TSTP Solution File: SWW176+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWW176+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Wed Jul 20 23:21:02 EDT 2022
% Result : Timeout 300.09s 300.50s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SWW176+1 : TPTP v8.1.0. Released v5.2.0.
% 0.12/0.13 % Command : bliksem %s
% 0.12/0.34 % Computer : n026.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % DateTime : Sun Jun 5 20:40:00 EDT 2022
% 0.12/0.35 % CPUTime :
% 0.97/1.59 *** allocated 10000 integers for termspace/termends
% 0.97/1.59 *** allocated 10000 integers for clauses
% 0.97/1.59 *** allocated 10000 integers for justifications
% 0.97/1.59 *** allocated 15000 integers for termspace/termends
% 0.97/1.59 *** allocated 22500 integers for termspace/termends
% 0.97/1.59 *** allocated 33750 integers for termspace/termends
% 0.97/1.59 Bliksem 1.12
% 0.97/1.59
% 0.97/1.59
% 0.97/1.59 Automatic Strategy Selection
% 0.97/1.59
% 0.97/1.59 *** allocated 50625 integers for termspace/termends
% 0.97/1.59 *** allocated 75937 integers for termspace/termends
% 0.97/1.59 *** allocated 113905 integers for termspace/termends
% 0.97/1.59
% 0.97/1.59 Clauses:
% 0.97/1.59
% 0.97/1.59 { ! hAPP( Y, skol1( X, Y ) ) = hAPP( X, skol1( X, Y ) ), Y = X }.
% 0.97/1.59 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.97/1.59 Y ) }.
% 0.97/1.59 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.97/1.59 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.59 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.59 Y ), ! Z = Y }.
% 0.97/1.59 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.97/1.59 Z ), ! Z = Y }.
% 0.97/1.59 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.97/1.59 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Z = Y }.
% 0.97/1.59 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.97/1.59 Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.59 { ! class_Orderings_Olinorder( X ), ! Z = Y, !
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.59 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.97/1.59 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.59 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.97/1.59 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Y = Z }.
% 0.97/1.59 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.97/1.59 ), ! Y = Z, ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.59 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.97/1.59 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.59 { ! class_Rings_Olinordered__idom( X ), Z = Y,
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.97/1.59 X, Y, Z ) }.
% 0.97/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.59 , ! Z = Y }.
% 0.97/1.59 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.59 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.59 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.59 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.59 , ! Z = Y }.
% 0.97/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.59 , ! Y = Z }.
% 0.97/1.59 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.97/1.59 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.59 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.59 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.59 , ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.97/1.59 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.59 Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.97/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.59 , ! Z = T, c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.97/1.59 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.97/1.59 ! Y = T, c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.97/1.59 { ! class_Orderings_Oorder( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless(
% 0.97/1.59 X, T, Y ), c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.97/1.59 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X
% 0.97/1.59 , Y, T ), c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.97/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.59 , ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.59 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.59 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.59 { ! class_Groups_Ozero( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y, Y =
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 0.97/1.59 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.59 , c_Groups_Osgn__class_Osgn( X, Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.97/1.59 .
% 0.97/1.59 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.59 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.97/1.59 , c_Groups_Osgn__class_Osgn( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }
% 0.97/1.59 .
% 0.97/1.59 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.59 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.97/1.59 .
% 0.97/1.59 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.59 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X
% 0.97/1.59 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) ) }
% 0.97/1.59 .
% 0.97/1.59 { ! class_Orderings_Oorder( Y ), ! class_Orderings_Oorder( X ), !
% 0.97/1.59 c_Orderings_Oorder__class_Ostrict__mono( X, Y, Z ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, U, T ), c_Orderings_Oord__class_Oless(
% 0.97/1.59 Y, hAPP( Z, U ), hAPP( Z, T ) ) }.
% 0.97/1.59 { ! class_Orderings_Oorder( Y ), ! class_Orderings_Olinorder( X ), !
% 0.97/1.59 c_Orderings_Oorder__class_Ostrict__mono( X, Y, Z ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( Y, hAPP( Z, U ), hAPP( Z, T ) ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, U, T ) }.
% 0.97/1.59 { ! class_Orderings_Oorder( Y ), ! class_Orderings_Olinorder( X ), !
% 0.97/1.59 c_Orderings_Oorder__class_Ostrict__mono( X, Y, Z ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, U, T ), c_Orderings_Oord__class_Oless(
% 0.97/1.59 Y, hAPP( Z, U ), hAPP( Z, T ) ) }.
% 0.97/1.59 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.97/1.59 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.97/1.59 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.59 ( X, c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero( X ) ) }
% 0.97/1.59 .
% 0.97/1.59 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.59 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.97/1.59 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP
% 0.97/1.59 ( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.97/1.59 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.59 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.97/1.59 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.97/1.59 ( c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.97/1.59 { ! class_Rings_Olinordered__comm__semiring__strict( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.59 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.97/1.59 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.97/1.59 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.59 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.59 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.97/1.59 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.97/1.59 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.59 { ! class_Rings_Olinordered__idom( X ), c_Groups_Osgn__class_Osgn( X,
% 0.97/1.59 c_Groups_Osgn__class_Osgn( X, Y ) ) = c_Groups_Osgn__class_Osgn( X, Y ) }
% 0.97/1.59 .
% 0.97/1.59 { ! class_Rings_Olinordered__idom( X ), c_Groups_Osgn__class_Osgn( X, hAPP
% 0.97/1.59 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Osgn__class_Osgn( X, Z ) ),
% 0.97/1.59 c_Groups_Osgn__class_Osgn( X, Y ) ) }.
% 0.97/1.59 { ! class_Groups_Oab__semigroup__mult( X ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.59 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.97/1.59 = Y }.
% 0.97/1.59 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.97/1.59 = Y }.
% 0.97/1.59 { ! class_Groups_Oone( X ), ! c_Groups_Oone__class_Oone( X ) = Y, Y =
% 0.97/1.59 c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.59 { ! class_Groups_Oone( X ), ! Y = c_Groups_Oone__class_Oone( X ),
% 0.97/1.59 c_Groups_Oone__class_Oone( X ) = Y }.
% 0.97/1.59 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.97/1.59 = Y }.
% 0.97/1.59 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.97/1.59 = Y }.
% 0.97/1.59 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.59 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.59 ( X, c_Groups_Oone__class_Oone( X ), Z ), c_Orderings_Oord__class_Oless(
% 0.97/1.59 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.59 { ! class_Orderings_Oorder( Y ), ! class_Orderings_Olinorder( X ), !
% 0.97/1.59 c_Orderings_Oorder__class_Ostrict__mono( X, Y, Z ), ! hAPP( Z, U ) = hAPP
% 0.97/1.59 ( Z, T ), U = T }.
% 0.97/1.59 { ! class_Orderings_Oorder( Y ), ! class_Orderings_Olinorder( X ), !
% 0.97/1.59 c_Orderings_Oorder__class_Ostrict__mono( X, Y, Z ), ! U = T, hAPP( Z, U )
% 0.97/1.59 = hAPP( Z, T ) }.
% 0.97/1.59 { ! class_Groups_Osgn__if( X ), c_Groups_Osgn__class_Osgn( X,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 0.97/1.59 = c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.97/1.59 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.59 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Groups_Osgn__class_Osgn( X, Y
% 0.97/1.59 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.59 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.59 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Groups_Osgn__class_Osgn( X, Y
% 0.97/1.59 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.59 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.59 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) =
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.59 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) =
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59 { ! class_Rings_Oring__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.59 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59 { ! class_Rings_Oring__no__zero__divisors( X ), ! Z =
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59 { ! class_Rings_Oring__no__zero__divisors( X ), ! Y =
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59 { ! class_Rings_Ono__zero__divisors( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.59 X ), Z = c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) =
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59 { ! class_Rings_Ono__zero__divisors( X ), ! hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.59 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Oone__class_Oone( X ) =
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.97/1.59 c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.59 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 0.97/1.59 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.59 }.
% 0.97/1.59 { ! class_Rings_Olinordered__idom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.59 X ), c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.59 }.
% 0.97/1.59 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.59 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.59 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha1( X, Y, Z, T ),
% 0.97/1.59 alpha19( X, Y, Z, T ) }.
% 0.97/1.59 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha1( X, Y, Z, T ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.59 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha19( X, Y, Z, T ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.59 { ! alpha19( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.59 { ! alpha19( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, T ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.59 , ! c_Orderings_Oord__class_Oless( X, Y, T ), alpha19( X, Y, Z, T ) }.
% 0.97/1.59 { ! alpha1( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.97/1.59 { ! alpha1( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.97/1.59 , ! c_Orderings_Oord__class_Oless( X, T, Y ), alpha1( X, Y, Z, T ) }.
% 0.97/1.59 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha2( X, Y, Z, T ),
% 0.97/1.59 alpha20( X, Y, Z, T ) }.
% 0.97/1.59 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha2( X, Y, Z, T ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.59 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha20( X, Y, Z, T ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.59 { ! alpha20( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.59 { ! alpha20( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( X, T, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.59 , ! c_Orderings_Oord__class_Oless( X, Y, Z ), alpha20( X, Y, Z, T ) }.
% 0.97/1.59 { ! alpha2( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ), T ) }.
% 0.97/1.59 { ! alpha2( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T )
% 0.97/1.59 , ! c_Orderings_Oord__class_Oless( X, Z, Y ), alpha2( X, Y, Z, T ) }.
% 0.97/1.59 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.59 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.97/1.59 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.59 ! c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless
% 0.97/1.59 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.97/1.59 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.59 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.59 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.97/1.59 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.59 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.59 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.59 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.97/1.59 ( X ) ) }.
% 0.97/1.59 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.59 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.59 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.97/1.59 ( X ) ) }.
% 0.97/1.59 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.97/1.59 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.97/1.59 .
% 0.97/1.59 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.97/1.59 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ) }
% 0.97/1.59 .
% 0.97/1.59 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.59 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.97/1.59 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.59 ! c_Orderings_Oord__class_Oless( X, Z, T ), c_Orderings_Oord__class_Oless
% 0.97/1.59 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.97/1.59 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.59 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.59 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.97/1.59 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.97/1.59 ( X ) ) }.
% 0.97/1.59 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.59 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.59 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.59 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.59 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.97/1.59 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP
% 0.97/1.59 ( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.97/1.59 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 0.97/1.59 c_Groups_Osgn__class_Osgn( X, c_Groups_Oone__class_Oone( X ) ) =
% 0.97/1.59 c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.59 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 0.97/1.59 c_Groups_Osgn__class_Osgn( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.59 X ), Z ), Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.97/1.59 c_Groups_Osgn__class_Osgn( X, Z ) ), c_Groups_Osgn__class_Osgn( X, Y ) )
% 0.97/1.59 }.
% 0.97/1.59 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Osgn__class_Osgn
% 0.97/1.59 ( X, c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X
% 0.97/1.59 ) }.
% 0.97/1.59 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.59 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) =
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.59 c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, X ) =
% 0.97/1.59 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.97/1.59 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ), X =
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.59 { ! X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 0.97/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.97/1.59 = Y }.
% 0.97/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.97/1.59 = Y }.
% 0.97/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP
% 0.97/1.59 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), Y ) ), X ) =
% 0.97/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), hAPP
% 0.97/1.59 ( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.97/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) =
% 0.97/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y )
% 0.97/1.59 }.
% 0.97/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.97/1.59 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) = X }.
% 0.97/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 0.97/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 0.97/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Z ) }.
% 0.97/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 0.97/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), Y ) ) }.
% 0.97/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.59 { ! c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) =
% 0.97/1.59 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.97/1.59 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) = hAPP( hAPP
% 0.97/1.59 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ), Z = Y }.
% 0.97/1.59 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP
% 0.97/1.59 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) = hAPP(
% 0.97/1.59 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) }.
% 0.97/1.59 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) = hAPP( hAPP
% 0.97/1.59 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ), Z = Y }.
% 0.97/1.59 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP
% 0.97/1.59 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) = hAPP(
% 0.97/1.59 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) }.
% 0.97/1.59 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.97/1.59 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.97/1.59 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.97/1.59 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.97/1.59 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.97/1.59 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.97/1.59 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59 { ! X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.97/1.59 c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, X ) =
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.59 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.59 c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, X ) =
% 0.97/1.59 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.97/1.59 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.59 c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, X ) =
% 0.97/1.59 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.97/1.59 { ! X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.97/1.59 c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, X ) =
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.59 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.59 c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, X ) =
% 0.97/1.59 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.97/1.59 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.59 c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, X ) =
% 0.97/1.59 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.97/1.59 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X,
% 0.97/1.59 c_Groups_Osgn__class_Osgn( X, Y ) ) = c_Groups_Ozero__class_Ozero(
% 0.97/1.59 tc_RealDef_Oreal ) }.
% 0.97/1.59 { ! class_RealVector_Oreal__normed__vector( X ), Y =
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X,
% 0.97/1.59 c_Groups_Osgn__class_Osgn( X, Y ) ) = c_Groups_Oone__class_Oone(
% 0.97/1.59 tc_RealDef_Oreal ) }.
% 0.97/1.59 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.59 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Osgn__class_Osgn( X, Y
% 0.97/1.59 ) = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) )
% 0.97/1.59 }.
% 0.97/1.59 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 0.97/1.59 = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.97/1.59 .
% 0.97/1.59 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.59 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Osgn__class_Osgn( X, Y
% 0.97/1.59 ) = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) )
% 0.97/1.59 }.
% 0.97/1.59 { ! class_Groups_Osgn__if( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.59 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59 { ! class_Groups_Osgn__if( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.59 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.59 { ! class_Groups_Osgn__if( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.59 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.97/1.59 c_Groups_Oone__class_Oone( X ) ) }.
% 0.97/1.59 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 0.97/1.59 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 0.97/1.59 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 0.97/1.59 { ! class_Orderings_Opreorder( X ), c_Orderings_Oord__class_Oless__eq( X, Y
% 0.97/1.59 , Y ) }.
% 0.97/1.59 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ) ), hAPP( hAPP
% 0.97/1.59 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) }.
% 0.97/1.59 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.97/1.59 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.97/1.59 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, X ) }.
% 0.97/1.59 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.97/1.59 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ouminus__class_Ouminus( X, Y
% 0.97/1.59 ) ) = c_RealVector_Onorm__class_Onorm( X, Y ) }.
% 0.97/1.59 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Z ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, Z ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ), Y = X }.
% 0.97/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.59 ) }.
% 0.97/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.59 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.97/1.59 ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.97/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 0.97/1.59 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.59 ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.97/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.97/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.59 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.59 ) }.
% 0.97/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.59 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 0.97/1.59 ( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.59 , Y ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.97/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.59 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 0.97/1.59 ( X, Y ), Y ) }.
% 0.97/1.59 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.97/1.59 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.97/1.59 hAPP( Y, U ) ) }.
% 0.97/1.59 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, hAPP
% 0.97/1.59 ( Z, skol2( X, Y, Z ) ), hAPP( Y, skol2( X, Y, Z ) ) ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }.
% 0.97/1.59 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.59 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.97/1.59 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.97/1.59 ( X, Z, Y ) }.
% 0.97/1.59 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.97/1.59 ( X, Y, Z ) }.
% 0.97/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.59 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.97/1.59 { ! class_Orderings_Opreorder( X ), ! Z = Y,
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.59 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.97/1.59 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.97/1.59 hAPP( Y, U ) ) }.
% 0.97/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.59 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.97/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.59 , Y ), ! Y = Z, c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.97/1.59 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.97/1.59 ( X, Y, T ), c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.97/1.59 { ! class_Orderings_Oorder( X ), ! Z = Y, !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.97/1.59 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y
% 0.97/1.59 ), ! Y = T, c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.97/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.59 , Y ), ! Z = T, c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.97/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.59 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.97/1.59 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.59 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.97/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.59 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.97/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.59 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.97/1.59 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.97/1.59 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.97/1.59 hAPP( Y, U ) ) }.
% 0.97/1.59 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.59 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.97/1.59 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.59 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.97/1.59 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.59 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.97/1.59 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.59 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.97/1.59 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.97/1.59 c_Groups_Ouminus__class_Ouminus( X, Z ) = c_Groups_Ouminus__class_Ouminus
% 0.97/1.59 ( X, Y ), Z = Y }.
% 0.97/1.59 { ! class_Lattices_Oboolean__algebra( X ), ! Z = Y,
% 0.97/1.59 c_Groups_Ouminus__class_Ouminus( X, Z ) = c_Groups_Ouminus__class_Ouminus
% 0.97/1.59 ( X, Y ) }.
% 0.97/1.59 { ! class_Groups_Ouminus( X ), hAPP( c_Groups_Ouminus__class_Ouminus(
% 0.97/1.59 tc_fun( T, X ), Z ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( Z, Y
% 0.97/1.59 ) ) }.
% 0.97/1.59 { ! class_Lattices_Oboolean__algebra( X ), c_Groups_Ouminus__class_Ouminus
% 0.97/1.59 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 0.97/1.59 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.97/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 0.97/1.59 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.59 , Y ), Y = c_Groups_Ouminus__class_Ouminus( X, Z ) }.
% 0.97/1.59 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.59 , Z ), Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.97/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ouminus__class_Ouminus
% 0.97/1.59 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.97/1.59 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.97/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 0.97/1.59 ( X, Z ) ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.97/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.97/1.59 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 0.97/1.59 ) = Y, c_Groups_Ouminus__class_Ouminus( X, Y ) = Z }.
% 0.97/1.59 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 0.97/1.59 ) = Z, c_Groups_Ouminus__class_Ouminus( X, Z ) = Y }.
% 0.97/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.59 , Z ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ), Z ) }.
% 0.97/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.59 , Y ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.59 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.97/1.59 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 0.97/1.59 ) = c_Groups_Ouminus__class_Ouminus( X, Y ), Z = Y }.
% 0.97/1.59 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ouminus__class_Ouminus
% 0.97/1.59 ( X, Z ) = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.97/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.59 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.97/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.59 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.97/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.59 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.97/1.59 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.59 c_RealVector_Onorm__class_Onorm( X, Y ), c_Groups_Ozero__class_Ozero(
% 0.97/1.59 tc_RealDef_Oreal ) ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq(
% 0.97/1.59 tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( X, Y ),
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.97/1.59 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.59 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.97/1.59 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 0.97/1.59 c_RealVector_Onorm__class_Onorm( X, Y ) ) ) }.
% 0.97/1.59 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.97/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Groups_Ozero__class_Ozero( X )
% 0.97/1.59 = Y }.
% 0.97/1.59 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Ouminus__class_Ouminus( X, Y
% 0.97/1.59 ) }.
% 0.97/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.97/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ), Y = c_Groups_Ozero__class_Ozero
% 0.97/1.59 ( X ) }.
% 0.97/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.59 , Y ) }.
% 0.97/1.59 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 0.97/1.59 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.97/1.59 ) }.
% 0.97/1.59 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.97/1.59 ) }.
% 0.97/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ) = Y, Y =
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.97/1.59 = Y }.
% 0.97/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ouminus__class_Ouminus( X,
% 0.97/1.59 Y ) ), c_Orderings_Oord__class_Oless( X, Y,
% 0.97/1.59 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.97/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ouminus__class_Ouminus( X,
% 0.97/1.59 Z ) ), c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.97/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.97/1.59 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 0.97/1.59 ( X, Y ), Z ) }.
% 0.97/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.97/1.59 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 0.97/1.59 ( X, Z ), Y ) }.
% 0.97/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.97/1.59 , c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, Y, Z ), c_Orderings_Oord__class_Oless(
% 0.97/1.59 X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.97/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.97/1.59 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 0.97/1.59 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.97/1.59 ( X, Y ) ) }.
% 0.97/1.59 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 0.97/1.59 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.97/1.59 ) ), Y ) }.
% 0.97/1.59 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.97/1.59 , c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.97/1.59 ( X, Y ) ) }.
% 0.97/1.59 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.97/1.59 , c_Groups_Ouminus__class_Ouminus( X, Z ) ),
% 0.97/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.97/1.59 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.97/1.59 ), Z ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 0.97/1.59 Z = Y, Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.97/1.59 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.97/1.59 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.97/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.97/1.59 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.97/1.59 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.59 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.97/1.59 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.59 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.97/1.59 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.59 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.97/1.59 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.59 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.97/1.59 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.97/1.59 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.59 , Y, Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.59 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.59 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.59 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.97/1.59 Z ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.59 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.59 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.59 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.59 , ! Z = Y }.
% 0.97/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.59 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.59 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.59 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.59 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.59 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.97/1.59 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.59 , Z, Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.59 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.97/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.59 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.59 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.97/1.59 ( X, Z, Y ) }.
% 0.97/1.59 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.97/1.59 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.97/1.59 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.59 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.59 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.97/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ), Z = Y }.
% 0.97/1.59 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.97/1.59 ), ! Z = Y, c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.59 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.97/1.59 ( X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.59 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.97/1.59 ( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.59 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.59 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.59 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.59 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.59 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.59 , Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.97/1.59 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.59 , Z, Y ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.59 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.97/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.59 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.59 , Y ), Y = Z, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.59 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.59 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.97/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.59 , ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.97/1.59 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.59 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.97/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.59 , Y ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), ! Y = X }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), Y = X,
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), Y = X }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.97/1.59 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.97/1.59 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Osgn__class_Osgn
% 0.97/1.59 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 0.97/1.59 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Osgn__class_Osgn( X, Y ) ) }
% 0.97/1.59 .
% 0.97/1.59 { ! class_Orderings_Oorder( Y ), ! class_Orderings_Olinorder( X ), !
% 0.97/1.59 c_Orderings_Oorder__class_Ostrict__mono( X, Y, Z ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( Y, hAPP( Z, U ), hAPP( Z, T ) ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, U, T ) }.
% 0.97/1.59 { ! class_Orderings_Oorder( Y ), ! class_Orderings_Olinorder( X ), !
% 0.97/1.59 c_Orderings_Oorder__class_Ostrict__mono( X, Y, Z ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( Y, hAPP( Z, U ), hAPP( Z, T ) ) }.
% 0.97/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.97/1.59 ( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.97/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.97/1.59 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.97/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.97/1.59 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.97/1.59 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.59 , Y ) }.
% 0.97/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.97/1.59 , Y ) }.
% 0.97/1.59 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.59 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.97/1.59 .
% 0.97/1.59 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.59 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.97/1.59 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.97/1.59 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.97/1.59 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.59 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.59 c_RealVector_Onorm__class_Onorm( X, Y ) = c_Groups_Ozero__class_Ozero(
% 0.97/1.59 tc_RealDef_Oreal ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X, Y )
% 0.97/1.59 = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.59 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = c_Groups_Oone__class_Oone
% 0.97/1.59 ( X ), Y = c_Groups_Oone__class_Oone( X ), Y =
% 0.97/1.59 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) }.
% 0.97/1.59 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.97/1.59 c_Groups_Oone__class_Oone( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.59 ( X ), Y ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.59 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.97/1.59 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 0.97/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) =
% 0.97/1.59 c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.59 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ouminus__class_Ouminus( X, Y
% 0.97/1.59 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.97/1.59 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) ), Y
% 0.97/1.59 ) }.
% 0.97/1.59 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 0.97/1.59 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.97/1.59 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 0.97/1.59 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.97/1.59 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_RealVector_Onorm__class_Onorm( X, Y ), c_Groups_Ozero__class_Ozero(
% 0.97/1.59 tc_RealDef_Oreal ) ) }.
% 0.97/1.59 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 0.97/1.59 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oone__class_Oone( X ) ) =
% 0.97/1.59 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.97/1.59 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.97/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.59 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.59 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.59 X ), Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.97/1.59 ( X ) ) }.
% 0.97/1.59 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.59 , c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.59 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.97/1.59 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.59 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.59 , Z, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.59 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.97/1.59 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.59 { ! class_Rings_Oordered__semiring( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.59 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.97/1.59 { ! class_Rings_Oordered__semiring( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.97/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.59 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.97/1.59 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.59 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.59 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.97/1.59 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.59 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.59 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.97/1.59 { ! class_Rings_Oordered__comm__semiring( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.97/1.59 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.59 { ! class_Rings_Oordered__semiring( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.97/1.59 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.59 { ! class_Rings_Oordered__semiring( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.97/1.59 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.97/1.59 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.59 , Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.59 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.97/1.59 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.59 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.59 X ), Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.97/1.59 ( X ) ) }.
% 0.97/1.59 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.59 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.59 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.59 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ),
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.59 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.59 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.59 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.97/1.59 ( X ) ), alpha3( X, Y, Z ), alpha21( X, Y, Z ) }.
% 0.97/1.59 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha3( X, Y, Z ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.97/1.59 ( X ) ) }.
% 0.97/1.59 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha21( X, Y, Z ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.97/1.59 ( X ) ) }.
% 0.97/1.59 { ! alpha21( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.59 { ! alpha21( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.97/1.59 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.97/1.59 ( X ), Y ), alpha21( X, Y, Z ) }.
% 0.97/1.59 { ! alpha3( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.97/1.59 { ! alpha3( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.59 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ) ), alpha3( X, Y, Z ) }.
% 0.97/1.59 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), alpha4( X, Y
% 0.97/1.59 , Z ), alpha22( X, Y, Z ) }.
% 0.97/1.59 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha4( X, Y, Z ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.59 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha22( X, Y, Z ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.59 { ! alpha22( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.59 { ! alpha22( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.97/1.59 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ) ), alpha22( X, Y, Z ) }.
% 0.97/1.59 { ! alpha4( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.97/1.59 { ! alpha4( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.59 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ), Y ), alpha4( X, Y, Z ) }.
% 0.97/1.60 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.97/1.60 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) }.
% 0.97/1.60 { ! class_Rings_Olinordered__semidom( X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.60 c_Groups_Oone__class_Oone( X ) ) }.
% 0.97/1.60 { ! class_Rings_Olinordered__semidom( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.97/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.60 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.97/1.60 c_RealVector_Onorm__class_Onorm( X, Y ) ), ! Y =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.60 { ! class_RealVector_Oreal__normed__vector( X ), Y =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless(
% 0.97/1.60 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.97/1.60 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.97/1.60 { ! class_RealVector_Oreal__normed__algebra( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.60 c_RealVector_Onorm__class_Onorm( X, Z ), Y ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.60 c_RealVector_Onorm__class_Onorm( X, U ), T ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.60 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), T ) ) }.
% 0.97/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.60 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.97/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.60 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.60 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.97/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.60 ! c_Orderings_Oord__class_Oless__eq( X, Z, T ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60 ( X, U, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.97/1.60 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.97/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60 ( X, U, T ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.97/1.60 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.97/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.97/1.60 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.60 , U ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.97/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( X, U, T ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.97/1.60 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.97/1.60 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.97/1.60 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.97/1.60 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.97/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.97/1.60 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.97/1.60 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.97/1.60 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.97/1.60 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.97/1.60 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.97/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.97/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.97/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.97/1.60 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) }.
% 0.97/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.97/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.97/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.97/1.60 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.97/1.60 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.60 c_RealVector_Onorm__class_Onorm( X, Z ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ),
% 0.97/1.60 c_RealVector_Onorm__class_Onorm( X, T ) ) ), Z =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.60 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol3( Y ) ) }.
% 0.97/1.60 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.60 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.97/1.60 c_RealVector_Onorm__class_Onorm( X, Y ) ),
% 0.97/1.60 c_RealVector_Onorm__class_Onorm( X, Z ) ) ), skol3( X ) ) ) }.
% 0.97/1.60 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol4( Z, T ) ) }.
% 0.97/1.60 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.60 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.97/1.60 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol4( X, Y ) ) ) }.
% 0.97/1.60 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol5( Z, T ) ) }.
% 0.97/1.60 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.60 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.97/1.60 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol5( X, Y ) ) ) }.
% 0.97/1.60 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal,
% 0.97/1.60 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ),
% 0.97/1.60 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) }.
% 0.97/1.60 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol6( Z, T ) ) }.
% 0.97/1.60 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.60 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.97/1.60 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol6( X, Y ) ) ) }.
% 0.97/1.60 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol7( Z, T ) ) }.
% 0.97/1.60 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.60 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.97/1.60 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol7( X, Y ) ) ) }.
% 0.97/1.60 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol8( Y ) ) }.
% 0.97/1.60 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.60 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.97/1.60 c_RealVector_Onorm__class_Onorm( X, Y ) ),
% 0.97/1.60 c_RealVector_Onorm__class_Onorm( X, Z ) ) ), skol8( X ) ) ) }.
% 0.97/1.60 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.60 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.97/1.60 c_RealVector_Onorm__class_Onorm( X, Y ) ),
% 0.97/1.60 c_RealVector_Onorm__class_Onorm( X, Z ) ) ), skol9( X ) ) ) }.
% 0.97/1.60 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.97/1.60 X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }
% 0.97/1.60 .
% 0.97/1.60 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.97/1.60 X ), Z, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z )
% 0.97/1.60 }.
% 0.97/1.60 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.97/1.60 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z
% 0.97/1.60 ), c_Orderings_Oord__class_Oless( tc_fun( T, X ), Z, Y ) }.
% 0.97/1.60 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.60 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.97/1.60 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol10( X, Y ) ) ) }.
% 0.97/1.60 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.60 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.97/1.60 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol11( X, Y ) ) ) }.
% 0.97/1.60 { ! class_Rings_Olinordered__semiring__1__strict( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60 ( X, T, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( X ), U ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), W
% 0.97/1.60 ), ! c_Groups_Oplus__class_Oplus( X, U, W ) = c_Groups_Oone__class_Oone
% 0.97/1.60 ( X ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X,
% 0.97/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), W ), T ) ), Y ) }.
% 0.97/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.60 skol12( X, T, U ) ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( X, skol12( X, T, U ),
% 0.97/1.60 c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.60 , Y ) }.
% 0.97/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), skol12( X, Y, Z ) ), Z ), Y ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.60 { c_RealDef_Opositive( X ), X = c_Groups_Ozero__class_Ozero(
% 0.97/1.60 tc_RealDef_Oreal ), c_RealDef_Opositive( c_Groups_Ouminus__class_Ouminus
% 0.97/1.60 ( tc_RealDef_Oreal, X ) ) }.
% 0.97/1.60 { ! class_Rings_Olinordered__semiring__1( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, T, Y ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.97/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.60 X ), W ), ! c_Groups_Oplus__class_Oplus( X, U, W ) =
% 0.97/1.60 c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.60 ( X ), U ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), T )
% 0.97/1.60 ), Y ) }.
% 0.97/1.60 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol13( Z, T ) ) }.
% 0.97/1.60 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.60 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, Z ) ), skol13( X, Y ) ) }.
% 0.97/1.60 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.60 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol50( X, Y, Z ) ) ), Z ),
% 0.97/1.60 c_SEQ_OBseq( X, Y ) }.
% 0.97/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.97/1.60 , Y ) = c_Groups_Oplus__class_Oplus( X, Y, Z ) }.
% 0.97/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.97/1.60 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.97/1.60 ( X, Z, c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.97/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.97/1.60 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.97/1.60 ( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) }.
% 0.97/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.97/1.60 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.97/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.97/1.60 ( X, c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 0.97/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.97/1.60 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X
% 0.97/1.60 , U, Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.97/1.60 { ! c_RealDef_Opositive( X ), ! c_RealDef_Opositive( Y ),
% 0.97/1.60 c_RealDef_Opositive( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X, Y
% 0.97/1.60 ) ) }.
% 0.97/1.60 { ! class_Groups_Oab__semigroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.97/1.60 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.97/1.60 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.97/1.60 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.97/1.60 T, Y ), Z = Y }.
% 0.97/1.60 { ! class_Groups_Ocancel__semigroup__add( X ), ! Z = Y,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.97/1.60 T, Y ) }.
% 0.97/1.60 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.97/1.60 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.97/1.60 Y, Z ), T = Y }.
% 0.97/1.60 { ! class_Groups_Ocancel__semigroup__add( X ), ! T = Y,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.97/1.60 Y, Z ) }.
% 0.97/1.60 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.97/1.60 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.97/1.60 T, Y ), Z = Y }.
% 0.97/1.60 { ! class_Groups_Ocancel__ab__semigroup__add( X ), !
% 0.97/1.60 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.97/1.60 T, Y ), Z = Y }.
% 0.97/1.60 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.97/1.60 c_Groups_Oplus__class_Oplus( X, Z, T ) = c_Groups_Oplus__class_Oplus( X,
% 0.97/1.60 Y, T ), Z = Y }.
% 0.97/1.60 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.60 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.97/1.60 ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.97/1.60 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.97/1.60 ( X, Y ) ) ) }.
% 0.97/1.60 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.60 c_RealVector_Onorm__class_Onorm( X, Z ), Y ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.60 c_RealVector_Onorm__class_Onorm( X, U ), T ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.60 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, Z, U
% 0.97/1.60 ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, T ) ) }.
% 0.97/1.60 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.97/1.60 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.97/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.60 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.97/1.60 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero( X ) =
% 0.97/1.60 c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 0.97/1.60 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.97/1.60 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.97/1.60 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.97/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.97/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.97/1.60 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.97/1.60 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.60 ( X ), ! Z = c_Groups_Oplus__class_Oplus( X, Z, Y ), Y =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.60 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.60 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.97/1.60 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 0.97/1.60 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.97/1.60 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.97/1.60 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.97/1.60 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.97/1.60 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.97/1.60 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.60 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.97/1.60 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.97/1.60 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.97/1.60 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.97/1.60 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.97/1.60 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.97/1.60 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.97/1.60 U ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.97/1.60 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.97/1.60 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.60 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.97/1.60 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.60 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.97/1.60 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ), c_Orderings_Oord__class_Oless
% 0.97/1.60 ( X, T, Y ) }.
% 0.97/1.60 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( X, T, Y ), c_Orderings_Oord__class_Oless(
% 0.97/1.60 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.97/1.60 , Y, Z ) ) }.
% 0.97/1.60 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.97/1.60 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.97/1.60 ( X, Z, Y ) }.
% 0.97/1.60 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.97/1.60 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.97/1.60 , T, Y ) ) }.
% 0.97/1.60 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.97/1.60 X, c_Groups_Oplus__class_Oplus( X, Z, T ), c_Groups_Oplus__class_Oplus( X
% 0.97/1.60 , Y, T ) ) }.
% 0.97/1.60 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.97/1.60 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.97/1.60 , T, Y ) ) }.
% 0.97/1.60 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60 ( X, U, T ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X, Y
% 0.97/1.60 , T ) ) }.
% 0.97/1.60 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, T )
% 0.97/1.60 , c_Groups_Oplus__class_Oplus( X, Y, T ) ), c_Orderings_Oord__class_Oless
% 0.97/1.60 ( X, Z, Y ) }.
% 0.97/1.60 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.97/1.60 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.97/1.60 ( X, Z, Y ) }.
% 0.97/1.60 { ! class_Rings_Ocomm__semiring( X ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.97/1.60 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.60 { ! class_Rings_Osemiring( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP
% 0.97/1.60 ( c_Groups_Otimes__class_Otimes( X ), U ), T ),
% 0.97/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.60 ( X ), Z ), T ), Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, U, Z
% 0.97/1.60 ) ), T ), Y ) }.
% 0.97/1.60 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.60 ( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.97/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.60 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.97/1.60 ), U = Z, T = Y }.
% 0.97/1.60 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.60 ( X ), ! U = Z, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.97/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.60 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.97/1.60 ) }.
% 0.97/1.60 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.60 ( X ), ! T = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.97/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.60 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.97/1.60 ) }.
% 0.97/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Y
% 0.97/1.60 ) ), Z ) }.
% 0.97/1.60 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.97/1.60 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.60 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.97/1.60 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.97/1.60 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.60 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.60 ( X ), U = T, Z = Y, ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.97/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.60 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.97/1.60 ) }.
% 0.97/1.60 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.60 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.97/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.60 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.97/1.60 ), ! U = T }.
% 0.97/1.60 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.60 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.97/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.60 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.97/1.60 ), ! Z = Y }.
% 0.97/1.60 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.60 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.60 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.60 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.60 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.60 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 0.97/1.60 , c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.97/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.97/1.60 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 0.97/1.60 , c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.97/1.60 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.97/1.60 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Z,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.97/1.60 Y ) ) = Y }.
% 0.97/1.60 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.60 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.60 Z, Y ) ) = Y }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ),
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, X ) ) }.
% 0.97/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ) ), X ) =
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.97/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.60 c_Groups_Oplus__class_Oplus( X, Y, Y ) ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.60 ) }.
% 0.97/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.60 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.97/1.60 ), c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.97/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Y,
% 0.97/1.60 Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.60 ) }.
% 0.97/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.60 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X
% 0.97/1.60 , Y, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.60 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.60 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.97/1.60 ) }.
% 0.97/1.60 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.60 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 0.97/1.60 .
% 0.97/1.60 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.60 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.97/1.60 .
% 0.97/1.60 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.60 X ), Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), ! Z =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.97/1.60 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.60 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.97/1.60 Y, Z ) ) }.
% 0.97/1.60 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.97/1.60 Z, Y ) ) }.
% 0.97/1.60 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.60 , c_Groups_Oplus__class_Oplus( X, Y, Z ), c_Groups_Ozero__class_Ozero( X
% 0.97/1.60 ) ) }.
% 0.97/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.60 c_Groups_Oplus__class_Oplus( X, Y, Y ) ), c_Orderings_Oord__class_Oless(
% 0.97/1.60 X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.97/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.60 c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.97/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.97/1.60 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Y
% 0.97/1.60 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.97/1.60 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.60 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.60 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.97/1.60 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.60 c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.97/1.60 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.60 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.60 , c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.97/1.60 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless(
% 0.97/1.60 X, T, c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.97/1.60 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( X, U, T ), c_Orderings_Oord__class_Oless(
% 0.97/1.60 X, c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X
% 0.97/1.60 , Y, T ) ) }.
% 0.97/1.60 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, U )
% 0.97/1.60 , c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.97/1.60 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.60 ( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! W = U, T = Z, !
% 0.97/1.60 c_Groups_Oplus__class_Oplus( X, W, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) =
% 0.97/1.60 c_Groups_Oplus__class_Oplus( X, U, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.60 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.97/1.60 , Y, c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) )
% 0.97/1.60 ) }.
% 0.97/1.60 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.97/1.60 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus
% 0.97/1.60 ( X, Z ) }.
% 0.97/1.60 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.60 , Z ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.60 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.97/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Ozero__class_Ozero(
% 0.97/1.60 X ) }.
% 0.97/1.60 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.60 , Y ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.60 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.97/1.60 = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ouminus__class_Ouminus
% 0.97/1.60 ( X, Y ) }.
% 0.97/1.60 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.60 { ! class_Groups_Oab__group__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.60 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.97/1.60 = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.97/1.60 Z ) = Y }.
% 0.97/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = hAPP(
% 0.97/1.60 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X
% 0.97/1.60 , Z, c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.97/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.97/1.60 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP
% 0.97/1.60 ( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.97/1.60 c_Groups_Oone__class_Oone( X ) ) ), Z ) }.
% 0.97/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.97/1.60 , Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.97/1.60 c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.97/1.60 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.97/1.60 { ! c_RealDef_Opositive( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) )
% 0.97/1.60 }.
% 0.97/1.60 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.60 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.60 { ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! X =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.60 { ! c_RealDef_Opositive( X ), ! c_RealDef_Opositive( Y ),
% 0.97/1.60 c_RealDef_Opositive( hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.60 tc_RealDef_Oreal ), X ), Y ) ) }.
% 0.97/1.60 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 0.97/1.60 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y = X }.
% 0.97/1.60 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 0.97/1.60 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.60 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X =
% 0.97/1.60 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) }.
% 0.97/1.60 { ! X = c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ),
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.60 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.60 ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.60 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.60 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.97/1.60 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.60 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.60 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.60 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.97/1.60 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.60 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.97/1.60 ) ) }.
% 0.97/1.60 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.60 ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.97/1.60 ) ) }.
% 0.97/1.60 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.60 ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.97/1.60 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.97/1.60 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.60 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.60 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.97/1.60 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.97/1.60 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.60 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.97/1.60 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.60 c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.97/1.60 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.97/1.60 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.97/1.60 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.97/1.60 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.97/1.60 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.60 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.97/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.60 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.97/1.60 ) ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.60 { ! class_Rings_Olinordered__ring__strict( X ), Z =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.97/1.60 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.97/1.60 { ! class_Rings_Olinordered__ring__strict( X ), Y =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.97/1.60 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.97/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.97/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.97/1.60 c_Groups_Ozero__class_Ozero( X ) ), Z = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.60 }.
% 0.97/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.97/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.97/1.60 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.60 }.
% 0.97/1.60 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.60 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.97/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.97/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.60 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.97/1.60 X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 0.97/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.97/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.60 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.97/1.60 ) = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X
% 0.97/1.60 ) }.
% 0.97/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.60 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.97/1.60 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.97/1.60 ) }.
% 0.97/1.60 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.60 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.60 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.97/1.60 ) ), c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 0.97/1.60 ) ) }.
% 0.97/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.60 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.97/1.60 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.97/1.60 ) ) }.
% 0.97/1.60 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol14( Z, T ) ) }.
% 0.97/1.60 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.60 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, hAPP
% 0.97/1.60 ( Y, Z ), c_Groups_Ouminus__class_Ouminus( X, hAPP( Y, skol51( X, Y ) ) )
% 0.97/1.60 ) ), skol14( X, Y ) ) }.
% 0.97/1.60 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.60 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, hAPP
% 0.97/1.60 ( Y, skol60( X, Y, Z, T ) ), c_Groups_Ouminus__class_Ouminus( X, hAPP( Y
% 0.97/1.60 , T ) ) ) ), Z ), c_SEQ_OBseq( X, Y ) }.
% 0.97/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.60 c_Groups_Oplus__class_Oplus( X, Y, Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.60 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.97/1.60 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.60 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol15( Z, T ) ) }.
% 0.97/1.60 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.60 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, hAPP
% 0.97/1.60 ( Y, Z ), c_Groups_Ouminus__class_Ouminus( X, skol52( X, Y ) ) ) ),
% 0.97/1.60 skol15( X, Y ) ) }.
% 0.97/1.60 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.60 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, hAPP
% 0.97/1.60 ( Y, skol61( X, Y, Z, T ) ), c_Groups_Ouminus__class_Ouminus( X, T ) ) )
% 0.97/1.60 , Z ), c_SEQ_OBseq( X, Y ) }.
% 0.97/1.60 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol16( Z, T ) ) }.
% 0.97/1.60 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.60 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, Z ) ), skol16( X, Y ) ) }.
% 0.97/1.60 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.60 c_RealVector_Onorm__class_Onorm( X, hAPP( Z, skol17( X, Y, Z ) ) ), Y ),
% 0.97/1.60 c_SEQ_OBseq( X, Z ) }.
% 0.97/1.60 { ! class_Fields_Olinordered__field( X ), c_Orderings_Oord__class_Oless( X
% 0.97/1.60 , c_Groups_Ozero__class_Ozero( X ), skol18( X, T, U ) ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.60 { ! class_Fields_Olinordered__field( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oplus__class_Oplus( X,
% 0.97/1.60 Y, skol18( X, Y, Z ) ) ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }
% 0.97/1.60 .
% 0.97/1.60 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, skol19( U, W, V0, T )
% 0.97/1.60 ), c_SEQ_OBseq( X, Y ) }.
% 0.97/1.60 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.60 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol19( X, Y, Z, T ) ) ), Z
% 0.97/1.60 ), c_SEQ_OBseq( X, Y ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol20( X, Y ) ) }.
% 0.97/1.60 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.60 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.97/1.60 { ! class_Orderings_Oorder( X ), ! c_SEQ_Odecseq( X, Y ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, T ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, T ), hAPP( Y, Z ) ) }.
% 0.97/1.60 { ! class_Orderings_Oorder( X ), c_Orderings_Oord__class_Oless__eq(
% 0.97/1.60 tc_Nat_Onat, skol21( X, Y ), skol53( X, Y ) ), c_SEQ_Odecseq( X, Y ) }.
% 0.97/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.60 hAPP( Y, skol53( X, Y ) ), hAPP( Y, skol21( X, Y ) ) ), c_SEQ_Odecseq( X
% 0.97/1.60 , Y ) }.
% 0.97/1.60 { ! class_Orderings_Oorder( X ), ! c_SEQ_Oincseq( X, Y ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, T ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, Z ), hAPP( Y, T ) ) }.
% 0.97/1.60 { ! class_Orderings_Oorder( X ), c_Orderings_Oord__class_Oless__eq(
% 0.97/1.60 tc_Nat_Onat, skol22( X, Y ), skol54( X, Y ) ), c_SEQ_Oincseq( X, Y ) }.
% 0.97/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.60 hAPP( Y, skol22( X, Y ) ), hAPP( Y, skol54( X, Y ) ) ), c_SEQ_Oincseq( X
% 0.97/1.60 , Y ) }.
% 0.97/1.60 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.60 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol23( X, Y, Z ) ) ), Z ),
% 0.97/1.60 c_SEQ_OBseq( X, Y ) }.
% 0.97/1.60 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.60 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.97/1.60 , Y ) ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.97/1.60 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, U,
% 0.97/1.60 Z ) ), c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus
% 0.97/1.60 ( X, T, Y ) ) ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.60 tc_Nat_Onat, X, Z ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), Z ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.97/1.60 tc_Nat_Onat, X, Y ), Z ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ), Y ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.60 tc_Nat_Onat, Z, X ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z, X =
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X =
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.97/1.60 tc_Nat_Onat, X, Y ), Y ) = X }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.60 tc_Nat_Onat, Z, X ), Y ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = X }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.60 tc_Nat_Onat, X, Z ), Y ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z,
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.60 tc_Nat_Onat, Z, Y ), X ) }.
% 0.97/1.60 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.97/1.60 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.97/1.60 ( X, Y ) ), c_RealVector_Onorm__class_Onorm( X,
% 0.97/1.60 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) }.
% 0.97/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.60 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.97/1.60 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.60 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.97/1.60 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, U, T ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ),
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.60 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.97/1.60 ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X = Z }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), ! X = Z,
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = Y }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, Z ),
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ),
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 0.97/1.60 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ), Y ) }.
% 0.97/1.60 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.60 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.97/1.60 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.60 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.97/1.60 ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.60 ( tc_Nat_Onat, Y, Z ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z )
% 0.97/1.60 ) }.
% 0.97/1.60 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.97/1.60 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) =
% 0.97/1.60 c_Groups_Ominus__class_Ominus( X, Y, Z ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.60 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.97/1.60 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.60 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.97/1.60 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.60 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.60 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.60 Y ), X ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.60 tc_Nat_Onat ), Z ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.60 ( tc_Nat_Onat ), Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 0.97/1.60 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.60 tc_Nat_Onat ), Y ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.60 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.97/1.60 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.60 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.97/1.60 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP
% 0.97/1.60 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.60 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.97/1.60 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP
% 0.97/1.60 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.97/1.60 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.60 tc_Nat_Onat ), X ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.60 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.60 ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.60 ( tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.60 tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 0.97/1.60 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.60 tc_Nat_Onat ), X ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.60 ( tc_Nat_Onat ), X ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 0.97/1.60 .
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.60 { ! class_Groups_Ominus( X ), hAPP( c_Groups_Ominus__class_Ominus( tc_fun(
% 0.97/1.60 U, X ), T, Z ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( T, Y ),
% 0.97/1.60 hAPP( Z, Y ) ) }.
% 0.97/1.60 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.97/1.60 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! U = T, Z = Y }.
% 0.97/1.60 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.97/1.60 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! Z = Y, U = T }.
% 0.97/1.60 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.97/1.60 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, X ) =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.60 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 0.97/1.60 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.60 tc_Nat_Onat ), X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.60 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.60 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.60 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.60 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.97/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Y = X
% 0.97/1.60 , Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.60 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.97/1.60 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.97/1.60 .
% 0.97/1.60 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.97/1.60 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.97/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = X
% 0.97/1.60 , Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.60 { ! Z = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.97/1.60 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }
% 0.97/1.60 .
% 0.97/1.60 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.97/1.60 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X )
% 0.97/1.60 , X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.60 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.60 c_Groups_Ominus__class_Ominus( X, Z, Y ), Y ) = Z }.
% 0.97/1.60 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = Z }.
% 0.97/1.60 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 0.97/1.60 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.60 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 0.97/1.60 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.60 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 0.97/1.60 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.60 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 0.97/1.60 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.60 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.97/1.60 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, U, T ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.60 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.97/1.60 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( X, U, T ) }.
% 0.97/1.60 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.97/1.60 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y, Y )
% 0.97/1.60 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.60 { ! class_Groups_Oab__group__add( X ), ! Z = Y,
% 0.97/1.60 c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.97/1.60 ) }.
% 0.97/1.60 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.97/1.60 Z, Y ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.97/1.60 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.97/1.60 ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.97/1.60 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ominus__class_Ominus(
% 0.97/1.60 X, Z, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.60 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.97/1.60 , ! alpha5( X, Y, Z ) }.
% 0.97/1.60 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.97/1.60 , ! alpha23( X, Y, Z ) }.
% 0.97/1.60 { alpha5( X, Y, Z ), alpha23( X, Y, Z ), hBOOL( hAPP( Z,
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.97/1.60 { ! alpha23( X, Y, Z ), ! hBOOL( hAPP( Z, skol24( T, U, Z ) ) ) }.
% 0.97/1.60 { ! alpha23( X, Y, Z ), Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.97/1.60 skol24( X, Y, Z ) ) }.
% 0.97/1.60 { ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, T ), hBOOL( hAPP( Z, T
% 0.97/1.60 ) ), alpha23( X, Y, Z ) }.
% 0.97/1.60 { ! alpha5( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }
% 0.97/1.60 .
% 0.97/1.60 { ! alpha5( X, Y, Z ), ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero(
% 0.97/1.60 tc_Nat_Onat ) ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), hBOOL( hAPP( Z,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha5( X, Y, Z ) }.
% 0.97/1.60 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.97/1.60 , alpha6( X, Y, Z ) }.
% 0.97/1.60 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.97/1.60 , alpha24( X, Y, Z ) }.
% 0.97/1.60 { ! alpha6( X, Y, Z ), ! alpha24( X, Y, Z ), hBOOL( hAPP( Z,
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.97/1.60 { ! alpha24( X, Y, Z ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.97/1.60 T ), hBOOL( hAPP( Z, T ) ) }.
% 0.97/1.60 { ! hBOOL( hAPP( Z, skol25( T, U, Z ) ) ), alpha24( X, Y, Z ) }.
% 0.97/1.60 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, skol25( X, Y, Z ) ),
% 0.97/1.60 alpha24( X, Y, Z ) }.
% 0.97/1.60 { ! alpha6( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 0.97/1.60 , hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.97/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), alpha6( X, Y, Z ) }.
% 0.97/1.60 { ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha6
% 0.97/1.60 ( X, Y, Z ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.60 ( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.60 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.60 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.97/1.60 tc_Nat_Onat, Y, X ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.60 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.97/1.60 tc_Nat_Onat, Y, X ) ) }.
% 0.97/1.60 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = Y, X =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.60 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.60 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.60 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.97/1.60 tc_Nat_Onat, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.60 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.60 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero
% 0.97/1.60 ( tc_Nat_Onat ) ) = X }.
% 0.97/1.60 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.60 tc_Nat_Onat ), X ) = X }.
% 0.97/1.60 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.97/1.60 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, c_Groups_Oplus__class_Oplus
% 0.97/1.60 ( tc_Nat_Onat, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.97/1.60 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.60 tc_Nat_Onat, Y, X ), X ) = Y }.
% 0.97/1.60 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.60 tc_Nat_Onat, Y, X ), Y ) = X }.
% 0.97/1.60 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.60 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.97/1.60 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.60 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.97/1.60 Z, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.97/1.60 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ), Y = X }.
% 0.97/1.60 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) }.
% 0.97/1.60 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ), Z = X }.
% 0.97/1.60 { ! Z = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.97/1.60 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.60 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) =
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 0.97/1.60 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.60 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) =
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.97/1.60 ( tc_Nat_Onat, Y, Z ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y
% 0.97/1.60 , X ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, X ) =
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.60 tc_Nat_Onat, Y, T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.97/1.60 .
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.60 tc_Nat_Onat, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.97/1.60 .
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.97/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) = Y }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.97/1.60 ( tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) )
% 0.97/1.60 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.60 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }
% 0.97/1.60 .
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z,
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.60 tc_Nat_Onat, Z, X ), Y ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.97/1.60 ( tc_Nat_Onat, Z, X ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z
% 0.97/1.60 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.97/1.60 ( tc_Nat_Onat, Y, X ), X ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.97/1.60 ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.97/1.60 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.60 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 0.97/1.60 ( tc_Nat_Onat ) ) ), X ) ) }.
% 0.97/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.97/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.60 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.97/1.60 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, Z,
% 0.97/1.60 Y ) ) = c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus
% 0.97/1.60 ( X, Y, Z ) ) }.
% 0.97/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 0.97/1.60 , Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 0.97/1.60 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.97/1.60 X, c_Groups_Ominus__class_Ominus( X, Z, Y ), c_Groups_Ozero__class_Ozero
% 0.97/1.60 ( X ) ) }.
% 0.97/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.97/1.60 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.97/1.60 , Z, Y ) }.
% 0.97/1.60 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.97/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.60 ( X ), Z ), U ), Y ), T = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.97/1.60 W ) ), U ), Y ) }.
% 0.97/1.60 { ! class_Rings_Oring( X ), ! T = c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.97/1.60 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.97/1.60 X, Z, W ) ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.97/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.60 ( X ), Z ), U ), Y ) }.
% 0.97/1.60 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.97/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.60 ( X ), Z ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.97/1.60 Z ) ), U ), T ) = Y }.
% 0.97/1.60 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.97/1.60 Z ) ), U ), T ) = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.97/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.60 ( X ), Z ), U ), Y ) }.
% 0.97/1.60 { ! class_Rings_Oring( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.97/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.60 ( X ), U ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 0.97/1.60 Z ) ), Y ) ) }.
% 0.97/1.60 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.97/1.60 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.97/1.60 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.97/1.60 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.97/1.60 X, U, Z ) ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 0.97/1.60 Z ) ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 0.97/1.60 c_Groups_Ominus__class_Ominus( X, T, Y ) ) ) }.
% 0.97/1.60 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.97/1.60 X, Y ) }.
% 0.97/1.60 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.97/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Oplus__class_Oplus(
% 0.97/1.60 X, Z, Y ) }.
% 0.97/1.60 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X, Z
% 0.97/1.60 , Y ) = c_Groups_Oplus__class_Oplus( X, Z,
% 0.97/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.97/1.60 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z, Y )
% 0.97/1.60 = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.60 , Y ) ) }.
% 0.97/1.60 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.97/1.60 ) = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus(
% 0.97/1.60 X, Y ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ),
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ),
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.97/1.60 { c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ) =
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 0.97/1.60 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) }.
% 0.97/1.60 { c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ) =
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 0.97/1.60 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) }.
% 0.97/1.60 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.97/1.60 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X ) ),
% 0.97/1.60 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y ) ),
% 0.97/1.60 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.97/1.60 c_RealDef_Opositive( c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X,
% 0.97/1.60 Y ) ) }.
% 0.97/1.60 { ! c_RealDef_Opositive( c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X
% 0.97/1.60 , Y ) ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ) }.
% 0.97/1.60 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.60 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.97/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.60 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.60 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ) }.
% 0.97/1.60 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.60 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.97/1.60 Z ) ), U ), T ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.60 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.97/1.60 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.60 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.97/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.60 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X, T,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.60 ( X ), c_Groups_Ominus__class_Ominus( X, Z, W ) ), U ), Y ) ) }.
% 0.97/1.60 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.60 , T, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.97/1.60 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.60 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.97/1.60 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.60 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.97/1.60 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.97/1.60 X, W, Z ) ), U ), T ), Y ) }.
% 0.97/1.60 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.60 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.97/1.60 hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.97/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.60 ( X ), Z ), U ), Y ) ) }.
% 0.97/1.60 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.60 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, hAPP
% 0.97/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus
% 0.97/1.60 ( X, Z, W ) ), U ), Y ) ) }.
% 0.97/1.60 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X, T
% 0.97/1.60 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.97/1.60 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.60 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.97/1.60 { ! class_Rings_Oring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP
% 0.97/1.60 ( c_Groups_Otimes__class_Otimes( X ), Y ), Y ), c_Groups_Oone__class_Oone
% 0.97/1.60 ( X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.97/1.60 c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) ) ),
% 0.97/1.60 c_Groups_Ominus__class_Ominus( X, Y, c_Groups_Oone__class_Oone( X ) ) ) }
% 0.97/1.60 .
% 0.97/1.60 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.97/1.60 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.97/1.60 ( X, Y ) ), c_RealVector_Onorm__class_Onorm( X,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) ) }.
% 0.97/1.60 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.60 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, Z,
% 0.97/1.60 Y ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.97/1.60 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.97/1.60 ( X, Y ) ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.60 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 0.97/1.60 ) }.
% 0.97/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.60 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 0.97/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 0.97/1.60 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.60 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X
% 0.97/1.60 ) }.
% 0.97/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.60 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 0.97/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 0.97/1.60 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.60 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.60 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.60 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.60 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.97/1.60 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, X ) }.
% 0.97/1.60 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ) }.
% 0.97/1.60 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ), Y = X }.
% 0.97/1.60 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) }.
% 0.97/1.60 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), T ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.97/1.60 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.97/1.60 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol26( X, Y ) ) }.
% 0.97/1.60 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, T ),
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ), X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.60 { ! class_RealVector_Oreal__normed__vector( Y ), ! class_Orderings_Oord( X
% 0.97/1.60 ), c_Orderings_Oord__class_Oless__eq( X, T, skol27( X, U, W, T ) ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, T, V0 ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.60 c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, V0 ) ),
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oone__class_Oone
% 0.97/1.60 ( tc_RealDef_Oreal ), c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, T ) )
% 0.97/1.60 ) ) }.
% 0.97/1.60 { ! class_RealVector_Oreal__normed__vector( Y ), ! class_Orderings_Oord( X
% 0.97/1.60 ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.60 c_RealVector_Onorm__class_Onorm( Y, c_Groups_Ominus__class_Ominus( Y,
% 0.97/1.60 hAPP( Z, T ), hAPP( Z, skol27( X, Y, Z, T ) ) ) ),
% 0.97/1.60 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, T, U ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.60 c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, U ) ),
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oone__class_Oone
% 0.97/1.60 ( tc_RealDef_Oreal ), c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, T ) )
% 0.97/1.60 ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.60 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 0.97/1.60 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.60 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 0.97/1.60 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.60 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 0.97/1.60 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.60 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.60 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.60 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 0.97/1.60 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.60 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 0.97/1.60 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) =
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.60 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.97/1.60 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.97/1.60 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X = Y }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.60 ( tc_Nat_Onat, Y, Z ), X ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.60 ( tc_Nat_Onat, Z, X ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.97/1.60 ) }.
% 0.97/1.60 { alpha54( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.97/1.60 hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.97/1.60 { alpha54( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP
% 0.97/1.60 ( X, Y ), Z ) ) }.
% 0.97/1.60 { ! alpha54( X, Y, Z ), alpha56( X, Y, Z ), Z = Y }.
% 0.97/1.60 { ! alpha54( X, Y, Z ), alpha56( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z
% 0.97/1.60 ) ) }.
% 0.97/1.60 { ! alpha56( X, Y, Z ), alpha54( X, Y, Z ) }.
% 0.97/1.60 { ! Z = Y, hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha54( X, Y, Z ) }.
% 0.97/1.60 { ! alpha56( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y )
% 0.97/1.60 }.
% 0.97/1.60 { ! alpha56( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP(
% 0.97/1.60 X, Y ), Z ) ), alpha56( X, Y, Z ) }.
% 0.97/1.60 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.60 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ), Y ) }.
% 0.97/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) = X }.
% 0.97/1.60 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), Y =
% 0.97/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.97/1.60 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X =
% 0.97/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.97/1.60 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.97/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Groups_Oone__class_Oone(
% 0.97/1.60 tc_Nat_Onat ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.97/1.60 , Y ), X ) }.
% 0.97/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.97/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.97/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP
% 0.97/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.97/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) =
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.97/1.60 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Oone__class_Oone(
% 0.97/1.60 tc_Nat_Onat ) }.
% 0.97/1.60 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X = c_Groups_Oone__class_Oone(
% 0.97/1.60 tc_Nat_Onat ) }.
% 0.97/1.60 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.97/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.97/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 0.97/1.60 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.60 { c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, Y, X ) =
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y,
% 0.97/1.60 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, X ) ) }.
% 0.97/1.60 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.97/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Z =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.97/1.60 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.97/1.60 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.97/1.60 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.97/1.60 .
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.60 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.97/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP(
% 0.97/1.60 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.60 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 0.97/1.60 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.60 ( tc_Nat_Onat ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.60 tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.60 tc_Nat_Onat ), X ), Y ), Z = Y }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.60 ( tc_Nat_Onat ), X ), ! Z = Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.60 ( tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.60 tc_Nat_Onat ), X ), Y ) }.
% 0.97/1.60 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), T ), Z ),
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), X ) ) =
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus
% 0.97/1.60 ( tc_Nat_Onat, T, Y ) ), Z ), X ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.60 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP
% 0.97/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.60 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z
% 0.97/1.60 , Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) =
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ), T =
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! T =
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ),
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) =
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.60 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 0.97/1.60 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) =
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, T,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ),
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ),
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) =
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ),
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) = Z }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) = Z,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) =
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.97/1.60 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.97/1.60 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Ouminus__class_Ouminus
% 0.97/1.60 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.97/1.60 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) }.
% 0.97/1.60 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.97/1.60 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus(
% 0.97/1.60 X, U, Z ), c_Groups_Ominus__class_Ominus( X, T, Y ) ) }.
% 0.97/1.60 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.97/1.60 hAPP( X, Y ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol28( Z, Y
% 0.97/1.60 ), Y ) }.
% 0.97/1.60 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.97/1.60 hAPP( X, Y ) ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.97/1.60 skol28( X, Y ) ), ! hBOOL( hAPP( X, Z ) ) }.
% 0.97/1.60 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.97/1.60 hAPP( X, Y ) ), hBOOL( hAPP( X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat
% 0.97/1.60 , skol28( X, Y ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.60 c_RComplete_Onatceiling( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X
% 0.97/1.60 , c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) =
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatceiling( X ),
% 0.97/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.60 c_RComplete_Onatfloor( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 0.97/1.60 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) =
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatfloor( X ),
% 0.97/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.97/1.60 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.60 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), hAPP( hAPP
% 0.97/1.60 ( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.60 c_Power_Opower__class_Opower( X ), Z ), c_Groups_Ominus__class_Ominus(
% 0.97/1.60 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ), Z ) =
% 0.97/1.60 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) }.
% 0.97/1.60 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.60 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 0.97/1.60 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.60 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.60 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.97/1.60 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.97/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.60 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.97/1.60 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.60 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) }.
% 0.97/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.60 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.97/1.60 tc_Nat_Onat ) ) = Y }.
% 0.97/1.60 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ),
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) = hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.60 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.60 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ) }.
% 0.97/1.60 { c_RComplete_Onatfloor( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) )
% 0.97/1.60 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.60 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) )
% 0.97/1.60 }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatfloor( Y
% 0.97/1.60 ), c_RComplete_Onatfloor( X ) ) }.
% 0.97/1.60 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.60 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.97/1.60 c_Power_Opower__class_Opower( X ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.60 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.97/1.60 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) ) }.
% 0.97/1.60 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 0.97/1.60 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.97/1.60 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.60 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.97/1.60 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) }.
% 0.97/1.60 { c_RComplete_Onatfloor( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) =
% 0.97/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.97/1.60 { c_RComplete_Onatceiling( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal )
% 0.97/1.60 ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.60 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_RComplete_Onatceiling( X )
% 0.97/1.60 ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 0.97/1.60 Y ), c_RComplete_Onatceiling( X ) ) }.
% 0.97/1.60 { c_RComplete_Onatceiling( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 0.97/1.60 = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.97/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.60 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ozero__class_Ozero(
% 0.97/1.60 tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.60 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.97/1.60 c_Power_Opower__class_Opower( X ), T ), Y ) ) = hAPP( hAPP(
% 0.97/1.60 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.97/1.60 tc_Nat_Onat, Z, Y ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_RComplete_Onatfloor
% 0.97/1.60 ( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.97/1.60 c_RComplete_Onatceiling( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.97/1.60 }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Groups_Oone__class_Oone
% 0.97/1.60 ( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling
% 0.97/1.60 ( X ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.97/1.60 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.97/1.60 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 0.97/1.60 X ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.97/1.60 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.60 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) =
% 0.97/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.97/1.60 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.60 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) = hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 0.97/1.60 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ),
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 0.97/1.60 ( tc_Nat_Onat ) ) ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_RComplete_Onatfloor( X )
% 0.97/1.60 ), c_RComplete_Onatfloor( Y ) ), c_RComplete_Onatfloor( hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) ) }.
% 0.97/1.60 { ! class_Power_Opower( X ), ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 0.97/1.60 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) =
% 0.97/1.60 c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.60 { ! class_Power_Opower( X ), Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.97/1.60 , hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) = hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.97/1.60 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ominus__class_Ominus(
% 0.97/1.60 tc_Nat_Onat, Z, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 0.97/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( X ), Z ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.60 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), T ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.60 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.97/1.60 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.97/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 0.97/1.60 hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.97/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ), X ) =
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.97/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ) =
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.97/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.97/1.60 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ), X ) =
% 0.97/1.60 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.97/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP(
% 0.97/1.60 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.97/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) = hAPP
% 0.97/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) }.
% 0.97/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 0.97/1.60 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = X }.
% 0.97/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.97/1.60 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) = X }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.60 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.60 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), X =
% 0.97/1.60 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.60 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.60 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), Y =
% 0.97/1.60 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.60 ( tc_Int_Oint ), X ), ! X = c_Groups_Oone__class_Oone( tc_Int_Oint ), ! Y
% 0.97/1.60 = c_Groups_Oone__class_Oone( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 0.97/1.60 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.60 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 0.97/1.60 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP
% 0.97/1.60 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.97/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ), X ) =
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.97/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) =
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.97/1.60 { ! class_Rings_Oring__1__no__zero__divisors( X ), Y =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.97/1.60 c_Power_Opower__class_Opower( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 0.97/1.60 ( X ) }.
% 0.97/1.60 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.97/1.60 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.60 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.97/1.60 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.97/1.60 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.60 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.97/1.60 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.97/1.60 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.97/1.60 c_Power_Opower__class_Opower( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.97/1.60 = c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.60 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.97/1.60 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), X =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.60 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.60 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.60 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.60 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.97/1.60 ), X ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.60 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.97/1.60 ( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Z ), hAPP( hAPP
% 0.97/1.60 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.97/1.60 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.97/1.60 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.60 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.97/1.60 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) }.
% 0.97/1.60 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.97/1.60 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.97/1.60 tc_Nat_Onat ) ) = Y }.
% 0.97/1.60 { ! class_Rings_Olinordered__semidom( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.97/1.60 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.60 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.97/1.60 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.97/1.60 { ! class_Rings_Olinordered__semidom( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.60 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.97/1.60 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.97/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless
% 0.97/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.97/1.60 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.97/1.60 { ! class_Rings_Olinordered__semidom( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 0.97/1.60 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.97/1.60 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.97/1.60 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.97/1.60 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.97/1.60 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.97/1.60 .
% 0.97/1.60 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.97/1.60 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.97/1.60 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.60 tc_Nat_Onat ) }.
% 0.97/1.60 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.97/1.60 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.97/1.60 , ! Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 0.97/1.60 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y )
% 0.97/1.60 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! hAPP( hAPP(
% 0.97/1.60 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.97/1.60 c_Power_Opower__class_Opower( X ), Y ), Z ), T = Z }.
% 0.97/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! T = Z, hAPP( hAPP(
% 0.97/1.60 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.97/1.60 c_Power_Opower__class_Opower( X ), Y ), Z ) }.
% 0.97/1.60 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.97/1.60 , Y ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.97/1.60 c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.60 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.97/1.60 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.97/1.60 tc_Nat_Onat, Z, Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.97/1.60 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.97/1.60 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.97/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP
% 0.97/1.60 ( c_Power_Opower__class_Opower( X ), Y ), T ) ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.60 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.97/1.60 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.97/1.60 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.97/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.97/1.60 X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.97/1.60 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.97/1.60 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), ! Y =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.60 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.97/1.60 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.60 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), Y =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.60 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.97/1.60 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.60 { ! class_Rings_Oring__1( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.97/1.60 ), c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.60 c_Power_Opower__class_Opower( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.97/1.60 c_Groups_Oone__class_Oone( X ) ) ), Y ) ), hAPP( hAPP(
% 0.97/1.60 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.97/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.97/1.60 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.97/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60 ( tc_Nat_Onat, T, Z ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.60 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.60 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.97/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.97/1.60 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.97/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.97/1.60 c_Groups_Oone__class_Oone( X ), T ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.60 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.60 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.97/1.60 { ! class_Rings_Olinordered__semidom( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), T )
% 0.97/1.60 , c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.60 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.60 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.97/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.97/1.60 c_Power_Opower__class_Opower( X ), Y ), Z ) ), hAPP( hAPP(
% 0.97/1.60 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.97/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.60 , T, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.60 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.97/1.60 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 0.97/1.60 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 0.97/1.60 c_Power_Opower__class_Opower( X ), T ), Z ) = hAPP( hAPP(
% 0.97/1.60 c_Power_Opower__class_Opower( X ), Y ), Z ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.97/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.60 X ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ), T = Y }.
% 0.97/1.60 { ! class_Rings_Olinordered__semidom( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.97/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oone__class_Oone
% 0.97/1.60 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.60 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.97/1.60 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 0.97/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.60 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.60 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.97/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.60 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.60 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.97/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.60 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.60 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.60 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.97/1.60 , Y ), X ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.60 tc_Nat_Onat ), Y ) }.
% 0.97/1.60 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.60 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.97/1.60 ), X ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.60 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.60 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.60 { ! class_Power_Opower( X ), c_Power_Opower__class_Opower( X ) =
% 0.97/1.60 c_Power_Opower_Opower( X, c_Groups_Oone__class_Oone( X ),
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.60 tc_Nat_Onat, Y ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.97/1.60 tc_RealDef_Oreal, X, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.97/1.60 c_RealDef_Oreal( tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone(
% 0.97/1.60 tc_RealDef_Oreal ) ) ), c_RComplete_Onatceiling( X ) =
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone(
% 0.97/1.60 tc_Nat_Onat ) ) }.
% 0.97/1.60 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.97/1.60 tc_Nat_Onat, X ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.60 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.60 tc_Int_Oint ), X ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.60 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.60 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.97/1.60 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X )
% 0.97/1.60 }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.97/1.60 tc_Int_Oint ) ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.97/1.60 tc_Int_Oint ) ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X )
% 0.97/1.60 }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.97/1.60 tc_Int_Oint ) ), X ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.60 tc_Int_Oint ), c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.97/1.60 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.97/1.60 tc_Int_Oint ) ), X ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Z ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.97/1.60 tc_Int_Oint, Y, T ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.97/1.60 .
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ),
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.97/1.60 { ! c_Groups_Ozero__class_Ozero( tc_Int_Oint ) = c_Groups_Oone__class_Oone
% 0.97/1.60 ( tc_Int_Oint ) }.
% 0.97/1.60 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero
% 0.97/1.60 ( tc_Int_Oint ) ) = X }.
% 0.97/1.60 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.60 tc_Int_Oint ), X ) = X }.
% 0.97/1.60 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) =
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) }.
% 0.97/1.60 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus
% 0.97/1.60 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.97/1.60 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.97/1.60 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.97/1.60 tc_Int_Oint, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.97/1.60 .
% 0.97/1.60 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.97/1.60 tc_Int_Oint, c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ) =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.97/1.60 ( tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.97/1.60 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.97/1.60 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.97/1.60 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.97/1.60 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y
% 0.97/1.60 = X }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.97/1.60 tc_Int_Oint ) ) ) }.
% 0.97/1.60 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.97/1.60 tc_Int_Oint ) ) ) }.
% 0.97/1.60 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.60 tc_Int_Oint ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.97/1.60 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y = X,
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), ! Y = X }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), Y = X,
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.97/1.60 { ! c_RealDef_Oreal( tc_Nat_Onat, Y ) = c_RealDef_Oreal( tc_Nat_Onat, X ),
% 0.97/1.60 Y = X }.
% 0.97/1.60 { ! Y = X, c_RealDef_Oreal( tc_Nat_Onat, Y ) = c_RealDef_Oreal( tc_Nat_Onat
% 0.97/1.60 , X ) }.
% 0.97/1.60 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.60 ( tc_Int_Oint ) ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.97/1.60 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint,
% 0.97/1.60 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) = X }.
% 0.97/1.60 { ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.97/1.60 c_Groups_Osgn__class_Osgn( tc_Int_Oint, X ) = c_Groups_Ozero__class_Ozero
% 0.97/1.60 ( tc_Int_Oint ) }.
% 0.97/1.60 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.60 tc_Int_Oint ), X ), c_Groups_Osgn__class_Osgn( tc_Int_Oint, X ) =
% 0.97/1.60 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.97/1.60 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.60 tc_Int_Oint ), X ), c_Groups_Osgn__class_Osgn( tc_Int_Oint, X ) =
% 0.97/1.60 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Oone__class_Oone(
% 0.97/1.60 tc_Int_Oint ) ) }.
% 0.97/1.60 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.97/1.60 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) }.
% 0.97/1.60 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) =
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.97/1.60 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.97/1.60 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.97/1.60 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.97/1.60 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ),
% 0.97/1.60 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.97/1.60 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.97/1.60 ( tc_Int_Oint, X ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ominus__class_Ominus
% 0.97/1.60 ( tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ),
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 0.97/1.60 ( tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.97/1.60 .
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 0.97/1.60 ( tc_Int_Oint ) ) ) }.
% 0.97/1.60 { c_RComplete_Onatceiling( c_RealDef_Oreal( tc_Nat_Onat, X ) ) = X }.
% 0.97/1.60 { c_RComplete_Onatfloor( c_RealDef_Oreal( tc_Nat_Onat, X ) ) = X }.
% 0.97/1.60 { ! c_RealDef_Oreal( tc_Nat_Onat, X ) = c_Groups_Ozero__class_Ozero(
% 0.97/1.60 tc_RealDef_Oreal ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.60 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_RealDef_Oreal(
% 0.97/1.60 tc_Nat_Onat, X ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.60 { c_RealDef_Oreal( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.97/1.60 ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.60 tc_Nat_Onat, X ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.60 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.60 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.60 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.60 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 0.97/1.60 { c_RealDef_Oreal( tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.60 tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.60 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ), c_RealDef_Oreal
% 0.97/1.60 ( tc_Nat_Onat, X ) ) }.
% 0.97/1.60 { c_RealDef_Oreal( tc_Nat_Onat, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y
% 0.97/1.60 , X ) ) = c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal
% 0.97/1.60 ( tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 0.97/1.60 { c_RealDef_Oreal( tc_Nat_Onat, c_Groups_Oone__class_Oone( tc_Nat_Onat ) )
% 0.97/1.60 = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.97/1.60 { c_RealDef_Oreal( tc_Nat_Onat, hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.97/1.60 tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.97/1.60 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ), X ) }.
% 0.97/1.60 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.97/1.60 c_RealDef_Oreal( tc_Nat_Onat, Y ) ), X ) = c_RealDef_Oreal( tc_Nat_Onat,
% 0.97/1.60 hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.60 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.97/1.60 tc_Nat_Onat, c_RComplete_Onatceiling( X ) ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.60 tc_Nat_Onat, X ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.60 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.60 tc_Nat_Onat, X ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), c_RealDef_Oreal
% 0.97/1.60 ( tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.60 tc_Nat_Onat, X ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.60 tc_Nat_Onat, c_RComplete_Onatfloor( X ) ), X ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.60 tc_Nat_Onat, Y ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.97/1.60 , c_RComplete_Onatfloor( X ) ) }.
% 0.97/1.60 { hAPP( hAPP( c_Power_Opower_Opower( T, Z, Y ), X ),
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = Z }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, c_RealDef_Oreal
% 0.97/1.60 ( tc_Nat_Onat, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.60 c_RComplete_Onatceiling( Y ), X ) }.
% 0.97/1.60 { ! X = c_RealDef_Oreal( tc_Nat_Onat, c_RComplete_Onatfloor( X ) ),
% 0.97/1.60 c_RComplete_Onatfloor( hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.97/1.60 tc_RealDef_Oreal ), X ), Y ) ) = hAPP( hAPP( c_Power_Opower__class_Opower
% 0.97/1.60 ( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ), Y ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.97/1.60 tc_Nat_Onat, X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.60 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.97/1.60 tc_Nat_Onat, X ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.60 tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.97/1.60 c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.60 tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.97/1.60 c_RealDef_Oreal( tc_Nat_Onat, X ) ), c_Orderings_Oord__class_Oless(
% 0.97/1.60 tc_Nat_Onat, Y, X ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.60 tc_Nat_Onat, Y ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.97/1.60 c_RealDef_Oreal( tc_Nat_Onat, X ), c_Groups_Oone__class_Oone(
% 0.97/1.60 tc_RealDef_Oreal ) ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.60 tc_Nat_Onat, Y ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.97/1.60 c_RealDef_Oreal( tc_Nat_Onat, X ), c_Groups_Oone__class_Oone(
% 0.97/1.60 tc_RealDef_Oreal ) ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.97/1.60 , X ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_RComplete_Onatfloor
% 0.97/1.60 ( X ) ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.60 c_RealDef_Oreal( tc_Nat_Onat, Y ), X ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.60 tc_Nat_Onat, Y ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.97/1.60 , c_RComplete_Onatfloor( X ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 0.97/1.60 X ), Y ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.97/1.60 c_RealDef_Oreal( tc_Nat_Onat, Y ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.97/1.60 tc_Nat_Onat, Y ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.60 c_RComplete_Onatceiling( X ), Y ) }.
% 0.97/1.60 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.60 tc_Nat_Onat, c_RComplete_Onatfloor( X ) ), c_Groups_Oone__class_Oone(
% 0.97/1.60 tc_RealDef_Oreal ) ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.60 tc_Nat_Onat, Y ), X ), c_RComplete_Onatfloor(
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.97/1.60 tc_Nat_Onat, Y ) ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.97/1.60 c_RComplete_Onatfloor( X ), Y ) }.
% 0.97/1.60 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X,
% 0.97/1.60 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), c_RealDef_Oreal(
% 0.97/1.60 tc_Nat_Onat, c_RComplete_Onatfloor( X ) ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.60 tc_Nat_Onat, Y ), X ), c_RComplete_Onatceiling(
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.97/1.60 tc_Nat_Onat, Y ) ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.97/1.60 c_RComplete_Onatceiling( X ), Y ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.97/1.60 tc_Nat_Onat, Y ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.60 c_RComplete_Onatfloor( X ), Y ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.60 c_RComplete_Onatfloor( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 0.97/1.60 c_RealDef_Oreal( tc_Nat_Onat, Y ) ) ) = c_Groups_Oplus__class_Oplus(
% 0.97/1.60 tc_Nat_Onat, c_RComplete_Onatfloor( X ), Y ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatfloor( Y ),
% 0.97/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, c_RealDef_Oreal(
% 0.97/1.60 tc_Nat_Onat, X ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.60 tc_Nat_Onat, Y ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal
% 0.97/1.60 , X, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.60 tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ),
% 0.97/1.60 c_RComplete_Onatfloor( X ) = Y }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.60 c_RComplete_Onatceiling( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X
% 0.97/1.60 , c_RealDef_Oreal( tc_Nat_Onat, Y ) ) ) = c_Groups_Oplus__class_Oplus(
% 0.97/1.60 tc_Nat_Onat, c_RComplete_Onatceiling( X ), Y ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.97/1.60 tc_Nat_Onat, Y ) ), X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 0.97/1.60 , hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 0.97/1.60 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ), Y ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.60 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.97/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.97/1.60 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.60 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.97/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oone__class_Oone
% 0.97/1.60 ( tc_Int_Oint ), Y ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.97/1.60 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.97/1.60 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.60 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ), Y = X }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Z ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, Z ) }.
% 0.97/1.60 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ) }.
% 0.97/1.60 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, X ) }.
% 0.97/1.60 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.97/1.60 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.97/1.60 ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, T, W ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.60 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.97/1.60 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, U ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, Z ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, T ) }.
% 0.97/1.60 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.97/1.60 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.97/1.60 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.60 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.97/1.60 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, U, Y ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, U ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, U ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Y ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.97/1.60 ( tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.97/1.60 Z ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.60 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.60 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.97/1.60 tc_Int_Oint, X, Y ) ) }.
% 0.97/1.60 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Ozero__class_Ozero(
% 0.97/1.60 tc_Int_Oint ) ) }.
% 0.97/1.60 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 0.97/1.60 tc_Int_Oint ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.60 tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, skol29( X ),
% 0.97/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ), X ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.97/1.60 tc_Nat_Onat, skol29( X ) ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.97/1.60 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ominus__class_Ominus(
% 0.97/1.60 tc_Int_Oint, X, Y ) }.
% 0.97/1.60 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.97/1.60 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint
% 0.97/1.60 ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.60 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol30( Z, T ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.60 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), hAPP( hAPP(
% 0.97/1.60 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), skol30( X, Y ) ), X ) =
% 0.97/1.60 Y }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.60 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), ! hAPP( hAPP(
% 0.97/1.60 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Z ), X ) = Y, Z =
% 0.97/1.60 skol30( X, Y ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Nat__Transfer_Otsub( X, Y )
% 0.97/1.60 ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.97/1.60 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ominus__class_Ominus(
% 0.97/1.60 tc_Int_Oint, X, Y ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.60 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol31( Z, T ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.60 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), hAPP( hAPP(
% 0.97/1.60 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), skol31( X, Y ) ), X ) =
% 0.97/1.60 Y }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.60 c_Transcendental_Oln( hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.97/1.60 tc_RealDef_Oreal ), X ), Y ) ) = hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.97/1.60 tc_Nat_Onat, Y ) ), c_Transcendental_Oln( X ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 0.97/1.60 ), X ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.97/1.60 c_Transcendental_Oln( X ) = c_Transcendental_Oln( Y ), X = Y }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), ! X = Y,
% 0.97/1.60 c_Transcendental_Oln( X ) = c_Transcendental_Oln( Y ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 0.97/1.60 ), c_Transcendental_Oln( Y ) ), c_Orderings_Oord__class_Oless(
% 0.97/1.60 tc_RealDef_Oreal, X, Y ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, Y ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 0.97/1.60 ), c_Transcendental_Oln( Y ) ) }.
% 0.97/1.60 { c_Transcendental_Oln( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_Transcendental_Oln
% 0.97/1.60 ( X ), c_Transcendental_Oln( Y ) ), c_Orderings_Oord__class_Oless__eq(
% 0.97/1.60 tc_RealDef_Oreal, X, Y ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_Transcendental_Oln
% 0.97/1.60 ( X ), c_Transcendental_Oln( Y ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 0.97/1.60 ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 0.97/1.60 ) ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.97/1.60 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 0.97/1.60 ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 0.97/1.60 ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.97/1.60 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.97/1.60 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 0.97/1.60 ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.60 c_Transcendental_Oln( X ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal
% 0.97/1.60 ), X = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), ! X =
% 0.97/1.60 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_Transcendental_Oln( X )
% 0.97/1.60 = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 0.97/1.60 ) ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 0.97/1.60 ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 0.97/1.60 ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 0.97/1.60 ) ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.61 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 0.97/1.61 ) ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.61 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.61 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 0.97/1.61 ) ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.97/1.61 c_Transcendental_Oln( hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.61 tc_RealDef_Oreal ), X ), Y ) ) = c_Groups_Oplus__class_Oplus(
% 0.97/1.61 tc_RealDef_Oreal, c_Transcendental_Oln( X ), c_Transcendental_Oln( Y ) )
% 0.97/1.61 }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_Transcendental_Oln
% 0.97/1.61 ( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.97/1.61 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) ), X ) }.
% 0.97/1.61 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.61 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol32( X, Y, Z ) ) ), Z ),
% 0.97/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.61 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, T ) ), c_RealDef_Oreal(
% 0.97/1.61 tc_Nat_Onat, c_Nat_OSuc( skol55( X, Y ) ) ) ) }.
% 0.97/1.61 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.61 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol62( X, Y, Z ) ) ),
% 0.97/1.61 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ),
% 0.97/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol64( T, U ) ) }.
% 0.97/1.61 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.61 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol62( X, Y, Z ) ) ),
% 0.97/1.61 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ),
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.61 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, T ) ), skol64( X, Y ) ) }.
% 0.97/1.61 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.61 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol33( X, Y, Z ) ) ), Z ),
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.61 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, T ) ), c_RealDef_Oreal(
% 0.97/1.61 tc_Nat_Onat, c_Nat_OSuc( skol56( X, Y ) ) ) ) }.
% 0.97/1.61 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.61 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol63( X, Y, Z ) ) ),
% 0.97/1.61 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ),
% 0.97/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol65( T, U ) ) }.
% 0.97/1.61 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.61 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol63( X, Y, Z ) ) ),
% 0.97/1.61 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ),
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.61 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, T ) ), skol65( X, Y ) ) }.
% 0.97/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( X ) ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.97/1.61 X ) ) }.
% 0.97/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.61 tc_Nat_Onat ), c_Nat_OSuc( X ) ) }.
% 0.97/1.61 { ! hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.61 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = c_Nat_OSuc(
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.61 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.61 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP(
% 0.97/1.61 hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc
% 0.97/1.61 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.61 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), c_Nat_OSuc(
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) = c_Nat_OSuc(
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.61 { hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), c_Nat_OSuc( X ) ) =
% 0.97/1.61 hAPP( hAPP( Z, Y ), hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), X
% 0.97/1.61 ) ) }.
% 0.97/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.97/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.97/1.61 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) )
% 0.97/1.61 }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.97/1.61 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.97/1.61 X ) ) }.
% 0.97/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y = X }
% 0.97/1.61 .
% 0.97/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X,
% 0.97/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.97/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), X = Y }
% 0.97/1.61 .
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) = X
% 0.97/1.61 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 0.97/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.97/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.97/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.97/1.61 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.61 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.97/1.61 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.97/1.61 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.61 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.61 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.97/1.61 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.61 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.97/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.97/1.61 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.97/1.61 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.97/1.61 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 0.97/1.61 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.97/1.61 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.61 ( tc_Nat_Onat, c_Nat_OSuc( Z ), Y ), c_Nat_OSuc( X ) ) =
% 0.97/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.61 ( tc_Nat_Onat, Z, Y ), X ) }.
% 0.97/1.61 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.97/1.61 X ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 0.97/1.61 { ! X = c_Nat_OSuc( X ) }.
% 0.97/1.61 { ! c_Nat_OSuc( X ) = X }.
% 0.97/1.61 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.97/1.61 { ! Y = X, c_Nat_OSuc( Y ) = c_Nat_OSuc( X ) }.
% 0.97/1.61 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.97/1.61 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z
% 0.97/1.61 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.61 c_Nat_OSuc( Z ) ), X ), Y = X }.
% 0.97/1.61 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.61 c_Nat_OSuc( Z ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.61 tc_Nat_Onat ), c_Nat_OSuc( Z ) ), X ) }.
% 0.97/1.61 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 0.97/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.61 ( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) }.
% 0.97/1.61 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 0.97/1.61 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.97/1.61 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.97/1.61 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X ) }.
% 0.97/1.61 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.97/1.61 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) =
% 0.97/1.61 c_Nat_OSuc( c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.97/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.97/1.61 ), X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.97/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.97/1.61 ), X ) ) }.
% 0.97/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), c_Nat_OSuc
% 0.97/1.61 ( X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Y )
% 0.97/1.61 ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.97/1.61 ( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.97/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.97/1.61 ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.97/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.97/1.61 ), X ) ) }.
% 0.97/1.61 { c_Groups_Oone__class_Oone( tc_Nat_Onat ) = c_Nat_OSuc(
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.97/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X = Y }
% 0.97/1.61 .
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X = Y,
% 0.97/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.97/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.97/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), X = c_Nat_OSuc(
% 0.97/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol34( X, Y ) ) ) }.
% 0.97/1.61 { ! X = c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ),
% 0.97/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 0.97/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ) }.
% 0.97/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 0.97/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.97/1.61 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.61 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y = c_Nat_OSuc
% 0.97/1.61 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.61 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.61 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X = c_Nat_OSuc
% 0.97/1.61 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.61 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.97/1.61 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.61 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha7( X, Y ), alpha25( X
% 0.97/1.61 , Y ) }.
% 0.97/1.61 { ! alpha7( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.97/1.61 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.61 { ! alpha25( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.97/1.61 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.61 { ! alpha25( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.61 { ! alpha25( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.97/1.61 tc_Nat_Onat ) ) }.
% 0.97/1.61 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha25( X, Y ) }.
% 0.97/1.61 { ! alpha7( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.97/1.61 tc_Nat_Onat ) ) }.
% 0.97/1.61 { ! alpha7( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.61 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha7( X, Y ) }.
% 0.97/1.61 { ! c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.97/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ), alpha8( X, Y ), alpha26
% 0.97/1.61 ( X, Y ) }.
% 0.97/1.61 { ! alpha8( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.97/1.61 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.97/1.61 { ! alpha26( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.97/1.61 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.97/1.61 { ! alpha26( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.61 { ! alpha26( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.97/1.61 tc_Nat_Onat ) ) }.
% 0.97/1.61 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha26( X, Y ) }.
% 0.97/1.61 { ! alpha8( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.97/1.61 tc_Nat_Onat ) ) }.
% 0.97/1.61 { ! alpha8( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.61 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha8( X, Y ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( c_Nat_OSuc(
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X =
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X = c_Nat_OSuc(
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y =
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha9( X, Y ) }.
% 0.97/1.61 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.97/1.61 { ! alpha9( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.97/1.61 c_Nat_OSuc( X ) ) }.
% 0.97/1.61 { ! alpha9( X, Y ), Y = c_Nat_OSuc( skol35( Z, Y ) ) }.
% 0.97/1.61 { ! alpha9( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol35( X,
% 0.97/1.61 Y ), X ) }.
% 0.97/1.61 { ! Y = c_Nat_OSuc( Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.97/1.61 ), alpha9( X, Y ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X =
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.61 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.61 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( skol36( X ) ) }.
% 0.97/1.61 { ! X = c_Nat_OSuc( Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.97/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 0.97/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 0.97/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.97/1.61 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.97/1.61 , Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.97/1.61 , Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.97/1.61 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) }.
% 0.97/1.61 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.61 c_Nat_OSuc( Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), X ) }
% 0.97/1.61 .
% 0.97/1.61 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 0.97/1.61 ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.97/1.61 { ! Y = c_Nat_OSuc( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.97/1.61 , c_Nat_OSuc( X ) ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 0.97/1.61 c_Nat_OSuc( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X )
% 0.97/1.61 }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 0.97/1.61 c_Nat_OSuc( X ) ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 0.97/1.61 ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.61 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ) = hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.97/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.61 X ), Y ), Z = Y }.
% 0.97/1.61 { ! class_Rings_Olinordered__semidom( X ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ), hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ) ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.61 ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.61 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.97/1.61 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ) ) }.
% 0.97/1.61 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.97/1.61 , Z ), c_Nat_OSuc( c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.97/1.61 ) ) ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc(
% 0.97/1.61 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), Z = Y, Z =
% 0.97/1.61 c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.97/1.61 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.97/1.61 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.97/1.61 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc(
% 0.97/1.61 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP
% 0.97/1.61 ( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.97/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.97/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.97/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.61 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.97/1.61 tc_Nat_Onat, X, c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) )
% 0.97/1.61 ) ) = X }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.61 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.61 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.97/1.61 tc_Nat_Onat, c_Nat_OSuc( X ) ) ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, c_Nat_OSuc(
% 0.97/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) ) =
% 0.97/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.61 tc_Nat_Onat, Z, Y ), c_Nat_OSuc( X ) ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), Z ) =
% 0.97/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 0.97/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ) }.
% 0.97/1.61 { c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.97/1.61 tc_Nat_Onat ) ) ) = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.97/1.61 { c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( X ) ) =
% 0.97/1.61 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.61 tc_Nat_Onat, X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ) }.
% 0.97/1.61 { ! class_Rings_Olinordered__semidom( X ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone
% 0.97/1.61 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ), Y ) }.
% 0.97/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.61 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.97/1.61 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ),
% 0.97/1.61 c_Groups_Oone__class_Oone( X ) ) }.
% 0.97/1.61 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.97/1.61 tc_Nat_Onat, Z, Y ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ),
% 0.97/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) ) = hAPP
% 0.97/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), T ), c_Groups_Ominus__class_Ominus(
% 0.97/1.61 tc_Nat_Onat, Y, Z ) ) ), T ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.61 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.97/1.61 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.61 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.97/1.61 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) = X }.
% 0.97/1.61 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = X }.
% 0.97/1.61 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.97/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.97/1.61 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) ) }.
% 0.97/1.61 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.61 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, Z ) ), c_RealDef_Oreal(
% 0.97/1.61 tc_Nat_Onat, c_Nat_OSuc( skol37( X, Y ) ) ) ) }.
% 0.97/1.61 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.61 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol57( X, Y, Z ) ) ),
% 0.97/1.61 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ), c_SEQ_OBseq( X, Y ) }
% 0.97/1.61 .
% 0.97/1.61 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.97/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.61 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, Z ) ), c_RealDef_Oreal(
% 0.97/1.61 tc_Nat_Onat, c_Nat_OSuc( skol38( X, Y ) ) ) ) }.
% 0.97/1.61 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.61 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol58( X, Y, Z ) ) ),
% 0.97/1.61 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ), c_SEQ_OBseq( X, Y ) }
% 0.97/1.61 .
% 0.97/1.61 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP
% 0.97/1.61 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) ) = hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.97/1.61 Y ) ), c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.97/1.61 tc_Nat_Onat, skol39( X, Y ) ) ), X ), Y ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.97/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.97/1.61 tc_Nat_Onat, c_Nat_OSuc( skol39( X, Y ) ) ) ), X ) ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.61 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.97/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ), Y ) = hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ),
% 0.97/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.97/1.61 { ! class_Divides_Osemiring__div( X ), ! T = c_Groups_Ozero__class_Ozero( X
% 0.97/1.61 ), c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.97/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.61 { ! class_Divides_Osemiring__div( X ), T = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.61 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.97/1.61 c_Divides_Odiv__class_Odiv( X, Z, Y ) }.
% 0.97/1.61 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.61 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = Z }.
% 0.97/1.61 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.61 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) = Z }.
% 0.97/1.61 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.61 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.97/1.61 c_Divides_Odiv__class_Odiv( X, T, Z ) }.
% 0.97/1.61 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.61 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) =
% 0.97/1.61 c_Divides_Odiv__class_Odiv( X, T, Z ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.61 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.97/1.61 tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.97/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.61 tc_Int_Oint ), Y ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.61 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ),
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.61 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ),
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.97/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.61 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.97/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.97/1.61 tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.61 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.97/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, X ) =
% 0.97/1.61 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.97/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X, Y,
% 0.97/1.61 c_Groups_Oone__class_Oone( X ) ) = Y }.
% 0.97/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X, Y,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.61 }.
% 0.97/1.61 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.61 tc_Int_Oint ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.97/1.61 tc_Int_Oint, X, Y ) ) }.
% 0.97/1.61 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.97/1.61 ( tc_Int_Oint, Y ), c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.97/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) }.
% 0.97/1.61 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y,
% 0.97/1.61 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.97/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.97/1.61 ( tc_Int_Oint, Y ), X ) }.
% 0.97/1.61 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.61 , c_Divides_Odiv__class_Odiv( X, Y, Y ) = c_Groups_Oone__class_Oone( X )
% 0.97/1.61 }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ),
% 0.97/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ) ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.61 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ),
% 0.97/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ) ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.97/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) =
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.61 tc_Int_Oint ), Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.97/1.61 Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 0.97/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ) ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.61 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.97/1.61 tc_Int_Oint, Y, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y
% 0.97/1.61 , c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.97/1.61 tc_Int_Oint, Y, X ) ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ),
% 0.97/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) =
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.61 tc_Int_Oint ), Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.97/1.61 Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ),
% 0.97/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.61 tc_Int_Oint ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ),
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.61 tc_Int_Oint ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ),
% 0.97/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.61 tc_Int_Oint ), Y ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.61 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.97/1.61 tc_Int_Oint, X, Y ) ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.61 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.97/1.61 tc_Int_Oint, Y, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X
% 0.97/1.61 , Y ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.61 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X
% 0.97/1.61 , Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.97/1.61 tc_Int_Oint, Y, X ) ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.61 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.97/1.61 tc_Int_Oint, Y, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.61 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.97/1.61 tc_Int_Oint, Y, X ) ) }.
% 0.97/1.61 { ! c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X =
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), alpha10( X, Y ) }.
% 0.97/1.61 { ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.97/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.97/1.61 { ! alpha10( X, Y ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.97/1.61 { ! alpha10( X, Y ), alpha27( X, Y ), alpha36( X, Y ) }.
% 0.97/1.61 { ! alpha27( X, Y ), alpha10( X, Y ) }.
% 0.97/1.61 { ! alpha36( X, Y ), alpha10( X, Y ) }.
% 0.97/1.61 { ! alpha36( X, Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.61 { ! alpha36( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ), alpha36( X, Y ) }.
% 0.97/1.61 { ! alpha27( X, Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.97/1.61 { ! alpha27( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), alpha27( X, Y ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.61 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.61 c_Groups_Oone__class_Oone( tc_Int_Oint ), Y ),
% 0.97/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.97/1.61 tc_Int_Oint, X, Y ), X ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.61 ( tc_Int_Oint ), X ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Z, hAPP(
% 0.97/1.61 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) =
% 0.97/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.97/1.61 tc_Int_Oint, Z, Y ), X ) }.
% 0.97/1.61 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.61 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, T, hAPP
% 0.97/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) =
% 0.97/1.61 c_Groups_Oplus__class_Oplus( X, Z, c_Divides_Odiv__class_Odiv( X, T, Y )
% 0.97/1.61 ) }.
% 0.97/1.61 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.61 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, T, hAPP
% 0.97/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) =
% 0.97/1.61 c_Groups_Oplus__class_Oplus( X, Z, c_Divides_Odiv__class_Odiv( X, T, Y )
% 0.97/1.61 ) }.
% 0.97/1.61 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.61 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, Y, Z ),
% 0.97/1.61 Y ) = c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Z, Y
% 0.97/1.61 ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.97/1.61 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.61 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, Z, Y ),
% 0.97/1.61 Y ) = c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Z, Y
% 0.97/1.61 ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.97/1.61 { ! T = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), alpha55( X,
% 0.97/1.61 Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), Z =
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.97/1.61 tc_Int_Oint, T, Z ) = Y }.
% 0.97/1.61 { ! T = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), alpha55( X,
% 0.97/1.61 Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Z =
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.97/1.61 tc_Int_Oint, T, Z ) = Y }.
% 0.97/1.61 { ! alpha55( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.97/1.61 { ! alpha55( X, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.61 ( tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), alpha55( X, Y ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.61 ( tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y )
% 0.97/1.61 , alpha55( X, Y ) }.
% 0.97/1.61 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ),
% 0.97/1.61 alpha11( X, Z ) }.
% 0.97/1.61 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ),
% 0.97/1.61 alpha28( X, Y, Z ) }.
% 0.97/1.61 { ! alpha11( X, Z ), ! alpha28( X, Y, Z ), hBOOL( hAPP( Z,
% 0.97/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ) }.
% 0.97/1.61 { ! alpha28( X, Y, Z ), alpha37( X, Y, Z ) }.
% 0.97/1.61 { ! alpha28( X, Y, Z ), alpha42( X, Y, Z ) }.
% 0.97/1.61 { ! alpha37( X, Y, Z ), ! alpha42( X, Y, Z ), alpha28( X, Y, Z ) }.
% 0.97/1.61 { ! alpha42( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha47( X, Y, Z ) }.
% 0.97/1.61 { c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha42( X, Y, Z ) }.
% 0.97/1.61 { ! alpha47( X, Y, Z ), alpha42( X, Y, Z ) }.
% 0.97/1.61 { ! alpha47( X, Y, Z ), ! alpha51( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 0.97/1.61 { ! hBOOL( hAPP( Z, skol40( T, U, Z ) ) ), alpha47( X, Y, Z ) }.
% 0.97/1.61 { alpha51( X, Y, skol40( X, Y, Z ) ), alpha47( X, Y, Z ) }.
% 0.97/1.61 { ! alpha51( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.61 skol41( X, T, U ) ) }.
% 0.97/1.61 { ! alpha51( X, Y, Z ), alpha53( X, Y, Z, skol41( X, Y, Z ) ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, T ), ! alpha53( X, Y, Z
% 0.97/1.61 , T ), alpha51( X, Y, Z ) }.
% 0.97/1.61 { ! alpha53( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.61 T, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.61 { ! alpha53( X, Y, Z, T ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.97/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ) }
% 0.97/1.61 .
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! Y =
% 0.97/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ), alpha53( X,
% 0.97/1.61 Y, Z, T ) }.
% 0.97/1.61 { ! alpha37( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), alpha43( X, Y, Z ) }.
% 0.97/1.61 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.61 tc_Int_Oint ), X ), alpha37( X, Y, Z ) }.
% 0.97/1.61 { ! alpha43( X, Y, Z ), alpha37( X, Y, Z ) }.
% 0.97/1.61 { ! alpha43( X, Y, Z ), ! alpha48( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 0.97/1.61 { ! hBOOL( hAPP( Z, skol42( T, U, Z ) ) ), alpha43( X, Y, Z ) }.
% 0.97/1.61 { alpha48( X, Y, skol42( X, Y, Z ) ), alpha43( X, Y, Z ) }.
% 0.97/1.61 { ! alpha48( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), skol43( T, U, W ) ) }.
% 0.97/1.61 { ! alpha48( X, Y, Z ), alpha52( X, Y, Z, skol43( X, Y, Z ) ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! alpha52( X, Y, Z, T )
% 0.97/1.61 , alpha48( X, Y, Z ) }.
% 0.97/1.61 { ! alpha52( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X
% 0.97/1.61 ) }.
% 0.97/1.61 { ! alpha52( X, Y, Z, T ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.97/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ) }
% 0.97/1.61 .
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X ), ! Y =
% 0.97/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ), alpha52( X,
% 0.97/1.61 Y, Z, T ) }.
% 0.97/1.61 { ! alpha11( X, Y ), ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.97/1.61 hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 0.97/1.61 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), alpha11( X, Y ) }.
% 0.97/1.61 { ! hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), alpha11
% 0.97/1.61 ( X, Y ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), c_SMT_Oz3div( X, Y ) =
% 0.97/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) }.
% 0.97/1.61 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), c_SMT_Oz3div( X, Y ) =
% 0.97/1.61 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Divides_Odiv__class_Odiv
% 0.97/1.61 ( tc_Int_Oint, X, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ) ) }
% 0.97/1.61 .
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.61 tc_Nat_Onat, skol44( X ) ), X ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.97/1.61 tc_Nat_Onat, c_Nat_OSuc( skol44( X ) ) ) ) }.
% 0.97/1.61 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) = X }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.61 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) =
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.61 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.61 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ), Y ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.61 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, Z ),
% 0.97/1.61 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, X, Z ) ) }.
% 0.97/1.61 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) =
% 0.97/1.61 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 0.97/1.61 tc_Nat_Onat, Z, Y ), X ) }.
% 0.97/1.61 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.61 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) =
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.61 { Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.61 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) =
% 0.97/1.61 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.61 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X
% 0.97/1.61 , Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.61 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, Y ),
% 0.97/1.61 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, X ) ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.61 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 0.97/1.61 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ) = Y }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.61 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 0.97/1.61 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ) = Y }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.61 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 0.97/1.61 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) =
% 0.97/1.61 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, Y ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.97/1.61 tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 0.97/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 0.97/1.61 tc_Nat_Onat, Y, X ), Y ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.61 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 0.97/1.61 , c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.97/1.61 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.97/1.61 tc_Nat_Onat, Y, X ), X ) ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.61 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 0.97/1.61 ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) =
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.61 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 0.97/1.61 , c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.97/1.61 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.97/1.61 tc_Nat_Onat, Y, X ), X ) ) }.
% 0.97/1.61 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 0.97/1.61 alpha12( X, Z ) }.
% 0.97/1.61 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 0.97/1.61 alpha29( X, Y, Z ) }.
% 0.97/1.61 { ! alpha12( X, Z ), ! alpha29( X, Y, Z ), hBOOL( hAPP( Z,
% 0.97/1.61 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ) }.
% 0.97/1.61 { ! alpha29( X, Y, Z ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.61 alpha38( X, Y, Z ) }.
% 0.97/1.61 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha29( X, Y, Z ) }.
% 0.97/1.61 { ! alpha38( X, Y, Z ), alpha29( X, Y, Z ) }.
% 0.97/1.61 { ! alpha38( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, X
% 0.97/1.61 ), alpha44( X, Y, Z, T ) }.
% 0.97/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol45( X, T, U ), X ),
% 0.97/1.61 alpha38( X, Y, Z ) }.
% 0.97/1.61 { ! alpha44( X, Y, Z, skol45( X, Y, Z ) ), alpha38( X, Y, Z ) }.
% 0.97/1.61 { ! alpha44( X, Y, Z, T ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.97/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 0.97/1.61 hBOOL( hAPP( Z, U ) ) }.
% 0.97/1.61 { ! hBOOL( hAPP( Z, skol46( U, W, Z, V0 ) ) ), alpha44( X, Y, Z, T ) }.
% 0.97/1.61 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol46( X, Y, Z, T ) )
% 0.97/1.61 , T ), alpha44( X, Y, Z, T ) }.
% 0.97/1.61 { ! alpha12( X, Y ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.61 hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.97/1.61 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha12( X, Y ) }.
% 0.97/1.61 { ! hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha12
% 0.97/1.61 ( X, Y ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.61 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), Y ),
% 0.97/1.61 ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), c_Nat_OSuc( Z ) ) ), Z
% 0.97/1.61 = c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.61 ( tc_Nat_Onat ), X ), ! Z = c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X
% 0.97/1.61 ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), Y ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.61 ( tc_Nat_Onat ), X ), ! Z = c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X
% 0.97/1.61 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), c_Nat_OSuc( Z ) ) ) }
% 0.97/1.61 .
% 0.97/1.61 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 0.97/1.61 alpha13( X, Z ), alpha30( X, Y, Z ) }.
% 0.97/1.61 { ! alpha13( X, Z ), hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv(
% 0.97/1.61 tc_Nat_Onat, Y, X ) ) ) }.
% 0.97/1.61 { ! alpha30( X, Y, Z ), hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv(
% 0.97/1.61 tc_Nat_Onat, Y, X ) ) ) }.
% 0.97/1.61 { ! alpha30( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol47( X
% 0.97/1.61 , Y, T ) ), Y ) }.
% 0.97/1.61 { ! alpha30( X, Y, Z ), alpha39( X, Y, Z, skol47( X, Y, Z ) ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), T ), Y ), ! alpha39( X
% 0.97/1.61 , Y, Z, T ), alpha30( X, Y, Z ) }.
% 0.97/1.61 { ! alpha39( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.97/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), c_Nat_OSuc
% 0.97/1.61 ( T ) ) ) }.
% 0.97/1.61 { ! alpha39( X, Y, Z, T ), hBOOL( hAPP( Z, T ) ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), c_Nat_OSuc( T ) ) ), !
% 0.97/1.61 hBOOL( hAPP( Z, T ) ), alpha39( X, Y, Z, T ) }.
% 0.97/1.61 { ! alpha13( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.61 { ! alpha13( X, Y ), hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero(
% 0.97/1.61 tc_Nat_Onat ) ) ) }.
% 0.97/1.61 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hBOOL( hAPP( Y,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha13( X, Y ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.61 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X
% 0.97/1.61 , Y ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.97/1.61 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.97/1.61 tc_Nat_Onat, Y, X ), X ) ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.61 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.61 tc_Nat_Onat ), Y ), c_RComplete_Onatfloor(
% 0.97/1.61 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.97/1.61 tc_Nat_Onat, Y ) ) ) = c_Divides_Odiv__class_Odiv( tc_Nat_Onat,
% 0.97/1.61 c_RComplete_Onatfloor( X ), Y ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.61 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( hAPP( Z, c_Divides_Odiv__class_Odiv
% 0.97/1.61 ( tc_Int_Oint, Y, X ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X )
% 0.97/1.61 ) ), ! alpha14( X, Y, T, U ), hBOOL( hAPP( hAPP( Z, T ), U ) ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.61 ( tc_Int_Oint ), X ), alpha14( X, Y, skol48( X, Y, Z ), skol59( X, Y, Z )
% 0.97/1.61 ), hBOOL( hAPP( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X )
% 0.97/1.61 ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.61 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( hAPP( Z, skol48( X, Y, Z ) ), skol59
% 0.97/1.61 ( X, Y, Z ) ) ), hBOOL( hAPP( hAPP( Z, c_Divides_Odiv__class_Odiv(
% 0.97/1.61 tc_Int_Oint, Y, X ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) )
% 0.97/1.61 ) }.
% 0.97/1.61 { ! alpha14( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ) }.
% 0.97/1.61 { ! alpha14( X, Y, Z, T ), alpha31( X, Y, Z, T ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! alpha31( X, Y, Z, T )
% 0.97/1.61 , alpha14( X, Y, Z, T ) }.
% 0.97/1.61 { ! alpha31( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X
% 0.97/1.61 ) }.
% 0.97/1.61 { ! alpha31( X, Y, Z, T ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.97/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ) }
% 0.97/1.61 .
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X ), ! Y =
% 0.97/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ), alpha31( X,
% 0.97/1.61 Y, Z, T ) }.
% 0.97/1.61 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.61 ( X ), c_Divides_Odiv__class_Odiv( X, T, Z ) ), Z ),
% 0.97/1.61 c_Divides_Odiv__class_Omod( X, T, Z ) ), Y ) =
% 0.97/1.61 c_Groups_Oplus__class_Oplus( X, T, Y ) }.
% 0.97/1.61 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.61 ( X ), T ), c_Divides_Odiv__class_Odiv( X, Z, T ) ),
% 0.97/1.61 c_Divides_Odiv__class_Omod( X, Z, T ) ), Y ) =
% 0.97/1.61 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 0.97/1.61 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 0.97/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X
% 0.97/1.61 , Z, Y ) ), Y ), c_Divides_Odiv__class_Omod( X, Z, Y ) ) = Z }.
% 0.97/1.61 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 0.97/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 0.97/1.61 c_Divides_Odiv__class_Odiv( X, Y, Z ) ), c_Divides_Odiv__class_Omod( X, Y
% 0.97/1.61 , Z ) ) = Y }.
% 0.97/1.61 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.61 c_Divides_Odiv__class_Omod( X, Z, Y ), hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X, Z, Y )
% 0.97/1.61 ), Y ) ) = Z }.
% 0.97/1.61 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.97/1.61 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.97/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.97/1.61 tc_Int_Oint, Z, X ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 0.97/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.97/1.61 tc_Int_Oint, c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, X ),
% 0.97/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) ) }.
% 0.97/1.61 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.61 tc_Nat_Onat, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ),
% 0.97/1.61 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.61 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) ) }.
% 0.97/1.61 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero(
% 0.97/1.61 tc_Int_Oint ) ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.97/1.61 { c_Divides_Odiv__class_Omod( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero(
% 0.97/1.61 tc_Int_Oint ) ) = X }.
% 0.97/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X,
% 0.97/1.61 c_Divides_Odiv__class_Omod( X, Z, Y ), Y ) = c_Groups_Ozero__class_Ozero
% 0.97/1.61 ( X ) }.
% 0.97/1.61 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Divides_Odiv__class_Omod(
% 0.97/1.61 tc_Int_Oint, Y, X ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.97/1.61 { ! class_Fields_Olinordered__field( X ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.61 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.61 , Z ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.97/1.61 ( X ), c_Rings_Oinverse__class_Odivide( X, Y, Z ) ) }.
% 0.97/1.61 { ! class_Fields_Olinordered__field( X ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.61 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.97/1.61 ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.61 c_Rings_Oinverse__class_Odivide( X, Y, Z ), c_Groups_Ozero__class_Ozero(
% 0.97/1.61 X ) ) }.
% 0.97/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.61 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( X, Y, Z ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.97/1.61 ! c_Orderings_Oord__class_Oless( X, T, U ), c_Orderings_Oord__class_Oless
% 0.97/1.61 ( X, c_Rings_Oinverse__class_Odivide( X, Y, U ),
% 0.97/1.61 c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 0.97/1.61 { ! class_Fields_Olinordered__field( X ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.61 ), ! c_Orderings_Oord__class_Oless( X, Y, Z ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.97/1.61 ! c_Orderings_Oord__class_Oless__eq( X, T, U ),
% 0.97/1.61 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, Y,
% 0.97/1.61 U ), c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 0.97/1.61 { ! class_Fields_Olinordered__field( X ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.97/1.61 ! c_Orderings_Oord__class_Oless__eq( X, T, U ),
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.97/1.61 , Y, U ), c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 0.97/1.61 { ! class_Fields_Olinordered__field( X ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.61 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.61 , Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.61 c_Rings_Oinverse__class_Odivide( X, Y, Z ), c_Groups_Ozero__class_Ozero(
% 0.97/1.61 X ) ) }.
% 0.97/1.61 { ! class_Fields_Olinordered__field( X ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.61 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.97/1.61 ) ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.61 X ), c_Rings_Oinverse__class_Odivide( X, Y, Z ) ) }.
% 0.97/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.97/1.61 Z, Y ) ), alpha32( X, Y, Z, T ) }.
% 0.97/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.97/1.61 Z, Y ) ), alpha40( X, Y, Z, T ) }.
% 0.97/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha32( X, Y, Z
% 0.97/1.61 , T ), ! alpha40( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 0.97/1.61 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.97/1.61 { ! alpha40( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( X ), Y ), alpha45( X, Y, Z, T ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.97/1.61 , alpha40( X, Y, Z, T ) }.
% 0.97/1.61 { ! alpha45( X, Y, Z, T ), alpha40( X, Y, Z, T ) }.
% 0.97/1.61 { ! alpha45( X, Y, Z, T ), alpha49( X, Y, Z, T ) }.
% 0.97/1.61 { ! alpha45( X, Y, Z, T ), alpha15( X, Y, T ) }.
% 0.97/1.61 { ! alpha49( X, Y, Z, T ), ! alpha15( X, Y, T ), alpha45( X, Y, Z, T ) }.
% 0.97/1.61 { ! alpha49( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.61 { c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.61 alpha49( X, Y, Z, T ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha49( X, Y, Z, T ) }.
% 0.97/1.61 { ! alpha32( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.97/1.61 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.61 alpha32( X, Y, Z, T ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ), alpha32( X, Y, Z, T )
% 0.97/1.61 }.
% 0.97/1.61 { ! alpha15( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.61 , alpha15( X, Y, Z ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.61 , alpha15( X, Y, Z ) }.
% 0.97/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.97/1.61 Z ), Y ), alpha33( X, Y, Z, T ) }.
% 0.97/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.97/1.61 Z ), Y ), alpha41( X, Y, Z, T ) }.
% 0.97/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha33( X, Y, Z
% 0.97/1.61 , T ), ! alpha41( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.61 c_Rings_Oinverse__class_Odivide( X, T, Z ), Y ) }.
% 0.97/1.61 { ! alpha41( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( X ), Z ), alpha46( X, Y, Z, T ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.97/1.61 , alpha41( X, Y, Z, T ) }.
% 0.97/1.61 { ! alpha46( X, Y, Z, T ), alpha41( X, Y, Z, T ) }.
% 0.97/1.61 { ! alpha46( X, Y, Z, T ), alpha50( X, Y, Z, T ) }.
% 0.97/1.61 { ! alpha46( X, Y, Z, T ), alpha16( X, Y, Z ) }.
% 0.97/1.61 { ! alpha50( X, Y, Z, T ), ! alpha16( X, Y, Z ), alpha46( X, Y, Z, T ) }.
% 0.97/1.61 { ! alpha50( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ) }.
% 0.97/1.61 { c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.61 alpha50( X, Y, Z, T ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ), alpha50( X, Y, Z, T )
% 0.97/1.61 }.
% 0.97/1.61 { ! alpha33( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.61 T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.61 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.97/1.61 alpha33( X, Y, Z, T ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha33( X, Y, Z, T ) }.
% 0.97/1.61 { ! alpha16( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.61 , alpha16( X, Y, Z ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.97/1.61 , alpha16( X, Y, Z ) }.
% 0.97/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.61 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.61 ( X, T, c_Rings_Oinverse__class_Odivide( X, Z, Y ) ),
% 0.97/1.61 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.97/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.61 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.61 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 0.97/1.61 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.97/1.61 Z, Y ) ) }.
% 0.97/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.61 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.61 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ),
% 0.97/1.61 c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.61 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.61 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.97/1.61 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.97/1.61 Y ), Z ) }.
% 0.97/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.61 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.61 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.97/1.61 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.97/1.61 Y ), Z ) }.
% 0.97/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.61 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.61 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 0.97/1.61 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.97/1.61 Z, Y ) ) }.
% 0.97/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.61 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.97/1.61 ( X, T, c_Rings_Oinverse__class_Odivide( X, Z, Y ) ),
% 0.97/1.61 c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.61 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.97/1.61 ( X, Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ),
% 0.97/1.61 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.97/1.61 Z, Y ) ) }.
% 0.97/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.61 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.97/1.61 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ),
% 0.97/1.61 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ) }.
% 0.97/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.61 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.97/1.61 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ),
% 0.97/1.61 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.97/1.61 Y ), Z ) }.
% 0.97/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.61 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.61 , c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.97/1.61 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.97/1.61 Y ), c_Rings_Oinverse__class_Odivide( X, T, Z ) ) }.
% 0.97/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.61 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, T,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless( X,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.97/1.61 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.97/1.61 Z ), c_Rings_Oinverse__class_Odivide( X, T, Y ) ) }.
% 0.97/1.61 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 0.97/1.61 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, T,
% 0.97/1.61 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 0.97/1.61 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.97/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Y ) }.
% 0.97/1.61 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.61 c_Groups_Oplus__class_Oplus( X, T, c_Rings_Oinverse__class_Odivide( X, Z
% 0.97/1.61 , Y ) ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus
% 0.97/1.61 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), Z ), Y ) }
% 0.97/1.61 .
% 0.97/1.61 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 0.97/1.61 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.61 c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ) =
% 0.97/1.61 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.97/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) }.
% 0.97/1.61 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.61 c_Groups_Oplus__class_Oplus( X, c_Rings_Oinverse__class_Odivide( X, T, Y
% 0.97/1.61 ), Z ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus
% 0.97/1.61 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) }
% 0.97/1.61 .
% 0.97/1.61 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.97/1.61 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.61 c_Rings_Oinverse__class_Odivide( X, U, Y ),
% 0.97/1.61 c_Rings_Oinverse__class_Odivide( X, T, Z ) ) =
% 0.97/1.61 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, hAPP
% 0.97/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.61 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.97/1.61 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ominus__class_Ominus( X,
% 0.97/1.61 c_Rings_Oinverse__class_Odivide( X, U, Y ),
% 0.97/1.61 c_Rings_Oinverse__class_Odivide( X, T, Z ) ) =
% 0.97/1.61 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus( X,
% 0.97/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.61 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.61 c_Groups_Ominus__class_Ominus( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.97/1.61 Y ), Z ) = c_Rings_Oinverse__class_Odivide( X,
% 0.97/1.61 c_Groups_Ominus__class_Ominus( X, T, hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) }.
% 0.97/1.61 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.61 c_Groups_Ominus__class_Ominus( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.97/1.61 Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X,
% 0.97/1.61 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ), Z ), Y ) }.
% 0.97/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.61 X, Z, Y ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.61 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.97/1.61 ), c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.97/1.61 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.97/1.61 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.61 X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.61 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.97/1.61 ), c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.97/1.61 c_Groups_Oone__class_Oone( X ) ) ) ) }.
% 0.97/1.61 { ! class_RealVector_Oreal__field( X ), c_Rings_Oinverse__class_Odivide( X
% 0.97/1.61 , c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), W ), U ), hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) =
% 0.97/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.61 ( X ), W ), c_Rings_Oinverse__class_Odivide( X,
% 0.97/1.61 c_Groups_Ominus__class_Ominus( X, U, Z ), Y ) ), hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.97/1.61 c_Groups_Ominus__class_Ominus( X, W, T ), Y ) ), Z ) ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.61 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.97/1.61 tc_Int_Oint, Y, X ) ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.61 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.97/1.61 tc_Int_Oint, Y, X ) ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.61 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ), X ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ),
% 0.97/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ) = X }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ),
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ),
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.97/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Divides_Odiv__class_Omod
% 0.97/1.61 ( tc_Int_Oint, Y, X ) ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.97/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ) = X }.
% 0.97/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.97/1.61 c_Groups_Oplus__class_Oplus( X, T, hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Z ) =
% 0.97/1.61 c_Divides_Odiv__class_Omod( X, T, Z ) }.
% 0.97/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.97/1.61 c_Groups_Oplus__class_Oplus( X, T, hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) =
% 0.97/1.61 c_Divides_Odiv__class_Omod( X, T, Y ) }.
% 0.97/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.97/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) =
% 0.97/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.97/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Z ) =
% 0.97/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.61 { ! c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y = hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), skol49( X, Y ) ) }.
% 0.97/1.61 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z )
% 0.97/1.61 , c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.97/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Divides_Odiv__class_Omod
% 0.97/1.61 ( tc_Int_Oint, Y, X ) ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.61 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ), X ) }.
% 0.97/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.97/1.61 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = c_Divides_Odiv__class_Omod
% 0.97/1.61 ( X, Z, Y ) }.
% 0.97/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.97/1.61 c_Groups_Oplus__class_Oplus( X, Z, Y ), Z ) = c_Divides_Odiv__class_Omod
% 0.97/1.61 ( X, Y, Z ) }.
% 0.97/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.97/1.61 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 0.97/1.61 ( X, c_Groups_Oplus__class_Oplus( X, T, c_Divides_Odiv__class_Omod( X, Z
% 0.97/1.61 , Y ) ), Y ) }.
% 0.97/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.97/1.61 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 0.97/1.61 ( X, c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Y
% 0.97/1.61 ), Z ), Y ) }.
% 0.97/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.97/1.61 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 0.97/1.61 ( X, c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Y
% 0.97/1.61 ), c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 0.97/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.97/1.61 c_Groups_Oplus__class_Oplus( X, T, c_Divides_Odiv__class_Omod( X, Z, Y )
% 0.97/1.61 ), Y ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X,
% 0.97/1.61 T, Z ), Y ) }.
% 0.97/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.97/1.61 c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Z ), Y
% 0.97/1.61 ), Z ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X,
% 0.97/1.61 T, Y ), Z ) }.
% 0.97/1.61 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, T,
% 0.97/1.61 Z ) = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod
% 0.97/1.61 ( X, W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 0.97/1.61 c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X, T, W ), Z
% 0.97/1.61 ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X, Y, U
% 0.97/1.61 ), Z ) }.
% 0.97/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y,
% 0.97/1.61 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y, Y
% 0.97/1.61 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.97/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.61 }.
% 0.97/1.61 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.61 tc_Int_Oint ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.97/1.61 { c_Divides_Odiv__class_Omod( tc_Int_Oint, X, X ) =
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.97/1.61 tc_Int_Oint, X, Y ) ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ), X ) }.
% 0.97/1.61 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.97/1.61 ( tc_Int_Oint, Y ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.97/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.97/1.61 { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y,
% 0.97/1.61 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), ! c_Divides_Odiv__class_Omod
% 0.97/1.61 ( tc_Int_Oint, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.97/1.61 { ! class_Divides_Oring__div( X ), ! c_Divides_Odiv__class_Omod( X, T, Z )
% 0.97/1.61 = c_Divides_Odiv__class_Omod( X, Y, Z ), c_Divides_Odiv__class_Omod( X,
% 0.97/1.61 c_Groups_Ouminus__class_Ouminus( X, T ), Z ) = c_Divides_Odiv__class_Omod
% 0.97/1.61 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ), Z ) }.
% 0.97/1.61 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.97/1.61 ( tc_Int_Oint, c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) =
% 0.97/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.97/1.61 ( tc_Int_Oint, Y ), X ) }.
% 0.97/1.61 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.97/1.61 ( tc_Int_Oint, Y ), c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.97/1.61 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Divides_Odiv__class_Omod
% 0.97/1.61 ( tc_Int_Oint, Y, X ) ) }.
% 0.97/1.61 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.97/1.61 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) = c_Divides_Odiv__class_Omod
% 0.97/1.61 ( X, c_Groups_Ouminus__class_Ouminus( X, c_Divides_Odiv__class_Omod( X, Z
% 0.97/1.61 , Y ) ), Y ) }.
% 0.97/1.61 { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y,
% 0.97/1.61 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.97/1.61 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Divides_Odiv__class_Omod
% 0.97/1.61 ( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) ) }
% 0.97/1.61 .
% 0.97/1.61 { ! class_Divides_Oring__div( X ), ! c_Divides_Odiv__class_Omod( X, T, Z )
% 0.97/1.61 = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod( X
% 0.97/1.61 , W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 0.97/1.61 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, T, W ),
% 0.97/1.61 Z ) = c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, Y
% 0.97/1.61 , U ), Z ) }.
% 0.97/1.61 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 0.97/1.61 tc_Int_Oint, c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y ), X ), Y ) =
% 0.97/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 0.97/1.61 tc_Int_Oint, Z, X ), Y ) }.
% 0.97/1.61 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 0.97/1.61 tc_Int_Oint, Z, c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) =
% 0.97/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 0.97/1.61 tc_Int_Oint, Z, Y ), X ) }.
% 0.97/1.61 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.97/1.61 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.97/1.61 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X,
% 0.97/1.61 c_Divides_Odiv__class_Omod( X, T, Y ), c_Divides_Odiv__class_Omod( X, Z,
% 0.97/1.61 Y ) ), Y ) }.
% 0.97/1.61 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.97/1.61 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.97/1.61 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X,
% 0.97/1.61 c_Divides_Odiv__class_Omod( X, T, Y ), Z ), Y ) }.
% 0.97/1.61 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.97/1.61 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.97/1.61 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, T,
% 0.97/1.61 c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 0.97/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.97/1.61 c_Divides_Odiv__class_Omod( X, Z, Y ), Y ) = c_Divides_Odiv__class_Omod(
% 0.97/1.61 X, Z, Y ) }.
% 0.97/1.61 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.97/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) =
% 0.97/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) }.
% 0.97/1.61 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) =
% 0.97/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.97/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) }.
% 0.97/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.97/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 0.97/1.61 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.61 ( X ), T ), c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 0.97/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.97/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 0.97/1.61 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.61 ( X ), c_Divides_Odiv__class_Omod( X, T, Y ) ), Z ), Y ) }.
% 0.97/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.97/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 0.97/1.61 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.61 ( X ), c_Divides_Odiv__class_Omod( X, T, Y ) ),
% 0.97/1.61 c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 0.97/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.97/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) = hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), T ), c_Divides_Odiv__class_Omod( X, Z
% 0.97/1.61 , Y ) ) }.
% 0.97/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.97/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Omod( X, T, Y )
% 0.97/1.61 ), Z ) }.
% 0.97/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.97/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Omod( X
% 0.97/1.61 , T, Z ) ), Y ), Z ) = c_Divides_Odiv__class_Omod( X, hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.97/1.61 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, T,
% 0.97/1.61 Z ) = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod
% 0.97/1.61 ( X, W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 0.97/1.61 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.61 ( X ), T ), W ), Z ) = c_Divides_Odiv__class_Omod( X, hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), U ), Z ) }.
% 0.97/1.61 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.97/1.61 tc_Int_Oint, Z, Y ) ), X ), Y ) = c_Divides_Odiv__class_Omod( tc_Int_Oint
% 0.97/1.61 , hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ), Y )
% 0.97/1.61 }.
% 0.97/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.61 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ), alpha17( X, Y, Z ), alpha34
% 0.97/1.61 ( X, Y, Z ) }.
% 0.97/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha17( X, Y, Z
% 0.97/1.61 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.97/1.61 ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.97/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha34( X, Y, Z
% 0.97/1.61 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.97/1.61 ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.97/1.61 { ! alpha34( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.61 { ! alpha34( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.97/1.61 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( X ) ), alpha34( X, Y, Z ) }.
% 0.97/1.61 { ! alpha17( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.97/1.61 { ! alpha17( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.61 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( X ), Y ), alpha17( X, Y, Z ) }.
% 0.97/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.97/1.61 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ), alpha18( X, Y, Z ), alpha35
% 0.97/1.61 ( X, Y, Z ) }.
% 0.97/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha18( X, Y, Z
% 0.97/1.61 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 0.97/1.61 ( X, Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha35( X, Y, Z
% 0.97/1.61 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 0.97/1.61 ( X, Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.61 { ! alpha35( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.61 { ! alpha35( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.97/1.61 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.97/1.61 ( X ), Y ), alpha35( X, Y, Z ) }.
% 0.97/1.61 { ! alpha18( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.97/1.61 { ! alpha18( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.61 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( X ) ), alpha18( X, Y, Z ) }.
% 0.97/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.97/1.61 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 0.97/1.61 ( X, Z, T ), c_Rings_Oinverse__class_Odivide( X, Y, T ) ) }.
% 0.97/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.61 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 0.97/1.61 ( X, Y, T ), c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 0.97/1.61 { ! class_Lattices_Oboolean__algebra( X ), class_Lattices_Oboolean__algebra
% 0.97/1.61 ( tc_fun( Y, X ) ) }.
% 0.97/1.61 { ! class_Orderings_Opreorder( X ), class_Orderings_Opreorder( tc_fun( Y, X
% 0.97/1.61 ) ) }.
% 0.97/1.61 { ! class_Orderings_Oorder( X ), class_Orderings_Oorder( tc_fun( Y, X ) ) }
% 0.97/1.61 .
% 0.97/1.61 { ! class_Orderings_Oord( X ), class_Orderings_Oord( tc_fun( Y, X ) ) }.
% 0.97/1.61 { ! class_Groups_Ouminus( X ), class_Groups_Ouminus( tc_fun( Y, X ) ) }.
% 0.97/1.61 { ! class_Groups_Ominus( X ), class_Groups_Ominus( tc_fun( Y, X ) ) }.
% 0.97/1.61 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.97/1.61 tc_Int_Oint ) }.
% 0.97/1.61 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.97/1.61 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Int_Oint ) }.
% 0.97/1.61 { class_Rings_Olinordered__comm__semiring__strict( tc_Int_Oint ) }.
% 0.97/1.61 { class_Rings_Olinordered__semiring__1__strict( tc_Int_Oint ) }.
% 0.97/1.61 { class_Rings_Olinordered__semiring__strict( tc_Int_Oint ) }.
% 0.97/1.61 { class_Groups_Oordered__ab__semigroup__add( tc_Int_Oint ) }.
% 0.97/1.61 { class_Groups_Oordered__comm__monoid__add( tc_Int_Oint ) }.
% 0.97/1.61 { class_Groups_Olinordered__ab__group__add( tc_Int_Oint ) }.
% 0.97/1.61 { class_Groups_Ocancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.97/1.61 { class_Rings_Oring__1__no__zero__divisors( tc_Int_Oint ) }.
% 0.97/1.61 { class_Rings_Oordered__cancel__semiring( tc_Int_Oint ) }.
% 0.97/1.61 { class_Rings_Olinordered__ring__strict( tc_Int_Oint ) }.
% 0.97/1.61 { class_Rings_Oring__no__zero__divisors( tc_Int_Oint ) }.
% 0.97/1.61 { class_Rings_Oordered__comm__semiring( tc_Int_Oint ) }.
% 0.97/1.61 { class_Rings_Olinordered__semiring__1( tc_Int_Oint ) }.
% 0.97/1.61 { class_Groups_Oordered__ab__group__add( tc_Int_Oint ) }.
% 0.97/1.61 { class_Groups_Ocancel__semigroup__add( tc_Int_Oint ) }.
% 0.97/1.61 { class_Rings_Olinordered__semiring( tc_Int_Oint ) }.
% 0.97/1.61 { class_Rings_Olinordered__semidom( tc_Int_Oint ) }.
% 0.97/1.61 { class_Groups_Oab__semigroup__mult( tc_Int_Oint ) }.
% 0.97/1.61 { class_Groups_Ocomm__monoid__mult( tc_Int_Oint ) }.
% 0.97/1.61 { class_Groups_Oab__semigroup__add( tc_Int_Oint ) }.
% 0.97/1.61 { class_Rings_Oordered__semiring( tc_Int_Oint ) }.
% 0.97/1.61 { class_Rings_Ono__zero__divisors( tc_Int_Oint ) }.
% 0.97/1.61 { class_Groups_Ocomm__monoid__add( tc_Int_Oint ) }.
% 0.97/1.61 { class_Rings_Olinordered__ring( tc_Int_Oint ) }.
% 0.97/1.61 { class_Rings_Olinordered__idom( tc_Int_Oint ) }.
% 0.97/1.61 { class_Rings_Ocomm__semiring__1( tc_Int_Oint ) }.
% 0.97/1.61 { class_Divides_Osemiring__div( tc_Int_Oint ) }.
% 0.97/1.61 { class_Rings_Ocomm__semiring( tc_Int_Oint ) }.
% 0.97/1.61 { class_Groups_Oab__group__add( tc_Int_Oint ) }.
% 0.97/1.61 { class_Rings_Ozero__neq__one( tc_Int_Oint ) }.
% 0.97/1.61 { class_Rings_Oordered__ring( tc_Int_Oint ) }.
% 0.97/1.61 { class_Orderings_Opreorder( tc_Int_Oint ) }.
% 0.97/1.61 { class_Orderings_Olinorder( tc_Int_Oint ) }.
% 0.97/1.61 { class_Groups_Omonoid__mult( tc_Int_Oint ) }.
% 0.97/1.61 { class_Rings_Ocomm__ring__1( tc_Int_Oint ) }.
% 0.97/1.61 { class_Groups_Omonoid__add( tc_Int_Oint ) }.
% 0.97/1.61 { class_Rings_Osemiring__0( tc_Int_Oint ) }.
% 0.97/1.61 { class_Groups_Ogroup__add( tc_Int_Oint ) }.
% 0.97/1.61 { class_Divides_Oring__div( tc_Int_Oint ) }.
% 0.97/1.61 { class_Rings_Omult__zero( tc_Int_Oint ) }.
% 0.97/1.61 { class_Orderings_Oorder( tc_Int_Oint ) }.
% 0.97/1.61 { class_Rings_Osemiring( tc_Int_Oint ) }.
% 0.97/1.61 { class_Orderings_Oord( tc_Int_Oint ) }.
% 0.97/1.61 { class_Groups_Ouminus( tc_Int_Oint ) }.
% 0.97/1.61 { class_Groups_Osgn__if( tc_Int_Oint ) }.
% 0.97/1.61 { class_Rings_Oring__1( tc_Int_Oint ) }.
% 0.97/1.61 { class_Groups_Ominus( tc_Int_Oint ) }.
% 0.97/1.61 { class_Power_Opower( tc_Int_Oint ) }.
% 0.97/1.61 { class_Groups_Ozero( tc_Int_Oint ) }.
% 0.97/1.61 { class_Rings_Oring( tc_Int_Oint ) }.
% 0.97/1.61 { class_Rings_Oidom( tc_Int_Oint ) }.
% 0.97/1.61 { class_Groups_Oone( tc_Int_Oint ) }.
% 0.97/1.61 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.97/1.61 tc_Nat_Onat ) }.
% 0.97/1.61 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.97/1.61 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Nat_Onat ) }.
% 0.97/1.61 { class_Rings_Olinordered__comm__semiring__strict( tc_Nat_Onat ) }.
% 0.97/1.61 { class_Rings_Olinordered__semiring__strict( tc_Nat_Onat ) }.
% 0.97/1.61 { class_Groups_Oordered__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.97/1.61 { class_Groups_Oordered__comm__monoid__add( tc_Nat_Onat ) }.
% 0.97/1.61 { class_Groups_Ocancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.97/1.61 { class_Rings_Oordered__cancel__semiring( tc_Nat_Onat ) }.
% 0.97/1.61 { class_Rings_Oordered__comm__semiring( tc_Nat_Onat ) }.
% 0.97/1.61 { class_Groups_Ocancel__semigroup__add( tc_Nat_Onat ) }.
% 0.97/1.61 { class_Rings_Olinordered__semiring( tc_Nat_Onat ) }.
% 0.97/1.61 { class_Rings_Olinordered__semidom( tc_Nat_Onat ) }.
% 0.97/1.61 { class_Groups_Oab__semigroup__mult( tc_Nat_Onat ) }.
% 0.97/1.61 { class_Groups_Ocomm__monoid__mult( tc_Nat_Onat ) }.
% 0.97/1.61 { class_Groups_Oab__semigroup__add( tc_Nat_Onat ) }.
% 0.97/1.61 { class_Rings_Oordered__semiring( tc_Nat_Onat ) }.
% 0.97/1.61 { class_Rings_Ono__zero__divisors( tc_Nat_Onat ) }.
% 0.97/1.61 { class_Groups_Ocomm__monoid__add( tc_Nat_Onat ) }.
% 0.97/1.61 { class_Rings_Ocomm__semiring__1( tc_Nat_Onat ) }.
% 0.97/1.61 { class_Divides_Osemiring__div( tc_Nat_Onat ) }.
% 0.97/1.61 { class_Rings_Ocomm__semiring( tc_Nat_Onat ) }.
% 0.97/1.61 { class_Rings_Ozero__neq__one( tc_Nat_Onat ) }.
% 0.97/1.61 { class_Orderings_Opreorder( tc_Nat_Onat ) }.
% 0.97/1.61 { class_Orderings_Olinorder( tc_Nat_Onat ) }.
% 0.97/1.61 { class_Groups_Omonoid__mult( tc_Nat_Onat ) }.
% 0.97/1.61 { class_Groups_Omonoid__add( tc_Nat_Onat ) }.
% 0.97/1.61 { class_Rings_Osemiring__0( tc_Nat_Onat ) }.
% 0.97/1.61 { class_Rings_Omult__zero( tc_Nat_Onat ) }.
% 0.97/1.61 { class_Orderings_Oorder( tc_Nat_Onat ) }.
% 0.97/1.61 { class_Rings_Osemiring( tc_Nat_Onat ) }.
% 0.97/1.61 { class_Orderings_Oord( tc_Nat_Onat ) }.
% 0.97/1.61 { class_Groups_Ominus( tc_Nat_Onat ) }.
% 0.97/1.61 { class_Power_Opower( tc_Nat_Onat ) }.
% 0.97/1.61 { class_Groups_Ozero( tc_Nat_Onat ) }.
% 0.97/1.61 { class_Groups_Oone( tc_Nat_Onat ) }.
% 0.97/1.61 { class_Lattices_Oboolean__algebra( tc_HOL_Obool ) }.
% 0.97/1.61 { class_Orderings_Opreorder( tc_HOL_Obool ) }.
% 0.97/1.61 { class_Orderings_Oorder( tc_HOL_Obool ) }.
% 0.97/1.61 { class_Orderings_Oord( tc_HOL_Obool ) }.
% 0.97/1.61 { class_Groups_Ouminus( tc_HOL_Obool ) }.
% 0.97/1.61 { class_Groups_Ominus( tc_HOL_Obool ) }.
% 0.97/1.61 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.97/1.61 tc_RealDef_Oreal ) }.
% 0.97/1.61 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.97/1.61 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_RealDef_Oreal ) }
% 0.97/1.61 .
% 0.97/1.61 { class_Rings_Olinordered__comm__semiring__strict( tc_RealDef_Oreal ) }.
% 0.97/1.61 { class_Fields_Olinordered__field__inverse__zero( tc_RealDef_Oreal ) }.
% 0.97/1.61 { class_Rings_Olinordered__semiring__1__strict( tc_RealDef_Oreal ) }.
% 0.97/1.61 { class_RealVector_Oreal__normed__div__algebra( tc_RealDef_Oreal ) }.
% 0.97/1.61 { class_Rings_Olinordered__semiring__strict( tc_RealDef_Oreal ) }.
% 0.97/1.61 { class_RealVector_Oreal__normed__algebra__1( tc_RealDef_Oreal ) }.
% 0.97/1.61 { class_Groups_Oordered__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.97/1.61 { class_RealVector_Oreal__normed__algebra( tc_RealDef_Oreal ) }.
% 0.97/1.61 { class_Groups_Oordered__comm__monoid__add( tc_RealDef_Oreal ) }.
% 0.97/1.61 { class_Groups_Olinordered__ab__group__add( tc_RealDef_Oreal ) }.
% 0.97/1.61 { class_Groups_Ocancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.97/1.61 { class_Rings_Oring__1__no__zero__divisors( tc_RealDef_Oreal ) }.
% 0.97/1.61 { class_Rings_Oordered__cancel__semiring( tc_RealDef_Oreal ) }.
% 0.97/1.61 { class_RealVector_Oreal__normed__vector( tc_RealDef_Oreal ) }.
% 0.97/1.61 { class_Rings_Olinordered__ring__strict( tc_RealDef_Oreal ) }.
% 0.97/1.61 { class_Rings_Oring__no__zero__divisors( tc_RealDef_Oreal ) }.
% 0.97/1.61 { class_Rings_Oordered__comm__semiring( tc_RealDef_Oreal ) }.
% 0.97/1.61 { class_Rings_Olinordered__semiring__1( tc_RealDef_Oreal ) }.
% 0.97/1.61 { class_Groups_Oordered__ab__group__add( tc_RealDef_Oreal ) }.
% 0.97/1.61 { class_Groups_Ocancel__semigroup__add( tc_RealDef_Oreal ) }.
% 0.97/1.61 { class_Rings_Olinordered__semiring( tc_RealDef_Oreal ) }.
% 0.97/1.61 { class_Fields_Ofield__inverse__zero( tc_RealDef_Oreal ) }.
% 0.97/1.61 { class_Rings_Olinordered__semidom( tc_RealDef_Oreal ) }.
% 0.97/1.61 { class_Groups_Oab__semigroup__mult( tc_RealDef_Oreal ) }.
% 0.97/1.61 { class_Groups_Ocomm__monoid__mult( tc_RealDef_Oreal ) }.
% 0.97/1.61 { class_Groups_Oab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.97/1.61 { class_Fields_Olinordered__field( tc_RealDef_Oreal ) }.
% 0.97/1.61 { class_Rings_Oordered__semiring( tc_RealDef_Oreal ) }.
% 0.97/1.61 { class_Rings_Ono__zero__divisors( tc_RealDef_Oreal ) }.
% 0.97/1.61 { class_Groups_Ocomm__monoid__add( tc_RealDef_Oreal ) }.
% 0.97/1.61 { class_Rings_Olinordered__ring( tc_RealDef_Oreal ) }.
% 0.97/1.61 { class_Rings_Olinordered__idom( tc_RealDef_Oreal ) }.
% 0.97/1.61 { class_Rings_Ocomm__semiring__1( tc_RealDef_Oreal ) }.
% 0.97/1.61 { class_RealVector_Oreal__field( tc_RealDef_Oreal ) }.
% 0.97/1.61 { class_Rings_Ocomm__semiring( tc_RealDef_Oreal ) }.
% 0.97/1.61 { class_Groups_Oab__group__add( tc_RealDef_Oreal ) }.
% 0.97/1.61 { class_Rings_Ozero__neq__one( tc_RealDef_Oreal ) }.
% 0.97/1.61 { class_Rings_Oordered__ring( tc_RealDef_Oreal ) }.
% 0.97/1.61 { class_Orderings_Opreorder( tc_RealDef_Oreal ) }.
% 0.97/1.61 { class_Orderings_Olinorder( tc_RealDef_Oreal ) }.
% 0.97/1.61 { class_Groups_Omonoid__mult( tc_RealDef_Oreal ) }.
% 0.97/1.61 { class_Rings_Ocomm__ring__1( tc_RealDef_Oreal ) }.
% 0.97/1.61 { class_Groups_Omonoid__add( tc_RealDef_Oreal ) }.
% 0.97/1.61 { class_Rings_Osemiring__0( tc_RealDef_Oreal ) }.
% 0.97/1.61 { class_Groups_Ogroup__add( tc_RealDef_Oreal ) }.
% 0.97/1.61 { class_Rings_Omult__zero( tc_RealDef_Oreal ) }.
% 0.97/1.61 { class_Orderings_Oorder( tc_RealDef_Oreal ) }.
% 0.97/1.61 { class_Rings_Osemiring( tc_RealDef_Oreal ) }.
% 0.97/1.61 { class_Orderings_Oord( tc_RealDef_Oreal ) }.
% 0.97/1.61 { class_Groups_Ouminus( tc_RealDef_Oreal ) }.
% 0.97/1.61 { class_Groups_Osgn__if( tc_RealDef_Oreal ) }.
% 0.97/1.61 { class_Rings_Oring__1( tc_RealDef_Oreal ) }.
% 0.97/1.61 { class_Groups_Ominus( tc_RealDef_Oreal ) }.
% 0.97/1.61 { class_Fields_Ofield( tc_RealDef_Oreal ) }.
% 0.97/1.61 { class_Power_Opower( tc_RealDef_Oreal ) }.
% 0.97/1.61 { class_Groups_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.61 { class_Rings_Oring( tc_RealDef_Oreal ) }.
% 0.97/1.61 { class_Rings_Oidom( tc_RealDef_Oreal ) }.
% 0.97/1.61 { class_Groups_Oone( tc_RealDef_Oreal ) }.
% 0.97/1.61 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.97/1.61 tc_Complex_Ocomplex ) }.
% 0.97/1.61 { class_RealVector_Oreal__normed__div__algebra( tc_Complex_Ocomplex ) }.
% 0.97/1.61 { class_RealVector_Oreal__normed__algebra__1( tc_Complex_Ocomplex ) }.
% 0.97/1.61 { class_RealVector_Oreal__normed__algebra( tc_Complex_Ocomplex ) }.
% 0.97/1.61 { class_Groups_Ocancel__ab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.97/1.61 { class_Rings_Oring__1__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.97/1.61 { class_RealVector_Oreal__normed__vector( tc_Complex_Ocomplex ) }.
% 0.97/1.61 { class_Rings_Oring__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.97/1.61 { class_Groups_Ocancel__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.97/1.61 { class_Fields_Ofield__inverse__zero( tc_Complex_Ocomplex ) }.
% 0.97/1.61 { class_Groups_Oab__semigroup__mult( tc_Complex_Ocomplex ) }.
% 0.97/1.61 { class_Groups_Ocomm__monoid__mult( tc_Complex_Ocomplex ) }.
% 0.97/1.61 { class_Groups_Oab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.97/1.61 { class_Rings_Ono__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.97/1.61 { class_Groups_Ocomm__monoid__add( tc_Complex_Ocomplex ) }.
% 0.97/1.61 { class_Rings_Ocomm__semiring__1( tc_Complex_Ocomplex ) }.
% 0.97/1.61 { class_RealVector_Oreal__field( tc_Complex_Ocomplex ) }.
% 0.97/1.61 { class_Rings_Ocomm__semiring( tc_Complex_Ocomplex ) }.
% 0.97/1.61 { class_Groups_Oab__group__add( tc_Complex_Ocomplex ) }.
% 0.97/1.61 { class_Rings_Ozero__neq__one( tc_Complex_Ocomplex ) }.
% 0.97/1.61 { class_Groups_Omonoid__mult( tc_Complex_Ocomplex ) }.
% 0.97/1.61 { class_Rings_Ocomm__ring__1( tc_Complex_Ocomplex ) }.
% 0.97/1.61 { class_Groups_Omonoid__add( tc_Complex_Ocomplex ) }.
% 0.97/1.61 { class_Rings_Osemiring__0( tc_Complex_Ocomplex ) }.
% 0.97/1.61 { class_Groups_Ogroup__add( tc_Complex_Ocomplex ) }.
% 0.97/1.61 { class_Rings_Omult__zero( tc_Complex_Ocomplex ) }.
% 0.97/1.61 { class_Rings_Osemiring( tc_Complex_Ocomplex ) }.
% 0.97/1.61 { class_Groups_Ouminus( tc_Complex_Ocomplex ) }.
% 0.97/1.61 { class_Rings_Oring__1( tc_Complex_Ocomplex ) }.
% 0.97/1.61 { class_Groups_Ominus( tc_Complex_Ocomplex ) }.
% 0.97/1.61 { class_Fields_Ofield( tc_Complex_Ocomplex ) }.
% 0.97/1.61 { class_Power_Opower( tc_Complex_Ocomplex ) }.
% 0.97/1.61 { class_Groups_Ozero( tc_Complex_Ocomplex ) }.
% 0.97/1.61 { class_Rings_Oring( tc_Complex_Ocomplex ) }.
% 0.97/1.61 { class_Rings_Oidom( tc_Complex_Ocomplex ) }.
% 0.97/1.61 { class_Groups_Oone( tc_Complex_Ocomplex ) }.
% 0.97/1.61 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), v_d1 ) }.
% 0.97/1.61 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), v_d2 ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, v_d1 ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, v_d2 ) }.
% 0.97/1.61
% 0.97/1.61 *** allocated 15000 integers for clauses
% 0.97/1.61 *** allocated 22500 integers for clauses
% 0.97/1.61 *** allocated 33750 integers for clauses
% 0.97/1.61 *** allocated 50625 integers for clauses
% 0.97/1.61 *** allocated 75937 integers for clauses
% 0.97/1.61 percentage equality = 0.240845, percentage horn = 0.911352
% 0.97/1.61 This is a problem with some equality
% 0.97/1.61
% 0.97/1.61
% 0.97/1.61
% 0.97/1.61 Options Used:
% 0.97/1.61
% 0.97/1.61 useres = 1
% 0.97/1.61 useparamod = 1
% 0.97/1.61 useeqrefl = 1
% 0.97/1.61 useeqfact = 1
% 0.97/1.61 usefactor = 1
% 0.97/1.61 usesimpsplitting = 0
% 0.97/1.61 usesimpdemod = 5
% 0.97/1.61 usesimpres = 3
% 0.97/1.61
% 0.97/1.61 resimpinuse = 1000
% 0.97/1.61 resimpclauses = 20000
% 0.97/1.61 substype = eqrewr
% 0.97/1.61 backwardsubs = 1
% 0.97/1.61 selectoldest = 5
% 0.97/1.61
% 0.97/1.61 litorderings [0] = split
% 0.97/1.61 litorderings [1] = extend the termordering, first sorting on arguments
% 0.97/1.61
% 0.97/1.61 termordering = kbo
% 0.97/1.61
% 0.97/1.61 litapriori = 0
% 0.97/1.61 termapriori = 1
% 0.97/1.61 litaposteriori = 0
% 0.97/1.61 termaposteriori = 0
% 0.97/1.61 demodaposteriori = 0
% 0.97/1.61 ordereqreflfact = 0
% 0.97/1.61
% 0.97/1.61 litselect = negord
% 0.97/1.61
% 0.97/1.61 maxweight = 15
% 0.97/1.61 maxdepth = 30000
% 0.97/1.61 maxlength = 115
% 0.97/1.61 maxnrvars = 195
% 0.97/1.61 excuselevel = 1
% 0.97/1.61 increasemaxweight = 1
% 0.97/1.61
% 0.97/1.61 maxselected = 10000000
% 0.97/1.61 maxnrclauses = 10000000
% 0.97/1.61
% 0.97/1.61 showgenerated = 0
% 0.97/1.61 showkept = 0
% 0.97/1.61 showselected = 0
% 0.97/1.61 showdeleted = 0
% 0.97/1.61 showresimp = 1
% 0.97/1.61 showstatus = 2000
% 0.97/1.61
% 0.97/1.61 prologoutput = 0
% 0.97/1.61 nrgoals = 5000000
% 0.97/1.61 totalproof = 1
% 0.97/1.61
% 0.97/1.61 Symbols occurring in the translation:
% 0.97/1.61
% 0.97/1.61 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.97/1.61 . [1, 2] (w:1, o:194, a:1, s:1, b:0),
% 0.97/1.61 ! [4, 1] (w:0, o:107, a:1, s:1, b:0),
% 0.97/1.61 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.97/1.61 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.97/1.61 hAPP [38, 2] (w:1, o:218, a:1, s:1, b:0),
% 0.97/1.61 class_Orderings_Opreorder [41, 1] (w:1, o:114, a:1, s:1, b:0),
% 0.97/1.61 c_Orderings_Oord__class_Oless [42, 3] (w:1, o:273, a:1, s:1, b:0),
% 0.97/1.61 class_Orderings_Olinorder [45, 1] (w:1, o:115, a:1, s:1, b:0),
% 0.97/1.61 class_Rings_Olinordered__idom [47, 1] (w:1, o:116, a:1, s:1, b:0),
% 0.97/1.61 class_Orderings_Oorder [48, 1] (w:1, o:112, a:1, s:1, b:0),
% 0.97/1.61 class_Orderings_Oord [53, 1] (w:1, o:113, a:1, s:1, b:0),
% 0.97/1.61 class_Groups_Ozero [54, 1] (w:1, o:121, a:1, s:1, b:0),
% 0.97/1.61 c_Groups_Ozero__class_Ozero [55, 1] (w:1, o:122, a:1, s:1, b:0),
% 0.97/1.61 c_Groups_Osgn__class_Osgn [57, 2] (w:1, o:219, a:1, s:1, b:0),
% 0.97/1.61 c_Orderings_Oorder__class_Ostrict__mono [59, 3] (w:1, o:274, a:1, s:1
% 0.97/1.61 , b:0),
% 0.97/1.61 class_Rings_Olinordered__semidom [60, 1] (w:1, o:125, a:1, s:1, b:0)
% 0.97/1.61 ,
% 0.97/1.61 c_Groups_Oone__class_Oone [61, 1] (w:1, o:126, a:1, s:1, b:0),
% 0.97/1.61 class_Rings_Olinordered__ring__strict [62, 1] (w:1, o:123, a:1, s:1
% 0.97/1.61 , b:0),
% 0.97/1.61 c_Groups_Otimes__class_Otimes [63, 1] (w:1, o:127, a:1, s:1, b:0),
% 0.97/1.61 class_Rings_Olinordered__comm__semiring__strict [64, 1] (w:1, o:128
% 0.97/1.61 , a:1, s:1, b:0),
% 0.97/1.61 class_Rings_Olinordered__semiring__strict [65, 1] (w:1, o:129, a:1
% 0.97/1.61 , s:1, b:0),
% 0.97/1.61 class_Groups_Oab__semigroup__mult [66, 1] (w:1, o:130, a:1, s:1, b:0)
% 0.97/1.61 ,
% 0.97/1.61 class_Groups_Ocomm__monoid__mult [67, 1] (w:1, o:131, a:1, s:1, b:0)
% 0.97/1.61 ,
% 0.97/1.61 class_Groups_Omonoid__mult [68, 1] (w:1, o:133, a:1, s:1, b:0),
% 0.97/1.61 class_Groups_Oone [69, 1] (w:1, o:134, a:1, s:1, b:0),
% 0.97/1.61 class_Groups_Osgn__if [72, 1] (w:1, o:135, a:1, s:1, b:0),
% 0.97/1.61 class_Rings_Omult__zero [73, 1] (w:1, o:139, a:1, s:1, b:0),
% 0.97/1.61 class_Rings_Oring__no__zero__divisors [75, 1] (w:1, o:140, a:1, s:1
% 0.97/1.61 , b:0),
% 0.97/1.61 class_Rings_Ono__zero__divisors [76, 1] (w:1, o:141, a:1, s:1, b:0),
% 0.97/1.61
% 0.97/1.61 class_Rings_Ozero__neq__one [77, 1] (w:1, o:142, a:1, s:1, b:0),
% 0.97/1.61 class_Rings_Olinordered__ring [78, 1] (w:1, o:124, a:1, s:1, b:0),
% 0.97/1.61 class_RealVector_Oreal__normed__algebra__1 [80, 1] (w:1, o:143, a:1
% 0.97/1.61 , s:1, b:0),
% 0.97/1.61 class_RealVector_Oreal__normed__div__algebra [81, 1] (w:1, o:144, a:1
% 0.97/1.61 , s:1, b:0),
% 0.97/1.61 class_RealVector_Oreal__normed__vector [82, 1] (w:1, o:145, a:1, s:1
% 0.97/1.61 , b:0),
% 0.97/1.61 tc_RealDef_Oreal [83, 0] (w:1, o:48, a:1, s:1, b:0),
% 0.97/1.61 class_Rings_Ocomm__semiring__1 [85, 1] (w:1, o:147, a:1, s:1, b:0),
% 0.97/1.61 class_RealVector_Oreal__normed__algebra [94, 1] (w:1, o:148, a:1, s:1
% 0.97/1.61 , b:0),
% 0.97/1.61 c_Groups_Ouminus__class_Ouminus [95, 2] (w:1, o:220, a:1, s:1, b:0),
% 0.97/1.61
% 0.97/1.61 c_RealVector_Onorm__class_Onorm [96, 2] (w:1, o:221, a:1, s:1, b:0),
% 0.97/1.61
% 0.97/1.61 class_Lattices_Oab__semigroup__idem__mult [97, 1] (w:1, o:149, a:1
% 0.97/1.61 , s:1, b:0),
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq [98, 3] (w:1, o:275, a:1, s:1, b:0)
% 0.97/1.61 ,
% 0.97/1.61 class_Groups_Oordered__ab__group__add [103, 1] (w:1, o:150, a:1, s:1
% 0.97/1.61 , b:0),
% 0.97/1.61 class_Groups_Olinordered__ab__group__add [104, 1] (w:1, o:132, a:1
% 0.97/1.61 , s:1, b:0),
% 0.97/1.61 tc_fun [105, 2] (w:1, o:254, a:1, s:1, b:0),
% 0.97/1.61 class_Lattices_Oboolean__algebra [106, 1] (w:1, o:151, a:1, s:1, b:0)
% 0.97/1.61 ,
% 0.97/1.61 class_Groups_Ouminus [108, 1] (w:1, o:152, a:1, s:1, b:0),
% 0.97/1.61 class_Groups_Ogroup__add [109, 1] (w:1, o:153, a:1, s:1, b:0),
% 0.97/1.61 class_Rings_Oring [110, 1] (w:1, o:154, a:1, s:1, b:0),
% 0.97/1.61 class_Rings_Oidom [111, 1] (w:1, o:155, a:1, s:1, b:0),
% 0.97/1.61 class_Rings_Oring__1__no__zero__divisors [113, 1] (w:1, o:156, a:1
% 0.97/1.61 , s:1, b:0),
% 0.97/1.61 class_Rings_Ocomm__ring__1 [114, 1] (w:1, o:146, a:1, s:1, b:0),
% 0.97/1.61 class_Rings_Oordered__cancel__semiring [115, 1] (w:1, o:157, a:1, s:1
% 0.97/1.61 , b:0),
% 0.97/1.61 class_Rings_Oordered__ring [116, 1] (w:1, o:158, a:1, s:1, b:0),
% 0.97/1.61 class_Rings_Oordered__semiring [118, 1] (w:1, o:159, a:1, s:1, b:0),
% 0.97/1.61
% 0.97/1.61 class_Rings_Oordered__comm__semiring [119, 1] (w:1, o:160, a:1, s:1
% 0.97/1.61 , b:0),
% 0.97/1.61 class_Rings_Olinordered__semiring [122, 1] (w:1, o:136, a:1, s:1, b:0
% 0.97/1.61 ),
% 0.97/1.61 tc_Complex_Ocomplex [126, 0] (w:1, o:78, a:1, s:1, b:0),
% 0.97/1.61 class_Rings_Olinordered__semiring__1__strict [128, 1] (w:1, o:137, a:
% 0.97/1.61 1, s:1, b:0),
% 0.97/1.61 c_Groups_Oplus__class_Oplus [129, 3] (w:1, o:276, a:1, s:1, b:0),
% 0.97/1.61 class_Fields_Olinordered__field__inverse__zero [130, 1] (w:1, o:117
% 0.97/1.61 , a:1, s:1, b:0),
% 0.97/1.61 c_RealDef_Opositive [132, 1] (w:1, o:161, a:1, s:1, b:0),
% 0.97/1.61 class_Rings_Olinordered__semiring__1 [133, 1] (w:1, o:138, a:1, s:1
% 0.97/1.61 , b:0),
% 0.97/1.61 c_SEQ_OBseq [135, 2] (w:1, o:256, a:1, s:1, b:0),
% 0.97/1.61 class_Groups_Oab__semigroup__add [137, 1] (w:1, o:162, a:1, s:1, b:0)
% 0.97/1.61 ,
% 0.97/1.61 class_Groups_Ocancel__semigroup__add [138, 1] (w:1, o:163, a:1, s:1
% 0.97/1.61 , b:0),
% 0.97/1.61 class_Groups_Ocancel__ab__semigroup__add [139, 1] (w:1, o:164, a:1
% 0.97/1.61 , s:1, b:0),
% 0.97/1.61 class_Groups_Omonoid__add [140, 1] (w:1, o:165, a:1, s:1, b:0),
% 0.97/1.61 class_Groups_Ocomm__monoid__add [141, 1] (w:1, o:166, a:1, s:1, b:0)
% 0.97/1.61 ,
% 0.97/1.61 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct [
% 0.97/1.61 142, 1] (w:1, o:172, a:1, s:1, b:0),
% 0.97/1.61 class_Groups_Oordered__ab__semigroup__add__imp__le [143, 1] (w:1, o:
% 0.97/1.61 173, a:1, s:1, b:0),
% 0.97/1.61 class_Groups_Oordered__ab__semigroup__add [144, 1] (w:1, o:174, a:1
% 0.97/1.61 , s:1, b:0),
% 0.97/1.61 class_Groups_Oordered__cancel__ab__semigroup__add [145, 1] (w:1, o:
% 0.97/1.61 175, a:1, s:1, b:0),
% 0.97/1.61 class_Rings_Ocomm__semiring [146, 1] (w:1, o:167, a:1, s:1, b:0),
% 0.97/1.61 class_Rings_Osemiring [148, 1] (w:1, o:169, a:1, s:1, b:0),
% 0.97/1.61 class_Groups_Oab__group__add [154, 1] (w:1, o:176, a:1, s:1, b:0),
% 0.97/1.61 class_Groups_Oordered__comm__monoid__add [155, 1] (w:1, o:177, a:1
% 0.97/1.61 , s:1, b:0),
% 0.97/1.61 class_Fields_Olinordered__field [159, 1] (w:1, o:118, a:1, s:1, b:0)
% 0.97/1.61 ,
% 0.97/1.61 tc_Nat_Onat [162, 0] (w:1, o:92, a:1, s:1, b:0),
% 0.97/1.61 c_SEQ_Odecseq [165, 2] (w:1, o:257, a:1, s:1, b:0),
% 0.97/1.61 c_SEQ_Oincseq [167, 2] (w:1, o:258, a:1, s:1, b:0),
% 0.97/1.61 c_Groups_Ominus__class_Ominus [168, 3] (w:1, o:277, a:1, s:1, b:0),
% 0.97/1.61 class_Groups_Ominus [175, 1] (w:1, o:178, a:1, s:1, b:0),
% 0.97/1.61 hBOOL [177, 1] (w:1, o:179, a:1, s:1, b:0),
% 0.97/1.61 class_Rings_Oring__1 [180, 1] (w:1, o:168, a:1, s:1, b:0),
% 0.97/1.61 c_RComplete_Onatceiling [185, 1] (w:1, o:180, a:1, s:1, b:0),
% 0.97/1.61 c_RComplete_Onatfloor [186, 1] (w:1, o:181, a:1, s:1, b:0),
% 0.97/1.61 c_Power_Opower__class_Opower [187, 1] (w:1, o:182, a:1, s:1, b:0),
% 0.97/1.61 tc_Int_Oint [188, 0] (w:1, o:98, a:1, s:1, b:0),
% 0.97/1.61 class_Power_Opower [191, 1] (w:1, o:183, a:1, s:1, b:0),
% 0.97/1.61 class_Rings_Osemiring__0 [192, 1] (w:1, o:170, a:1, s:1, b:0),
% 0.97/1.61 c_Power_Opower_Opower [194, 3] (w:1, o:278, a:1, s:1, b:0),
% 0.97/1.61 c_RealDef_Oreal [195, 2] (w:1, o:255, a:1, s:1, b:0),
% 0.97/1.61 c_Nat__Transfer_Otsub [202, 2] (w:1, o:259, a:1, s:1, b:0),
% 0.97/1.61 c_Transcendental_Oln [205, 1] (w:1, o:184, a:1, s:1, b:0),
% 0.97/1.61 c_Nat_OSuc [206, 1] (w:1, o:185, a:1, s:1, b:0),
% 0.97/1.61 c_Divides_Odiv__class_Odiv [212, 3] (w:1, o:279, a:1, s:1, b:0),
% 0.97/1.61 class_Divides_Osemiring__div [213, 1] (w:1, o:187, a:1, s:1, b:0),
% 0.97/1.61 c_SMT_Oz3div [217, 2] (w:1, o:260, a:1, s:1, b:0),
% 0.97/1.61 c_Rings_Oinverse__class_Odivide [220, 3] (w:1, o:280, a:1, s:1, b:0)
% 0.97/1.61 ,
% 0.97/1.61 c_Divides_Odiv__class_Omod [221, 3] (w:1, o:281, a:1, s:1, b:0),
% 0.97/1.61 class_Fields_Ofield__inverse__zero [222, 1] (w:1, o:119, a:1, s:1, b:
% 0.97/1.61 0),
% 0.97/1.61 class_Fields_Ofield [223, 1] (w:1, o:120, a:1, s:1, b:0),
% 0.97/1.61 class_RealVector_Oreal__field [225, 1] (w:1, o:171, a:1, s:1, b:0),
% 0.97/1.61 class_Divides_Oring__div [226, 1] (w:1, o:186, a:1, s:1, b:0),
% 0.97/1.61 tc_HOL_Obool [229, 0] (w:1, o:97, a:1, s:1, b:0),
% 0.97/1.61 v_d1 [230, 0] (w:1, o:105, a:1, s:1, b:0),
% 0.97/1.61 v_d2 [231, 0] (w:1, o:106, a:1, s:1, b:0),
% 0.97/1.61 alpha1 [232, 4] (w:1, o:330, a:1, s:1, b:1),
% 0.97/1.61 alpha2 [233, 4] (w:1, o:333, a:1, s:1, b:1),
% 0.97/1.61 alpha3 [234, 3] (w:1, o:288, a:1, s:1, b:1),
% 0.97/1.61 alpha4 [235, 3] (w:1, o:294, a:1, s:1, b:1),
% 0.97/1.61 alpha5 [236, 3] (w:1, o:299, a:1, s:1, b:1),
% 0.97/1.61 alpha6 [237, 3] (w:1, o:303, a:1, s:1, b:1),
% 0.97/1.61 alpha7 [238, 2] (w:1, o:261, a:1, s:1, b:1),
% 0.97/1.61 alpha8 [239, 2] (w:1, o:262, a:1, s:1, b:1),
% 0.97/1.61 alpha9 [240, 2] (w:1, o:263, a:1, s:1, b:1),
% 0.97/1.61 alpha10 [241, 2] (w:1, o:264, a:1, s:1, b:1),
% 0.97/1.61 alpha11 [242, 2] (w:1, o:265, a:1, s:1, b:1),
% 0.97/1.61 alpha12 [243, 2] (w:1, o:266, a:1, s:1, b:1),
% 0.97/1.61 alpha13 [244, 2] (w:1, o:267, a:1, s:1, b:1),
% 0.97/1.61 alpha14 [245, 4] (w:1, o:331, a:1, s:1, b:1),
% 0.97/1.61 alpha15 [246, 3] (w:1, o:304, a:1, s:1, b:1),
% 0.97/1.61 alpha16 [247, 3] (w:1, o:305, a:1, s:1, b:1),
% 0.97/1.61 alpha17 [248, 3] (w:1, o:306, a:1, s:1, b:1),
% 0.97/1.61 alpha18 [249, 3] (w:1, o:307, a:1, s:1, b:1),
% 0.97/1.61 alpha19 [250, 4] (w:1, o:332, a:1, s:1, b:1),
% 0.97/1.61 alpha20 [251, 4] (w:1, o:334, a:1, s:1, b:1),
% 0.97/1.61 alpha21 [252, 3] (w:1, o:282, a:1, s:1, b:1),
% 0.97/1.61 alpha22 [253, 3] (w:1, o:283, a:1, s:1, b:1),
% 0.97/1.61 alpha23 [254, 3] (w:1, o:284, a:1, s:1, b:1),
% 0.97/1.61 alpha24 [255, 3] (w:1, o:285, a:1, s:1, b:1),
% 0.97/1.61 alpha25 [256, 2] (w:1, o:268, a:1, s:1, b:1),
% 8.13/8.54 alpha26 [257, 2] (w:1, o:269, a:1, s:1, b:1),
% 8.13/8.54 alpha27 [258, 2] (w:1, o:270, a:1, s:1, b:1),
% 8.13/8.54 alpha28 [259, 3] (w:1, o:286, a:1, s:1, b:1),
% 8.13/8.54 alpha29 [260, 3] (w:1, o:287, a:1, s:1, b:1),
% 8.13/8.54 alpha30 [261, 3] (w:1, o:289, a:1, s:1, b:1),
% 8.13/8.54 alpha31 [262, 4] (w:1, o:335, a:1, s:1, b:1),
% 8.13/8.54 alpha32 [263, 4] (w:1, o:336, a:1, s:1, b:1),
% 8.13/8.54 alpha33 [264, 4] (w:1, o:337, a:1, s:1, b:1),
% 8.13/8.54 alpha34 [265, 3] (w:1, o:290, a:1, s:1, b:1),
% 8.13/8.54 alpha35 [266, 3] (w:1, o:291, a:1, s:1, b:1),
% 8.13/8.54 alpha36 [267, 2] (w:1, o:271, a:1, s:1, b:1),
% 8.13/8.54 alpha37 [268, 3] (w:1, o:292, a:1, s:1, b:1),
% 8.13/8.54 alpha38 [269, 3] (w:1, o:293, a:1, s:1, b:1),
% 8.13/8.54 alpha39 [270, 4] (w:1, o:338, a:1, s:1, b:1),
% 8.13/8.54 alpha40 [271, 4] (w:1, o:339, a:1, s:1, b:1),
% 8.13/8.54 alpha41 [272, 4] (w:1, o:340, a:1, s:1, b:1),
% 8.13/8.54 alpha42 [273, 3] (w:1, o:295, a:1, s:1, b:1),
% 8.13/8.54 alpha43 [274, 3] (w:1, o:296, a:1, s:1, b:1),
% 8.13/8.54 alpha44 [275, 4] (w:1, o:341, a:1, s:1, b:1),
% 8.13/8.54 alpha45 [276, 4] (w:1, o:342, a:1, s:1, b:1),
% 8.13/8.54 alpha46 [277, 4] (w:1, o:343, a:1, s:1, b:1),
% 8.13/8.54 alpha47 [278, 3] (w:1, o:297, a:1, s:1, b:1),
% 8.13/8.54 alpha48 [279, 3] (w:1, o:298, a:1, s:1, b:1),
% 8.13/8.54 alpha49 [280, 4] (w:1, o:344, a:1, s:1, b:1),
% 8.13/8.54 alpha50 [281, 4] (w:1, o:345, a:1, s:1, b:1),
% 8.13/8.54 alpha51 [282, 3] (w:1, o:300, a:1, s:1, b:1),
% 8.13/8.54 alpha52 [283, 4] (w:1, o:346, a:1, s:1, b:1),
% 8.13/8.54 alpha53 [284, 4] (w:1, o:347, a:1, s:1, b:1),
% 8.13/8.54 alpha54 [285, 3] (w:1, o:301, a:1, s:1, b:1),
% 8.13/8.54 alpha55 [286, 2] (w:1, o:272, a:1, s:1, b:1),
% 8.13/8.54 alpha56 [287, 3] (w:1, o:302, a:1, s:1, b:1),
% 8.13/8.54 skol1 [288, 2] (w:1, o:222, a:1, s:1, b:1),
% 8.13/8.54 skol2 [289, 3] (w:1, o:311, a:1, s:1, b:1),
% 8.13/8.54 skol3 [290, 1] (w:1, o:189, a:1, s:1, b:1),
% 8.13/8.54 skol4 [291, 2] (w:1, o:230, a:1, s:1, b:1),
% 8.13/8.54 skol5 [292, 2] (w:1, o:232, a:1, s:1, b:1),
% 8.13/8.54 skol6 [293, 2] (w:1, o:239, a:1, s:1, b:1),
% 8.13/8.54 skol7 [294, 2] (w:1, o:242, a:1, s:1, b:1),
% 8.13/8.54 skol8 [295, 1] (w:1, o:190, a:1, s:1, b:1),
% 8.13/8.54 skol9 [296, 1] (w:1, o:191, a:1, s:1, b:1),
% 8.13/8.54 skol10 [297, 2] (w:1, o:243, a:1, s:1, b:1),
% 8.13/8.54 skol11 [298, 2] (w:1, o:244, a:1, s:1, b:1),
% 8.13/8.54 skol12 [299, 3] (w:1, o:308, a:1, s:1, b:1),
% 8.13/8.54 skol13 [300, 2] (w:1, o:245, a:1, s:1, b:1),
% 8.13/8.54 skol14 [301, 2] (w:1, o:246, a:1, s:1, b:1),
% 8.13/8.54 skol15 [302, 2] (w:1, o:247, a:1, s:1, b:1),
% 8.13/8.54 skol16 [303, 2] (w:1, o:248, a:1, s:1, b:1),
% 8.13/8.54 skol17 [304, 3] (w:1, o:309, a:1, s:1, b:1),
% 8.13/8.54 skol18 [305, 3] (w:1, o:310, a:1, s:1, b:1),
% 8.13/8.54 skol19 [306, 4] (w:1, o:348, a:1, s:1, b:1),
% 8.13/8.54 skol20 [307, 2] (w:1, o:249, a:1, s:1, b:1),
% 8.13/8.54 skol21 [308, 2] (w:1, o:250, a:1, s:1, b:1),
% 8.13/8.54 skol22 [309, 2] (w:1, o:251, a:1, s:1, b:1),
% 8.13/8.54 skol23 [310, 3] (w:1, o:312, a:1, s:1, b:1),
% 8.13/8.54 skol24 [311, 3] (w:1, o:313, a:1, s:1, b:1),
% 8.13/8.54 skol25 [312, 3] (w:1, o:314, a:1, s:1, b:1),
% 8.13/8.54 skol26 [313, 2] (w:1, o:252, a:1, s:1, b:1),
% 8.13/8.54 skol27 [314, 4] (w:1, o:349, a:1, s:1, b:1),
% 8.13/8.54 skol28 [315, 2] (w:1, o:253, a:1, s:1, b:1),
% 8.13/8.54 skol29 [316, 1] (w:1, o:188, a:1, s:1, b:1),
% 8.13/8.54 skol30 [317, 2] (w:1, o:223, a:1, s:1, b:1),
% 8.13/8.54 skol31 [318, 2] (w:1, o:224, a:1, s:1, b:1),
% 8.13/8.54 skol32 [319, 3] (w:1, o:315, a:1, s:1, b:1),
% 8.13/8.54 skol33 [320, 3] (w:1, o:316, a:1, s:1, b:1),
% 8.13/8.54 skol34 [321, 2] (w:1, o:225, a:1, s:1, b:1),
% 8.13/8.54 skol35 [322, 2] (w:1, o:226, a:1, s:1, b:1),
% 8.13/8.54 skol36 [323, 1] (w:1, o:192, a:1, s:1, b:1),
% 8.13/8.54 skol37 [324, 2] (w:1, o:227, a:1, s:1, b:1),
% 8.13/8.54 skol38 [325, 2] (w:1, o:228, a:1, s:1, b:1),
% 8.13/8.54 skol39 [326, 2] (w:1, o:229, a:1, s:1, b:1),
% 8.13/8.54 skol40 [327, 3] (w:1, o:317, a:1, s:1, b:1),
% 8.13/8.54 skol41 [328, 3] (w:1, o:318, a:1, s:1, b:1),
% 8.13/8.54 skol42 [329, 3] (w:1, o:319, a:1, s:1, b:1),
% 8.13/8.54 skol43 [330, 3] (w:1, o:320, a:1, s:1, b:1),
% 8.13/8.54 skol44 [331, 1] (w:1, o:193, a:1, s:1, b:1),
% 8.13/8.54 skol45 [332, 3] (w:1, o:321, a:1, s:1, b:1),
% 8.13/8.54 skol46 [333, 4] (w:1, o:350, a:1, s:1, b:1),
% 8.13/8.54 skol47 [334, 3] (w:1, o:322, a:1, s:1, b:1),
% 50.45/50.85 skol48 [335, 3] (w:1, o:323, a:1, s:1, b:1),
% 50.45/50.85 skol49 [336, 2] (w:1, o:231, a:1, s:1, b:1),
% 50.45/50.85 skol50 [337, 3] (w:1, o:324, a:1, s:1, b:1),
% 50.45/50.85 skol51 [338, 2] (w:1, o:233, a:1, s:1, b:1),
% 50.45/50.85 skol52 [339, 2] (w:1, o:234, a:1, s:1, b:1),
% 50.45/50.85 skol53 [340, 2] (w:1, o:235, a:1, s:1, b:1),
% 50.45/50.85 skol54 [341, 2] (w:1, o:236, a:1, s:1, b:1),
% 50.45/50.85 skol55 [342, 2] (w:1, o:237, a:1, s:1, b:1),
% 50.45/50.85 skol56 [343, 2] (w:1, o:238, a:1, s:1, b:1),
% 50.45/50.85 skol57 [344, 3] (w:1, o:325, a:1, s:1, b:1),
% 50.45/50.85 skol58 [345, 3] (w:1, o:326, a:1, s:1, b:1),
% 50.45/50.85 skol59 [346, 3] (w:1, o:327, a:1, s:1, b:1),
% 50.45/50.85 skol60 [347, 4] (w:1, o:351, a:1, s:1, b:1),
% 50.45/50.85 skol61 [348, 4] (w:1, o:352, a:1, s:1, b:1),
% 50.45/50.85 skol62 [349, 3] (w:1, o:328, a:1, s:1, b:1),
% 50.45/50.85 skol63 [350, 3] (w:1, o:329, a:1, s:1, b:1),
% 50.45/50.85 skol64 [351, 2] (w:1, o:240, a:1, s:1, b:1),
% 50.45/50.85 skol65 [352, 2] (w:1, o:241, a:1, s:1, b:1).
% 50.45/50.85
% 50.45/50.85
% 50.45/50.85 Starting Search:
% 50.45/50.85
% 50.45/50.85 *** allocated 113905 integers for clauses
% 50.45/50.85 *** allocated 170857 integers for clauses
% 50.45/50.85 Resimplifying inuse:
% 50.45/50.85 Done
% 50.45/50.85
% 50.45/50.85
% 50.45/50.85 Intermediate Status:
% 50.45/50.85 Generated: 3057
% 50.45/50.85 Kept: 2002
% 50.45/50.85 Inuse: 52
% 50.45/50.85 Deleted: 0
% 50.45/50.85 Deletedinuse: 0
% 50.45/50.85
% 50.45/50.85 *** allocated 256285 integers for clauses
% 50.45/50.85 Resimplifying inuse:
% 50.45/50.85 Done
% 50.45/50.85
% 50.45/50.85 *** allocated 170857 integers for termspace/termends
% 50.45/50.85 Resimplifying inuse:
% 50.45/50.85 Done
% 50.45/50.85
% 50.45/50.85
% 50.45/50.85 Intermediate Status:
% 50.45/50.85 Generated: 8499
% 50.45/50.85 Kept: 4032
% 50.45/50.85 Inuse: 200
% 50.45/50.85 Deleted: 1
% 50.45/50.85 Deletedinuse: 0
% 50.45/50.85
% 50.45/50.85 *** allocated 384427 integers for clauses
% 50.45/50.85 Resimplifying inuse:
% 50.45/50.85 Done
% 50.45/50.85
% 50.45/50.85 *** allocated 256285 integers for termspace/termends
% 50.45/50.85
% 50.45/50.85 Intermediate Status:
% 50.45/50.85 Generated: 15073
% 50.45/50.85 Kept: 6322
% 50.45/50.85 Inuse: 255
% 50.45/50.85 Deleted: 1
% 50.45/50.85 Deletedinuse: 0
% 50.45/50.85
% 50.45/50.85 Resimplifying inuse:
% 50.45/50.85 Done
% 50.45/50.85
% 50.45/50.85 Resimplifying inuse:
% 50.45/50.85 Done
% 50.45/50.85
% 50.45/50.85 *** allocated 576640 integers for clauses
% 50.45/50.85
% 50.45/50.85 Intermediate Status:
% 50.45/50.85 Generated: 19856
% 50.45/50.85 Kept: 8379
% 50.45/50.85 Inuse: 360
% 50.45/50.85 Deleted: 1
% 50.45/50.85 Deletedinuse: 0
% 50.45/50.85
% 50.45/50.85 Resimplifying inuse:
% 50.45/50.85 Done
% 50.45/50.85
% 50.45/50.85 *** allocated 384427 integers for termspace/termends
% 50.45/50.85 Resimplifying inuse:
% 50.45/50.85 Done
% 50.45/50.85
% 50.45/50.85
% 50.45/50.85 Intermediate Status:
% 50.45/50.85 Generated: 25990
% 50.45/50.85 Kept: 10481
% 50.45/50.85 Inuse: 415
% 50.45/50.85 Deleted: 1
% 50.45/50.85 Deletedinuse: 0
% 50.45/50.85
% 50.45/50.85 Resimplifying inuse:
% 50.45/50.85 Done
% 50.45/50.85
% 50.45/50.85 Resimplifying inuse:
% 50.45/50.85 Done
% 50.45/50.85
% 50.45/50.85 *** allocated 864960 integers for clauses
% 50.45/50.85
% 50.45/50.85 Intermediate Status:
% 50.45/50.85 Generated: 31926
% 50.45/50.85 Kept: 12604
% 50.45/50.85 Inuse: 454
% 50.45/50.85 Deleted: 2
% 50.45/50.85 Deletedinuse: 0
% 50.45/50.85
% 50.45/50.85 Resimplifying inuse:
% 50.45/50.85 Done
% 50.45/50.85
% 50.45/50.85 *** allocated 576640 integers for termspace/termends
% 50.45/50.85 Resimplifying inuse:
% 50.45/50.85 Done
% 50.45/50.85
% 50.45/50.85
% 50.45/50.85 Intermediate Status:
% 50.45/50.85 Generated: 46196
% 50.45/50.85 Kept: 15428
% 50.45/50.85 Inuse: 515
% 50.45/50.85 Deleted: 11
% 50.45/50.85 Deletedinuse: 0
% 50.45/50.85
% 50.45/50.85 Resimplifying inuse:
% 50.45/50.85 Done
% 50.45/50.85
% 50.45/50.85 Resimplifying inuse:
% 50.45/50.85 Done
% 50.45/50.85
% 50.45/50.85
% 50.45/50.85 Intermediate Status:
% 50.45/50.85 Generated: 58516
% 50.45/50.85 Kept: 17482
% 50.45/50.85 Inuse: 527
% 50.45/50.85 Deleted: 11
% 50.45/50.85 Deletedinuse: 0
% 50.45/50.85
% 50.45/50.85 *** allocated 1297440 integers for clauses
% 50.45/50.85 Resimplifying inuse:
% 50.45/50.85 Done
% 50.45/50.85
% 50.45/50.85
% 50.45/50.85 Intermediate Status:
% 50.45/50.85 Generated: 65927
% 50.45/50.85 Kept: 19521
% 50.45/50.85 Inuse: 545
% 50.45/50.85 Deleted: 11
% 50.45/50.85 Deletedinuse: 0
% 50.45/50.85
% 50.45/50.85 *** allocated 864960 integers for termspace/termends
% 50.45/50.85 Resimplifying inuse:
% 50.45/50.85 Done
% 50.45/50.85
% 50.45/50.85 Resimplifying clauses:
% 50.45/50.85 Done
% 50.45/50.85
% 50.45/50.85
% 50.45/50.85 Intermediate Status:
% 50.45/50.85 Generated: 75650
% 50.45/50.85 Kept: 21913
% 50.45/50.85 Inuse: 565
% 50.45/50.85 Deleted: 412
% 50.45/50.85 Deletedinuse: 0
% 50.45/50.85
% 50.45/50.85 Resimplifying inuse:
% 50.45/50.85 Done
% 50.45/50.85
% 50.45/50.85 Resimplifying inuse:
% 50.45/50.85 Done
% 50.45/50.85
% 50.45/50.85
% 50.45/50.85 Intermediate Status:
% 50.45/50.85 Generated: 83561
% 50.45/50.85 Kept: 23916
% 50.45/50.85 Inuse: 590
% 50.45/50.85 Deleted: 414
% 50.45/50.85 Deletedinuse: 2
% 50.45/50.85
% 50.45/50.85 Resimplifying inuse:
% 50.45/50.85 Done
% 50.45/50.85
% 50.45/50.85 Resimplifying inuse:
% 50.45/50.85 Done
% 50.45/50.85
% 50.45/50.85
% 50.45/50.85 Intermediate Status:
% 50.45/50.85 Generated: 92598
% 50.45/50.85 Kept: 25999
% 50.45/50.85 Inuse: 640
% 50.45/50.85 Deleted: 414
% 50.45/50.85 Deletedinuse: 2
% 50.45/50.85
% 50.45/50.85 Resimplifying inuse:
% 50.45/50.85 Done
% 50.45/50.85
% 50.45/50.85 Resimplifying inuse:
% 50.45/50.85 Done
% 50.45/50.85
% 50.45/50.85
% 50.45/50.85 Intermediate Status:
% 50.45/50.85 Generated: 101615
% 50.45/50.85 Kept: 28278
% 50.45/50.85 Inuse: 705
% 50.45/50.85 Deleted: 414
% 50.45/50.85 Deletedinuse: 2
% 50.45/50.85
% 50.45/50.85 Resimplifying inuse:
% 50.45/50.85 Done
% 50.45/50.85
% 50.45/50.85 *** allocated 1946160 integers for clauses
% 50.45/50.85
% 50.45/50.85 Intermediate Status:
% 50.45/50.85 Generated: 110249
% 50.45/50.85 Kept: 30340
% 50.45/50.85 Inuse: 755
% 50.45/50.85 Deleted: 414
% 50.45/50.85 Deletedinuse: 2
% 50.45/50.85
% 50.45/50.85 Resimplifying inuse:
% 50.45/50.85 Done
% 50.45/50.85
% 50.45/50.85 Resimplifying inuse:
% 50.45/50.85 Done
% 50.45/50.85
% 50.45/50.85 *** allocated 1297440 integers for termspace/termends
% 50.45/50.85
% 50.45/50.85 Intermediate Status:
% 50.45/50.85 Generated: 122167
% 50.45/50.85 Kept: 33402
% 50.45/50.85 Inuse: 795
% 50.45/50.85 Deleted: 414
% 50.45/50.85 Deletedinuse: 2
% 50.45/50.85
% 50.45/50.85 Resimplifying inuse:
% 50.45/50.85 Done
% 50.45/50.85
% 50.45/50.85 Resimplifying inuse:
% 50.45/50.85 Done
% 50.45/50.85
% 135.45/135.82
% 135.45/135.82 Intermediate Status:
% 135.45/135.82 Generated: 128789
% 135.45/135.82 Kept: 35575
% 135.45/135.82 Inuse: 820
% 135.45/135.82 Deleted: 414
% 135.45/135.82 Deletedinuse: 2
% 135.45/135.82
% 135.45/135.82 Resimplifying inuse:
% 135.45/135.82 Done
% 135.45/135.82
% 135.45/135.82
% 135.45/135.82 Intermediate Status:
% 135.45/135.82 Generated: 136846
% 135.45/135.82 Kept: 38763
% 135.45/135.82 Inuse: 840
% 135.45/135.82 Deleted: 414
% 135.45/135.82 Deletedinuse: 2
% 135.45/135.82
% 135.45/135.82 Resimplifying inuse:
% 135.45/135.82 Done
% 135.45/135.82
% 135.45/135.82 Resimplifying inuse:
% 135.45/135.82 Done
% 135.45/135.82
% 135.45/135.82
% 135.45/135.82 Intermediate Status:
% 135.45/135.82 Generated: 155957
% 135.45/135.82 Kept: 42659
% 135.45/135.82 Inuse: 875
% 135.45/135.82 Deleted: 414
% 135.45/135.82 Deletedinuse: 2
% 135.45/135.82
% 135.45/135.82 Resimplifying inuse:
% 135.45/135.82 Done
% 135.45/135.82
% 135.45/135.82 Resimplifying clauses:
% 135.45/135.82 Done
% 135.45/135.82
% 135.45/135.82 Resimplifying inuse:
% 135.45/135.82 Done
% 135.45/135.82
% 135.45/135.82 *** allocated 2919240 integers for clauses
% 135.45/135.82
% 135.45/135.82 Intermediate Status:
% 135.45/135.82 Generated: 171110
% 135.45/135.82 Kept: 46689
% 135.45/135.82 Inuse: 915
% 135.45/135.82 Deleted: 1663
% 135.45/135.82 Deletedinuse: 3
% 135.45/135.82
% 135.45/135.82 Resimplifying inuse:
% 135.45/135.82 Done
% 135.45/135.82
% 135.45/135.82
% 135.45/135.82 Intermediate Status:
% 135.45/135.82 Generated: 179033
% 135.45/135.82 Kept: 49322
% 135.45/135.82 Inuse: 935
% 135.45/135.82 Deleted: 1663
% 135.45/135.82 Deletedinuse: 3
% 135.45/135.82
% 135.45/135.82 Resimplifying inuse:
% 135.45/135.82 Done
% 135.45/135.82
% 135.45/135.82 *** allocated 1946160 integers for termspace/termends
% 135.45/135.82 Resimplifying inuse:
% 135.45/135.82 Done
% 135.45/135.82
% 135.45/135.82
% 135.45/135.82 Intermediate Status:
% 135.45/135.82 Generated: 189762
% 135.45/135.82 Kept: 53470
% 135.45/135.82 Inuse: 970
% 135.45/135.82 Deleted: 1663
% 135.45/135.82 Deletedinuse: 3
% 135.45/135.82
% 135.45/135.82 Resimplifying inuse:
% 135.45/135.82 Done
% 135.45/135.82
% 135.45/135.82 Resimplifying inuse:
% 135.45/135.82 Done
% 135.45/135.82
% 135.45/135.82
% 135.45/135.82 Intermediate Status:
% 135.45/135.82 Generated: 196249
% 135.45/135.82 Kept: 55608
% 135.45/135.82 Inuse: 1005
% 135.45/135.82 Deleted: 1663
% 135.45/135.82 Deletedinuse: 3
% 135.45/135.82
% 135.45/135.82 Resimplifying inuse:
% 135.45/135.82 Done
% 135.45/135.82
% 135.45/135.82 Resimplifying inuse:
% 135.45/135.82 Done
% 135.45/135.82
% 135.45/135.82
% 135.45/135.82 Intermediate Status:
% 135.45/135.82 Generated: 204359
% 135.45/135.82 Kept: 59065
% 135.45/135.82 Inuse: 1035
% 135.45/135.82 Deleted: 1663
% 135.45/135.82 Deletedinuse: 3
% 135.45/135.82
% 135.45/135.82 Resimplifying inuse:
% 135.45/135.82 Done
% 135.45/135.82
% 135.45/135.82
% 135.45/135.82 Intermediate Status:
% 135.45/135.82 Generated: 214602
% 135.45/135.82 Kept: 61218
% 135.45/135.82 Inuse: 1045
% 135.45/135.82 Deleted: 1663
% 135.45/135.82 Deletedinuse: 3
% 135.45/135.82
% 135.45/135.82 Resimplifying inuse:
% 135.45/135.82 Done
% 135.45/135.82
% 135.45/135.82 Resimplifying inuse:
% 135.45/135.82 Done
% 135.45/135.82
% 135.45/135.82 Resimplifying clauses:
% 135.45/135.82 Done
% 135.45/135.82
% 135.45/135.82
% 135.45/135.82 Intermediate Status:
% 135.45/135.82 Generated: 222136
% 135.45/135.82 Kept: 63253
% 135.45/135.82 Inuse: 1077
% 135.45/135.82 Deleted: 1966
% 135.45/135.82 Deletedinuse: 3
% 135.45/135.82
% 135.45/135.82 Resimplifying inuse:
% 135.45/135.82 Done
% 135.45/135.82
% 135.45/135.82 Resimplifying inuse:
% 135.45/135.82 Done
% 135.45/135.82
% 135.45/135.82
% 135.45/135.82 Intermediate Status:
% 135.45/135.82 Generated: 233397
% 135.45/135.82 Kept: 65318
% 135.45/135.82 Inuse: 1100
% 135.45/135.82 Deleted: 1966
% 135.45/135.82 Deletedinuse: 3
% 135.45/135.82
% 135.45/135.82 Resimplifying inuse:
% 135.45/135.82 Done
% 135.45/135.82
% 135.45/135.82 Resimplifying inuse:
% 135.45/135.82 Done
% 135.45/135.82
% 135.45/135.82
% 135.45/135.82 Intermediate Status:
% 135.45/135.82 Generated: 245064
% 135.45/135.82 Kept: 67682
% 135.45/135.82 Inuse: 1125
% 135.45/135.82 Deleted: 1966
% 135.45/135.82 Deletedinuse: 3
% 135.45/135.82
% 135.45/135.82 Resimplifying inuse:
% 135.45/135.82 Done
% 135.45/135.82
% 135.45/135.82 Resimplifying inuse:
% 135.45/135.82 Done
% 135.45/135.82
% 135.45/135.82
% 135.45/135.82 Intermediate Status:
% 135.45/135.82 Generated: 255193
% 135.45/135.82 Kept: 69770
% 135.45/135.82 Inuse: 1155
% 135.45/135.82 Deleted: 1966
% 135.45/135.82 Deletedinuse: 3
% 135.45/135.82
% 135.45/135.82 Resimplifying inuse:
% 135.45/135.82 Done
% 135.45/135.82
% 135.45/135.82 *** allocated 4378860 integers for clauses
% 135.45/135.82
% 135.45/135.82 Intermediate Status:
% 135.45/135.82 Generated: 260512
% 135.45/135.82 Kept: 71780
% 135.45/135.82 Inuse: 1205
% 135.45/135.82 Deleted: 1966
% 135.45/135.82 Deletedinuse: 3
% 135.45/135.82
% 135.45/135.82 Resimplifying inuse:
% 135.45/135.82 Done
% 135.45/135.82
% 135.45/135.82 Resimplifying inuse:
% 135.45/135.82 Done
% 135.45/135.82
% 135.45/135.82 *** allocated 2919240 integers for termspace/termends
% 135.45/135.82
% 135.45/135.82 Intermediate Status:
% 135.45/135.82 Generated: 268413
% 135.45/135.82 Kept: 74822
% 135.45/135.82 Inuse: 1241
% 135.45/135.82 Deleted: 1970
% 135.45/135.82 Deletedinuse: 3
% 135.45/135.82
% 135.45/135.82 Resimplifying inuse:
% 135.45/135.82 Done
% 135.45/135.82
% 135.45/135.82 Resimplifying inuse:
% 135.45/135.82 Done
% 135.45/135.82
% 135.45/135.82
% 135.45/135.82 Intermediate Status:
% 135.45/135.82 Generated: 276722
% 135.45/135.82 Kept: 77245
% 135.45/135.82 Inuse: 1266
% 135.45/135.82 Deleted: 1970
% 135.45/135.82 Deletedinuse: 3
% 135.45/135.82
% 135.45/135.82 Resimplifying inuse:
% 135.45/135.82 Done
% 135.45/135.82
% 135.45/135.82 Resimplifying inuse:
% 135.45/135.82 Done
% 135.45/135.82
% 135.45/135.82
% 135.45/135.82 Intermediate Status:
% 135.45/135.82 Generated: 287402
% 135.45/135.82 Kept: 80725
% 135.45/135.82 Inuse: 1277
% 135.45/135.82 Deleted: 1970
% 135.45/135.82 Deletedinuse: 3
% 135.45/135.82
% 135.45/135.82 Resimplifying inuse:
% 135.45/135.82 Done
% 135.45/135.82
% 135.45/135.82 Resimplifying inuse:
% 135.45/135.82 Done
% 135.45/135.82
% 135.45/135.82
% 135.45/135.82 Intermediate Status:
% 135.45/135.82 Generated: 294871
% 135.45/135.82 Kept: 82802
% 135.45/135.82 Inuse: 1291
% 135.45/135.82 Deleted: 1970
% 135.45/135.82 Deletedinuse: 3
% 135.45/135.82
% 135.45/135.82 Resimplifying clauses:
% 135.45/135.82 Done
% 135.45/135.82
% 135.45/135.82 Resimplifying inuse:
% 135.45/135.82 Done
% 135.45/135.82
% 135.45/135.82 Resimplifying inuse:
% 135.45/135.82 Done
% 135.45/135.82
% 135.45/135.82
% 135.45/135.82 Intermediate Status:
% 135.45/135.82 Generated: 301342
% 135.45/135.82 Kept: 85265
% 135.45/135.82 Inuse: 1311
% 135.45/135.82 Deleted: 2336
% 135.45/135.82 Deletedinuse: 3
% 135.45/135.82
% 135.45/135.82 Resimplifying inuse:
% 135.45/135.82 Done
% 135.45/135.82
% 135.45/135.82 Resimplifying inuse:
% 135.45/135.82 Done
% 135.45/135.82
% 135.45/135.82
% 135.45/135.82 Intermediate Status:
% 135.45/135.82 Generated: 309666
% 135.45/135.82 Kept: 87517
% 135.45/135.82 Inuse: 1331
% 135.45/135.82 Deleted: 2336
% 135.45/135.82 Deletedinuse: 3
% 135.45/135.82
% 135.45/135.82 Resimplifying inuse:
% 135.45/135.82 Done
% 135.45/135.82
% 135.45/135.82
% 135.45/135.82 Intermediate Status:
% 135.45/135.82 Generated: 318528
% 135.45/135.82 Kept: 89780
% 135.45/135.82 Inuse: 1341
% 135.45/135.82 Deleted: 2336
% 135.45/135.82 Deletedinuse: 3
% 135.45/135.82
% 135.45/135.82 Resimplifying inuse:
% 135.45/135.82 Done
% 135.45/135.82
% 135.45/135.82 Resimplifying inuse:
% 135.45/135.82 Done
% 135.45/135.82
% 135.45/135.82
% 135.45/135.82 Intermediate Status:
% 135.45/135.82 Generated: 324120
% 135.45/135.82 Kept: 91806
% 135.45/135.82 Inuse: 1363
% 135.45/135.82 Deleted: 2337
% 135.45/135.82 Deletedinuse: 4
% 135.45/135.82
% 135.45/135.82 Resimplifying inuse:
% 135.45/135.82 Done
% 135.45/135.82
% 135.45/135.82 Resimplifying inuse:
% 135.45/135.82 Done
% 135.45/135.82
% 135.45/135.82
% 135.45/135.82 Intermediate Status:
% 135.45/135.82 Generated: 329923
% 135.45/135.82 Kept: 93938
% 135.45/135.82 Inuse: 1386
% 135.45/135.82 Deleted: 2339
% 135.45/135.82 Deletedinuse: 6
% 135.45/135.82
% 135.45/135.82 Resimplifying inuse:
% 135.45/135.82 Done
% 135.45/135.82
% 135.45/135.82 Resimplifying inuse:
% 135.45/135.82 Done
% 135.45/135.82
% 135.45/135.82
% 135.45/135.82 Intermediate Status:
% 246.71/247.12 Generated: 335506
% 246.71/247.12 Kept: 95957
% 246.71/247.12 Inuse: 1407
% 246.71/247.12 Deleted: 2342
% 246.71/247.12 Deletedinuse: 9
% 246.71/247.12
% 246.71/247.12 Resimplifying inuse:
% 246.71/247.12 Done
% 246.71/247.12
% 246.71/247.12 Resimplifying inuse:
% 246.71/247.12 Done
% 246.71/247.12
% 246.71/247.12
% 246.71/247.12 Intermediate Status:
% 246.71/247.12 Generated: 342089
% 246.71/247.12 Kept: 98316
% 246.71/247.12 Inuse: 1431
% 246.71/247.12 Deleted: 2342
% 246.71/247.12 Deletedinuse: 9
% 246.71/247.12
% 246.71/247.12 Resimplifying inuse:
% 246.71/247.12 Done
% 246.71/247.12
% 246.71/247.12 Resimplifying inuse:
% 246.71/247.12 Done
% 246.71/247.12
% 246.71/247.12
% 246.71/247.12 Intermediate Status:
% 246.71/247.12 Generated: 348660
% 246.71/247.12 Kept: 100343
% 246.71/247.12 Inuse: 1447
% 246.71/247.12 Deleted: 2342
% 246.71/247.12 Deletedinuse: 9
% 246.71/247.12
% 246.71/247.12 Resimplifying inuse:
% 246.71/247.12 Done
% 246.71/247.12
% 246.71/247.12 *** allocated 4378860 integers for termspace/termends
% 246.71/247.12
% 246.71/247.12 Intermediate Status:
% 246.71/247.12 Generated: 355802
% 246.71/247.12 Kept: 103683
% 246.71/247.12 Inuse: 1461
% 246.71/247.12 Deleted: 2342
% 246.71/247.12 Deletedinuse: 9
% 246.71/247.12
% 246.71/247.12 Resimplifying inuse:
% 246.71/247.12 Done
% 246.71/247.12
% 246.71/247.12 Resimplifying clauses:
% 246.71/247.12 Done
% 246.71/247.12
% 246.71/247.12 Resimplifying inuse:
% 246.71/247.12 Done
% 246.71/247.12
% 246.71/247.12
% 246.71/247.12 Intermediate Status:
% 246.71/247.12 Generated: 366289
% 246.71/247.12 Kept: 105817
% 246.71/247.12 Inuse: 1481
% 246.71/247.12 Deleted: 2732
% 246.71/247.12 Deletedinuse: 9
% 246.71/247.12
% 246.71/247.12 Resimplifying inuse:
% 246.71/247.12 Done
% 246.71/247.12
% 246.71/247.12 Resimplifying inuse:
% 246.71/247.12 Done
% 246.71/247.12
% 246.71/247.12 *** allocated 6568290 integers for clauses
% 246.71/247.12
% 246.71/247.12 Intermediate Status:
% 246.71/247.12 Generated: 381215
% 246.71/247.12 Kept: 108617
% 246.71/247.12 Inuse: 1516
% 246.71/247.12 Deleted: 2732
% 246.71/247.12 Deletedinuse: 9
% 246.71/247.12
% 246.71/247.12 Resimplifying inuse:
% 246.71/247.12 Done
% 246.71/247.12
% 246.71/247.12 Resimplifying inuse:
% 246.71/247.12 Done
% 246.71/247.12
% 246.71/247.12
% 246.71/247.12 Intermediate Status:
% 246.71/247.12 Generated: 393159
% 246.71/247.12 Kept: 110737
% 246.71/247.12 Inuse: 1531
% 246.71/247.12 Deleted: 2732
% 246.71/247.12 Deletedinuse: 9
% 246.71/247.12
% 246.71/247.12 Resimplifying inuse:
% 246.71/247.12 Done
% 246.71/247.12
% 246.71/247.12
% 246.71/247.12 Intermediate Status:
% 246.71/247.12 Generated: 404214
% 246.71/247.12 Kept: 112767
% 246.71/247.12 Inuse: 1542
% 246.71/247.12 Deleted: 2732
% 246.71/247.12 Deletedinuse: 9
% 246.71/247.12
% 246.71/247.12 Resimplifying inuse:
% 246.71/247.12 Done
% 246.71/247.12
% 246.71/247.12
% 246.71/247.12 Intermediate Status:
% 246.71/247.12 Generated: 413579
% 246.71/247.12 Kept: 115888
% 246.71/247.12 Inuse: 1559
% 246.71/247.12 Deleted: 2734
% 246.71/247.12 Deletedinuse: 9
% 246.71/247.12
% 246.71/247.12 Resimplifying inuse:
% 246.71/247.12 Done
% 246.71/247.12
% 246.71/247.12
% 246.71/247.12 Intermediate Status:
% 246.71/247.12 Generated: 423731
% 246.71/247.12 Kept: 119761
% 246.71/247.12 Inuse: 1589
% 246.71/247.12 Deleted: 2734
% 246.71/247.12 Deletedinuse: 9
% 246.71/247.12
% 246.71/247.12 Resimplifying inuse:
% 246.71/247.12 Done
% 246.71/247.12
% 246.71/247.12 Resimplifying inuse:
% 246.71/247.12 Done
% 246.71/247.12
% 246.71/247.12
% 246.71/247.12 Intermediate Status:
% 246.71/247.12 Generated: 431224
% 246.71/247.12 Kept: 121916
% 246.71/247.12 Inuse: 1619
% 246.71/247.12 Deleted: 2734
% 246.71/247.12 Deletedinuse: 9
% 246.71/247.12
% 246.71/247.12 Resimplifying inuse:
% 246.71/247.12 Done
% 246.71/247.12
% 246.71/247.12 Resimplifying inuse:
% 246.71/247.12 Done
% 246.71/247.12
% 246.71/247.12
% 246.71/247.12 Intermediate Status:
% 246.71/247.12 Generated: 441418
% 246.71/247.12 Kept: 123979
% 246.71/247.12 Inuse: 1644
% 246.71/247.12 Deleted: 2734
% 246.71/247.12 Deletedinuse: 9
% 246.71/247.12
% 246.71/247.12 Resimplifying clauses:
% 246.71/247.12 Done
% 246.71/247.12
% 246.71/247.12 Resimplifying inuse:
% 246.71/247.12 Done
% 246.71/247.12
% 246.71/247.12
% 246.71/247.12 Intermediate Status:
% 246.71/247.12 Generated: 448071
% 246.71/247.12 Kept: 127443
% 246.71/247.12 Inuse: 1653
% 246.71/247.12 Deleted: 2971
% 246.71/247.12 Deletedinuse: 9
% 246.71/247.12
% 246.71/247.12 Resimplifying inuse:
% 246.71/247.12 Done
% 246.71/247.12
% 246.71/247.12 Resimplifying inuse:
% 246.71/247.12 Done
% 246.71/247.12
% 246.71/247.12
% 246.71/247.12 Intermediate Status:
% 246.71/247.12 Generated: 454723
% 246.71/247.12 Kept: 129649
% 246.71/247.12 Inuse: 1674
% 246.71/247.12 Deleted: 2971
% 246.71/247.12 Deletedinuse: 9
% 246.71/247.12
% 246.71/247.12 Resimplifying inuse:
% 246.71/247.12 Done
% 246.71/247.12
% 246.71/247.12
% 246.71/247.12 Intermediate Status:
% 246.71/247.12 Generated: 491909
% 246.71/247.12 Kept: 133941
% 246.71/247.12 Inuse: 1679
% 246.71/247.12 Deleted: 2971
% 246.71/247.12 Deletedinuse: 9
% 246.71/247.12
% 246.71/247.12 Resimplifying inuse:
% 246.71/247.12 Done
% 246.71/247.12
% 246.71/247.12 Resimplifying inuse:
% 246.71/247.12 Done
% 246.71/247.12
% 246.71/247.12
% 246.71/247.12 Intermediate Status:
% 246.71/247.12 Generated: 502387
% 246.71/247.12 Kept: 136270
% 246.71/247.12 Inuse: 1699
% 246.71/247.12 Deleted: 2971
% 246.71/247.12 Deletedinuse: 9
% 246.71/247.12
% 246.71/247.12 Resimplifying inuse:
% 246.71/247.12 Done
% 246.71/247.12
% 246.71/247.12 Resimplifying inuse:
% 246.71/247.12 Done
% 246.71/247.12
% 246.71/247.12
% 246.71/247.12 Intermediate Status:
% 246.71/247.12 Generated: 511396
% 246.71/247.12 Kept: 138644
% 246.71/247.12 Inuse: 1728
% 246.71/247.12 Deleted: 2972
% 246.71/247.12 Deletedinuse: 9
% 246.71/247.12
% 246.71/247.12 Resimplifying inuse:
% 246.71/247.12 Done
% 246.71/247.12
% 246.71/247.12 Resimplifying inuse:
% 246.71/247.12 Done
% 246.71/247.12
% 246.71/247.12
% 246.71/247.12 Intermediate Status:
% 246.71/247.12 Generated: 526261
% 246.71/247.12 Kept: 142244
% 246.71/247.12 Inuse: 1753
% 246.71/247.12 Deleted: 2973
% 246.71/247.12 Deletedinuse: 10
% 246.71/247.12
% 246.71/247.12 Resimplifying inuse:
% 246.71/247.12 Done
% 246.71/247.12
% 246.71/247.12 Resimplifying inuse:
% 246.71/247.12 Done
% 246.71/247.12
% 246.71/247.12 Resimplifying clauses:
% 246.71/247.12 Done
% 246.71/247.12
% 246.71/247.12
% 246.71/247.12 Intermediate Status:
% 246.71/247.12 Generated: 536460
% 246.71/247.12 Kept: 144271
% 246.71/247.12 Inuse: 1760
% 246.71/247.12 Deleted: 3724
% 246.71/247.12 Deletedinuse: 10
% 246.71/247.12
% 246.71/247.12 Resimplifying inuse:
% 246.71/247.12 Done
% 246.71/247.12
% 246.71/247.12
% 246.71/247.12 Intermediate Status:
% 246.71/247.12 Generated: 545541
% 246.71/247.12 Kept: 146432
% 246.71/247.12 Inuse: 1778
% 246.71/247.12 Deleted: 3724
% 246.71/247.12 Deletedinuse: 10
% 246.71/247.12
% 246.71/247.12 Resimplifying inuse:
% 246.71/247.12 Done
% 246.71/247.12
% 246.71/247.12 Resimplifying inuse:
% 246.71/247.12 Done
% 246.71/247.12
% 246.71/247.12
% 246.71/247.12 Intermediate Status:
% 246.71/247.12 Generated: 552910
% 246.71/247.12 Kept: 148779
% 246.71/247.12 Inuse: 1803
% 246.71/247.12 Deleted: 3724
% 246.71/247.12 Deletedinuse: 10
% 246.71/247.12
% 246.71/247.12 Resimplifying inuse:
% 246.71/247.12 Done
% 246.71/247.12
% 246.71/247.12 Resimplifying inuse:
% 246.71/247.12 Done
% 246.71/247.12
% 246.71/247.12 *** allocated 6568290 integers for termspace/termends
% 246.71/247.12
% 246.71/247.12 Intermediate Status:
% 246.71/247.12 Generated: 559993
% 246.71/247.12 Kept: 151140
% 246.71/247.12 Inuse: 1823
% 246.71/247.12 Deleted: 3724
% 246.71/247.12 Deletedinuse: 10
% 246.71/247.12
% 246.71/247.12 Resimplifying inuse:
% 246.71/247.12 Done
% 246.71/247.12
% 246.71/247.12
% 246.71/247.12 Intermediate Status:
% 246.71/247.12 Generated: 596018
% 246.71/247.12 Kept: 154612
% 246.71/247.12 Inuse: 1828
% 246.71/247.12 Deleted: 3724
% 246.71/247.12 Deletedinuse: 10
% 246.71/247.12
% 246.71/247.12 Resimplifying inuse:
% 246.71/247.12 Done
% 246.71/247.12
% 246.71/247.12
% 246.71/247.12 Intermediate Status:
% 246.71/247.12 Generated: 603386
% 246.71/247.12 Kept: 156808
% 246.71/247.12 Inuse: 1838
% 246.71/247.12 Deleted: 3724
% 246.71/247.12 Deletedinuse: 10
% 246.71/247.12
% 246.71/247.12 RCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------