TSTP Solution File: SWW231+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWW231+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n018.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 23:21:25 EDT 2022
% Result : Timeout 288.43s 288.87s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SWW231+1 : TPTP v8.1.0. Released v5.2.0.
% 0.14/0.14 % Command : bliksem %s
% 0.14/0.36 % Computer : n018.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % DateTime : Sat Jun 4 11:57:32 EDT 2022
% 0.21/0.36 % CPUTime :
% 0.98/1.56 *** allocated 10000 integers for termspace/termends
% 0.98/1.56 *** allocated 10000 integers for clauses
% 0.98/1.56 *** allocated 10000 integers for justifications
% 0.98/1.56 *** allocated 15000 integers for termspace/termends
% 0.98/1.56 *** allocated 22500 integers for termspace/termends
% 0.98/1.56 *** allocated 33750 integers for termspace/termends
% 0.98/1.56 Bliksem 1.12
% 0.98/1.56
% 0.98/1.56
% 0.98/1.56 Automatic Strategy Selection
% 0.98/1.56
% 0.98/1.56 *** allocated 50625 integers for termspace/termends
% 0.98/1.56 *** allocated 75937 integers for termspace/termends
% 0.98/1.56 *** allocated 113905 integers for termspace/termends
% 0.98/1.56
% 0.98/1.56 Clauses:
% 0.98/1.56
% 0.98/1.56 { ! hAPP( Y, skol1( X, Y ) ) = hAPP( X, skol1( X, Y ) ), Y = X }.
% 0.98/1.56 { c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus
% 0.98/1.56 ( tc_RealDef_Oreal, Y, c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal
% 0.98/1.56 , X ) ) ) = c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 0.98/1.56 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 0.98/1.56 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) ) }.
% 0.98/1.56 { c_NthRoot_Osqrt( hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.98/1.56 tc_RealDef_Oreal ), X ), X ) ) = c_Groups_Oabs__class_Oabs(
% 0.98/1.56 tc_RealDef_Oreal, X ) }.
% 0.98/1.56 { c_NthRoot_Osqrt( c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) )
% 0.98/1.56 = c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, c_NthRoot_Osqrt( X
% 0.98/1.56 ) ) }.
% 0.98/1.56 { c_NthRoot_Osqrt( hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.98/1.56 tc_RealDef_Oreal ), Y ), X ) ) = hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_NthRoot_Osqrt( Y ) )
% 0.98/1.56 , c_NthRoot_Osqrt( X ) ) }.
% 0.98/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.98/1.56 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ) ), X ) =
% 0.98/1.56 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.98/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.98/1.56 c_Groups_Oabs__class_Oabs( X, c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 0.98/1.56 c_Groups_Oabs__class_Oabs( X, Y ) }.
% 0.98/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.98/1.56 c_Groups_Oabs__class_Oabs( X, c_Groups_Oplus__class_Oplus( X,
% 0.98/1.56 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ) )
% 0.98/1.56 = c_Groups_Oplus__class_Oplus( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.98/1.56 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.98/1.56 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, hAPP
% 0.98/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 0.98/1.56 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.98/1.56 { ! class_Rings_Olinordered__idom( X ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Y ) ),
% 0.98/1.56 c_Groups_Oabs__class_Oabs( X, Y ) ) = hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.98/1.56 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.98/1.56 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 0.98/1.56 , c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.98/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.98/1.56 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.98/1.56 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 0.98/1.56 , c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.98/1.56 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.98/1.56 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Z,
% 0.98/1.56 c_Groups_Oplus__class_Oplus( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.98/1.56 Y ) ) = Y }.
% 0.98/1.56 { ! class_Groups_Oab__semigroup__mult( X ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.56 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.98/1.56 c_Groups_Oplus__class_Oplus( X, Z, T ) = c_Groups_Oplus__class_Oplus( X,
% 0.98/1.56 Y, T ), Z = Y }.
% 0.98/1.56 { ! class_Groups_Ocancel__ab__semigroup__add( X ), !
% 0.98/1.56 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.98/1.56 T, Y ), Z = Y }.
% 0.98/1.56 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.98/1.56 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.98/1.56 T, Y ), Z = Y }.
% 0.98/1.56 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.98/1.56 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.98/1.56 Y, Z ), T = Y }.
% 0.98/1.56 { ! class_Groups_Ocancel__semigroup__add( X ), ! T = Y,
% 0.98/1.56 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.98/1.56 Y, Z ) }.
% 0.98/1.56 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.98/1.56 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.98/1.56 T, Y ), Z = Y }.
% 0.98/1.56 { ! class_Groups_Ocancel__semigroup__add( X ), ! Z = Y,
% 0.98/1.56 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.98/1.56 T, Y ) }.
% 0.98/1.56 { ! class_Groups_Oab__semigroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.56 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.98/1.56 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.98/1.56 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 0.98/1.56 ) = c_Groups_Ouminus__class_Ouminus( X, Y ), Z = Y }.
% 0.98/1.56 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ouminus__class_Ouminus
% 0.98/1.56 ( X, Z ) = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.98/1.56 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 0.98/1.56 ) = Y, c_Groups_Ouminus__class_Ouminus( X, Y ) = Z }.
% 0.98/1.56 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 0.98/1.56 ) = Z, c_Groups_Ouminus__class_Ouminus( X, Z ) = Y }.
% 0.98/1.56 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.56 , Y ), Y = c_Groups_Ouminus__class_Ouminus( X, Z ) }.
% 0.98/1.56 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.56 , Z ), Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.98/1.56 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.98/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 0.98/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP
% 0.98/1.56 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), Y ) ), X ) =
% 0.98/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), hAPP
% 0.98/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.98/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) =
% 0.98/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y )
% 0.98/1.56 }.
% 0.98/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.98/1.56 c_Groups_Oabs__class_Oabs( X, c_Groups_Oabs__class_Oabs( X, Y ) ) =
% 0.98/1.56 c_Groups_Oabs__class_Oabs( X, Y ) }.
% 0.98/1.56 { ! c_NthRoot_Osqrt( Y ) = c_NthRoot_Osqrt( X ), Y = X }.
% 0.98/1.56 { ! Y = X, c_NthRoot_Osqrt( Y ) = c_NthRoot_Osqrt( X ) }.
% 0.98/1.56 { ! class_Rings_Osemiring( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP
% 0.98/1.56 ( c_Groups_Otimes__class_Otimes( X ), U ), T ),
% 0.98/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.56 ( X ), Z ), T ), Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, U, Z
% 0.98/1.56 ) ), T ), Y ) }.
% 0.98/1.56 { ! class_Rings_Ocomm__semiring( X ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.98/1.56 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.56 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.98/1.56 ), Z ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 0.98/1.56 Z = Y, Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.98/1.56 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.98/1.56 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.98/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.98/1.56 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.98/1.56 , c_Groups_Ouminus__class_Ouminus( X, Z ) ),
% 0.98/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.98/1.56 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.98/1.56 , c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.98/1.56 ( X, Y ) ) }.
% 0.98/1.56 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 0.98/1.56 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.98/1.56 ) ), Y ) }.
% 0.98/1.56 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 0.98/1.56 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.98/1.56 ( X, Y ) ) }.
% 0.98/1.56 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.56 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.56 Z, Y ) ) = Y }.
% 0.98/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.98/1.56 c_Complex_Orcis( T, Z ) ), c_Complex_Orcis( Y, X ) ) = c_Complex_Orcis(
% 0.98/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), T ), Y ),
% 0.98/1.56 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, X ) ) }.
% 0.98/1.56 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.98/1.56 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.56 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.98/1.56 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.56 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.98/1.56 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.56 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.98/1.56 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.56 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.98/1.56 ( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.98/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.56 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.98/1.56 ), U = Z, T = Y }.
% 0.98/1.56 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.98/1.56 ( X ), ! U = Z, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.98/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.56 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.98/1.56 ) }.
% 0.98/1.56 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.98/1.56 ( X ), ! T = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.98/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.56 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.98/1.56 ) }.
% 0.98/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Y
% 0.98/1.56 ) ), Z ) }.
% 0.98/1.56 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.98/1.56 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.56 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.98/1.56 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.56 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.98/1.56 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.56 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.98/1.56 ( X ), U = T, Z = Y, ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.98/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.56 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.98/1.56 ) }.
% 0.98/1.56 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.98/1.56 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.98/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.56 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.98/1.56 ), ! U = T }.
% 0.98/1.56 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.98/1.56 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.98/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.56 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.98/1.56 ), ! Z = Y }.
% 0.98/1.56 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.56 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.56 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 0.98/1.56 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.56 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 0.98/1.56 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.56 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Z ) }.
% 0.98/1.56 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 0.98/1.56 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), Y ) ) }.
% 0.98/1.56 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.98/1.56 , Y ) = c_Groups_Oplus__class_Oplus( X, Y, Z ) }.
% 0.98/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.98/1.56 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.98/1.56 ( X, Z, c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.98/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.98/1.56 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.98/1.56 ( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) }.
% 0.98/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.56 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.98/1.56 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.98/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.56 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.98/1.56 ( X, c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 0.98/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.56 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.98/1.56 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X
% 0.98/1.56 , U, Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.98/1.56 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.56 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.56 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.56 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.56 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.56 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus
% 0.98/1.56 ( tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, T, Z )
% 0.98/1.56 , c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.98/1.56 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ),
% 0.98/1.56 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) ) ),
% 0.98/1.56 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs
% 0.98/1.56 ( tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, T,
% 0.98/1.56 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) ),
% 0.98/1.56 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus
% 0.98/1.56 ( tc_RealDef_Oreal, Z, c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal
% 0.98/1.56 , X ) ) ) ) ) }.
% 0.98/1.56 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, c_NthRoot_Osqrt(
% 0.98/1.56 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) ) ) }.
% 0.98/1.56 { ! class_Lattices_Oboolean__algebra( X ), c_Groups_Ouminus__class_Ouminus
% 0.98/1.56 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 0.98/1.56 { ! class_Groups_Ouminus( X ), hAPP( c_Groups_Ouminus__class_Ouminus(
% 0.98/1.56 tc_fun( T, X ), Z ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( Z, Y
% 0.98/1.56 ) ) }.
% 0.98/1.56 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.98/1.56 c_Groups_Ouminus__class_Ouminus( X, Z ) = c_Groups_Ouminus__class_Ouminus
% 0.98/1.56 ( X, Y ), Z = Y }.
% 0.98/1.56 { ! class_Lattices_Oboolean__algebra( X ), ! Z = Y,
% 0.98/1.56 c_Groups_Ouminus__class_Ouminus( X, Z ) = c_Groups_Ouminus__class_Ouminus
% 0.98/1.56 ( X, Y ) }.
% 0.98/1.56 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 0.98/1.56 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 0.98/1.56 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.98/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.98/1.56 c_Complex_Ocis( Y ) ), c_Complex_Ocis( X ) ) = c_Complex_Ocis(
% 0.98/1.56 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ) }.
% 0.98/1.56 { c_Complex_Oexpi( c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X )
% 0.98/1.56 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.98/1.56 c_Complex_Oexpi( Y ) ), c_Complex_Oexpi( X ) ) }.
% 0.98/1.56 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, Y ) =
% 0.98/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ),
% 0.98/1.56 c_Groups_Osgn__class_Osgn( X, Y ) ) }.
% 0.98/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ), Y = X }.
% 0.98/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Z ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, Z ) }.
% 0.98/1.56 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ) }.
% 0.98/1.56 { ! class_Rings_Olinordered__idom( X ), c_Groups_Osgn__class_Osgn( X,
% 0.98/1.56 c_Groups_Osgn__class_Osgn( X, Y ) ) = c_Groups_Osgn__class_Osgn( X, Y ) }
% 0.98/1.56 .
% 0.98/1.56 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, X ) }.
% 0.98/1.56 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.56 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.98/1.56 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.56 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.98/1.56 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.56 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.98/1.56 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.98/1.56 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.98/1.56 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.98/1.56 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.98/1.56 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.98/1.56 U ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.98/1.56 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.98/1.56 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.98/1.56 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.98/1.56 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.98/1.56 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.98/1.56 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.98/1.56 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.98/1.56 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.98/1.56 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.98/1.56 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.98/1.56 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.98/1.56 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.98/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.56 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.98/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.56 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.98/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.56 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.98/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.56 , Z ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ), Z ) }.
% 0.98/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.56 , Y ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.56 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.98/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ouminus__class_Ouminus
% 0.98/1.56 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.98/1.56 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.98/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 0.98/1.56 ( X, Z ) ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.98/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.98/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.98/1.56 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.98/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oabs__class_Oabs( X, Y
% 0.98/1.56 ) ) }.
% 0.98/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.56 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ),
% 0.98/1.56 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, X ) ) }.
% 0.98/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Osqrt( Y )
% 0.98/1.56 , c_NthRoot_Osqrt( X ) ) }.
% 0.98/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Osqrt( Y
% 0.98/1.56 ), c_NthRoot_Osqrt( X ) ), c_Orderings_Oord__class_Oless__eq(
% 0.98/1.56 tc_RealDef_Oreal, Y, X ) }.
% 0.98/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Osqrt( Y )
% 0.98/1.56 , c_NthRoot_Osqrt( X ) ) }.
% 0.98/1.56 { ! class_Rings_Olinordered__idom( X ), c_Groups_Osgn__class_Osgn( X, hAPP
% 0.98/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Osgn__class_Osgn( X, Z ) ),
% 0.98/1.56 c_Groups_Osgn__class_Osgn( X, Y ) ) }.
% 0.98/1.56 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 0.98/1.56 c_Groups_Osgn__class_Osgn( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.98/1.56 X ), Z ), Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.98/1.56 c_Groups_Osgn__class_Osgn( X, Z ) ), c_Groups_Osgn__class_Osgn( X, Y ) )
% 0.98/1.56 }.
% 0.98/1.56 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Osgn__class_Osgn
% 0.98/1.56 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 0.98/1.56 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Osgn__class_Osgn( X, Y ) ) }
% 0.98/1.56 .
% 0.98/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 0.98/1.56 c_Groups_Oplus__class_Oplus( X, Z, Y ) ), c_Groups_Oplus__class_Oplus( X
% 0.98/1.56 , c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) )
% 0.98/1.56 ) }.
% 0.98/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.98/1.56 Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.56 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.98/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.56 , Z ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.56 c_Groups_Oabs__class_Oabs( X, Z ), Y ) }.
% 0.98/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.98/1.56 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.98/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.98/1.56 Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.56 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.98/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.56 , Z ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.56 c_Groups_Oabs__class_Oabs( X, Z ), Y ) }.
% 0.98/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.56 , Y ), c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.98/1.56 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.56 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ) ), hAPP( hAPP
% 0.98/1.56 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) }.
% 0.98/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.56 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ), X ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.56 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ), Y ) }.
% 0.98/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.56 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ), X ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.98/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.56 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ), Y ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.56 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ), X ) }.
% 0.98/1.56 { ! class_Rings_Olinordered__idom( X ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Osgn__class_Osgn( X, Y ) ),
% 0.98/1.56 c_Groups_Oabs__class_Oabs( X, Y ) ) = Y }.
% 0.98/1.56 { ! class_Orderings_Opreorder( X ), c_Orderings_Oord__class_Oless__eq( X, Y
% 0.98/1.56 , Y ) }.
% 0.98/1.56 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt(
% 0.98/1.56 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) ) ) }.
% 0.98/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.56 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.98/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.98/1.56 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) }.
% 0.98/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.98/1.56 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.56 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.98/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.98/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.98/1.56 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.56 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ) }.
% 0.98/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.56 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.98/1.56 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ) }.
% 0.98/1.56 { c_Complex_Orcis( Y, X ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.98/1.56 tc_Complex_Ocomplex ), c_RealVector_Oof__real( tc_Complex_Ocomplex, Y ) )
% 0.98/1.56 , c_Complex_Ocis( X ) ) }.
% 0.98/1.56 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.56 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y ),
% 0.98/1.56 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.98/1.56 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.98/1.56 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X ) ),
% 0.98/1.56 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) ) }.
% 0.98/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.56 ), c_Groups_Oabs__class_Oabs( X, Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.98/1.56 X, Y ) }.
% 0.98/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.56 , c_Groups_Oabs__class_Oabs( X, Y ) ), c_Groups_Ozero__class_Ozero( X ) )
% 0.98/1.56 }.
% 0.98/1.56 { ! class_Rings_Oordered__ring__abs( X ), alpha13( X, Z ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.56 ), c_Groups_Oabs__class_Oabs( X, hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 0.98/1.56 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.98/1.56 { ! class_Rings_Oordered__ring__abs( X ), alpha13( X, Z ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.56 ), c_Groups_Oabs__class_Oabs( X, hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 0.98/1.56 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.98/1.56 { ! alpha13( X, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.98/1.56 { ! alpha13( X, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.56 { c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.56 ), c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero
% 0.98/1.56 ( X ) ), alpha13( X, Y ) }.
% 0.98/1.56 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.98/1.56 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 0.98/1.56 Y ) = c_Groups_Oabs__class_Oabs( X, hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.56 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.56 c_RealVector_Onorm__class_Onorm( X, Y ), c_Groups_Ozero__class_Ozero(
% 0.98/1.56 tc_RealDef_Oreal ) ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.56 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq(
% 0.98/1.56 tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( X, Y ),
% 0.98/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.98/1.56 { ! class_Groups_Ozero( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y, Y =
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.56 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 0.98/1.56 { ! class_RealVector_Oreal__algebra__1( X ), c_RealVector_Oof__real( X,
% 0.98/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) =
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.56 { ! class_RealVector_Oreal__algebra__1( X ), !
% 0.98/1.56 class_RealVector_Oreal__normed__vector( X ), c_RealVector_Oof__real( X,
% 0.98/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) =
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.56 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.98/1.56 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.98/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.98/1.56 { ! class_RealVector_Oreal__algebra__1( X ), ! c_RealVector_Oof__real( X, Y
% 0.98/1.56 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.56 tc_RealDef_Oreal ) }.
% 0.98/1.56 { ! class_RealVector_Oreal__algebra__1( X ), ! Y =
% 0.98/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealVector_Oof__real(
% 0.98/1.56 X, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.56 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.98/1.56 c_RealVector_Onorm__class_Onorm( X, Y ) = c_Groups_Ozero__class_Ozero(
% 0.98/1.56 tc_RealDef_Oreal ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.56 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X, Y )
% 0.98/1.56 = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.98/1.56 { ! class_RealVector_Oreal__algebra__1( X ), ! c_RealVector_Oof__real( X, Z
% 0.98/1.56 ) = c_RealVector_Oof__real( X, Y ), Z = Y }.
% 0.98/1.56 { ! class_RealVector_Oreal__algebra__1( X ), ! Z = Y,
% 0.98/1.56 c_RealVector_Oof__real( X, Z ) = c_RealVector_Oof__real( X, Y ) }.
% 0.98/1.56 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.98/1.56 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.98/1.56 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 0.98/1.56 c_RealVector_Onorm__class_Onorm( X, c_RealVector_Oof__real( X, Y ) ) =
% 0.98/1.56 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ) }.
% 0.98/1.56 { c_Complex_Orcis( X, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) =
% 0.98/1.56 c_RealVector_Oof__real( tc_Complex_Ocomplex, X ) }.
% 0.98/1.56 { c_Complex_Orcis( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ) =
% 0.98/1.56 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.98/1.56 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.98/1.56 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ouminus__class_Ouminus( X, Y
% 0.98/1.56 ) ) = c_RealVector_Onorm__class_Onorm( X, Y ) }.
% 0.98/1.56 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Oabs__class_Oabs
% 0.98/1.56 ( tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( X, Y ) ) =
% 0.98/1.56 c_RealVector_Onorm__class_Onorm( X, Y ) }.
% 0.98/1.56 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.98/1.56 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.56 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.98/1.56 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.56 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.98/1.56 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.56 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.98/1.56 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.56 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.98/1.56 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.56 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.98/1.56 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.56 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.56 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) =
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.56 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.56 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) =
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.56 { ! class_Rings_Oring__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.56 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.56 { ! class_Rings_Oring__no__zero__divisors( X ), ! Z =
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.56 { ! class_Rings_Oring__no__zero__divisors( X ), ! Y =
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.56 { ! class_Rings_Ono__zero__divisors( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.56 X ), Z = c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) =
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.56 { ! class_Rings_Ono__zero__divisors( X ), ! hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.56 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.98/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.98/1.56 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.98/1.56 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.98/1.56 ( X ), ! Z = c_Groups_Oplus__class_Oplus( X, Z, Y ), Y =
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.56 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.98/1.56 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.98/1.56 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 0.98/1.56 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.98/1.56 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.98/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.98/1.56 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero( X ) =
% 0.98/1.56 c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 0.98/1.56 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.98/1.56 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.98/1.56 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.98/1.56 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 0.98/1.56 c_Groups_Osgn__class_Osgn( X, c_RealVector_Oof__real( X, Y ) ) =
% 0.98/1.56 c_RealVector_Oof__real( X, c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, Y
% 0.98/1.56 ) ) }.
% 0.98/1.56 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.56 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.98/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Groups_Ozero__class_Ozero( X )
% 0.98/1.56 = Y }.
% 0.98/1.56 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y,
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Ouminus__class_Ouminus( X, Y
% 0.98/1.56 ) }.
% 0.98/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.98/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ), Y = c_Groups_Ozero__class_Ozero
% 0.98/1.56 ( X ) }.
% 0.98/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.56 , Y ) }.
% 0.98/1.56 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 0.98/1.56 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.98/1.56 ) }.
% 0.98/1.56 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.98/1.56 ) }.
% 0.98/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ) = Y, Y =
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.98/1.56 = Y }.
% 0.98/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.98/1.56 c_Groups_Oabs__class_Oabs( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.98/1.56 c_Groups_Oabs__class_Oabs( X, Y ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! Y =
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oabs__class_Oabs( X, Y ) =
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.56 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) = hAPP( hAPP
% 0.98/1.56 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ), Z = Y }.
% 0.98/1.56 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP
% 0.98/1.56 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) = hAPP(
% 0.98/1.56 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) }.
% 0.98/1.56 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) = hAPP( hAPP
% 0.98/1.56 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ), Z = Y }.
% 0.98/1.56 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP
% 0.98/1.56 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) = hAPP(
% 0.98/1.56 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) }.
% 0.98/1.56 { c_NthRoot_Osqrt( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) =
% 0.98/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.98/1.56 { ! c_NthRoot_Osqrt( X ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal )
% 0.98/1.56 , X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.98/1.56 { ! X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X
% 0.98/1.56 ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.98/1.56 { ! class_Groups_Osgn__if( X ), c_Groups_Osgn__class_Osgn( X,
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.56 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 0.98/1.56 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.56 }.
% 0.98/1.56 { ! class_Rings_Olinordered__idom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.56 X ), c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.56 }.
% 0.98/1.56 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Osgn__class_Osgn
% 0.98/1.56 ( X, c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X
% 0.98/1.56 ) }.
% 0.98/1.56 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.98/1.56 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.56 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) =
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.56 { ! class_RealVector_Oreal__algebra__1( X ), c_RealVector_Oof__real( X,
% 0.98/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), Y ) )
% 0.98/1.56 = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), c_RealVector_Oof__real
% 0.98/1.56 ( X, Z ) ), c_RealVector_Oof__real( X, Y ) ) }.
% 0.98/1.56 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 0.98/1.56 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.98/1.56 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 0.98/1.56 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.98/1.56 { ! class_RealVector_Oreal__algebra__1( X ), c_RealVector_Oof__real( X,
% 0.98/1.56 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ) ) =
% 0.98/1.56 c_Groups_Oplus__class_Oplus( X, c_RealVector_Oof__real( X, Z ),
% 0.98/1.56 c_RealVector_Oof__real( X, Y ) ) }.
% 0.98/1.56 { ! class_RealVector_Oreal__algebra__1( X ), !
% 0.98/1.56 class_RealVector_Oreal__normed__vector( X ), c_RealVector_Oof__real( X,
% 0.98/1.56 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ) ) =
% 0.98/1.56 c_Groups_Oplus__class_Oplus( X, c_RealVector_Oof__real( X, Z ),
% 0.98/1.56 c_RealVector_Oof__real( X, Y ) ) }.
% 0.98/1.56 { ! class_RealVector_Oreal__algebra__1( X ), c_RealVector_Oof__real( X,
% 0.98/1.56 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) =
% 0.98/1.56 c_Groups_Ouminus__class_Ouminus( X, c_RealVector_Oof__real( X, Y ) ) }.
% 0.98/1.56 { ! class_RealVector_Oreal__algebra__1( X ), !
% 0.98/1.56 class_RealVector_Oreal__normed__vector( X ), c_RealVector_Oof__real( X,
% 0.98/1.56 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) =
% 0.98/1.56 c_Groups_Ouminus__class_Ouminus( X, c_RealVector_Oof__real( X, Y ) ) }.
% 0.98/1.56 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.56 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal,
% 0.98/1.56 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ),
% 0.98/1.56 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) }.
% 0.98/1.56 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.98/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.56 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.56 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.98/1.56 X ), Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.98/1.56 ( X ) ) }.
% 0.98/1.56 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.56 , c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.56 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.98/1.56 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.56 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.56 , Z, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.56 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.98/1.56 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.56 { ! class_Rings_Oordered__semiring( X ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.98/1.56 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.98/1.56 { ! class_Rings_Oordered__semiring( X ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.98/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.98/1.56 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.98/1.56 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.56 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.56 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.98/1.56 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.56 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.56 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.98/1.56 { ! class_Rings_Oordered__comm__semiring( X ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.98/1.56 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.56 { ! class_Rings_Oordered__semiring( X ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.98/1.56 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.56 { ! class_Rings_Oordered__semiring( X ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.98/1.56 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.98/1.56 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.56 , Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.56 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.98/1.56 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.56 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.98/1.56 X ), Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.98/1.56 ( X ) ) }.
% 0.98/1.56 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.56 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.56 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.56 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ),
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.56 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.98/1.56 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.98/1.56 ( X ) ), alpha1( X, Y, Z ), alpha7( X, Y, Z ) }.
% 0.98/1.56 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha1( X, Y, Z ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.98/1.56 ( X ) ) }.
% 0.98/1.56 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha7( X, Y, Z ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.98/1.56 ( X ) ) }.
% 0.98/1.56 { ! alpha7( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.56 { ! alpha7( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.98/1.56 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.98/1.56 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.98/1.56 ( X ), Y ), alpha7( X, Y, Z ) }.
% 0.98/1.56 { ! alpha1( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.98/1.56 { ! alpha1( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.56 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.56 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ) ), alpha1( X, Y, Z ) }.
% 0.98/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), alpha2( X, Y
% 0.98/1.56 , Z ), alpha8( X, Y, Z ) }.
% 0.98/1.56 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha2( X, Y, Z ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.56 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha8( X, Y, Z ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.56 { ! alpha8( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.56 { ! alpha8( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.56 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.98/1.56 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ) ), alpha8( X, Y, Z ) }.
% 0.98/1.56 { ! alpha2( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.98/1.56 { ! alpha2( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.98/1.56 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.56 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ), Y ), alpha2( X, Y, Z ) }.
% 0.98/1.56 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.98/1.56 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) }.
% 0.98/1.56 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.56 , c_Groups_Oplus__class_Oplus( X, Y, Z ), c_Groups_Ozero__class_Ozero( X
% 0.98/1.56 ) ) }.
% 0.98/1.56 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.98/1.56 Z, Y ) ) }.
% 0.98/1.56 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.98/1.56 Y, Z ) ) }.
% 0.98/1.56 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.98/1.56 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 0.98/1.56 .
% 0.98/1.56 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.98/1.56 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.98/1.56 .
% 0.98/1.56 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.98/1.56 X ), Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), ! Z =
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.98/1.56 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.56 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.98/1.56 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.98/1.56 ) }.
% 0.98/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Y,
% 0.98/1.56 Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.56 ) }.
% 0.98/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.56 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X
% 0.98/1.56 , Y, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.56 c_Groups_Oplus__class_Oplus( X, Y, Y ) ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.56 ) }.
% 0.98/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.56 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.98/1.56 ), c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.98/1.56 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.98/1.56 ( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! W = U, T = Z, !
% 0.98/1.56 c_Groups_Oplus__class_Oplus( X, W, hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) =
% 0.98/1.56 c_Groups_Oplus__class_Oplus( X, U, hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.56 , Y ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.98/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.56 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 0.98/1.56 ( X, Y ), Y ) }.
% 0.98/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.56 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.56 ) }.
% 0.98/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.56 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 0.98/1.56 ( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 0.98/1.56 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.56 ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.98/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.98/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.56 ) }.
% 0.98/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.56 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.98/1.56 ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.98/1.56 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.98/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Ozero__class_Ozero(
% 0.98/1.56 X ) }.
% 0.98/1.56 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.56 , Y ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.56 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.98/1.56 = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ouminus__class_Ouminus
% 0.98/1.56 ( X, Y ) }.
% 0.98/1.56 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.56 { ! class_Groups_Oab__group__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.56 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.98/1.56 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus
% 0.98/1.56 ( X, Z ) }.
% 0.98/1.56 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.56 , Z ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.56 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.98/1.56 = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.98/1.56 Z ) = Y }.
% 0.98/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.56 ), c_Groups_Oabs__class_Oabs( X, Y ) = Y }.
% 0.98/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Y ),
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.56 }.
% 0.98/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! Y =
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.56 c_Groups_Oabs__class_Oabs( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.56 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.98/1.56 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 0.98/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y =
% 0.98/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.98/1.56 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 0.98/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X =
% 0.98/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.98/1.56 { ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! X =
% 0.98/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.98/1.56 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 0.98/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.98/1.56 { c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, c_Complex_Orcis( Y
% 0.98/1.56 , X ) ) = c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ) }.
% 0.98/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), ! c_NthRoot_Osqrt(
% 0.98/1.56 X ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X =
% 0.98/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.98/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ) }
% 0.98/1.56 .
% 0.98/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Osqrt( X
% 0.98/1.56 ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.98/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.98/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.98/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Osqrt( X )
% 0.98/1.56 , c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.98/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ) }.
% 0.98/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ) }
% 0.98/1.56 .
% 0.98/1.56 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) =
% 0.98/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X =
% 0.98/1.56 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) }.
% 0.98/1.56 { ! X = c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ),
% 0.98/1.56 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) =
% 0.98/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.98/1.56 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 0.98/1.56 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) =
% 0.98/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y = X }.
% 0.98/1.56 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 0.98/1.56 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) =
% 0.98/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.98/1.56 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.56 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.98/1.56 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 0.98/1.56 c_RealVector_Onorm__class_Onorm( X, Y ) ) ) }.
% 0.98/1.56 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.56 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.98/1.56 ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.98/1.56 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.98/1.56 ( X, Y ) ) ) }.
% 0.98/1.56 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.98/1.56 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.98/1.56 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.98/1.56 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.98/1.56 hAPP( Y, U ) ) }.
% 0.98/1.56 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.98/1.56 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.98/1.56 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.98/1.56 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.98/1.56 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.56 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.98/1.56 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.98/1.56 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.98/1.56 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.98/1.56 , Y ), ! Z = T, c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.98/1.56 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y
% 0.98/1.56 ), ! Y = T, c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.98/1.56 { ! class_Orderings_Oorder( X ), ! Z = Y, !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.98/1.56 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.98/1.56 ( X, Y, T ), c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.98/1.56 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.98/1.56 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.98/1.56 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.98/1.56 , Y ), ! Y = Z, c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.98/1.56 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.98/1.56 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.98/1.56 hAPP( Y, U ) ) }.
% 0.98/1.56 { ! class_Orderings_Opreorder( X ), ! Z = Y,
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.98/1.56 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.98/1.56 ( X, Z, Y ) }.
% 0.98/1.56 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.98/1.56 ( X, Y, Z ) }.
% 0.98/1.56 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.98/1.56 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.98/1.56 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.98/1.56 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.98/1.56 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.98/1.56 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.98/1.56 hAPP( Y, U ) ) }.
% 0.98/1.56 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, hAPP
% 0.98/1.56 ( Z, skol2( X, Y, Z ) ), hAPP( Y, skol2( X, Y, Z ) ) ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }.
% 0.98/1.56 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y,
% 0.98/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.56 c_RealVector_Onorm__class_Onorm( X, Z ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ),
% 0.98/1.56 c_RealVector_Onorm__class_Onorm( X, T ) ) ), Z =
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.98/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.56 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ),
% 0.98/1.56 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Z ) ) ), Y =
% 0.98/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.98/1.56 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.98/1.56 X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 0.98/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.98/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.98/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ) ), Z = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.56 }.
% 0.98/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.98/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.56 }.
% 0.98/1.56 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.56 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.98/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.56 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Opi ) }
% 0.98/1.56 .
% 0.98/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.56 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.98/1.56 ) = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X
% 0.98/1.56 ) }.
% 0.98/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.56 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.98/1.56 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.98/1.56 ) }.
% 0.98/1.56 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.56 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.56 { ! c_Transcendental_Opi = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal )
% 0.98/1.56 }.
% 0.98/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.56 c_Groups_Oplus__class_Oplus( X, Y, Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.56 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.98/1.56 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.56 { ! class_RealVector_Oreal__algebra__1( X ), !
% 0.98/1.56 class_RealVector_Oreal__normed__vector( X ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol3( Y ) ) }.
% 0.98/1.56 { ! class_RealVector_Oreal__algebra__1( X ), !
% 0.98/1.56 class_RealVector_Oreal__normed__vector( X ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.56 c_RealVector_Onorm__class_Onorm( X, c_RealVector_Oof__real( X, Y ) ),
% 0.98/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.98/1.56 c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, Y ) ), skol3( X ) ) )
% 0.98/1.56 }.
% 0.98/1.56 { c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, X ) =
% 0.98/1.56 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) }.
% 0.98/1.56 { ! class_RealVector_Oreal__algebra__1( X ), !
% 0.98/1.56 class_RealVector_Oreal__normed__vector( X ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.56 c_RealVector_Onorm__class_Onorm( X, c_RealVector_Oof__real( X, Y ) ),
% 0.98/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.98/1.56 c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, Y ) ), skol4( X ) ) )
% 0.98/1.56 }.
% 0.98/1.56 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol5( Y ) ) }.
% 0.98/1.56 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.56 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.98/1.56 c_RealVector_Onorm__class_Onorm( X, Y ) ),
% 0.98/1.56 c_RealVector_Onorm__class_Onorm( X, Z ) ) ), skol5( X ) ) ) }.
% 0.98/1.56 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol6( Z, T ) ) }.
% 0.98/1.56 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.56 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.98/1.56 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol6( X, Y ) ) ) }.
% 0.98/1.56 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol7( Z, T ) ) }.
% 0.98/1.56 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.56 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.98/1.56 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol7( X, Y ) ) ) }.
% 0.98/1.56 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.56 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.98/1.56 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol8( X, Y ) ) ) }.
% 0.98/1.56 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.56 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.98/1.56 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol9( X, Y ) ) ) }.
% 0.98/1.56 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.56 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.98/1.56 c_RealVector_Onorm__class_Onorm( X, Y ) ),
% 0.98/1.56 c_RealVector_Onorm__class_Onorm( X, Z ) ) ), skol10( X ) ) ) }.
% 0.98/1.56 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X,
% 0.98/1.56 c_Groups_Osgn__class_Osgn( X, Y ) ) = c_Groups_Ozero__class_Ozero(
% 0.98/1.56 tc_RealDef_Oreal ) }.
% 0.98/1.56 { ! class_RealVector_Oreal__normed__vector( X ), Y =
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X,
% 0.98/1.56 c_Groups_Osgn__class_Osgn( X, Y ) ) = c_Groups_Oone__class_Oone(
% 0.98/1.56 tc_RealDef_Oreal ) }.
% 0.98/1.56 { ! class_Rings_Olinordered__semiring__1( X ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, T, Y ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.98/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.98/1.56 X ), W ), ! c_Groups_Oplus__class_Oplus( X, U, W ) =
% 0.98/1.56 c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.56 ( X ), U ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), T )
% 0.98/1.56 ), Y ) }.
% 0.98/1.56 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.56 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X,
% 0.98/1.56 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.98/1.56 , Y ) ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.98/1.56 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, U,
% 0.98/1.56 Z ) ), c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus
% 0.98/1.56 ( X, T, Y ) ) ) ) }.
% 0.98/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.56 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, c_Transcendental_Opi )
% 0.98/1.56 , X ), ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y,
% 0.98/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.56 c_Transcendental_Ocos( X ), c_Transcendental_Ocos( Y ) ) }.
% 0.98/1.56 { c_RealDef_Opositive( X ), X = c_Groups_Ozero__class_Ozero(
% 0.98/1.56 tc_RealDef_Oreal ), c_RealDef_Opositive( c_Groups_Ouminus__class_Ouminus
% 0.98/1.56 ( tc_RealDef_Oreal, X ) ) }.
% 0.98/1.56 { c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, c_RealVector_Oof__real
% 0.98/1.56 ( tc_Complex_Ocomplex, Z ), c_Complex_Ocomplex_OComplex( Y, X ) ) =
% 0.98/1.56 c_Complex_Ocomplex_OComplex( c_Groups_Oplus__class_Oplus(
% 0.98/1.56 tc_RealDef_Oreal, Z, Y ), X ) }.
% 0.98/1.56 { c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex,
% 0.98/1.56 c_Complex_Ocomplex_OComplex( Z, Y ), c_RealVector_Oof__real(
% 0.98/1.56 tc_Complex_Ocomplex, X ) ) = c_Complex_Ocomplex_OComplex(
% 0.98/1.56 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, X ), Y ) }.
% 0.98/1.56 { c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex,
% 0.98/1.56 c_Complex_Ocomplex_OComplex( T, Z ), c_Complex_Ocomplex_OComplex( Y, X )
% 0.98/1.56 ) = c_Complex_Ocomplex_OComplex( c_Groups_Ominus__class_Ominus(
% 0.98/1.56 tc_RealDef_Oreal, T, Y ), c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal
% 0.98/1.56 , Z, X ) ) }.
% 0.98/1.56 { ! c_Complex_Ocomplex_OComplex( T, Z ) = c_Complex_Ocomplex_OComplex( Y, X
% 0.98/1.56 ), T = Y }.
% 0.98/1.56 { ! c_Complex_Ocomplex_OComplex( T, Z ) = c_Complex_Ocomplex_OComplex( Y, X
% 0.98/1.56 ), Z = X }.
% 0.98/1.56 { ! T = Y, ! Z = X, c_Complex_Ocomplex_OComplex( T, Z ) =
% 0.98/1.56 c_Complex_Ocomplex_OComplex( Y, X ) }.
% 0.98/1.56 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.98/1.56 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! U = T, Z = Y }.
% 0.98/1.56 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.98/1.56 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! Z = Y, U = T }.
% 0.98/1.56 { ! class_Groups_Oone( X ), ! c_Groups_Oone__class_Oone( X ) = Y, Y =
% 0.98/1.56 c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.56 { ! class_Groups_Oone( X ), ! Y = c_Groups_Oone__class_Oone( X ),
% 0.98/1.56 c_Groups_Oone__class_Oone( X ) = Y }.
% 0.98/1.56 { ! class_Groups_Ominus( X ), hAPP( c_Groups_Ominus__class_Ominus( tc_fun(
% 0.98/1.56 U, X ), T, Z ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( T, Y ),
% 0.98/1.56 hAPP( Z, Y ) ) }.
% 0.98/1.56 { ! c_Complex_Ocomplex_OComplex( Y, X ) = c_Groups_Oone__class_Oone(
% 0.98/1.56 tc_Complex_Ocomplex ), Y = c_Groups_Oone__class_Oone( tc_RealDef_Oreal )
% 0.98/1.56 }.
% 0.98/1.56 { ! c_Complex_Ocomplex_OComplex( Y, X ) = c_Groups_Oone__class_Oone(
% 0.98/1.56 tc_Complex_Ocomplex ), X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal
% 0.98/1.56 ) }.
% 0.98/1.56 { ! Y = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), ! X =
% 0.98/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.98/1.56 c_Complex_Ocomplex_OComplex( Y, X ) = c_Groups_Oone__class_Oone(
% 0.98/1.56 tc_Complex_Ocomplex ) }.
% 0.98/1.56 { ! class_RealVector_Oreal__algebra__1( X ), !
% 0.98/1.56 class_RealVector_Oreal__normed__vector( X ), c_RealVector_Oof__real( X,
% 0.98/1.56 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Z, Y ) ) =
% 0.98/1.56 c_Groups_Ominus__class_Ominus( X, c_RealVector_Oof__real( X, Z ),
% 0.98/1.56 c_RealVector_Oof__real( X, Y ) ) }.
% 0.98/1.56 { ! class_RealVector_Oreal__algebra__1( X ), c_RealVector_Oof__real( X,
% 0.98/1.56 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Z, Y ) ) =
% 0.98/1.56 c_Groups_Ominus__class_Ominus( X, c_RealVector_Oof__real( X, Z ),
% 0.98/1.56 c_RealVector_Oof__real( X, Y ) ) }.
% 0.98/1.56 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 0.98/1.56 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oone__class_Oone( X ) ) =
% 0.98/1.56 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.98/1.56 { ! class_RealVector_Oreal__algebra__1( X ), c_RealVector_Oof__real( X,
% 0.98/1.56 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) =
% 0.98/1.56 c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.56 { c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) =
% 0.98/1.56 c_Complex_Ocomplex_OComplex( c_Groups_Oone__class_Oone( tc_RealDef_Oreal
% 0.98/1.56 ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.98/1.56 { c_Transcendental_Ocos( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) )
% 0.98/1.56 = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.98/1.56 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.56 c_Transcendental_Ocos( X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal )
% 0.98/1.56 ) }.
% 0.98/1.56 { ! class_Rings_Oring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP
% 0.98/1.56 ( c_Groups_Otimes__class_Otimes( X ), Y ), Y ), c_Groups_Oone__class_Oone
% 0.98/1.56 ( X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.98/1.56 c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) ) ),
% 0.98/1.56 c_Groups_Ominus__class_Ominus( X, Y, c_Groups_Oone__class_Oone( X ) ) ) }
% 0.98/1.56 .
% 0.98/1.56 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.56 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.98/1.56 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.98/1.56 ( X, Y ) ), c_RealVector_Onorm__class_Onorm( X,
% 0.98/1.56 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) }.
% 0.98/1.56 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.56 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, c_Transcendental_Ocos( X ) )
% 0.98/1.56 , c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.98/1.56 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.98/1.56 ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.98/1.56 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ominus__class_Ominus(
% 0.98/1.56 X, Z, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.56 { ! class_Groups_Oab__group__add( X ), ! Z = Y,
% 0.98/1.56 c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.98/1.56 ) }.
% 0.98/1.56 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.98/1.56 Z, Y ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.98/1.56 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y, Y )
% 0.98/1.56 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.56 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y,
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.98/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.56 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.98/1.56 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.98/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.56 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.98/1.56 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, U, T ) }.
% 0.98/1.56 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 0.98/1.56 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.56 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 0.98/1.56 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.56 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 0.98/1.56 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.56 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 0.98/1.56 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.56 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.98/1.56 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = Z }.
% 0.98/1.56 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.56 c_Groups_Ominus__class_Ominus( X, Z, Y ), Y ) = Z }.
% 0.98/1.56 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.98/1.56 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) =
% 0.98/1.56 c_Groups_Ominus__class_Ominus( X, Y, Z ) }.
% 0.98/1.56 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.98/1.56 c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.56 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Oone__class_Oone( X ) =
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.98/1.56 c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Z, Y ) )
% 0.98/1.56 = c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Y, Z )
% 0.98/1.56 ) }.
% 0.98/1.56 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.98/1.56 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, Z,
% 0.98/1.56 Y ) ) = c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus
% 0.98/1.56 ( X, Y, Z ) ) }.
% 0.98/1.56 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.98/1.56 = Y }.
% 0.98/1.56 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.98/1.56 = Y }.
% 0.98/1.56 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.98/1.56 = Y }.
% 0.98/1.56 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.98/1.56 = Y }.
% 0.98/1.56 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.98/1.56 = Y }.
% 0.98/1.56 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.98/1.56 = Y }.
% 0.98/1.56 { c_RealVector_Oof__real( tc_Complex_Ocomplex,
% 0.98/1.56 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal,
% 0.98/1.56 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) =
% 0.98/1.56 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex,
% 0.98/1.56 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) }.
% 0.98/1.56 { c_Transcendental_Ocos( c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal
% 0.98/1.56 , X ) ) = c_Transcendental_Ocos( X ) }.
% 0.98/1.56 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X,
% 0.98/1.56 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.56 { c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex,
% 0.98/1.56 c_Complex_Ocomplex_OComplex( Y, X ) ) = c_Complex_Ocomplex_OComplex(
% 0.98/1.56 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ),
% 0.98/1.56 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) }.
% 0.98/1.56 { ! c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) =
% 0.98/1.56 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.98/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.98/1.56 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) = X }.
% 0.98/1.56 { ! c_NthRoot_Osqrt( X ) = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X
% 0.98/1.56 = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.98/1.56 { ! X = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X )
% 0.98/1.56 = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.98/1.56 { c_NthRoot_Osqrt( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) =
% 0.98/1.56 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.98/1.56 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 0.98/1.56 c_Groups_Osgn__class_Osgn( X, c_Groups_Oone__class_Oone( X ) ) =
% 0.98/1.56 c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.56 { c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, Y, X ) =
% 0.98/1.56 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y,
% 0.98/1.56 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, X ) ) }.
% 0.98/1.56 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.56 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 0.98/1.56 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.98/1.56 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.98/1.56 ( X, Y ) ) ), c_RealVector_Onorm__class_Onorm( X,
% 0.98/1.56 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) }.
% 0.98/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.98/1.56 c_Complex_Ocomplex_OComplex( T, Z ) ), c_Complex_Ocomplex_OComplex( Y, X
% 0.98/1.56 ) ) = c_Complex_Ocomplex_OComplex( c_Groups_Ominus__class_Ominus(
% 0.98/1.56 tc_RealDef_Oreal, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.98/1.56 tc_RealDef_Oreal ), T ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.98/1.56 tc_RealDef_Oreal ), Z ), X ) ), c_Groups_Oplus__class_Oplus(
% 0.98/1.56 tc_RealDef_Oreal, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.98/1.56 tc_RealDef_Oreal ), T ), X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.98/1.56 tc_RealDef_Oreal ), Z ), Y ) ) ) }.
% 0.98/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 0.98/1.56 , Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 0.98/1.56 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.98/1.56 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.98/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.56 ( X ), Z ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.98/1.56 Z ) ), U ), T ) = Y }.
% 0.98/1.56 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.98/1.56 Z ) ), U ), T ) = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.98/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.56 ( X ), Z ), U ), Y ) }.
% 0.98/1.56 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.98/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.56 ( X ), Z ), U ), Y ), T = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.98/1.56 W ) ), U ), Y ) }.
% 0.98/1.56 { ! class_Rings_Oring( X ), ! T = c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.98/1.56 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.98/1.56 X, Z, W ) ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.98/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.56 ( X ), Z ), U ), Y ) }.
% 0.98/1.56 { ! class_Rings_Oring( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.98/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.56 ( X ), U ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 0.98/1.56 Z ) ), Y ) ) }.
% 0.98/1.56 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.98/1.56 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.98/1.56 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.98/1.56 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.98/1.56 X, U, Z ) ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 0.98/1.56 Z ) ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 0.98/1.56 c_Groups_Ominus__class_Ominus( X, T, Y ) ) ) }.
% 0.98/1.56 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.98/1.56 X, Y ) }.
% 0.98/1.56 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.98/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Oplus__class_Oplus(
% 0.98/1.56 X, Z, Y ) }.
% 0.98/1.56 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X, Z
% 0.98/1.56 , Y ) = c_Groups_Oplus__class_Oplus( X, Z,
% 0.98/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.98/1.56 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z, Y )
% 0.98/1.56 = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.56 , Y ) ) }.
% 0.98/1.56 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.98/1.56 ) = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus(
% 0.98/1.56 X, Y ) ) }.
% 0.98/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 0.98/1.56 c_Groups_Ominus__class_Ominus( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.98/1.56 c_Groups_Oabs__class_Oabs( X, Y ) ) ), c_Groups_Oabs__class_Oabs( X,
% 0.98/1.56 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) }.
% 0.98/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X,
% 0.98/1.56 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ),
% 0.98/1.56 c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Z, Y ) )
% 0.98/1.56 ) }.
% 0.98/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X,
% 0.98/1.56 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ),
% 0.98/1.56 c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Y, Z ) )
% 0.98/1.56 ) }.
% 0.98/1.56 { ! class_Rings_Olinordered__semidom( X ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.98/1.56 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.56 { ! class_Rings_Olinordered__semidom( X ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.56 c_Groups_Oone__class_Oone( X ) ) }.
% 0.98/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.56 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ),
% 0.98/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.98/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.56 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ),
% 0.98/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.98/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = hAPP(
% 0.98/1.56 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X
% 0.98/1.56 , Z, c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.98/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.98/1.56 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP
% 0.98/1.56 ( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.98/1.56 c_Groups_Oone__class_Oone( X ) ) ), Z ) }.
% 0.98/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.98/1.56 , Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.98/1.56 c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.98/1.56 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.98/1.56 { ! c_RealDef_Opositive( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) )
% 0.98/1.56 }.
% 0.98/1.56 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = c_Groups_Oone__class_Oone
% 0.98/1.56 ( X ), Y = c_Groups_Oone__class_Oone( X ), Y =
% 0.98/1.56 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) }.
% 0.98/1.56 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.98/1.56 c_Groups_Oone__class_Oone( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.56 ( X ), Y ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.56 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.98/1.56 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 0.98/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) =
% 0.98/1.56 c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.56 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ouminus__class_Ouminus( X, Y
% 0.98/1.56 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.98/1.56 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) ), Y
% 0.98/1.56 ) }.
% 0.98/1.56 { ! c_RealDef_Opositive( X ), ! c_RealDef_Opositive( Y ),
% 0.98/1.56 c_RealDef_Opositive( hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.98/1.56 tc_RealDef_Oreal ), X ), Y ) ) }.
% 0.98/1.56 { ! c_RealDef_Opositive( X ), ! c_RealDef_Opositive( Y ),
% 0.98/1.56 c_RealDef_Opositive( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X, Y
% 0.98/1.56 ) ) }.
% 0.98/1.56 { c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ) =
% 0.98/1.56 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 0.98/1.56 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) }.
% 0.98/1.56 { c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ) =
% 0.98/1.56 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 0.98/1.56 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) }.
% 0.98/1.56 { ! c_Complex_Ocomplex_OComplex( Z, Y ) = c_RealVector_Oof__real(
% 0.98/1.56 tc_Complex_Ocomplex, X ), Z = X }.
% 0.98/1.56 { ! c_Complex_Ocomplex_OComplex( Z, Y ) = c_RealVector_Oof__real(
% 0.98/1.56 tc_Complex_Ocomplex, X ), Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.56 tc_RealDef_Oreal ) }.
% 0.98/1.56 { ! Z = X, ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.98/1.56 c_Complex_Ocomplex_OComplex( Z, Y ) = c_RealVector_Oof__real(
% 0.98/1.56 tc_Complex_Ocomplex, X ) }.
% 0.98/1.56 { c_RealVector_Oof__real( tc_Complex_Ocomplex, X ) =
% 0.98/1.56 c_Complex_Ocomplex_OComplex( X, c_Groups_Ozero__class_Ozero(
% 0.98/1.56 tc_RealDef_Oreal ) ) }.
% 0.98/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.56 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.56 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 0.98/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.56 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.56 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ) }.
% 0.98/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Osqrt( X
% 0.98/1.56 ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.98/1.56 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.98/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.98/1.56 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Osqrt( X )
% 0.98/1.56 , c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.98/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.56 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.56 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ) }.
% 0.98/1.56 { ! c_Complex_Ocomplex_OComplex( Y, X ) = c_Groups_Ozero__class_Ozero(
% 0.98/1.56 tc_Complex_Ocomplex ), Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal
% 0.98/1.56 ) }.
% 0.98/1.56 { ! c_Complex_Ocomplex_OComplex( Y, X ) = c_Groups_Ozero__class_Ozero(
% 0.98/1.56 tc_Complex_Ocomplex ), X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal
% 0.98/1.56 ) }.
% 0.98/1.56 { ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! X =
% 0.98/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.98/1.56 c_Complex_Ocomplex_OComplex( Y, X ) = c_Groups_Ozero__class_Ozero(
% 0.98/1.56 tc_Complex_Ocomplex ) }.
% 0.98/1.56 { c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) =
% 0.98/1.56 c_Complex_Ocomplex_OComplex( c_Groups_Ozero__class_Ozero(
% 0.98/1.56 tc_RealDef_Oreal ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.98/1.56 { c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex,
% 0.98/1.56 c_Complex_Ocomplex_OComplex( T, Z ), c_Complex_Ocomplex_OComplex( Y, X )
% 0.98/1.56 ) = c_Complex_Ocomplex_OComplex( c_Groups_Oplus__class_Oplus(
% 0.98/1.56 tc_RealDef_Oreal, T, Y ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.98/1.56 Z, X ) ) }.
% 0.98/1.56 { c_Complex_Ocis( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) =
% 0.98/1.56 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) }.
% 0.98/1.56 { c_Complex_Ocis( X ) = c_Complex_Orcis( c_Groups_Oone__class_Oone(
% 0.98/1.56 tc_RealDef_Oreal ), X ) }.
% 0.98/1.56 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.56 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.98/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.56 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.56 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ) }.
% 0.98/1.56 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.56 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.98/1.56 Z ) ), U ), T ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.56 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.98/1.56 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.56 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.98/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.56 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X, T,
% 0.98/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.56 ( X ), c_Groups_Ominus__class_Ominus( X, Z, W ) ), U ), Y ) ) }.
% 0.98/1.56 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.56 , T, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.98/1.56 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.56 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.98/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 0.98/1.56 c_Groups_Ominus__class_Ominus( X, c_Groups_Oplus__class_Oplus( X, U, T )
% 0.98/1.56 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) ), c_Groups_Oplus__class_Oplus
% 0.98/1.56 ( X, c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, U, Z
% 0.98/1.56 ) ), c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, T,
% 0.98/1.56 Y ) ) ) ) }.
% 0.98/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 0.98/1.56 c_Groups_Ominus__class_Ominus( X, Z, Y ) ), c_Groups_Oplus__class_Oplus(
% 0.98/1.56 X, c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) )
% 0.98/1.56 ) }.
% 0.98/1.56 { c_Complex_Oexpi( c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) =
% 0.98/1.56 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) }.
% 0.98/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y,
% 0.98/1.56 c_Transcendental_Opi ), c_Orderings_Oord__class_Oless__eq(
% 0.98/1.56 tc_RealDef_Oreal, c_Transcendental_Ocos( Y ), c_Transcendental_Ocos( X )
% 0.98/1.56 ) }.
% 0.98/1.56 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.98/1.56 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.98/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.98/1.56 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) }.
% 0.98/1.56 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.98/1.56 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.98/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.98/1.56 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) }.
% 0.98/1.56 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.56 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.98/1.56 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.98/1.56 ( X, Y ) ), c_RealVector_Onorm__class_Onorm( X,
% 0.98/1.56 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) ) }.
% 0.98/1.56 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.56 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, Z,
% 0.98/1.56 Y ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.98/1.56 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.98/1.56 ( X, Y ) ) ) }.
% 0.98/1.56 { c_Transcendental_Ocos( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 0.98/1.56 c_Transcendental_Opi ) ) = c_Groups_Ouminus__class_Ouminus(
% 0.98/1.56 tc_RealDef_Oreal, c_Transcendental_Ocos( X ) ) }.
% 0.98/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.98/1.56 c_Complex_Ocomplex_OComplex( Z, Y ) ), c_RealVector_Oof__real(
% 0.98/1.56 tc_Complex_Ocomplex, X ) ) = c_Complex_Ocomplex_OComplex( hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.98/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.98/1.56 c_RealVector_Oof__real( tc_Complex_Ocomplex, Z ) ),
% 0.98/1.56 c_Complex_Ocomplex_OComplex( Y, X ) ) = c_Complex_Ocomplex_OComplex( hAPP
% 0.98/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), Y ), hAPP
% 0.98/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) ) }.
% 0.98/1.56 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.56 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.98/1.56 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.98/1.56 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X ) ),
% 0.98/1.56 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y ) ),
% 0.98/1.56 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) }.
% 0.98/1.56 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.98/1.56 c_Transcendental_Ocos( c_Complex_Oarg( c_Complex_Ocomplex_OComplex(
% 0.98/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ) ) ) =
% 0.98/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.98/1.56 { c_Complex_Ocomplex_Ocomplex__size( c_Complex_Ocomplex_OComplex( Y, X ) )
% 0.98/1.56 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.56 { c_Complex_Ocomplex_Ocomplex__case( T, Z, c_Complex_Ocomplex_OComplex( Y,
% 0.98/1.56 X ) ) = hAPP( hAPP( Z, Y ), X ) }.
% 0.98/1.56 { c_Complex_Ocomplex_Ocomplex__rec( T, Z, c_Complex_Ocomplex_OComplex( Y, X
% 0.98/1.56 ) ) = hAPP( hAPP( Z, Y ), X ) }.
% 0.98/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.98/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.56 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, c_Transcendental_Opi )
% 0.98/1.56 , X ), c_Transcendental_Oarccos( c_Transcendental_Ocos( X ) ) =
% 0.98/1.56 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) }.
% 0.98/1.56 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.98/1.56 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Ouminus__class_Ouminus
% 0.98/1.56 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.98/1.56 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) }.
% 0.98/1.56 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.98/1.56 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.98/1.56 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus(
% 0.98/1.56 X, U, Z ), c_Groups_Ominus__class_Ominus( X, T, Y ) ) }.
% 0.98/1.56 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.98/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.56 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.98/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 0.98/1.56 ( tc_Nat_Onat ) ) ), X ) ) }.
% 0.98/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.98/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.98/1.56 c_Transcendental_Opi ), c_Transcendental_Oarccos( c_Transcendental_Ocos(
% 0.98/1.56 X ) ) = X }.
% 0.98/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.56 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ),
% 0.98/1.56 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), c_Transcendental_Ocos(
% 0.98/1.56 c_Transcendental_Oarccos( X ) ) = X }.
% 0.98/1.56 { c_Nat_Osize__class_Osize( tc_Complex_Ocomplex,
% 0.98/1.56 c_Complex_Ocomplex_OComplex( Y, X ) ) = c_Groups_Ozero__class_Ozero(
% 0.98/1.56 tc_Nat_Onat ) }.
% 0.98/1.56 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.98/1.56 { c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP( hAPP(
% 0.98/1.56 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.98/1.56 c_RealVector_Oof__real( tc_Complex_Ocomplex, Y ) ),
% 0.98/1.56 c_Complex_Ocomplex_OComplex( c_Transcendental_Ocos( X ),
% 0.98/1.56 c_Transcendental_Osin( X ) ) ) ) = c_Groups_Oabs__class_Oabs(
% 0.98/1.57 tc_RealDef_Oreal, Y ) }.
% 0.98/1.57 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.98/1.57 c_RealVector_Oof__real( tc_Complex_Ocomplex, X ) ), c_Complex_Oii ) =
% 0.98/1.57 c_Complex_Ocomplex_OComplex( c_Groups_Ozero__class_Ozero(
% 0.98/1.57 tc_RealDef_Oreal ), X ) }.
% 0.98/1.57 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.98/1.57 c_Complex_Oii ), c_RealVector_Oof__real( tc_Complex_Ocomplex, X ) ) =
% 0.98/1.57 c_Complex_Ocomplex_OComplex( c_Groups_Ozero__class_Ozero(
% 0.98/1.57 tc_RealDef_Oreal ), X ) }.
% 0.98/1.57 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.57 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) = X }.
% 0.98/1.57 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), Y =
% 0.98/1.57 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.98/1.57 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X =
% 0.98/1.57 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.98/1.57 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.98/1.57 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Groups_Oone__class_Oone(
% 0.98/1.57 tc_Nat_Onat ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.98/1.57 , Y ), X ) }.
% 0.98/1.57 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.98/1.57 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.98/1.57 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) =
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.98/1.57 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.98/1.57 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Oone__class_Oone(
% 0.98/1.57 tc_Nat_Onat ) }.
% 0.98/1.57 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.98/1.57 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X = c_Groups_Oone__class_Oone(
% 0.98/1.57 tc_Nat_Onat ) }.
% 0.98/1.57 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.98/1.57 c_Groups_Oone__class_Oone( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.98/1.57 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.98/1.57 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.98/1.57 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.98/1.57 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ), Y ) }.
% 0.98/1.57 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.57 tc_Nat_Onat, Y, X ), X ) = Y }.
% 0.98/1.57 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.57 tc_Nat_Onat, Y, X ), Y ) = X }.
% 0.98/1.57 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.98/1.57 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.98/1.57 Z, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.98/1.57 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.57 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) =
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 0.98/1.57 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.57 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) =
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z,
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.57 tc_Nat_Onat, Z, Y ), X ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.57 tc_Nat_Onat, X, Z ), Y ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = X }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.57 tc_Nat_Onat, Z, X ), Y ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.98/1.57 tc_Nat_Onat, X, Y ), Y ) = X }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z, X =
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X =
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.57 tc_Nat_Onat, Z, X ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.98/1.57 tc_Nat_Onat, X, Y ), Z ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ), Y ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.57 tc_Nat_Onat, X, Z ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), Z ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ),
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.98/1.57 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.98/1.57 ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X = Z }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), ! X = Z,
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = Y }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, Z ),
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ),
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 0.98/1.57 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ), Y ) }.
% 0.98/1.57 { c_Transcendental_Osin( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) )
% 0.98/1.57 = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.98/1.57 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP
% 0.98/1.57 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.98/1.57 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 0.98/1.57 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.98/1.57 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.98/1.57 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, c_Groups_Oplus__class_Oplus
% 0.98/1.57 ( tc_Nat_Onat, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.98/1.57 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.57 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.98/1.57 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ), Y = X }.
% 0.98/1.57 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) }.
% 0.98/1.57 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ), Z = X }.
% 0.98/1.57 { ! Z = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.98/1.57 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.98/1.57 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.98/1.57 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.98/1.57 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol11( X, Y ) ) }.
% 0.98/1.57 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol12( X, Y ) ) }.
% 0.98/1.57 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, T ),
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ), X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ), Y = X }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ) }.
% 0.98/1.57 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.98/1.57 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ) }.
% 0.98/1.57 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, X ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), T ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.98/1.57 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) ) }.
% 0.98/1.57 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) }.
% 0.98/1.57 { c_Transcendental_Osin( c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal
% 0.98/1.57 , X ) ) = c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal,
% 0.98/1.57 c_Transcendental_Osin( X ) ) }.
% 0.98/1.57 { ! c_Complex_Oii = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.98/1.57 { ! c_Complex_Oii = c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) }.
% 0.98/1.57 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.57 c_Transcendental_Osin( X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal )
% 0.98/1.57 ) }.
% 0.98/1.57 { c_Transcendental_Osin( c_Transcendental_Opi ) =
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.98/1.57 c_Transcendental_Opi ), c_Orderings_Oord__class_Oless__eq(
% 0.98/1.57 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.98/1.57 c_Transcendental_Osin( X ) ) }.
% 0.98/1.57 { ! c_Transcendental_Ocos( X ) = c_Groups_Oone__class_Oone(
% 0.98/1.57 tc_RealDef_Oreal ), c_Transcendental_Osin( X ) =
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.98/1.57 { c_Transcendental_Osin( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 0.98/1.57 X ) ) = c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_Transcendental_Osin
% 0.98/1.57 ( Y ) ), c_Transcendental_Ocos( X ) ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_Transcendental_Ocos
% 0.98/1.57 ( Y ) ), c_Transcendental_Osin( X ) ) ) }.
% 0.98/1.57 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, c_Transcendental_Osin( X ) )
% 0.98/1.57 , c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.98/1.57 { c_Transcendental_Osin( c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y
% 0.98/1.57 , X ) ) = c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_Transcendental_Osin
% 0.98/1.57 ( Y ) ), c_Transcendental_Ocos( X ) ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_Transcendental_Ocos
% 0.98/1.57 ( Y ) ), c_Transcendental_Osin( X ) ) ) }.
% 0.98/1.57 { c_Transcendental_Osin( c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y
% 0.98/1.57 , X ) ) = c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_Transcendental_Ocos
% 0.98/1.57 ( X ) ), c_Transcendental_Osin( Y ) ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_Transcendental_Osin
% 0.98/1.57 ( X ) ), c_Transcendental_Ocos( Y ) ) ) }.
% 0.98/1.57 { c_Transcendental_Osin( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 0.98/1.57 c_Transcendental_Opi ) ) = c_Groups_Ouminus__class_Ouminus(
% 0.98/1.57 tc_RealDef_Oreal, c_Transcendental_Osin( X ) ) }.
% 0.98/1.57 { c_Transcendental_Osin( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.98/1.57 c_Transcendental_Opi, X ) ) = c_Groups_Ouminus__class_Ouminus(
% 0.98/1.57 tc_RealDef_Oreal, c_Transcendental_Osin( X ) ) }.
% 0.98/1.57 { c_Complex_Ocis( X ) = c_Complex_Ocomplex_OComplex( c_Transcendental_Ocos
% 0.98/1.57 ( X ), c_Transcendental_Osin( X ) ) }.
% 0.98/1.57 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) =
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.57 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.57 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.57 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.57 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.57 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.98/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Y = X
% 0.98/1.57 , Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.57 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.98/1.57 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.98/1.57 .
% 0.98/1.57 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.98/1.57 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.98/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = X
% 0.98/1.57 , Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.57 { ! Z = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.98/1.57 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }
% 0.98/1.57 .
% 0.98/1.57 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.98/1.57 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.57 tc_Nat_Onat ), X ) = X }.
% 0.98/1.57 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero
% 0.98/1.57 ( tc_Nat_Onat ) ) = X }.
% 0.98/1.57 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.57 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.57 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X =
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.98/1.57 tc_Nat_Onat, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.57 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = Y, X =
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.57 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.57 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.98/1.57 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.57 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y,
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.57 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.98/1.57 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, X ) =
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.57 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 0.98/1.57 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.57 tc_Nat_Onat ), X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.57 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X )
% 0.98/1.57 , X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y =
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.57 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.98/1.57 c_Complex_Oii ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.98/1.57 tc_Complex_Ocomplex ), c_Complex_Oii ), X ) ) =
% 0.98/1.57 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, X ) }.
% 0.98/1.57 { c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_Transcendental_Ocos
% 0.98/1.57 ( X ) ), c_Transcendental_Ocos( X ) ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_Transcendental_Osin
% 0.98/1.57 ( X ) ), c_Transcendental_Osin( X ) ) ) = c_Groups_Oone__class_Oone(
% 0.98/1.57 tc_RealDef_Oreal ) }.
% 0.98/1.57 { ! c_Transcendental_Osin( X ) = c_Groups_Ozero__class_Ozero(
% 0.98/1.57 tc_RealDef_Oreal ), c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 0.98/1.57 c_Transcendental_Ocos( X ) ) = c_Groups_Oone__class_Oone(
% 0.98/1.57 tc_RealDef_Oreal ) }.
% 0.98/1.57 { c_Transcendental_Ocos( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 0.98/1.57 X ) ) = c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_Transcendental_Ocos
% 0.98/1.57 ( Y ) ), c_Transcendental_Ocos( X ) ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_Transcendental_Osin
% 0.98/1.57 ( Y ) ), c_Transcendental_Osin( X ) ) ) }.
% 0.98/1.57 { c_Transcendental_Ocos( c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y
% 0.98/1.57 , X ) ) = c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_Transcendental_Ocos
% 0.98/1.57 ( Y ) ), c_Transcendental_Ocos( X ) ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_Transcendental_Osin
% 0.98/1.57 ( Y ) ), c_Transcendental_Osin( X ) ) ) }.
% 0.98/1.57 { c_Transcendental_Ocos( c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y
% 0.98/1.57 , X ) ) = c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_Transcendental_Ocos
% 0.98/1.57 ( X ) ), c_Transcendental_Ocos( Y ) ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_Transcendental_Osin
% 0.98/1.57 ( X ) ), c_Transcendental_Osin( Y ) ) ) }.
% 0.98/1.57 { c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.98/1.57 c_Complex_Ocomplex_OComplex( c_Transcendental_Ocos( X ),
% 0.98/1.57 c_Transcendental_Osin( X ) ) ) = c_Groups_Oone__class_Oone(
% 0.98/1.57 tc_RealDef_Oreal ) }.
% 0.98/1.57 { c_Complex_Oii = c_Complex_Ocomplex_OComplex( c_Groups_Ozero__class_Ozero
% 0.98/1.57 ( tc_RealDef_Oreal ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.98/1.57 { ! c_Complex_Ocomplex_OComplex( Y, X ) = c_Complex_Oii, Y =
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.98/1.57 { ! c_Complex_Ocomplex_OComplex( Y, X ) = c_Complex_Oii, X =
% 0.98/1.57 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.98/1.57 { ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! X =
% 0.98/1.57 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ),
% 0.98/1.57 c_Complex_Ocomplex_OComplex( Y, X ) = c_Complex_Oii }.
% 0.98/1.57 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.98/1.57 c_Complex_Ocomplex_OComplex( Y, X ) ), c_Complex_Oii ) =
% 0.98/1.57 c_Complex_Ocomplex_OComplex( c_Groups_Ouminus__class_Ouminus(
% 0.98/1.57 tc_RealDef_Oreal, X ), Y ) }.
% 0.98/1.57 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.98/1.57 c_Complex_Oii ), c_Complex_Ocomplex_OComplex( Y, X ) ) =
% 0.98/1.57 c_Complex_Ocomplex_OComplex( c_Groups_Ouminus__class_Ouminus(
% 0.98/1.57 tc_RealDef_Oreal, X ), Y ) }.
% 0.98/1.57 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.98/1.57 c_Complex_Oii ), c_Complex_Oii ) = c_Groups_Ouminus__class_Ouminus(
% 0.98/1.57 tc_Complex_Ocomplex, c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) }
% 0.98/1.57 .
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.57 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 0.98/1.57 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) =
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.57 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) =
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ),
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) = Z }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) = Z,
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) =
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ),
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T,
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T,
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ),
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.57 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 0.98/1.57 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) =
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, T,
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 0.98/1.57 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.98/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Z =
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.98/1.57 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.98/1.57 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.98/1.57 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.98/1.57 .
% 0.98/1.57 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), T ), Z ),
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), X ) ) =
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus
% 0.98/1.57 ( tc_Nat_Onat, T, Y ) ), Z ), X ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) =
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ), T =
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! T =
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ),
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) =
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) }.
% 0.98/1.57 { ! c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) =
% 0.98/1.57 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, X,
% 0.98/1.57 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) ),
% 0.98/1.57 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, X,
% 0.98/1.57 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) ),
% 0.98/1.57 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, X, c_Complex_Oii ) ),
% 0.98/1.57 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, X, c_Complex_Oii ) )
% 0.98/1.57 , c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.98/1.57 c_RComplete_Onatceiling( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X
% 0.98/1.57 , c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) =
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatceiling( X ),
% 0.98/1.57 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.98/1.57 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ouminus__class_Ouminus( X,
% 0.98/1.57 Y ) ), c_Orderings_Oord__class_Oless( X, Y,
% 0.98/1.57 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.98/1.57 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ouminus__class_Ouminus( X,
% 0.98/1.57 Z ) ), c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.57 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.98/1.57 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.98/1.57 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 0.98/1.57 ( X, Y ), Z ) }.
% 0.98/1.57 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.98/1.57 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 0.98/1.57 ( X, Z ), Y ) }.
% 0.98/1.57 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.98/1.57 , c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.98/1.57 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, Y, Z ), c_Orderings_Oord__class_Oless(
% 0.98/1.57 X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.98/1.57 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), ! Y = X }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), Y = X,
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), Y = X }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.98/1.57 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Osqrt( Y ),
% 0.98/1.57 c_NthRoot_Osqrt( X ) ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 Y, X ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Osqrt( Y ),
% 0.98/1.57 c_NthRoot_Osqrt( X ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Osqrt( Y ),
% 0.98/1.57 c_NthRoot_Osqrt( X ) ) }.
% 0.98/1.57 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.98/1.57 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.98/1.57 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.57 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.98/1.57 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.98/1.57 , ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.98/1.57 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.57 Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.98/1.57 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.98/1.57 , ! Z = T, c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.98/1.57 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.98/1.57 ! Y = T, c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.98/1.57 { ! class_Orderings_Oorder( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless(
% 0.98/1.57 X, T, Y ), c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.98/1.57 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X
% 0.98/1.57 , Y, T ), c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.98/1.57 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.98/1.57 , ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.98/1.57 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.57 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.98/1.57 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.98/1.57 , ! Y = Z }.
% 0.98/1.57 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.98/1.57 , ! Z = Y }.
% 0.98/1.57 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.57 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.98/1.57 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.57 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.98/1.57 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.98/1.57 , ! Z = Y }.
% 0.98/1.57 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.98/1.57 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.98/1.57 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.98/1.57 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Y = Z }.
% 0.98/1.57 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.98/1.57 ), ! Y = Z, ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.98/1.57 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.98/1.57 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.98/1.57 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.98/1.57 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Z = Y }.
% 0.98/1.57 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.98/1.57 Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.98/1.57 { ! class_Orderings_Olinorder( X ), ! Z = Y, !
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.98/1.57 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.98/1.57 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.98/1.57 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.57 Y ), ! Z = Y }.
% 0.98/1.57 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.98/1.57 Z ), ! Z = Y }.
% 0.98/1.57 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.98/1.57 Y ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__idom( X ), Z = Y,
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.98/1.57 X, Y, Z ) }.
% 0.98/1.57 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.57 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.98/1.57 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, U, T ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.98/1.57 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.57 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.98/1.57 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, U, T ) }.
% 0.98/1.57 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.98/1.57 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ), c_Orderings_Oord__class_Oless
% 0.98/1.57 ( X, T, Y ) }.
% 0.98/1.57 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, T, Y ), c_Orderings_Oord__class_Oless(
% 0.98/1.57 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.98/1.57 , Y, Z ) ) }.
% 0.98/1.57 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.98/1.57 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.98/1.57 ( X, Z, Y ) }.
% 0.98/1.57 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.98/1.57 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.98/1.57 , T, Y ) ) }.
% 0.98/1.57 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.98/1.57 X, c_Groups_Oplus__class_Oplus( X, Z, T ), c_Groups_Oplus__class_Oplus( X
% 0.98/1.57 , Y, T ) ) }.
% 0.98/1.57 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.98/1.57 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.98/1.57 , T, Y ) ) }.
% 0.98/1.57 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.57 ( X, U, T ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.57 c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X, Y
% 0.98/1.57 , T ) ) }.
% 0.98/1.57 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, T )
% 0.98/1.57 , c_Groups_Oplus__class_Oplus( X, Y, T ) ), c_Orderings_Oord__class_Oless
% 0.98/1.57 ( X, Z, Y ) }.
% 0.98/1.57 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.98/1.57 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.98/1.57 ( X, Z, Y ) }.
% 0.98/1.57 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.98/1.57 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.98/1.57 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.57 , Y, Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.98/1.57 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.98/1.57 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.98/1.57 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.98/1.57 Z ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.98/1.57 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.98/1.57 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.98/1.57 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.98/1.57 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.98/1.57 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.98/1.57 , ! Z = Y }.
% 0.98/1.57 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.98/1.57 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.98/1.57 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.57 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.98/1.57 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.57 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.98/1.57 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.57 , Z, Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.98/1.57 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.98/1.57 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.98/1.57 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.98/1.57 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.98/1.57 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.98/1.57 ( X, Z, Y ) }.
% 0.98/1.57 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.98/1.57 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.98/1.57 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.98/1.57 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.98/1.57 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.98/1.57 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ), Z = Y }.
% 0.98/1.57 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.98/1.57 ), ! Z = Y, c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.98/1.57 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.98/1.57 ( X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.98/1.57 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.98/1.57 ( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.98/1.57 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.57 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.98/1.57 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.57 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.98/1.57 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.57 , Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.98/1.57 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.57 , Z, Y ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.98/1.57 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.98/1.57 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.98/1.57 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.98/1.57 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.98/1.57 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.98/1.57 , Y ), Y = Z, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.98/1.57 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.57 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.98/1.57 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.98/1.57 , ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.98/1.57 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.57 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.98/1.57 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.98/1.57 , Y ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.98/1.57 { c_RComplete_Onatceiling( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal )
% 0.98/1.57 ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.57 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_RComplete_Onatceiling( X )
% 0.98/1.57 ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 0.98/1.57 Y ), c_RComplete_Onatceiling( X ) ) }.
% 0.98/1.57 { c_RComplete_Onatceiling( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 0.98/1.57 = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.57 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.98/1.57 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP
% 0.98/1.57 ( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.57 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.98/1.57 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.98/1.57 ( c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__comm__semiring__strict( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.57 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.98/1.57 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.98/1.57 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.57 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.98/1.57 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.98/1.57 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.57 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.98/1.57 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP
% 0.98/1.57 ( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.57 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.98/1.57 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.57 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.98/1.57 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.98/1.57 ( X ) ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.57 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.57 ! c_Orderings_Oord__class_Oless( X, Z, T ), c_Orderings_Oord__class_Oless
% 0.98/1.57 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.98/1.57 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.98/1.57 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ) }
% 0.98/1.57 .
% 0.98/1.57 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.98/1.57 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.98/1.57 .
% 0.98/1.57 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.57 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.98/1.57 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.98/1.57 ( X ) ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.57 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.98/1.57 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.98/1.57 ( X ) ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.57 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.98/1.57 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.57 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.57 ! c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless
% 0.98/1.57 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.98/1.57 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha3( X, Y, Z, T ),
% 0.98/1.57 alpha9( X, Y, Z, T ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha3( X, Y, Z, T ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha9( X, Y, Z, T ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.57 { ! alpha9( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.57 { ! alpha9( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( X, T, c_Groups_Ozero__class_Ozero( X ) )
% 0.98/1.57 , ! c_Orderings_Oord__class_Oless( X, Y, Z ), alpha9( X, Y, Z, T ) }.
% 0.98/1.57 { ! alpha3( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( X ), T ) }.
% 0.98/1.57 { ! alpha3( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T )
% 0.98/1.57 , ! c_Orderings_Oord__class_Oless( X, Z, Y ), alpha3( X, Y, Z, T ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha4( X, Y, Z, T ),
% 0.98/1.57 alpha10( X, Y, Z, T ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha4( X, Y, Z, T ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha10( X, Y, Z, T ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.57 { ! alpha10( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.57 { ! alpha10( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, T ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.98/1.57 , ! c_Orderings_Oord__class_Oless( X, Y, T ), alpha10( X, Y, Z, T ) }.
% 0.98/1.57 { ! alpha4( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.98/1.57 { ! alpha4( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.98/1.57 , ! c_Orderings_Oord__class_Oless( X, T, Y ), alpha4( X, Y, Z, T ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.57 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 0.98/1.57 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.57 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.98/1.57 ) ), c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 0.98/1.57 ) ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.57 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.98/1.57 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.98/1.57 ) ) }.
% 0.98/1.57 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.57 c_Groups_Oplus__class_Oplus( X, Y, Y ) ), c_Orderings_Oord__class_Oless(
% 0.98/1.57 X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.98/1.57 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.57 c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.98/1.57 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.98/1.57 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Y
% 0.98/1.57 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.57 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.98/1.57 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.57 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.57 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.98/1.57 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.57 c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.57 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless(
% 0.98/1.57 X, T, c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.98/1.57 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.57 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.98/1.57 , c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.98/1.57 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.57 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, U )
% 0.98/1.57 , c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.98/1.57 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, U, T ), c_Orderings_Oord__class_Oless(
% 0.98/1.57 X, c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X
% 0.98/1.57 , Y, T ) ) }.
% 0.98/1.57 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.98/1.57 X, c_Groups_Ominus__class_Ominus( X, Z, Y ), c_Groups_Ozero__class_Ozero
% 0.98/1.57 ( X ) ) }.
% 0.98/1.57 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.98/1.57 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.98/1.57 , Z, Y ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.98/1.57 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.57 ( X, c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero( X ) ) }
% 0.98/1.57 .
% 0.98/1.57 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.57 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.98/1.57 ( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.57 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.57 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.57 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.98/1.57 .
% 0.98/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.57 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.98/1.57 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.98/1.57 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.98/1.57 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.98/1.57 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.98/1.57 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.57 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.98/1.57 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.57 , Y ) }.
% 0.98/1.57 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.98/1.57 , Y ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.57 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.57 ( X, c_Groups_Oone__class_Oone( X ), Z ), c_Orderings_Oord__class_Oless(
% 0.98/1.57 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.98/1.57 , Y, c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) )
% 0.98/1.57 ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.57 , c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, T, Z )
% 0.98/1.57 ), Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus
% 0.98/1.57 ( X, Z, Y ), T ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.57 , c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, T, Z )
% 0.98/1.57 ), Y ), c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus
% 0.98/1.57 ( X, Z, Y ) ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.57 , c_Groups_Ominus__class_Ominus( X, Z, Y ), T ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.98/1.57 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X,
% 0.98/1.57 c_Groups_Ominus__class_Ominus( X, T, Z ) ), Y ) }.
% 0.98/1.57 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X, Y ),
% 0.98/1.57 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.57 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.57 c_Groups_Oabs__class_Oabs( X, Y ) ), ! Y = c_Groups_Ozero__class_Ozero( X
% 0.98/1.57 ) }.
% 0.98/1.57 { ! class_Groups_Oordered__ab__group__add__abs( X ), Y =
% 0.98/1.57 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.98/1.57 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.57 c_Groups_Oabs__class_Oabs( X, Y ) = Y }.
% 0.98/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.57 , c_Groups_Oabs__class_Oabs( X, Z ), Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.57 ( X, c_Groups_Oabs__class_Oabs( X, U ), T ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 0.98/1.57 c_Groups_Oabs__class_Oabs( X, U ) ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.57 , c_Groups_Oabs__class_Oabs( X, Z ), Y ), c_Orderings_Oord__class_Oless(
% 0.98/1.57 X, Z, Y ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.57 , c_Groups_Oabs__class_Oabs( X, Z ), Y ), c_Orderings_Oord__class_Oless(
% 0.98/1.57 X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.57 , Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.98/1.57 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X, Z ), Y )
% 0.98/1.57 }.
% 0.98/1.57 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ), X =
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.98/1.57 { ! X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 0.98/1.57 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_RealVector_Onorm__class_Onorm( X, Y ), c_Groups_Ozero__class_Ozero(
% 0.98/1.57 tc_RealDef_Oreal ) ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.57 , c_Groups_Osgn__class_Osgn( X, Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.98/1.57 .
% 0.98/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.57 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.98/1.57 , c_Groups_Osgn__class_Osgn( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }
% 0.98/1.57 .
% 0.98/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.57 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.98/1.57 .
% 0.98/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.57 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X
% 0.98/1.57 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) ) }
% 0.98/1.57 .
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Opi,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.98/1.57 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Opi ) }
% 0.98/1.57 .
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ) }
% 0.98/1.57 .
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Osqrt( X ),
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Osqrt( X ),
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), ! c_NthRoot_Osqrt(
% 0.98/1.57 X ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ) }
% 0.98/1.57 .
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Osqrt( X ),
% 0.98/1.57 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.98/1.57 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.98/1.57 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Osqrt( X ),
% 0.98/1.57 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.98/1.57 c_RealDef_Opositive( c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X,
% 0.98/1.57 Y ) ) }.
% 0.98/1.57 { ! c_RealDef_Opositive( c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X
% 0.98/1.57 , Y ) ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.98/1.57 c_RComplete_Onatceiling( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.98/1.57 }.
% 0.98/1.57 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.57 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.57 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.57 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.57 ! c_Orderings_Oord__class_Oless__eq( X, Z, T ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.57 ( X, U, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.98/1.57 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.57 ( X, U, T ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.98/1.57 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.98/1.57 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.57 , U ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, U, T ), ! c_Orderings_Oord__class_Oless
% 0.98/1.57 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.98/1.57 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.57 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.98/1.57 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.98/1.57 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.98/1.57 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.57 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.98/1.57 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.98/1.57 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.98/1.57 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.98/1.57 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.57 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.98/1.57 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.98/1.57 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.57 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.57 ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.98/1.57 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.98/1.57 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.57 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.57 ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.98/1.57 ) ) }.
% 0.98/1.57 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.57 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.98/1.57 ) ) }.
% 0.98/1.57 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.57 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.57 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.57 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.98/1.57 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.57 ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.57 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.57 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.57 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.57 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.98/1.57 ) ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 0.98/1.57 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__ring__strict( X ), Z =
% 0.98/1.57 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.98/1.57 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__ring__strict( X ), Y =
% 0.98/1.57 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.98/1.57 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.57 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.98/1.57 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.98/1.57 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.57 c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ) ) }.
% 0.98/1.57 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.98/1.57 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.57 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.98/1.57 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.98/1.57 X, W, Z ) ), U ), T ), Y ) }.
% 0.98/1.57 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.98/1.57 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.57 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.98/1.57 hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.98/1.57 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.57 ( X ), Z ), U ), Y ) ) }.
% 0.98/1.57 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.98/1.57 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.57 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, hAPP
% 0.98/1.57 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus
% 0.98/1.57 ( X, Z, W ) ), U ), Y ) ) }.
% 0.98/1.57 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X, T
% 0.98/1.57 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.98/1.57 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.57 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.57 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.98/1.57 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.57 c_Groups_Oabs__class_Oabs( X, Y ) = c_Groups_Ouminus__class_Ouminus( X, Y
% 0.98/1.57 ) }.
% 0.98/1.57 { ! class_Groups_Oabs__if( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Oabs__class_Oabs( X, Y ) =
% 0.98/1.57 c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.98/1.57 { ! class_Groups_Oabs__if( X ), c_Orderings_Oord__class_Oless( X, Y,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Oabs__class_Oabs( X, Y ) = Y
% 0.98/1.57 }.
% 0.98/1.57 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.98/1.57 c_RealVector_Onorm__class_Onorm( X, Y ) ), ! Y =
% 0.98/1.57 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.57 { ! class_RealVector_Oreal__normed__vector( X ), Y =
% 0.98/1.57 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless(
% 0.98/1.57 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.98/1.57 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 0.98/1.57 = c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.57 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Groups_Osgn__class_Osgn( X, Y
% 0.98/1.57 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.57 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Groups_Osgn__class_Osgn( X, Y
% 0.98/1.57 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.57 { ! class_RealVector_Oreal__normed__algebra( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_RealVector_Onorm__class_Onorm( X, Z ), Y ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_RealVector_Onorm__class_Onorm( X, U ), T ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), T ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 0.98/1.57 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_RealVector_Onorm__class_Onorm( X, Z ), Y ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_RealVector_Onorm__class_Onorm( X, U ), T ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, Z, U
% 0.98/1.57 ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, T ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.98/1.57 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.98/1.57 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, c_Transcendental_Opi
% 0.98/1.57 ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Osin( X
% 0.98/1.57 ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.98/1.57 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) =
% 0.98/1.57 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) }.
% 0.98/1.57 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.98/1.57 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) = X }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.98/1.57 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) =
% 0.98/1.57 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) }.
% 0.98/1.57 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.98/1.57 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) = X }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs
% 0.98/1.57 ( tc_RealDef_Oreal, X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 0.98/1.57 , X ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.98/1.57 c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, X ) =
% 0.98/1.57 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling
% 0.98/1.57 ( X ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.98/1.57 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.98/1.57 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 0.98/1.57 X ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.57 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Osgn__class_Osgn( X, Y
% 0.98/1.57 ) = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) )
% 0.98/1.57 }.
% 0.98/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 0.98/1.57 = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.98/1.57 .
% 0.98/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.57 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Osgn__class_Osgn( X, Y
% 0.98/1.57 ) = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) )
% 0.98/1.57 }.
% 0.98/1.57 { ! class_Groups_Osgn__if( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.57 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.57 { ! class_Groups_Osgn__if( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.57 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.57 { ! class_Groups_Osgn__if( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.57 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.98/1.57 c_Groups_Oone__class_Oone( X ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, Y ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y,
% 0.98/1.57 c_Transcendental_Opi ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_Transcendental_Ocos( Y ), c_Transcendental_Ocos( X ) ) }.
% 0.98/1.57 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oone__class_Oone
% 0.98/1.57 ( tc_RealDef_Oreal ), c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) )
% 0.98/1.57 ) }.
% 0.98/1.57 { ! X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.98/1.57 c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, X ) =
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.98/1.57 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.98/1.57 c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, X ) =
% 0.98/1.57 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.98/1.57 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.98/1.57 c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, X ) =
% 0.98/1.57 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.98/1.57 { ! X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.98/1.57 c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, X ) =
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.98/1.57 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.98/1.57 c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, X ) =
% 0.98/1.57 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.98/1.57 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.98/1.57 c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, X ) =
% 0.98/1.57 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__semiring__1__strict( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.57 ( X, T, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( X ), U ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), W
% 0.98/1.57 ), ! c_Groups_Oplus__class_Oplus( X, U, W ) = c_Groups_Oone__class_Oone
% 0.98/1.57 ( X ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X,
% 0.98/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( X ), W ), T ) ), Y ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_Transcendental_Ocos
% 0.98/1.57 ( c_Complex_Oarg( c_Complex_Ocomplex_OComplex(
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ) ) ) =
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.98/1.57 c_Transcendental_Ocos( c_Complex_Oarg( c_Complex_Ocomplex_OComplex(
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ) ) ) =
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, c_Transcendental_Opi )
% 0.98/1.57 , X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, Y ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Ocos( X
% 0.98/1.57 ), c_Transcendental_Ocos( Y ) ) }.
% 0.98/1.57 { ! class_RealVector_Oreal__algebra__1( X ), !
% 0.98/1.57 class_RealVector_Oreal__normed__vector( X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol13( Y ) ) }.
% 0.98/1.57 { ! class_RealVector_Oreal__algebra__1( X ), !
% 0.98/1.57 class_RealVector_Oreal__normed__vector( X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.57 c_RealVector_Onorm__class_Onorm( X, c_RealVector_Oof__real( X, Y ) ),
% 0.98/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.98/1.57 c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, Y ) ), skol13( X ) ) )
% 0.98/1.57 }.
% 0.98/1.57 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol14( Y ) ) }.
% 0.98/1.57 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.57 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.98/1.57 c_RealVector_Onorm__class_Onorm( X, Y ) ),
% 0.98/1.57 c_RealVector_Onorm__class_Onorm( X, Z ) ) ), skol14( X ) ) ) }.
% 0.98/1.57 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol15( Z, T ) ) }.
% 0.98/1.57 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.57 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.98/1.57 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol15( X, Y ) ) ) }.
% 0.98/1.57 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol16( Z, T ) ) }.
% 0.98/1.57 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.57 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.98/1.57 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol16( X, Y ) ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.57 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.57 tc_Nat_Onat ), X ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.57 ( tc_Nat_Onat ), X ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 0.98/1.57 .
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X =
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.57 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.57 tc_Nat_Onat ), X ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.98/1.57 ( tc_Nat_Onat, Y, Z ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y
% 0.98/1.57 , X ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, X ) =
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.57 tc_Nat_Onat, Y, T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.98/1.57 .
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.57 tc_Nat_Onat, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.98/1.57 .
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.98/1.57 ( tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) )
% 0.98/1.57 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.57 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }
% 0.98/1.57 .
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.98/1.57 ( tc_Nat_Onat, Y, X ), X ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.98/1.57 ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.98/1.57 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.98/1.57 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.98/1.57 ( tc_Nat_Onat, Z, X ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.98/1.57 ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.98/1.57 ( tc_Nat_Onat, Y, Z ), X ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.98/1.57 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.98/1.57 X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }
% 0.98/1.57 .
% 0.98/1.57 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.98/1.57 X ), Z, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z )
% 0.98/1.57 }.
% 0.98/1.57 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.98/1.57 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z
% 0.98/1.57 ), c_Orderings_Oord__class_Oless( tc_fun( T, X ), Z, Y ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.57 ( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.57 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.57 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.98/1.57 tc_Nat_Onat, Y, X ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.57 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.98/1.57 tc_Nat_Onat, Y, X ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.57 ( tc_Nat_Onat ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.98/1.57 tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.98/1.57 tc_Nat_Onat ), X ), Y ), Z = Y }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.57 ( tc_Nat_Onat ), X ), ! Z = Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.57 ( tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.98/1.57 tc_Nat_Onat ), X ), Y ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.57 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.98/1.57 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP(
% 0.98/1.57 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.57 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 0.98/1.57 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.57 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.98/1.57 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.57 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.98/1.57 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.57 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.57 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.57 Y ), X ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.57 tc_Nat_Onat ), Z ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.57 ( tc_Nat_Onat ), Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 0.98/1.57 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.57 tc_Nat_Onat ), Y ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.57 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.98/1.57 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.57 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.98/1.57 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP
% 0.98/1.57 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.57 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.98/1.57 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP
% 0.98/1.57 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.57 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.98/1.57 ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.57 ( tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.57 tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 0.98/1.57 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) = Y }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z,
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.57 tc_Nat_Onat, Z, X ), Y ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.98/1.57 ( tc_Nat_Onat, Z, X ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z
% 0.98/1.57 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.98/1.57 ( tc_Nat_Onat, Y, Z ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z )
% 0.98/1.57 ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.98/1.57 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.98/1.57 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.98/1.57 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.98/1.57 ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.57 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP
% 0.98/1.57 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.57 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z
% 0.98/1.57 , Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.57 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X
% 0.98/1.57 ) }.
% 0.98/1.57 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.57 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 0.98/1.57 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 0.98/1.57 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.57 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 0.98/1.57 ) }.
% 0.98/1.57 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.57 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 0.98/1.57 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 0.98/1.57 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.98/1.57 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.98/1.57 , alpha5( X, Y, Z ) }.
% 0.98/1.57 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.98/1.57 , alpha11( X, Y, Z ) }.
% 0.98/1.57 { ! alpha5( X, Y, Z ), ! alpha11( X, Y, Z ), hBOOL( hAPP( Z,
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.98/1.57 { ! alpha11( X, Y, Z ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.98/1.57 T ), hBOOL( hAPP( Z, T ) ) }.
% 0.98/1.57 { ! hBOOL( hAPP( Z, skol17( T, U, Z ) ) ), alpha11( X, Y, Z ) }.
% 0.98/1.57 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, skol17( X, Y, Z ) ),
% 0.98/1.57 alpha11( X, Y, Z ) }.
% 0.98/1.57 { ! alpha5( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 0.98/1.57 , hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.98/1.57 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), alpha5( X, Y, Z ) }.
% 0.98/1.57 { ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha5
% 0.98/1.57 ( X, Y, Z ) }.
% 0.98/1.57 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.98/1.57 , ! alpha6( X, Y, Z ) }.
% 0.98/1.57 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.98/1.57 , ! alpha12( X, Y, Z ) }.
% 0.98/1.57 { alpha6( X, Y, Z ), alpha12( X, Y, Z ), hBOOL( hAPP( Z,
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.98/1.57 { ! alpha12( X, Y, Z ), ! hBOOL( hAPP( Z, skol18( T, U, Z ) ) ) }.
% 0.98/1.57 { ! alpha12( X, Y, Z ), Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.98/1.57 skol18( X, Y, Z ) ) }.
% 0.98/1.57 { ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, T ), hBOOL( hAPP( Z, T
% 0.98/1.57 ) ), alpha12( X, Y, Z ) }.
% 0.98/1.57 { ! alpha6( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }
% 0.98/1.57 .
% 0.98/1.57 { ! alpha6( X, Y, Z ), ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero(
% 0.98/1.57 tc_Nat_Onat ) ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), hBOOL( hAPP( Z,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha6( X, Y, Z ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.57 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 0.98/1.57 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T,
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T,
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.57 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 0.98/1.57 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.57 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 0.98/1.57 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.57 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.57 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.57 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 0.98/1.57 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.98/1.57 c_RComplete_Onatfloor( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 0.98/1.57 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) =
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatfloor( X ),
% 0.98/1.57 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.98/1.57 tc_Nat_Onat, Y ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.98/1.57 tc_RealDef_Oreal, X, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.98/1.57 c_RealDef_Oreal( tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone(
% 0.98/1.57 tc_RealDef_Oreal ) ) ), c_RComplete_Onatceiling( X ) =
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone(
% 0.98/1.57 tc_Nat_Onat ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, Z ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol19( T, U, W ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, Z ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, T ) ), skol19( X, Y,
% 0.98/1.57 Z ) ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, T ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, Z ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, T ) ), skol19( X, Y,
% 0.98/1.57 Z ) ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, T, Z ) }.
% 0.98/1.57 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.98/1.57 tc_Nat_Onat, X ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.98/1.57 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.98/1.57 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 0.98/1.57 { alpha14( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.98/1.57 hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.98/1.57 { alpha14( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP
% 0.98/1.57 ( X, Y ), Z ) ) }.
% 0.98/1.57 { ! alpha14( X, Y, Z ), alpha17( X, Y, Z ), Z = Y }.
% 0.98/1.57 { ! alpha14( X, Y, Z ), alpha17( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z
% 0.98/1.57 ) ) }.
% 0.98/1.57 { ! alpha17( X, Y, Z ), alpha14( X, Y, Z ) }.
% 0.98/1.57 { ! Z = Y, hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha14( X, Y, Z ) }.
% 0.98/1.57 { ! alpha17( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y )
% 0.98/1.57 }.
% 0.98/1.57 { ! alpha17( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP(
% 0.98/1.57 X, Y ), Z ) ), alpha17( X, Y, Z ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X = Y }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.98/1.57 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.98/1.57 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.98/1.57 tc_Nat_Onat, Y ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.57 c_RComplete_Onatfloor( X ), Y ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_RComplete_Onatfloor
% 0.98/1.57 ( X ) ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.57 c_RealDef_Oreal( tc_Nat_Onat, Y ), X ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.98/1.57 tc_Nat_Onat, Y ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.98/1.57 , c_RComplete_Onatfloor( X ) ) }.
% 0.98/1.57 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.98/1.57 tc_Nat_Onat, c_RComplete_Onatfloor( X ) ), c_Groups_Oone__class_Oone(
% 0.98/1.57 tc_RealDef_Oreal ) ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.98/1.57 tc_Nat_Onat, Y ), X ), c_RComplete_Onatfloor(
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.98/1.57 tc_Nat_Onat, Y ) ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.98/1.57 c_RComplete_Onatfloor( X ), Y ) }.
% 0.98/1.57 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X,
% 0.98/1.57 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), c_RealDef_Oreal(
% 0.98/1.57 tc_Nat_Onat, c_RComplete_Onatfloor( X ) ) ) }.
% 0.98/1.57 { c_RealDef_Oreal( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.98/1.57 ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.98/1.57 { ! c_RealDef_Oreal( tc_Nat_Onat, X ) = c_Groups_Ozero__class_Ozero(
% 0.98/1.57 tc_RealDef_Oreal ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.57 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_RealDef_Oreal(
% 0.98/1.57 tc_Nat_Onat, X ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.98/1.57 tc_Nat_Onat, X ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.98/1.57 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.98/1.57 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 0.98/1.57 { c_RealDef_Oreal( tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.98/1.57 tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.98/1.57 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ), c_RealDef_Oreal
% 0.98/1.57 ( tc_Nat_Onat, X ) ) }.
% 0.98/1.57 { c_RealDef_Oreal( tc_Nat_Onat, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y
% 0.98/1.57 , X ) ) = c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal
% 0.98/1.57 ( tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.98/1.57 c_RComplete_Onatfloor( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 0.98/1.57 c_RealDef_Oreal( tc_Nat_Onat, Y ) ) ) = c_Groups_Oplus__class_Oplus(
% 0.98/1.57 tc_Nat_Onat, c_RComplete_Onatfloor( X ), Y ) }.
% 0.98/1.57 { c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, c_RealDef_Oreal( tc_Nat_Onat
% 0.98/1.57 , X ) ) = c_RealDef_Oreal( tc_Nat_Onat, X ) }.
% 0.98/1.57 { ! c_RealDef_Oreal( tc_Nat_Onat, Y ) = c_RealDef_Oreal( tc_Nat_Onat, X ),
% 0.98/1.57 Y = X }.
% 0.98/1.57 { ! Y = X, c_RealDef_Oreal( tc_Nat_Onat, Y ) = c_RealDef_Oreal( tc_Nat_Onat
% 0.98/1.57 , X ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.98/1.57 tc_Nat_Onat, c_RComplete_Onatfloor( X ) ), X ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.98/1.57 tc_Nat_Onat, Y ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.98/1.57 , c_RComplete_Onatfloor( X ) ) }.
% 0.98/1.57 { c_RComplete_Onatceiling( c_RealDef_Oreal( tc_Nat_Onat, X ) ) = X }.
% 0.98/1.57 { c_RComplete_Onatfloor( c_RealDef_Oreal( tc_Nat_Onat, X ) ) = X }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatfloor( Y ),
% 0.98/1.57 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, c_RealDef_Oreal(
% 0.98/1.57 tc_Nat_Onat, X ) ) }.
% 0.98/1.57 { c_RealDef_Oreal( tc_Nat_Onat, c_Groups_Oone__class_Oone( tc_Nat_Onat ) )
% 0.98/1.57 = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.98/1.57 tc_Nat_Onat, Y ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal
% 0.98/1.57 , X, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.98/1.57 tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ),
% 0.98/1.57 c_RComplete_Onatfloor( X ) = Y }.
% 0.98/1.57 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.98/1.57 tc_Nat_Onat, c_RComplete_Onatceiling( X ) ) ) }.
% 0.98/1.57 { c_RComplete_Onatfloor( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) )
% 0.98/1.57 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.57 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) )
% 0.98/1.57 }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatfloor( Y
% 0.98/1.57 ), c_RComplete_Onatfloor( X ) ) }.
% 0.98/1.57 { c_RComplete_Onatfloor( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) =
% 0.98/1.57 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.98/1.57 tc_Nat_Onat, X ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X =
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.57 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.98/1.57 tc_Nat_Onat, X ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.98/1.57 tc_Nat_Onat, X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.57 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.98/1.57 tc_Nat_Onat, X ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.98/1.57 tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.98/1.57 c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.98/1.57 tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.98/1.57 c_RealDef_Oreal( tc_Nat_Onat, X ) ), c_Orderings_Oord__class_Oless(
% 0.98/1.57 tc_Nat_Onat, Y, X ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), c_RealDef_Oreal
% 0.98/1.57 ( tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.98/1.57 tc_Nat_Onat, X ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, c_RealDef_Oreal
% 0.98/1.57 ( tc_Nat_Onat, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.57 c_RComplete_Onatceiling( Y ), X ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_RComplete_Onatfloor
% 0.98/1.57 ( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.98/1.57 tc_Nat_Onat, Y ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.98/1.57 c_RealDef_Oreal( tc_Nat_Onat, X ), c_Groups_Oone__class_Oone(
% 0.98/1.57 tc_RealDef_Oreal ) ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.98/1.57 tc_Nat_Onat, Y ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.98/1.57 c_RealDef_Oreal( tc_Nat_Onat, X ), c_Groups_Oone__class_Oone(
% 0.98/1.57 tc_RealDef_Oreal ) ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.98/1.57 , X ) }.
% 0.98/1.57 { c_Transcendental_Osin( hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.98/1.57 tc_RealDef_Oreal ), c_Transcendental_Opi ), c_RealDef_Oreal( tc_Nat_Onat
% 0.98/1.57 , X ) ) ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.98/1.57 { c_Transcendental_Osin( hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.98/1.57 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, X ) ),
% 0.98/1.57 c_Transcendental_Opi ) ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal
% 0.98/1.57 ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 0.98/1.57 X ), Y ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.98/1.57 c_RealDef_Oreal( tc_Nat_Onat, Y ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.98/1.57 tc_Nat_Onat, Y ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.57 c_RComplete_Onatceiling( X ), Y ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.98/1.57 tc_Nat_Onat, Y ), X ), c_RComplete_Onatceiling(
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.98/1.57 tc_Nat_Onat, Y ) ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.98/1.57 c_RComplete_Onatceiling( X ), Y ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.57 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Groups_Oone__class_Oone
% 0.98/1.57 ( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.98/1.57 c_RComplete_Onatceiling( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X
% 0.98/1.57 , c_RealDef_Oreal( tc_Nat_Onat, Y ) ) ) = c_Groups_Oplus__class_Oplus(
% 0.98/1.57 tc_Nat_Onat, c_RComplete_Onatceiling( X ), Y ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_RComplete_Onatfloor( X )
% 0.98/1.57 ), c_RComplete_Onatfloor( Y ) ), c_RComplete_Onatfloor( hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.98/1.57 tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, skol20( X ),
% 0.98/1.57 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ), X ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.98/1.57 tc_Nat_Onat, skol20( X ) ) ) }.
% 0.98/1.57 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.98/1.57 hAPP( X, Y ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol21( Z, Y
% 0.98/1.57 ), Y ) }.
% 0.98/1.57 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.98/1.57 hAPP( X, Y ) ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.98/1.57 skol21( X, Y ) ), ! hBOOL( hAPP( X, Z ) ) }.
% 0.98/1.57 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.98/1.57 hAPP( X, Y ) ), hBOOL( hAPP( X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat
% 0.98/1.57 , skol21( X, Y ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, Z ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol22( T, U, W ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, Z ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, T ) ), skol22( X, Y,
% 0.98/1.57 Z ) ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, T ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, Z ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, T ) ), skol22( X, Y,
% 0.98/1.57 Z ) ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, T, Z ) }.
% 0.98/1.57 { ! class_RealVector_Oreal__normed__vector( Y ), ! class_Orderings_Oord( X
% 0.98/1.57 ), c_Orderings_Oord__class_Oless__eq( X, T, skol23( X, U, W, T ) ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( X, T, V0 ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, V0 ) ),
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oone__class_Oone
% 0.98/1.57 ( tc_RealDef_Oreal ), c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, T ) )
% 0.98/1.57 ) ) }.
% 0.98/1.57 { ! class_RealVector_Oreal__normed__vector( Y ), ! class_Orderings_Oord( X
% 0.98/1.57 ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_RealVector_Onorm__class_Onorm( Y, c_Groups_Ominus__class_Ominus( Y,
% 0.98/1.57 hAPP( Z, T ), hAPP( Z, skol23( X, Y, Z, T ) ) ) ),
% 0.98/1.57 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( X, T, U ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, U ) ),
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oone__class_Oone
% 0.98/1.57 ( tc_RealDef_Oreal ), c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, T ) )
% 0.98/1.57 ) ) }.
% 0.98/1.57 { ! class_Orderings_Oorder( X ), ! c_SEQ_Odecseq( X, Y ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, T ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, T ), hAPP( Y, Z ) ) }.
% 0.98/1.57 { ! class_Orderings_Oorder( X ), c_Orderings_Oord__class_Oless__eq(
% 0.98/1.57 tc_Nat_Onat, skol24( X, Y ), skol45( X, Y ) ), c_SEQ_Odecseq( X, Y ) }.
% 0.98/1.57 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.57 hAPP( Y, skol45( X, Y ) ), hAPP( Y, skol24( X, Y ) ) ), c_SEQ_Odecseq( X
% 0.98/1.57 , Y ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.98/1.57 tc_Nat_Onat, Y ) ), X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 0.98/1.57 , hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 0.98/1.57 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ), Y ) ) }.
% 0.98/1.57 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.57 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.98/1.57 c_Power_Opower__class_Opower( X ), Z ), Y ) ), hAPP( hAPP(
% 0.98/1.57 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.98/1.57 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) ) }.
% 0.98/1.57 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.57 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.57 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.98/1.57 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.98/1.57 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.57 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.98/1.57 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.98/1.57 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) }.
% 0.98/1.57 { ! class_RealVector_Oreal__algebra__1( X ), c_RealVector_Oof__real( X,
% 0.98/1.57 hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Z ), Y ) )
% 0.98/1.57 = hAPP( hAPP( c_Power_Opower__class_Opower( X ), c_RealVector_Oof__real(
% 0.98/1.57 X, Z ) ), Y ) }.
% 0.98/1.57 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 0.98/1.57 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.98/1.57 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.57 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.98/1.57 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) }.
% 0.98/1.57 { c_NthRoot_Osqrt( hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.98/1.57 tc_RealDef_Oreal ), Y ), X ) ) = hAPP( hAPP( c_Power_Opower__class_Opower
% 0.98/1.57 ( tc_RealDef_Oreal ), c_NthRoot_Osqrt( Y ) ), X ) }.
% 0.98/1.57 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.57 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.98/1.57 tc_Nat_Onat ) ) = Y }.
% 0.98/1.57 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.57 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.98/1.57 c_Power_Opower__class_Opower( X ), T ), Y ) ) = hAPP( hAPP(
% 0.98/1.57 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.98/1.57 tc_Nat_Onat, Z, Y ) ) }.
% 0.98/1.57 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.57 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ozero__class_Ozero(
% 0.98/1.57 tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.57 { ! class_Power_Opower( X ), ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 0.98/1.57 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) =
% 0.98/1.57 c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.57 { ! class_Power_Opower( X ), Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.98/1.57 , hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) = hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.98/1.57 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ominus__class_Ominus(
% 0.98/1.57 tc_Nat_Onat, Z, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 0.98/1.57 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.57 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), hAPP( hAPP
% 0.98/1.57 ( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.57 c_Power_Opower__class_Opower( X ), Z ), c_Groups_Ominus__class_Ominus(
% 0.98/1.57 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ), Z ) =
% 0.98/1.57 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.57 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( X ), Z ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.57 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), T ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.57 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.98/1.57 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.57 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.57 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 0.98/1.57 hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.57 ( tc_Int_Oint ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint )
% 0.98/1.57 , c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) ), X ) ), ! Y =
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X =
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.57 { Y = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.57 tc_Int_Oint ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ),
% 0.98/1.57 c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) ), X ) ) }.
% 0.98/1.57 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.57 tc_Int_Oint ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ),
% 0.98/1.57 c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) ), X ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.57 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.98/1.57 ( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Z ), hAPP( hAPP
% 0.98/1.57 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.57 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.98/1.57 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), X =
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.57 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.57 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.98/1.57 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.57 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.98/1.57 ), X ) ) }.
% 0.98/1.57 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.98/1.57 c_RealDef_Oreal( tc_Nat_Onat, Y ) ), X ) = c_RealDef_Oreal( tc_Nat_Onat,
% 0.98/1.57 hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.98/1.57 { c_RealDef_Oreal( tc_Nat_Onat, hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.98/1.57 tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.98/1.57 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ), X ) }.
% 0.98/1.57 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ),
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) = hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.98/1.57 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 0.98/1.57 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ) }.
% 0.98/1.57 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ),
% 0.98/1.57 c_RealVector_Oof__real( tc_Complex_Ocomplex, Y ) ), X ) =
% 0.98/1.57 c_RealVector_Oof__real( tc_Complex_Ocomplex, hAPP( hAPP(
% 0.98/1.57 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.98/1.57 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP( hAPP(
% 0.98/1.57 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 0.98/1.57 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.98/1.57 { ! X = c_RealDef_Oreal( tc_Nat_Onat, c_RComplete_Onatfloor( X ) ),
% 0.98/1.57 c_RComplete_Onatfloor( hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.98/1.57 tc_RealDef_Oreal ), X ), Y ) ) = hAPP( hAPP( c_Power_Opower__class_Opower
% 0.98/1.57 ( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ), Y ) }.
% 0.98/1.57 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ),
% 0.98/1.57 c_Complex_Ocis( Y ) ), X ) = c_Complex_Ocis( hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.98/1.57 tc_Nat_Onat, X ) ), Y ) ) }.
% 0.98/1.57 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.57 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) =
% 0.98/1.57 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.98/1.57 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.57 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) = hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 0.98/1.57 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ),
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 0.98/1.57 ( tc_Nat_Onat ) ) ) ) }.
% 0.98/1.57 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ),
% 0.98/1.57 c_Complex_Orcis( Z, Y ) ), X ) = c_Complex_Orcis( hAPP( hAPP(
% 0.98/1.57 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.98/1.57 tc_Nat_Onat, X ) ), Y ) ) }.
% 0.98/1.57 { ! class_Rings_Oring__1__no__zero__divisors( X ), Y =
% 0.98/1.57 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.98/1.57 c_Power_Opower__class_Opower( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 0.98/1.57 ( X ) }.
% 0.98/1.57 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.98/1.57 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.57 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.98/1.57 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.98/1.57 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.57 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.98/1.57 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.98/1.57 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.98/1.57 c_Power_Opower__class_Opower( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.98/1.57 = c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.57 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.98/1.57 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.57 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.98/1.57 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, hAPP
% 0.98/1.57 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.57 c_Power_Opower__class_Opower( X ), c_Groups_Oabs__class_Oabs( X, Z ) ), Y
% 0.98/1.57 ) }.
% 0.98/1.57 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.98/1.57 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.98/1.57 tc_Nat_Onat ) ) = Y }.
% 0.98/1.57 { ! class_Rings_Olinordered__semidom( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.57 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.98/1.57 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__semidom( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.98/1.57 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.57 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.98/1.57 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.57 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless
% 0.98/1.57 ( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.98/1.57 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__semidom( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 0.98/1.57 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.98/1.57 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.98/1.57 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.98/1.57 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.98/1.57 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.98/1.57 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.98/1.57 .
% 0.98/1.57 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.98/1.57 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.98/1.57 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.98/1.57 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.57 tc_Nat_Onat ) }.
% 0.98/1.57 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.98/1.57 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.98/1.57 , ! Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 0.98/1.57 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y )
% 0.98/1.57 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.57 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! hAPP( hAPP(
% 0.98/1.57 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.98/1.57 c_Power_Opower__class_Opower( X ), Y ), Z ), T = Z }.
% 0.98/1.57 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.57 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! T = Z, hAPP( hAPP(
% 0.98/1.57 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.98/1.57 c_Power_Opower__class_Opower( X ), Y ), Z ) }.
% 0.98/1.57 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.98/1.57 , Y ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.98/1.57 c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.57 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.98/1.57 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.98/1.57 tc_Nat_Onat, Z, Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.98/1.57 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.98/1.57 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, hAPP
% 0.98/1.57 ( hAPP( c_Power_Opower__class_Opower( X ),
% 0.98/1.57 c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) ) =
% 0.98/1.57 c_Groups_Oabs__class_Oabs( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.98/1.57 ), Z ), Y ) ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.57 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP
% 0.98/1.57 ( c_Power_Opower__class_Opower( X ), Y ), T ) ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.57 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.57 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.98/1.57 X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.98/1.57 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.57 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.98/1.57 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.98/1.57 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.98/1.57 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), ! Y =
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.57 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.98/1.57 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.57 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), Y =
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.57 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.98/1.57 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__idom( X ), c_Orderings_Oord__class_Oless__eq(
% 0.98/1.57 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.98/1.57 c_Power_Opower__class_Opower( X ), c_Groups_Oabs__class_Oabs( X, Z ) ), Y
% 0.98/1.57 ) ) }.
% 0.98/1.57 { ! class_Rings_Oring__1( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.98/1.57 ), c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.57 c_Power_Opower__class_Opower( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.98/1.57 c_Groups_Oone__class_Oone( X ) ) ), Y ) ), hAPP( hAPP(
% 0.98/1.57 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.57 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.57 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.98/1.57 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.57 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.57 ( tc_Nat_Onat, T, Z ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.57 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.98/1.57 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.57 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.57 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.98/1.57 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.57 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.98/1.57 c_Groups_Oone__class_Oone( X ), T ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.57 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.57 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__semidom( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), T )
% 0.98/1.57 , c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.57 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.57 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.57 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.98/1.57 c_Power_Opower__class_Opower( X ), Y ), Z ) ), hAPP( hAPP(
% 0.98/1.57 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.57 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.57 , T, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.57 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.98/1.57 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 0.98/1.57 c_Power_Opower__class_Opower( X ), T ), Z ) = hAPP( hAPP(
% 0.98/1.57 c_Power_Opower__class_Opower( X ), Y ), Z ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.98/1.57 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.98/1.57 X ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ), T = Y }.
% 0.98/1.57 { ! class_Rings_Olinordered__semidom( X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.98/1.57 ), ! c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oone__class_Oone
% 0.98/1.57 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.57 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.98/1.57 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.57 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.57 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.98/1.57 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.57 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.57 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.98/1.57 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.98/1.57 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.57 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.57 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.98/1.57 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.98/1.57 { X = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), Y =
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Orderings_Oord__class_Oless
% 0.98/1.57 ( tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex
% 0.98/1.57 , c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex,
% 0.98/1.57 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), X ), hAPP( hAPP(
% 0.98/1.57 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), skol25( X, Y ) ), Y
% 0.98/1.57 ) ) ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.98/1.57 { ! class_Power_Opower( X ), c_Power_Opower__class_Opower( X ) =
% 0.98/1.57 c_Power_Opower_Opower( X, c_Groups_Oone__class_Oone( X ),
% 0.98/1.57 c_Groups_Otimes__class_Otimes( X ) ) }.
% 0.98/1.57 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.98/1.57 c_Power_Opower__class_Opower( tc_Int_Oint ), c_Groups_Oabs__class_Oabs(
% 0.98/1.57 tc_Int_Oint, Y ) ), X ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Groups_Oabs__class_Oabs(
% 0.98/1.57 tc_Int_Oint, X ) = c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) }.
% 0.98/1.57 { c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Groups_Oabs__class_Oabs(
% 0.98/1.57 tc_Int_Oint, X ) = X }.
% 0.98/1.57 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y = X,
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), ! Y = X }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), Y = X,
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Z ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.98/1.57 tc_Int_Oint, Y, T ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.98/1.57 .
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.98/1.57 tc_Int_Oint, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.98/1.57 .
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.57 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 0.98/1.57 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP
% 0.98/1.57 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.57 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.57 tc_Int_Oint ), X ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.57 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.57 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 0.98/1.57 ( tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.98/1.57 .
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 0.98/1.57 ( tc_Int_Oint ) ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.98/1.57 tc_Int_Oint ) ), X ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.57 tc_Int_Oint ), c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.98/1.57 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.98/1.57 ( tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.98/1.57 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.98/1.57 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.98/1.57 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.98/1.57 tc_Int_Oint ) ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X )
% 0.98/1.57 }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.98/1.57 tc_Int_Oint ) ), X ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.98/1.57 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X )
% 0.98/1.57 }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.98/1.57 tc_Int_Oint ) ) ) }.
% 0.98/1.57 { ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.98/1.57 c_Groups_Osgn__class_Osgn( tc_Int_Oint, X ) = c_Groups_Ozero__class_Ozero
% 0.98/1.57 ( tc_Int_Oint ) }.
% 0.98/1.57 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.57 tc_Int_Oint ), X ), c_Groups_Osgn__class_Osgn( tc_Int_Oint, X ) =
% 0.98/1.57 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.98/1.57 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.57 tc_Int_Oint ), X ), c_Groups_Osgn__class_Osgn( tc_Int_Oint, X ) =
% 0.98/1.57 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Oone__class_Oone(
% 0.98/1.57 tc_Int_Oint ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oabs__class_Oabs(
% 0.98/1.57 tc_Int_Oint, X ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X =
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.98/1.57 { ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oabs__class_Oabs(
% 0.98/1.57 tc_Int_Oint, X ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ominus__class_Ominus
% 0.98/1.57 ( tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ),
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.98/1.57 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.57 tc_Int_Oint ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.57 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.98/1.57 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), X =
% 0.98/1.57 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.57 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.98/1.57 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), Y =
% 0.98/1.57 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.57 ( tc_Int_Oint ), X ), ! X = c_Groups_Oone__class_Oone( tc_Int_Oint ), ! Y
% 0.98/1.57 = c_Groups_Oone__class_Oone( tc_Int_Oint ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 0.98/1.57 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.98/1.57 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y
% 0.98/1.57 = X }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.98/1.57 tc_Int_Oint ) ) ) }.
% 0.98/1.57 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.98/1.57 tc_Int_Oint ) ) ) }.
% 0.98/1.57 { ! c_Groups_Oabs__class_Oabs( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) =
% 0.98/1.57 c_Groups_Oone__class_Oone( tc_Int_Oint ), c_Groups_Oabs__class_Oabs(
% 0.98/1.57 tc_Int_Oint, X ) = c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.98/1.57 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ), X ) =
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.98/1.57 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ) =
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.98/1.57 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 0.98/1.57 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = X }.
% 0.98/1.57 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.98/1.57 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) = X }.
% 0.98/1.57 { ! c_Groups_Ozero__class_Ozero( tc_Int_Oint ) = c_Groups_Oone__class_Oone
% 0.98/1.57 ( tc_Int_Oint ) }.
% 0.98/1.57 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.98/1.57 tc_Int_Oint, c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ) =
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.98/1.57 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.98/1.57 ( tc_Int_Oint, X ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.98/1.57 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero
% 0.98/1.57 ( tc_Int_Oint ) ) = X }.
% 0.98/1.57 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.57 tc_Int_Oint ), X ) = X }.
% 0.98/1.57 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.98/1.57 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ), X ) =
% 0.98/1.57 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.98/1.57 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) =
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.98/1.57 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ), X ) =
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.98/1.57 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP(
% 0.98/1.57 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.98/1.57 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) = hAPP
% 0.98/1.57 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) }.
% 0.98/1.57 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.57 ( tc_Int_Oint ) ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.98/1.57 { hAPP( hAPP( c_Power_Opower_Opower( T, Z, Y ), X ),
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = Z }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.57 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Z,
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Groups_Oplus__class_Oplus
% 0.98/1.57 ( tc_Int_Oint, c_Groups_Oabs__class_Oabs( tc_Int_Oint,
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, Z ) ),
% 0.98/1.57 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ), X ) ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.57 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Groups_Oplus__class_Oplus
% 0.98/1.57 ( tc_Int_Oint, c_Groups_Oabs__class_Oabs( tc_Int_Oint,
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ),
% 0.98/1.57 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ), X ) ), Y ) }.
% 0.98/1.57 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint,
% 0.98/1.57 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) = X }.
% 0.98/1.57 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, X ) }.
% 0.98/1.57 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Z ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, Z ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ), Y = X }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ),
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.98/1.57 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) =
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) }.
% 0.98/1.57 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus
% 0.98/1.57 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.98/1.57 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.98/1.57 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 0.98/1.57 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.98/1.57 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.98/1.57 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ),
% 0.98/1.57 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.98/1.57 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) =
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.98/1.57 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.98/1.57 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.98/1.57 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.98/1.57 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.57 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.98/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oone__class_Oone
% 0.98/1.57 ( tc_Int_Oint ), Y ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.57 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.98/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.98/1.57 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.98/1.57 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.98/1.57 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.98/1.57 ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, T, W ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.57 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.98/1.57 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, U ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, Z ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, T ) }.
% 0.98/1.57 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.98/1.57 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.98/1.57 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.57 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.98/1.57 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, U, Y ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 0.98/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, U ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, U ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Y ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.98/1.57 ( tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.98/1.57 Z ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.57 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.98/1.57 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.98/1.57 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.57 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.98/1.57 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.57 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.98/1.57 , Y ), X ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.57 tc_Nat_Onat ), Y ) }.
% 0.98/1.57 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.57 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.98/1.57 ), X ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.57 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.57 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.98/1.57 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Ozero__class_Ozero(
% 0.98/1.57 tc_Int_Oint ) ) }.
% 0.98/1.57 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 0.98/1.57 tc_Int_Oint ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.98/1.57 tc_Int_Oint, X, Y ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.98/1.57 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ominus__class_Ominus(
% 0.98/1.57 tc_Int_Oint, X, Y ) }.
% 0.98/1.57 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.98/1.57 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint
% 0.98/1.57 ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.57 ( tc_Int_Oint ), X ), hBOOL( hAPP( Y, skol26( Z, Y ) ) ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! hBOOL( hAPP( Y, U ) )
% 0.98/1.57 , hBOOL( hAPP( Y, c_Groups_Ominus__class_Ominus( tc_Int_Oint, U, hAPP(
% 0.98/1.57 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), T ), X ) ) ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.57 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( Y, c_Groups_Ominus__class_Ominus(
% 0.98/1.57 tc_Int_Oint, skol26( X, Y ), X ) ) ), ! c_Orderings_Oord__class_Oless__eq
% 0.98/1.57 ( tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), ! hBOOL(
% 0.98/1.57 hAPP( Y, T ) ), hBOOL( hAPP( Y, c_Groups_Ominus__class_Ominus(
% 0.98/1.57 tc_Int_Oint, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 0.98/1.57 , Z ), X ) ) ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Nat__Transfer_Otsub( X, Y )
% 0.98/1.57 ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.98/1.57 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ominus__class_Ominus(
% 0.98/1.57 tc_Int_Oint, X, Y ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.57 ( tc_Int_Oint ), X ), hBOOL( hAPP( Y, skol27( Z, Y ) ) ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! hBOOL( hAPP( Y, U ) )
% 0.98/1.57 , hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, hAPP( hAPP
% 0.98/1.57 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), T ), X ) ) ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.57 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus(
% 0.98/1.57 tc_Int_Oint, skol27( X, Y ), X ) ) ), ! c_Orderings_Oord__class_Oless__eq
% 0.98/1.57 ( tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), ! hBOOL(
% 0.98/1.57 hAPP( Y, T ) ), hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus( tc_Int_Oint
% 0.98/1.57 , T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) )
% 0.98/1.57 ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.57 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol28( Z, T ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.57 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), hAPP( hAPP(
% 0.98/1.57 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), skol28( X, Y ) ), X ) =
% 0.98/1.57 Y }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.57 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol29( Z, T ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.57 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), hAPP( hAPP(
% 0.98/1.57 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), skol29( X, Y ) ), X ) =
% 0.98/1.57 Y }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.57 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), ! hAPP( hAPP(
% 0.98/1.57 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Z ), X ) = Y, Z =
% 0.98/1.57 skol29( X, Y ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.98/1.57 c_Transcendental_Oln( hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.98/1.57 tc_RealDef_Oreal ), X ), Y ) ) = hAPP( hAPP(
% 0.98/1.57 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.98/1.57 tc_Nat_Onat, Y ) ), c_Transcendental_Oln( X ) ) }.
% 0.98/1.57 { c_Transcendental_Oln( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) =
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 0.98/1.57 ), X ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.98/1.57 c_Transcendental_Oln( X ) = c_Transcendental_Oln( Y ), X = Y }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), ! X = Y,
% 0.98/1.57 c_Transcendental_Oln( X ) = c_Transcendental_Oln( Y ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 0.98/1.57 ), c_Transcendental_Oln( Y ) ), c_Orderings_Oord__class_Oless(
% 0.98/1.57 tc_RealDef_Oreal, X, Y ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, Y ),
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 0.98/1.57 ), c_Transcendental_Oln( Y ) ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_Transcendental_Oln
% 0.98/1.57 ( X ), c_Transcendental_Oln( Y ) ), c_Orderings_Oord__class_Oless__eq(
% 0.98/1.57 tc_RealDef_Oreal, X, Y ) }.
% 0.98/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.98/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.98/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ),
% 0.98/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_Transcendental_Oln
% 0.98/1.58 ( X ), c_Transcendental_Oln( Y ) ) }.
% 0.98/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.58 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 0.98/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 0.98/1.58 ) ) }.
% 0.98/1.58 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 0.98/1.58 ) ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.98/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.58 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 0.98/1.58 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.98/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.98/1.58 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.98/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 0.98/1.58 ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.98/1.58 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.98/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 0.98/1.58 ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.98/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.98/1.58 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.98/1.58 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.98/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.98/1.58 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.98/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 0.98/1.58 ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.98/1.58 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.98/1.58 c_Transcendental_Oln( X ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal
% 0.98/1.58 ), X = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.98/1.58 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), ! X =
% 0.98/1.58 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_Transcendental_Oln( X )
% 0.98/1.58 = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.98/1.58 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.98/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 0.98/1.58 ) ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.58 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 0.98/1.58 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.98/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.58 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 0.98/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 0.98/1.58 ) ) }.
% 0.98/1.58 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.58 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 0.98/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 0.98/1.58 ) ) }.
% 0.98/1.58 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.98/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 0.98/1.58 ) ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.58 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 0.98/1.58 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.98/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.58 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 0.98/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 0.98/1.58 ) ) }.
% 0.98/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 0.98/1.58 ) ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.98/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.58 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 0.98/1.58 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.98/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.98/1.58 c_Transcendental_Oln( hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.98/1.58 tc_RealDef_Oreal ), X ), Y ) ) = c_Groups_Oplus__class_Oplus(
% 0.98/1.58 tc_RealDef_Oreal, c_Transcendental_Oln( X ), c_Transcendental_Oln( Y ) )
% 0.98/1.58 }.
% 0.98/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.98/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_Transcendental_Oln
% 0.98/1.58 ( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.98/1.58 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) ), X ) }.
% 0.98/1.58 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.98/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol30( Z, T ) ) }.
% 0.98/1.58 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.98/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.58 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, Z ) ), skol30( X, Y ) ) }.
% 0.98/1.58 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.98/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), !
% 0.98/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.58 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol46( X, Y, Z ) ) ), Z ),
% 0.98/1.58 c_SEQ_OBseq( X, Y ) }.
% 0.98/1.58 { ! class_Orderings_Oorder( X ), ! c_SEQ_Oincseq( X, Y ), !
% 0.98/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, T ),
% 0.98/1.58 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, Z ), hAPP( Y, T ) ) }.
% 0.98/1.58 { ! class_Orderings_Oorder( X ), c_Orderings_Oord__class_Oless__eq(
% 0.98/1.58 tc_Nat_Onat, skol31( X, Y ), skol47( X, Y ) ), c_SEQ_Oincseq( X, Y ) }.
% 0.98/1.58 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.58 hAPP( Y, skol31( X, Y ) ), hAPP( Y, skol47( X, Y ) ) ), c_SEQ_Oincseq( X
% 0.98/1.58 , Y ) }.
% 0.98/1.58 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.98/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol32( Z, T ) ) }.
% 0.98/1.58 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.98/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.58 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, hAPP
% 0.98/1.58 ( Y, Z ), c_Groups_Ouminus__class_Ouminus( X, skol48( X, Y ) ) ) ),
% 0.98/1.58 skol32( X, Y ) ) }.
% 0.98/1.58 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.98/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), !
% 0.98/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.58 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, hAPP
% 0.98/1.58 ( Y, skol50( X, Y, Z, T ) ), c_Groups_Ouminus__class_Ouminus( X, T ) ) )
% 0.98/1.58 , Z ), c_SEQ_OBseq( X, Y ) }.
% 0.98/1.58 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.98/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol33( Z, T ) ) }.
% 0.98/1.58 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.98/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.58 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, hAPP
% 0.98/1.58 ( Y, Z ), c_Groups_Ouminus__class_Ouminus( X, hAPP( Y, skol49( X, Y ) ) )
% 0.98/1.58 ) ), skol33( X, Y ) ) }.
% 0.98/1.58 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.98/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), !
% 0.98/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.58 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, hAPP
% 0.98/1.58 ( Y, skol51( X, Y, Z, T ) ), c_Groups_Ouminus__class_Ouminus( X, hAPP( Y
% 0.98/1.58 , T ) ) ) ), Z ), c_SEQ_OBseq( X, Y ) }.
% 0.98/1.58 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.98/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol34( Z, T ) ) }.
% 0.98/1.58 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.98/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.58 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, Z ) ), skol34( X, Y ) ) }.
% 0.98/1.58 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.98/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.98/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.58 c_RealVector_Onorm__class_Onorm( X, hAPP( Z, skol35( X, Y, Z ) ) ), Y ),
% 0.98/1.58 c_SEQ_OBseq( X, Z ) }.
% 0.98/1.58 { alpha15( X, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP(
% 0.98/1.58 X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Z ), !
% 0.98/1.58 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z, hAPP( X, Y ) ),
% 0.98/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, skol36( T, Y, U ), Y ) }
% 0.98/1.58 .
% 0.98/1.58 { alpha15( X, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP(
% 0.98/1.58 X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Z ), !
% 0.98/1.58 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z, hAPP( X, Y ) ), hAPP(
% 0.98/1.58 X, skol36( X, Y, Z ) ) = Z }.
% 0.98/1.58 { ! alpha15( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol37( Z
% 0.98/1.58 , Y ), Y ) }.
% 0.98/1.58 { ! alpha15( X, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.58 c_Groups_Oabs__class_Oabs( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 0.98/1.58 tc_Int_Oint, hAPP( X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, skol37( X
% 0.98/1.58 , Y ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ), hAPP( X, skol37( X,
% 0.98/1.58 Y ) ) ) ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.98/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ),
% 0.98/1.58 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oabs__class_Oabs
% 0.98/1.58 ( tc_Int_Oint, c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( X,
% 0.98/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, c_Groups_Oone__class_Oone(
% 0.98/1.58 tc_Nat_Onat ) ) ), hAPP( X, Z ) ) ), c_Groups_Oone__class_Oone(
% 0.98/1.58 tc_Int_Oint ) ), alpha15( X, Y ) }.
% 0.98/1.58 { alpha16( X, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP(
% 0.98/1.58 X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Z ), !
% 0.98/1.58 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z, hAPP( X, Y ) ),
% 0.98/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, skol38( T, Y, U ), Y ) }
% 0.98/1.58 .
% 0.98/1.58 { alpha16( X, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP(
% 0.98/1.58 X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Z ), !
% 0.98/1.58 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z, hAPP( X, Y ) ), hAPP(
% 0.98/1.58 X, skol38( X, Y, Z ) ) = Z }.
% 0.98/1.58 { ! alpha16( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol39( Z
% 0.98/1.58 , Y ), Y ) }.
% 0.98/1.58 { ! alpha16( X, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.58 c_Groups_Oabs__class_Oabs( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 0.98/1.58 tc_Int_Oint, hAPP( X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, skol39( X
% 0.98/1.58 , Y ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ), hAPP( X, skol39( X,
% 0.98/1.58 Y ) ) ) ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.98/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ),
% 0.98/1.58 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oabs__class_Oabs
% 0.98/1.58 ( tc_Int_Oint, c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( X,
% 0.98/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, c_Groups_Oone__class_Oone(
% 0.98/1.58 tc_Nat_Onat ) ) ), hAPP( X, Z ) ) ), c_Groups_Oone__class_Oone(
% 0.98/1.58 tc_Int_Oint ) ), alpha16( X, Y ) }.
% 0.98/1.58 { c_Transcendental_Osin( hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.98/1.58 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ), X ) ) =
% 0.98/1.58 c_Complex_OIm( hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.98/1.58 tc_Complex_Ocomplex ), c_Complex_Ocis( X ) ), Y ) ) }.
% 0.98/1.58 { c_Transcendental_Ocos( hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.98/1.58 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ), X ) ) =
% 0.98/1.58 c_Complex_ORe( hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.98/1.58 tc_Complex_Ocomplex ), c_Complex_Ocis( X ) ), Y ) ) }.
% 0.98/1.58 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.58 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, c_Complex_OIm( X ) ),
% 0.98/1.58 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) }.
% 0.98/1.58 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.58 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.98/1.58 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, Y, X ) ),
% 0.98/1.58 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs
% 0.98/1.58 ( tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.98/1.58 c_Complex_ORe( Y ), c_Complex_ORe( X ) ) ), c_Groups_Oabs__class_Oabs(
% 0.98/1.58 tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.98/1.58 c_Complex_OIm( Y ), c_Complex_OIm( X ) ) ) ) ) }.
% 0.98/1.58 { c_Complex_ORe( c_Complex_Oii ) = c_Groups_Ozero__class_Ozero(
% 0.98/1.58 tc_RealDef_Oreal ) }.
% 0.98/1.58 { c_Complex_OIm( c_RealVector_Oof__real( tc_Complex_Ocomplex, X ) ) =
% 0.98/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.98/1.58 { c_Complex_ORe( c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) =
% 0.98/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.98/1.58 { c_Complex_OIm( c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) =
% 0.98/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.98/1.58 { c_Complex_ORe( c_Complex_Ocomplex_OComplex( Y, X ) ) = Y }.
% 0.98/1.58 { c_Complex_OIm( c_Complex_Ocomplex_OComplex( Y, X ) ) = X }.
% 0.98/1.58 { c_Complex_ORe( c_RealVector_Oof__real( tc_Complex_Ocomplex, X ) ) = X }.
% 0.98/1.58 { ! c_Complex_ORe( Y ) = c_Complex_ORe( X ), ! c_Complex_OIm( Y ) =
% 0.98/1.58 c_Complex_OIm( X ), Y = X }.
% 0.98/1.58 { ! Y = X, c_Complex_ORe( Y ) = c_Complex_ORe( X ) }.
% 0.98/1.58 { ! Y = X, c_Complex_OIm( Y ) = c_Complex_OIm( X ) }.
% 0.98/1.58 { ! c_Complex_ORe( Y ) = c_Complex_ORe( X ), ! c_Complex_OIm( Y ) =
% 0.98/1.58 c_Complex_OIm( X ), Y = X }.
% 0.98/1.58 { c_Complex_Ocomplex_OComplex( c_Complex_ORe( X ), c_Complex_OIm( X ) ) = X
% 0.98/1.58 }.
% 0.98/1.58 { c_Complex_OIm( c_Complex_Ocis( X ) ) = c_Transcendental_Osin( X ) }.
% 0.98/1.58 { c_Complex_ORe( c_Complex_Ocis( X ) ) = c_Transcendental_Ocos( X ) }.
% 0.98/1.58 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_Complex_ORe( X ),
% 0.98/1.58 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) }.
% 0.98/1.58 { c_Complex_OIm( c_Complex_Oii ) = c_Groups_Oone__class_Oone(
% 0.98/1.58 tc_RealDef_Oreal ) }.
% 0.98/1.58 { c_Complex_ORe( c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X ) )
% 0.98/1.58 = c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Complex_ORe( Y ),
% 0.98/1.58 c_Complex_ORe( X ) ) }.
% 0.98/1.58 { c_Complex_OIm( c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X ) )
% 0.98/1.58 = c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Complex_OIm( Y ),
% 0.98/1.58 c_Complex_OIm( X ) ) }.
% 0.98/1.58 { c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, X ) =
% 0.98/1.58 c_Complex_Ocomplex_OComplex( c_Groups_Ouminus__class_Ouminus(
% 0.98/1.58 tc_RealDef_Oreal, c_Complex_ORe( X ) ), c_Groups_Ouminus__class_Ouminus(
% 0.98/1.58 tc_RealDef_Oreal, c_Complex_OIm( X ) ) ) }.
% 0.98/1.58 { c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X ) =
% 0.98/1.58 c_Complex_Ocomplex_OComplex( c_Groups_Oplus__class_Oplus(
% 0.98/1.58 tc_RealDef_Oreal, c_Complex_ORe( Y ), c_Complex_ORe( X ) ),
% 0.98/1.58 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Complex_OIm( Y ),
% 0.98/1.58 c_Complex_OIm( X ) ) ) }.
% 0.98/1.58 { c_Complex_OIm( c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, X )
% 0.98/1.58 ) = c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, c_Complex_OIm( X
% 0.98/1.58 ) ) }.
% 0.98/1.58 { c_Complex_ORe( c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, X )
% 0.98/1.58 ) = c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, c_Complex_ORe( X
% 0.98/1.58 ) ) }.
% 0.98/1.58 { c_Complex_OIm( c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, Y, X )
% 0.98/1.58 ) = c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, c_Complex_OIm( Y )
% 0.98/1.58 , c_Complex_OIm( X ) ) }.
% 0.98/1.58 { c_Complex_ORe( c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, Y, X )
% 0.98/1.58 ) = c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, c_Complex_ORe( Y )
% 0.98/1.58 , c_Complex_ORe( X ) ) }.
% 0.98/1.58 { c_Complex_ORe( c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) =
% 0.98/1.58 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.98/1.58 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), Y ), X
% 0.98/1.58 ) = c_Complex_Ocomplex_OComplex( c_Groups_Ominus__class_Ominus(
% 0.98/1.58 tc_RealDef_Oreal, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.98/1.58 tc_RealDef_Oreal ), c_Complex_ORe( Y ) ), c_Complex_ORe( X ) ), hAPP(
% 0.98/1.58 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_Complex_OIm( Y
% 0.98/1.58 ) ), c_Complex_OIm( X ) ) ), c_Groups_Oplus__class_Oplus(
% 0.98/1.58 tc_RealDef_Oreal, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.98/1.58 tc_RealDef_Oreal ), c_Complex_ORe( Y ) ), c_Complex_OIm( X ) ), hAPP(
% 0.98/1.58 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_Complex_OIm( Y
% 0.98/1.58 ) ), c_Complex_ORe( X ) ) ) ) }.
% 0.98/1.58 { c_Complex_OIm( hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.98/1.58 tc_Complex_Ocomplex ), Y ), X ) ) = c_Groups_Oplus__class_Oplus(
% 0.98/1.58 tc_RealDef_Oreal, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.98/1.58 tc_RealDef_Oreal ), c_Complex_ORe( Y ) ), c_Complex_OIm( X ) ), hAPP(
% 0.98/1.58 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_Complex_OIm( Y
% 0.98/1.58 ) ), c_Complex_ORe( X ) ) ) }.
% 0.98/1.58 { c_Complex_ORe( hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.98/1.58 tc_Complex_Ocomplex ), Y ), X ) ) = c_Groups_Ominus__class_Ominus(
% 0.98/1.58 tc_RealDef_Oreal, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.98/1.58 tc_RealDef_Oreal ), c_Complex_ORe( Y ) ), c_Complex_ORe( X ) ), hAPP(
% 0.98/1.58 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_Complex_OIm( Y
% 0.98/1.58 ) ), c_Complex_OIm( X ) ) ) }.
% 0.98/1.58 { c_Complex_OIm( c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) =
% 0.98/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.98/1.58 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.58 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, c_Complex_ORe( X ) ),
% 0.98/1.58 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) }.
% 0.98/1.58 { c_Complex_OIm( c_Complex_Orcis( Y, X ) ) = hAPP( hAPP(
% 0.98/1.58 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ),
% 0.98/1.58 c_Transcendental_Osin( X ) ) }.
% 0.98/1.58 { c_Complex_ORe( c_Complex_Orcis( Y, X ) ) = hAPP( hAPP(
% 0.98/1.58 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ),
% 0.98/1.58 c_Transcendental_Ocos( X ) ) }.
% 0.98/1.58 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol40 ) }.
% 0.98/1.58 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.58 c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, c_Complex_OIm( X ) ),
% 0.98/1.58 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.98/1.58 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ), skol40 ) ) }
% 0.98/1.58 .
% 0.98/1.58 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol41 ) }.
% 0.98/1.58 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.58 c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, c_Complex_ORe( X ) ),
% 0.98/1.58 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.98/1.58 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ), skol41 ) ) }
% 0.98/1.58 .
% 0.98/1.58 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol42 ) }.
% 0.98/1.58 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.58 c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, c_Complex_OIm( X ) ),
% 0.98/1.58 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.98/1.58 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ), skol42 ) ) }
% 0.98/1.58 .
% 0.98/1.58 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol43 ) }.
% 0.98/1.58 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.58 c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, c_Complex_ORe( X ) ),
% 0.98/1.58 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.98/1.58 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ), skol43 ) ) }
% 0.98/1.58 .
% 0.98/1.58 { c_Complex_Oexpi( X ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.98/1.58 tc_Complex_Ocomplex ), c_RealVector_Oof__real( tc_Complex_Ocomplex,
% 0.98/1.58 c_Transcendental_Oexp( tc_RealDef_Oreal, c_Complex_ORe( X ) ) ) ),
% 0.98/1.58 c_Complex_Ocis( c_Complex_OIm( X ) ) ) }.
% 0.98/1.58 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.58 c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, c_Complex_OIm( X ) ),
% 0.98/1.58 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.98/1.58 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ), skol44 ) ) }
% 0.98/1.58 .
% 0.98/1.58 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.98/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oexp(
% 0.98/1.58 tc_RealDef_Oreal, Y ), c_Transcendental_Oexp( tc_RealDef_Oreal, X ) ) }.
% 0.98/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.58 c_Transcendental_Oexp( tc_RealDef_Oreal, X ), c_Groups_Oone__class_Oone(
% 0.98/1.58 tc_RealDef_Oreal ) ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal
% 0.98/1.58 , X, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.98/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.98/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.98/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.58 c_Transcendental_Oexp( tc_RealDef_Oreal, X ), c_Groups_Oone__class_Oone(
% 0.98/1.58 tc_RealDef_Oreal ) ) }.
% 0.98/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.58 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_Transcendental_Oexp(
% 0.98/1.58 tc_RealDef_Oreal, X ) ), c_Orderings_Oord__class_Oless__eq(
% 0.98/1.58 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ) }
% 0.98/1.58 .
% 0.98/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.98/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.58 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_Transcendental_Oexp(
% 0.98/1.58 tc_RealDef_Oreal, X ) ) }.
% 0.98/1.58 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oexp(
% 0.98/1.58 tc_RealDef_Oreal, X ) ) }.
% 0.98/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.58 c_Transcendental_Oexp( tc_RealDef_Oreal, X ), c_Groups_Ozero__class_Ozero
% 0.98/1.58 ( tc_RealDef_Oreal ) ) }.
% 0.98/1.58 { ! c_Transcendental_Oexp( tc_RealDef_Oreal, X ) =
% 0.98/1.58 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X =
% 0.98/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.98/1.58 { ! X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.98/1.58 c_Transcendental_Oexp( tc_RealDef_Oreal, X ) = c_Groups_Oone__class_Oone
% 0.98/1.58 ( tc_RealDef_Oreal ) }.
% 0.98/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.58 c_Transcendental_Oexp( tc_RealDef_Oreal, Y ), c_Transcendental_Oexp(
% 0.98/1.58 tc_RealDef_Oreal, X ) ), c_Orderings_Oord__class_Oless__eq(
% 0.98/1.58 tc_RealDef_Oreal, Y, X ) }.
% 0.98/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.98/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.58 c_Transcendental_Oexp( tc_RealDef_Oreal, Y ), c_Transcendental_Oexp(
% 0.98/1.58 tc_RealDef_Oreal, X ) ) }.
% 0.98/1.58 { ! class_RealVector_Oreal__normed__field( X ), ! class_SEQ_Obanach( X ),
% 0.98/1.58 c_Transcendental_Oexp( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.98/1.58 c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.58 { ! class_RealVector_Oreal__normed__field( X ), ! class_SEQ_Obanach( X ),
% 0.98/1.58 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Transcendental_Oexp( X
% 0.98/1.58 , Z ) ), c_Transcendental_Oexp( X, Y ) ) = c_Transcendental_Oexp( X,
% 0.98/1.58 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.98/1.58 { ! class_RealVector_Oreal__normed__field( X ), ! class_SEQ_Obanach( X ),
% 0.98/1.58 c_Transcendental_Oexp( X, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = hAPP
% 0.98/1.58 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Transcendental_Oexp( X, Z )
% 0.98/1.58 ), c_Transcendental_Oexp( X, Y ) ) }.
% 0.98/1.58 { ! class_RealVector_Oreal__normed__field( X ), ! class_SEQ_Obanach( X ),
% 0.98/1.58 c_Transcendental_Oexp( X, c_RealVector_Oof__real( X, Y ) ) =
% 0.98/1.58 c_RealVector_Oof__real( X, c_Transcendental_Oexp( tc_RealDef_Oreal, Y ) )
% 0.98/1.58 }.
% 0.98/1.58 { ! c_Transcendental_Oexp( tc_RealDef_Oreal, Y ) = c_Transcendental_Oexp(
% 0.98/1.58 tc_RealDef_Oreal, X ), Y = X }.
% 0.98/1.58 { ! Y = X, c_Transcendental_Oexp( tc_RealDef_Oreal, Y ) =
% 0.98/1.58 c_Transcendental_Oexp( tc_RealDef_Oreal, X ) }.
% 0.98/1.58 { ! class_RealVector_Oreal__normed__field( X ), ! class_SEQ_Obanach( X ), !
% 0.98/1.58 c_Transcendental_Oexp( X, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.58 { c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, c_Transcendental_Oexp(
% 0.98/1.58 tc_RealDef_Oreal, X ) ) = c_Transcendental_Oexp( tc_RealDef_Oreal, X ) }
% 0.98/1.58 .
% 0.98/1.58 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oexp
% 0.98/1.58 ( tc_RealDef_Oreal, X ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal )
% 0.98/1.58 ) }.
% 0.98/1.58 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oexp(
% 0.98/1.58 tc_RealDef_Oreal, X ) ) }.
% 0.98/1.58 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oexp
% 0.98/1.58 ( tc_RealDef_Oreal, Y ), c_Transcendental_Oexp( tc_RealDef_Oreal, X ) ),
% 0.98/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ) }.
% 0.98/1.58 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.98/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oexp(
% 0.98/1.58 tc_RealDef_Oreal, Y ), c_Transcendental_Oexp( tc_RealDef_Oreal, X ) ) }.
% 0.98/1.58 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oexp
% 0.98/1.58 ( tc_RealDef_Oreal, Y ), c_Transcendental_Oexp( tc_RealDef_Oreal, X ) ),
% 0.98/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ) }.
% 0.98/1.58 { ! c_Transcendental_Oexp( tc_RealDef_Oreal, Y ) = X, c_Transcendental_Oln
% 0.98/1.58 ( X ) = Y }.
% 0.98/1.58 { ! c_Transcendental_Oexp( tc_RealDef_Oreal, Y ) = X, c_Transcendental_Oln
% 0.98/1.58 ( X ) = Y }.
% 0.98/1.58 { c_Transcendental_Oln( c_Transcendental_Oexp( tc_RealDef_Oreal, X ) ) = X
% 0.98/1.58 }.
% 0.98/1.58 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.58 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_Transcendental_Oexp(
% 0.98/1.58 tc_RealDef_Oreal, X ) ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal
% 0.98/1.58 , c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ) }.
% 0.98/1.58 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.98/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.58 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_Transcendental_Oexp(
% 0.98/1.58 tc_RealDef_Oreal, X ) ) }.
% 0.98/1.58 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oexp
% 0.98/1.58 ( tc_RealDef_Oreal, X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 0.98/1.58 , c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.98/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.98/1.58 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.98/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.98/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oexp(
% 0.98/1.58 tc_RealDef_Oreal, X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }
% 0.98/1.58 .
% 0.98/1.58 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.98/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.58 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_Transcendental_Oexp(
% 0.98/1.58 tc_RealDef_Oreal, X ) ) }.
% 0.98/1.58 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.98/1.58 c_Transcendental_Oexp( tc_RealDef_Oreal, c_Transcendental_Oln( X ) ) = X
% 0.98/1.58 }.
% 0.98/1.58 { ! c_Transcendental_Oexp( tc_RealDef_Oreal, c_Transcendental_Oln( X ) ) =
% 0.98/1.58 X, c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ) }.
% 0.98/1.58 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.98/1.58 c_Transcendental_Oexp( tc_RealDef_Oreal, c_Transcendental_Oln( X ) ) = X
% 0.98/1.58 }.
% 0.98/1.58 { ! class_Lattices_Oboolean__algebra( X ), class_Lattices_Oboolean__algebra
% 0.98/1.58 ( tc_fun( Y, X ) ) }.
% 0.98/1.58 { ! class_Orderings_Opreorder( X ), class_Orderings_Opreorder( tc_fun( Y, X
% 0.98/1.58 ) ) }.
% 0.98/1.58 { ! class_Orderings_Oorder( X ), class_Orderings_Oorder( tc_fun( Y, X ) ) }
% 0.98/1.58 .
% 0.98/1.58 { ! class_Orderings_Oord( X ), class_Orderings_Oord( tc_fun( Y, X ) ) }.
% 0.98/1.58 { ! class_Groups_Ouminus( X ), class_Groups_Ouminus( tc_fun( Y, X ) ) }.
% 0.98/1.58 { ! class_Groups_Ominus( X ), class_Groups_Ominus( tc_fun( Y, X ) ) }.
% 0.98/1.58 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.98/1.58 tc_Int_Oint ) }.
% 0.98/1.58 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.98/1.58 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Int_Oint ) }.
% 0.98/1.58 { class_Rings_Olinordered__comm__semiring__strict( tc_Int_Oint ) }.
% 0.98/1.58 { class_Rings_Olinordered__semiring__1__strict( tc_Int_Oint ) }.
% 0.98/1.58 { class_Rings_Olinordered__semiring__strict( tc_Int_Oint ) }.
% 0.98/1.58 { class_Groups_Oordered__ab__semigroup__add( tc_Int_Oint ) }.
% 0.98/1.58 { class_Groups_Oordered__ab__group__add__abs( tc_Int_Oint ) }.
% 0.98/1.58 { class_Groups_Oordered__comm__monoid__add( tc_Int_Oint ) }.
% 0.98/1.58 { class_Groups_Olinordered__ab__group__add( tc_Int_Oint ) }.
% 0.98/1.58 { class_Groups_Ocancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.98/1.58 { class_Rings_Oring__1__no__zero__divisors( tc_Int_Oint ) }.
% 0.98/1.58 { class_Rings_Oordered__cancel__semiring( tc_Int_Oint ) }.
% 0.98/1.58 { class_Rings_Olinordered__ring__strict( tc_Int_Oint ) }.
% 0.98/1.58 { class_Rings_Oring__no__zero__divisors( tc_Int_Oint ) }.
% 0.98/1.58 { class_Rings_Oordered__comm__semiring( tc_Int_Oint ) }.
% 0.98/1.58 { class_Rings_Olinordered__semiring__1( tc_Int_Oint ) }.
% 0.98/1.58 { class_Groups_Oordered__ab__group__add( tc_Int_Oint ) }.
% 0.98/1.58 { class_Groups_Ocancel__semigroup__add( tc_Int_Oint ) }.
% 0.98/1.58 { class_Rings_Olinordered__semiring( tc_Int_Oint ) }.
% 0.98/1.58 { class_Rings_Olinordered__semidom( tc_Int_Oint ) }.
% 0.98/1.58 { class_Groups_Oab__semigroup__mult( tc_Int_Oint ) }.
% 0.98/1.58 { class_Groups_Ocomm__monoid__mult( tc_Int_Oint ) }.
% 0.98/1.58 { class_Groups_Oab__semigroup__add( tc_Int_Oint ) }.
% 0.98/1.58 { class_Rings_Oordered__semiring( tc_Int_Oint ) }.
% 0.98/1.58 { class_Rings_Oordered__ring__abs( tc_Int_Oint ) }.
% 0.98/1.58 { class_Rings_Ono__zero__divisors( tc_Int_Oint ) }.
% 0.98/1.58 { class_Groups_Ocomm__monoid__add( tc_Int_Oint ) }.
% 0.98/1.58 { class_Rings_Olinordered__ring( tc_Int_Oint ) }.
% 0.98/1.58 { class_Rings_Olinordered__idom( tc_Int_Oint ) }.
% 0.98/1.58 { class_Rings_Ocomm__semiring__1( tc_Int_Oint ) }.
% 0.98/1.58 { class_Rings_Ocomm__semiring( tc_Int_Oint ) }.
% 0.98/1.58 { class_Groups_Oab__group__add( tc_Int_Oint ) }.
% 0.98/1.58 { class_Rings_Ozero__neq__one( tc_Int_Oint ) }.
% 0.98/1.58 { class_Rings_Oordered__ring( tc_Int_Oint ) }.
% 0.98/1.58 { class_Orderings_Opreorder( tc_Int_Oint ) }.
% 0.98/1.58 { class_Orderings_Olinorder( tc_Int_Oint ) }.
% 0.98/1.58 { class_Groups_Omonoid__mult( tc_Int_Oint ) }.
% 0.98/1.58 { class_Rings_Ocomm__ring__1( tc_Int_Oint ) }.
% 0.98/1.58 { class_Groups_Omonoid__add( tc_Int_Oint ) }.
% 0.98/1.58 { class_Rings_Osemiring__0( tc_Int_Oint ) }.
% 0.98/1.58 { class_Groups_Ogroup__add( tc_Int_Oint ) }.
% 0.98/1.58 { class_Rings_Omult__zero( tc_Int_Oint ) }.
% 0.98/1.58 { class_Orderings_Oorder( tc_Int_Oint ) }.
% 0.98/1.58 { class_Rings_Osemiring( tc_Int_Oint ) }.
% 0.98/1.58 { class_Orderings_Oord( tc_Int_Oint ) }.
% 0.98/1.58 { class_Groups_Ouminus( tc_Int_Oint ) }.
% 0.98/1.58 { class_Groups_Osgn__if( tc_Int_Oint ) }.
% 0.98/1.58 { class_Groups_Oabs__if( tc_Int_Oint ) }.
% 0.98/1.58 { class_Rings_Oring__1( tc_Int_Oint ) }.
% 0.98/1.58 { class_Groups_Ominus( tc_Int_Oint ) }.
% 0.98/1.58 { class_Power_Opower( tc_Int_Oint ) }.
% 0.98/1.58 { class_Groups_Ozero( tc_Int_Oint ) }.
% 0.98/1.58 { class_Rings_Oring( tc_Int_Oint ) }.
% 0.98/1.58 { class_Rings_Oidom( tc_Int_Oint ) }.
% 0.98/1.58 { class_Groups_Oone( tc_Int_Oint ) }.
% 0.98/1.58 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.98/1.58 tc_Nat_Onat ) }.
% 0.98/1.58 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.98/1.58 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Nat_Onat ) }.
% 0.98/1.58 { class_Rings_Olinordered__comm__semiring__strict( tc_Nat_Onat ) }.
% 0.98/1.58 { class_Rings_Olinordered__semiring__strict( tc_Nat_Onat ) }.
% 0.98/1.58 { class_Groups_Oordered__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.98/1.58 { class_Groups_Oordered__comm__monoid__add( tc_Nat_Onat ) }.
% 0.98/1.58 { class_Groups_Ocancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.98/1.58 { class_Rings_Oordered__cancel__semiring( tc_Nat_Onat ) }.
% 0.98/1.58 { class_Rings_Oordered__comm__semiring( tc_Nat_Onat ) }.
% 0.98/1.58 { class_Groups_Ocancel__semigroup__add( tc_Nat_Onat ) }.
% 0.98/1.58 { class_Rings_Olinordered__semiring( tc_Nat_Onat ) }.
% 0.98/1.58 { class_Rings_Olinordered__semidom( tc_Nat_Onat ) }.
% 0.98/1.58 { class_Groups_Oab__semigroup__mult( tc_Nat_Onat ) }.
% 0.98/1.58 { class_Groups_Ocomm__monoid__mult( tc_Nat_Onat ) }.
% 0.98/1.58 { class_Groups_Oab__semigroup__add( tc_Nat_Onat ) }.
% 0.98/1.58 { class_Rings_Oordered__semiring( tc_Nat_Onat ) }.
% 0.98/1.58 { class_Rings_Ono__zero__divisors( tc_Nat_Onat ) }.
% 0.98/1.58 { class_Groups_Ocomm__monoid__add( tc_Nat_Onat ) }.
% 0.98/1.58 { class_Rings_Ocomm__semiring__1( tc_Nat_Onat ) }.
% 0.98/1.58 { class_Rings_Ocomm__semiring( tc_Nat_Onat ) }.
% 0.98/1.58 { class_Rings_Ozero__neq__one( tc_Nat_Onat ) }.
% 0.98/1.58 { class_Orderings_Opreorder( tc_Nat_Onat ) }.
% 0.98/1.58 { class_Orderings_Olinorder( tc_Nat_Onat ) }.
% 0.98/1.58 { class_Groups_Omonoid__mult( tc_Nat_Onat ) }.
% 0.98/1.58 { class_Groups_Omonoid__add( tc_Nat_Onat ) }.
% 0.98/1.58 { class_Rings_Osemiring__0( tc_Nat_Onat ) }.
% 0.98/1.58 { class_Rings_Omult__zero( tc_Nat_Onat ) }.
% 0.98/1.58 { class_Orderings_Oorder( tc_Nat_Onat ) }.
% 0.98/1.58 { class_Rings_Osemiring( tc_Nat_Onat ) }.
% 0.98/1.58 { class_Orderings_Oord( tc_Nat_Onat ) }.
% 0.98/1.58 { class_Groups_Ominus( tc_Nat_Onat ) }.
% 0.98/1.58 { class_Power_Opower( tc_Nat_Onat ) }.
% 0.98/1.58 { class_Groups_Ozero( tc_Nat_Onat ) }.
% 0.98/1.58 { class_Groups_Oone( tc_Nat_Onat ) }.
% 0.98/1.58 { class_Lattices_Oboolean__algebra( tc_HOL_Obool ) }.
% 0.98/1.58 { class_Orderings_Opreorder( tc_HOL_Obool ) }.
% 0.98/1.58 { class_Orderings_Oorder( tc_HOL_Obool ) }.
% 0.98/1.58 { class_Orderings_Oord( tc_HOL_Obool ) }.
% 0.98/1.58 { class_Groups_Ouminus( tc_HOL_Obool ) }.
% 0.98/1.58 { class_Groups_Ominus( tc_HOL_Obool ) }.
% 0.98/1.58 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.98/1.58 tc_RealDef_Oreal ) }.
% 0.98/1.58 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.98/1.58 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_RealDef_Oreal ) }
% 0.98/1.58 .
% 0.98/1.58 { class_Rings_Olinordered__comm__semiring__strict( tc_RealDef_Oreal ) }.
% 0.98/1.58 { class_Rings_Olinordered__semiring__1__strict( tc_RealDef_Oreal ) }.
% 0.98/1.58 { class_RealVector_Oreal__normed__div__algebra( tc_RealDef_Oreal ) }.
% 0.98/1.58 { class_Rings_Olinordered__semiring__strict( tc_RealDef_Oreal ) }.
% 0.98/1.58 { class_RealVector_Oreal__normed__algebra__1( tc_RealDef_Oreal ) }.
% 0.98/1.58 { class_Groups_Oordered__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.98/1.58 { class_Groups_Oordered__ab__group__add__abs( tc_RealDef_Oreal ) }.
% 0.98/1.58 { class_RealVector_Oreal__normed__algebra( tc_RealDef_Oreal ) }.
% 0.98/1.58 { class_Groups_Oordered__comm__monoid__add( tc_RealDef_Oreal ) }.
% 0.98/1.58 { class_Groups_Olinordered__ab__group__add( tc_RealDef_Oreal ) }.
% 0.98/1.58 { class_Groups_Ocancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.98/1.58 { class_Rings_Oring__1__no__zero__divisors( tc_RealDef_Oreal ) }.
% 0.98/1.58 { class_Rings_Oordered__cancel__semiring( tc_RealDef_Oreal ) }.
% 0.98/1.58 { class_RealVector_Oreal__normed__vector( tc_RealDef_Oreal ) }.
% 0.98/1.58 { class_Rings_Olinordered__ring__strict( tc_RealDef_Oreal ) }.
% 0.98/1.58 { class_RealVector_Oreal__normed__field( tc_RealDef_Oreal ) }.
% 0.98/1.58 { class_Rings_Oring__no__zero__divisors( tc_RealDef_Oreal ) }.
% 0.98/1.58 { class_Rings_Oordered__comm__semiring( tc_RealDef_Oreal ) }.
% 0.98/1.58 { class_Rings_Olinordered__semiring__1( tc_RealDef_Oreal ) }.
% 0.98/1.58 { class_Groups_Oordered__ab__group__add( tc_RealDef_Oreal ) }.
% 0.98/1.58 { class_Groups_Ocancel__semigroup__add( tc_RealDef_Oreal ) }.
% 0.98/1.58 { class_Rings_Olinordered__semiring( tc_RealDef_Oreal ) }.
% 0.98/1.58 { class_RealVector_Oreal__algebra__1( tc_RealDef_Oreal ) }.
% 0.98/1.58 { class_Rings_Olinordered__semidom( tc_RealDef_Oreal ) }.
% 0.98/1.58 { class_Groups_Oab__semigroup__mult( tc_RealDef_Oreal ) }.
% 0.98/1.58 { class_Groups_Ocomm__monoid__mult( tc_RealDef_Oreal ) }.
% 0.98/1.58 { class_Groups_Oab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.98/1.58 { class_Rings_Oordered__semiring( tc_RealDef_Oreal ) }.
% 0.98/1.58 { class_Rings_Oordered__ring__abs( tc_RealDef_Oreal ) }.
% 0.98/1.58 { class_Rings_Ono__zero__divisors( tc_RealDef_Oreal ) }.
% 0.98/1.58 { class_Groups_Ocomm__monoid__add( tc_RealDef_Oreal ) }.
% 0.98/1.58 { class_Rings_Olinordered__ring( tc_RealDef_Oreal ) }.
% 0.98/1.58 { class_Rings_Olinordered__idom( tc_RealDef_Oreal ) }.
% 0.98/1.58 { class_Rings_Ocomm__semiring__1( tc_RealDef_Oreal ) }.
% 0.98/1.58 { class_Rings_Ocomm__semiring( tc_RealDef_Oreal ) }.
% 0.98/1.58 { class_Groups_Oab__group__add( tc_RealDef_Oreal ) }.
% 0.98/1.58 { class_Rings_Ozero__neq__one( tc_RealDef_Oreal ) }.
% 0.98/1.58 { class_Rings_Oordered__ring( tc_RealDef_Oreal ) }.
% 0.98/1.58 { class_Orderings_Opreorder( tc_RealDef_Oreal ) }.
% 0.98/1.58 { class_Orderings_Olinorder( tc_RealDef_Oreal ) }.
% 0.98/1.58 { class_Groups_Omonoid__mult( tc_RealDef_Oreal ) }.
% 0.98/1.58 { class_Rings_Ocomm__ring__1( tc_RealDef_Oreal ) }.
% 0.98/1.58 { class_Groups_Omonoid__add( tc_RealDef_Oreal ) }.
% 0.98/1.58 { class_Rings_Osemiring__0( tc_RealDef_Oreal ) }.
% 0.98/1.58 { class_Groups_Ogroup__add( tc_RealDef_Oreal ) }.
% 0.98/1.58 { class_Rings_Omult__zero( tc_RealDef_Oreal ) }.
% 0.98/1.58 { class_Orderings_Oorder( tc_RealDef_Oreal ) }.
% 0.98/1.58 { class_Rings_Osemiring( tc_RealDef_Oreal ) }.
% 0.98/1.58 { class_Orderings_Oord( tc_RealDef_Oreal ) }.
% 0.98/1.58 { class_Groups_Ouminus( tc_RealDef_Oreal ) }.
% 0.98/1.58 { class_Groups_Osgn__if( tc_RealDef_Oreal ) }.
% 0.98/1.58 { class_Groups_Oabs__if( tc_RealDef_Oreal ) }.
% 0.98/1.58 { class_Rings_Oring__1( tc_RealDef_Oreal ) }.
% 0.98/1.58 { class_Groups_Ominus( tc_RealDef_Oreal ) }.
% 0.98/1.58 { class_Power_Opower( tc_RealDef_Oreal ) }.
% 0.98/1.58 { class_Groups_Ozero( tc_RealDef_Oreal ) }.
% 0.98/1.58 { class_SEQ_Obanach( tc_RealDef_Oreal ) }.
% 0.98/1.58 { class_Rings_Oring( tc_RealDef_Oreal ) }.
% 0.98/1.58 { class_Rings_Oidom( tc_RealDef_Oreal ) }.
% 0.98/1.58 { class_Groups_Oone( tc_RealDef_Oreal ) }.
% 0.98/1.58 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.98/1.58 tc_Complex_Ocomplex ) }.
% 0.98/1.58 { class_RealVector_Oreal__normed__div__algebra( tc_Complex_Ocomplex ) }.
% 0.98/1.58 { class_RealVector_Oreal__normed__algebra__1( tc_Complex_Ocomplex ) }.
% 0.98/1.58 { class_RealVector_Oreal__normed__algebra( tc_Complex_Ocomplex ) }.
% 0.98/1.58 { class_Groups_Ocancel__ab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.98/1.58 { class_Rings_Oring__1__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.98/1.58 { class_RealVector_Oreal__normed__vector( tc_Complex_Ocomplex ) }.
% 0.98/1.58 { class_RealVector_Oreal__normed__field( tc_Complex_Ocomplex ) }.
% 0.98/1.58 { class_Rings_Oring__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.98/1.58 { class_Groups_Ocancel__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.98/1.58 { class_RealVector_Oreal__algebra__1( tc_Complex_Ocomplex ) }.
% 0.98/1.58 { class_Groups_Oab__semigroup__mult( tc_Complex_Ocomplex ) }.
% 0.98/1.58 { class_Groups_Ocomm__monoid__mult( tc_Complex_Ocomplex ) }.
% 0.98/1.58 { class_Groups_Oab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.98/1.58 { class_Rings_Ono__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.98/1.58 { class_Groups_Ocomm__monoid__add( tc_Complex_Ocomplex ) }.
% 0.98/1.58 { class_Rings_Ocomm__semiring__1( tc_Complex_Ocomplex ) }.
% 0.98/1.58 { class_Rings_Ocomm__semiring( tc_Complex_Ocomplex ) }.
% 0.98/1.58 { class_Groups_Oab__group__add( tc_Complex_Ocomplex ) }.
% 0.98/1.58 { class_Rings_Ozero__neq__one( tc_Complex_Ocomplex ) }.
% 0.98/1.58 { class_Groups_Omonoid__mult( tc_Complex_Ocomplex ) }.
% 0.98/1.58 { class_Rings_Ocomm__ring__1( tc_Complex_Ocomplex ) }.
% 0.98/1.58 { class_Groups_Omonoid__add( tc_Complex_Ocomplex ) }.
% 0.98/1.58 { class_Rings_Osemiring__0( tc_Complex_Ocomplex ) }.
% 0.98/1.58 { class_Groups_Ogroup__add( tc_Complex_Ocomplex ) }.
% 0.98/1.58 { class_Rings_Omult__zero( tc_Complex_Ocomplex ) }.
% 0.98/1.58 { class_Rings_Osemiring( tc_Complex_Ocomplex ) }.
% 0.98/1.58 { class_Groups_Ouminus( tc_Complex_Ocomplex ) }.
% 0.98/1.58 { class_Rings_Oring__1( tc_Complex_Ocomplex ) }.
% 0.98/1.58 { class_Groups_Ominus( tc_Complex_Ocomplex ) }.
% 0.98/1.58 { class_Power_Opower( tc_Complex_Ocomplex ) }.
% 0.98/1.58 { class_Groups_Ozero( tc_Complex_Ocomplex ) }.
% 0.98/1.58 { class_SEQ_Obanach( tc_Complex_Ocomplex ) }.
% 0.98/1.58 { class_Rings_Oring( tc_Complex_Ocomplex ) }.
% 0.98/1.58 { class_Rings_Oidom( tc_Complex_Ocomplex ) }.
% 0.98/1.58 { class_Groups_Oone( tc_Complex_Ocomplex ) }.
% 0.98/1.58 { ! c_Complex_Orcis( hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.98/1.58 tc_RealDef_Oreal ), c_NthRoot_Osqrt( c_Groups_Oabs__class_Oabs(
% 0.98/1.58 tc_RealDef_Oreal, v_r ) ) ), c_NthRoot_Osqrt( c_Groups_Oabs__class_Oabs(
% 0.98/1.58 tc_RealDef_Oreal, v_r ) ) ), c_Groups_Oplus__class_Oplus(
% 0.98/1.58 tc_RealDef_Oreal, c_Transcendental_Opi, v_a ) ) = c_Complex_Orcis(
% 0.98/1.58 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal,
% 0.98/1.58 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, v_r ) ), v_a ) }.
% 0.98/1.58
% 0.98/1.58 *** allocated 15000 integers for clauses
% 0.98/1.58 *** allocated 22500 integers for clauses
% 0.98/1.58 *** allocated 33750 integers for clauses
% 0.98/1.58 *** allocated 50625 integers for clauses
% 0.98/1.58 *** allocated 75937 integers for clauses
% 0.98/1.58 percentage equality = 0.271270, percentage horn = 0.935506
% 0.98/1.58 This is a problem with some equality
% 0.98/1.58
% 0.98/1.58
% 0.98/1.58
% 0.98/1.58 Options Used:
% 0.98/1.58
% 0.98/1.58 useres = 1
% 0.98/1.58 useparamod = 1
% 0.98/1.58 useeqrefl = 1
% 0.98/1.58 useeqfact = 1
% 0.98/1.58 usefactor = 1
% 0.98/1.58 usesimpsplitting = 0
% 0.98/1.58 usesimpdemod = 5
% 0.98/1.58 usesimpres = 3
% 0.98/1.58
% 0.98/1.58 resimpinuse = 1000
% 0.98/1.58 resimpclauses = 20000
% 0.98/1.58 substype = eqrewr
% 0.98/1.58 backwardsubs = 1
% 0.98/1.58 selectoldest = 5
% 0.98/1.58
% 0.98/1.58 litorderings [0] = split
% 0.98/1.58 litorderings [1] = extend the termordering, first sorting on arguments
% 0.98/1.58
% 0.98/1.58 termordering = kbo
% 0.98/1.58
% 0.98/1.58 litapriori = 0
% 0.98/1.58 termapriori = 1
% 0.98/1.58 litaposteriori = 0
% 0.98/1.58 termaposteriori = 0
% 0.98/1.58 demodaposteriori = 0
% 0.98/1.58 ordereqreflfact = 0
% 0.98/1.58
% 0.98/1.58 litselect = negord
% 0.98/1.58
% 0.98/1.58 maxweight = 15
% 0.98/1.58 maxdepth = 30000
% 0.98/1.58 maxlength = 115
% 0.98/1.58 maxnrvars = 195
% 0.98/1.58 excuselevel = 1
% 0.98/1.58 increasemaxweight = 1
% 0.98/1.58
% 0.98/1.58 maxselected = 10000000
% 0.98/1.58 maxnrclauses = 10000000
% 0.98/1.58
% 0.98/1.58 showgenerated = 0
% 0.98/1.58 showkept = 0
% 0.98/1.58 showselected = 0
% 0.98/1.58 showdeleted = 0
% 0.98/1.58 showresimp = 1
% 0.98/1.58 showstatus = 2000
% 0.98/1.58
% 0.98/1.58 prologoutput = 0
% 0.98/1.58 nrgoals = 5000000
% 0.98/1.58 totalproof = 1
% 0.98/1.58
% 0.98/1.58 Symbols occurring in the translation:
% 0.98/1.58
% 0.98/1.58 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.98/1.58 . [1, 2] (w:1, o:208, a:1, s:1, b:0),
% 0.98/1.58 ! [4, 1] (w:0, o:112, a:1, s:1, b:0),
% 0.98/1.58 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.98/1.58 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.98/1.58 hAPP [38, 2] (w:1, o:232, a:1, s:1, b:0),
% 0.98/1.58 tc_RealDef_Oreal [41, 0] (w:1, o:31, a:1, s:1, b:0),
% 0.98/1.58 c_Groups_Ouminus__class_Ouminus [42, 2] (w:1, o:233, a:1, s:1, b:0),
% 0.98/1.58
% 0.98/1.58 c_Groups_Oplus__class_Oplus [43, 3] (w:1, o:278, a:1, s:1, b:0),
% 0.98/1.58 c_Groups_Oabs__class_Oabs [44, 2] (w:1, o:234, a:1, s:1, b:0),
% 0.98/1.58 c_Groups_Otimes__class_Otimes [45, 1] (w:1, o:117, a:1, s:1, b:0),
% 0.98/1.58 c_NthRoot_Osqrt [46, 1] (w:1, o:118, a:1, s:1, b:0),
% 0.98/1.58 class_Groups_Oordered__ab__group__add__abs [52, 1] (w:1, o:119, a:1
% 0.98/1.58 , s:1, b:0),
% 0.98/1.58 class_Rings_Olinordered__idom [54, 1] (w:1, o:120, a:1, s:1, b:0),
% 0.98/1.58 class_Groups_Oab__group__add [55, 1] (w:1, o:121, a:1, s:1, b:0),
% 0.98/1.58 class_Groups_Ogroup__add [56, 1] (w:1, o:122, a:1, s:1, b:0),
% 0.98/1.58 class_Groups_Oab__semigroup__mult [58, 1] (w:1, o:123, a:1, s:1, b:0)
% 0.98/1.58 ,
% 0.98/1.58 class_Groups_Ocancel__semigroup__add [59, 1] (w:1, o:124, a:1, s:1
% 0.98/1.58 , b:0),
% 0.98/1.58 class_Groups_Ocancel__ab__semigroup__add [60, 1] (w:1, o:125, a:1, s:
% 0.98/1.58 1, b:0),
% 0.98/1.58 class_Groups_Oab__semigroup__add [64, 1] (w:1, o:126, a:1, s:1, b:0)
% 0.98/1.58 ,
% 0.98/1.58 class_Rings_Osemiring [70, 1] (w:1, o:131, a:1, s:1, b:0),
% 0.98/1.58 class_Rings_Ocomm__semiring [71, 1] (w:1, o:133, a:1, s:1, b:0),
% 0.98/1.58 class_Rings_Oidom [72, 1] (w:1, o:134, a:1, s:1, b:0),
% 0.98/1.58 class_Rings_Oring [73, 1] (w:1, o:127, a:1, s:1, b:0),
% 0.98/1.58 tc_Complex_Ocomplex [76, 0] (w:1, o:53, a:1, s:1, b:0),
% 0.98/1.58 c_Complex_Orcis [77, 2] (w:1, o:235, a:1, s:1, b:0),
% 0.98/1.58 class_RealVector_Oreal__normed__algebra [78, 1] (w:1, o:135, a:1, s:1
% 0.98/1.58 , b:0),
% 0.98/1.58 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct [82
% 0.98/1.58 , 1] (w:1, o:159, a:1, s:1, b:0),
% 0.98/1.58 class_Rings_Ocomm__semiring__1 [84, 1] (w:1, o:136, a:1, s:1, b:0),
% 0.98/1.58 c_Orderings_Oord__class_Oless__eq [95, 3] (w:1, o:279, a:1, s:1, b:0)
% 0.98/1.58 ,
% 0.98/1.58 class_Lattices_Oboolean__algebra [96, 1] (w:1, o:161, a:1, s:1, b:0)
% 0.98/1.58 ,
% 0.98/1.58 class_Groups_Ouminus [99, 1] (w:1, o:162, a:1, s:1, b:0),
% 0.98/1.58 tc_fun [100, 2] (w:1, o:263, a:1, s:1, b:0),
% 0.98/1.58 class_Lattices_Oab__semigroup__idem__mult [101, 1] (w:1, o:160, a:1
% 0.98/1.58 , s:1, b:0),
% 0.98/1.58 c_Complex_Ocis [102, 1] (w:1, o:163, a:1, s:1, b:0),
% 0.98/1.58 c_Complex_Oexpi [103, 1] (w:1, o:164, a:1, s:1, b:0),
% 0.98/1.58 c_Groups_Osgn__class_Osgn [105, 2] (w:1, o:264, a:1, s:1, b:0),
% 0.98/1.58 class_Groups_Oordered__ab__semigroup__add__imp__le [108, 1] (w:1, o:
% 0.98/1.58 165, a:1, s:1, b:0),
% 0.98/1.58 class_Groups_Oordered__ab__semigroup__add [109, 1] (w:1, o:166, a:1
% 0.98/1.58 , s:1, b:0),
% 0.98/1.58 class_Groups_Oordered__ab__group__add [110, 1] (w:1, o:167, a:1, s:1
% 0.98/1.58 , b:0),
% 0.98/1.58 class_RealVector_Oreal__normed__div__algebra [111, 1] (w:1, o:137, a:
% 0.98/1.58 1, s:1, b:0),
% 0.98/1.58 class_RealVector_Oreal__normed__vector [112, 1] (w:1, o:138, a:1, s:1
% 0.98/1.58 , b:0),
% 0.98/1.58 class_Orderings_Opreorder [115, 1] (w:1, o:170, a:1, s:1, b:0),
% 0.98/1.58 c_Groups_Ozero__class_Ozero [116, 1] (w:1, o:171, a:1, s:1, b:0),
% 0.98/1.58 c_RealVector_Oof__real [118, 2] (w:1, o:266, a:1, s:1, b:0),
% 0.98/1.58 c_RealVector_Onorm__class_Onorm [119, 2] (w:1, o:265, a:1, s:1, b:0)
% 0.98/1.58 ,
% 0.98/1.58 class_Rings_Oordered__ring__abs [120, 1] (w:1, o:140, a:1, s:1, b:0)
% 0.98/1.58 ,
% 0.98/1.58 class_Groups_Ozero [121, 1] (w:1, o:172, a:1, s:1, b:0),
% 0.98/1.58 class_RealVector_Oreal__algebra__1 [122, 1] (w:1, o:141, a:1, s:1, b:
% 0.98/1.58 0),
% 0.98/1.58 class_RealVector_Oreal__normed__algebra__1 [123, 1] (w:1, o:142, a:1
% 0.98/1.58 , s:1, b:0),
% 0.98/1.58 class_Rings_Omult__zero [124, 1] (w:1, o:151, a:1, s:1, b:0),
% 0.98/1.58 class_Rings_Oring__no__zero__divisors [125, 1] (w:1, o:128, a:1, s:1
% 0.98/1.58 , b:0),
% 0.98/1.58 class_Rings_Ono__zero__divisors [126, 1] (w:1, o:139, a:1, s:1, b:0)
% 0.98/1.58 ,
% 0.98/1.58 class_Groups_Omonoid__add [127, 1] (w:1, o:174, a:1, s:1, b:0),
% 0.98/1.58 class_Groups_Ocomm__monoid__add [128, 1] (w:1, o:175, a:1, s:1, b:0)
% 0.98/1.58 ,
% 0.98/1.58 class_Groups_Olinordered__ab__group__add [129, 1] (w:1, o:173, a:1
% 0.98/1.58 , s:1, b:0),
% 0.98/1.58 class_Groups_Osgn__if [130, 1] (w:1, o:176, a:1, s:1, b:0),
% 0.98/1.58 class_Rings_Oordered__cancel__semiring [131, 1] (w:1, o:152, a:1, s:1
% 0.98/1.58 , b:0),
% 0.98/1.58 class_Rings_Oordered__ring [132, 1] (w:1, o:153, a:1, s:1, b:0),
% 0.98/1.58 class_Rings_Oordered__semiring [133, 1] (w:1, o:154, a:1, s:1, b:0),
% 0.98/1.58
% 0.98/1.58 class_Rings_Oordered__comm__semiring [134, 1] (w:1, o:155, a:1, s:1
% 0.98/1.58 , b:0),
% 0.98/1.58 class_Rings_Olinordered__ring__strict [135, 1] (w:1, o:143, a:1, s:1
% 0.98/1.58 , b:0),
% 0.98/1.58 class_Rings_Olinordered__ring [136, 1] (w:1, o:144, a:1, s:1, b:0),
% 0.98/1.58 class_Groups_Oordered__comm__monoid__add [137, 1] (w:1, o:177, a:1
% 0.98/1.58 , s:1, b:0),
% 0.98/1.58 class_Orderings_Olinorder [138, 1] (w:1, o:178, a:1, s:1, b:0),
% 0.98/1.58 class_Orderings_Oord [139, 1] (w:1, o:168, a:1, s:1, b:0),
% 0.98/1.58 class_Orderings_Oorder [140, 1] (w:1, o:169, a:1, s:1, b:0),
% 0.98/1.58 c_Transcendental_Opi [141, 0] (w:1, o:73, a:1, s:1, b:0),
% 0.98/1.58 c_Groups_Oone__class_Oone [145, 1] (w:1, o:179, a:1, s:1, b:0),
% 0.98/1.58 class_Rings_Olinordered__semiring__1 [147, 1] (w:1, o:145, a:1, s:1
% 0.98/1.58 , b:0),
% 0.98/1.58 c_Groups_Ominus__class_Ominus [148, 3] (w:1, o:280, a:1, s:1, b:0),
% 0.98/1.58 c_Transcendental_Ocos [149, 1] (w:1, o:180, a:1, s:1, b:0),
% 0.98/1.58 c_RealDef_Opositive [150, 1] (w:1, o:181, a:1, s:1, b:0),
% 0.98/1.58 c_Complex_Ocomplex_OComplex [151, 2] (w:1, o:267, a:1, s:1, b:0),
% 0.98/1.58 class_Groups_Oone [156, 1] (w:1, o:182, a:1, s:1, b:0),
% 0.98/1.58 class_Groups_Ominus [158, 1] (w:1, o:183, a:1, s:1, b:0),
% 0.98/1.58 class_Rings_Oring__1 [159, 1] (w:1, o:129, a:1, s:1, b:0),
% 0.98/1.58 class_Rings_Ozero__neq__one [160, 1] (w:1, o:156, a:1, s:1, b:0),
% 0.98/1.58 class_Groups_Ocomm__monoid__mult [161, 1] (w:1, o:184, a:1, s:1, b:0)
% 0.98/1.58 ,
% 0.98/1.58 class_Groups_Omonoid__mult [162, 1] (w:1, o:185, a:1, s:1, b:0),
% 0.98/1.58 class_Rings_Ocomm__ring__1 [164, 1] (w:1, o:132, a:1, s:1, b:0),
% 0.98/1.58 class_Rings_Olinordered__semidom [165, 1] (w:1, o:146, a:1, s:1, b:0)
% 0.98/1.58 ,
% 0.98/1.58 class_Rings_Oring__1__no__zero__divisors [166, 1] (w:1, o:130, a:1
% 0.98/1.58 , s:1, b:0),
% 0.98/1.58 c_Complex_Oarg [169, 1] (w:1, o:186, a:1, s:1, b:0),
% 0.98/1.58 c_Complex_Ocomplex_Ocomplex__size [172, 1] (w:1, o:187, a:1, s:1, b:0
% 0.98/1.58 ),
% 0.98/1.58 tc_Nat_Onat [173, 0] (w:1, o:86, a:1, s:1, b:0),
% 0.98/1.58 c_Complex_Ocomplex_Ocomplex__case [175, 3] (w:1, o:281, a:1, s:1, b:0
% 0.98/1.58 ),
% 0.98/1.58 c_Complex_Ocomplex_Ocomplex__rec [176, 3] (w:1, o:282, a:1, s:1, b:0)
% 0.98/1.58 ,
% 0.98/1.58 c_Transcendental_Oarccos [177, 1] (w:1, o:188, a:1, s:1, b:0),
% 0.98/1.58 c_Nat_Osize__class_Osize [179, 2] (w:1, o:268, a:1, s:1, b:0),
% 0.98/1.58 c_Transcendental_Osin [180, 1] (w:1, o:189, a:1, s:1, b:0),
% 0.98/1.58 c_Complex_Oii [181, 0] (w:1, o:89, a:1, s:1, b:0),
% 0.98/1.58 c_Orderings_Oord__class_Oless [191, 3] (w:1, o:283, a:1, s:1, b:0),
% 0.98/1.58 c_RComplete_Onatceiling [192, 1] (w:1, o:190, a:1, s:1, b:0),
% 0.98/1.58 class_Groups_Oordered__cancel__ab__semigroup__add [193, 1] (w:1, o:
% 0.98/1.58 191, a:1, s:1, b:0),
% 0.98/1.58 class_Rings_Olinordered__comm__semiring__strict [194, 1] (w:1, o:147
% 0.98/1.58 , a:1, s:1, b:0),
% 0.98/1.58 class_Rings_Olinordered__semiring__strict [195, 1] (w:1, o:148, a:1
% 0.98/1.58 , s:1, b:0),
% 0.98/1.58 class_Rings_Olinordered__semiring [196, 1] (w:1, o:149, a:1, s:1, b:0
% 0.98/1.58 ),
% 0.98/1.58 class_Groups_Oabs__if [197, 1] (w:1, o:192, a:1, s:1, b:0),
% 0.98/1.58 class_Rings_Olinordered__semiring__1__strict [198, 1] (w:1, o:150, a:
% 0.98/1.58 1, s:1, b:0),
% 0.98/1.58 hBOOL [200, 1] (w:1, o:193, a:1, s:1, b:0),
% 0.98/1.58 c_RComplete_Onatfloor [202, 1] (w:1, o:194, a:1, s:1, b:0),
% 0.98/1.58 c_RealDef_Oreal [203, 2] (w:1, o:269, a:1, s:1, b:0),
% 0.98/1.58 c_SEQ_Odecseq [209, 2] (w:1, o:270, a:1, s:1, b:0),
% 0.98/1.58 c_Power_Opower__class_Opower [211, 1] (w:1, o:195, a:1, s:1, b:0),
% 0.98/1.58 class_Power_Opower [214, 1] (w:1, o:196, a:1, s:1, b:0),
% 0.98/1.58 tc_Int_Oint [215, 0] (w:1, o:101, a:1, s:1, b:0),
% 0.98/1.58 class_Rings_Osemiring__0 [216, 1] (w:1, o:157, a:1, s:1, b:0),
% 0.98/1.58 c_Power_Opower_Opower [219, 3] (w:1, o:284, a:1, s:1, b:0),
% 0.98/1.58 c_Nat__Transfer_Otsub [226, 2] (w:1, o:271, a:1, s:1, b:0),
% 17.84/18.18 c_Transcendental_Oln [228, 1] (w:1, o:197, a:1, s:1, b:0),
% 17.84/18.18 c_SEQ_OBseq [229, 2] (w:1, o:272, a:1, s:1, b:0),
% 17.84/18.18 c_SEQ_Oincseq [230, 2] (w:1, o:273, a:1, s:1, b:0),
% 17.84/18.18 c_Complex_OIm [233, 1] (w:1, o:198, a:1, s:1, b:0),
% 17.84/18.18 c_Complex_ORe [234, 1] (w:1, o:199, a:1, s:1, b:0),
% 17.84/18.18 c_Transcendental_Oexp [235, 2] (w:1, o:274, a:1, s:1, b:0),
% 17.84/18.18 class_RealVector_Oreal__normed__field [236, 1] (w:1, o:158, a:1, s:1
% 17.84/18.18 , b:0),
% 17.84/18.18 class_SEQ_Obanach [237, 1] (w:1, o:200, a:1, s:1, b:0),
% 17.84/18.18 tc_HOL_Obool [240, 0] (w:1, o:100, a:1, s:1, b:0),
% 17.84/18.18 v_r [241, 0] (w:1, o:110, a:1, s:1, b:0),
% 17.84/18.18 v_a [242, 0] (w:1, o:111, a:1, s:1, b:0),
% 17.84/18.18 alpha1 [243, 3] (w:1, o:285, a:1, s:1, b:1),
% 17.84/18.18 alpha2 [244, 3] (w:1, o:290, a:1, s:1, b:1),
% 17.84/18.18 alpha3 [245, 4] (w:1, o:304, a:1, s:1, b:1),
% 17.84/18.18 alpha4 [246, 4] (w:1, o:305, a:1, s:1, b:1),
% 17.84/18.18 alpha5 [247, 3] (w:1, o:291, a:1, s:1, b:1),
% 17.84/18.18 alpha6 [248, 3] (w:1, o:292, a:1, s:1, b:1),
% 17.84/18.18 alpha7 [249, 3] (w:1, o:293, a:1, s:1, b:1),
% 17.84/18.18 alpha8 [250, 3] (w:1, o:294, a:1, s:1, b:1),
% 17.84/18.18 alpha9 [251, 4] (w:1, o:306, a:1, s:1, b:1),
% 17.84/18.18 alpha10 [252, 4] (w:1, o:307, a:1, s:1, b:1),
% 17.84/18.18 alpha11 [253, 3] (w:1, o:286, a:1, s:1, b:1),
% 17.84/18.18 alpha12 [254, 3] (w:1, o:287, a:1, s:1, b:1),
% 17.84/18.18 alpha13 [255, 2] (w:1, o:275, a:1, s:1, b:1),
% 17.84/18.18 alpha14 [256, 3] (w:1, o:288, a:1, s:1, b:1),
% 17.84/18.18 alpha15 [257, 2] (w:1, o:276, a:1, s:1, b:1),
% 17.84/18.18 alpha16 [258, 2] (w:1, o:277, a:1, s:1, b:1),
% 17.84/18.18 alpha17 [259, 3] (w:1, o:289, a:1, s:1, b:1),
% 17.84/18.18 skol1 [260, 2] (w:1, o:236, a:1, s:1, b:1),
% 17.84/18.18 skol2 [261, 3] (w:1, o:298, a:1, s:1, b:1),
% 17.84/18.18 skol3 [262, 1] (w:1, o:202, a:1, s:1, b:1),
% 17.84/18.18 skol4 [263, 1] (w:1, o:203, a:1, s:1, b:1),
% 17.84/18.18 skol5 [264, 1] (w:1, o:204, a:1, s:1, b:1),
% 17.84/18.18 skol6 [265, 2] (w:1, o:237, a:1, s:1, b:1),
% 17.84/18.18 skol7 [266, 2] (w:1, o:238, a:1, s:1, b:1),
% 17.84/18.18 skol8 [267, 2] (w:1, o:239, a:1, s:1, b:1),
% 17.84/18.18 skol9 [268, 2] (w:1, o:240, a:1, s:1, b:1),
% 17.84/18.18 skol10 [269, 1] (w:1, o:205, a:1, s:1, b:1),
% 17.84/18.18 skol11 [270, 2] (w:1, o:241, a:1, s:1, b:1),
% 17.84/18.18 skol12 [271, 2] (w:1, o:242, a:1, s:1, b:1),
% 17.84/18.18 skol13 [272, 1] (w:1, o:206, a:1, s:1, b:1),
% 17.84/18.18 skol14 [273, 1] (w:1, o:207, a:1, s:1, b:1),
% 17.84/18.18 skol15 [274, 2] (w:1, o:243, a:1, s:1, b:1),
% 17.84/18.18 skol16 [275, 2] (w:1, o:244, a:1, s:1, b:1),
% 17.84/18.18 skol17 [276, 3] (w:1, o:295, a:1, s:1, b:1),
% 17.84/18.18 skol18 [277, 3] (w:1, o:296, a:1, s:1, b:1),
% 17.84/18.18 skol19 [278, 3] (w:1, o:297, a:1, s:1, b:1),
% 17.84/18.18 skol20 [279, 1] (w:1, o:201, a:1, s:1, b:1),
% 17.84/18.18 skol21 [280, 2] (w:1, o:245, a:1, s:1, b:1),
% 17.84/18.18 skol22 [281, 3] (w:1, o:299, a:1, s:1, b:1),
% 17.84/18.18 skol23 [282, 4] (w:1, o:308, a:1, s:1, b:1),
% 17.84/18.18 skol24 [283, 2] (w:1, o:246, a:1, s:1, b:1),
% 17.84/18.18 skol25 [284, 2] (w:1, o:247, a:1, s:1, b:1),
% 17.84/18.18 skol26 [285, 2] (w:1, o:248, a:1, s:1, b:1),
% 17.84/18.18 skol27 [286, 2] (w:1, o:249, a:1, s:1, b:1),
% 17.84/18.18 skol28 [287, 2] (w:1, o:250, a:1, s:1, b:1),
% 17.84/18.18 skol29 [288, 2] (w:1, o:251, a:1, s:1, b:1),
% 17.84/18.18 skol30 [289, 2] (w:1, o:252, a:1, s:1, b:1),
% 17.84/18.18 skol31 [290, 2] (w:1, o:253, a:1, s:1, b:1),
% 17.84/18.18 skol32 [291, 2] (w:1, o:254, a:1, s:1, b:1),
% 17.84/18.18 skol33 [292, 2] (w:1, o:255, a:1, s:1, b:1),
% 17.84/18.18 skol34 [293, 2] (w:1, o:256, a:1, s:1, b:1),
% 17.84/18.18 skol35 [294, 3] (w:1, o:300, a:1, s:1, b:1),
% 17.84/18.18 skol36 [295, 3] (w:1, o:301, a:1, s:1, b:1),
% 17.84/18.18 skol37 [296, 2] (w:1, o:257, a:1, s:1, b:1),
% 17.84/18.18 skol38 [297, 3] (w:1, o:302, a:1, s:1, b:1),
% 17.84/18.18 skol39 [298, 2] (w:1, o:258, a:1, s:1, b:1),
% 17.84/18.18 skol40 [299, 0] (w:1, o:26, a:1, s:1, b:1),
% 17.84/18.18 skol41 [300, 0] (w:1, o:27, a:1, s:1, b:1),
% 17.84/18.18 skol42 [301, 0] (w:1, o:28, a:1, s:1, b:1),
% 17.84/18.18 skol43 [302, 0] (w:1, o:29, a:1, s:1, b:1),
% 17.84/18.18 skol44 [303, 0] (w:1, o:30, a:1, s:1, b:1),
% 17.84/18.18 skol45 [304, 2] (w:1, o:259, a:1, s:1, b:1),
% 17.84/18.18 skol46 [305, 3] (w:1, o:303, a:1, s:1, b:1),
% 17.84/18.18 skol47 [306, 2] (w:1, o:260, a:1, s:1, b:1),
% 17.84/18.18 skol48 [307, 2] (w:1, o:261, a:1, s:1, b:1),
% 17.84/18.18 skol49 [308, 2] (w:1, o:262, a:1, s:1, b:1),
% 61.81/62.18 skol50 [309, 4] (w:1, o:309, a:1, s:1, b:1),
% 61.81/62.18 skol51 [310, 4] (w:1, o:310, a:1, s:1, b:1).
% 61.81/62.18
% 61.81/62.18
% 61.81/62.18 Starting Search:
% 61.81/62.18
% 61.81/62.18 *** allocated 113905 integers for clauses
% 61.81/62.18 *** allocated 170857 integers for clauses
% 61.81/62.18 Resimplifying inuse:
% 61.81/62.18 Done
% 61.81/62.18
% 61.81/62.18
% 61.81/62.18 Intermediate Status:
% 61.81/62.18 Generated: 3500
% 61.81/62.18 Kept: 2080
% 61.81/62.18 Inuse: 78
% 61.81/62.18 Deleted: 3
% 61.81/62.18 Deletedinuse: 0
% 61.81/62.18
% 61.81/62.18 *** allocated 256285 integers for clauses
% 61.81/62.18 Resimplifying inuse:
% 61.81/62.18 Done
% 61.81/62.18
% 61.81/62.18 *** allocated 170857 integers for termspace/termends
% 61.81/62.18 *** allocated 384427 integers for clauses
% 61.81/62.18
% 61.81/62.18 Intermediate Status:
% 61.81/62.18 Generated: 10804
% 61.81/62.18 Kept: 4118
% 61.81/62.18 Inuse: 158
% 61.81/62.18 Deleted: 3
% 61.81/62.18 Deletedinuse: 0
% 61.81/62.18
% 61.81/62.18 Resimplifying inuse:
% 61.81/62.18 Done
% 61.81/62.18
% 61.81/62.18 *** allocated 256285 integers for termspace/termends
% 61.81/62.18 Resimplifying inuse:
% 61.81/62.18 Done
% 61.81/62.18
% 61.81/62.18
% 61.81/62.18 Intermediate Status:
% 61.81/62.18 Generated: 22036
% 61.81/62.18 Kept: 6120
% 61.81/62.18 Inuse: 212
% 61.81/62.18 Deleted: 4
% 61.81/62.18 Deletedinuse: 0
% 61.81/62.18
% 61.81/62.18 *** allocated 576640 integers for clauses
% 61.81/62.18 Resimplifying inuse:
% 61.81/62.18 Done
% 61.81/62.18
% 61.81/62.18 *** allocated 384427 integers for termspace/termends
% 61.81/62.18 Resimplifying inuse:
% 61.81/62.18 Done
% 61.81/62.18
% 61.81/62.18
% 61.81/62.18 Intermediate Status:
% 61.81/62.18 Generated: 31949
% 61.81/62.18 Kept: 8196
% 61.81/62.18 Inuse: 290
% 61.81/62.18 Deleted: 6
% 61.81/62.18 Deletedinuse: 0
% 61.81/62.18
% 61.81/62.18 Resimplifying inuse:
% 61.81/62.18 Done
% 61.81/62.18
% 61.81/62.18 *** allocated 864960 integers for clauses
% 61.81/62.18
% 61.81/62.18 Intermediate Status:
% 61.81/62.18 Generated: 42128
% 61.81/62.18 Kept: 10608
% 61.81/62.18 Inuse: 349
% 61.81/62.18 Deleted: 7
% 61.81/62.18 Deletedinuse: 0
% 61.81/62.18
% 61.81/62.18 Resimplifying inuse:
% 61.81/62.18 Done
% 61.81/62.18
% 61.81/62.18 Resimplifying inuse:
% 61.81/62.18 Done
% 61.81/62.18
% 61.81/62.18
% 61.81/62.18 Intermediate Status:
% 61.81/62.18 Generated: 50912
% 61.81/62.18 Kept: 12724
% 61.81/62.18 Inuse: 400
% 61.81/62.18 Deleted: 7
% 61.81/62.18 Deletedinuse: 0
% 61.81/62.18
% 61.81/62.18 Resimplifying inuse:
% 61.81/62.18 Done
% 61.81/62.18
% 61.81/62.18 *** allocated 576640 integers for termspace/termends
% 61.81/62.18 Resimplifying inuse:
% 61.81/62.18 Done
% 61.81/62.18
% 61.81/62.18
% 61.81/62.18 Intermediate Status:
% 61.81/62.18 Generated: 60073
% 61.81/62.18 Kept: 14767
% 61.81/62.18 Inuse: 508
% 61.81/62.18 Deleted: 8
% 61.81/62.18 Deletedinuse: 0
% 61.81/62.18
% 61.81/62.18 Resimplifying inuse:
% 61.81/62.18 Done
% 61.81/62.18
% 61.81/62.18 Resimplifying inuse:
% 61.81/62.18 Done
% 61.81/62.18
% 61.81/62.18 *** allocated 1297440 integers for clauses
% 61.81/62.18
% 61.81/62.18 Intermediate Status:
% 61.81/62.18 Generated: 70706
% 61.81/62.18 Kept: 17610
% 61.81/62.18 Inuse: 593
% 61.81/62.18 Deleted: 8
% 61.81/62.18 Deletedinuse: 0
% 61.81/62.18
% 61.81/62.18 Resimplifying inuse:
% 61.81/62.18 Done
% 61.81/62.18
% 61.81/62.18 Resimplifying inuse:
% 61.81/62.18 Done
% 61.81/62.18
% 61.81/62.18
% 61.81/62.18 Intermediate Status:
% 61.81/62.18 Generated: 76460
% 61.81/62.18 Kept: 20002
% 61.81/62.18 Inuse: 626
% 61.81/62.18 Deleted: 10
% 61.81/62.18 Deletedinuse: 0
% 61.81/62.18
% 61.81/62.18 Resimplifying inuse:
% 61.81/62.18 Done
% 61.81/62.18
% 61.81/62.18 Resimplifying clauses:
% 61.81/62.18 Done
% 61.81/62.18
% 61.81/62.18 *** allocated 864960 integers for termspace/termends
% 61.81/62.18 Resimplifying inuse:
% 61.81/62.18 Done
% 61.81/62.18
% 61.81/62.18
% 61.81/62.18 Intermediate Status:
% 61.81/62.18 Generated: 86049
% 61.81/62.18 Kept: 22048
% 61.81/62.18 Inuse: 678
% 61.81/62.18 Deleted: 241
% 61.81/62.18 Deletedinuse: 0
% 61.81/62.18
% 61.81/62.18 Resimplifying inuse:
% 61.81/62.18 Done
% 61.81/62.18
% 61.81/62.18
% 61.81/62.18 Intermediate Status:
% 61.81/62.18 Generated: 97651
% 61.81/62.18 Kept: 24573
% 61.81/62.18 Inuse: 706
% 61.81/62.18 Deleted: 241
% 61.81/62.18 Deletedinuse: 0
% 61.81/62.18
% 61.81/62.18 Resimplifying inuse:
% 61.81/62.18 Done
% 61.81/62.18
% 61.81/62.18 *** allocated 1946160 integers for clauses
% 61.81/62.18
% 61.81/62.18 Intermediate Status:
% 61.81/62.18 Generated: 108587
% 61.81/62.18 Kept: 26730
% 61.81/62.18 Inuse: 718
% 61.81/62.18 Deleted: 245
% 61.81/62.18 Deletedinuse: 1
% 61.81/62.18
% 61.81/62.18 Resimplifying inuse:
% 61.81/62.18 Done
% 61.81/62.18
% 61.81/62.18
% 61.81/62.18 Intermediate Status:
% 61.81/62.18 Generated: 113939
% 61.81/62.18 Kept: 28901
% 61.81/62.18 Inuse: 733
% 61.81/62.18 Deleted: 245
% 61.81/62.18 Deletedinuse: 1
% 61.81/62.18
% 61.81/62.18 Resimplifying inuse:
% 61.81/62.18 Done
% 61.81/62.18
% 61.81/62.18 Resimplifying inuse:
% 61.81/62.18 Done
% 61.81/62.18
% 61.81/62.18
% 61.81/62.18 Intermediate Status:
% 61.81/62.18 Generated: 121762
% 61.81/62.18 Kept: 30908
% 61.81/62.18 Inuse: 761
% 61.81/62.18 Deleted: 245
% 61.81/62.18 Deletedinuse: 1
% 61.81/62.18
% 61.81/62.18 Resimplifying inuse:
% 61.81/62.18 Done
% 61.81/62.18
% 61.81/62.18
% 61.81/62.18 Intermediate Status:
% 61.81/62.18 Generated: 128698
% 61.81/62.18 Kept: 32928
% 61.81/62.18 Inuse: 784
% 61.81/62.18 Deleted: 247
% 61.81/62.18 Deletedinuse: 2
% 61.81/62.18
% 61.81/62.18 *** allocated 1297440 integers for termspace/termends
% 61.81/62.18 Resimplifying inuse:
% 61.81/62.18 Done
% 61.81/62.18
% 61.81/62.18
% 61.81/62.18 Intermediate Status:
% 61.81/62.18 Generated: 137432
% 61.81/62.18 Kept: 36233
% 61.81/62.18 Inuse: 807
% 61.81/62.18 Deleted: 247
% 61.81/62.18 Deletedinuse: 2
% 61.81/62.18
% 61.81/62.18 Resimplifying inuse:
% 61.81/62.18 Done
% 61.81/62.18
% 61.81/62.18 Resimplifying inuse:
% 61.81/62.18 Done
% 61.81/62.18
% 61.81/62.18
% 61.81/62.18 Intermediate Status:
% 61.81/62.18 Generated: 160420
% 61.81/62.18 Kept: 39060
% 61.81/62.18 Inuse: 822
% 61.81/62.18 Deleted: 248
% 61.81/62.18 Deletedinuse: 3
% 61.81/62.18
% 61.81/62.18 Resimplifying inuse:
% 61.81/62.18 Done
% 61.81/62.18
% 61.81/62.18 Resimplifying inuse:
% 61.81/62.18 Done
% 61.81/62.18
% 61.81/62.18 Resimplifying clauses:
% 61.81/62.18 Done
% 61.81/62.18
% 61.81/62.18 *** allocated 2919240 integers for clauses
% 61.81/62.18
% 61.81/62.18 Intermediate Status:
% 61.81/62.18 Generated: 184886
% 61.81/62.18 Kept: 41939
% 61.81/62.18 Inuse: 832
% 61.81/62.18 Deleted: 499
% 61.81/62.18 Deletedinuse: 3
% 61.81/62.18
% 61.81/62.18 Resimplifying inuse:
% 61.81/62.18 Done
% 61.81/62.18
% 61.81/62.18 Resimplifying inuse:
% 61.81/62.18 Done
% 61.81/62.18
% 61.81/62.18
% 61.81/62.18 Intermediate Status:
% 61.81/62.18 Generated: 193708
% 61.81/62.18 Kept: 45052
% 61.81/62.18 Inuse: 847
% 61.81/62.18 Deleted: 499
% 61.81/62.18 Deletedinuse: 3
% 61.81/62.18
% 61.81/62.18 Resimplifying inuse:
% 61.81/62.18 Done
% 61.81/62.18
% 61.81/62.18 Resimplifying inuse:
% 61.81/62.18 Done
% 61.81/62.18
% 61.81/62.18
% 61.81/62.18 Intermediate Status:
% 61.81/62.18 Generated: 200587
% 61.81/62.18 Kept: 47073
% 61.81/62.18 Inuse: 867
% 61.81/62.18 Deleted: 499
% 61.81/62.18 Deletedinuse: 3
% 61.81/62.18
% 61.81/62.18 Resimplifying inuse:
% 61.81/62.18 Done
% 61.81/62.18
% 61.81/62.18
% 61.81/62.18 Intermediate Status:
% 61.81/62.18 Generated: 211183
% 164.91/165.35 Kept: 49135
% 164.91/165.35 Inuse: 902
% 164.91/165.35 Deleted: 499
% 164.91/165.35 Deletedinuse: 3
% 164.91/165.35
% 164.91/165.35 Resimplifying inuse:
% 164.91/165.35 Done
% 164.91/165.35
% 164.91/165.35 *** allocated 1946160 integers for termspace/termends
% 164.91/165.35 Resimplifying inuse:
% 164.91/165.35 Done
% 164.91/165.35
% 164.91/165.35
% 164.91/165.35 Intermediate Status:
% 164.91/165.35 Generated: 225387
% 164.91/165.35 Kept: 51333
% 164.91/165.35 Inuse: 927
% 164.91/165.35 Deleted: 499
% 164.91/165.35 Deletedinuse: 3
% 164.91/165.35
% 164.91/165.35 Resimplifying inuse:
% 164.91/165.35 Done
% 164.91/165.35
% 164.91/165.35 Resimplifying inuse:
% 164.91/165.35 Done
% 164.91/165.35
% 164.91/165.35
% 164.91/165.35 Intermediate Status:
% 164.91/165.35 Generated: 235223
% 164.91/165.35 Kept: 53422
% 164.91/165.35 Inuse: 952
% 164.91/165.35 Deleted: 499
% 164.91/165.35 Deletedinuse: 3
% 164.91/165.35
% 164.91/165.35 Resimplifying inuse:
% 164.91/165.35 Done
% 164.91/165.35
% 164.91/165.35 Resimplifying inuse:
% 164.91/165.35 Done
% 164.91/165.35
% 164.91/165.35
% 164.91/165.35 Intermediate Status:
% 164.91/165.35 Generated: 242193
% 164.91/165.35 Kept: 55455
% 164.91/165.35 Inuse: 1002
% 164.91/165.35 Deleted: 499
% 164.91/165.35 Deletedinuse: 3
% 164.91/165.35
% 164.91/165.35 Resimplifying inuse:
% 164.91/165.35 Done
% 164.91/165.35
% 164.91/165.35 Resimplifying inuse:
% 164.91/165.35 Done
% 164.91/165.35
% 164.91/165.35
% 164.91/165.35 Intermediate Status:
% 164.91/165.35 Generated: 249089
% 164.91/165.35 Kept: 57510
% 164.91/165.35 Inuse: 1052
% 164.91/165.35 Deleted: 499
% 164.91/165.35 Deletedinuse: 3
% 164.91/165.35
% 164.91/165.35 Resimplifying inuse:
% 164.91/165.35 Done
% 164.91/165.35
% 164.91/165.35
% 164.91/165.35 Intermediate Status:
% 164.91/165.35 Generated: 258865
% 164.91/165.35 Kept: 59542
% 164.91/165.35 Inuse: 1067
% 164.91/165.35 Deleted: 499
% 164.91/165.35 Deletedinuse: 3
% 164.91/165.35
% 164.91/165.35 Resimplifying inuse:
% 164.91/165.35 Done
% 164.91/165.35
% 164.91/165.35 Resimplifying inuse:
% 164.91/165.35 Done
% 164.91/165.35
% 164.91/165.35 Resimplifying clauses:
% 164.91/165.35 Done
% 164.91/165.35
% 164.91/165.35
% 164.91/165.35 Intermediate Status:
% 164.91/165.35 Generated: 270545
% 164.91/165.35 Kept: 61557
% 164.91/165.35 Inuse: 1086
% 164.91/165.35 Deleted: 800
% 164.91/165.35 Deletedinuse: 3
% 164.91/165.35
% 164.91/165.35 Resimplifying inuse:
% 164.91/165.35 Done
% 164.91/165.35
% 164.91/165.35 *** allocated 4378860 integers for clauses
% 164.91/165.35
% 164.91/165.35 Intermediate Status:
% 164.91/165.35 Generated: 301288
% 164.91/165.35 Kept: 64716
% 164.91/165.35 Inuse: 1102
% 164.91/165.35 Deleted: 800
% 164.91/165.35 Deletedinuse: 3
% 164.91/165.35
% 164.91/165.35 Resimplifying inuse:
% 164.91/165.35 Done
% 164.91/165.35
% 164.91/165.35 Resimplifying inuse:
% 164.91/165.35 Done
% 164.91/165.35
% 164.91/165.35
% 164.91/165.35 Intermediate Status:
% 164.91/165.35 Generated: 311476
% 164.91/165.35 Kept: 66849
% 164.91/165.35 Inuse: 1142
% 164.91/165.35 Deleted: 800
% 164.91/165.35 Deletedinuse: 3
% 164.91/165.35
% 164.91/165.35 Resimplifying inuse:
% 164.91/165.35 Done
% 164.91/165.35
% 164.91/165.35 Resimplifying inuse:
% 164.91/165.35 Done
% 164.91/165.35
% 164.91/165.35
% 164.91/165.35 Intermediate Status:
% 164.91/165.35 Generated: 324334
% 164.91/165.35 Kept: 69840
% 164.91/165.35 Inuse: 1166
% 164.91/165.35 Deleted: 801
% 164.91/165.35 Deletedinuse: 3
% 164.91/165.35
% 164.91/165.35 Resimplifying inuse:
% 164.91/165.35 Done
% 164.91/165.35
% 164.91/165.35 *** allocated 2919240 integers for termspace/termends
% 164.91/165.35 Resimplifying inuse:
% 164.91/165.35 Done
% 164.91/165.35
% 164.91/165.35
% 164.91/165.35 Intermediate Status:
% 164.91/165.35 Generated: 332481
% 164.91/165.35 Kept: 71923
% 164.91/165.35 Inuse: 1183
% 164.91/165.35 Deleted: 813
% 164.91/165.35 Deletedinuse: 12
% 164.91/165.35
% 164.91/165.35 Resimplifying inuse:
% 164.91/165.35 Done
% 164.91/165.35
% 164.91/165.35
% 164.91/165.35 Intermediate Status:
% 164.91/165.35 Generated: 344384
% 164.91/165.35 Kept: 74747
% 164.91/165.35 Inuse: 1190
% 164.91/165.35 Deleted: 816
% 164.91/165.35 Deletedinuse: 12
% 164.91/165.35
% 164.91/165.35 Resimplifying inuse:
% 164.91/165.35 Done
% 164.91/165.35
% 164.91/165.35 Resimplifying inuse:
% 164.91/165.35 Done
% 164.91/165.35
% 164.91/165.35
% 164.91/165.35 Intermediate Status:
% 164.91/165.35 Generated: 356434
% 164.91/165.35 Kept: 77529
% 164.91/165.35 Inuse: 1218
% 164.91/165.35 Deleted: 818
% 164.91/165.35 Deletedinuse: 12
% 164.91/165.35
% 164.91/165.35 Resimplifying inuse:
% 164.91/165.35 Done
% 164.91/165.35
% 164.91/165.35 Resimplifying inuse:
% 164.91/165.35 Done
% 164.91/165.35
% 164.91/165.35
% 164.91/165.35 Intermediate Status:
% 164.91/165.35 Generated: 366048
% 164.91/165.35 Kept: 79633
% 164.91/165.35 Inuse: 1248
% 164.91/165.35 Deleted: 818
% 164.91/165.35 Deletedinuse: 12
% 164.91/165.35
% 164.91/165.35 Resimplifying inuse:
% 164.91/165.35 Done
% 164.91/165.35
% 164.91/165.35 Resimplifying clauses:
% 164.91/165.35 Done
% 164.91/165.35
% 164.91/165.35
% 164.91/165.35 Intermediate Status:
% 164.91/165.35 Generated: 382663
% 164.91/165.35 Kept: 81694
% 164.91/165.35 Inuse: 1260
% 164.91/165.35 Deleted: 1309
% 164.91/165.35 Deletedinuse: 19
% 164.91/165.35
% 164.91/165.35 Resimplifying inuse:
% 164.91/165.35 Done
% 164.91/165.35
% 164.91/165.35 Resimplifying inuse:
% 164.91/165.35 Done
% 164.91/165.35
% 164.91/165.35
% 164.91/165.35 Intermediate Status:
% 164.91/165.35 Generated: 392619
% 164.91/165.35 Kept: 83965
% 164.91/165.35 Inuse: 1290
% 164.91/165.35 Deleted: 1316
% 164.91/165.35 Deletedinuse: 26
% 164.91/165.35
% 164.91/165.35 Resimplifying inuse:
% 164.91/165.35 Done
% 164.91/165.35
% 164.91/165.35 Resimplifying inuse:
% 164.91/165.35 Done
% 164.91/165.35
% 164.91/165.35
% 164.91/165.35 Intermediate Status:
% 164.91/165.35 Generated: 401384
% 164.91/165.35 Kept: 86041
% 164.91/165.35 Inuse: 1297
% 164.91/165.35 Deleted: 1316
% 164.91/165.35 Deletedinuse: 26
% 164.91/165.35
% 164.91/165.35 Resimplifying inuse:
% 164.91/165.35 Done
% 164.91/165.35
% 164.91/165.35
% 164.91/165.35 Intermediate Status:
% 164.91/165.35 Generated: 410690
% 164.91/165.35 Kept: 88291
% 164.91/165.35 Inuse: 1304
% 164.91/165.35 Deleted: 1317
% 164.91/165.35 Deletedinuse: 26
% 164.91/165.35
% 164.91/165.35 Resimplifying inuse:
% 164.91/165.35 Done
% 164.91/165.35
% 164.91/165.35
% 164.91/165.35 Intermediate Status:
% 164.91/165.35 Generated: 418325
% 164.91/165.35 Kept: 90321
% 164.91/165.35 Inuse: 1308
% 164.91/165.35 Deleted: 1318
% 164.91/165.35 Deletedinuse: 26
% 164.91/165.35
% 164.91/165.35 Resimplifying inuse:
% 164.91/165.35 Done
% 164.91/165.35
% 164.91/165.35
% 164.91/165.35 Intermediate Status:
% 164.91/165.35 Generated: 426532
% 164.91/165.35 Kept: 92513
% 164.91/165.35 Inuse: 1313
% 164.91/165.35 Deleted: 1318
% 164.91/165.35 Deletedinuse: 26
% 164.91/165.35
% 164.91/165.35 Resimplifying inuse:
% 164.91/165.35 Done
% 164.91/165.35
% 164.91/165.35
% 164.91/165.35 Intermediate Status:
% 164.91/165.35 Generated: 434754
% 164.91/165.35 Kept: 94630
% 164.91/165.35 Inuse: 1318
% 164.91/165.35 Deleted: 1318
% 164.91/165.35 Deletedinuse: 26
% 164.91/165.35
% 164.91/165.35 Resimplifying inuse:
% 164.91/165.35 Done
% 164.91/165.35
% 164.91/165.35
% 164.91/165.35 Intermediate Status:
% 164.91/165.35 Generated: 442381
% 164.91/165.35 Kept: 96675
% 164.91/165.35 Inuse: 1323
% 164.91/165.35 Deleted: 1318
% 164.91/165.35 Deletedinuse: 26
% 164.91/165.35
% 164.91/165.35 Resimplifying inuse:
% 164.91/165.35 Done
% 164.91/165.35
% 164.91/165.35 Resimplifying inuse:
% 164.91/165.35 Done
% 164.91/165.35
% 164.91/165.35 *** allocated 6568290 integers for clauses
% 164.91/165.35
% 164.91/165.35 Intermediate Status:
% 164.91/165.35 Generated: 455650
% 164.91/165.35 Kept: 99123
% 164.91/165.35 Inuse: 1347
% 164.91/165.35 Deleted: 1319
% 164.91/165.35 Deletedinuse: 26
% 164.91/165.35
% 164.91/165.35 Resimplifying inuse:
% 164.91/165.35 Done
% 164.91/165.35
% 164.91/165.35 Resimplifying inuse:
% 164.91/165.35 Done
% 164.91/165.35
% 164.91/165.35
% 164.91/165.35 Intermediate Status:
% 164.91/165.35 Generated: 463529
% 164.91/165.35 Kept: 101619
% 164.91/165.35 Inuse: 1372
% 164.91/165.35 Deleted: 1323
% 164.91/165.35 Deletedinuse: 30
% 164.91/165.35
% 164.91/165.35 Resimplifying inuse:
% 164.91/165.35 Done
% 164.91/165.35
% 164.91/165.35 Resimplifying clauses:
% 288.43/288.87 Done
% 288.43/288.87
% 288.43/288.87 *** allocated 4378860 integers for termspace/termends
% 288.43/288.87 Resimplifying inuse:
% 288.43/288.87 Done
% 288.43/288.87
% 288.43/288.87
% 288.43/288.87 Intermediate Status:
% 288.43/288.87 Generated: 475885
% 288.43/288.87 Kept: 104921
% 288.43/288.87 Inuse: 1387
% 288.43/288.87 Deleted: 1794
% 288.43/288.87 Deletedinuse: 30
% 288.43/288.87
% 288.43/288.87 Resimplifying inuse:
% 288.43/288.87 Done
% 288.43/288.87
% 288.43/288.87 Resimplifying inuse:
% 288.43/288.87 Done
% 288.43/288.87
% 288.43/288.87
% 288.43/288.87 Intermediate Status:
% 288.43/288.87 Generated: 491747
% 288.43/288.87 Kept: 107191
% 288.43/288.87 Inuse: 1402
% 288.43/288.87 Deleted: 1794
% 288.43/288.87 Deletedinuse: 30
% 288.43/288.87
% 288.43/288.87 Resimplifying inuse:
% 288.43/288.87 Done
% 288.43/288.87
% 288.43/288.87
% 288.43/288.87 Intermediate Status:
% 288.43/288.87 Generated: 498729
% 288.43/288.87 Kept: 109972
% 288.43/288.87 Inuse: 1407
% 288.43/288.87 Deleted: 1794
% 288.43/288.87 Deletedinuse: 30
% 288.43/288.87
% 288.43/288.87 Resimplifying inuse:
% 288.43/288.87 Done
% 288.43/288.87
% 288.43/288.87
% 288.43/288.87 Intermediate Status:
% 288.43/288.87 Generated: 518597
% 288.43/288.87 Kept: 114329
% 288.43/288.87 Inuse: 1427
% 288.43/288.87 Deleted: 1794
% 288.43/288.87 Deletedinuse: 30
% 288.43/288.87
% 288.43/288.87 Resimplifying inuse:
% 288.43/288.87 Done
% 288.43/288.87
% 288.43/288.87
% 288.43/288.87 Intermediate Status:
% 288.43/288.87 Generated: 533177
% 288.43/288.87 Kept: 117871
% 288.43/288.87 Inuse: 1432
% 288.43/288.87 Deleted: 1794
% 288.43/288.87 Deletedinuse: 30
% 288.43/288.87
% 288.43/288.87 Resimplifying inuse:
% 288.43/288.87 Done
% 288.43/288.87
% 288.43/288.87 Resimplifying inuse:
% 288.43/288.87 Done
% 288.43/288.87
% 288.43/288.87
% 288.43/288.87 Intermediate Status:
% 288.43/288.87 Generated: 545129
% 288.43/288.87 Kept: 122051
% 288.43/288.87 Inuse: 1447
% 288.43/288.87 Deleted: 1794
% 288.43/288.87 Deletedinuse: 30
% 288.43/288.87
% 288.43/288.87 Resimplifying inuse:
% 288.43/288.87 Done
% 288.43/288.87
% 288.43/288.87 Resimplifying clauses:
% 288.43/288.87 Done
% 288.43/288.87
% 288.43/288.87
% 288.43/288.87 Intermediate Status:
% 288.43/288.87 Generated: 552436
% 288.43/288.87 Kept: 125249
% 288.43/288.87 Inuse: 1452
% 288.43/288.87 Deleted: 1919
% 288.43/288.87 Deletedinuse: 30
% 288.43/288.87
% 288.43/288.87 Resimplifying inuse:
% 288.43/288.87 Done
% 288.43/288.87
% 288.43/288.87 Resimplifying inuse:
% 288.43/288.87 Done
% 288.43/288.87
% 288.43/288.87
% 288.43/288.87 Intermediate Status:
% 288.43/288.87 Generated: 563647
% 288.43/288.87 Kept: 127265
% 288.43/288.87 Inuse: 1483
% 288.43/288.87 Deleted: 1919
% 288.43/288.87 Deletedinuse: 30
% 288.43/288.87
% 288.43/288.87 Resimplifying inuse:
% 288.43/288.87 Done
% 288.43/288.87
% 288.43/288.87
% 288.43/288.87 Intermediate Status:
% 288.43/288.87 Generated: 577984
% 288.43/288.87 Kept: 132351
% 288.43/288.87 Inuse: 1492
% 288.43/288.87 Deleted: 1919
% 288.43/288.87 Deletedinuse: 30
% 288.43/288.87
% 288.43/288.87 Resimplifying inuse:
% 288.43/288.87 Done
% 288.43/288.87
% 288.43/288.87
% 288.43/288.87 Intermediate Status:
% 288.43/288.87 Generated: 592800
% 288.43/288.87 Kept: 137290
% 288.43/288.87 Inuse: 1506
% 288.43/288.87 Deleted: 1920
% 288.43/288.87 Deletedinuse: 30
% 288.43/288.87
% 288.43/288.87 Resimplifying inuse:
% 288.43/288.87 Done
% 288.43/288.87
% 288.43/288.87 Resimplifying inuse:
% 288.43/288.87 Done
% 288.43/288.87
% 288.43/288.87
% 288.43/288.87 Intermediate Status:
% 288.43/288.87 Generated: 599905
% 288.43/288.87 Kept: 139350
% 288.43/288.87 Inuse: 1539
% 288.43/288.87 Deleted: 1922
% 288.43/288.87 Deletedinuse: 30
% 288.43/288.87
% 288.43/288.87 Resimplifying inuse:
% 288.43/288.87 Done
% 288.43/288.87
% 288.43/288.87 Resimplifying inuse:
% 288.43/288.87 Done
% 288.43/288.87
% 288.43/288.87
% 288.43/288.87 Intermediate Status:
% 288.43/288.87 Generated: 608835
% 288.43/288.87 Kept: 141422
% 288.43/288.87 Inuse: 1564
% 288.43/288.87 Deleted: 1936
% 288.43/288.87 Deletedinuse: 44
% 288.43/288.87
% 288.43/288.87 Resimplifying inuse:
% 288.43/288.87 Done
% 288.43/288.87
% 288.43/288.87 Resimplifying clauses:
% 288.43/288.87 Done
% 288.43/288.87
% 288.43/288.87 Resimplifying inuse:
% 288.43/288.87 Done
% 288.43/288.87
% 288.43/288.87
% 288.43/288.87 Intermediate Status:
% 288.43/288.87 Generated: 617854
% 288.43/288.87 Kept: 143422
% 288.43/288.87 Inuse: 1585
% 288.43/288.87 Deleted: 2537
% 288.43/288.87 Deletedinuse: 44
% 288.43/288.87
% 288.43/288.87 Resimplifying inuse:
% 288.43/288.87 Done
% 288.43/288.87
% 288.43/288.87 *** allocated 9852435 integers for clauses
% 288.43/288.87
% 288.43/288.87 Intermediate Status:
% 288.43/288.87 Generated: 630433
% 288.43/288.87 Kept: 147339
% 288.43/288.87 Inuse: 1603
% 288.43/288.87 Deleted: 2537
% 288.43/288.87 Deletedinuse: 44
% 288.43/288.87
% 288.43/288.87 Resimplifying inuse:
% 288.43/288.87 Done
% 288.43/288.87
% 288.43/288.87 Resimplifying inuse:
% 288.43/288.87 Done
% 288.43/288.87
% 288.43/288.87
% 288.43/288.87 Intermediate Status:
% 288.43/288.87 Generated: 640896
% 288.43/288.87 Kept: 149354
% 288.43/288.87 Inuse: 1623
% 288.43/288.87 Deleted: 2539
% 288.43/288.87 Deletedinuse: 46
% 288.43/288.87
% 288.43/288.87 Resimplifying inuse:
% 288.43/288.87 Done
% 288.43/288.87
% 288.43/288.87
% 288.43/288.87 Intermediate Status:
% 288.43/288.87 Generated: 656473
% 288.43/288.87 Kept: 152665
% 288.43/288.87 Inuse: 1638
% 288.43/288.87 Deleted: 2545
% 288.43/288.87 Deletedinuse: 52
% 288.43/288.87
% 288.43/288.87 Resimplifying inuse:
% 288.43/288.87 Done
% 288.43/288.87
% 288.43/288.87 Resimplifying inuse:
% 288.43/288.87 Done
% 288.43/288.87
% 288.43/288.87
% 288.43/288.87 Intermediate Status:
% 288.43/288.87 Generated: 668648
% 288.43/288.87 Kept: 154768
% 288.43/288.87 Inuse: 1658
% 288.43/288.87 Deleted: 2545
% 288.43/288.87 Deletedinuse: 52
% 288.43/288.87
% 288.43/288.87 Resimplifying inuse:
% 288.43/288.87 Done
% 288.43/288.87
% 288.43/288.87 Resimplifying inuse:
% 288.43/288.87 Done
% 288.43/288.87
% 288.43/288.87
% 288.43/288.87 Intermediate Status:
% 288.43/288.87 Generated: 680461
% 288.43/288.87 Kept: 157102
% 288.43/288.87 Inuse: 1683
% 288.43/288.87 Deleted: 2555
% 288.43/288.87 Deletedinuse: 52
% 288.43/288.87
% 288.43/288.87 Resimplifying inuse:
% 288.43/288.87 Done
% 288.43/288.87
% 288.43/288.87 *** allocated 6568290 integers for termspace/termends
% 288.43/288.87 Resimplifying inuse:
% 288.43/288.87 Done
% 288.43/288.87
% 288.43/288.87
% 288.43/288.87 Intermediate Status:
% 288.43/288.87 Generated: 688754
% 288.43/288.87 Kept: 159168
% 288.43/288.87 Inuse: 1708
% 288.43/288.87 Deleted: 2555
% 288.43/288.87 Deletedinuse: 52
% 288.43/288.87
% 288.43/288.87 Resimplifying inuse:
% 288.43/288.87 Done
% 288.43/288.87
% 288.43/288.87 Resimplifying inuse:
% 288.43/288.87 Done
% 288.43/288.87
% 288.43/288.87
% 288.43/288.87 Intermediate Status:
% 288.43/288.87 Generated: 714439
% 288.43/288.87 Kept: 164115
% 288.43/288.87 Inuse: 1723
% 288.43/288.87 Deleted: 2555
% 288.43/288.87 Deletedinuse: 52
% 288.43/288.87
% 288.43/288.87 Resimplifying inuse:
% 288.43/288.87 Done
% 288.43/288.87
% 288.43/288.87 Resimplifying clauses:
% 288.43/288.87 Done
% 288.43/288.87
% 288.43/288.87 Resimplifying inuse:
% 288.43/288.87 Done
% 288.43/288.87
% 288.43/288.87
% 288.43/288.87 Intermediate Status:
% 288.43/288.87 Generated: 728676
% 288.43/288.87 Kept: 166133
% 288.43/288.87 Inuse: 1745
% 288.43/288.87 Deleted: 6681
% 288.43/288.87 Deletedinuse: 52
% 288.43/288.87
% 288.43/288.87 Resimplifying inuse:
% 288.43/288.87 Done
% 288.43/288.87
% 288.43/288.87
% 288.43/288.87 Intermediate Status:
% 288.43/288.87 Generated: 747726
% 288.43/288.87 Kept: 175601
% 288.43/288.87 Inuse: 1758
% 288.43/288.87 Deleted: 6681
% 288.43/288.87 Deletedinuse: 52
% 288.43/288.87
% 288.43/288.87 Resimplifying inuse:
% 288.43/288.87 Done
% 288.43/288.87
% 288.43/288.87
% 288.43/288.87 Intermediate Status:
% 288.43/288.87 Generated: 756198
% 288.43/288.87 Kept: 179154
% 288.43/288.87 Inuse: 1763
% 288.43/288.87 Deleted: 6681
% 288.43/288.87 Deletedinuse: 52
% 288.43/288.87
% 288.43/288.87 Resimplifying inuse:
% 288.43/288.87 Done
% 288.43/288.87
% 288.43/288.87 Resimplifying inuse:
% 288.43/288.87 Done
% 288.43/288.87
% 288.43/288.87
% 288.43/288.87 Intermediate Status:
% 288.43/288.87 Generated: 765683
% 288.43/288.87 Kept: 181163
% 288.43/288.87 Inuse: 1778
% 288.43/288.87 DCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------