TSTP Solution File: SWW238+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWW238+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n020.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 23:21:28 EDT 2022
% Result : Theorem 4.20s 4.61s
% Output : Refutation 4.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SWW238+1 : TPTP v8.1.0. Released v5.2.0.
% 0.03/0.14 % Command : bliksem %s
% 0.13/0.35 % Computer : n020.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % DateTime : Sat Jun 4 12:14:52 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.28/1.63 *** allocated 10000 integers for termspace/termends
% 1.28/1.63 *** allocated 10000 integers for clauses
% 1.28/1.63 *** allocated 10000 integers for justifications
% 1.28/1.63 *** allocated 15000 integers for termspace/termends
% 1.28/1.63 *** allocated 22500 integers for termspace/termends
% 1.28/1.63 *** allocated 33750 integers for termspace/termends
% 1.28/1.63 Bliksem 1.12
% 1.28/1.63
% 1.28/1.63
% 1.28/1.63 Automatic Strategy Selection
% 1.28/1.63
% 1.28/1.63 *** allocated 50625 integers for termspace/termends
% 1.28/1.63 *** allocated 75937 integers for termspace/termends
% 1.28/1.63 *** allocated 113905 integers for termspace/termends
% 1.28/1.63
% 1.28/1.63 Clauses:
% 1.28/1.63
% 1.28/1.63 { ! hAPP( Y, skol1( X, Y ) ) = hAPP( X, skol1( X, Y ) ), Y = X }.
% 1.28/1.63 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.63 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), v_z____ ), v_c____
% 1.28/1.63 ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 1.28/1.63 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.28/1.63 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), v_z____ ), v_c____
% 1.28/1.63 ), v_aa____ ) ), c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.28/1.63 v_aa____ ) ) ) }.
% 1.28/1.63 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.63 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y ),
% 1.28/1.63 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 1.28/1.63 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.28/1.63 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X ) ),
% 1.28/1.63 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) ) }.
% 1.28/1.63 { ! v_p = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 1.28/1.63 tc_Complex_Ocomplex ) ) }.
% 1.28/1.63 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.63 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 1.28/1.63 ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 1.28/1.63 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 1.28/1.63 ( X, Y ) ) ) }.
% 1.28/1.63 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.63 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs
% 1.28/1.63 ( tc_RealDef_Oreal, v_da____ ), c_RealVector_Onorm__class_Onorm(
% 1.28/1.63 tc_Complex_Ocomplex, v_aa____ ) ), c_RealVector_Onorm__class_Onorm(
% 1.28/1.63 tc_Complex_Ocomplex, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.28/1.63 tc_Complex_Ocomplex ), v_z____ ), v_c____ ) ) ) }.
% 1.28/1.63 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.63 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.28/1.63 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 1.28/1.63 c_RealVector_Onorm__class_Onorm( X, Y ) ) ) }.
% 1.28/1.63 { ! class_Orderings_Opreorder( X ), c_Orderings_Oord__class_Oless__eq( X, Y
% 1.28/1.63 , Y ) }.
% 1.28/1.63 { ! v_c____ = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.63 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ),
% 1.28/1.63 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, X ) ) }.
% 1.28/1.63 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 1.28/1.63 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.28/1.63 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 1.28/1.63 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 1.28/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.63 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.63 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.28/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.63 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.28/1.63 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.28/1.63 ( X ), U = T, Z = Y, ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.63 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 1.28/1.63 ) }.
% 1.28/1.63 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.28/1.63 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.63 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 1.28/1.63 ), ! U = T }.
% 1.28/1.63 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.28/1.63 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.63 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 1.28/1.63 ), ! Z = Y }.
% 1.28/1.63 { v_cs____ = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 1.28/1.63 tc_Complex_Ocomplex ) ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z,
% 1.28/1.63 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.63 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs
% 1.28/1.63 ( tc_RealDef_Oreal, v_da____ ), X ), Z ),
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, v_da____, Y ) }.
% 1.28/1.63 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 1.28/1.63 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs
% 1.28/1.63 ( tc_RealDef_Oreal, v_da____ ), c_RealVector_Onorm__class_Onorm(
% 1.28/1.63 tc_Complex_Ocomplex, v_aa____ ) ), c_RealVector_Onorm__class_Onorm(
% 1.28/1.63 tc_Complex_Ocomplex, v_c____ ) ), c_RealVector_Onorm__class_Onorm(
% 1.28/1.63 tc_Complex_Ocomplex, v_z____ ) ) }.
% 1.28/1.63 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.28/1.63 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.28/1.63 { c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, X ) =
% 1.28/1.63 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) }.
% 1.28/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) =
% 1.28/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y )
% 1.28/1.63 }.
% 1.28/1.63 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.28/1.63 c_RealVector_Onorm__class_Onorm( X, Y ) = c_Groups_Ozero__class_Ozero(
% 1.28/1.63 tc_RealDef_Oreal ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.63 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X, Y )
% 1.28/1.63 = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.28/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP
% 1.28/1.63 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), Y ) ), X ) =
% 1.28/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), hAPP
% 1.28/1.63 ( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 1.28/1.63 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Oabs__class_Oabs
% 1.28/1.63 ( tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( X, Y ) ) =
% 1.28/1.63 c_RealVector_Onorm__class_Onorm( X, Y ) }.
% 1.28/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.28/1.63 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.28/1.63 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.28/1.63 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.28/1.63 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.28/1.63 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.28/1.63 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.63 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.28/1.63 ( X ), ! Z = c_Groups_Oplus__class_Oplus( X, Z, Y ), Y =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.63 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.28/1.63 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 1.28/1.63 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 1.28/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.28/1.63 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ) ), X ) =
% 1.28/1.63 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 1.28/1.63 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.63 c_RealVector_Onorm__class_Onorm( X, Y ), c_Groups_Ozero__class_Ozero(
% 1.28/1.63 tc_RealDef_Oreal ) ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.63 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq(
% 1.28/1.63 tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( X, Y ),
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 1.28/1.63 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.28/1.63 ( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! W = U, T = Z, !
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, W, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) =
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, U, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.28/1.63 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.28/1.63 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.28/1.63 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 1.28/1.63 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 1.28/1.63 hAPP( Y, U ) ) }.
% 1.28/1.63 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.28/1.63 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 1.28/1.63 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.28/1.63 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 1.28/1.63 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.63 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 1.28/1.63 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.28/1.63 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 1.28/1.63 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.28/1.63 , Y ), ! Z = T, c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 1.28/1.63 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y
% 1.28/1.63 ), ! Y = T, c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 1.28/1.63 { ! class_Orderings_Oorder( X ), ! Z = Y, !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 1.28/1.63 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 1.28/1.63 ( X, Y, T ), c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 1.28/1.63 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.28/1.63 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 1.28/1.63 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.28/1.63 , Y ), ! Y = Z, c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.28/1.63 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 1.28/1.63 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 1.28/1.63 hAPP( Y, U ) ) }.
% 1.28/1.63 { ! class_Orderings_Opreorder( X ), ! Z = Y,
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.28/1.63 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 1.28/1.63 ( X, Z, Y ) }.
% 1.28/1.63 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 1.28/1.63 ( X, Y, Z ) }.
% 1.28/1.63 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.28/1.63 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 1.28/1.63 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.28/1.63 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.28/1.63 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 1.28/1.63 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 1.28/1.63 hAPP( Y, U ) ) }.
% 1.28/1.63 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, hAPP
% 1.28/1.63 ( Z, skol2( X, Y, Z ) ), hAPP( Y, skol2( X, Y, Z ) ) ),
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), Y ) ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Z ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 1.28/1.63 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X
% 1.28/1.63 , U, Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.28/1.63 ( X, c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.28/1.63 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 1.28/1.63 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 1.28/1.63 ( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 1.28/1.63 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 1.28/1.63 ( X, Z, c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 1.28/1.63 , Y ) = c_Groups_Oplus__class_Oplus( X, Y, Z ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ), Y = X }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Z ),
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, Z ) }.
% 1.28/1.63 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ) }.
% 1.28/1.63 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, X ) }.
% 1.28/1.63 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.28/1.63 ( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.63 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 1.28/1.63 ), U = Z, T = Y }.
% 1.28/1.63 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.28/1.63 ( X ), ! U = Z, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.63 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 1.28/1.63 ) }.
% 1.28/1.63 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.28/1.63 ( X ), ! T = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.63 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 1.28/1.63 ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Y
% 1.28/1.63 ) ), Z ) }.
% 1.28/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.28/1.63 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.28/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.28/1.63 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.28/1.63 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.28/1.63 { v_cs____ = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 1.28/1.63 tc_Complex_Ocomplex ) ) }.
% 1.28/1.63 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.63 c_RealVector_Onorm__class_Onorm( X, Z ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ),
% 1.28/1.63 c_RealVector_Onorm__class_Onorm( X, T ) ) ), Z =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.63 { ! class_Rings_Oordered__ring__abs( X ), alpha81( X, Z ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.63 ), c_Groups_Oabs__class_Oabs( X, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 1.28/1.63 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 1.28/1.63 { ! class_Rings_Oordered__ring__abs( X ), alpha81( X, Z ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.63 ), c_Groups_Oabs__class_Oabs( X, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 1.28/1.63 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 1.28/1.63 { ! alpha81( X, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.28/1.63 { ! alpha81( X, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.63 { c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.63 ), c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero
% 1.28/1.63 ( X ) ), alpha81( X, Y ) }.
% 1.28/1.63 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 1.28/1.63 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 1.28/1.63 Y ) = c_Groups_Oabs__class_Oabs( X, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.28/1.63 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 1.28/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) ), Z = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.63 }.
% 1.28/1.63 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 1.28/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.63 }.
% 1.28/1.63 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.63 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 1.28/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.63 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 1.28/1.63 X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 1.28/1.63 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 1.28/1.63 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, Z, Y ) ), c_Groups_Oplus__class_Oplus( X
% 1.28/1.63 , c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) )
% 1.28/1.63 ) }.
% 1.28/1.63 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.63 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 1.28/1.63 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Y ),
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.63 }.
% 1.28/1.63 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! Y =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.63 c_Groups_Oabs__class_Oabs( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.63 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.63 ), c_Groups_Oabs__class_Oabs( X, Y ) = Y }.
% 1.28/1.63 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.63 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 1.28/1.63 ) = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X
% 1.28/1.63 ) }.
% 1.28/1.63 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.63 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 1.28/1.63 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 1.28/1.63 ) }.
% 1.28/1.63 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.63 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.63 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.63 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.63 , c_Groups_Oplus__class_Oplus( X, Y, Z ), c_Groups_Ozero__class_Ozero( X
% 1.28/1.63 ) ) }.
% 1.28/1.63 { ! c_Polynomial_OpCons( tc_Complex_Ocomplex, v_c____, v_cs____ ) =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) )
% 1.28/1.63 }.
% 1.28/1.63 { ! class_Fields_Ofield__inverse__zero( X ), !
% 1.28/1.63 class_RealVector_Oreal__normed__field( X ),
% 1.28/1.63 c_RealVector_Onorm__class_Onorm( X, c_Rings_Oinverse__class_Odivide( X, Z
% 1.28/1.63 , Y ) ) = c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 1.28/1.63 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 1.28/1.63 ( X, Y ) ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, Y, X ) ), alpha1( X, Y
% 1.28/1.63 ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, Y, X ) ), alpha26( X,
% 1.28/1.63 Y ) }.
% 1.28/1.63 { ! alpha1( X, Y ), ! alpha26( X, Y ), c_Orderings_Oord__class_Oless__eq(
% 1.28/1.63 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, Y, X ) ) }.
% 1.28/1.63 { ! alpha26( X, Y ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), alpha26( X, Y ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), alpha26( X, Y ) }.
% 1.28/1.63 { ! alpha1( X, Y ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y
% 1.28/1.63 , c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), alpha1( X, Y ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), alpha1( X, Y ) }.
% 1.28/1.63 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 1.28/1.63 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.63 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.63 }.
% 1.28/1.63 { ! class_Rings_Odivision__ring( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), c_Rings_Oinverse__class_Odivide
% 1.28/1.63 ( X, Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 1.28/1.63 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.28/1.63 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ),
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.28/1.63 { ! class_RealVector_Oreal__normed__field( X ), Y =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X,
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 1.28/1.63 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 1.28/1.63 ( X, Y ) ) }.
% 1.28/1.63 { ! class_RealVector_Oreal__normed__field( X ),
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 1.28/1.63 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.63 { ! class_RealVector_Oreal__normed__field( X ),
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, T, Z
% 1.28/1.63 ), Y ) = c_Groups_Oplus__class_Oplus( X, c_Rings_Oinverse__class_Odivide
% 1.28/1.63 ( X, T, Y ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.28/1.63 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.63 , ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, T =
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 1.28/1.63 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.63 , ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z }.
% 1.28/1.63 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.63 , ! c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z, T = hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 1.28/1.63 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.63 , ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z }.
% 1.28/1.63 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.63 , ! T = c_Rings_Oinverse__class_Odivide( X, Z, Y ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z }.
% 1.28/1.63 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.63 , ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, T =
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 1.28/1.63 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) = hAPP( hAPP
% 1.28/1.63 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ), Z = Y }.
% 1.28/1.63 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP
% 1.28/1.63 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) = hAPP(
% 1.28/1.63 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) }.
% 1.28/1.63 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) = hAPP( hAPP
% 1.28/1.63 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ), Z = Y }.
% 1.28/1.63 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP
% 1.28/1.63 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) = hAPP(
% 1.28/1.63 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.63 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ),
% 1.28/1.63 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Z ) ) ), Y =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.28/1.63 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.28/1.63 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 1.28/1.63 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.28/1.63 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.28/1.63 { ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! X =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.28/1.63 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.28/1.63 { ! class_Groups_Ozero( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y, Y =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.63 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 1.28/1.63 { ! class_Groups_Oab__semigroup__mult( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.28/1.63 { ! class_Groups_Oab__semigroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.28/1.63 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 1.28/1.63 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.28/1.63 T, Y ), Z = Y }.
% 1.28/1.63 { ! class_Groups_Ocancel__semigroup__add( X ), ! Z = Y,
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.28/1.63 T, Y ) }.
% 1.28/1.63 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.28/1.63 Y, Z ), T = Y }.
% 1.28/1.63 { ! class_Groups_Ocancel__semigroup__add( X ), ! T = Y,
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.28/1.63 Y, Z ) }.
% 1.28/1.63 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.28/1.63 T, Y ), Z = Y }.
% 1.28/1.63 { ! class_Groups_Ocancel__ab__semigroup__add( X ), !
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.28/1.63 T, Y ), Z = Y }.
% 1.28/1.63 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, Z, T ) = c_Groups_Oplus__class_Oplus( X,
% 1.28/1.63 Y, T ), Z = Y }.
% 1.28/1.63 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 1.28/1.63 c_Groups_Oabs__class_Oabs( X, c_Groups_Oabs__class_Oabs( X, Y ) ) =
% 1.28/1.63 c_Groups_Oabs__class_Oabs( X, Y ) }.
% 1.28/1.63 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.63 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.63 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.63 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.63 { ! class_Rings_Oring__no__zero__divisors( X ), ! hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.63 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.63 { ! class_Rings_Oring__no__zero__divisors( X ), ! Z =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.63 { ! class_Rings_Oring__no__zero__divisors( X ), ! Y =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.63 { ! class_Rings_Ono__zero__divisors( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.28/1.63 X ), Z = c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.63 { ! class_Rings_Ono__zero__divisors( X ), ! hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.63 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.63 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 1.28/1.63 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 1.28/1.63 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Oplus__class_Oplus( X, Y, Y )
% 1.28/1.63 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.63 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero( X ) =
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 1.28/1.63 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.28/1.63 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y
% 1.28/1.63 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.28/1.63 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.28/1.63 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ),
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 1.28/1.63 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.28/1.63 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.28/1.63 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.28/1.63 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.28/1.63 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.28/1.63 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 1.28/1.63 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 1.28/1.63 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 1.28/1.63 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.28/1.63 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 1.28/1.63 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 1.28/1.63 U ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 1.28/1.63 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 1.28/1.63 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ),
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.28/1.63 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.28/1.63 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.28/1.63 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.28/1.63 { ! class_Rings_Osemiring( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP
% 1.28/1.63 ( c_Groups_Otimes__class_Otimes( X ), U ), T ),
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.63 ( X ), Z ), T ), Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, U, Z
% 1.28/1.63 ) ), T ), Y ) }.
% 1.28/1.63 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 1.28/1.63 c_Groups_Oabs__class_Oabs( X, Y ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.63 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! Y =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oabs__class_Oabs( X, Y ) =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.63 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 1.28/1.63 c_Groups_Oabs__class_Oabs( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.63 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oabs__class_Oabs( X, Y
% 1.28/1.63 ) ) }.
% 1.28/1.63 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 1.28/1.63 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.28/1.63 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, hAPP
% 1.28/1.63 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 1.28/1.63 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 1.28/1.63 { ! class_Rings_Olinordered__idom( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Y ) ),
% 1.28/1.63 c_Groups_Oabs__class_Oabs( X, Y ) ) = hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 1.28/1.63 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 1.28/1.63 c_Groups_Oabs__class_Oabs( X, c_Groups_Oplus__class_Oplus( X,
% 1.28/1.63 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ) )
% 1.28/1.63 = c_Groups_Oplus__class_Oplus( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 1.28/1.63 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 1.28/1.63 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 1.28/1.63 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) }.
% 1.28/1.63 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), alpha2( X, Y
% 1.28/1.63 , Z ), alpha27( X, Y, Z ) }.
% 1.28/1.63 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha2( X, Y, Z ),
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.28/1.63 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha27( X, Y, Z ),
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.28/1.63 { ! alpha27( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.63 { ! alpha27( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.28/1.63 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) ), alpha27( X, Y, Z ) }.
% 1.28/1.63 { ! alpha2( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.28/1.63 { ! alpha2( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.63 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), Y ), alpha2( X, Y, Z ) }.
% 1.28/1.63 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.28/1.63 ( X ) ), alpha3( X, Y, Z ), alpha28( X, Y, Z ) }.
% 1.28/1.63 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha3( X, Y, Z ),
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.28/1.63 ( X ) ) }.
% 1.28/1.63 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha28( X, Y, Z ),
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.28/1.63 ( X ) ) }.
% 1.28/1.63 { ! alpha28( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.63 { ! alpha28( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.28/1.63 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 1.28/1.63 ( X ), Y ), alpha28( X, Y, Z ) }.
% 1.28/1.63 { ! alpha3( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.28/1.63 { ! alpha3( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.63 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) ), alpha3( X, Y, Z ) }.
% 1.28/1.63 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.63 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.28/1.63 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.28/1.63 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.63 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.63 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ),
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.63 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.63 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.63 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.63 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.63 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.28/1.63 X ), Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 1.28/1.63 ( X ) ) }.
% 1.28/1.63 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.63 , Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.63 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.28/1.63 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.28/1.63 { ! class_Rings_Oordered__semiring( X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.28/1.63 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.28/1.63 { ! class_Rings_Oordered__semiring( X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.28/1.63 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.28/1.63 { ! class_Rings_Oordered__comm__semiring( X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.28/1.63 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.28/1.63 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.63 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.63 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 1.28/1.63 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.63 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.63 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 1.28/1.63 { ! class_Rings_Oordered__semiring( X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.28/1.63 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.28/1.63 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.28/1.63 { ! class_Rings_Oordered__semiring( X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.63 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.28/1.63 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.28/1.63 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.63 , c_Groups_Ozero__class_Ozero( X ), Z ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.63 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.28/1.63 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.28/1.63 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.63 , Z, c_Groups_Ozero__class_Ozero( X ) ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.63 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.28/1.63 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.28/1.63 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.28/1.63 ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.63 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.63 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.63 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.28/1.63 X ), Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.28/1.63 ( X ) ) }.
% 1.28/1.63 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, Y, Y ) ),
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.63 ) }.
% 1.28/1.63 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.63 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.28/1.63 ), c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 1.28/1.63 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Y,
% 1.28/1.63 Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.63 ) }.
% 1.28/1.63 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.63 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X
% 1.28/1.63 , Y, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.63 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.63 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.28/1.63 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 1.28/1.63 ) }.
% 1.28/1.63 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.63 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.28/1.63 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 1.28/1.63 .
% 1.28/1.63 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.63 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.28/1.63 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 1.28/1.63 .
% 1.28/1.63 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.63 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.28/1.63 X ), Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), ! Z =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 1.28/1.63 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.63 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.63 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 1.28/1.63 Y, Z ) ) }.
% 1.28/1.63 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.63 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 1.28/1.63 Z, Y ) ) }.
% 1.28/1.63 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, T,
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z,
% 1.28/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Y ) }.
% 1.28/1.63 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, T, c_Rings_Oinverse__class_Odivide( X, Z
% 1.28/1.63 , Y ) ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus
% 1.28/1.63 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), Z ), Y ) }
% 1.28/1.63 .
% 1.28/1.63 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ) =
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.28/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) }.
% 1.28/1.63 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, c_Rings_Oinverse__class_Odivide( X, T, Y
% 1.28/1.63 ), Z ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus
% 1.28/1.63 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) }
% 1.28/1.63 .
% 1.28/1.63 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( X, U, Y ),
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( X, T, Z ) ) =
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, hAPP
% 1.28/1.63 ( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.28/1.63 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.28/1.63 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_c____ ) ) }.
% 1.28/1.63 { ! class_Fields_Olinordered__field( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.28/1.63 X ), c_Groups_Oabs__class_Oabs( X, c_Rings_Oinverse__class_Odivide( X, Z
% 1.28/1.63 , Y ) ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oabs__class_Oabs(
% 1.28/1.63 X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 1.28/1.63 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), ! c_Rings_Oinverse__class_Odivide( X, U
% 1.28/1.63 , Y ) = c_Rings_Oinverse__class_Odivide( X, T, Z ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), U ), Z ) = hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) }.
% 1.28/1.63 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), U ), Z ) = hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ),
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( X, U, Y ) =
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 1.28/1.63 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X,
% 1.28/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) =
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 1.28/1.63 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X,
% 1.28/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 1.28/1.63 { ! class_Rings_Olinordered__idom( X ), Z = Y,
% 1.28/1.63 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.28/1.63 X, Y, Z ) }.
% 1.28/1.63 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.28/1.63 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.28/1.63 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.28/1.63 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.28/1.63 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.28/1.63 , ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 1.28/1.63 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.28/1.63 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.28/1.63 Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 1.28/1.63 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.28/1.63 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.28/1.63 , ! Z = T, c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.28/1.63 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 1.28/1.63 ! Y = T, c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.28/1.63 { ! class_Orderings_Oorder( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless(
% 1.28/1.63 X, T, Y ), c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 1.28/1.63 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X
% 1.28/1.63 , Y, T ), c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.28/1.63 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.28/1.63 , ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.28/1.64 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.28/1.64 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.28/1.64 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.28/1.64 , ! Y = Z }.
% 1.28/1.64 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.28/1.64 , ! Z = Y }.
% 1.28/1.64 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.28/1.64 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.28/1.64 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.28/1.64 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.28/1.64 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.28/1.64 , ! Z = Y }.
% 1.28/1.64 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 1.28/1.64 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.28/1.64 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.28/1.64 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Y = Z }.
% 1.28/1.64 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.28/1.64 ), ! Y = Z, ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.28/1.64 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.28/1.64 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.28/1.64 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.28/1.64 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Z = Y }.
% 1.28/1.64 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.28/1.64 Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.28/1.64 { ! class_Orderings_Olinorder( X ), ! Z = Y, !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.28/1.64 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 1.28/1.64 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.28/1.64 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.28/1.64 Y ), ! Z = Y }.
% 1.28/1.64 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.28/1.64 Z ), ! Z = Y }.
% 1.28/1.64 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.28/1.64 Y ) }.
% 1.28/1.64 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.28/1.64 , Y ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.28/1.64 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.64 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.28/1.64 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.28/1.64 , ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.28/1.64 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.28/1.64 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.28/1.64 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.28/1.64 , Y ), Y = Z, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.28/1.64 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.28/1.64 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.28/1.64 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.28/1.64 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 1.28/1.64 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.64 , Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 1.28/1.64 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.64 , Z, Y ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.28/1.64 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.28/1.64 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.28/1.64 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.64 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.28/1.64 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 1.28/1.64 ( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.28/1.64 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 1.28/1.64 ( X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.28/1.64 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.28/1.64 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ), Z = Y }.
% 1.28/1.64 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.28/1.64 ), ! Z = Y, c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.28/1.64 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.28/1.64 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.28/1.64 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.28/1.64 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.28/1.64 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.28/1.64 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 1.28/1.64 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.28/1.64 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.28/1.64 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 1.28/1.64 ( X, Z, Y ) }.
% 1.28/1.64 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.28/1.64 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.28/1.64 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.28/1.64 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.28/1.64 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.64 , Z, Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.28/1.64 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.28/1.64 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.28/1.64 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.28/1.64 , ! Z = Y }.
% 1.28/1.64 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.28/1.64 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.28/1.64 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.28/1.64 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.28/1.64 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.28/1.64 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.28/1.64 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.28/1.64 Z ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.28/1.64 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.28/1.64 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.28/1.64 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.64 , Y, Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.28/1.64 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 1.28/1.64 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, Z, Y ) }.
% 1.28/1.64 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, T )
% 1.28/1.64 , c_Groups_Oplus__class_Oplus( X, Y, T ) ), c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, Z, Y ) }.
% 1.28/1.64 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, U, T ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X, Y
% 1.28/1.64 , T ) ) }.
% 1.28/1.64 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.28/1.64 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 1.28/1.64 , T, Y ) ) }.
% 1.28/1.64 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.28/1.64 X, c_Groups_Oplus__class_Oplus( X, Z, T ), c_Groups_Oplus__class_Oplus( X
% 1.28/1.64 , Y, T ) ) }.
% 1.28/1.64 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 1.28/1.64 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, Z, Y ) }.
% 1.28/1.64 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.28/1.64 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 1.28/1.64 , T, Y ) ) }.
% 1.28/1.64 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 1.28/1.64 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ), c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, T, Y ) }.
% 1.28/1.64 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, T, Y ), c_Orderings_Oord__class_Oless(
% 1.28/1.64 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 1.28/1.64 , Y, Z ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), Y = X }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 1.28/1.64 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), ! Y = X }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), Y = X,
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.64 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, T,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.64 c_Rings_Oinverse__class_Odivide( X, Y, T ),
% 1.28/1.64 c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.64 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.64 c_Rings_Oinverse__class_Odivide( X, Z, T ),
% 1.28/1.64 c_Rings_Oinverse__class_Odivide( X, Y, T ) ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.64 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, Z, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X
% 1.28/1.64 , Y, Z ) ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.64 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, c_Rings_Oinverse__class_Odivide( X, Y, Z ),
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.64 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, Z, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, c_Rings_Oinverse__class_Odivide( X, Y, Z ),
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.64 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X
% 1.28/1.64 , Y, Z ) ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, Z,
% 1.28/1.64 Y ), c_Groups_Ozero__class_Ozero( X ) ), alpha4( X, Y, Z ), alpha29( X, Y
% 1.28/1.64 , Z ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha4( X, Y, Z
% 1.28/1.64 ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X
% 1.28/1.64 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha29( X, Y, Z
% 1.28/1.64 ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X
% 1.28/1.64 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.64 { ! alpha29( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.64 { ! alpha29( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.28/1.64 , ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.64 ), alpha29( X, Y, Z ) }.
% 1.28/1.64 { ! alpha4( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.28/1.64 { ! alpha4( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.28/1.64 , ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.64 ), alpha4( X, Y, Z ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.64 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ), alpha5( X, Y, Z ), alpha30
% 1.28/1.64 ( X, Y, Z ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha5( X, Y, Z
% 1.28/1.64 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.64 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha30( X, Y, Z
% 1.28/1.64 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.64 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.28/1.64 { ! alpha30( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.64 { ! alpha30( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.28/1.64 , ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.64 ), alpha30( X, Y, Z ) }.
% 1.28/1.64 { ! alpha5( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.28/1.64 { ! alpha5( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.28/1.64 , ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.64 ), alpha5( X, Y, Z ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.64 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.64 , Z ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( X ), c_Rings_Oinverse__class_Odivide( X, Y, Z ) ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.64 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.28/1.64 ) ), c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.64 c_Rings_Oinverse__class_Odivide( X, Y, Z ), c_Groups_Ozero__class_Ozero(
% 1.28/1.64 X ) ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.64 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, Y, Z ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 1.28/1.64 ! c_Orderings_Oord__class_Oless( X, T, U ), c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, c_Rings_Oinverse__class_Odivide( X, Y, U ),
% 1.28/1.64 c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.64 ), ! c_Orderings_Oord__class_Oless( X, Y, Z ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 1.28/1.64 ! c_Orderings_Oord__class_Oless__eq( X, T, U ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, Y,
% 1.28/1.64 U ), c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.64 ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 1.28/1.64 ! c_Orderings_Oord__class_Oless__eq( X, T, U ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.28/1.64 , Y, U ), c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.64 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.64 , Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.64 c_Rings_Oinverse__class_Odivide( X, Y, Z ), c_Groups_Ozero__class_Ozero(
% 1.28/1.64 X ) ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.64 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.28/1.64 ) ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.28/1.64 X ), c_Rings_Oinverse__class_Odivide( X, Y, Z ) ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 1.28/1.64 Z, Y ) ), alpha31( X, Y, Z, T ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 1.28/1.64 Z, Y ) ), alpha48( X, Y, Z, T ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha31( X, Y, Z
% 1.28/1.64 , T ), ! alpha48( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 1.28/1.64 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.28/1.64 { ! alpha48( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), Y ), alpha57( X, Y, Z, T ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 1.28/1.64 , alpha48( X, Y, Z, T ) }.
% 1.28/1.64 { ! alpha57( X, Y, Z, T ), alpha48( X, Y, Z, T ) }.
% 1.28/1.64 { ! alpha57( X, Y, Z, T ), alpha67( X, Y, Z, T ) }.
% 1.28/1.64 { ! alpha57( X, Y, Z, T ), alpha6( X, Y, T ) }.
% 1.28/1.64 { ! alpha67( X, Y, Z, T ), ! alpha6( X, Y, T ), alpha57( X, Y, Z, T ) }.
% 1.28/1.64 { ! alpha67( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Z,
% 1.28/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.28/1.64 { c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.28/1.64 alpha67( X, Y, Z, T ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha67( X, Y, Z, T ) }.
% 1.28/1.64 { ! alpha31( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 1.28/1.64 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.28/1.64 alpha31( X, Y, Z, T ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ), alpha31( X, Y, Z, T )
% 1.28/1.64 }.
% 1.28/1.64 { ! alpha6( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Z,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 1.28/1.64 , alpha6( X, Y, Z ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.28/1.64 , alpha6( X, Y, Z ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.28/1.64 Z ), Y ), alpha32( X, Y, Z, T ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.28/1.64 Z ), Y ), alpha49( X, Y, Z, T ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha32( X, Y, Z
% 1.28/1.64 , T ), ! alpha49( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.64 c_Rings_Oinverse__class_Odivide( X, T, Z ), Y ) }.
% 1.28/1.64 { ! alpha49( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), Z ), alpha58( X, Y, Z, T ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.28/1.64 , alpha49( X, Y, Z, T ) }.
% 1.28/1.64 { ! alpha58( X, Y, Z, T ), alpha49( X, Y, Z, T ) }.
% 1.28/1.64 { ! alpha58( X, Y, Z, T ), alpha68( X, Y, Z, T ) }.
% 1.28/1.64 { ! alpha58( X, Y, Z, T ), alpha7( X, Y, Z ) }.
% 1.28/1.64 { ! alpha68( X, Y, Z, T ), ! alpha7( X, Y, Z ), alpha58( X, Y, Z, T ) }.
% 1.28/1.64 { ! alpha68( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ) }.
% 1.28/1.64 { c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) ),
% 1.28/1.64 alpha68( X, Y, Z, T ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ), alpha68( X, Y, Z, T )
% 1.28/1.64 }.
% 1.28/1.64 { ! alpha32( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.64 T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.28/1.64 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.28/1.64 alpha32( X, Y, Z, T ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha32( X, Y, Z, T ) }.
% 1.28/1.64 { ! alpha7( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.28/1.64 , alpha7( X, Y, Z ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 1.28/1.64 , alpha7( X, Y, Z ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.64 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, T, c_Rings_Oinverse__class_Odivide( X, Z, Y ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.64 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 1.28/1.64 Z, Y ) ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.64 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.64 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.28/1.64 Y ), Z ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.64 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.28/1.64 Y ), Z ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.64 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 1.28/1.64 Z, Y ) ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.64 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, T, c_Rings_Oinverse__class_Odivide( X, Z, Y ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.64 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 1.28/1.64 Z, Y ) ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.64 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.64 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.28/1.64 Y ), Z ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.64 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 1.28/1.64 , c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.28/1.64 Y ), c_Rings_Oinverse__class_Odivide( X, T, Z ) ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.64 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, T,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless( X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.28/1.64 Z ), c_Rings_Oinverse__class_Odivide( X, T, Y ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 1.28/1.64 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha8( X, Y, Z, T ),
% 1.28/1.64 alpha33( X, Y, Z, T ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha8( X, Y, Z, T ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha33( X, Y, Z, T ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.28/1.64 { ! alpha33( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.64 { ! alpha33( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, T ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.28/1.64 , ! c_Orderings_Oord__class_Oless( X, Y, T ), alpha33( X, Y, Z, T ) }.
% 1.28/1.64 { ! alpha8( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.28/1.64 { ! alpha8( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.28/1.64 , ! c_Orderings_Oord__class_Oless( X, T, Y ), alpha8( X, Y, Z, T ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha9( X, Y, Z, T ),
% 1.28/1.64 alpha34( X, Y, Z, T ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha9( X, Y, Z, T ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha34( X, Y, Z, T ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.28/1.64 { ! alpha34( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.64 { ! alpha34( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( X, T, c_Groups_Ozero__class_Ozero( X ) )
% 1.28/1.64 , ! c_Orderings_Oord__class_Oless( X, Y, Z ), alpha34( X, Y, Z, T ) }.
% 1.28/1.64 { ! alpha9( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), T ) }.
% 1.28/1.64 { ! alpha9( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T )
% 1.28/1.64 , ! c_Orderings_Oord__class_Oless( X, Z, Y ), alpha9( X, Y, Z, T ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.28/1.64 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.28/1.64 ! c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 1.28/1.64 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.28/1.64 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.28/1.64 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.28/1.64 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.28/1.64 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( X ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.28/1.64 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.28/1.64 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( X ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.28/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 1.28/1.64 .
% 1.28/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.28/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ) }
% 1.28/1.64 .
% 1.28/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.28/1.64 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.28/1.64 ! c_Orderings_Oord__class_Oless( X, Z, T ), c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 1.28/1.64 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.28/1.64 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.28/1.64 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( X ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.28/1.64 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.28/1.64 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP
% 1.28/1.64 ( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.28/1.64 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__comm__semiring__strict( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.28/1.64 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 1.28/1.64 ( c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP
% 1.28/1.64 ( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 1.28/1.64 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.64 c_Groups_Oplus__class_Oplus( X, Y, Y ) ), c_Orderings_Oord__class_Oless(
% 1.28/1.64 X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.28/1.64 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.64 c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 1.28/1.64 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 1.28/1.64 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Y
% 1.28/1.64 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.64 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 1.28/1.64 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.64 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.28/1.64 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.28/1.64 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.64 c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless(
% 1.28/1.64 X, T, c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.28/1.64 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.28/1.64 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.28/1.64 , c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Z
% 1.28/1.64 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.64 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, U, T ), c_Orderings_Oord__class_Oless(
% 1.28/1.64 X, c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X
% 1.28/1.64 , Y, T ) ) }.
% 1.28/1.64 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, U )
% 1.28/1.64 , c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.28/1.64 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oabs__class_Oabs( X, Z ), Y
% 1.28/1.64 ) = c_Groups_Oabs__class_Oabs( X, c_Rings_Oinverse__class_Odivide( X, Z
% 1.28/1.64 , Y ) ) }.
% 1.28/1.64 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X, Y ),
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.64 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.64 c_Groups_Oabs__class_Oabs( X, Y ) ), ! Y = c_Groups_Ozero__class_Ozero( X
% 1.28/1.64 ) }.
% 1.28/1.64 { ! class_Groups_Oordered__ab__group__add__abs( X ), Y =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 1.28/1.64 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.28/1.64 c_Groups_Oabs__class_Oabs( X, Y ) = Y }.
% 1.28/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.28/1.64 , c_Groups_Oabs__class_Oabs( X, Z ), Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, c_Groups_Oabs__class_Oabs( X, U ), T ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 1.28/1.64 c_Groups_Oabs__class_Oabs( X, U ) ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 1.28/1.64 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_RealVector_Onorm__class_Onorm( X, Y ), c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_RealDef_Oreal ) ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.64 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.64 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.28/1.64 , T, Z ), c_Rings_Oinverse__class_Odivide( X, T, Y ) ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.28/1.64 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.64 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.28/1.64 , T, Y ), c_Rings_Oinverse__class_Odivide( X, T, Z ) ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.64 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.28/1.64 , T, Y ), Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.64 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.28/1.64 , T, Y ), Z ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.64 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 1.28/1.64 ( X, Z, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Z, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.64 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 1.28/1.64 ( X, Z, Y ) ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.64 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 1.28/1.64 ( X, Z, Y ) ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.64 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.28/1.64 , T, Y ), Z ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.64 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.28/1.64 , T, Y ), Z ), c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.64 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.28/1.64 , T, Y ), Z ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.64 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 1.28/1.64 ( X, Z, Y ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.64 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 1.28/1.64 ( X, Z, Y ) ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.28/1.64 , T, Z ), Y ), alpha35( X, Y, Z, T ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.28/1.64 , T, Z ), Y ), alpha50( X, Y, Z, T ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha35( X, Y, Z
% 1.28/1.64 , T ), ! alpha50( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.64 c_Rings_Oinverse__class_Odivide( X, T, Z ), Y ) }.
% 1.28/1.64 { ! alpha50( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), Z ), alpha59( X, Y, Z, T ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.28/1.64 , alpha50( X, Y, Z, T ) }.
% 1.28/1.64 { ! alpha59( X, Y, Z, T ), alpha50( X, Y, Z, T ) }.
% 1.28/1.64 { ! alpha59( X, Y, Z, T ), alpha69( X, Y, Z, T ) }.
% 1.28/1.64 { ! alpha59( X, Y, Z, T ), alpha10( X, Y, Z ) }.
% 1.28/1.64 { ! alpha69( X, Y, Z, T ), ! alpha10( X, Y, Z ), alpha59( X, Y, Z, T ) }.
% 1.28/1.64 { ! alpha69( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.64 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ) }.
% 1.28/1.64 { c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) ),
% 1.28/1.64 alpha69( X, Y, Z, T ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ), alpha69( X, Y, Z, T )
% 1.28/1.64 }.
% 1.28/1.64 { ! alpha35( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless__eq
% 1.28/1.64 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.28/1.64 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.28/1.64 alpha35( X, Y, Z, T ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha35( X, Y, Z, T ) }.
% 1.28/1.64 { ! alpha10( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.64 , c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.28/1.64 , alpha10( X, Y, Z ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.64 , Y ), alpha10( X, Y, Z ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 1.28/1.64 ( X, Z, Y ) ), alpha36( X, Y, Z, T ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 1.28/1.64 ( X, Z, Y ) ), alpha51( X, Y, Z, T ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha36( X, Y, Z
% 1.28/1.64 , T ), ! alpha51( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( X, T,
% 1.28/1.64 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.28/1.64 { ! alpha51( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), Y ), alpha60( X, Y, Z, T ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 1.28/1.64 , alpha51( X, Y, Z, T ) }.
% 1.28/1.64 { ! alpha60( X, Y, Z, T ), alpha51( X, Y, Z, T ) }.
% 1.28/1.64 { ! alpha60( X, Y, Z, T ), alpha70( X, Y, Z, T ) }.
% 1.28/1.64 { ! alpha60( X, Y, Z, T ), alpha11( X, Y, T ) }.
% 1.28/1.64 { ! alpha70( X, Y, Z, T ), ! alpha11( X, Y, T ), alpha60( X, Y, Z, T ) }.
% 1.28/1.64 { ! alpha70( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.64 , Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.28/1.64 { c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.28/1.64 alpha70( X, Y, Z, T ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( X, Z, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha70( X, Y, Z, T ) }.
% 1.28/1.64 { ! alpha36( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless__eq
% 1.28/1.64 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 1.28/1.64 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.28/1.64 alpha36( X, Y, Z, T ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ), alpha36( X, Y, Z, T )
% 1.28/1.64 }.
% 1.28/1.64 { ! alpha11( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.64 , Z, c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 1.28/1.64 , alpha11( X, Y, Z ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.28/1.64 ) ), alpha11( X, Y, Z ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.28/1.64 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.28/1.64 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.28/1.64 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.28/1.64 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.28/1.64 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.28/1.64 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, U, T ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 1.28/1.64 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.28/1.64 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.64 , U ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, U, T ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 1.28/1.64 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, U, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 1.28/1.64 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.28/1.64 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.28/1.64 ! c_Orderings_Oord__class_Oless__eq( X, Z, T ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.28/1.64 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.28/1.64 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.28/1.64 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.64 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.28/1.64 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 1.28/1.64 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.64 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.28/1.64 ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.28/1.64 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 1.28/1.64 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.64 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.64 ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 1.28/1.64 ) ) }.
% 1.28/1.64 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.28/1.64 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 1.28/1.64 ) ) }.
% 1.28/1.64 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.64 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.64 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.64 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.28/1.64 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.28/1.64 ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.64 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.64 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.64 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 1.28/1.64 ) ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__ring__strict( X ), Z =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.28/1.64 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__ring__strict( X ), Y =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.28/1.64 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 1.28/1.64 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.64 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.28/1.64 c_RealVector_Onorm__class_Onorm( X, Y ) ), ! Y =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.64 { ! class_RealVector_Oreal__normed__vector( X ), Y =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless(
% 1.28/1.64 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.28/1.64 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 1.28/1.64 { ! class_RealVector_Oreal__normed__algebra( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_RealVector_Onorm__class_Onorm( X, Z ), Y ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_RealVector_Onorm__class_Onorm( X, U ), T ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), T ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 1.28/1.64 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_RealVector_Onorm__class_Onorm( X, Z ), Y ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_RealVector_Onorm__class_Onorm( X, U ), T ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, Z, U
% 1.28/1.64 ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, T ) ) }.
% 1.28/1.64 { ! class_Fields_Ofield__inverse__zero( X ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Odivide( X, U
% 1.28/1.64 , T ) ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 1.28/1.64 c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ),
% 1.28/1.64 c_Groups_Oabs__class_Oabs( X, c_Rings_Oinverse__class_Odivide( X, Z, Y )
% 1.28/1.64 ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oabs__class_Oabs( X, Z
% 1.28/1.64 ), c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.64 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ), alpha12( X, Y, Z ), alpha37
% 1.28/1.64 ( X, Y, Z ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha12( X, Y, Z
% 1.28/1.64 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.28/1.64 ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha37( X, Y, Z
% 1.28/1.64 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.28/1.64 ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.28/1.64 { ! alpha37( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.64 { ! alpha37( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.28/1.64 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ) ), alpha37( X, Y, Z ) }.
% 1.28/1.64 { ! alpha12( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.28/1.64 { ! alpha12( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.64 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), Y ), alpha12( X, Y, Z ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.28/1.64 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ), alpha13( X, Y, Z ), alpha38
% 1.28/1.64 ( X, Y, Z ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha13( X, Y, Z
% 1.28/1.64 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 1.28/1.64 ( X, Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha38( X, Y, Z
% 1.28/1.64 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 1.28/1.64 ( X, Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.64 { ! alpha38( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.64 { ! alpha38( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.28/1.64 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( X ), Y ), alpha38( X, Y, Z ) }.
% 1.28/1.64 { ! alpha13( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.28/1.64 { ! alpha13( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.64 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ) ), alpha13( X, Y, Z ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.28/1.64 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 1.28/1.64 ( X, Z, T ), c_Rings_Oinverse__class_Odivide( X, Y, T ) ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.64 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 1.28/1.64 ( X, Y, T ), c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 1.28/1.64 { ! class_Fields_Ofield__inverse__zero( X ), ! T =
% 1.28/1.64 c_Rings_Oinverse__class_Odivide( X, Z, Y ), alpha39( X, Y, Z, T ) }.
% 1.28/1.64 { ! class_Fields_Ofield__inverse__zero( X ), ! T =
% 1.28/1.64 c_Rings_Oinverse__class_Odivide( X, Z, Y ), alpha14( X, Y, T ) }.
% 1.28/1.64 { ! class_Fields_Ofield__inverse__zero( X ), ! alpha39( X, Y, Z, T ), !
% 1.28/1.64 alpha14( X, Y, T ), T = c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 1.28/1.64 { ! alpha39( X, Y, Z, T ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP
% 1.28/1.64 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z }.
% 1.28/1.64 { ! Y = c_Groups_Ozero__class_Ozero( X ), alpha39( X, Y, Z, T ) }.
% 1.28/1.64 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, alpha39(
% 1.28/1.64 X, Y, Z, T ) }.
% 1.28/1.64 { ! alpha14( X, Y, Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.64 { Y = c_Groups_Ozero__class_Ozero( X ), alpha14( X, Y, Z ) }.
% 1.28/1.64 { ! Z = c_Groups_Ozero__class_Ozero( X ), alpha14( X, Y, Z ) }.
% 1.28/1.64 { ! class_Fields_Ofield__inverse__zero( X ), !
% 1.28/1.64 c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y, alpha40( X, Y, Z, T ) }.
% 1.28/1.64 { ! class_Fields_Ofield__inverse__zero( X ), !
% 1.28/1.64 c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y, alpha15( X, Y, Z ) }.
% 1.28/1.64 { ! class_Fields_Ofield__inverse__zero( X ), ! alpha40( X, Y, Z, T ), !
% 1.28/1.64 alpha15( X, Y, Z ), c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y }.
% 1.28/1.64 { ! alpha40( X, Y, Z, T ), Z = c_Groups_Ozero__class_Ozero( X ), T = hAPP(
% 1.28/1.64 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 1.28/1.64 { ! Z = c_Groups_Ozero__class_Ozero( X ), alpha40( X, Y, Z, T ) }.
% 1.28/1.64 { ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), alpha40(
% 1.28/1.64 X, Y, Z, T ) }.
% 1.28/1.64 { ! alpha15( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero( X ), Y =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.64 { Z = c_Groups_Ozero__class_Ozero( X ), alpha15( X, Y, Z ) }.
% 1.28/1.64 { ! Y = c_Groups_Ozero__class_Ozero( X ), alpha15( X, Y, Z ) }.
% 1.28/1.64 { v_cs____ = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 1.28/1.64 tc_Complex_Ocomplex ) ), ! c_Orderings_Oord__class_Oless__eq(
% 1.28/1.64 tc_RealDef_Oreal, skol3, c_RealVector_Onorm__class_Onorm(
% 1.28/1.64 tc_Complex_Ocomplex, X ) ), c_Orderings_Oord__class_Oless__eq(
% 1.28/1.64 tc_RealDef_Oreal, v_da____, c_RealVector_Onorm__class_Onorm(
% 1.28/1.64 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 1.28/1.64 c_Polynomial_OpCons( tc_Complex_Ocomplex, v_aa____, c_Polynomial_OpCons(
% 1.28/1.64 tc_Complex_Ocomplex, v_c____, v_cs____ ) ) ), X ) ) ) }.
% 1.28/1.64 { ! class_Groups_Ozero( X ), c_Polynomial_OpCons( X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.64 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.64 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.64 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.28/1.64 c_Polynomial_OpCons( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.64 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ), X =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.28/1.64 { ! X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.28/1.64 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 1.28/1.64 ) ), c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 1.28/1.64 ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.28/1.64 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 1.28/1.64 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 1.28/1.64 ) ) }.
% 1.28/1.64 { ! class_RealVector_Oreal__normed__field( X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol4( Z, T ) ) }.
% 1.28/1.64 { ! class_RealVector_Oreal__normed__field( X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.64 c_RealVector_Onorm__class_Onorm( X, c_Rings_Oinverse__class_Odivide( X, Z
% 1.28/1.64 , Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.28/1.64 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol4( X, Y ) ) ) }.
% 1.28/1.64 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol5( Z, T ) ) }.
% 1.28/1.64 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.64 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.28/1.64 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol5( X, Y ) ) ) }.
% 1.28/1.64 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol6( Z, T ) ) }.
% 1.28/1.64 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.64 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.28/1.64 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol6( X, Y ) ) ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 1.28/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Z
% 1.28/1.64 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP(
% 1.28/1.64 c_Polynomial_Opoly( X, T ), Y ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 1.28/1.64 ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 1.28/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 1.28/1.64 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 1.28/1.64 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 1.28/1.64 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ), Z = Y }.
% 1.28/1.64 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Z = Y,
% 1.28/1.64 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ) }.
% 1.28/1.64 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 1.28/1.64 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.64 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Y =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.28/1.64 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 1.28/1.64 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 1.28/1.64 X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }
% 1.28/1.64 .
% 1.28/1.64 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 1.28/1.64 X ), Z, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z )
% 1.28/1.64 }.
% 1.28/1.64 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 1.28/1.64 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z
% 1.28/1.64 ), c_Orderings_Oord__class_Oless( tc_fun( T, X ), Z, Y ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.28/1.64 c_Polynomial_OpCons( X, T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus( X, T
% 1.28/1.64 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), hAPP(
% 1.28/1.64 c_Polynomial_Opoly( X, Z ), Y ) ) ) }.
% 1.28/1.64 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 1.28/1.64 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 1.28/1.64 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.64 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 1.28/1.64 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ), Y ) = Y }.
% 1.28/1.64 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.64 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 1.28/1.64 c_Polynomial_OpCons( X, Z, Y ), U = Z }.
% 1.28/1.64 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 1.28/1.64 c_Polynomial_OpCons( X, Z, Y ), T = Y }.
% 1.28/1.64 { ! class_Groups_Ozero( X ), ! U = Z, ! T = Y, c_Polynomial_OpCons( X, U, T
% 1.28/1.64 ) = c_Polynomial_OpCons( X, Z, Y ) }.
% 1.28/1.64 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.28/1.64 c_Groups_Oplus__class_Oplus( X, Y, Y ) = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.64 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.64 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Y )
% 1.28/1.64 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.64 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 1.28/1.64 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 1.28/1.64 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( X, U, Z ), c_Groups_Oplus__class_Oplus(
% 1.28/1.64 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 1.28/1.64 { c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ) ) =
% 1.28/1.64 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, X, Y ) }.
% 1.28/1.64 { v_cs____ = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 1.28/1.64 tc_Complex_Ocomplex ) ), ! c_Orderings_Oord__class_Oless__eq(
% 1.28/1.64 tc_RealDef_Oreal, skol7( X, Y ), c_RealVector_Onorm__class_Onorm(
% 1.28/1.64 tc_Complex_Ocomplex, Z ) ), c_Orderings_Oord__class_Oless__eq(
% 1.28/1.64 tc_RealDef_Oreal, Y, c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex
% 1.28/1.64 , hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_OpCons(
% 1.28/1.64 tc_Complex_Ocomplex, X, v_cs____ ) ), Z ) ) ) }.
% 1.28/1.64 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol8( Y ) ) }.
% 1.28/1.64 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.64 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.28/1.64 c_RealVector_Onorm__class_Onorm( X, Y ) ),
% 1.28/1.64 c_RealVector_Onorm__class_Onorm( X, Z ) ) ), skol8( X ) ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 1.28/1.64 c_Polynomial_OpCons( X, Z, Y ) ), c_Polynomial_Opos__poly( X, Y ),
% 1.28/1.64 alpha16( X, Y, Z ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 1.28/1.64 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__idom( X ), ! alpha16( X, Y, Z ),
% 1.28/1.64 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 1.28/1.64 { ! alpha16( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.64 { ! alpha16( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.28/1.64 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.28/1.64 alpha16( X, Y, Z ) }.
% 1.28/1.64 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol9( Z, T ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.64 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Z ), Y ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.64 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 1.28/1.64 c_Polynomial_Opoly( tc_Complex_Ocomplex, X ), Z ) ), skol9( X, Y ) ) }.
% 1.28/1.64 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ), ! c_Polynomial_Oorder( X, Y, Z ) =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.64 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.64 { ! class_Rings_Oidom( X ), c_Polynomial_Oorder( X, Y, Z ) =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( c_Polynomial_Opoly( X,
% 1.28/1.64 Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.64 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( W, X, Y,
% 1.28/1.64 Z, c_Polynomial_OpCons( X, U, T ) ) = hAPP( hAPP( hAPP( Z, U ), T ),
% 1.28/1.64 c_Polynomial_Opoly__rec( W, X, Y, Z, T ) ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ), hAPP
% 1.28/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y
% 1.28/1.64 ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 1.28/1.64 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 1.28/1.64 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X, hAPP( hAPP
% 1.28/1.64 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) }
% 1.28/1.64 .
% 1.28/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 1.28/1.64 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( T, X, Y,
% 1.28/1.64 Z, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) = Y }.
% 1.28/1.64 { ! class_Groups_Ozero( X ), c_Polynomial_Opoly__rec( W, X, U, T,
% 1.28/1.64 c_Polynomial_OpCons( X, Z, Y ) ) = hAPP( hAPP( hAPP( T, Z ), Y ), c_If( W
% 1.28/1.64 , c_fequal( Y, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) )
% 1.28/1.64 , U, c_Polynomial_Opoly__rec( W, X, U, T, Y ) ) ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 1.28/1.64 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus(
% 1.28/1.64 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, T,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 1.28/1.64 c_Polynomial_Opcompose( X, Z, Y ) ) ) }.
% 1.28/1.64 { ! class_Groups_Ozero( X ), !
% 1.28/1.64 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.64 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ),
% 1.28/1.64 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.28/1.64 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.28/1.64 { ! class_RealVector_Oreal__normed__field( X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol10( Z, T ) ) }.
% 1.28/1.64 { ! class_RealVector_Oreal__normed__field( X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.64 c_RealVector_Onorm__class_Onorm( X, c_Rings_Oinverse__class_Odivide( X, Z
% 1.28/1.64 , Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.28/1.64 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol10( X, Y ) ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.28/1.64 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.28/1.64 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 1.28/1.64 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ), ! Y = X }.
% 1.28/1.64 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X = Y }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 1.28/1.64 { alpha82( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 1.28/1.64 hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 1.28/1.64 { alpha82( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP
% 1.28/1.64 ( X, Y ), Z ) ) }.
% 1.28/1.64 { ! alpha82( X, Y, Z ), alpha85( X, Y, Z ), Z = Y }.
% 1.28/1.64 { ! alpha82( X, Y, Z ), alpha85( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z
% 1.28/1.64 ) ) }.
% 1.28/1.64 { ! alpha85( X, Y, Z ), alpha82( X, Y, Z ) }.
% 1.28/1.64 { ! Z = Y, hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha82( X, Y, Z ) }.
% 1.28/1.64 { ! alpha85( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y )
% 1.28/1.64 }.
% 1.28/1.64 { ! alpha85( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP(
% 1.28/1.64 X, Y ), Z ) ), alpha85( X, Y, Z ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.28/1.64 ( tc_Nat_Onat, Y, Z ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y
% 1.28/1.64 , X ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, X ) =
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.28/1.64 tc_Nat_Onat, Y, T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 1.28/1.64 .
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.28/1.64 tc_Nat_Onat, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 1.28/1.64 .
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.28/1.64 ( tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) )
% 1.28/1.64 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.28/1.64 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }
% 1.28/1.64 .
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.28/1.64 ( tc_Nat_Onat, Y, X ), X ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.28/1.64 ( tc_Nat_Onat, Y, X ), Y ) }.
% 1.28/1.64 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) }.
% 1.28/1.64 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 1.28/1.64 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.28/1.64 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol11( X, Y ) ) }.
% 1.28/1.64 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol12( X, Y ) ) }.
% 1.28/1.64 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, T ),
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), T ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ), X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ), Y = X }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ) }.
% 1.28/1.64 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.28/1.64 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ) }.
% 1.28/1.64 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, X ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.28/1.64 c_Polynomial_Opcompose( X, T, Z ) ), Y ) = hAPP( c_Polynomial_Opoly( X, T
% 1.28/1.64 ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 1.28/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.64 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.28/1.64 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Nat_Onat ), X ) = X }.
% 1.28/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.64 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ) ) = X }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.64 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.28/1.64 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.64 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.64 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 1.28/1.64 tc_Nat_Onat, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.64 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.64 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.64 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.64 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 1.28/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Y = X
% 1.28/1.64 , Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.64 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 1.28/1.64 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 1.28/1.64 .
% 1.28/1.64 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 1.28/1.64 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 1.28/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = X
% 1.28/1.64 , Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.64 { ! Z = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 1.28/1.64 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }
% 1.28/1.64 .
% 1.28/1.64 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 1.28/1.64 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = Y, X =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.64 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Nat_Onat ), X ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 1.28/1.64 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP
% 1.28/1.64 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 1.28/1.64 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP
% 1.28/1.64 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X
% 1.28/1.64 ) }.
% 1.28/1.64 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 1.28/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 1.28/1.64 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 1.28/1.64 ) }.
% 1.28/1.64 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 1.28/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 1.28/1.64 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Nat_Onat ), Y ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 1.28/1.64 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Nat_Onat ), Z ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 1.28/1.64 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 1.28/1.64 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 1.28/1.64 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.28/1.64 Y ), X ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 1.28/1.64 tc_Nat_Onat, Y, X ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 1.28/1.64 tc_Nat_Onat, Y, X ) ) }.
% 1.28/1.64 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Nat_Onat ), X ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 1.28/1.64 .
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.28/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP
% 1.28/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z
% 1.28/1.64 , Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 1.28/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP(
% 1.28/1.64 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 1.28/1.64 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.28/1.64 tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.28/1.64 tc_Nat_Onat ), X ), Y ), Z = Y }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! Z = Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.64 ( tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.28/1.64 tc_Nat_Onat ), X ), Y ) }.
% 1.28/1.64 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol13( Y ) ) }.
% 1.28/1.64 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.64 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.28/1.64 c_RealVector_Onorm__class_Onorm( X, Y ) ),
% 1.28/1.64 c_RealVector_Onorm__class_Onorm( X, Z ) ) ), skol13( X ) ) ) }.
% 1.28/1.64 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ), Z = X }.
% 1.28/1.64 { ! Z = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 1.28/1.64 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ), Y = X }.
% 1.28/1.64 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) }.
% 1.28/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ), X ) =
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.28/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 1.28/1.64 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.28/1.64 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.28/1.64 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.28/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.28/1.64 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, c_Groups_Oplus__class_Oplus
% 1.28/1.64 ( tc_Nat_Onat, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.28/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP
% 1.28/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 1.28/1.64 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 1.28/1.64 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), T ), Z ),
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), X ) ) =
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus
% 1.28/1.64 ( tc_Nat_Onat, T, Y ) ), Z ), X ) }.
% 1.28/1.64 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 1.28/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Z =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 1.28/1.64 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 1.28/1.64 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 1.28/1.64 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 1.28/1.64 .
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.28/1.64 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol14( Z, T ) ) }.
% 1.28/1.64 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.64 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.28/1.64 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol14( X, Y ) ) ) }.
% 1.28/1.64 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol15( Z, T ) ) }.
% 1.28/1.64 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.64 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.28/1.64 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol15( X, Y ) ) ) }.
% 1.28/1.64 { ! class_RealVector_Oreal__normed__field( X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.64 c_RealVector_Onorm__class_Onorm( X, c_Rings_Oinverse__class_Odivide( X, Z
% 1.28/1.64 , Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.28/1.64 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol16( X, Y ) ) ) }.
% 1.28/1.64 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.64 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.28/1.64 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol17( X, Y ) ) ) }.
% 1.28/1.64 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.64 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.28/1.64 c_RealVector_Onorm__class_Onorm( X, Y ) ),
% 1.28/1.64 c_RealVector_Onorm__class_Onorm( X, Z ) ) ), skol18( X ) ) ) }.
% 1.28/1.64 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.64 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.28/1.64 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol19( X, Y ) ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__semiring__1__strict( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, T, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), U ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), W
% 1.28/1.64 ), ! c_Groups_Oplus__class_Oplus( X, U, W ) = c_Groups_Oone__class_Oone
% 1.28/1.64 ( X ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X,
% 1.28/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), W ), T ) ), Y ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field( X ), c_Orderings_Oord__class_Oless( X
% 1.28/1.64 , c_Groups_Ozero__class_Ozero( X ), skol20( X, T, U ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oplus__class_Oplus( X,
% 1.28/1.64 Y, skol20( X, Y, Z ) ) ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }
% 1.28/1.64 .
% 1.28/1.64 { ! class_Groups_Oone( X ), ! c_Groups_Oone__class_Oone( X ) = Y, Y =
% 1.28/1.64 c_Groups_Oone__class_Oone( X ) }.
% 1.28/1.64 { ! class_Groups_Oone( X ), ! Y = c_Groups_Oone__class_Oone( X ),
% 1.28/1.64 c_Groups_Oone__class_Oone( X ) = Y }.
% 1.28/1.64 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 1.28/1.64 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oone__class_Oone( X ) ) =
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oone__class_Oone(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ) = c_Polynomial_OpCons( X,
% 1.28/1.64 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ) ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 1.28/1.64 c_Groups_Oone__class_Oone( X ) }.
% 1.28/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) = X }.
% 1.28/1.64 { ! c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) =
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X,
% 1.28/1.64 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Oone__class_Oone( X ) }.
% 1.28/1.64 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X, Y
% 1.28/1.64 , c_Groups_Oone__class_Oone( X ) ) = Y }.
% 1.28/1.64 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.28/1.64 = Y }.
% 1.28/1.64 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.28/1.64 = Y }.
% 1.28/1.64 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.28/1.64 = Y }.
% 1.28/1.64 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.28/1.64 = Y }.
% 1.28/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.28/1.64 = Y }.
% 1.28/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.28/1.64 = Y }.
% 1.28/1.64 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 1.28/1.64 c_Groups_Oone__class_Oone( X ) }.
% 1.28/1.64 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Oone__class_Oone( X ) =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) = X }.
% 1.28/1.64 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), Y =
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.28/1.64 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X =
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.28/1.64 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Groups_Oone__class_Oone(
% 1.28/1.64 tc_Nat_Onat ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 1.28/1.64 , Y ), X ) }.
% 1.28/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 1.28/1.64 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Oone__class_Oone(
% 1.28/1.64 tc_Nat_Onat ) }.
% 1.28/1.64 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X = c_Groups_Oone__class_Oone(
% 1.28/1.64 tc_Nat_Onat ) }.
% 1.28/1.64 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__semidom( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__semidom( X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.64 c_Groups_Oone__class_Oone( X ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero( X ) ) }
% 1.28/1.64 .
% 1.28/1.64 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 1.28/1.64 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oone__class_Oone( X ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, c_Groups_Oone__class_Oone( X ), Z ), c_Orderings_Oord__class_Oless(
% 1.28/1.64 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 1.28/1.64 , Y, c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) )
% 1.28/1.64 ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = hAPP(
% 1.28/1.64 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X
% 1.28/1.64 , Z, c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 1.28/1.64 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP
% 1.28/1.64 ( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 1.28/1.64 c_Groups_Oone__class_Oone( X ) ) ), Z ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 1.28/1.64 , Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.28/1.64 c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 1.28/1.64 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 1.28/1.64 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.64 , ! c_Rings_Oinverse__class_Odivide( X, Z, Y ) =
% 1.28/1.64 c_Groups_Oone__class_Oone( X ), Z = Y }.
% 1.28/1.64 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.64 , ! Z = Y, c_Rings_Oinverse__class_Odivide( X, Z, Y ) =
% 1.28/1.64 c_Groups_Oone__class_Oone( X ) }.
% 1.28/1.64 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.64 , c_Rings_Oinverse__class_Odivide( X, Y, Y ) = c_Groups_Oone__class_Oone
% 1.28/1.64 ( X ) }.
% 1.28/1.64 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Y =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X, Y,
% 1.28/1.64 Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.64 { ! class_Rings_Odivision__ring__inverse__zero( X ), Y =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X, Y,
% 1.28/1.64 Y ) = c_Groups_Oone__class_Oone( X ) }.
% 1.28/1.64 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X )
% 1.28/1.64 , X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 1.28/1.64 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.28/1.64 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 1.28/1.64 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 1.28/1.64 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.28/1.64 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 1.28/1.64 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 1.28/1.64 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.64 c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ) ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.64 X, Z, Y ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.64 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 1.28/1.64 ), c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 1.28/1.64 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.64 X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z,
% 1.28/1.64 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 1.28/1.64 ), c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 1.28/1.64 c_Groups_Oone__class_Oone( X ) ) ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs
% 1.28/1.64 ( tc_RealDef_Oreal, X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 1.28/1.64 , X ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__semiring__1( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, T, Y ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 1.28/1.64 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.28/1.64 X ), W ), ! c_Groups_Oplus__class_Oplus( X, U, W ) =
% 1.28/1.64 c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.64 ( X ), U ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), T )
% 1.28/1.64 ), Y ) }.
% 1.28/1.64 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oone__class_Oone
% 1.28/1.64 ( tc_RealDef_Oreal ), c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) )
% 1.28/1.64 ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.64 skol21( X, T, U ) ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, skol21( X, T, U ),
% 1.28/1.64 c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.28/1.64 , Y ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), skol21( X, Y, Z ) ), Z ), Y ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.28/1.64 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 1.28/1.64 hAPP( X, Y ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol22( Z, Y
% 1.28/1.64 ), Y ) }.
% 1.28/1.64 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 1.28/1.64 hAPP( X, Y ) ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.28/1.64 skol22( X, Y ) ), ! hBOOL( hAPP( X, Z ) ) }.
% 1.28/1.64 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 1.28/1.64 hAPP( X, Y ) ), hBOOL( hAPP( X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat
% 1.28/1.64 , skol22( X, Y ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), c_NthRoot_Oroot(
% 1.28/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z ) =
% 1.28/1.64 c_NthRoot_Oroot( X, c_NthRoot_Oroot( Y, Z ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 1.28/1.64 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), c_NthRoot_Oroot( X
% 1.28/1.64 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Z )
% 1.28/1.64 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.28/1.64 c_NthRoot_Oroot( X, Y ) ), c_NthRoot_Oroot( X, Z ) ) }.
% 1.28/1.64 { c_NthRoot_Oroot( X, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! c_NthRoot_Oroot( X, Z ) = c_NthRoot_Oroot( X, Y )
% 1.28/1.64 , Z = Y }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! Z = Y, c_NthRoot_Oroot( X, Z ) = c_NthRoot_Oroot
% 1.28/1.64 ( X, Y ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), c_NthRoot_Oroot( X,
% 1.28/1.64 c_NthRoot_Oroot( Y, Z ) ) = c_NthRoot_Oroot( Y, c_NthRoot_Oroot( X, Z ) )
% 1.28/1.64 }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! c_NthRoot_Oroot( X, Y ) =
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), Y =
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_RealDef_Oreal )
% 1.28/1.64 , c_NthRoot_Oroot( X, Y ) = c_Groups_Oone__class_Oone( tc_RealDef_Oreal )
% 1.28/1.64 }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), c_NthRoot_Oroot( X, c_Groups_Oone__class_Oone(
% 1.28/1.64 tc_RealDef_Oreal ) ) = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 1.28/1.64 tc_RealDef_Oreal, c_NthRoot_Oroot( X, Z ), c_NthRoot_Oroot( X, Y ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 1.28/1.64 tc_RealDef_Oreal, Z, Y ), c_Orderings_Oord__class_Oless__eq(
% 1.28/1.64 tc_RealDef_Oreal, c_NthRoot_Oroot( X, Z ), c_NthRoot_Oroot( X, Y ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 1.28/1.64 tc_RealDef_Oreal, Z, Y ), c_Orderings_Oord__class_Oless__eq(
% 1.28/1.64 tc_RealDef_Oreal, c_NthRoot_Oroot( X, Z ), c_NthRoot_Oroot( X, Y ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 1.28/1.64 tc_RealDef_Oreal, c_Groups_Oone__class_Oone( tc_RealDef_Oreal ),
% 1.28/1.64 c_NthRoot_Oroot( X, Y ) ), c_Orderings_Oord__class_Oless__eq(
% 1.28/1.64 tc_RealDef_Oreal, c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), Y ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 1.28/1.64 tc_RealDef_Oreal, c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), Y ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_NthRoot_Oroot( X, Y ) )
% 1.28/1.64 }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 1.28/1.64 tc_RealDef_Oreal, c_NthRoot_Oroot( X, Y ), c_Groups_Oone__class_Oone(
% 1.28/1.64 tc_RealDef_Oreal ) ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal
% 1.28/1.64 , Y, c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 1.28/1.64 tc_RealDef_Oreal, Y, c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Oroot( X,
% 1.28/1.64 Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y
% 1.28/1.64 ), ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), Z ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Oroot( Y,
% 1.28/1.64 Z ), c_NthRoot_Oroot( X, Z ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! c_NthRoot_Oroot( X, Y ) =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal
% 1.28/1.64 ), c_NthRoot_Oroot( X, Y ) = c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_RealDef_Oreal ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_NthRoot_Oroot( X, Z ), c_NthRoot_Oroot( X, Y ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 Z, Y ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Oroot
% 1.28/1.64 ( X, Z ), c_NthRoot_Oroot( X, Y ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 Z, Y ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Oroot
% 1.28/1.64 ( X, Z ), c_NthRoot_Oroot( X, Y ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_NthRoot_Oroot( X, Y ) )
% 1.28/1.64 , c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), Y ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), Y ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_NthRoot_Oroot( X, Y ) )
% 1.28/1.64 }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_NthRoot_Oroot( X, Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 1.28/1.64 , c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y,
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 Y, c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Oroot( X, Y )
% 1.28/1.64 , c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y
% 1.28/1.64 ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), Z ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Oroot( Y, Z )
% 1.28/1.64 , c_NthRoot_Oroot( X, Z ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), c_NthRoot_Oroot( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), Y ) ) = hAPP(
% 1.28/1.64 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_NthRoot_Oroot
% 1.28/1.64 ( X, Z ) ), c_NthRoot_Oroot( X, Y ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), c_NthRoot_Oroot( hAPP(
% 1.28/1.64 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z ) =
% 1.28/1.64 c_NthRoot_Oroot( X, c_NthRoot_Oroot( Y, Z ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), c_NthRoot_Oroot( X, c_Rings_Oinverse__class_Odivide
% 1.28/1.64 ( tc_RealDef_Oreal, Z, Y ) ) = c_Rings_Oinverse__class_Odivide(
% 1.28/1.64 tc_RealDef_Oreal, c_NthRoot_Oroot( X, Z ), c_NthRoot_Oroot( X, Y ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), c_NthRoot_Oroot( X, c_Groups_Oabs__class_Oabs(
% 1.28/1.64 tc_RealDef_Oreal, Y ) ) = c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 1.28/1.64 c_NthRoot_Oroot( X, Y ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 1.28/1.64 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Oroot( X, Y )
% 1.28/1.64 ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 1.28/1.64 tc_RealDef_Oreal, c_NthRoot_Oroot( X, Y ), c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_RealDef_Oreal ) ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal
% 1.28/1.64 , Y, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 1.28/1.64 tc_RealDef_Oreal, Y, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Oroot( X,
% 1.28/1.64 Y ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 1.28/1.64 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.28/1.64 c_NthRoot_Oroot( X, Y ) ), c_Orderings_Oord__class_Oless__eq(
% 1.28/1.64 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ) }
% 1.28/1.64 .
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 1.28/1.64 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Oroot( X, Y )
% 1.28/1.64 ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y
% 1.28/1.64 ), ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z,
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Oroot( X,
% 1.28/1.64 Z ), c_NthRoot_Oroot( Y, Z ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Oroot( X, Y )
% 1.28/1.64 ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Oroot( X, Y )
% 1.28/1.64 ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_NthRoot_Oroot( X, Y ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal )
% 1.28/1.64 ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 Y, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Oroot( X, Y )
% 1.28/1.64 , c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Oroot( X, Y )
% 1.28/1.64 ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y
% 1.28/1.64 ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z,
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Oroot( X, Z )
% 1.28/1.64 , c_NthRoot_Oroot( Y, Z ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 1.28/1.64 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, Z ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Oroot( X, Y )
% 1.28/1.64 , c_NthRoot_Oroot( X, Z ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Oroot( X, Y )
% 1.28/1.64 ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.28/1.64 c_RComplete_Onatceiling( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X
% 1.28/1.64 , c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) =
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatceiling( X ),
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.28/1.64 c_RComplete_Onatfloor( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) =
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatfloor( X ),
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), c_NthRoot_Oroot( X, Y )
% 1.28/1.64 ), X ) = Y }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 1.28/1.64 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 1.28/1.64 hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Y ), X ) =
% 1.28/1.64 Z, c_NthRoot_Oroot( X, Z ) = Y }.
% 1.28/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 1.28/1.64 tc_Nat_Onat ) ) = Y }.
% 1.28/1.64 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.64 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), Z ), Y ) ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 1.28/1.64 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) ) }.
% 1.28/1.64 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 1.28/1.64 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 1.28/1.64 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 1.28/1.64 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), T ), Z
% 1.28/1.64 ) ), Y ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), hAPP(
% 1.28/1.64 c_Polynomial_Opoly( X, T ), Y ) ), Z ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.28/1.64 { c_RComplete_Onatfloor( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) )
% 1.28/1.64 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.64 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) )
% 1.28/1.64 }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatfloor( Y
% 1.28/1.64 ), c_RComplete_Onatfloor( X ) ) }.
% 1.28/1.64 { c_RComplete_Onatfloor( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) =
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.28/1.64 { c_RComplete_Onatceiling( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal )
% 1.28/1.64 ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.64 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_RComplete_Onatceiling( X )
% 1.28/1.64 ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 1.28/1.64 Y ), c_RComplete_Onatceiling( X ) ) }.
% 1.28/1.64 { c_RComplete_Onatceiling( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 1.28/1.64 = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( X ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), T ), Y ) ) = hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 1.28/1.64 tc_Nat_Onat, Z, Y ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_RComplete_Onatfloor
% 1.28/1.64 ( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 1.28/1.64 c_RComplete_Onatceiling( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.28/1.64 }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), c_NthRoot_Oroot( X, hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Z ), Y ) ) = hAPP( hAPP
% 1.28/1.64 ( c_Power_Opower__class_Opower( tc_RealDef_Oreal ), c_NthRoot_Oroot( X, Z
% 1.28/1.64 ) ), Y ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Groups_Oone__class_Oone
% 1.28/1.64 ( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling
% 1.28/1.64 ( X ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 1.28/1.64 X ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_RComplete_Onatfloor( X )
% 1.28/1.64 ), c_RComplete_Onatfloor( Y ) ), c_RComplete_Onatfloor( hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 1.28/1.64 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 1.28/1.64 c_NthRoot_Oroot( X, hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.28/1.64 tc_RealDef_Oreal ), Y ), X ) ) = Y }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 1.28/1.64 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 1.28/1.64 hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 1.28/1.64 c_NthRoot_Oroot( X, Y ) ), X ) = Y }.
% 1.28/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), Z ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.64 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), T ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 1.28/1.64 hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Int_Oint ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint )
% 1.28/1.64 , c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) ), X ) ), ! Y =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.64 { Y = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Int_Oint ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ),
% 1.28/1.64 c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) ), X ) ) }.
% 1.28/1.64 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Int_Oint ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ),
% 1.28/1.64 c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) ), X ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 1.28/1.64 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), X =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 1.28/1.64 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 1.28/1.64 ), X ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 1.28/1.64 ( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Z ), hAPP( hAPP
% 1.28/1.64 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 1.28/1.64 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ),
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) = hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ) }.
% 1.28/1.64 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 1.28/1.64 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.28/1.64 { ! class_Rings_Oring__1__no__zero__divisors( X ), Y =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( X ) }.
% 1.28/1.64 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.28/1.64 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.28/1.64 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.28/1.64 = c_Groups_Oone__class_Oone( X ) }.
% 1.28/1.64 { ! class_Fields_Ofield__inverse__zero( X ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide( X, T
% 1.28/1.64 , Z ) ), Y ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, hAPP
% 1.28/1.64 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), c_Groups_Oabs__class_Oabs( X, Z ) ), Y
% 1.28/1.64 ) }.
% 1.28/1.64 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) }.
% 1.28/1.64 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 1.28/1.64 tc_Nat_Onat ) ) = Y }.
% 1.28/1.64 { ! class_Rings_Olinordered__semidom( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.64 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.28/1.64 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__semidom( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.28/1.64 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__semidom( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 1.28/1.64 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 1.28/1.64 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.28/1.64 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.28/1.64 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.28/1.64 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 1.28/1.64 .
% 1.28/1.64 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.28/1.64 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.28/1.64 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Nat_Onat ) }.
% 1.28/1.64 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.28/1.64 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.28/1.64 , ! Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y )
% 1.28/1.64 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), Y ), Z ), T = Z }.
% 1.28/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! T = Z, hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), Y ), Z ) }.
% 1.28/1.64 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP(
% 1.28/1.64 hAPP( c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide
% 1.28/1.64 ( X, T, Y ) ), Z ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.28/1.64 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 1.28/1.64 , Y ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.28/1.64 c_Groups_Oone__class_Oone( X ) }.
% 1.28/1.64 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 1.28/1.64 tc_Nat_Onat, Z, Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.28/1.64 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 1.28/1.64 { ! class_Fields_Ofield__inverse__zero( X ),
% 1.28/1.64 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oone__class_Oone( X ), hAPP
% 1.28/1.64 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide( X,
% 1.28/1.64 c_Groups_Oone__class_Oone( X ), Z ) ), Y ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP
% 1.28/1.64 ( c_Power_Opower__class_Opower( X ), Y ), T ) ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.64 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 1.28/1.64 X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 1.28/1.64 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.28/1.64 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), ! Y =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.28/1.64 ) = c_Groups_Oone__class_Oone( X ) }.
% 1.28/1.64 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), Y =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.28/1.64 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__idom( X ), c_Orderings_Oord__class_Oless__eq(
% 1.28/1.64 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), c_Groups_Oabs__class_Oabs( X, Z ) ), Y
% 1.28/1.64 ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.28/1.64 c_Groups_Oone__class_Oone( X ), T ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.64 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 1.28/1.64 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 1.28/1.64 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( tc_Nat_Onat, T, Z ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__semidom( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), T )
% 1.28/1.64 , c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), Y ), Z ) ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 1.28/1.64 , T, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.64 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), T ), Z ) = hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), Y ), Z ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.28/1.64 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.28/1.64 X ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ), T = Y }.
% 1.28/1.64 { ! class_Rings_Olinordered__semidom( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.28/1.64 ), ! c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oone__class_Oone
% 1.28/1.64 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 1.28/1.64 { X = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), Y =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Orderings_Oord__class_Oless
% 1.28/1.64 ( tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex
% 1.28/1.64 , c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex,
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), X ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), skol23( X, Y ) ), Y
% 1.28/1.64 ) ) ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 1.28/1.64 { ! class_Power_Opower( X ), c_Power_Opower__class_Opower( X ) =
% 1.28/1.64 c_Power_Opower_Opower( X, c_Groups_Oone__class_Oone( X ),
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.28/1.64 tc_Nat_Onat, Y ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 1.28/1.64 tc_RealDef_Oreal, X, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 1.28/1.64 c_RealDef_Oreal( tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone(
% 1.28/1.64 tc_RealDef_Oreal ) ) ), c_RComplete_Onatceiling( X ) =
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone(
% 1.28/1.64 tc_Nat_Onat ) ) }.
% 1.28/1.64 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.28/1.64 tc_Nat_Onat, X ) ) }.
% 1.28/1.64 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( tc_Int_Oint ), c_Groups_Oabs__class_Oabs(
% 1.28/1.64 tc_Int_Oint, Y ) ), X ) ) }.
% 1.28/1.64 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 1.28/1.64 c_RealDef_Oreal( tc_Nat_Onat, Y ) ), X ) = c_RealDef_Oreal( tc_Nat_Onat,
% 1.28/1.64 hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 1.28/1.64 { c_RealDef_Oreal( tc_Nat_Onat, hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.28/1.64 tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.28/1.64 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ), X ) }.
% 1.28/1.64 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Int_Oint ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Int_Oint ), X ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oabs__class_Oabs(
% 1.28/1.64 tc_Int_Oint, X ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.28/1.64 { ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oabs__class_Oabs(
% 1.28/1.64 tc_Int_Oint, X ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 1.28/1.64 { ! c_Groups_Ozero__class_Ozero( tc_Int_Oint ) = c_Groups_Oone__class_Oone
% 1.28/1.64 ( tc_Int_Oint ) }.
% 1.28/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) = X }.
% 1.28/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = X }.
% 1.28/1.64 { ! c_Groups_Oabs__class_Oabs( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) =
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_Int_Oint ), c_Groups_Oabs__class_Oabs(
% 1.28/1.64 tc_Int_Oint, X ) = c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.28/1.64 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.28/1.64 tc_Int_Oint, c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ) =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.28/1.64 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y
% 1.28/1.64 = X }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.28/1.64 tc_Int_Oint ) ) ) }.
% 1.28/1.64 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.28/1.64 tc_Int_Oint ) ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 1.28/1.64 tc_Int_Oint ) ), X ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.28/1.64 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), X =
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.28/1.64 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), Y =
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Int_Oint ), X ), ! X = c_Groups_Oone__class_Oone( tc_Int_Oint ), ! Y
% 1.28/1.64 = c_Groups_Oone__class_Oone( tc_Int_Oint ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Int_Oint ), c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 1.28/1.64 ( tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.28/1.64 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 1.28/1.64 tc_Int_Oint ) ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X )
% 1.28/1.64 }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 1.28/1.64 tc_Int_Oint ) ), X ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.28/1.64 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X )
% 1.28/1.64 }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.28/1.64 tc_Int_Oint ) ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), ! Y = X }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), Y = X,
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 1.28/1.64 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y = X,
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 1.28/1.64 { ! c_RealDef_Oreal( tc_Nat_Onat, Y ) = c_RealDef_Oreal( tc_Nat_Onat, X ),
% 1.28/1.64 Y = X }.
% 1.28/1.64 { ! Y = X, c_RealDef_Oreal( tc_Nat_Onat, Y ) = c_RealDef_Oreal( tc_Nat_Onat
% 1.28/1.64 , X ) }.
% 1.28/1.64 { c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, c_RealDef_Oreal( tc_Nat_Onat
% 1.28/1.64 , X ) ) = c_RealDef_Oreal( tc_Nat_Onat, X ) }.
% 1.28/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) = hAPP
% 1.28/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) }.
% 1.28/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) =
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 1.28/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP(
% 1.28/1.64 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.28/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ), X ) =
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.28/1.64 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Int_Oint ) ) = X }.
% 1.28/1.64 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Int_Oint ), X ) = X }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.28/1.64 tc_Int_Oint, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 1.28/1.64 .
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Z ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.28/1.64 tc_Int_Oint, Y, T ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 1.28/1.64 .
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 1.28/1.64 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP
% 1.28/1.64 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 1.28/1.64 { c_RComplete_Onatceiling( c_RealDef_Oreal( tc_Nat_Onat, X ) ) = X }.
% 1.28/1.64 { c_RComplete_Onatfloor( c_RealDef_Oreal( tc_Nat_Onat, X ) ) = X }.
% 1.28/1.64 { ! c_RealDef_Oreal( tc_Nat_Onat, X ) = c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_RealDef_Oreal ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.64 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_RealDef_Oreal(
% 1.28/1.64 tc_Nat_Onat, X ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.28/1.64 { c_RealDef_Oreal( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.28/1.64 ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.28/1.64 tc_Nat_Onat, X ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.28/1.64 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.28/1.64 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.28/1.64 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.28/1.64 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 1.28/1.64 { c_RealDef_Oreal( tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.28/1.64 tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.28/1.64 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ), c_RealDef_Oreal
% 1.28/1.64 ( tc_Nat_Onat, X ) ) }.
% 1.28/1.64 { c_RealDef_Oreal( tc_Nat_Onat, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y
% 1.28/1.64 , X ) ) = c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal
% 1.28/1.64 ( tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 1.28/1.64 { c_RealDef_Oreal( tc_Nat_Onat, c_Groups_Oone__class_Oone( tc_Nat_Onat ) )
% 1.28/1.64 = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 1.28/1.64 { ! X = c_RealDef_Oreal( tc_Nat_Onat, c_RComplete_Onatfloor( X ) ),
% 1.28/1.64 c_RComplete_Onatfloor( hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.28/1.64 tc_RealDef_Oreal ), X ), Y ) ) = hAPP( hAPP( c_Power_Opower__class_Opower
% 1.28/1.64 ( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ), Y ) }.
% 1.28/1.64 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 1.28/1.64 tc_Nat_Onat, c_RComplete_Onatceiling( X ) ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.28/1.64 tc_Nat_Onat, X ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.64 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.28/1.64 tc_Nat_Onat, X ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.28/1.64 tc_Nat_Onat, c_RComplete_Onatfloor( X ) ), X ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.28/1.64 tc_Nat_Onat, Y ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 1.28/1.64 , c_RComplete_Onatfloor( X ) ) }.
% 1.28/1.64 { hAPP( hAPP( c_Power_Opower_Opower( T, Z, Y ), X ),
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = Z }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, c_RealDef_Oreal
% 1.28/1.64 ( tc_Nat_Onat, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.28/1.64 c_RComplete_Onatceiling( Y ), X ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.28/1.64 tc_Nat_Onat, X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.28/1.64 tc_Nat_Onat, X ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.28/1.64 tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 1.28/1.64 c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.28/1.64 tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 1.28/1.64 c_RealDef_Oreal( tc_Nat_Onat, X ) ), c_Orderings_Oord__class_Oless(
% 1.28/1.64 tc_Nat_Onat, Y, X ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.28/1.64 tc_Nat_Onat, Y ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 1.28/1.64 c_RealDef_Oreal( tc_Nat_Onat, X ), c_Groups_Oone__class_Oone(
% 1.28/1.64 tc_RealDef_Oreal ) ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.28/1.64 tc_Nat_Onat, Y ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 1.28/1.64 c_RealDef_Oreal( tc_Nat_Onat, X ), c_Groups_Oone__class_Oone(
% 1.28/1.64 tc_RealDef_Oreal ) ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 1.28/1.64 , X ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_RComplete_Onatfloor
% 1.28/1.64 ( X ) ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.64 c_RealDef_Oreal( tc_Nat_Onat, Y ), X ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.28/1.64 tc_Nat_Onat, Y ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 1.28/1.64 , c_RComplete_Onatfloor( X ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 1.28/1.64 X ), Y ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 1.28/1.64 c_RealDef_Oreal( tc_Nat_Onat, Y ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 1.28/1.64 tc_Nat_Onat, Y ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.28/1.64 c_RComplete_Onatceiling( X ), Y ) }.
% 1.28/1.64 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.28/1.64 tc_Nat_Onat, c_RComplete_Onatfloor( X ) ), c_Groups_Oone__class_Oone(
% 1.28/1.64 tc_RealDef_Oreal ) ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 1.28/1.64 tc_Nat_Onat, Y ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.28/1.64 c_RComplete_Onatfloor( X ), Y ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.28/1.64 c_RComplete_Onatfloor( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 1.28/1.64 c_RealDef_Oreal( tc_Nat_Onat, Y ) ) ) = c_Groups_Oplus__class_Oplus(
% 1.28/1.64 tc_Nat_Onat, c_RComplete_Onatfloor( X ), Y ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatfloor( Y ),
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, c_RealDef_Oreal(
% 1.28/1.64 tc_Nat_Onat, X ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.28/1.64 tc_Nat_Onat, Y ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal
% 1.28/1.64 , X, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.28/1.64 tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ),
% 1.28/1.64 c_RComplete_Onatfloor( X ) = Y }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.28/1.64 c_RComplete_Onatceiling( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X
% 1.28/1.64 , c_RealDef_Oreal( tc_Nat_Onat, Y ) ) ) = c_Groups_Oplus__class_Oplus(
% 1.28/1.64 tc_Nat_Onat, c_RComplete_Onatceiling( X ), Y ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.28/1.64 tc_Nat_Onat, Y ) ), X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 1.28/1.64 , hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ), Y ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 1.28/1.64 , Y ), X ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Nat_Onat ), Y ) }.
% 1.28/1.64 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 1.28/1.64 ), X ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 1.28/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oone__class_Oone
% 1.28/1.64 ( tc_Int_Oint ), Y ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ),
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 1.28/1.64 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.28/1.64 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 1.28/1.64 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus
% 1.28/1.64 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 1.28/1.64 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) =
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ), Y = X }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Z ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, Z ) }.
% 1.28/1.64 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ) }.
% 1.28/1.64 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, X ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 1.28/1.64 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 1.28/1.64 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 1.28/1.64 ( tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.28/1.64 Z ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, U ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, U ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Y ) }.
% 1.28/1.64 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 1.28/1.64 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 1.28/1.64 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 1.28/1.64 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, U, Y ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, Z ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, T ) }.
% 1.28/1.64 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.28/1.64 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 1.28/1.64 ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, T, W ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 1.28/1.64 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, U ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 1.28/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ),
% 1.28/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 1.28/1.65 tc_Int_Oint, X, Y ) ) }.
% 1.28/1.65 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Ozero__class_Ozero(
% 1.28/1.65 tc_Int_Oint ) ) }.
% 1.28/1.65 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 1.28/1.65 tc_Int_Oint ) ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.65 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.28/1.65 tc_Nat_Onat ), Y ), c_RComplete_Onatfloor(
% 1.28/1.65 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 1.28/1.65 tc_Nat_Onat, Y ) ) ) = c_Divides_Odiv__class_Odiv( tc_Nat_Onat,
% 1.28/1.65 c_RComplete_Onatfloor( X ), Y ) }.
% 1.28/1.65 { ! class_Orderings_Oorder( X ), ! c_SEQ_Odecseq( X, Y ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, T ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, T ), hAPP( Y, Z ) ) }.
% 1.28/1.65 { ! class_Orderings_Oorder( X ), c_Orderings_Oord__class_Oless__eq(
% 1.28/1.65 tc_Nat_Onat, skol24( X, Y ), skol52( X, Y ) ), c_SEQ_Odecseq( X, Y ) }.
% 1.28/1.65 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.65 hAPP( Y, skol52( X, Y ) ), hAPP( Y, skol24( X, Y ) ) ), c_SEQ_Odecseq( X
% 1.28/1.65 , Y ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 1.28/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol25( Z, T ) ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), skol25( X, Y ) ), X ) =
% 1.28/1.65 Y }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), ! hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Z ), X ) = Y, Z =
% 1.28/1.65 skol25( X, Y ) }.
% 1.28/1.65 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.28/1.65 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.65 { Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.28/1.65 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) =
% 1.28/1.65 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.28/1.65 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, Z ),
% 1.28/1.65 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, X, Z ) ) }.
% 1.28/1.65 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.28/1.65 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ), Y ) }.
% 1.28/1.65 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) =
% 1.28/1.65 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 1.28/1.65 tc_Nat_Onat, Z, Y ), X ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.28/1.65 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.65 }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X, Y,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X, Y,
% 1.28/1.65 c_Groups_Oone__class_Oone( X ) ) = Y }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.65 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) =
% 1.28/1.65 c_Divides_Odiv__class_Odiv( X, T, Z ) }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.65 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.28/1.65 c_Divides_Odiv__class_Odiv( X, T, Z ) }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.65 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) = Z }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.65 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = Z }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), ! T = c_Groups_Ozero__class_Ozero( X
% 1.28/1.65 ), c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), T = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.65 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.28/1.65 c_Divides_Odiv__class_Odiv( X, Z, Y ) }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.65 , c_Divides_Odiv__class_Odiv( X, Y, Y ) = c_Groups_Oone__class_Oone( X )
% 1.28/1.65 }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X
% 1.28/1.65 , Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.28/1.65 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, Y ),
% 1.28/1.65 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, X ) ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 1.28/1.65 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ) = Y }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 1.28/1.65 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ) = Y }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 1.28/1.65 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) =
% 1.28/1.65 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, Y ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 1.28/1.65 tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 1.28/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 1.28/1.65 tc_Nat_Onat, Y, X ), Y ) }.
% 1.28/1.65 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.28/1.65 tc_Nat_Onat, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ),
% 1.28/1.65 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.28/1.65 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) ) }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.65 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, T, hAPP
% 1.28/1.65 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) =
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, Z, c_Divides_Odiv__class_Odiv( X, T, Y )
% 1.28/1.65 ) }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.65 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, T, hAPP
% 1.28/1.65 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) =
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, Z, c_Divides_Odiv__class_Odiv( X, T, Y )
% 1.28/1.65 ) }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.65 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, Y, Z ),
% 1.28/1.65 Y ) = c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Z, Y
% 1.28/1.65 ), c_Groups_Oone__class_Oone( X ) ) }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.65 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, Z, Y ),
% 1.28/1.65 Y ) = c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Z, Y
% 1.28/1.65 ), c_Groups_Oone__class_Oone( X ) ) }.
% 1.28/1.65 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 1.28/1.65 alpha17( X, Z ) }.
% 1.28/1.65 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 1.28/1.65 alpha41( X, Y, Z ) }.
% 1.28/1.65 { ! alpha17( X, Z ), ! alpha41( X, Y, Z ), hBOOL( hAPP( Z,
% 1.28/1.65 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ) }.
% 1.28/1.65 { ! alpha41( X, Y, Z ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.28/1.65 alpha52( X, Y, Z ) }.
% 1.28/1.65 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha41( X, Y, Z ) }.
% 1.28/1.65 { ! alpha52( X, Y, Z ), alpha41( X, Y, Z ) }.
% 1.28/1.65 { ! alpha52( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, X
% 1.28/1.65 ), alpha61( X, Y, Z, T ) }.
% 1.28/1.65 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol26( X, T, U ), X ),
% 1.28/1.65 alpha52( X, Y, Z ) }.
% 1.28/1.65 { ! alpha61( X, Y, Z, skol26( X, Y, Z ) ), alpha52( X, Y, Z ) }.
% 1.28/1.65 { ! alpha61( X, Y, Z, T ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 1.28/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 1.28/1.65 hBOOL( hAPP( Z, U ) ) }.
% 1.28/1.65 { ! hBOOL( hAPP( Z, skol27( U, W, Z, V0 ) ) ), alpha61( X, Y, Z, T ) }.
% 1.28/1.65 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol27( X, Y, Z, T ) )
% 1.28/1.65 , T ), alpha61( X, Y, Z, T ) }.
% 1.28/1.65 { ! alpha17( X, Y ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.28/1.65 hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.28/1.65 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha17( X, Y ) }.
% 1.28/1.65 { ! hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha17
% 1.28/1.65 ( X, Y ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 1.28/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol28( Z, T ) ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), skol28( X, Y ) ), X ) =
% 1.28/1.65 Y }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( tc_Nat_Onat ), X ), c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 1.28/1.65 c_RealDef_Oreal( tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) =
% 1.28/1.65 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.28/1.65 tc_Nat_Onat, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ),
% 1.28/1.65 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.28/1.65 tc_Nat_Onat, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ),
% 1.28/1.65 c_RealDef_Oreal( tc_Nat_Onat, X ) ) ) }.
% 1.28/1.65 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 1.28/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol29( Z, T ) ) }.
% 1.28/1.65 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.65 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, Z ) ), skol29( X, Y ) ) }.
% 1.28/1.65 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.65 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol53( X, Y, Z ) ) ), Z ),
% 1.28/1.65 c_SEQ_OBseq( X, Y ) }.
% 1.28/1.65 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Odiv(
% 1.28/1.65 tc_Polynomial_Opoly( X ), T, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.28/1.65 tc_Polynomial_Opoly( X ) ), Z ), Y ) ) = c_Divides_Odiv__class_Odiv(
% 1.28/1.65 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly
% 1.28/1.65 ( X ), T, Z ), Y ) }.
% 1.28/1.65 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.28/1.65 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 1.28/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 1.28/1.65 tc_Nat_Onat, Z, X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ),
% 1.28/1.65 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.28/1.65 tc_Nat_Onat, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, X ),
% 1.28/1.65 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ), X ) ) }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X,
% 1.28/1.65 c_Divides_Odiv__class_Omod( X, Z, Y ), Y ) = c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( X ) }.
% 1.28/1.65 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.28/1.65 tc_Int_Oint ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.28/1.65 tc_Int_Oint, X, Y ) ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.28/1.65 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.28/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 1.28/1.65 tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.28/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.28/1.65 tc_Int_Oint ), Y ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.28/1.65 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.28/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ),
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.28/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ),
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.28/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.28/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 1.28/1.65 tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.28/1.65 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.28/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, X ) =
% 1.28/1.65 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y,
% 1.28/1.65 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.28/1.65 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) = Y }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y, Y
% 1.28/1.65 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.65 }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.28/1.65 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ), X ) }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, T, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Z ) =
% 1.28/1.65 c_Divides_Odiv__class_Omod( X, T, Z ) }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, T, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) =
% 1.28/1.65 c_Divides_Odiv__class_Omod( X, T, Y ) }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.28/1.65 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Z ) =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.28/1.65 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.65 { ! c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol30( X, Y ) ) }.
% 1.28/1.65 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z )
% 1.28/1.65 , c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.28/1.65 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 1.28/1.65 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.65 ( X ), T ), c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.28/1.65 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 1.28/1.65 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.65 ( X ), c_Divides_Odiv__class_Omod( X, T, Y ) ), Z ), Y ) }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.28/1.65 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 1.28/1.65 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.65 ( X ), c_Divides_Odiv__class_Omod( X, T, Y ) ),
% 1.28/1.65 c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.28/1.65 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) = hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), c_Divides_Odiv__class_Omod( X, Z
% 1.28/1.65 , Y ) ) }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.28/1.65 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Omod( X, T, Y )
% 1.28/1.65 ), Z ) }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.28/1.65 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Omod( X
% 1.28/1.65 , T, Z ) ), Y ), Z ) = c_Divides_Odiv__class_Omod( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, T,
% 1.28/1.65 Z ) = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod
% 1.28/1.65 ( X, W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 1.28/1.65 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.65 ( X ), T ), W ), Z ) = c_Divides_Odiv__class_Omod( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), U ), Z ) }.
% 1.28/1.65 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.28/1.65 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z
% 1.28/1.65 ), Y ), X ), Y ) = c_Divides_Odiv__class_Omod( tc_Nat_Onat, X, Y ) }.
% 1.28/1.65 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.28/1.65 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, Y ) ), X ) =
% 1.28/1.65 c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.28/1.65 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 1.28/1.65 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) =
% 1.28/1.65 c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, T,
% 1.28/1.65 Z ) = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod
% 1.28/1.65 ( X, W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 1.28/1.65 c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X, T, W ), Z
% 1.28/1.65 ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X, Y, U
% 1.28/1.65 ), Z ) }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Z ), Y
% 1.28/1.65 ), Z ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X,
% 1.28/1.65 T, Y ), Z ) }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, T, c_Divides_Odiv__class_Omod( X, Z, Y )
% 1.28/1.65 ), Y ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X,
% 1.28/1.65 T, Z ), Y ) }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 1.28/1.65 ( X, c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Y
% 1.28/1.65 ), c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 1.28/1.65 ( X, c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Y
% 1.28/1.65 ), Z ), Y ) }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 1.28/1.65 ( X, c_Groups_Oplus__class_Oplus( X, T, c_Divides_Odiv__class_Omod( X, Z
% 1.28/1.65 , Y ) ), Y ) }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, Z, Y ), Z ) = c_Divides_Odiv__class_Omod
% 1.28/1.65 ( X, Y, Z ) }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = c_Divides_Odiv__class_Omod
% 1.28/1.65 ( X, Z, Y ) }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.28/1.65 c_Divides_Odiv__class_Omod( X, Z, Y ), Y ) = c_Divides_Odiv__class_Omod(
% 1.28/1.65 X, Z, Y ) }.
% 1.28/1.65 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.28/1.65 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ), Y ) }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.65 c_Divides_Odiv__class_Omod( X, Z, Y ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X, Z, Y )
% 1.28/1.65 ), Y ) ) = Z }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 1.28/1.65 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 1.28/1.65 c_Divides_Odiv__class_Odiv( X, Y, Z ) ), c_Divides_Odiv__class_Omod( X, Y
% 1.28/1.65 , Z ) ) = Y }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 1.28/1.65 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X
% 1.28/1.65 , Z, Y ) ), Y ), c_Divides_Odiv__class_Omod( X, Z, Y ) ) = Z }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.65 ( X ), T ), c_Divides_Odiv__class_Odiv( X, Z, T ) ),
% 1.28/1.65 c_Divides_Odiv__class_Omod( X, Z, T ) ), Y ) =
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.65 ( X ), c_Divides_Odiv__class_Odiv( X, T, Z ) ), Z ),
% 1.28/1.65 c_Divides_Odiv__class_Omod( X, T, Z ) ), Y ) =
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, T, Y ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ),
% 1.28/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ) ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.28/1.65 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ),
% 1.28/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ) ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.28/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.28/1.65 tc_Int_Oint ), Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.28/1.65 Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 1.28/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ) ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.28/1.65 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.28/1.65 tc_Int_Oint, Y, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y
% 1.28/1.65 , c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.28/1.65 tc_Int_Oint, Y, X ) ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ),
% 1.28/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.28/1.65 tc_Int_Oint ), Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.28/1.65 Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ),
% 1.28/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.28/1.65 tc_Int_Oint ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.28/1.65 tc_Int_Oint ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ),
% 1.28/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.28/1.65 tc_Int_Oint ), Y ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.28/1.65 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.28/1.65 tc_Int_Oint, X, Y ) ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.28/1.65 tc_Int_Oint, Y, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X
% 1.28/1.65 , Y ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X
% 1.28/1.65 , Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.28/1.65 tc_Int_Oint, Y, X ) ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.28/1.65 tc_Int_Oint, Y, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.28/1.65 tc_Int_Oint, Y, X ) ) }.
% 1.28/1.65 { ! c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), alpha18( X, Y ) }.
% 1.28/1.65 { ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.28/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.28/1.65 { ! alpha18( X, Y ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.28/1.65 { ! alpha18( X, Y ), alpha42( X, Y ), alpha53( X, Y ) }.
% 1.28/1.65 { ! alpha42( X, Y ), alpha18( X, Y ) }.
% 1.28/1.65 { ! alpha53( X, Y ), alpha18( X, Y ) }.
% 1.28/1.65 { ! alpha53( X, Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.28/1.65 { ! alpha53( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ), alpha53( X, Y ) }.
% 1.28/1.65 { ! alpha42( X, Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 1.28/1.65 { ! alpha42( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), alpha42( X, Y ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.28/1.65 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ), X ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.28/1.65 c_Groups_Oone__class_Oone( tc_Int_Oint ), Y ),
% 1.28/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 1.28/1.65 tc_Int_Oint, X, Y ), X ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( tc_Int_Oint ), X ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Z, hAPP(
% 1.28/1.65 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) =
% 1.28/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 1.28/1.65 tc_Int_Oint, Z, Y ), X ) }.
% 1.28/1.65 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), X ) =
% 1.28/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 1.28/1.65 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ),
% 1.28/1.65 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 1.28/1.65 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ), X ) ) }.
% 1.28/1.65 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) =
% 1.28/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ),
% 1.28/1.65 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 1.28/1.65 tc_Nat_Onat, Z, Y ), X ) ), c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, Y
% 1.28/1.65 ) ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 1.28/1.65 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.28/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ),
% 1.28/1.65 c_Divides_Odiv__class_Omod( tc_Nat_Onat, T, X ) ), Z ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.28/1.65 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) ),
% 1.28/1.65 alpha19( X, Y, Z ) }.
% 1.28/1.65 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) ),
% 1.28/1.65 alpha43( X, Y, Z ) }.
% 1.28/1.65 { ! alpha19( X, Y, Z ), ! alpha43( X, Y, Z ), hBOOL( hAPP( Z,
% 1.28/1.65 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) ) }.
% 1.28/1.65 { ! alpha43( X, Y, Z ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.28/1.65 alpha54( X, Y, Z ) }.
% 1.28/1.65 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha43( X, Y, Z ) }.
% 1.28/1.65 { ! alpha54( X, Y, Z ), alpha43( X, Y, Z ) }.
% 1.28/1.65 { ! alpha54( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, X
% 1.28/1.65 ), alpha62( X, Y, Z, T ) }.
% 1.28/1.65 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol31( X, T, U ), X ),
% 1.28/1.65 alpha54( X, Y, Z ) }.
% 1.28/1.65 { ! alpha62( X, Y, Z, skol31( X, Y, Z ) ), alpha54( X, Y, Z ) }.
% 1.28/1.65 { ! alpha62( X, Y, Z, T ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 1.28/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 1.28/1.65 hBOOL( hAPP( Z, T ) ) }.
% 1.28/1.65 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol32( X, Y, T ) ), T
% 1.28/1.65 ), alpha62( X, Y, Z, T ) }.
% 1.28/1.65 { ! hBOOL( hAPP( Z, T ) ), alpha62( X, Y, Z, T ) }.
% 1.28/1.65 { ! alpha19( X, Y, Z ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.28/1.65 hBOOL( hAPP( Z, Y ) ) }.
% 1.28/1.65 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha19( X, Y, Z ) }.
% 1.28/1.65 { ! hBOOL( hAPP( Z, Y ) ), alpha19( X, Y, Z ) }.
% 1.28/1.65 { ! T = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), alpha83( X,
% 1.28/1.65 Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), Z =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.28/1.65 tc_Int_Oint, T, Z ) = Y }.
% 1.28/1.65 { ! T = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), alpha83( X,
% 1.28/1.65 Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Z =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.28/1.65 tc_Int_Oint, T, Z ) = Y }.
% 1.28/1.65 { ! alpha83( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 1.28/1.65 { ! alpha83( X, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), alpha83( X, Y ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y )
% 1.28/1.65 , alpha83( X, Y ) }.
% 1.28/1.65 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ),
% 1.28/1.65 alpha20( X, Z ) }.
% 1.28/1.65 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ),
% 1.28/1.65 alpha44( X, Y, Z ) }.
% 1.28/1.65 { ! alpha20( X, Z ), ! alpha44( X, Y, Z ), hBOOL( hAPP( Z,
% 1.28/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ) }.
% 1.28/1.65 { ! alpha44( X, Y, Z ), alpha55( X, Y, Z ) }.
% 1.28/1.65 { ! alpha44( X, Y, Z ), alpha63( X, Y, Z ) }.
% 1.28/1.65 { ! alpha55( X, Y, Z ), ! alpha63( X, Y, Z ), alpha44( X, Y, Z ) }.
% 1.28/1.65 { ! alpha63( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha71( X, Y, Z ) }.
% 1.28/1.65 { c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha63( X, Y, Z ) }.
% 1.28/1.65 { ! alpha71( X, Y, Z ), alpha63( X, Y, Z ) }.
% 1.28/1.65 { ! alpha71( X, Y, Z ), ! alpha75( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 1.28/1.65 { ! hBOOL( hAPP( Z, skol33( T, U, Z ) ) ), alpha71( X, Y, Z ) }.
% 1.28/1.65 { alpha75( X, Y, skol33( X, Y, Z ) ), alpha71( X, Y, Z ) }.
% 1.28/1.65 { ! alpha75( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.28/1.65 skol34( X, T, U ) ) }.
% 1.28/1.65 { ! alpha75( X, Y, Z ), alpha79( X, Y, Z, skol34( X, Y, Z ) ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, T ), ! alpha79( X, Y, Z
% 1.28/1.65 , T ), alpha75( X, Y, Z ) }.
% 1.28/1.65 { ! alpha79( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.65 T, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.28/1.65 { ! alpha79( X, Y, Z, T ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.28/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ) }
% 1.28/1.65 .
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! Y =
% 1.28/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ), alpha79( X,
% 1.28/1.65 Y, Z, T ) }.
% 1.28/1.65 { ! alpha55( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), alpha64( X, Y, Z ) }.
% 1.28/1.65 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.28/1.65 tc_Int_Oint ), X ), alpha55( X, Y, Z ) }.
% 1.28/1.65 { ! alpha64( X, Y, Z ), alpha55( X, Y, Z ) }.
% 1.28/1.65 { ! alpha64( X, Y, Z ), ! alpha72( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 1.28/1.65 { ! hBOOL( hAPP( Z, skol35( T, U, Z ) ) ), alpha64( X, Y, Z ) }.
% 1.28/1.65 { alpha72( X, Y, skol35( X, Y, Z ) ), alpha64( X, Y, Z ) }.
% 1.28/1.65 { ! alpha72( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), skol36( T, U, W ) ) }.
% 1.28/1.65 { ! alpha72( X, Y, Z ), alpha76( X, Y, Z, skol36( X, Y, Z ) ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! alpha76( X, Y, Z, T )
% 1.28/1.65 , alpha72( X, Y, Z ) }.
% 1.28/1.65 { ! alpha76( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X
% 1.28/1.65 ) }.
% 1.28/1.65 { ! alpha76( X, Y, Z, T ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.28/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ) }
% 1.28/1.65 .
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X ), ! Y =
% 1.28/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ), alpha76( X,
% 1.28/1.65 Y, Z, T ) }.
% 1.28/1.65 { ! alpha20( X, Y ), ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.28/1.65 hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 1.28/1.65 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), alpha20( X, Y ) }.
% 1.28/1.65 { ! hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), alpha20
% 1.28/1.65 ( X, Y ) }.
% 1.28/1.65 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.65 c_RealVector_Onorm__class_Onorm( X, hAPP( Z, skol37( X, Y, Z ) ) ), Y ),
% 1.28/1.65 c_SEQ_OBseq( X, Z ) }.
% 1.28/1.65 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 1.28/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol38( Z, T ) ) }.
% 1.28/1.65 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.65 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, Z ) ), skol38( X, Y ) ) }.
% 1.28/1.65 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.28/1.65 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.28/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 1.28/1.65 tc_Int_Oint, Z, X ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 1.28/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.28/1.65 tc_Int_Oint, c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, X ),
% 1.28/1.65 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) ) }.
% 1.28/1.65 { Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 1.28/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 1.28/1.65 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) }.
% 1.28/1.65 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) =
% 1.28/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.28/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 1.28/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.28/1.65 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) ) }.
% 1.28/1.65 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.28/1.65 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 1.28/1.65 ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ) ),
% 1.28/1.65 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, Z ) ), X ) =
% 1.28/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) }.
% 1.28/1.65 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.28/1.65 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.28/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Z, Y ) ), Y ),
% 1.28/1.65 c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y ) ), X ) =
% 1.28/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) }.
% 1.28/1.65 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Divides_Odiv__class_Omod(
% 1.28/1.65 tc_Int_Oint, Y, X ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.28/1.65 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero(
% 1.28/1.65 tc_Int_Oint ) ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.28/1.65 { c_Divides_Odiv__class_Omod( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero(
% 1.28/1.65 tc_Int_Oint ) ) = X }.
% 1.28/1.65 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 1.28/1.65 tc_Int_Oint, Z, Y ) ), X ), Y ) = c_Divides_Odiv__class_Omod( tc_Int_Oint
% 1.28/1.65 , hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ), Y )
% 1.28/1.65 }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.28/1.65 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ), X ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.28/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Divides_Odiv__class_Omod
% 1.28/1.65 ( tc_Int_Oint, Y, X ) ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 1.28/1.65 tc_Int_Oint, X, Y ) ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.65 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ), X ) }.
% 1.28/1.65 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.28/1.65 tc_Int_Oint ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.28/1.65 { c_Divides_Odiv__class_Omod( tc_Int_Oint, X, X ) =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.28/1.65 { ! c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y = hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), skol39( X, Y ) ) }.
% 1.28/1.65 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z )
% 1.28/1.65 , c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.28/1.65 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.28/1.65 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) =
% 1.28/1.65 c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) }.
% 1.28/1.65 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) =
% 1.28/1.65 c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.28/1.65 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) }.
% 1.28/1.65 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Omod(
% 1.28/1.65 tc_Polynomial_Opoly( X ), T, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.28/1.65 tc_Polynomial_Opoly( X ) ), Z ), Y ) ) = c_Groups_Oplus__class_Oplus(
% 1.28/1.65 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.28/1.65 tc_Polynomial_Opoly( X ) ), Z ), c_Divides_Odiv__class_Omod(
% 1.28/1.65 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly
% 1.28/1.65 ( X ), T, Z ), Y ) ), c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X
% 1.28/1.65 ), T, Z ) ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 1.28/1.65 tc_Int_Oint, Y, X ) ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 1.28/1.65 tc_Int_Oint, Y, X ) ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.28/1.65 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ), X ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ),
% 1.28/1.65 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ) = X }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.65 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ),
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.65 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ),
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.28/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Divides_Odiv__class_Omod
% 1.28/1.65 ( tc_Int_Oint, Y, X ) ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.28/1.65 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ) = X }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ),
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Divides_Odiv__class_Omod
% 1.28/1.65 ( tc_Int_Oint, X, Y ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y )
% 1.28/1.65 }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( tc_Int_Oint ), X ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, hAPP(
% 1.28/1.65 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) =
% 1.28/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ),
% 1.28/1.65 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 1.28/1.65 tc_Int_Oint, Z, Y ), X ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y
% 1.28/1.65 ) ) }.
% 1.28/1.65 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ),
% 1.28/1.65 alpha21( X, Y, Z ) }.
% 1.28/1.65 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ),
% 1.28/1.65 alpha45( X, Y, Z ) }.
% 1.28/1.65 { ! alpha21( X, Y, Z ), ! alpha45( X, Y, Z ), hBOOL( hAPP( Z,
% 1.28/1.65 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 1.28/1.65 { ! alpha45( X, Y, Z ), alpha56( X, Y, Z ) }.
% 1.28/1.65 { ! alpha45( X, Y, Z ), alpha65( X, Y, Z ) }.
% 1.28/1.65 { ! alpha56( X, Y, Z ), ! alpha65( X, Y, Z ), alpha45( X, Y, Z ) }.
% 1.28/1.65 { ! alpha65( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha73( X, Y, Z ) }.
% 1.28/1.65 { c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha65( X, Y, Z ) }.
% 1.28/1.65 { ! alpha73( X, Y, Z ), alpha65( X, Y, Z ) }.
% 1.28/1.65 { ! alpha73( X, Y, Z ), ! alpha77( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 1.28/1.65 { ! hBOOL( hAPP( Z, skol40( T, U, Z ) ) ), alpha73( X, Y, Z ) }.
% 1.28/1.65 { alpha77( X, Y, skol40( X, Y, Z ) ), alpha73( X, Y, Z ) }.
% 1.28/1.65 { ! alpha77( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z )
% 1.28/1.65 }.
% 1.28/1.65 { ! alpha77( X, Y, Z ), alpha80( X, Y, Z ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), ! alpha80( X, Y, Z
% 1.28/1.65 ), alpha77( X, Y, Z ) }.
% 1.28/1.65 { ! alpha80( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.28/1.65 { ! alpha80( X, Y, Z ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP
% 1.28/1.65 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), skol41( X, Y,
% 1.28/1.65 Z ) ), Z ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! Y =
% 1.28/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), T ), Z ), alpha80( X,
% 1.28/1.65 Y, Z ) }.
% 1.28/1.65 { ! alpha56( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), alpha66( X, Y, Z ) }.
% 1.28/1.65 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.28/1.65 tc_Int_Oint ), X ), alpha56( X, Y, Z ) }.
% 1.28/1.65 { ! alpha66( X, Y, Z ), alpha56( X, Y, Z ) }.
% 1.28/1.65 { ! alpha66( X, Y, Z ), ! alpha74( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 1.28/1.65 { ! hBOOL( hAPP( Z, skol42( T, U, Z ) ) ), alpha66( X, Y, Z ) }.
% 1.28/1.65 { alpha74( X, Y, skol42( X, Y, Z ) ), alpha66( X, Y, Z ) }.
% 1.28/1.65 { ! alpha74( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ) }.
% 1.28/1.65 { ! alpha74( X, Y, Z ), alpha78( X, Y, Z ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), ! alpha78( X, Y, Z ),
% 1.28/1.65 alpha74( X, Y, Z ) }.
% 1.28/1.65 { ! alpha78( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X )
% 1.28/1.65 }.
% 1.28/1.65 { ! alpha78( X, Y, Z ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP
% 1.28/1.65 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), skol43( X, Y,
% 1.28/1.65 Z ) ), Z ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ), ! Y =
% 1.28/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), T ), Z ), alpha78( X,
% 1.28/1.65 Y, Z ) }.
% 1.28/1.65 { ! alpha21( X, Y, Z ), ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.28/1.65 hBOOL( hAPP( Z, Y ) ) }.
% 1.28/1.65 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), alpha21( X, Y, Z ) }.
% 1.28/1.65 { ! hBOOL( hAPP( Z, Y ) ), alpha21( X, Y, Z ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, Z ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 1.28/1.65 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 1.28/1.65 ), c_Divides_Odiv__class_Omod( tc_Int_Oint, T, X ) ), Y ) ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, Z ),
% 1.28/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.28/1.65 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 1.28/1.65 ), c_Divides_Odiv__class_Omod( tc_Int_Oint, T, X ) ), Y ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, Y
% 1.28/1.65 ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.28/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ),
% 1.28/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.28/1.65 c_Divides_Odiv__class_Omod( tc_Int_Oint, T, X ) ), Y ) ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, Y
% 1.28/1.65 ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.28/1.65 c_Divides_Odiv__class_Omod( tc_Int_Oint, T, X ) ), Y ),
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.28/1.65 { ! Z = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), T ), X ), alpha84( X,
% 1.28/1.65 Y ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), Y =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 1.28/1.65 tc_Int_Oint, Z, Y ) = X }.
% 1.28/1.65 { ! Z = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), T ), X ), alpha84( X,
% 1.28/1.65 Y ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 1.28/1.65 tc_Int_Oint, Z, Y ) = X }.
% 1.28/1.65 { ! alpha84( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 1.28/1.65 { ! alpha84( X, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), alpha84( X, Y ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y )
% 1.28/1.65 , alpha84( X, Y ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! hBOOL( hAPP( hAPP( Z,
% 1.28/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 1.28/1.65 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ), ! alpha22( X, Y, T,
% 1.28/1.65 U ), hBOOL( hAPP( hAPP( Z, T ), U ) ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha22( X, Y, skol44( X, Y
% 1.28/1.65 , Z ), skol54( X, Y, Z ) ), hBOOL( hAPP( hAPP( Z,
% 1.28/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 1.28/1.65 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! hBOOL( hAPP( hAPP( Z,
% 1.28/1.65 skol44( X, Y, Z ) ), skol54( X, Y, Z ) ) ), hBOOL( hAPP( hAPP( Z,
% 1.28/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 1.28/1.65 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 1.28/1.65 { ! alpha22( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, T
% 1.28/1.65 ) }.
% 1.28/1.65 { ! alpha22( X, Y, Z, T ), alpha46( X, Y, Z, T ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, T ), ! alpha46( X, Y, Z
% 1.28/1.65 , T ), alpha22( X, Y, Z, T ) }.
% 1.28/1.65 { ! alpha46( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.65 T, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.28/1.65 { ! alpha46( X, Y, Z, T ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.28/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ) }
% 1.28/1.65 .
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! Y =
% 1.28/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ), alpha46( X,
% 1.28/1.65 Y, Z, T ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( hAPP( Z, c_Divides_Odiv__class_Odiv
% 1.28/1.65 ( tc_Int_Oint, Y, X ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X )
% 1.28/1.65 ) ), ! alpha23( X, Y, T, U ), hBOOL( hAPP( hAPP( Z, T ), U ) ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( tc_Int_Oint ), X ), alpha23( X, Y, skol45( X, Y, Z ), skol55( X, Y, Z )
% 1.28/1.65 ), hBOOL( hAPP( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X )
% 1.28/1.65 ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( hAPP( Z, skol45( X, Y, Z ) ), skol55
% 1.28/1.65 ( X, Y, Z ) ) ), hBOOL( hAPP( hAPP( Z, c_Divides_Odiv__class_Odiv(
% 1.28/1.65 tc_Int_Oint, Y, X ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) )
% 1.28/1.65 ) }.
% 1.28/1.65 { ! alpha23( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ) }.
% 1.28/1.65 { ! alpha23( X, Y, Z, T ), alpha47( X, Y, Z, T ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! alpha47( X, Y, Z, T )
% 1.28/1.65 , alpha23( X, Y, Z, T ) }.
% 1.28/1.65 { ! alpha47( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X
% 1.28/1.65 ) }.
% 1.28/1.65 { ! alpha47( X, Y, Z, T ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.28/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ) }
% 1.28/1.65 .
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X ), ! Y =
% 1.28/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ), alpha47( X,
% 1.28/1.65 Y, Z, T ) }.
% 1.28/1.65 { ! class_Orderings_Oorder( X ), ! c_SEQ_Oincseq( X, Y ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, T ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, Z ), hAPP( Y, T ) ) }.
% 1.28/1.65 { ! class_Orderings_Oorder( X ), c_Orderings_Oord__class_Oless__eq(
% 1.28/1.65 tc_Nat_Onat, skol46( X, Y ), skol56( X, Y ) ), c_SEQ_Oincseq( X, Y ) }.
% 1.28/1.65 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.65 hAPP( Y, skol46( X, Y ) ), hAPP( Y, skol56( X, Y ) ) ), c_SEQ_Oincseq( X
% 1.28/1.65 , Y ) }.
% 1.28/1.65 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, skol47( U, W, V0, T )
% 1.28/1.65 ), c_SEQ_OBseq( X, Y ) }.
% 1.28/1.65 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.65 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol47( X, Y, Z, T ) ) ), Z
% 1.28/1.65 ), c_SEQ_OBseq( X, Y ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 1.28/1.65 c_RealDef_Oreal( tc_Nat_Onat, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y
% 1.28/1.65 , X ) ) = c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 1.28/1.65 c_RealDef_Oreal( tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) }
% 1.28/1.65 .
% 1.28/1.65 { ! c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, Y ) =
% 1.28/1.65 c_Divides_Odiv__class_Omod( tc_Nat_Onat, X, Y ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ), Z =
% 1.28/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), skol48( X, Y, Z ) ) )
% 1.28/1.65 }.
% 1.28/1.65 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, X ) }.
% 1.28/1.65 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Y,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.28/1.65 ), c_Divides_Odiv__class_Omod( X, Y, Z ) = c_Groups_Ozero__class_Ozero(
% 1.28/1.65 X ) }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, Y,
% 1.28/1.65 Z ) = c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.28/1.65 ) }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.28/1.65 ), c_Divides_Odiv__class_Omod( X, Y, Z ) = c_Groups_Ozero__class_Ozero(
% 1.28/1.65 X ) }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, T,
% 1.28/1.65 c_Divides_Odiv__class_Omod( X, Z, Y ) ), ! c_Rings_Odvd__class_Odvd( X, T
% 1.28/1.65 , Y ), c_Rings_Odvd__class_Odvd( X, T, Z ) }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.28/1.65 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X, Z
% 1.28/1.65 , c_Divides_Odiv__class_Omod( X, Y, T ) ) }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.28/1.65 ), c_Divides_Odiv__class_Omod( X, c_Divides_Odiv__class_Omod( X, T, Y )
% 1.28/1.65 , Z ) = c_Divides_Odiv__class_Omod( X, T, Z ) }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.28/1.65 ), ! c_Rings_Odvd__class_Odvd( X, Z, c_Divides_Odiv__class_Omod( X, T, Y
% 1.28/1.65 ) ), c_Rings_Odvd__class_Odvd( X, Z, T ) }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.28/1.65 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X, Z
% 1.28/1.65 , c_Divides_Odiv__class_Omod( X, T, Y ) ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y
% 1.28/1.65 ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.28/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), Z =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 1.28/1.65 tc_Nat_Onat, Y, X ) }.
% 1.28/1.65 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.28/1.65 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.28/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.28/1.65 ( tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.28/1.65 Z ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 1.28/1.65 X ) ) }.
% 1.28/1.65 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.28/1.65 Y ), c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Oabs__class_Oabs( X, Z )
% 1.28/1.65 = c_Groups_Oabs__class_Oabs( X, Y ), c_Rings_Odvd__class_Odvd( X, Z, Y )
% 1.28/1.65 }.
% 1.28/1.65 { ! class_Rings_Olinordered__idom( X ), ! c_Rings_Odvd__class_Odvd( X,
% 1.28/1.65 c_Groups_Oabs__class_Oabs( X, Z ), Y ), c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.28/1.65 ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__idom( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.28/1.65 ), c_Rings_Odvd__class_Odvd( X, c_Groups_Oabs__class_Oabs( X, Z ), Y ) }
% 1.28/1.65 .
% 1.28/1.65 { ! class_Rings_Olinordered__idom( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.28/1.65 c_Groups_Oabs__class_Oabs( X, Y ) ), c_Rings_Odvd__class_Odvd( X, Z, Y )
% 1.28/1.65 }.
% 1.28/1.65 { ! class_Rings_Olinordered__idom( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.28/1.65 ), c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oabs__class_Oabs( X, Y ) ) }
% 1.28/1.65 .
% 1.28/1.65 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ), Y ), Y = c_Groups_Ozero__class_Ozero( X
% 1.28/1.65 ) }.
% 1.28/1.65 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Z,
% 1.28/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.28/1.65 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Z,
% 1.28/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.28/1.65 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.28/1.65 Y ), c_Rings_Odvd__class_Odvd( X, Z, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.28/1.65 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.28/1.65 Y ), c_Rings_Odvd__class_Odvd( X, Z, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.28/1.65 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.28/1.65 Y ), ! c_Rings_Odvd__class_Odvd( X, U, T ), c_Rings_Odvd__class_Odvd( X,
% 1.28/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.28/1.65 { ! class_Rings_Odvd( X ), ! Z = hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.65 ( X ), Y ), T ), c_Rings_Odvd__class_Odvd( X, Y, Z ) }.
% 1.28/1.65 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 1.28/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), Y ),
% 1.28/1.65 c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 1.28/1.65 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 1.28/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ),
% 1.28/1.65 c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 1.28/1.65 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Z =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, T, Y ) }.
% 1.28/1.65 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.65 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 1.28/1.65 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) )
% 1.28/1.65 }.
% 1.28/1.65 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, T, Y ),
% 1.28/1.65 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 1.28/1.65 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) )
% 1.28/1.65 }.
% 1.28/1.65 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), T =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 1.28/1.65 { ! class_Rings_Oidom( X ), ! T = c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.65 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 1.28/1.65 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) )
% 1.28/1.65 }.
% 1.28/1.65 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y ),
% 1.28/1.65 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 1.28/1.65 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) )
% 1.28/1.65 }.
% 1.28/1.65 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Y, Y
% 1.28/1.65 ) }.
% 1.28/1.65 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.28/1.65 Y ), ! c_Rings_Odvd__class_Odvd( X, Y, T ), c_Rings_Odvd__class_Odvd( X,
% 1.28/1.65 Z, T ) }.
% 1.28/1.65 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.28/1.65 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 1.28/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.28/1.65 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 1.28/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), alpha24( X, Y ), Y = X }
% 1.28/1.65 .
% 1.28/1.65 { ! alpha24( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.28/1.65 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.28/1.65 { ! alpha24( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.28/1.65 { ! alpha24( X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 1.28/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.28/1.65 ( tc_Nat_Onat, X, Y ), alpha24( X, Y ) }.
% 1.28/1.65 { ! alpha25( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.28/1.65 { ! alpha25( X, Y ), ! Y = X }.
% 1.28/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X, alpha25( X, Y ) }
% 1.28/1.65 .
% 1.28/1.65 { ! alpha25( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.28/1.65 { ! alpha25( X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 1.28/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.28/1.65 ( tc_Nat_Onat, X, Y ), alpha25( X, Y ) }.
% 1.28/1.65 { Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ),
% 1.28/1.65 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.28/1.65 { Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.28/1.65 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 1.28/1.65 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.28/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.28/1.65 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), X = Y }.
% 1.28/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), ! X = Y,
% 1.28/1.65 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 1.28/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.28/1.65 ( tc_Nat_Onat, Y, X ), Y = X }.
% 1.28/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.28/1.65 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 1.28/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X,
% 1.28/1.65 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.28/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X, !
% 1.28/1.65 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 1.28/1.65 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 1.28/1.65 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 1.28/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), ! X = Z,
% 1.28/1.65 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 1.28/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.28/1.65 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 1.28/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.28/1.65 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 1.28/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.28/1.65 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 1.28/1.65 tc_Nat_Onat, Y, Z ) }.
% 1.28/1.65 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 1.28/1.65 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd(
% 1.28/1.65 tc_Nat_Onat, Y, Z ) }.
% 1.28/1.65 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 1.28/1.65 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd
% 1.28/1.65 ( tc_Nat_Onat, Z, Y ) }.
% 1.28/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.28/1.65 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 1.28/1.65 tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 1.28/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.28/1.65 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 1.28/1.65 tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 1.28/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.28/1.65 ( tc_Nat_Onat, X, Y ), ! Y = X }.
% 1.28/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.28/1.65 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 1.28/1.65 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.28/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.28/1.65 ( tc_Nat_Onat, X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.28/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.28/1.65 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 1.28/1.65 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.28/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.28/1.65 ( tc_Nat_Onat, X, Y ), ! Y = X }.
% 1.28/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.28/1.65 ( tc_Nat_Onat, X, Y ), ! X = Y }.
% 1.28/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.28/1.65 ( tc_Nat_Onat, X, Y ), ! X = Z, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 1.28/1.65 , Z ) }.
% 1.28/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.28/1.65 ( tc_Nat_Onat, X, Y ), ! X = Z, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat,
% 1.28/1.65 Z, Y ) }.
% 1.28/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.28/1.65 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 1.28/1.65 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 1.28/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.28/1.65 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), !
% 1.28/1.65 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 1.28/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.28/1.65 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 1.28/1.65 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.28/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.28/1.65 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 1.28/1.65 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd(
% 1.28/1.65 tc_Nat_Onat, Y, Z ) }.
% 1.28/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.28/1.65 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 1.28/1.65 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd
% 1.28/1.65 ( tc_Nat_Onat, Z, Y ) }.
% 1.28/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.28/1.65 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 1.28/1.65 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.28/1.65 { ! class_Rings_Ocomm__semiring__1( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 1.28/1.65 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 1.28/1.65 ), T ), Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ) ) }
% 1.28/1.65 .
% 1.28/1.65 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.28/1.65 Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, U, T ),
% 1.28/1.65 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 1.28/1.65 ), Z ), U ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ) ) }
% 1.28/1.65 .
% 1.28/1.65 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 1.28/1.65 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), Y ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, U, Z ),
% 1.28/1.65 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 1.28/1.65 ), T ), U ), Y ) }.
% 1.28/1.65 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.28/1.65 Y ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X,
% 1.28/1.65 Z, c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 1.28/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, c_Groups_Oplus__class_Oplus(
% 1.28/1.65 tc_Nat_Onat, X, Y ) ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.28/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.28/1.65 ( tc_Nat_Onat, Y, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 1.28/1.65 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X,
% 1.28/1.65 c_Groups_Oone__class_Oone( X ), Y ) }.
% 1.28/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Groups_Oone__class_Oone(
% 1.28/1.65 tc_Nat_Onat ) ), X = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.28/1.65 { ! X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd
% 1.28/1.65 ( tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.28/1.65 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ),
% 1.28/1.65 c_Divides_Odiv__class_Odiv( X, Y, Z ) ), T ) = c_Divides_Odiv__class_Odiv
% 1.28/1.65 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 1.28/1.65 ( c_Power_Opower__class_Opower( X ), Z ), T ) ) }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.28/1.65 ), ! c_Rings_Odvd__class_Odvd( X, U, T ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X, Y, Z )
% 1.28/1.65 ), c_Divides_Odiv__class_Odiv( X, T, U ) ) = c_Divides_Odiv__class_Odiv
% 1.28/1.65 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 1.28/1.65 ( c_Groups_Otimes__class_Otimes( X ), Z ), U ) ) }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.28/1.65 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.28/1.65 c_Divides_Odiv__class_Odiv( X, Y, Z ) ), T ) = c_Divides_Odiv__class_Odiv
% 1.28/1.65 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), Z ) }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.28/1.65 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.28/1.65 c_Divides_Odiv__class_Odiv( X, Y, Z ) ), Z ) = Y }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.28/1.65 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ),
% 1.28/1.65 c_Divides_Odiv__class_Odiv( X, Y, Z ) ) = c_Divides_Odiv__class_Odiv( X,
% 1.28/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.28/1.65 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 1.28/1.65 c_Divides_Odiv__class_Odiv( X, Y, Z ) ) = Y }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.28/1.65 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Divides_Odiv__class_Odiv( X
% 1.28/1.65 , c_Groups_Oplus__class_Oplus( X, Y, T ), Z ) =
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Y, Z ),
% 1.28/1.65 c_Divides_Odiv__class_Odiv( X, T, Z ) ) }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.28/1.65 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), ! c_Rings_Odvd__class_Odvd( X
% 1.28/1.65 , c_Divides_Odiv__class_Odiv( X, Y, Z ), c_Divides_Odiv__class_Odiv( X, T
% 1.28/1.65 , Z ) ), c_Rings_Odvd__class_Odvd( X, Y, T ) }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.28/1.65 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), ! c_Rings_Odvd__class_Odvd( X
% 1.28/1.65 , Y, T ), c_Rings_Odvd__class_Odvd( X, c_Divides_Odiv__class_Odiv( X, Y,
% 1.28/1.65 Z ), c_Divides_Odiv__class_Odiv( X, T, Z ) ) }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.65 , ! c_Rings_Odvd__class_Odvd( X, Y, Z ), ! c_Divides_Odiv__class_Odiv( X
% 1.28/1.65 , Z, Y ) = T, Z = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y
% 1.28/1.65 ) }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.65 , ! c_Rings_Odvd__class_Odvd( X, Y, Z ), ! Z = hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ), c_Divides_Odiv__class_Odiv
% 1.28/1.65 ( X, Z, Y ) = T }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.65 , Z = c_Groups_Ozero__class_Ozero( X ), ! c_Rings_Odvd__class_Odvd( X, Y
% 1.28/1.65 , T ), ! c_Rings_Odvd__class_Odvd( X, Z, U ), !
% 1.28/1.65 c_Divides_Odiv__class_Odiv( X, T, Y ) = c_Divides_Odiv__class_Odiv( X, U
% 1.28/1.65 , Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ) = hAPP(
% 1.28/1.65 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), U ) }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.65 , Z = c_Groups_Ozero__class_Ozero( X ), ! c_Rings_Odvd__class_Odvd( X, Y
% 1.28/1.65 , T ), ! c_Rings_Odvd__class_Odvd( X, Z, U ), ! hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ) = hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), U ), c_Divides_Odiv__class_Odiv
% 1.28/1.65 ( X, T, Y ) = c_Divides_Odiv__class_Odiv( X, U, Z ) }.
% 1.28/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.28/1.65 tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 1.28/1.65 ) }.
% 1.28/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.28/1.65 tc_Nat_Onat ), Z ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 1.28/1.65 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.28/1.65 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ),
% 1.28/1.65 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.28/1.65 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.65 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 1.28/1.65 c_Rings_Odvd__class_Odvd( X, Y, hAPP( hAPP( c_Power_Opower__class_Opower
% 1.28/1.65 ( X ), Y ), Z ) ) }.
% 1.28/1.65 { ! class_Rings_Ocomm__semiring__1( X ), ! Y = c_Groups_Oone__class_Oone( X
% 1.28/1.65 ), c_Rings_Odvd__class_Odvd( X, Y, hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 1.28/1.65 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ), Y =
% 1.28/1.65 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 1.28/1.65 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 1.28/1.65 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ), Y =
% 1.28/1.65 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 1.28/1.65 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ) }.
% 1.28/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ) ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 1.28/1.65 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 1.28/1.65 ) }.
% 1.28/1.65 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 1.28/1.65 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ), hBOOL(
% 1.28/1.65 hAPP( Z, skol49( U, W, Z ) ) ) }.
% 1.28/1.65 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 1.28/1.65 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ),
% 1.28/1.65 c_Rings_Odvd__class_Odvd( X, Y, c_Groups_Oplus__class_Oplus( X, skol49( X
% 1.28/1.65 , Y, Z ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.28/1.65 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), !
% 1.28/1.65 c_Rings_Odvd__class_Odvd( X, Y, c_Groups_Oplus__class_Oplus( X, T,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) ) ), ! hBOOL( hAPP( Z, T ) ), hBOOL(
% 1.28/1.65 hAPP( Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), skol57( X,
% 1.28/1.65 Y, Z ) ) ) ) }.
% 1.28/1.65 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 1.28/1.65 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ),
% 1.28/1.65 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 1.28/1.65 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 1.28/1.65 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ), c_Rings_Odvd__class_Odvd(
% 1.28/1.65 tc_Nat_Onat, hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Z )
% 1.28/1.65 , X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X )
% 1.28/1.65 ) }.
% 1.28/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, c_Divides_Odiv__class_Omod(
% 1.28/1.65 tc_Int_Oint, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, X ),
% 1.28/1.65 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 1.28/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 1.28/1.65 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, Z ), c_Rings_Odvd__class_Odvd(
% 1.28/1.65 tc_Int_Oint, Y, c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Z ) ) }.
% 1.28/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.28/1.65 tc_Int_Oint ) ), c_Groups_Oabs__class_Oabs( tc_Int_Oint, X ) =
% 1.28/1.65 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.28/1.65 { ! c_Groups_Oabs__class_Oabs( tc_Int_Oint, X ) = c_Groups_Oone__class_Oone
% 1.28/1.65 ( tc_Int_Oint ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, X,
% 1.28/1.65 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 1.28/1.65 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 1.28/1.65 c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ) ),
% 1.28/1.65 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 1.28/1.65 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 1.28/1.65 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd(
% 1.28/1.65 tc_Int_Oint, hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z )
% 1.28/1.65 , X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X )
% 1.28/1.65 ) }.
% 1.28/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ), Y =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 1.28/1.65 tc_Int_Oint, Z, X ) }.
% 1.28/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 1.28/1.65 c_Rings_Odvd__class_Odvd( tc_Int_Oint, X, Y ), c_Groups_Oabs__class_Oabs
% 1.28/1.65 ( tc_Int_Oint, Y ) = c_Groups_Oabs__class_Oabs( tc_Int_Oint, X ) }.
% 1.28/1.65 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 1.28/1.65 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd(
% 1.28/1.65 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X
% 1.28/1.65 ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y
% 1.28/1.65 ) ) }.
% 1.28/1.65 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 1.28/1.65 c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ),
% 1.28/1.65 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 1.28/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), Z =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Rings_Odvd__class_Odvd(
% 1.28/1.65 tc_Int_Oint, Y, X ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y
% 1.28/1.65 ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }.
% 1.28/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 1.28/1.65 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 1.28/1.65 tc_Int_Oint, U, T ) ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y,
% 1.28/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.28/1.65 tc_Int_Oint, U, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 1.28/1.65 , Z ), X ) ), T ) ) }.
% 1.28/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 1.28/1.65 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 1.28/1.65 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), T ) ),
% 1.28/1.65 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 1.28/1.65 tc_Int_Oint, U, T ) ) }.
% 1.28/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus(
% 1.28/1.65 tc_Int_Oint, Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 1.28/1.65 , Z ), X ) ) ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 1.28/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd
% 1.28/1.65 ( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP( hAPP
% 1.28/1.65 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), !
% 1.28/1.65 c_Rings_Odvd__class_Odvd( tc_Int_Oint, X, Y ), ! c_Rings_Odvd__class_Odvd
% 1.28/1.65 ( tc_Int_Oint, Y, X ), X = Y }.
% 1.28/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ),
% 1.28/1.65 c_Groups_Oabs__class_Oabs( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 1.28/1.65 tc_Int_Oint, X, Y ) ) = c_Divides_Odiv__class_Odiv( tc_Int_Oint,
% 1.28/1.65 c_Groups_Oabs__class_Oabs( tc_Int_Oint, X ), c_Groups_Oabs__class_Oabs(
% 1.28/1.65 tc_Int_Oint, Y ) ) }.
% 1.28/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ),
% 1.28/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) = X }.
% 1.28/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.28/1.65 tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 1.28/1.65 ) }.
% 1.28/1.65 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 1.28/1.65 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oabs__class_Oabs
% 1.28/1.65 ( tc_Int_Oint, Y ), c_Groups_Oabs__class_Oabs( tc_Int_Oint, X ) ) }.
% 1.28/1.65 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 1.28/1.65 c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ), X ),
% 1.28/1.65 c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) = c_Groups_Oone__class_Oone(
% 1.28/1.65 tc_Int_Oint ) }.
% 1.28/1.65 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 1.28/1.65 c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) = c_Groups_Oone__class_Oone(
% 1.28/1.65 tc_Int_Oint ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ), X ) }.
% 1.28/1.65 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero(
% 1.28/1.65 tc_Nat_Onat ) ) }.
% 1.28/1.65 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 1.28/1.65 tc_Nat_Onat ), X ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ),
% 1.28/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.28/1.65 tc_Nat_Onat ), Y ) }.
% 1.28/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ), Y =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 1.28/1.65 tc_Nat_Onat, Z, X ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( tc_Int_Oint ), X ), hBOOL( hAPP( Y, skol50( Z, Y ) ) ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! hBOOL( hAPP( Y, U ) )
% 1.28/1.65 , hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, hAPP( hAPP
% 1.28/1.65 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), T ), X ) ) ) ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus(
% 1.28/1.65 tc_Int_Oint, skol50( X, Y ), X ) ) ), ! c_Orderings_Oord__class_Oless__eq
% 1.28/1.65 ( tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), ! hBOOL(
% 1.28/1.65 hAPP( Y, T ) ), hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus( tc_Int_Oint
% 1.28/1.65 , T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) )
% 1.28/1.65 ) ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.28/1.65 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Groups_Oplus__class_Oplus
% 1.28/1.65 ( tc_Int_Oint, c_Groups_Oabs__class_Oabs( tc_Int_Oint,
% 1.28/1.65 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ),
% 1.28/1.65 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ), X ) ), Y ) }.
% 1.28/1.65 { ! c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y ) =
% 1.28/1.65 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ), c_Rings_Odvd__class_Odvd
% 1.28/1.65 ( tc_Int_Oint, Y, c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, X ) ) }
% 1.28/1.65 .
% 1.28/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Ominus__class_Ominus
% 1.28/1.65 ( tc_Int_Oint, Z, X ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y )
% 1.28/1.65 = c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ) }.
% 1.28/1.65 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 1.28/1.65 , ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X, Z,
% 1.28/1.65 c_Groups_Ominus__class_Ominus( X, Y, T ) ) }.
% 1.28/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, c_Groups_Ominus__class_Ominus
% 1.28/1.65 ( tc_Int_Oint, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, X )
% 1.28/1.65 , c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 1.28/1.65 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 1.28/1.65 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, U, T ) ), c_Rings_Odvd__class_Odvd( X, Z
% 1.28/1.65 , c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U,
% 1.28/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) }.
% 1.28/1.65 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 1.28/1.65 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U, hAPP
% 1.28/1.65 ( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ),
% 1.28/1.65 c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X, U, T ) )
% 1.28/1.65 }.
% 1.28/1.65 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 1.28/1.65 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, U, T ) ), c_Rings_Odvd__class_Odvd( X, Z
% 1.28/1.65 , c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U,
% 1.28/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) }.
% 1.28/1.65 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 1.28/1.65 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U, hAPP
% 1.28/1.65 ( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ),
% 1.28/1.65 c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X, U, T ) )
% 1.28/1.65 }.
% 1.28/1.65 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.65 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.65 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.65 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ) }.
% 1.28/1.65 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.65 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 1.28/1.65 Z ) ), U ), T ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.65 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 1.28/1.65 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.65 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.65 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X, T,
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.65 ( X ), c_Groups_Ominus__class_Ominus( X, Z, W ) ), U ), Y ) ) }.
% 1.28/1.65 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.65 , T, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.28/1.65 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.65 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 1.28/1.65 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.65 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 1.28/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.28/1.65 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 1.28/1.65 X, W, Z ) ), U ), T ), Y ) }.
% 1.28/1.65 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.65 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ),
% 1.28/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.28/1.65 hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.65 ( X ), Z ), U ), Y ) ) }.
% 1.28/1.65 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.65 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 1.28/1.65 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, hAPP
% 1.28/1.65 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus
% 1.28/1.65 ( X, Z, W ) ), U ), Y ) ) }.
% 1.28/1.65 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X, T
% 1.28/1.65 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.28/1.65 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.65 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 1.28/1.65 { ! class_Rings_Oring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP
% 1.28/1.65 ( c_Groups_Otimes__class_Otimes( X ), Y ), Y ), c_Groups_Oone__class_Oone
% 1.28/1.65 ( X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) ) ),
% 1.28/1.65 c_Groups_Ominus__class_Ominus( X, Y, c_Groups_Oone__class_Oone( X ) ) ) }
% 1.28/1.65 .
% 1.28/1.65 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.65 c_Groups_Ominus__class_Ominus( X, T, c_Rings_Oinverse__class_Odivide( X,
% 1.28/1.65 Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X,
% 1.28/1.65 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), T ), Z ), Y ) }.
% 1.28/1.65 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.65 c_Groups_Ominus__class_Ominus( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.28/1.65 Y ), Z ) = c_Rings_Oinverse__class_Odivide( X,
% 1.28/1.65 c_Groups_Ominus__class_Ominus( X, T, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) }.
% 1.28/1.65 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ominus__class_Ominus( X,
% 1.28/1.65 c_Rings_Oinverse__class_Odivide( X, U, Y ),
% 1.28/1.65 c_Rings_Oinverse__class_Odivide( X, T, Z ) ) =
% 1.28/1.65 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus( X,
% 1.28/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.28/1.65 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 1.28/1.65 c_Groups_Ominus__class_Ominus( X, c_Groups_Oplus__class_Oplus( X, U, T )
% 1.28/1.65 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) ), c_Groups_Oplus__class_Oplus
% 1.28/1.65 ( X, c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, U, Z
% 1.28/1.65 ) ), c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, T,
% 1.28/1.65 Y ) ) ) ) }.
% 1.28/1.65 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 1.28/1.65 c_Groups_Ominus__class_Ominus( X, Z, Y ) ), c_Groups_Oplus__class_Oplus(
% 1.28/1.65 X, c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) )
% 1.28/1.65 ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.28/1.65 , c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, T, Z )
% 1.28/1.65 ), Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus
% 1.28/1.65 ( X, Z, Y ), T ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.28/1.65 , c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, T, Z )
% 1.28/1.65 ), Y ), c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus
% 1.28/1.65 ( X, Z, Y ) ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.28/1.65 , c_Groups_Ominus__class_Ominus( X, Z, Y ), T ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y
% 1.28/1.65 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X,
% 1.28/1.65 c_Groups_Ominus__class_Ominus( X, T, Z ) ), Y ) }.
% 1.28/1.65 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.65 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, Z,
% 1.28/1.65 Y ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 1.28/1.65 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 1.28/1.65 ( X, Y ) ) ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.28/1.65 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 1.28/1.65 ( tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 1.28/1.65 .
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.28/1.65 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 1.28/1.65 ( tc_Int_Oint ) ) ) }.
% 1.28/1.65 { ! class_Divides_Oring__div( X ), ! c_Divides_Odiv__class_Omod( X, T, Z )
% 1.28/1.65 = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod( X
% 1.28/1.65 , W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 1.28/1.65 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, T, W ),
% 1.28/1.65 Z ) = c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, Y
% 1.28/1.65 , U ), Z ) }.
% 1.28/1.65 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 1.28/1.65 tc_Int_Oint, c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y ), X ), Y ) =
% 1.28/1.65 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 1.28/1.65 tc_Int_Oint, Z, X ), Y ) }.
% 1.28/1.65 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 1.28/1.65 tc_Int_Oint, Z, c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) =
% 1.28/1.65 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 1.28/1.65 tc_Int_Oint, Z, Y ), X ) }.
% 1.28/1.65 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.28/1.65 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 1.28/1.65 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X,
% 1.28/1.65 c_Divides_Odiv__class_Omod( X, T, Y ), c_Divides_Odiv__class_Omod( X, Z,
% 1.28/1.65 Y ) ), Y ) }.
% 1.28/1.65 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.28/1.65 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 1.28/1.65 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X,
% 1.28/1.65 c_Divides_Odiv__class_Omod( X, T, Y ), Z ), Y ) }.
% 1.28/1.65 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.28/1.65 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 1.28/1.65 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, T,
% 1.28/1.65 c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.28/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ominus__class_Ominus
% 1.28/1.65 ( tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.28/1.65 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ),
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.28/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 1.28/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.65 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.28/1.65 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, U, T ),
% 1.28/1.65 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.28/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.65 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.28/1.65 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 1.28/1.65 c_Orderings_Oord__class_Oless( X, U, T ) }.
% 1.28/1.65 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ominus__class_Ominus( X, Z, Y
% 1.28/1.65 ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 1.28/1.65 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ominus__class_Ominus(
% 1.28/1.65 X, Z, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.65 { ! class_Groups_Oab__group__add( X ), ! Z = Y,
% 1.28/1.65 c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X
% 1.28/1.65 ) }.
% 1.28/1.65 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 1.28/1.65 Z, Y ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 1.28/1.65 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y, Y )
% 1.28/1.65 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.65 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.28/1.65 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 1.28/1.65 c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Z, Y ) )
% 1.28/1.65 = c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Y, Z )
% 1.28/1.65 ) }.
% 1.28/1.65 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.28/1.65 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ) =
% 1.28/1.65 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 1.28/1.65 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.28/1.65 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ), X ) =
% 1.28/1.65 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.28/1.65 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 1.28/1.65 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.28/1.65 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 1.28/1.65 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.28/1.65 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 1.28/1.65 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.28/1.65 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 1.28/1.65 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.28/1.65 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 1.28/1.65 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 1.28/1.65 c_Groups_Ominus__class_Ominus( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.28/1.65 Y ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.28/1.65 { ! class_RealVector_Oreal__normed__field( X ),
% 1.28/1.65 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus( X, T,
% 1.28/1.65 Z ), Y ) = c_Groups_Ominus__class_Ominus( X,
% 1.28/1.65 c_Rings_Oinverse__class_Odivide( X, T, Y ),
% 1.28/1.65 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.28/1.65 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.28/1.65 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, Z,
% 1.28/1.65 Y ) ) = c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus
% 1.28/1.65 ( X, Y, Z ) ) }.
% 1.28/1.65 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 1.28/1.65 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 1.28/1.65 c_Groups_Ominus__class_Ominus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 1.28/1.65 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 1.28/1.65 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 1.28/1.65 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! U = T, Z = Y }.
% 1.28/1.65 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 1.28/1.65 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! Z = Y, U = T }.
% 1.28/1.65 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 1.28/1.65 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 1.28/1.65 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 1.28/1.65 c_Groups_Ominus__class_Ominus( X, U, Z ), c_Groups_Ominus__class_Ominus(
% 1.28/1.65 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 1.28/1.65 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 1.28/1.65 c_Groups_Ominus__class_Ominus( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 1.28/1.65 c_Groups_Oabs__class_Oabs( X, Y ) ) ), c_Groups_Oabs__class_Oabs( X,
% 1.28/1.65 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) }.
% 1.28/1.65 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X,
% 1.28/1.65 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ),
% 1.28/1.65 c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Z, Y ) )
% 1.28/1.65 ) }.
% 1.28/1.65 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X,
% 1.28/1.65 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ),
% 1.28/1.65 c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Y, Z ) )
% 1.28/1.65 ) }.
% 1.28/1.65 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.28/1.65 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.28/1.65 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 1.28/1.65 X, U, Z ) ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 1.28/1.65 Z ) ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 1.28/1.65 c_Groups_Ominus__class_Ominus( X, T, Y ) ) ) }.
% 1.28/1.65 { ! class_Rings_Oring( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.65 ( X ), U ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 1.28/1.65 Z ) ), Y ) ) }.
% 1.28/1.65 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.65 ( X ), Z ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 1.28/1.65 Z ) ), U ), T ) = Y }.
% 1.28/1.65 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 1.28/1.65 Z ) ), U ), T ) = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.65 ( X ), Z ), U ), Y ) }.
% 1.28/1.65 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.65 ( X ), Z ), U ), Y ), T = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.28/1.65 W ) ), U ), Y ) }.
% 1.28/1.65 { ! class_Rings_Oring( X ), ! T = c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.28/1.65 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 1.28/1.65 X, Z, W ) ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.65 ( X ), Z ), U ), Y ) }.
% 1.28/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.28/1.65 X, c_Groups_Ominus__class_Ominus( X, Z, Y ), c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( X ) ) }.
% 1.28/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 1.28/1.65 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 1.28/1.65 , Z, Y ) }.
% 1.28/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 1.28/1.65 , Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 1.28/1.65 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.28/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.65 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.28/1.65 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.28/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.65 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.28/1.65 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, U, T ) }.
% 1.28/1.65 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.65 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 1.28/1.65 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 1.28/1.65 ( X, Y ) ), c_RealVector_Onorm__class_Onorm( X,
% 1.28/1.65 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) }.
% 1.28/1.65 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = Z }.
% 1.28/1.65 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.65 c_Groups_Ominus__class_Ominus( X, Z, Y ), Y ) = Z }.
% 1.28/1.65 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.65 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 1.28/1.65 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 1.28/1.65 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 1.28/1.65 ( X, Y ) ) ), c_RealVector_Onorm__class_Onorm( X,
% 1.28/1.65 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) }.
% 1.28/1.65 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ),
% 1.28/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) =
% 1.28/1.65 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Divides_Odiv__class_Omod
% 1.28/1.65 ( tc_Int_Oint, X, Y ) ) }.
% 1.28/1.65 { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 1.28/1.65 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Divides_Odiv__class_Odiv
% 1.28/1.65 ( tc_Int_Oint, Y, X ) ), X ) ) }.
% 1.28/1.65 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.65 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X,
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 1.28/1.65 , Y ) ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 1.28/1.65 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, U,
% 1.28/1.65 Z ) ), c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus
% 1.28/1.65 ( X, T, Y ) ) ) ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Z,
% 1.28/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Groups_Oplus__class_Oplus
% 1.28/1.65 ( tc_Int_Oint, c_Groups_Oabs__class_Oabs( tc_Int_Oint,
% 1.28/1.65 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, Z ) ),
% 1.28/1.65 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ), X ) ) ) }.
% 1.28/1.65 { ! class_RealVector_Oreal__field( X ), c_Rings_Oinverse__class_Odivide( X
% 1.28/1.65 , c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), W ), U ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) =
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.65 ( X ), W ), c_Rings_Oinverse__class_Odivide( X,
% 1.28/1.65 c_Groups_Ominus__class_Ominus( X, U, Z ), Y ) ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Odivide( X,
% 1.28/1.65 c_Groups_Ominus__class_Ominus( X, W, T ), Y ) ), Z ) ) }.
% 1.28/1.65 { ! class_RealVector_Oreal__normed__vector( Y ), ! class_Orderings_Oord( X
% 1.28/1.65 ), c_Orderings_Oord__class_Oless__eq( X, T, skol51( X, U, W, T ) ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, T, V0 ),
% 1.28/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.65 c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, V0 ) ),
% 1.28/1.65 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oone__class_Oone
% 1.28/1.65 ( tc_RealDef_Oreal ), c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, T ) )
% 1.28/1.65 ) ) }.
% 1.28/1.65 { ! class_RealVector_Oreal__normed__vector( Y ), ! class_Orderings_Oord( X
% 1.28/1.65 ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.65 c_RealVector_Onorm__class_Onorm( Y, c_Groups_Ominus__class_Ominus( Y,
% 1.28/1.65 hAPP( Z, T ), hAPP( Z, skol51( X, Y, Z, T ) ) ) ),
% 1.28/1.65 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, T, U ),
% 1.28/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.65 c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, U ) ),
% 1.28/1.65 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oone__class_Oone
% 1.28/1.65 ( tc_RealDef_Oreal ), c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, T ) )
% 1.28/1.65 ) ) }.
% 1.28/1.65 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.28/1.65 class_Groups_Ocancel__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { class_Groups_Ocancel__comm__monoid__add( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_Groups_Ocancel__comm__monoid__add( tc_RealDef_Oreal ) }.
% 1.28/1.65 { class_Groups_Ocancel__comm__monoid__add( tc_Nat_Onat ) }.
% 1.28/1.65 { class_Groups_Ocancel__comm__monoid__add( tc_Int_Oint ) }.
% 1.28/1.65 { ! class_Orderings_Opreorder( X ), class_Orderings_Opreorder( tc_fun( Y, X
% 1.28/1.65 ) ) }.
% 1.28/1.65 { ! class_Orderings_Oorder( X ), class_Orderings_Oorder( tc_fun( Y, X ) ) }
% 1.28/1.65 .
% 1.28/1.65 { ! class_Orderings_Oord( X ), class_Orderings_Oord( tc_fun( Y, X ) ) }.
% 1.28/1.65 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.28/1.65 tc_Int_Oint ) }.
% 1.28/1.65 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Int_Oint ) }.
% 1.28/1.65 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Int_Oint ) }.
% 1.28/1.65 { class_Rings_Olinordered__comm__semiring__strict( tc_Int_Oint ) }.
% 1.28/1.65 { class_Rings_Olinordered__semiring__1__strict( tc_Int_Oint ) }.
% 1.28/1.65 { class_Rings_Olinordered__semiring__strict( tc_Int_Oint ) }.
% 1.28/1.65 { class_Groups_Oordered__ab__semigroup__add( tc_Int_Oint ) }.
% 1.28/1.65 { class_Groups_Oordered__ab__group__add__abs( tc_Int_Oint ) }.
% 1.28/1.65 { class_Groups_Oordered__comm__monoid__add( tc_Int_Oint ) }.
% 1.28/1.65 { class_Groups_Olinordered__ab__group__add( tc_Int_Oint ) }.
% 1.28/1.65 { class_Groups_Ocancel__ab__semigroup__add( tc_Int_Oint ) }.
% 1.28/1.65 { class_Rings_Oring__1__no__zero__divisors( tc_Int_Oint ) }.
% 1.28/1.65 { class_Rings_Oordered__cancel__semiring( tc_Int_Oint ) }.
% 1.28/1.65 { class_Rings_Olinordered__ring__strict( tc_Int_Oint ) }.
% 1.28/1.65 { class_Rings_Oring__no__zero__divisors( tc_Int_Oint ) }.
% 1.28/1.65 { class_Rings_Oordered__comm__semiring( tc_Int_Oint ) }.
% 1.28/1.65 { class_Rings_Olinordered__semiring__1( tc_Int_Oint ) }.
% 1.28/1.65 { class_Groups_Oordered__ab__group__add( tc_Int_Oint ) }.
% 1.28/1.65 { class_Groups_Ocancel__semigroup__add( tc_Int_Oint ) }.
% 1.28/1.65 { class_Rings_Olinordered__semiring( tc_Int_Oint ) }.
% 1.28/1.65 { class_Rings_Olinordered__semidom( tc_Int_Oint ) }.
% 1.28/1.65 { class_Groups_Oab__semigroup__mult( tc_Int_Oint ) }.
% 1.28/1.65 { class_Groups_Ocomm__monoid__mult( tc_Int_Oint ) }.
% 1.28/1.65 { class_Groups_Oab__semigroup__add( tc_Int_Oint ) }.
% 1.28/1.65 { class_Rings_Oordered__semiring( tc_Int_Oint ) }.
% 1.28/1.65 { class_Rings_Oordered__ring__abs( tc_Int_Oint ) }.
% 1.28/1.65 { class_Rings_Ono__zero__divisors( tc_Int_Oint ) }.
% 1.28/1.65 { class_Groups_Ocomm__monoid__add( tc_Int_Oint ) }.
% 1.28/1.65 { class_Rings_Olinordered__ring( tc_Int_Oint ) }.
% 1.28/1.65 { class_Rings_Olinordered__idom( tc_Int_Oint ) }.
% 1.28/1.65 { class_Rings_Ocomm__semiring__1( tc_Int_Oint ) }.
% 1.28/1.65 { class_Rings_Ocomm__semiring__0( tc_Int_Oint ) }.
% 1.28/1.65 { class_Divides_Osemiring__div( tc_Int_Oint ) }.
% 1.28/1.65 { class_Rings_Ocomm__semiring( tc_Int_Oint ) }.
% 1.28/1.65 { class_Groups_Oab__group__add( tc_Int_Oint ) }.
% 1.28/1.65 { class_Rings_Ozero__neq__one( tc_Int_Oint ) }.
% 1.28/1.65 { class_Rings_Oordered__ring( tc_Int_Oint ) }.
% 1.28/1.65 { class_Orderings_Opreorder( tc_Int_Oint ) }.
% 1.28/1.65 { class_Orderings_Olinorder( tc_Int_Oint ) }.
% 1.28/1.65 { class_Groups_Omonoid__mult( tc_Int_Oint ) }.
% 1.28/1.65 { class_Rings_Ocomm__ring__1( tc_Int_Oint ) }.
% 1.28/1.65 { class_Groups_Omonoid__add( tc_Int_Oint ) }.
% 1.28/1.65 { class_Rings_Osemiring__0( tc_Int_Oint ) }.
% 1.28/1.65 { class_Groups_Ogroup__add( tc_Int_Oint ) }.
% 1.28/1.65 { class_Divides_Oring__div( tc_Int_Oint ) }.
% 1.28/1.65 { class_Rings_Omult__zero( tc_Int_Oint ) }.
% 1.28/1.65 { class_Rings_Ocomm__ring( tc_Int_Oint ) }.
% 1.28/1.65 { class_Orderings_Oorder( tc_Int_Oint ) }.
% 1.28/1.65 { class_Int_Oring__char__0( tc_Int_Oint ) }.
% 1.28/1.65 { class_Rings_Osemiring( tc_Int_Oint ) }.
% 1.28/1.65 { class_Orderings_Oord( tc_Int_Oint ) }.
% 1.28/1.65 { class_Rings_Oring__1( tc_Int_Oint ) }.
% 1.28/1.65 { class_Power_Opower( tc_Int_Oint ) }.
% 1.28/1.65 { class_Groups_Ozero( tc_Int_Oint ) }.
% 1.28/1.65 { class_Rings_Oring( tc_Int_Oint ) }.
% 1.28/1.65 { class_Rings_Oidom( tc_Int_Oint ) }.
% 1.28/1.65 { class_Groups_Oone( tc_Int_Oint ) }.
% 1.28/1.65 { class_Rings_Odvd( tc_Int_Oint ) }.
% 1.28/1.65 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.28/1.65 tc_Nat_Onat ) }.
% 1.28/1.65 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.28/1.65 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Nat_Onat ) }.
% 1.28/1.65 { class_Rings_Olinordered__comm__semiring__strict( tc_Nat_Onat ) }.
% 1.28/1.65 { class_Rings_Olinordered__semiring__strict( tc_Nat_Onat ) }.
% 1.28/1.65 { class_Groups_Oordered__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.28/1.65 { class_Groups_Oordered__comm__monoid__add( tc_Nat_Onat ) }.
% 1.28/1.65 { class_Groups_Ocancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.28/1.65 { class_Rings_Oordered__cancel__semiring( tc_Nat_Onat ) }.
% 1.28/1.65 { class_Rings_Oordered__comm__semiring( tc_Nat_Onat ) }.
% 1.28/1.65 { class_Groups_Ocancel__semigroup__add( tc_Nat_Onat ) }.
% 1.28/1.65 { class_Rings_Olinordered__semiring( tc_Nat_Onat ) }.
% 1.28/1.65 { class_Rings_Olinordered__semidom( tc_Nat_Onat ) }.
% 1.28/1.65 { class_Groups_Oab__semigroup__mult( tc_Nat_Onat ) }.
% 1.28/1.65 { class_Groups_Ocomm__monoid__mult( tc_Nat_Onat ) }.
% 1.28/1.65 { class_Groups_Oab__semigroup__add( tc_Nat_Onat ) }.
% 1.28/1.65 { class_Rings_Oordered__semiring( tc_Nat_Onat ) }.
% 1.28/1.65 { class_Rings_Ono__zero__divisors( tc_Nat_Onat ) }.
% 1.28/1.65 { class_Groups_Ocomm__monoid__add( tc_Nat_Onat ) }.
% 1.28/1.65 { class_Rings_Ocomm__semiring__1( tc_Nat_Onat ) }.
% 1.28/1.65 { class_Rings_Ocomm__semiring__0( tc_Nat_Onat ) }.
% 1.28/1.65 { class_Divides_Osemiring__div( tc_Nat_Onat ) }.
% 1.28/1.65 { class_Rings_Ocomm__semiring( tc_Nat_Onat ) }.
% 1.28/1.65 { class_Rings_Ozero__neq__one( tc_Nat_Onat ) }.
% 1.28/1.65 { class_Orderings_Opreorder( tc_Nat_Onat ) }.
% 1.28/1.65 { class_Orderings_Olinorder( tc_Nat_Onat ) }.
% 1.28/1.65 { class_Groups_Omonoid__mult( tc_Nat_Onat ) }.
% 1.28/1.65 { class_Groups_Omonoid__add( tc_Nat_Onat ) }.
% 1.28/1.65 { class_Rings_Osemiring__0( tc_Nat_Onat ) }.
% 1.28/1.65 { class_Rings_Omult__zero( tc_Nat_Onat ) }.
% 1.28/1.65 { class_Orderings_Oorder( tc_Nat_Onat ) }.
% 1.28/1.65 { class_Rings_Osemiring( tc_Nat_Onat ) }.
% 1.28/1.65 { class_Orderings_Oord( tc_Nat_Onat ) }.
% 1.28/1.65 { class_Power_Opower( tc_Nat_Onat ) }.
% 1.28/1.65 { class_Groups_Ozero( tc_Nat_Onat ) }.
% 1.28/1.65 { class_Groups_Oone( tc_Nat_Onat ) }.
% 1.28/1.65 { class_Rings_Odvd( tc_Nat_Onat ) }.
% 1.28/1.65 { class_Orderings_Opreorder( tc_HOL_Obool ) }.
% 1.28/1.65 { class_Orderings_Oorder( tc_HOL_Obool ) }.
% 1.28/1.65 { class_Orderings_Oord( tc_HOL_Obool ) }.
% 1.28/1.65 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.28/1.65 tc_RealDef_Oreal ) }.
% 1.28/1.65 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 1.28/1.65 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_RealDef_Oreal ) }
% 1.28/1.65 .
% 1.28/1.65 { class_Rings_Olinordered__comm__semiring__strict( tc_RealDef_Oreal ) }.
% 1.28/1.65 { class_Fields_Olinordered__field__inverse__zero( tc_RealDef_Oreal ) }.
% 1.28/1.65 { class_Rings_Olinordered__semiring__1__strict( tc_RealDef_Oreal ) }.
% 1.28/1.65 { class_RealVector_Oreal__normed__div__algebra( tc_RealDef_Oreal ) }.
% 1.28/1.65 { class_Rings_Olinordered__semiring__strict( tc_RealDef_Oreal ) }.
% 1.28/1.65 { class_Rings_Odivision__ring__inverse__zero( tc_RealDef_Oreal ) }.
% 1.28/1.65 { class_RealVector_Oreal__normed__algebra__1( tc_RealDef_Oreal ) }.
% 1.28/1.65 { class_Groups_Oordered__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 1.28/1.65 { class_Groups_Oordered__ab__group__add__abs( tc_RealDef_Oreal ) }.
% 1.28/1.65 { class_RealVector_Oreal__normed__algebra( tc_RealDef_Oreal ) }.
% 1.28/1.65 { class_Groups_Oordered__comm__monoid__add( tc_RealDef_Oreal ) }.
% 1.28/1.65 { class_Groups_Olinordered__ab__group__add( tc_RealDef_Oreal ) }.
% 1.28/1.65 { class_Groups_Ocancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 1.28/1.65 { class_Rings_Oring__1__no__zero__divisors( tc_RealDef_Oreal ) }.
% 1.28/1.65 { class_Rings_Oordered__cancel__semiring( tc_RealDef_Oreal ) }.
% 1.28/1.65 { class_RealVector_Oreal__normed__vector( tc_RealDef_Oreal ) }.
% 1.28/1.65 { class_Rings_Olinordered__ring__strict( tc_RealDef_Oreal ) }.
% 1.28/1.65 { class_RealVector_Oreal__normed__field( tc_RealDef_Oreal ) }.
% 1.28/1.65 { class_Rings_Oring__no__zero__divisors( tc_RealDef_Oreal ) }.
% 1.28/1.65 { class_Rings_Oordered__comm__semiring( tc_RealDef_Oreal ) }.
% 1.28/1.65 { class_Rings_Olinordered__semiring__1( tc_RealDef_Oreal ) }.
% 1.28/1.65 { class_Groups_Oordered__ab__group__add( tc_RealDef_Oreal ) }.
% 1.28/1.65 { class_Groups_Ocancel__semigroup__add( tc_RealDef_Oreal ) }.
% 1.28/1.65 { class_Rings_Olinordered__semiring( tc_RealDef_Oreal ) }.
% 1.28/1.65 { class_Fields_Ofield__inverse__zero( tc_RealDef_Oreal ) }.
% 1.28/1.65 { class_Rings_Olinordered__semidom( tc_RealDef_Oreal ) }.
% 1.28/1.65 { class_Groups_Oab__semigroup__mult( tc_RealDef_Oreal ) }.
% 1.28/1.65 { class_Groups_Ocomm__monoid__mult( tc_RealDef_Oreal ) }.
% 1.28/1.65 { class_Groups_Oab__semigroup__add( tc_RealDef_Oreal ) }.
% 1.28/1.65 { class_Fields_Olinordered__field( tc_RealDef_Oreal ) }.
% 1.28/1.65 { class_Rings_Oordered__semiring( tc_RealDef_Oreal ) }.
% 1.28/1.65 { class_Rings_Oordered__ring__abs( tc_RealDef_Oreal ) }.
% 1.28/1.65 { class_Rings_Ono__zero__divisors( tc_RealDef_Oreal ) }.
% 1.28/1.65 { class_Groups_Ocomm__monoid__add( tc_RealDef_Oreal ) }.
% 1.28/1.65 { class_Rings_Olinordered__ring( tc_RealDef_Oreal ) }.
% 1.28/1.65 { class_Rings_Olinordered__idom( tc_RealDef_Oreal ) }.
% 1.28/1.65 { class_Rings_Ocomm__semiring__1( tc_RealDef_Oreal ) }.
% 1.28/1.65 { class_Rings_Ocomm__semiring__0( tc_RealDef_Oreal ) }.
% 1.28/1.65 { class_RealVector_Oreal__field( tc_RealDef_Oreal ) }.
% 1.28/1.65 { class_Rings_Odivision__ring( tc_RealDef_Oreal ) }.
% 1.28/1.65 { class_Rings_Ocomm__semiring( tc_RealDef_Oreal ) }.
% 1.28/1.65 { class_Groups_Oab__group__add( tc_RealDef_Oreal ) }.
% 1.28/1.65 { class_Rings_Ozero__neq__one( tc_RealDef_Oreal ) }.
% 1.28/1.65 { class_Rings_Oordered__ring( tc_RealDef_Oreal ) }.
% 1.28/1.65 { class_Orderings_Opreorder( tc_RealDef_Oreal ) }.
% 1.28/1.65 { class_Orderings_Olinorder( tc_RealDef_Oreal ) }.
% 1.28/1.65 { class_Groups_Omonoid__mult( tc_RealDef_Oreal ) }.
% 1.28/1.65 { class_Rings_Ocomm__ring__1( tc_RealDef_Oreal ) }.
% 1.28/1.65 { class_Groups_Omonoid__add( tc_RealDef_Oreal ) }.
% 1.28/1.65 { class_Rings_Osemiring__0( tc_RealDef_Oreal ) }.
% 1.28/1.65 { class_Groups_Ogroup__add( tc_RealDef_Oreal ) }.
% 1.28/1.65 { class_Rings_Omult__zero( tc_RealDef_Oreal ) }.
% 1.28/1.65 { class_Rings_Ocomm__ring( tc_RealDef_Oreal ) }.
% 1.28/1.65 { class_Orderings_Oorder( tc_RealDef_Oreal ) }.
% 1.28/1.65 { class_Int_Oring__char__0( tc_RealDef_Oreal ) }.
% 1.28/1.65 { class_Rings_Osemiring( tc_RealDef_Oreal ) }.
% 1.28/1.65 { class_Orderings_Oord( tc_RealDef_Oreal ) }.
% 1.28/1.65 { class_Rings_Oring__1( tc_RealDef_Oreal ) }.
% 1.28/1.65 { class_Fields_Ofield( tc_RealDef_Oreal ) }.
% 1.28/1.65 { class_Power_Opower( tc_RealDef_Oreal ) }.
% 1.28/1.65 { class_Groups_Ozero( tc_RealDef_Oreal ) }.
% 1.28/1.65 { class_Rings_Oring( tc_RealDef_Oreal ) }.
% 1.28/1.65 { class_Rings_Oidom( tc_RealDef_Oreal ) }.
% 1.28/1.65 { class_Groups_Oone( tc_RealDef_Oreal ) }.
% 1.28/1.65 { class_Rings_Odvd( tc_RealDef_Oreal ) }.
% 1.28/1.65 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.28/1.65 tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_RealVector_Oreal__normed__div__algebra( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_Rings_Odivision__ring__inverse__zero( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_RealVector_Oreal__normed__algebra__1( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_RealVector_Oreal__normed__algebra( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_Groups_Ocancel__ab__semigroup__add( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_Rings_Oring__1__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_RealVector_Oreal__normed__vector( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_RealVector_Oreal__normed__field( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_Rings_Oring__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_Groups_Ocancel__semigroup__add( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_Fields_Ofield__inverse__zero( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_Groups_Oab__semigroup__mult( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_Groups_Ocomm__monoid__mult( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_Groups_Oab__semigroup__add( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_Rings_Ono__zero__divisors( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_Groups_Ocomm__monoid__add( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_Rings_Ocomm__semiring__1( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_Rings_Ocomm__semiring__0( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_RealVector_Oreal__field( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_Rings_Odivision__ring( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_Rings_Ocomm__semiring( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_Groups_Oab__group__add( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_Rings_Ozero__neq__one( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_Groups_Omonoid__mult( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_Rings_Ocomm__ring__1( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_Groups_Omonoid__add( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_Rings_Osemiring__0( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_Groups_Ogroup__add( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_Rings_Omult__zero( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_Rings_Ocomm__ring( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_Int_Oring__char__0( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_Rings_Osemiring( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_Rings_Oring__1( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_Fields_Ofield( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_Power_Opower( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_Groups_Ozero( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_Rings_Oring( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_Rings_Oidom( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_Groups_Oone( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_Rings_Odvd( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { ! class_Rings_Oidom( X ),
% 1.28/1.65 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.28/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__idom( X ),
% 1.28/1.65 class_Groups_Oordered__cancel__ab__semigroup__add( tc_Polynomial_Opoly( X
% 1.28/1.65 ) ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__idom( X ),
% 1.28/1.65 class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Polynomial_Opoly(
% 1.28/1.65 X ) ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__idom( X ),
% 1.28/1.65 class_Rings_Olinordered__comm__semiring__strict( tc_Polynomial_Opoly( X )
% 1.28/1.65 ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__idom( X ),
% 1.28/1.65 class_Rings_Olinordered__semiring__1__strict( tc_Polynomial_Opoly( X ) )
% 1.28/1.65 }.
% 1.28/1.65 { ! class_Rings_Olinordered__idom( X ),
% 1.28/1.65 class_Rings_Olinordered__semiring__strict( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__idom( X ),
% 1.28/1.65 class_Groups_Oordered__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__idom( X ),
% 1.28/1.65 class_Groups_Oordered__ab__group__add__abs( tc_Polynomial_Opoly( X ) ) }
% 1.28/1.65 .
% 1.28/1.65 { ! class_Rings_Olinordered__idom( X ),
% 1.28/1.65 class_Groups_Oordered__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__idom( X ),
% 1.28/1.65 class_Groups_Olinordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.28/1.65 class_Groups_Ocancel__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Rings_Oidom( X ), class_Rings_Oring__1__no__zero__divisors(
% 1.28/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__idom( X ),
% 1.28/1.65 class_Rings_Oordered__cancel__semiring( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__idom( X ),
% 1.28/1.65 class_Rings_Olinordered__ring__strict( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Rings_Oidom( X ), class_Rings_Oring__no__zero__divisors(
% 1.28/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__idom( X ),
% 1.28/1.65 class_Rings_Oordered__comm__semiring( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__idom( X ),
% 1.28/1.65 class_Rings_Olinordered__semiring__1( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__idom( X ),
% 1.28/1.65 class_Groups_Oordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.28/1.65 class_Groups_Ocancel__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semiring(
% 1.28/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semidom(
% 1.28/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Oab__semigroup__mult
% 1.28/1.65 ( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Ocomm__monoid__mult(
% 1.28/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Oab__semigroup__add
% 1.28/1.65 ( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__semiring(
% 1.28/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__ring__abs(
% 1.28/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Rings_Oidom( X ), class_Rings_Ono__zero__divisors(
% 1.28/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Ocomm__monoid__add(
% 1.28/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__ring(
% 1.28/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__idom(
% 1.28/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ocomm__semiring__1(
% 1.28/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring__0(
% 1.28/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Fields_Ofield( X ), class_Divides_Osemiring__div(
% 1.28/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring(
% 1.28/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Groups_Oab__group__add( X ), class_Groups_Oab__group__add(
% 1.28/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ozero__neq__one(
% 1.28/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__ring(
% 1.28/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Opreorder(
% 1.28/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Olinorder(
% 1.28/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Omonoid__mult(
% 1.28/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Ocomm__ring__1(
% 1.28/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Omonoid__add(
% 1.28/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring__0(
% 1.28/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Groups_Oab__group__add( X ), class_Groups_Ogroup__add(
% 1.28/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Fields_Ofield( X ), class_Divides_Oring__div( tc_Polynomial_Opoly
% 1.28/1.65 ( X ) ) }.
% 1.28/1.65 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Omult__zero(
% 1.28/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Rings_Ocomm__ring( X ), class_Rings_Ocomm__ring(
% 1.28/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oorder(
% 1.28/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__idom( X ), class_Int_Oring__char__0(
% 1.28/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring(
% 1.28/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oord(
% 1.28/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Oring__1(
% 1.28/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Rings_Ocomm__semiring__1( X ), class_Power_Opower(
% 1.28/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Groups_Ozero( X ), class_Groups_Ozero( tc_Polynomial_Opoly( X ) )
% 1.28/1.65 }.
% 1.28/1.65 { ! class_Rings_Ocomm__ring( X ), class_Rings_Oring( tc_Polynomial_Opoly( X
% 1.28/1.65 ) ) }.
% 1.28/1.65 { ! class_Rings_Oidom( X ), class_Rings_Oidom( tc_Polynomial_Opoly( X ) ) }
% 1.28/1.65 .
% 1.28/1.65 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Oone(
% 1.28/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Odvd(
% 1.28/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! hBOOL( c_fequal( Y, X ) ), Y = X }.
% 1.28/1.65 { ! Y = X, hBOOL( c_fequal( Y, X ) ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.65 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), v_z____ ), v_c____
% 1.28/1.65 ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 1.28/1.65 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.28/1.65 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, v_aa____, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), v_z____ ), v_c____
% 1.28/1.65 ) ) ), c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_aa____ )
% 1.28/1.65 ) ) }.
% 1.28/1.65
% 1.28/1.65 *** allocated 15000 integers for clauses
% 1.28/1.65 *** allocated 22500 integers for clauses
% 1.28/1.65 *** allocated 33750 integers for clauses
% 1.28/1.65 *** allocated 50625 integers for clauses
% 1.28/1.65 *** allocated 75937 integers for clauses
% 1.28/1.65 *** allocated 113905 integers for clauses
% 1.28/1.65 percentage equality = 0.209274, percentage horn = 0.895109
% 1.28/1.65 This is a problem with some equality
% 1.28/1.65
% 1.28/1.65
% 1.28/1.65
% 1.28/1.65 Options Used:
% 1.28/1.65
% 1.28/1.65 useres = 1
% 1.28/1.65 useparamod = 1
% 1.28/1.65 useeqrefl = 1
% 1.28/1.65 useeqfact = 1
% 1.28/1.65 usefactor = 1
% 1.28/1.65 usesimpsplitting = 0
% 1.28/1.65 usesimpdemod = 5
% 1.28/1.65 usesimpres = 3
% 1.28/1.65
% 1.28/1.65 resimpinuse = 1000
% 1.28/1.65 resimpclauses = 20000
% 1.28/1.65 substype = eqrewr
% 1.28/1.65 backwardsubs = 1
% 1.28/1.65 selectoldest = 5
% 1.28/1.65
% 1.28/1.65 litorderings [0] = split
% 1.28/1.65 litorderings [1] = extend the termordering, first sorting on arguments
% 1.28/1.65
% 1.28/1.65 termordering = kbo
% 1.28/1.65
% 1.28/1.65 litapriori = 0
% 1.28/1.65 termapriori = 1
% 1.28/1.65 litaposteriori = 0
% 1.28/1.65 termaposteriori = 0
% 1.28/1.65 demodaposteriori = 0
% 1.28/1.65 ordereqreflfact = 0
% 1.28/1.65
% 1.28/1.65 litselect = negord
% 1.28/1.65
% 1.28/1.65 maxweight = 15
% 1.28/1.65 maxdepth = 30000
% 1.28/1.65 maxlength = 115
% 1.28/1.65 maxnrvars = 195
% 1.28/1.65 excuselevel = 1
% 1.28/1.65 increasemaxweight = 1
% 1.28/1.65
% 1.28/1.65 maxselected = 10000000
% 1.28/1.65 maxnrclauses = 10000000
% 1.28/1.65
% 1.28/1.65 showgenerated = 0
% 1.28/1.65 showkept = 0
% 1.28/1.65 showselected = 0
% 1.28/1.65 showdeleted = 0
% 1.28/1.65 showresimp = 1
% 1.28/1.65 showstatus = 2000
% 1.28/1.65
% 1.28/1.65 prologoutput = 0
% 1.28/1.65 nrgoals = 5000000
% 1.28/1.65 totalproof = 1
% 1.28/1.65
% 1.28/1.65 Symbols occurring in the translation:
% 1.28/1.65
% 1.28/1.65 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.28/1.65 . [1, 2] (w:1, o:200, a:1, s:1, b:0),
% 1.28/1.65 ! [4, 1] (w:0, o:113, a:1, s:1, b:0),
% 1.28/1.65 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.28/1.65 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.28/1.65 hAPP [38, 2] (w:1, o:224, a:1, s:1, b:0),
% 1.28/1.65 tc_RealDef_Oreal [39, 0] (w:1, o:13, a:1, s:1, b:0),
% 1.28/1.65 tc_Complex_Ocomplex [40, 0] (w:1, o:14, a:1, s:1, b:0),
% 1.28/1.65 c_Groups_Otimes__class_Otimes [41, 1] (w:1, o:118, a:1, s:1, b:0),
% 1.28/1.65 v_z____ [42, 0] (w:1, o:15, a:1, s:1, b:0),
% 1.28/1.65 v_c____ [43, 0] (w:1, o:16, a:1, s:1, b:0),
% 1.28/1.65 c_RealVector_Onorm__class_Onorm [44, 2] (w:1, o:225, a:1, s:1, b:0),
% 1.28/1.65
% 1.28/1.65 v_aa____ [45, 0] (w:1, o:17, a:1, s:1, b:0),
% 1.28/1.65 c_Groups_Oplus__class_Oplus [46, 3] (w:1, o:276, a:1, s:1, b:0),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq [47, 3] (w:1, o:277, a:1, s:1, b:0)
% 1.28/1.65 ,
% 1.28/1.65 v_p [50, 0] (w:1, o:29, a:1, s:1, b:0),
% 1.28/1.65 tc_Polynomial_Opoly [51, 1] (w:1, o:122, a:1, s:1, b:0),
% 1.28/1.65 c_Groups_Ozero__class_Ozero [52, 1] (w:1, o:123, a:1, s:1, b:0),
% 1.28/1.65 class_RealVector_Oreal__normed__vector [56, 1] (w:1, o:124, a:1, s:1
% 1.28/1.65 , b:0),
% 1.28/1.65 v_da____ [57, 0] (w:1, o:33, a:1, s:1, b:0),
% 1.28/1.65 c_Groups_Oabs__class_Oabs [58, 2] (w:1, o:227, a:1, s:1, b:0),
% 1.28/1.65 class_RealVector_Oreal__normed__algebra [59, 1] (w:1, o:125, a:1, s:1
% 1.28/1.65 , b:0),
% 1.28/1.65 class_Orderings_Opreorder [60, 1] (w:1, o:128, a:1, s:1, b:0),
% 1.28/1.65 class_RealVector_Oreal__normed__div__algebra [61, 1] (w:1, o:129, a:1
% 1.28/1.65 , s:1, b:0),
% 1.28/1.65 class_Rings_Ocomm__semiring__1 [65, 1] (w:1, o:133, a:1, s:1, b:0),
% 1.28/1.65 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct [71
% 1.28/1.65 , 1] (w:1, o:165, a:1, s:1, b:0),
% 1.28/1.65 v_cs____ [72, 0] (w:1, o:32, a:1, s:1, b:0),
% 1.28/1.65 c_Rings_Oinverse__class_Odivide [76, 3] (w:1, o:278, a:1, s:1, b:0),
% 1.28/1.65
% 1.28/1.65 class_Orderings_Olinorder [84, 1] (w:1, o:166, a:1, s:1, b:0),
% 1.28/1.65 class_Orderings_Oord [86, 1] (w:1, o:126, a:1, s:1, b:0),
% 1.28/1.65 tc_fun [87, 2] (w:1, o:255, a:1, s:1, b:0),
% 1.28/1.65 class_Orderings_Oorder [88, 1] (w:1, o:127, a:1, s:1, b:0),
% 1.28/1.65 class_Rings_Oordered__ring__abs [102, 1] (w:1, o:135, a:1, s:1, b:0)
% 1.28/1.65 ,
% 1.28/1.65 class_Rings_Olinordered__idom [103, 1] (w:1, o:136, a:1, s:1, b:0),
% 1.28/1.65 class_Rings_Olinordered__ring__strict [104, 1] (w:1, o:137, a:1, s:1
% 1.28/1.65 , b:0),
% 1.28/1.65 class_Rings_Olinordered__ring [105, 1] (w:1, o:138, a:1, s:1, b:0),
% 1.28/1.65 class_Groups_Oordered__ab__group__add__abs [106, 1] (w:1, o:171, a:1
% 1.28/1.65 , s:1, b:0),
% 1.28/1.65 class_Groups_Oordered__comm__monoid__add [107, 1] (w:1, o:172, a:1
% 1.28/1.65 , s:1, b:0),
% 1.28/1.65 c_Polynomial_OpCons [108, 3] (w:1, o:281, a:1, s:1, b:0),
% 1.28/1.65 class_Fields_Ofield__inverse__zero [109, 1] (w:1, o:167, a:1, s:1, b:
% 1.28/1.65 0),
% 1.28/1.65 class_RealVector_Oreal__normed__field [110, 1] (w:1, o:139, a:1, s:1
% 1.28/1.65 , b:0),
% 1.28/1.65 class_Rings_Odivision__ring__inverse__zero [111, 1] (w:1, o:141, a:1
% 1.28/1.65 , s:1, b:0),
% 1.28/1.65 class_Rings_Odivision__ring [112, 1] (w:1, o:142, a:1, s:1, b:0),
% 1.28/1.65 class_Groups_Ozero [113, 1] (w:1, o:173, a:1, s:1, b:0),
% 1.28/1.65 class_Groups_Oab__semigroup__mult [114, 1] (w:1, o:174, a:1, s:1, b:0
% 1.28/1.65 ),
% 1.28/1.65 class_Groups_Oab__semigroup__add [115, 1] (w:1, o:175, a:1, s:1, b:0)
% 1.28/1.65 ,
% 1.28/1.65 class_Groups_Ocancel__semigroup__add [116, 1] (w:1, o:176, a:1, s:1
% 1.28/1.65 , b:0),
% 1.28/1.65 class_Groups_Ocancel__ab__semigroup__add [117, 1] (w:1, o:177, a:1
% 1.28/1.65 , s:1, b:0),
% 1.28/1.65 class_Rings_Omult__zero [118, 1] (w:1, o:149, a:1, s:1, b:0),
% 1.28/1.65 class_Rings_Oring__no__zero__divisors [119, 1] (w:1, o:150, a:1, s:1
% 1.28/1.65 , b:0),
% 1.28/1.65 class_Rings_Ono__zero__divisors [120, 1] (w:1, o:134, a:1, s:1, b:0)
% 1.28/1.65 ,
% 1.28/1.65 class_Groups_Omonoid__add [121, 1] (w:1, o:179, a:1, s:1, b:0),
% 1.28/1.65 class_Groups_Ocomm__monoid__add [122, 1] (w:1, o:180, a:1, s:1, b:0)
% 1.28/1.65 ,
% 1.28/1.65 class_Groups_Olinordered__ab__group__add [123, 1] (w:1, o:178, a:1
% 1.28/1.65 , s:1, b:0),
% 1.28/1.65 class_Groups_Oordered__ab__semigroup__add__imp__le [124, 1] (w:1, o:
% 1.28/1.65 181, a:1, s:1, b:0),
% 1.28/1.65 class_Groups_Oordered__ab__semigroup__add [125, 1] (w:1, o:182, a:1
% 1.28/1.65 , s:1, b:0),
% 1.28/1.65 class_Rings_Ocomm__semiring [126, 1] (w:1, o:140, a:1, s:1, b:0),
% 1.28/1.65 class_Rings_Osemiring [128, 1] (w:1, o:154, a:1, s:1, b:0),
% 1.28/1.65 class_Rings_Oordered__cancel__semiring [129, 1] (w:1, o:155, a:1, s:1
% 1.28/1.65 , b:0),
% 1.28/1.66 class_Rings_Oordered__ring [130, 1] (w:1, o:156, a:1, s:1, b:0),
% 1.28/1.66 class_Rings_Oordered__semiring [131, 1] (w:1, o:157, a:1, s:1, b:0),
% 1.28/1.66
% 1.28/1.66 class_Rings_Oordered__comm__semiring [132, 1] (w:1, o:158, a:1, s:1
% 1.28/1.66 , b:0),
% 1.28/1.66 class_Fields_Ofield [133, 1] (w:1, o:168, a:1, s:1, b:0),
% 1.28/1.66 c_Orderings_Oord__class_Oless [134, 3] (w:1, o:279, a:1, s:1, b:0),
% 1.28/1.66 class_Fields_Olinordered__field [135, 1] (w:1, o:169, a:1, s:1, b:0)
% 1.28/1.66 ,
% 1.28/1.66 class_Groups_Oordered__cancel__ab__semigroup__add [136, 1] (w:1, o:
% 1.28/1.66 183, a:1, s:1, b:0),
% 1.28/1.66 class_Fields_Olinordered__field__inverse__zero [137, 1] (w:1, o:170
% 1.28/1.66 , a:1, s:1, b:0),
% 1.28/1.66 class_Rings_Olinordered__semiring__strict [138, 1] (w:1, o:143, a:1
% 1.28/1.66 , s:1, b:0),
% 1.28/1.66 class_Rings_Olinordered__comm__semiring__strict [139, 1] (w:1, o:144
% 1.28/1.66 , a:1, s:1, b:0),
% 1.28/1.66 class_Rings_Olinordered__semidom [140, 1] (w:1, o:145, a:1, s:1, b:0)
% 1.28/1.66 ,
% 1.28/1.66 class_Rings_Olinordered__semiring [141, 1] (w:1, o:146, a:1, s:1, b:0
% 1.28/1.66 ),
% 1.28/1.66 c_Polynomial_Opoly [145, 2] (w:1, o:256, a:1, s:1, b:0),
% 1.28/1.66 class_Rings_Ocomm__semiring__0 [150, 1] (w:1, o:132, a:1, s:1, b:0),
% 1.28/1.66
% 1.28/1.66 class_Int_Oring__char__0 [152, 1] (w:1, o:184, a:1, s:1, b:0),
% 1.28/1.66 class_Rings_Oidom [153, 1] (w:1, o:159, a:1, s:1, b:0),
% 1.28/1.66 c_Polynomial_Opos__poly [156, 2] (w:1, o:257, a:1, s:1, b:0),
% 1.28/1.66 c_Polynomial_Oorder [158, 3] (w:1, o:280, a:1, s:1, b:0),
% 1.28/1.66 tc_Nat_Onat [159, 0] (w:1, o:87, a:1, s:1, b:0),
% 1.28/1.66 c_Polynomial_Opoly__rec [160, 5] (w:1, o:388, a:1, s:1, b:0),
% 1.28/1.66 c_fequal [161, 2] (w:1, o:258, a:1, s:1, b:0),
% 1.28/1.66 c_If [162, 4] (w:1, o:354, a:1, s:1, b:0),
% 1.28/1.66 c_Polynomial_Opcompose [163, 3] (w:1, o:282, a:1, s:1, b:0),
% 1.28/1.66 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize [164, 2] (w:1, o:
% 1.28/1.66 226, a:1, s:1, b:0),
% 1.28/1.66 hBOOL [170, 1] (w:1, o:185, a:1, s:1, b:0),
% 1.28/1.66 class_Rings_Olinordered__semiring__1__strict [178, 1] (w:1, o:147, a:
% 1.28/1.66 1, s:1, b:0),
% 1.28/1.66 c_Groups_Oone__class_Oone [179, 1] (w:1, o:186, a:1, s:1, b:0),
% 1.28/1.66 class_Groups_Oone [181, 1] (w:1, o:187, a:1, s:1, b:0),
% 1.28/1.66 class_RealVector_Oreal__normed__algebra__1 [182, 1] (w:1, o:160, a:1
% 1.28/1.66 , s:1, b:0),
% 1.28/1.66 class_Groups_Omonoid__mult [183, 1] (w:1, o:188, a:1, s:1, b:0),
% 1.28/1.66 class_Groups_Ocomm__monoid__mult [184, 1] (w:1, o:189, a:1, s:1, b:0)
% 1.28/1.66 ,
% 1.28/1.66 class_Rings_Ozero__neq__one [185, 1] (w:1, o:161, a:1, s:1, b:0),
% 1.28/1.66 class_Rings_Olinordered__semiring__1 [186, 1] (w:1, o:148, a:1, s:1
% 1.28/1.66 , b:0),
% 1.28/1.66 c_NthRoot_Oroot [188, 2] (w:1, o:259, a:1, s:1, b:0),
% 1.28/1.66 c_RComplete_Onatceiling [192, 1] (w:1, o:190, a:1, s:1, b:0),
% 1.28/1.66 c_RComplete_Onatfloor [193, 1] (w:1, o:191, a:1, s:1, b:0),
% 1.28/1.66 c_Power_Opower__class_Opower [194, 1] (w:1, o:192, a:1, s:1, b:0),
% 1.28/1.66 tc_Int_Oint [195, 0] (w:1, o:105, a:1, s:1, b:0),
% 1.28/1.66 class_Rings_Oring__1__no__zero__divisors [196, 1] (w:1, o:151, a:1
% 1.28/1.66 , s:1, b:0),
% 1.28/1.66 class_Power_Opower [197, 1] (w:1, o:193, a:1, s:1, b:0),
% 1.28/1.66 class_Rings_Osemiring__0 [198, 1] (w:1, o:162, a:1, s:1, b:0),
% 1.28/1.66 c_Power_Opower_Opower [199, 3] (w:1, o:283, a:1, s:1, b:0),
% 1.28/1.66 c_RealDef_Oreal [200, 2] (w:1, o:260, a:1, s:1, b:0),
% 1.28/1.66 c_Divides_Odiv__class_Odiv [207, 3] (w:1, o:284, a:1, s:1, b:0),
% 1.28/1.66 c_SEQ_Odecseq [209, 2] (w:1, o:261, a:1, s:1, b:0),
% 1.28/1.66 class_Divides_Osemiring__div [211, 1] (w:1, o:195, a:1, s:1, b:0),
% 1.28/1.66 c_Divides_Odiv__class_Omod [213, 3] (w:1, o:285, a:1, s:1, b:0),
% 1.28/1.66 c_SEQ_OBseq [214, 2] (w:1, o:262, a:1, s:1, b:0),
% 1.28/1.66 c_SEQ_Oincseq [222, 2] (w:1, o:263, a:1, s:1, b:0),
% 1.28/1.66 c_Rings_Odvd__class_Odvd [224, 3] (w:1, o:286, a:1, s:1, b:0),
% 1.28/1.66 class_Rings_Odvd [225, 1] (w:1, o:163, a:1, s:1, b:0),
% 1.28/1.66 c_Groups_Ominus__class_Ominus [228, 3] (w:1, o:287, a:1, s:1, b:0),
% 1.28/1.66 class_Rings_Ocomm__ring__1 [229, 1] (w:1, o:130, a:1, s:1, b:0),
% 1.28/1.66 class_Rings_Ocomm__ring [231, 1] (w:1, o:131, a:1, s:1, b:0),
% 1.28/1.66 class_Rings_Oring__1 [233, 1] (w:1, o:152, a:1, s:1, b:0),
% 1.28/1.66 class_Divides_Oring__div [235, 1] (w:1, o:194, a:1, s:1, b:0),
% 1.28/1.66 class_Groups_Oordered__ab__group__add [236, 1] (w:1, o:196, a:1, s:1
% 1.33/1.70 , b:0),
% 1.33/1.70 class_Groups_Ogroup__add [237, 1] (w:1, o:197, a:1, s:1, b:0),
% 1.33/1.70 class_Groups_Oab__group__add [238, 1] (w:1, o:198, a:1, s:1, b:0),
% 1.33/1.70 class_Rings_Oring [239, 1] (w:1, o:153, a:1, s:1, b:0),
% 1.33/1.70 class_RealVector_Oreal__field [241, 1] (w:1, o:164, a:1, s:1, b:0),
% 1.33/1.70 class_Groups_Ocancel__comm__monoid__add [244, 1] (w:1, o:199, a:1, s:
% 1.33/1.70 1, b:0),
% 1.33/1.70 tc_HOL_Obool [246, 0] (w:1, o:104, a:1, s:1, b:0),
% 1.33/1.70 alpha1 [247, 2] (w:1, o:264, a:1, s:1, b:1),
% 1.33/1.70 alpha2 [248, 3] (w:1, o:296, a:1, s:1, b:1),
% 1.33/1.70 alpha3 [249, 3] (w:1, o:301, a:1, s:1, b:1),
% 1.33/1.70 alpha4 [250, 3] (w:1, o:305, a:1, s:1, b:1),
% 1.33/1.70 alpha5 [251, 3] (w:1, o:310, a:1, s:1, b:1),
% 1.33/1.70 alpha6 [252, 3] (w:1, o:315, a:1, s:1, b:1),
% 1.33/1.70 alpha7 [253, 3] (w:1, o:320, a:1, s:1, b:1),
% 1.33/1.70 alpha8 [254, 4] (w:1, o:358, a:1, s:1, b:1),
% 1.33/1.70 alpha9 [255, 4] (w:1, o:359, a:1, s:1, b:1),
% 1.33/1.70 alpha10 [256, 3] (w:1, o:288, a:1, s:1, b:1),
% 1.33/1.70 alpha11 [257, 3] (w:1, o:289, a:1, s:1, b:1),
% 1.33/1.70 alpha12 [258, 3] (w:1, o:290, a:1, s:1, b:1),
% 1.33/1.70 alpha13 [259, 3] (w:1, o:291, a:1, s:1, b:1),
% 1.33/1.70 alpha14 [260, 3] (w:1, o:292, a:1, s:1, b:1),
% 1.33/1.70 alpha15 [261, 3] (w:1, o:293, a:1, s:1, b:1),
% 1.33/1.70 alpha16 [262, 3] (w:1, o:294, a:1, s:1, b:1),
% 1.33/1.70 alpha17 [263, 2] (w:1, o:265, a:1, s:1, b:1),
% 1.33/1.70 alpha18 [264, 2] (w:1, o:266, a:1, s:1, b:1),
% 1.33/1.70 alpha19 [265, 3] (w:1, o:295, a:1, s:1, b:1),
% 1.33/1.70 alpha20 [266, 2] (w:1, o:267, a:1, s:1, b:1),
% 1.33/1.70 alpha21 [267, 3] (w:1, o:297, a:1, s:1, b:1),
% 1.33/1.70 alpha22 [268, 4] (w:1, o:360, a:1, s:1, b:1),
% 1.33/1.70 alpha23 [269, 4] (w:1, o:361, a:1, s:1, b:1),
% 1.33/1.70 alpha24 [270, 2] (w:1, o:268, a:1, s:1, b:1),
% 1.33/1.70 alpha25 [271, 2] (w:1, o:269, a:1, s:1, b:1),
% 1.33/1.70 alpha26 [272, 2] (w:1, o:270, a:1, s:1, b:1),
% 1.33/1.70 alpha27 [273, 3] (w:1, o:298, a:1, s:1, b:1),
% 1.33/1.70 alpha28 [274, 3] (w:1, o:299, a:1, s:1, b:1),
% 1.33/1.70 alpha29 [275, 3] (w:1, o:300, a:1, s:1, b:1),
% 1.33/1.70 alpha30 [276, 3] (w:1, o:302, a:1, s:1, b:1),
% 1.33/1.70 alpha31 [277, 4] (w:1, o:362, a:1, s:1, b:1),
% 1.33/1.70 alpha32 [278, 4] (w:1, o:363, a:1, s:1, b:1),
% 1.33/1.70 alpha33 [279, 4] (w:1, o:364, a:1, s:1, b:1),
% 1.33/1.70 alpha34 [280, 4] (w:1, o:365, a:1, s:1, b:1),
% 1.33/1.70 alpha35 [281, 4] (w:1, o:366, a:1, s:1, b:1),
% 1.33/1.70 alpha36 [282, 4] (w:1, o:367, a:1, s:1, b:1),
% 1.33/1.70 alpha37 [283, 3] (w:1, o:303, a:1, s:1, b:1),
% 1.33/1.70 alpha38 [284, 3] (w:1, o:304, a:1, s:1, b:1),
% 1.33/1.70 alpha39 [285, 4] (w:1, o:368, a:1, s:1, b:1),
% 1.33/1.70 alpha40 [286, 4] (w:1, o:369, a:1, s:1, b:1),
% 1.33/1.70 alpha41 [287, 3] (w:1, o:306, a:1, s:1, b:1),
% 1.33/1.70 alpha42 [288, 2] (w:1, o:271, a:1, s:1, b:1),
% 1.33/1.70 alpha43 [289, 3] (w:1, o:307, a:1, s:1, b:1),
% 1.33/1.70 alpha44 [290, 3] (w:1, o:308, a:1, s:1, b:1),
% 1.33/1.70 alpha45 [291, 3] (w:1, o:309, a:1, s:1, b:1),
% 1.33/1.70 alpha46 [292, 4] (w:1, o:370, a:1, s:1, b:1),
% 1.33/1.70 alpha47 [293, 4] (w:1, o:371, a:1, s:1, b:1),
% 1.33/1.70 alpha48 [294, 4] (w:1, o:372, a:1, s:1, b:1),
% 1.33/1.70 alpha49 [295, 4] (w:1, o:373, a:1, s:1, b:1),
% 1.33/1.70 alpha50 [296, 4] (w:1, o:374, a:1, s:1, b:1),
% 1.33/1.70 alpha51 [297, 4] (w:1, o:375, a:1, s:1, b:1),
% 1.33/1.70 alpha52 [298, 3] (w:1, o:311, a:1, s:1, b:1),
% 1.33/1.70 alpha53 [299, 2] (w:1, o:272, a:1, s:1, b:1),
% 1.33/1.70 alpha54 [300, 3] (w:1, o:312, a:1, s:1, b:1),
% 1.33/1.70 alpha55 [301, 3] (w:1, o:313, a:1, s:1, b:1),
% 1.33/1.70 alpha56 [302, 3] (w:1, o:314, a:1, s:1, b:1),
% 1.33/1.70 alpha57 [303, 4] (w:1, o:376, a:1, s:1, b:1),
% 1.33/1.70 alpha58 [304, 4] (w:1, o:377, a:1, s:1, b:1),
% 1.33/1.70 alpha59 [305, 4] (w:1, o:378, a:1, s:1, b:1),
% 1.33/1.70 alpha60 [306, 4] (w:1, o:379, a:1, s:1, b:1),
% 1.33/1.70 alpha61 [307, 4] (w:1, o:380, a:1, s:1, b:1),
% 1.33/1.70 alpha62 [308, 4] (w:1, o:381, a:1, s:1, b:1),
% 1.33/1.70 alpha63 [309, 3] (w:1, o:316, a:1, s:1, b:1),
% 1.33/1.70 alpha64 [310, 3] (w:1, o:317, a:1, s:1, b:1),
% 1.33/1.70 alpha65 [311, 3] (w:1, o:318, a:1, s:1, b:1),
% 1.33/1.70 alpha66 [312, 3] (w:1, o:319, a:1, s:1, b:1),
% 1.33/1.70 alpha67 [313, 4] (w:1, o:382, a:1, s:1, b:1),
% 1.33/1.70 alpha68 [314, 4] (w:1, o:383, a:1, s:1, b:1),
% 1.33/1.70 alpha69 [315, 4] (w:1, o:384, a:1, s:1, b:1),
% 4.20/4.61 alpha70 [316, 4] (w:1, o:355, a:1, s:1, b:1),
% 4.20/4.61 alpha71 [317, 3] (w:1, o:321, a:1, s:1, b:1),
% 4.20/4.61 alpha72 [318, 3] (w:1, o:322, a:1, s:1, b:1),
% 4.20/4.61 alpha73 [319, 3] (w:1, o:323, a:1, s:1, b:1),
% 4.20/4.61 alpha74 [320, 3] (w:1, o:324, a:1, s:1, b:1),
% 4.20/4.61 alpha75 [321, 3] (w:1, o:325, a:1, s:1, b:1),
% 4.20/4.61 alpha76 [322, 4] (w:1, o:356, a:1, s:1, b:1),
% 4.20/4.61 alpha77 [323, 3] (w:1, o:326, a:1, s:1, b:1),
% 4.20/4.61 alpha78 [324, 3] (w:1, o:327, a:1, s:1, b:1),
% 4.20/4.61 alpha79 [325, 4] (w:1, o:357, a:1, s:1, b:1),
% 4.20/4.61 alpha80 [326, 3] (w:1, o:328, a:1, s:1, b:1),
% 4.20/4.61 alpha81 [327, 2] (w:1, o:273, a:1, s:1, b:1),
% 4.20/4.61 alpha82 [328, 3] (w:1, o:329, a:1, s:1, b:1),
% 4.20/4.61 alpha83 [329, 2] (w:1, o:274, a:1, s:1, b:1),
% 4.20/4.61 alpha84 [330, 2] (w:1, o:275, a:1, s:1, b:1),
% 4.20/4.61 alpha85 [331, 3] (w:1, o:330, a:1, s:1, b:1),
% 4.20/4.61 skol1 [332, 2] (w:1, o:228, a:1, s:1, b:1),
% 4.20/4.61 skol2 [333, 3] (w:1, o:331, a:1, s:1, b:1),
% 4.20/4.61 skol3 [334, 0] (w:1, o:12, a:1, s:1, b:1),
% 4.20/4.61 skol4 [335, 2] (w:1, o:232, a:1, s:1, b:1),
% 4.20/4.61 skol5 [336, 2] (w:1, o:234, a:1, s:1, b:1),
% 4.20/4.61 skol6 [337, 2] (w:1, o:238, a:1, s:1, b:1),
% 4.20/4.61 skol7 [338, 2] (w:1, o:239, a:1, s:1, b:1),
% 4.20/4.61 skol8 [339, 1] (w:1, o:119, a:1, s:1, b:1),
% 4.20/4.61 skol9 [340, 2] (w:1, o:240, a:1, s:1, b:1),
% 4.20/4.61 skol10 [341, 2] (w:1, o:241, a:1, s:1, b:1),
% 4.20/4.61 skol11 [342, 2] (w:1, o:242, a:1, s:1, b:1),
% 4.20/4.61 skol12 [343, 2] (w:1, o:243, a:1, s:1, b:1),
% 4.20/4.61 skol13 [344, 1] (w:1, o:120, a:1, s:1, b:1),
% 4.20/4.61 skol14 [345, 2] (w:1, o:244, a:1, s:1, b:1),
% 4.20/4.61 skol15 [346, 2] (w:1, o:245, a:1, s:1, b:1),
% 4.20/4.61 skol16 [347, 2] (w:1, o:246, a:1, s:1, b:1),
% 4.20/4.61 skol17 [348, 2] (w:1, o:247, a:1, s:1, b:1),
% 4.20/4.61 skol18 [349, 1] (w:1, o:121, a:1, s:1, b:1),
% 4.20/4.61 skol19 [350, 2] (w:1, o:248, a:1, s:1, b:1),
% 4.20/4.61 skol20 [351, 3] (w:1, o:332, a:1, s:1, b:1),
% 4.20/4.61 skol21 [352, 3] (w:1, o:333, a:1, s:1, b:1),
% 4.20/4.61 skol22 [353, 2] (w:1, o:249, a:1, s:1, b:1),
% 4.20/4.61 skol23 [354, 2] (w:1, o:250, a:1, s:1, b:1),
% 4.20/4.61 skol24 [355, 2] (w:1, o:251, a:1, s:1, b:1),
% 4.20/4.61 skol25 [356, 2] (w:1, o:252, a:1, s:1, b:1),
% 4.20/4.61 skol26 [357, 3] (w:1, o:334, a:1, s:1, b:1),
% 4.20/4.61 skol27 [358, 4] (w:1, o:385, a:1, s:1, b:1),
% 4.20/4.61 skol28 [359, 2] (w:1, o:253, a:1, s:1, b:1),
% 4.20/4.61 skol29 [360, 2] (w:1, o:254, a:1, s:1, b:1),
% 4.20/4.61 skol30 [361, 2] (w:1, o:229, a:1, s:1, b:1),
% 4.20/4.61 skol31 [362, 3] (w:1, o:335, a:1, s:1, b:1),
% 4.20/4.61 skol32 [363, 3] (w:1, o:336, a:1, s:1, b:1),
% 4.20/4.61 skol33 [364, 3] (w:1, o:337, a:1, s:1, b:1),
% 4.20/4.61 skol34 [365, 3] (w:1, o:338, a:1, s:1, b:1),
% 4.20/4.61 skol35 [366, 3] (w:1, o:339, a:1, s:1, b:1),
% 4.20/4.61 skol36 [367, 3] (w:1, o:340, a:1, s:1, b:1),
% 4.20/4.61 skol37 [368, 3] (w:1, o:341, a:1, s:1, b:1),
% 4.20/4.61 skol38 [369, 2] (w:1, o:230, a:1, s:1, b:1),
% 4.20/4.61 skol39 [370, 2] (w:1, o:231, a:1, s:1, b:1),
% 4.20/4.61 skol40 [371, 3] (w:1, o:342, a:1, s:1, b:1),
% 4.20/4.61 skol41 [372, 3] (w:1, o:343, a:1, s:1, b:1),
% 4.20/4.61 skol42 [373, 3] (w:1, o:344, a:1, s:1, b:1),
% 4.20/4.61 skol43 [374, 3] (w:1, o:345, a:1, s:1, b:1),
% 4.20/4.61 skol44 [375, 3] (w:1, o:346, a:1, s:1, b:1),
% 4.20/4.61 skol45 [376, 3] (w:1, o:347, a:1, s:1, b:1),
% 4.20/4.61 skol46 [377, 2] (w:1, o:233, a:1, s:1, b:1),
% 4.20/4.61 skol47 [378, 4] (w:1, o:386, a:1, s:1, b:1),
% 4.20/4.61 skol48 [379, 3] (w:1, o:348, a:1, s:1, b:1),
% 4.20/4.61 skol49 [380, 3] (w:1, o:349, a:1, s:1, b:1),
% 4.20/4.61 skol50 [381, 2] (w:1, o:235, a:1, s:1, b:1),
% 4.20/4.61 skol51 [382, 4] (w:1, o:387, a:1, s:1, b:1),
% 4.20/4.61 skol52 [383, 2] (w:1, o:236, a:1, s:1, b:1),
% 4.20/4.61 skol53 [384, 3] (w:1, o:350, a:1, s:1, b:1),
% 4.20/4.61 skol54 [385, 3] (w:1, o:351, a:1, s:1, b:1),
% 4.20/4.61 skol55 [386, 3] (w:1, o:352, a:1, s:1, b:1),
% 4.20/4.61 skol56 [387, 2] (w:1, o:237, a:1, s:1, b:1),
% 4.20/4.61 skol57 [388, 3] (w:1, o:353, a:1, s:1, b:1).
% 4.20/4.61
% 4.20/4.61
% 4.20/4.61 Starting Search:
% 4.20/4.61
% 4.20/4.61 *** allocated 170857 integers for clauses
% 4.20/4.61
% 4.20/4.61 Intermediate Status:
% 4.20/4.61 Generated: 2772
% 4.20/4.61 Kept: 2038
% 4.20/4.61 Inuse: 0
% 4.20/4.61 Deleted: 0
% 4.20/4.61 Deletedinuse: 0
% 4.20/4.61
% 4.20/4.61 Resimplifying inuse:
% 4.20/4.61 Done
% 4.20/4.61
% 4.20/4.61 *** allocated 256285 integers for clauses
% 4.20/4.61 *** allocated 170857 integers for termspace/termends
% 4.20/4.61 Resimplifying inuse:
% 4.20/4.61 Done
% 4.20/4.61
% 4.20/4.61 *** allocated 384427 integers for clauses
% 4.20/4.61
% 4.20/4.61 Intermediate Status:
% 4.20/4.61 Generated: 10434
% 4.20/4.61 Kept: 4274
% 4.20/4.61 Inuse: 176
% 4.20/4.61 Deleted: 5
% 4.20/4.61 Deletedinuse: 0
% 4.20/4.61
% 4.20/4.61 Resimplifying inuse:
% 4.20/4.61 Done
% 4.20/4.61
% 4.20/4.61 *** allocated 256285 integers for termspace/termends
% 4.20/4.61 Resimplifying inuse:
% 4.20/4.61 Done
% 4.20/4.61
% 4.20/4.61
% 4.20/4.61 Intermediate Status:
% 4.20/4.61 Generated: 20012
% 4.20/4.61 Kept: 6350
% 4.20/4.61 Inuse: 266
% 4.20/4.61 Deleted: 10
% 4.20/4.61 Deletedinuse: 0
% 4.20/4.61
% 4.20/4.61 *** allocated 576640 integers for clauses
% 4.20/4.61 Resimplifying inuse:
% 4.20/4.61 Done
% 4.20/4.61
% 4.20/4.61 *** allocated 384427 integers for termspace/termends
% 4.20/4.61 Resimplifying inuse:
% 4.20/4.61 Done
% 4.20/4.61
% 4.20/4.61
% 4.20/4.61 Intermediate Status:
% 4.20/4.61 Generated: 28386
% 4.20/4.61 Kept: 8449
% 4.20/4.61 Inuse: 335
% 4.20/4.61 Deleted: 11
% 4.20/4.61 Deletedinuse: 0
% 4.20/4.61
% 4.20/4.61 Resimplifying inuse:
% 4.20/4.61 Done
% 4.20/4.61
% 4.20/4.61 Resimplifying inuse:
% 4.20/4.61 Done
% 4.20/4.61
% 4.20/4.61 *** allocated 864960 integers for clauses
% 4.20/4.61
% 4.20/4.61 Intermediate Status:
% 4.20/4.61 Generated: 34343
% 4.20/4.61 Kept: 10452
% 4.20/4.61 Inuse: 377
% 4.20/4.61 Deleted: 12
% 4.20/4.61 Deletedinuse: 1
% 4.20/4.61
% 4.20/4.61 Resimplifying inuse:
% 4.20/4.61 Done
% 4.20/4.61
% 4.20/4.61 *** allocated 576640 integers for termspace/termends
% 4.20/4.61 Resimplifying inuse:
% 4.20/4.61 Done
% 4.20/4.61
% 4.20/4.61
% 4.20/4.61 Intermediate Status:
% 4.20/4.61 Generated: 39420
% 4.20/4.61 Kept: 12626
% 4.20/4.61 Inuse: 413
% 4.20/4.61 Deleted: 14
% 4.20/4.61 Deletedinuse: 1
% 4.20/4.61
% 4.20/4.61 Resimplifying inuse:
% 4.20/4.61 Done
% 4.20/4.61
% 4.20/4.61 Resimplifying inuse:
% 4.20/4.61 Done
% 4.20/4.61
% 4.20/4.61
% 4.20/4.61 Intermediate Status:
% 4.20/4.61 Generated: 45957
% 4.20/4.61 Kept: 14636
% 4.20/4.61 Inuse: 463
% 4.20/4.61 Deleted: 14
% 4.20/4.61 Deletedinuse: 1
% 4.20/4.61
% 4.20/4.61 Resimplifying inuse:
% 4.20/4.61 Done
% 4.20/4.61
% 4.20/4.61 Resimplifying inuse:
% 4.20/4.61 Done
% 4.20/4.61
% 4.20/4.61 *** allocated 1297440 integers for clauses
% 4.20/4.61
% 4.20/4.61 Intermediate Status:
% 4.20/4.61 Generated: 52607
% 4.20/4.61 Kept: 16642
% 4.20/4.61 Inuse: 520
% 4.20/4.61 Deleted: 14
% 4.20/4.61 Deletedinuse: 1
% 4.20/4.61
% 4.20/4.61 *** allocated 864960 integers for termspace/termends
% 4.20/4.61 Resimplifying inuse:
% 4.20/4.61 Done
% 4.20/4.61
% 4.20/4.61
% 4.20/4.61 Intermediate Status:
% 4.20/4.61 Generated: 68720
% 4.20/4.61 Kept: 19580
% 4.20/4.61 Inuse: 528
% 4.20/4.61 Deleted: 14
% 4.20/4.61 Deletedinuse: 1
% 4.20/4.61
% 4.20/4.61 Resimplifying inuse:
% 4.20/4.61 Done
% 4.20/4.61
% 4.20/4.61 Resimplifying inuse:
% 4.20/4.61 Done
% 4.20/4.61
% 4.20/4.61 Resimplifying clauses:
% 4.20/4.61
% 4.20/4.61 Bliksems!, er is een bewijs:
% 4.20/4.61 % SZS status Theorem
% 4.20/4.61 % SZS output start Refutation
% 4.20/4.61
% 4.20/4.61 (2) {G0,W16,D5,L1,V2,M1} I { c_Orderings_Oord__class_Oless__eq(
% 4.20/4.61 tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y
% 4.20/4.61 ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 4.20/4.61 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 4.20/4.61 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X ) ),
% 4.20/4.61 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) ) }.
% 4.20/4.61 (62) {G0,W11,D3,L2,V3,M2} I { ! class_Rings_Ocomm__semiring__1( X ),
% 4.20/4.61 c_Groups_Oplus__class_Oplus( X, Z, Y ) = c_Groups_Oplus__class_Oplus( X,
% 4.20/4.61 Y, Z ) }.
% 4.20/4.61 (1570) {G0,W2,D2,L1,V0,M1} I { class_Rings_Ocomm__semiring__1(
% 4.20/4.61 tc_Complex_Ocomplex ) }.
% 4.20/4.61 (1654) {G0,W26,D8,L1,V0,M1} I { ! c_Orderings_Oord__class_Oless__eq(
% 4.20/4.61 tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 4.20/4.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), v_z____
% 4.20/4.61 ), v_c____ ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 4.20/4.61 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 4.20/4.61 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, v_aa____, hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), v_z____ ), v_c____
% 4.20/4.61 ) ) ), c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_aa____ )
% 4.20/4.61 ) ) }.
% 4.20/4.61 (6974) {G1,W16,D5,L1,V2,M1} P(62,2);r(1570) {
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 4.20/4.61 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ),
% 4.20/4.61 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 4.20/4.61 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 4.20/4.61 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X ) ),
% 4.20/4.61 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y ) ) ) }.
% 4.20/4.61 (20913) {G2,W0,D0,L0,V0,M0} S(1654);r(6974) { }.
% 4.20/4.61
% 4.20/4.61
% 4.20/4.61 % SZS output end Refutation
% 4.20/4.61 found a proof!
% 4.20/4.61
% 4.20/4.61
% 4.20/4.61 Unprocessed initial clauses:
% 4.20/4.61
% 4.20/4.61 (20915) {G0,W14,D4,L2,V2,M2} { ! hAPP( Y, skol1( X, Y ) ) = hAPP( X, skol1
% 4.20/4.61 ( X, Y ) ), Y = X }.
% 4.20/4.61 (20916) {G0,W26,D8,L1,V0,M1} { c_Orderings_Oord__class_Oless__eq(
% 4.20/4.61 tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 4.20/4.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), v_z____
% 4.20/4.61 ), v_c____ ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 4.20/4.61 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 4.20/4.61 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), v_z____ ), v_c____
% 4.20/4.61 ), v_aa____ ) ), c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 4.20/4.61 v_aa____ ) ) ) }.
% 4.20/4.61 (20917) {G0,W16,D5,L1,V2,M1} { c_Orderings_Oord__class_Oless__eq(
% 4.20/4.61 tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y
% 4.20/4.61 ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 4.20/4.61 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 4.20/4.61 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X ) ),
% 4.20/4.61 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) ) }.
% 4.20/4.61 (20918) {G0,W5,D4,L1,V0,M1} { ! v_p = c_Groups_Ozero__class_Ozero(
% 4.20/4.61 tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ) }.
% 4.20/4.61 (20919) {G0,W18,D4,L2,V3,M2} { ! class_RealVector_Oreal__normed__vector( X
% 4.20/4.61 ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 4.20/4.61 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 4.20/4.61 ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 4.20/4.61 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 4.20/4.61 ( X, Y ) ) ) }.
% 4.20/4.61 (20920) {G0,W18,D6,L1,V0,M1} { c_Orderings_Oord__class_Oless__eq(
% 4.20/4.61 tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 4.20/4.61 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, v_da____ ),
% 4.20/4.61 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_aa____ ) ),
% 4.20/4.61 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), v_z____ ), v_c____
% 4.20/4.61 ) ) ) }.
% 4.20/4.61 (20921) {G0,W22,D6,L2,V3,M2} { ! class_RealVector_Oreal__normed__algebra(
% 4.20/4.61 X ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 4.20/4.61 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 4.20/4.61 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 4.20/4.61 c_RealVector_Onorm__class_Onorm( X, Y ) ) ) }.
% 4.20/4.61 (20922) {G0,W6,D2,L2,V2,M2} { ! class_Orderings_Opreorder( X ),
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, Y, Y ) }.
% 4.20/4.61 (20923) {G0,W4,D3,L1,V0,M1} { ! v_c____ = c_Groups_Ozero__class_Ozero(
% 4.20/4.61 tc_Complex_Ocomplex ) }.
% 4.20/4.61 (20924) {G0,W14,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 4.20/4.61 tc_RealDef_Oreal, Y, X ), c_Orderings_Oord__class_Oless__eq(
% 4.20/4.61 tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ),
% 4.20/4.61 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, X ) ) }.
% 4.20/4.61 (20925) {G0,W21,D6,L2,V3,M2} { !
% 4.20/4.61 class_RealVector_Oreal__normed__div__algebra( X ),
% 4.20/4.61 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 4.20/4.61 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 4.20/4.61 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 4.20/4.61 (20926) {G0,W26,D6,L2,V4,M2} { ! class_RealVector_Oreal__normed__algebra(
% 4.20/4.61 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ),
% 4.20/4.61 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 4.20/4.61 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 4.20/4.61 (20927) {G0,W26,D6,L2,V4,M2} { ! class_Rings_Ocomm__semiring__1( X ), hAPP
% 4.20/4.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ),
% 4.20/4.61 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 4.20/4.61 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 4.20/4.61 (20928) {G0,W26,D6,L2,V4,M2} { ! class_RealVector_Oreal__normed__algebra(
% 4.20/4.61 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ),
% 4.20/4.61 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 4.20/4.61 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 4.20/4.61 (20929) {G0,W37,D6,L4,V5,M4} { !
% 4.20/4.61 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct( X
% 4.20/4.61 ), U = T, Z = Y, ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 4.20/4.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 4.20/4.61 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 4.20/4.61 ) }.
% 4.20/4.61 (20930) {G0,W34,D6,L3,V5,M3} { !
% 4.20/4.61 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct( X
% 4.20/4.61 ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 4.20/4.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 4.20/4.61 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 4.20/4.61 ), ! U = T }.
% 4.20/4.61 (20931) {G0,W34,D6,L3,V5,M3} { !
% 4.20/4.61 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct( X
% 4.20/4.61 ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 4.20/4.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 4.20/4.61 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 4.20/4.61 ), ! Z = Y }.
% 4.20/4.61 (20932) {G0,W5,D4,L1,V0,M1} { v_cs____ = c_Groups_Ozero__class_Ozero(
% 4.20/4.61 tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ) }.
% 4.20/4.61 (20933) {G0,W20,D4,L3,V3,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 4.20/4.61 tc_RealDef_Oreal, Z, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X
% 4.20/4.61 ) ), ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 4.20/4.61 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs
% 4.20/4.61 ( tc_RealDef_Oreal, v_da____ ), X ), Z ),
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, v_da____, Y ) }.
% 4.20/4.61 (20934) {G0,W18,D5,L1,V0,M1} { c_Orderings_Oord__class_Oless__eq(
% 4.20/4.61 tc_RealDef_Oreal, c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 4.20/4.61 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs
% 4.20/4.61 ( tc_RealDef_Oreal, v_da____ ), c_RealVector_Onorm__class_Onorm(
% 4.20/4.61 tc_Complex_Ocomplex, v_aa____ ) ), c_RealVector_Onorm__class_Onorm(
% 4.20/4.61 tc_Complex_Ocomplex, v_c____ ) ), c_RealVector_Onorm__class_Onorm(
% 4.20/4.61 tc_Complex_Ocomplex, v_z____ ) ) }.
% 4.20/4.61 (20935) {G0,W9,D4,L2,V1,M2} { ! class_RealVector_Oreal__normed__vector( X
% 4.20/4.61 ), c_RealVector_Onorm__class_Onorm( X, c_Groups_Ozero__class_Ozero( X )
% 4.20/4.61 ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 4.20/4.61 (20936) {G0,W7,D3,L1,V1,M1} { c_RealVector_Onorm__class_Onorm(
% 4.20/4.61 tc_RealDef_Oreal, X ) = c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X )
% 4.20/4.61 }.
% 4.20/4.61 (20937) {G0,W13,D5,L1,V2,M1} { hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 4.20/4.61 tc_RealDef_Oreal ), Y ), X ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 4.20/4.61 ( tc_RealDef_Oreal ), X ), Y ) }.
% 4.20/4.61 (20938) {G0,W12,D3,L3,V2,M3} { ! class_RealVector_Oreal__normed__vector( X
% 4.20/4.61 ), ! c_RealVector_Onorm__class_Onorm( X, Y ) =
% 4.20/4.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y =
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ) }.
% 4.20/4.61 (20939) {G0,W12,D3,L3,V2,M3} { ! class_RealVector_Oreal__normed__vector( X
% 4.20/4.61 ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 4.20/4.61 c_RealVector_Onorm__class_Onorm( X, Y ) = c_Groups_Ozero__class_Ozero(
% 4.20/4.61 tc_RealDef_Oreal ) }.
% 4.20/4.61 (20940) {G0,W23,D7,L1,V3,M1} { hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 4.20/4.61 tc_RealDef_Oreal ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 4.20/4.61 tc_RealDef_Oreal ), Z ), Y ) ), X ) = hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 4.20/4.61 (20941) {G0,W11,D4,L2,V2,M2} { ! class_RealVector_Oreal__normed__vector( X
% 4.20/4.61 ), c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 4.20/4.61 c_RealVector_Onorm__class_Onorm( X, Y ) ) =
% 4.20/4.61 c_RealVector_Onorm__class_Onorm( X, Y ) }.
% 4.20/4.61 (20942) {G0,W12,D5,L2,V2,M2} { ! class_RealVector_Oreal__normed__algebra(
% 4.20/4.61 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ),
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 4.20/4.61 (20943) {G0,W12,D5,L2,V2,M2} { ! class_RealVector_Oreal__normed__algebra(
% 4.20/4.61 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ),
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 4.20/4.61 (20944) {G0,W12,D5,L2,V2,M2} { ! class_Rings_Ocomm__semiring__1( X ), hAPP
% 4.20/4.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ),
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 4.20/4.61 (20945) {G0,W12,D5,L2,V2,M2} { ! class_RealVector_Oreal__normed__algebra(
% 4.20/4.61 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ) ), Y ) = c_Groups_Ozero__class_Ozero( X
% 4.20/4.61 ) }.
% 4.20/4.61 (20946) {G0,W12,D5,L2,V2,M2} { ! class_RealVector_Oreal__normed__algebra(
% 4.20/4.61 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ) ), Y ) = c_Groups_Ozero__class_Ozero( X
% 4.20/4.61 ) }.
% 4.20/4.61 (20947) {G0,W12,D5,L2,V2,M2} { ! class_Rings_Ocomm__semiring__1( X ), hAPP
% 4.20/4.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero(
% 4.20/4.61 X ) ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 4.20/4.61 (20948) {G0,W12,D3,L3,V3,M3} { !
% 4.20/4.61 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct( X
% 4.20/4.61 ), ! Z = c_Groups_Oplus__class_Oplus( X, Z, Y ), Y =
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ) }.
% 4.20/4.61 (20949) {G0,W12,D3,L3,V3,M3} { !
% 4.20/4.61 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct( X
% 4.20/4.61 ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 4.20/4.61 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 4.20/4.61 (20950) {G0,W9,D4,L2,V2,M2} { ! class_Rings_Ocomm__semiring__1( X ),
% 4.20/4.61 c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Ozero__class_Ozero( X ) ) = Y
% 4.20/4.61 }.
% 4.20/4.61 (20951) {G0,W9,D4,L2,V2,M2} { ! class_Rings_Ocomm__semiring__1( X ),
% 4.20/4.61 c_Groups_Oplus__class_Oplus( X, c_Groups_Ozero__class_Ozero( X ), Y ) = Y
% 4.20/4.61 }.
% 4.20/4.61 (20952) {G0,W24,D6,L1,V3,M1} { hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 4.20/4.61 tc_RealDef_Oreal ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y )
% 4.20/4.61 ), X ) = c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 4.20/4.61 (20953) {G0,W13,D3,L3,V2,M3} { ! class_RealVector_Oreal__normed__vector( X
% 4.20/4.61 ), ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 4.20/4.61 c_RealVector_Onorm__class_Onorm( X, Y ), c_Groups_Ozero__class_Ozero(
% 4.20/4.61 tc_RealDef_Oreal ) ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 4.20/4.61 (20954) {G0,W13,D3,L3,V2,M3} { ! class_RealVector_Oreal__normed__vector( X
% 4.20/4.61 ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 4.20/4.61 c_RealVector_Onorm__class_Onorm( X, Y ), c_Groups_Ozero__class_Ozero(
% 4.20/4.61 tc_RealDef_Oreal ) ) }.
% 4.20/4.61 (20955) {G0,W31,D6,L5,V6,M5} { !
% 4.20/4.61 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct( X
% 4.20/4.61 ), Y = c_Groups_Ozero__class_Ozero( X ), ! W = U, T = Z, !
% 4.20/4.61 c_Groups_Oplus__class_Oplus( X, W, hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) =
% 4.20/4.61 c_Groups_Oplus__class_Oplus( X, U, hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 4.20/4.61 (20956) {G0,W10,D2,L3,V3,M3} { ! class_Orderings_Olinorder( X ),
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 4.20/4.61 (20957) {G0,W16,D3,L3,V5,M3} { ! class_Orderings_Oord( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ),
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ), hAPP( Y, U ) ) }.
% 4.20/4.61 (20958) {G0,W14,D2,L4,V4,M4} { ! class_Orderings_Oorder( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 4.20/4.61 (20959) {G0,W13,D2,L4,V3,M4} { ! class_Orderings_Oorder( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 4.20/4.61 (20960) {G0,W14,D2,L4,V4,M4} { ! class_Orderings_Opreorder( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 4.20/4.61 (20961) {G0,W13,D2,L4,V3,M4} { ! class_Orderings_Oorder( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 4.20/4.61 (20962) {G0,W13,D2,L4,V4,M4} { ! class_Orderings_Oorder( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), ! Z = T,
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 4.20/4.61 (20963) {G0,W13,D2,L4,V4,M4} { ! class_Orderings_Oord( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), ! Y = T,
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 4.20/4.61 (20964) {G0,W13,D2,L4,V4,M4} { ! class_Orderings_Oorder( X ), ! Z = Y, !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 4.20/4.61 (20965) {G0,W13,D2,L4,V4,M4} { ! class_Orderings_Oord( X ), ! Z = Y, !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 4.20/4.61 (20966) {G0,W13,D2,L4,V3,M4} { ! class_Orderings_Oorder( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 4.20/4.61 (20967) {G0,W13,D2,L4,V3,M4} { ! class_Orderings_Oorder( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), ! Y = Z,
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 4.20/4.61 (20968) {G0,W16,D3,L3,V5,M3} { ! class_Orderings_Oord( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ),
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ), hAPP( Y, U ) ) }.
% 4.20/4.61 (20969) {G0,W9,D2,L3,V3,M3} { ! class_Orderings_Opreorder( X ), ! Z = Y,
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 4.20/4.61 (20970) {G0,W9,D2,L3,V3,M3} { ! class_Orderings_Oorder( X ), ! Z = Y,
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 4.20/4.61 (20971) {G0,W9,D2,L3,V3,M3} { ! class_Orderings_Oorder( X ), ! Z = Y,
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 4.20/4.61 (20972) {G0,W13,D2,L4,V3,M4} { ! class_Orderings_Oorder( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 4.20/4.61 (20973) {G0,W10,D2,L3,V3,M3} { ! class_Orderings_Olinorder( X ),
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 4.20/4.61 (20974) {G0,W16,D3,L3,V5,M3} { ! class_Orderings_Oord( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ),
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ), hAPP( Y, U ) ) }.
% 4.20/4.61 (20975) {G0,W22,D4,L3,V4,M3} { ! class_Orderings_Oord( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, skol2( X, Y, Z ) ), hAPP(
% 4.20/4.61 Y, skol2( X, Y, Z ) ) ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X
% 4.20/4.61 ), Z, Y ) }.
% 4.20/4.61 (20976) {G0,W35,D7,L2,V5,M2} { ! class_Rings_Ocomm__semiring__1( X ), hAPP
% 4.20/4.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 4.20/4.61 (20977) {G0,W35,D8,L2,V5,M2} { ! class_Rings_Ocomm__semiring__1( X ), hAPP
% 4.20/4.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), Y ) ) }.
% 4.20/4.61 (20978) {G0,W35,D7,L2,V5,M2} { ! class_Rings_Ocomm__semiring__1( X ), hAPP
% 4.20/4.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 4.20/4.61 (20979) {G0,W25,D7,L2,V4,M2} { ! class_Rings_Ocomm__semiring__1( X ), hAPP
% 4.20/4.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Z ) }.
% 4.20/4.61 (20980) {G0,W25,D7,L2,V4,M2} { ! class_Rings_Ocomm__semiring__1( X ), hAPP
% 4.20/4.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 4.20/4.61 (20981) {G0,W25,D7,L2,V4,M2} { ! class_Rings_Ocomm__semiring__1( X ), hAPP
% 4.20/4.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 4.20/4.61 (20982) {G0,W25,D6,L2,V4,M2} { ! class_Rings_Ocomm__semiring__1( X ), hAPP
% 4.20/4.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 4.20/4.61 (20983) {G0,W15,D5,L2,V3,M2} { ! class_Rings_Ocomm__semiring__1( X ), hAPP
% 4.20/4.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 4.20/4.61 (20984) {G0,W23,D4,L2,V5,M2} { ! class_Rings_Ocomm__semiring__1( X ),
% 4.20/4.61 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X, U, T ),
% 4.20/4.61 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 4.20/4.61 , c_Groups_Oplus__class_Oplus( X, U, Z ), c_Groups_Oplus__class_Oplus( X
% 4.20/4.61 , T, Y ) ) }.
% 4.20/4.61 (20985) {G0,W17,D4,L2,V4,M2} { ! class_Rings_Ocomm__semiring__1( X ),
% 4.20/4.61 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y
% 4.20/4.61 ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X, T, Y
% 4.20/4.61 ), Z ) }.
% 4.20/4.61 (20986) {G0,W17,D4,L2,V4,M2} { ! class_Rings_Ocomm__semiring__1( X ),
% 4.20/4.61 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y
% 4.20/4.61 ) = c_Groups_Oplus__class_Oplus( X, T, c_Groups_Oplus__class_Oplus( X, Z
% 4.20/4.61 , Y ) ) }.
% 4.20/4.61 (20987) {G0,W17,D4,L2,V4,M2} { ! class_Rings_Ocomm__semiring__1( X ),
% 4.20/4.61 c_Groups_Oplus__class_Oplus( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y )
% 4.20/4.61 ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X, T, Z
% 4.20/4.61 ), Y ) }.
% 4.20/4.61 (20988) {G0,W17,D4,L2,V4,M2} { ! class_Rings_Ocomm__semiring__1( X ),
% 4.20/4.61 c_Groups_Oplus__class_Oplus( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y )
% 4.20/4.61 ) = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Oplus__class_Oplus( X, T
% 4.20/4.61 , Y ) ) }.
% 4.20/4.61 (20989) {G0,W11,D3,L2,V3,M2} { ! class_Rings_Ocomm__semiring__1( X ),
% 4.20/4.61 c_Groups_Oplus__class_Oplus( X, Z, Y ) = c_Groups_Oplus__class_Oplus( X,
% 4.20/4.61 Y, Z ) }.
% 4.20/4.61 (20990) {G0,W11,D2,L3,V2,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 4.20/4.61 tc_RealDef_Oreal, Y, X ), ! c_Orderings_Oord__class_Oless__eq(
% 4.20/4.61 tc_RealDef_Oreal, X, Y ), Y = X }.
% 4.20/4.61 (20991) {G0,W12,D2,L3,V3,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 4.20/4.61 tc_RealDef_Oreal, Y, X ), ! c_Orderings_Oord__class_Oless__eq(
% 4.20/4.61 tc_RealDef_Oreal, X, Z ), c_Orderings_Oord__class_Oless__eq(
% 4.20/4.61 tc_RealDef_Oreal, Y, Z ) }.
% 4.20/4.61 (20992) {G0,W8,D2,L2,V2,M2} { c_Orderings_Oord__class_Oless__eq(
% 4.20/4.61 tc_RealDef_Oreal, Y, X ), c_Orderings_Oord__class_Oless__eq(
% 4.20/4.61 tc_RealDef_Oreal, X, Y ) }.
% 4.20/4.61 (20993) {G0,W4,D2,L1,V1,M1} { c_Orderings_Oord__class_Oless__eq(
% 4.20/4.61 tc_RealDef_Oreal, X, X ) }.
% 4.20/4.61 (20994) {G0,W37,D6,L4,V5,M4} { !
% 4.20/4.61 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct( X
% 4.20/4.61 ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 4.20/4.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 4.20/4.61 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 4.20/4.61 ), U = Z, T = Y }.
% 4.20/4.61 (20995) {G0,W34,D6,L3,V5,M3} { !
% 4.20/4.61 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct( X
% 4.20/4.61 ), ! U = Z, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 4.20/4.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 4.20/4.61 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 4.20/4.61 ) }.
% 4.20/4.61 (20996) {G0,W34,D6,L3,V5,M3} { !
% 4.20/4.61 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct( X
% 4.20/4.61 ), ! T = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 4.20/4.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 4.20/4.61 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 4.20/4.61 ) }.
% 4.20/4.61 (20997) {G0,W26,D6,L2,V4,M2} { ! class_Rings_Ocomm__semiring__1( X ),
% 4.20/4.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 4.20/4.61 ( X ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z )
% 4.20/4.61 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 4.20/4.61 c_Groups_Oplus__class_Oplus( X, T, Y ) ), Z ) }.
% 4.20/4.61 (20998) {G0,W26,D6,L2,V4,M2} { ! class_RealVector_Oreal__normed__algebra(
% 4.20/4.61 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 4.20/4.61 c_Groups_Oplus__class_Oplus( X, T, Z ) ), Y ) =
% 4.20/4.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 4.20/4.61 ( X ), T ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y )
% 4.20/4.61 ) }.
% 4.20/4.61 (20999) {G0,W26,D6,L2,V4,M2} { ! class_RealVector_Oreal__normed__algebra(
% 4.20/4.61 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 4.20/4.61 c_Groups_Oplus__class_Oplus( X, T, Z ) ), Y ) =
% 4.20/4.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 4.20/4.61 ( X ), T ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y )
% 4.20/4.61 ) }.
% 4.20/4.61 (21000) {G0,W26,D6,L2,V4,M2} { ! class_Rings_Ocomm__semiring__1( X ), hAPP
% 4.20/4.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus(
% 4.20/4.61 X, T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 4.20/4.61 (21001) {G0,W5,D4,L1,V0,M1} { v_cs____ = c_Groups_Ozero__class_Ozero(
% 4.20/4.61 tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ) }.
% 4.20/4.61 (21002) {G0,W24,D5,L4,V4,M4} { ! class_RealVector_Oreal__normed__vector( X
% 4.20/4.61 ), ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y,
% 4.20/4.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 4.20/4.61 c_RealVector_Onorm__class_Onorm( X, Z ), hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ),
% 4.20/4.61 c_RealVector_Onorm__class_Onorm( X, T ) ) ), Z =
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ) }.
% 4.20/4.61 (21003) {G0,W29,D6,L4,V3,M4} { ! class_Rings_Oordered__ring__abs( X ),
% 4.20/4.61 alpha81( X, Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ), Y ), c_Groups_Oabs__class_Oabs( X, hAPP
% 4.20/4.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 4.20/4.61 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 4.20/4.61 (21004) {G0,W29,D6,L4,V3,M4} { ! class_Rings_Oordered__ring__abs( X ),
% 4.20/4.61 alpha81( X, Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Oabs__class_Oabs( X, hAPP(
% 4.20/4.61 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 4.20/4.61 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 4.20/4.61 (21005) {G0,W8,D3,L2,V2,M2} { ! alpha81( X, Y ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 4.20/4.61 ) }.
% 4.20/4.61 (21006) {G0,W8,D3,L2,V2,M2} { ! alpha81( X, Y ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 4.20/4.61 ) }.
% 4.20/4.61 (21007) {G0,W13,D3,L3,V2,M3} { c_Orderings_Oord__class_Oless__eq( X,
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless__eq
% 4.20/4.61 ( X, Y, c_Groups_Ozero__class_Ozero( X ) ), alpha81( X, Y ) }.
% 4.20/4.61 (21008) {G0,W24,D6,L3,V3,M3} { ! class_Rings_Olinordered__idom( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 4.20/4.61 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 4.20/4.61 c_Groups_Oabs__class_Oabs( X, Z ) ), Y ) = c_Groups_Oabs__class_Oabs( X,
% 4.20/4.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 4.20/4.61 (21009) {G0,W24,D6,L3,V3,M3} { ! class_Rings_Olinordered__ring__strict( X
% 4.20/4.61 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus(
% 4.20/4.61 X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ) ), Z = c_Groups_Ozero__class_Ozero( X )
% 4.20/4.61 }.
% 4.20/4.61 (21010) {G0,W24,D6,L3,V3,M3} { ! class_Rings_Olinordered__ring__strict( X
% 4.20/4.61 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus(
% 4.20/4.61 X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 4.20/4.61 }.
% 4.20/4.61 (21011) {G0,W28,D6,L4,V3,M4} { ! class_Rings_Olinordered__ring__strict( X
% 4.20/4.61 ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq( X,
% 4.20/4.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 4.20/4.61 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 4.20/4.61 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 4.20/4.61 (21012) {G0,W20,D6,L2,V3,M2} { ! class_Rings_Olinordered__ring( X ),
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 4.20/4.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 4.20/4.61 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 4.20/4.61 ) ) }.
% 4.20/4.61 (21013) {G0,W18,D4,L2,V3,M2} { !
% 4.20/4.61 class_Groups_Oordered__ab__group__add__abs( X ),
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 4.20/4.61 c_Groups_Oplus__class_Oplus( X, Z, Y ) ), c_Groups_Oplus__class_Oplus( X
% 4.20/4.61 , c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) )
% 4.20/4.61 ) }.
% 4.20/4.61 (21014) {G0,W9,D3,L2,V2,M2} { ! class_Groups_Oordered__ab__group__add__abs
% 4.20/4.61 ( X ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 4.20/4.61 ( X ), c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 4.20/4.61 (21015) {G0,W13,D3,L3,V2,M3} { !
% 4.20/4.61 class_Groups_Oordered__ab__group__add__abs( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Y ),
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 4.20/4.61 }.
% 4.20/4.61 (21016) {G0,W13,D3,L3,V2,M3} { !
% 4.20/4.61 class_Groups_Oordered__ab__group__add__abs( X ), ! Y =
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq( X,
% 4.20/4.61 c_Groups_Oabs__class_Oabs( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 4.20/4.61 (21017) {G0,W12,D3,L3,V2,M3} { !
% 4.20/4.61 class_Groups_Oordered__ab__group__add__abs( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 4.20/4.61 ), c_Groups_Oabs__class_Oabs( X, Y ) = Y }.
% 4.20/4.61 (21018) {G0,W23,D6,L3,V3,M3} { ! class_Rings_Olinordered__ring__strict( X
% 4.20/4.61 ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X )
% 4.20/4.61 }.
% 4.20/4.61 (21019) {G0,W23,D6,L3,V3,M3} { ! class_Rings_Olinordered__ring__strict( X
% 4.20/4.61 ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 4.20/4.61 }.
% 4.20/4.61 (21020) {G0,W27,D6,L4,V3,M4} { ! class_Rings_Olinordered__ring__strict( X
% 4.20/4.61 ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 4.20/4.61 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ) }.
% 4.20/4.61 (21021) {G0,W20,D3,L4,V3,M4} { ! class_Groups_Oordered__comm__monoid__add
% 4.20/4.61 ( X ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless__eq(
% 4.20/4.61 X, Z, c_Groups_Ozero__class_Ozero( X ) ),
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Y,
% 4.20/4.61 Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 4.20/4.61 (21022) {G0,W8,D4,L1,V0,M1} { ! c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 4.20/4.61 v_c____, v_cs____ ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 4.20/4.61 tc_Complex_Ocomplex ) ) }.
% 4.20/4.61 (21023) {G0,W19,D4,L3,V3,M3} { ! class_Fields_Ofield__inverse__zero( X ),
% 4.20/4.61 ! class_RealVector_Oreal__normed__field( X ),
% 4.20/4.61 c_RealVector_Onorm__class_Onorm( X, c_Rings_Oinverse__class_Odivide( X, Z
% 4.20/4.61 , Y ) ) = c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 4.20/4.61 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 4.20/4.61 ( X, Y ) ) }.
% 4.20/4.61 (21024) {G0,W11,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 4.20/4.61 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 4.20/4.61 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, Y, X ) ), alpha1( X, Y
% 4.20/4.61 ) }.
% 4.20/4.61 (21025) {G0,W11,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 4.20/4.61 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 4.20/4.61 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, Y, X ) ), alpha26( X,
% 4.20/4.61 Y ) }.
% 4.20/4.61 (21026) {G0,W14,D3,L3,V2,M3} { ! alpha1( X, Y ), ! alpha26( X, Y ),
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 4.20/4.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 4.20/4.61 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, Y, X ) ) }.
% 4.20/4.61 (21027) {G0,W13,D3,L3,V2,M3} { ! alpha26( X, Y ),
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 4.20/4.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 4.20/4.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 4.20/4.61 (21028) {G0,W8,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 4.20/4.61 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 4.20/4.61 alpha26( X, Y ) }.
% 4.20/4.61 (21029) {G0,W8,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 4.20/4.61 tc_RealDef_Oreal, X, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 4.20/4.61 alpha26( X, Y ) }.
% 4.20/4.61 (21030) {G0,W13,D3,L3,V2,M3} { ! alpha1( X, Y ),
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y,
% 4.20/4.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 4.20/4.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ) }.
% 4.20/4.61 (21031) {G0,W8,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 4.20/4.61 tc_RealDef_Oreal, Y, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 4.20/4.61 alpha1( X, Y ) }.
% 4.20/4.61 (21032) {G0,W8,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 4.20/4.61 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 4.20/4.61 alpha1( X, Y ) }.
% 4.20/4.61 (21033) {G0,W10,D4,L2,V2,M2} { !
% 4.20/4.61 class_Rings_Odivision__ring__inverse__zero( X ),
% 4.20/4.61 c_Rings_Oinverse__class_Odivide( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 4.20/4.61 = c_Groups_Ozero__class_Ozero( X ) }.
% 4.20/4.61 (21034) {G0,W10,D4,L2,V2,M2} { ! class_Rings_Odivision__ring( X ),
% 4.20/4.61 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 4.20/4.61 = c_Groups_Ozero__class_Ozero( X ) }.
% 4.20/4.61 (21035) {G0,W21,D6,L2,V4,M2} { ! class_Rings_Odivision__ring( X ), hAPP(
% 4.20/4.61 hAPP( c_Groups_Otimes__class_Otimes( X ), T ),
% 4.20/4.61 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 4.20/4.61 c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 4.20/4.61 (21036) {G0,W20,D4,L2,V4,M2} { ! class_Rings_Odivision__ring( X ),
% 4.20/4.61 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, T, Z
% 4.20/4.61 ), Y ) = c_Groups_Oplus__class_Oplus( X, c_Rings_Oinverse__class_Odivide
% 4.20/4.61 ( X, T, Y ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 4.20/4.61 (21037) {G0,W21,D4,L3,V3,M3} { ! class_RealVector_Oreal__normed__field( X
% 4.20/4.61 ), Y = c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm
% 4.20/4.61 ( X, c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 4.20/4.61 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 4.20/4.61 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 4.20/4.61 ( X, Y ) ) }.
% 4.20/4.61 (21038) {G0,W10,D4,L2,V2,M2} { ! class_RealVector_Oreal__normed__field( X
% 4.20/4.61 ), c_Rings_Oinverse__class_Odivide( X, c_Groups_Ozero__class_Ozero( X )
% 4.20/4.61 , Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 4.20/4.61 (21039) {G0,W20,D4,L2,V4,M2} { ! class_RealVector_Oreal__normed__field( X
% 4.20/4.61 ), c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, T
% 4.20/4.61 , Z ), Y ) = c_Groups_Oplus__class_Oplus( X,
% 4.20/4.61 c_Rings_Oinverse__class_Odivide( X, T, Y ),
% 4.20/4.61 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 4.20/4.61 (21040) {G0,W20,D5,L4,V4,M4} { ! class_Rings_Odivision__ring( X ), Y =
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, T =
% 4.20/4.61 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 4.20/4.61 (21041) {G0,W20,D5,L4,V4,M4} { ! class_Rings_Odivision__ring( X ), Y =
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ), ! T = hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 4.20/4.61 c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z }.
% 4.20/4.61 (21042) {G0,W20,D5,L4,V4,M4} { ! class_Rings_Odivision__ring( X ), Y =
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ), ! c_Rings_Oinverse__class_Odivide( X, T
% 4.20/4.61 , Y ) = Z, T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y )
% 4.20/4.61 }.
% 4.20/4.61 (21043) {G0,W20,D5,L4,V4,M4} { ! class_Rings_Odivision__ring( X ), Y =
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ), ! T = hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 4.20/4.61 c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z }.
% 4.20/4.61 (21044) {G0,W20,D5,L4,V4,M4} { ! class_Rings_Odivision__ring( X ), Y =
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ), ! T = c_Rings_Oinverse__class_Odivide(
% 4.20/4.61 X, Z, Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z
% 4.20/4.61 }.
% 4.20/4.61 (21045) {G0,W20,D5,L4,V4,M4} { ! class_Rings_Odivision__ring( X ), Y =
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, T =
% 4.20/4.61 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 4.20/4.61 (21046) {G0,W20,D5,L3,V3,M3} { X = c_Groups_Ozero__class_Ozero(
% 4.20/4.61 tc_RealDef_Oreal ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 4.20/4.61 tc_RealDef_Oreal ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 4.20/4.61 ( tc_RealDef_Oreal ), X ), Y ), Z = Y }.
% 4.20/4.61 (21047) {G0,W20,D5,L3,V3,M3} { X = c_Groups_Ozero__class_Ozero(
% 4.20/4.61 tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 4.20/4.61 tc_RealDef_Oreal ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 4.20/4.61 ( tc_RealDef_Oreal ), X ), Y ) }.
% 4.20/4.61 (21048) {G0,W20,D5,L3,V3,M3} { X = c_Groups_Ozero__class_Ozero(
% 4.20/4.61 tc_RealDef_Oreal ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 4.20/4.61 tc_RealDef_Oreal ), Z ), X ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 4.20/4.61 ( tc_RealDef_Oreal ), Y ), X ), Z = Y }.
% 4.20/4.61 (21049) {G0,W20,D5,L3,V3,M3} { X = c_Groups_Ozero__class_Ozero(
% 4.20/4.61 tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 4.20/4.61 tc_RealDef_Oreal ), Z ), X ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 4.20/4.61 ( tc_RealDef_Oreal ), Y ), X ) }.
% 4.20/4.61 (21050) {G0,W22,D5,L3,V3,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 4.20/4.61 tc_RealDef_Oreal, X, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 4.20/4.61 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ), hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ),
% 4.20/4.61 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Z ) ) ), Y =
% 4.20/4.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 4.20/4.61 (21051) {G0,W9,D3,L2,V2,M2} { ! class_RealVector_Oreal__normed__vector( X
% 4.20/4.61 ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 4.20/4.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 4.20/4.61 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 4.20/4.61 (21052) {G0,W21,D6,L2,V2,M2} { ! c_Groups_Oplus__class_Oplus(
% 4.20/4.61 tc_RealDef_Oreal, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 4.20/4.61 tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 4.20/4.61 tc_RealDef_Oreal ), X ), X ) ) = c_Groups_Ozero__class_Ozero(
% 4.20/4.61 tc_RealDef_Oreal ), Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal )
% 4.20/4.61 }.
% 4.20/4.61 (21053) {G0,W21,D6,L2,V2,M2} { ! c_Groups_Oplus__class_Oplus(
% 4.20/4.61 tc_RealDef_Oreal, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 4.20/4.61 tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 4.20/4.61 tc_RealDef_Oreal ), X ), X ) ) = c_Groups_Ozero__class_Ozero(
% 4.20/4.61 tc_RealDef_Oreal ), X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal )
% 4.20/4.61 }.
% 4.20/4.61 (21054) {G0,W25,D6,L3,V2,M3} { ! Y = c_Groups_Ozero__class_Ozero(
% 4.20/4.61 tc_RealDef_Oreal ), ! X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal )
% 4.20/4.61 , c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 4.20/4.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 4.20/4.61 (21055) {G0,W10,D3,L3,V2,M3} { ! class_Groups_Ozero( X ), !
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ) = Y, Y = c_Groups_Ozero__class_Ozero( X
% 4.20/4.61 ) }.
% 4.20/4.61 (21056) {G0,W10,D3,L3,V2,M3} { ! class_Groups_Ozero( X ), ! Y =
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero( X ) = Y
% 4.20/4.61 }.
% 4.20/4.61 (21057) {G0,W25,D7,L2,V4,M2} { ! class_Groups_Oab__semigroup__mult( X ),
% 4.20/4.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 4.20/4.61 (21058) {G0,W17,D4,L2,V4,M2} { ! class_Groups_Oab__semigroup__add( X ),
% 4.20/4.61 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y
% 4.20/4.61 ) = c_Groups_Oplus__class_Oplus( X, T, c_Groups_Oplus__class_Oplus( X, Z
% 4.20/4.61 , Y ) ) }.
% 4.20/4.61 (21059) {G0,W14,D3,L3,V4,M3} { ! class_Groups_Ocancel__semigroup__add( X )
% 4.20/4.61 , ! c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus
% 4.20/4.61 ( X, T, Y ), Z = Y }.
% 4.20/4.61 (21060) {G0,W14,D3,L3,V4,M3} { ! class_Groups_Ocancel__semigroup__add( X )
% 4.20/4.61 , ! Z = Y, c_Groups_Oplus__class_Oplus( X, T, Z ) =
% 4.20/4.61 c_Groups_Oplus__class_Oplus( X, T, Y ) }.
% 4.20/4.61 (21061) {G0,W14,D3,L3,V4,M3} { ! class_Groups_Ocancel__semigroup__add( X )
% 4.20/4.61 , ! c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus
% 4.20/4.61 ( X, Y, Z ), T = Y }.
% 4.20/4.61 (21062) {G0,W14,D3,L3,V4,M3} { ! class_Groups_Ocancel__semigroup__add( X )
% 4.20/4.61 , ! T = Y, c_Groups_Oplus__class_Oplus( X, T, Z ) =
% 4.20/4.61 c_Groups_Oplus__class_Oplus( X, Y, Z ) }.
% 4.20/4.61 (21063) {G0,W14,D3,L3,V4,M3} { ! class_Groups_Ocancel__semigroup__add( X )
% 4.20/4.61 , ! c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus
% 4.20/4.61 ( X, T, Y ), Z = Y }.
% 4.20/4.61 (21064) {G0,W14,D3,L3,V4,M3} { ! class_Groups_Ocancel__ab__semigroup__add
% 4.20/4.61 ( X ), ! c_Groups_Oplus__class_Oplus( X, T, Z ) =
% 4.20/4.61 c_Groups_Oplus__class_Oplus( X, T, Y ), Z = Y }.
% 4.20/4.61 (21065) {G0,W14,D3,L3,V4,M3} { ! class_Groups_Ocancel__semigroup__add( X )
% 4.20/4.61 , ! c_Groups_Oplus__class_Oplus( X, Z, T ) = c_Groups_Oplus__class_Oplus
% 4.20/4.61 ( X, Y, T ), Z = Y }.
% 4.20/4.61 (21066) {G0,W11,D4,L2,V2,M2} { !
% 4.20/4.61 class_Groups_Oordered__ab__group__add__abs( X ),
% 4.20/4.61 c_Groups_Oabs__class_Oabs( X, c_Groups_Oabs__class_Oabs( X, Y ) ) =
% 4.20/4.61 c_Groups_Oabs__class_Oabs( X, Y ) }.
% 4.20/4.61 (21067) {G0,W12,D5,L2,V2,M2} { ! class_Rings_Omult__zero( X ), hAPP( hAPP
% 4.20/4.61 ( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) )
% 4.20/4.61 , Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 4.20/4.61 (21068) {G0,W12,D5,L2,V2,M2} { ! class_Rings_Omult__zero( X ), hAPP( hAPP
% 4.20/4.61 ( c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X
% 4.20/4.61 ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 4.20/4.61 (21069) {G0,W19,D5,L4,V3,M4} { ! class_Rings_Oring__no__zero__divisors( X
% 4.20/4.61 ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 4.20/4.61 = c_Groups_Ozero__class_Ozero( X ) }.
% 4.20/4.61 (21070) {G0,W15,D5,L3,V3,M3} { ! class_Rings_Oring__no__zero__divisors( X
% 4.20/4.61 ), ! Z = c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ) }.
% 4.20/4.61 (21071) {G0,W15,D5,L3,V3,M3} { ! class_Rings_Oring__no__zero__divisors( X
% 4.20/4.61 ), ! Y = c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ) }.
% 4.20/4.61 (21072) {G0,W19,D5,L4,V3,M4} { ! class_Rings_Ono__zero__divisors( X ), Y =
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ),
% 4.20/4.61 ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) =
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ) }.
% 4.20/4.61 (21073) {G0,W19,D5,L4,V3,M4} { ! class_Rings_Ono__zero__divisors( X ), !
% 4.20/4.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 4.20/4.61 = c_Groups_Ozero__class_Ozero( X ) }.
% 4.20/4.61 (21074) {G0,W9,D4,L2,V2,M2} { ! class_Groups_Omonoid__add( X ),
% 4.20/4.61 c_Groups_Oplus__class_Oplus( X, c_Groups_Ozero__class_Ozero( X ), Y ) = Y
% 4.20/4.61 }.
% 4.20/4.61 (21075) {G0,W9,D4,L2,V2,M2} { ! class_Groups_Ocomm__monoid__add( X ),
% 4.20/4.61 c_Groups_Oplus__class_Oplus( X, c_Groups_Ozero__class_Ozero( X ), Y ) = Y
% 4.20/4.61 }.
% 4.20/4.61 (21076) {G0,W13,D3,L3,V2,M3} { ! class_Groups_Olinordered__ab__group__add
% 4.20/4.61 ( X ), ! c_Groups_Ozero__class_Ozero( X ) = c_Groups_Oplus__class_Oplus(
% 4.20/4.61 X, Y, Y ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 4.20/4.61 (21077) {G0,W13,D3,L3,V2,M3} { ! class_Groups_Olinordered__ab__group__add
% 4.20/4.61 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Oplus__class_Oplus( X, Y, Y )
% 4.20/4.61 }.
% 4.20/4.61 (21078) {G0,W9,D4,L2,V2,M2} { ! class_Groups_Omonoid__add( X ),
% 4.20/4.61 c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Ozero__class_Ozero( X ) ) = Y
% 4.20/4.61 }.
% 4.20/4.61 (21079) {G0,W9,D4,L2,V2,M2} { ! class_Groups_Ocomm__monoid__add( X ),
% 4.20/4.61 c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Ozero__class_Ozero( X ) ) = Y
% 4.20/4.61 }.
% 4.20/4.61 (21080) {G0,W16,D3,L3,V4,M3} { !
% 4.20/4.61 class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 4.20/4.61 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ),
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 4.20/4.61 (21081) {G0,W16,D3,L3,V4,M3} { !
% 4.20/4.61 class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 4.20/4.61 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 4.20/4.61 (21082) {G0,W16,D3,L3,V4,M3} { !
% 4.20/4.61 class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 4.20/4.61 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 4.20/4.61 (21083) {G0,W16,D3,L3,V4,M3} { !
% 4.20/4.61 class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 4.20/4.61 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 4.20/4.61 (21084) {G0,W16,D3,L3,V4,M3} { ! class_Groups_Oordered__ab__semigroup__add
% 4.20/4.61 ( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 4.20/4.61 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 4.20/4.61 (21085) {G0,W16,D3,L3,V4,M3} { ! class_Groups_Oordered__ab__semigroup__add
% 4.20/4.61 ( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 4.20/4.61 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 4.20/4.61 (21086) {G0,W20,D3,L4,V5,M4} { ! class_Groups_Oordered__ab__semigroup__add
% 4.20/4.61 ( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 4.20/4.61 U ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 4.20/4.61 (21087) {G0,W16,D3,L3,V4,M3} { !
% 4.20/4.61 class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 4.20/4.61 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ),
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 4.20/4.61 (21088) {G0,W16,D3,L3,V4,M3} { !
% 4.20/4.61 class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 4.20/4.61 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 4.20/4.61 (21089) {G0,W26,D6,L2,V4,M2} { ! class_Rings_Ocomm__semiring( X ), hAPP(
% 4.20/4.61 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X
% 4.20/4.61 , T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 4.20/4.61 (21090) {G0,W32,D7,L2,V5,M2} { ! class_Rings_Osemiring( X ),
% 4.20/4.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 4.20/4.61 ( X ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), Z ), T ), Y ) ) =
% 4.20/4.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 4.20/4.61 ( X ), c_Groups_Oplus__class_Oplus( X, U, Z ) ), T ), Y ) }.
% 4.20/4.61 (21091) {G0,W12,D3,L3,V2,M3} { !
% 4.20/4.61 class_Groups_Oordered__ab__group__add__abs( X ), !
% 4.20/4.61 c_Groups_Oabs__class_Oabs( X, Y ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ) }.
% 4.20/4.61 (21092) {G0,W12,D3,L3,V2,M3} { !
% 4.20/4.61 class_Groups_Oordered__ab__group__add__abs( X ), ! Y =
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oabs__class_Oabs( X, Y ) =
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ) }.
% 4.20/4.61 (21093) {G0,W9,D4,L2,V1,M2} { ! class_Groups_Oordered__ab__group__add__abs
% 4.20/4.61 ( X ), c_Groups_Oabs__class_Oabs( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ) }.
% 4.20/4.61 (21094) {G0,W8,D3,L2,V2,M2} { ! class_Groups_Oordered__ab__group__add__abs
% 4.20/4.61 ( X ), c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oabs__class_Oabs
% 4.20/4.61 ( X, Y ) ) }.
% 4.20/4.61 (21095) {G0,W12,D3,L3,V3,M3} { !
% 4.20/4.61 class_Groups_Oordered__ab__group__add__abs( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 4.20/4.61 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 4.20/4.61 (21096) {G0,W21,D6,L2,V3,M2} { ! class_Rings_Olinordered__idom( X ),
% 4.20/4.61 c_Groups_Oabs__class_Oabs( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 4.20/4.61 X ), Z ), Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 4.20/4.61 c_Groups_Oabs__class_Oabs( X, Z ) ), c_Groups_Oabs__class_Oabs( X, Y ) )
% 4.20/4.61 }.
% 4.20/4.61 (21097) {G0,W19,D5,L2,V2,M2} { ! class_Rings_Olinordered__idom( X ), hAPP
% 4.20/4.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X
% 4.20/4.61 , Y ) ), c_Groups_Oabs__class_Oabs( X, Y ) ) = hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 4.20/4.61 (21098) {G0,W21,D5,L2,V3,M2} { !
% 4.20/4.61 class_Groups_Oordered__ab__group__add__abs( X ),
% 4.20/4.61 c_Groups_Oabs__class_Oabs( X, c_Groups_Oplus__class_Oplus( X,
% 4.20/4.61 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ) )
% 4.20/4.61 = c_Groups_Oplus__class_Oplus( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 4.20/4.61 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 4.20/4.61 (21099) {G0,W12,D5,L2,V2,M2} { ! class_Rings_Olinordered__ring( X ),
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 4.20/4.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) }.
% 4.20/4.61 (21100) {G0,W20,D5,L4,V3,M4} { ! class_Rings_Olinordered__ring__strict( X
% 4.20/4.61 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 4.20/4.61 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), alpha2(
% 4.20/4.61 X, Y, Z ), alpha27( X, Y, Z ) }.
% 4.20/4.61 (21101) {G0,W16,D5,L3,V3,M3} { ! class_Rings_Olinordered__ring__strict( X
% 4.20/4.61 ), ! alpha2( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 4.20/4.61 (21102) {G0,W16,D5,L3,V3,M3} { ! class_Rings_Olinordered__ring__strict( X
% 4.20/4.61 ), ! alpha27( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 4.20/4.61 (21103) {G0,W9,D3,L2,V3,M2} { ! alpha27( X, Y, Z ),
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 4.20/4.61 ) }.
% 4.20/4.61 (21104) {G0,W9,D3,L2,V3,M2} { ! alpha27( X, Y, Z ),
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 4.20/4.61 ) }.
% 4.20/4.61 (21105) {G0,W14,D3,L3,V3,M3} { ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless__eq(
% 4.20/4.61 X, Y, c_Groups_Ozero__class_Ozero( X ) ), alpha27( X, Y, Z ) }.
% 4.20/4.61 (21106) {G0,W9,D3,L2,V3,M2} { ! alpha2( X, Y, Z ),
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 4.20/4.61 ) }.
% 4.20/4.61 (21107) {G0,W9,D3,L2,V3,M2} { ! alpha2( X, Y, Z ),
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 4.20/4.61 ) }.
% 4.20/4.61 (21108) {G0,W14,D3,L3,V3,M3} { ! c_Orderings_Oord__class_Oless__eq( X,
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 4.20/4.61 ), alpha2( X, Y, Z ) }.
% 4.20/4.61 (21109) {G0,W20,D5,L4,V3,M4} { ! class_Rings_Olinordered__ring__strict( X
% 4.20/4.61 ), ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 4.20/4.61 ( X ) ), alpha3( X, Y, Z ), alpha28( X, Y, Z ) }.
% 4.20/4.61 (21110) {G0,W16,D5,L3,V3,M3} { ! class_Rings_Olinordered__ring__strict( X
% 4.20/4.61 ), ! alpha3( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP
% 4.20/4.61 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 4.20/4.61 (21111) {G0,W16,D5,L3,V3,M3} { ! class_Rings_Olinordered__ring__strict( X
% 4.20/4.61 ), ! alpha28( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 4.20/4.61 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 4.20/4.61 (21112) {G0,W9,D3,L2,V3,M2} { ! alpha28( X, Y, Z ),
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 4.20/4.61 ) }.
% 4.20/4.61 (21113) {G0,W9,D3,L2,V3,M2} { ! alpha28( X, Y, Z ),
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 4.20/4.61 ) }.
% 4.20/4.61 (21114) {G0,W14,D3,L3,V3,M3} { ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless__eq(
% 4.20/4.61 X, c_Groups_Ozero__class_Ozero( X ), Y ), alpha28( X, Y, Z ) }.
% 4.20/4.61 (21115) {G0,W9,D3,L2,V3,M2} { ! alpha3( X, Y, Z ),
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 4.20/4.61 ) }.
% 4.20/4.61 (21116) {G0,W9,D3,L2,V3,M2} { ! alpha3( X, Y, Z ),
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 4.20/4.61 ) }.
% 4.20/4.61 (21117) {G0,W14,D3,L3,V3,M3} { ! c_Orderings_Oord__class_Oless__eq( X,
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 4.20/4.61 ), alpha3( X, Y, Z ) }.
% 4.20/4.61 (21118) {G0,W22,D5,L4,V3,M4} { ! class_Rings_Oordered__cancel__semiring( X
% 4.20/4.61 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 4.20/4.61 X ), Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless__eq
% 4.20/4.61 ( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 4.20/4.61 (21119) {G0,W22,D5,L4,V3,M4} { ! class_Rings_Oordered__cancel__semiring( X
% 4.20/4.61 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 4.20/4.61 X ), Y ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 4.20/4.61 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ),
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 4.20/4.61 (21120) {G0,W22,D5,L4,V3,M4} { ! class_Rings_Oordered__cancel__semiring( X
% 4.20/4.61 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 4.20/4.61 X ), Y ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 4.20/4.61 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 4.20/4.61 (21121) {G0,W22,D5,L4,V3,M4} { ! class_Rings_Oordered__cancel__semiring( X
% 4.20/4.61 ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless__eq(
% 4.20/4.61 X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 4.20/4.61 ( X ) ) }.
% 4.20/4.61 (21122) {G0,W22,D5,L4,V3,M4} { ! class_Rings_Oordered__ring( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 4.20/4.61 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 4.20/4.61 , c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 4.20/4.61 (21123) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Oordered__semiring( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 4.20/4.61 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 4.20/4.61 (21124) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Oordered__semiring( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 4.20/4.61 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 4.20/4.61 (21125) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Oordered__comm__semiring( X )
% 4.20/4.61 , ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 4.20/4.61 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 4.20/4.61 (21126) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Oordered__ring( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Ozero__class_Ozero( X )
% 4.20/4.61 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 4.20/4.61 (21127) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Oordered__ring( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Ozero__class_Ozero( X )
% 4.20/4.61 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 4.20/4.61 (21128) {G0,W34,D5,L6,V5,M6} { ! class_Rings_Oordered__semiring( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 4.20/4.61 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 4.20/4.61 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 4.20/4.61 (21129) {G0,W34,D5,L6,V5,M6} { ! class_Rings_Oordered__semiring( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 4.20/4.61 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 4.20/4.61 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 4.20/4.61 (21130) {G0,W22,D5,L4,V3,M4} { ! class_Rings_Oordered__ring( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 4.20/4.61 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 4.20/4.61 X ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 4.20/4.61 (21131) {G0,W22,D5,L4,V3,M4} { ! class_Rings_Oordered__ring( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 4.20/4.61 ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 4.20/4.61 , c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 4.20/4.61 (21132) {G0,W22,D5,L4,V3,M4} { ! class_Rings_Oordered__cancel__semiring( X
% 4.20/4.61 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 4.20/4.61 X ), Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 4.20/4.61 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 4.20/4.61 (21133) {G0,W22,D5,L4,V3,M4} { ! class_Rings_Oordered__cancel__semiring( X
% 4.20/4.61 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless__eq(
% 4.20/4.61 X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 4.20/4.61 ( X ) ) }.
% 4.20/4.61 (21134) {G0,W15,D3,L3,V2,M3} { ! class_Groups_Olinordered__ab__group__add
% 4.20/4.61 ( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Y )
% 4.20/4.61 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 4.20/4.61 ), Y ) }.
% 4.20/4.61 (21135) {G0,W15,D3,L3,V2,M3} { ! class_Groups_Olinordered__ab__group__add
% 4.20/4.61 ( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless__eq
% 4.20/4.61 ( X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y
% 4.20/4.61 , Y ) ) }.
% 4.20/4.61 (21136) {G0,W15,D3,L3,V2,M3} { ! class_Groups_Olinordered__ab__group__add
% 4.20/4.61 ( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 4.20/4.61 c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X )
% 4.20/4.61 ), c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero
% 4.20/4.61 ( X ) ) }.
% 4.20/4.61 (21137) {G0,W15,D3,L3,V2,M3} { ! class_Groups_Olinordered__ab__group__add
% 4.20/4.61 ( X ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 4.20/4.61 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 4.20/4.61 ) ) }.
% 4.20/4.61 (21138) {G0,W20,D3,L4,V3,M4} { ! class_Groups_Oordered__comm__monoid__add
% 4.20/4.61 ( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 4.20/4.61 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 4.20/4.61 ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 4.20/4.61 (21139) {G0,W23,D3,L5,V3,M5} { ! class_Groups_Oordered__comm__monoid__add
% 4.20/4.61 ( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 4.20/4.61 ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 4.20/4.61 }.
% 4.20/4.61 (21140) {G0,W23,D3,L5,V3,M5} { ! class_Groups_Oordered__comm__monoid__add
% 4.20/4.61 ( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 4.20/4.61 ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X )
% 4.20/4.61 }.
% 4.20/4.61 (21141) {G0,W27,D3,L6,V3,M6} { ! class_Groups_Oordered__comm__monoid__add
% 4.20/4.61 ( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 4.20/4.61 ), ! Y = c_Groups_Ozero__class_Ozero( X ), ! Z =
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 4.20/4.61 = c_Groups_Ozero__class_Ozero( X ) }.
% 4.20/4.61 (21142) {G0,W18,D3,L4,V4,M4} { ! class_Groups_Oordered__comm__monoid__add
% 4.20/4.61 ( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 4.20/4.61 Y, Z ) ) }.
% 4.20/4.61 (21143) {G0,W18,D3,L4,V4,M4} { ! class_Groups_Oordered__comm__monoid__add
% 4.20/4.61 ( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 4.20/4.61 Z, Y ) ) }.
% 4.20/4.61 (21144) {G0,W26,D7,L3,V4,M3} { ! class_Fields_Ofield__inverse__zero( X ),
% 4.20/4.61 Y = c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, T,
% 4.20/4.61 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 4.20/4.61 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z,
% 4.20/4.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Y ) }.
% 4.20/4.61 (21145) {G0,W26,D7,L3,V4,M3} { ! class_Fields_Ofield( X ), Y =
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, T,
% 4.20/4.61 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 4.20/4.61 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, hAPP
% 4.20/4.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), Z ), Y ) }.
% 4.20/4.61 (21146) {G0,W26,D7,L3,V4,M3} { ! class_Fields_Ofield__inverse__zero( X ),
% 4.20/4.61 Y = c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 4.20/4.61 c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ) =
% 4.20/4.61 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, T,
% 4.20/4.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) }.
% 4.20/4.61 (21147) {G0,W26,D7,L3,V4,M3} { ! class_Fields_Ofield( X ), Y =
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 4.20/4.61 c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ) =
% 4.20/4.61 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, T,
% 4.20/4.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) }.
% 4.20/4.61 (21148) {G0,W43,D7,L4,V5,M4} { ! class_Fields_Ofield( X ), Y =
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ),
% 4.20/4.61 c_Groups_Oplus__class_Oplus( X, c_Rings_Oinverse__class_Odivide( X, U, Y
% 4.20/4.61 ), c_Rings_Oinverse__class_Odivide( X, T, Z ) ) =
% 4.20/4.61 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, hAPP
% 4.20/4.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 4.20/4.61 (21149) {G0,W7,D3,L1,V0,M1} { c_Orderings_Oord__class_Oless(
% 4.20/4.61 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 4.20/4.61 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_c____ ) ) }.
% 4.20/4.61 (21150) {G0,W21,D4,L3,V3,M3} { ! class_Fields_Olinordered__field( X ), Y =
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oabs__class_Oabs( X,
% 4.20/4.61 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 4.20/4.61 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 4.20/4.61 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 4.20/4.61 (21151) {G0,W32,D5,L5,V5,M5} { ! class_Fields_Ofield( X ), Y =
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), !
% 4.20/4.61 c_Rings_Oinverse__class_Odivide( X, U, Y ) =
% 4.20/4.61 c_Rings_Oinverse__class_Odivide( X, T, Z ), hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), U ), Z ) = hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) }.
% 4.20/4.61 (21152) {G0,W32,D5,L5,V5,M5} { ! class_Fields_Ofield( X ), Y =
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), !
% 4.20/4.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ) = hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ),
% 4.20/4.61 c_Rings_Oinverse__class_Odivide( X, U, Y ) =
% 4.20/4.61 c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 4.20/4.61 (21153) {G0,W25,D6,L3,V4,M3} { ! class_Fields_Ofield__inverse__zero( X ),
% 4.20/4.61 Y = c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X
% 4.20/4.61 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) =
% 4.20/4.61 c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 4.20/4.61 (21154) {G0,W25,D6,L3,V4,M3} { ! class_Fields_Ofield__inverse__zero( X ),
% 4.20/4.61 Y = c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X
% 4.20/4.61 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 4.20/4.61 c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 4.20/4.61 (21155) {G0,W13,D2,L4,V3,M4} { ! class_Rings_Olinordered__idom( X ), Z = Y
% 4.20/4.61 , c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless
% 4.20/4.61 ( X, Y, Z ) }.
% 4.20/4.61 (21156) {G0,W13,D2,L4,V3,M4} { ! class_Orderings_Olinorder( X ),
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y,
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 4.20/4.61 (21157) {G0,W10,D2,L3,V3,M3} { ! class_Orderings_Opreorder( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 4.20/4.61 ( X, Y, Z ) }.
% 4.20/4.61 (21158) {G0,W14,D2,L4,V4,M4} { ! class_Orderings_Oorder( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 4.20/4.61 ( X, T, Z ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 4.20/4.61 (21159) {G0,W14,D2,L4,V4,M4} { ! class_Orderings_Opreorder( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 4.20/4.61 ( X, Y, T ), c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 4.20/4.61 (21160) {G0,W13,D2,L4,V4,M4} { ! class_Orderings_Oorder( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Z, Y ), ! Z = T,
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 4.20/4.61 (21161) {G0,W13,D2,L4,V4,M4} { ! class_Orderings_Oord( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Z, Y ), ! Y = T,
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 4.20/4.61 (21162) {G0,W13,D2,L4,V4,M4} { ! class_Orderings_Oorder( X ), ! Z = Y, !
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, T, Y ), c_Orderings_Oord__class_Oless(
% 4.20/4.61 X, T, Z ) }.
% 4.20/4.61 (21163) {G0,W13,D2,L4,V4,M4} { ! class_Orderings_Oord( X ), ! Z = Y, !
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Y, T ), c_Orderings_Oord__class_Oless(
% 4.20/4.61 X, Z, T ) }.
% 4.20/4.61 (21164) {G0,W10,D2,L3,V3,M3} { ! class_Orderings_Oorder( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 4.20/4.61 ( X, Y, Z ) }.
% 4.20/4.61 (21165) {G0,W10,D2,L3,V3,M3} { ! class_Orderings_Opreorder( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 4.20/4.61 ( X, Y, Z ) }.
% 4.20/4.61 (21166) {G0,W9,D2,L3,V3,M3} { ! class_Orderings_Oorder( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Z, Y ), ! Y = Z }.
% 4.20/4.61 (21167) {G0,W9,D2,L3,V3,M3} { ! class_Orderings_Oorder( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Z, Y ), ! Z = Y }.
% 4.20/4.61 (21168) {G0,W10,D2,L3,V3,M3} { ! class_Orderings_Opreorder( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 4.20/4.61 ( X, Y, Z ) }.
% 4.20/4.61 (21169) {G0,W10,D2,L3,V3,M3} { ! class_Orderings_Opreorder( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 4.20/4.61 ( X, Y, Z ) }.
% 4.20/4.61 (21170) {G0,W9,D2,L3,V3,M3} { ! class_Orderings_Oorder( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Z, Y ), ! Z = Y }.
% 4.20/4.61 (21171) {G0,W13,D2,L4,V3,M4} { ! class_Orderings_Olinorder( X ), Z = Y,
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 4.20/4.61 X, Y, Z ) }.
% 4.20/4.61 (21172) {G0,W13,D2,L4,V3,M4} { ! class_Orderings_Olinorder( X ),
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 4.20/4.61 X, Y, Z ), Y = Z }.
% 4.20/4.61 (21173) {G0,W13,D2,L4,V3,M4} { ! class_Orderings_Olinorder( X ),
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Z, Y ), ! Y = Z, !
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 4.20/4.61 (21174) {G0,W13,D2,L4,V3,M4} { ! class_Orderings_Olinorder( X ),
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y,
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 4.20/4.61 (21175) {G0,W13,D2,L4,V3,M4} { ! class_Orderings_Olinorder( X ),
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 4.20/4.61 X, Y, Z ), Z = Y }.
% 4.20/4.61 (21176) {G0,W10,D2,L3,V3,M3} { ! class_Orderings_Olinorder( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Y, Z ), ! c_Orderings_Oord__class_Oless
% 4.20/4.61 ( X, Z, Y ) }.
% 4.20/4.61 (21177) {G0,W9,D2,L3,V3,M3} { ! class_Orderings_Olinorder( X ), ! Z = Y, !
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 4.20/4.61 (21178) {G0,W13,D2,L4,V3,M4} { ! class_Orderings_Olinorder( X ), Z = Y,
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 4.20/4.61 X, Y, Z ) }.
% 4.20/4.61 (21179) {G0,W9,D2,L3,V3,M3} { ! class_Orderings_Olinorder( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Z, Y ), ! Z = Y }.
% 4.20/4.61 (21180) {G0,W9,D2,L3,V3,M3} { ! class_Orderings_Olinorder( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Y, Z ), ! Z = Y }.
% 4.20/4.61 (21181) {G0,W6,D2,L2,V2,M2} { ! class_Orderings_Opreorder( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Y, Y ) }.
% 4.20/4.61 (21182) {G0,W14,D2,L4,V4,M4} { ! class_Orderings_Oorder( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless(
% 4.20/4.61 X, T, Y ) }.
% 4.20/4.61 (21183) {G0,W14,D2,L4,V4,M4} { ! class_Orderings_Opreorder( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Y, T ), c_Orderings_Oord__class_Oless(
% 4.20/4.61 X, Z, T ) }.
% 4.20/4.61 (21184) {G0,W14,D2,L4,V4,M4} { ! class_Orderings_Oorder( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 4.20/4.61 (21185) {G0,W14,D2,L4,V4,M4} { ! class_Orderings_Opreorder( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 4.20/4.61 (21186) {G0,W13,D2,L4,V3,M4} { ! class_Orderings_Oorder( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), Y = Z,
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 4.20/4.61 (21187) {G0,W13,D2,L4,V3,M4} { ! class_Orderings_Oorder( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), Z = Y,
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 4.20/4.61 (21188) {G0,W13,D2,L4,V3,M4} { ! class_Orderings_Oorder( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 4.20/4.61 (21189) {G0,W13,D2,L4,V3,M4} { ! class_Orderings_Olinorder( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 4.20/4.61 (21190) {G0,W13,D2,L4,V3,M4} { ! class_Orderings_Olinorder( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), ! Z = Y, !
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 4.20/4.61 (21191) {G0,W10,D2,L3,V3,M3} { ! class_Orderings_Opreorder( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Z, Y ),
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 4.20/4.61 (21192) {G0,W10,D2,L3,V3,M3} { ! class_Orderings_Olinorder( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 4.20/4.61 (21193) {G0,W13,D2,L4,V3,M4} { ! class_Orderings_Oorder( X ), Z = Y, !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 4.20/4.61 (21194) {G0,W13,D2,L4,V3,M4} { ! class_Orderings_Oorder( X ), Z = Y, !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 4.20/4.61 (21195) {G0,W13,D2,L4,V3,M4} { ! class_Orderings_Olinorder( X ),
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), Z = Y }.
% 4.20/4.61 (21196) {G0,W13,D2,L4,V3,M4} { ! class_Orderings_Olinorder( X ),
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Z, Y ), ! Z = Y,
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 4.20/4.61 (21197) {G0,W10,D2,L3,V3,M3} { ! class_Orderings_Olinorder( X ),
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 4.20/4.61 (21198) {G0,W10,D2,L3,V3,M3} { ! class_Orderings_Olinorder( X ),
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Z, Y ),
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 4.20/4.61 (21199) {G0,W13,D2,L4,V3,M4} { ! class_Orderings_Oorder( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 4.20/4.61 (21200) {G0,W10,D2,L3,V3,M3} { ! class_Orderings_Oorder( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Z, Y ),
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 4.20/4.61 (21201) {G0,W9,D2,L3,V3,M3} { ! class_Orderings_Oorder( X ), ! Z = Y,
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 4.20/4.61 (21202) {G0,W10,D2,L3,V3,M3} { ! class_Orderings_Opreorder( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Z, Y ),
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 4.20/4.61 (21203) {G0,W10,D2,L3,V3,M3} { ! class_Orderings_Opreorder( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 4.20/4.61 (21204) {G0,W14,D2,L4,V3,M4} { ! class_Orderings_Opreorder( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 4.20/4.61 (21205) {G0,W10,D2,L3,V3,M3} { ! class_Orderings_Oorder( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Z, Y ),
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 4.20/4.61 (21206) {G0,W9,D2,L3,V3,M3} { ! class_Orderings_Oorder( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Z, Y ), ! Z = Y }.
% 4.20/4.61 (21207) {G0,W13,D2,L4,V3,M4} { ! class_Orderings_Oorder( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), Z = Y,
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 4.20/4.61 (21208) {G0,W10,D2,L3,V3,M3} { ! class_Orderings_Olinorder( X ),
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 4.20/4.61 (21209) {G0,W10,D2,L3,V3,M3} { ! class_Orderings_Olinorder( X ),
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 4.20/4.61 (21210) {G0,W10,D2,L3,V3,M3} { ! class_Orderings_Olinorder( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Y, Z ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 4.20/4.61 (21211) {G0,W10,D2,L3,V3,M3} { ! class_Orderings_Olinorder( X ),
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Z, Y ),
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 4.20/4.61 (21212) {G0,W10,D2,L3,V3,M3} { ! class_Orderings_Olinorder( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, Y, Z ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 4.20/4.61 (21213) {G0,W16,D3,L3,V4,M3} { !
% 4.20/4.61 class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 4.20/4.61 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 4.20/4.61 ( X, Z, Y ) }.
% 4.20/4.61 (21214) {G0,W16,D3,L3,V4,M3} { !
% 4.20/4.61 class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, T )
% 4.20/4.61 , c_Groups_Oplus__class_Oplus( X, Y, T ) ), c_Orderings_Oord__class_Oless
% 4.20/4.61 ( X, Z, Y ) }.
% 4.20/4.61 (21215) {G0,W20,D3,L4,V5,M4} { !
% 4.20/4.61 class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 4.20/4.61 ( X, U, T ), c_Orderings_Oord__class_Oless( X,
% 4.20/4.61 c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X, Y
% 4.20/4.61 , T ) ) }.
% 4.20/4.61 (21216) {G0,W16,D3,L3,V4,M3} { !
% 4.20/4.61 class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 4.20/4.61 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 4.20/4.61 , T, Y ) ) }.
% 4.20/4.61 (21217) {G0,W16,D3,L3,V4,M3} { !
% 4.20/4.61 class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 4.20/4.61 X, c_Groups_Oplus__class_Oplus( X, Z, T ), c_Groups_Oplus__class_Oplus( X
% 4.20/4.61 , Y, T ) ) }.
% 4.20/4.61 (21218) {G0,W16,D3,L3,V4,M3} { !
% 4.20/4.61 class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 4.20/4.61 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 4.20/4.61 ( X, Z, Y ) }.
% 4.20/4.61 (21219) {G0,W16,D3,L3,V4,M3} { !
% 4.20/4.61 class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 4.20/4.61 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 4.20/4.61 , T, Y ) ) }.
% 4.20/4.61 (21220) {G0,W16,D3,L3,V4,M3} { !
% 4.20/4.61 class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 4.20/4.61 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ), c_Orderings_Oord__class_Oless
% 4.20/4.61 ( X, T, Y ) }.
% 4.20/4.61 (21221) {G0,W16,D3,L3,V4,M3} { !
% 4.20/4.61 class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, T, Y ), c_Orderings_Oord__class_Oless(
% 4.20/4.61 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 4.20/4.61 , Y, Z ) ) }.
% 4.20/4.61 (21222) {G0,W11,D2,L3,V2,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 4.20/4.61 tc_RealDef_Oreal, Y, X ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal
% 4.20/4.61 , Y, X ), Y = X }.
% 4.20/4.61 (21223) {G0,W8,D2,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 4.20/4.61 tc_RealDef_Oreal, Y, X ), c_Orderings_Oord__class_Oless__eq(
% 4.20/4.61 tc_RealDef_Oreal, Y, X ) }.
% 4.20/4.61 (21224) {G0,W7,D2,L2,V2,M2} { ! Y = X, c_Orderings_Oord__class_Oless__eq(
% 4.20/4.61 tc_RealDef_Oreal, Y, X ) }.
% 4.20/4.61 (21225) {G0,W8,D2,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 4.20/4.61 tc_RealDef_Oreal, Y, X ), c_Orderings_Oord__class_Oless__eq(
% 4.20/4.61 tc_RealDef_Oreal, Y, X ) }.
% 4.20/4.61 (21226) {G0,W7,D2,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 4.20/4.61 tc_RealDef_Oreal, Y, X ), ! Y = X }.
% 4.20/4.61 (21227) {G0,W11,D2,L3,V2,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 4.20/4.61 tc_RealDef_Oreal, Y, X ), Y = X, c_Orderings_Oord__class_Oless(
% 4.20/4.61 tc_RealDef_Oreal, Y, X ) }.
% 4.20/4.61 (21228) {G0,W21,D3,L4,V4,M4} { ! class_Fields_Olinordered__field( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 4.20/4.61 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 4.20/4.61 ( X, c_Rings_Oinverse__class_Odivide( X, Y, T ),
% 4.20/4.61 c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 4.20/4.61 (21229) {G0,W21,D3,L4,V4,M4} { ! class_Fields_Olinordered__field( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 4.20/4.61 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 4.20/4.61 ( X, c_Rings_Oinverse__class_Odivide( X, Z, T ),
% 4.20/4.61 c_Rings_Oinverse__class_Odivide( X, Y, T ) ) }.
% 4.20/4.61 (21230) {G0,W20,D3,L4,V3,M4} { ! class_Fields_Olinordered__field( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 4.20/4.61 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 4.20/4.61 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 4.20/4.61 c_Rings_Oinverse__class_Odivide( X, Y, Z ) ) }.
% 4.20/4.61 (21231) {G0,W20,D3,L4,V3,M4} { ! class_Fields_Olinordered__field( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 4.20/4.61 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 4.20/4.61 , c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, Y
% 4.20/4.61 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 4.20/4.61 (21232) {G0,W20,D3,L4,V3,M4} { ! class_Fields_Olinordered__field( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 4.20/4.61 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 4.20/4.61 , c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, Y
% 4.20/4.61 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 4.20/4.61 (21233) {G0,W20,D3,L4,V3,M4} { ! class_Fields_Olinordered__field( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 4.20/4.61 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 4.20/4.61 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 4.20/4.61 c_Rings_Oinverse__class_Odivide( X, Y, Z ) ) }.
% 4.20/4.61 (21234) {G0,W18,D3,L4,V3,M4} { !
% 4.20/4.61 class_Fields_Olinordered__field__inverse__zero( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, Z,
% 4.20/4.61 Y ), c_Groups_Ozero__class_Ozero( X ) ), alpha4( X, Y, Z ), alpha29( X, Y
% 4.20/4.61 , Z ) }.
% 4.20/4.61 (21235) {G0,W14,D3,L3,V3,M3} { !
% 4.20/4.61 class_Fields_Olinordered__field__inverse__zero( X ), ! alpha4( X, Y, Z )
% 4.20/4.61 , c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, Z
% 4.20/4.61 , Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 4.20/4.61 (21236) {G0,W14,D3,L3,V3,M3} { !
% 4.20/4.61 class_Fields_Olinordered__field__inverse__zero( X ), ! alpha29( X, Y, Z )
% 4.20/4.61 , c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, Z
% 4.20/4.61 , Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 4.20/4.61 (21237) {G0,W9,D3,L2,V3,M2} { ! alpha29( X, Y, Z ),
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 4.20/4.61 }.
% 4.20/4.61 (21238) {G0,W9,D3,L2,V3,M2} { ! alpha29( X, Y, Z ),
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 4.20/4.61 }.
% 4.20/4.61 (21239) {G0,W14,D3,L3,V3,M3} { ! c_Orderings_Oord__class_Oless( X, Z,
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless( X,
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ), Y ), alpha29( X, Y, Z ) }.
% 4.20/4.61 (21240) {G0,W9,D3,L2,V3,M2} { ! alpha4( X, Y, Z ),
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 4.20/4.61 }.
% 4.20/4.61 (21241) {G0,W9,D3,L2,V3,M2} { ! alpha4( X, Y, Z ),
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 4.20/4.61 }.
% 4.20/4.61 (21242) {G0,W14,D3,L3,V3,M3} { ! c_Orderings_Oord__class_Oless( X,
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ), Z ), ! c_Orderings_Oord__class_Oless( X
% 4.20/4.61 , Y, c_Groups_Ozero__class_Ozero( X ) ), alpha4( X, Y, Z ) }.
% 4.20/4.61 (21243) {G0,W18,D3,L4,V3,M4} { !
% 4.20/4.61 class_Fields_Olinordered__field__inverse__zero( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 4.20/4.61 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ), alpha5( X, Y, Z ), alpha30
% 4.20/4.61 ( X, Y, Z ) }.
% 4.20/4.61 (21244) {G0,W14,D3,L3,V3,M3} { !
% 4.20/4.61 class_Fields_Olinordered__field__inverse__zero( X ), ! alpha5( X, Y, Z )
% 4.20/4.61 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 4.20/4.61 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 4.20/4.61 (21245) {G0,W14,D3,L3,V3,M3} { !
% 4.20/4.61 class_Fields_Olinordered__field__inverse__zero( X ), ! alpha30( X, Y, Z )
% 4.20/4.61 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 4.20/4.61 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 4.20/4.61 (21246) {G0,W9,D3,L2,V3,M2} { ! alpha30( X, Y, Z ),
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 4.20/4.61 }.
% 4.20/4.61 (21247) {G0,W9,D3,L2,V3,M2} { ! alpha30( X, Y, Z ),
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 4.20/4.61 }.
% 4.20/4.61 (21248) {G0,W14,D3,L3,V3,M3} { ! c_Orderings_Oord__class_Oless( X, Z,
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless( X, Y
% 4.20/4.61 , c_Groups_Ozero__class_Ozero( X ) ), alpha30( X, Y, Z ) }.
% 4.20/4.61 (21249) {G0,W9,D3,L2,V3,M2} { ! alpha5( X, Y, Z ),
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 4.20/4.61 }.
% 4.20/4.61 (21250) {G0,W9,D3,L2,V3,M2} { ! alpha5( X, Y, Z ),
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 4.20/4.61 }.
% 4.20/4.61 (21251) {G0,W14,D3,L3,V3,M3} { ! c_Orderings_Oord__class_Oless( X,
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ), Z ), ! c_Orderings_Oord__class_Oless( X
% 4.20/4.61 , c_Groups_Ozero__class_Ozero( X ), Y ), alpha5( X, Y, Z ) }.
% 4.20/4.61 (21252) {G0,W20,D3,L4,V3,M4} { ! class_Fields_Olinordered__field( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 4.20/4.61 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 4.20/4.61 , Z ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 4.20/4.61 ( X ), c_Rings_Oinverse__class_Odivide( X, Y, Z ) ) }.
% 4.20/4.61 (21253) {G0,W20,D3,L4,V3,M4} { ! class_Fields_Olinordered__field( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 4.20/4.61 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 4.20/4.61 ) ), c_Orderings_Oord__class_Oless__eq( X,
% 4.20/4.61 c_Rings_Oinverse__class_Odivide( X, Y, Z ), c_Groups_Ozero__class_Ozero(
% 4.20/4.61 X ) ) }.
% 4.20/4.61 (21254) {G0,W30,D3,L6,V5,M6} { ! class_Fields_Olinordered__field( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 4.20/4.61 ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 4.20/4.61 ! c_Orderings_Oord__class_Oless( X, T, U ), c_Orderings_Oord__class_Oless
% 4.20/4.61 ( X, c_Rings_Oinverse__class_Odivide( X, Y, U ),
% 4.20/4.61 c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 4.20/4.61 (21255) {G0,W30,D3,L6,V5,M6} { ! class_Fields_Olinordered__field( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 4.20/4.61 ), ! c_Orderings_Oord__class_Oless( X, Y, Z ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 4.20/4.61 ! c_Orderings_Oord__class_Oless__eq( X, T, U ),
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, Y,
% 4.20/4.61 U ), c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 4.20/4.61 (21256) {G0,W30,D3,L6,V5,M6} { ! class_Fields_Olinordered__field( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 4.20/4.61 ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 4.20/4.61 ! c_Orderings_Oord__class_Oless__eq( X, T, U ),
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 4.20/4.61 , Y, U ), c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 4.20/4.61 (21257) {G0,W20,D3,L4,V3,M4} { ! class_Fields_Olinordered__field( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 4.20/4.61 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 4.20/4.61 , Z ), c_Orderings_Oord__class_Oless__eq( X,
% 4.20/4.61 c_Rings_Oinverse__class_Odivide( X, Y, Z ), c_Groups_Ozero__class_Ozero(
% 4.20/4.61 X ) ) }.
% 4.20/4.61 (21258) {G0,W20,D3,L4,V3,M4} { ! class_Fields_Olinordered__field( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 4.20/4.61 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 4.20/4.61 ) ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 4.20/4.61 X ), c_Rings_Oinverse__class_Odivide( X, Y, Z ) ) }.
% 4.20/4.61 (21259) {G0,W14,D3,L3,V4,M3} { !
% 4.20/4.61 class_Fields_Olinordered__field__inverse__zero( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 4.20/4.61 Z, Y ) ), alpha31( X, Y, Z, T ) }.
% 4.20/4.61 (21260) {G0,W14,D3,L3,V4,M3} { !
% 4.20/4.61 class_Fields_Olinordered__field__inverse__zero( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 4.20/4.61 Z, Y ) ), alpha48( X, Y, Z, T ) }.
% 4.20/4.61 (21261) {G0,W19,D3,L4,V4,M4} { !
% 4.20/4.61 class_Fields_Olinordered__field__inverse__zero( X ), ! alpha31( X, Y, Z,
% 4.20/4.61 T ), ! alpha48( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 4.20/4.61 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 4.20/4.61 (21262) {G0,W15,D3,L3,V4,M3} { ! alpha48( X, Y, Z, T ),
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 4.20/4.61 alpha57( X, Y, Z, T ) }.
% 4.20/4.61 (21263) {G0,W10,D3,L2,V4,M2} { ! c_Orderings_Oord__class_Oless( X,
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ), Y ), alpha48( X, Y, Z, T ) }.
% 4.20/4.61 (21264) {G0,W10,D2,L2,V4,M2} { ! alpha57( X, Y, Z, T ), alpha48( X, Y, Z,
% 4.20/4.61 T ) }.
% 4.20/4.61 (21265) {G0,W10,D2,L2,V4,M2} { ! alpha57( X, Y, Z, T ), alpha67( X, Y, Z,
% 4.20/4.61 T ) }.
% 4.20/4.61 (21266) {G0,W9,D2,L2,V4,M2} { ! alpha57( X, Y, Z, T ), alpha6( X, Y, T )
% 4.20/4.61 }.
% 4.20/4.61 (21267) {G0,W14,D2,L3,V4,M3} { ! alpha67( X, Y, Z, T ), ! alpha6( X, Y, T
% 4.20/4.61 ), alpha57( X, Y, Z, T ) }.
% 4.20/4.61 (21268) {G0,W19,D5,L3,V4,M3} { ! alpha67( X, Y, Z, T ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 4.20/4.61 (21269) {G0,W10,D3,L2,V4,M2} { c_Orderings_Oord__class_Oless( X, Y,
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ) ), alpha67( X, Y, Z, T ) }.
% 4.20/4.61 (21270) {G0,W14,D5,L2,V4,M2} { ! c_Orderings_Oord__class_Oless( X, Z, hAPP
% 4.20/4.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha67( X, Y, Z
% 4.20/4.61 , T ) }.
% 4.20/4.61 (21271) {G0,W19,D5,L3,V4,M3} { ! alpha31( X, Y, Z, T ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 4.20/4.61 (21272) {G0,W10,D3,L2,V4,M2} { c_Orderings_Oord__class_Oless( X,
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ), Y ), alpha31( X, Y, Z, T ) }.
% 4.20/4.61 (21273) {G0,W14,D5,L2,V4,M2} { ! c_Orderings_Oord__class_Oless( X, hAPP(
% 4.20/4.61 hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ), alpha31( X, Y, Z
% 4.20/4.61 , T ) }.
% 4.20/4.61 (21274) {G0,W14,D3,L3,V3,M3} { ! alpha6( X, Y, Z ),
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 4.20/4.61 }.
% 4.20/4.61 (21275) {G0,W9,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless( X, Y,
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ) ), alpha6( X, Y, Z ) }.
% 4.20/4.61 (21276) {G0,W9,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless( X, Z,
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ) ), alpha6( X, Y, Z ) }.
% 4.20/4.61 (21277) {G0,W14,D3,L3,V4,M3} { !
% 4.20/4.61 class_Fields_Olinordered__field__inverse__zero( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 4.20/4.61 Z ), Y ), alpha32( X, Y, Z, T ) }.
% 4.20/4.61 (21278) {G0,W14,D3,L3,V4,M3} { !
% 4.20/4.61 class_Fields_Olinordered__field__inverse__zero( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 4.20/4.61 Z ), Y ), alpha49( X, Y, Z, T ) }.
% 4.20/4.61 (21279) {G0,W19,D3,L4,V4,M4} { !
% 4.20/4.61 class_Fields_Olinordered__field__inverse__zero( X ), ! alpha32( X, Y, Z,
% 4.20/4.61 T ), ! alpha49( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 4.20/4.61 c_Rings_Oinverse__class_Odivide( X, T, Z ), Y ) }.
% 4.20/4.61 (21280) {G0,W15,D3,L3,V4,M3} { ! alpha49( X, Y, Z, T ),
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 4.20/4.61 alpha58( X, Y, Z, T ) }.
% 4.20/4.61 (21281) {G0,W10,D3,L2,V4,M2} { ! c_Orderings_Oord__class_Oless( X,
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ), Z ), alpha49( X, Y, Z, T ) }.
% 4.20/4.61 (21282) {G0,W10,D2,L2,V4,M2} { ! alpha58( X, Y, Z, T ), alpha49( X, Y, Z,
% 4.20/4.61 T ) }.
% 4.20/4.61 (21283) {G0,W10,D2,L2,V4,M2} { ! alpha58( X, Y, Z, T ), alpha68( X, Y, Z,
% 4.20/4.61 T ) }.
% 4.20/4.61 (21284) {G0,W9,D2,L2,V4,M2} { ! alpha58( X, Y, Z, T ), alpha7( X, Y, Z )
% 4.20/4.61 }.
% 4.20/4.61 (21285) {G0,W14,D2,L3,V4,M3} { ! alpha68( X, Y, Z, T ), ! alpha7( X, Y, Z
% 4.20/4.61 ), alpha58( X, Y, Z, T ) }.
% 4.20/4.61 (21286) {G0,W19,D5,L3,V4,M3} { ! alpha68( X, Y, Z, T ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) ),
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ) }.
% 4.20/4.61 (21287) {G0,W10,D3,L2,V4,M2} { c_Orderings_Oord__class_Oless( X, Z,
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ) ), alpha68( X, Y, Z, T ) }.
% 4.20/4.61 (21288) {G0,W14,D5,L2,V4,M2} { ! c_Orderings_Oord__class_Oless( X, hAPP(
% 4.20/4.61 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ), alpha68( X, Y, Z
% 4.20/4.61 , T ) }.
% 4.20/4.61 (21289) {G0,W19,D5,L3,V4,M3} { ! alpha32( X, Y, Z, T ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 4.20/4.61 (21290) {G0,W10,D3,L2,V4,M2} { c_Orderings_Oord__class_Oless( X,
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ), Z ), alpha32( X, Y, Z, T ) }.
% 4.20/4.61 (21291) {G0,W14,D5,L2,V4,M2} { ! c_Orderings_Oord__class_Oless( X, T, hAPP
% 4.20/4.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha32( X, Y, Z
% 4.20/4.61 , T ) }.
% 4.20/4.61 (21292) {G0,W14,D3,L3,V3,M3} { ! alpha7( X, Y, Z ),
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) ),
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 4.20/4.61 }.
% 4.20/4.61 (21293) {G0,W9,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless( X, Z,
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ) ), alpha7( X, Y, Z ) }.
% 4.20/4.61 (21294) {G0,W9,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless( X,
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ), Y ), alpha7( X, Y, Z ) }.
% 4.20/4.61 (21295) {G0,W23,D5,L4,V4,M4} { ! class_Fields_Olinordered__field( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 4.20/4.61 ! c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X
% 4.20/4.61 , Z, Y ) ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 4.20/4.61 (21296) {G0,W23,D5,L4,V4,M4} { ! class_Fields_Olinordered__field( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 4.20/4.61 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 4.20/4.61 Z, Y ) ) }.
% 4.20/4.61 (21297) {G0,W23,D5,L4,V4,M4} { ! class_Fields_Olinordered__field( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 4.20/4.61 ! c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T
% 4.20/4.61 , Y ), Z ), c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 4.20/4.61 (21298) {G0,W23,D5,L4,V4,M4} { ! class_Fields_Olinordered__field( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 4.20/4.61 ! c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 4.20/4.61 Y ), Z ) }.
% 4.20/4.61 (21299) {G0,W23,D5,L4,V4,M4} { ! class_Fields_Olinordered__field( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 4.20/4.61 ! c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 4.20/4.61 Y ), Z ) }.
% 4.20/4.61 (21300) {G0,W23,D5,L4,V4,M4} { ! class_Fields_Olinordered__field( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 4.20/4.61 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 4.20/4.61 Z, Y ) ) }.
% 4.20/4.61 (21301) {G0,W23,D5,L4,V4,M4} { ! class_Fields_Olinordered__field( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 4.20/4.61 ! c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X
% 4.20/4.61 , Z, Y ) ), c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 4.20/4.61 (21302) {G0,W23,D5,L4,V4,M4} { ! class_Fields_Olinordered__field( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 4.20/4.61 ! c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ),
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 4.20/4.61 Z, Y ) ) }.
% 4.20/4.61 (21303) {G0,W23,D5,L4,V4,M4} { ! class_Fields_Olinordered__field( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 4.20/4.61 ! c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T
% 4.20/4.61 , Y ), Z ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ) }.
% 4.20/4.61 (21304) {G0,W23,D5,L4,V4,M4} { ! class_Fields_Olinordered__field( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 4.20/4.61 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ),
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 4.20/4.61 Y ), Z ) }.
% 4.20/4.61 (21305) {G0,W31,D5,L5,V4,M5} { ! class_Fields_Olinordered__field( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 4.20/4.61 ( X, c_Groups_Ozero__class_Ozero( X ), T ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 4.20/4.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 4.20/4.61 Y ), c_Rings_Oinverse__class_Odivide( X, T, Z ) ) }.
% 4.20/4.61 (21306) {G0,W31,D5,L5,V4,M5} { ! class_Fields_Olinordered__field( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 4.20/4.61 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 4.20/4.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 4.20/4.61 Z ), c_Rings_Oinverse__class_Odivide( X, T, Y ) ) }.
% 4.20/4.61 (21307) {G0,W12,D5,L2,V2,M2} { ! class_Rings_Olinordered__ring( X ), !
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), Y ), Y ), c_Groups_Ozero__class_Ozero
% 4.20/4.61 ( X ) ) }.
% 4.20/4.61 (21308) {G0,W26,D5,L4,V4,M4} { ! class_Rings_Olinordered__ring__strict( X
% 4.20/4.61 ), ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha8( X, Y, Z, T ),
% 4.20/4.61 alpha33( X, Y, Z, T ) }.
% 4.20/4.61 (21309) {G0,W21,D5,L3,V4,M3} { ! class_Rings_Olinordered__ring__strict( X
% 4.20/4.61 ), ! alpha8( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP
% 4.20/4.61 ( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 4.20/4.61 (21310) {G0,W21,D5,L3,V4,M3} { ! class_Rings_Olinordered__ring__strict( X
% 4.20/4.61 ), ! alpha33( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP
% 4.20/4.61 ( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 4.20/4.61 (21311) {G0,W10,D3,L2,V4,M2} { ! alpha33( X, Y, Z, T ),
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 4.20/4.61 }.
% 4.20/4.61 (21312) {G0,W9,D2,L2,V4,M2} { ! alpha33( X, Y, Z, T ),
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Y, T ) }.
% 4.20/4.61 (21313) {G0,W14,D3,L3,V4,M3} { ! c_Orderings_Oord__class_Oless( X, Z,
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless( X, Y
% 4.20/4.61 , T ), alpha33( X, Y, Z, T ) }.
% 4.20/4.61 (21314) {G0,W10,D3,L2,V4,M2} { ! alpha8( X, Y, Z, T ),
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 4.20/4.61 }.
% 4.20/4.61 (21315) {G0,W9,D2,L2,V4,M2} { ! alpha8( X, Y, Z, T ),
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 4.20/4.61 (21316) {G0,W14,D3,L3,V4,M3} { ! c_Orderings_Oord__class_Oless( X,
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ), Z ), ! c_Orderings_Oord__class_Oless( X
% 4.20/4.61 , T, Y ), alpha8( X, Y, Z, T ) }.
% 4.20/4.61 (21317) {G0,W26,D5,L4,V4,M4} { ! class_Rings_Olinordered__ring__strict( X
% 4.20/4.61 ), ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha9( X, Y, Z, T ),
% 4.20/4.61 alpha34( X, Y, Z, T ) }.
% 4.20/4.61 (21318) {G0,W21,D5,L3,V4,M3} { ! class_Rings_Olinordered__ring__strict( X
% 4.20/4.61 ), ! alpha9( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP
% 4.20/4.61 ( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 4.20/4.61 (21319) {G0,W21,D5,L3,V4,M3} { ! class_Rings_Olinordered__ring__strict( X
% 4.20/4.61 ), ! alpha34( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP
% 4.20/4.61 ( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 4.20/4.61 (21320) {G0,W10,D3,L2,V4,M2} { ! alpha34( X, Y, Z, T ),
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, T, c_Groups_Ozero__class_Ozero( X ) )
% 4.20/4.61 }.
% 4.20/4.61 (21321) {G0,W9,D2,L2,V4,M2} { ! alpha34( X, Y, Z, T ),
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 4.20/4.61 (21322) {G0,W14,D3,L3,V4,M3} { ! c_Orderings_Oord__class_Oless( X, T,
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless( X, Y
% 4.20/4.61 , Z ), alpha34( X, Y, Z, T ) }.
% 4.20/4.61 (21323) {G0,W10,D3,L2,V4,M2} { ! alpha9( X, Y, Z, T ),
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T )
% 4.20/4.61 }.
% 4.20/4.61 (21324) {G0,W9,D2,L2,V4,M2} { ! alpha9( X, Y, Z, T ),
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 4.20/4.61 (21325) {G0,W14,D3,L3,V4,M3} { ! c_Orderings_Oord__class_Oless( X,
% 4.20/4.61 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 4.20/4.61 , Z, Y ), alpha9( X, Y, Z, T ) }.
% 4.20/4.61 (21326) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__ring__strict( X
% 4.20/4.61 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 4.20/4.61 , Y ), ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 4.20/4.61 (21327) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__ring__strict( X
% 4.20/4.61 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 4.20/4.61 , Y ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 4.20/4.61 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 4.20/4.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 4.20/4.61 (21328) {G0,W22,D5,L4,V3,M4} { ! class_Rings_Olinordered__semiring__strict
% 4.20/4.61 ( X ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X
% 4.20/4.61 ), Y ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero
% 4.20/4.61 ( X ), Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero
% 4.20/4.61 ( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 4.20/4.61 (21329) {G0,W22,D5,L4,V3,M4} { ! class_Rings_Olinordered__semiring__strict
% 4.20/4.61 ( X ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X
% 4.20/4.62 ), Y ), ! c_Orderings_Oord__class_Oless( X, Z,
% 4.20/4.62 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 4.20/4.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ),
% 4.20/4.62 c_Groups_Ozero__class_Ozero( X ) ) }.
% 4.20/4.62 (21330) {G0,W22,D5,L4,V3,M4} { ! class_Rings_Olinordered__semiring__strict
% 4.20/4.62 ( X ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X
% 4.20/4.62 ), Y ), ! c_Orderings_Oord__class_Oless( X, Z,
% 4.20/4.62 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 4.20/4.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 4.20/4.62 c_Groups_Ozero__class_Ozero( X ) ) }.
% 4.20/4.62 (21331) {G0,W22,D5,L4,V3,M4} { ! class_Rings_Olinordered__semiring__strict
% 4.20/4.62 ( X ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X
% 4.20/4.62 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 4.20/4.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 4.20/4.62 }.
% 4.20/4.62 (21332) {G0,W22,D5,L4,V3,M4} { ! class_Rings_Olinordered__semiring__strict
% 4.20/4.62 ( X ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X
% 4.20/4.62 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 4.20/4.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 4.20/4.62 }.
% 4.20/4.62 (21333) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__ring__strict( X
% 4.20/4.62 ), ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 4.20/4.62 ) ), ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 4.20/4.62 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 4.20/4.62 (21334) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__ring__strict( X
% 4.20/4.62 ), ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 4.20/4.62 ) ), ! c_Orderings_Oord__class_Oless( X, Z, T ),
% 4.20/4.62 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 4.20/4.62 (21335) {G0,W22,D5,L4,V3,M4} { ! class_Rings_Olinordered__semiring__strict
% 4.20/4.62 ( X ), ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero
% 4.20/4.62 ( X ) ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero
% 4.20/4.62 ( X ), Z ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 4.20/4.62 ( X ) ) }.
% 4.20/4.62 (21336) {G0,W22,D5,L4,V3,M4} { ! class_Rings_Olinordered__ring__strict( X
% 4.20/4.62 ), ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 4.20/4.62 ) ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero
% 4.20/4.62 ( X ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X
% 4.20/4.62 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 4.20/4.62 (21337) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__semiring__strict
% 4.20/4.62 ( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 4.20/4.62 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 4.20/4.62 (21338) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__semiring__strict
% 4.20/4.62 ( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 4.20/4.62 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 4.20/4.62 (21339) {G0,W25,D5,L4,V4,M4} { !
% 4.20/4.62 class_Rings_Olinordered__comm__semiring__strict( X ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 4.20/4.62 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 4.20/4.62 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 4.20/4.62 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 4.20/4.62 (21340) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__ring__strict( X
% 4.20/4.62 ), ! c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless( X, T, c_Groups_Ozero__class_Ozero( X ) ),
% 4.20/4.62 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 4.20/4.62 (21341) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__ring__strict( X
% 4.20/4.62 ), ! c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless( X, T, c_Groups_Ozero__class_Ozero( X ) ),
% 4.20/4.62 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 4.20/4.62 (21342) {G0,W15,D3,L3,V2,M3} { ! class_Groups_Olinordered__ab__group__add
% 4.20/4.62 ( X ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X
% 4.20/4.62 ), c_Groups_Oplus__class_Oplus( X, Y, Y ) ),
% 4.20/4.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 4.20/4.62 }.
% 4.20/4.62 (21343) {G0,W15,D3,L3,V2,M3} { ! class_Groups_Olinordered__ab__group__add
% 4.20/4.62 ( X ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X
% 4.20/4.62 ), Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X
% 4.20/4.62 ), c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 4.20/4.62 (21344) {G0,W15,D3,L3,V2,M3} { ! class_Groups_Olinordered__ab__group__add
% 4.20/4.62 ( X ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X
% 4.20/4.62 , Y, Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 4.20/4.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 4.20/4.62 }.
% 4.20/4.62 (21345) {G0,W15,D3,L3,V2,M3} { ! class_Groups_Olinordered__ab__group__add
% 4.20/4.62 ( X ), ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero
% 4.20/4.62 ( X ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X
% 4.20/4.62 , Y, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 4.20/4.62 (21346) {G0,W20,D3,L4,V3,M4} { ! class_Groups_Oordered__comm__monoid__add
% 4.20/4.62 ( X ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X
% 4.20/4.62 ), Y ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero
% 4.20/4.62 ( X ), Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero
% 4.20/4.62 ( X ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 4.20/4.62 (21347) {G0,W18,D3,L4,V4,M4} { ! class_Rings_Olinordered__semidom( X ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 4.20/4.62 ! c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless
% 4.20/4.62 ( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 4.20/4.62 (21348) {G0,W20,D3,L4,V3,M4} { ! class_Groups_Oordered__comm__monoid__add
% 4.20/4.62 ( X ), ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero
% 4.20/4.62 ( X ) ), ! c_Orderings_Oord__class_Oless( X, Z,
% 4.20/4.62 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 4.20/4.62 c_Groups_Oplus__class_Oplus( X, Y, Z ), c_Groups_Ozero__class_Ozero( X )
% 4.20/4.62 ) }.
% 4.20/4.62 (21349) {G0,W20,D3,L4,V5,M4} { !
% 4.20/4.62 class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless( X, U, T ), c_Orderings_Oord__class_Oless(
% 4.20/4.62 X, c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X
% 4.20/4.62 , Y, T ) ) }.
% 4.20/4.62 (21350) {G0,W20,D3,L4,V5,M4} { !
% 4.20/4.62 class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 4.20/4.62 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, U )
% 4.20/4.62 , c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 4.20/4.62 (21351) {G0,W20,D4,L3,V3,M3} { !
% 4.20/4.62 class_Fields_Olinordered__field__inverse__zero( X ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 4.20/4.62 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oabs__class_Oabs( X, Z ), Y
% 4.20/4.62 ) = c_Groups_Oabs__class_Oabs( X, c_Rings_Oinverse__class_Odivide( X, Z
% 4.20/4.62 , Y ) ) }.
% 4.20/4.62 (21352) {G0,W9,D3,L2,V2,M2} { ! class_Groups_Oordered__ab__group__add__abs
% 4.20/4.62 ( X ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X,
% 4.20/4.62 Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 4.20/4.62 (21353) {G0,W13,D3,L3,V2,M3} { !
% 4.20/4.62 class_Groups_Oordered__ab__group__add__abs( X ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 4.20/4.62 c_Groups_Oabs__class_Oabs( X, Y ) ), ! Y = c_Groups_Ozero__class_Ozero( X
% 4.20/4.62 ) }.
% 4.20/4.62 (21354) {G0,W13,D3,L3,V2,M3} { !
% 4.20/4.62 class_Groups_Oordered__ab__group__add__abs( X ), Y =
% 4.20/4.62 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 4.20/4.62 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 4.20/4.62 (21355) {G0,W12,D3,L3,V2,M3} { !
% 4.20/4.62 class_Groups_Oordered__ab__group__add__abs( X ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 4.20/4.62 c_Groups_Oabs__class_Oabs( X, Y ) = Y }.
% 4.20/4.62 (21356) {G0,W32,D5,L4,V5,M4} { ! class_Rings_Olinordered__idom( X ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X, Z ), Y )
% 4.20/4.62 , ! c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X, U ),
% 4.20/4.62 T ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 4.20/4.62 c_Groups_Oabs__class_Oabs( X, U ) ), hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 4.20/4.62 (21357) {G0,W23,D5,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 4.20/4.62 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ),
% 4.20/4.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ) }.
% 4.20/4.62 (21358) {G0,W23,D5,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 4.20/4.62 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 4.20/4.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 4.20/4.62 (21359) {G0,W20,D5,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 4.20/4.62 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 4.20/4.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 4.20/4.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 4.20/4.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 4.20/4.62 (21360) {G0,W23,D5,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 4.20/4.62 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 4.20/4.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 4.20/4.62 (21361) {G0,W9,D3,L2,V2,M2} { ! class_RealVector_Oreal__normed__vector( X
% 4.20/4.62 ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 4.20/4.62 c_RealVector_Onorm__class_Onorm( X, Y ), c_Groups_Ozero__class_Ozero(
% 4.20/4.62 tc_RealDef_Oreal ) ) }.
% 4.20/4.62 (21362) {G0,W31,D5,L5,V4,M5} { !
% 4.20/4.62 class_Fields_Olinordered__field__inverse__zero( X ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Ozero__class_Ozero( X )
% 4.20/4.62 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 4.20/4.62 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 4.20/4.62 , T, Z ), c_Rings_Oinverse__class_Odivide( X, T, Y ) ) }.
% 4.20/4.62 (21363) {G0,W31,D5,L5,V4,M5} { ! class_Fields_Olinordered__field( X ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 4.20/4.62 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 4.20/4.62 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 4.20/4.62 , T, Y ), c_Rings_Oinverse__class_Odivide( X, T, Z ) ) }.
% 4.20/4.62 (21364) {G0,W23,D5,L4,V4,M4} { ! class_Fields_Olinordered__field( X ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 4.20/4.62 ! c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide(
% 4.20/4.62 X, T, Y ), Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ) }.
% 4.20/4.62 (21365) {G0,W23,D5,L4,V4,M4} { ! class_Fields_Olinordered__field( X ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 4.20/4.62 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ),
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 4.20/4.62 , T, Y ), Z ) }.
% 4.20/4.62 (21366) {G0,W23,D5,L4,V4,M4} { ! class_Fields_Olinordered__field( X ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 4.20/4.62 ! c_Orderings_Oord__class_Oless__eq( X, T,
% 4.20/4.62 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ),
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( X, Z, hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 4.20/4.62 (21367) {G0,W23,D5,L4,V4,M4} { ! class_Fields_Olinordered__field( X ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 4.20/4.62 ! c_Orderings_Oord__class_Oless__eq( X, Z, hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ),
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 4.20/4.62 ( X, Z, Y ) ) }.
% 4.20/4.62 (21368) {G0,W23,D5,L4,V4,M4} { ! class_Fields_Olinordered__field( X ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 4.20/4.62 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 4.20/4.62 ( X, Z, Y ) ) }.
% 4.20/4.62 (21369) {G0,W23,D5,L4,V4,M4} { ! class_Fields_Olinordered__field( X ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 4.20/4.62 ! c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 4.20/4.62 , T, Y ), Z ) }.
% 4.20/4.62 (21370) {G0,W23,D5,L4,V4,M4} { ! class_Fields_Olinordered__field( X ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 4.20/4.62 ! c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide(
% 4.20/4.62 X, T, Y ), Z ), c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 4.20/4.62 (21371) {G0,W23,D5,L4,V4,M4} { ! class_Fields_Olinordered__field( X ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 4.20/4.62 ! c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 4.20/4.62 , T, Y ), Z ) }.
% 4.20/4.62 (21372) {G0,W23,D5,L4,V4,M4} { ! class_Fields_Olinordered__field( X ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 4.20/4.62 ! c_Orderings_Oord__class_Oless__eq( X, T,
% 4.20/4.62 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ),
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 4.20/4.62 (21373) {G0,W23,D5,L4,V4,M4} { ! class_Fields_Olinordered__field( X ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 4.20/4.62 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 4.20/4.62 ( X, Z, Y ) ) }.
% 4.20/4.62 (21374) {G0,W14,D3,L3,V4,M3} { !
% 4.20/4.62 class_Fields_Olinordered__field__inverse__zero( X ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 4.20/4.62 , T, Z ), Y ), alpha35( X, Y, Z, T ) }.
% 4.20/4.62 (21375) {G0,W14,D3,L3,V4,M3} { !
% 4.20/4.62 class_Fields_Olinordered__field__inverse__zero( X ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 4.20/4.62 , T, Z ), Y ), alpha50( X, Y, Z, T ) }.
% 4.20/4.62 (21376) {G0,W19,D3,L4,V4,M4} { !
% 4.20/4.62 class_Fields_Olinordered__field__inverse__zero( X ), ! alpha35( X, Y, Z,
% 4.20/4.62 T ), ! alpha50( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( X,
% 4.20/4.62 c_Rings_Oinverse__class_Odivide( X, T, Z ), Y ) }.
% 4.20/4.62 (21377) {G0,W15,D3,L3,V4,M3} { ! alpha50( X, Y, Z, T ),
% 4.20/4.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 4.20/4.62 alpha59( X, Y, Z, T ) }.
% 4.20/4.62 (21378) {G0,W10,D3,L2,V4,M2} { ! c_Orderings_Oord__class_Oless( X,
% 4.20/4.62 c_Groups_Ozero__class_Ozero( X ), Z ), alpha50( X, Y, Z, T ) }.
% 4.20/4.62 (21379) {G0,W10,D2,L2,V4,M2} { ! alpha59( X, Y, Z, T ), alpha50( X, Y, Z,
% 4.20/4.62 T ) }.
% 4.20/4.62 (21380) {G0,W10,D2,L2,V4,M2} { ! alpha59( X, Y, Z, T ), alpha69( X, Y, Z,
% 4.20/4.62 T ) }.
% 4.20/4.62 (21381) {G0,W9,D2,L2,V4,M2} { ! alpha59( X, Y, Z, T ), alpha10( X, Y, Z )
% 4.20/4.62 }.
% 4.20/4.62 (21382) {G0,W14,D2,L3,V4,M3} { ! alpha69( X, Y, Z, T ), ! alpha10( X, Y, Z
% 4.20/4.62 ), alpha59( X, Y, Z, T ) }.
% 4.20/4.62 (21383) {G0,W19,D5,L3,V4,M3} { ! alpha69( X, Y, Z, T ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) ),
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ) }.
% 4.20/4.62 (21384) {G0,W10,D3,L2,V4,M2} { c_Orderings_Oord__class_Oless( X, Z,
% 4.20/4.62 c_Groups_Ozero__class_Ozero( X ) ), alpha69( X, Y, Z, T ) }.
% 4.20/4.62 (21385) {G0,W14,D5,L2,V4,M2} { ! c_Orderings_Oord__class_Oless__eq( X,
% 4.20/4.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ), alpha69( X
% 4.20/4.62 , Y, Z, T ) }.
% 4.20/4.62 (21386) {G0,W19,D5,L3,V4,M3} { ! alpha35( X, Y, Z, T ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 4.20/4.62 (21387) {G0,W10,D3,L2,V4,M2} { c_Orderings_Oord__class_Oless( X,
% 4.20/4.62 c_Groups_Ozero__class_Ozero( X ), Z ), alpha35( X, Y, Z, T ) }.
% 4.20/4.62 (21388) {G0,W14,D5,L2,V4,M2} { ! c_Orderings_Oord__class_Oless__eq( X, T,
% 4.20/4.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha35( X, Y
% 4.20/4.62 , Z, T ) }.
% 4.20/4.62 (21389) {G0,W14,D3,L3,V3,M3} { ! alpha10( X, Y, Z ),
% 4.20/4.62 c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) ),
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 4.20/4.62 ) }.
% 4.20/4.62 (21390) {G0,W9,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless( X, Z,
% 4.20/4.62 c_Groups_Ozero__class_Ozero( X ) ), alpha10( X, Y, Z ) }.
% 4.20/4.62 (21391) {G0,W9,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless__eq( X,
% 4.20/4.62 c_Groups_Ozero__class_Ozero( X ), Y ), alpha10( X, Y, Z ) }.
% 4.20/4.62 (21392) {G0,W14,D3,L3,V4,M3} { !
% 4.20/4.62 class_Fields_Olinordered__field__inverse__zero( X ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 4.20/4.62 ( X, Z, Y ) ), alpha36( X, Y, Z, T ) }.
% 4.20/4.62 (21393) {G0,W14,D3,L3,V4,M3} { !
% 4.20/4.62 class_Fields_Olinordered__field__inverse__zero( X ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 4.20/4.62 ( X, Z, Y ) ), alpha51( X, Y, Z, T ) }.
% 4.20/4.62 (21394) {G0,W19,D3,L4,V4,M4} { !
% 4.20/4.62 class_Fields_Olinordered__field__inverse__zero( X ), ! alpha36( X, Y, Z,
% 4.20/4.62 T ), ! alpha51( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( X, T,
% 4.20/4.62 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 4.20/4.62 (21395) {G0,W15,D3,L3,V4,M3} { ! alpha51( X, Y, Z, T ),
% 4.20/4.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 4.20/4.62 alpha60( X, Y, Z, T ) }.
% 4.20/4.62 (21396) {G0,W10,D3,L2,V4,M2} { ! c_Orderings_Oord__class_Oless( X,
% 4.20/4.62 c_Groups_Ozero__class_Ozero( X ), Y ), alpha51( X, Y, Z, T ) }.
% 4.20/4.62 (21397) {G0,W10,D2,L2,V4,M2} { ! alpha60( X, Y, Z, T ), alpha51( X, Y, Z,
% 4.20/4.62 T ) }.
% 4.20/4.62 (21398) {G0,W10,D2,L2,V4,M2} { ! alpha60( X, Y, Z, T ), alpha70( X, Y, Z,
% 4.20/4.62 T ) }.
% 4.20/4.62 (21399) {G0,W9,D2,L2,V4,M2} { ! alpha60( X, Y, Z, T ), alpha11( X, Y, T )
% 4.20/4.62 }.
% 4.20/4.62 (21400) {G0,W14,D2,L3,V4,M3} { ! alpha70( X, Y, Z, T ), ! alpha11( X, Y, T
% 4.20/4.62 ), alpha60( X, Y, Z, T ) }.
% 4.20/4.62 (21401) {G0,W19,D5,L3,V4,M3} { ! alpha70( X, Y, Z, T ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( X, Z, hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 4.20/4.62 (21402) {G0,W10,D3,L2,V4,M2} { c_Orderings_Oord__class_Oless( X, Y,
% 4.20/4.62 c_Groups_Ozero__class_Ozero( X ) ), alpha70( X, Y, Z, T ) }.
% 4.20/4.62 (21403) {G0,W14,D5,L2,V4,M2} { ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 4.20/4.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha70( X, Y
% 4.20/4.62 , Z, T ) }.
% 4.20/4.62 (21404) {G0,W19,D5,L3,V4,M3} { ! alpha36( X, Y, Z, T ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 4.20/4.62 (21405) {G0,W10,D3,L2,V4,M2} { c_Orderings_Oord__class_Oless( X,
% 4.20/4.62 c_Groups_Ozero__class_Ozero( X ), Y ), alpha36( X, Y, Z, T ) }.
% 4.20/4.62 (21406) {G0,W14,D5,L2,V4,M2} { ! c_Orderings_Oord__class_Oless__eq( X,
% 4.20/4.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ), alpha36( X
% 4.20/4.62 , Y, Z, T ) }.
% 4.20/4.62 (21407) {G0,W14,D3,L3,V3,M3} { ! alpha11( X, Y, Z ),
% 4.20/4.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 4.20/4.62 ) }.
% 4.20/4.62 (21408) {G0,W9,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless( X, Y,
% 4.20/4.62 c_Groups_Ozero__class_Ozero( X ) ), alpha11( X, Y, Z ) }.
% 4.20/4.62 (21409) {G0,W9,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 4.20/4.62 c_Groups_Ozero__class_Ozero( X ) ), alpha11( X, Y, Z ) }.
% 4.20/4.62 (21410) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__semiring__strict
% 4.20/4.62 ( X ), ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 4.20/4.62 (21411) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__semiring__strict
% 4.20/4.62 ( X ), ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 4.20/4.62 (21412) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__semiring__strict
% 4.20/4.62 ( X ), ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 4.20/4.62 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 4.20/4.62 (21413) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__semiring( X ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 4.20/4.62 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 4.20/4.62 (21414) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__semiring__strict
% 4.20/4.62 ( X ), ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 4.20/4.62 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 4.20/4.62 (21415) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__semiring( X ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 4.20/4.62 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 4.20/4.62 (21416) {G0,W34,D5,L6,V5,M6} { ! class_Rings_Olinordered__semiring__strict
% 4.20/4.62 ( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless( X, U, T ), ! c_Orderings_Oord__class_Oless
% 4.20/4.62 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 4.20/4.62 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 4.20/4.62 (21417) {G0,W34,D5,L6,V5,M6} { ! class_Rings_Olinordered__semiring__strict
% 4.20/4.62 ( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 4.20/4.62 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 4.20/4.62 , U ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 4.20/4.62 (21418) {G0,W34,D5,L6,V5,M6} { ! class_Rings_Olinordered__semiring__strict
% 4.20/4.62 ( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless( X, U, T ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 4.20/4.62 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 4.20/4.62 X ), U ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 4.20/4.62 (21419) {G0,W34,D5,L6,V5,M6} { ! class_Rings_Olinordered__semiring__strict
% 4.20/4.62 ( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless( X, U, T ), ! c_Orderings_Oord__class_Oless
% 4.20/4.62 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 4.20/4.62 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 4.20/4.62 (21420) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__ring__strict( X
% 4.20/4.62 ), ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 4.20/4.62 ) ), ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 4.20/4.62 (21421) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__ring__strict( X
% 4.20/4.62 ), ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 4.20/4.62 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Z, T ),
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 4.20/4.62 (21422) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__ring__strict( X
% 4.20/4.62 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 4.20/4.62 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 4.20/4.62 (21423) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__ring__strict( X
% 4.20/4.62 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 4.20/4.62 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 4.20/4.62 (21424) {G0,W20,D3,L4,V3,M4} { ! class_Groups_Oordered__comm__monoid__add
% 4.20/4.62 ( X ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 4.20/4.62 c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless( X, Z
% 4.20/4.62 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 4.20/4.62 c_Groups_Oplus__class_Oplus( X, Y, Z ), c_Groups_Ozero__class_Ozero( X )
% 4.20/4.62 ) }.
% 4.20/4.62 (21425) {G0,W20,D3,L4,V3,M4} { ! class_Groups_Oordered__comm__monoid__add
% 4.20/4.62 ( X ), ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero
% 4.20/4.62 ( X ) ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 4.20/4.62 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 4.20/4.62 c_Groups_Oplus__class_Oplus( X, Y, Z ), c_Groups_Ozero__class_Ozero( X )
% 4.20/4.62 ) }.
% 4.20/4.62 (21426) {G0,W18,D3,L4,V4,M4} { ! class_Groups_Oordered__comm__monoid__add
% 4.20/4.62 ( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 4.20/4.62 c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless( X
% 4.20/4.62 , T, Z ), c_Orderings_Oord__class_Oless( X, T,
% 4.20/4.62 c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 4.20/4.62 (21427) {G0,W18,D3,L4,V4,M4} { ! class_Groups_Oordered__comm__monoid__add
% 4.20/4.62 ( X ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X
% 4.20/4.62 ), Y ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 4.20/4.62 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 4.20/4.62 ) ) }.
% 4.20/4.62 (21428) {G0,W20,D3,L4,V3,M4} { ! class_Groups_Oordered__comm__monoid__add
% 4.20/4.62 ( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 4.20/4.62 c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless( X
% 4.20/4.62 , c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless( X
% 4.20/4.62 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z
% 4.20/4.62 ) ) }.
% 4.20/4.62 (21429) {G0,W20,D3,L4,V3,M4} { ! class_Groups_Oordered__comm__monoid__add
% 4.20/4.62 ( X ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X
% 4.20/4.62 ), Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 4.20/4.62 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless( X,
% 4.20/4.62 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 4.20/4.62 ) }.
% 4.20/4.62 (21430) {G0,W28,D6,L4,V3,M4} { ! class_Rings_Olinordered__ring__strict( X
% 4.20/4.62 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 4.20/4.62 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ), ! Z =
% 4.20/4.62 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 4.20/4.62 }.
% 4.20/4.62 (21431) {G0,W24,D6,L3,V3,M3} { ! class_Rings_Olinordered__ring__strict( X
% 4.20/4.62 ), Z = c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless(
% 4.20/4.62 X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 4.20/4.62 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 4.20/4.62 (21432) {G0,W24,D6,L3,V3,M3} { ! class_Rings_Olinordered__ring__strict( X
% 4.20/4.62 ), Y = c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless(
% 4.20/4.62 X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 4.20/4.62 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 4.20/4.62 (21433) {G0,W20,D6,L2,V3,M2} { ! class_Rings_Olinordered__ring( X ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 4.20/4.62 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 4.20/4.62 c_Groups_Ozero__class_Ozero( X ) ) }.
% 4.20/4.62 (21434) {G0,W13,D3,L3,V2,M3} { ! class_RealVector_Oreal__normed__vector( X
% 4.20/4.62 ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 4.20/4.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 4.20/4.62 c_RealVector_Onorm__class_Onorm( X, Y ) ), ! Y =
% 4.20/4.62 c_Groups_Ozero__class_Ozero( X ) }.
% 4.20/4.62 (21435) {G0,W13,D3,L3,V2,M3} { ! class_RealVector_Oreal__normed__vector( X
% 4.20/4.62 ), Y = c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless(
% 4.20/4.62 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 4.20/4.62 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 4.20/4.62 (21436) {G0,W30,D6,L4,V5,M4} { ! class_RealVector_Oreal__normed__algebra(
% 4.20/4.62 X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 4.20/4.62 c_RealVector_Onorm__class_Onorm( X, Z ), Y ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 4.20/4.62 c_RealVector_Onorm__class_Onorm( X, U ), T ),
% 4.20/4.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 4.20/4.62 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), T ) ) }.
% 4.20/4.62 (21437) {G0,W23,D5,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 4.20/4.62 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ),
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 4.20/4.62 (21438) {G0,W23,D5,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 4.20/4.62 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ),
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 4.20/4.62 (21439) {G0,W23,D5,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 4.20/4.62 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ),
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 4.20/4.62 (21440) {G0,W23,D5,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 4.20/4.62 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ),
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 4.20/4.62 (21441) {G0,W26,D4,L4,V5,M4} { ! class_RealVector_Oreal__normed__vector( X
% 4.20/4.62 ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 4.20/4.62 c_RealVector_Onorm__class_Onorm( X, Z ), Y ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 4.20/4.62 c_RealVector_Onorm__class_Onorm( X, U ), T ),
% 4.20/4.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 4.20/4.62 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, Z, U
% 4.20/4.62 ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, T ) ) }.
% 4.20/4.62 (21442) {G0,W29,D6,L2,V5,M2} { ! class_Fields_Ofield__inverse__zero( X ),
% 4.20/4.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 4.20/4.62 c_Rings_Oinverse__class_Odivide( X, U, T ) ),
% 4.20/4.62 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 4.20/4.62 c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 4.20/4.62 (21443) {G0,W17,D4,L2,V3,M2} { !
% 4.20/4.62 class_Fields_Olinordered__field__inverse__zero( X ),
% 4.20/4.62 c_Groups_Oabs__class_Oabs( X, c_Rings_Oinverse__class_Odivide( X, Z, Y )
% 4.20/4.62 ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oabs__class_Oabs( X, Z
% 4.20/4.62 ), c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 4.20/4.62 (21444) {G0,W18,D3,L4,V3,M4} { !
% 4.20/4.62 class_Fields_Olinordered__field__inverse__zero( X ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 4.20/4.62 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ), alpha12( X, Y, Z ), alpha37
% 4.20/4.62 ( X, Y, Z ) }.
% 4.20/4.62 (21445) {G0,W14,D3,L3,V3,M3} { !
% 4.20/4.62 class_Fields_Olinordered__field__inverse__zero( X ), ! alpha12( X, Y, Z )
% 4.20/4.62 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 4.20/4.62 , c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 4.20/4.62 (21446) {G0,W14,D3,L3,V3,M3} { !
% 4.20/4.62 class_Fields_Olinordered__field__inverse__zero( X ), ! alpha37( X, Y, Z )
% 4.20/4.62 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 4.20/4.62 , c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 4.20/4.62 (21447) {G0,W9,D3,L2,V3,M2} { ! alpha37( X, Y, Z ),
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 4.20/4.62 ) }.
% 4.20/4.62 (21448) {G0,W9,D3,L2,V3,M2} { ! alpha37( X, Y, Z ),
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 4.20/4.62 ) }.
% 4.20/4.62 (21449) {G0,W14,D3,L3,V3,M3} { ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 4.20/4.62 c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless__eq(
% 4.20/4.62 X, Y, c_Groups_Ozero__class_Ozero( X ) ), alpha37( X, Y, Z ) }.
% 4.20/4.62 (21450) {G0,W9,D3,L2,V3,M2} { ! alpha12( X, Y, Z ),
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 4.20/4.62 ) }.
% 4.20/4.62 (21451) {G0,W9,D3,L2,V3,M2} { ! alpha12( X, Y, Z ),
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 4.20/4.62 ) }.
% 4.20/4.62 (21452) {G0,W14,D3,L3,V3,M3} { ! c_Orderings_Oord__class_Oless__eq( X,
% 4.20/4.62 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 4.20/4.62 ), alpha12( X, Y, Z ) }.
% 4.20/4.62 (21453) {G0,W18,D3,L4,V3,M4} { !
% 4.20/4.62 class_Fields_Olinordered__field__inverse__zero( X ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 4.20/4.62 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ), alpha13( X, Y, Z ), alpha38
% 4.20/4.62 ( X, Y, Z ) }.
% 4.20/4.62 (21454) {G0,W14,D3,L3,V3,M3} { !
% 4.20/4.62 class_Fields_Olinordered__field__inverse__zero( X ), ! alpha13( X, Y, Z )
% 4.20/4.62 , c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide(
% 4.20/4.62 X, Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 4.20/4.62 (21455) {G0,W14,D3,L3,V3,M3} { !
% 4.20/4.62 class_Fields_Olinordered__field__inverse__zero( X ), ! alpha38( X, Y, Z )
% 4.20/4.62 , c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide(
% 4.20/4.62 X, Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 4.20/4.62 (21456) {G0,W9,D3,L2,V3,M2} { ! alpha38( X, Y, Z ),
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 4.20/4.62 ) }.
% 4.20/4.62 (21457) {G0,W9,D3,L2,V3,M2} { ! alpha38( X, Y, Z ),
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 4.20/4.62 ) }.
% 4.20/4.62 (21458) {G0,W14,D3,L3,V3,M3} { ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 4.20/4.62 c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless__eq(
% 4.20/4.62 X, c_Groups_Ozero__class_Ozero( X ), Y ), alpha38( X, Y, Z ) }.
% 4.20/4.62 (21459) {G0,W9,D3,L2,V3,M2} { ! alpha13( X, Y, Z ),
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 4.20/4.62 ) }.
% 4.20/4.62 (21460) {G0,W9,D3,L2,V3,M2} { ! alpha13( X, Y, Z ),
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 4.20/4.62 ) }.
% 4.20/4.62 (21461) {G0,W14,D3,L3,V3,M3} { ! c_Orderings_Oord__class_Oless__eq( X,
% 4.20/4.62 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 4.20/4.62 ), alpha13( X, Y, Z ) }.
% 4.20/4.62 (21462) {G0,W21,D3,L4,V4,M4} { !
% 4.20/4.62 class_Fields_Olinordered__field__inverse__zero( X ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 4.20/4.62 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 4.20/4.62 ( X, Z, T ), c_Rings_Oinverse__class_Odivide( X, Y, T ) ) }.
% 4.20/4.62 (21463) {G0,W21,D3,L4,V4,M4} { !
% 4.20/4.62 class_Fields_Olinordered__field__inverse__zero( X ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Ozero__class_Ozero( X )
% 4.20/4.62 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 4.20/4.62 ( X, Y, T ), c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 4.20/4.62 (21464) {G0,W13,D3,L3,V4,M3} { ! class_Fields_Ofield__inverse__zero( X ),
% 4.20/4.62 ! T = c_Rings_Oinverse__class_Odivide( X, Z, Y ), alpha39( X, Y, Z, T )
% 4.20/4.62 }.
% 4.20/4.62 (21465) {G0,W12,D3,L3,V4,M3} { ! class_Fields_Ofield__inverse__zero( X ),
% 4.20/4.62 ! T = c_Rings_Oinverse__class_Odivide( X, Z, Y ), alpha14( X, Y, T ) }.
% 4.20/4.62 (21466) {G0,W17,D3,L4,V4,M4} { ! class_Fields_Ofield__inverse__zero( X ),
% 4.20/4.62 ! alpha39( X, Y, Z, T ), ! alpha14( X, Y, T ), T =
% 4.20/4.62 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 4.20/4.62 (21467) {G0,W17,D5,L3,V4,M3} { ! alpha39( X, Y, Z, T ), Y =
% 4.20/4.62 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z }.
% 4.20/4.62 (21468) {G0,W9,D3,L2,V4,M2} { ! Y = c_Groups_Ozero__class_Ozero( X ),
% 4.20/4.62 alpha39( X, Y, Z, T ) }.
% 4.20/4.62 (21469) {G0,W13,D5,L2,V4,M2} { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 4.20/4.62 ( X ), T ), Y ) = Z, alpha39( X, Y, Z, T ) }.
% 4.20/4.62 (21470) {G0,W12,D3,L3,V3,M3} { ! alpha14( X, Y, Z ), ! Y =
% 4.20/4.62 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X )
% 4.20/4.62 }.
% 4.20/4.62 (21471) {G0,W8,D3,L2,V3,M2} { Y = c_Groups_Ozero__class_Ozero( X ),
% 4.20/4.62 alpha14( X, Y, Z ) }.
% 4.20/4.62 (21472) {G0,W8,D3,L2,V3,M2} { ! Z = c_Groups_Ozero__class_Ozero( X ),
% 4.20/4.62 alpha14( X, Y, Z ) }.
% 4.20/4.62 (21473) {G0,W13,D3,L3,V4,M3} { ! class_Fields_Ofield__inverse__zero( X ),
% 4.20/4.62 ! c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y, alpha40( X, Y, Z, T )
% 4.20/4.62 }.
% 4.20/4.62 (21474) {G0,W12,D3,L3,V4,M3} { ! class_Fields_Ofield__inverse__zero( X ),
% 4.20/4.62 ! c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y, alpha15( X, Y, Z ) }.
% 4.20/4.62 (21475) {G0,W17,D3,L4,V4,M4} { ! class_Fields_Ofield__inverse__zero( X ),
% 4.20/4.62 ! alpha40( X, Y, Z, T ), ! alpha15( X, Y, Z ),
% 4.20/4.62 c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y }.
% 4.20/4.62 (21476) {G0,W17,D5,L3,V4,M3} { ! alpha40( X, Y, Z, T ), Z =
% 4.20/4.62 c_Groups_Ozero__class_Ozero( X ), T = hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 4.20/4.62 (21477) {G0,W9,D3,L2,V4,M2} { ! Z = c_Groups_Ozero__class_Ozero( X ),
% 4.20/4.62 alpha40( X, Y, Z, T ) }.
% 4.20/4.62 (21478) {G0,W13,D5,L2,V4,M2} { ! T = hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), alpha40( X, Y, Z, T ) }.
% 4.20/4.62 (21479) {G0,W12,D3,L3,V3,M3} { ! alpha15( X, Y, Z ), ! Z =
% 4.20/4.62 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 4.20/4.62 }.
% 4.20/4.62 (21480) {G0,W8,D3,L2,V3,M2} { Z = c_Groups_Ozero__class_Ozero( X ),
% 4.20/4.62 alpha15( X, Y, Z ) }.
% 4.20/4.62 (21481) {G0,W8,D3,L2,V3,M2} { ! Y = c_Groups_Ozero__class_Ozero( X ),
% 4.20/4.62 alpha15( X, Y, Z ) }.
% 4.20/4.62 (21482) {G0,W27,D7,L3,V1,M3} { v_cs____ = c_Groups_Ozero__class_Ozero(
% 4.20/4.62 tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, skol3,
% 4.20/4.62 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ),
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, v_da____,
% 4.20/4.62 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 4.20/4.62 c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_OpCons(
% 4.20/4.62 tc_Complex_Ocomplex, v_aa____, c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 4.20/4.62 v_c____, v_cs____ ) ) ), X ) ) ) }.
% 4.20/4.62 (21483) {G0,W13,D5,L2,V1,M2} { ! class_Groups_Ozero( X ),
% 4.20/4.62 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ),
% 4.20/4.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 4.20/4.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 4.20/4.62 (21484) {G0,W14,D4,L3,V3,M3} { ! class_Groups_Ozero( X ), !
% 4.20/4.62 c_Polynomial_OpCons( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 4.20/4.62 tc_Polynomial_Opoly( X ) ), Z = c_Groups_Ozero__class_Ozero( X ) }.
% 4.20/4.62 (21485) {G0,W15,D4,L3,V3,M3} { ! class_Groups_Ozero( X ), !
% 4.20/4.62 c_Polynomial_OpCons( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 4.20/4.62 tc_Polynomial_Opoly( X ) ), Y = c_Groups_Ozero__class_Ozero(
% 4.20/4.62 tc_Polynomial_Opoly( X ) ) }.
% 4.20/4.62 (21486) {G0,W19,D4,L4,V3,M4} { ! class_Groups_Ozero( X ), ! Z =
% 4.20/4.62 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 4.20/4.62 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X, Z, Y ) =
% 4.20/4.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 4.20/4.62 (21487) {G0,W14,D5,L2,V1,M2} { c_Orderings_Oord__class_Oless(
% 4.20/4.62 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP(
% 4.20/4.62 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ), X =
% 4.20/4.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 4.20/4.62 (21488) {G0,W14,D5,L2,V1,M2} { ! X = c_Groups_Ozero__class_Ozero(
% 4.20/4.62 tc_RealDef_Oreal ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 4.20/4.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) }.
% 4.20/4.62 (21489) {G0,W15,D3,L3,V2,M3} { ! class_Rings_Olinordered__idom( X ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 4.20/4.62 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Y
% 4.20/4.62 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 4.20/4.62 (21490) {G0,W15,D3,L3,V2,M3} { ! class_Rings_Olinordered__idom( X ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 4.20/4.62 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 4.20/4.62 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 4.20/4.62 (21491) {G0,W9,D3,L2,V3,M2} { ! class_RealVector_Oreal__normed__field( X )
% 4.20/4.62 , c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 4.20/4.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol4( Z, T ) ) }.
% 4.20/4.62 (21492) {G0,W20,D5,L2,V3,M2} { ! class_RealVector_Oreal__normed__field( X
% 4.20/4.62 ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 4.20/4.62 c_RealVector_Onorm__class_Onorm( X, c_Rings_Oinverse__class_Odivide( X, Z
% 4.20/4.62 , Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 4.20/4.62 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol4( X, Y ) ) ) }.
% 4.20/4.62 (21493) {G0,W9,D3,L2,V3,M2} { ! class_RealVector_Oreal__normed__algebra( X
% 4.20/4.62 ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 4.20/4.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol5( Z, T ) ) }.
% 4.20/4.62 (21494) {G0,W22,D6,L2,V3,M2} { ! class_RealVector_Oreal__normed__algebra(
% 4.20/4.62 X ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 4.20/4.62 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 4.20/4.62 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol5( X, Y ) ) ) }.
% 4.20/4.62 (21495) {G0,W9,D3,L2,V3,M2} { ! class_RealVector_Oreal__normed__algebra( X
% 4.20/4.62 ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 4.20/4.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol6( Z, T ) ) }.
% 4.20/4.62 (21496) {G0,W22,D6,L2,V3,M2} { ! class_RealVector_Oreal__normed__algebra(
% 4.20/4.62 X ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 4.20/4.62 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 4.20/4.62 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol6( X, Y ) ) ) }.
% 4.20/4.62 (21497) {G0,W28,D8,L2,V4,M2} { ! class_Rings_Ocomm__semiring__0( X ), hAPP
% 4.20/4.62 ( c_Polynomial_Opoly( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 4.20/4.62 tc_Polynomial_Opoly( X ) ), T ), Z ) ), Y ) = hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), hAPP( c_Polynomial_Opoly( X, T ), Y )
% 4.20/4.62 ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 4.20/4.62 (21498) {G0,W24,D6,L2,V4,M2} { ! class_Rings_Ocomm__semiring__0( X ), hAPP
% 4.20/4.62 ( c_Polynomial_Opoly( X, c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly
% 4.20/4.62 ( X ), T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP(
% 4.20/4.62 c_Polynomial_Opoly( X, T ), Y ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) )
% 4.20/4.62 }.
% 4.20/4.62 (21499) {G0,W14,D3,L4,V3,M4} { ! class_Int_Oring__char__0( X ), !
% 4.20/4.62 class_Rings_Oidom( X ), ! c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly
% 4.20/4.62 ( X, Y ), Z = Y }.
% 4.20/4.62 (21500) {G0,W14,D3,L4,V3,M4} { ! class_Int_Oring__char__0( X ), !
% 4.20/4.62 class_Rings_Oidom( X ), ! Z = Y, c_Polynomial_Opoly( X, Z ) =
% 4.20/4.62 c_Polynomial_Opoly( X, Y ) }.
% 4.20/4.62 (21501) {G0,W18,D5,L4,V2,M4} { ! class_Int_Oring__char__0( X ), !
% 4.20/4.62 class_Rings_Oidom( X ), ! c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly
% 4.20/4.62 ( X, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y =
% 4.20/4.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 4.20/4.62 (21502) {G0,W18,D5,L4,V2,M4} { ! class_Int_Oring__char__0( X ), !
% 4.20/4.62 class_Rings_Oidom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 4.20/4.62 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly( X, Y ) =
% 4.20/4.62 c_Polynomial_Opoly( X, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 4.20/4.62 X ) ) ) }.
% 4.20/4.62 (21503) {G0,W14,D3,L3,V4,M3} { ! class_Orderings_Oord( X ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless( tc_fun( T, X ), Z, Y ),
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }.
% 4.20/4.62 (21504) {G0,W14,D3,L3,V4,M3} { ! class_Orderings_Oord( X ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless( tc_fun( T, X ), Z, Y ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z ) }.
% 4.20/4.62 (21505) {G0,W20,D3,L4,V4,M4} { ! class_Orderings_Oord( X ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ),
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z ),
% 4.20/4.62 c_Orderings_Oord__class_Oless( tc_fun( T, X ), Z, Y ) }.
% 4.20/4.62 (21506) {G0,W12,D6,L2,V2,M2} { ! class_Rings_Ocomm__semiring__0( X ), hAPP
% 4.20/4.62 ( c_Polynomial_Opoly( X, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly
% 4.20/4.62 ( X ) ) ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 4.20/4.62 (21507) {G0,W24,D6,L2,V4,M2} { ! class_Rings_Ocomm__semiring__0( X ), hAPP
% 4.20/4.62 ( c_Polynomial_Opoly( X, c_Polynomial_OpCons( X, T, Z ) ), Y ) =
% 4.20/4.62 c_Groups_Oplus__class_Oplus( X, T, hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( c_Polynomial_Opoly( X, Z )
% 4.20/4.62 , Y ) ) ) }.
% 4.20/4.62 (21508) {G0,W11,D5,L2,V2,M2} { ! class_Groups_Ocomm__monoid__add( X ),
% 4.20/4.62 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Y,
% 4.20/4.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) = Y }.
% 4.20/4.62 (21509) {G0,W15,D6,L2,V2,M2} { ! class_Rings_Ocomm__semiring__0( X ), hAPP
% 4.20/4.62 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 4.20/4.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 4.20/4.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 4.20/4.62 (21510) {G0,W11,D5,L2,V2,M2} { ! class_Groups_Ocomm__monoid__add( X ),
% 4.20/4.62 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ),
% 4.20/4.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) = Y }.
% 4.20/4.62 (21511) {G0,W15,D6,L2,V2,M2} { ! class_Rings_Ocomm__semiring__0( X ), hAPP
% 4.20/4.62 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 4.20/4.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 4.20/4.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 4.20/4.62 (21512) {G0,W14,D3,L3,V5,M3} { ! class_Groups_Ozero( X ), !
% 4.20/4.62 c_Polynomial_OpCons( X, U, T ) = c_Polynomial_OpCons( X, Z, Y ), U = Z
% 4.20/4.62 }.
% 4.20/4.62 (21513) {G0,W14,D3,L3,V5,M3} { ! class_Groups_Ozero( X ), !
% 4.20/4.62 c_Polynomial_OpCons( X, U, T ) = c_Polynomial_OpCons( X, Z, Y ), T = Y
% 4.20/4.62 }.
% 4.20/4.62 (21514) {G0,W17,D3,L4,V5,M4} { ! class_Groups_Ozero( X ), ! U = Z, ! T = Y
% 4.20/4.62 , c_Polynomial_OpCons( X, U, T ) = c_Polynomial_OpCons( X, Z, Y ) }.
% 4.20/4.62 (21515) {G0,W13,D3,L3,V2,M3} { ! class_Groups_Olinordered__ab__group__add
% 4.20/4.62 ( X ), ! c_Groups_Oplus__class_Oplus( X, Y, Y ) =
% 4.20/4.62 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 4.20/4.62 }.
% 4.20/4.62 (21516) {G0,W13,D3,L3,V2,M3} { ! class_Groups_Olinordered__ab__group__add
% 4.20/4.62 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 4.20/4.62 c_Groups_Oplus__class_Oplus( X, Y, Y ) = c_Groups_Ozero__class_Ozero( X )
% 4.20/4.62 }.
% 4.20/4.62 (21517) {G0,W25,D5,L2,V5,M2} { ! class_Groups_Ocomm__monoid__add( X ),
% 4.20/4.62 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ),
% 4.20/4.62 c_Polynomial_OpCons( X, U, T ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 4.20/4.62 c_Polynomial_OpCons( X, c_Groups_Oplus__class_Oplus( X, U, Z ),
% 4.20/4.62 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 4.20/4.62 (21518) {G0,W19,D6,L1,V2,M1} { c_Rings_Oinverse__class_Odivide(
% 4.20/4.62 tc_RealDef_Oreal, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 4.20/4.62 tc_RealDef_Oreal ), Y ), X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 4.20/4.62 tc_RealDef_Oreal ), Y ), Y ) ) = c_Rings_Oinverse__class_Odivide(
% 4.20/4.62 tc_RealDef_Oreal, X, Y ) }.
% 4.20/4.62 (21519) {G0,W26,D6,L3,V3,M3} { v_cs____ = c_Groups_Ozero__class_Ozero(
% 4.20/4.62 tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, skol7( X, Y ),
% 4.20/4.62 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Z ) ),
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y,
% 4.20/4.62 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 4.20/4.62 c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_OpCons(
% 4.20/4.62 tc_Complex_Ocomplex, X, v_cs____ ) ), Z ) ) ) }.
% 4.20/4.62 (21520) {G0,W8,D3,L2,V2,M2} { ! class_RealVector_Oreal__normed__algebra( X
% 4.20/4.62 ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 4.20/4.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol8( Y ) ) }.
% 4.20/4.62 (21521) {G0,W28,D7,L2,V3,M2} { ! class_RealVector_Oreal__normed__algebra(
% 4.20/4.62 X ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 4.20/4.62 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 4.20/4.62 c_RealVector_Onorm__class_Onorm( X, Y ) ),
% 4.20/4.62 c_RealVector_Onorm__class_Onorm( X, Z ) ) ), skol8( X ) ) ) }.
% 4.20/4.62 (21522) {G0,W15,D3,L4,V3,M4} { ! class_Rings_Olinordered__idom( X ), !
% 4.20/4.62 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ),
% 4.20/4.62 c_Polynomial_Opos__poly( X, Y ), alpha16( X, Y, Z ) }.
% 4.20/4.62 (21523) {G0,W11,D3,L3,V3,M3} { ! class_Rings_Olinordered__idom( X ), !
% 4.20/4.62 c_Polynomial_Opos__poly( X, Y ), c_Polynomial_Opos__poly( X,
% 4.20/4.62 c_Polynomial_OpCons( X, Z, Y ) ) }.
% 4.20/4.62 (21524) {G0,W12,D3,L3,V3,M3} { ! class_Rings_Olinordered__idom( X ), !
% 4.20/4.62 alpha16( X, Y, Z ), c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z
% 4.20/4.62 , Y ) ) }.
% 4.20/4.62 (21525) {G0,W9,D4,L2,V3,M2} { ! alpha16( X, Y, Z ), Y =
% 4.20/4.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 4.20/4.62 (21526) {G0,W9,D3,L2,V3,M2} { ! alpha16( X, Y, Z ),
% 4.20/4.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 4.20/4.62 }.
% 4.20/4.62 (21527) {G0,W14,D4,L3,V3,M3} { ! Y = c_Groups_Ozero__class_Ozero(
% 4.20/4.62 tc_Polynomial_Opoly( X ) ), ! c_Orderings_Oord__class_Oless( X,
% 4.20/4.62 c_Groups_Ozero__class_Ozero( X ), Z ), alpha16( X, Y, Z ) }.
% 4.20/4.62 (21528) {G0,W7,D3,L1,V2,M1} { c_Orderings_Oord__class_Oless(
% 4.20/4.62 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol9
% 4.20/4.62 ( Z, T ) ) }.
% 4.20/4.62 (21529) {G0,W18,D5,L2,V3,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 4.20/4.62 tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Z
% 4.20/4.62 ), Y ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 4.20/4.62 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 4.20/4.62 c_Polynomial_Opoly( tc_Complex_Ocomplex, X ), Z ) ), skol9( X, Y ) ) }.
% 4.20/4.62 (21530) {G0,W22,D4,L4,V3,M4} { ! class_Rings_Oidom( X ), ! hAPP(
% 4.20/4.62 c_Polynomial_Opoly( X, Z ), Y ) = c_Groups_Ozero__class_Ozero( X ), Z =
% 4.20/4.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), !
% 4.20/4.62 c_Polynomial_Oorder( X, Y, Z ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 4.20/4.62 ) }.
% 4.20/4.62 (21531) {G0,W15,D4,L3,V3,M3} { ! class_Rings_Oidom( X ), ! Z =
% 4.20/4.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), hAPP(
% 4.20/4.62 c_Polynomial_Opoly( X, Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 4.20/4.62 (21532) {G0,W17,D4,L3,V3,M3} { ! class_Rings_Oidom( X ),
% 4.20/4.62 c_Polynomial_Oorder( X, Y, Z ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 4.20/4.62 ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) = c_Groups_Ozero__class_Ozero(
% 4.20/4.62 X ) }.
% 4.20/4.62 (21533) {G0,W36,D6,L3,V6,M3} { ! class_Groups_Ozero( X ), ! hAPP( hAPP(
% 4.20/4.62 hAPP( Z, c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero
% 4.20/4.62 ( tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( W, X, Y
% 4.20/4.62 , Z, c_Polynomial_OpCons( X, U, T ) ) = hAPP( hAPP( hAPP( Z, U ), T ),
% 4.20/4.62 c_Polynomial_Opoly__rec( W, X, Y, Z, T ) ) }.
% 4.20/4.62 (21534) {G0,W31,D7,L2,V4,M2} { ! class_Rings_Ocomm__semiring__0( X ), hAPP
% 4.20/4.62 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 4.20/4.62 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 4.20/4.62 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ), hAPP
% 4.20/4.62 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y
% 4.20/4.62 ) ) }.
% 4.20/4.62 (21535) {G0,W15,D4,L4,V3,M4} { ! class_Rings_Olinordered__idom( X ), !
% 4.20/4.62 c_Polynomial_Opos__poly( X, Y ), ! c_Polynomial_Opos__poly( X, Z ),
% 4.20/4.62 c_Polynomial_Opos__poly( X, c_Groups_Oplus__class_Oplus(
% 4.20/4.62 tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 4.20/4.62 (21536) {G0,W17,D6,L4,V3,M4} { ! class_Rings_Olinordered__idom( X ), !
% 4.20/4.62 c_Polynomial_Opos__poly( X, Y ), ! c_Polynomial_Opos__poly( X, Z ),
% 4.20/4.62 c_Polynomial_Opos__poly( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 4.20/4.62 tc_Polynomial_Opoly( X ) ), Y ), Z ) ) }.
% 4.20/4.62 (21537) {G0,W7,D4,L2,V1,M2} { ! class_Rings_Olinordered__idom( X ), !
% 4.20/4.62 c_Polynomial_Opos__poly( X, c_Groups_Ozero__class_Ozero(
% 4.20/4.62 tc_Polynomial_Opoly( X ) ) ) }.
% 4.20/4.62 (21538) {G0,W24,D6,L3,V4,M3} { ! class_Groups_Ozero( X ), ! hAPP( hAPP(
% 4.20/4.62 hAPP( Z, c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero
% 4.20/4.62 ( tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( T, X, Y
% 4.20/4.62 , Z, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) = Y }.
% 4.20/4.62 (21539) {G0,W32,D7,L2,V6,M2} { ! class_Groups_Ozero( X ),
% 4.20/4.62 c_Polynomial_Opoly__rec( W, X, U, T, c_Polynomial_OpCons( X, Z, Y ) ) =
% 4.20/4.62 hAPP( hAPP( hAPP( T, Z ), Y ), c_If( W, c_fequal( Y,
% 4.20/4.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), U,
% 4.20/4.62 c_Polynomial_Opoly__rec( W, X, U, T, Y ) ) ) }.
% 4.20/4.62 (21540) {G0,W29,D7,L2,V4,M2} { ! class_Rings_Ocomm__semiring__0( X ),
% 4.20/4.62 c_Polynomial_Opcompose( X, c_Polynomial_OpCons( X, T, Z ), Y ) =
% 4.20/4.62 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ),
% 4.20/4.62 c_Polynomial_OpCons( X, T, c_Groups_Ozero__class_Ozero(
% 4.20/4.62 tc_Polynomial_Opoly( X ) ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 4.20/4.62 tc_Polynomial_Opoly( X ) ), Y ), c_Polynomial_Opcompose( X, Z, Y ) ) )
% 4.20/4.62 }.
% 4.20/4.62 (21541) {G0,W13,D4,L3,V2,M3} { ! class_Groups_Ozero( X ), !
% 4.20/4.62 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 4.20/4.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 4.20/4.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 4.20/4.62 (21542) {G0,W13,D4,L3,V2,M3} { ! class_Groups_Ozero( X ), ! Y =
% 4.20/4.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 4.20/4.62 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 4.20/4.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 4.20/4.62 (21543) {G0,W5,D3,L1,V1,M1} { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 4.20/4.62 , X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 4.20/4.62 (21544) {G0,W5,D3,L1,V1,M1} { c_Orderings_Oord__class_Oless__eq(
% 4.20/4.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 4.20/4.62 (21545) {G0,W9,D3,L2,V3,M2} { ! class_RealVector_Oreal__normed__field( X )
% 4.20/4.62 , c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 4.20/4.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol10( Z, T ) ) }.
% 4.20/4.62 (21546) {G0,W20,D5,L2,V3,M2} { ! class_RealVector_Oreal__normed__field( X
% 4.20/4.62 ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 4.20/4.62 c_RealVector_Onorm__class_Onorm( X, c_Rings_Oinverse__class_Odivide( X, Z
% 4.20/4.62 , Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 4.20/4.62 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol10( X, Y ) ) ) }.
% 4.20/4.62 (21547) {G0,W8,D2,L2,V2,M2} { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 4.20/4.62 , Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 4.20/4.62 (21548) {G0,W7,D2,L2,V2,M2} { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 4.20/4.62 , Y, X ), ! Y = X }.
% 4.20/4.62 (21549) {G0,W11,D2,L3,V2,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 4.20/4.62 tc_Nat_Onat, Y, X ), Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y
% 4.20/4.62 , X ) }.
% 4.20/4.62 (21550) {G0,W11,D2,L3,V2,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 4.20/4.62 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 4.20/4.62 Y = X }.
% 4.20/4.62 (21551) {G0,W8,D2,L2,V2,M2} { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 4.20/4.62 , Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 4.20/4.62 (21552) {G0,W7,D2,L2,V2,M2} { ! Y = X, c_Orderings_Oord__class_Oless__eq(
% 4.20/4.62 tc_Nat_Onat, Y, X ) }.
% 4.20/4.62 (21553) {G0,W8,D2,L2,V2,M2} { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 4.20/4.62 , Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 4.20/4.62 (21554) {G0,W11,D2,L3,V2,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 4.20/4.62 tc_Nat_Onat, Y, X ), Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y
% 4.20/4.62 , X ) }.
% 4.20/4.62 (21555) {G0,W8,D2,L2,V2,M2} { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 4.20/4.62 , Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 4.20/4.62 (21556) {G0,W7,D2,L2,V2,M2} { ! Y = X, c_Orderings_Oord__class_Oless__eq(
% 4.20/4.62 tc_Nat_Onat, Y, X ) }.
% 4.20/4.62 (21557) {G0,W4,D2,L1,V1,M1} { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 4.20/4.62 , X, X ) }.
% 4.20/4.62 (21558) {G0,W11,D2,L3,V2,M3} { Y = X, c_Orderings_Oord__class_Oless(
% 4.20/4.62 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y )
% 4.20/4.62 }.
% 4.20/4.62 (21559) {G0,W7,D2,L2,V2,M2} { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 4.20/4.62 , Y, X ), ! Y = X }.
% 4.20/4.62 (21560) {G0,W7,D2,L2,V2,M2} { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 4.20/4.62 , X, Y ), ! Y = X }.
% 4.20/4.62 (21561) {G0,W11,D2,L3,V2,M3} { Y = X, c_Orderings_Oord__class_Oless(
% 4.20/4.62 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y )
% 4.20/4.62 }.
% 4.20/4.62 (21562) {G0,W4,D2,L1,V1,M1} { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 4.20/4.62 , X, X ) }.
% 4.20/4.62 (21563) {G0,W7,D2,L2,V2,M2} { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 4.20/4.62 , Y, X ), ! X = Y }.
% 4.20/4.62 (21564) {G0,W7,D2,L2,V2,M2} { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 4.20/4.62 , Y, X ), ! Y = X }.
% 4.20/4.62 (21565) {G0,W14,D4,L3,V3,M3} { alpha82( X, Y, Z ),
% 4.20/4.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ), hBOOL( hAPP( hAPP( X
% 4.20/4.62 , Y ), Z ) ) }.
% 4.20/4.62 (21566) {G0,W16,D4,L3,V3,M3} { alpha82( X, Y, Z ), ! hBOOL( hAPP( hAPP( X
% 4.20/4.62 , Y ), Z ) ), hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 4.20/4.62 (21567) {G0,W11,D2,L3,V3,M3} { ! alpha82( X, Y, Z ), alpha85( X, Y, Z ), Z
% 4.20/4.62 = Y }.
% 4.20/4.62 (21568) {G0,W14,D4,L3,V3,M3} { ! alpha82( X, Y, Z ), alpha85( X, Y, Z ), !
% 4.20/4.62 hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 4.20/4.62 (21569) {G0,W8,D2,L2,V3,M2} { ! alpha85( X, Y, Z ), alpha82( X, Y, Z ) }.
% 4.20/4.62 (21570) {G0,W13,D4,L3,V3,M3} { ! Z = Y, hBOOL( hAPP( hAPP( X, Y ), Z ) ),
% 4.20/4.62 alpha82( X, Y, Z ) }.
% 4.20/4.62 (21571) {G0,W8,D2,L2,V3,M2} { ! alpha85( X, Y, Z ),
% 4.20/4.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 4.20/4.62 (21572) {G0,W10,D4,L2,V3,M2} { ! alpha85( X, Y, Z ), ! hBOOL( hAPP( hAPP(
% 4.20/4.62 X, Y ), Z ) ) }.
% 4.20/4.62 (21573) {G0,W14,D4,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 4.20/4.62 tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha85( X, Y, Z )
% 4.20/4.62 }.
% 4.20/4.62 (21574) {G0,W11,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless(
% 4.20/4.62 tc_Nat_Onat, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ), X ),
% 4.20/4.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 4.20/4.62 (21575) {G0,W17,D3,L3,V4,M3} { ! c_Orderings_Oord__class_Oless(
% 4.20/4.62 tc_Nat_Onat, Y, X ), ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, X ) =
% 4.20/4.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 4.20/4.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 4.20/4.62 (21576) {G0,W18,D3,L3,V4,M3} { ! c_Orderings_Oord__class_Oless(
% 4.20/4.62 tc_Nat_Onat, Y, X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z )
% 4.20/4.62 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 4.20/4.62 ( tc_Nat_Onat, Y, T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) )
% 4.20/4.62 }.
% 4.20/4.62 (21577) {G0,W14,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless(
% 4.20/4.62 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 4.20/4.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 4.20/4.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 4.20/4.62 (21578) {G0,W11,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless(
% 4.20/4.62 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 4.20/4.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 4.20/4.62 (21579) {G0,W11,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless(
% 4.20/4.62 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 4.20/4.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 4.20/4.62 (21580) {G0,W14,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless(
% 4.20/4.62 tc_Nat_Onat, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 4.20/4.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ),
% 4.20/4.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 4.20/4.62 (21581) {G0,W14,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless(
% 4.20/4.62 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 4.20/4.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 4.20/4.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 4.20/4.62 (21582) {G0,W7,D3,L1,V2,M1} { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 4.20/4.62 , c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ), X ) }.
% 4.20/4.62 (21583) {G0,W7,D3,L1,V2,M1} { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 4.20/4.62 , c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ), Y ) }.
% 4.20/4.62 (21584) {G0,W9,D5,L1,V1,M1} { c_Orderings_Oord__class_Oless__eq(
% 4.20/4.62 tc_Nat_Onat, X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 4.20/4.62 , X ), X ) ) }.
% 4.20/4.62 (21585) {G0,W7,D3,L1,V2,M1} { c_Orderings_Oord__class_Oless__eq(
% 4.20/4.62 tc_Nat_Onat, Y, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 4.20/4.62 (21586) {G0,W7,D3,L1,V2,M1} { c_Orderings_Oord__class_Oless__eq(
% 4.20/4.62 tc_Nat_Onat, Y, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 4.20/4.62 (21587) {G0,W14,D6,L1,V1,M1} { c_Orderings_Oord__class_Oless__eq(
% 4.20/4.62 tc_Nat_Onat, X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 4.20/4.62 , X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X )
% 4.20/4.62 ) ) }.
% 4.20/4.62 (21588) {G0,W12,D4,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 4.20/4.62 tc_Nat_Onat, Y, X ), X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 4.20/4.62 skol11( X, Y ) ) }.
% 4.20/4.62 (21589) {G0,W10,D3,L2,V3,M2} { ! X = c_Groups_Oplus__class_Oplus(
% 4.20/4.62 tc_Nat_Onat, Y, Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 4.20/4.62 ) }.
% 4.20/4.62 (21590) {G0,W12,D4,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 4.20/4.62 tc_Nat_Onat, Y, X ), X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 4.20/4.62 skol12( X, Y ) ) }.
% 4.20/4.62 (21591) {G0,W10,D3,L2,V3,M2} { ! X = c_Groups_Oplus__class_Oplus(
% 4.20/4.62 tc_Nat_Onat, Y, Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 4.20/4.62 ) }.
% 4.20/4.62 (21592) {G0,W14,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 4.20/4.62 tc_Nat_Onat, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 4.20/4.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ),
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 4.20/4.62 (21593) {G0,W14,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 4.20/4.62 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 4.20/4.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 4.20/4.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 4.20/4.62 (21594) {G0,W11,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 4.20/4.62 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 4.20/4.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 4.20/4.62 (21595) {G0,W11,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 4.20/4.62 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 4.20/4.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 4.20/4.62 (21596) {G0,W14,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 4.20/4.62 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 4.20/4.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 4.20/4.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 4.20/4.62 (21597) {G0,W18,D5,L2,V3,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 4.20/4.62 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 4.20/4.62 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP(
% 4.20/4.62 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 4.20/4.62 (21598) {G0,W18,D5,L2,V3,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 4.20/4.62 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 4.20/4.62 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 4.20/4.62 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 4.20/4.62 (21599) {G0,W18,D3,L3,V4,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 4.20/4.62 tc_Nat_Onat, Y, X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T
% 4.20/4.62 , Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 4.20/4.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, T ),
% 4.20/4.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 4.20/4.62 (21600) {G0,W22,D5,L3,V4,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 4.20/4.62 tc_Nat_Onat, Y, X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T
% 4.20/4.62 , Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), T ), hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 4.20/4.62 (21601) {G0,W11,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 4.20/4.62 tc_Nat_Onat, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 4.20/4.62 (21602) {G0,W11,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 4.20/4.62 tc_Nat_Onat, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ), X ),
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 4.20/4.62 (21603) {G0,W11,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 4.20/4.62 tc_Nat_Onat, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ) }.
% 4.20/4.62 (21604) {G0,W11,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 4.20/4.62 tc_Nat_Onat, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 4.20/4.62 (21605) {G0,W11,D2,L3,V2,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 4.20/4.62 tc_Nat_Onat, Y, X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X
% 4.20/4.62 , Y ), Y = X }.
% 4.20/4.62 (21606) {G0,W12,D2,L3,V3,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 4.20/4.62 tc_Nat_Onat, Y, X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X
% 4.20/4.62 , Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ) }.
% 4.20/4.62 (21607) {G0,W7,D2,L2,V2,M2} { ! Y = X, c_Orderings_Oord__class_Oless__eq(
% 4.20/4.62 tc_Nat_Onat, Y, X ) }.
% 4.20/4.62 (21608) {G0,W8,D2,L2,V2,M2} { c_Orderings_Oord__class_Oless__eq(
% 4.20/4.62 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y
% 4.20/4.62 ) }.
% 4.20/4.62 (21609) {G0,W4,D2,L1,V1,M1} { c_Orderings_Oord__class_Oless__eq(
% 4.20/4.62 tc_Nat_Onat, X, X ) }.
% 4.20/4.62 (21610) {G0,W12,D5,L2,V2,M2} { ! class_Rings_Ocomm__semiring__0( X ),
% 4.20/4.62 c_Polynomial_Opcompose( X, c_Groups_Ozero__class_Ozero(
% 4.20/4.62 tc_Polynomial_Opoly( X ) ), Y ) = c_Groups_Ozero__class_Ozero(
% 4.20/4.62 tc_Polynomial_Opoly( X ) ) }.
% 4.20/4.62 (21611) {G0,W20,D5,L2,V4,M2} { ! class_Rings_Ocomm__semiring__0( X ), hAPP
% 4.20/4.62 ( c_Polynomial_Opoly( X, c_Polynomial_Opcompose( X, T, Z ) ), Y ) = hAPP
% 4.20/4.62 ( c_Polynomial_Opoly( X, T ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 4.20/4.62 (21612) {G0,W10,D5,L1,V1,M1} { hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 4.20/4.62 tc_Nat_Onat ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) =
% 4.20/4.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 4.20/4.62 (21613) {G0,W5,D3,L1,V1,M1} { c_Orderings_Oord__class_Oless__eq(
% 4.20/4.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 4.20/4.62 (21614) {G0,W7,D4,L1,V1,M1} { c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 4.20/4.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) = X }.
% 4.20/4.62 (21615) {G0,W10,D5,L1,V1,M1} { hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 4.20/4.62 tc_Nat_Onat ), X ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 4.20/4.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 4.20/4.62 (21616) {G0,W7,D4,L1,V1,M1} { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X
% 4.20/4.62 , c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 4.20/4.62 (21617) {G0,W9,D3,L2,V1,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 4.20/4.62 tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 4.20/4.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 4.20/4.62 (21618) {G0,W9,D3,L2,V1,M2} { ! X = c_Groups_Ozero__class_Ozero(
% 4.20/4.62 tc_Nat_Onat ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 4.20/4.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 4.20/4.62 (21619) {G0,W11,D3,L2,V2,M2} { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat
% 4.20/4.62 , Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 4.20/4.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 4.20/4.62 (21620) {G0,W11,D3,L2,V2,M2} { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat
% 4.20/4.62 , Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 4.20/4.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 4.20/4.62 (21621) {G0,W15,D3,L3,V2,M3} { ! Y = c_Groups_Ozero__class_Ozero(
% 4.20/4.62 tc_Nat_Onat ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 4.20/4.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 4.20/4.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 4.20/4.62 (21622) {G0,W17,D5,L3,V2,M3} { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 4.20/4.62 ( tc_Nat_Onat ), Y ), X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y
% 4.20/4.62 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 4.20/4.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 4.20/4.62 (21623) {G0,W13,D5,L2,V2,M2} { ! Y = c_Groups_Ozero__class_Ozero(
% 4.20/4.62 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 4.20/4.62 Y ), X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 4.20/4.62 (21624) {G0,W13,D5,L2,V2,M2} { ! X = c_Groups_Ozero__class_Ozero(
% 4.20/4.62 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 4.20/4.62 Y ), X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 4.20/4.62 (21625) {G0,W20,D5,L3,V3,M3} { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 4.20/4.62 ( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 4.20/4.62 tc_Nat_Onat ), Z ), X ), Y = X, Z = c_Groups_Ozero__class_Ozero(
% 4.20/4.62 tc_Nat_Onat ) }.
% 4.20/4.62 (21626) {G0,W16,D5,L2,V3,M2} { ! Y = X, hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 4.20/4.62 (21627) {G0,W17,D5,L2,V3,M2} { ! Z = c_Groups_Ozero__class_Ozero(
% 4.20/4.62 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 4.20/4.62 Z ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z )
% 4.20/4.62 , X ) }.
% 4.20/4.62 (21628) {G0,W20,D5,L3,V3,M3} { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 4.20/4.62 ( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 4.20/4.62 tc_Nat_Onat ), X ), Y ), Z = X, Y = c_Groups_Ozero__class_Ozero(
% 4.20/4.62 tc_Nat_Onat ) }.
% 4.20/4.62 (21629) {G0,W16,D5,L2,V3,M2} { ! Z = X, hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 4.20/4.62 (21630) {G0,W17,D5,L2,V3,M2} { ! Y = c_Groups_Ozero__class_Ozero(
% 4.20/4.62 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 4.20/4.62 Z ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X )
% 4.20/4.62 , Y ) }.
% 4.20/4.62 (21631) {G0,W10,D3,L2,V2,M2} { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat
% 4.20/4.62 , Y, X ) = Y, X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 4.20/4.62 (21632) {G0,W9,D3,L2,V1,M2} { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 4.20/4.62 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 4.20/4.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 4.20/4.62 (21633) {G0,W23,D5,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 4.20/4.62 tc_Nat_Onat, Y, X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 4.20/4.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 4.20/4.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 4.20/4.62 (21634) {G0,W23,D5,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 4.20/4.62 tc_Nat_Onat, Y, X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 4.20/4.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 4.20/4.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 4.20/4.62 (21635) {G0,W8,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 4.20/4.62 , Y, X ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 4.20/4.62 (21636) {G0,W23,D5,L3,V3,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 4.20/4.62 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z
% 4.20/4.62 ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y
% 4.20/4.62 ) ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 4.20/4.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ) }.
% 4.20/4.62 (21637) {G0,W19,D5,L2,V3,M2} { c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 4.20/4.62 , c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 4.20/4.62 (21638) {G0,W18,D5,L2,V3,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 4.20/4.62 tc_Nat_Onat, Z, X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 4.20/4.62 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 4.20/4.62 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 4.20/4.62 (21639) {G0,W23,D5,L3,V3,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 4.20/4.62 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z
% 4.20/4.62 ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X
% 4.20/4.62 ) ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 4.20/4.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 4.20/4.62 (21640) {G0,W19,D5,L2,V3,M2} { c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 4.20/4.62 , c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 4.20/4.62 (21641) {G0,W18,D5,L2,V3,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 4.20/4.62 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 4.20/4.62 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 4.20/4.62 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 4.20/4.62 (21642) {G0,W19,D5,L2,V3,M2} { ! c_Orderings_Oord__class_Oless(
% 4.20/4.62 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z
% 4.20/4.62 ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y
% 4.20/4.62 ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 4.20/4.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 4.20/4.62 (21643) {G0,W18,D5,L2,V3,M2} { ! c_Orderings_Oord__class_Oless(
% 4.20/4.62 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z
% 4.20/4.62 ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y
% 4.20/4.62 ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X ) }.
% 4.20/4.62 (21644) {G0,W23,D5,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 4.20/4.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X ),
% 4.20/4.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 4.20/4.62 (21645) {G0,W19,D5,L2,V3,M2} { ! c_Orderings_Oord__class_Oless(
% 4.20/4.62 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z
% 4.20/4.62 ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X
% 4.20/4.62 ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 4.20/4.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ) }.
% 4.20/4.62 (21646) {G0,W18,D5,L2,V3,M2} { ! c_Orderings_Oord__class_Oless(
% 4.20/4.62 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z
% 4.20/4.62 ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X
% 4.20/4.62 ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 4.20/4.62 (21647) {G0,W23,D5,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 4.20/4.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 4.20/4.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 4.20/4.62 (21648) {G0,W5,D3,L1,V1,M1} { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 4.20/4.62 , X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 4.20/4.62 (21649) {G0,W15,D5,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 4.20/4.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 4.20/4.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 4.20/4.62 tc_Nat_Onat ), Y ) }.
% 4.20/4.62 (21650) {G0,W15,D5,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 4.20/4.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 4.20/4.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 4.20/4.62 tc_Nat_Onat ), X ) }.
% 4.20/4.62 (21651) {G0,W20,D5,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 4.20/4.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 4.20/4.62 tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 4.20/4.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 4.20/4.62 (21652) {G0,W18,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 4.20/4.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 4.20/4.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ),
% 4.20/4.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 4.20/4.62 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 4.20/4.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 4.20/4.62 (21653) {G0,W13,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 4.20/4.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 4.20/4.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 4.20/4.62 tc_Nat_Onat ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 4.20/4.62 (21654) {G0,W13,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 4.20/4.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 4.20/4.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 4.20/4.62 tc_Nat_Onat ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 4.20/4.62 (21655) {G0,W9,D3,L2,V1,M2} { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 4.20/4.62 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 4.20/4.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 4.20/4.62 (21656) {G0,W9,D3,L2,V1,M2} { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 4.20/4.62 , c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), ! X =
% 4.20/4.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 4.20/4.62 (21657) {G0,W5,D3,L1,V1,M1} { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 4.20/4.62 , X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 4.20/4.62 (21658) {G0,W23,D5,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 4.20/4.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ) }.
% 4.20/4.62 (21659) {G0,W23,D5,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 4.20/4.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 4.20/4.62 (21660) {G0,W8,D2,L2,V2,M2} { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 4.20/4.62 , Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 4.20/4.62 (21661) {G0,W23,D5,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 4.20/4.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 4.20/4.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 4.20/4.62 (21662) {G0,W23,D5,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 4.20/4.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ),
% 4.20/4.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 4.20/4.62 (21663) {G0,W21,D5,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 4.20/4.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), ! hAPP(
% 4.20/4.62 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) = hAPP( hAPP
% 4.20/4.62 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = Y }.
% 4.20/4.62 (21664) {G0,W21,D5,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 4.20/4.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), ! Z = Y,
% 4.20/4.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) = hAPP
% 4.20/4.62 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 4.20/4.62 (21665) {G0,W8,D3,L2,V2,M2} { ! class_RealVector_Oreal__normed__algebra( X
% 4.20/4.62 ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 4.20/4.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol13( Y ) ) }.
% 4.20/4.62 (21666) {G0,W28,D7,L2,V3,M2} { ! class_RealVector_Oreal__normed__algebra(
% 4.20/4.62 X ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 4.20/4.62 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 4.20/4.62 c_RealVector_Onorm__class_Onorm( X, Y ) ),
% 4.20/4.62 c_RealVector_Onorm__class_Onorm( X, Z ) ) ), skol13( X ) ) ) }.
% 4.20/4.62 (21667) {G0,W12,D3,L2,V3,M2} { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat
% 4.20/4.62 , Z, Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ), Z = X }.
% 4.20/4.62 (21668) {G0,W12,D3,L2,V3,M2} { ! Z = X, c_Groups_Oplus__class_Oplus(
% 4.20/4.62 tc_Nat_Onat, Z, Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y )
% 4.20/4.62 }.
% 4.20/4.62 (21669) {G0,W12,D3,L2,V3,M2} { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat
% 4.20/4.62 , Z, Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ), Y = X }.
% 4.20/4.62 (21670) {G0,W12,D3,L2,V3,M2} { ! Y = X, c_Groups_Oplus__class_Oplus(
% 4.20/4.62 tc_Nat_Onat, Z, Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X )
% 4.20/4.62 }.
% 4.20/4.62 (21671) {G0,W24,D6,L1,V3,M1} { hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 4.20/4.62 tc_Nat_Onat ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ), X ) =
% 4.20/4.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 4.20/4.62 (21672) {G0,W23,D7,L1,V3,M1} { hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 4.20/4.62 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 4.20/4.62 Z ), Y ) ), X ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat
% 4.20/4.62 ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X
% 4.20/4.62 ) ) }.
% 4.20/4.62 (21673) {G0,W15,D4,L1,V3,M1} { c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 4.20/4.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ) =
% 4.20/4.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, c_Groups_Oplus__class_Oplus
% 4.20/4.62 ( tc_Nat_Onat, Y, X ) ) }.
% 4.20/4.62 (21674) {G0,W24,D6,L1,V3,M1} { hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 4.20/4.62 tc_Nat_Onat ), Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 4.20/4.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 4.20/4.62 (21675) {G0,W15,D4,L1,V3,M1} { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z
% 4.20/4.62 , c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 4.20/4.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Groups_Oplus__class_Oplus
% 4.20/4.62 ( tc_Nat_Onat, Z, X ) ) }.
% 4.20/4.62 (21676) {G0,W13,D5,L1,V2,M1} { hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 4.20/4.62 tc_Nat_Onat ), Y ), X ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 4.20/4.62 tc_Nat_Onat ), X ), Y ) }.
% 4.20/4.62 (21677) {G0,W9,D3,L1,V2,M1} { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y
% 4.20/4.62 , X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 4.20/4.62 (21678) {G0,W30,D7,L1,V4,M1} { c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 4.20/4.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), T ), Z ),
% 4.20/4.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), X ) ) =
% 4.20/4.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus
% 4.20/4.62 ( tc_Nat_Onat, T, Y ) ), Z ), X ) }.
% 4.20/4.62 (21679) {G0,W20,D5,L3,V3,M3} { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 4.20/4.62 ( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 4.20/4.62 tc_Nat_Onat ), Z ), X ), Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 4.20/4.62 Y = X }.
% 4.20/4.62 (21680) {G0,W17,D5,L2,V3,M2} { ! Z = c_Groups_Ozero__class_Ozero(
% 4.20/4.62 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 4.20/4.62 Z ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z )
% 4.20/4.62 , X ) }.
% 4.20/4.62 (21681) {G0,W16,D5,L2,V3,M2} { ! Y = X, hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 4.20/4.62 (21682) {G0,W11,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless(
% 4.20/4.62 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 4.20/4.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 4.20/4.62 (21683) {G0,W11,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless(
% 4.20/4.62 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 4.20/4.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 4.20/4.62 (21684) {G0,W11,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 4.20/4.62 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 4.20/4.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 4.20/4.62 (21685) {G0,W11,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 4.20/4.62 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 4.20/4.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 4.20/4.62 (21686) {G0,W9,D3,L2,V3,M2} { ! class_RealVector_Oreal__normed__algebra( X
% 4.20/4.62 ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 4.20/4.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol14( Z, T ) ) }.
% 4.20/4.62 (21687) {G0,W22,D6,L2,V3,M2} { ! class_RealVector_Oreal__normed__algebra(
% 4.20/4.62 X ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 4.20/4.62 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 4.20/4.62 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol14( X, Y ) ) ) }.
% 4.20/4.62 (21688) {G0,W9,D3,L2,V3,M2} { ! class_RealVector_Oreal__normed__algebra( X
% 4.20/4.62 ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 4.20/4.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol15( Z, T ) ) }.
% 4.20/4.62 (21689) {G0,W22,D6,L2,V3,M2} { ! class_RealVector_Oreal__normed__algebra(
% 4.20/4.62 X ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 4.20/4.62 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 4.20/4.62 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol15( X, Y ) ) ) }.
% 4.20/4.62 (21690) {G0,W20,D5,L2,V3,M2} { ! class_RealVector_Oreal__normed__field( X
% 4.20/4.62 ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 4.20/4.62 c_RealVector_Onorm__class_Onorm( X, c_Rings_Oinverse__class_Odivide( X, Z
% 4.20/4.62 , Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 4.20/4.62 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol16( X, Y ) ) ) }.
% 4.20/4.62 (21691) {G0,W22,D6,L2,V3,M2} { ! class_RealVector_Oreal__normed__algebra(
% 4.20/4.62 X ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 4.20/4.62 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 4.20/4.62 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol17( X, Y ) ) ) }.
% 4.20/4.62 (21692) {G0,W28,D7,L2,V3,M2} { ! class_RealVector_Oreal__normed__algebra(
% 4.20/4.62 X ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 4.20/4.62 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 4.20/4.62 c_RealVector_Onorm__class_Onorm( X, Y ) ),
% 4.20/4.62 c_RealVector_Onorm__class_Onorm( X, Z ) ) ), skol18( X ) ) ) }.
% 4.20/4.62 (21693) {G0,W22,D6,L2,V3,M2} { ! class_RealVector_Oreal__normed__algebra(
% 4.20/4.62 X ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 4.20/4.62 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 4.20/4.62 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol19( X, Y ) ) ) }.
% 4.20/4.62 (21694) {G0,W44,D6,L7,V6,M7} { !
% 4.20/4.62 class_Rings_Olinordered__semiring__1__strict( X ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 4.20/4.62 ( X, T, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 4.20/4.62 c_Groups_Ozero__class_Ozero( X ), U ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), W
% 4.20/4.62 ), ! c_Groups_Oplus__class_Oplus( X, U, W ) = c_Groups_Oone__class_Oone
% 4.20/4.62 ( X ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X,
% 4.20/4.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), W ), T ) ), Y ) }.
% 4.20/4.62 (21695) {G0,W14,D3,L3,V5,M3} { ! class_Fields_Olinordered__field( X ),
% 4.20/4.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 4.20/4.62 skol20( X, T, U ) ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 4.20/4.62 (21696) {G0,W16,D4,L3,V3,M3} { ! class_Fields_Olinordered__field( X ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oplus__class_Oplus( X,
% 4.20/4.62 Y, skol20( X, Y, Z ) ) ), c_Orderings_Oord__class_Oless__eq( X, Z, Y )
% 4.20/4.62 }.
% 4.20/4.62 (21697) {G0,W10,D3,L3,V2,M3} { ! class_Groups_Oone( X ), !
% 4.20/4.62 c_Groups_Oone__class_Oone( X ) = Y, Y = c_Groups_Oone__class_Oone( X )
% 4.20/4.62 }.
% 4.20/4.62 (21698) {G0,W10,D3,L3,V2,M3} { ! class_Groups_Oone( X ), ! Y =
% 4.20/4.62 c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) = Y }.
% 4.20/4.62 (21699) {G0,W9,D4,L2,V1,M2} { ! class_RealVector_Oreal__normed__algebra__1
% 4.20/4.62 ( X ), c_RealVector_Onorm__class_Onorm( X, c_Groups_Oone__class_Oone( X )
% 4.20/4.62 ) = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 4.20/4.62 (21700) {G0,W13,D5,L2,V1,M2} { ! class_Rings_Ocomm__semiring__1( X ),
% 4.20/4.62 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) =
% 4.20/4.62 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 4.20/4.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 4.20/4.62 (21701) {G0,W12,D6,L2,V2,M2} { ! class_Rings_Ocomm__semiring__1( X ), hAPP
% 4.20/4.62 ( c_Polynomial_Opoly( X, c_Groups_Oone__class_Oone( tc_Polynomial_Opoly(
% 4.20/4.62 X ) ) ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 4.20/4.62 (21702) {G0,W9,D5,L1,V1,M1} { hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 4.20/4.62 tc_RealDef_Oreal ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X )
% 4.20/4.62 = X }.
% 4.20/4.62 (21703) {G0,W5,D3,L1,V0,M1} { ! c_Groups_Ozero__class_Ozero(
% 4.20/4.62 tc_RealDef_Oreal ) = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 4.20/4.62 (21704) {G0,W9,D4,L2,V1,M2} { ! class_Rings_Olinordered__idom( X ),
% 4.20/4.62 c_Groups_Oabs__class_Oabs( X, c_Groups_Oone__class_Oone( X ) ) =
% 4.20/4.62 c_Groups_Oone__class_Oone( X ) }.
% 4.20/4.62 (21705) {G0,W9,D4,L2,V2,M2} { ! class_Rings_Odivision__ring( X ),
% 4.20/4.62 c_Rings_Oinverse__class_Odivide( X, Y, c_Groups_Oone__class_Oone( X ) ) =
% 4.20/4.62 Y }.
% 4.20/4.62 (21706) {G0,W11,D5,L2,V2,M2} { ! class_Groups_Omonoid__mult( X ), hAPP(
% 4.20/4.62 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X )
% 4.20/4.62 ), Y ) = Y }.
% 4.20/4.62 (21707) {G0,W11,D5,L2,V2,M2} { ! class_Groups_Ocomm__monoid__mult( X ),
% 4.20/4.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone
% 4.20/4.62 ( X ) ), Y ) = Y }.
% 4.20/4.62 (21708) {G0,W11,D5,L2,V2,M2} { ! class_Groups_Omonoid__mult( X ), hAPP(
% 4.20/4.62 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone
% 4.20/4.62 ( X ) ) = Y }.
% 4.20/4.62 (21709) {G0,W11,D5,L2,V2,M2} { ! class_Groups_Ocomm__monoid__mult( X ),
% 4.20/4.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ),
% 4.20/4.62 c_Groups_Oone__class_Oone( X ) ) = Y }.
% 4.20/4.62 (21710) {G0,W11,D5,L2,V2,M2} { ! class_Rings_Ocomm__semiring__1( X ), hAPP
% 4.20/4.62 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X
% 4.20/4.62 ) ), Y ) = Y }.
% 4.20/4.62 (21711) {G0,W11,D5,L2,V2,M2} { ! class_Rings_Ocomm__semiring__1( X ), hAPP
% 4.20/4.62 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ),
% 4.20/4.62 c_Groups_Oone__class_Oone( X ) ) = Y }.
% 4.20/4.62 (21712) {G0,W7,D3,L2,V1,M2} { ! class_Rings_Ozero__neq__one( X ), !
% 4.20/4.62 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Oone__class_Oone( X ) }.
% 4.20/4.62 (21713) {G0,W7,D3,L2,V1,M2} { ! class_Rings_Ozero__neq__one( X ), !
% 4.20/4.62 c_Groups_Oone__class_Oone( X ) = c_Groups_Ozero__class_Ozero( X ) }.
% 4.20/4.62 (21714) {G0,W9,D5,L1,V1,M1} { hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 4.20/4.62 tc_Nat_Onat ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) = X }.
% 4.20/4.62 (21715) {G0,W13,D5,L2,V2,M2} { ! c_Groups_Oone__class_Oone( tc_Nat_Onat )
% 4.20/4.62 = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), Y =
% 4.20/4.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 4.20/4.62 (21716) {G0,W13,D5,L2,V2,M2} { ! c_Groups_Oone__class_Oone( tc_Nat_Onat )
% 4.20/4.62 = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X =
% 4.20/4.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 4.20/4.62 (21717) {G0,W17,D5,L3,V2,M3} { ! Y = c_Groups_Oone__class_Oone(
% 4.20/4.62 tc_Nat_Onat ), ! X = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 4.20/4.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) }.
% 4.20/4.62 (21718) {G0,W9,D5,L1,V1,M1} { hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 4.20/4.62 tc_Nat_Onat ), X ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 4.20/4.62 (21719) {G0,W13,D5,L2,V2,M2} { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 4.20/4.62 ( tc_Nat_Onat ), Y ), X ) = c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y =
% 4.20/4.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 4.20/4.62 (21720) {G0,W13,D5,L2,V2,M2} { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 4.20/4.62 ( tc_Nat_Onat ), Y ), X ) = c_Groups_Oone__class_Oone( tc_Nat_Onat ), X =
% 4.20/4.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 4.20/4.62 (21721) {G0,W17,D5,L3,V2,M3} { ! Y = c_Groups_Oone__class_Oone(
% 4.20/4.62 tc_Nat_Onat ), ! X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), hAPP( hAPP
% 4.20/4.62 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 4.20/4.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 4.20/4.62 (21722) {G0,W8,D3,L2,V1,M2} { ! class_Rings_Olinordered__semidom( X ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 4.20/4.62 c_Groups_Ozero__class_Ozero( X ) ) }.
% 4.20/4.62 (21723) {G0,W8,D3,L2,V1,M2} { ! class_Rings_Olinordered__semidom( X ),
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 4.20/4.62 c_Groups_Oone__class_Oone( X ) ) }.
% 4.20/4.62 (21724) {G0,W8,D3,L2,V1,M2} { ! class_Rings_Olinordered__semidom( X ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 4.20/4.62 c_Groups_Ozero__class_Ozero( X ) ) }.
% 4.20/4.62 (21725) {G0,W8,D3,L2,V1,M2} { ! class_Rings_Olinordered__semidom( X ),
% 4.20/4.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 4.20/4.62 c_Groups_Oone__class_Oone( X ) ) }.
% 4.20/4.62 (21726) {G0,W22,D5,L4,V3,M4} { ! class_Rings_Olinordered__semidom( X ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), Z ),
% 4.20/4.62 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 4.20/4.62 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 4.20/4.62 (21727) {G0,W10,D4,L2,V2,M2} { ! class_Rings_Olinordered__semidom( X ),
% 4.20/4.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oplus__class_Oplus( X, Y,
% 4.20/4.62 c_Groups_Oone__class_Oone( X ) ) ) }.
% 4.20/4.62 (21728) {G0,W22,D6,L2,V3,M2} { ! class_Rings_Ocomm__semiring__1( X ),
% 4.20/4.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 4.20/4.62 ( X ), Z ), Y ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 4.20/4.62 c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Oone__class_Oone( X ) ) ), Y
% 4.20/4.62 ) }.
% 4.20/4.62 (21729) {G0,W22,D6,L2,V3,M2} { ! class_Rings_Ocomm__semiring__1( X ),
% 4.20/4.62 c_Groups_Oplus__class_Oplus( X, Z, hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 4.20/4.62 c_Groups_Oone__class_Oone( X ) ) ), Z ) }.
% 4.20/4.62 (21730) {G0,W18,D6,L2,V2,M2} { ! class_Rings_Ocomm__semiring__1( X ),
% 4.20/4.62 c_Groups_Oplus__class_Oplus( X, Y, Y ) = hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X,
% 4.20/4.62 c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ) ), Y )
% 4.20/4.62 }.
% 4.20/4.62 (21731) {G0,W16,D3,L4,V3,M4} { ! class_Rings_Odivision__ring( X ), Y =
% 4.20/4.62 c_Groups_Ozero__class_Ozero( X ), ! c_Rings_Oinverse__class_Odivide( X, Z
% 4.20/4.62 , Y ) = c_Groups_Oone__class_Oone( X ), Z = Y }.
% 4.20/4.62 (21732) {G0,W16,D3,L4,V3,M4} { ! class_Rings_Odivision__ring( X ), Y =
% 4.20/4.62 c_Groups_Ozero__class_Ozero( X ), ! Z = Y,
% 4.20/4.62 c_Rings_Oinverse__class_Odivide( X, Z, Y ) = c_Groups_Oone__class_Oone( X
% 4.20/4.62 ) }.
% 4.20/4.62 (21733) {G0,W13,D3,L3,V2,M3} { ! class_Rings_Odivision__ring( X ), Y =
% 4.20/4.62 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X, Y,
% 4.20/4.62 Y ) = c_Groups_Oone__class_Oone( X ) }.
% 4.20/4.62 (21734) {G0,W13,D3,L3,V2,M3} { !
% 4.20/4.62 class_Rings_Odivision__ring__inverse__zero( X ), ! Y =
% 4.20/4.62 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X, Y,
% 4.20/4.62 Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 4.20/4.62 (21735) {G0,W13,D3,L3,V2,M3} { !
% 4.20/4.62 class_Rings_Odivision__ring__inverse__zero( X ), Y =
% 4.20/4.62 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X, Y,
% 4.20/4.62 Y ) = c_Groups_Oone__class_Oone( X ) }.
% 4.20/4.62 (21736) {G0,W16,D5,L3,V2,M3} { ! Y = hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X =
% 4.20/4.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Ozero__class_Ozero
% 4.20/4.62 ( tc_Nat_Onat ) }.
% 4.20/4.62 (21737) {G0,W26,D5,L5,V3,M5} { ! class_Rings_Olinordered__idom( X ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 4.20/4.62 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 4.20/4.62 X ), Z ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 4.20/4.62 c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless__eq( X,
% 4.20/4.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) }.
% 4.20/4.62 (21738) {G0,W26,D5,L5,V3,M5} { ! class_Rings_Olinordered__idom( X ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 4.20/4.62 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 4.20/4.62 X ), Z ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 4.20/4.62 c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless__eq( X,
% 4.20/4.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) }.
% 4.20/4.62 (21739) {G0,W12,D4,L2,V1,M2} { ! class_Rings_Olinordered__semidom( X ),
% 4.20/4.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 4.20/4.62 c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 4.20/4.62 c_Groups_Oone__class_Oone( X ) ) ) }.
% 4.20/4.62 (21740) {G0,W21,D5,L3,V3,M3} { ! class_Fields_Olinordered__field( X ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 4.20/4.62 X, c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z
% 4.20/4.62 , Y ), c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 4.20/4.62 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 4.20/4.62 (21741) {G0,W21,D5,L3,V3,M3} { ! class_Fields_Olinordered__field( X ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 4.20/4.62 X, Z, c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X
% 4.20/4.62 , Z, Y ), c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X )
% 4.20/4.62 , c_Groups_Oone__class_Oone( X ) ) ) ) }.
% 4.20/4.62 (21742) {G0,W10,D4,L1,V1,M1} { ! c_Orderings_Oord__class_Oless(
% 4.20/4.62 tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 4.20/4.62 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ),
% 4.20/4.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) }.
% 4.20/4.62 (21743) {G0,W44,D6,L7,V6,M7} { ! class_Rings_Olinordered__semiring__1( X )
% 4.20/4.62 , ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( X, T, Y ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 4.20/4.62 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 4.20/4.62 X ), W ), ! c_Groups_Oplus__class_Oplus( X, U, W ) =
% 4.20/4.62 c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless__eq( X,
% 4.20/4.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 4.20/4.62 ( X ), U ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), T )
% 4.20/4.62 ), Y ) }.
% 4.20/4.62 (21744) {G0,W11,D4,L1,V1,M1} { c_Orderings_Oord__class_Oless(
% 4.20/4.62 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 4.20/4.62 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oone__class_Oone
% 4.20/4.62 ( tc_RealDef_Oreal ), c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) )
% 4.20/4.62 ) }.
% 4.20/4.62 (21745) {G0,W14,D3,L3,V5,M3} { !
% 4.20/4.62 class_Fields_Olinordered__field__inverse__zero( X ),
% 4.20/4.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 4.20/4.62 skol21( X, T, U ) ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 4.20/4.62 (21746) {G0,W14,D3,L3,V5,M3} { !
% 4.20/4.62 class_Fields_Olinordered__field__inverse__zero( X ),
% 4.20/4.62 c_Orderings_Oord__class_Oless( X, skol21( X, T, U ),
% 4.20/4.62 c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless__eq( X, Z
% 4.20/4.62 , Y ) }.
% 4.20/4.62 (21747) {G0,W18,D5,L3,V3,M3} { !
% 4.20/4.62 class_Fields_Olinordered__field__inverse__zero( X ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 4.20/4.62 c_Groups_Otimes__class_Otimes( X ), skol21( X, Y, Z ) ), Z ), Y ),
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 4.20/4.62 (21748) {G0,W15,D4,L3,V3,M3} { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero
% 4.20/4.62 ( tc_Nat_Onat ) ) ), ! hBOOL( hAPP( X, Y ) ),
% 4.20/4.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol22( Z, Y ), Y ) }.
% 4.20/4.62 (21749) {G0,W19,D4,L4,V3,M4} { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero
% 4.20/4.62 ( tc_Nat_Onat ) ) ), ! hBOOL( hAPP( X, Y ) ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, skol22( X, Y ) ), !
% 4.20/4.62 hBOOL( hAPP( X, Z ) ) }.
% 4.20/4.62 (21750) {G0,W19,D5,L3,V2,M3} { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero
% 4.20/4.62 ( tc_Nat_Onat ) ) ), ! hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X,
% 4.20/4.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, skol22( X, Y ),
% 4.20/4.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 4.20/4.62 (21751) {G0,W29,D6,L4,V3,M4} { ! c_Orderings_Oord__class_Oless(
% 4.20/4.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 4.20/4.62 tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 4.20/4.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), c_NthRoot_Oroot(
% 4.20/4.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z ) =
% 4.20/4.62 c_NthRoot_Oroot( X, c_NthRoot_Oroot( Y, Z ) ) }.
% 4.20/4.62 (21752) {G0,W34,D6,L4,V3,M4} { ! c_Orderings_Oord__class_Oless(
% 4.20/4.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 4.20/4.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 4.20/4.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), c_NthRoot_Oroot( X
% 4.20/4.62 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Z )
% 4.20/4.62 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 4.20/4.62 c_NthRoot_Oroot( X, Y ) ), c_NthRoot_Oroot( X, Z ) ) }.
% 4.20/4.62 (21753) {G0,W7,D4,L1,V1,M1} { c_NthRoot_Oroot( X,
% 4.20/4.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) =
% 4.20/4.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 4.20/4.62 (21754) {G0,W15,D3,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 4.20/4.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), !
% 4.20/4.62 c_NthRoot_Oroot( X, Z ) = c_NthRoot_Oroot( X, Y ), Z = Y }.
% 4.20/4.62 (21755) {G0,W15,D3,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 4.20/4.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), ! Z = Y,
% 4.20/4.62 c_NthRoot_Oroot( X, Z ) = c_NthRoot_Oroot( X, Y ) }.
% 4.20/4.62 (21756) {G0,W21,D4,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 4.20/4.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), !
% 4.20/4.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 4.20/4.62 tc_Nat_Onat ), Y ), c_NthRoot_Oroot( X, c_NthRoot_Oroot( Y, Z ) ) =
% 4.20/4.62 c_NthRoot_Oroot( Y, c_NthRoot_Oroot( X, Z ) ) }.
% 4.20/4.62 (21757) {G0,W15,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 4.20/4.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), !
% 4.20/4.62 c_NthRoot_Oroot( X, Y ) = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ),
% 4.20/4.62 Y = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 4.20/4.62 (21758) {G0,W15,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 4.20/4.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), ! Y =
% 4.29/4.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_NthRoot_Oroot( X, Y ) =
% 4.29/4.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 4.29/4.62 (21759) {G0,W12,D4,L2,V1,M2} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 4.29/4.62 c_NthRoot_Oroot( X, c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) =
% 4.29/4.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 4.29/4.62 (21760) {G0,W17,D3,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Oroot( X,
% 4.29/4.62 Z ), c_NthRoot_Oroot( X, Y ) ), c_Orderings_Oord__class_Oless__eq(
% 4.29/4.62 tc_RealDef_Oreal, Z, Y ) }.
% 4.29/4.62 (21761) {G0,W17,D3,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ),
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Oroot( X,
% 4.29/4.62 Z ), c_NthRoot_Oroot( X, Y ) ) }.
% 4.29/4.62 (21762) {G0,W17,D3,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ),
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Oroot( X,
% 4.29/4.62 Z ), c_NthRoot_Oroot( X, Y ) ) }.
% 4.29/4.62 (21763) {G0,W17,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 4.29/4.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_NthRoot_Oroot( X, Y ) )
% 4.29/4.62 , c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 4.29/4.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), Y ) }.
% 4.29/4.62 (21764) {G0,W17,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 4.29/4.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), Y ),
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 4.29/4.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_NthRoot_Oroot( X, Y ) )
% 4.29/4.62 }.
% 4.29/4.62 (21765) {G0,W17,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Oroot( X,
% 4.29/4.62 Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y,
% 4.29/4.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 4.29/4.62 (21766) {G0,W17,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y,
% 4.29/4.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Oroot( X,
% 4.29/4.62 Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 4.29/4.62 (21767) {G0,W22,D3,L4,V3,M4} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 4.29/4.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), Z ),
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Oroot( Y,
% 4.29/4.62 Z ), c_NthRoot_Oroot( X, Z ) ) }.
% 4.29/4.62 (21768) {G0,W15,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), !
% 4.29/4.62 c_NthRoot_Oroot( X, Y ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal )
% 4.29/4.62 , Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 4.29/4.62 (21769) {G0,W15,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), ! Y =
% 4.29/4.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Oroot( X, Y )
% 4.29/4.62 = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 4.29/4.62 (21770) {G0,W17,D3,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Oroot( X, Z )
% 4.29/4.62 , c_NthRoot_Oroot( X, Y ) ), c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_RealDef_Oreal, Z, Y ) }.
% 4.29/4.62 (21771) {G0,W17,D3,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 4.29/4.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Oroot( X, Z )
% 4.29/4.62 , c_NthRoot_Oroot( X, Y ) ) }.
% 4.29/4.62 (21772) {G0,W17,D3,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 4.29/4.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Oroot( X, Z )
% 4.29/4.62 , c_NthRoot_Oroot( X, Y ) ) }.
% 4.29/4.62 (21773) {G0,W17,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 4.29/4.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_NthRoot_Oroot( X, Y ) )
% 4.29/4.62 , c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 4.29/4.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), Y ) }.
% 4.29/4.62 (21774) {G0,W17,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 4.29/4.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), Y ),
% 4.29/4.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 4.29/4.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_NthRoot_Oroot( X, Y ) )
% 4.29/4.62 }.
% 4.29/4.62 (21775) {G0,W17,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Oroot( X, Y )
% 4.29/4.62 , c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 4.29/4.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y,
% 4.29/4.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 4.29/4.62 (21776) {G0,W17,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y,
% 4.29/4.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 4.29/4.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Oroot( X, Y )
% 4.29/4.62 , c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 4.29/4.62 (21777) {G0,W22,D3,L4,V3,M4} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 4.29/4.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), Z ),
% 4.29/4.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Oroot( Y, Z )
% 4.29/4.62 , c_NthRoot_Oroot( X, Z ) ) }.
% 4.29/4.62 (21778) {G0,W24,D6,L2,V3,M2} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 4.29/4.62 c_NthRoot_Oroot( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 4.29/4.62 tc_RealDef_Oreal ), Z ), Y ) ) = hAPP( hAPP(
% 4.29/4.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_NthRoot_Oroot( X, Z
% 4.29/4.62 ) ), c_NthRoot_Oroot( X, Y ) ) }.
% 4.29/4.62 (21779) {G0,W24,D6,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 4.29/4.62 tc_Nat_Onat ), Y ), c_NthRoot_Oroot( hAPP( hAPP(
% 4.29/4.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z ) =
% 4.29/4.62 c_NthRoot_Oroot( X, c_NthRoot_Oroot( Y, Z ) ) }.
% 4.29/4.62 (21780) {G0,W20,D4,L2,V3,M2} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 4.29/4.62 c_NthRoot_Oroot( X, c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, Z
% 4.29/4.62 , Y ) ) = c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 4.29/4.62 c_NthRoot_Oroot( X, Z ), c_NthRoot_Oroot( X, Y ) ) }.
% 4.29/4.62 (21781) {G0,W16,D4,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 4.29/4.62 c_NthRoot_Oroot( X, c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ) ) =
% 4.29/4.62 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, c_NthRoot_Oroot( X, Y ) )
% 4.29/4.62 }.
% 4.29/4.62 (21782) {G0,W17,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 4.29/4.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 4.29/4.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Oroot( X, Y )
% 4.29/4.62 ) }.
% 4.29/4.62 (21783) {G0,W17,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Oroot( X,
% 4.29/4.62 Y ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y,
% 4.29/4.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 4.29/4.62 (21784) {G0,W17,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y,
% 4.29/4.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Oroot( X,
% 4.29/4.62 Y ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 4.29/4.62 (21785) {G0,W17,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 4.29/4.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Oroot( X, Y )
% 4.29/4.62 ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 4.29/4.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ) }.
% 4.29/4.62 (21786) {G0,W17,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 4.29/4.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 4.29/4.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Oroot( X, Y )
% 4.29/4.62 ) }.
% 4.29/4.62 (21787) {G0,W27,D3,L5,V3,M5} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 4.29/4.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z,
% 4.29/4.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Oroot( X,
% 4.29/4.62 Z ), c_NthRoot_Oroot( Y, Z ) ) }.
% 4.29/4.62 (21788) {G0,W17,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 4.29/4.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Oroot( X, Y )
% 4.29/4.62 ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 4.29/4.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ) }.
% 4.29/4.62 (21789) {G0,W17,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 4.29/4.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 4.29/4.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 4.29/4.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Oroot( X, Y )
% 4.29/4.62 ) }.
% 4.29/4.62 (21790) {G0,W17,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Oroot( X, Y )
% 4.29/4.62 , c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 4.29/4.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y,
% 4.29/4.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 4.29/4.62 (21791) {G0,W17,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y,
% 4.29/4.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 4.29/4.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Oroot( X, Y )
% 4.29/4.62 , c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 4.29/4.62 (21792) {G0,W17,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 4.29/4.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 4.29/4.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 4.29/4.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Oroot( X, Y )
% 4.29/4.62 ) }.
% 4.29/4.62 (21793) {G0,W27,D3,L5,V3,M5} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 4.29/4.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z,
% 4.29/4.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 4.29/4.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Oroot( X, Z )
% 4.29/4.62 , c_NthRoot_Oroot( Y, Z ) ) }.
% 4.29/4.62 (21794) {G0,W22,D3,L4,V3,M4} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 4.29/4.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, Z ),
% 4.29/4.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Oroot( X, Y )
% 4.29/4.62 , c_NthRoot_Oroot( X, Z ) ) }.
% 4.29/4.62 (21795) {G0,W17,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 4.29/4.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 4.29/4.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Oroot( X, Y )
% 4.29/4.62 ) }.
% 4.29/4.62 (21796) {G0,W18,D5,L2,V1,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 4.29/4.62 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 4.29/4.62 c_RComplete_Onatceiling( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X
% 4.29/4.62 , c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) =
% 4.29/4.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatceiling( X ),
% 4.29/4.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 4.29/4.62 (21797) {G0,W18,D5,L2,V1,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 4.29/4.62 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 4.29/4.62 c_RComplete_Onatfloor( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 4.29/4.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) =
% 4.29/4.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatfloor( X ),
% 4.29/4.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 4.29/4.62 (21798) {G0,W20,D5,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 4.29/4.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), c_NthRoot_Oroot( X, Y )
% 4.29/4.62 ), X ) = Y }.
% 4.29/4.62 (21799) {G0,W23,D5,L4,V3,M4} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 4.29/4.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), ! hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Y ), X ) = Z,
% 4.29/4.62 c_NthRoot_Oroot( X, Z ) = Y }.
% 4.29/4.62 (21800) {G0,W11,D5,L2,V2,M2} { ! class_Rings_Ocomm__semiring__1( X ), hAPP
% 4.29/4.62 ( hAPP( c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone
% 4.29/4.62 ( tc_Nat_Onat ) ) = Y }.
% 4.29/4.62 (21801) {G0,W20,D6,L2,V3,M2} { !
% 4.29/4.62 class_RealVector_Oreal__normed__algebra__1( X ),
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 4.29/4.62 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( X ), Z ), Y ) ), hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 4.29/4.62 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) ) }.
% 4.29/4.62 (21802) {G0,W19,D6,L2,V3,M2} { !
% 4.29/4.62 class_RealVector_Oreal__normed__div__algebra( X ),
% 4.29/4.62 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 4.29/4.62 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) }.
% 4.29/4.62 (21803) {G0,W24,D8,L2,V4,M2} { ! class_Rings_Ocomm__semiring__1( X ), hAPP
% 4.29/4.62 ( c_Polynomial_Opoly( X, hAPP( hAPP( c_Power_Opower__class_Opower(
% 4.29/4.62 tc_Polynomial_Opoly( X ) ), T ), Z ) ), Y ) = hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( X ), hAPP( c_Polynomial_Opoly( X, T ), Y )
% 4.29/4.62 ), Z ) }.
% 4.29/4.62 (21804) {G0,W25,D7,L2,V4,M2} { ! class_Rings_Ocomm__semiring__1( X ), hAPP
% 4.29/4.62 ( hAPP( c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 4.29/4.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) }.
% 4.29/4.62 (21805) {G0,W30,D7,L2,V4,M2} { ! class_Rings_Ocomm__semiring__1( X ), hAPP
% 4.29/4.62 ( hAPP( c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 4.29/4.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 4.29/4.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 4.29/4.62 (21806) {G0,W6,D4,L1,V0,M1} { c_RComplete_Onatfloor(
% 4.29/4.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) =
% 4.29/4.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 4.29/4.62 (21807) {G0,W6,D3,L1,V1,M1} { c_Orderings_Oord__class_Oless__eq(
% 4.29/4.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 4.29/4.62 c_RComplete_Onatfloor( X ) ) }.
% 4.29/4.62 (21808) {G0,W10,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 4.29/4.62 tc_RealDef_Oreal, Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat
% 4.29/4.62 , c_RComplete_Onatfloor( Y ), c_RComplete_Onatfloor( X ) ) }.
% 4.29/4.62 (21809) {G0,W6,D4,L1,V0,M1} { c_RComplete_Onatfloor(
% 4.29/4.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) =
% 4.29/4.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 4.29/4.62 (21810) {G0,W6,D4,L1,V0,M1} { c_RComplete_Onatceiling(
% 4.29/4.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) =
% 4.29/4.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 4.29/4.62 (21811) {G0,W6,D3,L1,V1,M1} { c_Orderings_Oord__class_Oless__eq(
% 4.29/4.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 4.29/4.62 c_RComplete_Onatceiling( X ) ) }.
% 4.29/4.62 (21812) {G0,W10,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 4.29/4.62 tc_RealDef_Oreal, Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat
% 4.29/4.62 , c_RComplete_Onatceiling( Y ), c_RComplete_Onatceiling( X ) ) }.
% 4.29/4.62 (21813) {G0,W6,D4,L1,V0,M1} { c_RComplete_Onatceiling(
% 4.29/4.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) =
% 4.29/4.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 4.29/4.62 (21814) {G0,W12,D5,L2,V2,M2} { ! class_Rings_Ocomm__semiring__1( X ), hAPP
% 4.29/4.62 ( hAPP( c_Power_Opower__class_Opower( X ), Y ),
% 4.29/4.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone
% 4.29/4.62 ( X ) }.
% 4.29/4.62 (21815) {G0,W28,D7,L2,V4,M2} { ! class_Rings_Ocomm__semiring__1( X ), hAPP
% 4.29/4.62 ( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( X ), T ), Y ) ) = hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 4.29/4.62 tc_Nat_Onat, Z, Y ) ) }.
% 4.29/4.62 (21816) {G0,W10,D3,L2,V1,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 4.29/4.62 tc_RealDef_Oreal, X, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 4.29/4.62 c_RComplete_Onatfloor( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 4.29/4.62 }.
% 4.29/4.62 (21817) {G0,W10,D3,L2,V1,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 4.29/4.62 tc_RealDef_Oreal, X, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 4.29/4.62 c_RComplete_Onatceiling( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 4.29/4.62 }.
% 4.29/4.62 (21818) {G0,W22,D6,L2,V3,M2} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 4.29/4.62 c_NthRoot_Oroot( X, hAPP( hAPP( c_Power_Opower__class_Opower(
% 4.29/4.62 tc_RealDef_Oreal ), Z ), Y ) ) = hAPP( hAPP( c_Power_Opower__class_Opower
% 4.29/4.62 ( tc_RealDef_Oreal ), c_NthRoot_Oroot( X, Z ) ), Y ) }.
% 4.29/4.62 (21819) {G0,W11,D3,L2,V1,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 4.29/4.62 tc_Nat_Onat, c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 4.29/4.62 c_RComplete_Onatfloor( X ) ), c_Orderings_Oord__class_Oless__eq(
% 4.29/4.62 tc_RealDef_Oreal, c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 4.29/4.62 (21820) {G0,W11,D3,L2,V1,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 4.29/4.62 tc_RealDef_Oreal, c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Groups_Oone__class_Oone
% 4.29/4.62 ( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ) }.
% 4.29/4.62 (21821) {G0,W11,D3,L2,V1,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 4.29/4.62 tc_Nat_Onat, c_RComplete_Onatceiling( X ), c_Groups_Oone__class_Oone(
% 4.29/4.62 tc_Nat_Onat ) ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 4.29/4.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 4.29/4.62 (21822) {G0,W11,D3,L2,V1,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 4.29/4.62 tc_RealDef_Oreal, X, c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 4.29/4.62 X ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 4.29/4.62 (21823) {G0,W27,D6,L3,V2,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 4.29/4.62 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 4.29/4.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 4.29/4.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_RComplete_Onatfloor( X )
% 4.29/4.62 ), c_RComplete_Onatfloor( Y ) ), c_RComplete_Onatfloor( hAPP( hAPP(
% 4.29/4.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) ) }.
% 4.29/4.62 (21824) {G0,W20,D6,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 4.29/4.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), c_NthRoot_Oroot( X
% 4.29/4.62 , hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Y ), X )
% 4.29/4.62 ) = Y }.
% 4.29/4.62 (21825) {G0,W20,D5,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 4.29/4.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), c_NthRoot_Oroot( X, Y )
% 4.29/4.62 ), X ) = Y }.
% 4.29/4.62 (21826) {G0,W30,D5,L5,V4,M5} { ! class_Rings_Olinordered__semidom( X ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 4.29/4.62 ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 4.29/4.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), T ),
% 4.29/4.62 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 4.29/4.62 (21827) {G0,W22,D5,L4,V3,M4} { ! class_Rings_Olinordered__semidom( X ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 4.29/4.62 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( X,
% 4.29/4.62 c_Groups_Oone__class_Oone( X ), hAPP( hAPP( c_Power_Opower__class_Opower
% 4.29/4.62 ( X ), Y ), Z ) ) }.
% 4.29/4.62 (21828) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__semidom( X ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 4.29/4.62 (21829) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__semidom( X ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 4.29/4.62 (21830) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__semidom( X ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 4.29/4.62 (21831) {G0,W20,D5,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( tc_Int_Oint ), c_Groups_Oabs__class_Oabs(
% 4.29/4.62 tc_Int_Oint, Y ) ), X ) ), ! Y = c_Groups_Ozero__class_Ozero( tc_Int_Oint
% 4.29/4.62 ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 4.29/4.62 (21832) {G0,W16,D5,L2,V2,M2} { Y = c_Groups_Ozero__class_Ozero(
% 4.29/4.62 tc_Int_Oint ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 4.29/4.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( tc_Int_Oint ), c_Groups_Oabs__class_Oabs(
% 4.29/4.62 tc_Int_Oint, Y ) ), X ) ) }.
% 4.29/4.62 (21833) {G0,W16,D5,L2,V2,M2} { ! X = c_Groups_Ozero__class_Ozero(
% 4.29/4.62 tc_Nat_Onat ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 4.29/4.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( tc_Int_Oint ), c_Groups_Oabs__class_Oabs(
% 4.29/4.62 tc_Int_Oint, Y ) ), X ) ) }.
% 4.29/4.62 (21834) {G0,W19,D5,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ),
% 4.29/4.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 4.29/4.62 tc_Nat_Onat ), Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 4.29/4.62 (21835) {G0,W15,D5,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 4.29/4.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 4.29/4.62 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 4.29/4.62 ), X ) ) }.
% 4.29/4.62 (21836) {G0,W14,D5,L2,V2,M2} { ! X = c_Groups_Ozero__class_Ozero(
% 4.29/4.62 tc_Nat_Onat ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 4.29/4.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 4.29/4.62 (21837) {G0,W23,D5,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ),
% 4.29/4.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 4.29/4.62 (21838) {G0,W26,D7,L1,V3,M1} { hAPP( hAPP( c_Power_Opower__class_Opower(
% 4.29/4.62 tc_Int_Oint ), Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 4.29/4.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ) }.
% 4.29/4.62 (21839) {G0,W23,D7,L1,V3,M1} { hAPP( hAPP( c_Power_Opower__class_Opower(
% 4.29/4.62 tc_Int_Oint ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z
% 4.29/4.62 ), Y ) ), X ) = hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint )
% 4.29/4.62 , Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X )
% 4.29/4.62 ) }.
% 4.29/4.62 (21840) {G0,W15,D5,L3,V3,M3} { ! class_Rings_Oring__1__no__zero__divisors
% 4.29/4.62 ( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 4.29/4.62 ( X ) }.
% 4.29/4.62 (21841) {G0,W30,D7,L2,V4,M2} { ! class_Groups_Ocomm__monoid__mult( X ),
% 4.29/4.62 hAPP( hAPP( c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 4.29/4.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 4.29/4.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 4.29/4.62 (21842) {G0,W25,D7,L2,V3,M2} { ! class_Groups_Omonoid__mult( X ), hAPP(
% 4.29/4.62 hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 4.29/4.62 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 4.29/4.62 (21843) {G0,W12,D5,L2,V2,M2} { ! class_Groups_Omonoid__mult( X ), hAPP(
% 4.29/4.62 hAPP( c_Power_Opower__class_Opower( X ), c_Groups_Oone__class_Oone( X ) )
% 4.29/4.62 , Y ) = c_Groups_Oone__class_Oone( X ) }.
% 4.29/4.62 (21844) {G0,W26,D6,L2,V4,M2} { ! class_Fields_Ofield__inverse__zero( X ),
% 4.29/4.62 hAPP( hAPP( c_Power_Opower__class_Opower( X ),
% 4.29/4.62 c_Rings_Oinverse__class_Odivide( X, T, Z ) ), Y ) =
% 4.29/4.62 c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 4.29/4.62 (21845) {G0,W19,D6,L2,V3,M2} { ! class_Rings_Olinordered__idom( X ),
% 4.29/4.62 c_Groups_Oabs__class_Oabs( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 4.29/4.62 ), Z ), Y ) ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ),
% 4.29/4.62 c_Groups_Oabs__class_Oabs( X, Z ) ), Y ) }.
% 4.29/4.62 (21846) {G0,W25,D7,L2,V4,M2} { ! class_Groups_Omonoid__mult( X ), hAPP(
% 4.29/4.62 hAPP( c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 4.29/4.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) }.
% 4.29/4.62 (21847) {G0,W11,D5,L2,V2,M2} { ! class_Groups_Omonoid__mult( X ), hAPP(
% 4.29/4.62 hAPP( c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 4.29/4.62 tc_Nat_Onat ) ) = Y }.
% 4.29/4.62 (21848) {G0,W17,D5,L3,V3,M3} { ! class_Rings_Olinordered__semidom( X ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 4.29/4.62 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 4.29/4.62 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 4.29/4.62 (21849) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__semidom( X ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 4.29/4.62 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 4.29/4.62 (21850) {G0,W17,D5,L3,V3,M3} { ! class_Rings_Olinordered__semidom( X ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 4.29/4.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 4.29/4.62 ( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 4.29/4.62 (21851) {G0,W17,D5,L3,V3,M3} { ! class_Rings_Olinordered__semidom( X ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 4.29/4.62 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 4.29/4.62 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 4.29/4.62 (21852) {G0,W21,D5,L6,V3,M6} { ! class_Power_Opower( X ), !
% 4.29/4.62 class_Rings_Omult__zero( X ), ! class_Rings_Ono__zero__divisors( X ), !
% 4.29/4.62 class_Rings_Ozero__neq__one( X ), ! hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( X ), Z ), Y ) = c_Groups_Ozero__class_Ozero
% 4.29/4.62 ( X ), Z = c_Groups_Ozero__class_Ozero( X ) }.
% 4.29/4.62 (21853) {G0,W21,D5,L6,V3,M6} { ! class_Power_Opower( X ), !
% 4.29/4.62 class_Rings_Omult__zero( X ), ! class_Rings_Ono__zero__divisors( X ), !
% 4.29/4.62 class_Rings_Ozero__neq__one( X ), ! hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( X ), Z ), Y ) = c_Groups_Ozero__class_Ozero
% 4.29/4.62 ( X ), ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 4.29/4.62 (21854) {G0,W25,D5,L7,V3,M7} { ! class_Power_Opower( X ), !
% 4.29/4.62 class_Rings_Omult__zero( X ), ! class_Rings_Ono__zero__divisors( X ), !
% 4.29/4.62 class_Rings_Ozero__neq__one( X ), ! Z = c_Groups_Ozero__class_Ozero( X )
% 4.29/4.62 , Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( X ), Z ), Y ) = c_Groups_Ozero__class_Ozero
% 4.29/4.62 ( X ) }.
% 4.29/4.62 (21855) {G0,W23,D5,L4,V4,M4} { ! class_Rings_Olinordered__semidom( X ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 4.29/4.62 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( X ), Y ), Z ), T = Z }.
% 4.29/4.62 (21856) {G0,W23,D5,L4,V4,M4} { ! class_Rings_Olinordered__semidom( X ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 4.29/4.62 T = Z, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP(
% 4.29/4.62 hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) }.
% 4.29/4.62 (21857) {G0,W30,D6,L3,V4,M3} { ! class_Fields_Ofield( X ), Y =
% 4.29/4.62 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide( X, T
% 4.29/4.62 , Y ) ), Z ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 4.29/4.62 (21858) {G0,W12,D5,L2,V2,M2} { ! class_Power_Opower( X ), hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ozero__class_Ozero(
% 4.29/4.62 tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( X ) }.
% 4.29/4.62 (21859) {G0,W28,D7,L2,V4,M2} { ! class_Groups_Omonoid__mult( X ), hAPP(
% 4.29/4.62 hAPP( c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus
% 4.29/4.62 ( tc_Nat_Onat, Z, Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 4.29/4.62 , hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 4.29/4.62 (21860) {G0,W23,D6,L2,V3,M2} { ! class_Fields_Ofield__inverse__zero( X ),
% 4.29/4.62 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oone__class_Oone( X ), hAPP
% 4.29/4.62 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide( X,
% 4.29/4.62 c_Groups_Oone__class_Oone( X ), Z ) ), Y ) }.
% 4.29/4.62 (21861) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__semidom( X ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( X ), Y ), T ) ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 4.29/4.62 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 4.29/4.62 (21862) {G0,W26,D6,L3,V3,M3} { ! class_Rings_Olinordered__semidom( X ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), Y ),
% 4.29/4.62 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP(
% 4.29/4.62 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 4.29/4.62 (21863) {G0,W22,D6,L3,V3,M3} { ! class_Rings_Olinordered__semidom( X ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), Y ),
% 4.29/4.62 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 4.29/4.62 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 4.29/4.62 (21864) {G0,W18,D5,L4,V2,M4} { ! class_Power_Opower( X ), !
% 4.29/4.62 class_Rings_Osemiring__0( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 4.29/4.62 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( X ),
% 4.29/4.62 c_Groups_Ozero__class_Ozero( X ) ), Y ) = c_Groups_Oone__class_Oone( X )
% 4.29/4.62 }.
% 4.29/4.62 (21865) {G0,W18,D5,L4,V2,M4} { ! class_Power_Opower( X ), !
% 4.29/4.62 class_Rings_Osemiring__0( X ), Y = c_Groups_Ozero__class_Ozero(
% 4.29/4.62 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( X ),
% 4.29/4.62 c_Groups_Ozero__class_Ozero( X ) ), Y ) = c_Groups_Ozero__class_Ozero( X
% 4.29/4.62 ) }.
% 4.29/4.62 (21866) {G0,W14,D5,L2,V3,M2} { ! class_Rings_Olinordered__idom( X ),
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 4.29/4.62 hAPP( hAPP( c_Power_Opower__class_Opower( X ), c_Groups_Oabs__class_Oabs
% 4.29/4.62 ( X, Z ) ), Y ) ) }.
% 4.29/4.62 (21867) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__semidom( X ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), T ),
% 4.29/4.62 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 4.29/4.62 (21868) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__semidom( X ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 4.29/4.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 4.29/4.62 (21869) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__semidom( X ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 4.29/4.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 4.29/4.62 (21870) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__semidom( X ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ),
% 4.29/4.62 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 4.29/4.62 (21871) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__semidom( X ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), T )
% 4.29/4.62 , c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 4.29/4.62 (21872) {G0,W31,D6,L4,V3,M4} { ! class_Rings_Olinordered__semidom( X ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 4.29/4.62 ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 4.29/4.62 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 4.29/4.62 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( X ), Y ), Z ) ), hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 4.29/4.62 (21873) {G0,W30,D5,L5,V4,M5} { ! class_Rings_Olinordered__semidom( X ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 4.29/4.62 ! c_Orderings_Oord__class_Oless( X, T, c_Groups_Oone__class_Oone( X ) ),
% 4.29/4.62 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 4.29/4.62 (21874) {G0,W33,D5,L6,V4,M6} { ! class_Rings_Olinordered__semidom( X ), !
% 4.29/4.62 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ) = hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( X ), Y ), Z ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 4.29/4.62 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 4.29/4.62 X ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 4.29/4.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ), T = Y }.
% 4.29/4.62 (21875) {G0,W30,D5,L5,V4,M5} { ! class_Rings_Olinordered__semidom( X ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 4.29/4.62 ), ! c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oone__class_Oone
% 4.29/4.62 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 4.29/4.62 (21876) {G0,W31,D8,L3,V2,M3} { X = c_Groups_Ozero__class_Ozero(
% 4.29/4.62 tc_Complex_Ocomplex ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 4.29/4.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 4.29/4.62 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 4.29/4.62 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex,
% 4.29/4.62 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ), hAPP( hAPP(
% 4.29/4.62 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), X ), hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), skol23( X, Y ) ), Y
% 4.29/4.62 ) ) ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 4.29/4.62 (21877) {G0,W11,D4,L2,V1,M2} { ! class_Power_Opower( X ),
% 4.29/4.62 c_Power_Opower__class_Opower( X ) = c_Power_Opower_Opower( X,
% 4.29/4.62 c_Groups_Oone__class_Oone( X ), c_Groups_Otimes__class_Otimes( X ) ) }.
% 4.29/4.62 (21878) {G0,W24,D4,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_RealDef_Oreal, c_RealDef_Oreal( tc_Nat_Onat, Y ), X ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 4.29/4.62 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 4.29/4.62 tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ),
% 4.29/4.62 c_RComplete_Onatceiling( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 4.29/4.62 Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 4.29/4.62 (21879) {G0,W7,D3,L1,V1,M1} { c_Orderings_Oord__class_Oless__eq(
% 4.29/4.62 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 4.29/4.62 c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 4.29/4.62 (21880) {G0,W12,D5,L1,V2,M1} { c_Orderings_Oord__class_Oless__eq(
% 4.29/4.62 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( tc_Int_Oint ), c_Groups_Oabs__class_Oabs(
% 4.29/4.62 tc_Int_Oint, Y ) ), X ) ) }.
% 4.29/4.62 (21881) {G0,W17,D6,L1,V2,M1} { hAPP( hAPP( c_Power_Opower__class_Opower(
% 4.29/4.62 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ), X ) =
% 4.29/4.62 c_RealDef_Oreal( tc_Nat_Onat, hAPP( hAPP( c_Power_Opower__class_Opower(
% 4.29/4.62 tc_Nat_Onat ), Y ), X ) ) }.
% 4.29/4.62 (21882) {G0,W17,D6,L1,V2,M1} { c_RealDef_Oreal( tc_Nat_Onat, hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 4.29/4.62 tc_Nat_Onat, Y ) ), X ) }.
% 4.29/4.62 (21883) {G0,W6,D3,L1,V0,M1} { c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 4.29/4.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 4.29/4.62 tc_Int_Oint ) ) }.
% 4.29/4.62 (21884) {G0,W10,D3,L2,V1,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 4.29/4.62 tc_Int_Oint, c_Groups_Oone__class_Oone( tc_Int_Oint ), X ),
% 4.29/4.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 4.29/4.62 tc_Int_Oint ), X ) }.
% 4.29/4.62 (21885) {G0,W10,D3,L2,V1,M2} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oone__class_Oone
% 4.29/4.62 ( tc_Int_Oint ), X ) }.
% 4.29/4.62 (21886) {G0,W11,D3,L2,V1,M2} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_Int_Oint, c_Groups_Oabs__class_Oabs( tc_Int_Oint, X ),
% 4.29/4.62 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X =
% 4.29/4.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 4.29/4.62 (21887) {G0,W11,D3,L2,V1,M2} { ! X = c_Groups_Ozero__class_Ozero(
% 4.29/4.62 tc_Int_Oint ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 4.29/4.62 c_Groups_Oabs__class_Oabs( tc_Int_Oint, X ), c_Groups_Oone__class_Oone(
% 4.29/4.62 tc_Int_Oint ) ) }.
% 4.29/4.62 (21888) {G0,W5,D3,L1,V0,M1} { ! c_Groups_Ozero__class_Ozero( tc_Int_Oint )
% 4.29/4.62 = c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 4.29/4.62 (21889) {G0,W9,D5,L1,V1,M1} { hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 4.29/4.62 tc_Int_Oint ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) = X }.
% 4.29/4.62 (21890) {G0,W9,D5,L1,V1,M1} { hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 4.29/4.62 tc_Int_Oint ), X ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = X }.
% 4.29/4.62 (21891) {G0,W17,D6,L2,V2,M2} { ! c_Groups_Oabs__class_Oabs( tc_Int_Oint,
% 4.29/4.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) =
% 4.29/4.62 c_Groups_Oone__class_Oone( tc_Int_Oint ), c_Groups_Oabs__class_Oabs(
% 4.29/4.62 tc_Int_Oint, X ) = c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 4.29/4.62 (21892) {G0,W11,D5,L1,V1,M1} { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint
% 4.29/4.62 , c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oone__class_Oone(
% 4.29/4.62 tc_Int_Oint ), X ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 4.29/4.62 (21893) {G0,W15,D4,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus( tc_Int_Oint, X,
% 4.29/4.62 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ),
% 4.29/4.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y = X }.
% 4.29/4.62 (21894) {G0,W12,D4,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_Int_Oint, Y, X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 4.29/4.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 4.29/4.62 tc_Int_Oint ) ) ) }.
% 4.29/4.62 (21895) {G0,W11,D4,L2,V2,M2} { ! Y = X, c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus( tc_Int_Oint, X,
% 4.29/4.62 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ) }.
% 4.29/4.62 (21896) {G0,W12,D4,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_Int_Oint, Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 4.29/4.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 4.29/4.62 tc_Int_Oint ) ), X ) }.
% 4.29/4.62 (21897) {G0,W18,D5,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), ! hAPP(
% 4.29/4.62 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 4.29/4.62 c_Groups_Oone__class_Oone( tc_Int_Oint ), X = c_Groups_Oone__class_Oone(
% 4.29/4.62 tc_Int_Oint ) }.
% 4.29/4.62 (21898) {G0,W18,D5,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), ! hAPP(
% 4.29/4.62 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 4.29/4.62 c_Groups_Oone__class_Oone( tc_Int_Oint ), Y = c_Groups_Oone__class_Oone(
% 4.29/4.62 tc_Int_Oint ) }.
% 4.29/4.62 (21899) {G0,W22,D5,L4,V2,M4} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), ! X =
% 4.29/4.62 c_Groups_Oone__class_Oone( tc_Int_Oint ), ! Y = c_Groups_Oone__class_Oone
% 4.29/4.62 ( tc_Int_Oint ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 4.29/4.62 , X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 4.29/4.62 (21900) {G0,W14,D4,L2,V1,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 4.29/4.62 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 4.29/4.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 4.29/4.62 tc_Int_Oint ), c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 4.29/4.62 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) ) }.
% 4.29/4.62 (21901) {G0,W17,D5,L2,V1,M2} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 4.29/4.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oone__class_Oone(
% 4.29/4.62 tc_Int_Oint ), X ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 4.29/4.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 4.29/4.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 4.29/4.62 (21902) {G0,W17,D5,L2,V1,M2} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_Int_Oint, X, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 4.29/4.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 4.29/4.62 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 4.29/4.62 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 4.29/4.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 4.29/4.62 (21903) {G0,W12,D4,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 4.29/4.62 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 4.29/4.62 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ),
% 4.29/4.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 4.29/4.62 (21904) {G0,W12,D4,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_Int_Oint, Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 4.29/4.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 4.29/4.62 tc_Int_Oint ) ), X ) }.
% 4.29/4.62 (21905) {G0,W12,D4,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus( tc_Int_Oint, X,
% 4.29/4.62 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ),
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 4.29/4.62 (21906) {G0,W12,D4,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 4.29/4.62 tc_Int_Oint, Y, X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 4.29/4.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 4.29/4.62 tc_Int_Oint ) ) ) }.
% 4.29/4.62 (21907) {G0,W8,D2,L2,V2,M2} { ! c_Orderings_Oord__class_Oless( tc_Int_Oint
% 4.29/4.62 , Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 4.29/4.62 (21908) {G0,W7,D2,L2,V2,M2} { ! c_Orderings_Oord__class_Oless( tc_Int_Oint
% 4.29/4.62 , Y, X ), ! Y = X }.
% 4.29/4.62 (21909) {G0,W11,D2,L3,V2,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 4.29/4.62 tc_Int_Oint, Y, X ), Y = X, c_Orderings_Oord__class_Oless( tc_Int_Oint, Y
% 4.29/4.62 , X ) }.
% 4.29/4.62 (21910) {G0,W11,D2,L3,V2,M3} { c_Orderings_Oord__class_Oless( tc_Int_Oint
% 4.29/4.62 , Y, X ), Y = X, c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 4.29/4.62 (21911) {G0,W10,D3,L2,V2,M2} { ! c_RealDef_Oreal( tc_Nat_Onat, Y ) =
% 4.29/4.62 c_RealDef_Oreal( tc_Nat_Onat, X ), Y = X }.
% 4.29/4.62 (21912) {G0,W10,D3,L2,V2,M2} { ! Y = X, c_RealDef_Oreal( tc_Nat_Onat, Y )
% 4.29/4.62 = c_RealDef_Oreal( tc_Nat_Onat, X ) }.
% 4.29/4.62 (21913) {G0,W9,D4,L1,V1,M1} { c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal
% 4.29/4.62 , c_RealDef_Oreal( tc_Nat_Onat, X ) ) = c_RealDef_Oreal( tc_Nat_Onat, X )
% 4.29/4.62 }.
% 4.29/4.62 (21914) {G0,W13,D5,L1,V2,M1} { hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 4.29/4.62 tc_Int_Oint ), Y ), X ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 4.29/4.62 tc_Int_Oint ), X ), Y ) }.
% 4.29/4.62 (21915) {G0,W24,D6,L1,V3,M1} { hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 4.29/4.62 tc_Int_Oint ), Z ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) =
% 4.29/4.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 4.29/4.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 4.29/4.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 4.29/4.62 (21916) {G0,W23,D7,L1,V3,M1} { hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 4.29/4.62 tc_Int_Oint ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 4.29/4.62 Z ), Y ) ), X ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint
% 4.29/4.62 ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X
% 4.29/4.62 ) ) }.
% 4.29/4.62 (21917) {G0,W24,D6,L1,V3,M1} { hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 4.29/4.62 tc_Int_Oint ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ), X ) =
% 4.29/4.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 4.29/4.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 4.29/4.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 4.29/4.62 (21918) {G0,W7,D4,L1,V1,M1} { c_Groups_Oplus__class_Oplus( tc_Int_Oint, X
% 4.29/4.62 , c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) = X }.
% 4.29/4.62 (21919) {G0,W7,D4,L1,V1,M1} { c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 4.29/4.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ) = X }.
% 4.29/4.62 (21920) {G0,W14,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_Int_Oint, Y, X ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 4.29/4.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, Z ),
% 4.29/4.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }.
% 4.29/4.62 (21921) {G0,W18,D3,L3,V4,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_Int_Oint, Y, X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T
% 4.29/4.62 , Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 4.29/4.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, T ),
% 4.29/4.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }.
% 4.29/4.62 (21922) {G0,W23,D5,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_Int_Oint, Y, X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 4.29/4.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ),
% 4.29/4.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 4.29/4.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 4.29/4.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 4.29/4.62 (21923) {G0,W6,D4,L1,V1,M1} { c_RComplete_Onatceiling( c_RealDef_Oreal(
% 4.29/4.62 tc_Nat_Onat, X ) ) = X }.
% 4.29/4.62 (21924) {G0,W6,D4,L1,V1,M1} { c_RComplete_Onatfloor( c_RealDef_Oreal(
% 4.29/4.62 tc_Nat_Onat, X ) ) = X }.
% 4.29/4.62 (21925) {G0,W10,D3,L2,V1,M2} { ! c_RealDef_Oreal( tc_Nat_Onat, X ) =
% 4.29/4.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X =
% 4.29/4.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 4.29/4.62 (21926) {G0,W10,D3,L2,V1,M2} { ! X = c_Groups_Ozero__class_Ozero(
% 4.29/4.62 tc_Nat_Onat ), c_RealDef_Oreal( tc_Nat_Onat, X ) =
% 4.29/4.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 4.29/4.62 (21927) {G0,W7,D4,L1,V0,M1} { c_RealDef_Oreal( tc_Nat_Onat,
% 4.29/4.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 4.29/4.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 4.29/4.62 (21928) {G0,W7,D3,L1,V1,M1} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_RealDef_Oreal, c_RealDef_Oreal( tc_Nat_Onat, X ),
% 4.29/4.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 4.29/4.62 (21929) {G0,W12,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_RealDef_Oreal, c_RealDef_Oreal( tc_Nat_Onat, Y ), c_RealDef_Oreal(
% 4.29/4.62 tc_Nat_Onat, X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 4.29/4.62 }.
% 4.29/4.62 (21930) {G0,W12,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 4.29/4.62 c_RealDef_Oreal( tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) )
% 4.29/4.62 }.
% 4.29/4.62 (21931) {G0,W12,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 4.29/4.62 tc_RealDef_Oreal, c_RealDef_Oreal( tc_Nat_Onat, Y ), c_RealDef_Oreal(
% 4.29/4.62 tc_Nat_Onat, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 4.29/4.62 ) }.
% 4.29/4.62 (21932) {G0,W12,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 4.29/4.62 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal
% 4.29/4.62 , c_RealDef_Oreal( tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) )
% 4.29/4.62 }.
% 4.29/4.62 (21933) {G0,W19,D6,L1,V2,M1} { c_RealDef_Oreal( tc_Nat_Onat, hAPP( hAPP(
% 4.29/4.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP(
% 4.29/4.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 4.29/4.62 tc_Nat_Onat, Y ) ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 4.29/4.62 (21934) {G0,W15,D4,L1,V2,M1} { c_RealDef_Oreal( tc_Nat_Onat,
% 4.29/4.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 4.29/4.62 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 4.29/4.62 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 4.29/4.62 (21935) {G0,W7,D4,L1,V0,M1} { c_RealDef_Oreal( tc_Nat_Onat,
% 4.29/4.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone(
% 4.29/4.62 tc_RealDef_Oreal ) }.
% 4.29/4.62 (21936) {G0,W21,D6,L2,V2,M2} { ! X = c_RealDef_Oreal( tc_Nat_Onat,
% 4.29/4.62 c_RComplete_Onatfloor( X ) ), c_RComplete_Onatfloor( hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), X ), Y ) ) = hAPP( hAPP
% 4.29/4.62 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), c_RComplete_Onatfloor( X )
% 4.29/4.62 ), Y ) }.
% 4.29/4.62 (21937) {G0,W7,D4,L1,V1,M1} { c_Orderings_Oord__class_Oless__eq(
% 4.29/4.62 tc_RealDef_Oreal, X, c_RealDef_Oreal( tc_Nat_Onat,
% 4.29/4.62 c_RComplete_Onatceiling( X ) ) ) }.
% 4.29/4.62 (21938) {G0,W11,D3,L2,V1,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 4.29/4.62 tc_RealDef_Oreal, c_RealDef_Oreal( tc_Nat_Onat, X ),
% 4.29/4.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X =
% 4.29/4.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 4.29/4.62 (21939) {G0,W11,D3,L2,V1,M2} { ! X = c_Groups_Ozero__class_Ozero(
% 4.29/4.62 tc_Nat_Onat ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 4.29/4.62 c_RealDef_Oreal( tc_Nat_Onat, X ), c_Groups_Ozero__class_Ozero(
% 4.29/4.62 tc_RealDef_Oreal ) ) }.
% 4.29/4.62 (21940) {G0,W12,D4,L2,V1,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 4.29/4.62 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 4.29/4.62 tc_Nat_Onat, c_RComplete_Onatfloor( X ) ), X ) }.
% 4.29/4.62 (21941) {G0,W11,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 4.29/4.62 tc_RealDef_Oreal, c_RealDef_Oreal( tc_Nat_Onat, Y ), X ),
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_RComplete_Onatfloor
% 4.29/4.62 ( X ) ) }.
% 4.29/4.62 (21942) {G0,W11,D5,L1,V4,M1} { hAPP( hAPP( c_Power_Opower_Opower( T, Z, Y
% 4.29/4.62 ), X ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = Z }.
% 4.29/4.62 (21943) {G0,W11,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 4.29/4.62 tc_RealDef_Oreal, Y, c_RealDef_Oreal( tc_Nat_Onat, X ) ),
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 4.29/4.62 Y ), X ) }.
% 4.29/4.62 (21944) {G0,W12,D3,L2,V1,M2} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 4.29/4.62 c_RealDef_Oreal( tc_Nat_Onat, X ) ), c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 4.29/4.62 (21945) {G0,W12,D3,L2,V1,M2} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 4.29/4.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 4.29/4.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 4.29/4.62 tc_Nat_Onat, X ) ) }.
% 4.29/4.62 (21946) {G0,W16,D4,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal
% 4.29/4.62 , c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 4.29/4.62 tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 4.29/4.62 c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 4.29/4.62 (21947) {G0,W16,D4,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 4.29/4.62 tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 4.29/4.62 c_RealDef_Oreal( tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone(
% 4.29/4.62 tc_RealDef_Oreal ) ), c_RealDef_Oreal( tc_Nat_Onat, X ) ),
% 4.29/4.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 4.29/4.62 (21948) {G0,W16,D4,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 4.29/4.62 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 4.29/4.62 c_RealDef_Oreal( tc_Nat_Onat, Y ), c_Groups_Oplus__class_Oplus(
% 4.29/4.62 tc_RealDef_Oreal, c_RealDef_Oreal( tc_Nat_Onat, X ),
% 4.29/4.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) }.
% 4.29/4.62 (21949) {G0,W16,D4,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_RealDef_Oreal, c_RealDef_Oreal( tc_Nat_Onat, Y ),
% 4.29/4.62 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 4.29/4.62 tc_Nat_Onat, X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ),
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 4.29/4.62 (21950) {G0,W16,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 4.29/4.62 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_RComplete_Onatfloor
% 4.29/4.62 ( X ) ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 4.29/4.62 c_RealDef_Oreal( tc_Nat_Onat, Y ), X ) }.
% 4.29/4.62 (21951) {G0,W16,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 4.29/4.62 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 4.29/4.62 tc_Nat_Onat, Y ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 4.29/4.62 , c_RComplete_Onatfloor( X ) ) }.
% 4.29/4.62 (21952) {G0,W16,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 4.29/4.62 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling
% 4.29/4.62 ( X ), Y ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 4.29/4.62 c_RealDef_Oreal( tc_Nat_Onat, Y ) ) }.
% 4.29/4.62 (21953) {G0,W16,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 4.29/4.62 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, c_RealDef_Oreal
% 4.29/4.62 ( tc_Nat_Onat, Y ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 4.29/4.62 c_RComplete_Onatceiling( X ), Y ) }.
% 4.29/4.62 (21954) {G0,W11,D5,L1,V1,M1} { c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_RealDef_Oreal, X, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 4.29/4.62 c_RealDef_Oreal( tc_Nat_Onat, c_RComplete_Onatfloor( X ) ),
% 4.29/4.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) }.
% 4.29/4.62 (21955) {G0,W16,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 4.29/4.62 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 4.29/4.62 tc_Nat_Onat, Y ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 4.29/4.62 c_RComplete_Onatfloor( X ), Y ) }.
% 4.29/4.62 (21956) {G0,W18,D5,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 4.29/4.62 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 4.29/4.62 c_RComplete_Onatfloor( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 4.29/4.62 c_RealDef_Oreal( tc_Nat_Onat, Y ) ) ) = c_Groups_Oplus__class_Oplus(
% 4.29/4.62 tc_Nat_Onat, c_RComplete_Onatfloor( X ), Y ) }.
% 4.29/4.62 (21957) {G0,W15,D4,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 4.29/4.62 tc_Nat_Onat, c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 4.29/4.62 c_RComplete_Onatfloor( Y ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X
% 4.29/4.62 ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, c_RealDef_Oreal(
% 4.29/4.62 tc_Nat_Onat, X ) ) }.
% 4.29/4.62 (21958) {G0,W20,D4,L3,V2,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 4.29/4.62 tc_RealDef_Oreal, c_RealDef_Oreal( tc_Nat_Onat, Y ), X ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 4.29/4.62 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 4.29/4.62 tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ),
% 4.29/4.62 c_RComplete_Onatfloor( X ) = Y }.
% 4.29/4.62 (21959) {G0,W18,D5,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 4.29/4.62 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 4.29/4.62 c_RComplete_Onatceiling( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X
% 4.29/4.62 , c_RealDef_Oreal( tc_Nat_Onat, Y ) ) ) = c_Groups_Oplus__class_Oplus(
% 4.29/4.62 tc_Nat_Onat, c_RComplete_Onatceiling( X ), Y ) }.
% 4.29/4.62 (21960) {G0,W29,D6,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 4.29/4.62 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 4.29/4.62 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 4.29/4.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 4.29/4.62 tc_Nat_Onat, Y ) ), X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 4.29/4.62 , hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 4.29/4.62 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 4.29/4.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ), Y ) ) }.
% 4.29/4.62 (21961) {G0,W19,D5,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ), X =
% 4.29/4.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Orderings_Oord__class_Oless
% 4.29/4.62 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 4.29/4.62 (21962) {G0,W14,D5,L2,V2,M2} { ! X = c_Groups_Ozero__class_Ozero(
% 4.29/4.62 tc_Nat_Onat ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 4.29/4.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 4.29/4.62 (21963) {G0,W15,D5,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 4.29/4.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 4.29/4.62 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 4.29/4.62 ), X ) ) }.
% 4.29/4.62 (21964) {G0,W25,D6,L4,V3,M4} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), ! X =
% 4.29/4.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, hAPP( hAPP(
% 4.29/4.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ),
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oone__class_Oone
% 4.29/4.62 ( tc_Int_Oint ), Y ) }.
% 4.29/4.62 (21965) {G0,W14,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 4.29/4.62 tc_Int_Oint, Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 4.29/4.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ),
% 4.29/4.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 4.29/4.62 (21966) {G0,W15,D4,L1,V3,M1} { c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 4.29/4.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ), X ) =
% 4.29/4.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus
% 4.29/4.62 ( tc_Int_Oint, Y, X ) ) }.
% 4.29/4.62 (21967) {G0,W15,D4,L1,V3,M1} { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z
% 4.29/4.62 , c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) =
% 4.29/4.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus
% 4.29/4.62 ( tc_Int_Oint, Z, X ) ) }.
% 4.29/4.62 (21968) {G0,W9,D3,L1,V2,M1} { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y
% 4.29/4.62 , X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) }.
% 4.29/4.62 (21969) {G0,W11,D2,L3,V2,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 4.29/4.62 tc_Int_Oint, Y, X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X
% 4.29/4.62 , Y ), Y = X }.
% 4.29/4.62 (21970) {G0,W12,D2,L3,V3,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 4.29/4.62 tc_Int_Oint, Y, X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X
% 4.29/4.62 , Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, Z ) }.
% 4.29/4.62 (21971) {G0,W8,D2,L2,V2,M2} { c_Orderings_Oord__class_Oless__eq(
% 4.29/4.62 tc_Int_Oint, Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y
% 4.29/4.62 ) }.
% 4.29/4.62 (21972) {G0,W4,D2,L1,V1,M1} { c_Orderings_Oord__class_Oless__eq(
% 4.29/4.62 tc_Int_Oint, X, X ) }.
% 4.29/4.62 (21973) {G0,W27,D6,L4,V3,M4} { ! c_Orderings_Oord__class_Oless__eq(
% 4.29/4.62 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 4.29/4.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 4.29/4.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 4.29/4.62 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 4.29/4.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 4.29/4.62 (21974) {G0,W28,D6,L4,V3,M4} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 4.29/4.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ),
% 4.29/4.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 4.29/4.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 4.29/4.62 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 4.29/4.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 4.29/4.62 (21975) {G0,W37,D6,L5,V5,M5} { ! c_Orderings_Oord__class_Oless__eq(
% 4.29/4.62 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 4.29/4.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 4.29/4.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 4.29/4.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 4.29/4.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, U ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, U ),
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Y ) }.
% 4.29/4.62 (21976) {G0,W54,D6,L7,V6,M7} { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint
% 4.29/4.62 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T )
% 4.29/4.62 = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 4.29/4.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 4.29/4.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 4.29/4.62 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 4.29/4.62 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 4.29/4.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 4.29/4.62 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 4.29/4.62 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, U, Y ) }.
% 4.29/4.62 (21977) {G0,W37,D6,L5,V5,M5} { ! c_Orderings_Oord__class_Oless__eq(
% 4.29/4.62 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 4.29/4.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 4.29/4.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 4.29/4.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 4.29/4.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, X ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, Z ),
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, T ) }.
% 4.29/4.62 (21978) {G0,W54,D6,L7,V6,M7} { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint
% 4.29/4.62 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T )
% 4.29/4.62 = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 4.29/4.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 4.29/4.62 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 4.29/4.62 ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, T, W ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 4.29/4.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 4.29/4.62 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 4.29/4.62 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, U ) }.
% 4.29/4.62 (21979) {G0,W26,D6,L4,V3,M4} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), ! X =
% 4.29/4.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, hAPP( hAPP(
% 4.29/4.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 4.29/4.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ),
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 4.29/4.62 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 4.29/4.62 (21980) {G0,W15,D5,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 4.29/4.62 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 4.29/4.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) }.
% 4.29/4.62 (21981) {G0,W20,D5,L3,V2,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 4.29/4.62 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 4.29/4.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 4.29/4.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 4.29/4.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) }.
% 4.29/4.62 (21982) {G0,W18,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 4.29/4.62 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 4.29/4.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 4.29/4.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 4.29/4.62 tc_Int_Oint, X, Y ) ) }.
% 4.29/4.62 (21983) {G0,W6,D3,L1,V0,M1} { c_Orderings_Oord__class_Oless__eq(
% 4.29/4.62 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 4.29/4.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 4.29/4.62 (21984) {G0,W6,D3,L1,V0,M1} { c_Orderings_Oord__class_Oless__eq(
% 4.29/4.62 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 4.29/4.62 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 4.29/4.62 (21985) {G0,W23,D5,L3,V2,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 4.29/4.62 tc_RealDef_Oreal, c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 4.29/4.62 tc_Nat_Onat ), Y ), c_RComplete_Onatfloor(
% 4.29/4.62 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 4.29/4.62 tc_Nat_Onat, Y ) ) ) = c_Divides_Odiv__class_Odiv( tc_Nat_Onat,
% 4.29/4.62 c_RComplete_Onatfloor( X ), Y ) }.
% 4.29/4.62 (21986) {G0,W17,D3,L4,V4,M4} { ! class_Orderings_Oorder( X ), !
% 4.29/4.62 c_SEQ_Odecseq( X, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 4.29/4.62 Z, T ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, T ), hAPP( Y, Z )
% 4.29/4.62 ) }.
% 4.29/4.62 (21987) {G0,W13,D3,L3,V2,M3} { ! class_Orderings_Oorder( X ),
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, skol24( X, Y ), skol52( X
% 4.29/4.62 , Y ) ), c_SEQ_Odecseq( X, Y ) }.
% 4.29/4.62 (21988) {G0,W17,D4,L3,V2,M3} { ! class_Orderings_Oorder( X ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, skol52( X, Y ) ), hAPP( Y
% 4.29/4.62 , skol24( X, Y ) ) ), c_SEQ_Odecseq( X, Y ) }.
% 4.29/4.62 (21989) {G0,W17,D3,L3,V4,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 4.29/4.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 4.29/4.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 4.29/4.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol25( Z, T ) ) }.
% 4.29/4.62 (21990) {G0,W20,D5,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 4.29/4.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), skol25( X, Y ) ), X ) =
% 4.29/4.62 Y }.
% 4.29/4.62 (21991) {G0,W28,D5,L5,V3,M5} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 4.29/4.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 4.29/4.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), ! hAPP( hAPP(
% 4.29/4.62 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Z ), X ) = Y, Z =
% 4.29/4.62 skol25( X, Y ) }.
% 4.29/4.62 (21992) {G0,W21,D6,L2,V3,M2} { ! Z = c_Groups_Ozero__class_Ozero(
% 4.29/4.62 tc_Nat_Onat ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 4.29/4.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 4.29/4.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) =
% 4.29/4.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 4.29/4.62 (21993) {G0,W23,D6,L2,V3,M2} { Z = c_Groups_Ozero__class_Ozero(
% 4.29/4.62 tc_Nat_Onat ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 4.29/4.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 4.29/4.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) =
% 4.29/4.62 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) }.
% 4.29/4.62 (21994) {G0,W14,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 4.29/4.62 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 4.29/4.62 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, Z ),
% 4.29/4.62 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, X, Z ) ) }.
% 4.29/4.62 (21995) {G0,W7,D3,L1,V2,M1} { c_Orderings_Oord__class_Oless__eq(
% 4.29/4.62 tc_Nat_Onat, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ), Y ) }.
% 4.29/4.62 (21996) {G0,W17,D6,L1,V3,M1} { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z
% 4.29/4.62 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) =
% 4.29/4.62 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 4.29/4.62 tc_Nat_Onat, Z, Y ), X ) }.
% 4.29/4.62 (21997) {G0,W11,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_Nat_Onat, Y, X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) =
% 4.29/4.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 4.29/4.62 (21998) {G0,W10,D4,L2,V2,M2} { ! class_Divides_Osemiring__div( X ),
% 4.29/4.62 c_Divides_Odiv__class_Odiv( X, c_Groups_Ozero__class_Ozero( X ), Y ) =
% 4.29/4.62 c_Groups_Ozero__class_Ozero( X ) }.
% 4.29/4.62 (21999) {G0,W10,D4,L2,V2,M2} { ! class_Divides_Osemiring__div( X ),
% 4.29/4.62 c_Divides_Odiv__class_Odiv( X, Y, c_Groups_Ozero__class_Ozero( X ) ) =
% 4.29/4.62 c_Groups_Ozero__class_Ozero( X ) }.
% 4.29/4.62 (22000) {G0,W9,D4,L2,V2,M2} { ! class_Divides_Osemiring__div( X ),
% 4.29/4.62 c_Divides_Odiv__class_Odiv( X, Y, c_Groups_Oone__class_Oone( X ) ) = Y
% 4.29/4.62 }.
% 4.29/4.62 (22001) {G0,W25,D6,L3,V4,M3} { ! class_Divides_Osemiring__div( X ), Y =
% 4.29/4.62 c_Groups_Ozero__class_Ozero( X ), c_Divides_Odiv__class_Odiv( X, hAPP(
% 4.29/4.62 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 4.29/4.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) =
% 4.29/4.62 c_Divides_Odiv__class_Odiv( X, T, Z ) }.
% 4.29/4.62 (22002) {G0,W25,D6,L3,V4,M3} { ! class_Divides_Osemiring__div( X ), Y =
% 4.29/4.62 c_Groups_Ozero__class_Ozero( X ), c_Divides_Odiv__class_Odiv( X, hAPP(
% 4.29/4.62 hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 4.29/4.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 4.29/4.62 c_Divides_Odiv__class_Odiv( X, T, Z ) }.
% 4.29/4.62 (22003) {G0,W17,D6,L3,V3,M3} { ! class_Divides_Osemiring__div( X ), Y =
% 4.29/4.62 c_Groups_Ozero__class_Ozero( X ), c_Divides_Odiv__class_Odiv( X, hAPP(
% 4.29/4.62 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) = Z }.
% 4.29/4.62 (22004) {G0,W17,D6,L3,V3,M3} { ! class_Divides_Osemiring__div( X ), Y =
% 4.29/4.62 c_Groups_Ozero__class_Ozero( X ), c_Divides_Odiv__class_Odiv( X, hAPP(
% 4.29/4.62 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = Z }.
% 4.29/4.62 (22005) {G0,W23,D6,L3,V4,M3} { ! class_Divides_Osemiring__div( X ), ! T =
% 4.29/4.62 c_Groups_Ozero__class_Ozero( X ), c_Divides_Odiv__class_Odiv( X, hAPP(
% 4.29/4.62 hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 4.29/4.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 4.29/4.62 c_Groups_Ozero__class_Ozero( X ) }.
% 4.29/4.62 (22006) {G0,W25,D6,L3,V4,M3} { ! class_Divides_Osemiring__div( X ), T =
% 4.29/4.62 c_Groups_Ozero__class_Ozero( X ), c_Divides_Odiv__class_Odiv( X, hAPP(
% 4.29/4.62 hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 4.29/4.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 4.29/4.62 c_Divides_Odiv__class_Odiv( X, Z, Y ) }.
% 4.29/4.62 (22007) {G0,W13,D3,L3,V2,M3} { ! class_Divides_Osemiring__div( X ), Y =
% 4.29/4.62 c_Groups_Ozero__class_Ozero( X ), c_Divides_Odiv__class_Odiv( X, Y, Y ) =
% 4.29/4.62 c_Groups_Oone__class_Oone( X ) }.
% 4.29/4.62 (22008) {G0,W19,D3,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ),
% 4.29/4.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 4.29/4.62 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, Y ),
% 4.29/4.62 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, X ) ) }.
% 4.29/4.62 (22009) {G0,W16,D6,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 4.29/4.62 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 4.29/4.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ) = Y }.
% 4.29/4.62 (22010) {G0,W16,D6,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 4.29/4.62 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 4.29/4.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ) = Y }.
% 4.29/4.62 (22011) {G0,W24,D6,L2,V3,M2} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 4.29/4.62 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 4.29/4.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 4.29/4.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) =
% 4.29/4.62 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, Y ) }.
% 4.29/4.62 (22012) {G0,W17,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.62 tc_Nat_Onat, c_Groups_Oone__class_Oone( tc_Nat_Onat ), X ), !
% 4.29/4.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 4.29/4.62 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 4.29/4.62 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ), Y ) }.
% 4.29/4.62 (22013) {G0,W16,D4,L1,V2,M1} { c_Orderings_Oord__class_Oless__eq(
% 4.29/4.62 tc_RealDef_Oreal, c_RealDef_Oreal( tc_Nat_Onat,
% 4.29/4.62 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ),
% 4.29/4.62 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, c_RealDef_Oreal(
% 4.29/4.62 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) ) }.
% 4.29/4.62 (22014) {G0,W26,D7,L3,V4,M3} { ! class_Divides_Osemiring__div( X ), Y =
% 4.29/4.62 c_Groups_Ozero__class_Ozero( X ), c_Divides_Odiv__class_Odiv( X,
% 4.29/4.62 c_Groups_Oplus__class_Oplus( X, T, hAPP( hAPP(
% 4.29/4.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) =
% 4.29/4.62 c_Groups_Oplus__class_Oplus( X, Z, c_Divides_Odiv__class_Odiv( X, T, Y )
% 4.29/4.62 ) }.
% 4.29/4.62 (22015) {G0,W26,D7,L3,V4,M3} { ! class_Divides_Osemiring__div( X ), Y =
% 4.29/4.62 c_Groups_Ozero__class_Ozero( X ), c_Divides_Odiv__class_Odiv( X,
% 4.29/4.62 c_Groups_Oplus__class_Oplus( X, T, hAPP( hAPP(
% 4.29/4.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) =
% 4.29/4.62 c_Groups_Oplus__class_Oplus( X, Z, c_Divides_Odiv__class_Odiv( X, T, Y )
% 4.29/4.62 ) }.
% 4.29/4.62 (22016) {G0,W22,D4,L3,V3,M3} { ! class_Divides_Osemiring__div( X ), Y =
% 4.29/4.62 c_Groups_Ozero__class_Ozero( X ), c_Divides_Odiv__class_Odiv( X,
% 4.29/4.62 c_Groups_Oplus__class_Oplus( X, Y, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 4.29/4.62 ( X, c_Divides_Odiv__class_Odiv( X, Z, Y ), c_Groups_Oone__class_Oone( X
% 4.29/4.62 ) ) }.
% 4.29/4.62 (22017) {G0,W22,D4,L3,V3,M3} { ! class_Divides_Osemiring__div( X ), Y =
% 4.29/4.62 c_Groups_Ozero__class_Ozero( X ), c_Divides_Odiv__class_Odiv( X,
% 4.29/4.62 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = c_Groups_Oplus__class_Oplus
% 4.29/4.62 ( X, c_Divides_Odiv__class_Odiv( X, Z, Y ), c_Groups_Oone__class_Oone( X
% 4.29/4.62 ) ) }.
% 4.29/4.62 (22018) {G0,W10,D4,L2,V3,M2} { ! hBOOL( hAPP( Z,
% 4.29/4.63 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ), alpha17( X, Z ) }.
% 4.29/4.63 (22019) {G0,W11,D4,L2,V3,M2} { ! hBOOL( hAPP( Z,
% 4.29/4.63 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ), alpha41( X, Y, Z )
% 4.29/4.63 }.
% 4.29/4.63 (22020) {G0,W14,D4,L3,V3,M3} { ! alpha17( X, Z ), ! alpha41( X, Y, Z ),
% 4.29/4.63 hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ) }.
% 4.29/4.63 (22021) {G0,W12,D3,L3,V3,M3} { ! alpha41( X, Y, Z ), X =
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha52( X, Y, Z ) }.
% 4.29/4.63 (22022) {G0,W8,D3,L2,V3,M2} { ! X = c_Groups_Ozero__class_Ozero(
% 4.29/4.63 tc_Nat_Onat ), alpha41( X, Y, Z ) }.
% 4.29/4.63 (22023) {G0,W8,D2,L2,V3,M2} { ! alpha52( X, Y, Z ), alpha41( X, Y, Z ) }.
% 4.29/4.63 (22024) {G0,W13,D2,L3,V4,M3} { ! alpha52( X, Y, Z ), !
% 4.29/4.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, X ), alpha61( X, Y, Z, T )
% 4.29/4.63 }.
% 4.29/4.63 (22025) {G0,W11,D3,L2,V5,M2} { c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 4.29/4.63 , skol26( X, T, U ), X ), alpha52( X, Y, Z ) }.
% 4.29/4.63 (22026) {G0,W12,D3,L2,V3,M2} { ! alpha61( X, Y, Z, skol26( X, Y, Z ) ),
% 4.29/4.63 alpha52( X, Y, Z ) }.
% 4.29/4.63 (22027) {G0,W20,D6,L3,V5,M3} { ! alpha61( X, Y, Z, T ), ! Y =
% 4.29/4.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ), hBOOL( hAPP
% 4.29/4.63 ( Z, U ) ) }.
% 4.29/4.63 (22028) {G0,W13,D4,L2,V7,M2} { ! hBOOL( hAPP( Z, skol27( U, W, Z, V0 ) ) )
% 4.29/4.63 , alpha61( X, Y, Z, T ) }.
% 4.29/4.63 (22029) {G0,W20,D6,L2,V4,M2} { Y = c_Groups_Oplus__class_Oplus(
% 4.29/4.63 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 4.29/4.63 ), skol27( X, Y, Z, T ) ), T ), alpha61( X, Y, Z, T ) }.
% 4.29/4.63 (22030) {G0,W12,D4,L3,V2,M3} { ! alpha17( X, Y ), ! X =
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( Y,
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 4.29/4.63 (22031) {G0,W7,D3,L2,V2,M2} { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 4.29/4.63 ), alpha17( X, Y ) }.
% 4.29/4.63 (22032) {G0,W8,D4,L2,V2,M2} { ! hBOOL( hAPP( Y,
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha17( X, Y ) }.
% 4.29/4.63 (22033) {G0,W17,D3,L3,V4,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.63 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), !
% 4.29/4.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 4.29/4.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol28( Z, T ) ) }.
% 4.29/4.63 (22034) {G0,W20,D5,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.63 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), !
% 4.29/4.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), hAPP( hAPP(
% 4.29/4.63 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), skol28( X, Y ) ), X ) =
% 4.29/4.63 Y }.
% 4.29/4.63 (22035) {G0,W33,D6,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.63 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 4.29/4.63 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, c_RealDef_Oreal(
% 4.29/4.63 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) =
% 4.29/4.63 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 4.29/4.63 tc_Nat_Onat, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ),
% 4.29/4.63 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, c_RealDef_Oreal(
% 4.29/4.63 tc_Nat_Onat, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ),
% 4.29/4.63 c_RealDef_Oreal( tc_Nat_Onat, X ) ) ) }.
% 4.29/4.63 (22036) {G0,W12,D3,L3,V4,M3} { ! class_RealVector_Oreal__normed__vector( X
% 4.29/4.63 ), ! c_SEQ_OBseq( X, Y ), c_Orderings_Oord__class_Oless(
% 4.29/4.63 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol29
% 4.29/4.63 ( Z, T ) ) }.
% 4.29/4.63 (22037) {G0,W15,D4,L3,V3,M3} { ! class_RealVector_Oreal__normed__vector( X
% 4.29/4.63 ), ! c_SEQ_OBseq( X, Y ), c_Orderings_Oord__class_Oless__eq(
% 4.29/4.63 tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( X, hAPP( Y, Z ) ),
% 4.29/4.63 skol29( X, Y ) ) }.
% 4.29/4.63 (22038) {G0,W21,D5,L4,V3,M4} { ! class_RealVector_Oreal__normed__vector( X
% 4.29/4.63 ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), !
% 4.29/4.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 4.29/4.63 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol53( X, Y, Z ) ) ), Z ),
% 4.29/4.63 c_SEQ_OBseq( X, Y ) }.
% 4.29/4.63 (22039) {G0,W23,D7,L2,V4,M2} { ! class_Fields_Ofield( X ),
% 4.29/4.63 c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly( X ), T, hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y ) ) =
% 4.29/4.63 c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly( X ),
% 4.29/4.63 c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly( X ), T, Z ), Y ) }.
% 4.29/4.63 (22040) {G0,W33,D6,L1,V3,M1} { c_Divides_Odiv__class_Odiv( tc_Nat_Onat,
% 4.29/4.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ) =
% 4.29/4.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 4.29/4.63 tc_Nat_Onat, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, X ),
% 4.29/4.63 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ),
% 4.29/4.63 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 4.29/4.63 tc_Nat_Onat, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, X ),
% 4.29/4.63 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ), X ) ) }.
% 4.29/4.63 (22041) {G0,W12,D4,L2,V3,M2} { ! class_Divides_Osemiring__div( X ),
% 4.29/4.63 c_Divides_Odiv__class_Odiv( X, c_Divides_Odiv__class_Omod( X, Z, Y ), Y )
% 4.29/4.63 = c_Groups_Ozero__class_Ozero( X ) }.
% 4.29/4.63 (22042) {G0,W8,D4,L1,V1,M1} { c_Divides_Odiv__class_Odiv( tc_Int_Oint,
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ) =
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 4.29/4.63 (22043) {G0,W18,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 4.29/4.63 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 4.29/4.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 4.29/4.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 4.29/4.63 tc_Int_Oint, X, Y ) ) }.
% 4.29/4.63 (22044) {G0,W18,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.63 tc_Int_Oint, X, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 4.29/4.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 4.29/4.63 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 4.29/4.63 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 4.29/4.63 (22045) {G0,W18,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.63 tc_Int_Oint, X, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 4.29/4.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 4.29/4.63 tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 4.29/4.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 4.29/4.63 tc_Int_Oint ), Y ) }.
% 4.29/4.63 (22046) {G0,W18,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.63 tc_Int_Oint, X, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 4.29/4.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 4.29/4.63 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 4.29/4.63 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ),
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 4.29/4.63 (22047) {G0,W18,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.63 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 4.29/4.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 4.29/4.63 tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 4.29/4.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 4.29/4.63 (22048) {G0,W18,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.63 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 4.29/4.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 4.29/4.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 4.29/4.63 tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 4.29/4.63 (22049) {G0,W11,D3,L2,V1,M2} { X = c_Groups_Ozero__class_Ozero(
% 4.29/4.63 tc_Int_Oint ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, X ) =
% 4.29/4.63 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 4.29/4.63 (22050) {G0,W10,D4,L2,V2,M2} { ! class_Divides_Osemiring__div( X ),
% 4.29/4.63 c_Divides_Odiv__class_Omod( X, Y, c_Groups_Oone__class_Oone( X ) ) =
% 4.29/4.63 c_Groups_Ozero__class_Ozero( X ) }.
% 4.29/4.63 (22051) {G0,W10,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.63 tc_Nat_Onat, Y, X ), c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) = Y
% 4.29/4.63 }.
% 4.29/4.63 (22052) {G0,W9,D3,L2,V2,M2} { ! class_Divides_Osemiring__div( X ),
% 4.29/4.63 c_Divides_Odiv__class_Omod( X, Y, Y ) = c_Groups_Ozero__class_Ozero( X )
% 4.29/4.63 }.
% 4.29/4.63 (22053) {G0,W9,D4,L2,V2,M2} { ! class_Divides_Osemiring__div( X ),
% 4.29/4.63 c_Divides_Odiv__class_Omod( X, Y, c_Groups_Ozero__class_Ozero( X ) ) = Y
% 4.29/4.63 }.
% 4.29/4.63 (22054) {G0,W10,D4,L2,V2,M2} { ! class_Divides_Osemiring__div( X ),
% 4.29/4.63 c_Divides_Odiv__class_Omod( X, c_Groups_Ozero__class_Ozero( X ), Y ) =
% 4.29/4.63 c_Groups_Ozero__class_Ozero( X ) }.
% 4.29/4.63 (22055) {G0,W12,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.63 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 4.29/4.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Divides_Odiv__class_Omod(
% 4.29/4.63 tc_Nat_Onat, Y, X ), X ) }.
% 4.29/4.63 (22056) {G0,W19,D7,L2,V4,M2} { ! class_Divides_Osemiring__div( X ),
% 4.29/4.63 c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X, T, hAPP(
% 4.29/4.63 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Z ) =
% 4.29/4.63 c_Divides_Odiv__class_Omod( X, T, Z ) }.
% 4.29/4.63 (22057) {G0,W19,D7,L2,V4,M2} { ! class_Divides_Osemiring__div( X ),
% 4.29/4.63 c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X, T, hAPP(
% 4.29/4.63 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) =
% 4.29/4.63 c_Divides_Odiv__class_Omod( X, T, Y ) }.
% 4.29/4.63 (22058) {G0,W14,D6,L2,V3,M2} { ! class_Divides_Osemiring__div( X ),
% 4.29/4.63 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 4.29/4.63 ( X ), Z ), Y ), Z ) = c_Groups_Ozero__class_Ozero( X ) }.
% 4.29/4.63 (22059) {G0,W14,D6,L2,V3,M2} { ! class_Divides_Osemiring__div( X ),
% 4.29/4.63 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 4.29/4.63 ( X ), Z ), Y ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 4.29/4.63 (22060) {G0,W17,D5,L2,V2,M2} { ! c_Divides_Odiv__class_Omod( tc_Nat_Onat,
% 4.29/4.63 Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol30( X, Y ) ) }.
% 4.29/4.63 (22061) {G0,W15,D5,L2,V3,M2} { ! Y = hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ),
% 4.29/4.63 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 4.29/4.63 (22062) {G0,W24,D6,L2,V4,M2} { ! class_Divides_Osemiring__div( X ),
% 4.29/4.63 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 4.29/4.63 ( X ), T ), Z ), Y ) = c_Divides_Odiv__class_Omod( X, hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( X ), T ), c_Divides_Odiv__class_Omod( X, Z
% 4.29/4.63 , Y ) ), Y ) }.
% 4.29/4.63 (22063) {G0,W24,D6,L2,V4,M2} { ! class_Divides_Osemiring__div( X ),
% 4.29/4.63 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 4.29/4.63 ( X ), T ), Z ), Y ) = c_Divides_Odiv__class_Omod( X, hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Omod( X, T, Y )
% 4.29/4.63 ), Z ), Y ) }.
% 4.29/4.63 (22064) {G0,W27,D6,L2,V4,M2} { ! class_Divides_Osemiring__div( X ),
% 4.29/4.63 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 4.29/4.63 ( X ), T ), Z ), Y ) = c_Divides_Odiv__class_Omod( X, hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Omod( X, T, Y )
% 4.29/4.63 ), c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 4.29/4.63 (22065) {G0,W26,D6,L2,V4,M2} { ! class_Divides_Osemiring__div( X ),
% 4.29/4.63 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 4.29/4.63 ( X ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y )
% 4.29/4.63 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ),
% 4.29/4.63 c_Divides_Odiv__class_Omod( X, Z, Y ) ) }.
% 4.29/4.63 (22066) {G0,W26,D6,L2,V4,M2} { ! class_Divides_Osemiring__div( X ),
% 4.29/4.63 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 4.29/4.63 ( X ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z )
% 4.29/4.63 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 4.29/4.63 c_Divides_Odiv__class_Omod( X, T, Y ) ), Z ) }.
% 4.29/4.63 (22067) {G0,W24,D6,L2,V4,M2} { ! class_Divides_Osemiring__div( X ),
% 4.29/4.63 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 4.29/4.63 ( X ), c_Divides_Odiv__class_Omod( X, T, Z ) ), Y ), Z ) =
% 4.29/4.63 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 4.29/4.63 ( X ), T ), Y ), Z ) }.
% 4.29/4.63 (22068) {G0,W39,D6,L4,V6,M4} { ! class_Divides_Osemiring__div( X ), !
% 4.29/4.63 c_Divides_Odiv__class_Omod( X, T, Z ) = c_Divides_Odiv__class_Omod( X, Y
% 4.29/4.63 , Z ), ! c_Divides_Odiv__class_Omod( X, W, Z ) =
% 4.29/4.63 c_Divides_Odiv__class_Omod( X, U, Z ), c_Divides_Odiv__class_Omod( X,
% 4.29/4.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), W ), Z ) =
% 4.29/4.63 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 4.29/4.63 ( X ), Y ), U ), Z ) }.
% 4.29/4.63 (22069) {G0,W17,D7,L1,V3,M1} { c_Divides_Odiv__class_Omod( tc_Nat_Onat,
% 4.29/4.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), X ), Y ) =
% 4.29/4.63 c_Divides_Odiv__class_Omod( tc_Nat_Onat, X, Y ) }.
% 4.29/4.63 (22070) {G0,W24,D6,L1,V3,M1} { hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 4.29/4.63 tc_Nat_Onat ), c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, Y ) ), X ) =
% 4.29/4.63 c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 4.29/4.63 (22071) {G0,W24,D6,L1,V3,M1} { hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 4.29/4.63 tc_Nat_Onat ), Z ), c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) =
% 4.29/4.63 c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 4.29/4.63 (22072) {G0,W35,D4,L4,V6,M4} { ! class_Divides_Osemiring__div( X ), !
% 4.29/4.63 c_Divides_Odiv__class_Omod( X, T, Z ) = c_Divides_Odiv__class_Omod( X, Y
% 4.29/4.63 , Z ), ! c_Divides_Odiv__class_Omod( X, W, Z ) =
% 4.29/4.63 c_Divides_Odiv__class_Omod( X, U, Z ), c_Divides_Odiv__class_Omod( X,
% 4.29/4.63 c_Groups_Oplus__class_Oplus( X, T, W ), Z ) = c_Divides_Odiv__class_Omod
% 4.29/4.63 ( X, c_Groups_Oplus__class_Oplus( X, Y, U ), Z ) }.
% 4.29/4.63 (22073) {G0,W20,D5,L2,V4,M2} { ! class_Divides_Osemiring__div( X ),
% 4.29/4.63 c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X,
% 4.29/4.63 c_Divides_Odiv__class_Omod( X, T, Z ), Y ), Z ) =
% 4.29/4.63 c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X, T, Y ), Z
% 4.29/4.63 ) }.
% 4.29/4.63 (22074) {G0,W20,D5,L2,V4,M2} { ! class_Divides_Osemiring__div( X ),
% 4.29/4.63 c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X, T,
% 4.29/4.63 c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) = c_Divides_Odiv__class_Omod
% 4.29/4.63 ( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) }.
% 4.29/4.63 (22075) {G0,W23,D5,L2,V4,M2} { ! class_Divides_Osemiring__div( X ),
% 4.29/4.63 c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y
% 4.29/4.63 ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X,
% 4.29/4.63 c_Divides_Odiv__class_Omod( X, T, Y ), c_Divides_Odiv__class_Omod( X, Z,
% 4.29/4.63 Y ) ), Y ) }.
% 4.29/4.63 (22076) {G0,W20,D5,L2,V4,M2} { ! class_Divides_Osemiring__div( X ),
% 4.29/4.63 c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y
% 4.29/4.63 ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X,
% 4.29/4.63 c_Divides_Odiv__class_Omod( X, T, Y ), Z ), Y ) }.
% 4.29/4.63 (22077) {G0,W20,D5,L2,V4,M2} { ! class_Divides_Osemiring__div( X ),
% 4.29/4.63 c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y
% 4.29/4.63 ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X, T,
% 4.29/4.63 c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 4.29/4.63 (22078) {G0,W14,D4,L2,V3,M2} { ! class_Divides_Osemiring__div( X ),
% 4.29/4.63 c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X, Z, Y ), Z
% 4.29/4.63 ) = c_Divides_Odiv__class_Omod( X, Y, Z ) }.
% 4.29/4.63 (22079) {G0,W14,D4,L2,V3,M2} { ! class_Divides_Osemiring__div( X ),
% 4.29/4.63 c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X, Z, Y ), Y
% 4.29/4.63 ) = c_Divides_Odiv__class_Omod( X, Z, Y ) }.
% 4.29/4.63 (22080) {G0,W14,D4,L2,V3,M2} { ! class_Divides_Osemiring__div( X ),
% 4.29/4.63 c_Divides_Odiv__class_Omod( X, c_Divides_Odiv__class_Omod( X, Z, Y ), Y )
% 4.29/4.63 = c_Divides_Odiv__class_Omod( X, Z, Y ) }.
% 4.29/4.63 (22081) {G0,W7,D3,L1,V2,M1} { c_Orderings_Oord__class_Oless__eq(
% 4.29/4.63 tc_Nat_Onat, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ), Y ) }.
% 4.29/4.63 (22082) {G0,W19,D6,L2,V3,M2} { ! class_Divides_Osemiring__div( X ),
% 4.29/4.63 c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, Z, Y ),
% 4.29/4.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 4.29/4.63 c_Divides_Odiv__class_Odiv( X, Z, Y ) ), Y ) ) = Z }.
% 4.29/4.63 (22083) {G0,W19,D6,L2,V3,M2} { ! class_Divides_Osemiring__div( X ),
% 4.29/4.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 4.29/4.63 ( X ), Z ), c_Divides_Odiv__class_Odiv( X, Y, Z ) ),
% 4.29/4.63 c_Divides_Odiv__class_Omod( X, Y, Z ) ) = Y }.
% 4.29/4.63 (22084) {G0,W19,D6,L2,V3,M2} { ! class_Divides_Osemiring__div( X ),
% 4.29/4.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 4.29/4.63 ( X ), c_Divides_Odiv__class_Odiv( X, Z, Y ) ), Y ),
% 4.29/4.63 c_Divides_Odiv__class_Omod( X, Z, Y ) ) = Z }.
% 4.29/4.63 (22085) {G0,W25,D7,L2,V4,M2} { ! class_Divides_Osemiring__div( X ),
% 4.29/4.63 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 4.29/4.63 hAPP( c_Groups_Otimes__class_Otimes( X ), T ), c_Divides_Odiv__class_Odiv
% 4.29/4.63 ( X, Z, T ) ), c_Divides_Odiv__class_Omod( X, Z, T ) ), Y ) =
% 4.29/4.63 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 4.29/4.63 (22086) {G0,W25,D7,L2,V4,M2} { ! class_Divides_Osemiring__div( X ),
% 4.29/4.63 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 4.29/4.63 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X,
% 4.29/4.63 T, Z ) ), Z ), c_Divides_Odiv__class_Omod( X, T, Z ) ), Y ) =
% 4.29/4.63 c_Groups_Oplus__class_Oplus( X, T, Y ) }.
% 4.29/4.63 (22087) {G0,W19,D3,L3,V3,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 4.29/4.63 tc_Int_Oint, Y, X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Z,
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 4.29/4.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 4.29/4.63 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ),
% 4.29/4.63 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ) ) }.
% 4.29/4.63 (22088) {G0,W19,D3,L3,V3,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 4.29/4.63 tc_Int_Oint, Y, X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ),
% 4.29/4.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 4.29/4.63 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ),
% 4.29/4.63 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ) ) }.
% 4.29/4.63 (22089) {G0,W16,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 4.29/4.63 tc_Int_Oint, X, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 4.29/4.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 4.29/4.63 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) =
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 4.29/4.63 (22090) {G0,W24,D3,L4,V3,M4} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.63 tc_Int_Oint, X, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 4.29/4.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 4.29/4.63 tc_Int_Oint ), Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 4.29/4.63 Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 4.29/4.63 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 4.29/4.63 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ) ) }.
% 4.29/4.63 (22091) {G0,W18,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 4.29/4.63 tc_Int_Oint, X, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 4.29/4.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 4.29/4.63 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 4.29/4.63 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 4.29/4.63 (22092) {G0,W18,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.63 tc_Int_Oint, X, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 4.29/4.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 4.29/4.63 tc_Int_Oint, Y, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y
% 4.29/4.63 , c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 4.29/4.63 (22093) {G0,W18,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.63 tc_Int_Oint, X, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 4.29/4.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 4.29/4.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 4.29/4.63 tc_Int_Oint, Y, X ) ) }.
% 4.29/4.63 (22094) {G0,W16,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 4.29/4.63 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 4.29/4.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ),
% 4.29/4.63 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) =
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 4.29/4.63 (22095) {G0,W18,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 4.29/4.63 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 4.29/4.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 4.29/4.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 4.29/4.63 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 4.29/4.63 (22096) {G0,W24,D3,L4,V3,M4} { ! c_Orderings_Oord__class_Oless__eq(
% 4.29/4.63 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 4.29/4.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 4.29/4.63 tc_Int_Oint ), Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 4.29/4.63 Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 4.29/4.63 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ),
% 4.29/4.63 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) }.
% 4.29/4.63 (22097) {G0,W17,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 4.29/4.63 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 4.29/4.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 4.29/4.63 tc_Int_Oint ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ),
% 4.29/4.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 4.29/4.63 (22098) {G0,W18,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 4.29/4.63 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 4.29/4.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 4.29/4.63 tc_Int_Oint ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ),
% 4.29/4.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 4.29/4.63 tc_Int_Oint ), Y ) }.
% 4.29/4.63 (22099) {G0,W22,D3,L4,V2,M4} { ! c_Orderings_Oord__class_Oless__eq(
% 4.29/4.63 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 4.29/4.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 4.29/4.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 4.29/4.63 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 4.29/4.63 tc_Int_Oint, X, Y ) ) }.
% 4.29/4.63 (22100) {G0,W17,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.63 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 4.29/4.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 4.29/4.63 tc_Int_Oint ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 4.29/4.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ) }.
% 4.29/4.63 (22101) {G0,W17,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.63 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 4.29/4.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ),
% 4.29/4.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 4.29/4.63 tc_Int_Oint ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) }.
% 4.29/4.63 (22102) {G0,W18,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.63 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 4.29/4.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 4.29/4.63 tc_Int_Oint, Y, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 4.29/4.63 (22103) {G0,W18,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.63 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 4.29/4.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 4.29/4.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 4.29/4.63 tc_Int_Oint, Y, X ) ) }.
% 4.29/4.63 (22104) {G0,W14,D3,L3,V2,M3} { ! c_Divides_Odiv__class_Odiv( tc_Int_Oint,
% 4.29/4.63 Y, X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X =
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), alpha18( X, Y ) }.
% 4.29/4.63 (22105) {G0,W11,D3,L2,V2,M2} { ! X = c_Groups_Ozero__class_Ozero(
% 4.29/4.63 tc_Int_Oint ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 4.29/4.63 (22106) {G0,W10,D3,L2,V2,M2} { ! alpha18( X, Y ),
% 4.29/4.63 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 4.29/4.63 (22107) {G0,W9,D2,L3,V2,M3} { ! alpha18( X, Y ), alpha42( X, Y ), alpha53
% 4.29/4.63 ( X, Y ) }.
% 4.29/4.63 (22108) {G0,W6,D2,L2,V2,M2} { ! alpha42( X, Y ), alpha18( X, Y ) }.
% 4.29/4.63 (22109) {G0,W6,D2,L2,V2,M2} { ! alpha53( X, Y ), alpha18( X, Y ) }.
% 4.29/4.63 (22110) {G0,W8,D3,L2,V2,M2} { ! alpha53( X, Y ),
% 4.29/4.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 4.29/4.63 (22111) {G0,W7,D2,L2,V2,M2} { ! alpha53( X, Y ),
% 4.29/4.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 4.29/4.63 (22112) {G0,W12,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 4.29/4.63 tc_Int_Oint, Y, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 4.29/4.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ), alpha53( X, Y ) }.
% 4.29/4.63 (22113) {G0,W8,D3,L2,V2,M2} { ! alpha42( X, Y ),
% 4.29/4.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 4.29/4.63 (22114) {G0,W7,D2,L2,V2,M2} { ! alpha42( X, Y ),
% 4.29/4.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 4.29/4.63 (22115) {G0,W12,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 4.29/4.63 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), !
% 4.29/4.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), alpha42( X, Y ) }.
% 4.29/4.63 (22116) {G0,W12,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.63 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 4.29/4.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 4.29/4.63 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ), X ) }.
% 4.29/4.63 (22117) {G0,W17,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.63 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 4.29/4.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oone__class_Oone(
% 4.29/4.63 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 4.29/4.63 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ), X ) }.
% 4.29/4.63 (22118) {G0,W22,D6,L2,V3,M2} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.63 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 4.29/4.63 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Z, hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) =
% 4.29/4.63 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 4.29/4.63 tc_Int_Oint, Z, Y ), X ) }.
% 4.29/4.63 (22119) {G0,W33,D7,L1,V3,M1} { c_Divides_Odiv__class_Odiv( tc_Nat_Onat,
% 4.29/4.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), X ) =
% 4.29/4.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 4.29/4.63 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ),
% 4.29/4.63 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 4.29/4.63 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ), X ) ) }.
% 4.29/4.63 (22120) {G0,W28,D6,L1,V3,M1} { c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z
% 4.29/4.63 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) =
% 4.29/4.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ),
% 4.29/4.63 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 4.29/4.63 tc_Nat_Onat, Z, Y ), X ) ), c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, Y
% 4.29/4.63 ) ) }.
% 4.29/4.63 (22121) {G0,W29,D6,L3,V4,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.63 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), !
% 4.29/4.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ),
% 4.29/4.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 4.29/4.63 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 4.29/4.63 ), c_Divides_Odiv__class_Omod( tc_Nat_Onat, T, X ) ), Z ), hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 4.29/4.63 (22122) {G0,W11,D4,L2,V3,M2} { ! hBOOL( hAPP( Z,
% 4.29/4.63 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) ), alpha19( X, Y, Z )
% 4.29/4.63 }.
% 4.29/4.63 (22123) {G0,W11,D4,L2,V3,M2} { ! hBOOL( hAPP( Z,
% 4.29/4.63 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) ), alpha43( X, Y, Z )
% 4.29/4.63 }.
% 4.29/4.63 (22124) {G0,W15,D4,L3,V3,M3} { ! alpha19( X, Y, Z ), ! alpha43( X, Y, Z )
% 4.29/4.63 , hBOOL( hAPP( Z, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) ) }.
% 4.29/4.63 (22125) {G0,W12,D3,L3,V3,M3} { ! alpha43( X, Y, Z ), X =
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha54( X, Y, Z ) }.
% 4.29/4.63 (22126) {G0,W8,D3,L2,V3,M2} { ! X = c_Groups_Ozero__class_Ozero(
% 4.29/4.63 tc_Nat_Onat ), alpha43( X, Y, Z ) }.
% 4.29/4.63 (22127) {G0,W8,D2,L2,V3,M2} { ! alpha54( X, Y, Z ), alpha43( X, Y, Z ) }.
% 4.29/4.63 (22128) {G0,W13,D2,L3,V4,M3} { ! alpha54( X, Y, Z ), !
% 4.29/4.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, X ), alpha62( X, Y, Z, T )
% 4.29/4.63 }.
% 4.29/4.63 (22129) {G0,W11,D3,L2,V5,M2} { c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 4.29/4.63 , skol31( X, T, U ), X ), alpha54( X, Y, Z ) }.
% 4.29/4.63 (22130) {G0,W12,D3,L2,V3,M2} { ! alpha62( X, Y, Z, skol31( X, Y, Z ) ),
% 4.29/4.63 alpha54( X, Y, Z ) }.
% 4.29/4.63 (22131) {G0,W20,D6,L3,V5,M3} { ! alpha62( X, Y, Z, T ), ! Y =
% 4.29/4.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ), hBOOL( hAPP
% 4.29/4.63 ( Z, T ) ) }.
% 4.29/4.63 (22132) {G0,W19,D6,L2,V4,M2} { Y = c_Groups_Oplus__class_Oplus(
% 4.29/4.63 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 4.29/4.63 ), skol32( X, Y, T ) ), T ), alpha62( X, Y, Z, T ) }.
% 4.29/4.63 (22133) {G0,W9,D3,L2,V4,M2} { ! hBOOL( hAPP( Z, T ) ), alpha62( X, Y, Z, T
% 4.29/4.63 ) }.
% 4.29/4.63 (22134) {G0,W12,D3,L3,V3,M3} { ! alpha19( X, Y, Z ), ! X =
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( Z, Y ) ) }.
% 4.29/4.63 (22135) {G0,W8,D3,L2,V3,M2} { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 4.29/4.63 ), alpha19( X, Y, Z ) }.
% 4.29/4.63 (22136) {G0,W8,D3,L2,V3,M2} { ! hBOOL( hAPP( Z, Y ) ), alpha19( X, Y, Z )
% 4.29/4.63 }.
% 4.29/4.63 (22137) {G0,W29,D6,L5,V4,M5} { ! T = c_Groups_Oplus__class_Oplus(
% 4.29/4.63 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 4.29/4.63 ), Y ), X ), alpha83( X, Z ), ! c_Orderings_Oord__class_Oless(
% 4.29/4.63 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), Z =
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 4.29/4.63 tc_Int_Oint, T, Z ) = Y }.
% 4.29/4.63 (22138) {G0,W33,D6,L6,V4,M6} { ! T = c_Groups_Oplus__class_Oplus(
% 4.29/4.63 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 4.29/4.63 ), Y ), X ), alpha83( X, Z ), ! c_Orderings_Oord__class_Oless(
% 4.29/4.63 tc_Int_Oint, Z, X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X
% 4.29/4.63 , c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Z =
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 4.29/4.63 tc_Int_Oint, T, Z ) = Y }.
% 4.29/4.63 (22139) {G0,W8,D3,L2,V2,M2} { ! alpha83( X, Y ),
% 4.29/4.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 4.29/4.63 tc_Int_Oint ), Y ) }.
% 4.29/4.63 (22140) {G0,W12,D3,L3,V2,M3} { ! alpha83( X, Y ), !
% 4.29/4.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 4.29/4.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 4.29/4.63 (22141) {G0,W13,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.63 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 4.29/4.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), alpha83( X, Y ) }.
% 4.29/4.63 (22142) {G0,W12,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.63 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 4.29/4.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ), alpha83( X, Y ) }.
% 4.29/4.63 (22143) {G0,W10,D4,L2,V3,M2} { ! hBOOL( hAPP( Z,
% 4.29/4.63 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ), alpha20( X, Z ) }.
% 4.29/4.63 (22144) {G0,W11,D4,L2,V3,M2} { ! hBOOL( hAPP( Z,
% 4.29/4.63 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ), alpha44( X, Y, Z )
% 4.29/4.63 }.
% 4.29/4.63 (22145) {G0,W14,D4,L3,V3,M3} { ! alpha20( X, Z ), ! alpha44( X, Y, Z ),
% 4.29/4.63 hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ) }.
% 4.29/4.63 (22146) {G0,W8,D2,L2,V3,M2} { ! alpha44( X, Y, Z ), alpha55( X, Y, Z ) }.
% 4.29/4.63 (22147) {G0,W8,D2,L2,V3,M2} { ! alpha44( X, Y, Z ), alpha63( X, Y, Z ) }.
% 4.29/4.63 (22148) {G0,W12,D2,L3,V3,M3} { ! alpha55( X, Y, Z ), ! alpha63( X, Y, Z )
% 4.29/4.63 , alpha44( X, Y, Z ) }.
% 4.29/4.63 (22149) {G0,W13,D3,L3,V3,M3} { ! alpha63( X, Y, Z ), !
% 4.29/4.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha71( X, Y, Z ) }.
% 4.29/4.63 (22150) {G0,W9,D3,L2,V3,M2} { c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 4.29/4.63 X, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha63( X, Y, Z ) }.
% 4.29/4.63 (22151) {G0,W8,D2,L2,V3,M2} { ! alpha71( X, Y, Z ), alpha63( X, Y, Z ) }.
% 4.29/4.63 (22152) {G0,W12,D3,L3,V4,M3} { ! alpha71( X, Y, Z ), ! alpha75( X, Y, T )
% 4.29/4.63 , hBOOL( hAPP( Z, T ) ) }.
% 4.29/4.63 (22153) {G0,W11,D4,L2,V5,M2} { ! hBOOL( hAPP( Z, skol33( T, U, Z ) ) ),
% 4.29/4.63 alpha71( X, Y, Z ) }.
% 4.29/4.63 (22154) {G0,W11,D3,L2,V3,M2} { alpha75( X, Y, skol33( X, Y, Z ) ), alpha71
% 4.29/4.63 ( X, Y, Z ) }.
% 4.29/4.63 (22155) {G0,W11,D3,L2,V5,M2} { ! alpha75( X, Y, Z ),
% 4.29/4.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, skol34( X, T, U ) ) }.
% 4.29/4.63 (22156) {G0,W12,D3,L2,V3,M2} { ! alpha75( X, Y, Z ), alpha79( X, Y, Z,
% 4.29/4.63 skol34( X, Y, Z ) ) }.
% 4.29/4.63 (22157) {G0,W13,D2,L3,V4,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.63 tc_Int_Oint, X, T ), ! alpha79( X, Y, Z, T ), alpha75( X, Y, Z ) }.
% 4.29/4.63 (22158) {G0,W10,D3,L2,V4,M2} { ! alpha79( X, Y, Z, T ),
% 4.29/4.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T,
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 4.29/4.63 (22159) {G0,W16,D6,L2,V4,M2} { ! alpha79( X, Y, Z, T ), Y =
% 4.29/4.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ) }.
% 4.29/4.63 (22160) {G0,W21,D6,L3,V4,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 4.29/4.63 tc_Int_Oint, T, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! Y =
% 4.29/4.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ), alpha79( X,
% 4.29/4.63 Y, Z, T ) }.
% 4.29/4.63 (22161) {G0,W13,D3,L3,V3,M3} { ! alpha55( X, Y, Z ), !
% 4.29/4.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 4.29/4.63 tc_Int_Oint ), X ), alpha64( X, Y, Z ) }.
% 4.29/4.63 (22162) {G0,W9,D3,L2,V3,M2} { c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), alpha55( X, Y, Z ) }.
% 4.29/4.63 (22163) {G0,W8,D2,L2,V3,M2} { ! alpha64( X, Y, Z ), alpha55( X, Y, Z ) }.
% 4.29/4.63 (22164) {G0,W12,D3,L3,V4,M3} { ! alpha64( X, Y, Z ), ! alpha72( X, Y, T )
% 4.29/4.63 , hBOOL( hAPP( Z, T ) ) }.
% 4.29/4.63 (22165) {G0,W11,D4,L2,V5,M2} { ! hBOOL( hAPP( Z, skol35( T, U, Z ) ) ),
% 4.29/4.63 alpha64( X, Y, Z ) }.
% 4.29/4.63 (22166) {G0,W11,D3,L2,V3,M2} { alpha72( X, Y, skol35( X, Y, Z ) ), alpha64
% 4.29/4.63 ( X, Y, Z ) }.
% 4.29/4.63 (22167) {G0,W12,D3,L2,V6,M2} { ! alpha72( X, Y, Z ),
% 4.29/4.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), skol36( T, U, W ) ) }.
% 4.29/4.63 (22168) {G0,W12,D3,L2,V3,M2} { ! alpha72( X, Y, Z ), alpha76( X, Y, Z,
% 4.29/4.63 skol36( X, Y, Z ) ) }.
% 4.29/4.63 (22169) {G0,W14,D3,L3,V4,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 4.29/4.63 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! alpha76(
% 4.29/4.63 X, Y, Z, T ), alpha72( X, Y, Z ) }.
% 4.29/4.63 (22170) {G0,W9,D2,L2,V4,M2} { ! alpha76( X, Y, Z, T ),
% 4.29/4.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X ) }.
% 4.29/4.63 (22171) {G0,W16,D6,L2,V4,M2} { ! alpha76( X, Y, Z, T ), Y =
% 4.29/4.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ) }.
% 4.29/4.63 (22172) {G0,W20,D6,L3,V4,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.63 tc_Int_Oint, T, X ), ! Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP
% 4.29/4.63 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ),
% 4.29/4.63 alpha76( X, Y, Z, T ) }.
% 4.29/4.63 (22173) {G0,W12,D4,L3,V2,M3} { ! alpha20( X, Y ), ! X =
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hBOOL( hAPP( Y,
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 4.29/4.63 (22174) {G0,W7,D3,L2,V2,M2} { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint
% 4.29/4.63 ), alpha20( X, Y ) }.
% 4.29/4.63 (22175) {G0,W8,D4,L2,V2,M2} { ! hBOOL( hAPP( Y,
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), alpha20( X, Y ) }.
% 4.29/4.63 (22176) {G0,W21,D5,L4,V3,M4} { ! class_RealVector_Oreal__normed__vector( X
% 4.29/4.63 ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 4.29/4.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 4.29/4.63 c_RealVector_Onorm__class_Onorm( X, hAPP( Z, skol37( X, Y, Z ) ) ), Y ),
% 4.29/4.63 c_SEQ_OBseq( X, Z ) }.
% 4.29/4.63 (22177) {G0,W12,D3,L3,V4,M3} { ! class_RealVector_Oreal__normed__vector( X
% 4.29/4.63 ), ! c_SEQ_OBseq( X, Y ), c_Orderings_Oord__class_Oless(
% 4.29/4.63 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol38
% 4.29/4.63 ( Z, T ) ) }.
% 4.29/4.63 (22178) {G0,W15,D4,L3,V3,M3} { ! class_RealVector_Oreal__normed__vector( X
% 4.29/4.63 ), ! c_SEQ_OBseq( X, Y ), c_Orderings_Oord__class_Oless__eq(
% 4.29/4.63 tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( X, hAPP( Y, Z ) ),
% 4.29/4.63 skol38( X, Y ) ) }.
% 4.29/4.63 (22179) {G0,W33,D6,L1,V3,M1} { c_Divides_Odiv__class_Odiv( tc_Int_Oint,
% 4.29/4.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ), X ) =
% 4.29/4.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 4.29/4.63 tc_Int_Oint, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Z, X ),
% 4.29/4.63 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 4.29/4.63 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 4.29/4.63 tc_Int_Oint, c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, X ),
% 4.29/4.63 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) ) }.
% 4.29/4.63 (22180) {G0,W17,D6,L1,V2,M1} { Y = c_Groups_Oplus__class_Oplus(
% 4.29/4.63 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X
% 4.29/4.63 ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 4.29/4.63 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) }.
% 4.29/4.63 (22181) {G0,W33,D7,L1,V3,M1} { c_Divides_Odiv__class_Odiv( tc_Int_Oint,
% 4.29/4.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) =
% 4.29/4.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 4.29/4.63 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 4.29/4.63 c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 4.29/4.63 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) ) }.
% 4.29/4.63 (22182) {G0,W23,D7,L1,V3,M1} { c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 4.29/4.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 4.29/4.63 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ) ),
% 4.29/4.63 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, Z ) ), X ) =
% 4.29/4.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) }.
% 4.29/4.63 (22183) {G0,W23,D7,L1,V3,M1} { c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 4.29/4.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Divides_Odiv__class_Odiv
% 4.29/4.63 ( tc_Int_Oint, Z, Y ) ), Y ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Z
% 4.29/4.63 , Y ) ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) }.
% 4.29/4.63 (22184) {G0,W10,D4,L1,V2,M1} { c_Divides_Odiv__class_Odiv( tc_Int_Oint,
% 4.29/4.63 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ), X ) =
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 4.29/4.63 (22185) {G0,W8,D4,L1,V1,M1} { c_Divides_Odiv__class_Odiv( tc_Int_Oint, X,
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) =
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 4.29/4.63 (22186) {G0,W7,D4,L1,V1,M1} { c_Divides_Odiv__class_Omod( tc_Int_Oint, X,
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) = X }.
% 4.29/4.63 (22187) {G0,W22,D6,L1,V3,M1} { c_Divides_Odiv__class_Omod( tc_Int_Oint,
% 4.29/4.63 hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ),
% 4.29/4.63 c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y ) ), X ), Y ) =
% 4.29/4.63 c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 4.29/4.63 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ), Y ) }.
% 4.29/4.63 (22188) {G0,W12,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.63 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 4.29/4.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Omod(
% 4.29/4.63 tc_Int_Oint, Y, X ), X ) }.
% 4.29/4.63 (22189) {G0,W12,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.63 tc_Int_Oint, X, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 4.29/4.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Divides_Odiv__class_Omod
% 4.29/4.63 ( tc_Int_Oint, Y, X ) ) }.
% 4.29/4.63 (22190) {G0,W18,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 4.29/4.63 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 4.29/4.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 4.29/4.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 4.29/4.63 tc_Int_Oint, X, Y ) ) }.
% 4.29/4.63 (22191) {G0,W12,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 4.29/4.63 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 4.29/4.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 4.29/4.63 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ), X ) }.
% 4.29/4.63 (22192) {G0,W8,D4,L1,V1,M1} { c_Divides_Odiv__class_Omod( tc_Int_Oint,
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ) =
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 4.29/4.63 (22193) {G0,W7,D3,L1,V1,M1} { c_Divides_Odiv__class_Omod( tc_Int_Oint, X,
% 4.29/4.63 X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 4.29/4.63 (22194) {G0,W17,D5,L2,V2,M2} { ! c_Divides_Odiv__class_Omod( tc_Int_Oint,
% 4.29/4.63 Y, X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y = hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), skol39( X, Y ) ) }.
% 4.29/4.63 (22195) {G0,W15,D5,L2,V3,M2} { ! Y = hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ),
% 4.29/4.63 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 4.29/4.63 (22196) {G0,W22,D6,L1,V3,M1} { c_Divides_Odiv__class_Omod( tc_Int_Oint,
% 4.29/4.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 4.29/4.63 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) =
% 4.29/4.63 c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) }.
% 4.29/4.63 (22197) {G0,W22,D6,L1,V3,M1} { c_Divides_Odiv__class_Omod( tc_Int_Oint,
% 4.29/4.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) =
% 4.29/4.63 c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 4.29/4.63 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) }.
% 4.29/4.63 (22198) {G0,W37,D7,L2,V4,M2} { ! class_Fields_Ofield( X ),
% 4.29/4.63 c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), T, hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y ) ) =
% 4.29/4.63 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ),
% 4.29/4.63 c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ),
% 4.29/4.63 c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly( X ), T, Z ), Y ) ),
% 4.29/4.63 c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), T, Z ) ) }.
% 4.29/4.63 (22199) {G0,W13,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.63 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 4.29/4.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 4.29/4.63 tc_Int_Oint, Y, X ) ) }.
% 4.29/4.63 (22200) {G0,W13,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.63 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 4.29/4.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 4.29/4.63 tc_Int_Oint, Y, X ) ) }.
% 4.29/4.63 (22201) {G0,W12,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.63 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 4.29/4.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Omod(
% 4.29/4.63 tc_Int_Oint, Y, X ), X ) }.
% 4.29/4.63 (22202) {G0,W15,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 4.29/4.63 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 4.29/4.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ),
% 4.29/4.63 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ) = X }.
% 4.29/4.63 (22203) {G0,W13,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.63 tc_Int_Oint, X, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 4.29/4.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 4.29/4.63 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ),
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 4.29/4.63 (22204) {G0,W13,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.63 tc_Int_Oint, X, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 4.29/4.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 4.29/4.63 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ),
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 4.29/4.63 (22205) {G0,W12,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.63 tc_Int_Oint, X, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 4.29/4.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Divides_Odiv__class_Omod
% 4.29/4.63 ( tc_Int_Oint, Y, X ) ) }.
% 4.29/4.63 (22206) {G0,W15,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 4.29/4.63 tc_Int_Oint, X, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 4.29/4.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 4.29/4.63 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ) = X }.
% 4.29/4.63 (22207) {G0,W22,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.63 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 4.29/4.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 4.29/4.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ),
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Divides_Odiv__class_Omod
% 4.29/4.63 ( tc_Int_Oint, X, Y ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y )
% 4.29/4.63 }.
% 4.29/4.63 (22208) {G0,W33,D6,L2,V3,M2} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.63 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 4.29/4.63 c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) =
% 4.29/4.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ),
% 4.29/4.63 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 4.29/4.63 tc_Int_Oint, Z, Y ), X ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y
% 4.29/4.63 ) ) }.
% 4.29/4.63 (22209) {G0,W11,D4,L2,V3,M2} { ! hBOOL( hAPP( Z,
% 4.29/4.63 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ), alpha21( X, Y, Z )
% 4.29/4.63 }.
% 4.29/4.63 (22210) {G0,W11,D4,L2,V3,M2} { ! hBOOL( hAPP( Z,
% 4.29/4.63 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ), alpha45( X, Y, Z )
% 4.29/4.63 }.
% 4.29/4.63 (22211) {G0,W15,D4,L3,V3,M3} { ! alpha21( X, Y, Z ), ! alpha45( X, Y, Z )
% 4.29/4.63 , hBOOL( hAPP( Z, c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 4.29/4.63 (22212) {G0,W8,D2,L2,V3,M2} { ! alpha45( X, Y, Z ), alpha56( X, Y, Z ) }.
% 4.29/4.63 (22213) {G0,W8,D2,L2,V3,M2} { ! alpha45( X, Y, Z ), alpha65( X, Y, Z ) }.
% 4.29/4.63 (22214) {G0,W12,D2,L3,V3,M3} { ! alpha56( X, Y, Z ), ! alpha65( X, Y, Z )
% 4.29/4.63 , alpha45( X, Y, Z ) }.
% 4.29/4.63 (22215) {G0,W13,D3,L3,V3,M3} { ! alpha65( X, Y, Z ), !
% 4.29/4.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha73( X, Y, Z ) }.
% 4.29/4.63 (22216) {G0,W9,D3,L2,V3,M2} { c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 4.29/4.63 X, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha65( X, Y, Z ) }.
% 4.29/4.63 (22217) {G0,W8,D2,L2,V3,M2} { ! alpha73( X, Y, Z ), alpha65( X, Y, Z ) }.
% 4.29/4.63 (22218) {G0,W12,D3,L3,V4,M3} { ! alpha73( X, Y, Z ), ! alpha77( X, Y, T )
% 4.29/4.63 , hBOOL( hAPP( Z, T ) ) }.
% 4.29/4.63 (22219) {G0,W11,D4,L2,V5,M2} { ! hBOOL( hAPP( Z, skol40( T, U, Z ) ) ),
% 4.29/4.63 alpha73( X, Y, Z ) }.
% 4.29/4.63 (22220) {G0,W11,D3,L2,V3,M2} { alpha77( X, Y, skol40( X, Y, Z ) ), alpha73
% 4.29/4.63 ( X, Y, Z ) }.
% 4.29/4.63 (22221) {G0,W8,D2,L2,V3,M2} { ! alpha77( X, Y, Z ),
% 4.29/4.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ) }.
% 4.29/4.63 (22222) {G0,W8,D2,L2,V3,M2} { ! alpha77( X, Y, Z ), alpha80( X, Y, Z ) }.
% 4.29/4.63 (22223) {G0,W12,D2,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.63 tc_Int_Oint, X, Z ), ! alpha80( X, Y, Z ), alpha77( X, Y, Z ) }.
% 4.29/4.63 (22224) {G0,W9,D3,L2,V3,M2} { ! alpha80( X, Y, Z ),
% 4.29/4.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 4.29/4.63 (22225) {G0,W18,D6,L2,V3,M2} { ! alpha80( X, Y, Z ), Y =
% 4.29/4.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), skol41( X, Y, Z ) ), Z
% 4.29/4.63 ) }.
% 4.29/4.63 (22226) {G0,W20,D6,L3,V4,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 4.29/4.63 tc_Int_Oint, Z, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! Y =
% 4.29/4.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), T ), Z ), alpha80( X,
% 4.29/4.63 Y, Z ) }.
% 4.29/4.63 (22227) {G0,W13,D3,L3,V3,M3} { ! alpha56( X, Y, Z ), !
% 4.29/4.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 4.29/4.63 tc_Int_Oint ), X ), alpha66( X, Y, Z ) }.
% 4.29/4.63 (22228) {G0,W9,D3,L2,V3,M2} { c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), alpha56( X, Y, Z ) }.
% 4.29/4.63 (22229) {G0,W8,D2,L2,V3,M2} { ! alpha66( X, Y, Z ), alpha56( X, Y, Z ) }.
% 4.29/4.63 (22230) {G0,W12,D3,L3,V4,M3} { ! alpha66( X, Y, Z ), ! alpha74( X, Y, T )
% 4.29/4.63 , hBOOL( hAPP( Z, T ) ) }.
% 4.29/4.63 (22231) {G0,W11,D4,L2,V5,M2} { ! hBOOL( hAPP( Z, skol42( T, U, Z ) ) ),
% 4.29/4.63 alpha66( X, Y, Z ) }.
% 4.29/4.63 (22232) {G0,W11,D3,L2,V3,M2} { alpha74( X, Y, skol42( X, Y, Z ) ), alpha66
% 4.29/4.63 ( X, Y, Z ) }.
% 4.29/4.63 (22233) {G0,W9,D3,L2,V3,M2} { ! alpha74( X, Y, Z ),
% 4.29/4.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ) }.
% 4.29/4.63 (22234) {G0,W8,D2,L2,V3,M2} { ! alpha74( X, Y, Z ), alpha78( X, Y, Z ) }.
% 4.29/4.63 (22235) {G0,W13,D3,L3,V3,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 4.29/4.63 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), ! alpha78(
% 4.29/4.63 X, Y, Z ), alpha74( X, Y, Z ) }.
% 4.29/4.63 (22236) {G0,W8,D2,L2,V3,M2} { ! alpha78( X, Y, Z ),
% 4.29/4.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ) }.
% 4.29/4.63 (22237) {G0,W18,D6,L2,V3,M2} { ! alpha78( X, Y, Z ), Y =
% 4.29/4.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), skol43( X, Y, Z ) ), Z
% 4.29/4.63 ) }.
% 4.29/4.63 (22238) {G0,W19,D6,L3,V4,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.63 tc_Int_Oint, Z, X ), ! Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP
% 4.29/4.63 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), T ), Z ),
% 4.29/4.63 alpha78( X, Y, Z ) }.
% 4.29/4.63 (22239) {G0,W12,D3,L3,V3,M3} { ! alpha21( X, Y, Z ), ! X =
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hBOOL( hAPP( Z, Y ) ) }.
% 4.29/4.63 (22240) {G0,W8,D3,L2,V3,M2} { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint
% 4.29/4.63 ), alpha21( X, Y, Z ) }.
% 4.29/4.63 (22241) {G0,W8,D3,L2,V3,M2} { ! hBOOL( hAPP( Z, Y ) ), alpha21( X, Y, Z )
% 4.29/4.63 }.
% 4.29/4.63 (22242) {G0,W30,D6,L4,V4,M4} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.63 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 4.29/4.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), !
% 4.29/4.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, Z ),
% 4.29/4.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 4.29/4.63 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 4.29/4.63 ), c_Divides_Odiv__class_Omod( tc_Int_Oint, T, X ) ), Y ) ) }.
% 4.29/4.63 (22243) {G0,W34,D6,L4,V4,M4} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.63 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 4.29/4.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), !
% 4.29/4.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, Z ),
% 4.29/4.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 4.29/4.63 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 4.29/4.63 ), c_Divides_Odiv__class_Omod( tc_Int_Oint, T, X ) ), Y ), hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 4.29/4.63 (22244) {G0,W34,D6,L4,V4,M4} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.63 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 4.29/4.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, Y ), !
% 4.29/4.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 4.29/4.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ),
% 4.29/4.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 4.29/4.63 c_Divides_Odiv__class_Omod( tc_Int_Oint, T, X ) ), Y ) ) }.
% 4.29/4.63 (22245) {G0,W30,D6,L4,V4,M4} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.63 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 4.29/4.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, Y ), !
% 4.29/4.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 4.29/4.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 4.29/4.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 4.29/4.63 c_Divides_Odiv__class_Omod( tc_Int_Oint, T, X ) ), Y ),
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 4.29/4.63 (22246) {G0,W29,D6,L5,V4,M5} { ! Z = c_Groups_Oplus__class_Oplus(
% 4.29/4.63 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y
% 4.29/4.63 ), T ), X ), alpha84( X, Y ), ! c_Orderings_Oord__class_Oless(
% 4.29/4.63 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), Y =
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 4.29/4.63 tc_Int_Oint, Z, Y ) = X }.
% 4.29/4.63 (22247) {G0,W33,D6,L6,V4,M6} { ! Z = c_Groups_Oplus__class_Oplus(
% 4.29/4.63 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y
% 4.29/4.63 ), T ), X ), alpha84( X, Y ), ! c_Orderings_Oord__class_Oless(
% 4.29/4.63 tc_Int_Oint, Y, X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X
% 4.29/4.63 , c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y =
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 4.29/4.63 tc_Int_Oint, Z, Y ) = X }.
% 4.29/4.63 (22248) {G0,W8,D3,L2,V2,M2} { ! alpha84( X, Y ),
% 4.29/4.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 4.29/4.63 tc_Int_Oint ), Y ) }.
% 4.29/4.63 (22249) {G0,W12,D3,L3,V2,M3} { ! alpha84( X, Y ), !
% 4.29/4.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 4.29/4.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 4.29/4.63 (22250) {G0,W13,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.63 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 4.29/4.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), alpha84( X, Y ) }.
% 4.29/4.63 (22251) {G0,W12,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.63 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 4.29/4.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ), alpha84( X, Y ) }.
% 4.29/4.63 (22252) {G0,W28,D5,L4,V5,M4} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.63 tc_Int_Oint, X, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! hBOOL(
% 4.29/4.63 hAPP( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 4.29/4.63 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ), ! alpha22( X, Y, T,
% 4.29/4.63 U ), hBOOL( hAPP( hAPP( Z, T ), U ) ) }.
% 4.29/4.63 (22253) {G0,W28,D5,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.63 tc_Int_Oint, X, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha22( X
% 4.29/4.63 , Y, skol44( X, Y, Z ), skol54( X, Y, Z ) ), hBOOL( hAPP( hAPP( Z,
% 4.29/4.63 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 4.29/4.63 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 4.29/4.63 (22254) {G0,W29,D5,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.63 tc_Int_Oint, X, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! hBOOL(
% 4.29/4.63 hAPP( hAPP( Z, skol44( X, Y, Z ) ), skol54( X, Y, Z ) ) ), hBOOL( hAPP(
% 4.29/4.63 hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 4.29/4.63 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 4.29/4.63 (22255) {G0,W9,D2,L2,V4,M2} { ! alpha22( X, Y, Z, T ),
% 4.29/4.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, T ) }.
% 4.29/4.63 (22256) {G0,W10,D2,L2,V4,M2} { ! alpha22( X, Y, Z, T ), alpha46( X, Y, Z,
% 4.29/4.63 T ) }.
% 4.29/4.63 (22257) {G0,W14,D2,L3,V4,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.63 tc_Int_Oint, X, T ), ! alpha46( X, Y, Z, T ), alpha22( X, Y, Z, T ) }.
% 4.29/4.63 (22258) {G0,W10,D3,L2,V4,M2} { ! alpha46( X, Y, Z, T ),
% 4.29/4.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T,
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 4.29/4.63 (22259) {G0,W16,D6,L2,V4,M2} { ! alpha46( X, Y, Z, T ), Y =
% 4.29/4.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ) }.
% 4.29/4.63 (22260) {G0,W21,D6,L3,V4,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 4.29/4.63 tc_Int_Oint, T, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! Y =
% 4.29/4.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ), alpha46( X,
% 4.29/4.63 Y, Z, T ) }.
% 4.29/4.63 (22261) {G0,W28,D5,L4,V5,M4} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.63 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), ! hBOOL(
% 4.29/4.63 hAPP( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 4.29/4.63 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ), ! alpha23( X, Y, T,
% 4.29/4.63 U ), hBOOL( hAPP( hAPP( Z, T ), U ) ) }.
% 4.29/4.63 (22262) {G0,W28,D5,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.63 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), alpha23( X
% 4.29/4.63 , Y, skol45( X, Y, Z ), skol55( X, Y, Z ) ), hBOOL( hAPP( hAPP( Z,
% 4.29/4.63 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 4.29/4.63 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 4.29/4.63 (22263) {G0,W29,D5,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.63 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), ! hBOOL(
% 4.29/4.63 hAPP( hAPP( Z, skol45( X, Y, Z ) ), skol55( X, Y, Z ) ) ), hBOOL( hAPP(
% 4.29/4.63 hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 4.29/4.63 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 4.29/4.63 (22264) {G0,W10,D3,L2,V4,M2} { ! alpha23( X, Y, Z, T ),
% 4.29/4.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ) }.
% 4.29/4.63 (22265) {G0,W10,D2,L2,V4,M2} { ! alpha23( X, Y, Z, T ), alpha47( X, Y, Z,
% 4.29/4.63 T ) }.
% 4.29/4.63 (22266) {G0,W15,D3,L3,V4,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 4.29/4.63 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! alpha47(
% 4.29/4.63 X, Y, Z, T ), alpha23( X, Y, Z, T ) }.
% 4.29/4.63 (22267) {G0,W9,D2,L2,V4,M2} { ! alpha47( X, Y, Z, T ),
% 4.29/4.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X ) }.
% 4.29/4.63 (22268) {G0,W16,D6,L2,V4,M2} { ! alpha47( X, Y, Z, T ), Y =
% 4.29/4.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ) }.
% 4.29/4.63 (22269) {G0,W20,D6,L3,V4,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.63 tc_Int_Oint, T, X ), ! Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP
% 4.29/4.63 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ),
% 4.29/4.63 alpha47( X, Y, Z, T ) }.
% 4.29/4.63 (22270) {G0,W17,D3,L4,V4,M4} { ! class_Orderings_Oorder( X ), !
% 4.29/4.63 c_SEQ_Oincseq( X, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 4.29/4.63 Z, T ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, Z ), hAPP( Y, T )
% 4.29/4.63 ) }.
% 4.29/4.63 (22271) {G0,W13,D3,L3,V2,M3} { ! class_Orderings_Oorder( X ),
% 4.29/4.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, skol46( X, Y ), skol56( X
% 4.29/4.63 , Y ) ), c_SEQ_Oincseq( X, Y ) }.
% 4.29/4.63 (22272) {G0,W17,D4,L3,V2,M3} { ! class_Orderings_Oorder( X ), !
% 4.29/4.63 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, skol46( X, Y ) ), hAPP( Y
% 4.29/4.63 , skol56( X, Y ) ) ), c_SEQ_Oincseq( X, Y ) }.
% 4.29/4.63 (22273) {G0,W13,D3,L3,V6,M3} { ! class_RealVector_Oreal__normed__vector( X
% 4.29/4.63 ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, skol47( U, W, V0,
% 4.29/4.63 T ) ), c_SEQ_OBseq( X, Y ) }.
% 4.29/4.63 (22274) {G0,W17,D5,L3,V4,M3} { ! class_RealVector_Oreal__normed__vector( X
% 4.29/4.63 ), ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 4.29/4.63 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol47( X, Y, Z, T ) ) ), Z
% 4.29/4.63 ), c_SEQ_OBseq( X, Y ) }.
% 4.29/4.63 (22275) {G0,W24,D4,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.63 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), !
% 4.29/4.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), c_RealDef_Oreal(
% 4.29/4.63 tc_Nat_Onat, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) =
% 4.29/4.63 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, c_RealDef_Oreal(
% 4.29/4.63 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 4.29/4.63 (22276) {G0,W27,D6,L3,V3,M3} { ! c_Divides_Odiv__class_Omod( tc_Nat_Onat,
% 4.29/4.63 Z, Y ) = c_Divides_Odiv__class_Omod( tc_Nat_Onat, X, Y ), !
% 4.29/4.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ), Z =
% 4.29/4.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), skol48( X, Y, Z ) ) )
% 4.29/4.63 }.
% 4.29/4.63 (22277) {G0,W4,D2,L1,V1,M1} { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, X
% 4.29/4.63 ) }.
% 4.29/4.63 (22278) {G0,W7,D3,L2,V2,M2} { ! class_Rings_Ocomm__semiring__1( X ),
% 4.29/4.63 c_Rings_Odvd__class_Odvd( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 4.29/4.63 (22279) {G0,W13,D3,L3,V3,M3} { ! class_Divides_Osemiring__div( X ), !
% 4.29/4.63 c_Rings_Odvd__class_Odvd( X, Z, Y ), c_Divides_Odiv__class_Omod( X, Y, Z
% 4.29/4.63 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 4.29/4.63 (22280) {G0,W13,D3,L3,V3,M3} { ! class_Divides_Osemiring__div( X ), !
% 4.29/4.63 c_Divides_Odiv__class_Omod( X, Y, Z ) = c_Groups_Ozero__class_Ozero( X )
% 4.29/4.63 , c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 4.29/4.63 (22281) {G0,W13,D3,L3,V3,M3} { ! class_Divides_Osemiring__div( X ), !
% 4.29/4.63 c_Rings_Odvd__class_Odvd( X, Z, Y ), c_Divides_Odiv__class_Omod( X, Y, Z
% 4.29/4.63 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 4.29/4.63 (22282) {G0,W17,D3,L4,V4,M4} { ! class_Divides_Osemiring__div( X ), !
% 4.29/4.63 c_Rings_Odvd__class_Odvd( X, T, c_Divides_Odiv__class_Omod( X, Z, Y ) ),
% 4.29/4.63 ! c_Rings_Odvd__class_Odvd( X, T, Y ), c_Rings_Odvd__class_Odvd( X, T, Z
% 4.29/4.63 ) }.
% 4.29/4.63 (22283) {G0,W17,D3,L4,V4,M4} { ! class_Divides_Osemiring__div( X ), !
% 4.29/4.63 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z, T
% 4.29/4.63 ), c_Rings_Odvd__class_Odvd( X, Z, c_Divides_Odiv__class_Omod( X, Y, T )
% 4.29/4.63 ) }.
% 4.29/4.63 (22284) {G0,W18,D4,L3,V4,M3} { ! class_Divides_Osemiring__div( X ), !
% 4.29/4.63 c_Rings_Odvd__class_Odvd( X, Z, Y ), c_Divides_Odiv__class_Omod( X,
% 4.29/4.63 c_Divides_Odiv__class_Omod( X, T, Y ), Z ) = c_Divides_Odiv__class_Omod(
% 4.29/4.63 X, T, Z ) }.
% 4.29/4.63 (22285) {G0,W17,D3,L4,V4,M4} { ! class_Divides_Osemiring__div( X ), !
% 4.29/4.63 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 4.29/4.63 c_Divides_Odiv__class_Omod( X, T, Y ) ), c_Rings_Odvd__class_Odvd( X, Z,
% 4.29/4.63 T ) }.
% 4.29/4.63 (22286) {G0,W17,D3,L4,V4,M4} { ! class_Divides_Osemiring__div( X ), !
% 4.29/4.63 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z, T
% 4.29/4.63 ), c_Rings_Odvd__class_Odvd( X, Z, c_Divides_Odiv__class_Omod( X, T, Y )
% 4.29/4.63 ) }.
% 4.29/4.63 (22287) {G0,W13,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.63 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), !
% 4.29/4.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ), !
% 4.29/4.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 4.29/4.63 (22288) {G0,W22,D5,L3,V3,M3} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat,
% 4.29/4.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP
% 4.29/4.63 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), Z =
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 4.29/4.63 tc_Nat_Onat, Y, X ) }.
% 4.29/4.63 (22289) {G0,W18,D5,L2,V3,M2} { ! Z = c_Groups_Ozero__class_Ozero(
% 4.29/4.63 tc_Nat_Onat ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 4.29/4.63 (22290) {G0,W18,D5,L2,V3,M2} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 4.29/4.63 , X ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 4.29/4.63 (22291) {G0,W20,D5,L3,V4,M3} { ! class_Rings_Ocomm__semiring__1( X ), !
% 4.29/4.63 c_Rings_Odvd__class_Odvd( X, Z, Y ), c_Rings_Odvd__class_Odvd( X, hAPP(
% 4.29/4.63 hAPP( c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 4.29/4.63 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 4.29/4.63 (22292) {G0,W13,D3,L3,V3,M3} { ! class_Rings_Olinordered__idom( X ), !
% 4.29/4.63 c_Groups_Oabs__class_Oabs( X, Z ) = c_Groups_Oabs__class_Oabs( X, Y ),
% 4.29/4.63 c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 4.29/4.63 (22293) {G0,W12,D3,L3,V3,M3} { ! class_Rings_Olinordered__idom( X ), !
% 4.29/4.63 c_Rings_Odvd__class_Odvd( X, c_Groups_Oabs__class_Oabs( X, Z ), Y ),
% 4.29/4.63 c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 4.29/4.63 (22294) {G0,W12,D3,L3,V3,M3} { ! class_Rings_Olinordered__idom( X ), !
% 4.29/4.63 c_Rings_Odvd__class_Odvd( X, Z, Y ), c_Rings_Odvd__class_Odvd( X,
% 4.29/4.63 c_Groups_Oabs__class_Oabs( X, Z ), Y ) }.
% 4.29/4.63 (22295) {G0,W12,D3,L3,V3,M3} { ! class_Rings_Olinordered__idom( X ), !
% 4.29/4.63 c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oabs__class_Oabs( X, Y ) ),
% 4.29/4.63 c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 4.29/4.63 (22296) {G0,W12,D3,L3,V3,M3} { ! class_Rings_Olinordered__idom( X ), !
% 4.29/4.63 c_Rings_Odvd__class_Odvd( X, Z, Y ), c_Rings_Odvd__class_Odvd( X, Z,
% 4.29/4.63 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 4.29/4.63 (22297) {G0,W11,D3,L3,V2,M3} { ! class_Rings_Ocomm__semiring__1( X ), !
% 4.29/4.63 c_Rings_Odvd__class_Odvd( X, c_Groups_Ozero__class_Ozero( X ), Y ), Y =
% 4.29/4.63 c_Groups_Ozero__class_Ozero( X ) }.
% 4.29/4.63 (22298) {G0,W11,D5,L2,V3,M2} { ! class_Rings_Ocomm__semiring__1( X ),
% 4.29/4.63 c_Rings_Odvd__class_Odvd( X, Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 4.29/4.63 ( X ), Z ), Y ) ) }.
% 4.29/4.63 (22299) {G0,W11,D5,L2,V3,M2} { ! class_Rings_Ocomm__semiring__1( X ),
% 4.29/4.63 c_Rings_Odvd__class_Odvd( X, Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 4.29/4.63 ( X ), Y ), Z ) ) }.
% 4.29/4.63 (22300) {G0,W15,D5,L3,V4,M3} { ! class_Rings_Ocomm__semiring__1( X ), !
% 4.29/4.63 c_Rings_Odvd__class_Odvd( X, Z, Y ), c_Rings_Odvd__class_Odvd( X, Z, hAPP
% 4.29/4.63 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 4.29/4.63 (22301) {G0,W15,D5,L3,V4,M3} { ! class_Rings_Ocomm__semiring__1( X ), !
% 4.29/4.63 c_Rings_Odvd__class_Odvd( X, Z, Y ), c_Rings_Odvd__class_Odvd( X, Z, hAPP
% 4.29/4.63 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 4.29/4.63 (22302) {G0,W24,D5,L4,V5,M4} { ! class_Rings_Ocomm__semiring__1( X ), !
% 4.29/4.63 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, U, T
% 4.29/4.63 ), c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 4.29/4.63 (22303) {G0,W14,D5,L3,V4,M3} { ! class_Rings_Odvd( X ), ! Z = hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( X ), Y ), T ), c_Rings_Odvd__class_Odvd( X
% 4.29/4.63 , Y, Z ) }.
% 4.29/4.63 (22304) {G0,W15,D5,L3,V4,M3} { ! class_Rings_Ocomm__semiring__1( X ), !
% 4.29/4.63 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 4.29/4.63 ), Z ), T ), Y ), c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 4.29/4.63 (22305) {G0,W15,D5,L3,V4,M3} { ! class_Rings_Ocomm__semiring__1( X ), !
% 4.29/4.63 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 4.29/4.63 ), T ), Z ), Y ), c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 4.29/4.63 (22306) {G0,W24,D5,L4,V4,M4} { ! class_Rings_Oidom( X ), !
% 4.29/4.63 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 4.29/4.63 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) )
% 4.29/4.63 , Z = c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, T, Y
% 4.29/4.63 ) }.
% 4.29/4.63 (22307) {G0,W20,D5,L3,V4,M3} { ! class_Rings_Oidom( X ), ! Z =
% 4.29/4.63 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, hAPP( hAPP
% 4.29/4.63 ( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 4.29/4.63 (22308) {G0,W20,D5,L3,V4,M3} { ! class_Rings_Oidom( X ), !
% 4.29/4.63 c_Rings_Odvd__class_Odvd( X, T, Y ), c_Rings_Odvd__class_Odvd( X, hAPP(
% 4.29/4.63 hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 4.29/4.63 (22309) {G0,W24,D5,L4,V4,M4} { ! class_Rings_Oidom( X ), !
% 4.29/4.63 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 4.29/4.63 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) )
% 4.29/4.63 , T = c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, Z, Y
% 4.29/4.63 ) }.
% 4.29/4.63 (22310) {G0,W20,D5,L3,V4,M3} { ! class_Rings_Oidom( X ), ! T =
% 4.29/4.63 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, hAPP( hAPP
% 4.29/4.63 ( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 4.29/4.63 (22311) {G0,W20,D5,L3,V4,M3} { ! class_Rings_Oidom( X ), !
% 4.29/4.63 c_Rings_Odvd__class_Odvd( X, Z, Y ), c_Rings_Odvd__class_Odvd( X, hAPP(
% 4.29/4.63 hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 4.29/4.63 (22312) {G0,W6,D2,L2,V2,M2} { ! class_Rings_Ocomm__semiring__1( X ),
% 4.29/4.63 c_Rings_Odvd__class_Odvd( X, Y, Y ) }.
% 4.29/4.63 (22313) {G0,W14,D2,L4,V4,M4} { ! class_Rings_Ocomm__semiring__1( X ), !
% 4.29/4.63 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Y, T
% 4.29/4.63 ), c_Rings_Odvd__class_Odvd( X, Z, T ) }.
% 4.29/4.63 (22314) {G0,W7,D2,L2,V2,M2} { ! Y = X, c_Rings_Odvd__class_Odvd(
% 4.29/4.63 tc_Nat_Onat, Y, X ) }.
% 4.29/4.63 (22315) {G0,W7,D2,L2,V2,M2} { ! Y = X, c_Rings_Odvd__class_Odvd(
% 4.29/4.63 tc_Nat_Onat, X, Y ) }.
% 4.29/4.63 (22316) {G0,W11,D2,L3,V2,M3} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 4.29/4.63 , X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 4.29/4.63 (22317) {G0,W10,D2,L3,V2,M3} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 4.29/4.63 , X ), alpha24( X, Y ), Y = X }.
% 4.29/4.63 (22318) {G0,W7,D2,L2,V2,M2} { ! alpha24( X, Y ), c_Rings_Odvd__class_Odvd
% 4.29/4.63 ( tc_Nat_Onat, Y, X ) }.
% 4.29/4.63 (22319) {G0,W7,D2,L2,V2,M2} { ! Y = X, c_Rings_Odvd__class_Odvd(
% 4.29/4.63 tc_Nat_Onat, Y, X ) }.
% 4.29/4.63 (22320) {G0,W7,D2,L2,V2,M2} { ! alpha24( X, Y ), c_Rings_Odvd__class_Odvd
% 4.29/4.63 ( tc_Nat_Onat, Y, X ) }.
% 4.29/4.63 (22321) {G0,W7,D2,L2,V2,M2} { ! alpha24( X, Y ), !
% 4.29/4.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 4.29/4.63 (22322) {G0,W11,D2,L3,V2,M3} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 4.29/4.63 , X ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), alpha24( X, Y ) }.
% 4.29/4.63 (22323) {G0,W7,D2,L2,V2,M2} { ! alpha25( X, Y ), c_Rings_Odvd__class_Odvd
% 4.29/4.63 ( tc_Nat_Onat, Y, X ) }.
% 4.29/4.63 (22324) {G0,W6,D2,L2,V2,M2} { ! alpha25( X, Y ), ! Y = X }.
% 4.29/4.63 (22325) {G0,W10,D2,L3,V2,M3} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 4.29/4.63 , X ), Y = X, alpha25( X, Y ) }.
% 4.29/4.63 (22326) {G0,W7,D2,L2,V2,M2} { ! alpha25( X, Y ), c_Rings_Odvd__class_Odvd
% 4.29/4.63 ( tc_Nat_Onat, Y, X ) }.
% 4.29/4.63 (22327) {G0,W7,D2,L2,V2,M2} { ! alpha25( X, Y ), !
% 4.29/4.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 4.29/4.63 (22328) {G0,W11,D2,L3,V2,M3} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 4.29/4.63 , X ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), alpha25( X, Y ) }.
% 4.29/4.63 (22329) {G0,W11,D2,L3,V2,M3} { Y = X, ! c_Rings_Odvd__class_Odvd(
% 4.29/4.63 tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 4.29/4.63 (22330) {G0,W11,D2,L3,V2,M3} { Y = X, ! c_Rings_Odvd__class_Odvd(
% 4.29/4.63 tc_Nat_Onat, Y, X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 4.29/4.63 (22331) {G0,W7,D2,L2,V2,M2} { ! Y = X, c_Rings_Odvd__class_Odvd(
% 4.29/4.63 tc_Nat_Onat, Y, X ) }.
% 4.29/4.63 (22332) {G0,W11,D2,L3,V2,M3} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 4.29/4.63 , X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), X = Y }.
% 4.29/4.63 (22333) {G0,W11,D2,L3,V2,M3} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 4.29/4.63 , X ), ! X = Y, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 4.29/4.63 (22334) {G0,W11,D2,L3,V2,M3} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 4.29/4.63 , X ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X }.
% 4.29/4.63 (22335) {G0,W11,D2,L3,V2,M3} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 4.29/4.63 , X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 4.29/4.63 (22336) {G0,W11,D2,L3,V2,M3} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 4.29/4.63 , X ), Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 4.29/4.63 (22337) {G0,W11,D2,L3,V2,M3} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 4.29/4.63 , X ), Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 4.29/4.63 (22338) {G0,W11,D2,L3,V3,M3} { ! Y = X, ! c_Rings_Odvd__class_Odvd(
% 4.29/4.63 tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 4.29/4.63 (22339) {G0,W11,D2,L3,V3,M3} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 4.29/4.63 , X ), ! X = Z, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 4.29/4.63 (22340) {G0,W11,D2,L3,V2,M3} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 4.29/4.63 , X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 4.29/4.63 (22341) {G0,W11,D2,L3,V2,M3} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 4.29/4.63 , X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 4.29/4.63 (22342) {G0,W12,D2,L3,V3,M3} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 4.29/4.63 , X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 4.29/4.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 4.29/4.63 (22343) {G0,W15,D2,L4,V3,M4} { ! Y = X, ! c_Rings_Odvd__class_Odvd(
% 4.29/4.63 tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ),
% 4.29/4.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 4.29/4.63 (22344) {G0,W15,D2,L4,V3,M4} { ! Y = X, ! c_Rings_Odvd__class_Odvd(
% 4.29/4.63 tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), !
% 4.29/4.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 4.29/4.63 (22345) {G0,W16,D2,L4,V3,M4} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 4.29/4.63 , X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 4.29/4.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd(
% 4.29/4.63 tc_Nat_Onat, Y, Z ) }.
% 4.29/4.63 (22346) {G0,W16,D2,L4,V3,M4} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 4.29/4.63 , X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 4.29/4.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd
% 4.29/4.63 ( tc_Nat_Onat, Z, Y ) }.
% 4.29/4.63 (22347) {G0,W11,D2,L3,V2,M3} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 4.29/4.63 , X ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), ! Y = X }.
% 4.29/4.63 (22348) {G0,W16,D2,L4,V2,M4} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 4.29/4.63 , X ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), !
% 4.29/4.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), c_Rings_Odvd__class_Odvd(
% 4.29/4.63 tc_Nat_Onat, Y, X ) }.
% 4.29/4.63 (22349) {G0,W12,D2,L3,V2,M3} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 4.29/4.63 , X ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 4.29/4.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 4.29/4.63 (22350) {G0,W16,D2,L4,V2,M4} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 4.29/4.63 , X ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), !
% 4.29/4.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), c_Rings_Odvd__class_Odvd(
% 4.29/4.63 tc_Nat_Onat, Y, X ) }.
% 4.29/4.63 (22351) {G0,W11,D2,L3,V2,M3} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 4.29/4.63 , X ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), ! Y = X }.
% 4.29/4.63 (22352) {G0,W11,D2,L3,V2,M3} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 4.29/4.63 , X ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), ! X = Y }.
% 4.29/4.63 (22353) {G0,W15,D2,L4,V3,M4} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 4.29/4.63 , X ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), ! X = Z,
% 4.29/4.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 4.29/4.63 (22354) {G0,W15,D2,L4,V3,M4} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 4.29/4.63 , X ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), ! X = Z, !
% 4.29/4.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 4.29/4.63 (22355) {G0,W16,D2,L4,V3,M4} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 4.29/4.63 , X ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), !
% 4.29/4.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 4.29/4.63 tc_Nat_Onat, Y, Z ) }.
% 4.29/4.63 (22356) {G0,W16,D2,L4,V3,M4} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 4.29/4.63 , X ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), !
% 4.29/4.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), ! c_Rings_Odvd__class_Odvd
% 4.29/4.63 ( tc_Nat_Onat, Z, Y ) }.
% 4.29/4.63 (22357) {G0,W16,D2,L4,V2,M4} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 4.29/4.63 , X ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), !
% 4.29/4.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), c_Rings_Odvd__class_Odvd(
% 4.29/4.63 tc_Nat_Onat, Y, X ) }.
% 4.29/4.63 (22358) {G0,W20,D2,L5,V3,M5} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 4.29/4.63 , X ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), !
% 4.29/4.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 4.29/4.63 tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 4.29/4.63 (22359) {G0,W20,D2,L5,V3,M5} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 4.29/4.63 , X ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), !
% 4.29/4.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 4.29/4.63 tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 4.29/4.63 (22360) {G0,W16,D2,L4,V2,M4} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 4.29/4.63 , X ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), !
% 4.29/4.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), c_Rings_Odvd__class_Odvd(
% 4.29/4.63 tc_Nat_Onat, Y, X ) }.
% 4.29/4.63 (22361) {G0,W20,D5,L3,V4,M3} { ! class_Rings_Ocomm__semiring__1( X ), !
% 4.29/4.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 4.29/4.63 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 4.29/4.63 ), T ), Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ) )
% 4.29/4.63 }.
% 4.29/4.63 (22362) {G0,W24,D5,L4,V5,M4} { ! class_Rings_Ocomm__semiring__1( X ), !
% 4.29/4.63 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq
% 4.29/4.63 ( tc_Nat_Onat, U, T ), c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 4.29/4.63 c_Power_Opower__class_Opower( X ), Z ), U ), hAPP( hAPP(
% 4.29/4.63 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 4.29/4.63 (22363) {G0,W24,D5,L4,V5,M4} { ! class_Rings_Ocomm__semiring__1( X ), !
% 4.29/4.63 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 4.29/4.63 ), T ), Z ), Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, U, Z
% 4.29/4.63 ), c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower
% 4.29/4.63 ( X ), T ), U ), Y ) }.
% 4.29/4.63 (22364) {G0,W17,D3,L4,V4,M4} { ! class_Rings_Ocomm__semiring__1( X ), !
% 4.29/4.63 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z, T
% 4.29/4.63 ), c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X, Y, T
% 4.29/4.63 ) ) }.
% 4.29/4.63 (22365) {G0,W11,D3,L2,V2,M2} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 4.29/4.63 , c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ),
% 4.29/4.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 4.29/4.63 (22366) {G0,W11,D3,L2,V2,M2} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 4.29/4.63 , X ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y,
% 4.29/4.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 4.29/4.63 (22367) {G0,W7,D3,L2,V2,M2} { ! class_Rings_Ocomm__semiring__1( X ),
% 4.29/4.63 c_Rings_Odvd__class_Odvd( X, c_Groups_Oone__class_Oone( X ), Y ) }.
% 4.29/4.63 (22368) {G0,W9,D3,L2,V1,M2} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X,
% 4.29/4.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X = c_Groups_Oone__class_Oone
% 4.29/4.63 ( tc_Nat_Onat ) }.
% 4.29/4.63 (22369) {G0,W9,D3,L2,V1,M2} { ! X = c_Groups_Oone__class_Oone( tc_Nat_Onat
% 4.29/4.63 ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Groups_Oone__class_Oone(
% 4.29/4.63 tc_Nat_Onat ) ) }.
% 4.29/4.63 (22370) {G0,W30,D6,L3,V4,M3} { ! class_Divides_Osemiring__div( X ), !
% 4.29/4.63 c_Rings_Odvd__class_Odvd( X, Z, Y ), hAPP( hAPP(
% 4.29/4.63 c_Power_Opower__class_Opower( X ), c_Divides_Odiv__class_Odiv( X, Y, Z )
% 4.29/4.63 ), T ) = c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 4.29/4.63 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 4.29/4.63 c_Power_Opower__class_Opower( X ), Z ), T ) ) }.
% 4.29/4.63 (22371) {G0,W37,D6,L4,V5,M4} { ! class_Divides_Osemiring__div( X ), !
% 4.29/4.63 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, U, T
% 4.29/4.63 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 4.29/4.63 c_Divides_Odiv__class_Odiv( X, Y, Z ) ), c_Divides_Odiv__class_Odiv( X, T
% 4.29/4.63 , U ) ) = c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ) }.
% 4.29/4.63 (22372) {G0,W25,D6,L3,V4,M3} { ! class_Divides_Osemiring__div( X ), !
% 4.29/4.63 c_Rings_Odvd__class_Odvd( X, Z, Y ), hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X, Y, Z )
% 4.29/4.63 ), T ) = c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( X ), Y ), T ), Z ) }.
% 4.29/4.63 (22373) {G0,W17,D5,L3,V3,M3} { ! class_Divides_Osemiring__div( X ), !
% 4.29/4.63 c_Rings_Odvd__class_Odvd( X, Z, Y ), hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X, Y, Z )
% 4.29/4.63 ), Z ) = Y }.
% 4.29/4.63 (22374) {G0,W25,D6,L3,V4,M3} { ! class_Divides_Osemiring__div( X ), !
% 4.29/4.63 c_Rings_Odvd__class_Odvd( X, Z, Y ), hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( X ), T ), c_Divides_Odiv__class_Odiv( X, Y
% 4.29/4.63 , Z ) ) = c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 4.29/4.63 (22375) {G0,W17,D5,L3,V3,M3} { ! class_Divides_Osemiring__div( X ), !
% 4.29/4.63 c_Rings_Odvd__class_Odvd( X, Z, Y ), hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( X ), Z ), c_Divides_Odiv__class_Odiv( X, Y
% 4.29/4.63 , Z ) ) = Y }.
% 4.29/4.63 (22376) {G0,W28,D4,L4,V4,M4} { ! class_Divides_Osemiring__div( X ), !
% 4.29/4.63 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z, T
% 4.29/4.63 ), c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, Y, T )
% 4.29/4.63 , Z ) = c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Y
% 4.29/4.63 , Z ), c_Divides_Odiv__class_Odiv( X, T, Z ) ) }.
% 4.29/4.63 (22377) {G0,W24,D3,L5,V4,M5} { ! class_Divides_Osemiring__div( X ), !
% 4.29/4.63 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z, T
% 4.29/4.63 ), ! c_Rings_Odvd__class_Odvd( X, c_Divides_Odiv__class_Odiv( X, Y, Z )
% 4.29/4.63 , c_Divides_Odiv__class_Odiv( X, T, Z ) ), c_Rings_Odvd__class_Odvd( X, Y
% 4.29/4.63 , T ) }.
% 4.29/4.63 (22378) {G0,W24,D3,L5,V4,M5} { ! class_Divides_Osemiring__div( X ), !
% 4.29/4.63 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z, T
% 4.29/4.63 ), ! c_Rings_Odvd__class_Odvd( X, Y, T ), c_Rings_Odvd__class_Odvd( X,
% 4.29/4.63 c_Divides_Odiv__class_Odiv( X, Y, Z ), c_Divides_Odiv__class_Odiv( X, T,
% 4.29/4.63 Z ) ) }.
% 4.29/4.63 (22379) {G0,W24,D5,L5,V4,M5} { ! class_Divides_Osemiring__div( X ), Y =
% 4.29/4.63 c_Groups_Ozero__class_Ozero( X ), ! c_Rings_Odvd__class_Odvd( X, Y, Z ),
% 4.29/4.63 ! c_Divides_Odiv__class_Odiv( X, Z, Y ) = T, Z = hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) }.
% 4.29/4.63 (22380) {G0,W24,D5,L5,V4,M5} { ! class_Divides_Osemiring__div( X ), Y =
% 4.29/4.63 c_Groups_Ozero__class_Ozero( X ), ! c_Rings_Odvd__class_Odvd( X, Y, Z ),
% 4.29/4.63 ! Z = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ),
% 4.29/4.63 c_Divides_Odiv__class_Odiv( X, Z, Y ) = T }.
% 4.29/4.63 (22381) {G0,W40,D5,L7,V5,M7} { ! class_Divides_Osemiring__div( X ), Y =
% 4.29/4.63 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), !
% 4.29/4.63 c_Rings_Odvd__class_Odvd( X, Y, T ), ! c_Rings_Odvd__class_Odvd( X, Z, U
% 4.29/4.63 ), ! c_Divides_Odiv__class_Odiv( X, T, Y ) = c_Divides_Odiv__class_Odiv
% 4.29/4.63 ( X, U, Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ) =
% 4.29/4.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), U ) }.
% 4.29/4.63 (22382) {G0,W40,D5,L7,V5,M7} { ! class_Divides_Osemiring__div( X ), Y =
% 4.29/4.63 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), !
% 4.29/4.63 c_Rings_Odvd__class_Odvd( X, Y, T ), ! c_Rings_Odvd__class_Odvd( X, Z, U
% 4.29/4.63 ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ) = hAPP(
% 4.29/4.63 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), U ),
% 4.29/4.63 c_Divides_Odiv__class_Odiv( X, T, Y ) = c_Divides_Odiv__class_Odiv( X, U
% 4.29/4.63 , Z ) }.
% 4.29/4.63 (22383) {G0,W13,D3,L3,V2,M3} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 4.29/4.63 , X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 4.29/4.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 4.29/4.63 (22384) {G0,W23,D5,L3,V3,M3} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat,
% 4.29/4.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP
% 4.29/4.63 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 4.29/4.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 4.29/4.63 tc_Nat_Onat ), Z ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 4.29/4.63 (22385) {G0,W23,D5,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.63 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), !
% 4.29/4.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 4.29/4.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 4.29/4.63 (22386) {G0,W23,D5,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.63 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), !
% 4.29/4.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ), c_Rings_Odvd__class_Odvd(
% 4.29/4.63 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 4.29/4.63 ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y
% 4.29/4.63 ) ) }.
% 4.29/4.63 (22387) {G0,W16,D5,L3,V3,M3} { ! class_Rings_Ocomm__semiring__1( X ), !
% 4.29/4.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 4.29/4.63 tc_Nat_Onat ), Z ), c_Rings_Odvd__class_Odvd( X, Y, hAPP( hAPP(
% 4.29/4.63 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 4.29/4.63 (22388) {G0,W15,D5,L3,V3,M3} { ! class_Rings_Ocomm__semiring__1( X ), ! Y
% 4.29/4.63 = c_Groups_Oone__class_Oone( X ), c_Rings_Odvd__class_Odvd( X, Y, hAPP(
% 4.29/4.63 hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 4.29/4.63 (22389) {G0,W18,D5,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.63 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), !
% 4.29/4.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ), Y =
% 4.29/4.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 4.29/4.63 (22390) {G0,W18,D5,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.63 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), ! Y =
% 4.29/4.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 4.29/4.63 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 4.29/4.63 ), X ), X ) }.
% 4.29/4.63 (22391) {G0,W18,D5,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.63 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), !
% 4.29/4.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ), Y =
% 4.29/4.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 4.29/4.63 (22392) {G0,W18,D5,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.63 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), ! Y =
% 4.29/4.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 4.29/4.63 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 4.29/4.63 ), Y ), X ) }.
% 4.29/4.63 (22393) {G0,W23,D5,L3,V3,M3} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat,
% 4.29/4.63 hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ), hAPP(
% 4.29/4.63 hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ) ), !
% 4.29/4.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 4.29/4.63 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 4.29/4.63 ) }.
% 4.29/4.63 (22394) {G0,W20,D6,L4,V6,M4} { ! class_Rings_Odvd( X ), !
% 4.29/4.63 class_Rings_Osemiring__0( X ), ! hBOOL( hAPP( Z, hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ), hBOOL( hAPP( Z, skol49
% 4.29/4.63 ( U, W, Z ) ) ) }.
% 4.29/4.63 (22395) {G0,W24,D6,L4,V4,M4} { ! class_Rings_Odvd( X ), !
% 4.29/4.63 class_Rings_Osemiring__0( X ), ! hBOOL( hAPP( Z, hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ),
% 4.29/4.63 c_Rings_Odvd__class_Odvd( X, Y, c_Groups_Oplus__class_Oplus( X, skol49( X
% 4.29/4.63 , Y, Z ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 4.29/4.63 (22396) {G0,W28,D6,L5,V4,M5} { ! class_Rings_Odvd( X ), !
% 4.29/4.63 class_Rings_Osemiring__0( X ), ! c_Rings_Odvd__class_Odvd( X, Y,
% 4.29/4.63 c_Groups_Oplus__class_Oplus( X, T, c_Groups_Ozero__class_Ozero( X ) ) ),
% 4.29/4.63 ! hBOOL( hAPP( Z, T ) ), hBOOL( hAPP( Z, hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( X ), Y ), skol57( X, Y, Z ) ) ) ) }.
% 4.29/4.63 (22397) {G0,W22,D5,L3,V3,M3} { X = c_Groups_Ozero__class_Ozero(
% 4.29/4.63 tc_Nat_Onat ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 4.29/4.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 4.29/4.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ),
% 4.29/4.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 4.29/4.63 (22398) {G0,W22,D5,L3,V3,M3} { X = c_Groups_Ozero__class_Ozero(
% 4.29/4.63 tc_Nat_Onat ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ),
% 4.29/4.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 4.29/4.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 4.29/4.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 4.29/4.63 (22399) {G0,W15,D3,L3,V3,M3} { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z
% 4.29/4.63 , c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), !
% 4.29/4.63 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, X ), c_Rings_Odvd__class_Odvd(
% 4.29/4.63 tc_Int_Oint, Z, Y ) }.
% 4.29/4.63 (22400) {G0,W15,D3,L3,V3,M3} { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y
% 4.29/4.63 , X ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, Z ),
% 4.29/4.63 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Divides_Odiv__class_Omod(
% 4.29/4.63 tc_Int_Oint, X, Z ) ) }.
% 4.29/4.63 (22401) {G0,W11,D3,L2,V1,M2} { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, X
% 4.29/4.63 , c_Groups_Oone__class_Oone( tc_Int_Oint ) ), c_Groups_Oabs__class_Oabs(
% 4.29/4.63 tc_Int_Oint, X ) = c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 4.29/4.63 (22402) {G0,W11,D3,L2,V1,M2} { ! c_Groups_Oabs__class_Oabs( tc_Int_Oint, X
% 4.29/4.63 ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), c_Rings_Odvd__class_Odvd(
% 4.29/4.63 tc_Int_Oint, X, c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 4.29/4.63 (22403) {G0,W22,D5,L3,V3,M3} { X = c_Groups_Ozero__class_Ozero(
% 4.29/4.63 tc_Nat_Onat ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 4.29/4.63 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 4.29/4.63 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ) ),
% 4.29/4.63 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 4.29/4.63 (22404) {G0,W22,D5,L3,V3,M3} { X = c_Groups_Ozero__class_Ozero(
% 4.29/4.63 tc_Nat_Onat ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ),
% 4.29/4.63 c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 4.29/4.63 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 4.29/4.63 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ) ) }.
% 4.29/4.63 (22405) {G0,W22,D5,L3,V3,M3} { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint,
% 4.29/4.63 hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ), hAPP(
% 4.29/4.63 hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ), Y =
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 4.29/4.63 tc_Int_Oint, Z, X ) }.
% 4.29/4.63 (22406) {G0,W15,D3,L3,V2,M3} { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y
% 4.29/4.63 , X ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, X, Y ),
% 4.29/4.63 c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) = c_Groups_Oabs__class_Oabs(
% 4.29/4.63 tc_Int_Oint, X ) }.
% 4.29/4.63 (22407) {G0,W22,D5,L3,V3,M3} { X = c_Groups_Ozero__class_Ozero(
% 4.29/4.63 tc_Int_Oint ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ),
% 4.29/4.63 c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) }.
% 4.29/4.63 (22408) {G0,W22,D5,L3,V3,M3} { X = c_Groups_Ozero__class_Ozero(
% 4.29/4.63 tc_Int_Oint ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ),
% 4.29/4.63 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 4.29/4.63 (22409) {G0,W22,D5,L3,V3,M3} { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint,
% 4.29/4.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP
% 4.29/4.63 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), Z =
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Rings_Odvd__class_Odvd(
% 4.29/4.63 tc_Int_Oint, Y, X ) }.
% 4.29/4.63 (22410) {G0,W13,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.63 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 4.29/4.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ), !
% 4.29/4.63 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }.
% 4.29/4.63 (22411) {G0,W26,D7,L3,V5,M3} { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y
% 4.29/4.63 , X ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y,
% 4.29/4.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, T ) ),
% 4.29/4.63 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 4.29/4.63 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), T ) ) }.
% 4.29/4.63 (22412) {G0,W26,D7,L3,V5,M3} { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y
% 4.29/4.63 , X ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y,
% 4.29/4.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 4.29/4.63 tc_Int_Oint, U, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 4.29/4.63 , Z ), X ) ), T ) ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y,
% 4.29/4.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, T ) ) }.
% 4.29/4.63 (22413) {G0,W16,D6,L2,V3,M2} { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z
% 4.29/4.63 , c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ),
% 4.29/4.63 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 4.29/4.63 (22414) {G0,W16,D6,L2,V3,M2} { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z
% 4.29/4.63 , Y ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z,
% 4.29/4.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ) }.
% 4.29/4.63 (22415) {G0,W21,D3,L5,V2,M5} { ! c_Orderings_Oord__class_Oless__eq(
% 4.29/4.63 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 4.29/4.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), !
% 4.29/4.63 c_Rings_Odvd__class_Odvd( tc_Int_Oint, X, Y ), ! c_Rings_Odvd__class_Odvd
% 4.29/4.63 ( tc_Int_Oint, Y, X ), X = Y }.
% 4.29/4.63 (22416) {G0,W19,D4,L2,V2,M2} { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y
% 4.29/4.63 , X ), c_Groups_Oabs__class_Oabs( tc_Int_Oint, c_Divides_Odiv__class_Odiv
% 4.29/4.63 ( tc_Int_Oint, X, Y ) ) = c_Divides_Odiv__class_Odiv( tc_Int_Oint,
% 4.29/4.63 c_Groups_Oabs__class_Oabs( tc_Int_Oint, X ), c_Groups_Oabs__class_Oabs(
% 4.29/4.63 tc_Int_Oint, Y ) ) }.
% 4.29/4.63 (22417) {G0,W15,D5,L2,V2,M2} { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y
% 4.29/4.63 , X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ),
% 4.29/4.63 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) = X }.
% 4.29/4.63 (22418) {G0,W13,D3,L3,V2,M3} { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y
% 4.29/4.63 , X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 4.29/4.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 4.29/4.63 (22419) {G0,W16,D3,L3,V2,M3} { X = c_Groups_Ozero__class_Ozero(
% 4.29/4.63 tc_Int_Oint ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ),
% 4.29/4.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oabs__class_Oabs
% 4.29/4.63 ( tc_Int_Oint, Y ), c_Groups_Oabs__class_Oabs( tc_Int_Oint, X ) ) }.
% 4.29/4.63 (22420) {G0,W19,D5,L3,V2,M3} { X = c_Groups_Ozero__class_Ozero(
% 4.29/4.63 tc_Int_Oint ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ), X ),
% 4.29/4.63 c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) = c_Groups_Oone__class_Oone(
% 4.29/4.63 tc_Int_Oint ) }.
% 4.29/4.63 (22421) {G0,W19,D5,L3,V2,M3} { X = c_Groups_Ozero__class_Ozero(
% 4.29/4.63 tc_Int_Oint ), ! c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) =
% 4.29/4.63 c_Groups_Oone__class_Oone( tc_Int_Oint ), c_Rings_Odvd__class_Odvd(
% 4.29/4.63 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X
% 4.29/4.63 ), Y ), X ) }.
% 4.29/4.63 (22422) {G0,W5,D3,L1,V1,M1} { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X,
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 4.29/4.63 (22423) {G0,W5,D3,L1,V1,M1} { c_Rings_Odvd__class_Odvd( tc_Nat_Onat,
% 4.29/4.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X ) }.
% 4.29/4.63 (22424) {G0,W14,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.63 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), !
% 4.29/4.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ),
% 4.29/4.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 4.29/4.63 tc_Nat_Onat ), Y ) }.
% 4.29/4.63 (22425) {G0,W22,D5,L3,V3,M3} { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat,
% 4.29/4.63 hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ), hAPP(
% 4.29/4.63 hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ), Y =
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 4.29/4.63 tc_Nat_Onat, Z, X ) }.
% 4.29/4.63 (22426) {G0,W32,D7,L5,V5,M5} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.63 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), hBOOL( hAPP
% 4.29/4.63 ( Y, skol50( Z, Y ) ) ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint
% 4.29/4.63 , c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! hBOOL( hAPP( Y, U )
% 4.29/4.63 ), hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, hAPP(
% 4.29/4.63 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), T ), X ) ) ) ) }.
% 4.29/4.63 (22427) {G0,W35,D7,L5,V4,M5} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.63 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), ! hBOOL(
% 4.29/4.63 hAPP( Y, c_Groups_Oplus__class_Oplus( tc_Int_Oint, skol50( X, Y ), X ) )
% 4.29/4.63 ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), ! hBOOL( hAPP( Y, T ) )
% 4.29/4.63 , hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus( tc_Int_Oint, T, hAPP( hAPP
% 4.29/4.63 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ) ) }.
% 4.29/4.63 (22428) {G0,W26,D8,L2,V3,M2} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.63 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 4.29/4.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ominus__class_Ominus
% 4.29/4.63 ( tc_Int_Oint, Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint
% 4.29/4.63 ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oabs__class_Oabs(
% 4.29/4.63 tc_Int_Oint, c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ),
% 4.29/4.63 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ), X ) ), Y ) }.
% 4.29/4.63 (22429) {G0,W16,D3,L2,V3,M2} { ! c_Divides_Odiv__class_Omod( tc_Int_Oint,
% 4.29/4.63 Z, Y ) = c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ),
% 4.29/4.63 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Ominus__class_Ominus(
% 4.29/4.63 tc_Int_Oint, Z, X ) ) }.
% 4.29/4.63 (22430) {G0,W16,D3,L2,V3,M2} { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y
% 4.29/4.63 , c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, X ) ),
% 4.29/4.63 c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y ) =
% 4.29/4.63 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ) }.
% 4.29/4.63 (22431) {G0,W17,D3,L4,V4,M4} { ! class_Rings_Ocomm__ring__1( X ), !
% 4.29/4.63 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z, T
% 4.29/4.63 ), c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Ominus__class_Ominus( X, Y,
% 4.29/4.63 T ) ) }.
% 4.29/4.63 (22432) {G0,W15,D3,L3,V3,M3} { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z
% 4.29/4.63 , c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ), !
% 4.29/4.63 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, X ), c_Rings_Odvd__class_Odvd(
% 4.29/4.63 tc_Int_Oint, Z, Y ) }.
% 4.29/4.63 (22433) {G0,W30,D7,L5,V6,M5} { ! class_Rings_Ocomm__ring( X ), !
% 4.29/4.63 class_Rings_Odvd( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y ), !
% 4.29/4.63 c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X, U, T ) )
% 4.29/4.63 , c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X,
% 4.29/4.63 c_Groups_Ominus__class_Ominus( X, U, hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) }.
% 4.29/4.63 (22434) {G0,W30,D7,L5,V6,M5} { ! class_Rings_Ocomm__ring( X ), !
% 4.29/4.63 class_Rings_Odvd( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y ), !
% 4.29/4.63 c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X,
% 4.29/4.63 c_Groups_Ominus__class_Ominus( X, U, hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ),
% 4.29/4.63 c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X, U, T ) )
% 4.29/4.63 }.
% 4.29/4.63 (22435) {G0,W30,D7,L5,V6,M5} { ! class_Rings_Ocomm__ring( X ), !
% 4.29/4.63 class_Rings_Odvd( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y ), !
% 4.29/4.63 c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X, U, T ) )
% 4.29/4.63 , c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X,
% 4.29/4.63 c_Groups_Ominus__class_Ominus( X, U, hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) }.
% 4.29/4.63 (22436) {G0,W30,D7,L5,V6,M5} { ! class_Rings_Ocomm__ring( X ), !
% 4.29/4.63 class_Rings_Odvd( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y ), !
% 4.29/4.63 c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X,
% 4.29/4.63 c_Groups_Ominus__class_Ominus( X, U, hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ),
% 4.29/4.63 c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X, U, T ) )
% 4.29/4.63 }.
% 4.29/4.63 (22437) {G0,W37,D6,L3,V6,M3} { ! class_Rings_Oordered__ring( X ), !
% 4.29/4.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 4.29/4.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 4.29/4.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 4.29/4.63 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 4.29/4.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 4.29/4.63 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ) }.
% 4.29/4.63 (22438) {G0,W37,D6,L3,V6,M3} { ! class_Rings_Oordered__ring( X ), !
% 4.29/4.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 4.29/4.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 4.29/4.63 c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ),
% 4.29/4.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 4.29/4.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 4.29/4.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 4.29/4.63 ( X ), Z ), U ), Y ) ) }.
% 4.29/4.63 (22439) {G0,W37,D6,L3,V6,M3} { ! class_Rings_Oordered__ring( X ), !
% 4.29/4.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 4.29/4.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 4.29/4.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 4.29/4.63 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X, T,
% 4.29/4.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 4.29/4.63 ( X ), c_Groups_Ominus__class_Ominus( X, Z, W ) ), U ), Y ) ) }.
% 4.29/4.63 (22440) {G0,W37,D6,L3,V6,M3} { ! class_Rings_Oordered__ring( X ), !
% 4.29/4.63 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 4.29/4.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 4.29/4.63 c_Groups_Ominus__class_Ominus( X, Z, W ) ), U ), Y ) ),
% 4.29/4.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 4.29/4.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 4.29/4.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 4.29/4.63 ( X ), Z ), U ), Y ) ) }.
% 4.29/4.63 (22441) {G0,W37,D6,L3,V6,M3} { ! class_Rings_Oordered__ring( X ), !
% 4.29/4.63 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 4.29/4.63 hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 4.29/4.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 4.29/4.63 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless( X,
% 4.29/4.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 4.29/4.63 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ) }.
% 4.29/4.63 (22442) {G0,W37,D6,L3,V6,M3} { ! class_Rings_Oordered__ring( X ), !
% 4.29/4.63 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 4.29/4.63 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 4.29/4.63 X, W, Z ) ), U ), T ), Y ), c_Orderings_Oord__class_Oless( X,
% 4.29/4.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 4.29/4.63 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 4.29/4.63 (22443) {G0,W37,D6,L3,V6,M3} { ! class_Rings_Oordered__ring( X ), !
% 4.29/4.63 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 4.29/4.63 hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 4.29/4.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 4.29/4.63 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless( X, T,
% 4.29/4.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 4.29/4.63 ( X ), c_Groups_Ominus__class_Ominus( X, Z, W ) ), U ), Y ) ) }.
% 4.29/4.63 (22444) {G0,W37,D6,L3,V6,M3} { ! class_Rings_Oordered__ring( X ), !
% 4.29/4.63 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, hAPP
% 4.29/4.63 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus
% 4.29/4.63 ( X, Z, W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless( X,
% 4.29/4.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 4.29/4.63 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 4.29/4.63 (22445) {G0,W27,D6,L2,V2,M2} { ! class_Rings_Oring__1( X ),
% 4.29/4.63 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( X ), Y ), Y ), c_Groups_Oone__class_Oone(
% 4.29/4.63 X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 4.29/4.63 c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) ) ),
% 4.29/4.63 c_Groups_Ominus__class_Ominus( X, Y, c_Groups_Oone__class_Oone( X ) ) )
% 4.29/4.63 }.
% 4.29/4.63 (22446) {G0,W26,D7,L3,V4,M3} { ! class_Fields_Ofield( X ), Y =
% 4.29/4.63 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ominus__class_Ominus( X, T,
% 4.29/4.63 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 4.29/4.63 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus( X,
% 4.29/4.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), Z ), Y ) }.
% 4.29/4.63 (22447) {G0,W26,D7,L3,V4,M3} { ! class_Fields_Ofield( X ), Y =
% 4.29/4.63 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ominus__class_Ominus( X,
% 4.29/4.63 c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ) =
% 4.29/4.63 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus( X, T,
% 4.29/4.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) }.
% 4.29/4.63 (22448) {G0,W43,D7,L4,V5,M4} { ! class_Fields_Ofield( X ), Y =
% 4.29/4.63 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ),
% 4.29/4.63 c_Groups_Ominus__class_Ominus( X, c_Rings_Oinverse__class_Odivide( X, U,
% 4.29/4.63 Y ), c_Rings_Oinverse__class_Odivide( X, T, Z ) ) =
% 4.29/4.63 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus( X,
% 4.29/4.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 4.29/4.63 (22449) {G0,W30,D5,L2,V5,M2} { !
% 4.29/4.63 class_Groups_Oordered__ab__group__add__abs( X ),
% 4.29/4.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 4.29/4.63 c_Groups_Ominus__class_Ominus( X, c_Groups_Oplus__class_Oplus( X, U, T )
% 4.29/4.63 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) ), c_Groups_Oplus__class_Oplus
% 4.29/4.63 ( X, c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, U, Z
% 4.29/4.63 ) ), c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, T,
% 4.29/4.63 Y ) ) ) ) }.
% 4.29/4.63 (22450) {G0,W18,D4,L2,V3,M2} { !
% 4.29/4.63 class_Groups_Oordered__ab__group__add__abs( X ),
% 4.29/4.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 4.29/4.63 c_Groups_Ominus__class_Ominus( X, Z, Y ) ), c_Groups_Oplus__class_Oplus(
% 4.29/4.63 X, c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) )
% 4.29/4.63 ) }.
% 4.29/4.63 (22451) {G0,W18,D4,L3,V4,M3} { ! class_Rings_Olinordered__idom( X ), !
% 4.29/4.63 c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X,
% 4.29/4.63 c_Groups_Ominus__class_Ominus( X, T, Z ) ), Y ),
% 4.29/4.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 4.29/4.63 ), T ) }.
% 4.29/4.63 (22452) {G0,W18,D4,L3,V4,M3} { ! class_Rings_Olinordered__idom( X ), !
% 4.29/4.63 c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X,
% 4.29/4.63 c_Groups_Ominus__class_Ominus( X, T, Z ) ), Y ),
% 4.29/4.63 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y
% 4.29/4.63 ) ) }.
% 4.29/4.63 (22453) {G0,W25,D4,L4,V4,M4} { ! class_Rings_Olinordered__idom( X ), !
% 4.29/4.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 4.29/4.63 ), T ), ! c_Orderings_Oord__class_Oless( X, T,
% 4.29/4.63 c_Groups_Oplus__class_Oplus( X, Z, Y ) ), c_Orderings_Oord__class_Oless(
% 4.29/4.63 X, c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, T, Z )
% 4.29/4.63 ), Y ) }.
% 4.29/4.63 (22454) {G0,W18,D4,L2,V3,M2} { ! class_RealVector_Oreal__normed__vector( X
% 4.29/4.63 ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 4.29/4.63 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, Z,
% 4.29/4.63 Y ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 4.29/4.63 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 4.29/4.63 ( X, Y ) ) ) }.
% 4.29/4.63 (22455) {G0,W12,D4,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 4.29/4.63 tc_Int_Oint, Y, c_Groups_Ominus__class_Ominus( tc_Int_Oint, X,
% 4.29/4.63 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ),
% 4.29/4.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 4.29/4.63 (22456) {G0,W12,D4,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.63 tc_Int_Oint, Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 4.29/4.63 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 4.29/4.63 ( tc_Int_Oint ) ) ) }.
% 4.29/4.63 (22457) {G0,W35,D4,L4,V6,M4} { ! class_Divides_Oring__div( X ), !
% 4.29/4.63 c_Divides_Odiv__class_Omod( X, T, Z ) = c_Divides_Odiv__class_Omod( X, Y
% 4.29/4.63 , Z ), ! c_Divides_Odiv__class_Omod( X, W, Z ) =
% 4.29/4.63 c_Divides_Odiv__class_Omod( X, U, Z ), c_Divides_Odiv__class_Omod( X,
% 4.29/4.63 c_Groups_Ominus__class_Ominus( X, T, W ), Z ) =
% 4.29/4.63 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, Y, U ),
% 4.29/4.63 Z ) }.
% 4.29/4.63 (22458) {G0,W18,D5,L1,V3,M1} { c_Divides_Odiv__class_Omod( tc_Int_Oint,
% 4.29/4.63 c_Groups_Ominus__class_Ominus( tc_Int_Oint, c_Divides_Odiv__class_Omod(
% 4.29/4.63 tc_Int_Oint, Z, Y ), X ), Y ) = c_Divides_Odiv__class_Omod( tc_Int_Oint,
% 4.29/4.63 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, X ), Y ) }.
% 4.29/4.63 (22459) {G0,W18,D5,L1,V3,M1} { c_Divides_Odiv__class_Omod( tc_Int_Oint,
% 4.29/4.63 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, c_Divides_Odiv__class_Omod
% 4.29/4.63 ( tc_Int_Oint, Y, X ) ), X ) = c_Divides_Odiv__class_Omod( tc_Int_Oint,
% 4.29/4.63 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ), X ) }.
% 4.29/4.63 (22460) {G0,W23,D5,L2,V4,M2} { ! class_Divides_Oring__div( X ),
% 4.29/4.63 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, T, Z ),
% 4.29/4.63 Y ) = c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X,
% 4.29/4.63 c_Divides_Odiv__class_Omod( X, T, Y ), c_Divides_Odiv__class_Omod( X, Z,
% 4.29/4.63 Y ) ), Y ) }.
% 4.29/4.63 (22461) {G0,W20,D5,L2,V4,M2} { ! class_Divides_Oring__div( X ),
% 4.29/4.63 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, T, Z ),
% 4.29/4.63 Y ) = c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X,
% 4.29/4.63 c_Divides_Odiv__class_Omod( X, T, Y ), Z ), Y ) }.
% 4.29/4.63 (22462) {G0,W20,D5,L2,V4,M2} { ! class_Divides_Oring__div( X ),
% 4.29/4.63 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, T, Z ),
% 4.29/4.63 Y ) = c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, T
% 4.29/4.63 , c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 4.29/4.63 (22463) {G0,W12,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.63 tc_Int_Oint, Y, X ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 4.29/4.63 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ),
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 4.29/4.63 (22464) {G0,W12,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.63 tc_Int_Oint, c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ),
% 4.29/4.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 4.29/4.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 4.29/4.63 (22465) {G0,W19,D3,L4,V5,M4} { ! class_Groups_Oordered__ab__group__add( X
% 4.29/4.63 ), ! c_Groups_Ominus__class_Ominus( X, U, T ) =
% 4.29/4.63 c_Groups_Ominus__class_Ominus( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 4.29/4.63 ( X, U, T ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 4.29/4.63 (22466) {G0,W19,D3,L4,V5,M4} { ! class_Groups_Oordered__ab__group__add( X
% 4.29/4.63 ), ! c_Groups_Ominus__class_Ominus( X, U, T ) =
% 4.29/4.63 c_Groups_Ominus__class_Ominus( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 4.29/4.63 ( X, Z, Y ), c_Orderings_Oord__class_Oless( X, U, T ) }.
% 4.29/4.63 (22467) {G0,W12,D3,L3,V3,M3} { ! class_Groups_Ogroup__add( X ), !
% 4.29/4.63 c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X
% 4.29/4.63 ), Z = Y }.
% 4.29/4.63 (22468) {G0,W12,D3,L3,V3,M3} { ! class_Groups_Ogroup__add( X ), ! Z = Y,
% 4.29/4.63 c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X
% 4.29/4.63 ) }.
% 4.29/4.63 (22469) {G0,W12,D3,L3,V3,M3} { ! class_Groups_Oab__group__add( X ), ! Z =
% 4.29/4.63 Y, c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Ozero__class_Ozero
% 4.29/4.63 ( X ) }.
% 4.29/4.63 (22470) {G0,W12,D3,L3,V3,M3} { ! class_Groups_Oab__group__add( X ), !
% 4.29/4.63 c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X
% 4.29/4.63 ), Z = Y }.
% 4.29/4.63 (22471) {G0,W9,D3,L2,V2,M2} { ! class_Groups_Ogroup__add( X ),
% 4.29/4.63 c_Groups_Ominus__class_Ominus( X, Y, Y ) = c_Groups_Ozero__class_Ozero( X
% 4.29/4.63 ) }.
% 4.29/4.63 (22472) {G0,W9,D4,L2,V2,M2} { ! class_Groups_Ogroup__add( X ),
% 4.29/4.63 c_Groups_Ominus__class_Ominus( X, Y, c_Groups_Ozero__class_Ozero( X ) ) =
% 4.29/4.63 Y }.
% 4.29/4.63 (22473) {G0,W15,D4,L2,V3,M2} { !
% 4.29/4.63 class_Groups_Oordered__ab__group__add__abs( X ),
% 4.29/4.63 c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Z, Y ) )
% 4.29/4.63 = c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Y, Z )
% 4.29/4.63 ) }.
% 4.29/4.63 (22474) {G0,W24,D6,L1,V3,M1} { hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 4.29/4.63 tc_Int_Oint ), Z ), c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) )
% 4.29/4.63 = c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 4.29/4.63 (22475) {G0,W24,D6,L1,V3,M1} { hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 4.29/4.63 tc_Int_Oint ), c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ), X )
% 4.29/4.63 = c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 4.29/4.63 (22476) {G0,W26,D6,L2,V4,M2} { ! class_RealVector_Oreal__normed__algebra(
% 4.29/4.63 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 4.29/4.63 c_Groups_Ominus__class_Ominus( X, T, Z ) ), Y ) =
% 4.29/4.63 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 4.29/4.63 (22477) {G0,W26,D6,L2,V4,M2} { ! class_RealVector_Oreal__normed__algebra(
% 4.29/4.63 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 4.29/4.63 c_Groups_Ominus__class_Ominus( X, T, Z ) ), Y ) =
% 4.29/4.63 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 4.29/4.63 (22478) {G0,W26,D6,L2,V4,M2} { ! class_RealVector_Oreal__normed__algebra(
% 4.29/4.63 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ),
% 4.29/4.63 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) =
% 4.29/4.63 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 4.29/4.63 (22479) {G0,W26,D6,L2,V4,M2} { ! class_RealVector_Oreal__normed__algebra(
% 4.29/4.63 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ),
% 4.29/4.63 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) =
% 4.29/4.63 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 4.29/4.63 (22480) {G0,W20,D4,L2,V4,M2} { ! class_Rings_Odivision__ring( X ),
% 4.29/4.63 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus( X, T,
% 4.29/4.63 Z ), Y ) = c_Groups_Ominus__class_Ominus( X,
% 4.29/4.63 c_Rings_Oinverse__class_Odivide( X, T, Y ),
% 4.29/4.63 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 4.29/4.63 (22481) {G0,W20,D4,L2,V4,M2} { ! class_RealVector_Oreal__normed__field( X
% 4.29/4.63 ), c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus( X
% 4.29/4.63 , T, Z ), Y ) = c_Groups_Ominus__class_Ominus( X,
% 4.29/4.63 c_Rings_Oinverse__class_Odivide( X, T, Y ),
% 4.29/4.63 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 4.29/4.63 (22482) {G0,W15,D4,L2,V3,M2} { ! class_RealVector_Oreal__normed__vector( X
% 4.29/4.63 ), c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X
% 4.29/4.63 , Z, Y ) ) = c_RealVector_Onorm__class_Onorm( X,
% 4.29/4.63 c_Groups_Ominus__class_Ominus( X, Y, Z ) ) }.
% 4.29/4.63 (22483) {G0,W24,D6,L2,V4,M2} { ! class_Rings_Ocomm__ring( X ), hAPP(
% 4.29/4.63 c_Polynomial_Opoly( X, c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly
% 4.29/4.63 ( X ), T, Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP(
% 4.29/4.63 c_Polynomial_Opoly( X, T ), Y ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) )
% 4.29/4.63 }.
% 4.29/4.63 (22484) {G0,W17,D3,L4,V5,M4} { ! class_Groups_Oab__group__add( X ), !
% 4.29/4.63 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 4.29/4.63 ( X, Z, Y ), ! U = T, Z = Y }.
% 4.29/4.63 (22485) {G0,W17,D3,L4,V5,M4} { ! class_Groups_Oab__group__add( X ), !
% 4.29/4.63 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 4.29/4.63 ( X, Z, Y ), ! Z = Y, U = T }.
% 4.29/4.63 (22486) {G0,W25,D5,L2,V5,M2} { ! class_Groups_Oab__group__add( X ),
% 4.29/4.63 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ),
% 4.29/4.63 c_Polynomial_OpCons( X, U, T ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 4.29/4.63 c_Polynomial_OpCons( X, c_Groups_Ominus__class_Ominus( X, U, Z ),
% 4.29/4.63 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 4.29/4.63 (22487) {G0,W20,D5,L2,V3,M2} { !
% 4.29/4.63 class_Groups_Oordered__ab__group__add__abs( X ),
% 4.29/4.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 4.29/4.63 c_Groups_Ominus__class_Ominus( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 4.29/4.63 c_Groups_Oabs__class_Oabs( X, Y ) ) ), c_Groups_Oabs__class_Oabs( X,
% 4.29/4.63 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) }.
% 4.29/4.63 (22488) {G0,W18,D4,L2,V3,M2} { !
% 4.29/4.63 class_Groups_Oordered__ab__group__add__abs( X ),
% 4.29/4.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X,
% 4.29/4.63 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ),
% 4.29/4.63 c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Z, Y ) )
% 4.29/4.63 ) }.
% 4.29/4.63 (22489) {G0,W18,D4,L2,V3,M2} { !
% 4.29/4.63 class_Groups_Oordered__ab__group__add__abs( X ),
% 4.29/4.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X,
% 4.29/4.63 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ),
% 4.29/4.63 c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Y, Z ) )
% 4.29/4.63 ) }.
% 4.29/4.63 (22490) {G0,W51,D7,L2,V5,M2} { ! class_RealVector_Oreal__normed__algebra(
% 4.29/4.63 X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 4.29/4.63 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 4.29/4.63 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 4.29/4.63 X, U, Z ) ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 4.29/4.63 Z ) ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 4.29/4.63 c_Groups_Ominus__class_Ominus( X, T, Y ) ) ) }.
% 4.29/4.63 (22491) {G0,W37,D6,L2,V5,M2} { ! class_Rings_Oring( X ),
% 4.29/4.63 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 4.29/4.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 4.29/4.63 ( X ), U ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 4.29/4.63 Z ) ), Y ) ) }.
% 4.29/4.63 (22492) {G0,W35,D6,L3,V6,M3} { ! class_Rings_Oring( X ), !
% 4.29/4.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 4.29/4.63 ( X ), W ), U ), T ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ),
% 4.29/4.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 4.29/4.63 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ) = Y }.
% 4.29/4.63 (22493) {G0,W35,D6,L3,V6,M3} { ! class_Rings_Oring( X ), !
% 4.29/4.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 4.29/4.63 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ) = Y,
% 4.29/4.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 4.29/4.63 ( X ), W ), U ), T ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) }.
% 4.29/4.63 (22494) {G0,W35,D6,L3,V6,M3} { ! class_Rings_Oring( X ), !
% 4.29/4.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 4.29/4.63 ( X ), W ), U ), T ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ), T =
% 4.29/4.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 4.29/4.63 ( X ), c_Groups_Ominus__class_Ominus( X, Z, W ) ), U ), Y ) }.
% 4.29/4.63 (22495) {G0,W35,D6,L3,V6,M3} { ! class_Rings_Oring( X ), ! T =
% 4.29/4.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 4.29/4.63 ( X ), c_Groups_Ominus__class_Ominus( X, Z, W ) ), U ), Y ),
% 4.29/4.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 4.29/4.63 ( X ), W ), U ), T ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) }.
% 4.29/4.63 (22496) {G0,W14,D3,L3,V3,M3} { ! class_Groups_Oordered__ab__group__add( X
% 4.29/4.63 ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 4.29/4.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 4.29/4.63 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 4.29/4.63 (22497) {G0,W14,D3,L3,V3,M3} { ! class_Groups_Oordered__ab__group__add( X
% 4.29/4.63 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X
% 4.29/4.63 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 4.29/4.63 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 4.29/4.63 (22498) {G0,W14,D3,L3,V3,M3} { ! class_Groups_Oordered__ab__group__add( X
% 4.29/4.63 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 4.29/4.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 4.29/4.63 , Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 4.29/4.63 (22499) {G0,W14,D3,L3,V3,M3} { ! class_Groups_Oordered__ab__group__add( X
% 4.29/4.63 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus
% 4.29/4.63 ( X, Z, Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 4.29/4.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 4.29/4.63 (22500) {G0,W19,D3,L4,V5,M4} { ! class_Groups_Oordered__ab__group__add( X
% 4.29/4.63 ), ! c_Groups_Ominus__class_Ominus( X, U, T ) =
% 4.29/4.63 c_Groups_Ominus__class_Ominus( X, Z, Y ), !
% 4.29/4.63 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 4.29/4.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 4.29/4.63 (22501) {G0,W19,D3,L4,V5,M4} { ! class_Groups_Oordered__ab__group__add( X
% 4.29/4.63 ), ! c_Groups_Ominus__class_Ominus( X, U, T ) =
% 4.29/4.63 c_Groups_Ominus__class_Ominus( X, Z, Y ), !
% 4.29/4.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 4.29/4.63 c_Orderings_Oord__class_Oless__eq( X, U, T ) }.
% 4.29/4.63 (22502) {G0,W18,D4,L2,V3,M2} { ! class_RealVector_Oreal__normed__vector( X
% 4.29/4.63 ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 4.29/4.63 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 4.29/4.63 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 4.29/4.63 ( X, Y ) ), c_RealVector_Onorm__class_Onorm( X,
% 4.29/4.63 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) }.
% 4.29/4.63 (22503) {G0,W11,D4,L2,V3,M2} { ! class_Groups_Ogroup__add( X ),
% 4.29/4.63 c_Groups_Ominus__class_Ominus( X, c_Groups_Oplus__class_Oplus( X, Z, Y )
% 4.29/4.63 , Y ) = Z }.
% 4.29/4.63 (22504) {G0,W11,D4,L2,V3,M2} { ! class_Groups_Ogroup__add( X ),
% 4.29/4.63 c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, Z, Y )
% 4.29/4.63 , Y ) = Z }.
% 4.29/4.63 (22505) {G0,W20,D5,L2,V3,M2} { ! class_RealVector_Oreal__normed__vector( X
% 4.29/4.63 ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 4.29/4.63 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 4.29/4.63 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 4.29/4.63 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 4.29/4.63 ( X, Y ) ) ), c_RealVector_Onorm__class_Onorm( X,
% 4.29/4.63 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) }.
% 4.29/4.63 (22506) {G0,W17,D5,L1,V2,M1} { hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 4.29/4.63 tc_Int_Oint ), Y ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) =
% 4.29/4.63 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Divides_Odiv__class_Omod
% 4.29/4.63 ( tc_Int_Oint, X, Y ) ) }.
% 4.29/4.63 (22507) {G0,W17,D6,L1,V2,M1} { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y
% 4.29/4.63 , X ) = c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Divides_Odiv__class_Odiv
% 4.29/4.63 ( tc_Int_Oint, Y, X ) ), X ) ) }.
% 4.29/4.63 (22508) {G0,W30,D5,L2,V5,M2} { ! class_RealVector_Oreal__normed__vector( X
% 4.29/4.63 ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 4.29/4.63 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X,
% 4.29/4.63 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 4.29/4.63 , Y ) ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 4.29/4.63 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, U,
% 4.29/4.63 Z ) ), c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus
% 4.29/4.63 ( X, T, Y ) ) ) ) }.
% 4.29/4.63 (22509) {G0,W26,D8,L2,V3,M2} { ! c_Orderings_Oord__class_Oless(
% 4.29/4.63 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 4.29/4.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z,
% 4.29/4.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Groups_Oplus__class_Oplus
% 4.29/4.63 ( tc_Int_Oint, c_Groups_Oabs__class_Oabs( tc_Int_Oint,
% 4.29/4.63 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, Z ) ),
% 4.29/4.63 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ), X ) ) ) }.
% 4.29/4.63 (22510) {G0,W46,D7,L2,V6,M2} { ! class_RealVector_Oreal__field( X ),
% 4.29/4.63 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus( X,
% 4.29/4.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ), hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) =
% 4.29/4.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 4.29/4.63 ( X ), W ), c_Rings_Oinverse__class_Odivide( X,
% 4.29/4.63 c_Groups_Ominus__class_Ominus( X, U, Z ), Y ) ), hAPP( hAPP(
% 4.29/4.63 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Odivide( X,
% 4.29/4.63 c_Groups_Ominus__class_Ominus( X, W, T ), Y ) ), Z ) ) }.
% 4.29/4.63 (22511) {G0,W32,D5,L5,V7,M5} { ! class_RealVector_Oreal__normed__vector( Y
% 4.29/4.63 ), ! class_Orderings_Oord( X ), c_Orderings_Oord__class_Oless__eq( X, T
% 4.29/4.63 , skol51( X, U, W, T ) ), ! c_Orderings_Oord__class_Oless__eq( X, T, V0 )
% 4.29/4.63 , c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 4.29/4.63 c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, V0 ) ),
% 4.29/4.63 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oone__class_Oone
% 4.29/4.63 ( tc_RealDef_Oreal ), c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, T ) )
% 4.29/4.63 ) ) }.
% 4.29/4.63 (22512) {G0,W42,D6,L5,V5,M5} { ! class_RealVector_Oreal__normed__vector( Y
% 4.29/4.63 ), ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless(
% 4.29/4.63 tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( Y,
% 4.29/4.63 c_Groups_Ominus__class_Ominus( Y, hAPP( Z, T ), hAPP( Z, skol51( X, Y, Z
% 4.29/4.63 , T ) ) ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), !
% 4.29/4.63 c_Orderings_Oord__class_Oless__eq( X, T, U ),
% 4.29/4.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 4.29/4.63 c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, U ) ),
% 4.29/4.63 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oone__class_Oone
% 4.29/4.63 ( tc_RealDef_Oreal ), c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, T ) )
% 4.29/4.63 ) ) }.
% 4.29/4.63 (22513) {G0,W5,D3,L2,V1,M2} { ! class_Groups_Ocancel__comm__monoid__add( X
% 4.29/4.63 ), class_Groups_Ocancel__comm__monoid__add( tc_Polynomial_Opoly( X ) )
% 4.29/4.63 }.
% 4.29/4.63 (22514) {G0,W2,D2,L1,V0,M1} { class_Groups_Ocancel__comm__monoid__add(
% 4.29/4.63 tc_Complex_Ocomplex ) }.
% 4.29/4.63 (22515) {G0,W2,D2,L1,V0,M1} { class_Groups_Ocancel__comm__monoid__add(
% 4.29/4.63 tc_RealDef_Oreal ) }.
% 4.29/4.63 (22516) {G0,W2,D2,L1,V0,M1} { class_Groups_Ocancel__comm__monoid__add(
% 4.29/4.63 tc_Nat_Onat ) }.
% 4.29/4.63 (22517) {G0,W2,D2,L1,V0,M1} { class_Groups_Ocancel__comm__monoid__add(
% 4.29/4.63 tc_Int_Oint ) }.
% 4.29/4.63 (22518) {G0,W6,D3,L2,V2,M2} { ! class_Orderings_Opreorder( X ),
% 4.29/4.63 class_Orderings_Opreorder( tc_fun( Y, X ) ) }.
% 4.29/4.63 (22519) {G0,W6,D3,L2,V2,M2} { ! class_Orderings_Oorder( X ),
% 4.29/4.63 class_Orderings_Oorder( tc_fun( Y, X ) ) }.
% 4.29/4.63 (22520) {G0,W6,D3,L2,V2,M2} { ! class_Orderings_Oord( X ),
% 4.29/4.63 class_Orderings_Oord( tc_fun( Y, X ) ) }.
% 4.29/4.63 (22521) {G0,W2,D2,L1,V0,M1} {
% 4.29/4.63 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 4.29/4.63 tc_Int_Oint ) }.
% 4.29/4.63 (22522) {G0,W2,D2,L1,V0,M1} {
% 4.29/4.63 class_Groups_Oordered__cancel__ab__semigroup__add( tc_Int_Oint ) }.
% 4.29/4.63 (22523) {G0,W2,D2,L1,V0,M1} {
% 4.29/4.63 class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Int_Oint ) }.
% 4.29/4.63 (22524) {G0,W2,D2,L1,V0,M1} {
% 4.29/4.63 class_Rings_Olinordered__comm__semiring__strict( tc_Int_Oint ) }.
% 4.29/4.63 (22525) {G0,W2,D2,L1,V0,M1} { class_Rings_Olinordered__semiring__1__strict
% 4.29/4.63 ( tc_Int_Oint ) }.
% 4.29/4.63 (22526) {G0,W2,D2,L1,V0,M1} { class_Rings_Olinordered__semiring__strict(
% 4.29/4.63 tc_Int_Oint ) }.
% 4.29/4.63 (22527) {G0,W2,D2,L1,V0,M1} { class_Groups_Oordered__ab__semigroup__add(
% 4.29/4.63 tc_Int_Oint ) }.
% 4.29/4.63 (22528) {G0,W2,D2,L1,V0,M1} { class_Groups_Oordered__ab__group__add__abs(
% 4.29/4.63 tc_Int_Oint ) }.
% 4.29/4.63 (22529) {G0,W2,D2,L1,V0,M1} { class_Groups_Oordered__comm__monoid__add(
% 4.29/4.63 tc_Int_Oint ) }.
% 4.29/4.63 (22530) {G0,W2,D2,L1,V0,M1} { class_Groups_Olinordered__ab__group__add(
% 4.29/4.63 tc_Int_Oint ) }.
% 4.29/4.63 (22531) {G0,W2,D2,L1,V0,M1} { class_Groups_Ocancel__ab__semigroup__add(
% 4.29/4.63 tc_Int_Oint ) }.
% 4.29/4.63 (22532) {G0,W2,D2,L1,V0,M1} { class_Rings_Oring__1__no__zero__divisors(
% 4.29/4.63 tc_Int_Oint ) }.
% 4.29/4.63 (22533) {G0,W2,D2,L1,V0,M1} { class_Rings_Oordered__cancel__semiring(
% 4.29/4.63 tc_Int_Oint ) }.
% 4.29/4.63 (22534) {G0,W2,D2,L1,V0,M1} { class_Rings_Olinordered__ring__strict(
% 4.29/4.63 tc_Int_Oint ) }.
% 4.29/4.63 (22535) {G0,W2,D2,L1,V0,M1} { class_Rings_Oring__no__zero__divisors(
% 4.29/4.63 tc_Int_Oint ) }.
% 4.29/4.63 (22536) {G0,W2,D2,L1,V0,M1} { class_Rings_Oordered__comm__semiring(
% 4.29/4.63 tc_Int_Oint ) }.
% 4.29/4.63 (22537) {G0,W2,D2,L1,V0,M1} { class_Rings_Olinordered__semiring__1(
% 4.29/4.63 tc_Int_Oint ) }.
% 4.29/4.63 (22538) {G0,W2,D2,L1,V0,M1} { class_Groups_Oordered__ab__group__add(
% 4.29/4.63 tc_Int_Oint ) }.
% 4.29/4.63 (22539) {G0,W2,D2,L1,V0,M1} { class_Groups_Ocancel__semigroup__add(
% 4.29/4.63 tc_Int_Oint ) }.
% 4.29/4.63 (22540) {G0,W2,D2,L1,V0,M1} { class_Rings_Olinordered__semiring(
% 4.29/4.63 tc_Int_Oint ) }.
% 4.29/4.63 (22541) {G0,W2,D2,L1,V0,M1} { class_Rings_Olinordered__semidom(
% 4.29/4.63 tc_Int_Oint ) }.
% 4.29/4.63 (22542) {G0,W2,D2,L1,V0,M1} { class_Groups_Oab__semigroup__mult(
% 4.29/4.63 tc_Int_Oint ) }.
% 4.29/4.63 (22543) {G0,W2,D2,L1,V0,M1} { class_Groups_Ocomm__monoid__mult(
% 4.29/4.63 tc_Int_Oint ) }.
% 4.29/4.63 (22544) {G0,W2,D2,L1,V0,M1} { class_Groups_Oab__semigroup__add(
% 4.29/4.63 tc_Int_Oint ) }.
% 4.29/4.63 (22545) {G0,W2,D2,L1,V0,M1} { class_Rings_Oordered__semiring( tc_Int_Oint
% 4.29/4.63 ) }.
% 4.29/4.63 (22546) {G0,W2,D2,L1,V0,M1} { class_Rings_Oordered__ring__abs( tc_Int_Oint
% 4.29/4.63 ) }.
% 4.29/4.63 (22547) {G0,W2,D2,L1,V0,M1} { class_Rings_Ono__zero__divisors( tc_Int_Oint
% 4.29/4.63 ) }.
% 4.29/4.63 (22548) {G0,W2,D2,L1,V0,M1} { class_Groups_Ocomm__monoid__add( tc_Int_Oint
% 4.29/4.63 ) }.
% 4.29/4.63 (22549) {G0,W2,D2,L1,V0,M1} { class_Rings_Olinordered__ring( tc_Int_Oint )
% 4.29/4.63 }.
% 4.29/4.63 (22550) {G0,W2,D2,L1,V0,M1} { class_Rings_Olinordered__idom( tc_Int_Oint )
% 4.29/4.63 }.
% 4.29/4.63 (22551) {G0,W2,D2,L1,V0,M1} { class_Rings_Ocomm__semiring__1( tc_Int_Oint
% 4.29/4.63 ) }.
% 4.29/4.63 (22552) {G0,W2,D2,L1,V0,M1} { class_Rings_Ocomm__semiring__0( tc_Int_Oint
% 4.29/4.63 ) }.
% 4.29/4.63 (22553) {G0,W2,D2,L1,V0,M1} { class_Divides_Osemiring__div( tc_Int_Oint )
% 4.29/4.63 }.
% 4.29/4.63 (22554) {G0,W2,D2,L1,V0,M1} { class_Rings_Ocomm__semiring( tc_Int_Oint )
% 4.29/4.63 }.
% 4.29/4.63 (22555) {G0,W2,D2,L1,V0,M1} { class_Groups_Oab__group__add( tc_Int_Oint )
% 4.29/4.63 }.
% 4.29/4.63 (22556) {G0,W2,D2,L1,V0,M1} { class_Rings_Ozero__neq__one( tc_Int_Oint )
% 4.29/4.63 }.
% 4.29/4.63 (22557) {G0,W2,D2,L1,V0,M1} { class_Rings_Oordered__ring( tc_Int_Oint )
% 4.29/4.63 }.
% 4.29/4.63 (22558) {G0,W2,D2,L1,V0,M1} { class_Orderings_Opreorder( tc_Int_Oint ) }.
% 4.29/4.63 (22559) {G0,W2,D2,L1,V0,M1} { class_Orderings_Olinorder( tc_Int_Oint ) }.
% 4.29/4.63 (22560) {G0,W2,D2,L1,V0,M1} { class_Groups_Omonoid__mult( tc_Int_Oint )
% 4.29/4.63 }.
% 4.29/4.63 (22561) {G0,W2,D2,L1,V0,M1} { class_Rings_Ocomm__ring__1( tc_Int_Oint )
% 4.29/4.63 }.
% 4.29/4.63 (22562) {G0,W2,D2,L1,V0,M1} { class_Groups_Omonoid__add( tc_Int_Oint ) }.
% 4.29/4.63 (22563) {G0,W2,D2,L1,V0,M1} { class_Rings_Osemiring__0( tc_Int_Oint ) }.
% 4.29/4.63 (22564) {G0,W2,D2,L1,V0,M1} { class_Groups_Ogroup__add( tc_Int_Oint ) }.
% 4.29/4.63 (22565) {G0,W2,D2,L1,V0,M1} { class_Divides_Oring__div( tc_Int_Oint ) }.
% 4.29/4.63 (22566) {G0,W2,D2,L1,V0,M1} { class_Rings_Omult__zero( tc_Int_Oint ) }.
% 4.29/4.63 (22567) {G0,W2,D2,L1,V0,M1} { class_Rings_Ocomm__ring( tc_Int_Oint ) }.
% 4.29/4.63 (22568) {G0,W2,D2,L1,V0,M1} { class_Orderings_Oorder( tc_Int_Oint ) }.
% 4.29/4.63 (22569) {G0,W2,D2,L1,V0,M1} { class_Int_Oring__char__0( tc_Int_Oint ) }.
% 4.29/4.63 (22570) {G0,W2,D2,L1,V0,M1} { class_Rings_Osemiring( tc_Int_Oint ) }.
% 4.29/4.63 (22571) {G0,W2,D2,L1,V0,M1} { class_Orderings_Oord( tc_Int_Oint ) }.
% 4.29/4.63 (22572) {G0,W2,D2,L1,V0,M1} { class_Rings_Oring__1( tc_Int_Oint ) }.
% 4.29/4.63 (22573) {G0,W2,D2,L1,V0,M1} { class_Power_Opower( tc_Int_Oint ) }.
% 4.29/4.63 (22574) {G0,W2,D2,L1,V0,M1} { class_Groups_Ozero( tc_Int_Oint ) }.
% 4.29/4.63 (22575) {G0,W2,D2,L1,V0,M1} { class_Rings_Oring( tc_Int_Oint ) }.
% 4.29/4.63 (22576) {G0,W2,D2,L1,V0,M1} { class_Rings_Oidom( tc_Int_Oint ) }.
% 4.29/4.63 (22577) {G0,W2,D2,L1,V0,M1} { class_Groups_Oone( tc_Int_Oint ) }.
% 4.29/4.63 (22578) {G0,W2,D2,L1,V0,M1} { class_Rings_Odvd( tc_Int_Oint ) }.
% 4.29/4.63 (22579) {G0,W2,D2,L1,V0,M1} {
% 4.29/4.63 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 4.29/4.63 tc_Nat_Onat ) }.
% 4.29/4.63 (22580) {G0,W2,D2,L1,V0,M1} {
% 4.29/4.63 class_Groups_Oordered__cancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 4.29/4.63 (22581) {G0,W2,D2,L1,V0,M1} {
% 4.29/4.63 class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Nat_Onat ) }.
% 4.29/4.63 (22582) {G0,W2,D2,L1,V0,M1} {
% 4.29/4.63 class_Rings_Olinordered__comm__semiring__strict( tc_Nat_Onat ) }.
% 4.29/4.63 (22583) {G0,W2,D2,L1,V0,M1} { class_Rings_Olinordered__semiring__strict(
% 4.29/4.63 tc_Nat_Onat ) }.
% 4.29/4.63 (22584) {G0,W2,D2,L1,V0,M1} { class_Groups_Oordered__ab__semigroup__add(
% 4.29/4.63 tc_Nat_Onat ) }.
% 4.29/4.63 (22585) {G0,W2,D2,L1,V0,M1} { class_Groups_Oordered__comm__monoid__add(
% 4.29/4.63 tc_Nat_Onat ) }.
% 4.29/4.63 (22586) {G0,W2,D2,L1,V0,M1} { class_Groups_Ocancel__ab__semigroup__add(
% 4.29/4.63 tc_Nat_Onat ) }.
% 4.29/4.63 (22587) {G0,W2,D2,L1,V0,M1} { class_Rings_Oordered__cancel__semiring(
% 4.29/4.63 tc_Nat_Onat ) }.
% 4.29/4.63 (22588) {G0,W2,D2,L1,V0,M1} { class_Rings_Oordered__comm__semiring(
% 4.29/4.63 tc_Nat_Onat ) }.
% 4.29/4.63 (22589) {G0,W2,D2,L1,V0,M1} { class_Groups_Ocancel__semigroup__add(
% 4.29/4.63 tc_Nat_Onat ) }.
% 4.29/4.63 (22590) {G0,W2,D2,L1,V0,M1} { class_Rings_Olinordered__semiring(
% 4.29/4.63 tc_Nat_Onat ) }.
% 4.29/4.63 (22591) {G0,W2,D2,L1,V0,M1} { class_Rings_Olinordered__semidom(
% 4.29/4.63 tc_Nat_Onat ) }.
% 4.29/4.63 (22592) {G0,W2,D2,L1,V0,M1} { class_Groups_Oab__semigroup__mult(
% 4.29/4.63 tc_Nat_Onat ) }.
% 4.29/4.63 (22593) {G0,W2,D2,L1,V0,M1} { class_Groups_Ocomm__monoid__mult(
% 4.29/4.63 tc_Nat_Onat ) }.
% 4.29/4.63 (22594) {G0,W2,D2,L1,V0,M1} { class_Groups_Oab__semigroup__add(
% 4.29/4.63 tc_Nat_Onat ) }.
% 4.29/4.63 (22595) {G0,W2,D2,L1,V0,M1} { class_Rings_Oordered__semiring( tc_Nat_Onat
% 4.29/4.63 ) }.
% 4.29/4.63 (22596) {G0,W2,D2,L1,V0,M1} { class_Rings_Ono__zero__divisors( tc_Nat_Onat
% 4.29/4.63 ) }.
% 4.29/4.63 (22597) {G0,W2,D2,L1,V0,M1} { class_Groups_Ocomm__monoid__add( tc_Nat_Onat
% 4.29/4.63 ) }.
% 4.29/4.63 (22598) {G0,W2,D2,L1,V0,M1} { class_Rings_Ocomm__semiring__1( tc_Nat_Onat
% 4.29/4.63 ) }.
% 4.29/4.63 (22599) {G0,W2,D2,L1,V0,M1} { class_Rings_Ocomm__semiring__0( tc_Nat_Onat
% 4.29/4.63 ) }.
% 4.29/4.63 (22600) {G0,W2,D2,L1,V0,M1} { class_Divides_Osemiring__div( tc_Nat_Onat )
% 4.29/4.63 }.
% 4.29/4.63 (22601) {G0,W2,D2,L1,V0,M1} { class_Rings_Ocomm__semiring( tc_Nat_Onat )
% 4.29/4.63 }.
% 4.29/4.63 (22602) {G0,W2,D2,L1,V0,M1} { class_Rings_Ozero__neq__one( tc_Nat_Onat )
% 4.29/4.63 }.
% 4.29/4.63 (22603) {G0,W2,D2,L1,V0,M1} { class_Orderings_Opreorder( tc_Nat_Onat ) }.
% 4.29/4.63 (22604) {G0,W2,D2,L1,V0,M1} { class_Orderings_Olinorder( tc_Nat_Onat ) }.
% 4.29/4.63 (22605) {G0,W2,D2,L1,V0,M1} { class_Groups_Omonoid__mult( tc_Nat_Onat )
% 4.29/4.63 }.
% 4.29/4.63 (22606) {G0,W2,D2,L1,V0,M1} { class_Groups_Omonoid__add( tc_Nat_Onat ) }.
% 4.29/4.63 (22607) {G0,W2,D2,L1,V0,M1} { class_Rings_Osemiring__0( tc_Nat_Onat ) }.
% 4.29/4.63 (22608) {G0,W2,D2,L1,V0,M1} { class_Rings_Omult__zero( tc_Nat_Onat ) }.
% 4.29/4.63 (22609) {G0,W2,D2,L1,V0,M1} { class_Orderings_Oorder( tc_Nat_Onat ) }.
% 4.29/4.63 (22610) {G0,W2,D2,L1,V0,M1} { class_Rings_Osemiring( tc_Nat_Onat ) }.
% 4.29/4.63 (22611) {G0,W2,D2,L1,V0,M1} { class_Orderings_Oord( tc_Nat_Onat ) }.
% 4.29/4.63 (22612) {G0,W2,D2,L1,V0,M1} { class_Power_Opower( tc_Nat_Onat ) }.
% 4.29/4.63 (22613) {G0,W2,D2,L1,V0,M1} { class_Groups_Ozero( tc_Nat_Onat ) }.
% 4.29/4.63 (22614) {G0,W2,D2,L1,V0,M1} { class_Groups_Oone( tc_Nat_Onat ) }.
% 4.29/4.63 (22615) {G0,W2,D2,L1,V0,M1} { class_Rings_Odvd( tc_Nat_Onat ) }.
% 4.29/4.63 (22616) {G0,W2,D2,L1,V0,M1} { class_Orderings_Opreorder( tc_HOL_Obool )
% 4.29/4.63 }.
% 4.29/4.63 (22617) {G0,W2,D2,L1,V0,M1} { class_Orderings_Oorder( tc_HOL_Obool ) }.
% 4.29/4.63 (22618) {G0,W2,D2,L1,V0,M1} { class_Orderings_Oord( tc_HOL_Obool ) }.
% 4.29/4.63 (22619) {G0,W2,D2,L1,V0,M1} {
% 4.29/4.63 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 4.29/4.63 tc_RealDef_Oreal ) }.
% 4.29/4.63 (22620) {G0,W2,D2,L1,V0,M1} {
% 4.29/4.63 class_Groups_Oordered__cancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 4.29/4.63 (22621) {G0,W2,D2,L1,V0,M1} {
% 4.29/4.63 class_Groups_Oordered__ab__semigroup__add__imp__le( tc_RealDef_Oreal )
% 4.29/4.63 }.
% 4.29/4.63 (22622) {G0,W2,D2,L1,V0,M1} {
% 4.29/4.63 class_Rings_Olinordered__comm__semiring__strict( tc_RealDef_Oreal ) }.
% 4.29/4.63 (22623) {G0,W2,D2,L1,V0,M1} {
% 4.29/4.63 class_Fields_Olinordered__field__inverse__zero( tc_RealDef_Oreal ) }.
% 4.29/4.63 (22624) {G0,W2,D2,L1,V0,M1} { class_Rings_Olinordered__semiring__1__strict
% 4.29/4.63 ( tc_RealDef_Oreal ) }.
% 4.29/4.63 (22625) {G0,W2,D2,L1,V0,M1} { class_RealVector_Oreal__normed__div__algebra
% 4.29/4.63 ( tc_RealDef_Oreal ) }.
% 4.29/4.63 (22626) {G0,W2,D2,L1,V0,M1} { class_Rings_Olinordered__semiring__strict(
% 4.29/4.63 tc_RealDef_Oreal ) }.
% 4.29/4.63 (22627) {G0,W2,D2,L1,V0,M1} { class_Rings_Odivision__ring__inverse__zero(
% 4.29/4.63 tc_RealDef_Oreal ) }.
% 4.29/4.63 (22628) {G0,W2,D2,L1,V0,M1} { class_RealVector_Oreal__normed__algebra__1(
% 4.29/4.63 tc_RealDef_Oreal ) }.
% 4.29/4.63 (22629) {G0,W2,D2,L1,V0,M1} { class_Groups_Oordered__ab__semigroup__add(
% 4.29/4.63 tc_RealDef_Oreal ) }.
% 4.29/4.63 (22630) {G0,W2,D2,L1,V0,M1} { class_Groups_Oordered__ab__group__add__abs(
% 4.29/4.63 tc_RealDef_Oreal ) }.
% 4.29/4.63 (22631) {G0,W2,D2,L1,V0,M1} { class_RealVector_Oreal__normed__algebra(
% 4.29/4.63 tc_RealDef_Oreal ) }.
% 4.29/4.63 (22632) {G0,W2,D2,L1,V0,M1} { class_Groups_Oordered__comm__monoid__add(
% 4.29/4.63 tc_RealDef_Oreal ) }.
% 4.29/4.63 (22633) {G0,W2,D2,L1,V0,M1} { class_Groups_Olinordered__ab__group__add(
% 4.29/4.63 tc_RealDef_Oreal ) }.
% 4.29/4.63 (22634) {G0,W2,D2,L1,V0,M1} { class_Groups_Ocancel__ab__semigroup__add(
% 4.29/4.63 tc_RealDef_Oreal ) }.
% 4.29/4.63 (22635) {G0,W2,D2,L1,V0,M1} { class_Rings_Oring__1__no__zero__divisors(
% 4.29/4.63 tc_RealDef_Oreal ) }.
% 4.29/4.63 (22636) {G0,W2,D2,L1,V0,M1} { class_Rings_Oordered__cancel__semiring(
% 4.29/4.63 tc_RealDef_Oreal ) }.
% 4.29/4.63 (22637) {G0,W2,D2,L1,V0,M1} { class_RealVector_Oreal__normed__vector(
% 4.29/4.63 tc_RealDef_Oreal ) }.
% 4.29/4.63 (22638) {G0,W2,D2,L1,V0,M1} { class_Rings_Olinordered__ring__strict(
% 4.29/4.63 tc_RealDef_Oreal ) }.
% 4.29/4.63 (22639) {G0,W2,D2,L1,V0,M1} { class_RealVector_Oreal__normed__field(
% 4.29/4.63 tc_RealDef_Oreal ) }.
% 4.29/4.63 (22640) {G0,W2,D2,L1,V0,M1} { class_Rings_Oring__no__zero__divisors(
% 4.29/4.63 tc_RealDef_Oreal ) }.
% 4.29/4.63 (22641) {G0,W2,D2,L1,V0,M1} { class_Rings_Oordered__comm__semiring(
% 4.29/4.63 tc_RealDef_Oreal ) }.
% 4.29/4.63 (22642) {G0,W2,D2,L1,V0,M1} { class_Rings_Olinordered__semiring__1(
% 4.29/4.63 tc_RealDef_Oreal ) }.
% 4.29/4.63 (22643) {G0,W2,D2,L1,V0,M1} { class_Groups_Oordered__ab__group__add(
% 4.29/4.63 tc_RealDef_Oreal ) }.
% 4.29/4.63 (22644) {G0,W2,D2,L1,V0,M1} { class_Groups_Ocancel__semigroup__add(
% 4.29/4.63 tc_RealDef_Oreal ) }.
% 4.29/4.63 (22645) {G0,W2,D2,L1,V0,M1} { class_Rings_Olinordered__semiring(
% 4.29/4.63 tc_RealDef_Oreal ) }.
% 4.29/4.63 (22646) {G0,W2,D2,L1,V0,M1} { class_Fields_Ofield__inverse__zero(
% 4.29/4.63 tc_RealDef_Oreal ) }.
% 4.29/4.63 (22647) {G0,W2,D2,L1,V0,M1} { class_Rings_Olinordered__semidom(
% 4.29/4.63 tc_RealDef_Oreal ) }.
% 4.29/4.63 (22648) {G0,W2,D2,L1,V0,M1} { class_Groups_Oab__semigroup__mult(
% 4.29/4.63 tc_RealDef_Oreal ) }.
% 4.29/4.63 (22649) {G0,W2,D2,L1,V0,M1} { class_Groups_Ocomm__monoid__mult(
% 4.29/4.63 tc_RealDef_Oreal ) }.
% 4.29/4.63 (22650) {G0,W2,D2,L1,V0,M1} { class_Groups_Oab__semigroup__add(
% 4.29/4.63 tc_RealDef_Oreal ) }.
% 4.29/4.63 (22651) {G0,W2,D2,L1,V0,M1} { class_Fields_Olinordered__field(
% 4.29/4.63 tc_RealDef_Oreal ) }.
% 4.29/4.63 (22652) {G0,W2,D2,L1,V0,M1} { class_Rings_Oordered__semiring(
% 4.29/4.63 tc_RealDef_Oreal ) }.
% 4.29/4.63 (22653) {G0,W2,D2,L1,V0,M1} { class_Rings_Oordered__ring__abs(
% 4.29/4.63 tc_RealDef_Oreal ) }.
% 4.29/4.63 (22654) {G0,W2,D2,L1,V0,M1} { class_Rings_Ono__zero__divisors(
% 4.29/4.63 tc_RealDef_Oreal ) }.
% 4.29/4.63 (22655) {G0,W2,D2,L1,V0,M1} { class_Groups_Ocomm__monoid__add(
% 4.29/4.63 tc_RealDef_Oreal ) }.
% 4.29/4.63 (22656) {G0,W2,D2,L1,V0,M1} { class_Rings_Olinordered__ring(
% 4.29/4.63 tc_RealDef_Oreal ) }.
% 4.29/4.63 (22657) {G0,W2,D2,L1,V0,M1} { class_Rings_Olinordered__idom(
% 4.29/4.63 tc_RealDef_Oreal ) }.
% 4.29/4.63 (22658) {G0,W2,D2,L1,V0,M1} { class_Rings_Ocomm__semiring__1(
% 4.29/4.63 tc_RealDef_Oreal ) }.
% 4.29/4.63 (22659) {G0,W2,D2,L1,V0,M1} { class_Rings_Ocomm__semiring__0(
% 4.29/4.63 tc_RealDef_Oreal ) }.
% 4.29/4.63 (22660) {G0,W2,D2,L1,V0,M1} { class_RealVector_Oreal__field(
% 4.29/4.63 tc_RealDef_Oreal ) }.
% 4.29/4.63 (22661) {G0,W2,D2,L1,V0,M1} { class_Rings_Odivision__ring(
% 4.29/4.63 tc_RealDef_Oreal ) }.
% 4.29/4.63 (22662) {G0,W2,D2,L1,V0,M1} { class_Rings_Ocomm__semiring(
% 4.29/4.63 tc_RealDef_Oreal ) }.
% 4.29/4.63 (22663) {G0,W2,D2,L1,V0,M1} { class_Groups_Oab__group__add(
% 4.29/4.63 tc_RealDef_Oreal ) }.
% 4.29/4.63 (22664) {G0,W2,D2,L1,V0,M1} { class_Rings_Ozero__neq__one(
% 4.29/4.63 tc_RealDef_Oreal ) }.
% 4.29/4.63 (22665) {G0,W2,D2,L1,V0,M1} { class_Rings_Oordered__ring( tc_RealDef_Oreal
% 4.29/4.63 ) }.
% 4.29/4.63 (22666) {G0,W2,D2,L1,V0,M1} { class_Orderings_Opreorder( tc_RealDef_Oreal
% 4.29/4.63 ) }.
% 4.29/4.63 (22667) {G0,W2,D2,L1,V0,M1} { class_Orderings_Olinorder( tc_RealDef_Oreal
% 4.29/4.63 ) }.
% 4.29/4.63 (22668) {G0,W2,D2,L1,V0,M1} { class_Groups_Omonoid__mult( tc_RealDef_Oreal
% 4.29/4.63 ) }.
% 4.29/4.63 (22669) {G0,W2,D2,L1,V0,M1} { class_Rings_Ocomm__ring__1( tc_RealDef_Oreal
% 4.29/4.63 ) }.
% 4.29/4.63 (22670) {G0,W2,D2,L1,V0,M1} { class_Groups_Omonoid__add( tc_RealDef_Oreal
% 4.29/4.63 ) }.
% 4.29/4.63 (22671) {G0,W2,D2,L1,V0,M1} { class_Rings_Osemiring__0( tc_RealDef_Oreal )
% 4.29/4.63 }.
% 4.29/4.63 (22672) {G0,W2,D2,L1,V0,M1} { class_Groups_Ogroup__add( tc_RealDef_Oreal )
% 4.29/4.63 }.
% 4.29/4.63 (22673) {G0,W2,D2,L1,V0,M1} { class_Rings_Omult__zero( tc_RealDef_Oreal )
% 4.29/4.63 }.
% 4.29/4.63 (22674) {G0,W2,D2,L1,V0,M1} { class_Rings_Ocomm__ring( tc_RealDef_Oreal )
% 4.29/4.63 }.
% 4.29/4.63 (22675) {G0,W2,D2,L1,V0,M1} { class_Orderings_Oorder( tc_RealDef_Oreal )
% 4.29/4.63 }.
% 4.29/4.63 (22676) {G0,W2,D2,L1,V0,M1} { class_Int_Oring__char__0( tc_RealDef_Oreal )
% 4.29/4.63 }.
% 4.29/4.63 (22677) {G0,W2,D2,L1,V0,M1} { class_Rings_Osemiring( tc_RealDef_Oreal )
% 4.29/4.63 }.
% 4.29/4.63 (22678) {G0,W2,D2,L1,V0,M1} { class_Orderings_Oord( tc_RealDef_Oreal ) }.
% 4.29/4.63 (22679) {G0,W2,D2,L1,V0,M1} { class_Rings_Oring__1( tc_RealDef_Oreal ) }.
% 4.29/4.63 (22680) {G0,W2,D2,L1,V0,M1} { class_Fields_Ofield( tc_RealDef_Oreal ) }.
% 4.29/4.63 (22681) {G0,W2,D2,L1,V0,M1} { class_Power_Opower( tc_RealDef_Oreal ) }.
% 4.29/4.63 (22682) {G0,W2,D2,L1,V0,M1} { class_Groups_Ozero( tc_RealDef_Oreal ) }.
% 4.29/4.63 (22683) {G0,W2,D2,L1,V0,M1} { class_Rings_Oring( tc_RealDef_Oreal ) }.
% 4.29/4.63 (22684) {G0,W2,D2,L1,V0,M1} { class_Rings_Oidom( tc_RealDef_Oreal ) }.
% 4.29/4.63 (22685) {G0,W2,D2,L1,V0,M1} { class_Groups_Oone( tc_RealDef_Oreal ) }.
% 4.29/4.63 (22686) {G0,W2,D2,L1,V0,M1} { class_Rings_Odvd( tc_RealDef_Oreal ) }.
% 4.29/4.63 (22687) {G0,W2,D2,L1,V0,M1} {
% 4.29/4.63 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 4.29/4.63 tc_Complex_Ocomplex ) }.
% 4.29/4.63 (22688) {G0,W2,D2,L1,V0,M1} { class_RealVector_Oreal__normed__div__algebra
% 4.29/4.63 ( tc_Complex_Ocomplex ) }.
% 4.29/4.63 (22689) {G0,W2,D2,L1,V0,M1} { class_Rings_Odivision__ring__inverse__zero(
% 4.29/4.63 tc_Complex_Ocomplex ) }.
% 4.29/4.63 (22690) {G0,W2,D2,L1,V0,M1} { class_RealVector_Oreal__normed__algebra__1(
% 4.29/4.63 tc_Complex_Ocomplex ) }.
% 4.29/4.63 (22691) {G0,W2,D2,L1,V0,M1} { class_RealVector_Oreal__normed__algebra(
% 4.29/4.63 tc_Complex_Ocomplex ) }.
% 4.29/4.63 (22692) {G0,W2,D2,L1,V0,M1} { class_Groups_Ocancel__ab__semigroup__add(
% 4.29/4.63 tc_Complex_Ocomplex ) }.
% 4.29/4.63 (22693) {G0,W2,D2,L1,V0,M1} { class_Rings_Oring__1__no__zero__divisors(
% 4.29/4.63 tc_Complex_Ocomplex ) }.
% 4.29/4.63 (22694) {G0,W2,D2,L1,V0,M1} { class_RealVector_Oreal__normed__vector(
% 4.29/4.63 tc_Complex_Ocomplex ) }.
% 4.29/4.63 (22695) {G0,W2,D2,L1,V0,M1} { class_RealVector_Oreal__normed__field(
% 4.29/4.63 tc_Complex_Ocomplex ) }.
% 4.29/4.63 (22696) {G0,W2,D2,L1,V0,M1} { class_Rings_Oring__no__zero__divisors(
% 4.29/4.63 tc_Complex_Ocomplex ) }.
% 4.29/4.63 (22697) {G0,W2,D2,L1,V0,M1} { class_Groups_Ocancel__semigroup__add(
% 4.29/4.63 tc_Complex_Ocomplex ) }.
% 4.29/4.63 (22698) {G0,W2,D2,L1,V0,M1} { class_Fields_Ofield__inverse__zero(
% 4.29/4.63 tc_Complex_Ocomplex ) }.
% 4.29/4.63 (22699) {G0,W2,D2,L1,V0,M1} { class_Groups_Oab__semigroup__mult(
% 4.29/4.63 tc_Complex_Ocomplex ) }.
% 4.29/4.63 (22700) {G0,W2,D2,L1,V0,M1} { class_Groups_Ocomm__monoid__mult(
% 4.29/4.63 tc_Complex_Ocomplex ) }.
% 4.29/4.63 (22701) {G0,W2,D2,L1,V0,M1} { class_Groups_Oab__semigroup__add(
% 4.29/4.63 tc_Complex_Ocomplex ) }.
% 4.29/4.63 (22702) {G0,W2,D2,L1,V0,M1} { class_Rings_Ono__zero__divisors(
% 4.29/4.63 tc_Complex_Ocomplex ) }.
% 4.29/4.63 (22703) {G0,W2,D2,L1,V0,M1} { class_Groups_Ocomm__monoid__add(
% 4.29/4.63 tc_Complex_Ocomplex ) }.
% 4.29/4.63 (22704) {G0,W2,D2,L1,V0,M1} { class_Rings_Ocomm__semiring__1(
% 4.29/4.63 tc_Complex_Ocomplex ) }.
% 4.29/4.63 (22705) {G0,W2,D2,L1,V0,M1} { class_Rings_Ocomm__semiring__0(
% 4.29/4.63 tc_Complex_Ocomplex ) }.
% 4.29/4.63 (22706) {G0,W2,D2,L1,V0,M1} { class_RealVector_Oreal__field(
% 4.29/4.63 tc_Complex_Ocomplex ) }.
% 4.29/4.63 (22707) {G0,W2,D2,L1,V0,M1} { class_Rings_Odivision__ring(
% 4.29/4.63 tc_Complex_Ocomplex ) }.
% 4.29/4.63 (22708) {G0,W2,D2,L1,V0,M1} { class_Rings_Ocomm__semiring(
% 4.29/4.63 tc_Complex_Ocomplex ) }.
% 4.29/4.63 (22709) {G0,W2,D2,L1,V0,M1} { class_Groups_Oab__group__add(
% 4.29/4.63 tc_Complex_Ocomplex ) }.
% 4.29/4.63 (22710) {G0,W2,D2,L1,V0,M1} { class_Rings_Ozero__neq__one(
% 4.29/4.63 tc_Complex_Ocomplex ) }.
% 4.29/4.63 (22711) {G0,W2,D2,L1,V0,M1} { class_Groups_Omonoid__mult(
% 4.29/4.63 tc_Complex_Ocomplex ) }.
% 4.29/4.63 (22712) {G0,W2,D2,L1,V0,M1} { class_Rings_Ocomm__ring__1(
% 4.29/4.63 tc_Complex_Ocomplex ) }.
% 4.29/4.63 (22713) {G0,W2,D2,L1,V0,M1} { class_Groups_Omonoid__add(
% 4.29/4.63 tc_Complex_Ocomplex ) }.
% 4.29/4.63 (22714) {G0,W2,D2,L1,V0,M1} { class_Rings_Osemiring__0(
% 4.29/4.63 tc_Complex_Ocomplex ) }.
% 4.29/4.63 (22715) {G0,W2,D2,L1,V0,M1} { class_Groups_Ogroup__add(
% 4.29/4.63 tc_Complex_Ocomplex ) }.
% 4.29/4.63 (22716) {G0,W2,D2,L1,V0,M1} { class_Rings_Omult__zero( tc_Complex_Ocomplex
% 4.29/4.63 ) }.
% 4.29/4.63 (22717) {G0,W2,D2,L1,V0,M1} { class_Rings_Ocomm__ring( tc_Complex_Ocomplex
% 4.29/4.63 ) }.
% 4.29/4.63 (22718) {G0,W2,D2,L1,V0,M1} { class_Int_Oring__char__0(
% 4.29/4.63 tc_Complex_Ocomplex ) }.
% 4.29/4.63 (22719) {G0,W2,D2,L1,V0,M1} { class_Rings_Osemiring( tc_Complex_Ocomplex )
% 4.29/4.63 }.
% 4.29/4.63 (22720) {G0,W2,D2,L1,V0,M1} { class_Rings_Oring__1( tc_Complex_Ocomplex )
% 4.29/4.63 }.
% 4.29/4.63 (22721) {G0,W2,D2,L1,V0,M1} { class_Fields_Ofield( tc_Complex_Ocomplex )
% 4.29/4.63 }.
% 4.29/4.63 (22722) {G0,W2,D2,L1,V0,M1} { class_Power_Opower( tc_Complex_Ocomplex )
% 4.29/4.63 }.
% 4.29/4.63 (22723) {G0,W2,D2,L1,V0,M1} { class_Groups_Ozero( tc_Complex_Ocomplex )
% 4.29/4.63 }.
% 4.29/4.63 (22724) {G0,W2,D2,L1,V0,M1} { class_Rings_Oring( tc_Complex_Ocomplex ) }.
% 4.29/4.63 (22725) {G0,W2,D2,L1,V0,M1} { class_Rings_Oidom( tc_Complex_Ocomplex ) }.
% 4.29/4.63 (22726) {G0,W2,D2,L1,V0,M1} { class_Groups_Oone( tc_Complex_Ocomplex ) }.
% 4.29/4.63 (22727) {G0,W2,D2,L1,V0,M1} { class_Rings_Odvd( tc_Complex_Ocomplex ) }.
% 4.29/4.63 (22728) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Oidom( X ),
% 4.29/4.63 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 4.29/4.63 tc_Polynomial_Opoly( X ) ) }.
% 4.29/4.63 (22729) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Olinordered__idom( X ),
% 4.29/4.63 class_Groups_Oordered__cancel__ab__semigroup__add( tc_Polynomial_Opoly( X
% 4.29/4.63 ) ) }.
% 4.29/4.63 (22730) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Olinordered__idom( X ),
% 4.29/4.63 class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Polynomial_Opoly(
% 4.29/4.63 X ) ) }.
% 4.29/4.63 (22731) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Olinordered__idom( X ),
% 4.29/4.63 class_Rings_Olinordered__comm__semiring__strict( tc_Polynomial_Opoly( X )
% 4.29/4.63 ) }.
% 4.29/4.63 (22732) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Olinordered__idom( X ),
% 4.29/4.63 class_Rings_Olinordered__semiring__1__strict( tc_Polynomial_Opoly( X ) )
% 4.29/4.63 }.
% 4.29/4.63 (22733) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Olinordered__idom( X ),
% 4.29/4.63 class_Rings_Olinordered__semiring__strict( tc_Polynomial_Opoly( X ) ) }.
% 4.29/4.63 (22734) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Olinordered__idom( X ),
% 4.29/4.63 class_Groups_Oordered__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 4.29/4.63 (22735) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Olinordered__idom( X ),
% 4.29/4.63 class_Groups_Oordered__ab__group__add__abs( tc_Polynomial_Opoly( X ) )
% 4.29/4.63 }.
% 4.29/4.63 (22736) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Olinordered__idom( X ),
% 4.29/4.63 class_Groups_Oordered__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 4.29/4.63 (22737) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Olinordered__idom( X ),
% 4.29/4.63 class_Groups_Olinordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 4.29/4.63 (22738) {G0,W5,D3,L2,V1,M2} { ! class_Groups_Ocancel__comm__monoid__add( X
% 4.29/4.63 ), class_Groups_Ocancel__ab__semigroup__add( tc_Polynomial_Opoly( X ) )
% 4.29/4.63 }.
% 4.29/4.63 (22739) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Oidom( X ),
% 4.29/4.63 class_Rings_Oring__1__no__zero__divisors( tc_Polynomial_Opoly( X ) ) }.
% 4.29/4.63 (22740) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Olinordered__idom( X ),
% 4.29/4.63 class_Rings_Oordered__cancel__semiring( tc_Polynomial_Opoly( X ) ) }.
% 4.29/4.63 (22741) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Olinordered__idom( X ),
% 4.29/4.63 class_Rings_Olinordered__ring__strict( tc_Polynomial_Opoly( X ) ) }.
% 4.29/4.63 (22742) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Oidom( X ),
% 4.29/4.63 class_Rings_Oring__no__zero__divisors( tc_Polynomial_Opoly( X ) ) }.
% 4.29/4.63 (22743) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Olinordered__idom( X ),
% 4.29/4.63 class_Rings_Oordered__comm__semiring( tc_Polynomial_Opoly( X ) ) }.
% 4.29/4.63 (22744) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Olinordered__idom( X ),
% 4.29/4.63 class_Rings_Olinordered__semiring__1( tc_Polynomial_Opoly( X ) ) }.
% 4.29/4.63 (22745) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Olinordered__idom( X ),
% 4.29/4.63 class_Groups_Oordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 4.29/4.63 (22746) {G0,W5,D3,L2,V1,M2} { ! class_Groups_Ocancel__comm__monoid__add( X
% 4.29/4.63 ), class_Groups_Ocancel__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 4.29/4.63 (22747) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Olinordered__idom( X ),
% 4.29/4.63 class_Rings_Olinordered__semiring( tc_Polynomial_Opoly( X ) ) }.
% 4.29/4.63 (22748) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Olinordered__idom( X ),
% 4.29/4.63 class_Rings_Olinordered__semidom( tc_Polynomial_Opoly( X ) ) }.
% 4.29/4.63 (22749) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Ocomm__semiring__0( X ),
% 4.29/4.63 class_Groups_Oab__semigroup__mult( tc_Polynomial_Opoly( X ) ) }.
% 4.29/4.63 (22750) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Ocomm__semiring__1( X ),
% 4.29/4.63 class_Groups_Ocomm__monoid__mult( tc_Polynomial_Opoly( X ) ) }.
% 4.29/4.63 (22751) {G0,W5,D3,L2,V1,M2} { ! class_Groups_Ocomm__monoid__add( X ),
% 4.29/4.63 class_Groups_Oab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 4.29/4.63 (22752) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Olinordered__idom( X ),
% 4.29/4.63 class_Rings_Oordered__semiring( tc_Polynomial_Opoly( X ) ) }.
% 4.29/4.63 (22753) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Olinordered__idom( X ),
% 4.29/4.63 class_Rings_Oordered__ring__abs( tc_Polynomial_Opoly( X ) ) }.
% 4.29/4.63 (22754) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Oidom( X ),
% 4.29/4.63 class_Rings_Ono__zero__divisors( tc_Polynomial_Opoly( X ) ) }.
% 4.29/4.63 (22755) {G0,W5,D3,L2,V1,M2} { ! class_Groups_Ocomm__monoid__add( X ),
% 4.29/4.63 class_Groups_Ocomm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 4.29/4.63 (22756) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Olinordered__idom( X ),
% 4.29/4.63 class_Rings_Olinordered__ring( tc_Polynomial_Opoly( X ) ) }.
% 4.29/4.63 (22757) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Olinordered__idom( X ),
% 4.29/4.63 class_Rings_Olinordered__idom( tc_Polynomial_Opoly( X ) ) }.
% 4.29/4.63 (22758) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Ocomm__semiring__1( X ),
% 4.29/4.63 class_Rings_Ocomm__semiring__1( tc_Polynomial_Opoly( X ) ) }.
% 4.29/4.63 (22759) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Ocomm__semiring__0( X ),
% 4.29/4.63 class_Rings_Ocomm__semiring__0( tc_Polynomial_Opoly( X ) ) }.
% 4.29/4.63 (22760) {G0,W5,D3,L2,V1,M2} { ! class_Fields_Ofield( X ),
% 4.29/4.63 class_Divides_Osemiring__div( tc_Polynomial_Opoly( X ) ) }.
% 4.29/4.63 (22761) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Ocomm__semiring__0( X ),
% 4.29/4.63 class_Rings_Ocomm__semiring( tc_Polynomial_Opoly( X ) ) }.
% 4.29/4.63 (22762) {G0,W5,D3,L2,V1,M2} { ! class_Groups_Oab__group__add( X ),
% 4.29/4.63 class_Groups_Oab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 4.29/4.63 (22763) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Ocomm__semiring__1( X ),
% 4.29/4.63 class_Rings_Ozero__neq__one( tc_Polynomial_Opoly( X ) ) }.
% 4.29/4.63 (22764) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Olinordered__idom( X ),
% 4.29/4.63 class_Rings_Oordered__ring( tc_Polynomial_Opoly( X ) ) }.
% 4.29/4.63 (22765) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Olinordered__idom( X ),
% 4.29/4.63 class_Orderings_Opreorder( tc_Polynomial_Opoly( X ) ) }.
% 4.29/4.63 (22766) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Olinordered__idom( X ),
% 4.29/4.63 class_Orderings_Olinorder( tc_Polynomial_Opoly( X ) ) }.
% 4.29/4.63 (22767) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Ocomm__semiring__1( X ),
% 4.29/4.63 class_Groups_Omonoid__mult( tc_Polynomial_Opoly( X ) ) }.
% 4.29/4.63 (22768) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Ocomm__ring__1( X ),
% 4.29/4.63 class_Rings_Ocomm__ring__1( tc_Polynomial_Opoly( X ) ) }.
% 4.29/4.63 (22769) {G0,W5,D3,L2,V1,M2} { ! class_Groups_Ocomm__monoid__add( X ),
% 4.29/4.63 class_Groups_Omonoid__add( tc_Polynomial_Opoly( X ) ) }.
% 4.29/4.64 (22770) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Ocomm__semiring__0( X ),
% 4.29/4.64 class_Rings_Osemiring__0( tc_Polynomial_Opoly( X ) ) }.
% 4.29/4.64 (22771) {G0,W5,D3,L2,V1,M2} { ! class_Groups_Oab__group__add( X ),
% 4.29/4.64 class_Groups_Ogroup__add( tc_Polynomial_Opoly( X ) ) }.
% 4.29/4.64 (22772) {G0,W5,D3,L2,V1,M2} { ! class_Fields_Ofield( X ),
% 4.29/4.64 class_Divides_Oring__div( tc_Polynomial_Opoly( X ) ) }.
% 4.29/4.64 (22773) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Ocomm__semiring__0( X ),
% 4.29/4.64 class_Rings_Omult__zero( tc_Polynomial_Opoly( X ) ) }.
% 4.29/4.64 (22774) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Ocomm__ring( X ),
% 4.29/4.64 class_Rings_Ocomm__ring( tc_Polynomial_Opoly( X ) ) }.
% 4.29/4.64 (22775) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Olinordered__idom( X ),
% 4.29/4.64 class_Orderings_Oorder( tc_Polynomial_Opoly( X ) ) }.
% 4.29/4.64 (22776) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Olinordered__idom( X ),
% 4.29/4.64 class_Int_Oring__char__0( tc_Polynomial_Opoly( X ) ) }.
% 4.29/4.64 (22777) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Ocomm__semiring__0( X ),
% 4.29/4.64 class_Rings_Osemiring( tc_Polynomial_Opoly( X ) ) }.
% 4.29/4.64 (22778) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Olinordered__idom( X ),
% 4.29/4.64 class_Orderings_Oord( tc_Polynomial_Opoly( X ) ) }.
% 4.29/4.64 (22779) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Ocomm__ring__1( X ),
% 4.29/4.64 class_Rings_Oring__1( tc_Polynomial_Opoly( X ) ) }.
% 4.29/4.64 (22780) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Ocomm__semiring__1( X ),
% 4.29/4.64 class_Power_Opower( tc_Polynomial_Opoly( X ) ) }.
% 4.29/4.64 (22781) {G0,W5,D3,L2,V1,M2} { ! class_Groups_Ozero( X ),
% 4.29/4.64 class_Groups_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 4.29/4.64 (22782) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Ocomm__ring( X ),
% 4.29/4.64 class_Rings_Oring( tc_Polynomial_Opoly( X ) ) }.
% 4.29/4.64 (22783) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Oidom( X ), class_Rings_Oidom
% 4.29/4.64 ( tc_Polynomial_Opoly( X ) ) }.
% 4.29/4.64 (22784) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Ocomm__semiring__1( X ),
% 4.29/4.64 class_Groups_Oone( tc_Polynomial_Opoly( X ) ) }.
% 4.29/4.64 (22785) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Ocomm__semiring__1( X ),
% 4.29/4.64 class_Rings_Odvd( tc_Polynomial_Opoly( X ) ) }.
% 4.29/4.64 (22786) {G0,W7,D3,L2,V2,M2} { ! hBOOL( c_fequal( Y, X ) ), Y = X }.
% 4.29/4.64 (22787) {G0,W7,D3,L2,V2,M2} { ! Y = X, hBOOL( c_fequal( Y, X ) ) }.
% 4.29/4.64 (22788) {G0,W26,D8,L1,V0,M1} { ! c_Orderings_Oord__class_Oless__eq(
% 4.29/4.64 tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 4.29/4.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), v_z____
% 4.29/4.64 ), v_c____ ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 4.29/4.64 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 4.29/4.64 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, v_aa____, hAPP( hAPP(
% 4.29/4.64 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), v_z____ ), v_c____
% 4.29/4.64 ) ) ), c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_aa____ )
% 4.29/4.64 ) ) }.
% 4.29/4.64
% 4.29/4.64
% 4.29/4.64 Total Proof:
% 4.29/4.64
% 4.29/4.64 subsumption: (2) {G0,W16,D5,L1,V2,M1} I { c_Orderings_Oord__class_Oless__eq
% 4.29/4.64 ( tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex
% 4.29/4.64 , Y ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 4.29/4.64 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 4.29/4.64 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X ) ),
% 4.29/4.64 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) ) }.
% 4.29/4.64 parent0: (20917) {G0,W16,D5,L1,V2,M1} { c_Orderings_Oord__class_Oless__eq
% 4.29/4.64 ( tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex
% 4.29/4.64 , Y ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 4.29/4.64 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 4.29/4.64 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X ) ),
% 4.29/4.64 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) ) }.
% 4.29/4.64 substitution0:
% 4.29/4.64 X := X
% 4.29/4.64 Y := Y
% 4.29/4.64 end
% 4.29/4.64 permutation0:
% 4.29/4.64 0 ==> 0
% 4.29/4.64 end
% 4.29/4.64
% 4.29/4.64 subsumption: (62) {G0,W11,D3,L2,V3,M2} I { ! class_Rings_Ocomm__semiring__1
% 4.29/4.64 ( X ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 4.29/4.64 c_Groups_Oplus__class_Oplus( X, Y, Z ) }.
% 4.29/4.64 parent0: (20989) {G0,W11,D3,L2,V3,M2} { ! class_Rings_Ocomm__semiring__1(
% 4.29/4.64 X ), c_Groups_Oplus__class_Oplus( X, Z, Y ) = c_Groups_Oplus__class_Oplus
% 4.29/4.64 ( X, Y, Z ) }.
% 4.29/4.64 substitution0:
% 4.29/4.64 X := X
% 4.29/4.64 Y := Y
% 4.29/4.64 Z := Z
% 4.29/4.64 end
% 4.29/4.64 permutation0:
% 4.29/4.64 0 ==> 0
% 4.29/4.64 1 ==> 1
% 4.29/4.64 end
% 4.29/4.64
% 4.29/4.64 subsumption: (1570) {G0,W2,D2,L1,V0,M1} I { class_Rings_Ocomm__semiring__1
% 4.29/4.64 ( tc_Complex_Ocomplex ) }.
% 4.29/4.65 parent0: (22704) {G0,W2,D2,L1,V0,M1} { class_Rings_Ocomm__semiring__1(
% 4.29/4.65 tc_Complex_Ocomplex ) }.
% 4.29/4.65 substitution0:
% 4.29/4.65 end
% 4.29/4.65 permutation0:
% 4.29/4.65 0 ==> 0
% 4.29/4.65 end
% 4.29/4.65
% 4.29/4.65 subsumption: (1654) {G0,W26,D8,L1,V0,M1} I { !
% 4.29/4.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 4.29/4.65 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP( hAPP(
% 4.29/4.65 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), v_z____ ), v_c____
% 4.29/4.65 ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 4.29/4.65 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 4.29/4.65 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, v_aa____, hAPP( hAPP(
% 4.29/4.65 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), v_z____ ), v_c____
% 4.29/4.65 ) ) ), c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_aa____ )
% 4.29/4.65 ) ) }.
% 4.29/4.65 parent0: (22788) {G0,W26,D8,L1,V0,M1} { !
% 4.29/4.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 4.29/4.65 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP( hAPP(
% 4.29/4.65 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), v_z____ ), v_c____
% 4.29/4.65 ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 4.29/4.65 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 4.29/4.65 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, v_aa____, hAPP( hAPP(
% 4.29/4.65 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), v_z____ ), v_c____
% 4.29/4.65 ) ) ), c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_aa____ )
% 4.29/4.65 ) ) }.
% 4.29/4.65 substitution0:
% 4.29/4.65 end
% 4.29/4.65 permutation0:
% 4.29/4.65 0 ==> 0
% 4.29/4.65 end
% 4.29/4.65
% 4.29/4.65 paramod: (26229) {G1,W18,D5,L2,V2,M2} { c_Orderings_Oord__class_Oless__eq
% 4.29/4.65 ( tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex
% 4.29/4.65 , X ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 4.29/4.65 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 4.29/4.65 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X ) ),
% 4.29/4.65 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y ) ) ), !
% 4.29/4.65 class_Rings_Ocomm__semiring__1( tc_Complex_Ocomplex ) }.
% 4.29/4.65 parent0[1]: (62) {G0,W11,D3,L2,V3,M2} I { ! class_Rings_Ocomm__semiring__1
% 4.29/4.65 ( X ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 4.29/4.65 c_Groups_Oplus__class_Oplus( X, Y, Z ) }.
% 4.29/4.65 parent1[0; 9]: (2) {G0,W16,D5,L1,V2,M1} I {
% 4.29/4.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 4.29/4.65 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y ),
% 4.29/4.65 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 4.29/4.65 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 4.29/4.65 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X ) ),
% 4.29/4.65 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) ) }.
% 4.29/4.65 substitution0:
% 4.29/4.65 X := tc_Complex_Ocomplex
% 4.29/4.65 Y := Y
% 4.29/4.65 Z := X
% 4.29/4.65 end
% 4.29/4.65 substitution1:
% 4.29/4.65 X := Y
% 4.29/4.65 Y := X
% 4.29/4.65 end
% 4.29/4.65
% 4.29/4.65 resolution: (26269) {G1,W16,D5,L1,V2,M1} {
% 4.29/4.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 4.29/4.65 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ),
% 4.29/4.65 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 4.29/4.65 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 4.29/4.65 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X ) ),
% 4.29/4.65 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y ) ) ) }.
% 4.29/4.65 parent0[1]: (26229) {G1,W18,D5,L2,V2,M2} {
% 4.29/4.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 4.29/4.65 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ),
% 4.29/4.65 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 4.29/4.65 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 4.29/4.65 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X ) ),
% 4.29/4.65 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y ) ) ), !
% 4.29/4.65 class_Rings_Ocomm__semiring__1( tc_Complex_Ocomplex ) }.
% 4.29/4.65 parent1[0]: (1570) {G0,W2,D2,L1,V0,M1} I { class_Rings_Ocomm__semiring__1(
% 4.29/4.65 tc_Complex_Ocomplex ) }.
% 4.29/4.65 substitution0:
% 4.29/4.65 X := X
% 4.29/4.65 Y := Y
% 4.29/4.65 end
% 4.29/4.65 substitution1:
% 4.29/4.65 end
% 4.29/4.65
% 4.29/4.65 subsumption: (6974) {G1,W16,D5,L1,V2,M1} P(62,2);r(1570) {
% 4.29/4.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 4.29/4.65 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ),
% 4.29/4.65 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 4.29/4.65 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 4.29/4.65 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X ) ),
% 4.29/4.65 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y ) ) ) }.
% 4.29/4.65 parent0: (26269) {G1,W16,D5,L1,V2,M1} { c_Orderings_Oord__class_Oless__eq
% 4.29/4.65 ( tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex
% 4.29/4.65 , X ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 4.29/4.65 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 4.29/4.65 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X ) ),
% 4.29/4.65 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y ) ) ) }.
% 4.29/4.65 substitution0:
% 4.29/4.65 X := X
% 4.29/4.65 Y := Y
% 4.29/4.65 end
% 4.29/4.65 permutation0:
% 4.29/4.65 0 ==> 0
% 4.29/4.65 end
% 4.29/4.65
% 4.29/4.65 resolution: (26270) {G1,W0,D0,L0,V0,M0} { }.
% 4.29/4.65 parent0[0]: (1654) {G0,W26,D8,L1,V0,M1} I { !
% 4.29/4.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 4.29/4.65 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP( hAPP(
% 4.29/4.65 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), v_z____ ), v_c____
% 4.29/4.65 ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 4.29/4.65 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 4.29/4.65 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, v_aa____, hAPP( hAPP(
% 4.29/4.65 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), v_z____ ), v_c____
% 4.29/4.65 ) ) ), c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_aa____ )
% 4.29/4.65 ) ) }.
% 4.29/4.65 parent1[0]: (6974) {G1,W16,D5,L1,V2,M1} P(62,2);r(1570) {
% 4.29/4.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 4.29/4.65 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ),
% 4.29/4.65 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 4.29/4.65 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 4.29/4.65 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X ) ),
% 4.29/4.65 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y ) ) ) }.
% 4.29/4.65 substitution0:
% 4.29/4.65 end
% 4.29/4.65 substitution1:
% 4.29/4.65 X := hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 4.29/4.65 v_z____ ), v_c____ )
% 4.29/4.65 Y := v_aa____
% 4.29/4.65 end
% 4.29/4.65
% 4.29/4.65 subsumption: (20913) {G2,W0,D0,L0,V0,M0} S(1654);r(6974) { }.
% 4.29/4.65 parent0: (26270) {G1,W0,D0,L0,V0,M0} { }.
% 4.29/4.65 substitution0:
% 4.29/4.65 end
% 4.29/4.65 permutation0:
% 4.29/4.65 end
% 4.29/4.65
% 4.29/4.65 Proof check complete!
% 4.29/4.65
% 4.29/4.65 Memory use:
% 4.29/4.65
% 4.29/4.65 space for terms: 667843
% 4.29/4.65 space for clauses: 1063532
% 4.29/4.65
% 4.29/4.65
% 4.29/4.65 clauses generated: 80095
% 4.29/4.65 clauses kept: 20914
% 4.29/4.65 clauses selected: 533
% 4.29/4.65 clauses deleted: 125
% 4.29/4.65 clauses inuse deleted: 1
% 4.29/4.65
% 4.29/4.65 subsentry: 337836
% 4.29/4.65 literals s-matched: 164416
% 4.29/4.65 literals matched: 147122
% 4.29/4.65 full subsumption: 110575
% 4.29/4.65
% 4.29/4.65 checksum: 963501889
% 4.29/4.65
% 4.29/4.65
% 4.29/4.65 Bliksem ended
%------------------------------------------------------------------------------