TSTP Solution File: SWW236+1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWW236+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n028.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 23:21:27 EDT 2022
% Result : Timeout 300.05s 300.44s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SWW236+1 : TPTP v8.1.0. Released v5.2.0.
% 0.03/0.14 % Command : bliksem %s
% 0.14/0.35 % Computer : n028.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % DateTime : Sun Jun 5 15:45:12 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.99/1.61 *** allocated 10000 integers for termspace/termends
% 0.99/1.61 *** allocated 10000 integers for clauses
% 0.99/1.61 *** allocated 10000 integers for justifications
% 0.99/1.61 *** allocated 15000 integers for termspace/termends
% 0.99/1.61 *** allocated 22500 integers for termspace/termends
% 0.99/1.61 *** allocated 33750 integers for termspace/termends
% 0.99/1.61 Bliksem 1.12
% 0.99/1.61
% 0.99/1.61
% 0.99/1.61 Automatic Strategy Selection
% 0.99/1.61
% 0.99/1.61 *** allocated 50625 integers for termspace/termends
% 0.99/1.61 *** allocated 75937 integers for termspace/termends
% 0.99/1.61 *** allocated 113905 integers for termspace/termends
% 0.99/1.61
% 0.99/1.61 Clauses:
% 0.99/1.61
% 0.99/1.61 { ! hAPP( Y, skol1( X, Y ) ) = hAPP( X, skol1( X, Y ) ), Y = X }.
% 0.99/1.61 { ! v_c____ = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.99/1.61 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.61 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.99/1.61 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs
% 0.99/1.61 ( tc_RealDef_Oreal, v_da____ ), c_RealVector_Onorm__class_Onorm(
% 0.99/1.61 tc_Complex_Ocomplex, v_aa____ ) ), c_RealVector_Onorm__class_Onorm(
% 0.99/1.61 tc_Complex_Ocomplex, v_c____ ) ), c_RealVector_Onorm__class_Onorm(
% 0.99/1.61 tc_Complex_Ocomplex, v_z____ ) ) }.
% 0.99/1.61 { ! v_p = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.99/1.61 tc_Complex_Ocomplex ) ) }.
% 0.99/1.61 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.61 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.99/1.61 ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.99/1.61 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.99/1.61 ( X, Y ) ) ) }.
% 0.99/1.61 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.61 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.99/1.61 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 0.99/1.61 c_RealVector_Onorm__class_Onorm( X, Y ) ) ) }.
% 0.99/1.61 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 0.99/1.61 c_Groups_Oplus__class_Oplus( X, Z, Y ) ), c_Groups_Oplus__class_Oplus( X
% 0.99/1.61 , c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) )
% 0.99/1.61 ) }.
% 0.99/1.61 { ! class_Orderings_Opreorder( X ), c_Orderings_Oord__class_Oless__eq( X, Y
% 0.99/1.61 , Y ) }.
% 0.99/1.61 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Oabs__class_Oabs
% 0.99/1.61 ( tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( X, Y ) ) =
% 0.99/1.61 c_RealVector_Onorm__class_Onorm( X, Y ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.61 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ),
% 0.99/1.61 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, X ) ) }.
% 0.99/1.61 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.99/1.61 c_Groups_Oabs__class_Oabs( X, c_Groups_Oplus__class_Oplus( X,
% 0.99/1.61 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ) )
% 0.99/1.61 = c_Groups_Oplus__class_Oplus( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.99/1.61 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, hAPP
% 0.99/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 0.99/1.61 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__idom( X ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Y ) ),
% 0.99/1.61 c_Groups_Oabs__class_Oabs( X, Y ) ) = hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.99/1.61 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 0.99/1.61 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.99/1.61 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 0.99/1.61 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.99/1.61 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oabs__class_Oabs( X, Y
% 0.99/1.61 ) ) }.
% 0.99/1.61 { v_cs____ = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.99/1.61 tc_Complex_Ocomplex ) ) }.
% 0.99/1.61 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.99/1.61 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.99/1.61 { ! class_Fields_Ofield__inverse__zero( X ), !
% 0.99/1.61 class_RealVector_Oreal__normed__field( X ),
% 0.99/1.61 c_RealVector_Onorm__class_Onorm( X, c_Rings_Oinverse__class_Odivide( X, Z
% 0.99/1.61 , Y ) ) = c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.99/1.61 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.99/1.61 ( X, Y ) ) }.
% 0.99/1.61 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.61 }.
% 0.99/1.61 { ! class_RealVector_Oreal__normed__field( X ),
% 0.99/1.61 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.99/1.61 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.61 { ! class_Groups_Ozero( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y, Y =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.61 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 0.99/1.61 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.99/1.61 c_Rings_Oinverse__class_Odivide( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.61 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) =
% 0.99/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y )
% 0.99/1.61 }.
% 0.99/1.61 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.99/1.61 c_RealVector_Onorm__class_Onorm( X, Y ) = c_Groups_Ozero__class_Ozero(
% 0.99/1.61 tc_RealDef_Oreal ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.61 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X, Y )
% 0.99/1.61 = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.99/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP
% 0.99/1.61 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), Y ) ), X ) =
% 0.99/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), hAPP
% 0.99/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.99/1.61 { ! class_RealVector_Oreal__normed__field( X ), Y =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X,
% 0.99/1.61 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 0.99/1.61 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.99/1.61 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.99/1.61 ( X, Y ) ) }.
% 0.99/1.61 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.61 , ! T = c_Rings_Oinverse__class_Odivide( X, Z, Y ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z }.
% 0.99/1.61 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.61 , ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, T =
% 0.99/1.61 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.99/1.61 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.61 , ! c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z, T = hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.99/1.61 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.61 , ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.99/1.61 c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z }.
% 0.99/1.61 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.61 , ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.99/1.61 c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z }.
% 0.99/1.61 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.61 , ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, T =
% 0.99/1.61 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.99/1.61 { ! class_Rings_Odivision__ring( X ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), T ), c_Rings_Oinverse__class_Odivide
% 0.99/1.61 ( X, Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 0.99/1.61 { ! class_RealVector_Oreal__normed__field( X ),
% 0.99/1.61 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, T, Z
% 0.99/1.61 ), Y ) = c_Groups_Oplus__class_Oplus( X, c_Rings_Oinverse__class_Odivide
% 0.99/1.61 ( X, T, Y ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.99/1.61 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.99/1.61 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.99/1.61 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ),
% 0.99/1.61 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.99/1.61 { ! class_Rings_Ono__zero__divisors( X ), ! hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.61 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.61 { ! class_Rings_Ono__zero__divisors( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.99/1.61 X ), Z = c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.61 { ! class_Rings_Oring__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.61 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.61 { ! class_Rings_Oring__no__zero__divisors( X ), ! Z =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.61 { ! class_Rings_Oring__no__zero__divisors( X ), ! Y =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.61 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.99/1.61 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.61 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.99/1.61 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.61 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.61 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.61 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.99/1.61 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.61 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.99/1.61 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.61 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.61 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.61 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.99/1.61 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.99/1.61 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.99/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.99/1.61 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero( X ) =
% 0.99/1.61 c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 0.99/1.61 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.99/1.61 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.99/1.61 { c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, X ) =
% 0.99/1.61 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) }.
% 0.99/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.99/1.61 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ) ), X ) =
% 0.99/1.61 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.99/1.61 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.99/1.61 c_Groups_Oabs__class_Oabs( X, Y ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.61 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! Y =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oabs__class_Oabs( X, Y ) =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.61 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.99/1.61 c_Groups_Oabs__class_Oabs( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.61 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.61 c_RealVector_Onorm__class_Onorm( X, Y ), c_Groups_Ozero__class_Ozero(
% 0.99/1.61 tc_RealDef_Oreal ) ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.61 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq(
% 0.99/1.61 tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( X, Y ),
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.99/1.61 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.99/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.61 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.61 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.99/1.61 X ), Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( X ) ) }.
% 0.99/1.61 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.61 , c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.61 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.99/1.61 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.61 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.61 , Z, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.61 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.99/1.61 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.61 { ! class_Rings_Oordered__semiring( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.99/1.61 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.99/1.61 { ! class_Rings_Oordered__semiring( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.99/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.99/1.61 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.99/1.61 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.61 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.61 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.99/1.61 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.61 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.61 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.99/1.61 { ! class_Rings_Oordered__comm__semiring( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.99/1.61 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.99/1.61 { ! class_Rings_Oordered__semiring( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.99/1.61 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.99/1.61 { ! class_Rings_Oordered__semiring( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.99/1.61 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.99/1.61 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.61 , Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.61 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.99/1.61 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.99/1.61 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.99/1.61 X ), Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( X ) ) }.
% 0.99/1.61 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.61 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.61 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.61 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ),
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.61 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.99/1.61 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( X ) ), alpha1( X, Y, Z ), alpha26( X, Y, Z ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha1( X, Y, Z ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( X ) ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha26( X, Y, Z ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( X ) ) }.
% 0.99/1.61 { ! alpha26( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.61 { ! alpha26( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.99/1.61 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( X ), Y ), alpha26( X, Y, Z ) }.
% 0.99/1.61 { ! alpha1( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.99/1.61 { ! alpha1( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.61 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ) ), alpha1( X, Y, Z ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), alpha2( X, Y
% 0.99/1.61 , Z ), alpha27( X, Y, Z ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha2( X, Y, Z ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha27( X, Y, Z ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.61 { ! alpha27( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.61 { ! alpha27( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.99/1.61 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ) ), alpha27( X, Y, Z ) }.
% 0.99/1.61 { ! alpha2( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.99/1.61 { ! alpha2( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.61 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ), Y ), alpha2( X, Y, Z ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.99/1.61 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) }.
% 0.99/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.61 , c_Groups_Oplus__class_Oplus( X, Y, Z ), c_Groups_Ozero__class_Ozero( X
% 0.99/1.61 ) ) }.
% 0.99/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.99/1.61 Z, Y ) ) }.
% 0.99/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.99/1.61 Y, Z ) ) }.
% 0.99/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.99/1.61 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 0.99/1.61 .
% 0.99/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.99/1.61 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.99/1.61 .
% 0.99/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.99/1.61 X ), Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), ! Z =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.99/1.61 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.99/1.61 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.99/1.61 ) }.
% 0.99/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Y,
% 0.99/1.61 Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.61 ) }.
% 0.99/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.61 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X
% 0.99/1.61 , Y, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.61 c_Groups_Oplus__class_Oplus( X, Y, Y ) ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.61 ) }.
% 0.99/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.61 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.99/1.61 ), c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.99/1.61 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.61 ), c_Groups_Oabs__class_Oabs( X, Y ) = Y }.
% 0.99/1.61 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Y ),
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.61 }.
% 0.99/1.61 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! Y =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.61 c_Groups_Oabs__class_Oabs( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.61 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.61 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.99/1.61 { ! class_Rings_Oordered__ring__abs( X ), alpha73( X, Z ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.61 ), c_Groups_Oabs__class_Oabs( X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 0.99/1.61 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.99/1.61 { ! class_Rings_Oordered__ring__abs( X ), alpha73( X, Z ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.61 ), c_Groups_Oabs__class_Oabs( X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 0.99/1.61 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.99/1.61 { ! alpha73( X, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.99/1.61 { ! alpha73( X, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.61 { c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.61 ), c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( X ) ), alpha73( X, Y ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.99/1.61 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 0.99/1.61 Y ) = c_Groups_Oabs__class_Oabs( X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.61 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.99/1.61 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.99/1.61 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.99/1.61 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.99/1.61 hAPP( Y, U ) ) }.
% 0.99/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.99/1.61 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.99/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.99/1.61 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.99/1.61 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.61 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.99/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.99/1.61 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.99/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.99/1.61 , Y ), ! Z = T, c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.99/1.61 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y
% 0.99/1.61 ), ! Y = T, c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.99/1.61 { ! class_Orderings_Oorder( X ), ! Z = Y, !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.99/1.61 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.99/1.61 ( X, Y, T ), c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.99/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.99/1.61 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.99/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.99/1.61 , Y ), ! Y = Z, c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.99/1.61 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.99/1.61 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.99/1.61 hAPP( Y, U ) ) }.
% 0.99/1.61 { ! class_Orderings_Opreorder( X ), ! Z = Y,
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.99/1.61 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.99/1.61 ( X, Z, Y ) }.
% 0.99/1.61 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.99/1.61 ( X, Y, Z ) }.
% 0.99/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.99/1.61 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.99/1.61 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.99/1.61 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.99/1.61 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.99/1.61 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.99/1.61 hAPP( Y, U ) ) }.
% 0.99/1.61 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, hAPP
% 0.99/1.61 ( Z, skol2( X, Y, Z ) ), hAPP( Y, skol2( X, Y, Z ) ) ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }.
% 0.99/1.61 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.61 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y ),
% 0.99/1.61 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.99/1.61 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.99/1.61 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X ) ),
% 0.99/1.61 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) ) }.
% 0.99/1.61 { ! class_Groups_Oab__semigroup__mult( X ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.61 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.99/1.61 c_Groups_Oplus__class_Oplus( X, Z, T ) = c_Groups_Oplus__class_Oplus( X,
% 0.99/1.61 Y, T ), Z = Y }.
% 0.99/1.61 { ! class_Groups_Ocancel__ab__semigroup__add( X ), !
% 0.99/1.61 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.99/1.61 T, Y ), Z = Y }.
% 0.99/1.61 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.99/1.61 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.99/1.61 T, Y ), Z = Y }.
% 0.99/1.61 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.99/1.61 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.99/1.61 Y, Z ), T = Y }.
% 0.99/1.61 { ! class_Groups_Ocancel__semigroup__add( X ), ! T = Y,
% 0.99/1.61 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.99/1.61 Y, Z ) }.
% 0.99/1.61 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.99/1.61 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.99/1.61 T, Y ), Z = Y }.
% 0.99/1.61 { ! class_Groups_Ocancel__semigroup__add( X ), ! Z = Y,
% 0.99/1.61 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.99/1.61 T, Y ) }.
% 0.99/1.61 { ! class_Groups_Oab__semigroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.99/1.61 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.99/1.61 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ), Y = X }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Z ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, Z ) }.
% 0.99/1.61 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ) }.
% 0.99/1.61 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, X ) }.
% 0.99/1.61 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.99/1.61 c_Groups_Oabs__class_Oabs( X, c_Groups_Oabs__class_Oabs( X, Y ) ) =
% 0.99/1.61 c_Groups_Oabs__class_Oabs( X, Y ) }.
% 0.99/1.61 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.99/1.61 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.99/1.61 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.99/1.61 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.99/1.61 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.99/1.61 U ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.99/1.61 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.99/1.61 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.99/1.61 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.99/1.61 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.99/1.61 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.99/1.61 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.99/1.61 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.99/1.61 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.99/1.61 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.99/1.61 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.99/1.61 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.99/1.61 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.99/1.61 { ! class_Rings_Osemiring( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP
% 0.99/1.61 ( c_Groups_Otimes__class_Otimes( X ), U ), T ),
% 0.99/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.61 ( X ), Z ), T ), Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, U, Z
% 0.99/1.61 ) ), T ), Y ) }.
% 0.99/1.61 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.99/1.61 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.61 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.99/1.61 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.61 { ! class_Rings_Ocomm__semiring( X ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.99/1.61 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.61 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.99/1.61 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.99/1.61 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.99/1.61 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.99/1.61 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.99/1.61 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.99/1.61 { v_cs____ = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.99/1.61 tc_Complex_Ocomplex ) ) }.
% 0.99/1.61 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.61 c_RealVector_Onorm__class_Onorm( X, Z ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ),
% 0.99/1.61 c_RealVector_Onorm__class_Onorm( X, T ) ) ), Z =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.61 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.99/1.61 c_Rings_Oinverse__class_Odivide( X, U, Y ),
% 0.99/1.61 c_Rings_Oinverse__class_Odivide( X, T, Z ) ) =
% 0.99/1.61 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, hAPP
% 0.99/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.99/1.61 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.61 c_Groups_Oplus__class_Oplus( X, c_Rings_Oinverse__class_Odivide( X, T, Y
% 0.99/1.61 ), Z ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus
% 0.99/1.61 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) }
% 0.99/1.61 .
% 0.99/1.61 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.99/1.61 c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ) =
% 0.99/1.61 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.99/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) }.
% 0.99/1.61 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.61 c_Groups_Oplus__class_Oplus( X, T, c_Rings_Oinverse__class_Odivide( X, Z
% 0.99/1.61 , Y ) ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus
% 0.99/1.61 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), Z ), Y ) }
% 0.99/1.61 .
% 0.99/1.61 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, T,
% 0.99/1.61 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 0.99/1.61 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.99/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Y ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.99/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ) ), Z = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.61 }.
% 0.99/1.61 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.99/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.61 }.
% 0.99/1.61 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.61 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.99/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.99/1.61 X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 0.99/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.99/1.61 { ! class_Fields_Olinordered__field( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.99/1.61 X ), c_Groups_Oabs__class_Oabs( X, c_Rings_Oinverse__class_Odivide( X, Z
% 0.99/1.61 , Y ) ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oabs__class_Oabs(
% 0.99/1.61 X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.99/1.61 { ! class_Fields_Ofield__inverse__zero( X ), ! T =
% 0.99/1.61 c_Rings_Oinverse__class_Odivide( X, Z, Y ), alpha28( X, Y, Z, T ) }.
% 0.99/1.61 { ! class_Fields_Ofield__inverse__zero( X ), ! T =
% 0.99/1.61 c_Rings_Oinverse__class_Odivide( X, Z, Y ), alpha3( X, Y, T ) }.
% 0.99/1.61 { ! class_Fields_Ofield__inverse__zero( X ), ! alpha28( X, Y, Z, T ), !
% 0.99/1.61 alpha3( X, Y, T ), T = c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.99/1.61 { ! alpha28( X, Y, Z, T ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP
% 0.99/1.61 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z }.
% 0.99/1.61 { ! Y = c_Groups_Ozero__class_Ozero( X ), alpha28( X, Y, Z, T ) }.
% 0.99/1.61 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, alpha28(
% 0.99/1.61 X, Y, Z, T ) }.
% 0.99/1.61 { ! alpha3( X, Y, Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.61 { Y = c_Groups_Ozero__class_Ozero( X ), alpha3( X, Y, Z ) }.
% 0.99/1.61 { ! Z = c_Groups_Ozero__class_Ozero( X ), alpha3( X, Y, Z ) }.
% 0.99/1.61 { ! class_Fields_Ofield__inverse__zero( X ), !
% 0.99/1.61 c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y, alpha29( X, Y, Z, T ) }.
% 0.99/1.61 { ! class_Fields_Ofield__inverse__zero( X ), !
% 0.99/1.61 c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y, alpha4( X, Y, Z ) }.
% 0.99/1.61 { ! class_Fields_Ofield__inverse__zero( X ), ! alpha29( X, Y, Z, T ), !
% 0.99/1.61 alpha4( X, Y, Z ), c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y }.
% 0.99/1.61 { ! alpha29( X, Y, Z, T ), Z = c_Groups_Ozero__class_Ozero( X ), T = hAPP(
% 0.99/1.61 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 0.99/1.61 { ! Z = c_Groups_Ozero__class_Ozero( X ), alpha29( X, Y, Z, T ) }.
% 0.99/1.61 { ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), alpha29(
% 0.99/1.61 X, Y, Z, T ) }.
% 0.99/1.61 { ! alpha4( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.61 { Z = c_Groups_Ozero__class_Ozero( X ), alpha4( X, Y, Z ) }.
% 0.99/1.61 { ! Y = c_Groups_Ozero__class_Ozero( X ), alpha4( X, Y, Z ) }.
% 0.99/1.61 { ! c_Polynomial_OpCons( tc_Complex_Ocomplex, v_c____, v_cs____ ) =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) )
% 0.99/1.61 }.
% 0.99/1.61 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) = hAPP( hAPP
% 0.99/1.61 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ), Z = Y }.
% 0.99/1.61 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP
% 0.99/1.61 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) = hAPP(
% 0.99/1.61 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) }.
% 0.99/1.61 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) = hAPP( hAPP
% 0.99/1.61 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ), Z = Y }.
% 0.99/1.61 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP
% 0.99/1.61 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) = hAPP(
% 0.99/1.61 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.61 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ),
% 0.99/1.61 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Z ) ) ), Y =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.99/1.61 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.99/1.61 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.99/1.61 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, Y, X ) ), alpha5( X, Y
% 0.99/1.61 ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.99/1.61 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, Y, X ) ), alpha30( X,
% 0.99/1.61 Y ) }.
% 0.99/1.61 { ! alpha5( X, Y ), ! alpha30( X, Y ), c_Orderings_Oord__class_Oless__eq(
% 0.99/1.61 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.99/1.61 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, Y, X ) ) }.
% 0.99/1.61 { ! alpha30( X, Y ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), alpha30( X, Y ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), alpha30( X, Y ) }.
% 0.99/1.61 { ! alpha5( X, Y ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y
% 0.99/1.61 , c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), alpha5( X, Y ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), alpha5( X, Y ) }.
% 0.99/1.61 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.99/1.61 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.99/1.61 { ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! X =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.99/1.61 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.99/1.61 { ! class_Fields_Ofield__inverse__zero( X ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Odivide( X, U
% 0.99/1.61 , T ) ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 0.99/1.61 c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.99/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ),
% 0.99/1.61 c_Groups_Oabs__class_Oabs( X, c_Rings_Oinverse__class_Odivide( X, Z, Y )
% 0.99/1.61 ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oabs__class_Oabs( X, Z
% 0.99/1.61 ), c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.99/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.61 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.99/1.61 ) = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X
% 0.99/1.61 ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.99/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.61 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.99/1.61 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.99/1.61 ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.61 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.61 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 0.99/1.61 ( X, Y, T ), c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 0.99/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.99/1.61 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 0.99/1.61 ( X, Z, T ), c_Rings_Oinverse__class_Odivide( X, Y, T ) ) }.
% 0.99/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.99/1.61 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ), alpha6( X, Y, Z ), alpha31
% 0.99/1.61 ( X, Y, Z ) }.
% 0.99/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha6( X, Y, Z
% 0.99/1.61 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 0.99/1.61 ( X, Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha31( X, Y, Z
% 0.99/1.61 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 0.99/1.61 ( X, Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.61 { ! alpha31( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.61 { ! alpha31( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.99/1.61 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( X ), Y ), alpha31( X, Y, Z ) }.
% 0.99/1.61 { ! alpha6( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.99/1.61 { ! alpha6( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.61 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ) ), alpha6( X, Y, Z ) }.
% 0.99/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.61 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ), alpha7( X, Y, Z ), alpha32
% 0.99/1.61 ( X, Y, Z ) }.
% 0.99/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha7( X, Y, Z
% 0.99/1.61 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.99/1.61 ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.99/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha32( X, Y, Z
% 0.99/1.61 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.99/1.61 ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.99/1.61 { ! alpha32( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.61 { ! alpha32( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.99/1.61 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ) ), alpha32( X, Y, Z ) }.
% 0.99/1.61 { ! alpha7( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.99/1.61 { ! alpha7( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.61 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ), Y ), alpha7( X, Y, Z ) }.
% 0.99/1.61 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ), ! c_Rings_Oinverse__class_Odivide( X, U
% 0.99/1.61 , Y ) = c_Rings_Oinverse__class_Odivide( X, T, Z ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), U ), Z ) = hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) }.
% 0.99/1.61 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), U ), Z ) = hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ),
% 0.99/1.61 c_Rings_Oinverse__class_Odivide( X, U, Y ) =
% 0.99/1.61 c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 0.99/1.61 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.99/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) =
% 0.99/1.61 c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 0.99/1.61 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.99/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.99/1.61 c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 0.99/1.61 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.99/1.61 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_c____ ) ) }.
% 0.99/1.61 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.99/1.61 ( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! W = U, T = Z, !
% 0.99/1.61 c_Groups_Oplus__class_Oplus( X, W, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) =
% 0.99/1.61 c_Groups_Oplus__class_Oplus( X, U, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.99/1.61 { c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ) ) =
% 0.99/1.61 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, X, Y ) }.
% 0.99/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.99/1.61 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.99/1.61 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.99/1.61 ( X ), U = T, Z = Y, ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.99/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.61 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.99/1.61 ) }.
% 0.99/1.61 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.99/1.61 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.99/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.61 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.99/1.61 ), ! U = T }.
% 0.99/1.61 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.99/1.61 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.99/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.61 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.99/1.61 ), ! Z = Y }.
% 0.99/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.99/1.61 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.99/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Y
% 0.99/1.61 ) ), Z ) }.
% 0.99/1.61 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.99/1.61 ( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.99/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.61 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.99/1.61 ), U = Z, T = Y }.
% 0.99/1.61 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.99/1.61 ( X ), ! U = Z, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.99/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.61 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.99/1.61 ) }.
% 0.99/1.61 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.99/1.61 ( X ), ! T = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.99/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.61 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.99/1.61 ) }.
% 0.99/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.99/1.61 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.99/1.61 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.99/1.61 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.99/1.61 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.99/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.99/1.61 , ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.99/1.61 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.99/1.61 Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.99/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.99/1.61 , ! Z = T, c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.99/1.61 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.99/1.61 ! Y = T, c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.99/1.61 { ! class_Orderings_Oorder( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless(
% 0.99/1.61 X, T, Y ), c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.99/1.61 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X
% 0.99/1.61 , Y, T ), c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.99/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.99/1.61 , ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.99/1.61 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.99/1.61 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.99/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.99/1.61 , ! Y = Z }.
% 0.99/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.99/1.61 , ! Z = Y }.
% 0.99/1.61 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.99/1.61 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.99/1.61 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.99/1.61 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.99/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.99/1.61 , ! Z = Y }.
% 0.99/1.61 { ! class_Rings_Olinordered__idom( X ), Z = Y,
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.99/1.61 X, Y, Z ) }.
% 0.99/1.61 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.99/1.61 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.99/1.61 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.99/1.61 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Y = Z }.
% 0.99/1.61 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.99/1.61 ), ! Y = Z, ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.99/1.61 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.99/1.61 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.99/1.61 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.99/1.61 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Z = Y }.
% 0.99/1.61 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.99/1.61 Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.99/1.61 { ! class_Orderings_Olinorder( X ), ! Z = Y, !
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.99/1.61 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.99/1.61 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.99/1.61 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.99/1.61 Y ), ! Z = Y }.
% 0.99/1.61 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.99/1.61 Z ), ! Z = Y }.
% 0.99/1.61 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.99/1.61 Y ) }.
% 0.99/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.99/1.61 , Y ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.99/1.61 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.61 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.99/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.99/1.61 , ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.99/1.61 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.99/1.61 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.99/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.99/1.61 , Y ), Y = Z, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.99/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.99/1.61 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.99/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.99/1.61 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.99/1.61 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.61 , Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.99/1.61 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.61 , Z, Y ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.99/1.61 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.99/1.61 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.99/1.61 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.61 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.99/1.61 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.99/1.61 ( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.99/1.61 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.99/1.61 ( X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.99/1.61 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.99/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ), Z = Y }.
% 0.99/1.61 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.99/1.61 ), ! Z = Y, c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.99/1.61 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.99/1.61 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.99/1.61 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.99/1.61 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.99/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.99/1.61 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.99/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.99/1.61 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.99/1.61 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.99/1.61 ( X, Z, Y ) }.
% 0.99/1.61 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.99/1.61 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.99/1.61 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.99/1.61 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.99/1.61 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.61 , Z, Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.99/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.99/1.61 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.99/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.99/1.61 , ! Z = Y }.
% 0.99/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.99/1.61 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.99/1.61 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.99/1.61 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.99/1.61 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.99/1.61 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.99/1.61 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.99/1.61 Z ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.99/1.61 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.99/1.61 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.99/1.61 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.61 , Y, Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.99/1.61 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.99/1.61 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.99/1.61 ( X, Z, Y ) }.
% 0.99/1.61 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, T )
% 0.99/1.61 , c_Groups_Oplus__class_Oplus( X, Y, T ) ), c_Orderings_Oord__class_Oless
% 0.99/1.61 ( X, Z, Y ) }.
% 0.99/1.61 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.99/1.61 ( X, U, T ), c_Orderings_Oord__class_Oless( X,
% 0.99/1.61 c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X, Y
% 0.99/1.61 , T ) ) }.
% 0.99/1.61 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.99/1.61 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.99/1.61 , T, Y ) ) }.
% 0.99/1.61 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.99/1.61 X, c_Groups_Oplus__class_Oplus( X, Z, T ), c_Groups_Oplus__class_Oplus( X
% 0.99/1.61 , Y, T ) ) }.
% 0.99/1.61 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.99/1.61 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.99/1.61 ( X, Z, Y ) }.
% 0.99/1.61 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.99/1.61 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.99/1.61 , T, Y ) ) }.
% 0.99/1.61 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.99/1.61 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ), c_Orderings_Oord__class_Oless
% 0.99/1.61 ( X, T, Y ) }.
% 0.99/1.61 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, T, Y ), c_Orderings_Oord__class_Oless(
% 0.99/1.61 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.99/1.61 , Y, Z ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), Y = X }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.99/1.61 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), ! Y = X }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), Y = X,
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ) }.
% 0.99/1.61 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ), X =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.99/1.61 { ! X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.99/1.61 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha8( X, Y, Z, T ),
% 0.99/1.61 alpha33( X, Y, Z, T ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha8( X, Y, Z, T ),
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha33( X, Y, Z, T ),
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.99/1.61 { ! alpha33( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.61 { ! alpha33( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, T ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.61 , ! c_Orderings_Oord__class_Oless( X, Y, T ), alpha33( X, Y, Z, T ) }.
% 0.99/1.61 { ! alpha8( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.99/1.61 { ! alpha8( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.99/1.61 , ! c_Orderings_Oord__class_Oless( X, T, Y ), alpha8( X, Y, Z, T ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha9( X, Y, Z, T ),
% 0.99/1.61 alpha34( X, Y, Z, T ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha9( X, Y, Z, T ),
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha34( X, Y, Z, T ),
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.99/1.61 { ! alpha34( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.61 { ! alpha34( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( X, T, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.61 , ! c_Orderings_Oord__class_Oless( X, Y, Z ), alpha34( X, Y, Z, T ) }.
% 0.99/1.61 { ! alpha9( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ), T ) }.
% 0.99/1.61 { ! alpha9( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T )
% 0.99/1.61 , ! c_Orderings_Oord__class_Oless( X, Z, Y ), alpha9( X, Y, Z, T ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.99/1.61 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.99/1.61 ! c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless
% 0.99/1.61 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.99/1.61 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.99/1.61 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.99/1.61 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.99/1.61 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.61 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( X ) ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.99/1.61 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.61 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( X ) ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.99/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.99/1.61 .
% 0.99/1.61 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.99/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ) }
% 0.99/1.61 .
% 0.99/1.61 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.61 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.61 ! c_Orderings_Oord__class_Oless( X, Z, T ), c_Orderings_Oord__class_Oless
% 0.99/1.61 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.99/1.61 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.61 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.99/1.61 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( X ) ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.61 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.61 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.99/1.61 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.99/1.61 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP
% 0.99/1.61 ( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.99/1.61 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.99/1.61 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.99/1.61 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__comm__semiring__strict( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.99/1.61 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.99/1.61 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.99/1.61 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.99/1.61 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.99/1.61 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.99/1.61 ( c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.99/1.61 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.99/1.61 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP
% 0.99/1.61 ( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.99/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.61 c_Groups_Oplus__class_Oplus( X, Y, Y ) ), c_Orderings_Oord__class_Oless(
% 0.99/1.61 X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.99/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.61 c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.99/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.99/1.61 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Y
% 0.99/1.61 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.99/1.61 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.99/1.61 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.99/1.61 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.61 c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.61 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless(
% 0.99/1.61 X, T, c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.99/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.61 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.61 , c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.99/1.61 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.61 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, U, T ), c_Orderings_Oord__class_Oless(
% 0.99/1.61 X, c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X
% 0.99/1.61 , Y, T ) ) }.
% 0.99/1.61 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, U )
% 0.99/1.61 , c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.99/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.61 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ), alpha10( X, Y, Z ), alpha35
% 0.99/1.61 ( X, Y, Z ) }.
% 0.99/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha10( X, Y, Z
% 0.99/1.61 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.61 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.99/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha35( X, Y, Z
% 0.99/1.61 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.61 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.99/1.61 { ! alpha35( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.61 { ! alpha35( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.61 , ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.61 ), alpha35( X, Y, Z ) }.
% 0.99/1.61 { ! alpha10( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.99/1.61 { ! alpha10( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.99/1.61 , ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.61 ), alpha10( X, Y, Z ) }.
% 0.99/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, Z,
% 0.99/1.61 Y ), c_Groups_Ozero__class_Ozero( X ) ), alpha11( X, Y, Z ), alpha36( X,
% 0.99/1.61 Y, Z ) }.
% 0.99/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha11( X, Y, Z
% 0.99/1.61 ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X
% 0.99/1.61 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha36( X, Y, Z
% 0.99/1.61 ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X
% 0.99/1.61 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.61 { ! alpha36( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.61 { ! alpha36( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.61 , ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.61 ), alpha36( X, Y, Z ) }.
% 0.99/1.61 { ! alpha11( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.99/1.61 { ! alpha11( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.99/1.61 , ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.61 ), alpha11( X, Y, Z ) }.
% 0.99/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.99/1.61 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.99/1.61 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless
% 0.99/1.61 ( X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X
% 0.99/1.61 , Y, Z ) ) }.
% 0.99/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.99/1.61 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.99/1.61 ( X, Z, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.99/1.61 ( X, c_Rings_Oinverse__class_Odivide( X, Y, Z ),
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.99/1.61 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.99/1.61 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless
% 0.99/1.61 ( X, c_Rings_Oinverse__class_Odivide( X, Y, Z ),
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.99/1.61 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.99/1.61 ( X, Z, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.99/1.61 ( X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X
% 0.99/1.61 , Y, Z ) ) }.
% 0.99/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.99/1.61 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless( X,
% 0.99/1.61 c_Rings_Oinverse__class_Odivide( X, Z, T ),
% 0.99/1.61 c_Rings_Oinverse__class_Odivide( X, Y, T ) ) }.
% 0.99/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.99/1.61 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, T,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.99/1.61 c_Rings_Oinverse__class_Odivide( X, Y, T ),
% 0.99/1.61 c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 0.99/1.61 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X, Y ),
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.61 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.61 c_Groups_Oabs__class_Oabs( X, Y ) ), ! Y = c_Groups_Ozero__class_Ozero( X
% 0.99/1.61 ) }.
% 0.99/1.61 { ! class_Groups_Oordered__ab__group__add__abs( X ), Y =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.99/1.61 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.99/1.61 c_Groups_Oabs__class_Oabs( X, Y ) = Y }.
% 0.99/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.99/1.61 , c_Groups_Oabs__class_Oabs( X, Z ), Y ), ! c_Orderings_Oord__class_Oless
% 0.99/1.61 ( X, c_Groups_Oabs__class_Oabs( X, U ), T ),
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 0.99/1.61 c_Groups_Oabs__class_Oabs( X, U ) ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ),
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 0.99/1.61 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.61 c_RealVector_Onorm__class_Onorm( X, Y ), c_Groups_Ozero__class_Ozero(
% 0.99/1.61 tc_RealDef_Oreal ) ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.99/1.61 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.61 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.99/1.61 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.99/1.61 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.99/1.61 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.61 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.99/1.61 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.99/1.61 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, U, T ), ! c_Orderings_Oord__class_Oless
% 0.99/1.61 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.99/1.61 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.99/1.61 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.61 , U ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.99/1.61 ( X, U, T ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.99/1.61 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.99/1.61 ( X, U, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.99/1.61 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.61 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.61 ! c_Orderings_Oord__class_Oless__eq( X, Z, T ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.99/1.61 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.99/1.61 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.99/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.61 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.99/1.61 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.99/1.61 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.61 ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.99/1.61 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.99/1.61 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.61 ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.99/1.61 ) ) }.
% 0.99/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.99/1.61 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.99/1.61 ) ) }.
% 0.99/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.61 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.61 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.61 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.99/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.99/1.61 ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.61 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.61 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.61 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.99/1.61 ) ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__ring__strict( X ), Z =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.99/1.61 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__ring__strict( X ), Y =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.99/1.61 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.99/1.61 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.61 { ! class_Fields_Olinordered__field( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.61 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.61 , Z ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( X ), c_Rings_Oinverse__class_Odivide( X, Y, Z ) ) }.
% 0.99/1.61 { ! class_Fields_Olinordered__field( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.61 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.99/1.61 ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.61 c_Rings_Oinverse__class_Odivide( X, Y, Z ), c_Groups_Ozero__class_Ozero(
% 0.99/1.61 X ) ) }.
% 0.99/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.99/1.61 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, Y, Z ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.99/1.61 ! c_Orderings_Oord__class_Oless( X, T, U ), c_Orderings_Oord__class_Oless
% 0.99/1.61 ( X, c_Rings_Oinverse__class_Odivide( X, Y, U ),
% 0.99/1.61 c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 0.99/1.61 { ! class_Fields_Olinordered__field( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.61 ), ! c_Orderings_Oord__class_Oless( X, Y, Z ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.99/1.61 ! c_Orderings_Oord__class_Oless__eq( X, T, U ),
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, Y,
% 0.99/1.61 U ), c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 0.99/1.61 { ! class_Fields_Olinordered__field( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.99/1.61 ! c_Orderings_Oord__class_Oless__eq( X, T, U ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.99/1.61 , Y, U ), c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 0.99/1.61 { ! class_Fields_Olinordered__field( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.61 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.61 , Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.61 c_Rings_Oinverse__class_Odivide( X, Y, Z ), c_Groups_Ozero__class_Ozero(
% 0.99/1.61 X ) ) }.
% 0.99/1.61 { ! class_Fields_Olinordered__field( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.61 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.99/1.61 ) ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.99/1.61 X ), c_Rings_Oinverse__class_Odivide( X, Y, Z ) ) }.
% 0.99/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.99/1.61 Z, Y ) ), alpha37( X, Y, Z, T ) }.
% 0.99/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.99/1.61 Z, Y ) ), alpha49( X, Y, Z, T ) }.
% 0.99/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha37( X, Y, Z
% 0.99/1.61 , T ), ! alpha49( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 0.99/1.61 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.99/1.61 { ! alpha49( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ), Y ), alpha57( X, Y, Z, T ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.99/1.61 , alpha49( X, Y, Z, T ) }.
% 0.99/1.61 { ! alpha57( X, Y, Z, T ), alpha49( X, Y, Z, T ) }.
% 0.99/1.61 { ! alpha57( X, Y, Z, T ), alpha64( X, Y, Z, T ) }.
% 0.99/1.61 { ! alpha57( X, Y, Z, T ), alpha12( X, Y, T ) }.
% 0.99/1.61 { ! alpha64( X, Y, Z, T ), ! alpha12( X, Y, T ), alpha57( X, Y, Z, T ) }.
% 0.99/1.61 { ! alpha64( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Z,
% 0.99/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.99/1.61 { c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.61 alpha64( X, Y, Z, T ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha64( X, Y, Z, T ) }.
% 0.99/1.61 { ! alpha37( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X,
% 0.99/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.99/1.61 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.99/1.61 alpha37( X, Y, Z, T ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ), alpha37( X, Y, Z, T )
% 0.99/1.61 }.
% 0.99/1.61 { ! alpha12( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Z,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.61 , alpha12( X, Y, Z ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.61 , alpha12( X, Y, Z ) }.
% 0.99/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.99/1.61 Z ), Y ), alpha38( X, Y, Z, T ) }.
% 0.99/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.99/1.61 Z ), Y ), alpha50( X, Y, Z, T ) }.
% 0.99/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha38( X, Y, Z
% 0.99/1.61 , T ), ! alpha50( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.99/1.61 c_Rings_Oinverse__class_Odivide( X, T, Z ), Y ) }.
% 0.99/1.61 { ! alpha50( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ), Z ), alpha58( X, Y, Z, T ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.99/1.61 , alpha50( X, Y, Z, T ) }.
% 0.99/1.61 { ! alpha58( X, Y, Z, T ), alpha50( X, Y, Z, T ) }.
% 0.99/1.61 { ! alpha58( X, Y, Z, T ), alpha65( X, Y, Z, T ) }.
% 0.99/1.61 { ! alpha58( X, Y, Z, T ), alpha13( X, Y, Z ) }.
% 0.99/1.61 { ! alpha65( X, Y, Z, T ), ! alpha13( X, Y, Z ), alpha58( X, Y, Z, T ) }.
% 0.99/1.61 { ! alpha65( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.99/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ) }.
% 0.99/1.61 { c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.61 alpha65( X, Y, Z, T ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ), alpha65( X, Y, Z, T )
% 0.99/1.61 }.
% 0.99/1.61 { ! alpha38( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless( X,
% 0.99/1.61 T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.99/1.61 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.99/1.61 alpha38( X, Y, Z, T ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha38( X, Y, Z, T ) }.
% 0.99/1.61 { ! alpha13( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.61 , alpha13( X, Y, Z ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.99/1.61 , alpha13( X, Y, Z ) }.
% 0.99/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.99/1.61 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.99/1.61 ( X, T, c_Rings_Oinverse__class_Odivide( X, Z, Y ) ),
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.99/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.99/1.61 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.99/1.61 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.99/1.61 Z, Y ) ) }.
% 0.99/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.99/1.61 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.99/1.61 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ),
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.99/1.61 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.99/1.61 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.99/1.61 Y ), Z ) }.
% 0.99/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.99/1.61 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.99/1.61 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.99/1.61 Y ), Z ) }.
% 0.99/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.99/1.61 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.99/1.61 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.99/1.61 Z, Y ) ) }.
% 0.99/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.99/1.61 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.99/1.61 ( X, T, c_Rings_Oinverse__class_Odivide( X, Z, Y ) ),
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.99/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.99/1.61 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.99/1.61 ( X, Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ),
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.99/1.61 Z, Y ) ) }.
% 0.99/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.99/1.61 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.99/1.61 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ),
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ) }.
% 0.99/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.99/1.61 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.99/1.61 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ),
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.99/1.61 Y ), Z ) }.
% 0.99/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.99/1.61 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 0.99/1.61 , c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.99/1.61 Y ), c_Rings_Oinverse__class_Odivide( X, T, Z ) ) }.
% 0.99/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.99/1.61 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, T,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless( X,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.99/1.61 Z ), c_Rings_Oinverse__class_Odivide( X, T, Y ) ) }.
% 0.99/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.99/1.61 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oabs__class_Oabs( X, Z ), Y
% 0.99/1.61 ) = c_Groups_Oabs__class_Oabs( X, c_Rings_Oinverse__class_Odivide( X, Z
% 0.99/1.61 , Y ) ) }.
% 0.99/1.61 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.99/1.61 c_RealVector_Onorm__class_Onorm( X, Y ) ), ! Y =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.61 { ! class_RealVector_Oreal__normed__vector( X ), Y =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless(
% 0.99/1.61 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.99/1.61 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.99/1.61 { ! class_RealVector_Oreal__normed__algebra( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.61 c_RealVector_Onorm__class_Onorm( X, Z ), Y ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.61 c_RealVector_Onorm__class_Onorm( X, U ), T ),
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.61 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), T ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 0.99/1.61 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.61 c_RealVector_Onorm__class_Onorm( X, Z ), Y ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.61 c_RealVector_Onorm__class_Onorm( X, U ), T ),
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.61 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, Z, U
% 0.99/1.61 ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, T ) ) }.
% 0.99/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.99/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), Y ) ) }.
% 0.99/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 0.99/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Z ) }.
% 0.99/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 0.99/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.99/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 0.99/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.99/1.61 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.99/1.61 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X
% 0.99/1.61 , U, Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.99/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.99/1.61 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.99/1.61 ( X, c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 0.99/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.99/1.61 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.99/1.61 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.99/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.99/1.61 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.99/1.61 ( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) }.
% 0.99/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.99/1.61 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.99/1.61 ( X, Z, c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.99/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.99/1.61 , Y ) = c_Groups_Oplus__class_Oplus( X, Y, Z ) }.
% 0.99/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.61 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.61 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.99/1.61 , T, Z ), c_Rings_Oinverse__class_Odivide( X, T, Y ) ) }.
% 0.99/1.61 { ! class_Fields_Olinordered__field( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.99/1.61 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.61 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.99/1.61 , T, Y ), c_Rings_Oinverse__class_Odivide( X, T, Z ) ) }.
% 0.99/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.99/1.61 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.99/1.61 , T, Y ), Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ) }.
% 0.99/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.99/1.61 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.99/1.61 , T, Y ), Z ) }.
% 0.99/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.99/1.61 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.99/1.61 ( X, Z, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Z, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.99/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.99/1.61 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.99/1.61 ( X, Z, Y ) ) }.
% 0.99/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.99/1.61 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.99/1.61 ( X, Z, Y ) ) }.
% 0.99/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.99/1.61 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.99/1.61 , T, Y ), Z ) }.
% 0.99/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.99/1.61 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.99/1.61 , T, Y ), Z ), c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.99/1.61 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.99/1.61 , T, Y ), Z ) }.
% 0.99/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.99/1.61 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.99/1.61 ( X, Z, Y ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.99/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.99/1.61 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.99/1.61 ( X, Z, Y ) ) }.
% 0.99/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.99/1.61 , T, Z ), Y ), alpha39( X, Y, Z, T ) }.
% 0.99/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.99/1.61 , T, Z ), Y ), alpha51( X, Y, Z, T ) }.
% 0.99/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha39( X, Y, Z
% 0.99/1.61 , T ), ! alpha51( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.61 c_Rings_Oinverse__class_Odivide( X, T, Z ), Y ) }.
% 0.99/1.61 { ! alpha51( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ), Z ), alpha59( X, Y, Z, T ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.99/1.61 , alpha51( X, Y, Z, T ) }.
% 0.99/1.61 { ! alpha59( X, Y, Z, T ), alpha51( X, Y, Z, T ) }.
% 0.99/1.61 { ! alpha59( X, Y, Z, T ), alpha66( X, Y, Z, T ) }.
% 0.99/1.61 { ! alpha59( X, Y, Z, T ), alpha14( X, Y, Z ) }.
% 0.99/1.61 { ! alpha66( X, Y, Z, T ), ! alpha14( X, Y, Z ), alpha59( X, Y, Z, T ) }.
% 0.99/1.61 { ! alpha66( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.61 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ) }.
% 0.99/1.61 { c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.61 alpha66( X, Y, Z, T ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ), alpha66( X, Y, Z, T )
% 0.99/1.61 }.
% 0.99/1.61 { ! alpha39( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless__eq
% 0.99/1.61 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.99/1.61 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.99/1.61 alpha39( X, Y, Z, T ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha39( X, Y, Z, T ) }.
% 0.99/1.61 { ! alpha14( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.61 , c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.61 , alpha14( X, Y, Z ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.61 , Y ), alpha14( X, Y, Z ) }.
% 0.99/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.99/1.61 ( X, Z, Y ) ), alpha40( X, Y, Z, T ) }.
% 0.99/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.99/1.61 ( X, Z, Y ) ), alpha52( X, Y, Z, T ) }.
% 0.99/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha40( X, Y, Z
% 0.99/1.61 , T ), ! alpha52( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( X, T,
% 0.99/1.61 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.99/1.61 { ! alpha52( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ), Y ), alpha60( X, Y, Z, T ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.99/1.61 , alpha52( X, Y, Z, T ) }.
% 0.99/1.61 { ! alpha60( X, Y, Z, T ), alpha52( X, Y, Z, T ) }.
% 0.99/1.61 { ! alpha60( X, Y, Z, T ), alpha67( X, Y, Z, T ) }.
% 0.99/1.61 { ! alpha60( X, Y, Z, T ), alpha15( X, Y, T ) }.
% 0.99/1.61 { ! alpha67( X, Y, Z, T ), ! alpha15( X, Y, T ), alpha60( X, Y, Z, T ) }.
% 0.99/1.61 { ! alpha67( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.61 , Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.99/1.61 { c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.61 alpha67( X, Y, Z, T ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless__eq( X, Z, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha67( X, Y, Z, T ) }.
% 0.99/1.61 { ! alpha40( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless__eq
% 0.99/1.61 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.99/1.61 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.99/1.61 alpha40( X, Y, Z, T ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ), alpha40( X, Y, Z, T )
% 0.99/1.61 }.
% 0.99/1.61 { ! alpha15( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.61 , Z, c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.61 , alpha15( X, Y, Z ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.99/1.61 ) ), alpha15( X, Y, Z ) }.
% 0.99/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.99/1.61 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.99/1.61 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.61 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.99/1.61 ( X ), ! Z = c_Groups_Oplus__class_Oplus( X, Z, Y ), Y =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.61 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.99/1.61 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.99/1.61 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 0.99/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.99/1.61 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.99/1.61 { v_cs____ = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.99/1.61 tc_Complex_Ocomplex ) ), ! c_Orderings_Oord__class_Oless__eq(
% 0.99/1.61 tc_RealDef_Oreal, skol3, c_RealVector_Onorm__class_Onorm(
% 0.99/1.61 tc_Complex_Ocomplex, X ) ), c_Orderings_Oord__class_Oless__eq(
% 0.99/1.61 tc_RealDef_Oreal, v_da____, c_RealVector_Onorm__class_Onorm(
% 0.99/1.61 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 0.99/1.61 c_Polynomial_OpCons( tc_Complex_Ocomplex, v_aa____, c_Polynomial_OpCons(
% 0.99/1.61 tc_Complex_Ocomplex, v_c____, v_cs____ ) ) ), X ) ) ) }.
% 0.99/1.61 { ! class_Groups_Ozero( X ), c_Polynomial_OpCons( X,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero(
% 0.99/1.61 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 0.99/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.61 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.61 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.61 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.99/1.61 c_Polynomial_OpCons( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.99/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.99/1.61 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.99/1.61 ) ), c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 0.99/1.61 ) ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.99/1.61 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.99/1.61 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.99/1.61 ) ) }.
% 0.99/1.61 { ! class_RealVector_Oreal__normed__field( X ),
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol4( Z, T ) ) }.
% 0.99/1.61 { ! class_RealVector_Oreal__normed__field( X ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.61 c_RealVector_Onorm__class_Onorm( X, c_Rings_Oinverse__class_Odivide( X, Z
% 0.99/1.61 , Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.99/1.61 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol4( X, Y ) ) ) }.
% 0.99/1.61 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol5( Z, T ) ) }.
% 0.99/1.61 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.61 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.99/1.61 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol5( X, Y ) ) ) }.
% 0.99/1.61 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol6( Z, T ) ) }.
% 0.99/1.61 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.61 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.99/1.61 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol6( X, Y ) ) ) }.
% 0.99/1.61 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol7( Y ) ) }.
% 0.99/1.61 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.61 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.99/1.61 c_RealVector_Onorm__class_Onorm( X, Y ) ),
% 0.99/1.61 c_RealVector_Onorm__class_Onorm( X, Z ) ) ), skol7( X ) ) ) }.
% 0.99/1.61 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 0.99/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Z
% 0.99/1.61 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP(
% 0.99/1.61 c_Polynomial_Opoly( X, T ), Y ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 0.99/1.61 ) }.
% 0.99/1.61 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.99/1.61 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.99/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 0.99/1.61 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.99/1.61 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 0.99/1.61 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ), Z = Y }.
% 0.99/1.61 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Z = Y,
% 0.99/1.61 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ) }.
% 0.99/1.61 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 0.99/1.61 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.61 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Y =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.99/1.61 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.99/1.61 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.99/1.61 X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }
% 0.99/1.61 .
% 0.99/1.61 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.99/1.61 X ), Z, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z )
% 0.99/1.61 }.
% 0.99/1.61 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.99/1.61 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z
% 0.99/1.61 ), c_Orderings_Oord__class_Oless( tc_fun( T, X ), Z, Y ) }.
% 0.99/1.61 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.61 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.99/1.61 c_Polynomial_OpCons( X, T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus( X, T
% 0.99/1.61 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), hAPP(
% 0.99/1.61 c_Polynomial_Opoly( X, Z ), Y ) ) ) }.
% 0.99/1.61 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.99/1.61 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 0.99/1.61 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.99/1.61 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.61 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.99/1.61 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.99/1.61 tc_Polynomial_Opoly( X ) ), Y ) = Y }.
% 0.99/1.61 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.61 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 0.99/1.61 c_Polynomial_OpCons( X, Z, Y ), U = Z }.
% 0.99/1.61 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 0.99/1.61 c_Polynomial_OpCons( X, Z, Y ), T = Y }.
% 0.99/1.61 { ! class_Groups_Ozero( X ), ! U = Z, ! T = Y, c_Polynomial_OpCons( X, U, T
% 0.99/1.61 ) = c_Polynomial_OpCons( X, Z, Y ) }.
% 0.99/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.99/1.61 c_Groups_Oplus__class_Oplus( X, Y, Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.61 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.99/1.61 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.61 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.99/1.61 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 0.99/1.61 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 0.99/1.61 c_Groups_Oplus__class_Oplus( X, U, Z ), c_Groups_Oplus__class_Oplus(
% 0.99/1.61 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 0.99/1.61 { v_cs____ = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.99/1.61 tc_Complex_Ocomplex ) ), ! c_Orderings_Oord__class_Oless__eq(
% 0.99/1.61 tc_RealDef_Oreal, skol8( X, Y ), c_RealVector_Onorm__class_Onorm(
% 0.99/1.61 tc_Complex_Ocomplex, Z ) ), c_Orderings_Oord__class_Oless__eq(
% 0.99/1.61 tc_RealDef_Oreal, Y, c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex
% 0.99/1.61 , hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_OpCons(
% 0.99/1.61 tc_Complex_Ocomplex, X, v_cs____ ) ), Z ) ) ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.99/1.61 c_Polynomial_OpCons( X, Z, Y ) ), c_Polynomial_Opos__poly( X, Y ),
% 0.99/1.61 alpha16( X, Y, Z ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.99/1.61 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__idom( X ), ! alpha16( X, Y, Z ),
% 0.99/1.61 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 0.99/1.61 { ! alpha16( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero(
% 0.99/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.61 { ! alpha16( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.99/1.61 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.99/1.61 alpha16( X, Y, Z ) }.
% 0.99/1.61 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol9( Z, T ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.61 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Z ), Y ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.61 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.99/1.61 c_Polynomial_Opoly( tc_Complex_Ocomplex, X ), Z ) ), skol9( X, Y ) ) }.
% 0.99/1.61 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 0.99/1.61 tc_Polynomial_Opoly( X ) ), ! c_Polynomial_Oorder( X, Y, Z ) =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.61 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.99/1.61 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.61 { ! class_Rings_Oidom( X ), c_Polynomial_Oorder( X, Y, Z ) =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( c_Polynomial_Opoly( X,
% 0.99/1.61 Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.61 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 0.99/1.61 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( W, X, Y,
% 0.99/1.61 Z, c_Polynomial_OpCons( X, U, T ) ) = hAPP( hAPP( hAPP( Z, U ), T ),
% 0.99/1.61 c_Polynomial_Opoly__rec( W, X, Y, Z, T ) ) }.
% 0.99/1.61 { ! class_RealVector_Oreal__normed__field( X ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol10( Z, T ) ) }.
% 0.99/1.61 { ! class_RealVector_Oreal__normed__field( X ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.61 c_RealVector_Onorm__class_Onorm( X, c_Rings_Oinverse__class_Odivide( X, Z
% 0.99/1.61 , Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.99/1.61 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol10( X, Y ) ) ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.99/1.61 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X, hAPP( hAPP
% 0.99/1.61 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) }
% 0.99/1.61 .
% 0.99/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.99/1.61 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X,
% 0.99/1.61 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 0.99/1.61 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.99/1.61 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.99/1.61 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ), hAPP
% 0.99/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y
% 0.99/1.61 ) ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.99/1.61 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 0.99/1.61 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( T, X, Y,
% 0.99/1.61 Z, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.99/1.61 { ! class_Groups_Ozero( X ), c_Polynomial_Opoly__rec( W, X, U, T,
% 0.99/1.61 c_Polynomial_OpCons( X, Z, Y ) ) = hAPP( hAPP( hAPP( T, Z ), Y ), c_If( W
% 0.99/1.61 , c_fequal( Y, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) )
% 0.99/1.61 , U, c_Polynomial_Opoly__rec( W, X, U, T, Y ) ) ) }.
% 0.99/1.61 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 0.99/1.61 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus(
% 0.99/1.61 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, T,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 0.99/1.61 c_Polynomial_Opcompose( X, Z, Y ) ) ) }.
% 0.99/1.61 { ! class_Groups_Ozero( X ), !
% 0.99/1.61 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.61 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.99/1.61 tc_Polynomial_Opoly( X ) ),
% 0.99/1.61 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.99/1.61 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.99/1.61 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol11( Z, T ) ) }.
% 0.99/1.61 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.61 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.99/1.61 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol11( X, Y ) ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.99/1.61 ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.99/1.61 ( tc_Nat_Onat, Y, X ), X ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.99/1.61 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.99/1.61 ( tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) )
% 0.99/1.61 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.61 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }
% 0.99/1.61 .
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.99/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.99/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.61 tc_Nat_Onat, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.99/1.61 .
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ),
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.61 tc_Nat_Onat, Y, T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.99/1.61 .
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.99/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, X ) =
% 0.99/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.99/1.61 ( tc_Nat_Onat, Y, Z ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y
% 0.99/1.61 , X ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.99/1.61 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.99/1.61 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.99/1.61 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X = Y }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.99/1.61 { alpha74( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.99/1.61 hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.99/1.61 { alpha74( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP
% 0.99/1.61 ( X, Y ), Z ) ) }.
% 0.99/1.61 { ! alpha74( X, Y, Z ), alpha76( X, Y, Z ), Z = Y }.
% 0.99/1.61 { ! alpha74( X, Y, Z ), alpha76( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z
% 0.99/1.61 ) ) }.
% 0.99/1.61 { ! alpha76( X, Y, Z ), alpha74( X, Y, Z ) }.
% 0.99/1.61 { ! Z = Y, hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha74( X, Y, Z ) }.
% 0.99/1.61 { ! alpha76( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y )
% 0.99/1.61 }.
% 0.99/1.61 { ! alpha76( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP(
% 0.99/1.61 X, Y ), Z ) ), alpha76( X, Y, Z ) }.
% 0.99/1.61 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) }.
% 0.99/1.61 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.99/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.99/1.61 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.99/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.99/1.61 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 0.99/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol12( X, Y ) ) }.
% 0.99/1.61 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 0.99/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol13( X, Y ) ) }.
% 0.99/1.61 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.99/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.99/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.99/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.99/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.99/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, T ),
% 0.99/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), T ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ), X ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ), Y = X }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ) }.
% 0.99/1.61 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.99/1.61 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ) }.
% 0.99/1.61 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, X ) }.
% 0.99/1.61 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.61 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.99/1.61 c_Polynomial_Opcompose( X, T, Z ) ), Y ) = hAPP( c_Polynomial_Opoly( X, T
% 0.99/1.61 ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.99/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.61 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.99/1.61 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.61 tc_Nat_Onat ), X ) = X }.
% 0.99/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.61 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( tc_Nat_Onat ) ) = X }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.61 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.99/1.61 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.61 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.61 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.99/1.61 tc_Nat_Onat, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.61 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.61 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.61 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.61 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.99/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Y = X
% 0.99/1.61 , Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.61 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.99/1.61 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.99/1.61 .
% 0.99/1.61 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.99/1.61 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.99/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = X
% 0.99/1.61 , Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.61 { ! Z = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.99/1.61 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }
% 0.99/1.61 .
% 0.99/1.61 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.99/1.61 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = Y, X =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.61 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.61 tc_Nat_Onat ), X ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.61 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.99/1.61 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP
% 0.99/1.61 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.61 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.99/1.61 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP
% 0.99/1.61 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.61 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X
% 0.99/1.61 ) }.
% 0.99/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.61 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 0.99/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 0.99/1.61 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.61 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 0.99/1.61 ) }.
% 0.99/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.61 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 0.99/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 0.99/1.61 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.61 tc_Nat_Onat ), Y ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.99/1.61 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.61 tc_Nat_Onat ), Z ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( tc_Nat_Onat ), Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 0.99/1.61 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.99/1.61 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.99/1.61 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.61 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.61 Y ), X ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ),
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.61 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.99/1.61 tc_Nat_Onat, Y, X ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.99/1.61 tc_Nat_Onat, Y, X ) ) }.
% 0.99/1.61 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.61 tc_Nat_Onat ), X ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( tc_Nat_Onat ), X ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 0.99/1.61 .
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP
% 0.99/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z
% 0.99/1.61 , Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.99/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP(
% 0.99/1.61 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 0.99/1.61 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( tc_Nat_Onat ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.99/1.61 tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.99/1.61 tc_Nat_Onat ), X ), Y ), Z = Y }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( tc_Nat_Onat ), X ), ! Z = Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.61 ( tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.99/1.61 tc_Nat_Onat ), X ), Y ) }.
% 0.99/1.61 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol14( Y ) ) }.
% 0.99/1.61 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.61 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.99/1.61 c_RealVector_Onorm__class_Onorm( X, Y ) ),
% 0.99/1.61 c_RealVector_Onorm__class_Onorm( X, Z ) ) ), skol14( X ) ) ) }.
% 0.99/1.61 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.99/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.99/1.61 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, c_Groups_Oplus__class_Oplus
% 0.99/1.61 ( tc_Nat_Onat, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.99/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.99/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.99/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 0.99/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.99/1.61 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.61 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.99/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.99/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.99/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.99/1.61 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.99/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ), Y = X }.
% 0.99/1.61 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.99/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) }.
% 0.99/1.61 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.99/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ), Z = X }.
% 0.99/1.61 { ! Z = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.99/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.99/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 0.99/1.61 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.99/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP
% 0.99/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.99/1.61 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), T ), Z ),
% 0.99/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), X ) ) =
% 0.99/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus
% 0.99/1.61 ( tc_Nat_Onat, T, Y ) ), Z ), X ) }.
% 0.99/1.61 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.99/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Z =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.99/1.61 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.99/1.61 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.99/1.61 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.99/1.61 .
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.99/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.99/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.99/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.99/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.99/1.61 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol15( Z, T ) ) }.
% 0.99/1.61 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.61 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.99/1.61 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol15( X, Y ) ) ) }.
% 0.99/1.61 { ! class_RealVector_Oreal__normed__field( X ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.61 c_RealVector_Onorm__class_Onorm( X, c_Rings_Oinverse__class_Odivide( X, Z
% 0.99/1.61 , Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.99/1.61 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol16( X, Y ) ) ) }.
% 0.99/1.61 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.61 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.99/1.61 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol17( X, Y ) ) ) }.
% 0.99/1.61 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.61 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.99/1.61 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol18( X, Y ) ) ) }.
% 0.99/1.61 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.61 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.99/1.61 c_RealVector_Onorm__class_Onorm( X, Y ) ),
% 0.99/1.61 c_RealVector_Onorm__class_Onorm( X, Z ) ) ), skol19( X ) ) ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__semiring__1__strict( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.99/1.61 ( X, T, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ), U ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), W
% 0.99/1.61 ), ! c_Groups_Oplus__class_Oplus( X, U, W ) = c_Groups_Oone__class_Oone
% 0.99/1.61 ( X ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X,
% 0.99/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), W ), T ) ), Y ) }.
% 0.99/1.61 { ! class_Fields_Olinordered__field( X ), c_Orderings_Oord__class_Oless( X
% 0.99/1.61 , c_Groups_Ozero__class_Ozero( X ), skol20( X, T, U ) ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.99/1.61 { ! class_Fields_Olinordered__field( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oplus__class_Oplus( X,
% 0.99/1.61 Y, skol20( X, Y, Z ) ) ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }
% 0.99/1.61 .
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), c_NthRoot_Oroot(
% 0.99/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z ) =
% 0.99/1.61 c_NthRoot_Oroot( X, c_NthRoot_Oroot( Y, Z ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( tc_Nat_Onat ), X ), c_NthRoot_Oroot( X, c_Groups_Oone__class_Oone(
% 0.99/1.61 tc_RealDef_Oreal ) ) = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( tc_Nat_Onat ), X ), ! c_NthRoot_Oroot( X, Y ) =
% 0.99/1.61 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), Y =
% 0.99/1.61 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_RealDef_Oreal )
% 0.99/1.61 , c_NthRoot_Oroot( X, Y ) = c_Groups_Oone__class_Oone( tc_RealDef_Oreal )
% 0.99/1.61 }.
% 0.99/1.61 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 0.99/1.61 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oone__class_Oone( X ) ) =
% 0.99/1.61 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.99/1.61 { ! class_Groups_Oone( X ), ! c_Groups_Oone__class_Oone( X ) = Y, Y =
% 0.99/1.61 c_Groups_Oone__class_Oone( X ) }.
% 0.99/1.61 { ! class_Groups_Oone( X ), ! Y = c_Groups_Oone__class_Oone( X ),
% 0.99/1.61 c_Groups_Oone__class_Oone( X ) = Y }.
% 0.99/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oone__class_Oone(
% 0.99/1.61 tc_Polynomial_Opoly( X ) ) = c_Polynomial_OpCons( X,
% 0.99/1.61 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.99/1.61 tc_Polynomial_Opoly( X ) ) ) }.
% 0.99/1.61 { c_NthRoot_Oroot( X, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.99/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 0.99/1.61 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.99/1.61 c_Groups_Oone__class_Oone( X ) }.
% 0.99/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.99/1.61 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) = X }.
% 0.99/1.61 { ! c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) =
% 0.99/1.61 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X,
% 0.99/1.61 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.99/1.61 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X, Y
% 0.99/1.61 , c_Groups_Oone__class_Oone( X ) ) = Y }.
% 0.99/1.61 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.99/1.61 = Y }.
% 0.99/1.61 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.99/1.61 = Y }.
% 0.99/1.61 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.99/1.61 = Y }.
% 0.99/1.61 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.99/1.61 = Y }.
% 0.99/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.99/1.61 = Y }.
% 0.99/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.99/1.61 = Y }.
% 0.99/1.61 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.99/1.61 c_Groups_Oone__class_Oone( X ) }.
% 0.99/1.61 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Oone__class_Oone( X ) =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.61 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) = X }.
% 0.99/1.61 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), Y =
% 0.99/1.61 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.99/1.61 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X =
% 0.99/1.61 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.99/1.61 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.99/1.61 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Groups_Oone__class_Oone(
% 0.99/1.61 tc_Nat_Onat ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.99/1.61 , Y ), X ) }.
% 0.99/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.99/1.61 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.99/1.61 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.99/1.61 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Oone__class_Oone(
% 0.99/1.61 tc_Nat_Onat ) }.
% 0.99/1.61 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.99/1.61 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X = c_Groups_Oone__class_Oone(
% 0.99/1.61 tc_Nat_Onat ) }.
% 0.99/1.61 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.99/1.61 c_Groups_Oone__class_Oone( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.99/1.61 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y
% 0.99/1.61 ), ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.61 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), Z ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Oroot( Y,
% 0.99/1.61 Z ), c_NthRoot_Oroot( X, Z ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.99/1.61 tc_RealDef_Oreal, c_NthRoot_Oroot( X, Y ), c_Groups_Oone__class_Oone(
% 0.99/1.61 tc_RealDef_Oreal ) ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal
% 0.99/1.61 , Y, c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.99/1.61 tc_RealDef_Oreal, Y, c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Oroot( X,
% 0.99/1.61 Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.99/1.61 tc_RealDef_Oreal, c_Groups_Oone__class_Oone( tc_RealDef_Oreal ),
% 0.99/1.61 c_NthRoot_Oroot( X, Y ) ), c_Orderings_Oord__class_Oless__eq(
% 0.99/1.61 tc_RealDef_Oreal, c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), Y ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.99/1.61 tc_RealDef_Oreal, c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), Y ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.61 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_NthRoot_Oroot( X, Y ) )
% 0.99/1.61 }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y
% 0.99/1.61 ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.61 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), Z ),
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Oroot( Y, Z )
% 0.99/1.61 , c_NthRoot_Oroot( X, Z ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.61 c_NthRoot_Oroot( X, Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 0.99/1.61 , c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y,
% 0.99/1.61 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.61 Y, c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Oroot( X, Y )
% 0.99/1.61 , c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.61 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_NthRoot_Oroot( X, Y ) )
% 0.99/1.61 , c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.61 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), Y ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.61 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), Y ),
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.61 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_NthRoot_Oroot( X, Y ) )
% 0.99/1.61 }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y
% 0.99/1.61 ), ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z,
% 0.99/1.61 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Oroot( X,
% 0.99/1.61 Z ), c_NthRoot_Oroot( Y, Z ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y
% 0.99/1.61 ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z,
% 0.99/1.61 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Oroot( X, Z )
% 0.99/1.61 , c_NthRoot_Oroot( Y, Z ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), c_NthRoot_Oroot( X,
% 0.99/1.61 c_NthRoot_Oroot( Y, Z ) ) = c_NthRoot_Oroot( Y, c_NthRoot_Oroot( X, Z ) )
% 0.99/1.61 }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( tc_Nat_Onat ), X ), ! c_NthRoot_Oroot( X, Z ) = c_NthRoot_Oroot( X, Y )
% 0.99/1.61 , Z = Y }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( tc_Nat_Onat ), X ), ! Z = Y, c_NthRoot_Oroot( X, Z ) = c_NthRoot_Oroot
% 0.99/1.61 ( X, Y ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__semidom( X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__semidom( X ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.61 c_Groups_Oone__class_Oone( X ) ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.99/1.61 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.61 ( X, c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero( X ) ) }
% 0.99/1.61 .
% 0.99/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.61 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.99/1.61 ( X, c_Groups_Oone__class_Oone( X ), Z ), c_Orderings_Oord__class_Oless(
% 0.99/1.61 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.99/1.61 , Y, c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) )
% 0.99/1.61 ) }.
% 0.99/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.99/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = hAPP(
% 0.99/1.61 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X
% 0.99/1.61 , Z, c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.99/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.99/1.61 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP
% 0.99/1.61 ( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.99/1.61 c_Groups_Oone__class_Oone( X ) ) ), Z ) }.
% 0.99/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.99/1.61 , Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.99/1.61 c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.99/1.61 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.99/1.61 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Y =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X, Y,
% 0.99/1.61 Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.61 { ! class_Rings_Odivision__ring__inverse__zero( X ), Y =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X, Y,
% 0.99/1.61 Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.99/1.61 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.61 , c_Rings_Oinverse__class_Odivide( X, Y, Y ) = c_Groups_Oone__class_Oone
% 0.99/1.61 ( X ) }.
% 0.99/1.61 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.61 , ! c_Rings_Oinverse__class_Odivide( X, Z, Y ) =
% 0.99/1.61 c_Groups_Oone__class_Oone( X ), Z = Y }.
% 0.99/1.61 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.61 , ! Z = Y, c_Rings_Oinverse__class_Odivide( X, Z, Y ) =
% 0.99/1.62 c_Groups_Oone__class_Oone( X ) }.
% 0.99/1.62 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X )
% 0.99/1.62 , X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.99/1.62 tc_RealDef_Oreal, Z, Y ), c_Orderings_Oord__class_Oless__eq(
% 0.99/1.62 tc_RealDef_Oreal, c_NthRoot_Oroot( X, Z ), c_NthRoot_Oroot( X, Y ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.99/1.62 tc_RealDef_Oreal, c_NthRoot_Oroot( X, Z ), c_NthRoot_Oroot( X, Y ) ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.99/1.62 tc_RealDef_Oreal, Z, Y ), c_Orderings_Oord__class_Oless__eq(
% 0.99/1.62 tc_RealDef_Oreal, c_NthRoot_Oroot( X, Z ), c_NthRoot_Oroot( X, Y ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Nat_Onat ), X ), ! c_NthRoot_Oroot( X, Y ) =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal
% 0.99/1.62 ), c_NthRoot_Oroot( X, Y ) = c_Groups_Ozero__class_Ozero(
% 0.99/1.62 tc_RealDef_Oreal ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.62 Z, Y ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Oroot
% 0.99/1.62 ( X, Z ), c_NthRoot_Oroot( X, Y ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.62 c_NthRoot_Oroot( X, Z ), c_NthRoot_Oroot( X, Y ) ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.62 Z, Y ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Oroot
% 0.99/1.62 ( X, Z ), c_NthRoot_Oroot( X, Y ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Nat_Onat ), X ), c_NthRoot_Oroot( X, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), Y ) ) = hAPP(
% 0.99/1.62 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_NthRoot_Oroot
% 0.99/1.62 ( X, Z ) ), c_NthRoot_Oroot( X, Y ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), c_NthRoot_Oroot( hAPP(
% 0.99/1.62 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z ) =
% 0.99/1.62 c_NthRoot_Oroot( X, c_NthRoot_Oroot( Y, Z ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Nat_Onat ), X ), c_NthRoot_Oroot( X, c_Rings_Oinverse__class_Odivide
% 0.99/1.62 ( tc_RealDef_Oreal, Z, Y ) ) = c_Rings_Oinverse__class_Odivide(
% 0.99/1.62 tc_RealDef_Oreal, c_NthRoot_Oroot( X, Z ), c_NthRoot_Oroot( X, Y ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Nat_Onat ), X ), c_NthRoot_Oroot( X, c_Groups_Oabs__class_Oabs(
% 0.99/1.62 tc_RealDef_Oreal, Y ) ) = c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 0.99/1.62 c_NthRoot_Oroot( X, Y ) ) }.
% 0.99/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.99/1.62 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.99/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.99/1.62 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) }.
% 0.99/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.99/1.62 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.99/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.99/1.62 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) }.
% 0.99/1.62 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.99/1.62 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.99/1.62 c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ) ) }.
% 0.99/1.62 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.99/1.62 X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z,
% 0.99/1.62 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.99/1.62 ), c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.99/1.62 c_Groups_Oone__class_Oone( X ) ) ) ) }.
% 0.99/1.62 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.99/1.62 X, Z, Y ), c_Orderings_Oord__class_Oless( X,
% 0.99/1.62 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.99/1.62 ), c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.99/1.62 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs
% 0.99/1.62 ( tc_RealDef_Oreal, X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 0.99/1.62 , X ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.99/1.62 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Oroot( X, Y )
% 0.99/1.62 ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.99/1.62 tc_RealDef_Oreal, c_NthRoot_Oroot( X, Y ), c_Groups_Ozero__class_Ozero(
% 0.99/1.62 tc_RealDef_Oreal ) ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal
% 0.99/1.62 , Y, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.99/1.62 tc_RealDef_Oreal, Y, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Oroot( X,
% 0.99/1.62 Y ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.99/1.62 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.99/1.62 c_NthRoot_Oroot( X, Y ) ), c_Orderings_Oord__class_Oless__eq(
% 0.99/1.62 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ) }
% 0.99/1.62 .
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.99/1.62 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Oroot( X, Y )
% 0.99/1.62 ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Oroot( X, Y )
% 0.99/1.62 ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Oroot( X, Y )
% 0.99/1.62 ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.62 c_NthRoot_Oroot( X, Y ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal )
% 0.99/1.62 ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.62 Y, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Oroot( X, Y )
% 0.99/1.62 , c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Oroot( X, Y )
% 0.99/1.62 ) }.
% 0.99/1.62 { ! class_Rings_Olinordered__semiring__1( X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, T, Y ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.99/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.99/1.62 X ), W ), ! c_Groups_Oplus__class_Oplus( X, U, W ) =
% 0.99/1.62 c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.62 ( X ), U ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), T )
% 0.99/1.62 ), Y ) }.
% 0.99/1.62 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oone__class_Oone
% 0.99/1.62 ( tc_RealDef_Oreal ), c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) )
% 0.99/1.62 ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Oroot( X, Y )
% 0.99/1.62 ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.99/1.62 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, Z ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Oroot( X, Y )
% 0.99/1.62 , c_NthRoot_Oroot( X, Z ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.99/1.62 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), c_NthRoot_Oroot( X
% 0.99/1.62 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Z )
% 0.99/1.62 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.99/1.62 c_NthRoot_Oroot( X, Y ) ), c_NthRoot_Oroot( X, Z ) ) }.
% 0.99/1.62 { ! class_Fields_Olinordered__field__inverse__zero( X ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.62 skol21( X, T, U ) ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.99/1.62 { ! class_Fields_Olinordered__field__inverse__zero( X ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( X, skol21( X, T, U ),
% 0.99/1.62 c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.99/1.62 , Y ) }.
% 0.99/1.62 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), skol21( X, Y, Z ) ), Z ), Y ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), c_NthRoot_Oroot( X, Y )
% 0.99/1.62 ), X ) = Y }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.99/1.62 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.99/1.62 c_NthRoot_Oroot( X, hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.99/1.62 tc_RealDef_Oreal ), Y ), X ) ) = Y }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.99/1.62 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.99/1.62 hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.99/1.62 c_NthRoot_Oroot( X, Y ) ), X ) = Y }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.99/1.62 tc_Nat_Onat ) ) = Y }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 0.99/1.62 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), T ), Z
% 0.99/1.62 ) ), Y ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), hAPP(
% 0.99/1.62 c_Polynomial_Opoly( X, T ), Y ) ), Z ) }.
% 0.99/1.62 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 0.99/1.62 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.99/1.62 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) }.
% 0.99/1.62 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.62 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), Z ), Y ) ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.99/1.62 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ozero__class_Ozero(
% 0.99/1.62 tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), T ), Y ) ) = hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.99/1.62 tc_Nat_Onat, Z, Y ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Nat_Onat ), X ), c_NthRoot_Oroot( X, hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Z ), Y ) ) = hAPP( hAPP
% 0.99/1.62 ( c_Power_Opower__class_Opower( tc_RealDef_Oreal ), c_NthRoot_Oroot( X, Z
% 0.99/1.62 ) ), Y ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.99/1.62 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.99/1.62 hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Y ), X ) =
% 0.99/1.62 Z, c_NthRoot_Oroot( X, Z ) = Y }.
% 0.99/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.62 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ), Z ), ! c_Orderings_Oord__class_Oless(
% 0.99/1.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), T ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.99/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.62 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.99/1.62 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 0.99/1.62 hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.99/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.62 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.99/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.62 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.99/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.62 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.99/1.62 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ),
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) = hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ) }.
% 0.99/1.62 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 0.99/1.62 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Int_Oint ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint )
% 0.99/1.62 , c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) ), X ) ), ! Y =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.62 { Y = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.62 tc_Int_Oint ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ),
% 0.99/1.62 c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) ), X ) ) }.
% 0.99/1.62 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.62 tc_Int_Oint ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ),
% 0.99/1.62 c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) ), X ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.99/1.62 ( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Z ), hAPP( hAPP
% 0.99/1.62 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.99/1.62 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), X =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.99/1.62 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.62 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.99/1.62 ), X ) ) }.
% 0.99/1.62 { ! class_Rings_Oring__1__no__zero__divisors( X ), Y =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( X ) }.
% 0.99/1.62 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.99/1.62 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.99/1.62 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.99/1.62 = c_Groups_Oone__class_Oone( X ) }.
% 0.99/1.62 { ! class_Fields_Ofield__inverse__zero( X ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide( X, T
% 0.99/1.62 , Z ) ), Y ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.99/1.62 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, hAPP
% 0.99/1.62 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), c_Groups_Oabs__class_Oabs( X, Z ) ), Y
% 0.99/1.62 ) }.
% 0.99/1.62 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) }.
% 0.99/1.62 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.99/1.62 tc_Nat_Onat ) ) = Y }.
% 0.99/1.62 { ! class_Rings_Olinordered__semidom( X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.99/1.62 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.99/1.62 { ! class_Rings_Olinordered__semidom( X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.62 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.99/1.62 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.99/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.62 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless
% 0.99/1.62 ( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.99/1.62 { ! class_Rings_Olinordered__semidom( X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 0.99/1.62 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.99/1.62 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.99/1.62 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.99/1.62 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.99/1.62 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.99/1.62 .
% 0.99/1.62 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.99/1.62 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.99/1.62 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.99/1.62 tc_Nat_Onat ) }.
% 0.99/1.62 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.99/1.62 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.99/1.62 , ! Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y )
% 0.99/1.62 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.62 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), Y ), Z ), T = Z }.
% 0.99/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.62 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! T = Z, hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), Y ), Z ) }.
% 0.99/1.62 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP(
% 0.99/1.62 hAPP( c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide
% 0.99/1.62 ( X, T, Y ) ), Z ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.99/1.62 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.99/1.62 , Y ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.99/1.62 c_Groups_Oone__class_Oone( X ) }.
% 0.99/1.62 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.99/1.62 tc_Nat_Onat, Z, Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.99/1.62 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.99/1.62 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.99/1.62 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oone__class_Oone( X ), hAPP
% 0.99/1.62 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.99/1.62 c_Groups_Oone__class_Oone( X ), Z ) ), Y ) }.
% 0.99/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.62 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP
% 0.99/1.62 ( c_Power_Opower__class_Opower( X ), Y ), T ) ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.62 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.99/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.62 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.99/1.62 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.99/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.62 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.99/1.62 X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.99/1.62 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), ! Y =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.99/1.62 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.99/1.62 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), Y =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.99/1.62 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.62 { ! class_Rings_Olinordered__idom( X ), c_Orderings_Oord__class_Oless__eq(
% 0.99/1.62 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), c_Groups_Oabs__class_Oabs( X, Z ) ), Y
% 0.99/1.62 ) ) }.
% 0.99/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.62 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.99/1.62 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.99/1.62 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.99/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.62 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.99/1.62 ( tc_Nat_Onat, T, Z ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.99/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.62 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.99/1.62 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.99/1.62 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.99/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.62 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.99/1.62 c_Groups_Oone__class_Oone( X ), T ), c_Orderings_Oord__class_Oless( X,
% 0.99/1.62 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.99/1.62 { ! class_Rings_Olinordered__semidom( X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), T )
% 0.99/1.62 , c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.99/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.62 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), Y ), Z ) ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.99/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.62 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 0.99/1.62 , T, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.99/1.62 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 0.99/1.62 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), T ), Z ) = hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), Y ), Z ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.99/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.99/1.62 X ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ), T = Y }.
% 0.99/1.62 { ! class_Rings_Olinordered__semidom( X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.99/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oone__class_Oone
% 0.99/1.62 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 0.99/1.62 { X = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), Y =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Orderings_Oord__class_Oless
% 0.99/1.62 ( tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex
% 0.99/1.62 , c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex,
% 0.99/1.62 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), X ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), skol22( X, Y ) ), Y
% 0.99/1.62 ) ) ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.99/1.62 { ! class_Power_Opower( X ), c_Power_Opower__class_Opower( X ) =
% 0.99/1.62 c_Power_Opower_Opower( X, c_Groups_Oone__class_Oone( X ),
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.99/1.62 , Y ), X ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.62 tc_Nat_Onat ), Y ) }.
% 0.99/1.62 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.62 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.99/1.62 ), X ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.99/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( tc_Int_Oint ), c_Groups_Oabs__class_Oabs(
% 0.99/1.62 tc_Int_Oint, Y ) ), X ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.99/1.62 tc_Int_Oint, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.99/1.62 .
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.62 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 0.99/1.62 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP
% 0.99/1.62 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Z ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.99/1.62 tc_Int_Oint, Y, T ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.99/1.62 .
% 0.99/1.62 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.62 tc_Int_Oint ), X ) = X }.
% 0.99/1.62 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Int_Oint ) ) = X }.
% 0.99/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) =
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.99/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ), X ) =
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.99/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP(
% 0.99/1.62 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.99/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) = hAPP
% 0.99/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) }.
% 0.99/1.62 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y = X,
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), ! Y = X }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), Y = X,
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.99/1.62 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X )
% 0.99/1.62 }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.99/1.62 tc_Int_Oint ) ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.99/1.62 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y
% 0.99/1.62 = X }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.99/1.62 tc_Int_Oint ) ) ) }.
% 0.99/1.62 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.99/1.62 tc_Int_Oint ) ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.99/1.62 tc_Int_Oint ) ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X )
% 0.99/1.62 }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.99/1.62 tc_Int_Oint ) ), X ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.99/1.62 ( tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.99/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.99/1.62 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.99/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.62 tc_Int_Oint ), c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.99/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.99/1.62 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), X =
% 0.99/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.99/1.62 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), Y =
% 0.99/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Int_Oint ), X ), ! X = c_Groups_Oone__class_Oone( tc_Int_Oint ), ! Y
% 0.99/1.62 = c_Groups_Oone__class_Oone( tc_Int_Oint ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 0.99/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.99/1.62 tc_Int_Oint ) ), X ) }.
% 0.99/1.62 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.99/1.62 tc_Int_Oint, c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ) =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.99/1.62 { ! c_Groups_Oabs__class_Oabs( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) =
% 0.99/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ), c_Groups_Oabs__class_Oabs(
% 0.99/1.62 tc_Int_Oint, X ) = c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.99/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 0.99/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = X }.
% 0.99/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.99/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) = X }.
% 0.99/1.62 { ! c_Groups_Ozero__class_Ozero( tc_Int_Oint ) = c_Groups_Oone__class_Oone
% 0.99/1.62 ( tc_Int_Oint ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oabs__class_Oabs(
% 0.99/1.62 tc_Int_Oint, X ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.99/1.62 { ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oabs__class_Oabs(
% 0.99/1.62 tc_Int_Oint, X ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.62 tc_Int_Oint ), X ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) }.
% 0.99/1.62 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.62 tc_Int_Oint ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.99/1.62 { hAPP( hAPP( c_Power_Opower_Opower( T, Z, Y ), X ),
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = Z }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.99/1.62 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.99/1.62 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.62 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.99/1.62 ( tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.99/1.62 Z ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.62 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, U ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, U ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Y ) }.
% 0.99/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, X ) }.
% 0.99/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Z ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, Z ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ), Y = X }.
% 0.99/1.62 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.99/1.62 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 0.99/1.62 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus
% 0.99/1.62 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.99/1.62 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) =
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ),
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.99/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oone__class_Oone
% 0.99/1.62 ( tc_Int_Oint ), Y ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.99/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.99/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.99/1.62 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.99/1.62 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.99/1.62 ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, T, W ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.62 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.99/1.62 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, U ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, Z ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, T ) }.
% 0.99/1.62 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.99/1.62 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.99/1.62 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.62 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.99/1.62 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, U, Y ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.99/1.62 tc_Int_Oint, X, Y ) ) }.
% 0.99/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Ozero__class_Ozero(
% 0.99/1.62 tc_Int_Oint ) ) }.
% 0.99/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 0.99/1.62 tc_Int_Oint ) ) }.
% 0.99/1.62 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.99/1.62 hAPP( X, Y ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol23( Z, Y
% 0.99/1.62 ), Y ) }.
% 0.99/1.62 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.99/1.62 hAPP( X, Y ) ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.99/1.62 skol23( X, Y ) ), ! hBOOL( hAPP( X, Z ) ) }.
% 0.99/1.62 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.99/1.62 hAPP( X, Y ) ), hBOOL( hAPP( X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat
% 0.99/1.62 , skol23( X, Y ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol24( Z, T ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), skol24( X, Y ) ), X ) =
% 0.99/1.62 Y }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol25( Z, T ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), skol25( X, Y ) ), X ) =
% 0.99/1.62 Y }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), ! hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Z ), X ) = Y, Z =
% 0.99/1.62 skol25( X, Y ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.99/1.62 c_RComplete_Onatceiling( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X
% 0.99/1.62 , c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) =
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatceiling( X ),
% 0.99/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.99/1.62 c_RComplete_Onatfloor( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 0.99/1.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) =
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatfloor( X ),
% 0.99/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.99/1.62 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless(
% 0.99/1.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), hAPP( hAPP
% 0.99/1.62 ( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), Z ), c_Groups_Ominus__class_Ominus(
% 0.99/1.62 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ), Z ) =
% 0.99/1.62 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) }.
% 0.99/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 0.99/1.62 , Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 0.99/1.62 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.99/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.99/1.62 X, c_Groups_Ominus__class_Ominus( X, Z, Y ), c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( X ) ) }.
% 0.99/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.99/1.62 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.99/1.62 , Z, Y ) }.
% 0.99/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) )
% 0.99/1.62 }.
% 0.99/1.62 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.99/1.62 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.99/1.62 ( X, Y ) ) ), c_RealVector_Onorm__class_Onorm( X,
% 0.99/1.62 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) }.
% 0.99/1.62 { c_RComplete_Onatfloor( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) =
% 0.99/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.99/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_RComplete_Onatceiling( X )
% 0.99/1.62 ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 0.99/1.62 Y ), c_RComplete_Onatceiling( X ) ) }.
% 0.99/1.62 { c_RComplete_Onatceiling( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 0.99/1.62 = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatfloor( Y
% 0.99/1.62 ), c_RComplete_Onatfloor( X ) ) }.
% 0.99/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.62 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.99/1.62 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.99/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.62 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.99/1.62 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, U, T ) }.
% 0.99/1.62 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.99/1.62 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.99/1.62 ( X, Y ) ), c_RealVector_Onorm__class_Onorm( X,
% 0.99/1.62 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ),
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.99/1.62 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.99/1.62 ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X = Z }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), ! X = Z,
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = Y }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, Z ),
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ),
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 0.99/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ), Y ) }.
% 0.99/1.62 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = Z }.
% 0.99/1.62 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.99/1.62 c_Groups_Ominus__class_Ominus( X, Z, Y ), Y ) = Z }.
% 0.99/1.62 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.62 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) =
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ) }.
% 0.99/1.62 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.62 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) =
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 0.99/1.62 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.99/1.62 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.99/1.62 Z, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.99/1.62 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.62 tc_Nat_Onat, Y, X ), Y ) = X }.
% 0.99/1.62 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.62 tc_Nat_Onat, Y, X ), X ) = Y }.
% 0.99/1.62 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.99/1.62 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.99/1.62 c_Groups_Ominus__class_Ominus( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.99/1.62 Y ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.99/1.62 { ! class_RealVector_Oreal__normed__field( X ),
% 0.99/1.62 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus( X, T,
% 0.99/1.62 Z ), Y ) = c_Groups_Ominus__class_Ominus( X,
% 0.99/1.62 c_Rings_Oinverse__class_Odivide( X, T, Y ),
% 0.99/1.62 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.99/1.62 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.99/1.62 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, Z,
% 0.99/1.62 Y ) ) = c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus
% 0.99/1.62 ( X, Y, Z ) ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.99/1.62 c_Groups_Ominus__class_Ominus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 0.99/1.62 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.99/1.62 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.99/1.62 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! U = T, Z = Y }.
% 0.99/1.62 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.99/1.62 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! Z = Y, U = T }.
% 0.99/1.62 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.99/1.62 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 0.99/1.62 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 0.99/1.62 c_Groups_Ominus__class_Ominus( X, U, Z ), c_Groups_Ominus__class_Ominus(
% 0.99/1.62 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 0.99/1.62 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.99/1.62 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ), Y ) }.
% 0.99/1.62 { c_RComplete_Onatceiling( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal )
% 0.99/1.62 ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.62 { c_RComplete_Onatfloor( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) )
% 0.99/1.62 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.62 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.99/1.62 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, U, T ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.99/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.62 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.99/1.62 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( X, U, T ) }.
% 0.99/1.62 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.99/1.62 ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.99/1.62 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ominus__class_Ominus(
% 0.99/1.62 X, Z, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.62 { ! class_Groups_Oab__group__add( X ), ! Z = Y,
% 0.99/1.62 c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.99/1.62 ) }.
% 0.99/1.62 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.99/1.62 Z, Y ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.99/1.62 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y, Y )
% 0.99/1.62 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.62 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.99/1.62 ( tc_Nat_Onat, Y, Z ), X ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.99/1.62 ( tc_Nat_Onat, Z, X ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.99/1.62 ) }.
% 0.99/1.62 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.99/1.62 c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Z, Y ) )
% 0.99/1.62 = c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Y, Z )
% 0.99/1.62 ) }.
% 0.99/1.62 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.99/1.62 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, X ) =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.62 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 0.99/1.62 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.62 tc_Nat_Onat ), X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 0.99/1.62 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 0.99/1.62 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 0.99/1.62 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.99/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 0.99/1.62 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.99/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) =
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.99/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.99/1.62 { ! class_Rings_Oring( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.62 ( X ), U ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 0.99/1.62 Z ) ), Y ) ) }.
% 0.99/1.62 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.99/1.62 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.99/1.62 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.99/1.62 X, U, Z ) ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 0.99/1.62 Z ) ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 0.99/1.62 c_Groups_Ominus__class_Ominus( X, T, Y ) ) ) }.
% 0.99/1.62 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.62 ( X ), Z ), U ), Y ), T = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.99/1.62 W ) ), U ), Y ) }.
% 0.99/1.62 { ! class_Rings_Oring( X ), ! T = c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.99/1.62 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.99/1.62 X, Z, W ) ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.62 ( X ), Z ), U ), Y ) }.
% 0.99/1.62 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.62 ( X ), Z ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.99/1.62 Z ) ), U ), T ) = Y }.
% 0.99/1.62 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.99/1.62 Z ) ), U ), T ) = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.62 ( X ), Z ), U ), Y ) }.
% 0.99/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.99/1.62 , c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, T, Z )
% 0.99/1.62 ), Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus
% 0.99/1.62 ( X, Z, Y ), T ) }.
% 0.99/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.99/1.62 , c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, T, Z )
% 0.99/1.62 ), Y ), c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus
% 0.99/1.62 ( X, Z, Y ) ) }.
% 0.99/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.99/1.62 , c_Groups_Ominus__class_Ominus( X, Z, Y ), T ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.99/1.62 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X,
% 0.99/1.62 c_Groups_Ominus__class_Ominus( X, T, Z ) ), Y ) }.
% 0.99/1.62 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 0.99/1.62 c_Groups_Ominus__class_Ominus( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.99/1.62 c_Groups_Oabs__class_Oabs( X, Y ) ) ), c_Groups_Oabs__class_Oabs( X,
% 0.99/1.62 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) }.
% 0.99/1.62 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X,
% 0.99/1.62 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ),
% 0.99/1.62 c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Z, Y ) )
% 0.99/1.62 ) }.
% 0.99/1.62 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X,
% 0.99/1.62 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ),
% 0.99/1.62 c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Y, Z ) )
% 0.99/1.62 ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.62 tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.99/1.62 ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.99/1.62 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y,
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.62 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z,
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.62 tc_Nat_Onat, Z, X ), Y ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.99/1.62 ( tc_Nat_Onat, Z, X ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z
% 0.99/1.62 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 0.99/1.62 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) = Y }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.99/1.62 ( tc_Nat_Onat, Y, Z ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z )
% 0.99/1.62 ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.99/1.62 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.99/1.62 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.99/1.62 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.99/1.62 ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z,
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.62 tc_Nat_Onat, Z, Y ), X ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.62 tc_Nat_Onat, X, Z ), Y ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = X }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.62 tc_Nat_Onat, Z, X ), Y ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.99/1.62 tc_Nat_Onat, X, Y ), Y ) = X }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z, X =
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X =
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.62 tc_Nat_Onat, Z, X ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.99/1.62 tc_Nat_Onat, X, Y ), Z ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ), Y ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.62 tc_Nat_Onat, X, Z ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), Z ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_RComplete_Onatfloor
% 0.99/1.62 ( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.99/1.62 c_RComplete_Onatceiling( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.99/1.62 }.
% 0.99/1.62 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.62 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.62 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X, T,
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.62 ( X ), c_Groups_Ominus__class_Ominus( X, Z, W ) ), U ), Y ) ) }.
% 0.99/1.62 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.62 , T, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.99/1.62 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.62 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.99/1.62 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.62 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.62 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.62 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ) }.
% 0.99/1.62 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.62 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.99/1.62 Z ) ), U ), T ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.62 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.99/1.62 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.62 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, hAPP
% 0.99/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus
% 0.99/1.62 ( X, Z, W ) ), U ), Y ) ) }.
% 0.99/1.62 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X, T
% 0.99/1.62 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.99/1.62 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless( X,
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.62 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.99/1.62 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.62 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.99/1.62 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.99/1.62 X, W, Z ) ), U ), T ), Y ) }.
% 0.99/1.62 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.62 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.99/1.62 hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.62 ( X ), Z ), U ), Y ) ) }.
% 0.99/1.62 { ! class_Rings_Oring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP
% 0.99/1.62 ( c_Groups_Otimes__class_Otimes( X ), Y ), Y ), c_Groups_Oone__class_Oone
% 0.99/1.62 ( X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) ) ),
% 0.99/1.62 c_Groups_Ominus__class_Ominus( X, Y, c_Groups_Oone__class_Oone( X ) ) ) }
% 0.99/1.62 .
% 0.99/1.62 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ominus__class_Ominus( X,
% 0.99/1.62 c_Rings_Oinverse__class_Odivide( X, U, Y ),
% 0.99/1.62 c_Rings_Oinverse__class_Odivide( X, T, Z ) ) =
% 0.99/1.62 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus( X,
% 0.99/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.99/1.62 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.62 c_Groups_Ominus__class_Ominus( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.99/1.62 Y ), Z ) = c_Rings_Oinverse__class_Odivide( X,
% 0.99/1.62 c_Groups_Ominus__class_Ominus( X, T, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) }.
% 0.99/1.62 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.62 c_Groups_Ominus__class_Ominus( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.99/1.62 Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X,
% 0.99/1.62 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ), Z ), Y ) }.
% 0.99/1.62 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 0.99/1.62 c_Groups_Ominus__class_Ominus( X, Z, Y ) ), c_Groups_Oplus__class_Oplus(
% 0.99/1.62 X, c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) )
% 0.99/1.62 ) }.
% 0.99/1.62 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 0.99/1.62 c_Groups_Ominus__class_Ominus( X, c_Groups_Oplus__class_Oplus( X, U, T )
% 0.99/1.62 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) ), c_Groups_Oplus__class_Oplus
% 0.99/1.62 ( X, c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, U, Z
% 0.99/1.62 ) ), c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, T,
% 0.99/1.62 Y ) ) ) ) }.
% 0.99/1.62 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.62 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, Z,
% 0.99/1.62 Y ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.99/1.62 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.99/1.62 ( X, Y ) ) ) }.
% 0.99/1.62 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.99/1.62 , ! alpha17( X, Y, Z ) }.
% 0.99/1.62 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.99/1.62 , ! alpha41( X, Y, Z ) }.
% 0.99/1.62 { alpha17( X, Y, Z ), alpha41( X, Y, Z ), hBOOL( hAPP( Z,
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.99/1.62 { ! alpha41( X, Y, Z ), ! hBOOL( hAPP( Z, skol26( T, U, Z ) ) ) }.
% 0.99/1.62 { ! alpha41( X, Y, Z ), Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.99/1.62 skol26( X, Y, Z ) ) }.
% 0.99/1.62 { ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, T ), hBOOL( hAPP( Z, T
% 0.99/1.62 ) ), alpha41( X, Y, Z ) }.
% 0.99/1.62 { ! alpha17( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 0.99/1.62 }.
% 0.99/1.62 { ! alpha17( X, Y, Z ), ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero(
% 0.99/1.62 tc_Nat_Onat ) ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), hBOOL( hAPP( Z,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha17( X, Y, Z ) }.
% 0.99/1.62 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.99/1.62 , alpha18( X, Y, Z ) }.
% 0.99/1.62 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.99/1.62 , alpha42( X, Y, Z ) }.
% 0.99/1.62 { ! alpha18( X, Y, Z ), ! alpha42( X, Y, Z ), hBOOL( hAPP( Z,
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.99/1.62 { ! alpha42( X, Y, Z ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.99/1.62 T ), hBOOL( hAPP( Z, T ) ) }.
% 0.99/1.62 { ! hBOOL( hAPP( Z, skol27( T, U, Z ) ) ), alpha42( X, Y, Z ) }.
% 0.99/1.62 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, skol27( X, Y, Z ) ),
% 0.99/1.62 alpha42( X, Y, Z ) }.
% 0.99/1.62 { ! alpha18( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 0.99/1.62 ), hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.99/1.62 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), alpha18( X, Y, Z ) }
% 0.99/1.62 .
% 0.99/1.62 { ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha18
% 0.99/1.62 ( X, Y, Z ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.62 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 0.99/1.62 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) =
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.62 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) =
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ),
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) = Z }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) = Z,
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) =
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ),
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T,
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T,
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ),
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.62 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 0.99/1.62 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) =
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, T,
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) =
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ), T =
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! T =
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ),
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) =
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Groups_Oone__class_Oone
% 0.99/1.62 ( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling
% 0.99/1.62 ( X ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.99/1.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.99/1.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 0.99/1.62 X ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.99/1.62 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.62 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X,
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.99/1.62 , Y ) ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.99/1.62 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, U,
% 0.99/1.62 Z ) ), c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus
% 0.99/1.62 ( X, T, Y ) ) ) ) }.
% 0.99/1.62 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ominus__class_Ominus(
% 0.99/1.62 tc_Nat_Onat, Z, T ) ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.62 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 0.99/1.62 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T,
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T,
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.62 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 0.99/1.62 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.62 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 0.99/1.62 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.62 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.62 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.62 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 0.99/1.62 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) }.
% 0.99/1.62 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.62 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 0.99/1.62 ( tc_Nat_Onat ) ) ), X ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_RComplete_Onatfloor( X )
% 0.99/1.62 ), c_RComplete_Onatfloor( Y ) ), c_RComplete_Onatfloor( hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) ) }.
% 0.99/1.62 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) =
% 0.99/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.99/1.62 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) = hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ),
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 0.99/1.62 ( tc_Nat_Onat ) ) ) ) }.
% 0.99/1.62 { ! class_Power_Opower( X ), ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 0.99/1.62 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) =
% 0.99/1.62 c_Groups_Oone__class_Oone( X ) }.
% 0.99/1.62 { ! class_Power_Opower( X ), Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.99/1.62 , hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) = hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ominus__class_Ominus(
% 0.99/1.62 tc_Nat_Onat, Z, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 0.99/1.62 { ! class_RealVector_Oreal__field( X ), c_Rings_Oinverse__class_Odivide( X
% 0.99/1.62 , c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), W ), U ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) =
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.62 ( X ), W ), c_Rings_Oinverse__class_Odivide( X,
% 0.99/1.62 c_Groups_Ominus__class_Ominus( X, U, Z ), Y ) ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.99/1.62 c_Groups_Ominus__class_Ominus( X, W, T ), Y ) ), Z ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.99/1.62 tc_Nat_Onat, Y ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.99/1.62 tc_RealDef_Oreal, X, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.99/1.62 c_RealDef_Oreal( tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone(
% 0.99/1.62 tc_RealDef_Oreal ) ) ), c_RComplete_Onatceiling( X ) =
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone(
% 0.99/1.62 tc_Nat_Onat ) ) }.
% 0.99/1.62 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.99/1.62 tc_Nat_Onat, X ) ) }.
% 0.99/1.62 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X,
% 0.99/1.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), c_RealDef_Oreal(
% 0.99/1.62 tc_Nat_Onat, c_RComplete_Onatfloor( X ) ) ) }.
% 0.99/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.99/1.62 ( tc_Polynomial_Opoly( X ), Z, Y ), Z = Y, c_Polynomial_Opos__poly( X,
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 0.99/1.62 { ! class_Rings_Olinordered__idom( X ), ! Z = Y,
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.99/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.99/1.62 tc_Nat_Onat, Y ), X ), c_RComplete_Onatceiling(
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.99/1.62 tc_Nat_Onat, Y ) ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.99/1.62 c_RComplete_Onatceiling( X ), Y ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.99/1.62 tc_Nat_Onat, Y ), X ), c_RComplete_Onatfloor(
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.99/1.62 tc_Nat_Onat, Y ) ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.99/1.62 c_RComplete_Onatfloor( X ), Y ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), c_RealDef_Oreal
% 0.99/1.62 ( tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.99/1.62 tc_Nat_Onat, X ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ) }.
% 0.99/1.62 { c_RComplete_Onatceiling( c_RealDef_Oreal( tc_Nat_Onat, X ) ) = X }.
% 0.99/1.62 { c_RComplete_Onatfloor( c_RealDef_Oreal( tc_Nat_Onat, X ) ) = X }.
% 0.99/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless(
% 0.99/1.62 tc_Polynomial_Opoly( X ), Z, Y ), c_Polynomial_Opos__poly( X,
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 0.99/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.99/1.62 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.99/1.62 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 0.99/1.62 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.99/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ) =
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.99/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ), X ) =
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.99/1.62 { c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, hAPP( Z, Y ), hAPP( hAPP
% 0.99/1.62 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.99/1.62 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, hAPP( Z, X ), hAPP( Z, Y
% 0.99/1.62 ) ), c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, Y ) ) ), Y ) )
% 0.99/1.62 = c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, hAPP( Z, X ), hAPP(
% 0.99/1.62 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.99/1.62 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, hAPP( Z, X ), hAPP( Z, Y
% 0.99/1.62 ) ), c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, Y ) ) ), X ) )
% 0.99/1.62 }.
% 0.99/1.62 { c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, c_RealDef_Oreal( tc_Nat_Onat
% 0.99/1.62 , X ) ) = c_RealDef_Oreal( tc_Nat_Onat, X ) }.
% 0.99/1.62 { ! c_RealDef_Oreal( tc_Nat_Onat, Y ) = c_RealDef_Oreal( tc_Nat_Onat, X ),
% 0.99/1.62 Y = X }.
% 0.99/1.62 { ! Y = X, c_RealDef_Oreal( tc_Nat_Onat, Y ) = c_RealDef_Oreal( tc_Nat_Onat
% 0.99/1.62 , X ) }.
% 0.99/1.62 { ! c_RealDef_Oreal( tc_Nat_Onat, X ) = c_Groups_Ozero__class_Ozero(
% 0.99/1.62 tc_RealDef_Oreal ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.62 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_RealDef_Oreal(
% 0.99/1.62 tc_Nat_Onat, X ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.99/1.62 { c_RealDef_Oreal( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.99/1.62 ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.99/1.62 tc_Nat_Onat, X ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.99/1.62 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.99/1.62 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.99/1.62 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.99/1.62 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 0.99/1.62 { c_RealDef_Oreal( tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.99/1.62 tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.99/1.62 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ), c_RealDef_Oreal
% 0.99/1.62 ( tc_Nat_Onat, X ) ) }.
% 0.99/1.62 { c_RealDef_Oreal( tc_Nat_Onat, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y
% 0.99/1.62 , X ) ) = c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal
% 0.99/1.62 ( tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ),
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ),
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.99/1.62 { c_RealDef_Oreal( tc_Nat_Onat, c_Groups_Oone__class_Oone( tc_Nat_Onat ) )
% 0.99/1.62 = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ominus__class_Ominus
% 0.99/1.62 ( tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ),
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.99/1.62 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.99/1.62 c_RealDef_Oreal( tc_Nat_Onat, Y ) ), X ) = c_RealDef_Oreal( tc_Nat_Onat,
% 0.99/1.62 hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.99/1.62 { c_RealDef_Oreal( tc_Nat_Onat, hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.99/1.62 tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.99/1.62 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ), X ) }.
% 0.99/1.62 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.99/1.62 tc_Nat_Onat, c_RComplete_Onatceiling( X ) ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.99/1.62 tc_Nat_Onat, X ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.62 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.99/1.62 tc_Nat_Onat, X ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.99/1.62 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.99/1.62 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.99/1.62 ( X, Y ) ), c_RealVector_Onorm__class_Onorm( X,
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.99/1.62 tc_Nat_Onat, c_RComplete_Onatfloor( X ) ), X ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 0.99/1.62 ( tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.99/1.62 .
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 0.99/1.62 ( tc_Int_Oint ) ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.99/1.62 tc_Nat_Onat, Y ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.99/1.62 , c_RComplete_Onatfloor( X ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, c_RealDef_Oreal
% 0.99/1.62 ( tc_Nat_Onat, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.62 c_RComplete_Onatceiling( Y ), X ) }.
% 0.99/1.62 { ! X = c_RealDef_Oreal( tc_Nat_Onat, c_RComplete_Onatfloor( X ) ),
% 0.99/1.62 c_RComplete_Onatfloor( hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.99/1.62 tc_RealDef_Oreal ), X ), Y ) ) = hAPP( hAPP( c_Power_Opower__class_Opower
% 0.99/1.62 ( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ), Y ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.99/1.62 tc_Nat_Onat, X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.99/1.62 tc_Nat_Onat, X ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.99/1.62 tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.99/1.62 c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.99/1.62 tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.99/1.62 c_RealDef_Oreal( tc_Nat_Onat, X ) ), c_Orderings_Oord__class_Oless(
% 0.99/1.62 tc_Nat_Onat, Y, X ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.99/1.62 tc_Nat_Onat, Y ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.99/1.62 c_RealDef_Oreal( tc_Nat_Onat, X ), c_Groups_Oone__class_Oone(
% 0.99/1.62 tc_RealDef_Oreal ) ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.99/1.62 tc_Nat_Onat, Y ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.99/1.62 c_RealDef_Oreal( tc_Nat_Onat, X ), c_Groups_Oone__class_Oone(
% 0.99/1.62 tc_RealDef_Oreal ) ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.99/1.62 , X ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_RComplete_Onatfloor
% 0.99/1.62 ( X ) ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.62 c_RealDef_Oreal( tc_Nat_Onat, Y ), X ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.99/1.62 tc_Nat_Onat, Y ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.99/1.62 , c_RComplete_Onatfloor( X ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 0.99/1.62 X ), Y ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.99/1.62 c_RealDef_Oreal( tc_Nat_Onat, Y ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.99/1.62 tc_Nat_Onat, Y ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.62 c_RComplete_Onatceiling( X ), Y ) }.
% 0.99/1.62 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.99/1.62 tc_Nat_Onat, c_RComplete_Onatfloor( X ) ), c_Groups_Oone__class_Oone(
% 0.99/1.62 tc_RealDef_Oreal ) ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.99/1.62 tc_Nat_Onat, Y ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.62 c_RComplete_Onatfloor( X ), Y ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.99/1.62 c_RComplete_Onatfloor( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 0.99/1.62 c_RealDef_Oreal( tc_Nat_Onat, Y ) ) ) = c_Groups_Oplus__class_Oplus(
% 0.99/1.62 tc_Nat_Onat, c_RComplete_Onatfloor( X ), Y ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatfloor( Y ),
% 0.99/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, c_RealDef_Oreal(
% 0.99/1.62 tc_Nat_Onat, X ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.99/1.62 tc_Nat_Onat, Y ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal
% 0.99/1.62 , X, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.99/1.62 tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ),
% 0.99/1.62 c_RComplete_Onatfloor( X ) = Y }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.99/1.62 c_RComplete_Onatceiling( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X
% 0.99/1.62 , c_RealDef_Oreal( tc_Nat_Onat, Y ) ) ) = c_Groups_Oplus__class_Oplus(
% 0.99/1.62 tc_Nat_Onat, c_RComplete_Onatceiling( X ), Y ) }.
% 0.99/1.62 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.99/1.62 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus(
% 0.99/1.62 X, U, Z ), c_Groups_Ominus__class_Ominus( X, T, Y ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.99/1.62 tc_Nat_Onat, Y ) ), X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 0.99/1.62 , hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 0.99/1.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ), Y ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Groups_Oplus__class_Oplus
% 0.99/1.62 ( tc_Int_Oint, c_Groups_Oabs__class_Oabs( tc_Int_Oint,
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ),
% 0.99/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ), X ) ), Y ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Z,
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Groups_Oplus__class_Oplus
% 0.99/1.62 ( tc_Int_Oint, c_Groups_Oabs__class_Oabs( tc_Int_Oint,
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, Z ) ),
% 0.99/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ), X ) ) ) }.
% 0.99/1.62 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.99/1.62 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X ) ),
% 0.99/1.62 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y ) ),
% 0.99/1.62 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ),
% 0.99/1.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ),
% 0.99/1.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Transcendental_Oarctan(
% 0.99/1.62 X ), c_Transcendental_Oarctan( Y ) ) = c_Transcendental_Oarctan(
% 0.99/1.62 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X, Y ),
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oarctan
% 0.99/1.62 ( Y ), c_Transcendental_Oarctan( X ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.62 c_Transcendental_Oarctan( Y ), c_Transcendental_Oarctan( X ) ) }.
% 0.99/1.62 { c_Transcendental_Oarctan( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal )
% 0.99/1.62 ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.99/1.62 tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, skol28( X ),
% 0.99/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ), X ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.99/1.62 tc_Nat_Onat, skol28( X ) ) ) }.
% 0.99/1.62 { ! c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) =
% 0.99/1.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.62 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, X,
% 0.99/1.62 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) ),
% 0.99/1.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.62 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, X,
% 0.99/1.62 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) ),
% 0.99/1.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.62 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, X, c_Complex_Oii ) ),
% 0.99/1.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.62 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, X, c_Complex_Oii ) )
% 0.99/1.62 , c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.99/1.62 { ! c_Complex_Oii = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.99/1.62 { ! c_Complex_Oii = c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) }.
% 0.99/1.62 { ! class_RealVector_Oreal__normed__vector( Y ), ! class_Orderings_Oord( X
% 0.99/1.62 ), c_Orderings_Oord__class_Oless__eq( X, T, skol29( X, U, W, T ) ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, T, V0 ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.62 c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, V0 ) ),
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oone__class_Oone
% 0.99/1.62 ( tc_RealDef_Oreal ), c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, T ) )
% 0.99/1.62 ) ) }.
% 0.99/1.62 { ! class_RealVector_Oreal__normed__vector( Y ), ! class_Orderings_Oord( X
% 0.99/1.62 ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.62 c_RealVector_Onorm__class_Onorm( Y, c_Groups_Ominus__class_Ominus( Y,
% 0.99/1.62 hAPP( Z, T ), hAPP( Z, skol29( X, Y, Z, T ) ) ) ),
% 0.99/1.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, T, U ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.62 c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, U ) ),
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oone__class_Oone
% 0.99/1.62 ( tc_RealDef_Oreal ), c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, T ) )
% 0.99/1.62 ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol30( T, U, W ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.99/1.62 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, T, Z ) ) ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.62 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, T, Z ) ), skol30( X,
% 0.99/1.62 Y, Z ) ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.62 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, hAPP(
% 0.99/1.62 c_Polynomial_Opoly( tc_Complex_Ocomplex, Y ), T ), hAPP(
% 0.99/1.62 c_Polynomial_Opoly( tc_Complex_Ocomplex, Y ), Z ) ) ), X ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.99/1.62 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ominus__class_Ominus(
% 0.99/1.62 tc_Int_Oint, X, Y ) }.
% 0.99/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.99/1.62 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint
% 0.99/1.62 ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.62 tc_Nat_Onat ), Y ), c_RComplete_Onatfloor(
% 0.99/1.62 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.99/1.62 tc_Nat_Onat, Y ) ) ) = c_Divides_Odiv__class_Odiv( tc_Nat_Onat,
% 0.99/1.62 c_RComplete_Onatfloor( X ), Y ) }.
% 0.99/1.62 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.99/1.62 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.62 { Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.99/1.62 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) =
% 0.99/1.62 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) }.
% 0.99/1.62 { ! class_Divides_Osemiring__div( X ), ! T = c_Groups_Ozero__class_Ozero( X
% 0.99/1.62 ), c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.62 { ! class_Divides_Osemiring__div( X ), T = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.62 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.99/1.62 c_Divides_Odiv__class_Odiv( X, Z, Y ) }.
% 0.99/1.62 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.62 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = Z }.
% 0.99/1.62 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.62 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) = Z }.
% 0.99/1.62 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.62 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.99/1.62 c_Divides_Odiv__class_Odiv( X, T, Z ) }.
% 0.99/1.62 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.62 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) =
% 0.99/1.62 c_Divides_Odiv__class_Odiv( X, T, Z ) }.
% 0.99/1.62 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.62 , c_Divides_Odiv__class_Odiv( X, Y, Y ) = c_Groups_Oone__class_Oone( X )
% 0.99/1.62 }.
% 0.99/1.62 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) =
% 0.99/1.62 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 0.99/1.62 tc_Nat_Onat, Z, Y ), X ) }.
% 0.99/1.62 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.62 }.
% 0.99/1.62 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X, Y,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.62 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X, Y,
% 0.99/1.62 c_Groups_Oone__class_Oone( X ) ) = Y }.
% 0.99/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.62 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ), Y ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.62 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, Z ),
% 0.99/1.62 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, X, Z ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.62 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X
% 0.99/1.62 , Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.62 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, Y ),
% 0.99/1.62 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, X ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 0.99/1.62 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) =
% 0.99/1.62 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, Y ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 0.99/1.62 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ) = Y }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 0.99/1.62 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ) = Y }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.99/1.62 tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 0.99/1.62 tc_Nat_Onat, Y, X ), Y ) }.
% 0.99/1.62 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.99/1.62 tc_Nat_Onat, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ),
% 0.99/1.62 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.99/1.62 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) ) }.
% 0.99/1.62 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.62 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, T, hAPP
% 0.99/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) =
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X, Z, c_Divides_Odiv__class_Odiv( X, T, Y )
% 0.99/1.62 ) }.
% 0.99/1.62 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.62 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, T, hAPP
% 0.99/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) =
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X, Z, c_Divides_Odiv__class_Odiv( X, T, Y )
% 0.99/1.62 ) }.
% 0.99/1.62 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.62 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, Z, Y ),
% 0.99/1.62 Y ) = c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Z, Y
% 0.99/1.62 ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.99/1.62 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.62 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, Y, Z ),
% 0.99/1.62 Y ) = c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Z, Y
% 0.99/1.62 ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.99/1.62 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 0.99/1.62 alpha19( X, Z ) }.
% 0.99/1.62 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 0.99/1.62 alpha43( X, Y, Z ) }.
% 0.99/1.62 { ! alpha19( X, Z ), ! alpha43( X, Y, Z ), hBOOL( hAPP( Z,
% 0.99/1.62 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ) }.
% 0.99/1.62 { ! alpha43( X, Y, Z ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.99/1.62 alpha53( X, Y, Z ) }.
% 0.99/1.62 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha43( X, Y, Z ) }.
% 0.99/1.62 { ! alpha53( X, Y, Z ), alpha43( X, Y, Z ) }.
% 0.99/1.62 { ! alpha53( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, X
% 0.99/1.62 ), alpha61( X, Y, Z, T ) }.
% 0.99/1.62 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol31( X, T, U ), X ),
% 0.99/1.62 alpha53( X, Y, Z ) }.
% 0.99/1.62 { ! alpha61( X, Y, Z, skol31( X, Y, Z ) ), alpha53( X, Y, Z ) }.
% 0.99/1.62 { ! alpha61( X, Y, Z, T ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.99/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 0.99/1.62 hBOOL( hAPP( Z, U ) ) }.
% 0.99/1.62 { ! hBOOL( hAPP( Z, skol32( U, W, Z, V0 ) ) ), alpha61( X, Y, Z, T ) }.
% 0.99/1.62 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol32( X, Y, Z, T ) )
% 0.99/1.62 , T ), alpha61( X, Y, Z, T ) }.
% 0.99/1.62 { ! alpha19( X, Y ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.99/1.62 hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.99/1.62 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha19( X, Y ) }.
% 0.99/1.62 { ! hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha19
% 0.99/1.62 ( X, Y ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Nat__Transfer_Otsub( X, Y )
% 0.99/1.62 ) }.
% 0.99/1.62 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.99/1.62 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.99/1.62 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ), c_RealDef_Oreal(
% 0.99/1.62 tc_Nat_Onat, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ) ) }.
% 0.99/1.62 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.99/1.62 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.99/1.62 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ), c_RealDef_Oreal(
% 0.99/1.62 tc_Nat_Onat, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 0.99/1.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.99/1.62 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ominus__class_Ominus(
% 0.99/1.62 tc_Int_Oint, X, Y ) }.
% 0.99/1.62 { ! class_Orderings_Oorder( X ), ! c_SEQ_Odecseq( X, Y ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, T ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, T ), hAPP( Y, Z ) ) }.
% 0.99/1.62 { ! class_Orderings_Oorder( X ), c_Orderings_Oord__class_Oless__eq(
% 0.99/1.62 tc_Nat_Onat, skol33( X, Y ), skol49( X, Y ) ), c_SEQ_Odecseq( X, Y ) }.
% 0.99/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.62 hAPP( Y, skol49( X, Y ) ), hAPP( Y, skol33( X, Y ) ) ), c_SEQ_Odecseq( X
% 0.99/1.62 , Y ) }.
% 0.99/1.62 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ),
% 0.99/1.62 c_Complex_Orcis( Z, Y ) ), X ) = c_Complex_Orcis( hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.99/1.62 tc_Nat_Onat, X ) ), Y ) ) }.
% 0.99/1.62 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.99/1.62 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, X ) =
% 0.99/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.99/1.62 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.62 tc_Int_Oint ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.99/1.62 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Odiv(
% 0.99/1.62 tc_Polynomial_Opoly( X ), T, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.99/1.62 tc_Polynomial_Opoly( X ) ), Z ), Y ) ) = c_Divides_Odiv__class_Odiv(
% 0.99/1.62 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly
% 0.99/1.62 ( X ), T, Z ), Y ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.99/1.62 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ),
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.99/1.62 tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.99/1.62 tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.62 tc_Int_Oint ), Y ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.62 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.99/1.62 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ),
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.62 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.99/1.62 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.99/1.62 tc_Int_Oint, X, Y ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.62 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ),
% 0.99/1.62 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.62 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.62 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ),
% 0.99/1.62 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.99/1.62 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.62 tc_Int_Oint ), Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.99/1.62 Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.62 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 0.99/1.62 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.62 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.62 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.99/1.62 tc_Int_Oint, Y, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y
% 0.99/1.62 , c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.99/1.62 tc_Int_Oint, Y, X ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ),
% 0.99/1.62 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.62 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.62 tc_Int_Oint ), Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.99/1.62 Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.62 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ),
% 0.99/1.62 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.62 tc_Int_Oint ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.62 tc_Int_Oint ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.62 tc_Int_Oint ), Y ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.62 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.99/1.62 tc_Int_Oint, X, Y ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.99/1.62 tc_Int_Oint, Y, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X
% 0.99/1.62 , Y ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X
% 0.99/1.62 , Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.99/1.62 tc_Int_Oint, Y, X ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.99/1.62 tc_Int_Oint, Y, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.99/1.62 tc_Int_Oint, Y, X ) ) }.
% 0.99/1.62 { ! c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), alpha20( X, Y ) }.
% 0.99/1.62 { ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.99/1.62 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.99/1.62 { ! alpha20( X, Y ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.99/1.62 { ! alpha20( X, Y ), alpha44( X, Y ), alpha54( X, Y ) }.
% 0.99/1.62 { ! alpha44( X, Y ), alpha20( X, Y ) }.
% 0.99/1.62 { ! alpha54( X, Y ), alpha20( X, Y ) }.
% 0.99/1.62 { ! alpha54( X, Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.99/1.62 { ! alpha54( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ), alpha54( X, Y ) }.
% 0.99/1.62 { ! alpha44( X, Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.99/1.62 { ! alpha44( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), alpha44( X, Y ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.99/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ), Y ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.99/1.62 tc_Int_Oint, X, Y ), X ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Int_Oint ), X ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Z, hAPP(
% 0.99/1.62 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) =
% 0.99/1.62 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.99/1.62 tc_Int_Oint, Z, Y ), X ) }.
% 0.99/1.62 { c_Rings_Oinverse__class_Odivide( tc_Complex_Ocomplex, c_Complex_Orcis( T
% 0.99/1.62 , Z ), c_Complex_Orcis( Y, X ) ) = c_Complex_Orcis(
% 0.99/1.62 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, T, Y ),
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Z, X ) ) }.
% 0.99/1.62 { c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, c_Complex_Orcis( Y
% 0.99/1.62 , X ) ) = c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ) }.
% 0.99/1.62 { c_Complex_Orcis( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ) =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.99/1.62 { ! T = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), alpha75( X,
% 0.99/1.62 Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), Z =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.99/1.62 tc_Int_Oint, T, Z ) = Y }.
% 0.99/1.62 { ! T = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), alpha75( X,
% 0.99/1.62 Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Z =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.99/1.62 tc_Int_Oint, T, Z ) = Y }.
% 0.99/1.62 { ! alpha75( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.99/1.62 { ! alpha75( X, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), alpha75( X, Y ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y )
% 0.99/1.62 , alpha75( X, Y ) }.
% 0.99/1.62 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ),
% 0.99/1.62 alpha21( X, Z ) }.
% 0.99/1.62 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ),
% 0.99/1.62 alpha45( X, Y, Z ) }.
% 0.99/1.62 { ! alpha21( X, Z ), ! alpha45( X, Y, Z ), hBOOL( hAPP( Z,
% 0.99/1.62 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ) }.
% 0.99/1.62 { ! alpha45( X, Y, Z ), alpha55( X, Y, Z ) }.
% 0.99/1.62 { ! alpha45( X, Y, Z ), alpha62( X, Y, Z ) }.
% 0.99/1.62 { ! alpha55( X, Y, Z ), ! alpha62( X, Y, Z ), alpha45( X, Y, Z ) }.
% 0.99/1.62 { ! alpha62( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha68( X, Y, Z ) }.
% 0.99/1.62 { c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha62( X, Y, Z ) }.
% 0.99/1.62 { ! alpha68( X, Y, Z ), alpha62( X, Y, Z ) }.
% 0.99/1.62 { ! alpha68( X, Y, Z ), ! alpha70( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 0.99/1.62 { ! hBOOL( hAPP( Z, skol34( T, U, Z ) ) ), alpha68( X, Y, Z ) }.
% 0.99/1.62 { alpha70( X, Y, skol34( X, Y, Z ) ), alpha68( X, Y, Z ) }.
% 0.99/1.62 { ! alpha70( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.99/1.62 skol35( X, T, U ) ) }.
% 0.99/1.62 { ! alpha70( X, Y, Z ), alpha72( X, Y, Z, skol35( X, Y, Z ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, T ), ! alpha72( X, Y, Z
% 0.99/1.62 , T ), alpha70( X, Y, Z ) }.
% 0.99/1.62 { ! alpha72( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.62 T, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.99/1.62 { ! alpha72( X, Y, Z, T ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.99/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ) }
% 0.99/1.62 .
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! Y =
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ), alpha72( X,
% 0.99/1.62 Y, Z, T ) }.
% 0.99/1.62 { ! alpha55( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), alpha63( X, Y, Z ) }.
% 0.99/1.62 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.62 tc_Int_Oint ), X ), alpha55( X, Y, Z ) }.
% 0.99/1.62 { ! alpha63( X, Y, Z ), alpha55( X, Y, Z ) }.
% 0.99/1.62 { ! alpha63( X, Y, Z ), ! alpha69( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 0.99/1.62 { ! hBOOL( hAPP( Z, skol36( T, U, Z ) ) ), alpha63( X, Y, Z ) }.
% 0.99/1.62 { alpha69( X, Y, skol36( X, Y, Z ) ), alpha63( X, Y, Z ) }.
% 0.99/1.62 { ! alpha69( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), skol37( T, U, W ) ) }.
% 0.99/1.62 { ! alpha69( X, Y, Z ), alpha71( X, Y, Z, skol37( X, Y, Z ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! alpha71( X, Y, Z, T )
% 0.99/1.62 , alpha69( X, Y, Z ) }.
% 0.99/1.62 { ! alpha71( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X
% 0.99/1.62 ) }.
% 0.99/1.62 { ! alpha71( X, Y, Z, T ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.99/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ) }
% 0.99/1.62 .
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X ), ! Y =
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ), alpha71( X,
% 0.99/1.62 Y, Z, T ) }.
% 0.99/1.62 { ! alpha21( X, Y ), ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.99/1.62 hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 0.99/1.62 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), alpha21( X, Y ) }.
% 0.99/1.62 { ! hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), alpha21
% 0.99/1.62 ( X, Y ) }.
% 0.99/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.99/1.62 c_Complex_Orcis( T, Z ) ), c_Complex_Orcis( Y, X ) ) = c_Complex_Orcis(
% 0.99/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), T ), Y ),
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, X ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, Z ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol38( T, U, W ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, Z ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, T ) ), skol38( X, Y,
% 0.99/1.62 Z ) ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, T ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, Z ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, T ) ), skol38( X, Y,
% 0.99/1.62 Z ) ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, T, Z ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Int_Oint ), X ), hBOOL( hAPP( Y, skol39( Z, Y ) ) ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! hBOOL( hAPP( Y, U ) )
% 0.99/1.62 , hBOOL( hAPP( Y, c_Groups_Ominus__class_Ominus( tc_Int_Oint, U, hAPP(
% 0.99/1.62 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), T ), X ) ) ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( Y, c_Groups_Ominus__class_Ominus(
% 0.99/1.62 tc_Int_Oint, skol39( X, Y ), X ) ) ), ! c_Orderings_Oord__class_Oless__eq
% 0.99/1.62 ( tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), ! hBOOL(
% 0.99/1.62 hAPP( Y, T ) ), hBOOL( hAPP( Y, c_Groups_Ominus__class_Ominus(
% 0.99/1.62 tc_Int_Oint, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 0.99/1.62 , Z ), X ) ) ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.99/1.62 c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ), Y ) = hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ),
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Int_Oint ), X ), hBOOL( hAPP( Y, skol40( Z, Y ) ) ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! hBOOL( hAPP( Y, U ) )
% 0.99/1.62 , hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, hAPP( hAPP
% 0.99/1.62 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), T ), X ) ) ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus(
% 0.99/1.62 tc_Int_Oint, skol40( X, Y ), X ) ) ), ! c_Orderings_Oord__class_Oless__eq
% 0.99/1.62 ( tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), ! hBOOL(
% 0.99/1.62 hAPP( Y, T ) ), hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus( tc_Int_Oint
% 0.99/1.62 , T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) )
% 0.99/1.62 ) ) }.
% 0.99/1.62 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( X ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.99/1.62 X ) ) }.
% 0.99/1.62 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.62 tc_Nat_Onat ), c_Nat_OSuc( X ) ) }.
% 0.99/1.62 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) = X }.
% 0.99/1.62 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ) = hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.99/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.99/1.62 X ), Y ), Z = Y }.
% 0.99/1.62 { ! class_Rings_Olinordered__semidom( X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ) ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.62 ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.99/1.62 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.99/1.62 ( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) }.
% 0.99/1.62 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 0.99/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) =
% 0.99/1.62 c_Nat_OSuc( c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.99/1.62 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.99/1.62 ( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) ) }.
% 0.99/1.62 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.99/1.62 ( tc_Nat_Onat, c_Nat_OSuc( Z ), Y ), c_Nat_OSuc( X ) ) =
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.99/1.62 ( tc_Nat_Onat, Z, Y ), X ) }.
% 0.99/1.62 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.99/1.62 X ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha22( X, Y ) }.
% 0.99/1.62 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.99/1.62 { ! alpha22( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.99/1.62 c_Nat_OSuc( X ) ) }.
% 0.99/1.62 { ! alpha22( X, Y ), Y = c_Nat_OSuc( skol41( Z, Y ) ) }.
% 0.99/1.62 { ! alpha22( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol41( X
% 0.99/1.62 , Y ), X ) }.
% 0.99/1.62 { ! Y = c_Nat_OSuc( Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.99/1.62 ), alpha22( X, Y ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.62 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( skol42( X ) ) }.
% 0.99/1.62 { ! X = c_Nat_OSuc( Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( c_Nat_OSuc(
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X = c_Nat_OSuc(
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), X = c_Nat_OSuc(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol43( X, Y ) ) ) }.
% 0.99/1.62 { ! X = c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.99/1.62 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ) }.
% 0.99/1.62 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X = Y }
% 0.99/1.62 .
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X = Y,
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.99/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.99/1.62 ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.99/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.99/1.62 ), X ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.99/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.99/1.62 ), X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.99/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.99/1.62 ), X ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 0.99/1.62 ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 0.99/1.62 c_Nat_OSuc( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X )
% 0.99/1.62 }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 0.99/1.62 c_Nat_OSuc( X ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 0.99/1.62 ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.99/1.62 { ! Y = c_Nat_OSuc( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.99/1.62 , c_Nat_OSuc( X ) ) }.
% 0.99/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), X ) }
% 0.99/1.62 .
% 0.99/1.62 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.99/1.62 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) )
% 0.99/1.62 }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.99/1.62 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.99/1.62 X ) ) }.
% 0.99/1.62 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y = X }
% 0.99/1.62 .
% 0.99/1.62 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X,
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.99/1.62 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), X = Y }
% 0.99/1.62 .
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) = X
% 0.99/1.62 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.99/1.62 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.99/1.62 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z
% 0.99/1.62 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.62 c_Nat_OSuc( Z ) ), X ), Y = X }.
% 0.99/1.62 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.62 c_Nat_OSuc( Z ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.99/1.62 tc_Nat_Onat ), c_Nat_OSuc( Z ) ), X ) }.
% 0.99/1.62 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.99/1.62 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.99/1.62 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.62 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.62 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.99/1.62 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.62 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.99/1.62 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.99/1.62 { ! Y = X, c_Nat_OSuc( Y ) = c_Nat_OSuc( X ) }.
% 0.99/1.62 { ! c_Nat_OSuc( X ) = X }.
% 0.99/1.62 { ! X = c_Nat_OSuc( X ) }.
% 0.99/1.62 { hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), c_Nat_OSuc( X ) ) =
% 0.99/1.62 hAPP( hAPP( Z, Y ), hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), X
% 0.99/1.62 ) ) }.
% 0.99/1.62 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 0.99/1.62 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.99/1.62 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.99/1.62 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.99/1.62 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.99/1.62 { ! hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) =
% 0.99/1.62 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = c_Nat_OSuc(
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.99/1.62 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.99/1.62 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP(
% 0.99/1.62 hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc
% 0.99/1.62 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.99/1.62 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), c_Nat_OSuc(
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) = c_Nat_OSuc(
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.99/1.62 { c_NthRoot_Oroot( c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) )
% 0.99/1.62 , X ) = X }.
% 0.99/1.62 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.99/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X ) }.
% 0.99/1.62 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.99/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.99/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Y )
% 0.99/1.62 ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.99/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), c_Nat_OSuc
% 0.99/1.62 ( X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.99/1.62 { c_Groups_Oone__class_Oone( tc_Nat_Onat ) = c_Nat_OSuc(
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.99/1.62 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.99/1.62 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y = c_Nat_OSuc
% 0.99/1.62 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.99/1.62 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.99/1.62 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X = c_Nat_OSuc
% 0.99/1.62 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.99/1.62 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.99/1.62 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.99/1.62 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha23( X, Y ), alpha46( X
% 0.99/1.62 , Y ) }.
% 0.99/1.62 { ! alpha23( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.99/1.62 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.99/1.62 { ! alpha46( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.99/1.62 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.99/1.62 { ! alpha46( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.62 { ! alpha46( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.99/1.62 tc_Nat_Onat ) ) }.
% 0.99/1.62 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha46( X, Y ) }.
% 0.99/1.62 { ! alpha23( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.99/1.62 tc_Nat_Onat ) ) }.
% 0.99/1.62 { ! alpha23( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.62 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha23( X, Y ) }.
% 0.99/1.62 { ! c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ), alpha24( X, Y ),
% 0.99/1.62 alpha47( X, Y ) }.
% 0.99/1.62 { ! alpha24( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.99/1.62 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.99/1.62 { ! alpha47( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.99/1.62 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.99/1.62 { ! alpha47( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.62 { ! alpha47( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.99/1.62 tc_Nat_Onat ) ) }.
% 0.99/1.62 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha47( X, Y ) }.
% 0.99/1.62 { ! alpha24( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.99/1.62 tc_Nat_Onat ) ) }.
% 0.99/1.62 { ! alpha24( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.62 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha24( X, Y ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.99/1.62 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) }.
% 0.99/1.62 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.99/1.62 , Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.99/1.62 , Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.99/1.62 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.62 c_Nat_OSuc( Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.62 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.99/1.62 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.99/1.62 tc_Nat_Onat, X, c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) )
% 0.99/1.62 ) ) = X }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.99/1.62 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.99/1.62 tc_Nat_Onat, c_Nat_OSuc( X ) ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, c_Nat_OSuc(
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) ) =
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.62 tc_Nat_Onat, Z, Y ), c_Nat_OSuc( X ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc(
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), Z ) =
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ) }.
% 0.99/1.62 { c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.99/1.62 tc_Nat_Onat ) ) ) = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.99/1.62 { c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( X ) ) =
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.99/1.62 tc_Nat_Onat, X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ) }.
% 0.99/1.62 { ! class_Rings_Olinordered__semidom( X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone
% 0.99/1.62 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ), Y ) }.
% 0.99/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.62 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ),
% 0.99/1.62 c_Groups_Oone__class_Oone( X ) ) }.
% 0.99/1.62 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.99/1.62 tc_Nat_Onat, Z, Y ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ),
% 0.99/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) ) = hAPP
% 0.99/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), T ), c_Groups_Ominus__class_Ominus(
% 0.99/1.62 tc_Nat_Onat, Y, Z ) ) ), T ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.99/1.62 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.99/1.62 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) = X }.
% 0.99/1.62 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = X }.
% 0.99/1.62 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.99/1.62 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 0.99/1.62 ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 0.99/1.62 , c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.99/1.62 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.99/1.62 tc_Nat_Onat, Y, X ), X ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 0.99/1.62 , c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.99/1.62 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.99/1.62 tc_Nat_Onat, Y, X ), X ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), c_NthRoot_Oroot(
% 0.99/1.62 c_Nat_OSuc( Y ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.99/1.62 tc_RealDef_Oreal ), X ), c_Nat_OSuc( Y ) ) ) = X }.
% 0.99/1.62 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP
% 0.99/1.62 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) ) = hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.99/1.62 Y ) ), c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.99/1.62 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.62 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol44( X, Y, Z ) ) ), Z ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.62 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, T ) ), c_RealDef_Oreal(
% 0.99/1.62 tc_Nat_Onat, c_Nat_OSuc( skol50( X, Y ) ) ) ) }.
% 0.99/1.62 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.62 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol52( X, Y, Z ) ) ),
% 0.99/1.62 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol54( T, U ) ) }.
% 0.99/1.62 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.62 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol52( X, Y, Z ) ) ),
% 0.99/1.62 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.62 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, T ) ), skol54( X, Y ) ) }.
% 0.99/1.62 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.62 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol45( X, Y, Z ) ) ), Z ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.62 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, T ) ), c_RealDef_Oreal(
% 0.99/1.62 tc_Nat_Onat, c_Nat_OSuc( skol51( X, Y ) ) ) ) }.
% 0.99/1.62 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.62 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol53( X, Y, Z ) ) ),
% 0.99/1.62 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol55( T, U ) ) }.
% 0.99/1.62 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.62 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol53( X, Y, Z ) ) ),
% 0.99/1.62 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.62 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, T ) ), skol55( X, Y ) ) }.
% 0.99/1.62 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 0.99/1.62 alpha25( X, Z ), alpha48( X, Y, Z ) }.
% 0.99/1.62 { ! alpha25( X, Z ), hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv(
% 0.99/1.62 tc_Nat_Onat, Y, X ) ) ) }.
% 0.99/1.62 { ! alpha48( X, Y, Z ), hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv(
% 0.99/1.62 tc_Nat_Onat, Y, X ) ) ) }.
% 0.99/1.62 { ! alpha48( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol46( X
% 0.99/1.62 , Y, T ) ), Y ) }.
% 0.99/1.62 { ! alpha48( X, Y, Z ), alpha56( X, Y, Z, skol46( X, Y, Z ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), T ), Y ), ! alpha56( X
% 0.99/1.62 , Y, Z, T ), alpha48( X, Y, Z ) }.
% 0.99/1.62 { ! alpha56( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.99/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), c_Nat_OSuc
% 0.99/1.62 ( T ) ) ) }.
% 0.99/1.62 { ! alpha56( X, Y, Z, T ), hBOOL( hAPP( Z, T ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), c_Nat_OSuc( T ) ) ), !
% 0.99/1.62 hBOOL( hAPP( Z, T ) ), alpha56( X, Y, Z, T ) }.
% 0.99/1.62 { ! alpha25( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.62 { ! alpha25( X, Y ), hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero(
% 0.99/1.62 tc_Nat_Onat ) ) ) }.
% 0.99/1.62 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hBOOL( hAPP( Y,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha25( X, Y ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), Y ),
% 0.99/1.62 ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), c_Nat_OSuc( Z ) ) ), Z
% 0.99/1.62 = c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Nat_Onat ), X ), ! Z = c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X
% 0.99/1.62 ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), Y ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Nat_Onat ), X ), ! Z = c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X
% 0.99/1.62 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), c_Nat_OSuc( Z ) ) ) }
% 0.99/1.62 .
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X
% 0.99/1.62 , Y ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.99/1.62 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.99/1.62 tc_Nat_Onat, Y, X ), X ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.99/1.62 tc_Nat_Onat, skol47( X, Y ) ) ), X ), Y ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.99/1.62 tc_Nat_Onat, c_Nat_OSuc( skol47( X, Y ) ) ) ), X ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.99/1.62 tc_Nat_Onat, skol48( X ) ), X ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.99/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.99/1.62 tc_Nat_Onat, c_Nat_OSuc( skol48( X ) ) ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.99/1.62 c_Transcendental_Oln( hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.99/1.62 tc_RealDef_Oreal ), X ), Y ) ) = hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.99/1.62 tc_Nat_Onat, Y ) ), c_Transcendental_Oln( X ) ) }.
% 0.99/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Nat_Onat ), X ), c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.99/1.62 c_RealDef_Oreal( tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) =
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.99/1.62 tc_Nat_Onat, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ),
% 0.99/1.62 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.99/1.62 tc_Nat_Onat, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ),
% 0.99/1.62 c_RealDef_Oreal( tc_Nat_Onat, X ) ) ) }.
% 0.99/1.62 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), X ) =
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.99/1.62 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ),
% 0.99/1.62 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.99/1.62 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ), X ) ) }.
% 0.99/1.62 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) =
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ),
% 0.99/1.62 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 0.99/1.62 tc_Nat_Onat, Z, Y ), X ) ), c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, Y
% 0.99/1.62 ) ) }.
% 0.99/1.62 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.99/1.62 class_Groups_Ocancel__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.62 { class_Groups_Ocancel__comm__monoid__add( tc_Complex_Ocomplex ) }.
% 0.99/1.62 { class_Groups_Ocancel__comm__monoid__add( tc_RealDef_Oreal ) }.
% 0.99/1.62 { class_Groups_Ocancel__comm__monoid__add( tc_Nat_Onat ) }.
% 0.99/1.62 { class_Groups_Ocancel__comm__monoid__add( tc_Int_Oint ) }.
% 0.99/1.62 { ! class_Orderings_Opreorder( X ), class_Orderings_Opreorder( tc_fun( Y, X
% 0.99/1.62 ) ) }.
% 0.99/1.62 { ! class_Orderings_Oorder( X ), class_Orderings_Oorder( tc_fun( Y, X ) ) }
% 0.99/1.62 .
% 0.99/1.62 { ! class_Orderings_Oord( X ), class_Orderings_Oord( tc_fun( Y, X ) ) }.
% 0.99/1.62 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.99/1.62 tc_Int_Oint ) }.
% 0.99/1.62 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.99/1.62 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Int_Oint ) }.
% 0.99/1.62 { class_Rings_Olinordered__comm__semiring__strict( tc_Int_Oint ) }.
% 0.99/1.62 { class_Rings_Olinordered__semiring__1__strict( tc_Int_Oint ) }.
% 0.99/1.62 { class_Rings_Olinordered__semiring__strict( tc_Int_Oint ) }.
% 0.99/1.62 { class_Groups_Oordered__ab__semigroup__add( tc_Int_Oint ) }.
% 0.99/1.62 { class_Groups_Oordered__ab__group__add__abs( tc_Int_Oint ) }.
% 0.99/1.62 { class_Groups_Oordered__comm__monoid__add( tc_Int_Oint ) }.
% 0.99/1.62 { class_Groups_Olinordered__ab__group__add( tc_Int_Oint ) }.
% 0.99/1.62 { class_Groups_Ocancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.99/1.62 { class_Rings_Oring__1__no__zero__divisors( tc_Int_Oint ) }.
% 0.99/1.62 { class_Rings_Oordered__cancel__semiring( tc_Int_Oint ) }.
% 0.99/1.62 { class_Rings_Olinordered__ring__strict( tc_Int_Oint ) }.
% 0.99/1.62 { class_Rings_Oring__no__zero__divisors( tc_Int_Oint ) }.
% 0.99/1.62 { class_Rings_Oordered__comm__semiring( tc_Int_Oint ) }.
% 0.99/1.62 { class_Rings_Olinordered__semiring__1( tc_Int_Oint ) }.
% 0.99/1.62 { class_Groups_Oordered__ab__group__add( tc_Int_Oint ) }.
% 0.99/1.62 { class_Groups_Ocancel__semigroup__add( tc_Int_Oint ) }.
% 0.99/1.62 { class_Rings_Olinordered__semiring( tc_Int_Oint ) }.
% 0.99/1.62 { class_Rings_Olinordered__semidom( tc_Int_Oint ) }.
% 0.99/1.62 { class_Groups_Oab__semigroup__mult( tc_Int_Oint ) }.
% 0.99/1.62 { class_Groups_Ocomm__monoid__mult( tc_Int_Oint ) }.
% 0.99/1.62 { class_Groups_Oab__semigroup__add( tc_Int_Oint ) }.
% 0.99/1.62 { class_Rings_Oordered__semiring( tc_Int_Oint ) }.
% 0.99/1.62 { class_Rings_Oordered__ring__abs( tc_Int_Oint ) }.
% 0.99/1.62 { class_Rings_Ono__zero__divisors( tc_Int_Oint ) }.
% 0.99/1.62 { class_Groups_Ocomm__monoid__add( tc_Int_Oint ) }.
% 0.99/1.62 { class_Rings_Olinordered__ring( tc_Int_Oint ) }.
% 0.99/1.62 { class_Rings_Olinordered__idom( tc_Int_Oint ) }.
% 0.99/1.62 { class_Rings_Ocomm__semiring__1( tc_Int_Oint ) }.
% 0.99/1.62 { class_Rings_Ocomm__semiring__0( tc_Int_Oint ) }.
% 0.99/1.62 { class_Divides_Osemiring__div( tc_Int_Oint ) }.
% 0.99/1.62 { class_Rings_Ocomm__semiring( tc_Int_Oint ) }.
% 0.99/1.62 { class_Groups_Oab__group__add( tc_Int_Oint ) }.
% 0.99/1.62 { class_Rings_Ozero__neq__one( tc_Int_Oint ) }.
% 0.99/1.62 { class_Rings_Oordered__ring( tc_Int_Oint ) }.
% 0.99/1.62 { class_Orderings_Opreorder( tc_Int_Oint ) }.
% 0.99/1.62 { class_Orderings_Olinorder( tc_Int_Oint ) }.
% 0.99/1.62 { class_Groups_Omonoid__mult( tc_Int_Oint ) }.
% 0.99/1.62 { class_Rings_Ocomm__ring__1( tc_Int_Oint ) }.
% 0.99/1.62 { class_Groups_Omonoid__add( tc_Int_Oint ) }.
% 0.99/1.62 { class_Rings_Osemiring__0( tc_Int_Oint ) }.
% 0.99/1.62 { class_Groups_Ogroup__add( tc_Int_Oint ) }.
% 0.99/1.62 { class_Rings_Omult__zero( tc_Int_Oint ) }.
% 0.99/1.62 { class_Rings_Ocomm__ring( tc_Int_Oint ) }.
% 0.99/1.62 { class_Orderings_Oorder( tc_Int_Oint ) }.
% 0.99/1.62 { class_Int_Oring__char__0( tc_Int_Oint ) }.
% 0.99/1.62 { class_Rings_Osemiring( tc_Int_Oint ) }.
% 0.99/1.62 { class_Orderings_Oord( tc_Int_Oint ) }.
% 0.99/1.62 { class_Rings_Oring__1( tc_Int_Oint ) }.
% 0.99/1.62 { class_Power_Opower( tc_Int_Oint ) }.
% 0.99/1.62 { class_Groups_Ozero( tc_Int_Oint ) }.
% 0.99/1.62 { class_Rings_Oring( tc_Int_Oint ) }.
% 0.99/1.62 { class_Rings_Oidom( tc_Int_Oint ) }.
% 0.99/1.62 { class_Groups_Oone( tc_Int_Oint ) }.
% 0.99/1.62 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.99/1.62 tc_Nat_Onat ) }.
% 0.99/1.62 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.99/1.62 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Nat_Onat ) }.
% 0.99/1.62 { class_Rings_Olinordered__comm__semiring__strict( tc_Nat_Onat ) }.
% 0.99/1.62 { class_Rings_Olinordered__semiring__strict( tc_Nat_Onat ) }.
% 0.99/1.62 { class_Groups_Oordered__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.99/1.62 { class_Groups_Oordered__comm__monoid__add( tc_Nat_Onat ) }.
% 0.99/1.62 { class_Groups_Ocancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.99/1.62 { class_Rings_Oordered__cancel__semiring( tc_Nat_Onat ) }.
% 0.99/1.62 { class_Rings_Oordered__comm__semiring( tc_Nat_Onat ) }.
% 0.99/1.62 { class_Groups_Ocancel__semigroup__add( tc_Nat_Onat ) }.
% 0.99/1.62 { class_Rings_Olinordered__semiring( tc_Nat_Onat ) }.
% 0.99/1.62 { class_Rings_Olinordered__semidom( tc_Nat_Onat ) }.
% 0.99/1.62 { class_Groups_Oab__semigroup__mult( tc_Nat_Onat ) }.
% 0.99/1.63 { class_Groups_Ocomm__monoid__mult( tc_Nat_Onat ) }.
% 0.99/1.63 { class_Groups_Oab__semigroup__add( tc_Nat_Onat ) }.
% 0.99/1.63 { class_Rings_Oordered__semiring( tc_Nat_Onat ) }.
% 0.99/1.63 { class_Rings_Ono__zero__divisors( tc_Nat_Onat ) }.
% 0.99/1.63 { class_Groups_Ocomm__monoid__add( tc_Nat_Onat ) }.
% 0.99/1.63 { class_Rings_Ocomm__semiring__1( tc_Nat_Onat ) }.
% 0.99/1.63 { class_Rings_Ocomm__semiring__0( tc_Nat_Onat ) }.
% 0.99/1.63 { class_Divides_Osemiring__div( tc_Nat_Onat ) }.
% 0.99/1.63 { class_Rings_Ocomm__semiring( tc_Nat_Onat ) }.
% 0.99/1.63 { class_Rings_Ozero__neq__one( tc_Nat_Onat ) }.
% 0.99/1.63 { class_Orderings_Opreorder( tc_Nat_Onat ) }.
% 0.99/1.63 { class_Orderings_Olinorder( tc_Nat_Onat ) }.
% 0.99/1.63 { class_Groups_Omonoid__mult( tc_Nat_Onat ) }.
% 0.99/1.63 { class_Groups_Omonoid__add( tc_Nat_Onat ) }.
% 0.99/1.63 { class_Rings_Osemiring__0( tc_Nat_Onat ) }.
% 0.99/1.63 { class_Rings_Omult__zero( tc_Nat_Onat ) }.
% 0.99/1.63 { class_Orderings_Oorder( tc_Nat_Onat ) }.
% 0.99/1.63 { class_Rings_Osemiring( tc_Nat_Onat ) }.
% 0.99/1.63 { class_Orderings_Oord( tc_Nat_Onat ) }.
% 0.99/1.63 { class_Power_Opower( tc_Nat_Onat ) }.
% 0.99/1.63 { class_Groups_Ozero( tc_Nat_Onat ) }.
% 0.99/1.63 { class_Groups_Oone( tc_Nat_Onat ) }.
% 0.99/1.63 { class_Orderings_Opreorder( tc_HOL_Obool ) }.
% 0.99/1.63 { class_Orderings_Oorder( tc_HOL_Obool ) }.
% 0.99/1.63 { class_Orderings_Oord( tc_HOL_Obool ) }.
% 0.99/1.63 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.99/1.63 tc_RealDef_Oreal ) }.
% 0.99/1.63 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.99/1.63 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_RealDef_Oreal ) }
% 0.99/1.63 .
% 0.99/1.63 { class_Rings_Olinordered__comm__semiring__strict( tc_RealDef_Oreal ) }.
% 0.99/1.63 { class_Fields_Olinordered__field__inverse__zero( tc_RealDef_Oreal ) }.
% 0.99/1.63 { class_Rings_Olinordered__semiring__1__strict( tc_RealDef_Oreal ) }.
% 0.99/1.63 { class_RealVector_Oreal__normed__div__algebra( tc_RealDef_Oreal ) }.
% 0.99/1.63 { class_Rings_Olinordered__semiring__strict( tc_RealDef_Oreal ) }.
% 0.99/1.63 { class_Rings_Odivision__ring__inverse__zero( tc_RealDef_Oreal ) }.
% 0.99/1.63 { class_RealVector_Oreal__normed__algebra__1( tc_RealDef_Oreal ) }.
% 0.99/1.63 { class_Groups_Oordered__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.99/1.63 { class_Groups_Oordered__ab__group__add__abs( tc_RealDef_Oreal ) }.
% 0.99/1.63 { class_RealVector_Oreal__normed__algebra( tc_RealDef_Oreal ) }.
% 0.99/1.63 { class_Groups_Oordered__comm__monoid__add( tc_RealDef_Oreal ) }.
% 0.99/1.63 { class_Groups_Olinordered__ab__group__add( tc_RealDef_Oreal ) }.
% 0.99/1.63 { class_Groups_Ocancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.99/1.63 { class_Rings_Oring__1__no__zero__divisors( tc_RealDef_Oreal ) }.
% 0.99/1.63 { class_Rings_Oordered__cancel__semiring( tc_RealDef_Oreal ) }.
% 0.99/1.63 { class_RealVector_Oreal__normed__vector( tc_RealDef_Oreal ) }.
% 0.99/1.63 { class_Rings_Olinordered__ring__strict( tc_RealDef_Oreal ) }.
% 0.99/1.63 { class_RealVector_Oreal__normed__field( tc_RealDef_Oreal ) }.
% 0.99/1.63 { class_Rings_Oring__no__zero__divisors( tc_RealDef_Oreal ) }.
% 0.99/1.63 { class_Rings_Oordered__comm__semiring( tc_RealDef_Oreal ) }.
% 0.99/1.63 { class_Rings_Olinordered__semiring__1( tc_RealDef_Oreal ) }.
% 0.99/1.63 { class_Groups_Oordered__ab__group__add( tc_RealDef_Oreal ) }.
% 0.99/1.63 { class_Groups_Ocancel__semigroup__add( tc_RealDef_Oreal ) }.
% 0.99/1.63 { class_Rings_Olinordered__semiring( tc_RealDef_Oreal ) }.
% 0.99/1.63 { class_Fields_Ofield__inverse__zero( tc_RealDef_Oreal ) }.
% 0.99/1.63 { class_Rings_Olinordered__semidom( tc_RealDef_Oreal ) }.
% 0.99/1.63 { class_Groups_Oab__semigroup__mult( tc_RealDef_Oreal ) }.
% 0.99/1.63 { class_Groups_Ocomm__monoid__mult( tc_RealDef_Oreal ) }.
% 0.99/1.63 { class_Groups_Oab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.99/1.63 { class_Fields_Olinordered__field( tc_RealDef_Oreal ) }.
% 0.99/1.63 { class_Rings_Oordered__semiring( tc_RealDef_Oreal ) }.
% 0.99/1.63 { class_Rings_Oordered__ring__abs( tc_RealDef_Oreal ) }.
% 0.99/1.63 { class_Rings_Ono__zero__divisors( tc_RealDef_Oreal ) }.
% 0.99/1.63 { class_Groups_Ocomm__monoid__add( tc_RealDef_Oreal ) }.
% 0.99/1.63 { class_Rings_Olinordered__ring( tc_RealDef_Oreal ) }.
% 0.99/1.63 { class_Rings_Olinordered__idom( tc_RealDef_Oreal ) }.
% 0.99/1.63 { class_Rings_Ocomm__semiring__1( tc_RealDef_Oreal ) }.
% 0.99/1.63 { class_Rings_Ocomm__semiring__0( tc_RealDef_Oreal ) }.
% 0.99/1.63 { class_RealVector_Oreal__field( tc_RealDef_Oreal ) }.
% 0.99/1.63 { class_Rings_Odivision__ring( tc_RealDef_Oreal ) }.
% 0.99/1.63 { class_Rings_Ocomm__semiring( tc_RealDef_Oreal ) }.
% 0.99/1.63 { class_Groups_Oab__group__add( tc_RealDef_Oreal ) }.
% 0.99/1.63 { class_Rings_Ozero__neq__one( tc_RealDef_Oreal ) }.
% 0.99/1.63 { class_Rings_Oordered__ring( tc_RealDef_Oreal ) }.
% 0.99/1.63 { class_Orderings_Opreorder( tc_RealDef_Oreal ) }.
% 0.99/1.63 { class_Orderings_Olinorder( tc_RealDef_Oreal ) }.
% 0.99/1.63 { class_Groups_Omonoid__mult( tc_RealDef_Oreal ) }.
% 0.99/1.63 { class_Rings_Ocomm__ring__1( tc_RealDef_Oreal ) }.
% 0.99/1.63 { class_Groups_Omonoid__add( tc_RealDef_Oreal ) }.
% 0.99/1.63 { class_Rings_Osemiring__0( tc_RealDef_Oreal ) }.
% 0.99/1.63 { class_Groups_Ogroup__add( tc_RealDef_Oreal ) }.
% 0.99/1.63 { class_Rings_Omult__zero( tc_RealDef_Oreal ) }.
% 0.99/1.63 { class_Rings_Ocomm__ring( tc_RealDef_Oreal ) }.
% 0.99/1.63 { class_Orderings_Oorder( tc_RealDef_Oreal ) }.
% 0.99/1.63 { class_Int_Oring__char__0( tc_RealDef_Oreal ) }.
% 0.99/1.63 { class_Rings_Osemiring( tc_RealDef_Oreal ) }.
% 0.99/1.63 { class_Orderings_Oord( tc_RealDef_Oreal ) }.
% 0.99/1.63 { class_Rings_Oring__1( tc_RealDef_Oreal ) }.
% 0.99/1.63 { class_Fields_Ofield( tc_RealDef_Oreal ) }.
% 0.99/1.63 { class_Power_Opower( tc_RealDef_Oreal ) }.
% 0.99/1.63 { class_Groups_Ozero( tc_RealDef_Oreal ) }.
% 0.99/1.63 { class_Rings_Oring( tc_RealDef_Oreal ) }.
% 0.99/1.63 { class_Rings_Oidom( tc_RealDef_Oreal ) }.
% 0.99/1.63 { class_Groups_Oone( tc_RealDef_Oreal ) }.
% 0.99/1.63 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.99/1.63 tc_Complex_Ocomplex ) }.
% 0.99/1.63 { class_RealVector_Oreal__normed__div__algebra( tc_Complex_Ocomplex ) }.
% 0.99/1.63 { class_Rings_Odivision__ring__inverse__zero( tc_Complex_Ocomplex ) }.
% 0.99/1.63 { class_RealVector_Oreal__normed__algebra__1( tc_Complex_Ocomplex ) }.
% 0.99/1.63 { class_RealVector_Oreal__normed__algebra( tc_Complex_Ocomplex ) }.
% 0.99/1.63 { class_Groups_Ocancel__ab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.99/1.63 { class_Rings_Oring__1__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.99/1.63 { class_RealVector_Oreal__normed__vector( tc_Complex_Ocomplex ) }.
% 0.99/1.63 { class_RealVector_Oreal__normed__field( tc_Complex_Ocomplex ) }.
% 0.99/1.63 { class_Rings_Oring__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.99/1.63 { class_Groups_Ocancel__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.99/1.63 { class_Fields_Ofield__inverse__zero( tc_Complex_Ocomplex ) }.
% 0.99/1.63 { class_Groups_Oab__semigroup__mult( tc_Complex_Ocomplex ) }.
% 0.99/1.63 { class_Groups_Ocomm__monoid__mult( tc_Complex_Ocomplex ) }.
% 0.99/1.63 { class_Groups_Oab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.99/1.63 { class_Rings_Ono__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.99/1.63 { class_Groups_Ocomm__monoid__add( tc_Complex_Ocomplex ) }.
% 0.99/1.63 { class_Rings_Ocomm__semiring__1( tc_Complex_Ocomplex ) }.
% 0.99/1.63 { class_Rings_Ocomm__semiring__0( tc_Complex_Ocomplex ) }.
% 0.99/1.63 { class_RealVector_Oreal__field( tc_Complex_Ocomplex ) }.
% 0.99/1.63 { class_Rings_Odivision__ring( tc_Complex_Ocomplex ) }.
% 0.99/1.63 { class_Rings_Ocomm__semiring( tc_Complex_Ocomplex ) }.
% 0.99/1.63 { class_Groups_Oab__group__add( tc_Complex_Ocomplex ) }.
% 0.99/1.63 { class_Rings_Ozero__neq__one( tc_Complex_Ocomplex ) }.
% 0.99/1.63 { class_Groups_Omonoid__mult( tc_Complex_Ocomplex ) }.
% 0.99/1.63 { class_Rings_Ocomm__ring__1( tc_Complex_Ocomplex ) }.
% 0.99/1.63 { class_Groups_Omonoid__add( tc_Complex_Ocomplex ) }.
% 0.99/1.63 { class_Rings_Osemiring__0( tc_Complex_Ocomplex ) }.
% 0.99/1.63 { class_Groups_Ogroup__add( tc_Complex_Ocomplex ) }.
% 0.99/1.63 { class_Rings_Omult__zero( tc_Complex_Ocomplex ) }.
% 0.99/1.63 { class_Rings_Ocomm__ring( tc_Complex_Ocomplex ) }.
% 0.99/1.63 { class_Int_Oring__char__0( tc_Complex_Ocomplex ) }.
% 0.99/1.63 { class_Rings_Osemiring( tc_Complex_Ocomplex ) }.
% 0.99/1.63 { class_Rings_Oring__1( tc_Complex_Ocomplex ) }.
% 0.99/1.63 { class_Fields_Ofield( tc_Complex_Ocomplex ) }.
% 0.99/1.63 { class_Power_Opower( tc_Complex_Ocomplex ) }.
% 0.99/1.63 { class_Groups_Ozero( tc_Complex_Ocomplex ) }.
% 0.99/1.63 { class_Rings_Oring( tc_Complex_Ocomplex ) }.
% 0.99/1.63 { class_Rings_Oidom( tc_Complex_Ocomplex ) }.
% 0.99/1.63 { class_Groups_Oone( tc_Complex_Ocomplex ) }.
% 0.99/1.63 { ! class_Rings_Oidom( X ),
% 0.99/1.63 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.99/1.63 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__idom( X ),
% 0.99/1.63 class_Groups_Oordered__cancel__ab__semigroup__add( tc_Polynomial_Opoly( X
% 0.99/1.63 ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__idom( X ),
% 0.99/1.63 class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Polynomial_Opoly(
% 0.99/1.63 X ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__idom( X ),
% 0.99/1.63 class_Rings_Olinordered__comm__semiring__strict( tc_Polynomial_Opoly( X )
% 0.99/1.63 ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__idom( X ),
% 0.99/1.63 class_Rings_Olinordered__semiring__1__strict( tc_Polynomial_Opoly( X ) )
% 0.99/1.63 }.
% 0.99/1.63 { ! class_Rings_Olinordered__idom( X ),
% 0.99/1.63 class_Rings_Olinordered__semiring__strict( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__idom( X ),
% 0.99/1.63 class_Groups_Oordered__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__idom( X ),
% 0.99/1.63 class_Groups_Oordered__ab__group__add__abs( tc_Polynomial_Opoly( X ) ) }
% 0.99/1.63 .
% 0.99/1.63 { ! class_Rings_Olinordered__idom( X ),
% 0.99/1.63 class_Groups_Oordered__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__idom( X ),
% 0.99/1.63 class_Groups_Olinordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.63 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.99/1.63 class_Groups_Ocancel__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.63 { ! class_Rings_Oidom( X ), class_Rings_Oring__1__no__zero__divisors(
% 0.99/1.63 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__idom( X ),
% 0.99/1.63 class_Rings_Oordered__cancel__semiring( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__idom( X ),
% 0.99/1.63 class_Rings_Olinordered__ring__strict( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.63 { ! class_Rings_Oidom( X ), class_Rings_Oring__no__zero__divisors(
% 0.99/1.63 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__idom( X ),
% 0.99/1.63 class_Rings_Oordered__comm__semiring( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__idom( X ),
% 0.99/1.63 class_Rings_Olinordered__semiring__1( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__idom( X ),
% 0.99/1.63 class_Groups_Oordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.63 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.99/1.63 class_Groups_Ocancel__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semiring(
% 0.99/1.63 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semidom(
% 0.99/1.63 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.63 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Oab__semigroup__mult
% 0.99/1.63 ( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.63 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Ocomm__monoid__mult(
% 0.99/1.63 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.63 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Oab__semigroup__add
% 0.99/1.63 ( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__semiring(
% 0.99/1.63 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__ring__abs(
% 0.99/1.63 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.63 { ! class_Rings_Oidom( X ), class_Rings_Ono__zero__divisors(
% 0.99/1.63 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.63 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Ocomm__monoid__add(
% 0.99/1.63 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__ring(
% 0.99/1.63 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__idom(
% 0.99/1.63 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.63 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ocomm__semiring__1(
% 0.99/1.63 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.63 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring__0(
% 0.99/1.63 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.63 { ! class_Fields_Ofield( X ), class_Divides_Osemiring__div(
% 0.99/1.63 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.63 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring(
% 0.99/1.63 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.63 { ! class_Groups_Oab__group__add( X ), class_Groups_Oab__group__add(
% 0.99/1.63 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.63 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ozero__neq__one(
% 0.99/1.63 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__ring(
% 0.99/1.63 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Opreorder(
% 0.99/1.63 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Olinorder(
% 0.99/1.63 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.63 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Omonoid__mult(
% 0.99/1.63 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.63 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Ocomm__ring__1(
% 0.99/1.63 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.63 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Omonoid__add(
% 0.99/1.63 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.63 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring__0(
% 0.99/1.63 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.63 { ! class_Groups_Oab__group__add( X ), class_Groups_Ogroup__add(
% 0.99/1.63 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.63 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Omult__zero(
% 0.99/1.63 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.63 { ! class_Rings_Ocomm__ring( X ), class_Rings_Ocomm__ring(
% 0.99/1.63 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oorder(
% 0.99/1.63 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__idom( X ), class_Int_Oring__char__0(
% 0.99/1.63 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.63 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring(
% 0.99/1.63 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oord(
% 0.99/1.63 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.63 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Oring__1(
% 0.99/1.63 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.63 { ! class_Rings_Ocomm__semiring__1( X ), class_Power_Opower(
% 0.99/1.63 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.63 { ! class_Groups_Ozero( X ), class_Groups_Ozero( tc_Polynomial_Opoly( X ) )
% 0.99/1.63 }.
% 0.99/1.63 { ! class_Rings_Ocomm__ring( X ), class_Rings_Oring( tc_Polynomial_Opoly( X
% 0.99/1.63 ) ) }.
% 0.99/1.63 { ! class_Rings_Oidom( X ), class_Rings_Oidom( tc_Polynomial_Opoly( X ) ) }
% 0.99/1.63 .
% 0.99/1.63 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Oone(
% 0.99/1.63 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.63 { ! hBOOL( c_fequal( Y, X ) ), Y = X }.
% 0.99/1.63 { ! Y = X, hBOOL( c_fequal( Y, X ) ) }.
% 0.99/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.63 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs
% 0.99/1.63 ( tc_RealDef_Oreal, v_da____ ), c_RealVector_Onorm__class_Onorm(
% 0.99/1.63 tc_Complex_Ocomplex, v_aa____ ) ), c_RealVector_Onorm__class_Onorm(
% 0.99/1.63 tc_Complex_Ocomplex, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.99/1.63 tc_Complex_Ocomplex ), v_z____ ), v_c____ ) ) ) }.
% 0.99/1.63
% 0.99/1.63 *** allocated 15000 integers for clauses
% 0.99/1.63 *** allocated 22500 integers for clauses
% 0.99/1.63 *** allocated 33750 integers for clauses
% 0.99/1.63 *** allocated 50625 integers for clauses
% 0.99/1.63 *** allocated 75937 integers for clauses
% 0.99/1.63 *** allocated 113905 integers for clauses
% 0.99/1.63 percentage equality = 0.222167, percentage horn = 0.899941
% 0.99/1.63 This is a problem with some equality
% 0.99/1.63
% 0.99/1.63
% 0.99/1.63
% 0.99/1.63 Options Used:
% 0.99/1.63
% 0.99/1.63 useres = 1
% 0.99/1.63 useparamod = 1
% 0.99/1.63 useeqrefl = 1
% 0.99/1.63 useeqfact = 1
% 0.99/1.63 usefactor = 1
% 0.99/1.63 usesimpsplitting = 0
% 0.99/1.63 usesimpdemod = 5
% 0.99/1.63 usesimpres = 3
% 0.99/1.63
% 0.99/1.63 resimpinuse = 1000
% 0.99/1.63 resimpclauses = 20000
% 0.99/1.63 substype = eqrewr
% 0.99/1.63 backwardsubs = 1
% 0.99/1.63 selectoldest = 5
% 0.99/1.63
% 0.99/1.63 litorderings [0] = split
% 0.99/1.63 litorderings [1] = extend the termordering, first sorting on arguments
% 0.99/1.63
% 0.99/1.63 termordering = kbo
% 0.99/1.63
% 0.99/1.63 litapriori = 0
% 0.99/1.63 termapriori = 1
% 0.99/1.63 litaposteriori = 0
% 0.99/1.63 termaposteriori = 0
% 0.99/1.63 demodaposteriori = 0
% 0.99/1.63 ordereqreflfact = 0
% 0.99/1.63
% 0.99/1.63 litselect = negord
% 0.99/1.63
% 0.99/1.63 maxweight = 15
% 0.99/1.63 maxdepth = 30000
% 0.99/1.63 maxlength = 115
% 0.99/1.63 maxnrvars = 195
% 0.99/1.63 excuselevel = 1
% 0.99/1.63 increasemaxweight = 1
% 0.99/1.63
% 0.99/1.63 maxselected = 10000000
% 0.99/1.63 maxnrclauses = 10000000
% 0.99/1.63
% 0.99/1.63 showgenerated = 0
% 0.99/1.63 showkept = 0
% 0.99/1.63 showselected = 0
% 0.99/1.63 showdeleted = 0
% 0.99/1.63 showresimp = 1
% 0.99/1.63 showstatus = 2000
% 0.99/1.63
% 0.99/1.63 prologoutput = 0
% 0.99/1.63 nrgoals = 5000000
% 0.99/1.63 totalproof = 1
% 0.99/1.63
% 0.99/1.63 Symbols occurring in the translation:
% 0.99/1.63
% 0.99/1.63 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.99/1.63 . [1, 2] (w:1, o:207, a:1, s:1, b:0),
% 0.99/1.63 ! [4, 1] (w:0, o:116, a:1, s:1, b:0),
% 0.99/1.63 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.99/1.63 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.99/1.63 hAPP [38, 2] (w:1, o:231, a:1, s:1, b:0),
% 0.99/1.63 v_c____ [39, 0] (w:1, o:13, a:1, s:1, b:0),
% 0.99/1.63 tc_Complex_Ocomplex [40, 0] (w:1, o:15, a:1, s:1, b:0),
% 0.99/1.63 c_Groups_Ozero__class_Ozero [41, 1] (w:1, o:121, a:1, s:1, b:0),
% 0.99/1.63 tc_RealDef_Oreal [42, 0] (w:1, o:16, a:1, s:1, b:0),
% 0.99/1.63 v_da____ [43, 0] (w:1, o:18, a:1, s:1, b:0),
% 0.99/1.63 c_Groups_Oabs__class_Oabs [44, 2] (w:1, o:233, a:1, s:1, b:0),
% 0.99/1.63 v_aa____ [45, 0] (w:1, o:19, a:1, s:1, b:0),
% 0.99/1.63 c_RealVector_Onorm__class_Onorm [46, 2] (w:1, o:234, a:1, s:1, b:0),
% 0.99/1.63
% 0.99/1.63 c_Groups_Oplus__class_Oplus [47, 3] (w:1, o:288, a:1, s:1, b:0),
% 0.99/1.63 c_Rings_Oinverse__class_Odivide [48, 3] (w:1, o:289, a:1, s:1, b:0),
% 0.99/1.63
% 0.99/1.63 v_z____ [49, 0] (w:1, o:20, a:1, s:1, b:0),
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq [50, 3] (w:1, o:290, a:1, s:1, b:0)
% 0.99/1.63 ,
% 0.99/1.63 v_p [51, 0] (w:1, o:21, a:1, s:1, b:0),
% 0.99/1.63 tc_Polynomial_Opoly [52, 1] (w:1, o:128, a:1, s:1, b:0),
% 0.99/1.63 class_RealVector_Oreal__normed__vector [56, 1] (w:1, o:129, a:1, s:1
% 0.99/1.63 , b:0),
% 0.99/1.63 class_RealVector_Oreal__normed__algebra [57, 1] (w:1, o:130, a:1, s:1
% 0.99/1.63 , b:0),
% 0.99/1.63 c_Groups_Otimes__class_Otimes [58, 1] (w:1, o:131, a:1, s:1, b:0),
% 0.99/1.63 class_Groups_Oordered__ab__group__add__abs [61, 1] (w:1, o:136, a:1
% 0.99/1.63 , s:1, b:0),
% 0.99/1.63 class_Orderings_Opreorder [62, 1] (w:1, o:139, a:1, s:1, b:0),
% 0.99/1.63 class_Rings_Olinordered__idom [64, 1] (w:1, o:140, a:1, s:1, b:0),
% 0.99/1.63 class_RealVector_Oreal__normed__div__algebra [65, 1] (w:1, o:141, a:1
% 0.99/1.63 , s:1, b:0),
% 0.99/1.63 v_cs____ [66, 0] (w:1, o:17, a:1, s:1, b:0),
% 0.99/1.63 class_Fields_Ofield__inverse__zero [67, 1] (w:1, o:132, a:1, s:1, b:0
% 0.99/1.63 ),
% 0.99/1.63 class_RealVector_Oreal__normed__field [68, 1] (w:1, o:142, a:1, s:1
% 0.99/1.63 , b:0),
% 0.99/1.63 class_Rings_Odivision__ring [69, 1] (w:1, o:148, a:1, s:1, b:0),
% 0.99/1.63 class_Groups_Ozero [71, 1] (w:1, o:149, a:1, s:1, b:0),
% 0.99/1.63 class_Rings_Odivision__ring__inverse__zero [72, 1] (w:1, o:150, a:1
% 0.99/1.63 , s:1, b:0),
% 0.99/1.63 class_Rings_Ono__zero__divisors [82, 1] (w:1, o:160, a:1, s:1, b:0),
% 0.99/1.63
% 0.99/1.63 class_Rings_Oring__no__zero__divisors [83, 1] (w:1, o:161, a:1, s:1
% 0.99/1.63 , b:0),
% 0.99/1.63 class_Rings_Omult__zero [84, 1] (w:1, o:159, a:1, s:1, b:0),
% 0.99/1.63 class_Groups_Ocomm__monoid__add [85, 1] (w:1, o:162, a:1, s:1, b:0),
% 0.99/1.63
% 0.99/1.63 class_Groups_Omonoid__add [86, 1] (w:1, o:164, a:1, s:1, b:0),
% 0.99/1.63 class_Groups_Olinordered__ab__group__add [87, 1] (w:1, o:163, a:1, s:
% 0.99/1.63 1, b:0),
% 0.99/1.63 class_Rings_Oordered__cancel__semiring [89, 1] (w:1, o:165, a:1, s:1
% 0.99/1.63 , b:0),
% 0.99/1.63 class_Rings_Oordered__ring [90, 1] (w:1, o:166, a:1, s:1, b:0),
% 0.99/1.63 class_Rings_Oordered__semiring [92, 1] (w:1, o:168, a:1, s:1, b:0),
% 0.99/1.63 class_Rings_Oordered__comm__semiring [93, 1] (w:1, o:169, a:1, s:1
% 0.99/1.63 , b:0),
% 0.99/1.63 class_Rings_Olinordered__ring__strict [94, 1] (w:1, o:151, a:1, s:1
% 0.99/1.63 , b:0),
% 0.99/1.63 class_Rings_Olinordered__ring [95, 1] (w:1, o:152, a:1, s:1, b:0),
% 0.99/1.63 class_Groups_Oordered__comm__monoid__add [96, 1] (w:1, o:170, a:1, s:
% 0.99/1.63 1, b:0),
% 0.99/1.63 class_Rings_Oordered__ring__abs [98, 1] (w:1, o:167, a:1, s:1, b:0),
% 0.99/1.63
% 0.99/1.63 class_Orderings_Olinorder [99, 1] (w:1, o:171, a:1, s:1, b:0),
% 0.99/1.63 class_Orderings_Oord [101, 1] (w:1, o:137, a:1, s:1, b:0),
% 0.99/1.63 tc_fun [102, 2] (w:1, o:264, a:1, s:1, b:0),
% 0.99/1.63 class_Orderings_Oorder [103, 1] (w:1, o:138, a:1, s:1, b:0),
% 0.99/1.63 class_Groups_Oab__semigroup__mult [104, 1] (w:1, o:172, a:1, s:1, b:0
% 0.99/1.63 ),
% 0.99/1.63 class_Groups_Ocancel__semigroup__add [105, 1] (w:1, o:173, a:1, s:1
% 0.99/1.63 , b:0),
% 0.99/1.63 class_Groups_Ocancel__ab__semigroup__add [106, 1] (w:1, o:174, a:1
% 0.99/1.63 , s:1, b:0),
% 0.99/1.63 class_Groups_Oab__semigroup__add [107, 1] (w:1, o:175, a:1, s:1, b:0)
% 0.99/1.63 ,
% 0.99/1.63 class_Groups_Oordered__ab__semigroup__add__imp__le [111, 1] (w:1, o:
% 0.99/1.63 176, a:1, s:1, b:0),
% 0.99/1.63 class_Groups_Oordered__ab__semigroup__add [112, 1] (w:1, o:177, a:1
% 0.99/1.63 , s:1, b:0),
% 0.99/1.63 class_Rings_Osemiring [114, 1] (w:1, o:181, a:1, s:1, b:0),
% 0.99/1.63 class_Rings_Ocomm__semiring [116, 1] (w:1, o:145, a:1, s:1, b:0),
% 0.99/1.63 class_Fields_Ofield [119, 1] (w:1, o:133, a:1, s:1, b:0),
% 0.99/1.63 class_Fields_Olinordered__field [120, 1] (w:1, o:134, a:1, s:1, b:0)
% 0.99/1.63 ,
% 0.99/1.63 c_Polynomial_OpCons [121, 3] (w:1, o:293, a:1, s:1, b:0),
% 0.99/1.63 class_Fields_Olinordered__field__inverse__zero [122, 1] (w:1, o:135
% 0.99/1.63 , a:1, s:1, b:0),
% 0.99/1.63 c_Orderings_Oord__class_Oless [125, 3] (w:1, o:291, a:1, s:1, b:0),
% 0.99/1.63 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct [
% 0.99/1.63 126, 1] (w:1, o:187, a:1, s:1, b:0),
% 0.99/1.63 class_Rings_Ocomm__semiring__1 [127, 1] (w:1, o:147, a:1, s:1, b:0),
% 0.99/1.63
% 0.99/1.63 class_Groups_Oordered__cancel__ab__semigroup__add [130, 1] (w:1, o:
% 0.99/1.63 188, a:1, s:1, b:0),
% 0.99/1.63 class_Rings_Olinordered__semiring__strict [131, 1] (w:1, o:153, a:1
% 0.99/1.63 , s:1, b:0),
% 0.99/1.63 class_Rings_Olinordered__comm__semiring__strict [132, 1] (w:1, o:154
% 0.99/1.63 , a:1, s:1, b:0),
% 0.99/1.63 class_Rings_Olinordered__semidom [133, 1] (w:1, o:155, a:1, s:1, b:0)
% 0.99/1.63 ,
% 0.99/1.63 class_Rings_Olinordered__semiring [134, 1] (w:1, o:156, a:1, s:1, b:0
% 0.99/1.63 ),
% 0.99/1.63 c_Polynomial_Opoly [142, 2] (w:1, o:265, a:1, s:1, b:0),
% 0.99/1.63 class_Rings_Ocomm__semiring__0 [149, 1] (w:1, o:146, a:1, s:1, b:0),
% 0.99/1.63
% 0.99/1.63 class_Int_Oring__char__0 [151, 1] (w:1, o:189, a:1, s:1, b:0),
% 0.99/1.63 class_Rings_Oidom [152, 1] (w:1, o:182, a:1, s:1, b:0),
% 0.99/1.63 c_Polynomial_Opos__poly [153, 2] (w:1, o:266, a:1, s:1, b:0),
% 0.99/1.63 c_Polynomial_Oorder [155, 3] (w:1, o:292, a:1, s:1, b:0),
% 0.99/1.63 tc_Nat_Onat [156, 0] (w:1, o:91, a:1, s:1, b:0),
% 0.99/1.63 c_Polynomial_Opoly__rec [157, 5] (w:1, o:380, a:1, s:1, b:0),
% 0.99/1.63 c_fequal [158, 2] (w:1, o:267, a:1, s:1, b:0),
% 0.99/1.63 c_If [159, 4] (w:1, o:351, a:1, s:1, b:0),
% 0.99/1.63 c_Polynomial_Opcompose [160, 3] (w:1, o:294, a:1, s:1, b:0),
% 0.99/1.63 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize [161, 2] (w:1, o:
% 0.99/1.63 232, a:1, s:1, b:0),
% 0.99/1.63 hBOOL [169, 1] (w:1, o:190, a:1, s:1, b:0),
% 0.99/1.63 class_Rings_Olinordered__semiring__1__strict [175, 1] (w:1, o:157, a:
% 0.99/1.63 1, s:1, b:0),
% 0.99/1.63 c_Groups_Oone__class_Oone [176, 1] (w:1, o:191, a:1, s:1, b:0),
% 0.99/1.63 c_NthRoot_Oroot [178, 2] (w:1, o:268, a:1, s:1, b:0),
% 0.99/1.63 class_RealVector_Oreal__normed__algebra__1 [179, 1] (w:1, o:183, a:1
% 0.99/1.63 , s:1, b:0),
% 0.99/1.63 class_Groups_Oone [180, 1] (w:1, o:192, a:1, s:1, b:0),
% 0.99/1.63 class_Groups_Omonoid__mult [181, 1] (w:1, o:193, a:1, s:1, b:0),
% 0.99/1.63 class_Groups_Ocomm__monoid__mult [182, 1] (w:1, o:194, a:1, s:1, b:0)
% 0.99/1.63 ,
% 0.99/1.63 class_Rings_Ozero__neq__one [183, 1] (w:1, o:184, a:1, s:1, b:0),
% 0.99/1.63 class_Rings_Olinordered__semiring__1 [185, 1] (w:1, o:158, a:1, s:1
% 0.99/1.63 , b:0),
% 0.99/1.63 c_Power_Opower__class_Opower [188, 1] (w:1, o:195, a:1, s:1, b:0),
% 0.99/1.63 tc_Int_Oint [189, 0] (w:1, o:108, a:1, s:1, b:0),
% 0.99/1.63 class_Rings_Oring__1__no__zero__divisors [190, 1] (w:1, o:178, a:1
% 0.99/1.63 , s:1, b:0),
% 0.99/1.63 class_Power_Opower [191, 1] (w:1, o:196, a:1, s:1, b:0),
% 0.99/1.63 class_Rings_Osemiring__0 [192, 1] (w:1, o:185, a:1, s:1, b:0),
% 0.99/1.63 c_Power_Opower_Opower [193, 3] (w:1, o:295, a:1, s:1, b:0),
% 0.99/1.63 c_RComplete_Onatceiling [202, 1] (w:1, o:197, a:1, s:1, b:0),
% 0.99/1.63 c_RComplete_Onatfloor [203, 1] (w:1, o:198, a:1, s:1, b:0),
% 0.99/1.63 c_Groups_Ominus__class_Ominus [204, 3] (w:1, o:296, a:1, s:1, b:0),
% 0.99/1.63 class_Groups_Oordered__ab__group__add [205, 1] (w:1, o:199, a:1, s:1
% 0.99/1.63 , b:0),
% 0.99/1.63 class_Groups_Ogroup__add [206, 1] (w:1, o:200, a:1, s:1, b:0),
% 0.99/1.63 class_Rings_Ocomm__ring [207, 1] (w:1, o:143, a:1, s:1, b:0),
% 0.99/1.63 class_Groups_Oab__group__add [208, 1] (w:1, o:201, a:1, s:1, b:0),
% 0.99/1.63 class_Rings_Oring [209, 1] (w:1, o:179, a:1, s:1, b:0),
% 0.99/1.63 class_Rings_Oring__1 [214, 1] (w:1, o:180, a:1, s:1, b:0),
% 0.99/1.63 class_RealVector_Oreal__field [218, 1] (w:1, o:186, a:1, s:1, b:0),
% 0.99/1.63 c_RealDef_Oreal [219, 2] (w:1, o:269, a:1, s:1, b:0),
% 0.99/1.63 c_Transcendental_Oarctan [220, 1] (w:1, o:202, a:1, s:1, b:0),
% 0.99/1.63 c_Complex_Oii [221, 0] (w:1, o:111, a:1, s:1, b:0),
% 0.99/1.63 c_Nat__Transfer_Otsub [225, 2] (w:1, o:270, a:1, s:1, b:0),
% 0.99/1.63 c_Divides_Odiv__class_Odiv [226, 3] (w:1, o:297, a:1, s:1, b:0),
% 0.99/1.63 class_Divides_Osemiring__div [227, 1] (w:1, o:203, a:1, s:1, b:0),
% 0.99/1.63 c_SEQ_Odecseq [229, 2] (w:1, o:271, a:1, s:1, b:0),
% 0.99/1.63 c_Complex_Orcis [230, 2] (w:1, o:272, a:1, s:1, b:0),
% 0.99/1.63 c_Nat_OSuc [236, 1] (w:1, o:204, a:1, s:1, b:0),
% 0.99/1.63 class_Rings_Ocomm__ring__1 [241, 1] (w:1, o:144, a:1, s:1, b:0),
% 0.99/1.63 c_Transcendental_Oln [244, 1] (w:1, o:205, a:1, s:1, b:0),
% 0.99/1.63 c_Divides_Odiv__class_Omod [245, 3] (w:1, o:298, a:1, s:1, b:0),
% 0.99/1.63 class_Groups_Ocancel__comm__monoid__add [247, 1] (w:1, o:206, a:1, s:
% 0.99/1.63 1, b:0),
% 0.99/1.63 tc_HOL_Obool [249, 0] (w:1, o:107, a:1, s:1, b:0),
% 0.99/1.63 alpha1 [250, 3] (w:1, o:299, a:1, s:1, b:1),
% 0.99/1.63 alpha2 [251, 3] (w:1, o:309, a:1, s:1, b:1),
% 0.99/1.63 alpha3 [252, 3] (w:1, o:312, a:1, s:1, b:1),
% 0.99/1.63 alpha4 [253, 3] (w:1, o:317, a:1, s:1, b:1),
% 0.99/1.63 alpha5 [254, 2] (w:1, o:276, a:1, s:1, b:1),
% 0.99/1.63 alpha6 [255, 3] (w:1, o:320, a:1, s:1, b:1),
% 0.99/1.63 alpha7 [256, 3] (w:1, o:325, a:1, s:1, b:1),
% 0.99/1.63 alpha8 [257, 4] (w:1, o:354, a:1, s:1, b:1),
% 0.99/1.63 alpha9 [258, 4] (w:1, o:355, a:1, s:1, b:1),
% 0.99/1.63 alpha10 [259, 3] (w:1, o:300, a:1, s:1, b:1),
% 0.99/1.63 alpha11 [260, 3] (w:1, o:301, a:1, s:1, b:1),
% 0.99/1.63 alpha12 [261, 3] (w:1, o:302, a:1, s:1, b:1),
% 0.99/1.63 alpha13 [262, 3] (w:1, o:303, a:1, s:1, b:1),
% 0.99/1.63 alpha14 [263, 3] (w:1, o:304, a:1, s:1, b:1),
% 0.99/1.63 alpha15 [264, 3] (w:1, o:305, a:1, s:1, b:1),
% 0.99/1.63 alpha16 [265, 3] (w:1, o:306, a:1, s:1, b:1),
% 0.99/1.63 alpha17 [266, 3] (w:1, o:307, a:1, s:1, b:1),
% 0.99/1.63 alpha18 [267, 3] (w:1, o:308, a:1, s:1, b:1),
% 0.99/1.63 alpha19 [268, 2] (w:1, o:277, a:1, s:1, b:1),
% 0.99/1.63 alpha20 [269, 2] (w:1, o:278, a:1, s:1, b:1),
% 0.99/1.63 alpha21 [270, 2] (w:1, o:279, a:1, s:1, b:1),
% 0.99/1.63 alpha22 [271, 2] (w:1, o:280, a:1, s:1, b:1),
% 0.99/1.63 alpha23 [272, 2] (w:1, o:281, a:1, s:1, b:1),
% 0.99/1.63 alpha24 [273, 2] (w:1, o:282, a:1, s:1, b:1),
% 0.99/1.63 alpha25 [274, 2] (w:1, o:283, a:1, s:1, b:1),
% 0.99/1.63 alpha26 [275, 3] (w:1, o:310, a:1, s:1, b:1),
% 0.99/1.63 alpha27 [276, 3] (w:1, o:311, a:1, s:1, b:1),
% 0.99/1.63 alpha28 [277, 4] (w:1, o:356, a:1, s:1, b:1),
% 0.99/1.63 alpha29 [278, 4] (w:1, o:357, a:1, s:1, b:1),
% 0.99/1.63 alpha30 [279, 2] (w:1, o:284, a:1, s:1, b:1),
% 0.99/1.63 alpha31 [280, 3] (w:1, o:313, a:1, s:1, b:1),
% 0.99/1.63 alpha32 [281, 3] (w:1, o:314, a:1, s:1, b:1),
% 0.99/1.63 alpha33 [282, 4] (w:1, o:358, a:1, s:1, b:1),
% 0.99/1.63 alpha34 [283, 4] (w:1, o:359, a:1, s:1, b:1),
% 0.99/1.63 alpha35 [284, 3] (w:1, o:315, a:1, s:1, b:1),
% 0.99/1.63 alpha36 [285, 3] (w:1, o:316, a:1, s:1, b:1),
% 0.99/1.63 alpha37 [286, 4] (w:1, o:360, a:1, s:1, b:1),
% 0.99/1.63 alpha38 [287, 4] (w:1, o:361, a:1, s:1, b:1),
% 0.99/1.63 alpha39 [288, 4] (w:1, o:362, a:1, s:1, b:1),
% 0.99/1.63 alpha40 [289, 4] (w:1, o:363, a:1, s:1, b:1),
% 0.99/1.63 alpha41 [290, 3] (w:1, o:326, a:1, s:1, b:1),
% 0.99/1.63 alpha42 [291, 3] (w:1, o:327, a:1, s:1, b:1),
% 0.99/1.63 alpha43 [292, 3] (w:1, o:328, a:1, s:1, b:1),
% 0.99/1.63 alpha44 [293, 2] (w:1, o:273, a:1, s:1, b:1),
% 0.99/1.63 alpha45 [294, 3] (w:1, o:329, a:1, s:1, b:1),
% 0.99/1.63 alpha46 [295, 2] (w:1, o:274, a:1, s:1, b:1),
% 0.99/1.63 alpha47 [296, 2] (w:1, o:275, a:1, s:1, b:1),
% 0.99/1.63 alpha48 [297, 3] (w:1, o:330, a:1, s:1, b:1),
% 0.99/1.63 alpha49 [298, 4] (w:1, o:364, a:1, s:1, b:1),
% 7.54/7.93 alpha50 [299, 4] (w:1, o:365, a:1, s:1, b:1),
% 7.54/7.93 alpha51 [300, 4] (w:1, o:366, a:1, s:1, b:1),
% 7.54/7.93 alpha52 [301, 4] (w:1, o:367, a:1, s:1, b:1),
% 7.54/7.93 alpha53 [302, 3] (w:1, o:318, a:1, s:1, b:1),
% 7.54/7.93 alpha54 [303, 2] (w:1, o:285, a:1, s:1, b:1),
% 7.54/7.93 alpha55 [304, 3] (w:1, o:319, a:1, s:1, b:1),
% 7.54/7.93 alpha56 [305, 4] (w:1, o:368, a:1, s:1, b:1),
% 7.54/7.93 alpha57 [306, 4] (w:1, o:369, a:1, s:1, b:1),
% 7.54/7.93 alpha58 [307, 4] (w:1, o:370, a:1, s:1, b:1),
% 7.54/7.93 alpha59 [308, 4] (w:1, o:371, a:1, s:1, b:1),
% 7.54/7.93 alpha60 [309, 4] (w:1, o:372, a:1, s:1, b:1),
% 7.54/7.93 alpha61 [310, 4] (w:1, o:373, a:1, s:1, b:1),
% 7.54/7.93 alpha62 [311, 3] (w:1, o:321, a:1, s:1, b:1),
% 7.54/7.93 alpha63 [312, 3] (w:1, o:322, a:1, s:1, b:1),
% 7.54/7.93 alpha64 [313, 4] (w:1, o:374, a:1, s:1, b:1),
% 7.54/7.93 alpha65 [314, 4] (w:1, o:375, a:1, s:1, b:1),
% 7.54/7.93 alpha66 [315, 4] (w:1, o:376, a:1, s:1, b:1),
% 7.54/7.93 alpha67 [316, 4] (w:1, o:377, a:1, s:1, b:1),
% 7.54/7.93 alpha68 [317, 3] (w:1, o:323, a:1, s:1, b:1),
% 7.54/7.93 alpha69 [318, 3] (w:1, o:324, a:1, s:1, b:1),
% 7.54/7.93 alpha70 [319, 3] (w:1, o:331, a:1, s:1, b:1),
% 7.54/7.93 alpha71 [320, 4] (w:1, o:352, a:1, s:1, b:1),
% 7.54/7.93 alpha72 [321, 4] (w:1, o:353, a:1, s:1, b:1),
% 7.54/7.93 alpha73 [322, 2] (w:1, o:286, a:1, s:1, b:1),
% 7.54/7.93 alpha74 [323, 3] (w:1, o:332, a:1, s:1, b:1),
% 7.54/7.93 alpha75 [324, 2] (w:1, o:287, a:1, s:1, b:1),
% 7.54/7.93 alpha76 [325, 3] (w:1, o:333, a:1, s:1, b:1),
% 7.54/7.93 skol1 [326, 2] (w:1, o:235, a:1, s:1, b:1),
% 7.54/7.93 skol2 [327, 3] (w:1, o:334, a:1, s:1, b:1),
% 7.54/7.93 skol3 [328, 0] (w:1, o:14, a:1, s:1, b:1),
% 7.54/7.93 skol4 [329, 2] (w:1, o:238, a:1, s:1, b:1),
% 7.54/7.93 skol5 [330, 2] (w:1, o:244, a:1, s:1, b:1),
% 7.54/7.93 skol6 [331, 2] (w:1, o:249, a:1, s:1, b:1),
% 7.54/7.93 skol7 [332, 1] (w:1, o:122, a:1, s:1, b:1),
% 7.54/7.93 skol8 [333, 2] (w:1, o:250, a:1, s:1, b:1),
% 7.54/7.93 skol9 [334, 2] (w:1, o:251, a:1, s:1, b:1),
% 7.54/7.93 skol10 [335, 2] (w:1, o:252, a:1, s:1, b:1),
% 7.54/7.93 skol11 [336, 2] (w:1, o:253, a:1, s:1, b:1),
% 7.54/7.93 skol12 [337, 2] (w:1, o:254, a:1, s:1, b:1),
% 7.54/7.93 skol13 [338, 2] (w:1, o:255, a:1, s:1, b:1),
% 7.54/7.93 skol14 [339, 1] (w:1, o:123, a:1, s:1, b:1),
% 7.54/7.93 skol15 [340, 2] (w:1, o:256, a:1, s:1, b:1),
% 7.54/7.93 skol16 [341, 2] (w:1, o:257, a:1, s:1, b:1),
% 7.54/7.93 skol17 [342, 2] (w:1, o:258, a:1, s:1, b:1),
% 7.54/7.93 skol18 [343, 2] (w:1, o:259, a:1, s:1, b:1),
% 7.54/7.93 skol19 [344, 1] (w:1, o:124, a:1, s:1, b:1),
% 7.54/7.93 skol20 [345, 3] (w:1, o:335, a:1, s:1, b:1),
% 7.54/7.93 skol21 [346, 3] (w:1, o:336, a:1, s:1, b:1),
% 7.54/7.93 skol22 [347, 2] (w:1, o:260, a:1, s:1, b:1),
% 7.54/7.93 skol23 [348, 2] (w:1, o:261, a:1, s:1, b:1),
% 7.54/7.93 skol24 [349, 2] (w:1, o:262, a:1, s:1, b:1),
% 7.54/7.93 skol25 [350, 2] (w:1, o:263, a:1, s:1, b:1),
% 7.54/7.93 skol26 [351, 3] (w:1, o:337, a:1, s:1, b:1),
% 7.54/7.93 skol27 [352, 3] (w:1, o:338, a:1, s:1, b:1),
% 7.54/7.93 skol28 [353, 1] (w:1, o:125, a:1, s:1, b:1),
% 7.54/7.93 skol29 [354, 4] (w:1, o:378, a:1, s:1, b:1),
% 7.54/7.93 skol30 [355, 3] (w:1, o:339, a:1, s:1, b:1),
% 7.54/7.93 skol31 [356, 3] (w:1, o:340, a:1, s:1, b:1),
% 7.54/7.93 skol32 [357, 4] (w:1, o:379, a:1, s:1, b:1),
% 7.54/7.93 skol33 [358, 2] (w:1, o:236, a:1, s:1, b:1),
% 7.54/7.93 skol34 [359, 3] (w:1, o:341, a:1, s:1, b:1),
% 7.54/7.93 skol35 [360, 3] (w:1, o:342, a:1, s:1, b:1),
% 7.54/7.93 skol36 [361, 3] (w:1, o:343, a:1, s:1, b:1),
% 7.54/7.93 skol37 [362, 3] (w:1, o:344, a:1, s:1, b:1),
% 7.54/7.93 skol38 [363, 3] (w:1, o:345, a:1, s:1, b:1),
% 7.54/7.93 skol39 [364, 2] (w:1, o:237, a:1, s:1, b:1),
% 7.54/7.93 skol40 [365, 2] (w:1, o:239, a:1, s:1, b:1),
% 7.54/7.93 skol41 [366, 2] (w:1, o:240, a:1, s:1, b:1),
% 7.54/7.93 skol42 [367, 1] (w:1, o:126, a:1, s:1, b:1),
% 7.54/7.93 skol43 [368, 2] (w:1, o:241, a:1, s:1, b:1),
% 7.54/7.93 skol44 [369, 3] (w:1, o:346, a:1, s:1, b:1),
% 7.54/7.93 skol45 [370, 3] (w:1, o:347, a:1, s:1, b:1),
% 7.54/7.93 skol46 [371, 3] (w:1, o:348, a:1, s:1, b:1),
% 7.54/7.93 skol47 [372, 2] (w:1, o:242, a:1, s:1, b:1),
% 7.54/7.93 skol48 [373, 1] (w:1, o:127, a:1, s:1, b:1),
% 7.54/7.93 skol49 [374, 2] (w:1, o:243, a:1, s:1, b:1),
% 7.54/7.93 skol50 [375, 2] (w:1, o:245, a:1, s:1, b:1),
% 7.54/7.93 skol51 [376, 2] (w:1, o:246, a:1, s:1, b:1),
% 94.49/94.91 skol52 [377, 3] (w:1, o:349, a:1, s:1, b:1),
% 94.49/94.91 skol53 [378, 3] (w:1, o:350, a:1, s:1, b:1),
% 94.49/94.91 skol54 [379, 2] (w:1, o:247, a:1, s:1, b:1),
% 94.49/94.91 skol55 [380, 2] (w:1, o:248, a:1, s:1, b:1).
% 94.49/94.91
% 94.49/94.91
% 94.49/94.91 Starting Search:
% 94.49/94.91
% 94.49/94.91 *** allocated 170857 integers for clauses
% 94.49/94.91 Resimplifying inuse:
% 94.49/94.91 Done
% 94.49/94.91
% 94.49/94.91
% 94.49/94.91 Intermediate Status:
% 94.49/94.91 Generated: 2704
% 94.49/94.91 Kept: 2000
% 94.49/94.91 Inuse: 6
% 94.49/94.91 Deleted: 0
% 94.49/94.91 Deletedinuse: 0
% 94.49/94.91
% 94.49/94.91 *** allocated 256285 integers for clauses
% 94.49/94.91 *** allocated 170857 integers for termspace/termends
% 94.49/94.91 Resimplifying inuse:
% 94.49/94.91 Done
% 94.49/94.91
% 94.49/94.91 *** allocated 384427 integers for clauses
% 94.49/94.91
% 94.49/94.91 Intermediate Status:
% 94.49/94.91 Generated: 8757
% 94.49/94.91 Kept: 4164
% 94.49/94.91 Inuse: 145
% 94.49/94.91 Deleted: 1
% 94.49/94.91 Deletedinuse: 0
% 94.49/94.91
% 94.49/94.91 Resimplifying inuse:
% 94.49/94.91 Done
% 94.49/94.91
% 94.49/94.91 *** allocated 256285 integers for termspace/termends
% 94.49/94.91 Resimplifying inuse:
% 94.49/94.91 Done
% 94.49/94.91
% 94.49/94.91
% 94.49/94.91 Intermediate Status:
% 94.49/94.91 Generated: 17010
% 94.49/94.91 Kept: 6176
% 94.49/94.91 Inuse: 196
% 94.49/94.91 Deleted: 1
% 94.49/94.91 Deletedinuse: 0
% 94.49/94.91
% 94.49/94.91 *** allocated 576640 integers for clauses
% 94.49/94.91 Resimplifying inuse:
% 94.49/94.91 Done
% 94.49/94.91
% 94.49/94.91 Resimplifying inuse:
% 94.49/94.91 Done
% 94.49/94.91
% 94.49/94.91
% 94.49/94.91 Intermediate Status:
% 94.49/94.91 Generated: 22430
% 94.49/94.91 Kept: 8575
% 94.49/94.91 Inuse: 260
% 94.49/94.91 Deleted: 1
% 94.49/94.91 Deletedinuse: 0
% 94.49/94.91
% 94.49/94.91 *** allocated 384427 integers for termspace/termends
% 94.49/94.91 Resimplifying inuse:
% 94.49/94.91 Done
% 94.49/94.91
% 94.49/94.91 Resimplifying inuse:
% 94.49/94.91 Done
% 94.49/94.91
% 94.49/94.91
% 94.49/94.91 Intermediate Status:
% 94.49/94.91 Generated: 29403
% 94.49/94.91 Kept: 10585
% 94.49/94.91 Inuse: 314
% 94.49/94.91 Deleted: 2
% 94.49/94.91 Deletedinuse: 0
% 94.49/94.91
% 94.49/94.91 Resimplifying inuse:
% 94.49/94.91 Done
% 94.49/94.91
% 94.49/94.91 *** allocated 864960 integers for clauses
% 94.49/94.91 Resimplifying inuse:
% 94.49/94.91 Done
% 94.49/94.91
% 94.49/94.91
% 94.49/94.91 Intermediate Status:
% 94.49/94.91 Generated: 33758
% 94.49/94.91 Kept: 12598
% 94.49/94.91 Inuse: 386
% 94.49/94.91 Deleted: 2
% 94.49/94.91 Deletedinuse: 0
% 94.49/94.91
% 94.49/94.91 *** allocated 576640 integers for termspace/termends
% 94.49/94.91 Resimplifying inuse:
% 94.49/94.91 Done
% 94.49/94.91
% 94.49/94.91
% 94.49/94.91 Intermediate Status:
% 94.49/94.91 Generated: 39942
% 94.49/94.91 Kept: 14707
% 94.49/94.91 Inuse: 439
% 94.49/94.91 Deleted: 2
% 94.49/94.91 Deletedinuse: 0
% 94.49/94.91
% 94.49/94.91 Resimplifying inuse:
% 94.49/94.91 Done
% 94.49/94.91
% 94.49/94.91 Resimplifying inuse:
% 94.49/94.91 Done
% 94.49/94.91
% 94.49/94.91
% 94.49/94.91 Intermediate Status:
% 94.49/94.91 Generated: 48080
% 94.49/94.91 Kept: 17426
% 94.49/94.91 Inuse: 479
% 94.49/94.91 Deleted: 2
% 94.49/94.91 Deletedinuse: 0
% 94.49/94.91
% 94.49/94.91 Resimplifying inuse:
% 94.49/94.91 Done
% 94.49/94.91
% 94.49/94.91 *** allocated 1297440 integers for clauses
% 94.49/94.91 Resimplifying inuse:
% 94.49/94.91 Done
% 94.49/94.91
% 94.49/94.91
% 94.49/94.91 Intermediate Status:
% 94.49/94.91 Generated: 53270
% 94.49/94.91 Kept: 19432
% 94.49/94.91 Inuse: 535
% 94.49/94.91 Deleted: 3
% 94.49/94.91 Deletedinuse: 0
% 94.49/94.91
% 94.49/94.91 Resimplifying inuse:
% 94.49/94.91 Done
% 94.49/94.91
% 94.49/94.91 *** allocated 864960 integers for termspace/termends
% 94.49/94.91 Resimplifying clauses:
% 94.49/94.91 Done
% 94.49/94.91
% 94.49/94.91 Resimplifying inuse:
% 94.49/94.91 Done
% 94.49/94.91
% 94.49/94.91
% 94.49/94.91 Intermediate Status:
% 94.49/94.91 Generated: 60358
% 94.49/94.91 Kept: 21467
% 94.49/94.91 Inuse: 563
% 94.49/94.91 Deleted: 275
% 94.49/94.91 Deletedinuse: 0
% 94.49/94.91
% 94.49/94.91 Resimplifying inuse:
% 94.49/94.91 Done
% 94.49/94.91
% 94.49/94.91 Resimplifying inuse:
% 94.49/94.91 Done
% 94.49/94.91
% 94.49/94.91
% 94.49/94.91 Intermediate Status:
% 94.49/94.91 Generated: 67192
% 94.49/94.91 Kept: 23716
% 94.49/94.91 Inuse: 593
% 94.49/94.91 Deleted: 277
% 94.49/94.91 Deletedinuse: 2
% 94.49/94.91
% 94.49/94.91 Resimplifying inuse:
% 94.49/94.91 Done
% 94.49/94.91
% 94.49/94.91 Resimplifying inuse:
% 94.49/94.91 Done
% 94.49/94.91
% 94.49/94.91
% 94.49/94.91 Intermediate Status:
% 94.49/94.91 Generated: 75729
% 94.49/94.91 Kept: 26166
% 94.49/94.91 Inuse: 603
% 94.49/94.91 Deleted: 277
% 94.49/94.91 Deletedinuse: 2
% 94.49/94.91
% 94.49/94.91 Resimplifying inuse:
% 94.49/94.91 Done
% 94.49/94.91
% 94.49/94.91 *** allocated 1946160 integers for clauses
% 94.49/94.91 Resimplifying inuse:
% 94.49/94.91 Done
% 94.49/94.91
% 94.49/94.91
% 94.49/94.91 Intermediate Status:
% 94.49/94.91 Generated: 83328
% 94.49/94.91 Kept: 28300
% 94.49/94.91 Inuse: 628
% 94.49/94.91 Deleted: 277
% 94.49/94.91 Deletedinuse: 2
% 94.49/94.91
% 94.49/94.91 Resimplifying inuse:
% 94.49/94.91 Done
% 94.49/94.91
% 94.49/94.91 Resimplifying inuse:
% 94.49/94.91 Done
% 94.49/94.91
% 94.49/94.91
% 94.49/94.91 Intermediate Status:
% 94.49/94.91 Generated: 88559
% 94.49/94.91 Kept: 30321
% 94.49/94.91 Inuse: 669
% 94.49/94.91 Deleted: 277
% 94.49/94.91 Deletedinuse: 2
% 94.49/94.91
% 94.49/94.91 Resimplifying inuse:
% 94.49/94.91 Done
% 94.49/94.91
% 94.49/94.91 *** allocated 1297440 integers for termspace/termends
% 94.49/94.91
% 94.49/94.91 Intermediate Status:
% 94.49/94.91 Generated: 96961
% 94.49/94.91 Kept: 32996
% 94.49/94.91 Inuse: 703
% 94.49/94.91 Deleted: 277
% 94.49/94.91 Deletedinuse: 2
% 94.49/94.91
% 94.49/94.91 Resimplifying inuse:
% 94.49/94.91 Done
% 94.49/94.91
% 94.49/94.91 Resimplifying inuse:
% 94.49/94.91 Done
% 94.49/94.91
% 94.49/94.91
% 94.49/94.91 Intermediate Status:
% 94.49/94.91 Generated: 110054
% 94.49/94.91 Kept: 35019
% 94.49/94.91 Inuse: 712
% 94.49/94.91 Deleted: 277
% 94.49/94.91 Deletedinuse: 2
% 94.49/94.91
% 94.49/94.91 Resimplifying inuse:
% 94.49/94.91 Done
% 94.49/94.91
% 94.49/94.91
% 94.49/94.91 Intermediate Status:
% 94.49/94.91 Generated: 117160
% 94.49/94.91 Kept: 37036
% 94.49/94.91 Inuse: 718
% 94.49/94.91 Deleted: 277
% 94.49/94.91 Deletedinuse: 2
% 94.49/94.91
% 94.49/94.91 Resimplifying inuse:
% 94.49/94.91 Done
% 94.49/94.91
% 94.49/94.91 Resimplifying inuse:
% 94.49/94.91 Done
% 94.49/94.91
% 94.49/94.91
% 94.49/94.91 Intermediate Status:
% 94.49/94.91 Generated: 127394
% 94.49/94.91 Kept: 39427
% 94.49/94.91 Inuse: 733
% 94.49/94.91 Deleted: 277
% 94.49/94.91 Deletedinuse: 2
% 94.49/94.91
% 94.49/94.91 Resimplifying inuse:
% 94.49/94.91 Done
% 94.49/94.91
% 94.49/94.91 Resimplifying inuse:
% 94.49/94.91 Done
% 94.49/94.91
% 94.49/94.91 Resimplifying clauses:
% 94.49/94.91 Done
% 94.49/94.91
% 94.49/94.91 *** allocated 2919240 integers for clauses
% 94.49/94.91
% 94.49/94.91 Intermediate Status:
% 94.49/94.91 Generated: 136090
% 94.49/94.91 Kept: 42122
% 94.49/94.91 Inuse: 748
% 94.49/94.91 Deleted: 458
% 94.49/94.91 Deletedinuse: 2
% 94.49/94.91
% 94.49/94.91 Resimplifying inuse:
% 94.49/94.91 Done
% 94.49/94.91
% 94.49/94.91 Resimplifying inuse:
% 94.49/94.91 Done
% 94.49/94.91
% 94.49/94.91 *** allocated 1946160 integers for termspace/termends
% 200.84/201.22
% 200.84/201.22 Intermediate Status:
% 200.84/201.22 Generated: 149591
% 200.84/201.22 Kept: 45224
% 200.84/201.22 Inuse: 768
% 200.84/201.22 Deleted: 459
% 200.84/201.22 Deletedinuse: 3
% 200.84/201.22
% 200.84/201.22 Resimplifying inuse:
% 200.84/201.22 Done
% 200.84/201.22
% 200.84/201.22
% 200.84/201.22 Intermediate Status:
% 200.84/201.22 Generated: 156366
% 200.84/201.22 Kept: 48748
% 200.84/201.22 Inuse: 783
% 200.84/201.22 Deleted: 459
% 200.84/201.22 Deletedinuse: 3
% 200.84/201.22
% 200.84/201.22 Resimplifying inuse:
% 200.84/201.22 Done
% 200.84/201.22
% 200.84/201.22 Resimplifying inuse:
% 200.84/201.22 Done
% 200.84/201.22
% 200.84/201.22
% 200.84/201.22 Intermediate Status:
% 200.84/201.22 Generated: 159865
% 200.84/201.22 Kept: 50793
% 200.84/201.22 Inuse: 798
% 200.84/201.22 Deleted: 459
% 200.84/201.22 Deletedinuse: 3
% 200.84/201.22
% 200.84/201.22 Resimplifying inuse:
% 200.84/201.22 Done
% 200.84/201.22
% 200.84/201.22
% 200.84/201.22 Intermediate Status:
% 200.84/201.22 Generated: 174227
% 200.84/201.22 Kept: 53841
% 200.84/201.22 Inuse: 813
% 200.84/201.22 Deleted: 459
% 200.84/201.22 Deletedinuse: 3
% 200.84/201.22
% 200.84/201.22 Resimplifying inuse:
% 200.84/201.22 Done
% 200.84/201.22
% 200.84/201.22
% 200.84/201.22 Intermediate Status:
% 200.84/201.22 Generated: 182139
% 200.84/201.22 Kept: 57671
% 200.84/201.22 Inuse: 828
% 200.84/201.22 Deleted: 459
% 200.84/201.22 Deletedinuse: 3
% 200.84/201.22
% 200.84/201.22 Resimplifying inuse:
% 200.84/201.22 Done
% 200.84/201.22
% 200.84/201.22 Resimplifying inuse:
% 200.84/201.22 Done
% 200.84/201.22
% 200.84/201.22
% 200.84/201.22 Intermediate Status:
% 200.84/201.22 Generated: 185610
% 200.84/201.22 Kept: 59750
% 200.84/201.22 Inuse: 838
% 200.84/201.22 Deleted: 459
% 200.84/201.22 Deletedinuse: 3
% 200.84/201.22
% 200.84/201.22
% 200.84/201.22 Intermediate Status:
% 200.84/201.22 Generated: 204240
% 200.84/201.22 Kept: 61821
% 200.84/201.22 Inuse: 848
% 200.84/201.22 Deleted: 459
% 200.84/201.22 Deletedinuse: 3
% 200.84/201.22
% 200.84/201.22 Resimplifying inuse:
% 200.84/201.22 Done
% 200.84/201.22
% 200.84/201.22 Resimplifying clauses:
% 200.84/201.22 Done
% 200.84/201.22
% 200.84/201.22 Resimplifying inuse:
% 200.84/201.22 Done
% 200.84/201.22
% 200.84/201.22 *** allocated 4378860 integers for clauses
% 200.84/201.22
% 200.84/201.22 Intermediate Status:
% 200.84/201.22 Generated: 231603
% 200.84/201.22 Kept: 65169
% 200.84/201.22 Inuse: 858
% 200.84/201.22 Deleted: 491
% 200.84/201.22 Deletedinuse: 3
% 200.84/201.22
% 200.84/201.22 Resimplifying inuse:
% 200.84/201.22 Done
% 200.84/201.22
% 200.84/201.22 Resimplifying inuse:
% 200.84/201.22 Done
% 200.84/201.22
% 200.84/201.22
% 200.84/201.22 Intermediate Status:
% 200.84/201.22 Generated: 246576
% 200.84/201.22 Kept: 67901
% 200.84/201.22 Inuse: 868
% 200.84/201.22 Deleted: 491
% 200.84/201.22 Deletedinuse: 3
% 200.84/201.22
% 200.84/201.22 Resimplifying inuse:
% 200.84/201.22 Done
% 200.84/201.22
% 200.84/201.22 Resimplifying inuse:
% 200.84/201.22 Done
% 200.84/201.22
% 200.84/201.22
% 200.84/201.22 Intermediate Status:
% 200.84/201.22 Generated: 254898
% 200.84/201.22 Kept: 69939
% 200.84/201.22 Inuse: 897
% 200.84/201.22 Deleted: 491
% 200.84/201.22 Deletedinuse: 3
% 200.84/201.22
% 200.84/201.22 Resimplifying inuse:
% 200.84/201.22 Done
% 200.84/201.22
% 200.84/201.22 *** allocated 2919240 integers for termspace/termends
% 200.84/201.22 Resimplifying inuse:
% 200.84/201.22 Done
% 200.84/201.22
% 200.84/201.22
% 200.84/201.22 Intermediate Status:
% 200.84/201.22 Generated: 265691
% 200.84/201.22 Kept: 72673
% 200.84/201.22 Inuse: 923
% 200.84/201.22 Deleted: 491
% 200.84/201.22 Deletedinuse: 3
% 200.84/201.22
% 200.84/201.22 Resimplifying inuse:
% 200.84/201.22 Done
% 200.84/201.22
% 200.84/201.22 Resimplifying inuse:
% 200.84/201.22 Done
% 200.84/201.22
% 200.84/201.22
% 200.84/201.22 Intermediate Status:
% 200.84/201.22 Generated: 274496
% 200.84/201.22 Kept: 74719
% 200.84/201.22 Inuse: 935
% 200.84/201.22 Deleted: 491
% 200.84/201.22 Deletedinuse: 3
% 200.84/201.22
% 200.84/201.22 Resimplifying inuse:
% 200.84/201.22 Done
% 200.84/201.22
% 200.84/201.22
% 200.84/201.22 Intermediate Status:
% 200.84/201.22 Generated: 287955
% 200.84/201.22 Kept: 77999
% 200.84/201.22 Inuse: 948
% 200.84/201.22 Deleted: 491
% 200.84/201.22 Deletedinuse: 3
% 200.84/201.22
% 200.84/201.22 Resimplifying inuse:
% 200.84/201.22 Done
% 200.84/201.22
% 200.84/201.22 Resimplifying inuse:
% 200.84/201.22 Done
% 200.84/201.22
% 200.84/201.22
% 200.84/201.22 Intermediate Status:
% 200.84/201.22 Generated: 297141
% 200.84/201.22 Kept: 80126
% 200.84/201.22 Inuse: 968
% 200.84/201.22 Deleted: 491
% 200.84/201.22 Deletedinuse: 3
% 200.84/201.22
% 200.84/201.22 Resimplifying inuse:
% 200.84/201.22 Done
% 200.84/201.22
% 200.84/201.22 Resimplifying inuse:
% 200.84/201.22 Done
% 200.84/201.22
% 200.84/201.22 Resimplifying clauses:
% 200.84/201.22 Done
% 200.84/201.22
% 200.84/201.22
% 200.84/201.22 Intermediate Status:
% 200.84/201.22 Generated: 304783
% 200.84/201.22 Kept: 82305
% 200.84/201.22 Inuse: 998
% 200.84/201.22 Deleted: 584
% 200.84/201.22 Deletedinuse: 3
% 200.84/201.22
% 200.84/201.22 Resimplifying inuse:
% 200.84/201.22 Done
% 200.84/201.22
% 200.84/201.22 Resimplifying inuse:
% 200.84/201.22 Done
% 200.84/201.22
% 200.84/201.22
% 200.84/201.22 Intermediate Status:
% 200.84/201.22 Generated: 318734
% 200.84/201.22 Kept: 86096
% 200.84/201.22 Inuse: 1026
% 200.84/201.22 Deleted: 584
% 200.84/201.22 Deletedinuse: 3
% 200.84/201.22
% 200.84/201.22 Resimplifying inuse:
% 200.84/201.22 Done
% 200.84/201.22
% 200.84/201.22 Resimplifying inuse:
% 200.84/201.22 Done
% 200.84/201.22
% 200.84/201.22
% 200.84/201.22 Intermediate Status:
% 200.84/201.22 Generated: 348115
% 200.84/201.22 Kept: 89164
% 200.84/201.22 Inuse: 1058
% 200.84/201.22 Deleted: 584
% 200.84/201.22 Deletedinuse: 3
% 200.84/201.22
% 200.84/201.22 Resimplifying inuse:
% 200.84/201.22 Done
% 200.84/201.22
% 200.84/201.22 Resimplifying inuse:
% 200.84/201.22 Done
% 200.84/201.22
% 200.84/201.22
% 200.84/201.22 Intermediate Status:
% 200.84/201.22 Generated: 381819
% 200.84/201.22 Kept: 91167
% 200.84/201.22 Inuse: 1079
% 200.84/201.22 Deleted: 584
% 200.84/201.22 Deletedinuse: 3
% 200.84/201.22
% 200.84/201.22
% 200.84/201.22 Intermediate Status:
% 200.84/201.22 Generated: 412076
% 200.84/201.22 Kept: 93563
% 200.84/201.22 Inuse: 1083
% 200.84/201.22 Deleted: 584
% 200.84/201.22 Deletedinuse: 3
% 200.84/201.22
% 200.84/201.22 Resimplifying inuse:
% 200.84/201.22 Done
% 200.84/201.22
% 200.84/201.22
% 200.84/201.22 Intermediate Status:
% 200.84/201.22 Generated: 450264
% 200.84/201.22 Kept: 97087
% 200.84/201.22 Inuse: 1093
% 200.84/201.22 Deleted: 584
% 200.84/201.22 Deletedinuse: 3
% 200.84/201.22
% 200.84/201.22 Resimplifying inuse:
% 200.84/201.22 Done
% 200.84/201.22
% 200.84/201.22 Resimplifying inuse:
% 200.84/201.22 Done
% 200.84/201.22
% 200.84/201.22 *** allocated 4378860 integers for termspace/termends
% 200.84/201.22 *** allocated 6568290 integers for clauses
% 200.84/201.22
% 200.84/201.22 Intermediate Status:
% 200.84/201.22 Generated: 469390
% 200.84/201.22 Kept: 100746
% 200.84/201.22 Inuse: 1118
% 200.84/201.22 Deleted: 584
% 200.84/201.22 Deletedinuse: 3
% 200.84/201.22
% 200.84/201.22 Resimplifying inuse:
% 200.84/201.22 Done
% 200.84/201.22
% 200.84/201.22 Resimplifying inuse:
% 200.84/201.22 Done
% 200.84/201.22
% 200.84/201.22
% 200.84/201.22 Intermediate Status:
% 200.84/201.22 Generated: 484279
% 200.84/201.22 Kept: 103839
% 200.84/201.22 Inuse: 1168
% 200.84/201.22 Deleted: 584
% 200.84/201.22 Deletedinuse: 3
% 200.84/201.22
% 200.84/201.22 Resimplifying inuse:
% 200.84/201.22 Done
% 200.84/201.22
% 200.84/201.22 Resimplifying clauses:
% 200.84/201.22 Done
% 200.84/201.22
% 200.84/201.22 Resimplifying inuse:
% 200.84/201.22 Done
% 200.84/201.22
% 200.84/201.22
% 200.84/201.22 Intermediate Status:
% 200.84/201.22 Generated: 498025
% 200.84/201.22 Kept: 108751
% 200.84/201.22 Inuse: 1208
% 200.84/201.22 Deleted: 1825
% 200.84/201.22 Deletedinuse: 3
% 200.84/201.22
% 200.84/201.22 Resimplifying inuse:
% 200.84/201.22 Done
% 200.84/201.22
% 200.84/201.22
% 200.84/201.22 Intermediate Status:
% 200.84/201.22 Generated: 507129
% 200.84/201.22 Kept: 112685
% 200.84/201.22 Inuse: 1213
% 200.84/201.22 Deleted: 1825
% 200.84/201.22 Deletedinuse: 3
% 200.84/201.22
% 200.84/201.22 Resimplifying inCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------