_Oint, X ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.58 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.97/1.58 tc_Int_Oint, X ) ) }.
% 0.97/1.58 { c_RealDef_Oreal( tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y
% 0.97/1.58 , X ) ) = c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal
% 0.97/1.58 ( tc_Int_Oint, Y ), c_RealDef_Oreal( tc_Int_Oint, X ) ) }.
% 0.97/1.58 { c_RealDef_Oreal( tc_Int_Oint, c_Groups_Ominus__class_Ominus( tc_Int_Oint
% 0.97/1.58 , Y, X ) ) = c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.97/1.58 c_RealDef_Oreal( tc_Int_Oint, Y ), c_RealDef_Oreal( tc_Int_Oint, X ) ) }
% 0.97/1.58 .
% 0.97/1.58 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.58 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) =
% 0.97/1.58 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.58 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.97/1.58 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.58 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.58 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) =
% 0.97/1.58 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.58 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.97/1.58 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.58 { ! class_Rings_Oring__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.97/1.58 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.58 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.58 { ! class_Rings_Oring__no__zero__divisors( X ), ! Z =
% 0.97/1.58 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.97/1.58 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.58 { ! class_Rings_Oring__no__zero__divisors( X ), ! Y =
% 0.97/1.58 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.97/1.58 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.58 { ! class_Rings_Ono__zero__divisors( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.58 X ), Z = c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) =
% 0.97/1.58 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.58 { ! class_Rings_Ono__zero__divisors( X ), ! hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.97/1.58 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.58 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.58 { c_RealDef_Oreal( tc_Int_Oint, c_Groups_Oabs__class_Oabs( tc_Int_Oint, X )
% 0.97/1.58 ) = c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.58 tc_Int_Oint, X ) ) }.
% 0.97/1.58 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.58 ( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.97/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.58 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.97/1.58 ), U = Z, T = Y }.
% 0.97/1.58 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.58 ( X ), ! U = Z, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.97/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.58 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.97/1.58 ) }.
% 0.97/1.58 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.58 ( X ), ! T = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.97/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.58 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.97/1.58 ) }.
% 0.97/1.58 { ! class_Rings_Osemiring( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP
% 0.97/1.58 ( c_Groups_Otimes__class_Otimes( X ), U ), T ),
% 0.97/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.58 ( X ), Z ), T ), Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, U, Z
% 0.97/1.58 ) ), T ), Y ) }.
% 0.97/1.58 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.58 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Y
% 0.97/1.58 ) ), Z ) }.
% 0.97/1.58 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.97/1.58 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.58 { ! class_Rings_Ocomm__semiring( X ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.97/1.58 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.58 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.58 ( X ), U = T, Z = Y, ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.97/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.58 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.97/1.58 ) }.
% 0.97/1.58 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.58 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.97/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.58 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.97/1.58 ), ! U = T }.
% 0.97/1.58 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.58 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.97/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.58 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.97/1.58 ), ! Z = Y }.
% 0.97/1.58 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.58 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.58 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.97/1.58 = Y }.
% 0.97/1.58 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.97/1.58 = Y }.
% 0.97/1.58 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.97/1.58 = Y }.
% 0.97/1.58 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.97/1.58 = Y }.
% 0.97/1.58 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.97/1.58 = Y }.
% 0.97/1.58 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.97/1.58 = Y }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 0.97/1.58 { ! class_Rings_Olinordered__idom( X ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Y ) ),
% 0.97/1.58 c_Groups_Oabs__class_Oabs( X, Y ) ) = hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.97/1.58 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, hAPP
% 0.97/1.58 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 0.97/1.58 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.97/1.58 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.97/1.58 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) = X }.
% 0.97/1.58 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ) ), X ) =
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.97/1.58 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y =
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.58 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X =
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.58 { ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! X =
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.58 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 0.97/1.58 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.58 }.
% 0.97/1.58 { ! class_Rings_Olinordered__idom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.58 X ), c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.58 }.
% 0.97/1.58 { ! class_Groups_Osgn__if( X ), c_Groups_Osgn__class_Osgn( X,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.58 { ! c_RealDef_Opositive( X ), ! c_RealDef_Opositive( Y ),
% 0.97/1.58 c_RealDef_Opositive( hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.58 tc_RealDef_Oreal ), X ), Y ) ) }.
% 0.97/1.58 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.97/1.58 ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.58 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.97/1.58 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.58 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.58 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.58 X ), Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.97/1.58 ( X ) ) }.
% 0.97/1.58 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.58 , c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.58 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.97/1.58 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.58 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.58 , Z, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.58 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.97/1.58 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.58 { ! class_Rings_Oordered__semiring( X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.58 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.58 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.97/1.58 { ! class_Rings_Oordered__semiring( X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.97/1.58 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.58 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.97/1.58 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.58 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.58 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.97/1.58 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.58 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.58 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.97/1.58 { ! class_Rings_Oordered__comm__semiring( X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.97/1.58 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.58 { ! class_Rings_Oordered__semiring( X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.97/1.58 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.58 { ! class_Rings_Oordered__semiring( X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.97/1.58 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.97/1.58 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.58 , Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.58 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.97/1.58 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.58 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.58 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.58 X ), Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.97/1.58 ( X ) ) }.
% 0.97/1.58 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.58 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.58 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.97/1.58 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.58 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.58 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.58 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ),
% 0.97/1.58 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.58 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.58 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.58 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.58 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.97/1.58 ( X ) ), alpha1( X, Y, Z ), alpha17( X, Y, Z ) }.
% 0.97/1.58 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha1( X, Y, Z ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.97/1.58 ( X ) ) }.
% 0.97/1.58 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha17( X, Y, Z ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.97/1.58 ( X ) ) }.
% 0.97/1.58 { ! alpha17( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.58 { ! alpha17( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.97/1.58 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.97/1.58 ( X ), Y ), alpha17( X, Y, Z ) }.
% 0.97/1.58 { ! alpha1( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.97/1.58 { ! alpha1( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.58 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( X ) ), alpha1( X, Y, Z ) }.
% 0.97/1.58 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.58 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), alpha2( X, Y
% 0.97/1.58 , Z ), alpha18( X, Y, Z ) }.
% 0.97/1.58 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha2( X, Y, Z ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.58 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.58 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha18( X, Y, Z ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.58 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.58 { ! alpha18( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.58 { ! alpha18( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.97/1.58 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( X ) ), alpha18( X, Y, Z ) }.
% 0.97/1.58 { ! alpha2( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.97/1.58 { ! alpha2( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.58 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( X ), Y ), alpha2( X, Y, Z ) }.
% 0.97/1.58 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.97/1.58 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) }.
% 0.97/1.58 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.58 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.97/1.58 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP
% 0.97/1.58 ( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.97/1.58 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.58 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.97/1.58 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.97/1.58 ( c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.97/1.58 { ! class_Rings_Olinordered__comm__semiring__strict( X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.58 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.97/1.58 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.97/1.58 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.58 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.58 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.97/1.58 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.97/1.58 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.58 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.58 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.97/1.58 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP
% 0.97/1.58 ( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.97/1.58 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.58 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.58 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.58 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.58 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.58 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.97/1.58 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.97/1.58 ( X ) ) }.
% 0.97/1.58 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.58 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.97/1.58 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.58 ! c_Orderings_Oord__class_Oless( X, Z, T ), c_Orderings_Oord__class_Oless
% 0.97/1.58 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.97/1.58 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.58 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.97/1.58 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ) }
% 0.97/1.58 .
% 0.97/1.58 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.97/1.58 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.97/1.58 .
% 0.97/1.58 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.58 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.58 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.97/1.58 ( X ) ) }.
% 0.97/1.58 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.58 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.58 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.97/1.58 ( X ) ) }.
% 0.97/1.58 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.58 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.97/1.58 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.58 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.58 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.58 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.97/1.58 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.58 ! c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless
% 0.97/1.58 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.97/1.58 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.58 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha3( X, Y, Z, T ),
% 0.97/1.58 alpha19( X, Y, Z, T ) }.
% 0.97/1.58 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha3( X, Y, Z, T ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.58 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha19( X, Y, Z, T ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.58 { ! alpha19( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.58 { ! alpha19( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( X, T, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.58 , ! c_Orderings_Oord__class_Oless( X, Y, Z ), alpha19( X, Y, Z, T ) }.
% 0.97/1.58 { ! alpha3( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( X ), T ) }.
% 0.97/1.58 { ! alpha3( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T )
% 0.97/1.58 , ! c_Orderings_Oord__class_Oless( X, Z, Y ), alpha3( X, Y, Z, T ) }.
% 0.97/1.58 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha4( X, Y, Z, T ),
% 0.97/1.58 alpha20( X, Y, Z, T ) }.
% 0.97/1.58 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha4( X, Y, Z, T ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.58 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha20( X, Y, Z, T ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.58 { ! alpha20( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.58 { ! alpha20( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, T ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.58 , ! c_Orderings_Oord__class_Oless( X, Y, T ), alpha20( X, Y, Z, T ) }.
% 0.97/1.58 { ! alpha4( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.97/1.58 { ! alpha4( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.97/1.58 , ! c_Orderings_Oord__class_Oless( X, T, Y ), alpha4( X, Y, Z, T ) }.
% 0.97/1.58 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.58 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 0.97/1.58 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.58 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.58 ( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! W = U, T = Z, !
% 0.97/1.58 c_Groups_Oplus__class_Oplus( X, W, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) =
% 0.97/1.58 c_Groups_Oplus__class_Oplus( X, U, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.58 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.58 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.58 ( X, c_Groups_Oone__class_Oone( X ), Z ), c_Orderings_Oord__class_Oless(
% 0.97/1.58 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.58 { ! class_Rings_Oring( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.97/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.58 ( X ), U ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 0.97/1.58 Z ) ), Y ) ) }.
% 0.97/1.58 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.97/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.58 ( X ), Z ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.97/1.58 Z ) ), U ), T ) = Y }.
% 0.97/1.58 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.97/1.58 Z ) ), U ), T ) = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.97/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.58 ( X ), Z ), U ), Y ) }.
% 0.97/1.58 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.97/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.58 ( X ), Z ), U ), Y ), T = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.97/1.58 W ) ), U ), Y ) }.
% 0.97/1.58 { ! class_Rings_Oring( X ), ! T = c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.97/1.58 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.97/1.58 X, Z, W ) ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.97/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.58 ( X ), Z ), U ), Y ) }.
% 0.97/1.58 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.58 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = hAPP(
% 0.97/1.58 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X
% 0.97/1.58 , Z, c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.97/1.58 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.97/1.58 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP
% 0.97/1.58 ( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.97/1.58 c_Groups_Oone__class_Oone( X ) ) ), Z ) }.
% 0.97/1.58 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.97/1.58 , Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.97/1.58 c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.97/1.58 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.97/1.58 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.58 , c_Groups_Oabs__class_Oabs( X, Z ), Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.58 ( X, c_Groups_Oabs__class_Oabs( X, U ), T ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 0.97/1.58 c_Groups_Oabs__class_Oabs( X, U ) ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.97/1.58 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.58 , c_Groups_Osgn__class_Osgn( X, Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.97/1.58 .
% 0.97/1.58 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.58 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.97/1.58 , c_Groups_Osgn__class_Osgn( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }
% 0.97/1.58 .
% 0.97/1.58 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.58 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.97/1.58 .
% 0.97/1.58 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.58 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X
% 0.97/1.58 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) ) }
% 0.97/1.58 .
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.58 tc_Int_Oint, Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.97/1.58 c_RealDef_Oreal( tc_Int_Oint, X ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.58 tc_Int_Oint, Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.97/1.58 c_RealDef_Oreal( tc_Int_Oint, X ) ), c_Orderings_Oord__class_Oless(
% 0.97/1.58 tc_Int_Oint, Y, X ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.58 tc_Int_Oint, Y ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.97/1.58 c_RealDef_Oreal( tc_Int_Oint, X ), c_Groups_Oone__class_Oone(
% 0.97/1.58 tc_RealDef_Oreal ) ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y
% 0.97/1.58 , X ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.58 tc_Int_Oint, Y ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.97/1.58 c_RealDef_Oreal( tc_Int_Oint, X ), c_Groups_Oone__class_Oone(
% 0.97/1.58 tc_RealDef_Oreal ) ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.58 tc_Int_Oint, Y ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.97/1.58 c_RealDef_Oreal( tc_Int_Oint, X ), c_Groups_Oone__class_Oone(
% 0.97/1.58 tc_RealDef_Oreal ) ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y
% 0.97/1.58 , X ) }.
% 0.97/1.58 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.58 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.97/1.58 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.97/1.58 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.58 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.58 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.97/1.58 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.97/1.58 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.58 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.97/1.58 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.97/1.58 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.58 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.97/1.58 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.97/1.58 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.97/1.58 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless( X, U, T ), ! c_Orderings_Oord__class_Oless
% 0.97/1.58 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.97/1.58 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.97/1.58 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.97/1.58 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.58 , U ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.97/1.58 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.58 ( X, U, T ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.97/1.58 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.97/1.58 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.58 ( X, U, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.97/1.58 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.97/1.58 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.58 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.97/1.58 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.58 ! c_Orderings_Oord__class_Oless__eq( X, Z, T ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.58 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.58 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.97/1.58 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.58 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.58 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.97/1.58 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.97/1.58 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.97/1.58 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) }.
% 0.97/1.58 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.97/1.58 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.97/1.58 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.97/1.58 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) }.
% 0.97/1.58 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.58 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.97/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.58 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.58 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ) }.
% 0.97/1.58 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.58 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.97/1.58 Z ) ), U ), T ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.58 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.97/1.58 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.58 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.97/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.58 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X, T,
% 0.97/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.58 ( X ), c_Groups_Ominus__class_Ominus( X, Z, W ) ), U ), Y ) ) }.
% 0.97/1.58 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.58 , T, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.97/1.58 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.58 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.97/1.58 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.97/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.58 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.97/1.58 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.97/1.58 X, W, Z ) ), U ), T ), Y ) }.
% 0.97/1.58 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.97/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.58 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.97/1.58 hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.97/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.58 ( X ), Z ), U ), Y ) ) }.
% 0.97/1.58 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.97/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.58 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, hAPP
% 0.97/1.58 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus
% 0.97/1.58 ( X, Z, W ) ), U ), Y ) ) }.
% 0.97/1.58 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X, T
% 0.97/1.58 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.97/1.58 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.58 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.97/1.58 { ! class_Rings_Oring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP
% 0.97/1.58 ( c_Groups_Otimes__class_Otimes( X ), Y ), Y ), c_Groups_Oone__class_Oone
% 0.97/1.58 ( X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.97/1.58 c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) ) ),
% 0.97/1.58 c_Groups_Ominus__class_Ominus( X, Y, c_Groups_Oone__class_Oone( X ) ) ) }
% 0.97/1.58 .
% 0.97/1.58 { ! class_Rings_Oordered__ring__abs( X ), alpha52( X, Z ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.58 ), c_Groups_Oabs__class_Oabs( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 0.97/1.58 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.97/1.58 { ! class_Rings_Oordered__ring__abs( X ), alpha52( X, Z ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.58 ), c_Groups_Oabs__class_Oabs( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 0.97/1.58 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.97/1.58 { ! alpha52( X, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.97/1.58 { ! alpha52( X, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.58 { c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.58 ), c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero
% 0.97/1.58 ( X ) ), alpha52( X, Y ) }.
% 0.97/1.58 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.97/1.58 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 0.97/1.58 Y ) = c_Groups_Oabs__class_Oabs( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.58 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.58 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_w____ ), v_r ) }
% 0.97/1.58 .
% 0.97/1.58 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.58 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.97/1.58 ) ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 0.97/1.58 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.58 { ! class_Rings_Olinordered__ring__strict( X ), Z =
% 0.97/1.58 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.97/1.58 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.97/1.58 { ! class_Rings_Olinordered__ring__strict( X ), Y =
% 0.97/1.58 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.97/1.58 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.97/1.58 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.58 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.97/1.58 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.58 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.97/1.58 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.97/1.58 c_Groups_Ozero__class_Ozero( X ) ), Z = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.58 }.
% 0.97/1.58 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.97/1.58 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.97/1.58 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.58 }.
% 0.97/1.58 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.97/1.58 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.58 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.97/1.58 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.97/1.58 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.58 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.97/1.58 X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 0.97/1.58 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.58 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ),
% 0.97/1.58 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Z ) ) ), Y =
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.58 c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, X ) =
% 0.97/1.58 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.97/1.58 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.97/1.58 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.97/1.58 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.97/1.58 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.97/1.58 X, U, Z ) ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 0.97/1.58 Z ) ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 0.97/1.58 c_Groups_Ominus__class_Ominus( X, T, Y ) ) ) }.
% 0.97/1.58 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.58 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_g____( X ) ), v_r
% 0.97/1.58 ) }.
% 0.97/1.58 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.97/1.58 tc_Int_Oint, c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ) =
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.97/1.58 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.58 tc_Int_Oint ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.97/1.58 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.58 tc_Int_Oint ), X ) = X }.
% 0.97/1.58 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero
% 0.97/1.58 ( tc_Int_Oint ) ) = X }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ominus__class_Ominus
% 0.97/1.58 ( tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ),
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.97/1.58 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y
% 0.97/1.58 = X }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.97/1.58 tc_Int_Oint ) ) ) }.
% 0.97/1.58 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.97/1.58 tc_Int_Oint ) ) ) }.
% 0.97/1.58 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ) =
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oabs__class_Oabs(
% 0.97/1.58 tc_Int_Oint, X ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X =
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.97/1.58 { ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oabs__class_Oabs(
% 0.97/1.58 tc_Int_Oint, X ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.97/1.58 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ), X ) =
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.97/1.58 ( tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.97/1.58 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.97/1.58 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.97/1.58 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.58 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.58 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), X =
% 0.97/1.58 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.58 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.58 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), Y =
% 0.97/1.58 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.58 ( tc_Int_Oint ), X ), ! X = c_Groups_Oone__class_Oone( tc_Int_Oint ), ! Y
% 0.97/1.58 = c_Groups_Oone__class_Oone( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 0.97/1.58 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.58 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 0.97/1.58 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP
% 0.97/1.58 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.97/1.58 { ! c_Groups_Oabs__class_Oabs( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) =
% 0.97/1.58 c_Groups_Oone__class_Oone( tc_Int_Oint ), c_Groups_Oabs__class_Oabs(
% 0.97/1.58 tc_Int_Oint, X ) = c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.97/1.58 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 0.97/1.58 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = X }.
% 0.97/1.58 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.97/1.58 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) = X }.
% 0.97/1.58 { ! c_Groups_Ozero__class_Ozero( tc_Int_Oint ) = c_Groups_Oone__class_Oone
% 0.97/1.58 ( tc_Int_Oint ) }.
% 0.97/1.58 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 0.97/1.58 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.97/1.58 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 0.97/1.58 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.97/1.58 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) = hAPP
% 0.97/1.58 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) }.
% 0.97/1.58 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP(
% 0.97/1.58 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.97/1.58 tc_Int_Oint, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.97/1.58 .
% 0.97/1.58 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ), X ) =
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.97/1.58 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP
% 0.97/1.58 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), Y ) ), X ) =
% 0.97/1.58 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), hAPP
% 0.97/1.58 ( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.97/1.58 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.97/1.58 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 0.97/1.58 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) =
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.97/1.58 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus
% 0.97/1.58 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.97/1.58 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y = X,
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.97/1.58 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) =
% 0.97/1.58 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y )
% 0.97/1.58 }.
% 0.97/1.58 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) =
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) }.
% 0.97/1.58 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Oabs__class_Oabs
% 0.97/1.58 ( tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( X, Y ) ) =
% 0.97/1.58 c_RealVector_Onorm__class_Onorm( X, Y ) }.
% 0.97/1.58 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.97/1.58 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, Z,
% 0.97/1.58 Y ) ) = c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus
% 0.97/1.58 ( X, Y, Z ) ) }.
% 0.97/1.58 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.97/1.58 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.58 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.58 c_RealVector_Onorm__class_Onorm( X, Y ) = c_Groups_Ozero__class_Ozero(
% 0.97/1.58 tc_RealDef_Oreal ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.58 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.97/1.58 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X, Y )
% 0.97/1.58 = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.58 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.58 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.97/1.58 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 0.97/1.58 c_RealVector_Onorm__class_Onorm( X, Y ) ) ) }.
% 0.97/1.58 { ! class_RealVector_Oreal__normed__algebra( X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.58 c_RealVector_Onorm__class_Onorm( X, Z ), Y ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.58 c_RealVector_Onorm__class_Onorm( X, U ), T ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.58 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), T ) ) }.
% 0.97/1.58 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.97/1.58 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.97/1.58 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.58 c_RealVector_Onorm__class_Onorm( X, Y ), c_Groups_Ozero__class_Ozero(
% 0.97/1.58 tc_RealDef_Oreal ) ) }.
% 0.97/1.58 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 0.97/1.58 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oone__class_Oone( X ) ) =
% 0.97/1.58 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.97/1.58 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.58 c_RealVector_Onorm__class_Onorm( X, Y ), c_Groups_Ozero__class_Ozero(
% 0.97/1.58 tc_RealDef_Oreal ) ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.58 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.97/1.58 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq(
% 0.97/1.58 tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( X, Y ),
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.97/1.58 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.58 c_RealVector_Onorm__class_Onorm( X, Z ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ),
% 0.97/1.58 c_RealVector_Onorm__class_Onorm( X, T ) ) ), Z =
% 0.97/1.58 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.58 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.97/1.58 c_RealVector_Onorm__class_Onorm( X, Y ) ), ! Y =
% 0.97/1.58 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.58 { ! class_RealVector_Oreal__normed__vector( X ), Y =
% 0.97/1.58 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless(
% 0.97/1.58 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.97/1.58 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.97/1.58 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.58 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.97/1.58 ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.97/1.58 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.97/1.58 ( X, Y ) ) ) }.
% 0.97/1.58 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.58 c_RealVector_Onorm__class_Onorm( X, Z ), Y ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.58 c_RealVector_Onorm__class_Onorm( X, U ), T ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.58 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, Z, U
% 0.97/1.58 ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, T ) ) }.
% 0.97/1.58 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.58 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, Z,
% 0.97/1.58 Y ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.97/1.58 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.97/1.58 ( X, Y ) ) ) }.
% 0.97/1.58 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.97/1.58 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.97/1.58 ( X, Y ) ), c_RealVector_Onorm__class_Onorm( X,
% 0.97/1.58 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) ) }.
% 0.97/1.58 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.97/1.58 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.97/1.58 ( X, Y ) ), c_RealVector_Onorm__class_Onorm( X,
% 0.97/1.58 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) }.
% 0.97/1.58 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.58 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y ),
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.97/1.58 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X ) ),
% 0.97/1.58 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) ) }.
% 0.97/1.58 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.58 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X,
% 0.97/1.58 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.97/1.58 , Y ) ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.97/1.58 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, U,
% 0.97/1.58 Z ) ), c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus
% 0.97/1.58 ( X, T, Y ) ) ) ) }.
% 0.97/1.58 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.97/1.58 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X,
% 0.97/1.58 c_Groups_Osgn__class_Osgn( X, Y ) ) = c_Groups_Ozero__class_Ozero(
% 0.97/1.58 tc_RealDef_Oreal ) }.
% 0.97/1.58 { ! class_RealVector_Oreal__normed__vector( X ), Y =
% 0.97/1.58 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X,
% 0.97/1.58 c_Groups_Osgn__class_Osgn( X, Y ) ) = c_Groups_Oone__class_Oone(
% 0.97/1.58 tc_RealDef_Oreal ) }.
% 0.97/1.58 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.58 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.97/1.58 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.97/1.58 ( X, Y ) ) ), c_RealVector_Onorm__class_Onorm( X,
% 0.97/1.58 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) }.
% 0.97/1.58 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.97/1.58 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.58 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.97/1.58 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.58 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.97/1.58 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.58 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.97/1.58 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.58 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.97/1.58 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.58 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.97/1.58 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.58 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.58 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.58 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.58 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.58 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 0.97/1.58 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.58 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 0.97/1.58 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.58 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 0.97/1.58 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.58 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 0.97/1.58 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.58 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.58 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.97/1.58 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.58 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.97/1.58 c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) =
% 0.97/1.58 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.58 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Osgn__class_Osgn
% 0.97/1.58 ( X, c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X
% 0.97/1.58 ) }.
% 0.97/1.58 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 0.97/1.58 c_Groups_Osgn__class_Osgn( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.58 X ), Z ), Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.97/1.58 c_Groups_Osgn__class_Osgn( X, Z ) ), c_Groups_Osgn__class_Osgn( X, Y ) )
% 0.97/1.58 }.
% 0.97/1.58 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 0.97/1.58 c_Groups_Osgn__class_Osgn( X, c_Groups_Oone__class_Oone( X ) ) =
% 0.97/1.58 c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.58 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.58 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.97/1.58 ) = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X
% 0.97/1.58 ) }.
% 0.97/1.58 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.58 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.97/1.58 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.97/1.58 ) }.
% 0.97/1.58 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.97/1.58 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.58 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 0.97/1.58 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.58 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Z,
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Groups_Oplus__class_Oplus
% 0.97/1.58 ( tc_Int_Oint, c_Groups_Oabs__class_Oabs( tc_Int_Oint,
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, Z ) ),
% 0.97/1.58 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ), X ) ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.58 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Groups_Oplus__class_Oplus
% 0.97/1.58 ( tc_Int_Oint, c_Groups_Oabs__class_Oabs( tc_Int_Oint,
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ),
% 0.97/1.58 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ), X ) ), Y ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.58 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.97/1.58 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oone__class_Oone
% 0.97/1.58 ( tc_Int_Oint ), Y ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.58 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.97/1.58 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.97/1.58 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.97/1.58 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.97/1.58 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.97/1.58 ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Int_Oint, T, W ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.58 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.97/1.58 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, U ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, Z ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, T ) }.
% 0.97/1.58 { c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, X ) =
% 0.97/1.58 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.97/1.58 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.97/1.58 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.58 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.97/1.58 ( tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.97/1.58 Z ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.58 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, U ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, U ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Y ) }.
% 0.97/1.58 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.97/1.58 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.97/1.58 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.58 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.97/1.58 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, U, Y ) }.
% 0.97/1.58 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.97/1.58 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X ) ),
% 0.97/1.58 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y ) ),
% 0.97/1.58 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.97/1.58 tc_Int_Oint, X, Y ) ) }.
% 0.97/1.58 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 0.97/1.58 tc_Int_Oint ) ) }.
% 0.97/1.58 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ), X =
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.58 { ! X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) }.
% 0.97/1.58 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Ozero__class_Ozero(
% 0.97/1.58 tc_Int_Oint ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.58 tc_Int_Oint, skol5( X ) ), X ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.97/1.58 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint, skol5( X ),
% 0.97/1.58 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.58 tc_Int_Oint, skol6( X ) ), X ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.97/1.58 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint, skol6( X ),
% 0.97/1.58 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ) ) }.
% 0.97/1.58 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol7( Z, T ) ) }.
% 0.97/1.58 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.58 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.97/1.58 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol7( X, Y ) ) ) }.
% 0.97/1.58 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol8( Z, T ) ) }.
% 0.97/1.58 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.58 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.97/1.58 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol8( X, Y ) ) ) }.
% 0.97/1.58 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol9( Y ) ) }.
% 0.97/1.58 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.58 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.97/1.58 c_RealVector_Onorm__class_Onorm( X, Y ) ),
% 0.97/1.58 c_RealVector_Onorm__class_Onorm( X, Z ) ) ), skol9( X ) ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.58 tc_Int_Oint, Y ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.97/1.58 tc_RealDef_Oreal, X, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.97/1.58 c_RealDef_Oreal( tc_Int_Oint, Y ), c_Groups_Oone__class_Oone(
% 0.97/1.58 tc_RealDef_Oreal ) ) ), c_Archimedean__Field_Oceiling( tc_RealDef_Oreal,
% 0.97/1.58 X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.97/1.58 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.97/1.58 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ominus__class_Ominus(
% 0.97/1.58 tc_Int_Oint, X, Y ) }.
% 0.97/1.58 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.97/1.58 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint
% 0.97/1.58 ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.58 ( tc_Int_Oint ), X ), hBOOL( hAPP( Y, skol10( Z, Y ) ) ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! hBOOL( hAPP( Y, U ) )
% 0.97/1.58 , hBOOL( hAPP( Y, c_Groups_Ominus__class_Ominus( tc_Int_Oint, U, hAPP(
% 0.97/1.58 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), T ), X ) ) ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.58 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( Y, c_Groups_Ominus__class_Ominus(
% 0.97/1.58 tc_Int_Oint, skol10( X, Y ), X ) ) ), ! c_Orderings_Oord__class_Oless__eq
% 0.97/1.58 ( tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), ! hBOOL(
% 0.97/1.58 hAPP( Y, T ) ), hBOOL( hAPP( Y, c_Groups_Ominus__class_Ominus(
% 0.97/1.58 tc_Int_Oint, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 0.97/1.58 , Z ), X ) ) ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, v_N1____, X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.58 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, v_g____( hAPP(
% 0.97/1.58 v_f____, X ) ), v_z____ ) ), v_d____ ) }.
% 0.97/1.58 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.58 tc_Int_Oint, skol11( X ) ), X ) }.
% 0.97/1.58 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.97/1.58 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint, skol11( X ),
% 0.97/1.58 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ) ) }.
% 0.97/1.58 { c_SEQ_Osubseq( v_f____ ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, skol12( X ), Y ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.58 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, v_g____( hAPP(
% 0.97/1.58 v_f____, Y ) ), v_z____ ) ), X ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol13( X, Y ) ) }.
% 0.97/1.58 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.58 { ! c_RealDef_Oreal( tc_Int_Oint, c_Archimedean__Field_Oceiling(
% 0.97/1.58 tc_RealDef_Oreal, X ) ) = X, X = c_RealDef_Oreal( tc_Int_Oint, skol14( X
% 0.97/1.58 ) ) }.
% 0.97/1.58 { ! X = c_RealDef_Oreal( tc_Int_Oint, Y ), c_RealDef_Oreal( tc_Int_Oint,
% 0.97/1.58 c_Archimedean__Field_Oceiling( tc_RealDef_Oreal, X ) ) = X }.
% 0.97/1.58 { c_Archimedean__Field_Oceiling( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.58 tc_Int_Oint, X ) ) = X }.
% 0.97/1.58 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.97/1.58 tc_Int_Oint, c_Archimedean__Field_Oceiling( tc_RealDef_Oreal, X ) ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.58 c_Archimedean__Field_Oceiling( tc_RealDef_Oreal, Y ), X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, c_RealDef_Oreal(
% 0.97/1.58 tc_Int_Oint, X ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, c_RealDef_Oreal
% 0.97/1.58 ( tc_Int_Oint, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.58 c_Archimedean__Field_Oceiling( tc_RealDef_Oreal, Y ), X ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, c_RealDef_Oreal
% 0.97/1.58 ( tc_Int_Oint, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.58 c_Archimedean__Field_Oceiling( tc_RealDef_Oreal, Y ), X ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.58 c_Archimedean__Field_Oceiling( tc_RealDef_Oreal, Y ), X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, c_RealDef_Oreal(
% 0.97/1.58 tc_Int_Oint, X ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.97/1.58 c_Archimedean__Field_Oceiling( tc_RealDef_Oreal, X ) ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.58 tc_Int_Oint, Y ), X ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.58 tc_Int_Oint, Y ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.97/1.58 c_Archimedean__Field_Oceiling( tc_RealDef_Oreal, X ) ) }.
% 0.97/1.58 { c_Archimedean__Field_Oceiling( tc_RealDef_Oreal,
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, c_RealDef_Oreal(
% 0.97/1.58 tc_Int_Oint, X ) ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.97/1.58 c_Archimedean__Field_Oceiling( tc_RealDef_Oreal, Y ), X ) }.
% 0.97/1.58 { c_Archimedean__Field_Oceiling( tc_RealDef_Oreal,
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, c_RealDef_Oreal(
% 0.97/1.58 tc_Int_Oint, X ) ) ) = c_Groups_Ominus__class_Ominus( tc_Int_Oint,
% 0.97/1.58 c_Archimedean__Field_Oceiling( tc_RealDef_Oreal, Y ), X ) }.
% 0.97/1.58 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.58 tc_Int_Oint, c_Archimedean__Field_Oceiling( tc_RealDef_Oreal, X ) ),
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 0.97/1.58 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) }.
% 0.97/1.58 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.58 tc_Int_Oint, c_Archimedean__Field_Oceiling( tc_RealDef_Oreal, X ) ),
% 0.97/1.58 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Nat__Transfer_Otsub( X, Y )
% 0.97/1.58 ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.97/1.58 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ominus__class_Ominus(
% 0.97/1.58 tc_Int_Oint, X, Y ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.58 tc_Int_Oint, Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, c_RealDef_Oreal
% 0.97/1.58 ( tc_Int_Oint, Y ) ), c_Archimedean__Field_Oceiling( tc_RealDef_Oreal, X
% 0.97/1.58 ) = Y }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.97/1.58 c_Archimedean__Field_Oceiling( tc_RealDef_Oreal, X ) ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.58 tc_Int_Oint, Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) }
% 0.97/1.58 .
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.58 tc_Int_Oint, Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.97/1.58 c_Archimedean__Field_Oceiling( tc_RealDef_Oreal, X ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.58 c_Archimedean__Field_Oceiling( tc_RealDef_Oreal, Y ), X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y,
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.58 tc_Int_Oint, X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y,
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.58 tc_Int_Oint, X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Archimedean__Field_Oceiling
% 0.97/1.58 ( tc_RealDef_Oreal, Y ), X ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.58 tc_Int_Oint, Y ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal
% 0.97/1.58 , X, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.58 tc_Int_Oint, Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ),
% 0.97/1.58 c_Archimedean__Field_Oceiling( tc_RealDef_Oreal, X ) =
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.97/1.58 tc_Int_Oint ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, skol15, X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.58 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, v_g____( hAPP(
% 0.97/1.58 v_f____, X ) ), v_z____ ) ), v_d____ ) }.
% 0.97/1.58 { ! class_Archimedean__Field_Oarchimedean__field( X ),
% 0.97/1.58 c_Archimedean__Field_Oceiling( X, c_Groups_Ominus__class_Ominus( X, Y,
% 0.97/1.58 c_Groups_Oone__class_Oone( X ) ) ) = c_Groups_Ominus__class_Ominus(
% 0.97/1.58 tc_Int_Oint, c_Archimedean__Field_Oceiling( X, Y ),
% 0.97/1.58 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.97/1.58 { ! class_Archimedean__Field_Oarchimedean__field( X ),
% 0.97/1.58 c_Archimedean__Field_Oceiling( X, c_Groups_Oplus__class_Oplus( X, Y,
% 0.97/1.58 c_Groups_Oone__class_Oone( X ) ) ) = c_Groups_Oplus__class_Oplus(
% 0.97/1.58 tc_Int_Oint, c_Archimedean__Field_Oceiling( X, Y ),
% 0.97/1.58 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.97/1.58 { ! class_Archimedean__Field_Oarchimedean__field( X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oone__class_Oone(
% 0.97/1.58 tc_Int_Oint ), c_Archimedean__Field_Oceiling( X, Y ) ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), Y ) }.
% 0.97/1.58 { ! class_Archimedean__Field_Oarchimedean__field( X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), Y ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oone__class_Oone(
% 0.97/1.58 tc_Int_Oint ), c_Archimedean__Field_Oceiling( X, Y ) ) }.
% 0.97/1.58 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.58 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 0.97/1.58 ( tc_Nat_Onat ) ) ), X ) ) }.
% 0.97/1.58 { ! class_Archimedean__Field_Oarchimedean__field( X ),
% 0.97/1.58 c_Archimedean__Field_Oceiling( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.97/1.58 { ! class_Archimedean__Field_Oarchimedean__field( X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.58 c_Archimedean__Field_Oceiling( X, Z ), c_Archimedean__Field_Oceiling( X,
% 0.97/1.58 Y ) ) }.
% 0.97/1.58 { ! class_Archimedean__Field_Oarchimedean__field( X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Archimedean__Field_Oceiling
% 0.97/1.58 ( X, Z ), c_Archimedean__Field_Oceiling( X, Y ) ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.58 { ! class_Archimedean__Field_Oarchimedean__field( X ),
% 0.97/1.58 c_Archimedean__Field_Oceiling( X, c_Groups_Oone__class_Oone( X ) ) =
% 0.97/1.58 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.97/1.58 { ! class_Archimedean__Field_Oarchimedean__field( X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.58 c_Archimedean__Field_Oceiling( X, Y ), c_Groups_Ozero__class_Ozero(
% 0.97/1.58 tc_Int_Oint ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.58 { ! class_Archimedean__Field_Oarchimedean__field( X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.58 ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.58 c_Archimedean__Field_Oceiling( X, Y ), c_Groups_Ozero__class_Ozero(
% 0.97/1.58 tc_Int_Oint ) ) }.
% 0.97/1.58 { ! class_Archimedean__Field_Oarchimedean__field( X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.58 tc_Int_Oint ), c_Archimedean__Field_Oceiling( X, Y ) ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.97/1.58 .
% 0.97/1.58 { ! class_Archimedean__Field_Oarchimedean__field( X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.58 tc_Int_Oint ), c_Archimedean__Field_Oceiling( X, Y ) ) }.
% 0.97/1.58 { ! class_Archimedean__Field_Oarchimedean__field( X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oone__class_Oone
% 0.97/1.58 ( tc_Int_Oint ), c_Archimedean__Field_Oceiling( X, Y ) ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.97/1.58 .
% 0.97/1.58 { ! class_Archimedean__Field_Oarchimedean__field( X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oone__class_Oone
% 0.97/1.58 ( tc_Int_Oint ), c_Archimedean__Field_Oceiling( X, Y ) ) }.
% 0.97/1.58 { ! class_Archimedean__Field_Oarchimedean__field( X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Archimedean__Field_Oceiling
% 0.97/1.58 ( X, Y ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.58 ) }.
% 0.97/1.58 { ! class_Archimedean__Field_Oarchimedean__field( X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.58 ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.58 c_Archimedean__Field_Oceiling( X, Y ), c_Groups_Oone__class_Oone(
% 0.97/1.58 tc_Int_Oint ) ) }.
% 0.97/1.58 { ! class_Archimedean__Field_Oarchimedean__field( X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.58 c_Archimedean__Field_Oceiling( X, Y ), c_Groups_Oone__class_Oone(
% 0.97/1.58 tc_Int_Oint ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.97/1.58 c_Groups_Oone__class_Oone( X ) ) }.
% 0.97/1.58 { ! class_Archimedean__Field_Oarchimedean__field( X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone( X ) )
% 0.97/1.58 , c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.58 c_Archimedean__Field_Oceiling( X, Y ), c_Groups_Oone__class_Oone(
% 0.97/1.58 tc_Int_Oint ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, skol16, X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.58 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, v_g____( hAPP(
% 0.97/1.58 v_f____, X ) ), v_z____ ) ), v_d____ ) }.
% 0.97/1.58 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.97/1.58 { ! c_SEQ_Osubseq( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.97/1.58 hAPP( X, Y ) ) }.
% 0.97/1.58 { ! c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) =
% 0.97/1.58 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.58 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, X,
% 0.97/1.58 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) ),
% 0.97/1.58 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.58 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, X,
% 0.97/1.58 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) ),
% 0.97/1.58 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.58 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, X, c_Complex_Oii ) ),
% 0.97/1.58 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.58 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, X, c_Complex_Oii ) )
% 0.97/1.58 , c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.58 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 0.97/1.58 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.58 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP
% 0.97/1.58 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.97/1.58 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) =
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.58 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.58 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) = X }.
% 0.97/1.58 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), Y =
% 0.97/1.58 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.97/1.58 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X =
% 0.97/1.58 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.97/1.58 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.97/1.58 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Groups_Oone__class_Oone(
% 0.97/1.58 tc_Nat_Onat ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.97/1.58 , Y ), X ) }.
% 0.97/1.58 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.58 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.97/1.58 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.97/1.58 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.58 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Oone__class_Oone(
% 0.97/1.58 tc_Nat_Onat ) }.
% 0.97/1.58 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.58 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X = c_Groups_Oone__class_Oone(
% 0.97/1.58 tc_Nat_Onat ) }.
% 0.97/1.58 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.97/1.58 c_Groups_Oone__class_Oone( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.58 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.97/1.58 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.58 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.58 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.58 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.97/1.58 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Y = X
% 0.97/1.58 , Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.58 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.97/1.58 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.97/1.58 .
% 0.97/1.58 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.97/1.58 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.97/1.58 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = X
% 0.97/1.58 , Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.58 { ! Z = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.97/1.58 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }
% 0.97/1.58 .
% 0.97/1.58 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.97/1.58 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X )
% 0.97/1.58 , X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y =
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.58 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.58 tc_Nat_Onat ), X ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.58 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.97/1.58 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP
% 0.97/1.58 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.58 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.97/1.58 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP
% 0.97/1.58 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X =
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.58 tc_Nat_Onat ), Y ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.58 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.97/1.58 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.58 tc_Nat_Onat ), Z ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.58 ( tc_Nat_Onat ), Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 0.97/1.58 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.58 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.97/1.58 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.58 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.97/1.58 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.58 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.58 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.58 Y ), X ) ) }.
% 0.97/1.58 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.58 tc_Nat_Onat ), X ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.58 ( tc_Nat_Onat ), X ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 0.97/1.58 .
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.58 { ! c_Complex_Oii = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.97/1.58 { ! c_Complex_Oii = c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) }.
% 0.97/1.58 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.58 tc_Nat_Onat ), X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.58 ( tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.58 tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 0.97/1.58 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 0.97/1.58 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, X ) =
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.58 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) =
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.97/1.58 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.58 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.58 ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.58 ( tc_Nat_Onat, Y, Z ), X ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.58 ( tc_Nat_Onat, Z, X ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.97/1.58 ) }.
% 0.97/1.58 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.97/1.58 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.58 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ), Y ) }.
% 0.97/1.58 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.58 tc_Nat_Onat ), X ) = X }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.58 ( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.58 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.58 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.97/1.58 tc_Nat_Onat, Y, X ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.58 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.97/1.58 tc_Nat_Onat, Y, X ) ) }.
% 0.97/1.58 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero
% 0.97/1.58 ( tc_Nat_Onat ) ) = X }.
% 0.97/1.58 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.58 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.58 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X =
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.97/1.58 tc_Nat_Onat, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.58 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = Y, X =
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.97/1.58 ( tc_Nat_Onat, Y, Z ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y
% 0.97/1.58 , X ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, X ) =
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.58 tc_Nat_Onat, Y, T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.97/1.58 .
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.58 tc_Nat_Onat, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.97/1.58 .
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.97/1.58 ( tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) )
% 0.97/1.58 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.58 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }
% 0.97/1.58 .
% 0.97/1.58 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.58 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.97/1.58 ( tc_Nat_Onat, Y, X ), X ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.97/1.58 ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.97/1.58 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.97/1.58 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, c_Groups_Oplus__class_Oplus
% 0.97/1.58 ( tc_Nat_Onat, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.97/1.58 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.58 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.97/1.58 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ), Y = X }.
% 0.97/1.58 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) }.
% 0.97/1.58 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ), Z = X }.
% 0.97/1.58 { ! Z = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.97/1.58 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.58 tc_Nat_Onat, Y, X ), X ) = Y }.
% 0.97/1.58 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.58 tc_Nat_Onat, Y, X ), Y ) = X }.
% 0.97/1.58 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.58 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.97/1.58 Z, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.97/1.58 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.58 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) =
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 0.97/1.58 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.58 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) =
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ) }.
% 0.97/1.58 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) = Y }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z,
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.58 tc_Nat_Onat, Z, X ), Y ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.97/1.58 ( tc_Nat_Onat, Z, X ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z
% 0.97/1.58 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 0.97/1.58 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y,
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.58 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.97/1.58 , alpha5( X, Y, Z ) }.
% 0.97/1.58 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.97/1.58 , alpha21( X, Y, Z ) }.
% 0.97/1.58 { ! alpha5( X, Y, Z ), ! alpha21( X, Y, Z ), hBOOL( hAPP( Z,
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.97/1.58 { ! alpha21( X, Y, Z ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.97/1.58 T ), hBOOL( hAPP( Z, T ) ) }.
% 0.97/1.58 { ! hBOOL( hAPP( Z, skol17( T, U, Z ) ) ), alpha21( X, Y, Z ) }.
% 0.97/1.58 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, skol17( X, Y, Z ) ),
% 0.97/1.58 alpha21( X, Y, Z ) }.
% 0.97/1.58 { ! alpha5( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 0.97/1.58 , hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.97/1.58 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), alpha5( X, Y, Z ) }.
% 0.97/1.58 { ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha5
% 0.97/1.58 ( X, Y, Z ) }.
% 0.97/1.58 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.97/1.58 , ! alpha6( X, Y, Z ) }.
% 0.97/1.58 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.97/1.58 , ! alpha22( X, Y, Z ) }.
% 0.97/1.58 { alpha6( X, Y, Z ), alpha22( X, Y, Z ), hBOOL( hAPP( Z,
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.97/1.58 { ! alpha22( X, Y, Z ), ! hBOOL( hAPP( Z, skol18( T, U, Z ) ) ) }.
% 0.97/1.58 { ! alpha22( X, Y, Z ), Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.97/1.58 skol18( X, Y, Z ) ) }.
% 0.97/1.58 { ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, T ), hBOOL( hAPP( Z, T
% 0.97/1.58 ) ), alpha22( X, Y, Z ) }.
% 0.97/1.58 { ! alpha6( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }
% 0.97/1.58 .
% 0.97/1.58 { ! alpha6( X, Y, Z ), ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero(
% 0.97/1.58 tc_Nat_Onat ) ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), hBOOL( hAPP( Z,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha6( X, Y, Z ) }.
% 0.97/1.58 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, X ) }.
% 0.97/1.58 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ) }.
% 0.97/1.58 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ), Y = X }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.58 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.58 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.97/1.58 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.58 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.97/1.58 ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ),
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.58 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.97/1.58 ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X = Z }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), ! X = Z,
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), T ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.58 ( tc_Nat_Onat, Y, Z ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z )
% 0.97/1.58 ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = Y }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, Z ),
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ),
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.58 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X
% 0.97/1.58 ) }.
% 0.97/1.58 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.58 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 0.97/1.58 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 0.97/1.58 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.58 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 0.97/1.58 ) }.
% 0.97/1.58 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.58 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 0.97/1.58 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 0.97/1.58 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.97/1.58 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.58 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.58 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ), Y ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.58 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.58 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.97/1.58 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) ) }.
% 0.97/1.58 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) }.
% 0.97/1.58 { ! c_SEQ_Osubseq( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z
% 0.97/1.58 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( X, Y ), hAPP( X, Z
% 0.97/1.58 ) ) }.
% 0.97/1.58 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol19( X ), skol65( X ) ),
% 0.97/1.58 c_SEQ_Osubseq( X ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( X, skol19( X ) ),
% 0.97/1.58 hAPP( X, skol65( X ) ) ), c_SEQ_Osubseq( X ) }.
% 0.97/1.58 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.97/1.58 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol20( X, Y ) ) }.
% 0.97/1.58 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z,
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.58 tc_Nat_Onat, Z, Y ), X ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.58 tc_Nat_Onat, X, Z ), Y ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = X }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.58 tc_Nat_Onat, Z, X ), Y ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.97/1.58 tc_Nat_Onat, X, Y ), Y ) = X }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z, X =
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X =
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.58 tc_Nat_Onat, Z, X ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.97/1.58 tc_Nat_Onat, X, Y ), Z ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ), Y ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.58 tc_Nat_Onat, X, Z ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), Z ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, T ),
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ), X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) =
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ), T =
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! T =
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ),
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) =
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.58 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 0.97/1.58 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) =
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, T,
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.58 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 0.97/1.58 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T,
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T,
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.58 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 0.97/1.58 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ),
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T,
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T,
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ),
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.97/1.58 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.97/1.58 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X = Y }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.97/1.58 { alpha53( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.97/1.58 hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.97/1.58 { alpha53( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP
% 0.97/1.58 ( X, Y ), Z ) ) }.
% 0.97/1.58 { ! alpha53( X, Y, Z ), alpha58( X, Y, Z ), Z = Y }.
% 0.97/1.58 { ! alpha53( X, Y, Z ), alpha58( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z
% 0.97/1.58 ) ) }.
% 0.97/1.58 { ! alpha58( X, Y, Z ), alpha53( X, Y, Z ) }.
% 0.97/1.58 { ! Z = Y, hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha53( X, Y, Z ) }.
% 0.97/1.58 { ! alpha58( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y )
% 0.97/1.58 }.
% 0.97/1.58 { ! alpha58( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP(
% 0.97/1.58 X, Y ), Z ) ), alpha58( X, Y, Z ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.58 ( tc_Nat_Onat ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.58 tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.58 tc_Nat_Onat ), X ), Y ), Z = Y }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.58 ( tc_Nat_Onat ), X ), ! Z = Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.58 ( tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.58 tc_Nat_Onat ), X ), Y ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.58 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.97/1.58 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP(
% 0.97/1.58 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.58 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 0.97/1.58 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.97/1.58 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.97/1.58 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Z =
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.97/1.58 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.97/1.58 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.97/1.58 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.97/1.58 .
% 0.97/1.58 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), T ), Z ),
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), X ) ) =
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus
% 0.97/1.58 ( tc_Nat_Onat, T, Y ) ), Z ), X ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.58 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.58 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP
% 0.97/1.58 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.58 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z
% 0.97/1.58 , Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.58 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 0.97/1.58 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.58 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.58 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.58 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 0.97/1.58 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.58 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 0.97/1.58 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) =
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.58 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) =
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ),
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) = Z }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) = Z,
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) =
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.58 c_RComplete_Onatceiling( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X
% 0.97/1.58 , c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) =
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatceiling( X ),
% 0.97/1.58 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.97/1.58 { ! class_RealVector_Oreal__normed__vector( Y ), ! class_Orderings_Oord( X
% 0.97/1.58 ), c_Orderings_Oord__class_Oless__eq( X, T, skol21( X, U, W, T ) ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( X, T, V0 ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.58 c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, V0 ) ),
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oone__class_Oone
% 0.97/1.58 ( tc_RealDef_Oreal ), c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, T ) )
% 0.97/1.58 ) ) }.
% 0.97/1.58 { ! class_RealVector_Oreal__normed__vector( Y ), ! class_Orderings_Oord( X
% 0.97/1.58 ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.58 c_RealVector_Onorm__class_Onorm( Y, c_Groups_Ominus__class_Ominus( Y,
% 0.97/1.58 hAPP( Z, T ), hAPP( Z, skol21( X, Y, Z, T ) ) ) ),
% 0.97/1.58 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( X, T, U ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.58 c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, U ) ),
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oone__class_Oone
% 0.97/1.58 ( tc_RealDef_Oreal ), c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, T ) )
% 0.97/1.58 ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.58 c_RComplete_Onatfloor( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 0.97/1.58 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) =
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatfloor( X ),
% 0.97/1.58 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.97/1.58 { c_RComplete_Onatfloor( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) )
% 0.97/1.58 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.58 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) )
% 0.97/1.58 }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatfloor( Y
% 0.97/1.58 ), c_RComplete_Onatfloor( X ) ) }.
% 0.97/1.58 { c_RComplete_Onatfloor( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) =
% 0.97/1.58 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.97/1.58 { c_RComplete_Onatceiling( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal )
% 0.97/1.58 ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.58 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_RComplete_Onatceiling( X )
% 0.97/1.58 ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 0.97/1.58 Y ), c_RComplete_Onatceiling( X ) ) }.
% 0.97/1.58 { c_RComplete_Onatceiling( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 0.97/1.58 = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_RComplete_Onatfloor
% 0.97/1.58 ( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.97/1.58 c_RComplete_Onatceiling( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.97/1.58 }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.58 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.58 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.58 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Groups_Oone__class_Oone
% 0.97/1.58 ( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling
% 0.97/1.58 ( X ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.97/1.58 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.97/1.58 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 0.97/1.58 X ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_RComplete_Onatfloor( X )
% 0.97/1.58 ), c_RComplete_Onatfloor( Y ) ), c_RComplete_Onatfloor( hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.58 tc_Nat_Onat, Y ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.97/1.58 tc_RealDef_Oreal, X, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.97/1.58 c_RealDef_Oreal( tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone(
% 0.97/1.58 tc_RealDef_Oreal ) ) ), c_RComplete_Onatceiling( X ) =
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone(
% 0.97/1.58 tc_Nat_Onat ) ) }.
% 0.97/1.58 { ! class_Orderings_Oorder( X ), ! c_SEQ_Odecseq( X, Y ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, T ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, T ), hAPP( Y, Z ) ) }.
% 0.97/1.58 { ! class_Orderings_Oorder( X ), c_Orderings_Oord__class_Oless__eq(
% 0.97/1.58 tc_Nat_Onat, skol22( X, Y ), skol66( X, Y ) ), c_SEQ_Odecseq( X, Y ) }.
% 0.97/1.58 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.58 hAPP( Y, skol66( X, Y ) ), hAPP( Y, skol22( X, Y ) ) ), c_SEQ_Odecseq( X
% 0.97/1.58 , Y ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.58 ( tc_Int_Oint ), X ), hBOOL( hAPP( Y, skol23( Z, Y ) ) ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! hBOOL( hAPP( Y, U ) )
% 0.97/1.58 , hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, hAPP( hAPP
% 0.97/1.58 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), T ), X ) ) ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.58 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus(
% 0.97/1.58 tc_Int_Oint, skol23( X, Y ), X ) ) ), ! c_Orderings_Oord__class_Oless__eq
% 0.97/1.58 ( tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), ! hBOOL(
% 0.97/1.58 hAPP( Y, T ) ), hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus( tc_Int_Oint
% 0.97/1.58 , T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) )
% 0.97/1.58 ) ) }.
% 0.97/1.58 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.97/1.58 tc_Nat_Onat, X ) ) }.
% 0.97/1.58 { c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, c_RealDef_Oreal( tc_Nat_Onat
% 0.97/1.58 , X ) ) = c_RealDef_Oreal( tc_Nat_Onat, X ) }.
% 0.97/1.58 { ! c_RealDef_Oreal( tc_Nat_Onat, Y ) = c_RealDef_Oreal( tc_Nat_Onat, X ),
% 0.97/1.58 Y = X }.
% 0.97/1.58 { ! Y = X, c_RealDef_Oreal( tc_Nat_Onat, Y ) = c_RealDef_Oreal( tc_Nat_Onat
% 0.97/1.58 , X ) }.
% 0.97/1.58 { c_RComplete_Onatfloor( c_RealDef_Oreal( tc_Nat_Onat, X ) ) = X }.
% 0.97/1.58 { c_RComplete_Onatceiling( c_RealDef_Oreal( tc_Nat_Onat, X ) ) = X }.
% 0.97/1.58 { c_RealDef_Oreal( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.97/1.58 ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.58 { ! c_RealDef_Oreal( tc_Nat_Onat, X ) = c_Groups_Ozero__class_Ozero(
% 0.97/1.58 tc_RealDef_Oreal ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.58 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_RealDef_Oreal(
% 0.97/1.58 tc_Nat_Onat, X ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.58 tc_Nat_Onat, X ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.58 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.58 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.58 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.58 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 0.97/1.58 { c_RealDef_Oreal( tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.58 tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.58 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ), c_RealDef_Oreal
% 0.97/1.58 ( tc_Nat_Onat, X ) ) }.
% 0.97/1.58 { c_RealDef_Oreal( tc_Nat_Onat, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y
% 0.97/1.58 , X ) ) = c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal
% 0.97/1.58 ( tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 0.97/1.58 { c_RealDef_Oreal( tc_Nat_Onat, c_Groups_Oone__class_Oone( tc_Nat_Onat ) )
% 0.97/1.58 = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.97/1.58 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.97/1.58 tc_Nat_Onat, c_RComplete_Onatceiling( X ) ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.58 tc_Nat_Onat, X ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X =
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.58 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.58 tc_Nat_Onat, X ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), c_RealDef_Oreal
% 0.97/1.58 ( tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.58 tc_Nat_Onat, X ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.58 tc_Nat_Onat, c_RComplete_Onatfloor( X ) ), X ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.58 tc_Nat_Onat, Y ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.97/1.58 , c_RComplete_Onatfloor( X ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, c_RealDef_Oreal
% 0.97/1.58 ( tc_Nat_Onat, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.58 c_RComplete_Onatceiling( Y ), X ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.97/1.58 tc_Nat_Onat, X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.58 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.97/1.58 tc_Nat_Onat, X ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.58 tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.97/1.58 c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.58 tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.97/1.58 c_RealDef_Oreal( tc_Nat_Onat, X ) ), c_Orderings_Oord__class_Oless(
% 0.97/1.58 tc_Nat_Onat, Y, X ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.58 tc_Nat_Onat, Y ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.97/1.58 c_RealDef_Oreal( tc_Nat_Onat, X ), c_Groups_Oone__class_Oone(
% 0.97/1.58 tc_RealDef_Oreal ) ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.58 tc_Nat_Onat, Y ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.97/1.58 c_RealDef_Oreal( tc_Nat_Onat, X ), c_Groups_Oone__class_Oone(
% 0.97/1.58 tc_RealDef_Oreal ) ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.97/1.58 , X ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_RComplete_Onatfloor
% 0.97/1.58 ( X ) ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.58 c_RealDef_Oreal( tc_Nat_Onat, Y ), X ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.58 tc_Nat_Onat, Y ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.97/1.58 , c_RComplete_Onatfloor( X ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 0.97/1.58 X ), Y ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.97/1.58 c_RealDef_Oreal( tc_Nat_Onat, Y ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.97/1.58 tc_Nat_Onat, Y ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.58 c_RComplete_Onatceiling( X ), Y ) }.
% 0.97/1.58 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.58 tc_Nat_Onat, c_RComplete_Onatfloor( X ) ), c_Groups_Oone__class_Oone(
% 0.97/1.58 tc_RealDef_Oreal ) ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.58 tc_Nat_Onat, Y ), X ), c_RComplete_Onatfloor(
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.97/1.58 tc_Nat_Onat, Y ) ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.97/1.58 c_RComplete_Onatfloor( X ), Y ) }.
% 0.97/1.58 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X,
% 0.97/1.58 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), c_RealDef_Oreal(
% 0.97/1.58 tc_Nat_Onat, c_RComplete_Onatfloor( X ) ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.58 tc_Nat_Onat, Y ), X ), c_RComplete_Onatceiling(
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.97/1.58 tc_Nat_Onat, Y ) ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.97/1.58 c_RComplete_Onatceiling( X ), Y ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.97/1.58 tc_Nat_Onat, Y ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.58 c_RComplete_Onatfloor( X ), Y ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.58 c_RComplete_Onatfloor( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 0.97/1.58 c_RealDef_Oreal( tc_Nat_Onat, Y ) ) ) = c_Groups_Oplus__class_Oplus(
% 0.97/1.58 tc_Nat_Onat, c_RComplete_Onatfloor( X ), Y ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatfloor( Y ),
% 0.97/1.58 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, c_RealDef_Oreal(
% 0.97/1.58 tc_Nat_Onat, X ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.58 tc_Nat_Onat, Y ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal
% 0.97/1.58 , X, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.58 tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ),
% 0.97/1.58 c_RComplete_Onatfloor( X ) = Y }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.58 c_RComplete_Onatceiling( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X
% 0.97/1.58 , c_RealDef_Oreal( tc_Nat_Onat, Y ) ) ) = c_Groups_Oplus__class_Oplus(
% 0.97/1.58 tc_Nat_Onat, c_RComplete_Onatceiling( X ), Y ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.58 tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, skol24( X ),
% 0.97/1.58 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ), X ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.97/1.58 tc_Nat_Onat, skol24( X ) ) ) }.
% 0.97/1.58 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.97/1.58 hAPP( X, Y ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol25( Z, Y
% 0.97/1.58 ), Y ) }.
% 0.97/1.58 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.97/1.58 hAPP( X, Y ) ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.97/1.58 skol25( X, Y ) ), ! hBOOL( hAPP( X, Z ) ) }.
% 0.97/1.58 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.97/1.58 hAPP( X, Y ) ), hBOOL( hAPP( X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat
% 0.97/1.58 , skol25( X, Y ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 0.97/1.58 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol26( Z, T ) ) }.
% 0.97/1.58 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.58 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.97/1.58 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol26( X, Y ) ) ) }.
% 0.97/1.58 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol27( Y ) ) }.
% 0.97/1.58 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.58 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.97/1.58 c_RealVector_Onorm__class_Onorm( X, Y ) ),
% 0.97/1.58 c_RealVector_Onorm__class_Onorm( X, Z ) ) ), skol27( X ) ) ) }.
% 0.97/1.58 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol28( Z, T ) ) }.
% 0.97/1.58 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.58 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.97/1.58 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol28( X, Y ) ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.97/1.58 tc_Nat_Onat, Y ) ), X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 0.97/1.58 , hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 0.97/1.58 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ), Y ) ) }.
% 0.97/1.58 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.58 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ozero__class_Ozero(
% 0.97/1.58 tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.58 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.58 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.97/1.58 c_Power_Opower__class_Opower( X ), T ), Y ) ) = hAPP( hAPP(
% 0.97/1.58 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.97/1.58 tc_Nat_Onat, Z, Y ) ) }.
% 0.97/1.58 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 0.97/1.58 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.97/1.58 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.58 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.97/1.58 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) }.
% 0.97/1.58 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.58 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.97/1.58 c_Power_Opower__class_Opower( X ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.58 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.97/1.58 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) ) }.
% 0.97/1.58 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.58 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.97/1.58 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.58 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) }.
% 0.97/1.58 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.58 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.97/1.58 tc_Nat_Onat ) ) = Y }.
% 0.97/1.58 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.58 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.58 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.97/1.58 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.97/1.58 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.58 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), hAPP( hAPP
% 0.97/1.58 ( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.58 c_Power_Opower__class_Opower( X ), Z ), c_Groups_Ominus__class_Ominus(
% 0.97/1.58 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ), Z ) =
% 0.97/1.58 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) }.
% 0.97/1.58 { ! class_Power_Opower( X ), ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 0.97/1.58 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) =
% 0.97/1.58 c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.58 { ! class_Power_Opower( X ), Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.97/1.58 , hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) = hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.97/1.58 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ominus__class_Ominus(
% 0.97/1.58 tc_Nat_Onat, Z, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 0.97/1.58 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.58 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( X ), Z ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.58 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), T ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.58 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.97/1.58 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.97/1.58 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.58 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.58 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 0.97/1.58 hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.58 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.97/1.58 ( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Z ), hAPP( hAPP
% 0.97/1.58 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.58 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.97/1.58 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), X =
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.58 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.58 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.58 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.58 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.97/1.58 ), X ) ) }.
% 0.97/1.58 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.58 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 0.97/1.58 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.97/1.58 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.58 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) }.
% 0.97/1.58 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ),
% 0.97/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) = hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.58 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.58 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ) }.
% 0.97/1.58 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.97/1.58 c_RealDef_Oreal( tc_Nat_Onat, Y ) ), X ) = c_RealDef_Oreal( tc_Nat_Onat,
% 0.97/1.58 hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.58 { c_RealDef_Oreal( tc_Nat_Onat, hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.97/1.58 tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.97/1.58 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ), X ) }.
% 0.97/1.58 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.97/1.58 c_RealDef_Oreal( tc_Int_Oint, Y ) ), X ) = c_RealDef_Oreal( tc_Int_Oint,
% 0.97/1.58 hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ) ) }.
% 0.97/1.58 { c_RealDef_Oreal( tc_Int_Oint, hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.97/1.58 tc_Int_Oint ), Y ), X ) ) = hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.97/1.58 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Int_Oint, Y ) ), X ) }.
% 0.97/1.58 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.58 c_Power_Opower__class_Opower( tc_Int_Oint ), c_Groups_Oabs__class_Oabs(
% 0.97/1.58 tc_Int_Oint, Y ) ), X ) ) }.
% 0.97/1.58 { ! X = c_RealDef_Oreal( tc_Nat_Onat, c_RComplete_Onatfloor( X ) ),
% 0.97/1.58 c_RComplete_Onatfloor( hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.97/1.58 tc_RealDef_Oreal ), X ), Y ) ) = hAPP( hAPP( c_Power_Opower__class_Opower
% 0.97/1.58 ( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ), Y ) }.
% 0.97/1.58 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.58 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) =
% 0.97/1.58 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.97/1.58 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.58 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) = hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 0.97/1.58 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ),
% 0.97/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 0.97/1.58 ( tc_Nat_Onat ) ) ) ) }.
% 0.97/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.58 ( tc_Int_Oint ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint )
% 0.97/1.58 , c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) ), X ) ), ! Y =
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X =
% 0.97/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.58 { Y = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.58 tc_Int_Oint ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ),
% 0.97/1.58 c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) ), X ) ) }.
% 0.97/1.58 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.58 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.58 tc_Int_Oint ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ),
% 0.97/1.58 c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) ), X ) ) }.
% 0.97/1.58 { ! class_Rings_Oring__1__no__zero__divisors( X ), Y =
% 0.97/1.58 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.97/1.58 c_Power_Opower__class_Opower( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 0.97/1.58 ( X ) }.
% 0.97/1.58 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.97/1.58 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.58 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.97/1.58 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.97/1.58 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.58 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.97/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.97/1.58 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.97/1.58 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.97/1.58 c_Power_Opower__class_Opower( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.97/1.58 = c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.58 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, hAPP
% 0.97/1.58 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.58 c_Power_Opower__class_Opower( X ), c_Groups_Oabs__class_Oabs( X, Z ) ), Y
% 0.97/1.59 ) }.
% 0.97/1.59 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.97/1.59 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.59 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.97/1.59 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) }.
% 0.97/1.59 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.97/1.59 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.97/1.59 tc_Nat_Onat ) ) = Y }.
% 0.97/1.59 { ! class_Rings_Olinordered__semidom( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.97/1.59 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.59 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.97/1.59 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.97/1.59 { ! class_Rings_Olinordered__semidom( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.59 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.97/1.59 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.97/1.59 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.59 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless
% 0.97/1.59 ( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.97/1.59 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.97/1.59 { ! class_Rings_Olinordered__semidom( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 0.97/1.59 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.97/1.59 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.97/1.59 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.59 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! hAPP( hAPP(
% 0.97/1.59 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.97/1.59 c_Power_Opower__class_Opower( X ), Y ), Z ), T = Z }.
% 0.97/1.59 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.59 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! T = Z, hAPP( hAPP(
% 0.97/1.59 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.97/1.59 c_Power_Opower__class_Opower( X ), Y ), Z ) }.
% 0.97/1.59 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.97/1.59 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.97/1.59 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.97/1.59 .
% 0.97/1.59 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.97/1.59 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.97/1.59 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.59 tc_Nat_Onat ) }.
% 0.97/1.59 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.97/1.59 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.97/1.59 , ! Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 0.97/1.59 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y )
% 0.97/1.59 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.97/1.59 , Y ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.97/1.59 c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.59 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.97/1.59 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.97/1.59 tc_Nat_Onat, Z, Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.97/1.59 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.97/1.59 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.97/1.59 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.59 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP
% 0.97/1.59 ( c_Power_Opower__class_Opower( X ), Y ), T ) ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.59 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.59 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.59 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.97/1.59 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.97/1.59 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.97/1.59 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.59 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.97/1.59 X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.97/1.59 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.97/1.59 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), ! Y =
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.59 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.97/1.59 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.59 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), Y =
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.59 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.97/1.59 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59 { ! class_Rings_Olinordered__idom( X ), c_Orderings_Oord__class_Oless__eq(
% 0.97/1.59 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.97/1.59 c_Power_Opower__class_Opower( X ), c_Groups_Oabs__class_Oabs( X, Z ) ), Y
% 0.97/1.59 ) ) }.
% 0.97/1.59 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.59 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.59 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.97/1.59 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.97/1.59 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.59 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.59 ( tc_Nat_Onat, T, Z ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.59 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.59 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.97/1.59 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.59 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.59 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.97/1.59 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.97/1.59 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.59 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.97/1.59 c_Groups_Oone__class_Oone( X ), T ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.59 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.59 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.97/1.59 { ! class_Rings_Olinordered__semidom( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), T )
% 0.97/1.59 , c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.59 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.59 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.97/1.59 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.59 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.97/1.59 c_Power_Opower__class_Opower( X ), Y ), Z ) ), hAPP( hAPP(
% 0.97/1.59 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.97/1.59 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.59 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.59 , T, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.59 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.97/1.59 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 0.97/1.59 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 0.97/1.59 c_Power_Opower__class_Opower( X ), T ), Z ) = hAPP( hAPP(
% 0.97/1.59 c_Power_Opower__class_Opower( X ), Y ), Z ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.97/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.59 X ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ), T = Y }.
% 0.97/1.59 { ! class_Rings_Olinordered__semidom( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.97/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oone__class_Oone
% 0.97/1.59 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.59 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.97/1.59 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 0.97/1.59 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.59 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.59 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.59 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.97/1.59 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.59 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.59 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.59 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.97/1.59 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.59 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.59 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.59 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.97/1.59 { X = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), Y =
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Orderings_Oord__class_Oless
% 0.97/1.59 ( tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex
% 0.97/1.59 , c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex,
% 0.97/1.59 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), X ), hAPP( hAPP(
% 0.97/1.59 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), skol29( X, Y ) ), Y
% 0.97/1.59 ) ) ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.97/1.59 { ! class_Power_Opower( X ), c_Power_Opower__class_Opower( X ) =
% 0.97/1.59 c_Power_Opower_Opower( X, c_Groups_Oone__class_Oone( X ),
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.59 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.97/1.59 , Y ), X ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.59 tc_Nat_Onat ), Y ) }.
% 0.97/1.59 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.59 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.97/1.59 ), X ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.59 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.59 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.59 { hAPP( hAPP( c_Power_Opower_Opower( T, Z, Y ), X ),
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = Z }.
% 0.97/1.59 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ),
% 0.97/1.59 c_Complex_Orcis( Z, Y ) ), X ) = c_Complex_Orcis( hAPP( hAPP(
% 0.97/1.59 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.97/1.59 tc_Nat_Onat, X ) ), Y ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.59 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol30( Z, T ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.59 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), hAPP( hAPP(
% 0.97/1.59 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), skol30( X, Y ) ), X ) =
% 0.97/1.59 Y }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.59 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), ! hAPP( hAPP(
% 0.97/1.59 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Z ), X ) = Y, Z =
% 0.97/1.59 skol30( X, Y ) }.
% 0.97/1.59 { c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, c_Complex_Orcis( Y
% 0.97/1.59 , X ) ) = c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ) }.
% 0.97/1.59 { c_Complex_Orcis( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ) =
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.97/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.97/1.59 c_Complex_Orcis( T, Z ) ), c_Complex_Orcis( Y, X ) ) = c_Complex_Orcis(
% 0.97/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), T ), Y ),
% 0.97/1.59 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, X ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.59 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol31( Z, T ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.59 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), hAPP( hAPP(
% 0.97/1.59 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), skol31( X, Y ) ), X ) =
% 0.97/1.59 Y }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.59 c_Transcendental_Oln( hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.97/1.59 tc_RealDef_Oreal ), X ), Y ) ) = hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.97/1.59 tc_Nat_Onat, Y ) ), c_Transcendental_Oln( X ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 0.97/1.59 ), c_Transcendental_Oln( Y ) ), c_Orderings_Oord__class_Oless(
% 0.97/1.59 tc_RealDef_Oreal, X, Y ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, Y ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 0.97/1.59 ), c_Transcendental_Oln( Y ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.97/1.59 c_Transcendental_Oln( X ) = c_Transcendental_Oln( Y ), X = Y }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), ! X = Y,
% 0.97/1.59 c_Transcendental_Oln( X ) = c_Transcendental_Oln( Y ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 0.97/1.59 ), X ) }.
% 0.97/1.59 { c_Transcendental_Oln( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) =
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_Transcendental_Oln
% 0.97/1.59 ( X ), c_Transcendental_Oln( Y ) ), c_Orderings_Oord__class_Oless__eq(
% 0.97/1.59 tc_RealDef_Oreal, X, Y ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_Transcendental_Oln
% 0.97/1.59 ( X ), c_Transcendental_Oln( Y ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 0.97/1.59 ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 0.97/1.59 ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 0.97/1.59 ) ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 0.97/1.59 ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.59 c_Transcendental_Oln( X ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal
% 0.97/1.59 ), X = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), ! X =
% 0.97/1.59 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_Transcendental_Oln( X )
% 0.97/1.59 = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 0.97/1.59 ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.97/1.59 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.97/1.59 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 0.97/1.59 ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.97/1.59 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 0.97/1.59 ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 0.97/1.59 ) ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 0.97/1.59 ) ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 0.97/1.59 ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 0.97/1.59 ) ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.97/1.59 c_Transcendental_Oln( hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.59 tc_RealDef_Oreal ), X ), Y ) ) = c_Groups_Oplus__class_Oplus(
% 0.97/1.59 tc_RealDef_Oreal, c_Transcendental_Oln( X ), c_Transcendental_Oln( Y ) )
% 0.97/1.59 }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_Transcendental_Oln
% 0.97/1.59 ( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) ), X ) }.
% 0.97/1.59 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol32( Z, T ) ) }.
% 0.97/1.59 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.59 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, Z ) ), skol32( X, Y ) ) }.
% 0.97/1.59 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.59 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol67( X, Y, Z ) ) ), Z ),
% 0.97/1.59 c_SEQ_OBseq( X, Y ) }.
% 0.97/1.59 { ! class_Orderings_Oorder( X ), ! c_SEQ_Oincseq( X, Y ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, T ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, Z ), hAPP( Y, T ) ) }.
% 0.97/1.59 { ! class_Orderings_Oorder( X ), c_Orderings_Oord__class_Oless__eq(
% 0.97/1.59 tc_Nat_Onat, skol33( X, Y ), skol68( X, Y ) ), c_SEQ_Oincseq( X, Y ) }.
% 0.97/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.59 hAPP( Y, skol33( X, Y ) ), hAPP( Y, skol68( X, Y ) ) ), c_SEQ_Oincseq( X
% 0.97/1.59 , Y ) }.
% 0.97/1.59 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol34( Z, T ) ) }.
% 0.97/1.59 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.59 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, Z ) ), skol34( X, Y ) ) }.
% 0.97/1.59 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.59 c_RealVector_Onorm__class_Onorm( X, hAPP( Z, skol35( X, Y, Z ) ) ), Y ),
% 0.97/1.59 c_SEQ_OBseq( X, Z ) }.
% 0.97/1.59 { c_Complex_Oexpi( c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) =
% 0.97/1.59 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) }.
% 0.97/1.59 { alpha54( X, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP(
% 0.97/1.59 X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Z ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z, hAPP( X, Y ) ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, skol36( T, Y, U ), Y ) }
% 0.97/1.59 .
% 0.97/1.59 { alpha54( X, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP(
% 0.97/1.59 X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Z ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z, hAPP( X, Y ) ), hAPP(
% 0.97/1.59 X, skol36( X, Y, Z ) ) = Z }.
% 0.97/1.59 { ! alpha54( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol37( Z
% 0.97/1.59 , Y ), Y ) }.
% 0.97/1.59 { ! alpha54( X, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.59 c_Groups_Oabs__class_Oabs( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 0.97/1.59 tc_Int_Oint, hAPP( X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, skol37( X
% 0.97/1.59 , Y ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ), hAPP( X, skol37( X,
% 0.97/1.59 Y ) ) ) ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oabs__class_Oabs
% 0.97/1.59 ( tc_Int_Oint, c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( X,
% 0.97/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, c_Groups_Oone__class_Oone(
% 0.97/1.59 tc_Nat_Onat ) ) ), hAPP( X, Z ) ) ), c_Groups_Oone__class_Oone(
% 0.97/1.59 tc_Int_Oint ) ), alpha54( X, Y ) }.
% 0.97/1.59 { c_Complex_Oexpi( c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X )
% 0.97/1.59 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.97/1.59 c_Complex_Oexpi( Y ) ), c_Complex_Oexpi( X ) ) }.
% 0.97/1.59 { alpha55( X, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP(
% 0.97/1.59 X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Z ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z, hAPP( X, Y ) ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, skol38( T, Y, U ), Y ) }
% 0.97/1.59 .
% 0.97/1.59 { alpha55( X, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP(
% 0.97/1.59 X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Z ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z, hAPP( X, Y ) ), hAPP(
% 0.97/1.59 X, skol38( X, Y, Z ) ) = Z }.
% 0.97/1.59 { ! alpha55( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol39( Z
% 0.97/1.59 , Y ), Y ) }.
% 0.97/1.59 { ! alpha55( X, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.59 c_Groups_Oabs__class_Oabs( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 0.97/1.59 tc_Int_Oint, hAPP( X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, skol39( X
% 0.97/1.59 , Y ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ), hAPP( X, skol39( X,
% 0.97/1.59 Y ) ) ) ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oabs__class_Oabs
% 0.97/1.59 ( tc_Int_Oint, c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( X,
% 0.97/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, c_Groups_Oone__class_Oone(
% 0.97/1.59 tc_Nat_Onat ) ) ), hAPP( X, Z ) ) ), c_Groups_Oone__class_Oone(
% 0.97/1.59 tc_Int_Oint ) ), alpha55( X, Y ) }.
% 0.97/1.59 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, skol40( U, W, V0, T )
% 0.97/1.59 ), c_SEQ_OBseq( X, Y ) }.
% 0.97/1.59 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.59 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol40( X, Y, Z, T ) ) ), Z
% 0.97/1.59 ), c_SEQ_OBseq( X, Y ) }.
% 0.97/1.59 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.59 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol41( X, Y, Z ) ) ), Z ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.59 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, T ) ), c_RealDef_Oreal(
% 0.97/1.59 tc_Nat_Onat, c_Nat_OSuc( skol69( X, Y ) ) ) ) }.
% 0.97/1.59 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.59 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol75( X, Y, Z ) ) ),
% 0.97/1.59 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol77( T, U ) ) }.
% 0.97/1.59 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.59 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol75( X, Y, Z ) ) ),
% 0.97/1.59 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.59 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, T ) ), skol77( X, Y ) ) }.
% 0.97/1.59 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.59 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol42( X, Y, Z ) ) ), Z ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, T ) ), c_RealDef_Oreal(
% 0.97/1.59 tc_Nat_Onat, c_Nat_OSuc( skol70( X, Y ) ) ) ) }.
% 0.97/1.59 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol76( X, Y, Z ) ) ),
% 0.97/1.59 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol78( T, U ) ) }.
% 0.97/1.59 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol76( X, Y, Z ) ) ),
% 0.97/1.59 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.59 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, T ) ), skol78( X, Y ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.97/1.59 X ) ) }.
% 0.97/1.59 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( X ) ) }.
% 0.97/1.59 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.59 tc_Nat_Onat ), c_Nat_OSuc( X ) ) }.
% 0.97/1.59 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), hAPP( hAPP(
% 0.97/1.59 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.59 c_Nat_OSuc( Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), c_Nat_OSuc(
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) = c_Nat_OSuc(
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.59 { ! hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.59 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = c_Nat_OSuc(
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.59 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.59 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.59 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP(
% 0.97/1.59 hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc
% 0.97/1.59 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.59 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.97/1.59 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 0.97/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.97/1.59 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.59 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 0.97/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.59 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.97/1.59 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.97/1.59 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.97/1.59 , Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.97/1.59 , Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.97/1.59 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.97/1.59 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.59 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) }.
% 0.97/1.59 { hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), c_Nat_OSuc( X ) ) =
% 0.97/1.59 hAPP( hAPP( Z, Y ), hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), X
% 0.97/1.59 ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( c_Nat_OSuc(
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X =
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X = c_Nat_OSuc(
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.59 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z
% 0.97/1.59 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.59 c_Nat_OSuc( Z ) ), X ), Y = X }.
% 0.97/1.59 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.59 c_Nat_OSuc( Z ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.59 tc_Nat_Onat ), c_Nat_OSuc( Z ) ), X ) }.
% 0.97/1.59 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.59 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y = c_Nat_OSuc
% 0.97/1.59 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.59 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.59 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X = c_Nat_OSuc
% 0.97/1.59 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.59 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.97/1.59 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), X = c_Nat_OSuc(
% 0.97/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol43( X, Y ) ) ) }.
% 0.97/1.59 { ! X = c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.59 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 0.97/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ) }.
% 0.97/1.59 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 0.97/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X = Y }
% 0.97/1.59 .
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X = Y,
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.59 { c_Groups_Oone__class_Oone( tc_Nat_Onat ) = c_Nat_OSuc(
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.97/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.97/1.59 ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.97/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.97/1.59 ), X ) ) }.
% 0.97/1.59 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.59 ( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) ) }.
% 0.97/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), c_Nat_OSuc
% 0.97/1.59 ( X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Y )
% 0.97/1.59 ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.97/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.97/1.59 ), X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.97/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.97/1.59 ), X ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) =
% 0.97/1.59 c_Nat_OSuc( c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.97/1.59 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.97/1.59 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.97/1.59 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.97/1.59 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X ) }.
% 0.97/1.59 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 0.97/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.59 ( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) }.
% 0.97/1.59 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 0.97/1.59 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.97/1.59 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.97/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.97/1.59 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.97/1.59 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.97/1.59 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 0.97/1.59 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.97/1.59 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.97/1.59 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.97/1.59 { ! Y = X, c_Nat_OSuc( Y ) = c_Nat_OSuc( X ) }.
% 0.97/1.59 { ! c_Nat_OSuc( X ) = X }.
% 0.97/1.59 { ! X = c_Nat_OSuc( X ) }.
% 0.97/1.59 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.59 ( tc_Nat_Onat, c_Nat_OSuc( Z ), Y ), c_Nat_OSuc( X ) ) =
% 0.97/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.59 ( tc_Nat_Onat, Z, Y ), X ) }.
% 0.97/1.59 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.97/1.59 X ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 0.97/1.59 ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 0.97/1.59 c_Nat_OSuc( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X )
% 0.97/1.59 }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 0.97/1.59 c_Nat_OSuc( X ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 0.97/1.59 ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.97/1.59 { ! Y = c_Nat_OSuc( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.97/1.59 , c_Nat_OSuc( X ) ) }.
% 0.97/1.59 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), X ) }
% 0.97/1.59 .
% 0.97/1.59 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.59 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.97/1.59 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.59 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.59 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.97/1.59 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.97/1.59 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) = X
% 0.97/1.59 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.97/1.59 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), X = Y }
% 0.97/1.59 .
% 0.97/1.59 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y = X }
% 0.97/1.59 .
% 0.97/1.59 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X,
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.97/1.59 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.97/1.59 X ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.97/1.59 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) )
% 0.97/1.59 }.
% 0.97/1.59 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.59 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha7( X, Y ), alpha23( X
% 0.97/1.59 , Y ) }.
% 0.97/1.59 { ! alpha7( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.97/1.59 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.59 { ! alpha23( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.97/1.59 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.59 { ! alpha23( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.59 { ! alpha23( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.97/1.59 tc_Nat_Onat ) ) }.
% 0.97/1.59 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha23( X, Y ) }.
% 0.97/1.59 { ! alpha7( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.97/1.59 tc_Nat_Onat ) ) }.
% 0.97/1.59 { ! alpha7( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.59 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha7( X, Y ) }.
% 0.97/1.59 { ! c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.97/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ), alpha8( X, Y ), alpha24
% 0.97/1.59 ( X, Y ) }.
% 0.97/1.59 { ! alpha8( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.97/1.59 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.97/1.59 { ! alpha24( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.97/1.59 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.97/1.59 { ! alpha24( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.59 { ! alpha24( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.97/1.59 tc_Nat_Onat ) ) }.
% 0.97/1.59 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha24( X, Y ) }.
% 0.97/1.59 { ! alpha8( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.97/1.59 tc_Nat_Onat ) ) }.
% 0.97/1.59 { ! alpha8( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.59 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha8( X, Y ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.59 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( skol44( X ) ) }.
% 0.97/1.59 { ! X = c_Nat_OSuc( Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X =
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.59 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y =
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha9( X, Y ) }.
% 0.97/1.59 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.97/1.59 { ! alpha9( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.97/1.59 c_Nat_OSuc( X ) ) }.
% 0.97/1.59 { ! alpha9( X, Y ), Y = c_Nat_OSuc( skol45( Z, Y ) ) }.
% 0.97/1.59 { ! alpha9( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol45( X,
% 0.97/1.59 Y ), X ) }.
% 0.97/1.59 { ! Y = c_Nat_OSuc( Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.97/1.59 ), alpha9( X, Y ) }.
% 0.97/1.59 { ! c_SEQ_Osubseq( X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( X
% 0.97/1.59 , Y ), hAPP( X, c_Nat_OSuc( Y ) ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( X, skol46( X ) ),
% 0.97/1.59 hAPP( X, c_Nat_OSuc( skol46( X ) ) ) ), c_SEQ_Osubseq( X ) }.
% 0.97/1.59 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 0.97/1.59 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ) = hAPP( hAPP(
% 0.97/1.59 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.97/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.59 X ), Y ), Z = Y }.
% 0.97/1.59 { ! class_Rings_Olinordered__semidom( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.59 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ), hAPP( hAPP(
% 0.97/1.59 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ) ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.59 ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.59 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.59 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.97/1.59 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.97/1.59 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.59 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.59 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.97/1.59 tc_Nat_Onat, X, c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) )
% 0.97/1.59 ) ) = X }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.59 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.97/1.59 tc_Nat_Onat, c_Nat_OSuc( X ) ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), Z ) =
% 0.97/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 0.97/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, c_Nat_OSuc(
% 0.97/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) ) =
% 0.97/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.59 tc_Nat_Onat, Z, Y ), c_Nat_OSuc( X ) ) }.
% 0.97/1.59 { c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.97/1.59 tc_Nat_Onat ) ) ) = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.97/1.59 { c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( X ) ) =
% 0.97/1.59 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.59 tc_Nat_Onat, X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.97/1.59 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ) }.
% 0.97/1.59 { ! class_Rings_Olinordered__semidom( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone
% 0.97/1.59 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.59 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ), Y ) }.
% 0.97/1.59 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.59 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.59 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ),
% 0.97/1.59 c_Groups_Oone__class_Oone( X ) ) }.
% 0.97/1.59 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.97/1.59 tc_Nat_Onat, Z, Y ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ),
% 0.97/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) ) = hAPP
% 0.97/1.59 ( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.59 c_Power_Opower__class_Opower( X ), T ), c_Groups_Ominus__class_Ominus(
% 0.97/1.59 tc_Nat_Onat, Y, Z ) ) ), T ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.59 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.97/1.59 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) = X }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.59 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.97/1.59 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) }.
% 0.97/1.59 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = X }.
% 0.97/1.59 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.97/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.97/1.59 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) ) }.
% 0.97/1.59 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.59 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, Z ) ), c_RealDef_Oreal(
% 0.97/1.59 tc_Nat_Onat, c_Nat_OSuc( skol47( X, Y ) ) ) ) }.
% 0.97/1.59 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.59 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol71( X, Y, Z ) ) ),
% 0.97/1.59 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ), c_SEQ_OBseq( X, Y ) }
% 0.97/1.59 .
% 0.97/1.59 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, Z ) ), c_RealDef_Oreal(
% 0.97/1.59 tc_Nat_Onat, c_Nat_OSuc( skol48( X, Y ) ) ) ) }.
% 0.97/1.59 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol72( X, Y, Z ) ) ),
% 0.97/1.59 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ), c_SEQ_OBseq( X, Y ) }
% 0.97/1.59 .
% 0.97/1.59 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP
% 0.97/1.59 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), hAPP( hAPP(
% 0.97/1.59 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) ) = hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.97/1.59 Y ) ), c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.97/1.59 tc_Nat_Onat, skol49( X, Y ) ) ), X ), Y ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.97/1.59 tc_Nat_Onat, c_Nat_OSuc( skol49( X, Y ) ) ) ), X ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.59 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.97/1.59 c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.59 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ), Y ) = hAPP( hAPP(
% 0.97/1.59 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ),
% 0.97/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.97/1.59 tc_Int_Oint, X, Y ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.59 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.59 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.97/1.59 tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.59 tc_Int_Oint ), Y ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.59 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.59 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ),
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.59 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.59 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ),
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.59 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.97/1.59 tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.59 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.97/1.59 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, X ) =
% 0.97/1.59 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.97/1.59 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.59 tc_Int_Oint ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.97/1.59 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.59 }.
% 0.97/1.59 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X, Y,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X, Y,
% 0.97/1.59 c_Groups_Oone__class_Oone( X ) ) = Y }.
% 0.97/1.59 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.59 , c_Divides_Odiv__class_Odiv( X, Y, Y ) = c_Groups_Oone__class_Oone( X )
% 0.97/1.59 }.
% 0.97/1.59 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.59 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) =
% 0.97/1.59 c_Divides_Odiv__class_Odiv( X, T, Z ) }.
% 0.97/1.59 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.59 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.97/1.59 c_Divides_Odiv__class_Odiv( X, T, Z ) }.
% 0.97/1.59 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.59 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) = Z }.
% 0.97/1.59 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.59 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = Z }.
% 0.97/1.59 { ! class_Divides_Osemiring__div( X ), ! T = c_Groups_Ozero__class_Ozero( X
% 0.97/1.59 ), c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59 { ! class_Divides_Osemiring__div( X ), T = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.59 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.97/1.59 c_Divides_Odiv__class_Odiv( X, Z, Y ) }.
% 0.97/1.59 { ! c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X =
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), alpha10( X, Y ) }.
% 0.97/1.59 { ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.97/1.59 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.97/1.59 { ! alpha10( X, Y ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.97/1.59 { ! alpha10( X, Y ), alpha25( X, Y ), alpha32( X, Y ) }.
% 0.97/1.59 { ! alpha25( X, Y ), alpha10( X, Y ) }.
% 0.97/1.59 { ! alpha32( X, Y ), alpha10( X, Y ) }.
% 0.97/1.59 { ! alpha32( X, Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.59 { ! alpha32( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ), alpha32( X, Y ) }.
% 0.97/1.59 { ! alpha25( X, Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.97/1.59 { ! alpha25( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), alpha25( X, Y ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.59 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.97/1.59 tc_Int_Oint, Y, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.59 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.97/1.59 tc_Int_Oint, Y, X ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.59 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.97/1.59 tc_Int_Oint, Y, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X
% 0.97/1.59 , Y ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.59 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X
% 0.97/1.59 , Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.97/1.59 tc_Int_Oint, Y, X ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.59 tc_Int_Oint ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.59 tc_Int_Oint ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.59 tc_Int_Oint ), Y ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.59 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.97/1.59 tc_Int_Oint, X, Y ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.59 tc_Int_Oint ), Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.97/1.59 Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.59 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ),
% 0.97/1.59 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.59 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ),
% 0.97/1.59 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) =
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.97/1.59 tc_Int_Oint, Y, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y
% 0.97/1.59 , c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.97/1.59 tc_Int_Oint, Y, X ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.59 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.59 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.59 tc_Int_Oint ), Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.97/1.59 Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.59 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 0.97/1.59 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.97/1.59 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) =
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.59 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.59 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ),
% 0.97/1.59 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.59 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ),
% 0.97/1.59 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.59 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.59 c_Groups_Oone__class_Oone( tc_Int_Oint ), Y ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.97/1.59 tc_Int_Oint, X, Y ), X ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.59 ( tc_Int_Oint ), X ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Z, hAPP(
% 0.97/1.59 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) =
% 0.97/1.59 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.97/1.59 tc_Int_Oint, Z, Y ), X ) }.
% 0.97/1.59 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.59 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, T, hAPP
% 0.97/1.59 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) =
% 0.97/1.59 c_Groups_Oplus__class_Oplus( X, Z, c_Divides_Odiv__class_Odiv( X, T, Y )
% 0.97/1.59 ) }.
% 0.97/1.59 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.59 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, T, hAPP
% 0.97/1.59 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) =
% 0.97/1.59 c_Groups_Oplus__class_Oplus( X, Z, c_Divides_Odiv__class_Odiv( X, T, Y )
% 0.97/1.59 ) }.
% 0.97/1.59 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.59 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, Z, Y ),
% 0.97/1.59 Y ) = c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Z, Y
% 0.97/1.59 ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.97/1.59 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.59 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, Y, Z ),
% 0.97/1.59 Y ) = c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Z, Y
% 0.97/1.59 ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.97/1.59 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ),
% 0.97/1.59 alpha11( X, Z ) }.
% 0.97/1.59 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ),
% 0.97/1.59 alpha26( X, Y, Z ) }.
% 0.97/1.59 { ! alpha11( X, Z ), ! alpha26( X, Y, Z ), hBOOL( hAPP( Z,
% 0.97/1.59 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ) }.
% 0.97/1.59 { ! alpha26( X, Y, Z ), alpha33( X, Y, Z ) }.
% 0.97/1.59 { ! alpha26( X, Y, Z ), alpha37( X, Y, Z ) }.
% 0.97/1.59 { ! alpha33( X, Y, Z ), ! alpha37( X, Y, Z ), alpha26( X, Y, Z ) }.
% 0.97/1.59 { ! alpha37( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha42( X, Y, Z ) }.
% 0.97/1.59 { c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha37( X, Y, Z ) }.
% 0.97/1.59 { ! alpha42( X, Y, Z ), alpha37( X, Y, Z ) }.
% 0.97/1.59 { ! alpha42( X, Y, Z ), ! alpha46( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 0.97/1.59 { ! hBOOL( hAPP( Z, skol50( T, U, Z ) ) ), alpha42( X, Y, Z ) }.
% 0.97/1.59 { alpha46( X, Y, skol50( X, Y, Z ) ), alpha42( X, Y, Z ) }.
% 0.97/1.59 { ! alpha46( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.59 skol51( X, T, U ) ) }.
% 0.97/1.59 { ! alpha46( X, Y, Z ), alpha50( X, Y, Z, skol51( X, Y, Z ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, T ), ! alpha50( X, Y, Z
% 0.97/1.59 , T ), alpha46( X, Y, Z ) }.
% 0.97/1.59 { ! alpha50( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.59 T, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.59 { ! alpha50( X, Y, Z, T ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.97/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ) }
% 0.97/1.59 .
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! Y =
% 0.97/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ), alpha50( X,
% 0.97/1.59 Y, Z, T ) }.
% 0.97/1.59 { ! alpha33( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), alpha38( X, Y, Z ) }.
% 0.97/1.59 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.59 tc_Int_Oint ), X ), alpha33( X, Y, Z ) }.
% 0.97/1.59 { ! alpha38( X, Y, Z ), alpha33( X, Y, Z ) }.
% 0.97/1.59 { ! alpha38( X, Y, Z ), ! alpha43( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 0.97/1.59 { ! hBOOL( hAPP( Z, skol52( T, U, Z ) ) ), alpha38( X, Y, Z ) }.
% 0.97/1.59 { alpha43( X, Y, skol52( X, Y, Z ) ), alpha38( X, Y, Z ) }.
% 0.97/1.59 { ! alpha43( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), skol53( T, U, W ) ) }.
% 0.97/1.59 { ! alpha43( X, Y, Z ), alpha47( X, Y, Z, skol53( X, Y, Z ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! alpha47( X, Y, Z, T )
% 0.97/1.59 , alpha43( X, Y, Z ) }.
% 0.97/1.59 { ! alpha47( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X
% 0.97/1.59 ) }.
% 0.97/1.59 { ! alpha47( X, Y, Z, T ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.97/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ) }
% 0.97/1.59 .
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X ), ! Y =
% 0.97/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ), alpha47( X,
% 0.97/1.59 Y, Z, T ) }.
% 0.97/1.59 { ! alpha11( X, Y ), ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.97/1.59 hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 0.97/1.59 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), alpha11( X, Y ) }.
% 0.97/1.59 { ! hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), alpha11
% 0.97/1.59 ( X, Y ) }.
% 0.97/1.59 { ! T = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), alpha56( X,
% 0.97/1.59 Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), Z =
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.97/1.59 tc_Int_Oint, T, Z ) = Y }.
% 0.97/1.59 { ! T = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), alpha56( X,
% 0.97/1.59 Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Z =
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.97/1.59 tc_Int_Oint, T, Z ) = Y }.
% 0.97/1.59 { ! alpha56( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.97/1.59 { ! alpha56( X, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.59 ( tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), alpha56( X, Y ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.59 ( tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y )
% 0.97/1.59 , alpha56( X, Y ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.59 tc_Nat_Onat, skol54( X ) ), X ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.97/1.59 tc_Nat_Onat, c_Nat_OSuc( skol54( X ) ) ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! hBOOL( hAPP( hAPP( Z,
% 0.97/1.59 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 0.97/1.59 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ), ! alpha12( X, Y, T,
% 0.97/1.59 U ), hBOOL( hAPP( hAPP( Z, T ), U ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha12( X, Y, skol55( X, Y
% 0.97/1.59 , Z ), skol73( X, Y, Z ) ), hBOOL( hAPP( hAPP( Z,
% 0.97/1.59 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 0.97/1.59 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! hBOOL( hAPP( hAPP( Z,
% 0.97/1.59 skol55( X, Y, Z ) ), skol73( X, Y, Z ) ) ), hBOOL( hAPP( hAPP( Z,
% 0.97/1.59 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 0.97/1.59 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 0.97/1.59 { ! alpha12( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, T
% 0.97/1.59 ) }.
% 0.97/1.59 { ! alpha12( X, Y, Z, T ), alpha27( X, Y, Z, T ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, T ), ! alpha27( X, Y, Z
% 0.97/1.59 , T ), alpha12( X, Y, Z, T ) }.
% 0.97/1.59 { ! alpha27( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.59 T, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.59 { ! alpha27( X, Y, Z, T ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.97/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ) }
% 0.97/1.59 .
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! Y =
% 0.97/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ), alpha27( X,
% 0.97/1.59 Y, Z, T ) }.
% 0.97/1.59 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) = X }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.59 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) =
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.59 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Divides_Odiv__class_Omod(
% 0.97/1.59 tc_Int_Oint, Y, X ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.97/1.59 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X,
% 0.97/1.59 c_Divides_Odiv__class_Omod( X, Z, Y ), Y ) = c_Groups_Ozero__class_Ozero
% 0.97/1.59 ( X ) }.
% 0.97/1.59 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero(
% 0.97/1.59 tc_Int_Oint ) ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.97/1.59 { c_Divides_Odiv__class_Omod( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero(
% 0.97/1.59 tc_Int_Oint ) ) = X }.
% 0.97/1.59 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.97/1.59 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.97/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.97/1.59 tc_Int_Oint, Z, X ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 0.97/1.59 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.97/1.59 tc_Int_Oint, c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, X ),
% 0.97/1.59 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) ) }.
% 0.97/1.59 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.59 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ), Y ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.59 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, Z ),
% 0.97/1.59 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, X, Z ) ) }.
% 0.97/1.59 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.59 c_Divides_Odiv__class_Omod( X, Z, Y ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X, Z, Y )
% 0.97/1.59 ), Y ) ) = Z }.
% 0.97/1.59 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 0.97/1.59 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 0.97/1.59 c_Divides_Odiv__class_Odiv( X, Y, Z ) ), c_Divides_Odiv__class_Omod( X, Y
% 0.97/1.59 , Z ) ) = Y }.
% 0.97/1.59 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 0.97/1.59 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X
% 0.97/1.59 , Z, Y ) ), Y ), c_Divides_Odiv__class_Omod( X, Z, Y ) ) = Z }.
% 0.97/1.59 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.59 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.59 ( X ), T ), c_Divides_Odiv__class_Odiv( X, Z, T ) ),
% 0.97/1.59 c_Divides_Odiv__class_Omod( X, Z, T ) ), Y ) =
% 0.97/1.59 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 0.97/1.59 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.59 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.59 ( X ), c_Divides_Odiv__class_Odiv( X, T, Z ) ), Z ),
% 0.97/1.59 c_Divides_Odiv__class_Omod( X, T, Z ) ), Y ) =
% 0.97/1.59 c_Groups_Oplus__class_Oplus( X, T, Y ) }.
% 0.97/1.59 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) =
% 0.97/1.59 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 0.97/1.59 tc_Nat_Onat, Z, Y ), X ) }.
% 0.97/1.59 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.59 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) =
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.59 { Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.59 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) =
% 0.97/1.59 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.59 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X
% 0.97/1.59 , Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.59 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, Y ),
% 0.97/1.59 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, X ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.59 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 0.97/1.59 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ) = Y }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.59 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 0.97/1.59 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ) = Y }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.59 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 0.97/1.59 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) =
% 0.97/1.59 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, Y ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.97/1.59 tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 0.97/1.59 tc_Nat_Onat, Y, X ), Y ) }.
% 0.97/1.59 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.59 c_Power_Opower__class_Opower( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.97/1.59 tc_Int_Oint, Z, Y ) ), X ), Y ) = c_Divides_Odiv__class_Omod( tc_Int_Oint
% 0.97/1.59 , hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ), Y )
% 0.97/1.59 }.
% 0.97/1.59 { ! c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y = hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), skol56( X, Y ) ) }.
% 0.97/1.59 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z )
% 0.97/1.59 , c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.97/1.59 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, T,
% 0.97/1.59 Z ) = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod
% 0.97/1.59 ( X, W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 0.97/1.59 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.59 ( X ), T ), W ), Z ) = c_Divides_Odiv__class_Omod( X, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), U ), Z ) }.
% 0.97/1.59 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.97/1.59 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Omod( X
% 0.97/1.59 , T, Z ) ), Y ), Z ) = c_Divides_Odiv__class_Omod( X, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.97/1.59 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.97/1.59 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) =
% 0.97/1.59 c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) }.
% 0.97/1.59 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.97/1.59 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Omod( X, T, Y )
% 0.97/1.59 ), Z ) }.
% 0.97/1.59 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.97/1.59 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) = hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), T ), c_Divides_Odiv__class_Omod( X, Z
% 0.97/1.59 , Y ) ) }.
% 0.97/1.59 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.97/1.59 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 0.97/1.59 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.59 ( X ), c_Divides_Odiv__class_Omod( X, T, Y ) ),
% 0.97/1.59 c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 0.97/1.59 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.97/1.59 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 0.97/1.59 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.59 ( X ), c_Divides_Odiv__class_Omod( X, T, Y ) ), Z ), Y ) }.
% 0.97/1.59 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) =
% 0.97/1.59 c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.97/1.59 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) }.
% 0.97/1.59 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.97/1.59 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 0.97/1.59 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.59 ( X ), T ), c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 0.97/1.59 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.97/1.59 c_Groups_Oplus__class_Oplus( X, T, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) =
% 0.97/1.59 c_Divides_Odiv__class_Omod( X, T, Y ) }.
% 0.97/1.59 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.97/1.59 c_Groups_Oplus__class_Oplus( X, T, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Z ) =
% 0.97/1.59 c_Divides_Odiv__class_Omod( X, T, Z ) }.
% 0.97/1.59 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.97/1.59 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Z ) =
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.97/1.59 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) =
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y,
% 0.97/1.59 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 0.97/1.59 tc_Int_Oint, Z, c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) =
% 0.97/1.59 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 0.97/1.59 tc_Int_Oint, Z, Y ), X ) }.
% 0.97/1.59 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 0.97/1.59 tc_Int_Oint, c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y ), X ), Y ) =
% 0.97/1.59 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 0.97/1.59 tc_Int_Oint, Z, X ), Y ) }.
% 0.97/1.59 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.97/1.59 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.97/1.59 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, T,
% 0.97/1.59 c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 0.97/1.59 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.97/1.59 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.97/1.59 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X,
% 0.97/1.59 c_Divides_Odiv__class_Omod( X, T, Y ), Z ), Y ) }.
% 0.97/1.59 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.97/1.59 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.97/1.59 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X,
% 0.97/1.59 c_Divides_Odiv__class_Omod( X, T, Y ), c_Divides_Odiv__class_Omod( X, Z,
% 0.97/1.59 Y ) ), Y ) }.
% 0.97/1.59 { ! class_Divides_Oring__div( X ), ! c_Divides_Odiv__class_Omod( X, T, Z )
% 0.97/1.59 = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod( X
% 0.97/1.59 , W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 0.97/1.59 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, T, W ),
% 0.97/1.59 Z ) = c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, Y
% 0.97/1.59 , U ), Z ) }.
% 0.97/1.59 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.97/1.59 c_Divides_Odiv__class_Omod( X, Z, Y ), Y ) = c_Divides_Odiv__class_Omod(
% 0.97/1.59 X, Z, Y ) }.
% 0.97/1.59 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, T,
% 0.97/1.59 Z ) = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod
% 0.97/1.59 ( X, W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 0.97/1.59 c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X, T, W ), Z
% 0.97/1.59 ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X, Y, U
% 0.97/1.59 ), Z ) }.
% 0.97/1.59 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.97/1.59 c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Z ), Y
% 0.97/1.59 ), Z ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X,
% 0.97/1.59 T, Y ), Z ) }.
% 0.97/1.59 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.97/1.59 c_Groups_Oplus__class_Oplus( X, T, c_Divides_Odiv__class_Omod( X, Z, Y )
% 0.97/1.59 ), Y ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X,
% 0.97/1.59 T, Z ), Y ) }.
% 0.97/1.59 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.97/1.59 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 0.97/1.59 ( X, c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Y
% 0.97/1.59 ), c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 0.97/1.59 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.97/1.59 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 0.97/1.59 ( X, c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Y
% 0.97/1.59 ), Z ), Y ) }.
% 0.97/1.59 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.97/1.59 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 0.97/1.59 ( X, c_Groups_Oplus__class_Oplus( X, T, c_Divides_Odiv__class_Omod( X, Z
% 0.97/1.59 , Y ) ), Y ) }.
% 0.97/1.59 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.97/1.59 c_Groups_Oplus__class_Oplus( X, Z, Y ), Z ) = c_Divides_Odiv__class_Omod
% 0.97/1.59 ( X, Y, Z ) }.
% 0.97/1.59 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.97/1.59 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = c_Divides_Odiv__class_Omod
% 0.97/1.59 ( X, Z, Y ) }.
% 0.97/1.59 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.59 }.
% 0.97/1.59 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.59 tc_Int_Oint ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.97/1.59 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.97/1.59 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y, Y
% 0.97/1.59 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59 { c_Divides_Odiv__class_Omod( tc_Int_Oint, X, X ) =
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.59 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.59 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ), X ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Divides_Odiv__class_Omod
% 0.97/1.59 ( tc_Int_Oint, Y, X ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.59 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ), X ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.97/1.59 tc_Int_Oint, X, Y ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.97/1.59 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ) = X }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.59 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ),
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Divides_Odiv__class_Omod
% 0.97/1.59 ( tc_Int_Oint, Y, X ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.59 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ),
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ),
% 0.97/1.59 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ) = X }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.59 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.97/1.59 tc_Int_Oint, Y, X ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.59 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.59 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ), X ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.59 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.97/1.59 tc_Int_Oint, Y, X ) ) }.
% 0.97/1.59 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.97/1.59 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.97/1.59 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Z, Y ) ), Y ),
% 0.97/1.59 c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y ) ), X ) =
% 0.97/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) }.
% 0.97/1.59 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.97/1.59 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.97/1.59 ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ) ),
% 0.97/1.59 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, Z ) ), X ) =
% 0.97/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) }.
% 0.97/1.59 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) =
% 0.97/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.97/1.59 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 0.97/1.59 c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.97/1.59 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) ) }.
% 0.97/1.59 { Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 0.97/1.59 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 0.97/1.59 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) }.
% 0.97/1.59 { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.97/1.59 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Divides_Odiv__class_Odiv
% 0.97/1.59 ( tc_Int_Oint, Y, X ) ), X ) ) }.
% 0.97/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ),
% 0.97/1.59 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) =
% 0.97/1.59 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Divides_Odiv__class_Omod
% 0.97/1.59 ( tc_Int_Oint, X, Y ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.59 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 0.97/1.59 ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) =
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.59 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 0.97/1.59 , c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.97/1.59 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.97/1.59 tc_Nat_Onat, Y, X ), X ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.59 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 0.97/1.59 , c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.97/1.59 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.97/1.59 tc_Nat_Onat, Y, X ), X ) ) }.
% 0.97/1.59 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 0.97/1.59 alpha13( X, Z ) }.
% 0.97/1.59 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 0.97/1.59 alpha28( X, Y, Z ) }.
% 0.97/1.59 { ! alpha13( X, Z ), ! alpha28( X, Y, Z ), hBOOL( hAPP( Z,
% 0.97/1.59 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ) }.
% 0.97/1.59 { ! alpha28( X, Y, Z ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.59 alpha34( X, Y, Z ) }.
% 0.97/1.59 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha28( X, Y, Z ) }.
% 0.97/1.59 { ! alpha34( X, Y, Z ), alpha28( X, Y, Z ) }.
% 0.97/1.59 { ! alpha34( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, X
% 0.97/1.59 ), alpha39( X, Y, Z, T ) }.
% 0.97/1.59 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol57( X, T, U ), X ),
% 0.97/1.59 alpha34( X, Y, Z ) }.
% 0.97/1.59 { ! alpha39( X, Y, Z, skol57( X, Y, Z ) ), alpha34( X, Y, Z ) }.
% 0.97/1.59 { ! alpha39( X, Y, Z, T ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.97/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 0.97/1.59 hBOOL( hAPP( Z, U ) ) }.
% 0.97/1.59 { ! hBOOL( hAPP( Z, skol58( U, W, Z, V0 ) ) ), alpha39( X, Y, Z, T ) }.
% 0.97/1.59 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol58( X, Y, Z, T ) )
% 0.97/1.59 , T ), alpha39( X, Y, Z, T ) }.
% 0.97/1.59 { ! alpha13( X, Y ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.59 hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.97/1.59 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha13( X, Y ) }.
% 0.97/1.59 { ! hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha13
% 0.97/1.59 ( X, Y ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.59 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ),
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Divides_Odiv__class_Omod
% 0.97/1.59 ( tc_Int_Oint, X, Y ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y )
% 0.97/1.59 }.
% 0.97/1.59 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 0.97/1.59 alpha14( X, Z ), alpha29( X, Y, Z ) }.
% 0.97/1.59 { ! alpha14( X, Z ), hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv(
% 0.97/1.59 tc_Nat_Onat, Y, X ) ) ) }.
% 0.97/1.59 { ! alpha29( X, Y, Z ), hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv(
% 0.97/1.59 tc_Nat_Onat, Y, X ) ) ) }.
% 0.97/1.59 { ! alpha29( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol59( X
% 0.97/1.59 , Y, T ) ), Y ) }.
% 0.97/1.59 { ! alpha29( X, Y, Z ), alpha35( X, Y, Z, skol59( X, Y, Z ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), T ), Y ), ! alpha35( X
% 0.97/1.59 , Y, Z, T ), alpha29( X, Y, Z ) }.
% 0.97/1.59 { ! alpha35( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.97/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), c_Nat_OSuc
% 0.97/1.59 ( T ) ) ) }.
% 0.97/1.59 { ! alpha35( X, Y, Z, T ), hBOOL( hAPP( Z, T ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), c_Nat_OSuc( T ) ) ), !
% 0.97/1.59 hBOOL( hAPP( Z, T ) ), alpha35( X, Y, Z, T ) }.
% 0.97/1.59 { ! alpha14( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.59 { ! alpha14( X, Y ), hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero(
% 0.97/1.59 tc_Nat_Onat ) ) ) }.
% 0.97/1.59 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hBOOL( hAPP( Y,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha14( X, Y ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.59 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), Y ),
% 0.97/1.59 ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), c_Nat_OSuc( Z ) ) ), Z
% 0.97/1.59 = c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.59 ( tc_Nat_Onat ), X ), ! Z = c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X
% 0.97/1.59 ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), Y ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.59 ( tc_Nat_Onat ), X ), ! Z = c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X
% 0.97/1.59 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), c_Nat_OSuc( Z ) ) ) }
% 0.97/1.59 .
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.59 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X
% 0.97/1.59 , Y ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.97/1.59 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.97/1.59 tc_Nat_Onat, Y, X ), X ) ) }.
% 0.97/1.59 { ! Z = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), T ), X ), alpha57( X,
% 0.97/1.59 Y ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), Y =
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.97/1.59 tc_Int_Oint, Z, Y ) = X }.
% 0.97/1.59 { ! Z = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), T ), X ), alpha57( X,
% 0.97/1.59 Y ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y =
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.97/1.59 tc_Int_Oint, Z, Y ) = X }.
% 0.97/1.59 { ! alpha57( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.97/1.59 { ! alpha57( X, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.59 ( tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), alpha57( X, Y ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.59 ( tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y )
% 0.97/1.59 , alpha57( X, Y ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.59 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, Y
% 0.97/1.59 ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.97/1.59 c_Divides_Odiv__class_Omod( tc_Int_Oint, T, X ) ), Y ),
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.59 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, Y
% 0.97/1.59 ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ),
% 0.97/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.97/1.59 c_Divides_Odiv__class_Omod( tc_Int_Oint, T, X ) ), Y ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.59 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, Z ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.97/1.59 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.97/1.59 ), c_Divides_Odiv__class_Omod( tc_Int_Oint, T, X ) ), Y ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.59 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, Z ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.97/1.59 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.97/1.59 ), c_Divides_Odiv__class_Omod( tc_Int_Oint, T, X ) ), Y ) ) }.
% 0.97/1.59 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ),
% 0.97/1.59 alpha15( X, Y, Z ) }.
% 0.97/1.59 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ),
% 0.97/1.59 alpha30( X, Y, Z ) }.
% 0.97/1.59 { ! alpha15( X, Y, Z ), ! alpha30( X, Y, Z ), hBOOL( hAPP( Z,
% 0.97/1.59 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 0.97/1.59 { ! alpha30( X, Y, Z ), alpha36( X, Y, Z ) }.
% 0.97/1.59 { ! alpha30( X, Y, Z ), alpha40( X, Y, Z ) }.
% 0.97/1.59 { ! alpha36( X, Y, Z ), ! alpha40( X, Y, Z ), alpha30( X, Y, Z ) }.
% 0.97/1.59 { ! alpha40( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha44( X, Y, Z ) }.
% 0.97/1.59 { c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha40( X, Y, Z ) }.
% 0.97/1.59 { ! alpha44( X, Y, Z ), alpha40( X, Y, Z ) }.
% 0.97/1.59 { ! alpha44( X, Y, Z ), ! alpha48( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 0.97/1.59 { ! hBOOL( hAPP( Z, skol60( T, U, Z ) ) ), alpha44( X, Y, Z ) }.
% 0.97/1.59 { alpha48( X, Y, skol60( X, Y, Z ) ), alpha44( X, Y, Z ) }.
% 0.97/1.59 { ! alpha48( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z )
% 0.97/1.59 }.
% 0.97/1.59 { ! alpha48( X, Y, Z ), alpha51( X, Y, Z ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), ! alpha51( X, Y, Z
% 0.97/1.59 ), alpha48( X, Y, Z ) }.
% 0.97/1.59 { ! alpha51( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.59 { ! alpha51( X, Y, Z ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP
% 0.97/1.59 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), skol61( X, Y,
% 0.97/1.59 Z ) ), Z ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! Y =
% 0.97/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), T ), Z ), alpha51( X,
% 0.97/1.59 Y, Z ) }.
% 0.97/1.59 { ! alpha36( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), alpha41( X, Y, Z ) }.
% 0.97/1.59 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.59 tc_Int_Oint ), X ), alpha36( X, Y, Z ) }.
% 0.97/1.59 { ! alpha41( X, Y, Z ), alpha36( X, Y, Z ) }.
% 0.97/1.59 { ! alpha41( X, Y, Z ), ! alpha45( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 0.97/1.59 { ! hBOOL( hAPP( Z, skol62( T, U, Z ) ) ), alpha41( X, Y, Z ) }.
% 0.97/1.59 { alpha45( X, Y, skol62( X, Y, Z ) ), alpha41( X, Y, Z ) }.
% 0.97/1.59 { ! alpha45( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ) }.
% 0.97/1.59 { ! alpha45( X, Y, Z ), alpha49( X, Y, Z ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), ! alpha49( X, Y, Z ),
% 0.97/1.59 alpha45( X, Y, Z ) }.
% 0.97/1.59 { ! alpha49( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X )
% 0.97/1.59 }.
% 0.97/1.59 { ! alpha49( X, Y, Z ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP
% 0.97/1.59 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), skol63( X, Y,
% 0.97/1.59 Z ) ), Z ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ), ! Y =
% 0.97/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), T ), Z ), alpha49( X,
% 0.97/1.59 Y, Z ) }.
% 0.97/1.59 { ! alpha15( X, Y, Z ), ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.97/1.59 hBOOL( hAPP( Z, Y ) ) }.
% 0.97/1.59 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), alpha15( X, Y, Z ) }.
% 0.97/1.59 { ! hBOOL( hAPP( Z, Y ) ), alpha15( X, Y, Z ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.59 ( tc_Int_Oint ), X ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, hAPP(
% 0.97/1.59 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) =
% 0.97/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ),
% 0.97/1.59 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.97/1.59 tc_Int_Oint, Z, Y ), X ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y
% 0.97/1.59 ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.59 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( hAPP( Z, c_Divides_Odiv__class_Odiv
% 0.97/1.59 ( tc_Int_Oint, Y, X ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X )
% 0.97/1.59 ) ), ! alpha16( X, Y, T, U ), hBOOL( hAPP( hAPP( Z, T ), U ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.59 ( tc_Int_Oint ), X ), alpha16( X, Y, skol64( X, Y, Z ), skol74( X, Y, Z )
% 0.97/1.59 ), hBOOL( hAPP( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X )
% 0.97/1.59 ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.59 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( hAPP( Z, skol64( X, Y, Z ) ), skol74
% 0.97/1.59 ( X, Y, Z ) ) ), hBOOL( hAPP( hAPP( Z, c_Divides_Odiv__class_Odiv(
% 0.97/1.59 tc_Int_Oint, Y, X ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) )
% 0.97/1.59 ) }.
% 0.97/1.59 { ! alpha16( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ) }.
% 0.97/1.59 { ! alpha16( X, Y, Z, T ), alpha31( X, Y, Z, T ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! alpha31( X, Y, Z, T )
% 0.97/1.59 , alpha16( X, Y, Z, T ) }.
% 0.97/1.59 { ! alpha31( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X
% 0.97/1.59 ) }.
% 0.97/1.59 { ! alpha31( X, Y, Z, T ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.97/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ) }
% 0.97/1.59 .
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X ), ! Y =
% 0.97/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ), alpha31( X,
% 0.97/1.59 Y, Z, T ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.59 tc_Nat_Onat ), Y ), c_RComplete_Onatfloor(
% 0.97/1.59 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.97/1.59 tc_Nat_Onat, Y ) ) ) = c_Divides_Odiv__class_Odiv( tc_Nat_Onat,
% 0.97/1.59 c_RComplete_Onatfloor( X ), Y ) }.
% 0.97/1.59 { c_Complex_Ocis( hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.59 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Y ) ) ), X
% 0.97/1.59 ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.97/1.59 c_Complex_Ocis( X ) ), c_Complex_Ocis( hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.97/1.59 tc_Nat_Onat, Y ) ), X ) ) ) }.
% 0.97/1.59 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.97/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.59 tc_Nat_Onat, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ),
% 0.97/1.59 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ),
% 0.97/1.59 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.59 tc_Nat_Onat, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ),
% 0.97/1.59 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), X ) ) }.
% 0.97/1.59 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.59 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.97/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 0.97/1.59 tc_Nat_Onat, Z, X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ),
% 0.97/1.59 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.59 tc_Nat_Onat, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, X ),
% 0.97/1.59 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ), X ) ) }.
% 0.97/1.59 { ! class_Orderings_Opreorder( X ), class_Orderings_Opreorder( tc_fun( Y, X
% 0.97/1.59 ) ) }.
% 0.97/1.59 { ! class_Orderings_Oorder( X ), class_Orderings_Oorder( tc_fun( Y, X ) ) }
% 0.97/1.59 .
% 0.97/1.59 { ! class_Orderings_Oord( X ), class_Orderings_Oord( tc_fun( Y, X ) ) }.
% 0.97/1.59 { ! class_Groups_Ominus( X ), class_Groups_Ominus( tc_fun( Y, X ) ) }.
% 0.97/1.59 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.97/1.59 tc_Int_Oint ) }.
% 0.97/1.59 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.97/1.59 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Int_Oint ) }.
% 0.97/1.59 { class_Rings_Olinordered__comm__semiring__strict( tc_Int_Oint ) }.
% 0.97/1.59 { class_Rings_Olinordered__semiring__1__strict( tc_Int_Oint ) }.
% 0.97/1.59 { class_Rings_Olinordered__semiring__strict( tc_Int_Oint ) }.
% 0.97/1.59 { class_Groups_Oordered__ab__semigroup__add( tc_Int_Oint ) }.
% 0.97/1.59 { class_Groups_Oordered__ab__group__add__abs( tc_Int_Oint ) }.
% 0.97/1.59 { class_Groups_Oordered__comm__monoid__add( tc_Int_Oint ) }.
% 0.97/1.59 { class_Groups_Olinordered__ab__group__add( tc_Int_Oint ) }.
% 0.97/1.59 { class_Groups_Ocancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.97/1.59 { class_Rings_Oring__1__no__zero__divisors( tc_Int_Oint ) }.
% 0.97/1.59 { class_Rings_Oordered__cancel__semiring( tc_Int_Oint ) }.
% 0.97/1.59 { class_Rings_Olinordered__ring__strict( tc_Int_Oint ) }.
% 0.97/1.59 { class_Rings_Oring__no__zero__divisors( tc_Int_Oint ) }.
% 0.97/1.59 { class_Rings_Oordered__comm__semiring( tc_Int_Oint ) }.
% 0.97/1.59 { class_Rings_Olinordered__semiring__1( tc_Int_Oint ) }.
% 0.97/1.59 { class_Groups_Oordered__ab__group__add( tc_Int_Oint ) }.
% 0.97/1.59 { class_Groups_Ocancel__semigroup__add( tc_Int_Oint ) }.
% 0.97/1.59 { class_Rings_Olinordered__semiring( tc_Int_Oint ) }.
% 0.97/1.59 { class_Rings_Olinordered__semidom( tc_Int_Oint ) }.
% 0.97/1.59 { class_Groups_Oab__semigroup__mult( tc_Int_Oint ) }.
% 0.97/1.59 { class_Groups_Ocomm__monoid__mult( tc_Int_Oint ) }.
% 0.97/1.59 { class_Groups_Oab__semigroup__add( tc_Int_Oint ) }.
% 0.97/1.59 { class_Rings_Oordered__semiring( tc_Int_Oint ) }.
% 0.97/1.59 { class_Rings_Oordered__ring__abs( tc_Int_Oint ) }.
% 0.97/1.59 { class_Rings_Ono__zero__divisors( tc_Int_Oint ) }.
% 0.97/1.59 { class_Groups_Ocomm__monoid__add( tc_Int_Oint ) }.
% 0.97/1.59 { class_Rings_Olinordered__ring( tc_Int_Oint ) }.
% 0.97/1.59 { class_Rings_Olinordered__idom( tc_Int_Oint ) }.
% 0.97/1.59 { class_Rings_Ocomm__semiring__1( tc_Int_Oint ) }.
% 0.97/1.59 { class_Divides_Osemiring__div( tc_Int_Oint ) }.
% 0.97/1.59 { class_Rings_Ocomm__semiring( tc_Int_Oint ) }.
% 0.97/1.59 { class_Groups_Oab__group__add( tc_Int_Oint ) }.
% 0.97/1.59 { class_Rings_Ozero__neq__one( tc_Int_Oint ) }.
% 0.97/1.59 { class_Rings_Oordered__ring( tc_Int_Oint ) }.
% 0.97/1.59 { class_Orderings_Opreorder( tc_Int_Oint ) }.
% 0.97/1.59 { class_Orderings_Olinorder( tc_Int_Oint ) }.
% 0.97/1.59 { class_Groups_Omonoid__mult( tc_Int_Oint ) }.
% 0.97/1.59 { class_Rings_Ocomm__ring__1( tc_Int_Oint ) }.
% 0.97/1.59 { class_Groups_Omonoid__add( tc_Int_Oint ) }.
% 0.97/1.59 { class_Rings_Osemiring__0( tc_Int_Oint ) }.
% 0.97/1.59 { class_Groups_Ogroup__add( tc_Int_Oint ) }.
% 0.97/1.59 { class_Divides_Oring__div( tc_Int_Oint ) }.
% 0.97/1.59 { class_Rings_Omult__zero( tc_Int_Oint ) }.
% 0.97/1.59 { class_Orderings_Oorder( tc_Int_Oint ) }.
% 0.97/1.59 { class_Rings_Osemiring( tc_Int_Oint ) }.
% 0.97/1.59 { class_Orderings_Oord( tc_Int_Oint ) }.
% 0.97/1.59 { class_Groups_Osgn__if( tc_Int_Oint ) }.
% 0.97/1.59 { class_Rings_Oring__1( tc_Int_Oint ) }.
% 0.97/1.59 { class_Groups_Ominus( tc_Int_Oint ) }.
% 0.97/1.59 { class_Power_Opower( tc_Int_Oint ) }.
% 0.97/1.59 { class_Groups_Ozero( tc_Int_Oint ) }.
% 0.97/1.59 { class_Rings_Oring( tc_Int_Oint ) }.
% 0.97/1.59 { class_Groups_Oone( tc_Int_Oint ) }.
% 0.97/1.59 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.97/1.59 tc_Nat_Onat ) }.
% 0.97/1.59 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.97/1.59 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Nat_Onat ) }.
% 0.97/1.59 { class_Rings_Olinordered__comm__semiring__strict( tc_Nat_Onat ) }.
% 0.97/1.59 { class_Rings_Olinordered__semiring__strict( tc_Nat_Onat ) }.
% 0.97/1.59 { class_Groups_Oordered__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.97/1.59 { class_Groups_Oordered__comm__monoid__add( tc_Nat_Onat ) }.
% 0.97/1.59 { class_Groups_Ocancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.97/1.59 { class_Rings_Oordered__cancel__semiring( tc_Nat_Onat ) }.
% 0.97/1.59 { class_Rings_Oordered__comm__semiring( tc_Nat_Onat ) }.
% 0.97/1.59 { class_Groups_Ocancel__semigroup__add( tc_Nat_Onat ) }.
% 0.97/1.59 { class_Rings_Olinordered__semiring( tc_Nat_Onat ) }.
% 0.97/1.59 { class_Rings_Olinordered__semidom( tc_Nat_Onat ) }.
% 0.97/1.59 { class_Groups_Oab__semigroup__mult( tc_Nat_Onat ) }.
% 0.97/1.59 { class_Groups_Ocomm__monoid__mult( tc_Nat_Onat ) }.
% 0.97/1.59 { class_Groups_Oab__semigroup__add( tc_Nat_Onat ) }.
% 0.97/1.59 { class_Rings_Oordered__semiring( tc_Nat_Onat ) }.
% 0.97/1.59 { class_Rings_Ono__zero__divisors( tc_Nat_Onat ) }.
% 0.97/1.59 { class_Groups_Ocomm__monoid__add( tc_Nat_Onat ) }.
% 0.97/1.59 { class_Rings_Ocomm__semiring__1( tc_Nat_Onat ) }.
% 0.97/1.59 { class_Divides_Osemiring__div( tc_Nat_Onat ) }.
% 0.97/1.59 { class_Rings_Ocomm__semiring( tc_Nat_Onat ) }.
% 0.97/1.59 { class_Rings_Ozero__neq__one( tc_Nat_Onat ) }.
% 0.97/1.59 { class_Orderings_Opreorder( tc_Nat_Onat ) }.
% 0.97/1.59 { class_Orderings_Olinorder( tc_Nat_Onat ) }.
% 0.97/1.59 { class_Groups_Omonoid__mult( tc_Nat_Onat ) }.
% 0.97/1.59 { class_Groups_Omonoid__add( tc_Nat_Onat ) }.
% 0.97/1.59 { class_Rings_Osemiring__0( tc_Nat_Onat ) }.
% 0.97/1.59 { class_Rings_Omult__zero( tc_Nat_Onat ) }.
% 0.97/1.59 { class_Orderings_Oorder( tc_Nat_Onat ) }.
% 0.97/1.59 { class_Rings_Osemiring( tc_Nat_Onat ) }.
% 0.97/1.59 { class_Orderings_Oord( tc_Nat_Onat ) }.
% 0.97/1.59 { class_Groups_Ominus( tc_Nat_Onat ) }.
% 0.97/1.59 { class_Power_Opower( tc_Nat_Onat ) }.
% 0.97/1.59 { class_Groups_Ozero( tc_Nat_Onat ) }.
% 0.97/1.59 { class_Groups_Oone( tc_Nat_Onat ) }.
% 0.97/1.59 { class_Orderings_Opreorder( tc_HOL_Obool ) }.
% 0.97/1.59 { class_Orderings_Oorder( tc_HOL_Obool ) }.
% 0.97/1.59 { class_Orderings_Oord( tc_HOL_Obool ) }.
% 0.97/1.59 { class_Groups_Ominus( tc_HOL_Obool ) }.
% 0.97/1.59 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.97/1.59 tc_RealDef_Oreal ) }.
% 0.97/1.59 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.97/1.59 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_RealDef_Oreal ) }
% 0.97/1.59 .
% 0.97/1.59 { class_Rings_Olinordered__comm__semiring__strict( tc_RealDef_Oreal ) }.
% 0.97/1.59 { class_Archimedean__Field_Oarchimedean__field( tc_RealDef_Oreal ) }.
% 0.97/1.59 { class_Rings_Olinordered__semiring__1__strict( tc_RealDef_Oreal ) }.
% 0.97/1.59 { class_RealVector_Oreal__normed__div__algebra( tc_RealDef_Oreal ) }.
% 0.97/1.59 { class_Rings_Olinordered__semiring__strict( tc_RealDef_Oreal ) }.
% 0.97/1.59 { class_RealVector_Oreal__normed__algebra__1( tc_RealDef_Oreal ) }.
% 0.97/1.59 { class_Groups_Oordered__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.97/1.59 { class_Groups_Oordered__ab__group__add__abs( tc_RealDef_Oreal ) }.
% 0.97/1.59 { class_RealVector_Oreal__normed__algebra( tc_RealDef_Oreal ) }.
% 0.97/1.59 { class_Groups_Oordered__comm__monoid__add( tc_RealDef_Oreal ) }.
% 0.97/1.59 { class_Groups_Olinordered__ab__group__add( tc_RealDef_Oreal ) }.
% 0.97/1.59 { class_Groups_Ocancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.97/1.59 { class_Rings_Oring__1__no__zero__divisors( tc_RealDef_Oreal ) }.
% 0.97/1.59 { class_Rings_Oordered__cancel__semiring( tc_RealDef_Oreal ) }.
% 0.97/1.59 { class_RealVector_Oreal__normed__vector( tc_RealDef_Oreal ) }.
% 0.97/1.59 { class_Rings_Olinordered__ring__strict( tc_RealDef_Oreal ) }.
% 0.97/1.59 { class_Rings_Oring__no__zero__divisors( tc_RealDef_Oreal ) }.
% 0.97/1.59 { class_Rings_Oordered__comm__semiring( tc_RealDef_Oreal ) }.
% 0.97/1.59 { class_Rings_Olinordered__semiring__1( tc_RealDef_Oreal ) }.
% 0.97/1.59 { class_Groups_Oordered__ab__group__add( tc_RealDef_Oreal ) }.
% 0.97/1.59 { class_Groups_Ocancel__semigroup__add( tc_RealDef_Oreal ) }.
% 0.97/1.59 { class_Rings_Olinordered__semiring( tc_RealDef_Oreal ) }.
% 0.97/1.59 { class_Rings_Olinordered__semidom( tc_RealDef_Oreal ) }.
% 0.97/1.59 { class_Groups_Oab__semigroup__mult( tc_RealDef_Oreal ) }.
% 0.97/1.59 { class_Groups_Ocomm__monoid__mult( tc_RealDef_Oreal ) }.
% 0.97/1.59 { class_Groups_Oab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.97/1.59 { class_Rings_Oordered__semiring( tc_RealDef_Oreal ) }.
% 0.97/1.59 { class_Rings_Oordered__ring__abs( tc_RealDef_Oreal ) }.
% 0.97/1.59 { class_Rings_Ono__zero__divisors( tc_RealDef_Oreal ) }.
% 0.97/1.59 { class_Groups_Ocomm__monoid__add( tc_RealDef_Oreal ) }.
% 0.97/1.59 { class_Rings_Olinordered__ring( tc_RealDef_Oreal ) }.
% 0.97/1.59 { class_Rings_Olinordered__idom( tc_RealDef_Oreal ) }.
% 0.97/1.59 { class_Rings_Ocomm__semiring__1( tc_RealDef_Oreal ) }.
% 0.97/1.59 { class_Rings_Ocomm__semiring( tc_RealDef_Oreal ) }.
% 0.97/1.59 { class_Groups_Oab__group__add( tc_RealDef_Oreal ) }.
% 0.97/1.59 { class_Rings_Ozero__neq__one( tc_RealDef_Oreal ) }.
% 0.97/1.59 { class_Rings_Oordered__ring( tc_RealDef_Oreal ) }.
% 0.97/1.59 { class_Orderings_Opreorder( tc_RealDef_Oreal ) }.
% 0.97/1.59 { class_Orderings_Olinorder( tc_RealDef_Oreal ) }.
% 0.97/1.59 { class_Groups_Omonoid__mult( tc_RealDef_Oreal ) }.
% 0.97/1.59 { class_Rings_Ocomm__ring__1( tc_RealDef_Oreal ) }.
% 0.97/1.59 { class_Groups_Omonoid__add( tc_RealDef_Oreal ) }.
% 0.97/1.59 { class_Rings_Osemiring__0( tc_RealDef_Oreal ) }.
% 0.97/1.59 { class_Groups_Ogroup__add( tc_RealDef_Oreal ) }.
% 0.97/1.59 { class_Rings_Omult__zero( tc_RealDef_Oreal ) }.
% 0.97/1.59 { class_Orderings_Oorder( tc_RealDef_Oreal ) }.
% 0.97/1.59 { class_Rings_Osemiring( tc_RealDef_Oreal ) }.
% 0.97/1.59 { class_Orderings_Oord( tc_RealDef_Oreal ) }.
% 0.97/1.59 { class_Groups_Osgn__if( tc_RealDef_Oreal ) }.
% 0.97/1.59 { class_Rings_Oring__1( tc_RealDef_Oreal ) }.
% 0.97/1.59 { class_Groups_Ominus( tc_RealDef_Oreal ) }.
% 0.97/1.59 { class_Power_Opower( tc_RealDef_Oreal ) }.
% 0.97/1.59 { class_Groups_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.59 { class_Rings_Oring( tc_RealDef_Oreal ) }.
% 0.97/1.59 { class_Groups_Oone( tc_RealDef_Oreal ) }.
% 0.97/1.59 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.97/1.59 tc_Complex_Ocomplex ) }.
% 0.97/1.59 { class_RealVector_Oreal__normed__div__algebra( tc_Complex_Ocomplex ) }.
% 0.97/1.59 { class_RealVector_Oreal__normed__algebra__1( tc_Complex_Ocomplex ) }.
% 0.97/1.59 { class_RealVector_Oreal__normed__algebra( tc_Complex_Ocomplex ) }.
% 0.97/1.59 { class_Groups_Ocancel__ab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.97/1.59 { class_Rings_Oring__1__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.97/1.59 { class_RealVector_Oreal__normed__vector( tc_Complex_Ocomplex ) }.
% 0.97/1.59 { class_Rings_Oring__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.97/1.59 { class_Groups_Ocancel__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.97/1.59 { class_Groups_Oab__semigroup__mult( tc_Complex_Ocomplex ) }.
% 0.97/1.59 { class_Groups_Ocomm__monoid__mult( tc_Complex_Ocomplex ) }.
% 0.97/1.59 { class_Groups_Oab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.97/1.59 { class_Rings_Ono__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.97/1.59 { class_Groups_Ocomm__monoid__add( tc_Complex_Ocomplex ) }.
% 0.97/1.59 { class_Rings_Ocomm__semiring__1( tc_Complex_Ocomplex ) }.
% 0.97/1.59 { class_Rings_Ocomm__semiring( tc_Complex_Ocomplex ) }.
% 0.97/1.59 { class_Groups_Oab__group__add( tc_Complex_Ocomplex ) }.
% 0.97/1.59 { class_Rings_Ozero__neq__one( tc_Complex_Ocomplex ) }.
% 0.97/1.59 { class_Groups_Omonoid__mult( tc_Complex_Ocomplex ) }.
% 0.97/1.59 { class_Rings_Ocomm__ring__1( tc_Complex_Ocomplex ) }.
% 0.97/1.59 { class_Groups_Omonoid__add( tc_Complex_Ocomplex ) }.
% 0.97/1.59 { class_Rings_Osemiring__0( tc_Complex_Ocomplex ) }.
% 0.97/1.59 { class_Groups_Ogroup__add( tc_Complex_Ocomplex ) }.
% 0.97/1.59 { class_Rings_Omult__zero( tc_Complex_Ocomplex ) }.
% 0.97/1.59 { class_Rings_Osemiring( tc_Complex_Ocomplex ) }.
% 0.97/1.59 { class_Rings_Oring__1( tc_Complex_Ocomplex ) }.
% 0.97/1.59 { class_Groups_Ominus( tc_Complex_Ocomplex ) }.
% 0.97/1.59 { class_Power_Opower( tc_Complex_Ocomplex ) }.
% 0.97/1.59 { class_Groups_Ozero( tc_Complex_Ocomplex ) }.
% 0.97/1.59 { class_Rings_Oring( tc_Complex_Ocomplex ) }.
% 0.97/1.59 { class_Groups_Oone( tc_Complex_Ocomplex ) }.
% 0.97/1.59 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, v_m, v_x ) }.
% 0.97/1.59 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, v_x,
% 0.97/1.59 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, v_m, v_e ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, v_x, v_m ) ), v_e ) }.
% 0.97/1.59
% 0.97/1.59 *** allocated 15000 integers for clauses
% 0.97/1.59 *** allocated 22500 integers for clauses
% 0.97/1.59 *** allocated 33750 integers for clauses
% 0.97/1.59 *** allocated 50625 integers for clauses
% 0.97/1.59 *** allocated 75937 integers for clauses
% 0.97/1.59 percentage equality = 0.233838, percentage horn = 0.913517
% 0.97/1.59 This is a problem with some equality
% 0.97/1.59
% 0.97/1.59
% 0.97/1.59
% 0.97/1.59 Options Used:
% 0.97/1.59
% 0.97/1.59 useres = 1
% 0.97/1.59 useparamod = 1
% 0.97/1.59 useeqrefl = 1
% 0.97/1.59 useeqfact = 1
% 0.97/1.59 usefactor = 1
% 0.97/1.59 usesimpsplitting = 0
% 0.97/1.59 usesimpdemod = 5
% 0.97/1.59 usesimpres = 3
% 0.97/1.59
% 0.97/1.59 resimpinuse = 1000
% 0.97/1.59 resimpclauses = 20000
% 0.97/1.59 substype = eqrewr
% 0.97/1.59 backwardsubs = 1
% 0.97/1.59 selectoldest = 5
% 0.97/1.59
% 0.97/1.59 litorderings [0] = split
% 0.97/1.59 litorderings [1] = extend the termordering, first sorting on arguments
% 0.97/1.59
% 0.97/1.59 termordering = kbo
% 0.97/1.59
% 0.97/1.59 litapriori = 0
% 0.97/1.59 termapriori = 1
% 0.97/1.59 litaposteriori = 0
% 0.97/1.59 termaposteriori = 0
% 0.97/1.59 demodaposteriori = 0
% 0.97/1.59 ordereqreflfact = 0
% 0.97/1.59
% 0.97/1.59 litselect = negord
% 0.97/1.59
% 0.97/1.59 maxweight = 15
% 0.97/1.59 maxdepth = 30000
% 0.97/1.59 maxlength = 115
% 0.97/1.59 maxnrvars = 195
% 0.97/1.59 excuselevel = 1
% 0.97/1.59 increasemaxweight = 1
% 0.97/1.59
% 0.97/1.59 maxselected = 10000000
% 0.97/1.59 maxnrclauses = 10000000
% 0.97/1.59
% 0.97/1.59 showgenerated = 0
% 0.97/1.59 showkept = 0
% 0.97/1.59 showselected = 0
% 0.97/1.59 showdeleted = 0
% 0.97/1.59 showresimp = 1
% 0.97/1.59 showstatus = 2000
% 0.97/1.59
% 0.97/1.59 prologoutput = 0
% 0.97/1.59 nrgoals = 5000000
% 0.97/1.59 totalproof = 1
% 0.97/1.59
% 0.97/1.59 Symbols occurring in the translation:
% 0.97/1.59
% 0.97/1.59 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.97/1.59 . [1, 2] (w:1, o:214, a:1, s:1, b:0),
% 0.97/1.59 ! [4, 1] (w:0, o:121, a:1, s:1, b:0),
% 0.97/1.59 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.97/1.59 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.97/1.59 hAPP [38, 2] (w:1, o:238, a:1, s:1, b:0),
% 0.97/1.59 class_Rings_Olinordered__idom [43, 1] (w:1, o:126, a:1, s:1, b:0),
% 0.97/1.59 c_Groups_Ominus__class_Ominus [44, 3] (w:1, o:297, a:1, s:1, b:0),
% 0.97/1.59 c_Groups_Oabs__class_Oabs [45, 2] (w:1, o:239, a:1, s:1, b:0),
% 0.97/1.59 c_Orderings_Oord__class_Oless [46, 3] (w:1, o:298, a:1, s:1, b:0),
% 0.97/1.59 c_Groups_Oplus__class_Oplus [47, 3] (w:1, o:299, a:1, s:1, b:0),
% 0.97/1.59 class_Groups_Oordered__ab__group__add__abs [50, 1] (w:1, o:127, a:1
% 0.97/1.59 , s:1, b:0),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq [51, 3] (w:1, o:300, a:1, s:1, b:0)
% 0.97/1.59 ,
% 0.97/1.59 class_Groups_Oordered__cancel__ab__semigroup__add [54, 1] (w:1, o:128
% 0.97/1.59 , a:1, s:1, b:0),
% 0.97/1.59 class_Orderings_Opreorder [56, 1] (w:1, o:131, a:1, s:1, b:0),
% 0.97/1.59 tc_RealDef_Oreal [59, 0] (w:1, o:50, a:1, s:1, b:0),
% 0.97/1.59 class_Orderings_Olinorder [60, 1] (w:1, o:132, a:1, s:1, b:0),
% 0.97/1.59 class_Orderings_Oord [62, 1] (w:1, o:129, a:1, s:1, b:0),
% 0.97/1.59 tc_fun [63, 2] (w:1, o:271, a:1, s:1, b:0),
% 0.97/1.59 class_Orderings_Oorder [64, 1] (w:1, o:130, a:1, s:1, b:0),
% 0.97/1.59 class_Groups_Ocancel__semigroup__add [66, 1] (w:1, o:133, a:1, s:1
% 0.97/1.59 , b:0),
% 0.97/1.59 class_Groups_Ocancel__ab__semigroup__add [67, 1] (w:1, o:134, a:1, s:
% 0.97/1.59 1, b:0),
% 0.97/1.59 class_Groups_Oab__semigroup__add [70, 1] (w:1, o:135, a:1, s:1, b:0)
% 0.97/1.59 ,
% 0.97/1.59 class_Groups_Oab__group__add [72, 1] (w:1, o:136, a:1, s:1, b:0),
% 0.97/1.59 class_Groups_Oordered__ab__semigroup__add__imp__le [77, 1] (w:1, o:
% 0.97/1.59 137, a:1, s:1, b:0),
% 0.97/1.59 class_Groups_Oordered__ab__semigroup__add [78, 1] (w:1, o:138, a:1
% 0.97/1.59 , s:1, b:0),
% 0.97/1.59 class_Groups_Oordered__ab__group__add [79, 1] (w:1, o:139, a:1, s:1
% 0.97/1.59 , b:0),
% 0.97/1.59 class_Groups_Ogroup__add [80, 1] (w:1, o:140, a:1, s:1, b:0),
% 0.97/1.59 c_RealDef_Opositive [81, 1] (w:1, o:141, a:1, s:1, b:0),
% 0.97/1.59 c_Groups_Oone__class_Oone [82, 1] (w:1, o:142, a:1, s:1, b:0),
% 0.97/1.59 class_Groups_Ominus [85, 1] (w:1, o:144, a:1, s:1, b:0),
% 0.97/1.59 class_Rings_Ocomm__semiring__1 [86, 1] (w:1, o:146, a:1, s:1, b:0),
% 0.97/1.59 class_Groups_Oordered__comm__monoid__add [87, 1] (w:1, o:147, a:1, s:
% 0.97/1.59 1, b:0),
% 0.97/1.59 c_Groups_Ozero__class_Ozero [88, 1] (w:1, o:148, a:1, s:1, b:0),
% 0.97/1.59 v_d____ [89, 0] (w:1, o:60, a:1, s:1, b:0),
% 0.97/1.59 v_r [90, 0] (w:1, o:61, a:1, s:1, b:0),
% 0.97/1.59 class_Rings_Olinordered__semidom [91, 1] (w:1, o:151, a:1, s:1, b:0)
% 0.97/1.59 ,
% 0.97/1.59 class_Groups_Oone [92, 1] (w:1, o:152, a:1, s:1, b:0),
% 0.97/1.59 class_Groups_Ozero [93, 1] (w:1, o:153, a:1, s:1, b:0),
% 0.97/1.59 class_Rings_Ozero__neq__one [94, 1] (w:1, o:154, a:1, s:1, b:0),
% 0.97/1.59 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct [95
% 0.97/1.59 , 1] (w:1, o:178, a:1, s:1, b:0),
% 0.97/1.59 class_Groups_Omonoid__add [96, 1] (w:1, o:179, a:1, s:1, b:0),
% 0.97/1.59 class_Groups_Ocomm__monoid__add [97, 1] (w:1, o:180, a:1, s:1, b:0),
% 0.97/1.59
% 0.97/1.59 class_Groups_Olinordered__ab__group__add [98, 1] (w:1, o:143, a:1, s:
% 0.97/1.59 1, b:0),
% 0.97/1.59 class_Rings_Olinordered__semiring__1__strict [103, 1] (w:1, o:155, a:
% 0.97/1.59 1, s:1, b:0),
% 0.97/1.59 c_Groups_Otimes__class_Otimes [104, 1] (w:1, o:181, a:1, s:1, b:0),
% 0.97/1.59 class_Rings_Olinordered__semiring__1 [105, 1] (w:1, o:156, a:1, s:1
% 0.97/1.59 , b:0),
% 0.97/1.59 tc_Int_Oint [109, 0] (w:1, o:75, a:1, s:1, b:0),
% 0.97/1.59 c_RealDef_Oreal [110, 2] (w:1, o:272, a:1, s:1, b:0),
% 0.97/1.59 c_Groups_Osgn__class_Osgn [111, 2] (w:1, o:273, a:1, s:1, b:0),
% 0.97/1.59 class_Lattices_Oab__semigroup__idem__mult [120, 1] (w:1, o:182, a:1
% 0.97/1.59 , s:1, b:0),
% 0.97/1.59 class_Groups_Oab__semigroup__mult [121, 1] (w:1, o:183, a:1, s:1, b:0
% 0.97/1.59 ),
% 0.97/1.59 class_Rings_Omult__zero [123, 1] (w:1, o:160, a:1, s:1, b:0),
% 0.97/1.59 class_Rings_Oring__no__zero__divisors [124, 1] (w:1, o:161, a:1, s:1
% 0.97/1.59 , b:0),
% 0.97/1.59 class_Rings_Ono__zero__divisors [125, 1] (w:1, o:162, a:1, s:1, b:0)
% 0.97/1.59 ,
% 0.97/1.59 class_Rings_Osemiring [127, 1] (w:1, o:166, a:1, s:1, b:0),
% 0.97/1.59 class_Rings_Ocomm__semiring [128, 1] (w:1, o:167, a:1, s:1, b:0),
% 0.97/1.59 class_Groups_Ocomm__monoid__mult [129, 1] (w:1, o:184, a:1, s:1, b:0)
% 0.97/1.59 ,
% 0.97/1.59 class_Groups_Omonoid__mult [130, 1] (w:1, o:185, a:1, s:1, b:0),
% 0.97/1.59 class_Groups_Osgn__if [133, 1] (w:1, o:186, a:1, s:1, b:0),
% 0.97/1.59 class_Rings_Oordered__cancel__semiring [134, 1] (w:1, o:168, a:1, s:1
% 0.97/1.59 , b:0),
% 0.97/1.59 class_Rings_Oordered__ring [135, 1] (w:1, o:169, a:1, s:1, b:0),
% 0.97/1.59 class_Rings_Oordered__semiring [136, 1] (w:1, o:171, a:1, s:1, b:0),
% 0.97/1.59
% 0.97/1.59 class_Rings_Oordered__comm__semiring [137, 1] (w:1, o:172, a:1, s:1
% 0.97/1.59 , b:0),
% 0.97/1.59 class_Rings_Olinordered__ring__strict [138, 1] (w:1, o:149, a:1, s:1
% 0.97/1.59 , b:0),
% 0.97/1.59 class_Rings_Olinordered__ring [139, 1] (w:1, o:150, a:1, s:1, b:0),
% 0.97/1.59 class_Rings_Olinordered__comm__semiring__strict [140, 1] (w:1, o:157
% 0.97/1.59 , a:1, s:1, b:0),
% 0.97/1.59 class_Rings_Olinordered__semiring__strict [141, 1] (w:1, o:158, a:1
% 0.97/1.59 , s:1, b:0),
% 0.97/1.59 class_Rings_Oring [142, 1] (w:1, o:163, a:1, s:1, b:0),
% 0.97/1.59 class_Rings_Olinordered__semiring [145, 1] (w:1, o:159, a:1, s:1, b:0
% 0.97/1.59 ),
% 0.97/1.59 class_Rings_Oring__1 [146, 1] (w:1, o:164, a:1, s:1, b:0),
% 0.97/1.59 class_Rings_Oordered__ring__abs [147, 1] (w:1, o:170, a:1, s:1, b:0)
% 0.97/1.59 ,
% 0.97/1.59 tc_Complex_Ocomplex [148, 0] (w:1, o:83, a:1, s:1, b:0),
% 0.97/1.59 v_w____ [149, 0] (w:1, o:84, a:1, s:1, b:0),
% 0.97/1.59 c_RealVector_Onorm__class_Onorm [150, 2] (w:1, o:274, a:1, s:1, b:0)
% 0.97/1.59 ,
% 0.97/1.59 class_RealVector_Oreal__normed__algebra [151, 1] (w:1, o:173, a:1, s:
% 0.97/1.59 1, b:0),
% 0.97/1.60 v_g____ [153, 1] (w:1, o:187, a:1, s:1, b:0),
% 0.97/1.60 class_RealVector_Oreal__normed__div__algebra [156, 1] (w:1, o:174, a:
% 0.97/1.60 1, s:1, b:0),
% 0.97/1.60 class_RealVector_Oreal__normed__vector [158, 1] (w:1, o:175, a:1, s:1
% 0.97/1.60 , b:0),
% 0.97/1.60 class_RealVector_Oreal__normed__algebra__1 [160, 1] (w:1, o:176, a:1
% 0.97/1.60 , s:1, b:0),
% 0.97/1.60 c_Archimedean__Field_Oceiling [171, 2] (w:1, o:275, a:1, s:1, b:0),
% 0.97/1.60 c_Nat__Transfer_Otsub [172, 2] (w:1, o:276, a:1, s:1, b:0),
% 0.97/1.60 hBOOL [174, 1] (w:1, o:188, a:1, s:1, b:0),
% 0.97/1.60 tc_Nat_Onat [175, 0] (w:1, o:97, a:1, s:1, b:0),
% 0.97/1.60 v_N1____ [176, 0] (w:1, o:98, a:1, s:1, b:0),
% 0.97/1.60 v_f____ [177, 0] (w:1, o:100, a:1, s:1, b:0),
% 0.97/1.60 v_z____ [178, 0] (w:1, o:101, a:1, s:1, b:0),
% 0.97/1.60 c_SEQ_Osubseq [179, 1] (w:1, o:191, a:1, s:1, b:0),
% 0.97/1.60 class_Archimedean__Field_Oarchimedean__field [182, 1] (w:1, o:192, a:
% 0.97/1.60 1, s:1, b:0),
% 0.97/1.60 c_Complex_Oii [184, 0] (w:1, o:105, a:1, s:1, b:0),
% 0.97/1.60 c_RComplete_Onatceiling [192, 1] (w:1, o:189, a:1, s:1, b:0),
% 0.97/1.60 c_RComplete_Onatfloor [195, 1] (w:1, o:190, a:1, s:1, b:0),
% 0.97/1.60 c_SEQ_Odecseq [196, 2] (w:1, o:277, a:1, s:1, b:0),
% 0.97/1.60 c_Power_Opower__class_Opower [198, 1] (w:1, o:193, a:1, s:1, b:0),
% 0.97/1.60 class_Power_Opower [200, 1] (w:1, o:194, a:1, s:1, b:0),
% 0.97/1.60 class_Rings_Oring__1__no__zero__divisors [201, 1] (w:1, o:165, a:1
% 0.97/1.60 , s:1, b:0),
% 0.97/1.60 class_Rings_Osemiring__0 [202, 1] (w:1, o:177, a:1, s:1, b:0),
% 0.97/1.60 c_Power_Opower_Opower [205, 3] (w:1, o:301, a:1, s:1, b:0),
% 0.97/1.60 c_Complex_Orcis [208, 2] (w:1, o:278, a:1, s:1, b:0),
% 0.97/1.60 c_Transcendental_Oln [212, 1] (w:1, o:195, a:1, s:1, b:0),
% 0.97/1.60 c_SEQ_OBseq [213, 2] (w:1, o:279, a:1, s:1, b:0),
% 0.97/1.60 c_SEQ_Oincseq [214, 2] (w:1, o:280, a:1, s:1, b:0),
% 0.97/1.60 c_Complex_Oexpi [216, 1] (w:1, o:196, a:1, s:1, b:0),
% 0.97/1.60 c_Nat_OSuc [218, 1] (w:1, o:197, a:1, s:1, b:0),
% 0.97/1.60 class_Rings_Ocomm__ring__1 [224, 1] (w:1, o:145, a:1, s:1, b:0),
% 0.97/1.60 c_Divides_Odiv__class_Odiv [225, 3] (w:1, o:302, a:1, s:1, b:0),
% 0.97/1.60 class_Divides_Osemiring__div [226, 1] (w:1, o:199, a:1, s:1, b:0),
% 0.97/1.60 c_Divides_Odiv__class_Omod [230, 3] (w:1, o:303, a:1, s:1, b:0),
% 0.97/1.60 class_Divides_Oring__div [232, 1] (w:1, o:198, a:1, s:1, b:0),
% 0.97/1.60 c_Rings_Oinverse__class_Odivide [235, 3] (w:1, o:304, a:1, s:1, b:0)
% 0.97/1.60 ,
% 0.97/1.60 c_Complex_Ocis [236, 1] (w:1, o:200, a:1, s:1, b:0),
% 0.97/1.60 tc_HOL_Obool [239, 0] (w:1, o:74, a:1, s:1, b:0),
% 0.97/1.60 v_m [240, 0] (w:1, o:119, a:1, s:1, b:0),
% 0.97/1.60 v_x [241, 0] (w:1, o:120, a:1, s:1, b:0),
% 0.97/1.60 v_e [242, 0] (w:1, o:99, a:1, s:1, b:0),
% 0.97/1.60 alpha1 [243, 3] (w:1, o:305, a:1, s:1, b:1),
% 0.97/1.60 alpha2 [244, 3] (w:1, o:309, a:1, s:1, b:1),
% 0.97/1.60 alpha3 [245, 4] (w:1, o:366, a:1, s:1, b:1),
% 0.97/1.60 alpha4 [246, 4] (w:1, o:370, a:1, s:1, b:1),
% 0.97/1.60 alpha5 [247, 3] (w:1, o:319, a:1, s:1, b:1),
% 0.97/1.60 alpha6 [248, 3] (w:1, o:323, a:1, s:1, b:1),
% 0.97/1.60 alpha7 [249, 2] (w:1, o:281, a:1, s:1, b:1),
% 0.97/1.60 alpha8 [250, 2] (w:1, o:282, a:1, s:1, b:1),
% 0.97/1.60 alpha9 [251, 2] (w:1, o:283, a:1, s:1, b:1),
% 0.97/1.60 alpha10 [252, 2] (w:1, o:284, a:1, s:1, b:1),
% 1.91/2.27 alpha11 [253, 2] (w:1, o:285, a:1, s:1, b:1),
% 1.91/2.27 alpha12 [254, 4] (w:1, o:371, a:1, s:1, b:1),
% 1.91/2.27 alpha13 [255, 2] (w:1, o:286, a:1, s:1, b:1),
% 1.91/2.27 alpha14 [256, 2] (w:1, o:287, a:1, s:1, b:1),
% 1.91/2.27 alpha15 [257, 3] (w:1, o:306, a:1, s:1, b:1),
% 1.91/2.27 alpha16 [258, 4] (w:1, o:372, a:1, s:1, b:1),
% 1.91/2.27 alpha17 [259, 3] (w:1, o:307, a:1, s:1, b:1),
% 1.91/2.27 alpha18 [260, 3] (w:1, o:308, a:1, s:1, b:1),
% 1.91/2.27 alpha19 [261, 4] (w:1, o:373, a:1, s:1, b:1),
% 1.91/2.27 alpha20 [262, 4] (w:1, o:364, a:1, s:1, b:1),
% 1.91/2.27 alpha21 [263, 3] (w:1, o:324, a:1, s:1, b:1),
% 1.91/2.27 alpha22 [264, 3] (w:1, o:325, a:1, s:1, b:1),
% 1.91/2.27 alpha23 [265, 2] (w:1, o:288, a:1, s:1, b:1),
% 1.91/2.27 alpha24 [266, 2] (w:1, o:289, a:1, s:1, b:1),
% 1.91/2.27 alpha25 [267, 2] (w:1, o:290, a:1, s:1, b:1),
% 1.91/2.27 alpha26 [268, 3] (w:1, o:326, a:1, s:1, b:1),
% 1.91/2.27 alpha27 [269, 4] (w:1, o:365, a:1, s:1, b:1),
% 1.91/2.27 alpha28 [270, 3] (w:1, o:327, a:1, s:1, b:1),
% 1.91/2.27 alpha29 [271, 3] (w:1, o:328, a:1, s:1, b:1),
% 1.91/2.27 alpha30 [272, 3] (w:1, o:329, a:1, s:1, b:1),
% 1.91/2.27 alpha31 [273, 4] (w:1, o:367, a:1, s:1, b:1),
% 1.91/2.27 alpha32 [274, 2] (w:1, o:291, a:1, s:1, b:1),
% 1.91/2.27 alpha33 [275, 3] (w:1, o:330, a:1, s:1, b:1),
% 1.91/2.27 alpha34 [276, 3] (w:1, o:331, a:1, s:1, b:1),
% 1.91/2.27 alpha35 [277, 4] (w:1, o:368, a:1, s:1, b:1),
% 1.91/2.27 alpha36 [278, 3] (w:1, o:332, a:1, s:1, b:1),
% 1.91/2.27 alpha37 [279, 3] (w:1, o:333, a:1, s:1, b:1),
% 1.91/2.27 alpha38 [280, 3] (w:1, o:334, a:1, s:1, b:1),
% 1.91/2.27 alpha39 [281, 4] (w:1, o:369, a:1, s:1, b:1),
% 1.91/2.27 alpha40 [282, 3] (w:1, o:310, a:1, s:1, b:1),
% 1.91/2.27 alpha41 [283, 3] (w:1, o:311, a:1, s:1, b:1),
% 1.91/2.27 alpha42 [284, 3] (w:1, o:312, a:1, s:1, b:1),
% 1.91/2.27 alpha43 [285, 3] (w:1, o:313, a:1, s:1, b:1),
% 1.91/2.27 alpha44 [286, 3] (w:1, o:314, a:1, s:1, b:1),
% 1.91/2.27 alpha45 [287, 3] (w:1, o:315, a:1, s:1, b:1),
% 1.91/2.27 alpha46 [288, 3] (w:1, o:316, a:1, s:1, b:1),
% 1.91/2.27 alpha47 [289, 4] (w:1, o:374, a:1, s:1, b:1),
% 1.91/2.27 alpha48 [290, 3] (w:1, o:317, a:1, s:1, b:1),
% 1.91/2.27 alpha49 [291, 3] (w:1, o:318, a:1, s:1, b:1),
% 1.91/2.27 alpha50 [292, 4] (w:1, o:375, a:1, s:1, b:1),
% 1.91/2.27 alpha51 [293, 3] (w:1, o:320, a:1, s:1, b:1),
% 1.91/2.27 alpha52 [294, 2] (w:1, o:292, a:1, s:1, b:1),
% 1.91/2.27 alpha53 [295, 3] (w:1, o:321, a:1, s:1, b:1),
% 1.91/2.27 alpha54 [296, 2] (w:1, o:293, a:1, s:1, b:1),
% 1.91/2.27 alpha55 [297, 2] (w:1, o:294, a:1, s:1, b:1),
% 1.91/2.27 alpha56 [298, 2] (w:1, o:295, a:1, s:1, b:1),
% 1.91/2.27 alpha57 [299, 2] (w:1, o:296, a:1, s:1, b:1),
% 1.91/2.27 alpha58 [300, 3] (w:1, o:322, a:1, s:1, b:1),
% 1.91/2.27 skol1 [301, 2] (w:1, o:240, a:1, s:1, b:1),
% 1.91/2.27 skol2 [302, 3] (w:1, o:337, a:1, s:1, b:1),
% 1.91/2.27 skol3 [303, 3] (w:1, o:338, a:1, s:1, b:1),
% 1.91/2.27 skol4 [304, 3] (w:1, o:342, a:1, s:1, b:1),
% 1.91/2.27 skol5 [305, 1] (w:1, o:203, a:1, s:1, b:1),
% 1.91/2.27 skol6 [306, 1] (w:1, o:205, a:1, s:1, b:1),
% 1.91/2.27 skol7 [307, 2] (w:1, o:244, a:1, s:1, b:1),
% 1.91/2.27 skol8 [308, 2] (w:1, o:248, a:1, s:1, b:1),
% 1.91/2.27 skol9 [309, 1] (w:1, o:206, a:1, s:1, b:1),
% 1.91/2.27 skol10 [310, 2] (w:1, o:249, a:1, s:1, b:1),
% 1.91/2.27 skol11 [311, 1] (w:1, o:207, a:1, s:1, b:1),
% 1.91/2.27 skol12 [312, 1] (w:1, o:208, a:1, s:1, b:1),
% 1.91/2.27 skol13 [313, 2] (w:1, o:250, a:1, s:1, b:1),
% 1.91/2.27 skol14 [314, 1] (w:1, o:209, a:1, s:1, b:1),
% 1.91/2.27 skol15 [315, 0] (w:1, o:48, a:1, s:1, b:1),
% 1.91/2.27 skol16 [316, 0] (w:1, o:49, a:1, s:1, b:1),
% 1.91/2.27 skol17 [317, 3] (w:1, o:335, a:1, s:1, b:1),
% 1.91/2.27 skol18 [318, 3] (w:1, o:336, a:1, s:1, b:1),
% 1.91/2.27 skol19 [319, 1] (w:1, o:210, a:1, s:1, b:1),
% 1.91/2.27 skol20 [320, 2] (w:1, o:251, a:1, s:1, b:1),
% 1.91/2.27 skol21 [321, 4] (w:1, o:376, a:1, s:1, b:1),
% 1.91/2.27 skol22 [322, 2] (w:1, o:252, a:1, s:1, b:1),
% 1.91/2.27 skol23 [323, 2] (w:1, o:253, a:1, s:1, b:1),
% 1.91/2.27 skol24 [324, 1] (w:1, o:211, a:1, s:1, b:1),
% 1.91/2.27 skol25 [325, 2] (w:1, o:254, a:1, s:1, b:1),
% 1.91/2.27 skol26 [326, 2] (w:1, o:255, a:1, s:1, b:1),
% 1.91/2.27 skol27 [327, 1] (w:1, o:212, a:1, s:1, b:1),
% 1.91/2.27 skol28 [328, 2] (w:1, o:256, a:1, s:1, b:1),
% 1.91/2.27 skol29 [329, 2] (w:1, o:257, a:1, s:1, b:1),
% 1.91/2.27 skol30 [330, 2] (w:1, o:258, a:1, s:1, b:1),
% 23.34/23.70 skol31 [331, 2] (w:1, o:259, a:1, s:1, b:1),
% 23.34/23.70 skol32 [332, 2] (w:1, o:260, a:1, s:1, b:1),
% 23.34/23.70 skol33 [333, 2] (w:1, o:261, a:1, s:1, b:1),
% 23.34/23.70 skol34 [334, 2] (w:1, o:262, a:1, s:1, b:1),
% 23.34/23.70 skol35 [335, 3] (w:1, o:339, a:1, s:1, b:1),
% 23.34/23.70 skol36 [336, 3] (w:1, o:340, a:1, s:1, b:1),
% 23.34/23.70 skol37 [337, 2] (w:1, o:263, a:1, s:1, b:1),
% 23.34/23.70 skol38 [338, 3] (w:1, o:341, a:1, s:1, b:1),
% 23.34/23.70 skol39 [339, 2] (w:1, o:264, a:1, s:1, b:1),
% 23.34/23.70 skol40 [340, 4] (w:1, o:377, a:1, s:1, b:1),
% 23.34/23.70 skol41 [341, 3] (w:1, o:343, a:1, s:1, b:1),
% 23.34/23.70 skol42 [342, 3] (w:1, o:344, a:1, s:1, b:1),
% 23.34/23.70 skol43 [343, 2] (w:1, o:265, a:1, s:1, b:1),
% 23.34/23.70 skol44 [344, 1] (w:1, o:201, a:1, s:1, b:1),
% 23.34/23.70 skol45 [345, 2] (w:1, o:266, a:1, s:1, b:1),
% 23.34/23.70 skol46 [346, 1] (w:1, o:202, a:1, s:1, b:1),
% 23.34/23.70 skol47 [347, 2] (w:1, o:267, a:1, s:1, b:1),
% 23.34/23.70 skol48 [348, 2] (w:1, o:268, a:1, s:1, b:1),
% 23.34/23.70 skol49 [349, 2] (w:1, o:269, a:1, s:1, b:1),
% 23.34/23.70 skol50 [350, 3] (w:1, o:345, a:1, s:1, b:1),
% 23.34/23.70 skol51 [351, 3] (w:1, o:346, a:1, s:1, b:1),
% 23.34/23.70 skol52 [352, 3] (w:1, o:347, a:1, s:1, b:1),
% 23.34/23.70 skol53 [353, 3] (w:1, o:348, a:1, s:1, b:1),
% 23.34/23.70 skol54 [354, 1] (w:1, o:204, a:1, s:1, b:1),
% 23.34/23.70 skol55 [355, 3] (w:1, o:349, a:1, s:1, b:1),
% 23.34/23.70 skol56 [356, 2] (w:1, o:270, a:1, s:1, b:1),
% 23.34/23.70 skol57 [357, 3] (w:1, o:350, a:1, s:1, b:1),
% 23.34/23.70 skol58 [358, 4] (w:1, o:378, a:1, s:1, b:1),
% 23.34/23.70 skol59 [359, 3] (w:1, o:351, a:1, s:1, b:1),
% 23.34/23.70 skol60 [360, 3] (w:1, o:352, a:1, s:1, b:1),
% 23.34/23.70 skol61 [361, 3] (w:1, o:353, a:1, s:1, b:1),
% 23.34/23.70 skol62 [362, 3] (w:1, o:354, a:1, s:1, b:1),
% 23.34/23.70 skol63 [363, 3] (w:1, o:355, a:1, s:1, b:1),
% 23.34/23.70 skol64 [364, 3] (w:1, o:356, a:1, s:1, b:1),
% 23.34/23.70 skol65 [365, 1] (w:1, o:213, a:1, s:1, b:1),
% 23.34/23.70 skol66 [366, 2] (w:1, o:241, a:1, s:1, b:1),
% 23.34/23.70 skol67 [367, 3] (w:1, o:357, a:1, s:1, b:1),
% 23.34/23.70 skol68 [368, 2] (w:1, o:242, a:1, s:1, b:1),
% 23.34/23.70 skol69 [369, 2] (w:1, o:243, a:1, s:1, b:1),
% 23.34/23.70 skol70 [370, 2] (w:1, o:245, a:1, s:1, b:1),
% 23.34/23.70 skol71 [371, 3] (w:1, o:358, a:1, s:1, b:1),
% 23.34/23.70 skol72 [372, 3] (w:1, o:359, a:1, s:1, b:1),
% 23.34/23.70 skol73 [373, 3] (w:1, o:360, a:1, s:1, b:1),
% 23.34/23.70 skol74 [374, 3] (w:1, o:361, a:1, s:1, b:1),
% 23.34/23.70 skol75 [375, 3] (w:1, o:362, a:1, s:1, b:1),
% 23.34/23.70 skol76 [376, 3] (w:1, o:363, a:1, s:1, b:1),
% 23.34/23.70 skol77 [377, 2] (w:1, o:246, a:1, s:1, b:1),
% 23.34/23.70 skol78 [378, 2] (w:1, o:247, a:1, s:1, b:1).
% 23.34/23.70
% 23.34/23.70
% 23.34/23.70 Starting Search:
% 23.34/23.70
% 23.34/23.70 *** allocated 113905 integers for clauses
% 23.34/23.70 *** allocated 170857 integers for clauses
% 23.34/23.70 Resimplifying inuse:
% 23.34/23.70 Done
% 23.34/23.70
% 23.34/23.70
% 23.34/23.70 Intermediate Status:
% 23.34/23.70 Generated: 2859
% 23.34/23.70 Kept: 2010
% 23.34/23.70 Inuse: 61
% 23.34/23.70 Deleted: 0
% 23.34/23.70 Deletedinuse: 0
% 23.34/23.70
% 23.34/23.70 *** allocated 256285 integers for clauses
% 23.34/23.70 Resimplifying inuse:
% 23.34/23.70 Done
% 23.34/23.70
% 23.34/23.70 *** allocated 170857 integers for termspace/termends
% 23.34/23.70 Resimplifying inuse:
% 23.34/23.70 Done
% 23.34/23.70
% 23.34/23.70
% 23.34/23.70 Intermediate Status:
% 23.34/23.70 Generated: 8739
% 23.34/23.70 Kept: 4070
% 23.34/23.70 Inuse: 224
% 23.34/23.70 Deleted: 2
% 23.34/23.70 Deletedinuse: 0
% 23.34/23.70
% 23.34/23.70 *** allocated 384427 integers for clauses
% 23.34/23.70 Resimplifying inuse:
% 23.34/23.70 Done
% 23.34/23.70
% 23.34/23.70 *** allocated 256285 integers for termspace/termends
% 23.34/23.70 Resimplifying inuse:
% 23.34/23.70 Done
% 23.34/23.70
% 23.34/23.70
% 23.34/23.70 Intermediate Status:
% 23.34/23.70 Generated: 14227
% 23.34/23.70 Kept: 6070
% 23.34/23.70 Inuse: 289
% 23.34/23.70 Deleted: 3
% 23.34/23.70 Deletedinuse: 0
% 23.34/23.70
% 23.34/23.70 Resimplifying inuse:
% 23.34/23.70 Done
% 23.34/23.70
% 23.34/23.70 *** allocated 576640 integers for clauses
% 23.34/23.70 Resimplifying inuse:
% 23.34/23.70 Done
% 23.34/23.70
% 23.34/23.70
% 23.34/23.70 Intermediate Status:
% 23.34/23.70 Generated: 20454
% 23.34/23.70 Kept: 8093
% 23.34/23.70 Inuse: 357
% 23.34/23.70 Deleted: 3
% 23.34/23.70 Deletedinuse: 0
% 23.34/23.70
% 23.34/23.70 Resimplifying inuse:
% 23.34/23.70 Done
% 23.34/23.70
% 23.34/23.70 *** allocated 384427 integers for termspace/termends
% 23.34/23.70 Resimplifying inuse:
% 23.34/23.70 Done
% 23.34/23.70
% 23.34/23.70
% 23.34/23.70 Intermediate Status:
% 23.34/23.70 Generated: 26980
% 23.34/23.70 Kept: 10146
% 23.34/23.70 Inuse: 418
% 23.34/23.70 Deleted: 3
% 23.34/23.70 Deletedinuse: 0
% 23.34/23.70
% 23.34/23.70 Resimplifying inuse:
% 23.34/23.70 Done
% 23.34/23.70
% 23.34/23.70 *** allocated 864960 integers for clauses
% 23.34/23.70
% 23.34/23.70 Intermediate Status:
% 23.34/23.70 Generated: 32084
% 23.34/23.70 Kept: 12280
% 23.34/23.70 Inuse: 468
% 23.34/23.70 Deleted: 3
% 23.34/23.70 Deletedinuse: 0
% 23.34/23.70
% 23.34/23.70 Resimplifying inuse:
% 23.34/23.70 Done
% 23.34/23.70
% 23.34/23.70 Resimplifying inuse:
% 23.34/23.70 Done
% 23.34/23.70
% 23.34/23.70
% 23.34/23.70 Intermediate Status:
% 23.34/23.70 Generated: 40329
% 23.34/23.70 Kept: 14339
% 23.34/23.70 Inuse: 545
% 23.34/23.70 Deleted: 6
% 23.34/23.70 Deletedinuse: 0
% 23.34/23.70
% 23.34/23.70 Resimplifying inuse:
% 23.34/23.70 Done
% 23.34/23.70
% 23.34/23.70 Resimplifying inuse:
% 85.04/85.44 Done
% 85.04/85.44
% 85.04/85.44 *** allocated 576640 integers for termspace/termends
% 85.04/85.44
% 85.04/85.44 Intermediate Status:
% 85.04/85.44 Generated: 46164
% 85.04/85.44 Kept: 16788
% 85.04/85.44 Inuse: 595
% 85.04/85.44 Deleted: 6
% 85.04/85.44 Deletedinuse: 0
% 85.04/85.44
% 85.04/85.44 Resimplifying inuse:
% 85.04/85.44 Done
% 85.04/85.44
% 85.04/85.44 *** allocated 1297440 integers for clauses
% 85.04/85.44
% 85.04/85.44 Intermediate Status:
% 85.04/85.44 Generated: 51122
% 85.04/85.44 Kept: 19057
% 85.04/85.44 Inuse: 629
% 85.04/85.44 Deleted: 7
% 85.04/85.44 Deletedinuse: 0
% 85.04/85.44
% 85.04/85.44 Resimplifying inuse:
% 85.04/85.44 Done
% 85.04/85.44
% 85.04/85.44 Resimplifying inuse:
% 85.04/85.44 Done
% 85.04/85.44
% 85.04/85.44 Resimplifying clauses:
% 85.04/85.44 Done
% 85.04/85.44
% 85.04/85.44
% 85.04/85.44 Intermediate Status:
% 85.04/85.44 Generated: 54636
% 85.04/85.44 Kept: 21062
% 85.04/85.44 Inuse: 640
% 85.04/85.44 Deleted: 329
% 85.04/85.44 Deletedinuse: 1
% 85.04/85.44
% 85.04/85.44 Resimplifying inuse:
% 85.04/85.44 Done
% 85.04/85.44
% 85.04/85.44
% 85.04/85.44 Intermediate Status:
% 85.04/85.44 Generated: 60404
% 85.04/85.44 Kept: 23155
% 85.04/85.44 Inuse: 669
% 85.04/85.44 Deleted: 329
% 85.04/85.44 Deletedinuse: 1
% 85.04/85.44
% 85.04/85.44 Resimplifying inuse:
% 85.04/85.44 Done
% 85.04/85.44
% 85.04/85.44 Resimplifying inuse:
% 85.04/85.44 Done
% 85.04/85.44
% 85.04/85.44
% 85.04/85.44 Intermediate Status:
% 85.04/85.44 Generated: 68813
% 85.04/85.44 Kept: 25347
% 85.04/85.44 Inuse: 699
% 85.04/85.44 Deleted: 329
% 85.04/85.44 Deletedinuse: 1
% 85.04/85.44
% 85.04/85.44 *** allocated 864960 integers for termspace/termends
% 85.04/85.44 Resimplifying inuse:
% 85.04/85.44 Done
% 85.04/85.44
% 85.04/85.44 Resimplifying inuse:
% 85.04/85.44 Done
% 85.04/85.44
% 85.04/85.44
% 85.04/85.44 Intermediate Status:
% 85.04/85.44 Generated: 77774
% 85.04/85.44 Kept: 27460
% 85.04/85.44 Inuse: 738
% 85.04/85.44 Deleted: 331
% 85.04/85.44 Deletedinuse: 2
% 85.04/85.44
% 85.04/85.44 Resimplifying inuse:
% 85.04/85.44 Done
% 85.04/85.44
% 85.04/85.44 Resimplifying inuse:
% 85.04/85.44 Done
% 85.04/85.44
% 85.04/85.44 *** allocated 1946160 integers for clauses
% 85.04/85.44
% 85.04/85.44 Intermediate Status:
% 85.04/85.44 Generated: 85840
% 85.04/85.44 Kept: 29519
% 85.04/85.44 Inuse: 777
% 85.04/85.44 Deleted: 331
% 85.04/85.44 Deletedinuse: 2
% 85.04/85.44
% 85.04/85.44 Resimplifying inuse:
% 85.04/85.44 Done
% 85.04/85.44
% 85.04/85.44
% 85.04/85.44 Intermediate Status:
% 85.04/85.44 Generated: 92475
% 85.04/85.44 Kept: 32152
% 85.04/85.44 Inuse: 796
% 85.04/85.44 Deleted: 335
% 85.04/85.44 Deletedinuse: 4
% 85.04/85.44
% 85.04/85.44 Resimplifying inuse:
% 85.04/85.44 Done
% 85.04/85.44
% 85.04/85.44 Resimplifying inuse:
% 85.04/85.44 Done
% 85.04/85.44
% 85.04/85.44
% 85.04/85.44 Intermediate Status:
% 85.04/85.44 Generated: 100544
% 85.04/85.44 Kept: 34164
% 85.04/85.44 Inuse: 831
% 85.04/85.44 Deleted: 345
% 85.04/85.44 Deletedinuse: 14
% 85.04/85.44
% 85.04/85.44 Resimplifying inuse:
% 85.04/85.44 Done
% 85.04/85.44
% 85.04/85.44 Resimplifying inuse:
% 85.04/85.44 Done
% 85.04/85.44
% 85.04/85.44
% 85.04/85.44 Intermediate Status:
% 85.04/85.44 Generated: 112181
% 85.04/85.44 Kept: 36320
% 85.04/85.44 Inuse: 868
% 85.04/85.44 Deleted: 349
% 85.04/85.44 Deletedinuse: 15
% 85.04/85.44
% 85.04/85.44 *** allocated 1297440 integers for termspace/termends
% 85.04/85.44 Resimplifying inuse:
% 85.04/85.44 Done
% 85.04/85.44
% 85.04/85.44
% 85.04/85.44 Intermediate Status:
% 85.04/85.44 Generated: 120912
% 85.04/85.44 Kept: 38764
% 85.04/85.44 Inuse: 886
% 85.04/85.44 Deleted: 350
% 85.04/85.44 Deletedinuse: 16
% 85.04/85.44
% 85.04/85.44 Resimplifying inuse:
% 85.04/85.44 Done
% 85.04/85.44
% 85.04/85.44 Resimplifying inuse:
% 85.04/85.44 Done
% 85.04/85.44
% 85.04/85.44
% 85.04/85.44 Intermediate Status:
% 85.04/85.44 Generated: 130819
% 85.04/85.44 Kept: 42917
% 85.04/85.44 Inuse: 928
% 85.04/85.44 Deleted: 350
% 85.04/85.44 Deletedinuse: 16
% 85.04/85.44
% 85.04/85.44 Resimplifying inuse:
% 85.04/85.44 Done
% 85.04/85.44
% 85.04/85.44 Resimplifying clauses:
% 85.04/85.44 Done
% 85.04/85.44
% 85.04/85.44 Resimplifying inuse:
% 85.04/85.44 Done
% 85.04/85.44
% 85.04/85.44 *** allocated 2919240 integers for clauses
% 85.04/85.44
% 85.04/85.44 Intermediate Status:
% 85.04/85.44 Generated: 137390
% 85.04/85.44 Kept: 45846
% 85.04/85.44 Inuse: 953
% 85.04/85.44 Deleted: 1015
% 85.04/85.44 Deletedinuse: 16
% 85.04/85.44
% 85.04/85.44 Resimplifying inuse:
% 85.04/85.44 Done
% 85.04/85.44
% 85.04/85.44 Resimplifying inuse:
% 85.04/85.44 Done
% 85.04/85.44
% 85.04/85.44
% 85.04/85.44 Intermediate Status:
% 85.04/85.44 Generated: 152255
% 85.04/85.44 Kept: 48468
% 85.04/85.44 Inuse: 978
% 85.04/85.44 Deleted: 1015
% 85.04/85.44 Deletedinuse: 16
% 85.04/85.44
% 85.04/85.44 Resimplifying inuse:
% 85.04/85.44 Done
% 85.04/85.44
% 85.04/85.44 Resimplifying inuse:
% 85.04/85.44 Done
% 85.04/85.44
% 85.04/85.44
% 85.04/85.44 Intermediate Status:
% 85.04/85.44 Generated: 170124
% 85.04/85.44 Kept: 51166
% 85.04/85.44 Inuse: 988
% 85.04/85.44 Deleted: 1015
% 85.04/85.44 Deletedinuse: 16
% 85.04/85.44
% 85.04/85.44 Resimplifying inuse:
% 85.04/85.44 Done
% 85.04/85.44
% 85.04/85.44 Resimplifying inuse:
% 85.04/85.44 Done
% 85.04/85.44
% 85.04/85.44
% 85.04/85.44 Intermediate Status:
% 85.04/85.44 Generated: 185135
% 85.04/85.44 Kept: 54457
% 85.04/85.44 Inuse: 1008
% 85.04/85.44 Deleted: 1015
% 85.04/85.44 Deletedinuse: 16
% 85.04/85.44
% 85.04/85.44 Resimplifying inuse:
% 85.04/85.44 Done
% 85.04/85.44
% 85.04/85.44 *** allocated 1946160 integers for termspace/termends
% 85.04/85.44 Resimplifying inuse:
% 85.04/85.44 Done
% 85.04/85.44
% 85.04/85.44
% 85.04/85.44 Intermediate Status:
% 85.04/85.44 Generated: 192980
% 85.04/85.44 Kept: 56457
% 85.04/85.44 Inuse: 1046
% 85.04/85.44 Deleted: 1015
% 85.04/85.44 Deletedinuse: 16
% 85.04/85.44
% 85.04/85.44 Resimplifying inuse:
% 85.04/85.44 Done
% 85.04/85.44
% 85.04/85.44
% 85.04/85.44 Intermediate Status:
% 85.04/85.44 Generated: 202955
% 85.04/85.44 Kept: 59152
% 85.04/85.44 Inuse: 1063
% 85.04/85.44 Deleted: 1015
% 85.04/85.44 Deletedinuse: 16
% 85.04/85.44
% 85.04/85.44 Resimplifying inuse:
% 85.04/85.44 Done
% 85.04/85.44
% 85.04/85.44 Resimplifying inuse:
% 85.04/85.44 Done
% 85.04/85.44
% 85.04/85.44
% 85.04/85.44 Intermediate Status:
% 85.04/85.44 Generated: 209601
% 85.04/85.44 Kept: 61275
% 85.04/85.44 Inuse: 1093
% 85.04/85.44 Deleted: 1015
% 85.04/85.44 Deletedinuse: 16
% 85.04/85.44
% 85.04/85.44 Resimplifying inuse:
% 85.04/85.44 Done
% 85.04/85.44
% 85.04/85.44 Resimplifying inuse:
% 85.04/85.44 Done
% 85.04/85.44
% 85.04/85.44 Resimplifying clauses:
% 85.04/85.44 Done
% 85.04/85.44
% 85.04/85.44
% 85.04/85.44 Intermediate Status:
% 85.04/85.44 Generated: 216089
% 85.04/85.44 Kept: 63437
% 85.04/85.44 Inuse: 1123
% 85.04/85.44 Deleted: 1126
% 85.04/85.44 Deletedinuse: 16
% 85.04/85.44
% 85.04/85.44 Resimplifying inuse:
% 85.04/85.44 Done
% 85.04/85.44
% 85.04/85.44 Resimplifying inuse:
% 85.04/85.44 Done
% 85.04/85.44
% 85.04/85.44
% 85.04/85.44 Intermediate Status:
% 85.04/85.44 Generated: 223577
% 85.04/85.44 Kept: 65513
% 85.04/85.44 Inuse: 1157
% 85.04/85.44 Deleted: 1127
% 85.04/85.44 Deletedinuse: 17
% 85.04/85.44
% 85.04/85.44 Resimplifying inuse:
% 85.04/85.44 Done
% 85.04/85.44
% 85.04/85.44 *** allocated 4378860 integers for clauses
% 85.04/85.44
% 85.04/85.44 Intermediate Status:
% 85.04/85.44 Generated: 238128
% 85.04/85.44 Kept: 68266
% 85.04/85.44 Inuse: 1168
% 85.04/85.44 Deleted: 1129
% 85.04/85.44 Deletedinuse: 19
% 85.04/85.44
% 85.04/85.44 Resimplifying inuse:
% 85.04/85.44 Done
% 85.04/85.44
% 85.04/85.44
% 85.04/85.44 Intermediate Status:
% 85.04/85.44 Generated: 254794
% 176.46/176.91 Kept: 71053
% 176.46/176.91 Inuse: 1183
% 176.46/176.91 Deleted: 1129
% 176.46/176.91 Deletedinuse: 19
% 176.46/176.91
% 176.46/176.91 Resimplifying inuse:
% 176.46/176.91 Done
% 176.46/176.91
% 176.46/176.91
% 176.46/176.91 Intermediate Status:
% 176.46/176.91 Generated: 259971
% 176.46/176.91 Kept: 73543
% 176.46/176.91 Inuse: 1192
% 176.46/176.91 Deleted: 1129
% 176.46/176.91 Deletedinuse: 19
% 176.46/176.91
% 176.46/176.91 Resimplifying inuse:
% 176.46/176.91 Done
% 176.46/176.91
% 176.46/176.91
% 176.46/176.91 Intermediate Status:
% 176.46/176.91 Generated: 285534
% 176.46/176.91 Kept: 76289
% 176.46/176.91 Inuse: 1193
% 176.46/176.91 Deleted: 1129
% 176.46/176.91 Deletedinuse: 19
% 176.46/176.91
% 176.46/176.91 Resimplifying inuse:
% 176.46/176.91 Done
% 176.46/176.91
% 176.46/176.91 Resimplifying inuse:
% 176.46/176.91 Done
% 176.46/176.91
% 176.46/176.91
% 176.46/176.91 Intermediate Status:
% 176.46/176.91 Generated: 294167
% 176.46/176.91 Kept: 78335
% 176.46/176.91 Inuse: 1213
% 176.46/176.91 Deleted: 1129
% 176.46/176.91 Deletedinuse: 19
% 176.46/176.91
% 176.46/176.91 Resimplifying inuse:
% 176.46/176.91 Done
% 176.46/176.91
% 176.46/176.91 *** allocated 2919240 integers for termspace/termends
% 176.46/176.91 Resimplifying inuse:
% 176.46/176.91 Done
% 176.46/176.91
% 176.46/176.91
% 176.46/176.91 Intermediate Status:
% 176.46/176.91 Generated: 301621
% 176.46/176.91 Kept: 80403
% 176.46/176.91 Inuse: 1243
% 176.46/176.91 Deleted: 1129
% 176.46/176.91 Deletedinuse: 19
% 176.46/176.91
% 176.46/176.91 Resimplifying inuse:
% 176.46/176.91 Done
% 176.46/176.91
% 176.46/176.91 Resimplifying inuse:
% 176.46/176.91 Done
% 176.46/176.91
% 176.46/176.91
% 176.46/176.91 Intermediate Status:
% 176.46/176.91 Generated: 310076
% 176.46/176.91 Kept: 82616
% 176.46/176.91 Inuse: 1268
% 176.46/176.91 Deleted: 1129
% 176.46/176.91 Deletedinuse: 19
% 176.46/176.91
% 176.46/176.91 Resimplifying inuse:
% 176.46/176.91 Done
% 176.46/176.91
% 176.46/176.91 Resimplifying clauses:
% 176.46/176.91 Done
% 176.46/176.91
% 176.46/176.91 Resimplifying inuse:
% 176.46/176.91 Done
% 176.46/176.91
% 176.46/176.91
% 176.46/176.91 Intermediate Status:
% 176.46/176.91 Generated: 322927
% 176.46/176.91 Kept: 85792
% 176.46/176.91 Inuse: 1293
% 176.46/176.91 Deleted: 1846
% 176.46/176.91 Deletedinuse: 19
% 176.46/176.91
% 176.46/176.91 Resimplifying inuse:
% 176.46/176.91 Done
% 176.46/176.91
% 176.46/176.91 Resimplifying inuse:
% 176.46/176.91 Done
% 176.46/176.91
% 176.46/176.91
% 176.46/176.91 Intermediate Status:
% 176.46/176.91 Generated: 334161
% 176.46/176.91 Kept: 89873
% 176.46/176.91 Inuse: 1303
% 176.46/176.91 Deleted: 1846
% 176.46/176.91 Deletedinuse: 19
% 176.46/176.91
% 176.46/176.91 Resimplifying inuse:
% 176.46/176.91 Done
% 176.46/176.91
% 176.46/176.91 Resimplifying inuse:
% 176.46/176.91 Done
% 176.46/176.91
% 176.46/176.91
% 176.46/176.91 Intermediate Status:
% 176.46/176.91 Generated: 341392
% 176.46/176.91 Kept: 91903
% 176.46/176.91 Inuse: 1329
% 176.46/176.91 Deleted: 1846
% 176.46/176.91 Deletedinuse: 19
% 176.46/176.91
% 176.46/176.91 Resimplifying inuse:
% 176.46/176.91 Done
% 176.46/176.91
% 176.46/176.91 Resimplifying inuse:
% 176.46/176.91 Done
% 176.46/176.91
% 176.46/176.91
% 176.46/176.91 Intermediate Status:
% 176.46/176.91 Generated: 351687
% 176.46/176.91 Kept: 93925
% 176.46/176.91 Inuse: 1347
% 176.46/176.91 Deleted: 1846
% 176.46/176.91 Deletedinuse: 19
% 176.46/176.91
% 176.46/176.91 Resimplifying inuse:
% 176.46/176.91 Done
% 176.46/176.91
% 176.46/176.91 Resimplifying inuse:
% 176.46/176.91 Done
% 176.46/176.91
% 176.46/176.91
% 176.46/176.91 Intermediate Status:
% 176.46/176.91 Generated: 361707
% 176.46/176.91 Kept: 95936
% 176.46/176.91 Inuse: 1361
% 176.46/176.91 Deleted: 1846
% 176.46/176.91 Deletedinuse: 19
% 176.46/176.91
% 176.46/176.91 Resimplifying inuse:
% 176.46/176.91 Done
% 176.46/176.91
% 176.46/176.91
% 176.46/176.91 Intermediate Status:
% 176.46/176.91 Generated: 370077
% 176.46/176.91 Kept: 98198
% 176.46/176.91 Inuse: 1378
% 176.46/176.91 Deleted: 1846
% 176.46/176.91 Deletedinuse: 19
% 176.46/176.91
% 176.46/176.91 Resimplifying inuse:
% 176.46/176.91 Done
% 176.46/176.91
% 176.46/176.91 Resimplifying inuse:
% 176.46/176.91 Done
% 176.46/176.91
% 176.46/176.91
% 176.46/176.91 Intermediate Status:
% 176.46/176.91 Generated: 375464
% 176.46/176.91 Kept: 100350
% 176.46/176.91 Inuse: 1408
% 176.46/176.91 Deleted: 1846
% 176.46/176.91 Deletedinuse: 19
% 176.46/176.91
% 176.46/176.91 Resimplifying inuse:
% 176.46/176.91 Done
% 176.46/176.91
% 176.46/176.91 Resimplifying inuse:
% 176.46/176.91 Done
% 176.46/176.91
% 176.46/176.91
% 176.46/176.91 Intermediate Status:
% 176.46/176.91 Generated: 380605
% 176.46/176.91 Kept: 102490
% 176.46/176.91 Inuse: 1438
% 176.46/176.91 Deleted: 1846
% 176.46/176.91 Deletedinuse: 19
% 176.46/176.91
% 176.46/176.91 Resimplifying inuse:
% 176.46/176.91 Done
% 176.46/176.91
% 176.46/176.91 Resimplifying clauses:
% 176.46/176.91 Done
% 176.46/176.91
% 176.46/176.91 Resimplifying inuse:
% 176.46/176.91 Done
% 176.46/176.91
% 176.46/176.91 *** allocated 6568290 integers for clauses
% 176.46/176.91
% 176.46/176.91 Intermediate Status:
% 176.46/176.91 Generated: 385441
% 176.46/176.91 Kept: 104525
% 176.46/176.91 Inuse: 1476
% 176.46/176.91 Deleted: 2026
% 176.46/176.91 Deletedinuse: 19
% 176.46/176.91
% 176.46/176.91 Resimplifying inuse:
% 176.46/176.91 Done
% 176.46/176.91
% 176.46/176.91 Resimplifying inuse:
% 176.46/176.91 Done
% 176.46/176.91
% 176.46/176.91
% 176.46/176.91 Intermediate Status:
% 176.46/176.91 Generated: 392423
% 176.46/176.91 Kept: 106637
% 176.46/176.91 Inuse: 1491
% 176.46/176.91 Deleted: 2028
% 176.46/176.91 Deletedinuse: 19
% 176.46/176.91
% 176.46/176.91 Resimplifying inuse:
% 176.46/176.91 Done
% 176.46/176.91
% 176.46/176.91 Resimplifying inuse:
% 176.46/176.91 Done
% 176.46/176.91
% 176.46/176.91
% 176.46/176.91 Intermediate Status:
% 176.46/176.91 Generated: 402115
% 176.46/176.91 Kept: 111033
% 176.46/176.91 Inuse: 1505
% 176.46/176.91 Deleted: 2030
% 176.46/176.91 Deletedinuse: 19
% 176.46/176.91
% 176.46/176.91 Resimplifying inuse:
% 176.46/176.91 Done
% 176.46/176.91
% 176.46/176.91 Resimplifying inuse:
% 176.46/176.91 Done
% 176.46/176.91
% 176.46/176.91 *** allocated 4378860 integers for termspace/termends
% 176.46/176.91
% 176.46/176.91 Intermediate Status:
% 176.46/176.91 Generated: 408420
% 176.46/176.91 Kept: 113256
% 176.46/176.91 Inuse: 1524
% 176.46/176.91 Deleted: 2030
% 176.46/176.91 Deletedinuse: 19
% 176.46/176.91
% 176.46/176.91 Resimplifying inuse:
% 176.46/176.91 Done
% 176.46/176.91
% 176.46/176.91 Resimplifying inuse:
% 176.46/176.91 Done
% 176.46/176.91
% 176.46/176.91
% 176.46/176.91 Intermediate Status:
% 176.46/176.91 Generated: 415147
% 176.46/176.91 Kept: 115435
% 176.46/176.91 Inuse: 1544
% 176.46/176.91 Deleted: 2030
% 176.46/176.91 Deletedinuse: 19
% 176.46/176.91
% 176.46/176.91 Resimplifying inuse:
% 176.46/176.91 Done
% 176.46/176.91
% 176.46/176.91 Resimplifying inuse:
% 176.46/176.91 Done
% 176.46/176.91
% 176.46/176.91
% 176.46/176.91 Intermediate Status:
% 176.46/176.91 Generated: 419897
% 176.46/176.91 Kept: 117688
% 176.46/176.91 Inuse: 1584
% 176.46/176.91 Deleted: 2030
% 176.46/176.91 Deletedinuse: 19
% 176.46/176.91
% 176.46/176.91 Resimplifying inuse:
% 176.46/176.91 Done
% 176.46/176.91
% 176.46/176.91 Resimplifying inuse:
% 176.46/176.91 Done
% 176.46/176.91
% 176.46/176.91
% 176.46/176.91 Intermediate Status:
% 176.46/176.91 Generated: 424293
% 176.46/176.91 Kept: 119873
% 176.46/176.91 Inuse: 1619
% 176.46/176.91 Deleted: 2030
% 176.46/176.91 Deletedinuse: 19
% 176.46/176.91
% 176.46/176.91 Resimplifying inuse:
% 176.46/176.91 Done
% 176.46/176.91
% 176.46/176.91
% 176.46/176.91 Intermediate Status:
% 176.46/176.91 Generated: 455923
% 176.46/176.91 Kept: 123551
% 176.46/176.91 Inuse: 1639
% 176.46/176.91 Deleted: 2030
% 176.46/176.91 Deletedinuse: 19
% 176.46/176.91
% 176.46/176.91 Resimplifying inuse:
% 176.46/176.91 Done
% 176.46/176.91
% 176.46/176.91 Resimplifying clauses:
% 176.46/176.91 Done
% 176.46/176.91
% 176.46/176.91 Resimplifying inuse:
% 176.46/176.91 Done
% 176.46/176.91
% 176.46/176.91
% 176.46/176.91 Intermediate Status:
% 176.46/176.91 Generated: 469790
% 176.46/176.91 Kept: 126875
% 176.46/176.91 Inuse: 1654
% 176.46/176.91 Deleted: 2220
% 176.46/176.91 Deletedinuse: 19
% 176.46/176.91
% 176.46/176.91 Resimplifying inuse:
% 176.46/176.91 Done
% 176.46/176.91
% 176.46/176.91 Resimplifying inuse:
% 176.46/176.91 Done
% 176.46/176.91
% 176.46/176.91
% 176.46/176.91 Intermediate StaCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------