TSTP Solution File: SWW215+1 by Bliksem---1.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWW215+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n022.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 23:21:17 EDT 2022
% Result : Timeout 300.08s 300.50s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWW215+1 : TPTP v8.1.0. Released v5.2.0.
% 0.11/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n022.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % DateTime : Mon Jun 6 02:14:05 EDT 2022
% 0.13/0.34 % 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 { ! v_w____ = v_z }.
% 0.97/1.59 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, v_da____,
% 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_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.97/1.59 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, v_w____, v_z ) ),
% 0.97/1.59 v_da____ ) }.
% 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_RealVector_Oreal__normed__vector( X ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.97/1.59 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.97/1.59 ( X, Y ) ), c_RealVector_Onorm__class_Onorm( X,
% 0.97/1.59 c_Groups_Ominus__class_Ominus( X, Z, 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 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.97/1.59 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, Z,
% 0.97/1.59 Y ) ) = c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus
% 0.97/1.59 ( X, Y, Z ) ) }.
% 0.97/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.59 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.97/1.59 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.59 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.97/1.59 ( X, Z, Y ), ! 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( tc_RealDef_Oreal, X, 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__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_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_Ominus( X ), hAPP( c_Groups_Ominus__class_Ominus( tc_fun(
% 0.97/1.59 U, X ), T, Z ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( T, Y ),
% 0.97/1.59 hAPP( Z, Y ) ) }.
% 0.97/1.59 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, v_d____,
% 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 ), v_da____ ) }.
% 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_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_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, Y, 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 ), ! 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 ), ! 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 ), ! 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_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 , ! 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, 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_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 { ! 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( 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( 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__eq( X, Z
% 0.97/1.59 , Y ), Y = Z, 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 ), 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_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_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, Y, Z ) }.
% 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_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_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_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, 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( 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_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( 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_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__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( 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_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.59 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.97/1.59 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, U, T ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.59 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.97/1.59 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, U, T ) }.
% 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 { ! 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 { ! 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_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, T, Z ),
% 0.97/1.59 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 ), 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, 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 ), Z = Y }.
% 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_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 ), ! 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 ), ! 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 ), ! 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 ), ! 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_Opreorder( 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_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_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_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_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.97/1.59 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! U = T, Z = Y }.
% 0.97/1.59 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.97/1.59 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! Z = Y, U = T }.
% 0.97/1.59 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 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 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, v_da____,
% 0.97/1.59 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, v_e, v_m____ ) ) }.
% 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_Oabs__class_Oabs( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.97/1.59 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.97/1.59 ( X, Y ) ) ), c_RealVector_Onorm__class_Onorm( X,
% 0.97/1.59 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.97/1.59 c_RealDef_Opositive( c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X,
% 0.97/1.59 Y ) ) }.
% 0.97/1.59 { ! c_RealDef_Opositive( c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X
% 0.97/1.59 , Y ) ), c_Orderings_Oord__class_Oless( 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 ), v_d____ ) }.
% 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_RealVector_Oreal__normed__vector( X ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.97/1.59 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.97/1.59 ( X, Y ) ), c_RealVector_Onorm__class_Onorm( X,
% 0.97/1.59 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) ) }.
% 0.97/1.59 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.59 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, Z,
% 0.97/1.59 Y ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.97/1.59 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.97/1.59 ( X, Y ) ) ) }.
% 0.97/1.59 { ! class_Orderings_Odense__linorder( X ), c_Orderings_Oord__class_Oless( X
% 0.97/1.59 , skol3( X, T, Z ), Z ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.59 { ! class_Orderings_Odense__linorder( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, skol3( X, Y, Z ), Y ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.59 { ! class_Orderings_Odense__linorder( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.59 ( X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z, skol4( X, U, Z, W ) ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, Y, T ) }.
% 0.97/1.59 { ! class_Orderings_Odense__linorder( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.59 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, skol4( X, U, Z, T )
% 0.97/1.59 , T ), c_Orderings_Oord__class_Oless__eq( X, Y, T ) }.
% 0.97/1.59 { ! class_Orderings_Odense__linorder( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.59 ( X, Z, Y ), c_Orderings_Oord__class_Oless( X, skol4( X, Y, Z, T ), Y ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, Y, T ) }.
% 0.97/1.59 { ! class_Orderings_Oorder( Y ), ! class_Orderings_Oorder( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, T, Z ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( Y, W, hAPP( U, T ) ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, skol51( X, Y, U ), skol5( X, Y, U ) ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( Y, W, hAPP( U, Z ) ) }.
% 0.97/1.59 { ! class_Orderings_Oorder( Y ), ! class_Orderings_Oorder( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, T, Z ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( Y, W, hAPP( U, T ) ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( Y, hAPP( U, skol51( X, Y, U ) ), hAPP( U,
% 0.97/1.59 skol5( X, Y, U ) ) ), c_Orderings_Oord__class_Oless( Y, W, hAPP( U, Z ) )
% 0.97/1.59 }.
% 0.97/1.59 { ! class_Orderings_Oorder( Y ), ! class_Orderings_Oorder( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, T, Z ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( Y, W, hAPP( U, T ) ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, skol52( X, Y, U ), skol6( X, Y, U )
% 0.97/1.59 ), c_Orderings_Oord__class_Oless( Y, W, hAPP( U, Z ) ) }.
% 0.97/1.59 { ! class_Orderings_Oorder( Y ), ! class_Orderings_Oorder( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, T, Z ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( Y, W, hAPP( U, T ) ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( Y, hAPP( U, skol52( X, Y, U ) ), hAPP
% 0.97/1.59 ( U, skol6( X, Y, U ) ) ), c_Orderings_Oord__class_Oless( Y, W, hAPP( U,
% 0.97/1.59 Z ) ) }.
% 0.97/1.59 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), v_m____ ) }.
% 0.97/1.59 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), v_e ) }.
% 0.97/1.59 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, v_d____,
% 0.97/1.59 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, v_e, v_m____ ) ) }.
% 0.97/1.59 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.97/1.59 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, v_e, v_m____ ) ) }.
% 0.97/1.59 { ! c_RealDef_Opositive( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) )
% 0.97/1.59 }.
% 0.97/1.59 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.97/1.59 c_Groups_Oabs__class_Oabs( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59 { c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, X ) =
% 0.97/1.59 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) }.
% 0.97/1.59 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.97/1.59 c_Groups_Oabs__class_Oabs( X, c_Groups_Oabs__class_Oabs( X, Y ) ) =
% 0.97/1.59 c_Groups_Oabs__class_Oabs( X, Y ) }.
% 0.97/1.59 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.97/1.59 c_Groups_Oabs__class_Oabs( X, c_Groups_Oplus__class_Oplus( X,
% 0.97/1.59 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ) )
% 0.97/1.59 = c_Groups_Oplus__class_Oplus( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.97/1.59 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.97/1.59 { ! class_RealVector_Oreal__normed__field( X ),
% 0.97/1.59 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.97/1.59 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.97/1.59 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 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_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.97/1.59 , Y = 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_Ozero__class_Ozero( X ) =
% 0.97/1.59 c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 0.97/1.59 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.97/1.59 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.97/1.59 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.97/1.59 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.97/1.59 X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }
% 0.97/1.59 .
% 0.97/1.59 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.97/1.59 X ), Z, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z )
% 0.97/1.59 }.
% 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( tc_fun( T, X ), Y, Z
% 0.97/1.59 ), c_Orderings_Oord__class_Oless( tc_fun( T, X ), Z, Y ) }.
% 0.97/1.59 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Y =
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X, Y,
% 0.97/1.59 Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59 { ! class_Rings_Odivision__ring__inverse__zero( X ), Y =
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X, Y,
% 0.97/1.59 Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.59 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.97/1.59 c_Groups_Oabs__class_Oabs( X, Y ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! Y =
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oabs__class_Oabs( X, Y ) =
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59 { ! class_Groups_Oab__semigroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.59 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.97/1.59 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.97/1.59 { ! class_RealVector_Oreal__normed__field( X ),
% 0.97/1.59 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, T, Z
% 0.97/1.59 ), Y ) = c_Groups_Oplus__class_Oplus( X, c_Rings_Oinverse__class_Odivide
% 0.97/1.59 ( X, T, Y ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.97/1.59 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.97/1.59 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.97/1.59 T, Y ), Z = Y }.
% 0.97/1.59 { ! class_Groups_Ocancel__semigroup__add( X ), ! Z = Y,
% 0.97/1.59 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.97/1.59 T, Y ) }.
% 0.97/1.59 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.97/1.59 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.97/1.59 Y, Z ), T = Y }.
% 0.97/1.59 { ! class_Groups_Ocancel__semigroup__add( X ), ! T = Y,
% 0.97/1.59 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.97/1.59 Y, Z ) }.
% 0.97/1.59 { ! c_RealDef_Opositive( X ), ! c_RealDef_Opositive( Y ),
% 0.97/1.59 c_RealDef_Opositive( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X, Y
% 0.97/1.59 ) ) }.
% 0.97/1.59 { ! class_RealVector_Oreal__normed__field( X ), Y =
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X,
% 0.97/1.59 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 0.97/1.59 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.97/1.59 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.97/1.59 ( X, Y ) ) }.
% 0.97/1.59 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.59 , c_Rings_Oinverse__class_Odivide( X, Y, Y ) = c_Groups_Oone__class_Oone
% 0.97/1.59 ( X ) }.
% 0.97/1.59 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.59 , ! c_Rings_Oinverse__class_Odivide( X, Z, Y ) =
% 0.97/1.59 c_Groups_Oone__class_Oone( X ), Z = Y }.
% 0.97/1.59 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.59 , ! Z = Y, c_Rings_Oinverse__class_Odivide( X, Z, Y ) =
% 0.97/1.59 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_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, T, c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.97/1.59 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.97/1.59 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.97/1.59 T, Y ), Z = Y }.
% 0.97/1.59 { ! class_Groups_Ocancel__ab__semigroup__add( X ), !
% 0.97/1.59 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.97/1.59 T, Y ), Z = Y }.
% 0.97/1.59 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.97/1.59 c_Groups_Oplus__class_Oplus( X, Z, T ) = c_Groups_Oplus__class_Oplus( X,
% 0.97/1.59 Y, T ), Z = Y }.
% 0.97/1.59 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.97/1.59 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.97/1.59 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ),
% 0.97/1.59 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.97/1.59 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.97/1.59 c_Rings_Oinverse__class_Odivide( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.59 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.59 }.
% 0.97/1.59 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 0.97/1.59 c_Groups_Oplus__class_Oplus( X, Z, Y ) ), c_Groups_Oplus__class_Oplus( X
% 0.97/1.59 , c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) )
% 0.97/1.59 ) }.
% 0.97/1.59 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.59 ), c_Groups_Oabs__class_Oabs( X, Y ) = Y }.
% 0.97/1.59 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( 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_Oordered__ab__group__add__abs( X ), ! Y =
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.59 c_Groups_Oabs__class_Oabs( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.59 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.59 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.97/1.59 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.59 c_Groups_Oabs__class_Oabs( X, Y ) = Y }.
% 0.97/1.59 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.59 c_Groups_Oabs__class_Oabs( X, Y ) ), ! Y = c_Groups_Ozero__class_Ozero( X
% 0.97/1.59 ) }.
% 0.97/1.59 { ! class_Groups_Oordered__ab__group__add__abs( 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 ), c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.97/1.59 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X, Y ),
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.59 { ! class_Groups_Oordered__comm__monoid__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, Z,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.59 , c_Groups_Oplus__class_Oplus( X, Y, Z ), c_Groups_Ozero__class_Ozero( X
% 0.97/1.59 ) ) }.
% 0.97/1.59 { ! class_Groups_Oordered__comm__monoid__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, T, Z ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.97/1.59 Z, Y ) ) }.
% 0.97/1.59 { ! class_Groups_Oordered__comm__monoid__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, T, Z ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.97/1.59 Y, Z ) ) }.
% 0.97/1.59 { ! class_Groups_Oordered__comm__monoid__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_Ozero__class_Ozero(
% 0.97/1.59 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 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_Oordered__comm__monoid__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_Ozero__class_Ozero(
% 0.97/1.59 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.97/1.59 .
% 0.97/1.59 { ! class_Groups_Oordered__comm__monoid__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_Ozero__class_Ozero(
% 0.97/1.59 X ), Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), ! Z =
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.97/1.59 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59 { ! class_Groups_Oordered__comm__monoid__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_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 ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.97/1.59 ) }.
% 0.97/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Y,
% 0.97/1.59 Y ), 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 ) }.
% 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, c_Groups_Oplus__class_Oplus( X
% 0.97/1.59 , Y, 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_Ozero__class_Ozero( X ),
% 0.97/1.59 c_Groups_Oplus__class_Oplus( X, Y, Y ) ),
% 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_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_Ozero__class_Ozero( X
% 0.97/1.59 ), c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.97/1.59 { ! class_Fields_Ofield__inverse__zero( X ), !
% 0.97/1.59 class_RealVector_Oreal__normed__field( X ),
% 0.97/1.59 c_RealVector_Onorm__class_Onorm( X, c_Rings_Oinverse__class_Odivide( X, Z
% 0.97/1.59 , Y ) ) = c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.97/1.59 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.97/1.59 ( X, Y ) ) }.
% 0.97/1.59 { ! class_Groups_Oordered__comm__monoid__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, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.59 , c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.97/1.59 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.59 { ! class_Groups_Oordered__comm__monoid__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_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 c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.97/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.97/1.59 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( 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, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, 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_Ozero__class_Ozero( X ),
% 0.97/1.59 c_Groups_Oplus__class_Oplus( X, Y, Y ) ), c_Orderings_Oord__class_Oless(
% 0.97/1.59 X, 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( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.59 c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.97/1.59 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, Y, X ) ), alpha1( X, Y
% 0.97/1.59 ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.97/1.59 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, Y, X ) ), alpha27( X,
% 0.97/1.59 Y ) }.
% 0.97/1.59 { ! alpha1( X, Y ), ! alpha27( X, Y ), c_Orderings_Oord__class_Oless__eq(
% 0.97/1.59 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.97/1.59 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, Y, X ) ) }.
% 0.97/1.59 { ! alpha27( X, Y ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), alpha27( X, Y ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), alpha27( X, Y ) }.
% 0.97/1.59 { ! alpha1( X, Y ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y
% 0.97/1.59 , c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), alpha1( X, Y ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), alpha1( X, Y ) }.
% 0.97/1.59 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X,
% 0.97/1.59 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.59 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.97/1.59 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.97/1.59 c_Groups_Ominus__class_Ominus( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.97/1.59 Y ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.97/1.59 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X, Y
% 0.97/1.59 , c_Groups_Oone__class_Oone( X ) ) = Y }.
% 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_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_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 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.97/1.59 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oone__class_Oone
% 0.97/1.59 ( tc_RealDef_Oreal ), c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) )
% 0.97/1.59 ) }.
% 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_Oplus__class_Oplus( X,
% 0.97/1.59 c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ) ) }.
% 0.97/1.59 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 0.97/1.59 c_Groups_Ominus__class_Ominus( X, Z, Y ) ), c_Groups_Oplus__class_Oplus(
% 0.97/1.59 X, c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) )
% 0.97/1.59 ) }.
% 0.97/1.59 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 0.97/1.59 c_Groups_Ominus__class_Ominus( X, c_Groups_Oplus__class_Oplus( X, U, T )
% 0.97/1.59 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) ), c_Groups_Oplus__class_Oplus
% 0.97/1.59 ( X, c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, U, Z
% 0.97/1.59 ) ), c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, T,
% 0.97/1.59 Y ) ) ) ) }.
% 0.97/1.59 { ! class_Groups_Oordered__comm__monoid__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( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.97/1.59 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.97/1.59 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.59 { ! class_Groups_Oordered__comm__monoid__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__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.97/1.59 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.97/1.59 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.59 { ! class_Groups_Oordered__comm__monoid__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( X, T, Z ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.97/1.59 ) ) }.
% 0.97/1.59 { ! class_Groups_Oordered__comm__monoid__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__eq( X, T, Z ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.97/1.59 ) ) }.
% 0.97/1.59 { ! class_Groups_Oordered__comm__monoid__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( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.59 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.59 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.97/1.59 { ! class_Groups_Oordered__comm__monoid__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__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.59 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.59 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs
% 0.97/1.59 ( tc_RealDef_Oreal, X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 0.97/1.59 , 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_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.97/1.59 ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.97/1.59 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.97/1.59 ( 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, Z ), Y ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_RealVector_Onorm__class_Onorm( X, U ), T ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, Z, U
% 0.97/1.59 ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, T ) ) }.
% 0.97/1.59 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oabs__class_Oabs( X, Y
% 0.97/1.59 ) ) }.
% 0.97/1.59 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.97/1.59 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.59 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.97/1.59 c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Z, Y ) )
% 0.97/1.59 = c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Y, Z )
% 0.97/1.59 ) }.
% 0.97/1.59 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.59 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y ),
% 0.97/1.59 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.97/1.59 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.97/1.59 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X ) ),
% 0.97/1.59 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, 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_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__vector( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.97/1.59 c_RealVector_Onorm__class_Onorm( X, Y ) ), ! 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_Orderings_Oord__class_Oless(
% 0.97/1.59 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.97/1.59 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.97/1.59 { ! class_RealVector_Oreal__normed__field( X ),
% 0.97/1.59 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus( X, T,
% 0.97/1.59 Z ), Y ) = c_Groups_Ominus__class_Ominus( X,
% 0.97/1.59 c_Rings_Oinverse__class_Odivide( X, T, Y ),
% 0.97/1.59 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.97/1.59 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.97/1.59 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.97/1.59 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.97/1.59 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.97/1.59 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.97/1.59 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.59 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( 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_Oplus__class_Oplus( X, T,
% 0.97/1.59 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.97/1.59 { ! class_Groups_Oordered__ab__semigroup__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_Oplus__class_Oplus( X, Z,
% 0.97/1.59 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.97/1.59 { ! class_Groups_Oordered__ab__semigroup__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_Oplus__class_Oplus( X, T,
% 0.97/1.59 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.97/1.59 { ! class_Groups_Oordered__ab__semigroup__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, U, T ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.97/1.59 U ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.97/1.59 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.97/1.59 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.59 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.97/1.59 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.59 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.97/1.59 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.97/1.59 ( X, Z, Y ) }.
% 0.97/1.59 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, T )
% 0.97/1.59 , c_Groups_Oplus__class_Oplus( X, Y, T ) ), c_Orderings_Oord__class_Oless
% 0.97/1.59 ( X, Z, Y ) }.
% 0.97/1.59 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.59 ( X, U, T ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.59 c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X, Y
% 0.97/1.59 , T ) ) }.
% 0.97/1.59 { ! class_Groups_Oordered__cancel__ab__semigroup__add( 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_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.97/1.59 , T, Y ) ) }.
% 0.97/1.59 { ! class_Groups_Oordered__cancel__ab__semigroup__add( 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_Oplus__class_Oplus( X, Z, T ), c_Groups_Oplus__class_Oplus( X
% 0.97/1.59 , Y, T ) ) }.
% 0.97/1.59 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.97/1.59 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.97/1.59 ( X, Z, Y ) }.
% 0.97/1.59 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( 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_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.97/1.59 , T, Y ) ) }.
% 0.97/1.59 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.97/1.59 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ), c_Orderings_Oord__class_Oless
% 0.97/1.59 ( X, T, Y ) }.
% 0.97/1.59 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, T, Y ), c_Orderings_Oord__class_Oless(
% 0.97/1.59 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.97/1.59 , Y, Z ) ) }.
% 0.97/1.59 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Oabs__class_Oabs
% 0.97/1.59 ( tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( X, Y ) ) =
% 0.97/1.59 c_RealVector_Onorm__class_Onorm( X, Y ) }.
% 0.97/1.59 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.59 c_Groups_Ominus__class_Ominus( X, Z, Y ), Y ) = Z }.
% 0.97/1.59 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.97/1.59 c_Groups_Oplus__class_Oplus( X, Z, Y ), 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,
% 0.97/1.59 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ),
% 0.97/1.59 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, X ) ) }.
% 0.97/1.59 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.97/1.59 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y, Y )
% 0.97/1.59 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59 { ! class_Groups_Oab__group__add( X ), ! Z = Y,
% 0.97/1.59 c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.97/1.59 ) }.
% 0.97/1.59 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.97/1.59 Z, Y ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.97/1.59 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.97/1.59 ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.97/1.59 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ominus__class_Ominus(
% 0.97/1.59 X, Z, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.97/1.59 , Y, c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) )
% 0.97/1.59 ) }.
% 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 { ! class_Rings_Olinordered__semidom( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.59 { ! class_Rings_Olinordered__semidom( X ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.59 c_Groups_Oone__class_Oone( X ) ) }.
% 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_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, c_Groups_Ominus__class_Ominus( X,
% 0.97/1.59 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.97/1.59 , Y ) ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.97/1.59 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, U,
% 0.97/1.59 Z ) ), c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus
% 0.97/1.59 ( X, T, Y ) ) ) ) }.
% 0.97/1.59 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 0.97/1.59 c_Groups_Ominus__class_Ominus( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.97/1.59 c_Groups_Oabs__class_Oabs( X, Y ) ) ), c_Groups_Oabs__class_Oabs( X,
% 0.97/1.59 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) }.
% 0.97/1.59 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X,
% 0.97/1.59 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ),
% 0.97/1.59 c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Z, Y ) )
% 0.97/1.59 ) }.
% 0.97/1.59 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X,
% 0.97/1.59 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ),
% 0.97/1.59 c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Y, Z ) )
% 0.97/1.59 ) }.
% 0.97/1.59 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, U, T ), c_Orderings_Oord__class_Oless(
% 0.97/1.59 X, c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X
% 0.97/1.59 , Y, T ) ) }.
% 0.97/1.59 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( 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( X, c_Groups_Oplus__class_Oplus( X, Z, U )
% 0.97/1.59 , c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 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_Ominus__class_Ominus( X, Z
% 0.97/1.59 , 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__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 0.97/1.59 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.59 { ! class_Groups_Oordered__ab__group__add( 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_Ominus__class_Ominus( X, Z, Y ), c_Groups_Ozero__class_Ozero
% 0.97/1.59 ( X ) ) }.
% 0.97/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.97/1.59 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.97/1.59 , Z, Y ) }.
% 0.97/1.59 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 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 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ),
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ),
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 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,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol7 ) }.
% 0.97/1.59 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, skol7,
% 0.97/1.59 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.97/1.59 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, skol7,
% 0.97/1.59 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, v_e, v_m____ ) ) }.
% 0.97/1.59 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol8 ) }.
% 0.97/1.59 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, skol8,
% 0.97/1.59 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.97/1.59 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, skol8,
% 0.97/1.59 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, v_e, v_m____ ) ) }.
% 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 ), v_d____ ), v_m____ ),
% 0.97/1.59 v_e ) }.
% 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 ), v_d____ ), v_m____ ) )
% 0.97/1.59 }.
% 0.97/1.59 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.59 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oabs__class_Oabs( X, Z ), Y
% 0.97/1.59 ) = c_Groups_Oabs__class_Oabs( X, c_Rings_Oinverse__class_Odivide( X, Z
% 0.97/1.59 , Y ) ) }.
% 0.97/1.59 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.59 , c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, T, Z )
% 0.97/1.59 ), Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus
% 0.97/1.59 ( X, Z, Y ), T ) }.
% 0.97/1.59 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.59 , c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, T, Z )
% 0.97/1.59 ), Y ), c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus
% 0.97/1.59 ( X, Z, Y ) ) }.
% 0.97/1.59 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.59 , c_Groups_Ominus__class_Ominus( X, Z, Y ), T ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.97/1.59 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X,
% 0.97/1.59 c_Groups_Ominus__class_Ominus( X, T, Z ) ), Y ) }.
% 0.97/1.59 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.59 X, Z, Y ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.59 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.97/1.59 ), c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.97/1.59 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.97/1.59 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.59 X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.59 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.97/1.59 ), c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.97/1.59 c_Groups_Oone__class_Oone( X ) ) ) ) }.
% 0.97/1.59 { ! class_Fields_Olinordered__field( 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( 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 ), c_Rings_Oinverse__class_Odivide( X, Y, Z ) ) }.
% 0.97/1.59 { ! class_Fields_Olinordered__field( 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( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.59 , Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.59 c_Rings_Oinverse__class_Odivide( X, Y, Z ), c_Groups_Ozero__class_Ozero(
% 0.97/1.59 X ) ) }.
% 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 { 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 { ! 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_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 { 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 { ! 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_Fields_Ofield__inverse__zero( X ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Odivide( X, U
% 0.97/1.59 , T ) ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 0.97/1.59 c_Rings_Oinverse__class_Odivide( 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 { ! 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_RealVector_Oreal__normed__algebra( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_RealVector_Onorm__class_Onorm( X, Z ), Y ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.59 c_RealVector_Onorm__class_Onorm( X, U ), T ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( 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 ), U ) ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), T ) ) }.
% 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_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_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( X ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.97/1.59 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.59 { ! class_Rings_Osemiring( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP
% 0.97/1.59 ( c_Groups_Otimes__class_Otimes( X ), U ), T ),
% 0.97/1.59 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.59 ( X ), Z ), T ), Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, U, Z
% 0.97/1.59 ) ), T ), 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_Oplus__class_Oplus( X, T, Z
% 0.97/1.59 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.59 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.97/1.59 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.59 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.59 Z, Y ) ) = c_Groups_Oplus__class_Oplus( 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_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.59 Z, Y ) ) = c_Groups_Oplus__class_Oplus( 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_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 0.97/1.59 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.59 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 0.97/1.59 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.59 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 0.97/1.59 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( 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_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 0.97/1.59 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( 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_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_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_Odivision__ring( X ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), T ), c_Rings_Oinverse__class_Odivide
% 0.97/1.59 ( X, Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ), 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 ), 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_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( 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_Oabs__class_Oabs( X, Z ) ),
% 0.97/1.59 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.97/1.59 { ! class_Rings_Olinordered__idom( X ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Y ) ),
% 0.97/1.59 c_Groups_Oabs__class_Oabs( X, Y ) ) = hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 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 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.97/1.59 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ) ), X ) =
% 0.97/1.59 c_Groups_Oplus__class_Oplus( 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 { ! class_Fields_Ofield__inverse__zero( X ), ! T =
% 0.97/1.59 c_Rings_Oinverse__class_Odivide( X, Z, Y ), alpha28( X, Y, Z, T ) }.
% 0.97/1.59 { ! class_Fields_Ofield__inverse__zero( X ), ! T =
% 0.97/1.59 c_Rings_Oinverse__class_Odivide( X, Z, Y ), alpha2( X, Y, T ) }.
% 0.97/1.59 { ! class_Fields_Ofield__inverse__zero( X ), ! alpha28( X, Y, Z, T ), !
% 0.97/1.59 alpha2( X, Y, T ), T = c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.97/1.59 { ! alpha28( X, Y, Z, T ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP
% 0.97/1.59 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z }.
% 0.97/1.59 { ! Y = c_Groups_Ozero__class_Ozero( X ), alpha28( X, Y, Z, T ) }.
% 0.97/1.59 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, alpha28(
% 0.97/1.59 X, Y, Z, T ) }.
% 0.97/1.59 { ! alpha2( X, Y, Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59 { Y = c_Groups_Ozero__class_Ozero( X ), alpha2( X, Y, Z ) }.
% 0.97/1.59 { ! Z = c_Groups_Ozero__class_Ozero( X ), alpha2( X, Y, Z ) }.
% 0.97/1.59 { ! class_Fields_Ofield__inverse__zero( X ), !
% 0.97/1.59 c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y, alpha29( X, Y, Z, T ) }.
% 0.97/1.59 { ! class_Fields_Ofield__inverse__zero( X ), !
% 0.97/1.59 c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y, alpha3( X, Y, Z ) }.
% 0.97/1.59 { ! class_Fields_Ofield__inverse__zero( X ), ! alpha29( X, Y, Z, T ), !
% 0.97/1.59 alpha3( X, Y, Z ), c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y }.
% 0.97/1.59 { ! alpha29( X, Y, Z, T ), Z = c_Groups_Ozero__class_Ozero( X ), T = hAPP(
% 0.97/1.59 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 0.97/1.59 { ! Z = c_Groups_Ozero__class_Ozero( X ), alpha29( X, Y, Z, T ) }.
% 0.97/1.59 { ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), alpha29(
% 0.97/1.59 X, Y, Z, T ) }.
% 0.97/1.59 { ! alpha3( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.59 { Z = c_Groups_Ozero__class_Ozero( X ), alpha3( X, Y, Z ) }.
% 0.97/1.59 { ! Y = c_Groups_Ozero__class_Ozero( X ), alpha3( X, Y, Z ) }.
% 0.97/1.59 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( 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 ), Z ), Y ) ) =
% 0.97/1.59 c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 0.97/1.59 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( 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 ), Y ), Z ) ) =
% 0.97/1.59 c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 0.97/1.59 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ), ! c_Rings_Oinverse__class_Odivide( X, U
% 0.97/1.59 , Y ) = c_Rings_Oinverse__class_Odivide( X, T, Z ), 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 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.97/1.59 c_Groups_Ozero__class_Ozero( 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_Rings_Oinverse__class_Odivide( X, U, Y ) =
% 0.97/1.59 c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 0.97/1.59 { ! c_RealDef_Opositive( X ), ! c_RealDef_Opositive( Y ),
% 0.97/1.59 c_RealDef_Opositive( hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.59 tc_RealDef_Oreal ), X ), Y ) ) }.
% 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 ) ), alpha4( X, Y, Z ), alpha30( 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, 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 ), ! alpha30( 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 { ! alpha30( 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 { ! alpha30( 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 ), alpha30( 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, 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 ) ), alpha4( 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 ) ), alpha5( X, Y
% 0.97/1.59 , Z ), alpha31( X, Y, Z ) }.
% 0.97/1.59 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha5( 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 ), ! alpha31( 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 { ! alpha31( 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 { ! alpha31( 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 ) ), alpha31( X, Y, Z ) }.
% 0.97/1.59 { ! alpha5( 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 { ! alpha5( 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 ), alpha5( X, Y, Z ) }.
% 0.97/1.59 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.97/1.59 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) }.
% 0.97/1.59 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.59 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, T,
% 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 ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.97/1.59 Z ), c_Rings_Oinverse__class_Odivide( X, T, Y ) ) }.
% 0.97/1.59 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.59 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.59 , 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_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.97/1.59 Y ), c_Rings_Oinverse__class_Odivide( X, T, Z ) ) }.
% 0.97/1.59 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.59 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.97/1.59 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ) }.
% 0.97/1.59 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.59 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.97/1.59 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.97/1.59 Y ), Z ) }.
% 0.97/1.59 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.59 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.97/1.59 ( X, T, c_Rings_Oinverse__class_Odivide( X, Z, Y ) ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.59 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.59 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.97/1.59 ( X, Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.97/1.59 Z, Y ) ) }.
% 0.97/1.59 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.59 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.59 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.97/1.59 Z, Y ) ) }.
% 0.97/1.59 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.59 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.59 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.97/1.59 Y ), Z ) }.
% 0.97/1.59 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.59 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.59 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.59 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.59 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.59 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.97/1.59 Y ), Z ) }.
% 0.97/1.59 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.59 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.59 ( X, T, c_Rings_Oinverse__class_Odivide( X, Z, Y ) ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.97/1.59 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.59 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.59 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.97/1.59 Z, Y ) ) }.
% 0.97/1.59 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.97/1.59 Z ), Y ), alpha32( X, Y, Z, T ) }.
% 0.97/1.59 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.97/1.59 Z ), Y ), alpha51( X, Y, Z, T ) }.
% 0.97/1.59 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha32( X, Y, Z
% 0.97/1.59 , T ), ! alpha51( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.59 c_Rings_Oinverse__class_Odivide( X, T, Z ), Y ) }.
% 0.97/1.59 { ! alpha51( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ), Z ), alpha61( X, Y, Z, T ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.97/1.59 , alpha51( X, Y, Z, T ) }.
% 0.97/1.59 { ! alpha61( X, Y, Z, T ), alpha51( X, Y, Z, T ) }.
% 0.97/1.59 { ! alpha61( X, Y, Z, T ), alpha71( X, Y, Z, T ) }.
% 0.97/1.59 { ! alpha61( X, Y, Z, T ), alpha6( X, Y, Z ) }.
% 0.97/1.59 { ! alpha71( X, Y, Z, T ), ! alpha6( X, Y, Z ), alpha61( X, Y, Z, T ) }.
% 0.97/1.59 { ! alpha71( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ) }.
% 0.97/1.59 { c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.59 alpha71( 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 ), Y ), Z ), T ), alpha71( X, Y, Z, T )
% 0.97/1.59 }.
% 0.97/1.59 { ! alpha32( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.59 T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.59 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.97/1.59 alpha32( X, Y, Z, T ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha32( X, Y, Z, T ) }.
% 0.97/1.59 { ! alpha6( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 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 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.59 , alpha6( X, Y, Z ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.97/1.59 , alpha6( X, Y, Z ) }.
% 0.97/1.59 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.97/1.59 Z, Y ) ), alpha33( X, Y, Z, T ) }.
% 0.97/1.59 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.97/1.59 Z, Y ) ), alpha52( X, Y, Z, T ) }.
% 0.97/1.59 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha33( X, Y, Z
% 0.97/1.59 , T ), ! alpha52( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 0.97/1.59 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.97/1.59 { ! alpha52( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ), Y ), alpha62( X, Y, Z, T ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.97/1.59 , alpha52( X, Y, Z, T ) }.
% 0.97/1.59 { ! alpha62( X, Y, Z, T ), alpha52( X, Y, Z, T ) }.
% 0.97/1.59 { ! alpha62( X, Y, Z, T ), alpha72( X, Y, Z, T ) }.
% 0.97/1.59 { ! alpha62( X, Y, Z, T ), alpha7( X, Y, T ) }.
% 0.97/1.59 { ! alpha72( X, Y, Z, T ), ! alpha7( X, Y, T ), alpha62( X, Y, Z, T ) }.
% 0.97/1.59 { ! alpha72( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.59 { c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.59 alpha72( X, Y, Z, T ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha72( X, Y, Z, T ) }.
% 0.97/1.59 { ! alpha33( X, Y, Z, T ), ! 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 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.97/1.59 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.59 alpha33( 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 ), Y ), Z ), alpha33( X, Y, Z, T )
% 0.97/1.59 }.
% 0.97/1.59 { ! alpha7( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.59 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 , alpha7( X, Y, Z ) }.
% 0.97/1.59 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.59 , alpha7( X, Y, 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 ), 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__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_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, 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, 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, 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__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 ), 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 ), 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, 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__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__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 ) ), alpha8( X, Y, Z, T ),
% 0.97/1.59 alpha34( X, Y, Z, T ) }.
% 0.97/1.59 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha8( 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 ), ! alpha34( 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 { ! alpha34( 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 { ! alpha34( 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 ), alpha34( X, Y, Z, T ) }.
% 0.97/1.59 { ! alpha8( 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 { ! alpha8( 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 ), alpha8( 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 ), Y ), Z ) ), alpha9( X, Y, Z, T ),
% 0.97/1.59 alpha35( X, Y, Z, T ) }.
% 0.97/1.59 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha9( 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 ), ! alpha35( 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 { ! alpha35( 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 { ! alpha35( 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 ), alpha35( X, Y, Z, T ) }.
% 0.97/1.59 { ! alpha9( 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 { ! alpha9( 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 ), alpha9( X, Y, Z, T ) }.
% 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_Fields_Ofield__inverse__zero( X ), Y =
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, T,
% 0.97/1.59 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 0.97/1.59 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.97/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Y ) }.
% 0.97/1.59 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.59 c_Groups_Oplus__class_Oplus( X, T, c_Rings_Oinverse__class_Odivide( X, Z
% 0.97/1.59 , Y ) ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus
% 0.97/1.59 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), Z ), Y ) }
% 0.97/1.59 .
% 0.97/1.59 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.59 c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ) =
% 0.97/1.59 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.97/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) }.
% 0.97/1.59 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.59 c_Groups_Oplus__class_Oplus( X, c_Rings_Oinverse__class_Odivide( X, T, Y
% 0.97/1.59 ), Z ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus
% 0.97/1.59 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) }
% 0.97/1.59 .
% 0.97/1.59 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.59 c_Rings_Oinverse__class_Odivide( X, U, Y ),
% 0.97/1.59 c_Rings_Oinverse__class_Odivide( X, T, Z ) ) =
% 0.97/1.59 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, hAPP
% 0.97/1.59 ( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.59 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.97/1.59 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ominus__class_Ominus( X,
% 0.97/1.59 c_Rings_Oinverse__class_Odivide( X, U, Y ),
% 0.97/1.59 c_Rings_Oinverse__class_Odivide( X, T, Z ) ) =
% 0.97/1.59 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus( X,
% 0.97/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.59 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.59 c_Groups_Ominus__class_Ominus( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.97/1.59 Y ), Z ) = c_Rings_Oinverse__class_Odivide( X,
% 0.97/1.59 c_Groups_Ominus__class_Ominus( X, T, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) }.
% 0.97/1.59 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.59 c_Groups_Ominus__class_Ominus( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.97/1.59 Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X,
% 0.97/1.59 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), T ), Z ), Y ) }.
% 0.97/1.59 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.59 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.59 ( X, c_Groups_Oone__class_Oone( X ), 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_Rings_Oring( X ), c_Groups_Ominus__class_Ominus( 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 ) ) =
% 0.97/1.59 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.59 ( X ), U ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 0.97/1.59 Z ) ), Y ) ) }.
% 0.97/1.59 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.97/1.59 c_Groups_Ominus__class_Ominus( 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 ) ) =
% 0.97/1.59 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.97/1.59 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.97/1.59 X, U, Z ) ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 0.97/1.59 Z ) ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 0.97/1.59 c_Groups_Ominus__class_Ominus( X, T, Y ) ) ) }.
% 0.97/1.59 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.97/1.59 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.59 ( X ), Z ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.97/1.59 Z ) ), U ), T ) = Y }.
% 0.97/1.59 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.97/1.59 Z ) ), U ), T ) = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.97/1.59 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.59 ( X ), Z ), U ), Y ) }.
% 0.97/1.59 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.97/1.59 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.59 ( X ), Z ), U ), Y ), T = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.97/1.59 W ) ), U ), Y ) }.
% 0.97/1.59 { ! class_Rings_Oring( X ), ! T = c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.97/1.59 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.97/1.59 X, Z, W ) ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.97/1.59 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.59 ( X ), Z ), U ), Y ) }.
% 0.97/1.59 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.59 , ! T = c_Rings_Oinverse__class_Odivide( X, Z, Y ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z }.
% 0.97/1.59 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.59 , ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, T =
% 0.97/1.59 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.97/1.59 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.59 , ! c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z, T = hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.97/1.59 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.59 , ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.97/1.59 c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z }.
% 0.97/1.59 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.59 , ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.97/1.59 c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z }.
% 0.97/1.59 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.59 , ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, T =
% 0.97/1.59 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.97/1.59 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.59 , c_Groups_Oabs__class_Oabs( X, Z ), Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.59 ( X, c_Groups_Oabs__class_Oabs( X, U ), T ),
% 0.97/1.59 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 0.97/1.59 c_Groups_Oabs__class_Oabs( X, U ) ), hAPP( hAPP(
% 0.97/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 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 { ! c_Groups_Oplus__class_Oplus( 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 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y =
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.59 { ! c_Groups_Oplus__class_Oplus( 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 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X =
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.59 { ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! X =
% 0.97/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.97/1.59 c_Groups_Oplus__class_Oplus( 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 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.59 { ! class_Fields_Olinordered__field__inverse__zero( 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, T, 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 ), Z ), Y ) ),
% 0.97/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.97/1.59 , T, Z ), c_Rings_Oinverse__class_Odivide( X, T, Y ) ) }.
% 0.97/1.59 { ! class_Fields_Olinordered__field( 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
% 0.97/1.60 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.60 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.97/1.60 , T, Y ), c_Rings_Oinverse__class_Odivide( X, T, Z ) ) }.
% 0.97/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.60 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.97/1.60 , T, Y ), Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ) }.
% 0.97/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.60 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 ), Z ), Y ), T ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.97/1.60 , T, Y ), Z ) }.
% 0.97/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.60 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.97/1.60 ( X, Z, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Z, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.60 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, 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, T, c_Rings_Oinverse__class_Odivide
% 0.97/1.60 ( X, Z, Y ) ) }.
% 0.97/1.60 { ! class_Fields_Olinordered__field( 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__eq( X, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.97/1.60 ( X, Z, Y ) ) }.
% 0.97/1.60 { ! class_Fields_Olinordered__field( 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__eq( X, T, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.97/1.60 , T, Y ), Z ) }.
% 0.97/1.60 { ! class_Fields_Olinordered__field( 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__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.97/1.60 , T, Y ), Z ), c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.60 { ! class_Fields_Olinordered__field( 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__eq( X, T, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.97/1.60 , T, Y ), Z ) }.
% 0.97/1.60 { ! class_Fields_Olinordered__field( 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__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.97/1.60 ( X, Z, Y ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.97/1.60 { ! class_Fields_Olinordered__field( 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__eq( X, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.97/1.60 ( X, Z, Y ) ) }.
% 0.97/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.97/1.60 , T, Z ), Y ), alpha36( X, Y, Z, T ) }.
% 0.97/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.97/1.60 , T, Z ), Y ), alpha53( X, Y, Z, T ) }.
% 0.97/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha36( X, Y, Z
% 0.97/1.60 , T ), ! alpha53( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.60 c_Rings_Oinverse__class_Odivide( X, T, Z ), Y ) }.
% 0.97/1.60 { ! alpha53( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( X ), Z ), alpha63( X, Y, Z, T ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.97/1.60 , alpha53( X, Y, Z, T ) }.
% 0.97/1.60 { ! alpha63( X, Y, Z, T ), alpha53( X, Y, Z, T ) }.
% 0.97/1.60 { ! alpha63( X, Y, Z, T ), alpha73( X, Y, Z, T ) }.
% 0.97/1.60 { ! alpha63( X, Y, Z, T ), alpha10( X, Y, Z ) }.
% 0.97/1.60 { ! alpha73( X, Y, Z, T ), ! alpha10( X, Y, Z ), alpha63( X, Y, Z, T ) }.
% 0.97/1.60 { ! alpha73( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.60 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ) }.
% 0.97/1.60 { c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.60 alpha73( X, Y, 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 ), Z ), T ), alpha73( X, Y, Z, T )
% 0.97/1.60 }.
% 0.97/1.60 { ! alpha36( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless__eq
% 0.97/1.60 ( X, T, hAPP( hAPP( 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 alpha36( X, Y, Z, T ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha36( X, Y, Z, T ) }.
% 0.97/1.60 { ! alpha10( X, Y, Z ), c_Orderings_Oord__class_Oless( 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_Ozero__class_Ozero( X ), Y ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.60 , alpha10( X, Y, Z ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.60 , Y ), alpha10( X, Y, Z ) }.
% 0.97/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.97/1.60 ( X, Z, Y ) ), alpha37( X, Y, Z, T ) }.
% 0.97/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.97/1.60 ( X, Z, Y ) ), alpha54( X, Y, Z, T ) }.
% 0.97/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha37( X, Y, Z
% 0.97/1.60 , T ), ! alpha54( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( X, T,
% 0.97/1.60 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.97/1.60 { ! alpha54( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( X ), Y ), alpha64( X, Y, Z, T ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.97/1.60 , alpha54( X, Y, Z, T ) }.
% 0.97/1.60 { ! alpha64( X, Y, Z, T ), alpha54( X, Y, Z, T ) }.
% 0.97/1.60 { ! alpha64( X, Y, Z, T ), alpha74( X, Y, Z, T ) }.
% 0.97/1.60 { ! alpha64( X, Y, Z, T ), alpha11( X, Y, T ) }.
% 0.97/1.60 { ! alpha74( X, Y, Z, T ), ! alpha11( X, Y, T ), alpha64( X, Y, Z, T ) }.
% 0.97/1.60 { ! alpha74( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.60 , Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.60 { c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.60 alpha74( X, Y, Z, T ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( X, Z, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha74( X, Y, Z, T ) }.
% 0.97/1.60 { ! alpha37( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless__eq
% 0.97/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.97/1.60 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.60 alpha37( X, Y, 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 ), T ), Y ), Z ), alpha37( X, Y, Z, T )
% 0.97/1.60 }.
% 0.97/1.60 { ! alpha11( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.60 , Z, 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 , alpha11( X, Y, Z ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.97/1.60 ) ), alpha11( X, Y, 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, 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 ), Z ), Y ), 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_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, 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_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_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_Rings_Oordered__ring__abs( X ), alpha85( X, Z ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.60 ), c_Groups_Oabs__class_Oabs( 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( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 0.97/1.60 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.97/1.60 { ! class_Rings_Oordered__ring__abs( X ), alpha85( X, Z ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.60 ), c_Groups_Oabs__class_Oabs( 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( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 0.97/1.60 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.97/1.60 { ! alpha85( X, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.97/1.60 { ! alpha85( X, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( 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, Y, c_Groups_Ozero__class_Ozero
% 0.97/1.60 ( X ) ), alpha85( X, 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 ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 0.97/1.60 Y ) = c_Groups_Oabs__class_Oabs( X, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), 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, 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 { ! 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 ), X ), Z ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ),
% 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 ), X ), Z ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 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_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_Groups_Oabs__class_Oabs( X, c_Rings_Oinverse__class_Odivide( X, Z, Y )
% 0.97/1.60 ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oabs__class_Oabs( X, Z
% 0.97/1.60 ), c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.97/1.60 { ! class_Fields_Olinordered__field__inverse__zero( 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, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.60 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 0.97/1.60 ( X, Y, T ), c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 0.97/1.60 { ! class_Fields_Olinordered__field__inverse__zero( 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 ), T
% 0.97/1.60 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 0.97/1.60 ( X, Z, T ), c_Rings_Oinverse__class_Odivide( X, Y, T ) ) }.
% 0.97/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.97/1.60 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ), alpha12( X, Y, Z ), alpha38
% 0.97/1.60 ( X, Y, Z ) }.
% 0.97/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha12( X, Y, Z
% 0.97/1.60 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 0.97/1.60 ( X, Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha38( X, Y, Z
% 0.97/1.60 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 0.97/1.60 ( X, Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.60 { ! alpha38( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.60 { ! alpha38( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 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__eq( X, c_Groups_Ozero__class_Ozero
% 0.97/1.60 ( X ), Y ), alpha38( X, Y, Z ) }.
% 0.97/1.60 { ! alpha12( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.97/1.60 { ! alpha12( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 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__eq( X, Y,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( X ) ), alpha12( X, Y, Z ) }.
% 0.97/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.60 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ), alpha13( X, Y, Z ), alpha39
% 0.97/1.60 ( X, Y, Z ) }.
% 0.97/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha13( X, Y, Z
% 0.97/1.60 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.97/1.60 ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.97/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha39( X, Y, Z
% 0.97/1.60 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.97/1.60 ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.97/1.60 { ! alpha39( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.60 { ! alpha39( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.97/1.60 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__eq( X, Y,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( X ) ), alpha39( X, Y, Z ) }.
% 0.97/1.60 { ! alpha13( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.97/1.60 { ! alpha13( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( 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 )
% 0.97/1.60 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( X ), Y ), alpha13( X, Y, Z ) }.
% 0.97/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.60 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, T,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.60 c_Rings_Oinverse__class_Odivide( X, Y, T ),
% 0.97/1.60 c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 0.97/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.60 X, 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 c_Rings_Oinverse__class_Odivide( X, Z, T ),
% 0.97/1.60 c_Rings_Oinverse__class_Odivide( X, Y, T ) ) }.
% 0.97/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.60 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60 ( X, Z, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.97/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X
% 0.97/1.60 , Y, Z ) ) }.
% 0.97/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.60 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.97/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless
% 0.97/1.60 ( X, c_Rings_Oinverse__class_Odivide( X, Y, Z ),
% 0.97/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.60 { ! class_Fields_Olinordered__field( 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, Z, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.97/1.60 ( X, c_Rings_Oinverse__class_Odivide( X, Y, Z ),
% 0.97/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.60 { ! class_Fields_Olinordered__field( 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 ), Z ), c_Orderings_Oord__class_Oless
% 0.97/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X
% 0.97/1.60 , Y, Z ) ) }.
% 0.97/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, Z,
% 0.97/1.60 Y ), c_Groups_Ozero__class_Ozero( X ) ), alpha14( X, Y, Z ), alpha40( X,
% 0.97/1.60 Y, Z ) }.
% 0.97/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha14( X, Y, Z
% 0.97/1.60 ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X
% 0.97/1.60 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha40( X, Y, Z
% 0.97/1.60 ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X
% 0.97/1.60 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.60 { ! alpha40( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.60 { ! alpha40( X, Y, Z ), 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( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.60 , ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.60 ), alpha40( X, Y, Z ) }.
% 0.97/1.60 { ! alpha14( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.97/1.60 { ! alpha14( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 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, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.60 ), alpha14( X, Y, Z ) }.
% 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 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ), alpha15( X, Y, Z ), alpha41
% 0.97/1.60 ( X, Y, Z ) }.
% 0.97/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha15( X, Y, Z
% 0.97/1.60 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.60 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.97/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha41( X, Y, Z
% 0.97/1.60 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.60 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.97/1.60 { ! alpha41( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.60 { ! alpha41( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 0.97/1.60 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, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.60 ), alpha41( X, Y, Z ) }.
% 0.97/1.60 { ! alpha15( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.97/1.60 { ! alpha15( X, Y, Z ), 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( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.97/1.60 , ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.60 ), alpha15( X, Y, Z ) }.
% 0.97/1.60 { ! class_Fields_Olinordered__field( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.60 X ), c_Groups_Oabs__class_Oabs( X, c_Rings_Oinverse__class_Odivide( X, Z
% 0.97/1.60 , Y ) ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oabs__class_Oabs(
% 0.97/1.60 X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.97/1.60 { ! class_Fields_Olinordered__field( 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__eq( X, c_Groups_Ozero__class_Ozero
% 0.97/1.60 ( X ), c_Rings_Oinverse__class_Odivide( X, Y, Z ) ) }.
% 0.97/1.60 { ! class_Fields_Olinordered__field( 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, Z, c_Groups_Ozero__class_Ozero( X
% 0.97/1.60 ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.60 c_Rings_Oinverse__class_Odivide( X, Y, Z ), c_Groups_Ozero__class_Ozero(
% 0.97/1.60 X ) ) }.
% 0.97/1.60 { ! class_Fields_Olinordered__field( 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__eq( X, Y, Z ), !
% 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( X, T, U ), c_Orderings_Oord__class_Oless
% 0.97/1.60 ( X, c_Rings_Oinverse__class_Odivide( X, Y, U ),
% 0.97/1.60 c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 0.97/1.60 { ! class_Fields_Olinordered__field( 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, Y, Z ), !
% 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, T, U ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, Y,
% 0.97/1.60 U ), c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 0.97/1.60 { ! class_Fields_Olinordered__field( 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, Y, Z ), !
% 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, T, U ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.97/1.60 , Y, U ), c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 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 { 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__eq( tc_RealDef_Oreal, 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_Oabs__class_Oabs( tc_RealDef_Oreal, Y ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ),
% 0.97/1.60 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Z ) ) ), Y =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.60 { ! class_RealVector_Oreal__field( X ), c_Rings_Oinverse__class_Odivide( X
% 0.97/1.60 , c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), W ), U ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) =
% 0.97/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.60 ( X ), W ), c_Rings_Oinverse__class_Odivide( X,
% 0.97/1.60 c_Groups_Ominus__class_Ominus( X, U, Z ), Y ) ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.97/1.60 c_Groups_Ominus__class_Ominus( X, W, T ), Y ) ), 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 ),
% 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( 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__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_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 { ! 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 { c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, hAPP( Z, Y ), hAPP( hAPP
% 0.97/1.60 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.97/1.60 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, hAPP( Z, X ), hAPP( Z, Y
% 0.97/1.60 ) ), c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, Y ) ) ), Y ) )
% 0.97/1.60 = c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, hAPP( Z, X ), hAPP(
% 0.97/1.60 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.97/1.60 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, hAPP( Z, X ), hAPP( Z, Y
% 0.97/1.60 ) ), c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, Y ) ) ), X ) )
% 0.97/1.60 }.
% 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 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ), X =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.60 { ! X = 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 ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) }.
% 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 { ! 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,
% 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_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_Ocomm__semiring__1( 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( X ), Y ), Z ) }.
% 0.97/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), T ), 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( X ), 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 ), 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( X ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 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_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), T ), 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 ), 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_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Z ) }.
% 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_Groups_Otimes__class_Otimes( X ), U ), T ) ), 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( X ), U ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), T ), 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 ), 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 ) ) = hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), Y ) ) }.
% 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_Groups_Otimes__class_Otimes( X ), U ), T ) ), 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( 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 { ! 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 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.97/1.60 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.97/1.60 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 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_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_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_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_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_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 ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.97/1.60 = 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_Oone__class_Oone( X ) ), Y )
% 0.97/1.60 = Y }.
% 0.97/1.60 { c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ) ) =
% 0.97/1.60 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, X, Y ) }.
% 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__field( 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 ), skol9( Z, T ) ) }.
% 0.97/1.60 { ! class_RealVector_Oreal__normed__field( 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_Rings_Oinverse__class_Odivide( X, Z
% 0.97/1.60 , Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.97/1.60 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol9( X, Y ) ) ) }.
% 0.97/1.60 { ! c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, 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_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, X,
% 0.97/1.60 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) ),
% 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_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, X,
% 0.97/1.60 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) ),
% 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_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, X, c_Complex_Oii ) ),
% 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_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, X, c_Complex_Oii ) )
% 0.97/1.60 , c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 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 ), skol10( 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 ) ) ), skol10( 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 ), skol11( 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 ) ), skol11( X, Y ) ) ) }.
% 0.97/1.60 { ! c_Complex_Oii = c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) }.
% 0.97/1.60 { ! c_Complex_Oii = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 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__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 ), skol12( 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 ) ), skol12( X, Y ) ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Oabs__class_Oabs( 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_Oabs__class_Oabs( tc_RealDef_Oreal, Y ),
% 0.97/1.60 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Transcendental_Oarctan(
% 0.97/1.60 X ), c_Transcendental_Oarctan( Y ) ) = c_Transcendental_Oarctan(
% 0.97/1.60 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X, Y ),
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( 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 ), skol13 ) }.
% 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( tc_Complex_Ocomplex,
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, X, v_z ) ) ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.60 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, X, v_z ) ), skol13 )
% 0.97/1.60 , c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.60 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, hAPP(
% 0.97/1.60 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_cs____ ),
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, X, v_z ) ), hAPP(
% 0.97/1.60 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_cs____ ),
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, v_z, v_z ) ) ) ), v_e
% 0.97/1.60 ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, Z ),
% 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( T, U, W ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, Z ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, T ) ), skol14( X, Y,
% 0.97/1.60 Z ) ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, T ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, Z ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, T ) ), skol14( X, Y,
% 0.97/1.60 Z ) ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, T, Z ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.60 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, 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,
% 0.97/1.60 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.97/1.60 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_cs____ ), X ) ), v_m____ ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oarctan
% 0.97/1.60 ( Y ), c_Transcendental_Oarctan( X ) ) }.
% 0.97/1.60 { c_Transcendental_Oarctan( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal )
% 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_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.60 c_Transcendental_Oarctan( Y ), c_Transcendental_Oarctan( 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 ), skol15 ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.60 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, 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,
% 0.97/1.60 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.97/1.60 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_cs____ ), X ) ), skol15 ) }.
% 0.97/1.60 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ), X ) = hAPP(
% 0.97/1.60 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_p ),
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, v_z, X ) ) }.
% 0.97/1.60 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, X, v_z ) ) = hAPP(
% 0.97/1.60 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_p ), 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 ), skol16 ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.60 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, 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,
% 0.97/1.60 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.97/1.60 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_cs____ ), X ) ), skol16 ) }.
% 0.97/1.60 { c_Polynomial_Odegree( tc_Complex_Ocomplex, v_q____ ) =
% 0.97/1.60 c_Polynomial_Odegree( tc_Complex_Ocomplex, v_p ) }.
% 0.97/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 0.97/1.60 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.97/1.60 c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.60 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.97/1.60 c_Groups_Ominus__class_Ominus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 0.97/1.60 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.97/1.60 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.97/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 0.97/1.60 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.97/1.60 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 0.97/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Z
% 0.97/1.60 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP(
% 0.97/1.60 c_Polynomial_Opoly( X, T ), Y ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 0.97/1.60 ) }.
% 0.97/1.60 { ! class_Rings_Ocomm__semiring__0( X ), c_Orderings_Oord__class_Oless__eq
% 0.97/1.60 ( tc_Nat_Onat, c_Polynomial_Odegree( X, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y ) ),
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Polynomial_Odegree( X, Z ),
% 0.97/1.60 c_Polynomial_Odegree( X, Y ) ) ) }.
% 0.97/1.60 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ), hAPP
% 0.97/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y
% 0.97/1.60 ) ) }.
% 0.97/1.60 { ! class_Groups_Oab__group__add( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.97/1.60 ( tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 0.97/1.60 T ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.60 c_Polynomial_Odegree( X, c_Groups_Ominus__class_Ominus(
% 0.97/1.60 tc_Polynomial_Opoly( X ), Z, T ) ), Y ) }.
% 0.97/1.60 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.60 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) )
% 0.97/1.60 , c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 0.97/1.60 tc_Polynomial_Opoly( X ), Y, Z ) ) = c_Polynomial_Odegree( X, Y ) }.
% 0.97/1.60 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.60 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) )
% 0.97/1.60 , c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 0.97/1.60 tc_Polynomial_Opoly( X ), Z, Y ) ) = c_Polynomial_Odegree( X, Y ) }.
% 0.97/1.60 { ! class_Groups_Ocomm__monoid__add( X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 0.97/1.60 Z ), Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.60 c_Polynomial_Odegree( X, T ), Y ), c_Orderings_Oord__class_Oless__eq(
% 0.97/1.60 tc_Nat_Onat, c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 0.97/1.60 tc_Polynomial_Opoly( X ), Z, T ) ), Y ) }.
% 0.97/1.60 { ! class_Groups_Oab__group__add( X ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.60 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, T )
% 0.97/1.60 , Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree(
% 0.97/1.60 X, c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Z, T ) ), Y )
% 0.97/1.60 }.
% 0.97/1.60 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.60 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, T )
% 0.97/1.60 , Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree(
% 0.97/1.60 X, c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Z, T ) ), Y ) }
% 0.97/1.60 .
% 0.97/1.60 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.97/1.60 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 0.97/1.60 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.97/1.60 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.97/1.60 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 0.97/1.60 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.97/1.60 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.97/1.60 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.97/1.60 tc_Polynomial_Opoly( X ) ), Y ) = Y }.
% 0.97/1.60 { ! class_Groups_Ozero( X ), c_Polynomial_Odegree( X,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.60 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.60 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.60 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.60 tc_Polynomial_Opoly( X ) ), Z = c_Groups_Ozero__class_Ozero(
% 0.97/1.60 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) =
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Polynomial_Odegree( X, Y ),
% 0.97/1.60 c_Polynomial_Odegree( X, Z ) ) }.
% 0.97/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Odegree( X,
% 0.97/1.60 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ) =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.60 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 0.97/1.60 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ), Z = Y }.
% 0.97/1.60 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Z = Y,
% 0.97/1.60 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ) }.
% 0.97/1.60 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 0.97/1.60 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.60 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Y =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.97/1.60 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.97/1.60 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.60 { c_Polynomial_Odegree( tc_Complex_Ocomplex, skol17 ) =
% 0.97/1.60 c_Polynomial_Odegree( tc_Complex_Ocomplex, v_p ) }.
% 0.97/1.60 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, skol17 ), X ) = hAPP(
% 0.97/1.60 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_p ),
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, v_z, 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 ), skol18( Z, T ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.60 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Z ), Y ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.60 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.97/1.60 c_Polynomial_Opoly( tc_Complex_Ocomplex, X ), Z ) ), skol18( X, Y ) ) }.
% 0.97/1.60 { ! class_RealVector_Oreal__normed__field( 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 ), skol19( Z, T ) ) }.
% 0.97/1.60 { ! class_RealVector_Oreal__normed__field( 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_Rings_Oinverse__class_Odivide( X, Z
% 0.97/1.60 , Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.97/1.60 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol19( 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 ), skol20( 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 ) ) ), skol20( 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, skol21( 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 { ! 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 { 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( 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_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_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 ), 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 ),
% 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 { 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 ), 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 ), 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 ), X ),
% 0.97/1.60 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 ), 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 ),
% 0.97/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) = X }.
% 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 { ! 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 { ! 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 ), 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 { ! 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 ), 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 ),
% 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 { ! 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 { alpha86( 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 { alpha86( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP
% 0.97/1.60 ( X, Y ), Z ) ) }.
% 0.97/1.60 { ! alpha86( X, Y, Z ), alpha89( X, Y, Z ), Z = Y }.
% 0.97/1.60 { ! alpha86( X, Y, Z ), alpha89( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z
% 0.97/1.60 ) ) }.
% 0.97/1.60 { ! alpha89( X, Y, Z ), alpha86( X, Y, Z ) }.
% 0.97/1.60 { ! Z = Y, hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha86( X, Y, Z ) }.
% 0.97/1.60 { ! alpha89( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y )
% 0.97/1.60 }.
% 0.97/1.60 { ! alpha89( 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 ) ), alpha89( X, Y, Z ) }.
% 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 ), ! X = Y }.
% 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 { 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 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, 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 { 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_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_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_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_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, 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_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_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 { 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 { 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__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, 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_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, 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, 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, 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, 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( 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( 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 { ! 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 { 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 ), 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, 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_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, 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 { ! 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, 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 { 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, 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, 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_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_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_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,
% 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, 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_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( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.97/1.60 ( 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, Y, X ), X ) }.
% 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, 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, 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, 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 { ! 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, 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_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, 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_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, 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 { ! 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( 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( 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 { ! 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__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, skol22( 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, 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 { ! 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,
% 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, 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, 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_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_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_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, 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_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_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_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, 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_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 { ! 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__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,
% 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_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_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( 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 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.97/1.60 , alpha16( X, Y, Z ) }.
% 0.97/1.60 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.97/1.60 , alpha42( X, Y, Z ) }.
% 0.97/1.60 { ! alpha16( X, Y, Z ), ! alpha42( X, Y, Z ), hBOOL( hAPP( Z,
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.97/1.60 { ! alpha42( 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, skol23( T, U, Z ) ) ), alpha42( X, Y, Z ) }.
% 0.97/1.60 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, skol23( X, Y, Z ) ),
% 0.97/1.60 alpha42( X, Y, Z ) }.
% 0.97/1.60 { ! alpha16( 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 ), alpha16( X, Y, Z ) }
% 0.97/1.60 .
% 0.97/1.60 { ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha16
% 0.97/1.60 ( X, Y, Z ) }.
% 0.97/1.60 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.97/1.60 , ! alpha17( X, Y, Z ) }.
% 0.97/1.60 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.97/1.60 , ! alpha43( X, Y, Z ) }.
% 0.97/1.60 { alpha17( X, Y, Z ), alpha43( X, Y, Z ), hBOOL( hAPP( Z,
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.97/1.60 { ! alpha43( X, Y, Z ), ! hBOOL( hAPP( Z, skol24( T, U, Z ) ) ) }.
% 0.97/1.60 { ! alpha43( 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 ) ), alpha43( X, Y, Z ) }.
% 0.97/1.60 { ! alpha17( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 0.97/1.60 }.
% 0.97/1.60 { ! alpha17( 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 ) ) ), alpha17( X, Y, 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 ), 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, 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 { ! class_Groups_Ozero( X ), !
% 0.97/1.60 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.60 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.60 tc_Polynomial_Opoly( X ) ),
% 0.97/1.60 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.60 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 0.97/1.60 tc_Polynomial_Opoly( X ) ), ! c_Polynomial_Oorder( X, Y, Z ) =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.60 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.97/1.60 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.60 { ! class_Rings_Oidom( X ), c_Polynomial_Oorder( X, Y, Z ) =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( c_Polynomial_Opoly( X,
% 0.97/1.60 Z ), Y ) = c_Groups_Ozero__class_Ozero( 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_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 { 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 { 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 { ! 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 { ! 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_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.60 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless__eq(
% 0.97/1.60 tc_Nat_Onat, c_Polynomial_Oorder( X, Z, Y ), c_Polynomial_Odegree( X, Y )
% 0.97/1.60 ) }.
% 0.97/1.60 { ! class_Rings_Ocomm__semiring__0( X ), c_Orderings_Oord__class_Oless__eq
% 0.97/1.60 ( tc_Nat_Onat, c_Polynomial_Odegree( X, c_Polynomial_Opcompose( X, Z, Y )
% 0.97/1.60 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.60 c_Polynomial_Odegree( X, Z ) ), c_Polynomial_Odegree( X, Y ) ) ) }.
% 0.97/1.60 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.97/1.60 , U = c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), T ), Y )
% 0.97/1.60 }.
% 0.97/1.60 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.97/1.60 , alpha55( X, Y, Z, T ) }.
% 0.97/1.60 { ! class_Fields_Ofield( X ), ! U = c_Groups_Oplus__class_Oplus(
% 0.97/1.60 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.60 tc_Polynomial_Opoly( X ) ), Z ), T ), Y ), ! alpha55( X, Y, Z, T ),
% 0.97/1.60 c_Polynomial_Opdivmod__rel( X, U, T, Z, Y ) }.
% 0.97/1.60 { ! alpha55( X, Y, Z, T ), alpha18( X, Z, T ) }.
% 0.97/1.60 { ! alpha55( X, Y, Z, T ), alpha44( X, Y, T ) }.
% 0.97/1.60 { ! alpha18( X, Z, T ), ! alpha44( X, Y, T ), alpha55( X, Y, Z, T ) }.
% 0.97/1.60 { ! alpha44( X, Y, Z ), Z = c_Groups_Ozero__class_Ozero(
% 0.97/1.60 tc_Polynomial_Opoly( X ) ), alpha56( X, Y, Z ) }.
% 0.97/1.60 { ! Z = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha44( X
% 0.97/1.60 , Y, Z ) }.
% 0.97/1.60 { ! alpha56( X, Y, Z ), alpha44( X, Y, Z ) }.
% 0.97/1.60 { ! alpha56( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.60 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.60 c_Polynomial_Odegree( X, Y ), c_Polynomial_Odegree( X, Z ) ) }.
% 0.97/1.60 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha56( X
% 0.97/1.60 , Y, Z ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, Y
% 0.97/1.60 ), c_Polynomial_Odegree( X, Z ) ), alpha56( X, Y, Z ) }.
% 0.97/1.60 { ! alpha18( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.97/1.60 tc_Polynomial_Opoly( X ) ), Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.60 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.60 { Z = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha18( X,
% 0.97/1.60 Y, Z ) }.
% 0.97/1.60 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha18( X
% 0.97/1.60 , 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, Y,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.97/1.60 { ! class_Fields_Ofield( X ), c_Polynomial_Opdivmod__rel( X, Y,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) }.
% 0.97/1.60 { ! class_Fields_Ofield( X ), c_Polynomial_Opdivmod__rel( X,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.97/1.60 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ), Z =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.60 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ), Y = T }
% 0.97/1.60 .
% 0.97/1.60 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.97/1.60 tc_Polynomial_Opoly( X ) ), ! Y = T, c_Polynomial_Opdivmod__rel( X, T,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ) }.
% 0.97/1.60 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ), Z =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.60 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ), Y =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.60 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.97/1.60 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.60 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opdivmod__rel( X,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ) }.
% 0.97/1.60 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.97/1.60 , ! c_Polynomial_Opdivmod__rel( X, U, T, V0, W ), Z = V0 }.
% 0.97/1.60 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.97/1.60 , ! c_Polynomial_Opdivmod__rel( X, U, T, V0, W ), Y = W }.
% 0.97/1.60 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, U, Y )
% 0.97/1.60 , ! c_Polynomial_Opdivmod__rel( X, T, Z, V0, W ), Y = W }.
% 0.97/1.60 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, Y, U )
% 0.97/1.60 , ! c_Polynomial_Opdivmod__rel( X, T, Z, W, V0 ), Y = W }.
% 0.97/1.60 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.60 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.97/1.60 c_Polynomial_Opcompose( X, T, Z ) ), Y ) = hAPP( c_Polynomial_Opoly( X, T
% 0.97/1.60 ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.97/1.60 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.97/1.60 , ! c_Polynomial_Opdivmod__rel( X, Z, V1, V0, W ),
% 0.97/1.60 c_Polynomial_Opdivmod__rel( X, U, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), V1 ), V0
% 0.97/1.60 , c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), W ), 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( 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 { ! 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 ),
% 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_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 { 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, skol25( 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 skol25( 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 , skol25( X, Y ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 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 ), skol26( 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 ) ), skol26( 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 ), c_RealDef_Oreal(
% 0.97/1.60 tc_Nat_Onat, 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_Oabs__class_Oabs( tc_RealDef_Oreal, c_RealDef_Oreal( tc_Nat_Onat
% 0.97/1.60 , X ) ) = c_RealDef_Oreal( tc_Nat_Onat, X ) }.
% 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_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 { ! 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 { ! 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, c_RealDef_Oreal(
% 0.97/1.60 tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, skol27( 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, skol27( 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( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.60 tc_Nat_Onat ), Y ), c_RComplete_Onatfloor(
% 0.97/1.60 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.97/1.60 tc_Nat_Onat, Y ) ) ) = c_Divides_Odiv__class_Odiv( tc_Nat_Onat,
% 0.97/1.60 c_RComplete_Onatfloor( 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 ), skol28( 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 ) ), skol28( X, Y ) ) ) }.
% 0.97/1.60 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.60 c_Divides_Odiv__class_Odiv( 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_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.60 { Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.60 c_Divides_Odiv__class_Odiv( 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_Divides_Odiv__class_Odiv( 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_Divides_Odiv__class_Odiv( 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_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, Y ) }.
% 0.97/1.60 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.60 tc_Nat_Onat, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ),
% 0.97/1.60 c_Rings_Oinverse__class_Odivide( 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,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.97/1.60 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.60 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ), c_RealDef_Oreal(
% 0.97/1.60 tc_Nat_Onat, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, 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,
% 0.97/1.60 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.60 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ), c_RealDef_Oreal(
% 0.97/1.60 tc_Nat_Onat, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 0.97/1.60 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.97/1.60 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 0.97/1.60 alpha19( X, Z ) }.
% 0.97/1.60 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 0.97/1.60 alpha45( X, Y, Z ) }.
% 0.97/1.60 { ! alpha19( X, Z ), ! alpha45( X, Y, Z ), hBOOL( hAPP( Z,
% 0.97/1.60 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ) }.
% 0.97/1.60 { ! alpha45( X, Y, Z ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.60 alpha57( X, Y, Z ) }.
% 0.97/1.60 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha45( X, Y, Z ) }.
% 0.97/1.60 { ! alpha57( X, Y, Z ), alpha45( X, Y, Z ) }.
% 0.97/1.60 { ! alpha57( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, X
% 0.97/1.60 ), alpha65( X, Y, Z, T ) }.
% 0.97/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol29( X, T, U ), X ),
% 0.97/1.60 alpha57( X, Y, Z ) }.
% 0.97/1.60 { ! alpha65( X, Y, Z, skol29( X, Y, Z ) ), alpha57( X, Y, Z ) }.
% 0.97/1.60 { ! alpha65( X, Y, Z, T ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.97/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 0.97/1.60 hBOOL( hAPP( Z, U ) ) }.
% 0.97/1.60 { ! hBOOL( hAPP( Z, skol30( U, W, Z, V0 ) ) ), alpha65( X, Y, Z, T ) }.
% 0.97/1.60 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol30( X, Y, Z, T ) )
% 0.97/1.60 , T ), alpha65( X, Y, Z, T ) }.
% 0.97/1.60 { ! alpha19( X, Y ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.60 hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.97/1.60 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha19( X, Y ) }.
% 0.97/1.60 { ! hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha19
% 0.97/1.60 ( X, Y ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 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_Divides_Odiv__class_Odiv(
% 0.97/1.60 tc_Nat_Onat, Y, 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_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 0.97/1.60 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ) = Y }.
% 0.97/1.60 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X,
% 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_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X, Y,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.60 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X, Y,
% 0.97/1.60 c_Groups_Oone__class_Oone( X ) ) = Y }.
% 0.97/1.60 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.60 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ), 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_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, Z ),
% 0.97/1.60 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, X, Z ) ) }.
% 0.97/1.60 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) =
% 0.97/1.60 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 0.97/1.60 tc_Nat_Onat, Z, Y ), X ) }.
% 0.97/1.60 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.60 , c_Divides_Odiv__class_Odiv( 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_Divides_Odiv__class_Odiv( X, T, Z ) }.
% 0.97/1.60 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.60 , c_Divides_Odiv__class_Odiv( 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 c_Divides_Odiv__class_Odiv( X, T, Z ) }.
% 0.97/1.60 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.60 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) = Z }.
% 0.97/1.60 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.60 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = Z }.
% 0.97/1.60 { ! class_Divides_Osemiring__div( X ), ! T = c_Groups_Ozero__class_Ozero( X
% 0.97/1.60 ), c_Divides_Odiv__class_Odiv( 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_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.60 { ! class_Divides_Osemiring__div( X ), T = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.60 , c_Divides_Odiv__class_Odiv( 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_Divides_Odiv__class_Odiv( X, Z, Y ) }.
% 0.97/1.60 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.60 , c_Divides_Odiv__class_Odiv( X, Y, Y ) = c_Groups_Oone__class_Oone( X )
% 0.97/1.60 }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.60 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.60 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.60 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, T, hAPP
% 0.97/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) =
% 0.97/1.60 c_Groups_Oplus__class_Oplus( X, Z, c_Divides_Odiv__class_Odiv( X, T, Y )
% 0.97/1.60 ) }.
% 0.97/1.60 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.60 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, T, hAPP
% 0.97/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) =
% 0.97/1.60 c_Groups_Oplus__class_Oplus( X, Z, c_Divides_Odiv__class_Odiv( X, T, Y )
% 0.97/1.60 ) }.
% 0.97/1.60 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.60 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, Z, Y ),
% 0.97/1.60 Y ) = c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Z, Y
% 0.97/1.60 ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.97/1.60 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.60 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, Y, Z ),
% 0.97/1.60 Y ) = c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Z, 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 ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X
% 0.97/1.60 , Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.60 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, Y ),
% 0.97/1.60 c_Divides_Odiv__class_Odiv( 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 ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 0.97/1.60 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ) = 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 skol31( 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, skol31( 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 ), skol31( X, Y, Z ) ), Z ), Y ),
% 0.97/1.60 c_Orderings_Oord__class_Oless__eq( X, 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_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.97/1.60 c_RealDef_Oreal( tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) =
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.60 tc_Nat_Onat, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ),
% 0.97/1.60 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.60 tc_Nat_Onat, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ),
% 0.97/1.60 c_RealDef_Oreal( tc_Nat_Onat, X ) ) ) }.
% 0.97/1.60 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Odegree( X,
% 0.97/1.60 c_Polynomial_Osynthetic__div( X, Z, Y ) ) = c_Groups_Ominus__class_Ominus
% 0.97/1.60 ( tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Groups_Oone__class_Oone(
% 0.97/1.60 tc_Nat_Onat ) ) }.
% 0.97/1.60 { c_Divides_Odiv__class_Odiv( 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,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 0.97/1.60 tc_Nat_Onat, Z, X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ),
% 0.97/1.60 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.60 tc_Nat_Onat, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, X ),
% 0.97/1.60 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ), X ) ) }.
% 0.97/1.60 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X,
% 0.97/1.60 c_Divides_Odiv__class_Omod( X, Z, Y ), Y ) = c_Groups_Ozero__class_Ozero
% 0.97/1.60 ( X ) }.
% 0.97/1.60 { c_Divides_Odiv__class_Omod( 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 ), Z
% 0.97/1.60 ), Y ), X ), Y ) = c_Divides_Odiv__class_Omod( tc_Nat_Onat, X, Y ) }.
% 0.97/1.60 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( X, T, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Z ) =
% 0.97/1.60 c_Divides_Odiv__class_Omod( X, T, Z ) }.
% 0.97/1.60 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( X, T, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) =
% 0.97/1.60 c_Divides_Odiv__class_Omod( X, T, Y ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.60 c_Divides_Odiv__class_Omod( tc_Nat_Onat, X, Y ) =
% 0.97/1.60 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.97/1.60 tc_Nat_Onat, X, Y ), Y ) }.
% 0.97/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.60 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 0.97/1.60 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.97/1.60 tc_Nat_Onat, Y, X ), X ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.60 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) = Y }.
% 0.97/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.60 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 0.97/1.60 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.97/1.60 tc_Nat_Onat, Y, X ), X ) }.
% 0.97/1.60 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.97/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Z ) =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.60 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.97/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.60 { ! c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol32( X, Y ) ) }.
% 0.97/1.60 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z )
% 0.97/1.60 , c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.60 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y,
% 0.97/1.60 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.60 { ! class_Divides_Oring__div( X ), ! c_Divides_Odiv__class_Omod( X, T, Z )
% 0.97/1.60 = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod( X
% 0.97/1.60 , W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 0.97/1.60 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, T, W ),
% 0.97/1.60 Z ) = c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, Y
% 0.97/1.60 , U ), Z ) }.
% 0.97/1.60 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.97/1.60 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.97/1.60 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X,
% 0.97/1.60 c_Divides_Odiv__class_Omod( X, T, Y ), c_Divides_Odiv__class_Omod( X, Z,
% 0.97/1.60 Y ) ), Y ) }.
% 0.97/1.60 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.97/1.60 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.97/1.60 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X,
% 0.97/1.60 c_Divides_Odiv__class_Omod( X, T, Y ), Z ), Y ) }.
% 0.97/1.60 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.97/1.60 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.97/1.60 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, T,
% 0.97/1.60 c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 0.97/1.60 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, T,
% 0.97/1.60 Z ) = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod
% 0.97/1.60 ( X, W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 0.97/1.60 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.60 ( X ), T ), W ), Z ) = c_Divides_Odiv__class_Omod( X, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), U ), Z ) }.
% 0.97/1.60 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.97/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Omod( X
% 0.97/1.60 , T, Z ) ), Y ), Z ) = c_Divides_Odiv__class_Omod( X, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.97/1.60 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.97/1.60 ( 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_Divides_Odiv__class_Omod( X, T, Y )
% 0.97/1.60 ), Z ) }.
% 0.97/1.60 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.97/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), 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 ), T ), c_Divides_Odiv__class_Omod( X, Z
% 0.97/1.60 , Y ) ) }.
% 0.97/1.60 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.97/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 0.97/1.60 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.60 ( X ), c_Divides_Odiv__class_Omod( X, T, Y ) ),
% 0.97/1.60 c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 0.97/1.60 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.97/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 0.97/1.60 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.60 ( X ), c_Divides_Odiv__class_Omod( X, T, Y ) ), Z ), Y ) }.
% 0.97/1.60 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.97/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 0.97/1.60 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.60 ( X ), T ), c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 0.97/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.60 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.97/1.60 c_Divides_Odiv__class_Omod( 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 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.97/1.60 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) =
% 0.97/1.60 c_Divides_Odiv__class_Omod( 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 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.97/1.60 c_Divides_Odiv__class_Omod( X, Z, Y ), Y ) = c_Divides_Odiv__class_Omod(
% 0.97/1.60 X, Z, Y ) }.
% 0.97/1.60 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.60 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ), Y ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.60 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, 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_Nat_Onat,
% 0.97/1.60 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ), X ) }.
% 0.97/1.60 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y, Y
% 0.97/1.60 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.60 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.97/1.60 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 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_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, T,
% 0.97/1.60 Z ) = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod
% 0.97/1.60 ( X, W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 0.97/1.60 c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X, T, W ), Z
% 0.97/1.60 ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X, Y, U
% 0.97/1.60 ), Z ) }.
% 0.97/1.60 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Z ), Y
% 0.97/1.60 ), Z ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X,
% 0.97/1.60 T, Y ), Z ) }.
% 0.97/1.60 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( X, T, c_Divides_Odiv__class_Omod( X, Z, Y )
% 0.97/1.60 ), Y ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X,
% 0.97/1.60 T, Z ), Y ) }.
% 0.97/1.60 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 0.97/1.60 ( X, c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Y
% 0.97/1.60 ), c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 0.97/1.60 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 0.97/1.60 ( X, c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Y
% 0.97/1.60 ), Z ), Y ) }.
% 0.97/1.60 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 0.97/1.60 ( X, c_Groups_Oplus__class_Oplus( X, T, c_Divides_Odiv__class_Omod( X, Z
% 0.97/1.60 , Y ) ), Y ) }.
% 0.97/1.60 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( X, Z, Y ), Z ) = c_Divides_Odiv__class_Omod
% 0.97/1.60 ( X, Y, Z ) }.
% 0.97/1.60 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = c_Divides_Odiv__class_Omod
% 0.97/1.60 ( X, Z, Y ) }.
% 0.97/1.60 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, Y, U )
% 0.97/1.60 , c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly( X ), T, Z ) = Y }.
% 0.97/1.60 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Odiv(
% 0.97/1.60 tc_Polynomial_Opoly( X ), T, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.60 tc_Polynomial_Opoly( X ) ), Z ), Y ) ) = c_Divides_Odiv__class_Odiv(
% 0.97/1.60 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly
% 0.97/1.60 ( X ), T, Z ), Y ) }.
% 0.97/1.60 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.60 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.60 ( X ), c_Divides_Odiv__class_Odiv( X, T, Z ) ), Z ),
% 0.97/1.60 c_Divides_Odiv__class_Omod( X, T, Z ) ), Y ) =
% 0.97/1.60 c_Groups_Oplus__class_Oplus( X, T, Y ) }.
% 0.97/1.60 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.60 ( X ), T ), c_Divides_Odiv__class_Odiv( X, Z, T ) ),
% 0.97/1.60 c_Divides_Odiv__class_Omod( X, Z, T ) ), Y ) =
% 0.97/1.60 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 0.97/1.60 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 0.97/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X
% 0.97/1.60 , Z, Y ) ), Y ), c_Divides_Odiv__class_Omod( X, Z, Y ) ) = Z }.
% 0.97/1.60 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 0.97/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 0.97/1.60 c_Divides_Odiv__class_Odiv( X, Y, Z ) ), c_Divides_Odiv__class_Omod( X, Y
% 0.97/1.60 , Z ) ) = Y }.
% 0.97/1.60 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.60 c_Divides_Odiv__class_Omod( X, Z, Y ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X, Z, Y )
% 0.97/1.60 ), 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 ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.60 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ), X ) }.
% 0.97/1.60 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( 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 ),
% 0.97/1.60 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ),
% 0.97/1.60 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.97/1.60 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ), X ) ) }.
% 0.97/1.60 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, 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, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ),
% 0.97/1.60 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 0.97/1.60 tc_Nat_Onat, Z, Y ), X ) ), c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, Y
% 0.97/1.60 ) ) }.
% 0.97/1.60 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Divides_Odiv__class_Odiv
% 0.97/1.60 ( tc_Nat_Onat, Y, X ) ), X ) ) }.
% 0.97/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ),
% 0.97/1.60 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, X, Y ) ) =
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Divides_Odiv__class_Omod
% 0.97/1.60 ( tc_Nat_Onat, X, Y ) ) }.
% 0.97/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.60 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ), X ) =
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Divides_Odiv__class_Omod
% 0.97/1.60 ( tc_Nat_Onat, Y, X ) ) }.
% 0.97/1.60 { ! class_Fields_Ofield( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 0.97/1.60 , c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) ),
% 0.97/1.60 c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly( X ), Z, Y ) =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.60 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) ),
% 0.97/1.60 alpha20( X, Y, Z ) }.
% 0.97/1.60 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) ),
% 0.97/1.60 alpha46( X, Y, Z ) }.
% 0.97/1.60 { ! alpha20( X, Y, Z ), ! alpha46( X, Y, Z ), hBOOL( hAPP( Z,
% 0.97/1.60 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) ) }.
% 0.97/1.60 { ! alpha46( X, Y, Z ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.60 alpha58( X, Y, Z ) }.
% 0.97/1.60 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha46( X, Y, Z ) }.
% 0.97/1.60 { ! alpha58( X, Y, Z ), alpha46( X, Y, Z ) }.
% 0.97/1.60 { ! alpha58( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, X
% 0.97/1.60 ), alpha66( X, Y, Z, T ) }.
% 0.97/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol33( X, T, U ), X ),
% 0.97/1.60 alpha58( X, Y, Z ) }.
% 0.97/1.60 { ! alpha66( X, Y, Z, skol33( X, Y, Z ) ), alpha58( X, Y, Z ) }.
% 0.97/1.60 { ! alpha66( X, Y, Z, T ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.97/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 0.97/1.60 hBOOL( hAPP( Z, T ) ) }.
% 0.97/1.60 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol34( X, Y, T ) ), T
% 0.97/1.60 ), alpha66( X, Y, Z, T ) }.
% 0.97/1.60 { ! hBOOL( hAPP( Z, T ) ), alpha66( X, Y, Z, T ) }.
% 0.97/1.60 { ! alpha20( X, Y, Z ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.60 hBOOL( hAPP( Z, Y ) ) }.
% 0.97/1.60 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha20( X, Y, Z ) }.
% 0.97/1.60 { ! hBOOL( hAPP( Z, Y ) ), alpha20( 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 ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 0.97/1.60 ), c_Orderings_Oord__class_Oless( 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 ),
% 0.97/1.60 c_Divides_Odiv__class_Omod( tc_Nat_Onat, T, X ) ), 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__0( X ), ! c_Polynomial_Osynthetic__div( X
% 0.97/1.60 , Z, Y ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.97/1.60 c_Polynomial_Odegree( X, Z ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.97/1.60 }.
% 0.97/1.60 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Odegree( X, Z ) =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Polynomial_Osynthetic__div
% 0.97/1.60 ( X, Z, Y ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.60 { c_Complex_Oexpi( c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) =
% 0.97/1.60 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, Z ),
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol35( T, U, W ) ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, Z ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, T ) ), skol35( X, Y,
% 0.97/1.60 Z ) ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, T ) }.
% 0.97/1.60 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, Z ), !
% 0.97/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 0.97/1.60 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, T ) ), skol35( X, Y,
% 0.97/1.60 Z ) ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, T, Z ) }.
% 0.97/1.60 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, U, Y )
% 0.97/1.60 , c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), T, Z ) = Y }.
% 0.97/1.60 { ! class_Fields_Ofield( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 0.97/1.60 , c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) ),
% 0.97/1.60 c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), Z, Y ) = Z }.
% 0.97/1.60 { ! class_Fields_Ofield( X ), c_Polynomial_Opdivmod__rel( X, Z, Y,
% 0.97/1.60 c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly( X ), Z, Y ),
% 0.97/1.60 c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), Z, Y ) ) }.
% 0.97/1.60 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Omod(
% 0.97/1.60 tc_Polynomial_Opoly( X ), T, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.60 tc_Polynomial_Opoly( X ) ), Z ), Y ) ) = c_Groups_Oplus__class_Oplus(
% 0.97/1.60 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.60 tc_Polynomial_Opoly( X ) ), Z ), c_Divides_Odiv__class_Omod(
% 0.97/1.60 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly
% 0.97/1.60 ( X ), T, Z ), Y ) ), c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X
% 0.97/1.60 ), T, Z ) ) }.
% 0.97/1.60 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.60 tc_Polynomial_Opoly( X ) ), c_Divides_Odiv__class_Omod(
% 0.97/1.60 tc_Polynomial_Opoly( X ), Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.97/1.60 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.60 c_Polynomial_Odegree( X, c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly
% 0.97/1.60 ( X ), Z, Y ) ), c_Polynomial_Odegree( X, Y ) ) }.
% 0.97/1.60 { c_Complex_Oexpi( c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X )
% 0.97/1.60 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.97/1.60 c_Complex_Oexpi( Y ) ), c_Complex_Oexpi( 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_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 0.97/1.60 c_RealDef_Oreal( tc_Nat_Onat, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y
% 0.97/1.60 , X ) ) = c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.97/1.60 c_RealDef_Oreal( tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) }
% 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__eq( X, T, skol36( 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, skol36( 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_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, X ) }.
% 0.97/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Y,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.60 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.97/1.60 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Divides_Odiv__class_Odiv( X
% 0.97/1.60 , c_Groups_Oplus__class_Oplus( X, Y, T ), Z ) =
% 0.97/1.60 c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Y, Z ),
% 0.97/1.60 c_Divides_Odiv__class_Odiv( X, T, Z ) ) }.
% 0.97/1.60 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.97/1.60 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), ! c_Rings_Odvd__class_Odvd( X
% 0.97/1.60 , c_Divides_Odiv__class_Odiv( X, Y, Z ), c_Divides_Odiv__class_Odiv( X, T
% 0.97/1.60 , Z ) ), c_Rings_Odvd__class_Odvd( X, Y, T ) }.
% 0.97/1.60 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.97/1.60 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), ! c_Rings_Odvd__class_Odvd( X
% 0.97/1.60 , Y, T ), c_Rings_Odvd__class_Odvd( X, c_Divides_Odiv__class_Odiv( X, Y,
% 0.97/1.60 Z ), c_Divides_Odiv__class_Odiv( X, T, Z ) ) }.
% 0.97/1.60 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.97/1.60 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 0.97/1.60 c_Divides_Odiv__class_Odiv( X, Y, Z ) ) = Y }.
% 0.97/1.60 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.97/1.60 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ),
% 0.97/1.60 c_Divides_Odiv__class_Odiv( X, Y, Z ) ) = c_Divides_Odiv__class_Odiv( X,
% 0.97/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.97/1.60 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.97/1.60 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.97/1.60 c_Divides_Odiv__class_Odiv( X, Y, Z ) ), Z ) = Y }.
% 0.97/1.60 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.97/1.60 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.97/1.60 c_Divides_Odiv__class_Odiv( X, Y, Z ) ), T ) = c_Divides_Odiv__class_Odiv
% 0.97/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), Z ) }.
% 0.97/1.60 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.97/1.60 ), ! c_Rings_Odvd__class_Odvd( X, U, T ), hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X, Y, Z )
% 0.97/1.60 ), c_Divides_Odiv__class_Odiv( X, T, U ) ) = c_Divides_Odiv__class_Odiv
% 0.97/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.97/1.60 ( c_Groups_Otimes__class_Otimes( X ), Z ), U ) ) }.
% 0.97/1.60 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, T,
% 0.97/1.60 c_Divides_Odiv__class_Omod( X, Z, Y ) ), ! c_Rings_Odvd__class_Odvd( X, T
% 0.97/1.60 , Y ), c_Rings_Odvd__class_Odvd( X, T, Z ) }.
% 0.97/1.60 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.97/1.60 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X, Z
% 0.97/1.60 , c_Divides_Odiv__class_Omod( X, Y, T ) ) }.
% 0.97/1.60 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.97/1.60 ), c_Divides_Odiv__class_Omod( X, c_Divides_Odiv__class_Omod( X, T, Y )
% 0.97/1.60 , Z ) = c_Divides_Odiv__class_Omod( X, T, Z ) }.
% 0.97/1.60 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.97/1.60 ), ! c_Rings_Odvd__class_Odvd( X, Z, c_Divides_Odiv__class_Omod( X, T, Y
% 0.97/1.60 ) ), c_Rings_Odvd__class_Odvd( X, Z, T ) }.
% 0.97/1.60 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.97/1.60 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X, Z
% 0.97/1.60 , c_Divides_Odiv__class_Omod( X, T, Y ) ) }.
% 0.97/1.60 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.97/1.60 ), c_Divides_Odiv__class_Omod( X, Y, Z ) = c_Groups_Ozero__class_Ozero(
% 0.97/1.60 X ) }.
% 0.97/1.60 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.97/1.60 ), c_Divides_Odiv__class_Omod( X, Y, Z ) = c_Groups_Ozero__class_Ozero(
% 0.97/1.60 X ) }.
% 0.97/1.60 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, Y,
% 0.97/1.60 Z ) = c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.97/1.60 ) }.
% 0.97/1.60 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( 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 ) ), Z =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, T, Y ) }.
% 0.97/1.60 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.60 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.97/1.60 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) )
% 0.97/1.60 }.
% 0.97/1.60 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, T, Y ),
% 0.97/1.60 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.97/1.60 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) )
% 0.97/1.60 }.
% 0.97/1.60 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( 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 ) ), T =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 0.97/1.60 { ! class_Rings_Oidom( X ), ! T = c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.60 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.97/1.60 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) )
% 0.97/1.60 }.
% 0.97/1.60 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y ),
% 0.97/1.60 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.97/1.60 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) )
% 0.97/1.60 }.
% 0.97/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.97/1.60 Y ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X,
% 0.97/1.60 Z, c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.97/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.97/1.60 c_Groups_Ozero__class_Ozero( X ), Y ), Y = c_Groups_Ozero__class_Ozero( X
% 0.97/1.60 ) }.
% 0.97/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Oabs__class_Oabs( X, Z )
% 0.97/1.60 = c_Groups_Oabs__class_Oabs( X, Y ), c_Rings_Odvd__class_Odvd( X, Z, Y )
% 0.97/1.60 }.
% 0.97/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.97/1.60 c_Groups_Oabs__class_Oabs( X, Z ), Y ), c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.97/1.60 ) }.
% 0.97/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.97/1.60 ), c_Rings_Odvd__class_Odvd( X, c_Groups_Oabs__class_Oabs( X, Z ), Y ) }
% 0.97/1.60 .
% 0.97/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.97/1.60 c_Groups_Oabs__class_Oabs( X, Y ) ), c_Rings_Odvd__class_Odvd( X, Z, Y )
% 0.97/1.60 }.
% 0.97/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.97/1.60 ), c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oabs__class_Oabs( X, Y ) ) }
% 0.97/1.60 .
% 0.97/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.97/1.60 Y ), ! c_Rings_Odvd__class_Odvd( X, Y, T ), c_Rings_Odvd__class_Odvd( X,
% 0.97/1.60 Z, T ) }.
% 0.97/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Y, Y
% 0.97/1.60 ) }.
% 0.97/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Groups_Oone__class_Oone(
% 0.97/1.60 tc_Nat_Onat ) ), X = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.97/1.60 { ! X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd
% 0.97/1.60 ( tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.97/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X,
% 0.97/1.60 c_Groups_Oone__class_Oone( X ), Y ) }.
% 0.97/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Z,
% 0.97/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Z,
% 0.97/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.97/1.60 Y ), c_Rings_Odvd__class_Odvd( X, Z, hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.97/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.97/1.60 Y ), c_Rings_Odvd__class_Odvd( X, 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 ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.97/1.60 Y ), ! c_Rings_Odvd__class_Odvd( X, U, T ), c_Rings_Odvd__class_Odvd( X,
% 0.97/1.60 hAPP( hAPP( 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_Odvd( X ), ! Z = hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.60 ( X ), Y ), T ), c_Rings_Odvd__class_Odvd( X, Y, Z ) }.
% 0.97/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.97/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), Y ),
% 0.97/1.60 c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 0.97/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.97/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ),
% 0.97/1.60 c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 0.97/1.60 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 0.97/1.60 , ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X, Z,
% 0.97/1.60 c_Groups_Ominus__class_Ominus( X, Y, T ) ) }.
% 0.97/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.97/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ), c_Rings_Odvd__class_Odvd(
% 0.97/1.60 tc_Nat_Onat, Y, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) }.
% 0.97/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.97/1.60 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 0.97/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.97/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.97/1.60 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.97/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd(
% 0.97/1.60 tc_Nat_Onat, Y, Z ) }.
% 0.97/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.97/1.60 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.97/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd
% 0.97/1.60 ( tc_Nat_Onat, Z, Y ) }.
% 0.97/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.97/1.60 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 0.97/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.97/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.97/1.60 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.97/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 0.97/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.97/1.60 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), !
% 0.97/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.97/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.97/1.60 ( tc_Nat_Onat, X, Y ), ! X = Z, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 0.97/1.60 , Z ) }.
% 0.97/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.97/1.60 ( tc_Nat_Onat, X, Y ), ! X = Z, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat,
% 0.97/1.60 Z, Y ) }.
% 0.97/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.97/1.60 ( tc_Nat_Onat, X, Y ), ! X = Y }.
% 0.97/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.97/1.60 ( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.97/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.97/1.60 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 0.97/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.97/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.97/1.60 ( tc_Nat_Onat, X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.97/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.97/1.60 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 0.97/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.97/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.97/1.60 ( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.97/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.97/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 0.97/1.60 tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 0.97/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.97/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 0.97/1.60 tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.97/1.60 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.97/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd(
% 0.97/1.60 tc_Nat_Onat, Y, Z ) }.
% 0.97/1.60 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.97/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd
% 0.97/1.60 ( tc_Nat_Onat, Z, Y ) }.
% 0.97/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.97/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 0.97/1.60 tc_Nat_Onat, Y, Z ) }.
% 0.97/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.97/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 0.97/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.97/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 0.97/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), ! X = Z,
% 0.97/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 0.97/1.60 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.97/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 0.97/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X,
% 0.97/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.97/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X, !
% 0.97/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.97/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.97/1.60 ( tc_Nat_Onat, Y, X ), Y = X }.
% 0.97/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.97/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 0.97/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.97/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), X = Y }.
% 0.97/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), ! X = Y,
% 0.97/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.97/1.60 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.97/1.60 { Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ),
% 0.97/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.97/1.60 { Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.97/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.97/1.60 { ! alpha21( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.97/1.60 { ! alpha21( X, Y ), ! Y = X }.
% 0.97/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X, alpha21( X, Y ) }
% 0.97/1.60 .
% 0.97/1.60 { ! alpha21( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.97/1.60 { ! alpha21( X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.97/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.97/1.60 ( tc_Nat_Onat, X, Y ), alpha21( X, Y ) }.
% 0.97/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), alpha22( X, Y ), Y = X }
% 0.97/1.60 .
% 0.97/1.60 { ! alpha22( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.97/1.60 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.97/1.60 { ! alpha22( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.97/1.60 { ! alpha22( X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.97/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.97/1.60 ( tc_Nat_Onat, X, Y ), alpha22( X, Y ) }.
% 0.97/1.60 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.97/1.60 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.97/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.97/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 0.97/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, c_Groups_Oplus__class_Oplus(
% 0.97/1.60 tc_Nat_Onat, X, Y ) ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.97/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.97/1.60 ( tc_Nat_Onat, Y, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.97/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, c_Groups_Ominus__class_Ominus
% 0.97/1.60 ( tc_Nat_Onat, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X )
% 0.97/1.60 , ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ),
% 0.97/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.97/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, c_Groups_Ominus__class_Ominus
% 0.97/1.60 ( tc_Nat_Onat, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y )
% 0.97/1.60 , ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ),
% 0.97/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ) }.
% 0.97/1.60 { ! c_Rings_Odvd__class_Odvd( 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 ) ), Z =
% 0.97/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 0.97/1.60 tc_Nat_Onat, Y, X ) }.
% 0.97/1.60 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.60 c_Rings_Odvd__class_Odvd( 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_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.97/1.60 ( tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.60 Z ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 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, X, Y
% 0.97/1.60 ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.97/1.60 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.60 , Z = c_Groups_Ozero__class_Ozero( X ), ! c_Rings_Odvd__class_Odvd( X, Y
% 0.97/1.60 , T ), ! c_Rings_Odvd__class_Odvd( X, Z, U ), !
% 0.97/1.60 c_Divides_Odiv__class_Odiv( X, T, Y ) = c_Divides_Odiv__class_Odiv( X, U
% 0.97/1.60 , Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ) = hAPP(
% 0.97/1.60 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), U ) }.
% 0.97/1.60 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.60 , Z = c_Groups_Ozero__class_Ozero( X ), ! c_Rings_Odvd__class_Odvd( X, Y
% 0.97/1.60 , T ), ! c_Rings_Odvd__class_Odvd( X, Z, U ), ! 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 ), U ), c_Divides_Odiv__class_Odiv
% 0.97/1.60 ( X, T, Y ) = c_Divides_Odiv__class_Odiv( X, U, Z ) }.
% 0.97/1.60 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.60 , ! c_Rings_Odvd__class_Odvd( X, Y, Z ), ! c_Divides_Odiv__class_Odiv( X
% 0.97/1.60 , Z, Y ) = T, Z = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y
% 0.97/1.60 ) }.
% 0.97/1.60 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.60 , ! c_Rings_Odvd__class_Odvd( X, Y, Z ), ! Z = hAPP( hAPP(
% 0.97/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ), c_Divides_Odiv__class_Odiv
% 0.97/1.60 ( X, Z, Y ) = T }.
% 0.97/1.60 { ! c_Rings_Odvd__class_Odvd( 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__eq( tc_Nat_Onat, Y, X
% 0.97/1.60 ) }.
% 0.97/1.60 { ! c_Rings_Odvd__class_Odvd( 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_Rings_Odvd__class_Odvd( 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_Rings_Odvd__class_Odvd( 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_Rings_Odvd__class_Odvd( 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_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ),
% 0.97/1.60 c_Rings_Odvd__class_Odvd( 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 ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 0.97/1.60 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ), Y =
% 0.97/1.61 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 ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 0.97/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), 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_Rings_Odvd__class_Odvd( 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_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 ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 0.97/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ) }.
% 0.97/1.61 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 0.97/1.61 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.97/1.61 c_Groups_Oplus__class_Oplus( X, U, T ) ), c_Rings_Odvd__class_Odvd( X, Z
% 0.97/1.61 , c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U,
% 0.97/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) }.
% 0.97/1.61 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 0.97/1.61 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.97/1.61 c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U, hAPP
% 0.97/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ),
% 0.97/1.61 c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X, U, T ) )
% 0.97/1.61 }.
% 0.97/1.61 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 0.97/1.61 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.97/1.61 c_Groups_Oplus__class_Oplus( X, U, T ) ), c_Rings_Odvd__class_Odvd( X, Z
% 0.97/1.61 , c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U,
% 0.97/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) }.
% 0.97/1.61 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 0.97/1.61 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.97/1.61 c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U, hAPP
% 0.97/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ),
% 0.97/1.61 c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X, U, T ) )
% 0.97/1.61 }.
% 0.97/1.61 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.97/1.61 ( X ), Z, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X )
% 0.97/1.61 ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree
% 0.97/1.61 ( X, Z ), c_Polynomial_Odegree( X, Y ) ) }.
% 0.97/1.61 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 0.97/1.61 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ), hBOOL(
% 0.97/1.61 hAPP( Z, skol37( U, W, Z ) ) ) }.
% 0.97/1.61 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 0.97/1.61 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ),
% 0.97/1.61 c_Rings_Odvd__class_Odvd( X, Y, c_Groups_Oplus__class_Oplus( X, skol37( X
% 0.97/1.61 , Y, Z ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.97/1.61 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), !
% 0.97/1.61 c_Rings_Odvd__class_Odvd( X, Y, c_Groups_Oplus__class_Oplus( X, T,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( X ) ) ), ! hBOOL( hAPP( Z, T ) ), hBOOL(
% 0.97/1.61 hAPP( Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), skol53( X,
% 0.97/1.61 Y, Z ) ) ) ) }.
% 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_Rings_Odvd__class_Odvd( 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 ), Y ) }.
% 0.97/1.61 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.97/1.61 tc_Nat_Onat ), X ) }.
% 0.97/1.61 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero(
% 0.97/1.61 tc_Nat_Onat ) ) }.
% 0.97/1.61 { ! class_Orderings_Oorder( X ), ! c_SEQ_Odecseq( X, Y ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, T ),
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, T ), hAPP( Y, Z ) ) }.
% 0.97/1.61 { ! class_Orderings_Oorder( X ), c_Orderings_Oord__class_Oless__eq(
% 0.97/1.61 tc_Nat_Onat, skol38( X, Y ), skol54( X, Y ) ), c_SEQ_Odecseq( X, Y ) }.
% 0.97/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.61 hAPP( Y, skol54( X, Y ) ), hAPP( Y, skol38( X, Y ) ) ), c_SEQ_Odecseq( X
% 0.97/1.61 , Y ) }.
% 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,
% 0.97/1.61 c_Groups_Oplus__class_Oplus( 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, Y ) ), X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 0.97/1.61 , hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.97/1.61 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 0.97/1.61 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ), Y ) ) }.
% 0.97/1.61 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.97/1.61 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ),
% 0.97/1.61 c_Divides_Odiv__class_Odiv( X, Y, Z ) ), T ) = c_Divides_Odiv__class_Odiv
% 0.97/1.61 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.97/1.61 ( c_Power_Opower__class_Opower( X ), Z ), T ) ) }.
% 0.97/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), 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 ), T ), Y ) ), hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.97/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) }.
% 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 ), T ), Z ) ), hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), T ), Y ) ) = hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.97/1.61 tc_Nat_Onat, Z, Y ) ) }.
% 0.97/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ozero__class_Ozero(
% 0.97/1.61 tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.97/1.61 tc_Nat_Onat ) ) = Y }.
% 0.97/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 0.97/1.61 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), T ), Z
% 0.97/1.61 ) ), Y ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), hAPP(
% 0.97/1.61 c_Polynomial_Opoly( X, T ), Y ) ), Z ) }.
% 0.97/1.61 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 0.97/1.61 c_RealVector_Onorm__class_Onorm( X, 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( tc_RealDef_Oreal ),
% 0.97/1.61 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) }.
% 0.97/1.61 { ! class_RealVector_Oreal__normed__algebra__1( 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( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.97/1.61 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) ) }.
% 0.97/1.61 { ! class_Power_Opower( X ), ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 0.97/1.61 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) =
% 0.97/1.61 c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.61 { ! class_Power_Opower( X ), Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.97/1.61 , hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) = hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ominus__class_Ominus(
% 0.97/1.61 tc_Nat_Onat, Z, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 0.97/1.61 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.61 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), 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 ), c_Groups_Ominus__class_Ominus(
% 0.97/1.61 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ), Z ) =
% 0.97/1.61 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) }.
% 0.97/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.61 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( X ), Z ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.61 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), T ),
% 0.97/1.61 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.97/1.61 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ), hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ominus__class_Ominus(
% 0.97/1.61 tc_Nat_Onat, Z, T ) ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.97/1.61 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.97/1.61 c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ) ),
% 0.97/1.61 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.97/1.61 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.97/1.61 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd(
% 0.97/1.61 tc_Int_Oint, hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z )
% 0.97/1.61 , X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X )
% 0.97/1.61 ) }.
% 0.97/1.61 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.97/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ),
% 0.97/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.97/1.61 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.97/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ), c_Rings_Odvd__class_Odvd(
% 0.97/1.61 tc_Nat_Onat, hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Z )
% 0.97/1.61 , X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X )
% 0.97/1.61 ) }.
% 0.97/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ), Y =
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 0.97/1.61 tc_Int_Oint, Z, X ) }.
% 0.97/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ), Y =
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 0.97/1.61 tc_Nat_Onat, Z, X ) }.
% 0.97/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ) ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.97/1.61 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 0.97/1.61 ) }.
% 0.97/1.61 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 0.97/1.61 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.61 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ),
% 0.97/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) = hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( tc_Int_Oint ), 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 ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.97/1.61 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( 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 ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 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 ), Y ), X ) ) }.
% 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, c_Groups_Ozero__class_Ozero(
% 0.97/1.61 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 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, hAPP
% 0.97/1.61 ( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Z ), hAPP( hAPP
% 0.97/1.61 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ),
% 0.97/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, 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 ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint )
% 0.97/1.61 , c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) ), X ) ), ! Y =
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X =
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.61 { Y = 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 ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ),
% 0.97/1.61 c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) ), X ) ) }.
% 0.97/1.61 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.61 tc_Int_Oint ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ),
% 0.97/1.61 c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) ), X ) ) }.
% 0.97/1.61 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.97/1.61 c_RealDef_Oreal( tc_Nat_Onat, Y ) ), X ) = c_RealDef_Oreal( tc_Nat_Onat,
% 0.97/1.61 hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.61 { c_RealDef_Oreal( tc_Nat_Onat, hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.97/1.61 tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.97/1.61 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ), X ) }.
% 0.97/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Orderings_Oord__class_Oless__eq
% 0.97/1.61 ( tc_Nat_Onat, c_Polynomial_Odegree( X, hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), Z ), Y ) ),
% 0.97/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.61 c_Polynomial_Odegree( X, Z ) ), Y ) ) }.
% 0.97/1.61 { ! X = c_RealDef_Oreal( tc_Nat_Onat, c_RComplete_Onatfloor( X ) ),
% 0.97/1.61 c_RComplete_Onatfloor( hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.97/1.61 tc_RealDef_Oreal ), X ), Y ) ) = hAPP( hAPP( c_Power_Opower__class_Opower
% 0.97/1.61 ( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ), Y ) }.
% 0.97/1.61 { ! Y = 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 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.97/1.61 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) = hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ),
% 0.97/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 0.97/1.61 ( tc_Nat_Onat ) ) ) ) }.
% 0.97/1.61 { ! class_Rings_Oring__1__no__zero__divisors( X ), Y =
% 0.97/1.61 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 0.97/1.61 ( X ) }.
% 0.97/1.61 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), 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 ), T ), Y ) ), hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.97/1.61 { ! class_Groups_Omonoid__mult( 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_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_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.97/1.61 = c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.61 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.97/1.61 Y ), c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.97/1.61 { ! class_Fields_Ofield__inverse__zero( X ), hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide( X, T
% 0.97/1.61 , Z ) ), Y ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.97/1.61 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 ), T ), hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) }.
% 0.97/1.61 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, hAPP
% 0.97/1.61 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), c_Groups_Oabs__class_Oabs( X, Z ) ), Y
% 0.97/1.61 ) }.
% 0.97/1.61 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.97/1.61 tc_Nat_Onat ) ) = 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, c_Groups_Ozero__class_Ozero( X
% 0.97/1.61 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.97/1.61 { ! class_Rings_Olinordered__semidom( 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 ), Z
% 0.97/1.61 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 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 ), c_Orderings_Oord__class_Oless
% 0.97/1.61 ( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.97/1.61 { ! class_Rings_Olinordered__semidom( X ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 0.97/1.61 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.97/1.61 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.97/1.61 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.97/1.61 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.97/1.61 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.97/1.61 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.97/1.61 .
% 0.97/1.61 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.97/1.61 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.97/1.61 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.97/1.61 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.61 tc_Nat_Onat ) }.
% 0.97/1.61 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.97/1.61 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.97/1.61 , ! Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 0.97/1.61 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y )
% 0.97/1.61 = c_Groups_Ozero__class_Ozero( X ) }.
% 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 ), ! hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ), T = Z }.
% 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 ), ! T = Z, hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) }.
% 0.97/1.61 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP(
% 0.97/1.61 hAPP( c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide
% 0.97/1.61 ( X, T, Y ) ), Z ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.97/1.61 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.97/1.61 , Y ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.97/1.61 c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.61 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.97/1.61 tc_Nat_Onat, Z, Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.97/1.61 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.97/1.61 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.97/1.61 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oone__class_Oone( X ), hAPP
% 0.97/1.61 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.97/1.61 c_Groups_Oone__class_Oone( X ), Z ) ), Y ) }.
% 0.97/1.61 { ! class_Rings_Ocomm__semiring__1( X ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 0.97/1.61 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.97/1.61 ), T ), Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ) ) }
% 0.97/1.61 .
% 0.97/1.61 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.97/1.61 Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, U, T ),
% 0.97/1.61 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.97/1.61 ), Z ), U ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ) ) }
% 0.97/1.61 .
% 0.97/1.61 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.97/1.61 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), Y ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, U, Z ),
% 0.97/1.61 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.97/1.61 ), T ), U ), Y ) }.
% 0.97/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.61 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP
% 0.97/1.61 ( c_Power_Opower__class_Opower( X ), Y ), 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( 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_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 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, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.97/1.61 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), ! Y =
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.97/1.61 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.61 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), Y =
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.97/1.61 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.61 { ! class_Rings_Olinordered__idom( X ), c_Orderings_Oord__class_Oless__eq(
% 0.97/1.61 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), c_Groups_Oabs__class_Oabs( X, Z ) ), Y
% 0.97/1.61 ) ) }.
% 0.97/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.61 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.97/1.61 c_Groups_Oone__class_Oone( X ), T ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.61 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), T ), 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, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.97/1.61 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.97/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 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, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.97/1.61 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.97/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 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 ( tc_Nat_Onat, T, Z ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.97/1.61 { ! class_Rings_Olinordered__semidom( X ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), T )
% 0.97/1.61 , c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), T ), 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_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) ), hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.97/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.61 ( tc_Nat_Onat, 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 , T, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.61 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 0.97/1.61 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), T ), Z ) = hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ), !
% 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_Groups_Ozero__class_Ozero(
% 0.97/1.61 X ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ), T = Y }.
% 0.97/1.61 { ! class_Rings_Olinordered__semidom( X ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, 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, T, 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 ), T ), Y ), hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 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 ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 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 ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 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 ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 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 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 0.97/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 0.97/1.61 hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.97/1.61 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.61 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 0.97/1.61 c_Rings_Odvd__class_Odvd( X, Y, hAPP( hAPP( c_Power_Opower__class_Opower
% 0.97/1.61 ( X ), Y ), Z ) ) }.
% 0.97/1.61 { ! class_Rings_Ocomm__semiring__1( X ), ! Y = c_Groups_Oone__class_Oone( X
% 0.97/1.61 ), c_Rings_Odvd__class_Odvd( X, Y, hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.97/1.61 { X = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), Y =
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Orderings_Oord__class_Oless
% 0.97/1.61 ( tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex
% 0.97/1.61 , c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex,
% 0.97/1.61 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ), hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), X ), hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), skol39( X, Y ) ), Y
% 0.97/1.61 ) ) ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.97/1.61 { ! class_Power_Opower( X ), c_Power_Opower__class_Opower( X ) =
% 0.97/1.61 c_Power_Opower_Opower( X, c_Groups_Oone__class_Oone( X ),
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ) ) }.
% 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 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.61 c_Power_Opower__class_Opower( tc_Int_Oint ), c_Groups_Oabs__class_Oabs(
% 0.97/1.61 tc_Int_Oint, Y ) ), X ) ) }.
% 0.97/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ),
% 0.97/1.61 c_Groups_Oabs__class_Oabs( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.97/1.61 tc_Int_Oint, X, Y ) ) = c_Divides_Odiv__class_Odiv( tc_Int_Oint,
% 0.97/1.61 c_Groups_Oabs__class_Oabs( tc_Int_Oint, X ), c_Groups_Oabs__class_Oabs(
% 0.97/1.61 tc_Int_Oint, Y ) ) }.
% 0.97/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ),
% 0.97/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) = X }.
% 0.97/1.61 { ! c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y ) =
% 0.97/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ), c_Rings_Odvd__class_Odvd
% 0.97/1.61 ( tc_Int_Oint, Y, c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, X ) ) }
% 0.97/1.61 .
% 0.97/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Ominus__class_Ominus
% 0.97/1.61 ( tc_Int_Oint, Z, X ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y )
% 0.97/1.61 = c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ) }.
% 0.97/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, c_Divides_Odiv__class_Omod(
% 0.97/1.61 tc_Int_Oint, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, X ),
% 0.97/1.61 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.97/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 0.97/1.61 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, Z ), c_Rings_Odvd__class_Odvd(
% 0.97/1.61 tc_Int_Oint, Y, c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Z ) ) }.
% 0.97/1.61 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.97/1.61 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ),
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oabs__class_Oabs
% 0.97/1.61 ( tc_Int_Oint, Y ), c_Groups_Oabs__class_Oabs( 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 ), 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_Rings_Odvd__class_Odvd( tc_Int_Oint, X, Y ), ! c_Rings_Odvd__class_Odvd
% 0.97/1.61 ( tc_Int_Oint, Y, X ), 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, X, Y
% 0.97/1.61 ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }.
% 0.97/1.61 { ! c_Rings_Odvd__class_Odvd( 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, Y, X
% 0.97/1.61 ) }.
% 0.97/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 0.97/1.61 c_Rings_Odvd__class_Odvd( tc_Int_Oint, X, Y ), c_Groups_Oabs__class_Oabs
% 0.97/1.61 ( tc_Int_Oint, Y ) = c_Groups_Oabs__class_Oabs( tc_Int_Oint, X ) }.
% 0.97/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.97/1.61 tc_Int_Oint ) ), c_Groups_Oabs__class_Oabs( tc_Int_Oint, X ) =
% 0.97/1.61 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.97/1.61 { ! c_Groups_Oabs__class_Oabs( tc_Int_Oint, X ) = c_Groups_Oone__class_Oone
% 0.97/1.61 ( tc_Int_Oint ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, X,
% 0.97/1.61 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.97/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, c_Groups_Ominus__class_Ominus
% 0.97/1.61 ( tc_Int_Oint, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, X )
% 0.97/1.61 , c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.97/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), Z =
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Rings_Odvd__class_Odvd(
% 0.97/1.61 tc_Int_Oint, Y, X ) }.
% 0.97/1.61 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.97/1.61 c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ), X ),
% 0.97/1.61 c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) = c_Groups_Oone__class_Oone(
% 0.97/1.61 tc_Int_Oint ) }.
% 0.97/1.61 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.97/1.61 c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) = c_Groups_Oone__class_Oone(
% 0.97/1.61 tc_Int_Oint ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ), X ) }.
% 0.97/1.61 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.97/1.61 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd(
% 0.97/1.61 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X
% 0.97/1.61 ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y
% 0.97/1.61 ) ) }.
% 0.97/1.61 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.97/1.61 c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ),
% 0.97/1.61 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.97/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 0.97/1.61 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 0.97/1.61 tc_Int_Oint, U, T ) ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y,
% 0.97/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.97/1.61 tc_Int_Oint, U, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 0.97/1.61 , Z ), X ) ), T ) ) }.
% 0.97/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 0.97/1.61 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 0.97/1.61 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), T ) ),
% 0.97/1.61 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 0.97/1.61 tc_Int_Oint, U, T ) ) }.
% 0.97/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus(
% 0.97/1.61 tc_Int_Oint, Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 0.97/1.61 , Z ), X ) ) ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.97/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd
% 0.97/1.61 ( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP( hAPP
% 0.97/1.61 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), 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 { 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 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ),
% 0.97/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) =
% 0.97/1.61 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Divides_Odiv__class_Omod
% 0.97/1.61 ( tc_Int_Oint, X, Y ) ) }.
% 0.97/1.61 { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.97/1.61 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Divides_Odiv__class_Odiv
% 0.97/1.61 ( tc_Int_Oint, Y, X ) ), X ) ) }.
% 0.97/1.61 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ),
% 0.97/1.61 alpha23( X, Z ) }.
% 0.97/1.61 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ),
% 0.97/1.61 alpha47( X, Y, Z ) }.
% 0.97/1.61 { ! alpha23( X, Z ), ! alpha47( X, Y, Z ), hBOOL( hAPP( Z,
% 0.97/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ) }.
% 0.97/1.61 { ! alpha47( X, Y, Z ), alpha59( X, Y, Z ) }.
% 0.97/1.61 { ! alpha47( X, Y, Z ), alpha67( X, Y, Z ) }.
% 0.97/1.61 { ! alpha59( X, Y, Z ), ! alpha67( X, Y, Z ), alpha47( X, Y, Z ) }.
% 0.97/1.61 { ! alpha67( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha75( 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 ) ), alpha67( X, Y, Z ) }.
% 0.97/1.61 { ! alpha75( X, Y, Z ), alpha67( X, Y, Z ) }.
% 0.97/1.61 { ! alpha75( X, Y, Z ), ! alpha79( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 0.97/1.61 { ! hBOOL( hAPP( Z, skol40( T, U, Z ) ) ), alpha75( X, Y, Z ) }.
% 0.97/1.61 { alpha79( X, Y, skol40( X, Y, Z ) ), alpha75( X, Y, Z ) }.
% 0.97/1.61 { ! alpha79( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.61 skol41( X, T, U ) ) }.
% 0.97/1.61 { ! alpha79( X, Y, Z ), alpha83( X, Y, Z, skol41( X, Y, Z ) ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, T ), ! alpha83( X, Y, Z
% 0.97/1.61 , T ), alpha79( X, Y, Z ) }.
% 0.97/1.61 { ! alpha83( 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 { ! alpha83( 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 ), alpha83( X,
% 0.97/1.61 Y, Z, T ) }.
% 0.97/1.61 { ! alpha59( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), alpha68( 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 ), alpha59( X, Y, Z ) }.
% 0.97/1.61 { ! alpha68( X, Y, Z ), alpha59( X, Y, Z ) }.
% 0.97/1.61 { ! alpha68( X, Y, Z ), ! alpha76( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 0.97/1.61 { ! hBOOL( hAPP( Z, skol42( T, U, Z ) ) ), alpha68( X, Y, Z ) }.
% 0.97/1.61 { alpha76( X, Y, skol42( X, Y, Z ) ), alpha68( X, Y, Z ) }.
% 0.97/1.61 { ! alpha76( 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 { ! alpha76( X, Y, Z ), alpha80( 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 ), ! alpha80( X, Y, Z, T )
% 0.97/1.61 , alpha76( X, Y, Z ) }.
% 0.97/1.61 { ! alpha80( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X
% 0.97/1.61 ) }.
% 0.97/1.61 { ! alpha80( 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 ), alpha80( X,
% 0.97/1.61 Y, Z, T ) }.
% 0.97/1.61 { ! alpha23( 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 ), alpha23( X, Y ) }.
% 0.97/1.61 { ! hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), alpha23
% 0.97/1.61 ( 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_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 { ! 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_Omod( 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_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ),
% 0.97/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.97/1.61 tc_Int_Oint, Z, Y ), X ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y
% 0.97/1.61 ) ) }.
% 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 ) ), ! alpha24( 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 ), alpha24( X, Y, skol44( X, Y, Z ), skol55( 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, skol44( X, Y, Z ) ), skol55
% 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 { ! alpha24( 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 { ! alpha24( X, Y, Z, T ), alpha48( 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 ), ! alpha48( X, Y, Z, T )
% 0.97/1.61 , alpha24( X, Y, Z, T ) }.
% 0.97/1.61 { ! alpha48( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X
% 0.97/1.61 ) }.
% 0.97/1.61 { ! alpha48( 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 ), alpha48( X,
% 0.97/1.61 Y, Z, T ) }.
% 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 ) ), ! hBOOL( hAPP( hAPP( Z,
% 0.97/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 0.97/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ), ! alpha25( X, Y, T,
% 0.97/1.61 U ), hBOOL( hAPP( hAPP( Z, T ), U ) ) }.
% 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 ) ), alpha25( X, Y, skol45( X, Y
% 0.97/1.61 , Z ), skol56( X, Y, Z ) ), hBOOL( hAPP( hAPP( Z,
% 0.97/1.61 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, X,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! hBOOL( hAPP( hAPP( Z,
% 0.97/1.61 skol45( X, Y, Z ) ), skol56( X, Y, Z ) ) ), hBOOL( hAPP( hAPP( Z,
% 0.97/1.61 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 { ! alpha25( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, T
% 0.97/1.61 ) }.
% 0.97/1.61 { ! alpha25( X, Y, Z, T ), alpha49( X, Y, Z, T ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, T ), ! alpha49( X, Y, Z
% 0.97/1.61 , T ), alpha25( X, Y, Z, T ) }.
% 0.97/1.61 { ! alpha49( 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 { ! alpha49( 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 ), alpha49( X,
% 0.97/1.61 Y, Z, T ) }.
% 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 ), alpha87( 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 ), alpha87( 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 { ! alpha87( 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 { ! alpha87( 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 ), alpha87( 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 , alpha87( X, Y ) }.
% 0.97/1.61 { Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( 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_Omod( tc_Int_Oint, Y, X ) ) }.
% 0.97/1.61 { c_Divides_Odiv__class_Odiv( 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_Groups_Oplus__class_Oplus( 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_Odiv( tc_Int_Oint, Y, X ) ),
% 0.97/1.61 c_Divides_Odiv__class_Odiv( 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_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.97/1.61 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.97/1.61 ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ) ),
% 0.97/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, Z ) ), X ) =
% 0.97/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) }.
% 0.97/1.61 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.97/1.61 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.97/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Z, Y ) ), Y ),
% 0.97/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y ) ), X ) =
% 0.97/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, 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 ), skol46( 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 { ! Z = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), T ), X ), alpha88( 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 ), Y ), Y =
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.97/1.61 tc_Int_Oint, Z, Y ) = X }.
% 0.97/1.61 { ! Z = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), T ), X ), alpha88( X,
% 0.97/1.61 Y ), ! c_Orderings_Oord__class_Oless( 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 ) ), Y =
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.97/1.61 tc_Int_Oint, Z, Y ) = X }.
% 0.97/1.61 { ! alpha88( 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 { ! alpha88( 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 ), alpha88( 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 , alpha88( 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, Z, 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__eq( tc_Int_Oint,
% 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 ), Z ),
% 0.97/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, T, 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, c_Groups_Ozero__class_Ozero
% 0.97/1.61 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, 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, hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ),
% 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 ), Z ),
% 0.97/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, T, 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__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, Z ),
% 0.97/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.97/1.61 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.97/1.61 ), c_Divides_Odiv__class_Omod( tc_Int_Oint, T, X ) ), Y ), hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), 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 ), Y ), !
% 0.97/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, 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 ), c_Groups_Oplus__class_Oplus(
% 0.97/1.61 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.97/1.61 ), c_Divides_Odiv__class_Omod( tc_Int_Oint, T, X ) ), Y ) ) }.
% 0.97/1.61 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ),
% 0.97/1.61 alpha26( X, Y, Z ) }.
% 0.97/1.61 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ),
% 0.97/1.61 alpha50( X, Y, Z ) }.
% 0.97/1.61 { ! alpha26( X, Y, Z ), ! alpha50( X, Y, Z ), hBOOL( hAPP( Z,
% 0.97/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 0.97/1.61 { ! alpha50( X, Y, Z ), alpha60( X, Y, Z ) }.
% 0.97/1.61 { ! alpha50( X, Y, Z ), alpha69( X, Y, Z ) }.
% 0.97/1.61 { ! alpha60( X, Y, Z ), ! alpha69( X, Y, Z ), alpha50( X, Y, Z ) }.
% 0.97/1.61 { ! alpha69( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha77( 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 ) ), alpha69( X, Y, Z ) }.
% 0.97/1.61 { ! alpha77( X, Y, Z ), alpha69( X, Y, Z ) }.
% 0.97/1.61 { ! alpha77( X, Y, Z ), ! alpha81( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 0.97/1.61 { ! hBOOL( hAPP( Z, skol47( T, U, Z ) ) ), alpha77( X, Y, Z ) }.
% 0.97/1.61 { alpha81( X, Y, skol47( X, Y, Z ) ), alpha77( X, Y, Z ) }.
% 0.97/1.61 { ! alpha81( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z )
% 0.97/1.61 }.
% 0.97/1.61 { ! alpha81( X, Y, Z ), alpha84( X, Y, Z ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), ! alpha84( X, Y, Z
% 0.97/1.61 ), alpha81( X, Y, Z ) }.
% 0.97/1.61 { ! alpha84( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.61 { ! alpha84( X, Y, Z ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP
% 0.97/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), skol48( X, Y,
% 0.97/1.61 Z ) ), Z ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 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 ), T ), Z ), alpha84( X,
% 0.97/1.61 Y, Z ) }.
% 0.97/1.61 { ! alpha60( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), alpha70( 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 ), alpha60( X, Y, Z ) }.
% 0.97/1.61 { ! alpha70( X, Y, Z ), alpha60( X, Y, Z ) }.
% 0.97/1.61 { ! alpha70( X, Y, Z ), ! alpha78( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 0.97/1.61 { ! hBOOL( hAPP( Z, skol49( T, U, Z ) ) ), alpha70( X, Y, Z ) }.
% 0.97/1.61 { alpha78( X, Y, skol49( X, Y, Z ) ), alpha70( X, Y, Z ) }.
% 0.97/1.61 { ! alpha78( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ) }.
% 0.97/1.61 { ! alpha78( X, Y, Z ), alpha82( 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 ), Z ), ! alpha82( X, Y, Z ),
% 0.97/1.61 alpha78( X, Y, Z ) }.
% 0.97/1.61 { ! alpha82( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X )
% 0.97/1.61 }.
% 0.97/1.61 { ! alpha82( X, Y, Z ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP
% 0.97/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), skol50( X, Y,
% 0.97/1.61 Z ) ), Z ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, 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 ), T ), Z ), alpha82( X,
% 0.97/1.61 Y, Z ) }.
% 0.97/1.61 { ! alpha26( X, Y, Z ), ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.97/1.61 hBOOL( hAPP( Z, Y ) ) }.
% 0.97/1.61 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), alpha26( X, Y, Z ) }.
% 0.97/1.61 { ! hBOOL( hAPP( Z, Y ) ), alpha26( X, Y, Z ) }.
% 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 { ! 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( 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__eq( tc_Int_Oint,
% 0.97/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, 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__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( 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( 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, 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 { 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_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 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.97/1.61 class_Groups_Ocancel__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.61 { class_Groups_Ocancel__comm__monoid__add( tc_Complex_Ocomplex ) }.
% 0.97/1.61 { class_Groups_Ocancel__comm__monoid__add( tc_RealDef_Oreal ) }.
% 0.97/1.61 { class_Groups_Ocancel__comm__monoid__add( tc_Nat_Onat ) }.
% 0.97/1.61 { class_Groups_Ocancel__comm__monoid__add( tc_Int_Oint ) }.
% 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_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__ab__group__add__abs( 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_Oordered__ring__abs( 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_Rings_Ocomm__semiring__0( 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_Rings_Ocomm__ring( tc_Int_Oint ) }.
% 0.97/1.61 { class_Orderings_Oorder( tc_Int_Oint ) }.
% 0.97/1.61 { class_Int_Oring__char__0( 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_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_Rings_Odvd( 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_Rings_Ocomm__semiring__0( 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_Rings_Odvd( tc_Nat_Onat ) }.
% 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_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_Rings_Odivision__ring__inverse__zero( 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_Groups_Oordered__ab__group__add__abs( 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_RealVector_Oreal__normed__field( 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_Orderings_Odense__linorder( 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_Oordered__ring__abs( 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_Rings_Ocomm__semiring__0( tc_RealDef_Oreal ) }.
% 0.97/1.61 { class_RealVector_Oreal__field( tc_RealDef_Oreal ) }.
% 0.97/1.61 { class_Rings_Odivision__ring( 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_Rings_Ocomm__ring( tc_RealDef_Oreal ) }.
% 0.97/1.61 { class_Orderings_Oorder( tc_RealDef_Oreal ) }.
% 0.97/1.61 { class_Int_Oring__char__0( 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_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_Rings_Odvd( 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_Rings_Odivision__ring__inverse__zero( 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_RealVector_Oreal__normed__field( 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_Rings_Ocomm__semiring__0( tc_Complex_Ocomplex ) }.
% 0.97/1.61 { class_RealVector_Oreal__field( tc_Complex_Ocomplex ) }.
% 0.97/1.61 { class_Rings_Odivision__ring( 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_Ocomm__ring( tc_Complex_Ocomplex ) }.
% 0.97/1.61 { class_Int_Oring__char__0( tc_Complex_Ocomplex ) }.
% 0.97/1.61 { class_Rings_Osemiring( 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 { class_Rings_Odvd( tc_Complex_Ocomplex ) }.
% 0.97/1.61 { ! class_Rings_Oidom( X ),
% 0.97/1.61 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.97/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.97/1.61 class_Groups_Oordered__cancel__ab__semigroup__add( tc_Polynomial_Opoly( X
% 0.97/1.61 ) ) }.
% 0.97/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.97/1.61 class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Polynomial_Opoly(
% 0.97/1.61 X ) ) }.
% 0.97/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.97/1.61 class_Rings_Olinordered__comm__semiring__strict( tc_Polynomial_Opoly( X )
% 0.97/1.61 ) }.
% 0.97/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.97/1.61 class_Rings_Olinordered__semiring__1__strict( tc_Polynomial_Opoly( X ) )
% 0.97/1.61 }.
% 0.97/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.97/1.61 class_Rings_Olinordered__semiring__strict( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.97/1.61 class_Groups_Oordered__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.97/1.61 class_Groups_Oordered__ab__group__add__abs( tc_Polynomial_Opoly( X ) ) }
% 0.97/1.61 .
% 0.97/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.97/1.61 class_Groups_Oordered__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.97/1.61 class_Groups_Olinordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.61 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.97/1.61 class_Groups_Ocancel__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.61 { ! class_Rings_Oidom( X ), class_Rings_Oring__1__no__zero__divisors(
% 0.97/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.97/1.61 class_Rings_Oordered__cancel__semiring( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.97/1.61 class_Rings_Olinordered__ring__strict( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.61 { ! class_Rings_Oidom( X ), class_Rings_Oring__no__zero__divisors(
% 0.97/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.97/1.61 class_Rings_Oordered__comm__semiring( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.97/1.61 class_Rings_Olinordered__semiring__1( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.97/1.61 class_Groups_Oordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.61 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.97/1.61 class_Groups_Ocancel__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.61 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semiring(
% 0.97/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.61 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semidom(
% 0.97/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.61 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Oab__semigroup__mult
% 0.97/1.61 ( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.61 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Ocomm__monoid__mult(
% 0.97/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.61 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Oab__semigroup__add
% 0.97/1.61 ( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.61 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__semiring(
% 0.97/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.61 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__ring__abs(
% 0.97/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.61 { ! class_Rings_Oidom( X ), class_Rings_Ono__zero__divisors(
% 0.97/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.61 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Ocomm__monoid__add(
% 0.97/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.61 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__ring(
% 0.97/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.61 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__idom(
% 0.97/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.61 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ocomm__semiring__1(
% 0.97/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.61 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring__0(
% 0.97/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.61 { ! class_Fields_Ofield( X ), class_Divides_Osemiring__div(
% 0.97/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.61 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring(
% 0.97/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.61 { ! class_Groups_Oab__group__add( X ), class_Groups_Oab__group__add(
% 0.97/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.61 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ozero__neq__one(
% 0.97/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.61 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__ring(
% 0.97/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.61 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Opreorder(
% 0.97/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.61 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Olinorder(
% 0.97/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.61 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Omonoid__mult(
% 0.97/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.61 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Ocomm__ring__1(
% 0.97/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.61 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Omonoid__add(
% 0.97/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.61 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring__0(
% 0.97/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.61 { ! class_Groups_Oab__group__add( X ), class_Groups_Ogroup__add(
% 0.97/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.61 { ! class_Fields_Ofield( X ), class_Divides_Oring__div( tc_Polynomial_Opoly
% 0.97/1.61 ( X ) ) }.
% 0.97/1.61 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Omult__zero(
% 0.97/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.61 { ! class_Rings_Ocomm__ring( X ), class_Rings_Ocomm__ring(
% 0.97/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.61 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oorder(
% 0.97/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.61 { ! class_Rings_Olinordered__idom( X ), class_Int_Oring__char__0(
% 0.97/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.61 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring(
% 0.97/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.61 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oord(
% 0.97/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.61 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Oring__1(
% 0.97/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.61 { ! class_Groups_Oab__group__add( X ), class_Groups_Ominus(
% 0.97/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.61 { ! class_Rings_Ocomm__semiring__1( X ), class_Power_Opower(
% 0.97/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.61 { ! class_Groups_Ozero( X ), class_Groups_Ozero( tc_Polynomial_Opoly( X ) )
% 0.97/1.61 }.
% 0.97/1.61 { ! class_Rings_Ocomm__ring( X ), class_Rings_Oring( tc_Polynomial_Opoly( X
% 0.97/1.61 ) ) }.
% 0.97/1.61 { ! class_Rings_Oidom( X ), class_Rings_Oidom( tc_Polynomial_Opoly( X ) ) }
% 0.97/1.61 .
% 0.97/1.61 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Oone(
% 0.97/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.61 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Odvd(
% 0.97/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.61 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.97/1.61 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, v_w____, v_z ) ),
% 0.97/1.61 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 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 *** allocated 113905 integers for clauses
% 0.97/1.61 percentage equality = 0.212332, percentage horn = 0.886311
% 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:214, a:1, s:1, b:0),
% 0.97/1.61 ! [4, 1] (w:0, o:121, 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:238, a:1, s:1, b:0),
% 0.97/1.61 v_w____ [39, 0] (w:1, o:13, a:1, s:1, b:0),
% 0.97/1.61 v_z [40, 0] (w:1, o:14, a:1, s:1, b:0),
% 0.97/1.61 tc_RealDef_Oreal [41, 0] (w:1, o:21, a:1, s:1, b:0),
% 0.97/1.61 v_da____ [42, 0] (w:1, o:23, a:1, s:1, b:0),
% 0.97/1.61 c_Groups_Oone__class_Oone [43, 1] (w:1, o:126, a:1, s:1, b:0),
% 0.97/1.61 c_Orderings_Oord__class_Oless [44, 3] (w:1, o:272, a:1, s:1, b:0),
% 0.97/1.61 tc_Complex_Ocomplex [45, 0] (w:1, o:24, a:1, s:1, b:0),
% 0.97/1.61 c_Groups_Ominus__class_Ominus [46, 3] (w:1, o:273, a:1, s:1, b:0),
% 0.97/1.61 c_RealVector_Onorm__class_Onorm [47, 2] (w:1, o:239, a:1, s:1, b:0),
% 0.97/1.61
% 0.97/1.61 class_RealVector_Oreal__normed__algebra__1 [49, 1] (w:1, o:127, a:1
% 0.97/1.61 , s:1, b:0),
% 0.97/1.61 class_RealVector_Oreal__normed__vector [52, 1] (w:1, o:128, a:1, s:1
% 0.97/1.61 , b:0),
% 0.97/1.61 c_Orderings_Oord__class_Oless__eq [53, 3] (w:1, o:274, a:1, s:1, b:0)
% 0.97/1.61 ,
% 0.97/1.61 class_Orderings_Opreorder [55, 1] (w:1, o:131, a:1, s:1, b:0),
% 0.97/1.61 class_Groups_Oordered__ab__group__add [60, 1] (w:1, o:136, a:1, s:1
% 0.97/1.61 , b:0),
% 0.97/1.61 class_Groups_Oone [67, 1] (w:1, o:137, a:1, s:1, b:0),
% 0.97/1.61 class_Groups_Ominus [71, 1] (w:1, o:139, a:1, s:1, b:0),
% 0.97/1.61 tc_fun [72, 2] (w:1, o:256, a:1, s:1, b:0),
% 0.97/1.61 v_d____ [73, 0] (w:1, o:60, a:1, s:1, b:0),
% 0.97/1.61 c_Groups_Ozero__class_Ozero [74, 1] (w:1, o:140, a:1, s:1, b:0),
% 0.97/1.61 class_Orderings_Olinorder [76, 1] (w:1, o:141, a:1, s:1, b:0),
% 0.97/1.61 class_Orderings_Oorder [78, 1] (w:1, o:129, a:1, s:1, b:0),
% 0.97/1.61 class_Orderings_Oord [80, 1] (w:1, o:130, a:1, s:1, b:0),
% 0.97/1.61 class_Groups_Oab__group__add [81, 1] (w:1, o:142, a:1, s:1, b:0),
% 0.97/1.61 v_e [82, 0] (w:1, o:61, a:1, s:1, b:0),
% 0.97/1.61 v_m____ [83, 0] (w:1, o:62, a:1, s:1, b:0),
% 0.97/1.61 c_Rings_Oinverse__class_Odivide [84, 3] (w:1, o:275, a:1, s:1, b:0),
% 0.97/1.61
% 0.97/1.61 c_Groups_Oabs__class_Oabs [85, 2] (w:1, o:258, a:1, s:1, b:0),
% 0.97/1.61 c_RealDef_Opositive [86, 1] (w:1, o:143, a:1, s:1, b:0),
% 0.97/1.61 class_Rings_Olinordered__idom [87, 1] (w:1, o:144, a:1, s:1, b:0),
% 0.97/1.61 c_Groups_Oplus__class_Oplus [88, 3] (w:1, o:276, a:1, s:1, b:0),
% 0.97/1.61 class_Orderings_Odense__linorder [89, 1] (w:1, o:145, a:1, s:1, b:0)
% 0.97/1.61 ,
% 0.97/1.61 class_Groups_Oordered__ab__group__add__abs [92, 1] (w:1, o:146, a:1
% 0.97/1.61 , s:1, b:0),
% 0.97/1.61 class_RealVector_Oreal__normed__field [94, 1] (w:1, o:147, a:1, s:1
% 0.97/1.61 , b:0),
% 0.97/1.61 class_Groups_Omonoid__add [95, 1] (w:1, o:148, a:1, s:1, b:0),
% 0.97/1.61 class_Groups_Ocomm__monoid__add [96, 1] (w:1, o:149, a:1, s:1, b:0),
% 0.97/1.61
% 0.97/1.61 class_Groups_Ozero [97, 1] (w:1, o:150, a:1, s:1, b:0),
% 0.97/1.61 class_Groups_Olinordered__ab__group__add [98, 1] (w:1, o:138, a:1, s:
% 0.97/1.61 1, b:0),
% 0.97/1.61 class_Rings_Odivision__ring__inverse__zero [99, 1] (w:1, o:156, a:1
% 0.97/1.61 , s:1, b:0),
% 0.97/1.61 class_Groups_Oab__semigroup__add [100, 1] (w:1, o:157, a:1, s:1, b:0)
% 0.97/1.61 ,
% 0.97/1.61 class_Groups_Ocancel__semigroup__add [102, 1] (w:1, o:158, a:1, s:1
% 0.97/1.61 , b:0),
% 0.97/1.61 class_Rings_Odivision__ring [103, 1] (w:1, o:159, a:1, s:1, b:0),
% 0.97/1.61 class_Rings_Olinordered__semidom [104, 1] (w:1, o:162, a:1, s:1, b:0)
% 0.97/1.61 ,
% 0.97/1.61 class_Groups_Ocancel__ab__semigroup__add [105, 1] (w:1, o:163, a:1
% 0.97/1.61 , s:1, b:0),
% 0.97/1.61 class_Groups_Oordered__comm__monoid__add [106, 1] (w:1, o:164, a:1
% 0.97/1.61 , s:1, b:0),
% 0.97/1.61 class_Fields_Ofield__inverse__zero [107, 1] (w:1, o:132, a:1, s:1, b:
% 0.97/1.61 0),
% 0.97/1.61 class_Rings_Ozero__neq__one [108, 1] (w:1, o:165, a:1, s:1, b:0),
% 0.97/1.61 class_Groups_Oordered__ab__semigroup__add__imp__le [111, 1] (w:1, o:
% 0.97/1.61 166, a:1, s:1, b:0),
% 0.97/1.61 class_Groups_Oordered__ab__semigroup__add [112, 1] (w:1, o:167, a:1
% 0.97/1.61 , s:1, b:0),
% 0.97/1.61 class_Groups_Oordered__cancel__ab__semigroup__add [113, 1] (w:1, o:
% 0.97/1.61 168, a:1, s:1, b:0),
% 0.97/1.61 class_Groups_Ogroup__add [114, 1] (w:1, o:169, a:1, s:1, b:0),
% 0.97/1.61 c_Groups_Otimes__class_Otimes [117, 1] (w:1, o:170, a:1, s:1, b:0),
% 0.97/1.61 class_Fields_Olinordered__field__inverse__zero [118, 1] (w:1, o:133
% 0.97/1.61 , a:1, s:1, b:0),
% 0.97/1.61 class_Fields_Olinordered__field [120, 1] (w:1, o:134, a:1, s:1, b:0)
% 0.97/1.61 ,
% 0.97/1.61 class_RealVector_Oreal__normed__div__algebra [121, 1] (w:1, o:171, a:
% 0.97/1.61 1, s:1, b:0),
% 0.97/1.61 class_Groups_Oab__semigroup__mult [125, 1] (w:1, o:172, a:1, s:1, b:0
% 0.97/1.61 ),
% 0.97/1.61 class_Lattices_Oab__semigroup__idem__mult [126, 1] (w:1, o:173, a:1
% 0.97/1.61 , s:1, b:0),
% 0.97/1.61 class_RealVector_Oreal__normed__algebra [127, 1] (w:1, o:174, a:1, s:
% 0.97/1.61 1, b:0),
% 0.97/1.61 class_Rings_Omult__zero [128, 1] (w:1, o:180, a:1, s:1, b:0),
% 0.97/1.61 class_Rings_Oring__no__zero__divisors [129, 1] (w:1, o:181, a:1, s:1
% 0.97/1.61 , b:0),
% 0.97/1.61 class_Rings_Ono__zero__divisors [130, 1] (w:1, o:182, a:1, s:1, b:0)
% 0.97/1.61 ,
% 0.97/1.61 class_Rings_Ocomm__semiring [131, 1] (w:1, o:153, a:1, s:1, b:0),
% 0.97/1.61 class_Rings_Osemiring [133, 1] (w:1, o:186, a:1, s:1, b:0),
% 0.97/1.61 class_Groups_Ocomm__monoid__mult [137, 1] (w:1, o:187, a:1, s:1, b:0)
% 0.97/1.61 ,
% 0.97/1.61 class_Groups_Omonoid__mult [138, 1] (w:1, o:188, a:1, s:1, b:0),
% 0.97/1.61 class_Fields_Ofield [141, 1] (w:1, o:135, a:1, s:1, b:0),
% 0.97/1.61 class_Rings_Oordered__cancel__semiring [142, 1] (w:1, o:189, a:1, s:1
% 0.97/1.61 , b:0),
% 0.97/1.61 class_Rings_Oordered__ring [143, 1] (w:1, o:190, a:1, s:1, b:0),
% 0.97/1.61 class_Rings_Oordered__semiring [144, 1] (w:1, o:192, a:1, s:1, b:0),
% 0.97/1.61
% 0.97/1.61 class_Rings_Oordered__comm__semiring [145, 1] (w:1, o:193, a:1, s:1
% 0.97/1.61 , b:0),
% 0.97/1.61 class_Rings_Olinordered__ring__strict [146, 1] (w:1, o:160, a:1, s:1
% 0.97/1.61 , b:0),
% 0.97/1.61 class_Rings_Olinordered__ring [147, 1] (w:1, o:161, a:1, s:1, b:0),
% 0.97/1.61 class_Rings_Olinordered__comm__semiring__strict [148, 1] (w:1, o:175
% 0.97/1.61 , a:1, s:1, b:0),
% 0.97/1.61 class_Rings_Olinordered__semiring__strict [149, 1] (w:1, o:176, a:1
% 0.97/1.61 , s:1, b:0),
% 0.97/1.61 class_Rings_Oring [152, 1] (w:1, o:183, a:1, s:1, b:0),
% 0.97/1.61 class_Rings_Olinordered__semiring [154, 1] (w:1, o:177, a:1, s:1, b:0
% 0.97/1.61 ),
% 0.97/1.61 class_Rings_Oring__1 [155, 1] (w:1, o:184, a:1, s:1, b:0),
% 0.97/1.61 class_Rings_Oordered__ring__abs [156, 1] (w:1, o:191, a:1, s:1, b:0)
% 0.97/1.61 ,
% 0.97/1.61 class_Rings_Olinordered__semiring__1 [159, 1] (w:1, o:178, a:1, s:1
% 0.97/1.61 , b:0),
% 0.97/1.61 class_Rings_Olinordered__semiring__1__strict [160, 1] (w:1, o:179, a:
% 0.97/1.61 1, s:1, b:0),
% 0.97/1.61 class_RealVector_Oreal__field [162, 1] (w:1, o:194, a:1, s:1, b:0),
% 0.97/1.61 class_Rings_Ocomm__semiring__1 [163, 1] (w:1, o:155, a:1, s:1, b:0),
% 0.97/1.61
% 0.97/1.61 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct [
% 0.97/1.61 164, 1] (w:1, o:198, a:1, s:1, b:0),
% 0.97/1.61 c_Complex_Oii [170, 0] (w:1, o:97, a:1, s:1, b:0),
% 0.97/1.61 c_Transcendental_Oarctan [173, 1] (w:1, o:199, a:1, s:1, b:0),
% 0.97/1.61 v_cs____ [174, 0] (w:1, o:22, a:1, s:1, b:0),
% 0.97/1.61 c_Polynomial_Opoly [175, 2] (w:1, o:259, a:1, s:1, b:0),
% 0.97/1.61 v_q____ [178, 0] (w:1, o:103, a:1, s:1, b:0),
% 0.97/1.61 v_p [179, 0] (w:1, o:102, a:1, s:1, b:0),
% 0.97/1.61 c_Polynomial_Odegree [181, 2] (w:1, o:260, a:1, s:1, b:0),
% 0.97/1.61 tc_Polynomial_Opoly [182, 1] (w:1, o:203, a:1, s:1, b:0),
% 0.97/1.61 class_Rings_Ocomm__ring [185, 1] (w:1, o:151, a:1, s:1, b:0),
% 0.97/1.61 class_Rings_Ocomm__semiring__0 [186, 1] (w:1, o:154, a:1, s:1, b:0),
% 0.97/1.61
% 0.97/1.61 tc_Nat_Onat [187, 0] (w:1, o:105, a:1, s:1, b:0),
% 0.97/1.61 class_Rings_Oidom [188, 1] (w:1, o:195, a:1, s:1, b:0),
% 0.97/1.61 class_Int_Oring__char__0 [191, 1] (w:1, o:204, a:1, s:1, b:0),
% 0.97/1.61 hBOOL [202, 1] (w:1, o:205, a:1, s:1, b:0),
% 0.97/1.61 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize [206, 2] (w:1, o:
% 0.97/1.61 257, a:1, s:1, b:0),
% 0.97/1.61 c_Polynomial_Oorder [207, 3] (w:1, o:277, a:1, s:1, b:0),
% 0.97/1.61 c_RComplete_Onatceiling [208, 1] (w:1, o:206, a:1, s:1, b:0),
% 0.97/1.61 c_RComplete_Onatfloor [209, 1] (w:1, o:207, a:1, s:1, b:0),
% 0.97/1.61 c_Polynomial_Opcompose [210, 3] (w:1, o:278, a:1, s:1, b:0),
% 0.97/1.61 c_Polynomial_Opdivmod__rel [211, 5] (w:1, o:395, a:1, s:1, b:0),
% 0.97/1.61 c_RealDef_Oreal [218, 2] (w:1, o:261, a:1, s:1, b:0),
% 0.97/1.61 c_Divides_Odiv__class_Odiv [220, 3] (w:1, o:279, a:1, s:1, b:0),
% 0.97/1.61 class_Divides_Osemiring__div [222, 1] (w:1, o:209, a:1, s:1, b:0),
% 0.97/1.61 c_Divides_Odiv__class_Omod [223, 3] (w:1, o:280, a:1, s:1, b:0),
% 0.97/1.61 c_Polynomial_Osynthetic__div [224, 3] (w:1, o:281, a:1, s:1, b:0),
% 0.97/1.61 class_Divides_Oring__div [225, 1] (w:1, o:208, a:1, s:1, b:0),
% 0.97/1.61 c_Complex_Oexpi [226, 1] (w:1, o:210, a:1, s:1, b:0),
% 0.97/1.61 c_Rings_Odvd__class_Odvd [227, 3] (w:1, o:282, a:1, s:1, b:0),
% 0.97/1.61 class_Rings_Odvd [230, 1] (w:1, o:196, a:1, s:1, b:0),
% 0.97/1.61 class_Rings_Ocomm__ring__1 [231, 1] (w:1, o:152, a:1, s:1, b:0),
% 0.97/1.61 class_Rings_Osemiring__0 [234, 1] (w:1, o:197, a:1, s:1, b:0),
% 0.97/1.61 c_SEQ_Odecseq [235, 2] (w:1, o:262, a:1, s:1, b:0),
% 0.97/1.61 c_Power_Opower__class_Opower [236, 1] (w:1, o:211, a:1, s:1, b:0),
% 0.97/1.61 class_Power_Opower [237, 1] (w:1, o:212, a:1, s:1, b:0),
% 0.97/1.61 tc_Int_Oint [238, 0] (w:1, o:117, a:1, s:1, b:0),
% 0.97/1.61 class_Rings_Oring__1__no__zero__divisors [239, 1] (w:1, o:185, a:1
% 0.97/1.61 , s:1, b:0),
% 0.97/1.61 c_Power_Opower_Opower [241, 3] (w:1, o:283, a:1, s:1, b:0),
% 0.97/1.61 class_Groups_Ocancel__comm__monoid__add [248, 1] (w:1, o:213, a:1, s:
% 0.97/1.61 1, b:0),
% 0.97/1.61 tc_HOL_Obool [250, 0] (w:1, o:116, a:1, s:1, b:0),
% 0.97/1.61 alpha1 [251, 2] (w:1, o:263, a:1, s:1, b:1),
% 0.97/1.61 alpha2 [252, 3] (w:1, o:293, a:1, s:1, b:1),
% 0.97/1.61 alpha3 [253, 3] (w:1, o:296, a:1, s:1, b:1),
% 0.97/1.61 alpha4 [254, 3] (w:1, o:301, a:1, s:1, b:1),
% 0.97/1.61 alpha5 [255, 3] (w:1, o:310, a:1, s:1, b:1),
% 0.97/1.61 alpha6 [256, 3] (w:1, o:316, a:1, s:1, b:1),
% 0.97/1.61 alpha7 [257, 3] (w:1, o:321, a:1, s:1, b:1),
% 0.97/1.61 alpha8 [258, 4] (w:1, o:365, a:1, s:1, b:1),
% 0.97/1.61 alpha9 [259, 4] (w:1, o:368, a:1, s:1, b:1),
% 0.97/1.61 alpha10 [260, 3] (w:1, o:284, a:1, s:1, b:1),
% 0.97/1.61 alpha11 [261, 3] (w:1, o:285, a:1, s:1, b:1),
% 0.97/1.61 alpha12 [262, 3] (w:1, o:286, a:1, s:1, b:1),
% 0.97/1.61 alpha13 [263, 3] (w:1, o:287, a:1, s:1, b:1),
% 0.97/1.61 alpha14 [264, 3] (w:1, o:288, a:1, s:1, b:1),
% 0.97/1.61 alpha15 [265, 3] (w:1, o:289, a:1, s:1, b:1),
% 0.97/1.61 alpha16 [266, 3] (w:1, o:290, a:1, s:1, b:1),
% 0.97/1.61 alpha17 [267, 3] (w:1, o:291, a:1, s:1, b:1),
% 1.79/2.16 alpha18 [268, 3] (w:1, o:292, a:1, s:1, b:1),
% 1.79/2.16 alpha19 [269, 2] (w:1, o:264, a:1, s:1, b:1),
% 1.79/2.16 alpha20 [270, 3] (w:1, o:294, a:1, s:1, b:1),
% 1.79/2.16 alpha21 [271, 2] (w:1, o:265, a:1, s:1, b:1),
% 1.79/2.16 alpha22 [272, 2] (w:1, o:266, a:1, s:1, b:1),
% 1.79/2.16 alpha23 [273, 2] (w:1, o:267, a:1, s:1, b:1),
% 1.79/2.16 alpha24 [274, 4] (w:1, o:369, a:1, s:1, b:1),
% 1.79/2.16 alpha25 [275, 4] (w:1, o:370, a:1, s:1, b:1),
% 1.79/2.16 alpha26 [276, 3] (w:1, o:295, a:1, s:1, b:1),
% 1.79/2.16 alpha27 [277, 2] (w:1, o:268, a:1, s:1, b:1),
% 1.79/2.16 alpha28 [278, 4] (w:1, o:371, a:1, s:1, b:1),
% 1.79/2.16 alpha29 [279, 4] (w:1, o:372, a:1, s:1, b:1),
% 1.79/2.16 alpha30 [280, 3] (w:1, o:297, a:1, s:1, b:1),
% 1.79/2.16 alpha31 [281, 3] (w:1, o:298, a:1, s:1, b:1),
% 1.79/2.16 alpha32 [282, 4] (w:1, o:373, a:1, s:1, b:1),
% 1.79/2.16 alpha33 [283, 4] (w:1, o:374, a:1, s:1, b:1),
% 1.79/2.16 alpha34 [284, 4] (w:1, o:375, a:1, s:1, b:1),
% 1.79/2.16 alpha35 [285, 4] (w:1, o:376, a:1, s:1, b:1),
% 1.79/2.16 alpha36 [286, 4] (w:1, o:377, a:1, s:1, b:1),
% 1.79/2.16 alpha37 [287, 4] (w:1, o:378, a:1, s:1, b:1),
% 1.79/2.16 alpha38 [288, 3] (w:1, o:299, a:1, s:1, b:1),
% 1.79/2.16 alpha39 [289, 3] (w:1, o:300, a:1, s:1, b:1),
% 1.79/2.16 alpha40 [290, 3] (w:1, o:302, a:1, s:1, b:1),
% 1.79/2.16 alpha41 [291, 3] (w:1, o:303, a:1, s:1, b:1),
% 1.79/2.16 alpha42 [292, 3] (w:1, o:304, a:1, s:1, b:1),
% 1.79/2.16 alpha43 [293, 3] (w:1, o:305, a:1, s:1, b:1),
% 1.79/2.16 alpha44 [294, 3] (w:1, o:306, a:1, s:1, b:1),
% 1.79/2.16 alpha45 [295, 3] (w:1, o:307, a:1, s:1, b:1),
% 1.79/2.16 alpha46 [296, 3] (w:1, o:308, a:1, s:1, b:1),
% 1.79/2.16 alpha47 [297, 3] (w:1, o:309, a:1, s:1, b:1),
% 1.79/2.16 alpha48 [298, 4] (w:1, o:379, a:1, s:1, b:1),
% 1.79/2.16 alpha49 [299, 4] (w:1, o:380, a:1, s:1, b:1),
% 1.79/2.16 alpha50 [300, 3] (w:1, o:311, a:1, s:1, b:1),
% 1.79/2.16 alpha51 [301, 4] (w:1, o:381, a:1, s:1, b:1),
% 1.79/2.16 alpha52 [302, 4] (w:1, o:382, a:1, s:1, b:1),
% 1.79/2.16 alpha53 [303, 4] (w:1, o:383, a:1, s:1, b:1),
% 1.79/2.16 alpha54 [304, 4] (w:1, o:384, a:1, s:1, b:1),
% 1.79/2.16 alpha55 [305, 4] (w:1, o:385, a:1, s:1, b:1),
% 1.79/2.16 alpha56 [306, 3] (w:1, o:312, a:1, s:1, b:1),
% 1.79/2.16 alpha57 [307, 3] (w:1, o:313, a:1, s:1, b:1),
% 1.79/2.16 alpha58 [308, 3] (w:1, o:314, a:1, s:1, b:1),
% 1.79/2.16 alpha59 [309, 3] (w:1, o:315, a:1, s:1, b:1),
% 1.79/2.16 alpha60 [310, 3] (w:1, o:317, a:1, s:1, b:1),
% 1.79/2.16 alpha61 [311, 4] (w:1, o:386, a:1, s:1, b:1),
% 1.79/2.16 alpha62 [312, 4] (w:1, o:387, a:1, s:1, b:1),
% 1.79/2.16 alpha63 [313, 4] (w:1, o:388, a:1, s:1, b:1),
% 1.79/2.16 alpha64 [314, 4] (w:1, o:389, a:1, s:1, b:1),
% 1.79/2.16 alpha65 [315, 4] (w:1, o:390, a:1, s:1, b:1),
% 1.79/2.16 alpha66 [316, 4] (w:1, o:391, a:1, s:1, b:1),
% 1.79/2.16 alpha67 [317, 3] (w:1, o:318, a:1, s:1, b:1),
% 1.79/2.16 alpha68 [318, 3] (w:1, o:319, a:1, s:1, b:1),
% 1.79/2.16 alpha69 [319, 3] (w:1, o:320, a:1, s:1, b:1),
% 1.79/2.16 alpha70 [320, 3] (w:1, o:322, a:1, s:1, b:1),
% 1.79/2.16 alpha71 [321, 4] (w:1, o:361, a:1, s:1, b:1),
% 1.79/2.16 alpha72 [322, 4] (w:1, o:362, a:1, s:1, b:1),
% 1.79/2.16 alpha73 [323, 4] (w:1, o:363, a:1, s:1, b:1),
% 1.79/2.16 alpha74 [324, 4] (w:1, o:364, a:1, s:1, b:1),
% 1.79/2.16 alpha75 [325, 3] (w:1, o:323, a:1, s:1, b:1),
% 1.79/2.16 alpha76 [326, 3] (w:1, o:324, a:1, s:1, b:1),
% 1.79/2.16 alpha77 [327, 3] (w:1, o:325, a:1, s:1, b:1),
% 1.79/2.16 alpha78 [328, 3] (w:1, o:326, a:1, s:1, b:1),
% 1.79/2.16 alpha79 [329, 3] (w:1, o:327, a:1, s:1, b:1),
% 1.79/2.16 alpha80 [330, 4] (w:1, o:366, a:1, s:1, b:1),
% 1.79/2.16 alpha81 [331, 3] (w:1, o:328, a:1, s:1, b:1),
% 1.79/2.16 alpha82 [332, 3] (w:1, o:329, a:1, s:1, b:1),
% 1.79/2.16 alpha83 [333, 4] (w:1, o:367, a:1, s:1, b:1),
% 1.79/2.16 alpha84 [334, 3] (w:1, o:330, a:1, s:1, b:1),
% 1.79/2.16 alpha85 [335, 2] (w:1, o:269, a:1, s:1, b:1),
% 1.79/2.16 alpha86 [336, 3] (w:1, o:331, a:1, s:1, b:1),
% 1.79/2.16 alpha87 [337, 2] (w:1, o:270, a:1, s:1, b:1),
% 1.79/2.16 alpha88 [338, 2] (w:1, o:271, a:1, s:1, b:1),
% 1.79/2.16 alpha89 [339, 3] (w:1, o:332, a:1, s:1, b:1),
% 1.79/2.16 skol1 [340, 2] (w:1, o:240, a:1, s:1, b:1),
% 1.79/2.16 skol2 [341, 3] (w:1, o:334, a:1, s:1, b:1),
% 1.79/2.16 skol3 [342, 3] (w:1, o:338, a:1, s:1, b:1),
% 1.79/2.16 skol4 [343, 4] (w:1, o:394, a:1, s:1, b:1),
% 1.79/2.16 skol5 [344, 3] (w:1, o:348, a:1, s:1, b:1),
% 9.86/10.21 skol6 [345, 3] (w:1, o:355, a:1, s:1, b:1),
% 9.86/10.21 skol7 [346, 0] (w:1, o:15, a:1, s:1, b:1),
% 9.86/10.21 skol8 [347, 0] (w:1, o:16, a:1, s:1, b:1),
% 9.86/10.21 skol9 [348, 2] (w:1, o:241, a:1, s:1, b:1),
% 9.86/10.21 skol10 [349, 1] (w:1, o:200, a:1, s:1, b:1),
% 9.86/10.21 skol11 [350, 2] (w:1, o:242, a:1, s:1, b:1),
% 9.86/10.21 skol12 [351, 2] (w:1, o:243, a:1, s:1, b:1),
% 9.86/10.21 skol13 [352, 0] (w:1, o:17, a:1, s:1, b:1),
% 9.86/10.21 skol14 [353, 3] (w:1, o:333, a:1, s:1, b:1),
% 9.86/10.21 skol15 [354, 0] (w:1, o:18, a:1, s:1, b:1),
% 9.86/10.21 skol16 [355, 0] (w:1, o:19, a:1, s:1, b:1),
% 9.86/10.21 skol17 [356, 0] (w:1, o:20, a:1, s:1, b:1),
% 9.86/10.21 skol18 [357, 2] (w:1, o:244, a:1, s:1, b:1),
% 9.86/10.21 skol19 [358, 2] (w:1, o:245, a:1, s:1, b:1),
% 9.86/10.21 skol20 [359, 1] (w:1, o:201, a:1, s:1, b:1),
% 9.86/10.21 skol21 [360, 2] (w:1, o:246, a:1, s:1, b:1),
% 9.86/10.21 skol22 [361, 2] (w:1, o:247, a:1, s:1, b:1),
% 9.86/10.21 skol23 [362, 3] (w:1, o:335, a:1, s:1, b:1),
% 9.86/10.21 skol24 [363, 3] (w:1, o:336, a:1, s:1, b:1),
% 9.86/10.21 skol25 [364, 2] (w:1, o:248, a:1, s:1, b:1),
% 9.86/10.21 skol26 [365, 2] (w:1, o:249, a:1, s:1, b:1),
% 9.86/10.21 skol27 [366, 1] (w:1, o:202, a:1, s:1, b:1),
% 9.86/10.21 skol28 [367, 2] (w:1, o:250, a:1, s:1, b:1),
% 9.86/10.21 skol29 [368, 3] (w:1, o:337, a:1, s:1, b:1),
% 9.86/10.21 skol30 [369, 4] (w:1, o:392, a:1, s:1, b:1),
% 9.86/10.21 skol31 [370, 3] (w:1, o:356, a:1, s:1, b:1),
% 9.86/10.21 skol32 [371, 2] (w:1, o:251, a:1, s:1, b:1),
% 9.86/10.21 skol33 [372, 3] (w:1, o:357, a:1, s:1, b:1),
% 9.86/10.21 skol34 [373, 3] (w:1, o:358, a:1, s:1, b:1),
% 9.86/10.21 skol35 [374, 3] (w:1, o:359, a:1, s:1, b:1),
% 9.86/10.21 skol36 [375, 4] (w:1, o:393, a:1, s:1, b:1),
% 9.86/10.21 skol37 [376, 3] (w:1, o:360, a:1, s:1, b:1),
% 9.86/10.21 skol38 [377, 2] (w:1, o:252, a:1, s:1, b:1),
% 9.86/10.21 skol39 [378, 2] (w:1, o:253, a:1, s:1, b:1),
% 9.86/10.21 skol40 [379, 3] (w:1, o:339, a:1, s:1, b:1),
% 9.86/10.21 skol41 [380, 3] (w:1, o:340, a:1, s:1, b:1),
% 9.86/10.21 skol42 [381, 3] (w:1, o:341, a:1, s:1, b:1),
% 9.86/10.21 skol43 [382, 3] (w:1, o:342, a:1, s:1, b:1),
% 9.86/10.21 skol44 [383, 3] (w:1, o:343, a:1, s:1, b:1),
% 9.86/10.21 skol45 [384, 3] (w:1, o:344, a:1, s:1, b:1),
% 9.86/10.21 skol46 [385, 2] (w:1, o:254, a:1, s:1, b:1),
% 9.86/10.21 skol47 [386, 3] (w:1, o:345, a:1, s:1, b:1),
% 9.86/10.21 skol48 [387, 3] (w:1, o:346, a:1, s:1, b:1),
% 9.86/10.21 skol49 [388, 3] (w:1, o:347, a:1, s:1, b:1),
% 9.86/10.21 skol50 [389, 3] (w:1, o:349, a:1, s:1, b:1),
% 9.86/10.21 skol51 [390, 3] (w:1, o:350, a:1, s:1, b:1),
% 9.86/10.21 skol52 [391, 3] (w:1, o:351, a:1, s:1, b:1),
% 9.86/10.21 skol53 [392, 3] (w:1, o:352, a:1, s:1, b:1),
% 9.86/10.21 skol54 [393, 2] (w:1, o:255, a:1, s:1, b:1),
% 9.86/10.21 skol55 [394, 3] (w:1, o:353, a:1, s:1, b:1),
% 9.86/10.21 skol56 [395, 3] (w:1, o:354, a:1, s:1, b:1).
% 9.86/10.21
% 9.86/10.21
% 9.86/10.21 Starting Search:
% 9.86/10.21
% 9.86/10.21 *** allocated 170857 integers for clauses
% 9.86/10.21
% 9.86/10.21 Intermediate Status:
% 9.86/10.21 Generated: 2820
% 9.86/10.21 Kept: 2073
% 9.86/10.21 Inuse: 0
% 9.86/10.21 Deleted: 0
% 9.86/10.21 Deletedinuse: 0
% 9.86/10.21
% 9.86/10.21 Resimplifying inuse:
% 9.86/10.21 Done
% 9.86/10.21
% 9.86/10.21 *** allocated 256285 integers for clauses
% 9.86/10.21 *** allocated 170857 integers for termspace/termends
% 9.86/10.21 Resimplifying inuse:
% 9.86/10.21 Done
% 9.86/10.21
% 9.86/10.21
% 9.86/10.21 Intermediate Status:
% 9.86/10.21 Generated: 6905
% 9.86/10.21 Kept: 4075
% 9.86/10.21 Inuse: 186
% 9.86/10.21 Deleted: 0
% 9.86/10.21 Deletedinuse: 0
% 9.86/10.21
% 9.86/10.21 Resimplifying inuse:
% 9.86/10.21 Done
% 9.86/10.21
% 9.86/10.21 *** allocated 384427 integers for clauses
% 9.86/10.21 Resimplifying inuse:
% 9.86/10.21 Done
% 9.86/10.21
% 9.86/10.21
% 9.86/10.21 Intermediate Status:
% 9.86/10.21 Generated: 11315
% 9.86/10.21 Kept: 6092
% 9.86/10.21 Inuse: 286
% 9.86/10.21 Deleted: 0
% 9.86/10.21 Deletedinuse: 0
% 9.86/10.21
% 9.86/10.21 Resimplifying inuse:
% 9.86/10.21 Done
% 9.86/10.21
% 9.86/10.21 *** allocated 256285 integers for termspace/termends
% 9.86/10.21 Resimplifying inuse:
% 9.86/10.21 Done
% 9.86/10.21
% 9.86/10.21 *** allocated 576640 integers for clauses
% 9.86/10.21
% 9.86/10.21 Intermediate Status:
% 9.86/10.21 Generated: 17403
% 9.86/10.21 Kept: 8093
% 9.86/10.21 Inuse: 346
% 9.86/10.21 Deleted: 3
% 9.86/10.21 Deletedinuse: 1
% 9.86/10.21
% 9.86/10.21 Resimplifying inuse:
% 9.86/10.21 Done
% 9.86/10.21
% 9.86/10.21 Resimplifying inuse:
% 9.86/10.21 Done
% 9.86/10.21
% 9.86/10.21
% 9.86/10.21 Intermediate Status:
% 9.86/10.21 Generated: 22752
% 9.86/10.21 Kept: 10106
% 9.86/10.21 Inuse: 393
% 9.86/10.21 Deleted: 3
% 9.86/10.21 Deletedinuse: 1
% 9.86/10.21
% 9.86/10.21 *** allocated 384427 integers for termspace/termends
% 9.86/10.21 Resimplifying inuse:
% 9.86/10.21 Done
% 9.86/10.21
% 9.86/10.21 Resimplifying inuse:
% 9.86/10.21 Done
% 9.86/10.21
% 9.86/10.21 *** allocated 864960 integers for clauses
% 9.86/10.21
% 9.86/10.21 Intermediate Status:
% 9.86/10.21 Generated: 27232
% 9.86/10.21 Kept: 12185
% 9.86/10.21 Inuse: 448
% 9.86/10.21 Deleted: 4
% 9.86/10.21 Deletedinuse: 1
% 9.86/10.21
% 9.86/10.21 Resimplifying inuse:
% 9.86/10.21 Done
% 9.86/10.21
% 9.86/10.21 Resimplifying inuse:
% 9.86/10.21 Done
% 9.86/10.21
% 9.86/10.21
% 9.86/10.21 Intermediate Status:
% 9.86/10.21 Generated: 31730
% 9.86/10.21 Kept: 14875
% 80.65/81.03 Inuse: 493
% 80.65/81.03 Deleted: 4
% 80.65/81.03 Deletedinuse: 1
% 80.65/81.03
% 80.65/81.03 Resimplifying inuse:
% 80.65/81.03 Done
% 80.65/81.03
% 80.65/81.03 Resimplifying inuse:
% 80.65/81.03 Done
% 80.65/81.03
% 80.65/81.03
% 80.65/81.03 Intermediate Status:
% 80.65/81.03 Generated: 38791
% 80.65/81.03 Kept: 17161
% 80.65/81.03 Inuse: 523
% 80.65/81.03 Deleted: 4
% 80.65/81.03 Deletedinuse: 1
% 80.65/81.03
% 80.65/81.03 Resimplifying inuse:
% 80.65/81.03 Done
% 80.65/81.03
% 80.65/81.03 *** allocated 576640 integers for termspace/termends
% 80.65/81.03 *** allocated 1297440 integers for clauses
% 80.65/81.03 Resimplifying inuse:
% 80.65/81.03 Done
% 80.65/81.03
% 80.65/81.03
% 80.65/81.03 Intermediate Status:
% 80.65/81.03 Generated: 42967
% 80.65/81.03 Kept: 19199
% 80.65/81.03 Inuse: 543
% 80.65/81.03 Deleted: 4
% 80.65/81.03 Deletedinuse: 1
% 80.65/81.03
% 80.65/81.03 Resimplifying inuse:
% 80.65/81.03 Done
% 80.65/81.03
% 80.65/81.03 Resimplifying inuse:
% 80.65/81.03 Done
% 80.65/81.03
% 80.65/81.03 Resimplifying clauses:
% 80.65/81.03 Done
% 80.65/81.03
% 80.65/81.03
% 80.65/81.03 Intermediate Status:
% 80.65/81.03 Generated: 50214
% 80.65/81.03 Kept: 21579
% 80.65/81.03 Inuse: 553
% 80.65/81.03 Deleted: 276
% 80.65/81.03 Deletedinuse: 1
% 80.65/81.03
% 80.65/81.03 Resimplifying inuse:
% 80.65/81.03 Done
% 80.65/81.03
% 80.65/81.03 Resimplifying inuse:
% 80.65/81.03 Done
% 80.65/81.03
% 80.65/81.03
% 80.65/81.03 Intermediate Status:
% 80.65/81.03 Generated: 56257
% 80.65/81.03 Kept: 23580
% 80.65/81.03 Inuse: 578
% 80.65/81.03 Deleted: 276
% 80.65/81.03 Deletedinuse: 1
% 80.65/81.03
% 80.65/81.03 Resimplifying inuse:
% 80.65/81.03 Done
% 80.65/81.03
% 80.65/81.03 Resimplifying inuse:
% 80.65/81.03 Done
% 80.65/81.03
% 80.65/81.03
% 80.65/81.03 Intermediate Status:
% 80.65/81.03 Generated: 59923
% 80.65/81.03 Kept: 25603
% 80.65/81.03 Inuse: 597
% 80.65/81.03 Deleted: 276
% 80.65/81.03 Deletedinuse: 1
% 80.65/81.03
% 80.65/81.03 *** allocated 864960 integers for termspace/termends
% 80.65/81.03 Resimplifying inuse:
% 80.65/81.03 Done
% 80.65/81.03
% 80.65/81.03
% 80.65/81.03 Intermediate Status:
% 80.65/81.03 Generated: 63641
% 80.65/81.03 Kept: 27639
% 80.65/81.03 Inuse: 615
% 80.65/81.03 Deleted: 276
% 80.65/81.03 Deletedinuse: 1
% 80.65/81.03
% 80.65/81.03 *** allocated 1946160 integers for clauses
% 80.65/81.03 Resimplifying inuse:
% 80.65/81.03 Done
% 80.65/81.03
% 80.65/81.03 Resimplifying inuse:
% 80.65/81.03 Done
% 80.65/81.03
% 80.65/81.03
% 80.65/81.03 Intermediate Status:
% 80.65/81.03 Generated: 72391
% 80.65/81.03 Kept: 30235
% 80.65/81.03 Inuse: 638
% 80.65/81.03 Deleted: 276
% 80.65/81.03 Deletedinuse: 1
% 80.65/81.03
% 80.65/81.03 Resimplifying inuse:
% 80.65/81.03 Done
% 80.65/81.03
% 80.65/81.03 Resimplifying inuse:
% 80.65/81.03 Done
% 80.65/81.03
% 80.65/81.03
% 80.65/81.03 Intermediate Status:
% 80.65/81.03 Generated: 77882
% 80.65/81.03 Kept: 32259
% 80.65/81.03 Inuse: 669
% 80.65/81.03 Deleted: 276
% 80.65/81.03 Deletedinuse: 1
% 80.65/81.03
% 80.65/81.03 Resimplifying inuse:
% 80.65/81.03 Done
% 80.65/81.03
% 80.65/81.03 Resimplifying inuse:
% 80.65/81.03 Done
% 80.65/81.03
% 80.65/81.03
% 80.65/81.03 Intermediate Status:
% 80.65/81.03 Generated: 82977
% 80.65/81.03 Kept: 34362
% 80.65/81.03 Inuse: 703
% 80.65/81.03 Deleted: 276
% 80.65/81.03 Deletedinuse: 1
% 80.65/81.03
% 80.65/81.03 Resimplifying inuse:
% 80.65/81.03 Done
% 80.65/81.03
% 80.65/81.03 Resimplifying inuse:
% 80.65/81.03 Done
% 80.65/81.03
% 80.65/81.03
% 80.65/81.03 Intermediate Status:
% 80.65/81.03 Generated: 89901
% 80.65/81.03 Kept: 37761
% 80.65/81.03 Inuse: 763
% 80.65/81.03 Deleted: 277
% 80.65/81.03 Deletedinuse: 2
% 80.65/81.03
% 80.65/81.03 Resimplifying inuse:
% 80.65/81.03 Done
% 80.65/81.03
% 80.65/81.03 Resimplifying inuse:
% 80.65/81.03 Done
% 80.65/81.03
% 80.65/81.03
% 80.65/81.03 Intermediate Status:
% 80.65/81.03 Generated: 94613
% 80.65/81.03 Kept: 39833
% 80.65/81.03 Inuse: 798
% 80.65/81.03 Deleted: 278
% 80.65/81.03 Deletedinuse: 3
% 80.65/81.03
% 80.65/81.03 Resimplifying inuse:
% 80.65/81.03 Done
% 80.65/81.03
% 80.65/81.03 *** allocated 1297440 integers for termspace/termends
% 80.65/81.03 Resimplifying inuse:
% 80.65/81.03 Done
% 80.65/81.03
% 80.65/81.03 Resimplifying clauses:
% 80.65/81.03 Done
% 80.65/81.03
% 80.65/81.03
% 80.65/81.03 Intermediate Status:
% 80.65/81.03 Generated: 99425
% 80.65/81.03 Kept: 41923
% 80.65/81.03 Inuse: 828
% 80.65/81.03 Deleted: 460
% 80.65/81.03 Deletedinuse: 3
% 80.65/81.03
% 80.65/81.03 Resimplifying inuse:
% 80.65/81.03 Done
% 80.65/81.03
% 80.65/81.03 *** allocated 2919240 integers for clauses
% 80.65/81.03 Resimplifying inuse:
% 80.65/81.03 Done
% 80.65/81.03
% 80.65/81.03
% 80.65/81.03 Intermediate Status:
% 80.65/81.03 Generated: 106475
% 80.65/81.03 Kept: 45502
% 80.65/81.03 Inuse: 858
% 80.65/81.03 Deleted: 460
% 80.65/81.03 Deletedinuse: 3
% 80.65/81.03
% 80.65/81.03 Resimplifying inuse:
% 80.65/81.03 Done
% 80.65/81.03
% 80.65/81.03 Resimplifying inuse:
% 80.65/81.03 Done
% 80.65/81.03
% 80.65/81.03
% 80.65/81.03 Intermediate Status:
% 80.65/81.03 Generated: 109649
% 80.65/81.03 Kept: 47506
% 80.65/81.03 Inuse: 865
% 80.65/81.03 Deleted: 460
% 80.65/81.03 Deletedinuse: 3
% 80.65/81.03
% 80.65/81.03 Resimplifying inuse:
% 80.65/81.03 Done
% 80.65/81.03
% 80.65/81.03
% 80.65/81.03 Intermediate Status:
% 80.65/81.03 Generated: 113720
% 80.65/81.03 Kept: 49551
% 80.65/81.03 Inuse: 893
% 80.65/81.03 Deleted: 460
% 80.65/81.03 Deletedinuse: 3
% 80.65/81.03
% 80.65/81.03 Resimplifying inuse:
% 80.65/81.03 Done
% 80.65/81.03
% 80.65/81.03 Resimplifying inuse:
% 80.65/81.03 Done
% 80.65/81.03
% 80.65/81.03
% 80.65/81.03 Intermediate Status:
% 80.65/81.03 Generated: 118274
% 80.65/81.03 Kept: 51607
% 80.65/81.03 Inuse: 919
% 80.65/81.03 Deleted: 460
% 80.65/81.03 Deletedinuse: 3
% 80.65/81.03
% 80.65/81.03 Resimplifying inuse:
% 80.65/81.03 Done
% 80.65/81.03
% 80.65/81.03 Resimplifying inuse:
% 80.65/81.03 Done
% 80.65/81.03
% 80.65/81.03
% 80.65/81.03 Intermediate Status:
% 80.65/81.03 Generated: 124292
% 80.65/81.03 Kept: 53655
% 80.65/81.03 Inuse: 953
% 80.65/81.03 Deleted: 460
% 80.65/81.03 Deletedinuse: 3
% 80.65/81.03
% 80.65/81.03 Resimplifying inuse:
% 80.65/81.03 Done
% 80.65/81.03
% 80.65/81.03 Resimplifying inuse:
% 80.65/81.03 Done
% 80.65/81.03
% 80.65/81.03
% 80.65/81.03 Intermediate Status:
% 80.65/81.03 Generated: 132975
% 80.65/81.03 Kept: 58625
% 80.65/81.03 Inuse: 978
% 80.65/81.03 Deleted: 461
% 80.65/81.03 Deletedinuse: 4
% 80.65/81.03
% 80.65/81.03 Resimplifying inuse:
% 80.65/81.03 Done
% 80.65/81.03
% 80.65/81.03 *** allocated 1946160 integers for termspace/termends
% 80.65/81.03
% 80.65/81.03 Intermediate Status:
% 80.65/81.03 Generated: 138297
% 80.65/81.03 Kept: 62689
% 80.65/81.03 Inuse: 983
% 80.65/81.03 Deleted: 461
% 80.65/81.03 Deletedinuse: 4
% 80.65/81.03
% 80.65/81.03 Resimplifying inuse:
% 80.65/81.03 Done
% 80.65/81.03
% 80.65/81.03 Resimplifying clauses:
% 80.65/81.03 Done
% 80.65/81.03
% 80.65/81.03 Resimplifying inuse:
% 80.65/81.03 Done
% 80.65/81.03
% 80.65/81.03
% 80.65/81.03 Intermediate Status:
% 80.65/81.03 Generated: 142817
% 80.65/81.03 Kept: 64692
% 80.65/81.03 Inuse: 1017
% 80.65/81.03 Deleted: 597
% 80.65/81.03 Deletedinuse: 4
% 80.65/81.03
% 80.65/81.03 Resimplifying inuse:
% 80.65/81.03 Done
% 80.65/81.03
% 80.65/81.03 *** allocated 4378860 integers for clauses
% 80.65/81.03 Resimplifying inuse:
% 80.65/81.03 Done
% 80.65/81.03
% 80.65/81.03
% 80.65/81.03 Intermediate Status:
% 80.65/81.03 Generated: 147388
% 80.65/81.03 Kept: 66748
% 80.65/81.03 Inuse: 1036
% 80.65/81.03 Deleted: 597
% 80.65/81.03 Deletedinuse: 4
% 80.65/81.03
% 80.65/81.03 Resimplifying inuse:
% 80.65/81.03 Done
% 80.65/81.03
% 80.65/81.03 Resimplifying inuse:
% 80.65/81.03 Done
% 80.65/81.03
% 80.65/81.03
% 80.65/81.03 Intermediate Status:
% 80.65/81.03 Generated: 152152
% 224.81/225.31 Kept: 68766
% 224.81/225.31 Inuse: 1057
% 224.81/225.31 Deleted: 597
% 224.81/225.31 Deletedinuse: 4
% 224.81/225.31
% 224.81/225.31 Resimplifying inuse:
% 224.81/225.31 Done
% 224.81/225.31
% 224.81/225.31 Resimplifying inuse:
% 224.81/225.31 Done
% 224.81/225.31
% 224.81/225.31
% 224.81/225.31 Intermediate Status:
% 224.81/225.31 Generated: 157344
% 224.81/225.31 Kept: 70774
% 224.81/225.31 Inuse: 1082
% 224.81/225.31 Deleted: 597
% 224.81/225.31 Deletedinuse: 4
% 224.81/225.31
% 224.81/225.31 Resimplifying inuse:
% 224.81/225.31 Done
% 224.81/225.31
% 224.81/225.31 Resimplifying inuse:
% 224.81/225.31 Done
% 224.81/225.31
% 224.81/225.31
% 224.81/225.31 Intermediate Status:
% 224.81/225.31 Generated: 162312
% 224.81/225.31 Kept: 72838
% 224.81/225.31 Inuse: 1103
% 224.81/225.31 Deleted: 597
% 224.81/225.31 Deletedinuse: 4
% 224.81/225.31
% 224.81/225.31 Resimplifying inuse:
% 224.81/225.31 Done
% 224.81/225.31
% 224.81/225.31 Resimplifying inuse:
% 224.81/225.31 Done
% 224.81/225.31
% 224.81/225.31
% 224.81/225.31 Intermediate Status:
% 224.81/225.31 Generated: 167224
% 224.81/225.31 Kept: 74881
% 224.81/225.31 Inuse: 1126
% 224.81/225.31 Deleted: 597
% 224.81/225.31 Deletedinuse: 4
% 224.81/225.31
% 224.81/225.31 Resimplifying inuse:
% 224.81/225.31 Done
% 224.81/225.31
% 224.81/225.31 Resimplifying inuse:
% 224.81/225.31 Done
% 224.81/225.31
% 224.81/225.31
% 224.81/225.31 Intermediate Status:
% 224.81/225.31 Generated: 172149
% 224.81/225.31 Kept: 76934
% 224.81/225.31 Inuse: 1147
% 224.81/225.31 Deleted: 597
% 224.81/225.31 Deletedinuse: 4
% 224.81/225.31
% 224.81/225.31
% 224.81/225.31 Intermediate Status:
% 224.81/225.31 Generated: 181366
% 224.81/225.31 Kept: 79612
% 224.81/225.31 Inuse: 1155
% 224.81/225.31 Deleted: 597
% 224.81/225.31 Deletedinuse: 4
% 224.81/225.31
% 224.81/225.31 Resimplifying inuse:
% 224.81/225.31 Done
% 224.81/225.31
% 224.81/225.31 Resimplifying inuse:
% 224.81/225.31 Done
% 224.81/225.31
% 224.81/225.31
% 224.81/225.31 Intermediate Status:
% 224.81/225.31 Generated: 187760
% 224.81/225.31 Kept: 82023
% 224.81/225.31 Inuse: 1188
% 224.81/225.31 Deleted: 599
% 224.81/225.31 Deletedinuse: 6
% 224.81/225.31
% 224.81/225.31 Resimplifying inuse:
% 224.81/225.31 Done
% 224.81/225.31
% 224.81/225.31
% 224.81/225.31 Intermediate Status:
% 224.81/225.31 Generated: 200188
% 224.81/225.31 Kept: 84676
% 224.81/225.31 Inuse: 1203
% 224.81/225.31 Deleted: 599
% 224.81/225.31 Deletedinuse: 6
% 224.81/225.31
% 224.81/225.31 Resimplifying inuse:
% 224.81/225.31 Done
% 224.81/225.31
% 224.81/225.31 Resimplifying clauses:
% 224.81/225.31 Done
% 224.81/225.31
% 224.81/225.31
% 224.81/225.31 Intermediate Status:
% 224.81/225.31 Generated: 213891
% 224.81/225.31 Kept: 87367
% 224.81/225.31 Inuse: 1218
% 224.81/225.31 Deleted: 1020
% 224.81/225.31 Deletedinuse: 6
% 224.81/225.31
% 224.81/225.31 Resimplifying inuse:
% 224.81/225.31 Done
% 224.81/225.31
% 224.81/225.31 Resimplifying inuse:
% 224.81/225.31 Done
% 224.81/225.31
% 224.81/225.31 *** allocated 2919240 integers for termspace/termends
% 224.81/225.31
% 224.81/225.31 Intermediate Status:
% 224.81/225.31 Generated: 219580
% 224.81/225.31 Kept: 89418
% 224.81/225.31 Inuse: 1248
% 224.81/225.31 Deleted: 1020
% 224.81/225.31 Deletedinuse: 6
% 224.81/225.31
% 224.81/225.31 Resimplifying inuse:
% 224.81/225.31 Done
% 224.81/225.31
% 224.81/225.31 Resimplifying inuse:
% 224.81/225.31 Done
% 224.81/225.31
% 224.81/225.31
% 224.81/225.31 Intermediate Status:
% 224.81/225.31 Generated: 243715
% 224.81/225.31 Kept: 93421
% 224.81/225.31 Inuse: 1288
% 224.81/225.31 Deleted: 1020
% 224.81/225.31 Deletedinuse: 6
% 224.81/225.31
% 224.81/225.31 Resimplifying inuse:
% 224.81/225.31 Done
% 224.81/225.31
% 224.81/225.31 Resimplifying inuse:
% 224.81/225.31 Done
% 224.81/225.31
% 224.81/225.31
% 224.81/225.31 Intermediate Status:
% 224.81/225.31 Generated: 270736
% 224.81/225.31 Kept: 96877
% 224.81/225.31 Inuse: 1298
% 224.81/225.31 Deleted: 1020
% 224.81/225.31 Deletedinuse: 6
% 224.81/225.31
% 224.81/225.31 Resimplifying inuse:
% 224.81/225.31 Done
% 224.81/225.31
% 224.81/225.31 Resimplifying inuse:
% 224.81/225.31 Done
% 224.81/225.31
% 224.81/225.31 *** allocated 6568290 integers for clauses
% 224.81/225.31
% 224.81/225.31 Intermediate Status:
% 224.81/225.31 Generated: 281506
% 224.81/225.31 Kept: 98974
% 224.81/225.31 Inuse: 1318
% 224.81/225.31 Deleted: 1020
% 224.81/225.31 Deletedinuse: 6
% 224.81/225.31
% 224.81/225.31 Resimplifying inuse:
% 224.81/225.31 Done
% 224.81/225.31
% 224.81/225.31 Resimplifying inuse:
% 224.81/225.31 Done
% 224.81/225.31
% 224.81/225.31
% 224.81/225.31 Intermediate Status:
% 224.81/225.31 Generated: 288730
% 224.81/225.31 Kept: 100979
% 224.81/225.31 Inuse: 1341
% 224.81/225.31 Deleted: 1020
% 224.81/225.31 Deletedinuse: 6
% 224.81/225.31
% 224.81/225.31
% 224.81/225.31 Intermediate Status:
% 224.81/225.31 Generated: 301497
% 224.81/225.31 Kept: 103318
% 224.81/225.31 Inuse: 1343
% 224.81/225.31 Deleted: 1020
% 224.81/225.31 Deletedinuse: 6
% 224.81/225.31
% 224.81/225.31 Resimplifying inuse:
% 224.81/225.31 Done
% 224.81/225.31
% 224.81/225.31
% 224.81/225.31 Intermediate Status:
% 224.81/225.31 Generated: 311844
% 224.81/225.31 Kept: 109673
% 224.81/225.31 Inuse: 1358
% 224.81/225.31 Deleted: 1020
% 224.81/225.31 Deletedinuse: 6
% 224.81/225.31
% 224.81/225.31 Resimplifying inuse:
% 224.81/225.31 Done
% 224.81/225.31
% 224.81/225.31 Resimplifying clauses:
% 224.81/225.31 Done
% 224.81/225.31
% 224.81/225.31
% 224.81/225.31 Intermediate Status:
% 224.81/225.31 Generated: 316618
% 224.81/225.31 Kept: 112893
% 224.81/225.31 Inuse: 1363
% 224.81/225.31 Deleted: 1096
% 224.81/225.31 Deletedinuse: 6
% 224.81/225.31
% 224.81/225.31 Resimplifying inuse:
% 224.81/225.31 Done
% 224.81/225.31
% 224.81/225.31 Resimplifying inuse:
% 224.81/225.31 Done
% 224.81/225.31
% 224.81/225.31
% 224.81/225.31 Intermediate Status:
% 224.81/225.31 Generated: 335495
% 224.81/225.31 Kept: 116960
% 224.81/225.31 Inuse: 1388
% 224.81/225.31 Deleted: 1096
% 224.81/225.31 Deletedinuse: 6
% 224.81/225.31
% 224.81/225.31 Resimplifying inuse:
% 224.81/225.31 Done
% 224.81/225.31
% 224.81/225.31
% 224.81/225.31 Intermediate Status:
% 224.81/225.31 Generated: 346318
% 224.81/225.31 Kept: 123516
% 224.81/225.31 Inuse: 1403
% 224.81/225.31 Deleted: 1096
% 224.81/225.31 Deletedinuse: 6
% 224.81/225.31
% 224.81/225.31 Resimplifying inuse:
% 224.81/225.31 Done
% 224.81/225.31
% 224.81/225.31
% 224.81/225.31 Intermediate Status:
% 224.81/225.31 Generated: 351211
% 224.81/225.31 Kept: 126809
% 224.81/225.31 Inuse: 1408
% 224.81/225.31 Deleted: 1096
% 224.81/225.31 Deletedinuse: 6
% 224.81/225.31
% 224.81/225.31 Resimplifying inuse:
% 224.81/225.31 Done
% 224.81/225.31
% 224.81/225.31 Resimplifying inuse:
% 224.81/225.31 Done
% 224.81/225.31
% 224.81/225.31
% 224.81/225.31 Intermediate Status:
% 224.81/225.31 Generated: 384695
% 224.81/225.31 Kept: 128825
% 224.81/225.31 Inuse: 1432
% 224.81/225.31 Deleted: 1096
% 224.81/225.31 Deletedinuse: 6
% 224.81/225.31
% 224.81/225.31 *** allocated 4378860 integers for termspace/termends
% 224.81/225.31 Resimplifying inuse:
% 224.81/225.31 Done
% 224.81/225.31
% 224.81/225.31 Resimplifying clauses:
% 224.81/225.31 Done
% 224.81/225.31
% 224.81/225.31
% 224.81/225.31 Intermediate Status:
% 224.81/225.31 Generated: 410261
% 224.81/225.31 Kept: 130852
% 224.81/225.31 Inuse: 1439
% 224.81/225.31 Deleted: 1118
% 224.81/225.31 Deletedinuse: 6
% 224.81/225.31
% 224.81/225.31 Resimplifying inuse:
% 224.81/225.31 Done
% 224.81/225.31
% 224.81/225.31 Resimplifying inuse:
% 224.81/225.31 Done
% 224.81/225.31
% 224.81/225.31
% 224.81/225.31 Intermediate Status:
% 224.81/225.31 Generated: 417881
% 224.81/225.31 Kept: 133014
% 224.81/225.31 Inuse: 1458
% 224.81/225.31 Deleted: 1118
% 224.81/225.31 Deletedinuse: 6
% 224.81/225.31
% 224.81/225.31 Resimplifying inuse:
% 224.81/225.31 Done
% 224.81/225.31
% 224.81/225.31
% 224.81/225.31 Intermediate Status:
% 224.81/225.31 Generated: 431953
% 224.81/225.31 Kept: 135248
% 224.81/225.31 Inuse: 1473
% 224.81/225.31 Deleted: 1118
% 224.81/225.31 Deletedinuse: 6
% 224.81/225.31
% 224.81/225.31 Resimplifying inuse:
% 224.81/225.31 Done
% 224.81/225.31
% 224.81/225.31 Resimplifying inuse:
% 224.81/225.31 Done
% 224.81/225.31
% 224.81/225.31
% 224.81/225.31 Intermediate Status:
% 224.81/225.31 Generated: 438941
% 224.81/225.31 Kept: 137403
% 224.81/225.31 Inuse: 1493
% 224.81/225.31 Deleted: Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------