TSTP Solution File: SWW239+1 by Bliksem---1.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWW239+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n032.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 23:21:29 EDT 2022
% Result : Timeout 300.03s 300.54s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09 % Problem : SWW239+1 : TPTP v8.1.0. Released v5.2.0.
% 0.05/0.10 % Command : bliksem %s
% 0.09/0.29 % Computer : n032.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % DateTime : Mon Jun 6 05:16:19 EDT 2022
% 0.09/0.29 % CPUTime :
% 0.77/1.33 *** allocated 10000 integers for termspace/termends
% 0.77/1.33 *** allocated 10000 integers for clauses
% 0.77/1.33 *** allocated 10000 integers for justifications
% 0.77/1.33 *** allocated 15000 integers for termspace/termends
% 0.77/1.33 *** allocated 22500 integers for termspace/termends
% 0.77/1.33 *** allocated 33750 integers for termspace/termends
% 0.77/1.33 Bliksem 1.12
% 0.77/1.33
% 0.77/1.33
% 0.77/1.33 Automatic Strategy Selection
% 0.77/1.33
% 0.77/1.33 *** allocated 50625 integers for termspace/termends
% 0.77/1.33 *** allocated 75937 integers for termspace/termends
% 0.77/1.33 *** allocated 113905 integers for termspace/termends
% 0.77/1.33
% 0.77/1.33 Clauses:
% 0.77/1.33
% 0.77/1.33 { ! hAPP( Y, skol1( X, Y ) ) = hAPP( X, skol1( X, Y ) ), Y = X }.
% 0.77/1.33 { c_Nat_OSuc( c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) =
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.77/1.33 c_Int_OPls ) ) ) }.
% 0.77/1.33 { c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.77/1.33 c_Int_OPls ) ) ) = c_Nat_OSuc( c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.77/1.33 tc_Nat_Onat ) ) ) }.
% 0.77/1.33 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.77/1.33 { c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit1( c_Int_OPls )
% 0.77/1.33 ) = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.77/1.33 { c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit1( c_Int_OBit1(
% 0.77/1.33 c_Int_OPls ) ) ) = c_Nat_OSuc( c_Nat_OSuc( c_Nat_OSuc(
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.77/1.33 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.77/1.33 tc_Polynomial_Opoly( X ) ),
% 0.77/1.33 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.77/1.33 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.77/1.33 tc_Polynomial_Opoly( X ) ),
% 0.77/1.33 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) = c_Nat_OSuc(
% 0.77/1.33 c_Polynomial_Odegree( X, Y ) ) }.
% 0.77/1.33 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( X, Y ) ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, Y ) }.
% 0.77/1.33 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, Y ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.77/1.33 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 0.77/1.33 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, c_Int_OPls ) }.
% 0.77/1.33 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, c_Int_OPls ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 0.77/1.33 , Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.77/1.33 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( X ) }.
% 0.77/1.33 { ! class_Groups_Ozero( X ), c_Polynomial_Odegree( X,
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.77/1.33 { c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) =
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OPls ) }.
% 0.77/1.33 { c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OPls ) =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.77/1.33 { c_Groups_Ozero__class_Ozero( tc_Int_Oint ) =
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OPls ) }.
% 0.77/1.33 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, X ) }.
% 0.77/1.33 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Z ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, Z ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ), Y = X }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( Y ),
% 0.77/1.33 c_Int_OBit1( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 0.77/1.33 ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( Y ),
% 0.77/1.33 c_Int_OBit1( X ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( Y ),
% 0.77/1.33 c_Int_OBit1( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 0.77/1.33 ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( Y ),
% 0.77/1.33 c_Int_OBit1( X ) ) }.
% 0.77/1.33 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, c_Int_OPls )
% 0.77/1.33 }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.77/1.33 c_Int_OBit0( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 0.77/1.33 ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.77/1.33 c_Int_OBit0( X ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.77/1.33 c_Int_OBit0( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 0.77/1.33 ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.77/1.33 c_Int_OBit0( X ) ) }.
% 0.77/1.33 { c_Int_OPls = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, c_Int_OBit1
% 0.77/1.33 ( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, X )
% 0.77/1.33 }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, c_Int_OBit1(
% 0.77/1.33 X ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.77/1.33 c_Int_OBit1( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 0.77/1.33 ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.77/1.33 c_Int_OBit1( X ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.77/1.33 c_Int_OBit1( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 0.77/1.33 ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.77/1.33 c_Int_OBit1( X ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( X ),
% 0.77/1.33 c_Int_OPls ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.77/1.33 c_Int_OPls ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, c_Int_OPls ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( X ),
% 0.77/1.33 c_Int_OPls ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, c_Int_OBit0
% 0.77/1.33 ( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, X )
% 0.77/1.33 }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, c_Int_OBit0(
% 0.77/1.33 X ) ) }.
% 0.77/1.33 { ! c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, c_Int_OPls ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, c_Int_OPls ),
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.77/1.33 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) =
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, c_Int_OPls ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, c_Int_OPls ),
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) =
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, c_Int_OPls ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, c_Int_OPls ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) }.
% 0.77/1.33 { ! class_Int_Onumber__ring( X ), ! class_Int_Oring__char__0( X ), !
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( X, Z ) =
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( X, Y ), Z = Y }.
% 0.77/1.33 { ! class_Int_Onumber__ring( X ), ! class_Int_Oring__char__0( X ), ! Z = Y
% 0.77/1.33 , c_Int_Onumber__class_Onumber__of( X, Z ) =
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( X, Y ) }.
% 0.77/1.33 { ! class_Int_Onumber( X ), ! c_Int_Onumber__class_Onumber__of( X, Z ) = Y
% 0.77/1.33 , Y = c_Int_Onumber__class_Onumber__of( X, Z ) }.
% 0.77/1.33 { ! class_Int_Onumber( X ), ! Y = c_Int_Onumber__class_Onumber__of( X, Z )
% 0.77/1.33 , c_Int_Onumber__class_Onumber__of( X, Z ) = Y }.
% 0.77/1.33 { ! c_Int_OBit1( Y ) = c_Int_OBit1( X ), Y = X }.
% 0.77/1.33 { ! Y = X, c_Int_OBit1( Y ) = c_Int_OBit1( X ) }.
% 0.77/1.33 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.77/1.33 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.77/1.33 { ! Y = X, c_Nat_OSuc( Y ) = c_Nat_OSuc( X ) }.
% 0.77/1.33 { ! c_Nat_OSuc( X ) = X }.
% 0.77/1.33 { ! X = c_Nat_OSuc( X ) }.
% 0.77/1.33 { ! c_Int_OBit0( Y ) = c_Int_OBit0( X ), Y = X }.
% 0.77/1.33 { ! Y = X, c_Int_OBit0( Y ) = c_Int_OBit0( X ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ), Y = X }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ) }.
% 0.77/1.33 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.77/1.33 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ) }.
% 0.77/1.33 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, X ) }.
% 0.77/1.33 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 0.77/1.33 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ), Z = Y }.
% 0.77/1.33 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Z = Y,
% 0.77/1.33 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ) }.
% 0.77/1.33 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 0.77/1.33 , Z ), c_Int_Onumber__class_Onumber__of( X, Y ) ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z, Y ) }.
% 0.77/1.33 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z, Y ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 0.77/1.33 , Z ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.77/1.33 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.77/1.33 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.77/1.33 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.77/1.33 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.77/1.33 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.77/1.33 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.77/1.33 { ! c_Int_OBit1( X ) = c_Int_OPls }.
% 0.77/1.33 { ! c_Int_OPls = c_Int_OBit1( X ) }.
% 0.77/1.33 { ! c_Int_OBit1( Y ) = c_Int_OBit0( X ) }.
% 0.77/1.33 { ! c_Int_OBit0( Y ) = c_Int_OBit1( X ) }.
% 0.77/1.33 { ! c_Int_OBit0( X ) = c_Int_OPls, X = c_Int_OPls }.
% 0.77/1.33 { ! X = c_Int_OPls, c_Int_OBit0( X ) = c_Int_OPls }.
% 0.77/1.33 { ! c_Int_OPls = c_Int_OBit0( X ), c_Int_OPls = X }.
% 0.77/1.33 { ! c_Int_OPls = X, c_Int_OPls = c_Int_OBit0( X ) }.
% 0.77/1.33 { c_Int_OBit0( c_Int_OPls ) = c_Int_OPls }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.77/1.33 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.77/1.33 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 0.77/1.33 ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 0.77/1.33 c_Nat_OSuc( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X )
% 0.77/1.33 }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 0.77/1.33 c_Nat_OSuc( X ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 0.77/1.33 ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.77/1.33 { ! Y = c_Nat_OSuc( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.77/1.33 , c_Nat_OSuc( X ) ) }.
% 0.77/1.33 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), X ) }
% 0.77/1.33 .
% 0.77/1.33 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 0.77/1.33 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.77/1.33 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Y =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.77/1.33 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.77/1.33 { ! class_Groups_Ozero( X ), !
% 0.77/1.33 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.77/1.33 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.77/1.33 tc_Polynomial_Opoly( X ) ),
% 0.77/1.33 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.77/1.33 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.77/1.33 c_Int_OPls ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.77/1.33 { ! class_Int_Onumber__ring( X ), c_Groups_Ozero__class_Ozero( X ) =
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( X, c_Int_OPls ) }.
% 0.77/1.33 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0( c_Int_OBit1(
% 0.77/1.33 c_Int_OPls ) ) ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0( X ) ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit1( X ) ) ) }.
% 0.77/1.33 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit1( c_Int_OBit1(
% 0.77/1.33 c_Int_OPls ) ) ) ) }.
% 0.77/1.33 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 0.77/1.33 tc_Polynomial_Opoly( X ) ), ! c_Polynomial_Oorder( X, Y, Z ) =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.77/1.33 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.77/1.33 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( X ) }.
% 0.77/1.33 { ! class_Rings_Oidom( X ), c_Polynomial_Oorder( X, Y, Z ) =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( c_Polynomial_Opoly( X,
% 0.77/1.33 Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.77/1.33 { ! class_Orderings_Opreorder( X ), c_Orderings_Oord__class_Oless__eq( X, Y
% 0.77/1.33 , Y ) }.
% 0.77/1.33 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OPls ) ) }.
% 0.77/1.33 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.77/1.33 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless__eq(
% 0.77/1.33 tc_Nat_Onat, c_Polynomial_Oorder( X, Z, Y ), c_Polynomial_Odegree( X, Y )
% 0.77/1.33 ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.77/1.33 c_Int_OPls ) ) ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.77/1.33 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.77/1.33 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Osynthetic__div( X
% 0.77/1.33 , Z, Y ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.77/1.33 c_Polynomial_Odegree( X, Z ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.77/1.33 }.
% 0.77/1.33 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Odegree( X, Z ) =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Polynomial_Osynthetic__div
% 0.77/1.33 ( X, Z, Y ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.77/1.33 { ! class_Rings_Olinordered__semidom( X ), ! c_Power_Opower__class_Opower(
% 0.77/1.33 X, Z, c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0(
% 0.77/1.33 c_Int_OBit1( c_Int_OPls ) ) ) ) = c_Power_Opower__class_Opower( X, Y,
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.77/1.33 c_Int_OPls ) ) ) ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.77/1.33 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.77/1.33 ), Z = Y }.
% 0.77/1.33 { ! class_Rings_Olinordered__semidom( X ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( X, c_Power_Opower__class_Opower( X, Z
% 0.77/1.33 , c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1
% 0.77/1.33 ( c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( X, Y,
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.77/1.33 c_Int_OPls ) ) ) ) ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.77/1.33 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless__eq
% 0.77/1.33 ( X, Z, Y ) }.
% 0.77/1.33 { ! class_Rings_Olinordered__idom( X ), c_Orderings_Oord__class_Oless__eq(
% 0.77/1.33 X, c_Groups_Ozero__class_Ozero( X ), c_Power_Opower__class_Opower( X, Y,
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.77/1.33 c_Int_OPls ) ) ) ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.77/1.33 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( X ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.77/1.33 X ) ) }.
% 0.77/1.33 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.77/1.33 tc_Nat_Onat ), c_Nat_OSuc( X ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.77/1.33 { c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) = X }.
% 0.77/1.33 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.77/1.33 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X = Y }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.77/1.33 { alpha61( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.77/1.33 hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.77/1.33 { alpha61( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP
% 0.77/1.33 ( X, Y ), Z ) ) }.
% 0.77/1.33 { ! alpha61( X, Y, Z ), alpha64( X, Y, Z ), Z = Y }.
% 0.77/1.33 { ! alpha61( X, Y, Z ), alpha64( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z
% 0.77/1.33 ) ) }.
% 0.77/1.33 { ! alpha64( X, Y, Z ), alpha61( X, Y, Z ) }.
% 0.77/1.33 { ! Z = Y, hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha61( X, Y, Z ) }.
% 0.77/1.33 { ! alpha64( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y )
% 0.77/1.33 }.
% 0.77/1.33 { ! alpha64( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP(
% 0.77/1.33 X, Y ), Z ) ), alpha64( X, Y, Z ) }.
% 0.77/1.33 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.77/1.33 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.77/1.33 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.77/1.33 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.77/1.33 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.77/1.33 , ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.77/1.33 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.77/1.33 Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.77/1.33 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.77/1.33 , ! Z = T, c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.77/1.33 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.77/1.33 ! Y = T, c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.77/1.33 { ! class_Orderings_Oorder( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless(
% 0.77/1.33 X, T, Y ), c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.77/1.33 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X
% 0.77/1.33 , Y, T ), c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.77/1.33 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.77/1.33 , ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.77/1.33 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.77/1.33 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.77/1.33 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.77/1.33 , ! Y = Z }.
% 0.77/1.33 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.77/1.33 , ! Z = Y }.
% 0.77/1.33 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.77/1.33 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.77/1.33 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.77/1.33 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.77/1.33 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.77/1.33 , ! Z = Y }.
% 0.77/1.33 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.77/1.33 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.77/1.33 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.77/1.33 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Y = Z }.
% 0.77/1.33 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.77/1.33 ), ! Y = Z, ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.77/1.33 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.77/1.33 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.77/1.33 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.77/1.33 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Z = Y }.
% 0.77/1.33 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.77/1.33 Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.77/1.33 { ! class_Orderings_Olinorder( X ), ! Z = Y, !
% 0.77/1.33 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.77/1.33 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.77/1.33 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.77/1.33 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.77/1.33 Y ), ! Z = Y }.
% 0.77/1.33 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.77/1.33 Z ), ! Z = Y }.
% 0.77/1.33 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.77/1.33 Y ) }.
% 0.77/1.33 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Z
% 0.77/1.33 ), c_Int_Onumber__class_Onumber__of( X, Y ) ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, Y ) }.
% 0.77/1.33 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, Y ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Z
% 0.77/1.33 ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.77/1.33 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 0.77/1.33 c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.77/1.33 c_Power_Opower__class_Opower( X, hAPP( c_Polynomial_Opoly( X, T ), Y ), Z
% 0.77/1.33 ) }.
% 0.77/1.33 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.77/1.33 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.77/1.33 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.77/1.33 , Y, Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.77/1.33 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.77/1.33 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.77/1.33 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.77/1.33 Z ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.77/1.33 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.77/1.33 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.77/1.33 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.77/1.33 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.77/1.33 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.77/1.33 , ! Z = Y }.
% 0.77/1.33 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.77/1.33 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.77/1.33 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.77/1.33 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.77/1.33 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.77/1.33 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.77/1.33 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.77/1.33 , Z, Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.77/1.33 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.77/1.33 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.77/1.33 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.77/1.33 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.77/1.33 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.77/1.33 ( X, Z, Y ) }.
% 0.77/1.33 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.77/1.33 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.77/1.33 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.77/1.33 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.77/1.33 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.77/1.33 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ), Z = Y }.
% 0.77/1.33 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.77/1.33 ), ! Z = Y, c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.77/1.33 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.77/1.33 ( X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.77/1.33 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.77/1.33 ( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.77/1.33 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.77/1.33 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.77/1.33 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.77/1.33 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.77/1.33 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.77/1.33 , Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.77/1.33 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.77/1.33 , Z, Y ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.77/1.33 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.77/1.33 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.77/1.33 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.77/1.33 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.77/1.33 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.77/1.33 , Y ), Y = Z, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.77/1.33 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.77/1.33 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.77/1.33 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.77/1.33 , ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.77/1.33 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.77/1.33 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.77/1.33 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.77/1.33 , Y ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Power_Opower__class_Opower
% 0.77/1.33 ( tc_Int_Oint, X, Y ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.77/1.33 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.77/1.33 tc_Nat_Onat ), X ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.77/1.33 ( tc_Nat_Onat ), X ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 0.77/1.33 .
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.77/1.33 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.77/1.33 tc_Nat_Onat ), X ) }.
% 0.77/1.33 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.77/1.33 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) )
% 0.77/1.33 }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.77/1.33 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.77/1.33 X ) ) }.
% 0.77/1.33 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y = X }
% 0.77/1.33 .
% 0.77/1.33 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X,
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.77/1.33 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), X = Y }
% 0.77/1.33 .
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) = X
% 0.77/1.33 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.77/1.33 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.77/1.33 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.77/1.33 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.77/1.33 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.77/1.33 ( tc_Int_Oint, c_Int_OPls, Y ) }.
% 0.77/1.33 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, Y ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.77/1.33 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Y
% 0.77/1.33 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless(
% 0.77/1.33 tc_Int_Oint, Y, c_Int_OPls ) }.
% 0.77/1.33 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, c_Int_OPls ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Y
% 0.77/1.33 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.77/1.33 { ! class_Int_Onumber( X ), ! class_Orderings_Olinorder( X ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 0.77/1.33 , Z ), c_Int_Onumber__class_Onumber__of( X, Y ) ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Y
% 0.77/1.33 ), c_Int_Onumber__class_Onumber__of( X, Z ) ) }.
% 0.77/1.33 { ! class_Int_Onumber( X ), ! class_Orderings_Olinorder( X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Y
% 0.77/1.33 ), c_Int_Onumber__class_Onumber__of( X, Z ) ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 0.77/1.33 , Z ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.77/1.33 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( skol2( X ) ) }.
% 0.77/1.33 { ! X = c_Nat_OSuc( Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.77/1.33 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha1( X, Y ) }.
% 0.77/1.33 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.77/1.33 { ! alpha1( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.77/1.33 c_Nat_OSuc( X ) ) }.
% 0.77/1.33 { ! alpha1( X, Y ), Y = c_Nat_OSuc( skol3( Z, Y ) ) }.
% 0.77/1.33 { ! alpha1( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol3( X, Y
% 0.77/1.33 ), X ) }.
% 0.77/1.33 { ! Y = c_Nat_OSuc( Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.77/1.33 ), alpha1( X, Y ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X = Y }
% 0.77/1.33 .
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X = Y,
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.77/1.33 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.77/1.33 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.77/1.33 , c_Power_Opower__class_Opower( X, Y, c_Int_Onumber__class_Onumber__of(
% 0.77/1.33 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ),
% 0.77/1.33 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.77/1.33 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.77/1.33 , c_Groups_Ozero__class_Ozero( X ), c_Power_Opower__class_Opower( X, Y,
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.77/1.33 c_Int_OPls ) ) ) ) ), ! Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.77/1.33 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.77/1.33 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.77/1.33 c_Power_Opower__class_Opower( X, Y, c_Int_Onumber__class_Onumber__of(
% 0.77/1.33 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) }.
% 0.77/1.33 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.77/1.33 ( X, c_Power_Opower__class_Opower( X, Z, c_Int_Onumber__class_Onumber__of
% 0.77/1.33 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ),
% 0.77/1.33 c_Power_Opower__class_Opower( X, Y, c_Int_Onumber__class_Onumber__of(
% 0.77/1.33 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.77/1.33 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.77/1.33 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.77/1.33 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.77/1.33 hAPP( Y, U ) ) }.
% 0.77/1.33 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, hAPP
% 0.77/1.33 ( Z, skol4( X, Y, Z ) ), hAPP( Y, skol4( X, Y, Z ) ) ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }.
% 0.77/1.33 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.77/1.33 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.77/1.33 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.77/1.33 ( X, Z, Y ) }.
% 0.77/1.33 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.77/1.33 ( X, Y, Z ) }.
% 0.77/1.33 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.77/1.33 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.77/1.33 { ! class_Orderings_Opreorder( X ), ! Z = Y,
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.77/1.33 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.77/1.33 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.77/1.33 hAPP( Y, U ) ) }.
% 0.77/1.33 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.77/1.33 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.77/1.33 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.77/1.33 , Y ), ! Y = Z, c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.77/1.33 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.77/1.33 ( X, Y, T ), c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.77/1.33 { ! class_Orderings_Oorder( X ), ! Z = Y, !
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.77/1.33 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y
% 0.77/1.33 ), ! Y = T, c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.77/1.33 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.77/1.33 , Y ), ! Z = T, c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.77/1.33 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.77/1.33 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.77/1.33 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.77/1.33 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.77/1.33 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.77/1.33 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.77/1.33 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.77/1.33 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.77/1.33 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.77/1.33 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.77/1.33 hAPP( Y, U ) ) }.
% 0.77/1.33 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.77/1.33 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.77/1.33 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Ozero__class_Ozero(
% 0.77/1.33 tc_Int_Oint ) ) }.
% 0.77/1.33 { ! class_Rings_Osemiring__1( X ), c_Power_Opower__class_Opower( X,
% 0.77/1.33 c_Groups_Ozero__class_Ozero( X ), c_Int_Onumber__class_Onumber__of(
% 0.77/1.33 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( X ) }.
% 0.77/1.33 { ! class_Rings_Oring__1__no__zero__divisors( X ), !
% 0.77/1.33 c_Power_Opower__class_Opower( X, Y, c_Int_Onumber__class_Onumber__of(
% 0.77/1.33 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 0.77/1.33 .
% 0.77/1.33 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( X ), c_Power_Opower__class_Opower( X, Y,
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.77/1.33 c_Int_OPls ) ) ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.77/1.33 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.77/1.33 tc_Nat_Onat ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0
% 0.77/1.33 ( c_Int_OBit1( c_Int_OPls ) ) ) ) }.
% 0.77/1.33 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.77/1.33 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.77/1.33 c_Groups_Ozero__class_Ozero( X ), Z ), ! c_Orderings_Oord__class_Oless(
% 0.77/1.33 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), T ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( X, c_Power_Opower__class_Opower( X, Z, T )
% 0.77/1.33 , c_Power_Opower__class_Opower( X, Y, T ) ) }.
% 0.77/1.33 { ! class_Rings_Olinordered__semidom( X ), ! c_Power_Opower__class_Opower(
% 0.77/1.33 X, T, Z ) = c_Power_Opower__class_Opower( X, Y, Z ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.77/1.33 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.77/1.33 X ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ), T = Y }.
% 0.77/1.33 { c_Power_Opower__class_Opower( tc_Complex_Ocomplex,
% 0.77/1.33 c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt( X ),
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.77/1.33 c_Int_OPls ) ) ) ) = X }.
% 0.77/1.33 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.77/1.33 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.77/1.33 , ! c_Power_Opower__class_Opower( X, Z, c_Int_Onumber__class_Onumber__of
% 0.77/1.33 ( tc_Nat_Onat, Y ) ) = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( X ) }.
% 0.77/1.33 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.77/1.33 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.77/1.33 , ! c_Power_Opower__class_Opower( X, Z, c_Int_Onumber__class_Onumber__of
% 0.77/1.33 ( tc_Nat_Onat, Y ) ) = c_Groups_Ozero__class_Ozero( X ), !
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.77/1.33 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.77/1.33 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.77/1.33 , ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Power_Opower__class_Opower
% 0.77/1.33 ( X, Z, c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) ) =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( X ) }.
% 0.77/1.33 { ! class_Rings_Olinordered__semidom( X ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( X, c_Power_Opower__class_Opower( X, Z
% 0.77/1.33 , c_Nat_OSuc( T ) ), c_Power_Opower__class_Opower( X, Y, c_Nat_OSuc( T )
% 0.77/1.33 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.77/1.33 ( X ), Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.77/1.33 { ! class_Rings_Olinordered__semidom( X ), ! c_Power_Opower__class_Opower(
% 0.77/1.33 X, Z, c_Nat_OSuc( T ) ) = c_Power_Opower__class_Opower( X, Y, c_Nat_OSuc
% 0.77/1.33 ( T ) ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.77/1.33 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.77/1.33 ), Z = Y }.
% 0.77/1.33 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.77/1.33 ( X, c_Power_Opower__class_Opower( X, Z, T ),
% 0.77/1.33 c_Power_Opower__class_Opower( X, Y, T ) ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.77/1.33 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.77/1.33 ( tc_Nat_Onat ), c_Power_Opower__class_Opower( tc_Nat_Onat, Y,
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) ),
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Orderings_Oord__class_Oless
% 0.77/1.33 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 0.77/1.33 { ! c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Orderings_Oord__class_Oless
% 0.77/1.33 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.77/1.33 c_Power_Opower__class_Opower( tc_Nat_Onat, Y,
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.77/1.33 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Power_Opower__class_Opower
% 0.77/1.33 ( tc_Nat_Onat, Y, c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) )
% 0.77/1.33 }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 0.77/1.33 c_Power_Opower__class_Opower( tc_Nat_Onat, X, Y ) ) }.
% 0.77/1.33 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.77/1.33 X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }
% 0.77/1.33 .
% 0.77/1.33 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.77/1.33 X ), Z, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z )
% 0.77/1.33 }.
% 0.77/1.33 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.77/1.33 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z
% 0.77/1.33 ), c_Orderings_Oord__class_Oless( tc_fun( T, X ), Z, Y ) }.
% 0.77/1.33 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y = X,
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( Y ),
% 0.77/1.33 c_Int_OBit1( X ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.77/1.33 .
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( Y ), c_Int_OBit1
% 0.77/1.33 ( X ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( Y ),
% 0.77/1.33 c_Int_OBit1( X ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.77/1.33 .
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( Y ), c_Int_OBit1
% 0.77/1.33 ( X ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, c_Int_OPls ) }
% 0.77/1.33 .
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.77/1.33 c_Int_OBit0( X ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.77/1.33 .
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( Y ), c_Int_OBit0
% 0.77/1.33 ( X ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.77/1.33 c_Int_OBit0( X ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.77/1.33 .
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( Y ), c_Int_OBit0
% 0.77/1.33 ( X ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), ! Y = X }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), Y = X,
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( X ),
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( X ),
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( X ),
% 0.77/1.33 c_Int_OPls ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Int_OPls )
% 0.77/1.33 }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Int_OPls ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( X ), c_Int_OPls
% 0.77/1.33 ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls,
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( Y ),
% 0.77/1.33 c_Int_OBit0( X ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.77/1.33 .
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( Y ), c_Int_OBit0
% 0.77/1.33 ( X ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( Y ),
% 0.77/1.33 c_Int_OBit0( X ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.77/1.33 .
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( Y ), c_Int_OBit0
% 0.77/1.33 ( X ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( X ),
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( X ),
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( X ),
% 0.77/1.33 c_Int_OPls ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Int_OPls )
% 0.77/1.33 }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Int_OPls ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( X ), c_Int_OPls
% 0.77/1.33 ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, c_Int_OBit0( X
% 0.77/1.33 ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, X ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, c_Int_OBit0( X )
% 0.77/1.33 ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( X ),
% 0.77/1.33 c_Int_OPls ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Int_OPls )
% 0.77/1.33 }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Int_OPls ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( X ),
% 0.77/1.33 c_Int_OPls ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, c_Int_OBit1( X
% 0.77/1.33 ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, X ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, c_Int_OBit1( X )
% 0.77/1.33 ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( Y ),
% 0.77/1.33 c_Int_OBit0( X ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.77/1.33 .
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( Y ),
% 0.77/1.33 c_Int_OBit0( X ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( Y ),
% 0.77/1.33 c_Int_OBit0( X ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.77/1.33 .
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( Y ),
% 0.77/1.33 c_Int_OBit0( X ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.77/1.33 c_Int_OBit1( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 0.77/1.33 ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( Y ), c_Int_OBit1
% 0.77/1.33 ( X ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.77/1.33 c_Int_OBit1( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 0.77/1.33 ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( Y ), c_Int_OBit1
% 0.77/1.33 ( X ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ), alpha2( X, Y ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.77/1.33 { ! alpha2( X, Y ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) }.
% 0.77/1.33 { ! alpha2( X, Y ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, X ) }.
% 0.77/1.33 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), alpha2( X, Y ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, X ), alpha2( X
% 0.77/1.33 , Y ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.77/1.33 ( tc_Nat_Onat ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, X ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.77/1.33 tc_Nat_Onat ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) }.
% 0.77/1.33 { ! class_Rings_Oring__1__no__zero__divisors( X ), Y =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( X ), ! c_Power_Opower__class_Opower( X, Y, Z
% 0.77/1.33 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.77/1.33 { ! c_Power_Opower__class_Opower( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = c_Nat_OSuc(
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.77/1.33 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.77/1.33 c_Power_Opower__class_Opower( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.77/1.33 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 0.77/1.33 c_Power_Opower__class_Opower( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.77/1.33 { c_Power_Opower__class_Opower( tc_Nat_Onat, c_Nat_OSuc(
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) = c_Nat_OSuc(
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.77/1.33 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.77/1.33 c_Power_Opower__class_Opower( tc_Nat_Onat, X, Z ),
% 0.77/1.33 c_Power_Opower__class_Opower( tc_Nat_Onat, X, Y ) ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.77/1.33 ( tc_Nat_Onat ), c_Power_Opower__class_Opower( tc_Nat_Onat, Y, X ) ), X =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.77/1.33 tc_Nat_Onat ), Y ) }.
% 0.77/1.33 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.77/1.33 tc_Nat_Onat ), c_Power_Opower__class_Opower( tc_Nat_Onat, Y, X ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.77/1.33 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Power_Opower__class_Opower
% 0.77/1.33 ( tc_Nat_Onat, Y, X ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.77/1.33 ( tc_Nat_Onat ), c_Power_Opower__class_Opower( tc_Nat_Onat, Y, X ) ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.77/1.33 tc_Nat_Onat ), Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.77/1.33 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Power_Opower__class_Opower
% 0.77/1.33 ( tc_Nat_Onat, Y, X ) ) }.
% 0.77/1.33 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.77/1.33 tc_Nat_Onat ), c_Power_Opower__class_Opower( tc_Nat_Onat, Y, X ) ) }.
% 0.77/1.33 { ! class_Rings_Olinordered__semidom( X ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.77/1.33 ), c_Orderings_Oord__class_Oless__eq( X, c_Power_Opower__class_Opower( X
% 0.77/1.33 , Z, T ), c_Power_Opower__class_Opower( X, Y, T ) ) }.
% 0.77/1.33 { ! class_Rings_Olinordered__semidom( X ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.77/1.33 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.77/1.33 ), c_Power_Opower__class_Opower( X, Y, Z ) ) }.
% 0.77/1.33 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.77/1.33 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless
% 0.77/1.33 ( X, c_Groups_Ozero__class_Ozero( X ), c_Power_Opower__class_Opower( X, Y
% 0.77/1.33 , Z ) ) }.
% 0.77/1.33 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.77/1.33 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.77/1.33 , ! c_Power_Opower__class_Opower( X, Z, Y ) = c_Groups_Ozero__class_Ozero
% 0.77/1.33 ( X ), Z = c_Groups_Ozero__class_Ozero( X ) }.
% 0.77/1.33 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.77/1.33 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.77/1.33 , ! c_Power_Opower__class_Opower( X, Z, Y ) = c_Groups_Ozero__class_Ozero
% 0.77/1.33 ( X ), ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.77/1.33 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.77/1.33 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.77/1.33 , ! Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 0.77/1.33 ( tc_Nat_Onat ), c_Power_Opower__class_Opower( X, Z, Y ) =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( X ) }.
% 0.77/1.33 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ),
% 0.77/1.33 c_Power_Opower__class_Opower( X, c_Groups_Ozero__class_Ozero( X ),
% 0.77/1.33 c_Nat_OSuc( Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( c_Nat_OSuc(
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X = c_Nat_OSuc(
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.77/1.33 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.77/1.33 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.77/1.33 , c_Power_Opower__class_Opower( X, Y, c_Nat_OSuc(
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat,
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.77/1.33 c_Int_OPls ) ) ), Z ) ) ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.77/1.33 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.77/1.33 ( X, c_Groups_Ozero__class_Ozero( X ), c_Power_Opower__class_Opower( X, Y
% 0.77/1.33 , c_Nat_OSuc( c_Groups_Otimes__class_Otimes( tc_Nat_Onat,
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.77/1.33 c_Int_OPls ) ) ), Z ) ) ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.77/1.33 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0( c_Int_OBit1(
% 0.77/1.33 c_Int_OPls ) ) ) ), X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X =
% 0.77/1.33 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.77/1.33 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.77/1.33 ( X, c_Power_Opower__class_Opower( X, Y, c_Groups_Otimes__class_Otimes(
% 0.77/1.33 tc_Nat_Onat, c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0(
% 0.77/1.33 c_Int_OBit1( c_Int_OPls ) ) ), Z ) ), c_Groups_Ozero__class_Ozero( X ) )
% 0.77/1.33 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.77/1.33 { ! class_Rings_Olinordered__idom( X ), c_Orderings_Oord__class_Oless__eq(
% 0.77/1.33 X, c_Groups_Ozero__class_Ozero( X ), c_Power_Opower__class_Opower( X, Z,
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat,
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.77/1.33 c_Int_OPls ) ) ), Y ) ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.77/1.33 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.77/1.33 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.77/1.33 c_Power_Opower__class_Opower( X, Z, c_Int_Onumber__class_Onumber__of(
% 0.77/1.33 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ),
% 0.77/1.33 c_Power_Opower__class_Opower( X, Y, c_Int_Onumber__class_Onumber__of(
% 0.77/1.33 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) ), ! Z =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.77/1.33 }.
% 0.77/1.33 { ! class_Rings_Olinordered__idom( X ), Z = c_Groups_Ozero__class_Ozero( X
% 0.77/1.33 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.77/1.33 c_Groups_Oplus__class_Oplus( X, c_Power_Opower__class_Opower( X, Z,
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.77/1.33 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( X, Y,
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.77/1.33 c_Int_OPls ) ) ) ) ) ) }.
% 0.77/1.33 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.77/1.33 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.77/1.33 c_Groups_Oplus__class_Oplus( X, c_Power_Opower__class_Opower( X, Z,
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.77/1.33 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( X, Y,
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.77/1.33 c_Int_OPls ) ) ) ) ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.77/1.33 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.77/1.33 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y
% 0.77/1.33 = X }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.77/1.33 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.77/1.33 tc_Int_Oint ) ) ) }.
% 0.77/1.33 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.77/1.33 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.77/1.33 tc_Int_Oint ) ) ) }.
% 0.77/1.33 { ! class_Groups_Omonoid__mult( X ), c_Power_Opower__class_Opower( X, T,
% 0.77/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ) =
% 0.77/1.33 c_Groups_Otimes__class_Otimes( X, c_Power_Opower__class_Opower( X, T, Z )
% 0.77/1.33 , c_Power_Opower__class_Opower( X, T, Y ) ) }.
% 0.77/1.33 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.77/1.33 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.77/1.33 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 0.77/1.33 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.77/1.33 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.77/1.33 c_Groups_Otimes__class_Otimes( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 0.77/1.33 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.77/1.33 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 0.77/1.33 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.77/1.33 c_Groups_Oone__class_Oone( X ) }.
% 0.77/1.33 { ! class_Int_Onumber__ring( X ), c_Groups_Otimes__class_Otimes( X,
% 0.77/1.33 c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.77/1.33 c_Groups_Oone__class_Oone( X ) ), c_Int_Onumber__class_Onumber__of( X, Y
% 0.77/1.33 ) ) = c_Int_Onumber__class_Onumber__of( X, c_Int_OBit0( Y ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.77/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.77/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.77/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.77/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.77/1.33 { c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) =
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Y ) }.
% 0.77/1.33 { c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z,
% 0.77/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 0.77/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.77/1.33 tc_Nat_Onat, Z, Y ), c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ) )
% 0.77/1.33 }.
% 0.77/1.33 { c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Groups_Otimes__class_Otimes
% 0.77/1.33 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Otimes__class_Otimes( tc_Nat_Onat,
% 0.77/1.33 Z, c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) ) }.
% 0.77/1.33 { c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.77/1.33 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ),
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) ) }.
% 0.77/1.33 { c_Int_OBit1( X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.77/1.33 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oone__class_Oone(
% 0.77/1.33 tc_Int_Oint ), X ), X ) }.
% 0.77/1.33 { c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 0.77/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) ) }.
% 0.77/1.33 { c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.77/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) ) }.
% 0.77/1.33 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Int_Oint, Z, Y ) ) =
% 0.77/1.33 c_Groups_Otimes__class_Otimes( X, c_Int_Onumber__class_Onumber__of( X, Z
% 0.77/1.33 ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.77/1.33 { ! class_Int_Onumber__ring( X ), c_Groups_Otimes__class_Otimes( X,
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( X, Z ),
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( X, Y ) ) =
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( X, c_Groups_Otimes__class_Otimes(
% 0.77/1.33 tc_Int_Oint, Z, Y ) ) }.
% 0.77/1.33 { ! class_Int_Onumber__ring( X ), c_Groups_Otimes__class_Otimes( X,
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( X, T ), c_Groups_Otimes__class_Otimes(
% 0.77/1.33 X, c_Int_Onumber__class_Onumber__of( X, Z ), Y ) ) =
% 0.77/1.33 c_Groups_Otimes__class_Otimes( X, c_Int_Onumber__class_Onumber__of( X,
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Int_Oint, T, Z ) ), Y ) }.
% 0.77/1.33 { ! class_Int_Onumber( X ), ! class_Rings_Osemiring( X ),
% 0.77/1.33 c_Groups_Otimes__class_Otimes( X, c_Int_Onumber__class_Onumber__of( X, T
% 0.77/1.33 ), c_Groups_Oplus__class_Oplus( X, Z, Y ) ) =
% 0.77/1.33 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( X, T ), Z ),
% 0.77/1.33 c_Groups_Otimes__class_Otimes( X, c_Int_Onumber__class_Onumber__of( X, T
% 0.77/1.33 ), Y ) ) }.
% 0.77/1.33 { ! class_Int_Onumber( X ), ! class_Rings_Osemiring( X ),
% 0.77/1.33 c_Groups_Otimes__class_Otimes( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.77/1.33 , c_Int_Onumber__class_Onumber__of( X, Y ) ) =
% 0.77/1.33 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, T,
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( X, Y ) ), c_Groups_Otimes__class_Otimes
% 0.77/1.33 ( X, Z, c_Int_Onumber__class_Onumber__of( X, Y ) ) ) }.
% 0.77/1.33 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.77/1.33 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ) =
% 0.77/1.33 c_Groups_Oplus__class_Oplus( X, c_Int_Onumber__class_Onumber__of( X, Z )
% 0.77/1.33 , c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.77/1.33 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X,
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( X, Z ),
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( X, Y ) ) =
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( X, c_Groups_Oplus__class_Oplus(
% 0.77/1.33 tc_Int_Oint, Z, Y ) ) }.
% 0.77/1.33 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X,
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( X, T ), c_Groups_Oplus__class_Oplus( X
% 0.77/1.33 , c_Int_Onumber__class_Onumber__of( X, Z ), Y ) ) =
% 0.77/1.33 c_Groups_Oplus__class_Oplus( X, c_Int_Onumber__class_Onumber__of( X,
% 0.77/1.33 c_Groups_Oplus__class_Oplus( tc_Int_Oint, T, Z ) ), Y ) }.
% 0.77/1.33 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.77/1.33 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, Z, Z )
% 0.77/1.33 , c_Groups_Otimes__class_Otimes( X, Y, Y ) ) =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.77/1.33 .
% 0.77/1.33 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.77/1.33 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, Z, Z )
% 0.77/1.33 , c_Groups_Otimes__class_Otimes( X, Y, Y ) ) =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 0.77/1.33 .
% 0.77/1.33 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.77/1.33 , c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, Z, Z
% 0.77/1.33 ), c_Groups_Otimes__class_Otimes( X, Y, Y ) ) =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( X ) }.
% 0.77/1.33 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.77/1.33 tc_Int_Oint, c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ) =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.77/1.33 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X,
% 0.77/1.33 c_Groups_Oone__class_Oone( X ), c_Int_Onumber__class_Onumber__of( X, Y )
% 0.77/1.33 ) = c_Int_Onumber__class_Onumber__of( X, c_Groups_Oplus__class_Oplus(
% 0.77/1.33 tc_Int_Oint, c_Int_OBit1( c_Int_OPls ), Y ) ) }.
% 0.77/1.33 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X,
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( X, Y ), c_Groups_Oone__class_Oone( X )
% 0.77/1.33 ) = c_Int_Onumber__class_Onumber__of( X, c_Groups_Oplus__class_Oplus(
% 0.77/1.33 tc_Int_Oint, Y, c_Int_OBit1( c_Int_OPls ) ) ) }.
% 0.77/1.33 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.77/1.33 X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.77/1.33 c_Groups_Otimes__class_Otimes( X, Z, Z ), c_Groups_Otimes__class_Otimes(
% 0.77/1.33 X, Y, Y ) ) ) }.
% 0.77/1.33 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.77/1.33 c_Groups_Otimes__class_Otimes( X, Z, Z ), c_Groups_Otimes__class_Otimes(
% 0.77/1.33 X, Y, Y ) ), c_Groups_Ozero__class_Ozero( X ) ), Z =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( X ) }.
% 0.77/1.33 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.77/1.33 c_Groups_Otimes__class_Otimes( X, Z, Z ), c_Groups_Otimes__class_Otimes(
% 0.77/1.33 X, Y, Y ) ), c_Groups_Ozero__class_Ozero( X ) ), Y =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( X ) }.
% 0.77/1.33 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.77/1.33 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.77/1.33 c_Groups_Otimes__class_Otimes( X, Z, Z ), c_Groups_Otimes__class_Otimes(
% 0.77/1.33 X, Y, Y ) ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.77/1.33 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.77/1.33 , c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, Z, Z
% 0.77/1.33 ), c_Groups_Otimes__class_Otimes( X, Y, Y ) ),
% 0.77/1.33 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.77/1.33 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.77/1.33 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, Z, Z )
% 0.77/1.33 , c_Groups_Otimes__class_Otimes( X, Y, Y ) ) ), ! Z =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.77/1.33 }.
% 0.77/1.33 { ! class_Rings_Olinordered__ring__strict( X ), Z =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.77/1.33 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.77/1.33 c_Groups_Otimes__class_Otimes( X, Z, Z ), c_Groups_Otimes__class_Otimes(
% 0.77/1.33 X, Y, Y ) ) ) }.
% 0.77/1.33 { ! class_Rings_Olinordered__ring__strict( X ), Y =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.77/1.33 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.77/1.33 c_Groups_Otimes__class_Otimes( X, Z, Z ), c_Groups_Otimes__class_Otimes(
% 0.77/1.33 X, Y, Y ) ) ) }.
% 0.77/1.33 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.77/1.33 c_Int_OBit1( Y ) ) = c_Groups_Oplus__class_Oplus( X,
% 0.77/1.33 c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( X, Y ) ),
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.77/1.33 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.77/1.33 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.77/1.33 X, c_Power_Opower__class_Opower( X, Y, Z ), c_Groups_Otimes__class_Otimes
% 0.77/1.33 ( X, Y, c_Power_Opower__class_Opower( X, Y, Z ) ) ) }.
% 0.77/1.33 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.77/1.33 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.77/1.33 X, c_Groups_Oone__class_Oone( X ), c_Groups_Otimes__class_Otimes( X, Y,
% 0.77/1.33 c_Power_Opower__class_Opower( X, Y, Z ) ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.77/1.33 ( tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.77/1.33 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.77/1.33 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.77/1.33 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.33 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.77/1.33 tc_Int_Oint ) ), X ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.33 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.77/1.33 tc_Int_Oint ) ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X )
% 0.77/1.33 }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.33 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.77/1.33 tc_Int_Oint ) ), X ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.77/1.33 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.77/1.33 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X )
% 0.77/1.33 }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.77/1.33 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.77/1.33 tc_Int_Oint ) ) ) }.
% 0.77/1.33 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.77/1.33 c_Groups_Oplus__class_Oplus( X, Y, Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.77/1.33 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.77/1.33 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.77/1.33 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.77/1.33 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.77/1.33 tc_Nat_Onat ), X ) = X }.
% 0.77/1.33 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero
% 0.77/1.33 ( tc_Nat_Onat ) ) = X }.
% 0.77/1.33 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.77/1.33 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.77/1.33 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.77/1.33 tc_Nat_Onat, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.77/1.33 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = Y, X =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.77/1.33 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.77/1.33 tc_Int_Oint ), X ) = X }.
% 0.77/1.33 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero
% 0.77/1.33 ( tc_Int_Oint ) ) = X }.
% 0.77/1.33 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Int_OPls, X ) = X }.
% 0.77/1.33 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Int_OPls ) = X }.
% 0.77/1.33 { ! class_Groups_Ocomm__monoid__mult( X ), c_Power_Opower__class_Opower( X
% 0.77/1.33 , c_Groups_Otimes__class_Otimes( X, T, Z ), Y ) =
% 0.77/1.33 c_Groups_Otimes__class_Otimes( X, c_Power_Opower__class_Opower( X, T, Y )
% 0.77/1.33 , c_Power_Opower__class_Opower( X, Z, Y ) ) }.
% 0.77/1.33 { ! class_Groups_Omonoid__mult( X ), c_Groups_Otimes__class_Otimes( X,
% 0.77/1.33 c_Power_Opower__class_Opower( X, Z, Y ), Z ) =
% 0.77/1.33 c_Groups_Otimes__class_Otimes( X, Z, c_Power_Opower__class_Opower( X, Z,
% 0.77/1.33 Y ) ) }.
% 0.77/1.33 { c_Int_OBit0( X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, X ) }.
% 0.77/1.33 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Int_OBit0( Y ), c_Int_OBit0(
% 0.77/1.33 X ) ) = c_Int_OBit0( c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }
% 0.77/1.33 .
% 0.77/1.33 { c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.77/1.33 tc_Nat_Onat ), X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.77/1.33 { c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X,
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.77/1.33 { ! c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.77/1.33 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.77/1.33 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.77/1.33 { ! c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ) =
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ), Y = X, Z =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.77/1.33 { ! Y = X, c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ) =
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ) }.
% 0.77/1.33 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ) =
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ) }.
% 0.77/1.33 { ! c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ) =
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Y ), Z = X, Y =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.77/1.33 { ! Z = X, c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ) =
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Y ) }.
% 0.77/1.33 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ) =
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Y ) }.
% 0.77/1.33 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 0.77/1.33 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.77/1.33 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.77/1.33 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.77/1.33 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.77/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.77/1.33 { ! class_Groups_Omonoid__mult( X ), c_Power_Opower__class_Opower( X,
% 0.77/1.33 c_Groups_Oone__class_Oone( X ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.77/1.33 ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.77/1.33 ( tc_Nat_Onat, Y, X ), X ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.77/1.33 ( tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) )
% 0.77/1.33 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.77/1.33 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }
% 0.77/1.33 .
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.77/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.77/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.77/1.33 tc_Nat_Onat, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.77/1.33 .
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.77/1.33 tc_Nat_Onat, Y, T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.77/1.33 .
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.77/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, X ) =
% 0.77/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.77/1.33 ( tc_Nat_Onat, Y, Z ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y
% 0.77/1.33 , X ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.33 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ),
% 0.77/1.33 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.77/1.33 { ! class_Groups_Omonoid__mult( X ), c_Power_Opower__class_Opower( X, T,
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ) ) =
% 0.77/1.33 c_Power_Opower__class_Opower( X, c_Power_Opower__class_Opower( X, T, Z )
% 0.77/1.33 , Y ) }.
% 0.77/1.33 { ! c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Nat_OSuc( Z ), Y ) =
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Nat_OSuc( Z ), X ), Y = X }
% 0.77/1.33 .
% 0.77/1.33 { ! Y = X, c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Nat_OSuc( Z ), Y )
% 0.77/1.33 = c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Nat_OSuc( Z ), X ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.77/1.33 tc_Int_Oint, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.77/1.33 .
% 0.77/1.33 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.77/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.77/1.33 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.77/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 0.77/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol5( X, Y ) ) }.
% 0.77/1.33 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.77/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.77/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.77/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.77/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.77/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.77/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.77/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.77/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.77/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, T ),
% 0.77/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.77/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.77/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ), X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.77/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.77/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.77/1.33 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, X ) ) }.
% 0.77/1.33 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X,
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, X ) ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, Z ),
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Z ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ),
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, T ),
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Z ) ) }.
% 0.77/1.33 { c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) =
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Int_Oint,
% 0.77/1.33 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 0.77/1.33 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.77/1.33 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.77/1.33 tc_Polynomial_Opoly( X ) ), Y ) = Y }.
% 0.77/1.33 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.77/1.33 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 0.77/1.33 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.77/1.33 { ! c_Groups_Ozero__class_Ozero( tc_Int_Oint ) = c_Groups_Oone__class_Oone
% 0.77/1.33 ( tc_Int_Oint ) }.
% 0.77/1.33 { c_Power_Opower__class_Opower( tc_Int_Oint, c_Power_Opower__class_Opower(
% 0.77/1.33 tc_Int_Oint, Z, Y ), X ) = c_Power_Opower__class_Opower( tc_Int_Oint, Z,
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) ) }.
% 0.77/1.33 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.77/1.33 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, Y,
% 0.77/1.33 c_Power_Opower__class_Opower( X, Y, Z ) ), c_Power_Opower__class_Opower(
% 0.77/1.33 X, Y, Z ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, c_Int_OPls ),
% 0.77/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) =
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) }.
% 0.77/1.33 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, c_Int_OPls ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Int_OPls ),
% 0.77/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) =
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) }.
% 0.77/1.33 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, c_Int_OPls ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Int_OPls ),
% 0.77/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) =
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 0.77/1.33 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.77/1.33 tc_Int_Oint ), c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.77/1.33 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) ) }.
% 0.77/1.33 { ! class_Int_Onumber__ring( X ), c_Groups_Otimes__class_Otimes( X, Y,
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( X, c_Int_OBit0( c_Int_OBit1( c_Int_OPls
% 0.77/1.33 ) ) ) ) = c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 0.77/1.33 { ! class_Int_Onumber__ring( X ), c_Groups_Otimes__class_Otimes( X,
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( X, c_Int_OBit0( c_Int_OBit1( c_Int_OPls
% 0.77/1.33 ) ) ), Y ) = c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 0.77/1.33 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X,
% 0.77/1.33 c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ) =
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( X, c_Int_OBit0( c_Int_OBit1( c_Int_OPls
% 0.77/1.33 ) ) ) }.
% 0.77/1.33 { c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X,
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.77/1.33 c_Int_OPls ) ) ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, X ) }.
% 0.77/1.33 { c_Groups_Otimes__class_Otimes( tc_Nat_Onat,
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.77/1.33 c_Int_OPls ) ) ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, X )
% 0.77/1.33 }.
% 0.77/1.33 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.77/1.33 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.77/1.33 ) ), c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 0.77/1.33 ) ) }.
% 0.77/1.33 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.77/1.33 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.77/1.33 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.77/1.33 ) ) }.
% 0.77/1.33 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( X, c_Int_OPls ) ) = Y }.
% 0.77/1.33 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X,
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( X, c_Int_OPls ), Y ) = Y }.
% 0.77/1.33 { ! class_Rings_Olinordered__semidom( X ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 0.77/1.33 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.77/1.33 c_Power_Opower__class_Opower( X, Y, Z ) ) }.
% 0.77/1.33 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.77/1.33 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Power_Opower__class_Opower
% 0.77/1.33 ( X, Y, T ) = c_Power_Opower__class_Opower( X, Y, Z ), T = Z }.
% 0.77/1.33 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.77/1.33 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! T = Z,
% 0.77/1.33 c_Power_Opower__class_Opower( X, Y, T ) = c_Power_Opower__class_Opower( X
% 0.77/1.33 , Y, Z ) }.
% 0.77/1.33 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Int_OBit0( Y ), c_Int_OBit1(
% 0.77/1.33 X ) ) = c_Int_OBit1( c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }
% 0.77/1.33 .
% 0.77/1.33 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Int_OBit1( Y ), c_Int_OBit0(
% 0.77/1.33 X ) ) = c_Int_OBit1( c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }
% 0.77/1.33 .
% 0.77/1.33 { ! c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.77/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ), alpha3( X, Y ), alpha21
% 0.77/1.33 ( X, Y ) }.
% 0.77/1.33 { ! alpha3( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.77/1.33 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.77/1.33 { ! alpha21( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.77/1.33 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.77/1.33 { ! alpha21( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.77/1.33 { ! alpha21( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.77/1.33 tc_Nat_Onat ) ) }.
% 0.77/1.33 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha21( X, Y ) }.
% 0.77/1.33 { ! alpha3( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.77/1.33 tc_Nat_Onat ) ) }.
% 0.77/1.33 { ! alpha3( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.77/1.33 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha3( X, Y ) }.
% 0.77/1.33 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha4( X, Y ), alpha22( X
% 0.77/1.33 , Y ) }.
% 0.77/1.33 { ! alpha4( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.77/1.33 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.77/1.33 { ! alpha22( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.77/1.33 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.77/1.33 { ! alpha22( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.77/1.33 { ! alpha22( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.77/1.33 tc_Nat_Onat ) ) }.
% 0.77/1.33 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha22( X, Y ) }.
% 0.77/1.33 { ! alpha4( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.77/1.33 tc_Nat_Onat ) ) }.
% 0.77/1.33 { ! alpha4( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.77/1.33 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha4( X, Y ) }.
% 0.77/1.33 { ! class_Groups_Omonoid__mult( X ), c_Power_Opower__class_Opower( X, Z,
% 0.77/1.33 c_Nat_OSuc( Y ) ) = c_Groups_Otimes__class_Otimes( X,
% 0.77/1.33 c_Power_Opower__class_Opower( X, Z, Y ), Z ) }.
% 0.77/1.33 { ! class_Power_Opower( X ), c_Power_Opower__class_Opower( X, Z, c_Nat_OSuc
% 0.77/1.33 ( Y ) ) = c_Groups_Otimes__class_Otimes( X, Z,
% 0.77/1.33 c_Power_Opower__class_Opower( X, Z, Y ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.77/1.33 ( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.77/1.33 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.77/1.33 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.77/1.33 tc_Nat_Onat, Y, X ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.77/1.33 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.77/1.33 tc_Nat_Onat, Y, X ) ) }.
% 0.77/1.33 { ! class_Power_Opower( X ), c_Power_Opower__class_Opower( X, Y,
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone
% 0.77/1.33 ( X ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.77/1.33 tc_Int_Oint, X, Y ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), X = c_Nat_OSuc(
% 0.77/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol6( X, Y ) ) ) }.
% 0.77/1.33 { ! X = c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.77/1.33 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 0.77/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ) }.
% 0.77/1.33 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 0.77/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.77/1.33 { ! c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y = c_Nat_OSuc(
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.77/1.33 { ! c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X = c_Nat_OSuc(
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.77/1.33 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.77/1.33 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.77/1.33 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ),
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.77/1.33 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, Z ),
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Z ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ),
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Y ) ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.77/1.33 tc_Nat_Onat ), Y ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ),
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Y ) ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.77/1.33 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.77/1.33 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ),
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Y ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ),
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ) ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.77/1.33 tc_Nat_Onat ), Z ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ),
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ) ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.77/1.33 ( tc_Nat_Onat ), Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 0.77/1.33 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ),
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.77/1.33 ( tc_Nat_Onat ), c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.77/1.33 tc_Nat_Onat ), Y ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.77/1.33 ( tc_Nat_Onat ), c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.77/1.33 tc_Nat_Onat ), X ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.77/1.33 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.77/1.33 tc_Nat_Onat ), c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Nat_OSuc( Z ), Y ),
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Nat_OSuc( Z ), X ) ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Otimes__class_Otimes
% 0.77/1.33 ( tc_Nat_Onat, c_Nat_OSuc( Z ), Y ), c_Groups_Otimes__class_Otimes(
% 0.77/1.33 tc_Nat_Onat, c_Nat_OSuc( Z ), X ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Z ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.77/1.33 tc_Int_Oint, Y, T ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.77/1.33 .
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Nat_OSuc( Z ), Y ),
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Nat_OSuc( Z ), X ) ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Nat_OSuc( Z ), Y ),
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Nat_OSuc( Z ), X ) ) }.
% 0.77/1.33 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 0.77/1.33 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) )
% 0.77/1.33 , c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 0.77/1.33 tc_Polynomial_Opoly( X ), Y, Z ) ) = c_Polynomial_Odegree( X, Y ) }.
% 0.77/1.33 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 0.77/1.33 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) )
% 0.77/1.33 , c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 0.77/1.33 tc_Polynomial_Opoly( X ), Z, Y ) ) = c_Polynomial_Odegree( X, Y ) }.
% 0.77/1.33 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 0.77/1.33 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, T )
% 0.77/1.33 , Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree(
% 0.77/1.33 X, c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Z, T ) ), Y ) }
% 0.77/1.33 .
% 0.77/1.33 { ! class_Groups_Ocomm__monoid__add( X ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 0.77/1.33 Z ), Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.77/1.33 c_Polynomial_Odegree( X, T ), Y ), c_Orderings_Oord__class_Oless__eq(
% 0.77/1.33 tc_Nat_Onat, c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 0.77/1.33 tc_Polynomial_Opoly( X ), Z, T ) ), Y ) }.
% 0.77/1.33 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 0.77/1.33 tc_Int_Oint ) ) }.
% 0.77/1.33 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.77/1.33 tc_Int_Oint ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.77/1.33 { ! class_Int_Onumber__ring( X ), c_Power_Opower__class_Opower( X,
% 0.77/1.33 c_Groups_Oplus__class_Oplus( X, Z, Y ), c_Int_Onumber__class_Onumber__of
% 0.77/1.33 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) =
% 0.77/1.33 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X,
% 0.77/1.33 c_Power_Opower__class_Opower( X, Z, c_Int_Onumber__class_Onumber__of(
% 0.77/1.33 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ),
% 0.77/1.33 c_Power_Opower__class_Opower( X, Y, c_Int_Onumber__class_Onumber__of(
% 0.77/1.33 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ),
% 0.77/1.33 c_Groups_Otimes__class_Otimes( X, c_Groups_Otimes__class_Otimes( X,
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( X, c_Int_OBit0( c_Int_OBit1( c_Int_OPls
% 0.77/1.33 ) ) ), Z ), Y ) ) }.
% 0.77/1.33 { ! class_Groups_Omonoid__mult( X ), c_Power_Opower__class_Opower( X, Z,
% 0.77/1.33 c_Nat_OSuc( c_Groups_Otimes__class_Otimes( tc_Nat_Onat,
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.77/1.33 c_Int_OPls ) ) ), Y ) ) ) = c_Groups_Otimes__class_Otimes( X, Z,
% 0.77/1.33 c_Power_Opower__class_Opower( X, c_Power_Opower__class_Opower( X, Z, Y )
% 0.77/1.33 , c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1
% 0.77/1.33 ( c_Int_OPls ) ) ) ) ) }.
% 0.77/1.33 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.77/1.33 c_Int_OBit0( Y ) ) = c_Groups_Oplus__class_Oplus( X,
% 0.77/1.33 c_Groups_Oplus__class_Oplus( X, c_Groups_Ozero__class_Ozero( X ),
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( X, Y ) ),
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.77/1.33 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), ! Y =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Power_Opower__class_Opower
% 0.77/1.33 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Oone__class_Oone( X
% 0.77/1.33 ) }.
% 0.77/1.33 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), Y =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Power_Opower__class_Opower
% 0.77/1.33 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero
% 0.77/1.33 ( X ) }.
% 0.77/1.33 { ! class_Int_Onumber__ring( X ), c_Groups_Otimes__class_Otimes( X, Y,
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( X, c_Int_OBit1( c_Int_OPls ) ) ) = Y }
% 0.77/1.33 .
% 0.77/1.33 { ! class_Int_Onumber__ring( X ), c_Groups_Otimes__class_Otimes( X,
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( X, c_Int_OBit1( c_Int_OPls ) ), Y ) = Y
% 0.77/1.33 }.
% 0.77/1.33 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.77/1.33 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.77/1.33 X, c_Groups_Oone__class_Oone( X ), c_Power_Opower__class_Opower( X, Y,
% 0.77/1.33 c_Nat_OSuc( Z ) ) ) }.
% 0.77/1.33 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.77/1.33 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.77/1.33 c_Groups_Oone__class_Oone( X ), T ), c_Orderings_Oord__class_Oless( X,
% 0.77/1.33 c_Power_Opower__class_Opower( X, T, Z ), c_Power_Opower__class_Opower( X
% 0.77/1.33 , T, Y ) ) }.
% 0.77/1.33 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.77/1.33 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.77/1.33 ( X, c_Power_Opower__class_Opower( X, Y, T ),
% 0.77/1.33 c_Power_Opower__class_Opower( X, Y, Z ) ), c_Orderings_Oord__class_Oless
% 0.77/1.33 ( tc_Nat_Onat, T, Z ) }.
% 0.77/1.33 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.77/1.33 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.77/1.33 ( X, c_Power_Opower__class_Opower( X, Y, T ),
% 0.77/1.33 c_Power_Opower__class_Opower( X, Y, Z ) ), c_Orderings_Oord__class_Oless
% 0.77/1.33 ( tc_Nat_Onat, T, Z ) }.
% 0.77/1.33 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.77/1.33 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.77/1.33 ( tc_Nat_Onat, T, Z ), c_Orderings_Oord__class_Oless( X,
% 0.77/1.33 c_Power_Opower__class_Opower( X, Y, T ), c_Power_Opower__class_Opower( X
% 0.77/1.33 , Y, Z ) ) }.
% 0.77/1.33 { ! class_Rings_Olinordered__semidom( X ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), T )
% 0.77/1.33 , c_Orderings_Oord__class_Oless__eq( X, c_Power_Opower__class_Opower( X,
% 0.77/1.33 T, Z ), c_Power_Opower__class_Opower( X, T, Y ) ) }.
% 0.77/1.33 { ! class_Int_Onumber__ring( X ), c_Groups_Oone__class_Oone( X ) =
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( X, c_Int_OBit1( c_Int_OPls ) ) }.
% 0.77/1.33 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.77/1.33 c_Int_OBit1( c_Int_OPls ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Y ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ),
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ) ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.77/1.33 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 0.77/1.33 ) }.
% 0.77/1.33 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.77/1.33 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ),
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ),
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ),
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Y ) ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.77/1.33 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X
% 0.77/1.33 ) }.
% 0.77/1.33 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.77/1.33 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ),
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Y ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ),
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Y ) ) }.
% 0.77/1.33 { c_Groups_Oone__class_Oone( tc_Int_Oint ) =
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit1( c_Int_OPls )
% 0.77/1.33 ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.33 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.77/1.33 tc_Int_Oint ), X ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.77/1.33 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.33 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) }.
% 0.77/1.33 { ! class_Rings_Ocomm__semiring__1( X ), c_Orderings_Oord__class_Oless__eq
% 0.77/1.33 ( tc_Nat_Onat, c_Polynomial_Odegree( X, c_Power_Opower__class_Opower(
% 0.77/1.33 tc_Polynomial_Opoly( X ), Z, Y ) ), c_Groups_Otimes__class_Otimes(
% 0.77/1.33 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ) ) }.
% 0.77/1.33 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.77/1.33 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( X, c_Power_Opower__class_Opower( X, Y,
% 0.77/1.33 c_Nat_OSuc( Z ) ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.77/1.33 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.77/1.33 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.77/1.33 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 0.77/1.33 , T, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.77/1.33 c_Power_Opower__class_Opower( X, T, Y ), c_Power_Opower__class_Opower( X
% 0.77/1.33 , T, Z ) ) }.
% 0.77/1.33 { ! class_Rings_Olinordered__semidom( X ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.77/1.33 ), ! c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oone__class_Oone
% 0.77/1.33 ( X ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.77/1.33 c_Power_Opower__class_Opower( X, T, Y ), c_Power_Opower__class_Opower( X
% 0.77/1.33 , T, Z ) ) }.
% 0.77/1.33 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.77/1.33 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( X, c_Power_Opower__class_Opower( X, Y
% 0.77/1.33 , T ), c_Power_Opower__class_Opower( X, Y, Z ) ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.77/1.33 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.77/1.33 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( X, c_Power_Opower__class_Opower( X, Y
% 0.77/1.33 , T ), c_Power_Opower__class_Opower( X, Y, Z ) ) }.
% 0.77/1.33 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.77/1.33 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( X, c_Power_Opower__class_Opower( X, Y
% 0.77/1.33 , T ), c_Power_Opower__class_Opower( X, Y, Z ) ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.77/1.33 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.77/1.33 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.77/1.33 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 0.77/1.33 c_Power_Opower__class_Opower( X, Y, Z ) ) }.
% 0.77/1.33 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), !
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Power_Opower__class_Opower
% 0.77/1.33 ( X, c_Groups_Ozero__class_Ozero( X ), c_Int_Onumber__class_Onumber__of(
% 0.77/1.33 tc_Nat_Onat, Y ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.77/1.33 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ),
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Power_Opower__class_Opower
% 0.77/1.33 ( X, c_Groups_Ozero__class_Ozero( X ), c_Int_Onumber__class_Onumber__of(
% 0.77/1.33 tc_Nat_Onat, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.77/1.33 { ! class_Groups_Omonoid__mult( X ), c_Power_Opower__class_Opower( X, Y,
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit1( c_Int_OBit1(
% 0.77/1.33 c_Int_OPls ) ) ) ) = c_Groups_Otimes__class_Otimes( X,
% 0.77/1.33 c_Groups_Otimes__class_Otimes( X, Y, Y ), Y ) }.
% 0.77/1.33 { c_Nat_OSuc( c_Nat_OSuc( c_Nat_OSuc( X ) ) ) = c_Groups_Oplus__class_Oplus
% 0.77/1.33 ( tc_Nat_Onat, c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit1
% 0.77/1.33 ( c_Int_OBit1( c_Int_OPls ) ) ), X ) }.
% 0.77/1.33 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( X, Y ) ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( c_Int_OPls )
% 0.77/1.33 , Y ) }.
% 0.77/1.33 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( c_Int_OPls )
% 0.77/1.33 , Y ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X
% 0.77/1.33 ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.77/1.33 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 0.77/1.33 , Y ), c_Groups_Oone__class_Oone( X ) ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, c_Int_OBit1(
% 0.77/1.33 c_Int_OPls ) ) }.
% 0.77/1.33 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, c_Int_OBit1(
% 0.77/1.33 c_Int_OPls ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( X, Y ), c_Groups_Oone__class_Oone( X )
% 0.77/1.33 ) }.
% 0.77/1.33 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.77/1.33 ( tc_Int_Oint, c_Int_OBit1( c_Int_OPls ), Y ) }.
% 0.77/1.33 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( c_Int_OPls ), Y
% 0.77/1.33 ), c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.77/1.33 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Y
% 0.77/1.33 ), c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless(
% 0.77/1.33 tc_Int_Oint, Y, c_Int_OBit1( c_Int_OPls ) ) }.
% 0.77/1.33 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, c_Int_OBit1( c_Int_OPls )
% 0.77/1.33 ), c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X
% 0.77/1.33 , Y ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.77/1.33 { ! class_Groups_Omonoid__mult( X ), c_Power_Opower__class_Opower( X, Y,
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.77/1.33 c_Int_OPls ) ) ) ) = c_Groups_Otimes__class_Otimes( X, Y, Y ) }.
% 0.77/1.33 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.77/1.33 c_Int_OPls ) ) ) ) = c_Nat_OSuc( c_Nat_OSuc( X ) ) }.
% 0.77/1.33 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.77/1.33 c_Int_OPls ) ) ), X ) = c_Nat_OSuc( c_Nat_OSuc( X ) ) }.
% 0.77/1.33 { ! class_Rings_Osemiring__1( X ), c_Power_Opower__class_Opower( X,
% 0.77/1.33 c_Groups_Oone__class_Oone( X ), c_Int_Onumber__class_Onumber__of(
% 0.77/1.33 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) =
% 0.77/1.33 c_Groups_Oone__class_Oone( X ) }.
% 0.77/1.33 { ! class_Groups_Omonoid__mult( X ), c_Power_Opower__class_Opower( X, Z,
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat,
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.77/1.33 c_Int_OPls ) ) ), Y ) ) = c_Power_Opower__class_Opower( X,
% 0.77/1.33 c_Power_Opower__class_Opower( X, Z, Y ), c_Int_Onumber__class_Onumber__of
% 0.77/1.33 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) }.
% 0.77/1.33 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Oplus__class_Oplus( X,
% 0.77/1.33 c_Power_Opower__class_Opower( X, Z, c_Int_Onumber__class_Onumber__of(
% 0.77/1.33 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ),
% 0.77/1.33 c_Power_Opower__class_Opower( X, Y, c_Int_Onumber__class_Onumber__of(
% 0.77/1.33 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.77/1.33 .
% 0.77/1.33 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Oplus__class_Oplus( X,
% 0.77/1.33 c_Power_Opower__class_Opower( X, Z, c_Int_Onumber__class_Onumber__of(
% 0.77/1.33 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ),
% 0.77/1.33 c_Power_Opower__class_Opower( X, Y, c_Int_Onumber__class_Onumber__of(
% 0.77/1.33 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 0.77/1.33 .
% 0.77/1.33 { ! class_Rings_Olinordered__idom( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.77/1.33 X ), ! Y = c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus
% 0.77/1.33 ( X, c_Power_Opower__class_Opower( X, Z, c_Int_Onumber__class_Onumber__of
% 0.77/1.33 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ),
% 0.77/1.33 c_Power_Opower__class_Opower( X, Y, c_Int_Onumber__class_Onumber__of(
% 0.77/1.33 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( X ) }.
% 0.77/1.33 { ! class_Groups_Omonoid__mult( X ), ! class_Int_Onumber( X ),
% 0.77/1.33 c_Power_Opower__class_Opower( X, c_Int_Onumber__class_Onumber__of( X, Y )
% 0.77/1.33 , c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1
% 0.77/1.33 ( c_Int_OPls ) ) ) ) = c_Groups_Otimes__class_Otimes( X,
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( X, Y ),
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.77/1.33 { ! class_Rings_Olinordered__idom( X ), c_Orderings_Oord__class_Oless__eq(
% 0.77/1.33 X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.77/1.33 c_Power_Opower__class_Opower( X, Z, c_Int_Onumber__class_Onumber__of(
% 0.77/1.33 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ),
% 0.77/1.33 c_Power_Opower__class_Opower( X, Y, c_Int_Onumber__class_Onumber__of(
% 0.77/1.33 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) ) }.
% 0.77/1.33 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.77/1.33 ( X, c_Groups_Oplus__class_Oplus( X, c_Power_Opower__class_Opower( X, Z,
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.77/1.33 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( X, Y,
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.77/1.33 c_Int_OPls ) ) ) ) ), c_Groups_Ozero__class_Ozero( X ) ), Z =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( X ) }.
% 0.77/1.33 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.77/1.33 ( X, c_Groups_Oplus__class_Oplus( X, c_Power_Opower__class_Opower( X, Z,
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.77/1.33 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( X, Y,
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.77/1.33 c_Int_OPls ) ) ) ) ), c_Groups_Ozero__class_Ozero( X ) ), Y =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( X ) }.
% 0.77/1.33 { ! class_Rings_Olinordered__idom( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.77/1.33 X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.77/1.33 c_Power_Opower__class_Opower( X, Z, c_Int_Onumber__class_Onumber__of(
% 0.77/1.33 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ),
% 0.77/1.33 c_Power_Opower__class_Opower( X, Y, c_Int_Onumber__class_Onumber__of(
% 0.77/1.33 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ),
% 0.77/1.33 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.77/1.33 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.77/1.33 , c_Groups_Oplus__class_Oplus( X, c_Power_Opower__class_Opower( X, Z,
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.77/1.33 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( X, Y,
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.77/1.33 c_Int_OPls ) ) ) ) ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.77/1.33 { ! class_Rings_Ocomm__semiring__1( X ), c_Power_Opower__class_Opower( X, Z
% 0.77/1.33 , c_Nat_OSuc( c_Groups_Otimes__class_Otimes( tc_Nat_Onat,
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.77/1.33 c_Int_OPls ) ) ), Y ) ) ) = c_Groups_Otimes__class_Otimes( X, Z,
% 0.77/1.33 c_Groups_Otimes__class_Otimes( X, c_Power_Opower__class_Opower( X, Z, Y )
% 0.77/1.33 , c_Power_Opower__class_Opower( X, Z, Y ) ) ) }.
% 0.77/1.33 { ! class_Rings_Ocomm__semiring__1( X ), c_Power_Opower__class_Opower( X, Z
% 0.77/1.33 , c_Groups_Otimes__class_Otimes( tc_Nat_Onat,
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.77/1.33 c_Int_OPls ) ) ), Y ) ) = c_Groups_Otimes__class_Otimes( X,
% 0.77/1.33 c_Power_Opower__class_Opower( X, Z, Y ), c_Power_Opower__class_Opower( X
% 0.77/1.33 , Z, Y ) ) }.
% 0.77/1.33 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.77/1.33 Y, Y ) = c_Power_Opower__class_Opower( X, Y,
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.77/1.33 c_Int_OPls ) ) ) ) }.
% 0.77/1.33 { ! class_Rings_Olinordered__semiring__1__strict( X ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.77/1.33 ( X, T, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.77/1.33 c_Groups_Ozero__class_Ozero( X ), U ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), W
% 0.77/1.33 ), ! c_Groups_Oplus__class_Oplus( X, U, W ) = c_Groups_Oone__class_Oone
% 0.77/1.33 ( X ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X,
% 0.77/1.33 c_Groups_Otimes__class_Otimes( X, U, Z ), c_Groups_Otimes__class_Otimes(
% 0.77/1.33 X, W, T ) ), Y ) }.
% 0.77/1.33 { ! class_Rings_Olinordered__semidom( X ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.77/1.33 ), ! c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone
% 0.77/1.33 ( X ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.77/1.33 c_Power_Opower__class_Opower( X, Y, c_Nat_OSuc( Z ) ), Y ) }.
% 0.77/1.33 { ! class_Rings_Olinordered__semiring__1( X ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( X, T, Y ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.77/1.33 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.77/1.33 X ), W ), ! c_Groups_Oplus__class_Oplus( X, U, W ) =
% 0.77/1.33 c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless__eq( X,
% 0.77/1.33 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, U, Z )
% 0.77/1.33 , c_Groups_Otimes__class_Otimes( X, W, T ) ), Y ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.77/1.33 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Z ),
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Y ) ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.77/1.33 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z
% 0.77/1.33 , Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Z ),
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Y ) ) }.
% 0.77/1.33 { ! class_Rings_Ocomm__semiring__1( X ), c_Power_Opower__class_Opower( X, Y
% 0.77/1.33 , c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = Y }.
% 0.77/1.33 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.77/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.77/1.33 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) =
% 0.77/1.33 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) }.
% 0.77/1.33 { c_Groups_Otimes__class_Otimes( tc_Int_Oint, Y, X ) =
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Int_Oint, X, Y ) }.
% 0.77/1.33 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus
% 0.77/1.33 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.77/1.33 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.77/1.33 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, c_Groups_Oplus__class_Oplus
% 0.77/1.33 ( tc_Nat_Onat, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.77/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.77/1.33 { c_Groups_Otimes__class_Otimes( tc_Int_Oint, Z,
% 0.77/1.33 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) =
% 0.77/1.33 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Otimes__class_Otimes(
% 0.77/1.33 tc_Int_Oint, Z, Y ), c_Groups_Otimes__class_Otimes( tc_Int_Oint, Z, X ) )
% 0.77/1.33 }.
% 0.77/1.33 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.77/1.33 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.77/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.77/1.33 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.77/1.33 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.77/1.33 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 0.77/1.33 { c_Groups_Otimes__class_Otimes( tc_Int_Oint, c_Groups_Otimes__class_Otimes
% 0.77/1.33 ( tc_Int_Oint, Z, Y ), X ) = c_Groups_Otimes__class_Otimes( tc_Int_Oint,
% 0.77/1.33 Z, c_Groups_Otimes__class_Otimes( tc_Int_Oint, Y, X ) ) }.
% 0.77/1.33 { ! class_Rings_Ocomm__semiring__0( X ), c_Groups_Otimes__class_Otimes(
% 0.77/1.33 tc_Polynomial_Opoly( X ), c_Groups_Oplus__class_Oplus(
% 0.77/1.33 tc_Polynomial_Opoly( X ), T, Z ), Y ) = c_Groups_Oplus__class_Oplus(
% 0.77/1.33 tc_Polynomial_Opoly( X ), c_Groups_Otimes__class_Otimes(
% 0.77/1.33 tc_Polynomial_Opoly( X ), T, Y ), c_Groups_Otimes__class_Otimes(
% 0.77/1.33 tc_Polynomial_Opoly( X ), Z, Y ) ) }.
% 0.77/1.33 { c_Groups_Otimes__class_Otimes( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.77/1.33 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Int_Oint, Z, X ),
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Int_Oint, Y, X ) ) }.
% 0.77/1.33 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.77/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ), Y = X }.
% 0.77/1.33 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.77/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) }.
% 0.77/1.33 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.77/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ), Z = X }.
% 0.77/1.33 { ! Z = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.77/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.77/1.33 { c_Groups_Otimes__class_Otimes( tc_Int_Oint, c_Int_OPls, X ) = c_Int_OPls
% 0.77/1.33 }.
% 0.77/1.33 { c_Groups_Otimes__class_Otimes( tc_Int_Oint, c_Int_OBit0( Y ), X ) =
% 0.77/1.33 c_Int_OBit0( c_Groups_Otimes__class_Otimes( tc_Int_Oint, Y, X ) ) }.
% 0.77/1.33 { ! class_Groups_Omonoid__mult( X ), c_Power_Opower__class_Opower( X, Y,
% 0.77/1.33 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = Y }.
% 0.77/1.33 { c_Groups_Otimes__class_Otimes( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 0.77/1.33 ( tc_Int_Oint ) ) = X }.
% 0.77/1.33 { c_Groups_Otimes__class_Otimes( tc_Int_Oint, c_Groups_Oone__class_Oone(
% 0.77/1.33 tc_Int_Oint ), X ) = X }.
% 0.77/1.33 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.77/1.33 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.77/1.33 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.77/1.33 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X ) }.
% 0.77/1.33 { c_Groups_Otimes__class_Otimes( tc_Int_Oint,
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) =
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Int_Oint,
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Int_Oint, Y, X ) ) }.
% 0.77/1.33 { ! class_Rings_Ocomm__semiring__0( X ), c_Groups_Otimes__class_Otimes(
% 0.77/1.33 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 0.77/1.33 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 0.77/1.33 tc_Polynomial_Opoly( X ) ) }.
% 0.77/1.33 { ! class_Rings_Ocomm__semiring__0( X ), c_Groups_Otimes__class_Otimes(
% 0.77/1.33 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.77/1.33 tc_Polynomial_Opoly( X ) ), Y ) = c_Groups_Ozero__class_Ozero(
% 0.77/1.33 tc_Polynomial_Opoly( X ) ) }.
% 0.77/1.33 { ! c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) =
% 0.77/1.33 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Oone__class_Oone(
% 0.77/1.33 tc_Nat_Onat ) }.
% 0.77/1.33 { ! c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) =
% 0.77/1.33 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X = c_Groups_Oone__class_Oone(
% 0.77/1.33 tc_Nat_Onat ) }.
% 0.77/1.33 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.77/1.33 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Groups_Otimes__class_Otimes(
% 0.77/1.33 tc_Nat_Onat, Y, X ) = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.77/1.33 { c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, c_Groups_Oone__class_Oone
% 0.77/1.33 ( tc_Nat_Onat ) ) = X }.
% 0.77/1.33 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) =
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ), Y =
% 0.77/1.33 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.77/1.33 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) =
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ), X =
% 0.77/1.33 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.77/1.33 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.77/1.33 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Groups_Oone__class_Oone(
% 0.77/1.33 tc_Nat_Onat ) = c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) }.
% 0.77/1.33 { c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.77/1.33 tc_Nat_Onat ), X ) = X }.
% 0.77/1.33 { c_Power_Opower__class_Opower( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus
% 0.77/1.33 ( tc_Nat_Onat, Y, X ) ) = c_Groups_Otimes__class_Otimes( tc_Int_Oint,
% 0.77/1.33 c_Power_Opower__class_Opower( tc_Int_Oint, Z, Y ),
% 0.77/1.33 c_Power_Opower__class_Opower( tc_Int_Oint, Z, X ) ) }.
% 0.77/1.33 { c_Groups_Otimes__class_Otimes( tc_Int_Oint, c_Int_OBit1( Y ), X ) =
% 0.77/1.33 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Int_OBit0(
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Int_Oint, Y, X ) ), X ) }.
% 0.77/1.33 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.77/1.33 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ),
% 0.77/1.33 c_Power_Opower__class_Opower( tc_RealDef_Oreal,
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.77/1.33 c_Int_OBit1( c_Int_OPls ) ) ), X ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Otimes__class_Otimes
% 0.77/1.33 ( tc_Int_Oint, X, Y ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.77/1.33 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Int_Oint, Z, Y ),
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Int_Oint, Z, X ) ) }.
% 0.77/1.33 { c_Groups_Oone__class_Oone( tc_Nat_Onat ) = c_Nat_OSuc(
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.77/1.33 { ! Y = c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ), X =
% 0.77/1.33 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Ozero__class_Ozero
% 0.77/1.33 ( tc_Nat_Onat ) }.
% 0.77/1.33 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Odegree( X,
% 0.77/1.33 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ) =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.77/1.33 { ! class_Rings_Ocomm__semiring__0( X ), c_Orderings_Oord__class_Oless__eq
% 0.77/1.33 ( tc_Nat_Onat, c_Polynomial_Odegree( X, c_Groups_Otimes__class_Otimes(
% 0.77/1.33 tc_Polynomial_Opoly( X ), Z, Y ) ), c_Groups_Oplus__class_Oplus(
% 0.77/1.33 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) )
% 0.77/1.33 ) }.
% 0.77/1.33 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.77/1.33 tc_Polynomial_Opoly( X ) ), Z = c_Groups_Ozero__class_Ozero(
% 0.77/1.33 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X,
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ), Y, Z ) ) =
% 0.77/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Polynomial_Odegree( X, Y ),
% 0.77/1.33 c_Polynomial_Odegree( X, Z ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.77/1.33 ( tc_Int_Oint ), X ), ! c_Groups_Otimes__class_Otimes( tc_Int_Oint, X, Y
% 0.77/1.33 ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), X =
% 0.77/1.33 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.77/1.33 ( tc_Int_Oint ), X ), ! c_Groups_Otimes__class_Otimes( tc_Int_Oint, X, Y
% 0.77/1.33 ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), Y =
% 0.77/1.33 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.77/1.33 ( tc_Int_Oint ), X ), ! X = c_Groups_Oone__class_Oone( tc_Int_Oint ), ! Y
% 0.77/1.33 = c_Groups_Oone__class_Oone( tc_Int_Oint ),
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Int_Oint, X, Y ) =
% 0.77/1.33 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.77/1.33 { ! class_Rings_Olinordered__idom( X ), Z = Y,
% 0.77/1.33 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.77/1.33 X, Y, Z ) }.
% 0.77/1.33 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.77/1.33 Z, Y ) = c_Groups_Otimes__class_Otimes( X, Y, Z ) }.
% 0.77/1.33 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.77/1.33 T, c_Groups_Otimes__class_Otimes( X, Z, Y ) ) =
% 0.77/1.33 c_Groups_Otimes__class_Otimes( X, Z, c_Groups_Otimes__class_Otimes( X, T
% 0.77/1.33 , Y ) ) }.
% 0.77/1.33 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.77/1.33 T, c_Groups_Otimes__class_Otimes( X, Z, Y ) ) =
% 0.77/1.33 c_Groups_Otimes__class_Otimes( X, c_Groups_Otimes__class_Otimes( X, T, Z
% 0.77/1.33 ), Y ) }.
% 0.77/1.33 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.77/1.33 c_Groups_Otimes__class_Otimes( X, T, Z ), Y ) =
% 0.77/1.33 c_Groups_Otimes__class_Otimes( X, T, c_Groups_Otimes__class_Otimes( X, Z
% 0.77/1.33 , Y ) ) }.
% 0.77/1.33 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.77/1.33 c_Groups_Otimes__class_Otimes( X, T, Z ), Y ) =
% 0.77/1.33 c_Groups_Otimes__class_Otimes( X, c_Groups_Otimes__class_Otimes( X, T, Y
% 0.77/1.33 ), Z ) }.
% 0.77/1.33 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.77/1.33 c_Groups_Otimes__class_Otimes( X, U, T ), c_Groups_Otimes__class_Otimes(
% 0.77/1.33 X, Z, Y ) ) = c_Groups_Otimes__class_Otimes( X, U,
% 0.77/1.33 c_Groups_Otimes__class_Otimes( X, T, c_Groups_Otimes__class_Otimes( X, Z
% 0.77/1.33 , Y ) ) ) }.
% 0.77/1.33 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.77/1.33 c_Groups_Otimes__class_Otimes( X, U, T ), c_Groups_Otimes__class_Otimes(
% 0.77/1.33 X, Z, Y ) ) = c_Groups_Otimes__class_Otimes( X, Z,
% 0.77/1.33 c_Groups_Otimes__class_Otimes( X, c_Groups_Otimes__class_Otimes( X, U, T
% 0.77/1.33 ), Y ) ) }.
% 0.77/1.33 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.77/1.33 c_Groups_Otimes__class_Otimes( X, U, T ), c_Groups_Otimes__class_Otimes(
% 0.77/1.33 X, Z, Y ) ) = c_Groups_Otimes__class_Otimes( X,
% 0.77/1.33 c_Groups_Otimes__class_Otimes( X, U, Z ), c_Groups_Otimes__class_Otimes(
% 0.77/1.33 X, T, Y ) ) }.
% 0.77/1.33 { c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit1( c_Int_OPls )
% 0.77/1.33 ) = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.77/1.33 { c_Groups_Oone__class_Oone( tc_Nat_Onat ) =
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit1( c_Int_OPls )
% 0.77/1.33 ) }.
% 0.77/1.33 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.77/1.33 , Y ) = c_Groups_Oplus__class_Oplus( X, Y, Z ) }.
% 0.77/1.33 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.77/1.33 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.77/1.33 ( X, Z, c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.77/1.33 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.77/1.33 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.77/1.33 ( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) }.
% 0.77/1.33 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.77/1.33 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.77/1.33 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.77/1.33 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.77/1.33 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.77/1.33 ( X, c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 0.77/1.33 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.77/1.33 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.77/1.33 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X
% 0.77/1.33 , U, Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.77/1.33 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.77/1.33 tc_Nat_Onat, T, Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, Z ), X ) ) =
% 0.77/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.77/1.33 tc_Nat_Onat, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, Y ), Z ), X ) }
% 0.77/1.33 .
% 0.77/1.33 { c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal,
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.77/1.33 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ),
% 0.77/1.33 c_Power_Opower__class_Opower( tc_RealDef_Oreal, X,
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.77/1.33 c_Int_OPls ) ) ) ) ) = c_Power_Opower__class_Opower( tc_RealDef_Oreal,
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal,
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.77/1.33 c_Int_OBit1( c_Int_OPls ) ) ), X ), c_Int_Onumber__class_Onumber__of(
% 0.77/1.33 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) }.
% 0.77/1.33 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.77/1.33 tc_Nat_Onat ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) =
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.77/1.33 c_Int_OPls ) ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, c_Int_OPls ),
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat,
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Z ),
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat,
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ), X ) ) =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.77/1.33 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, c_Int_OPls ),
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat,
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Z ),
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat,
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ), X ) ) =
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat,
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Int_Oint, Z, Y ) ), X ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, c_Int_OPls ),
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat,
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.77/1.33 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, c_Int_OPls ),
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat,
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) =
% 0.77/1.33 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Int_Oint, Y, X ) ) }.
% 0.77/1.33 { ! class_Rings_Omult__zero( X ), c_Groups_Otimes__class_Otimes( X,
% 0.77/1.33 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.77/1.33 }.
% 0.77/1.33 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.77/1.33 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.77/1.33 }.
% 0.77/1.33 { ! class_Rings_Omult__zero( X ), c_Groups_Otimes__class_Otimes( X, Y,
% 0.77/1.33 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.77/1.33 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.77/1.33 Y, c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X )
% 0.77/1.33 }.
% 0.77/1.33 { ! class_Rings_Oring__no__zero__divisors( X ), !
% 0.77/1.33 c_Groups_Otimes__class_Otimes( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.77/1.33 ), Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 0.77/1.33 ( X ) }.
% 0.77/1.33 { ! class_Rings_Oring__no__zero__divisors( X ), ! Z =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( X ), c_Groups_Otimes__class_Otimes( X, Z, Y
% 0.77/1.33 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.77/1.33 { ! class_Rings_Oring__no__zero__divisors( X ), ! Y =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( X ), c_Groups_Otimes__class_Otimes( X, Z, Y
% 0.77/1.33 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.77/1.33 { ! class_Rings_Ono__zero__divisors( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.77/1.33 X ), Z = c_Groups_Ozero__class_Ozero( X ), !
% 0.77/1.33 c_Groups_Otimes__class_Otimes( X, Y, Z ) = c_Groups_Ozero__class_Ozero( X
% 0.77/1.33 ) }.
% 0.77/1.33 { ! class_Rings_Ono__zero__divisors( X ), ! c_Groups_Otimes__class_Otimes(
% 0.77/1.33 X, Z, Y ) = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 0.77/1.33 .
% 0.77/1.33 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.77/1.33 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.77/1.33 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.77/1.33 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.77/1.33 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.77/1.33 ( X ), ! Z = c_Groups_Oplus__class_Oplus( X, Z, Y ), Y =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( X ) }.
% 0.77/1.33 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.77/1.33 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.77/1.33 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 0.77/1.33 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Oone__class_Oone( X ) =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( X ) }.
% 0.77/1.33 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.77/1.33 c_Groups_Oone__class_Oone( X ) }.
% 0.77/1.33 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.77/1.33 T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.77/1.33 ( X, c_Groups_Otimes__class_Otimes( X, T, Z ),
% 0.77/1.33 c_Groups_Otimes__class_Otimes( X, T, Y ) ) }.
% 0.77/1.33 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.77/1.33 ( X ), U = T, Z = Y, ! c_Groups_Oplus__class_Oplus( X,
% 0.77/1.33 c_Groups_Otimes__class_Otimes( X, U, Z ), c_Groups_Otimes__class_Otimes(
% 0.77/1.33 X, T, Y ) ) = c_Groups_Oplus__class_Oplus( X,
% 0.77/1.33 c_Groups_Otimes__class_Otimes( X, U, Y ), c_Groups_Otimes__class_Otimes(
% 0.77/1.33 X, T, Z ) ) }.
% 0.77/1.33 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.77/1.33 ( X ), c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.77/1.33 U, Z ), c_Groups_Otimes__class_Otimes( X, T, Y ) ) =
% 0.77/1.33 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, U, Y )
% 0.77/1.33 , c_Groups_Otimes__class_Otimes( X, T, Z ) ), ! U = T }.
% 0.77/1.33 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.77/1.33 ( X ), c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.77/1.33 U, Z ), c_Groups_Otimes__class_Otimes( X, T, Y ) ) =
% 0.77/1.33 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, U, Y )
% 0.77/1.33 , c_Groups_Otimes__class_Otimes( X, T, Z ) ), ! Z = Y }.
% 0.77/1.33 { ! class_Rings_Ocomm__semiring( X ), c_Groups_Otimes__class_Otimes( X,
% 0.77/1.33 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.77/1.33 ( X, c_Groups_Otimes__class_Otimes( X, T, Y ),
% 0.77/1.33 c_Groups_Otimes__class_Otimes( X, Z, Y ) ) }.
% 0.77/1.33 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.77/1.33 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.77/1.33 ( X, c_Groups_Otimes__class_Otimes( X, T, Y ),
% 0.77/1.33 c_Groups_Otimes__class_Otimes( X, Z, Y ) ) }.
% 0.77/1.33 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.77/1.33 c_Groups_Otimes__class_Otimes( X, T, Z ), c_Groups_Otimes__class_Otimes(
% 0.77/1.33 X, Y, Z ) ) = c_Groups_Otimes__class_Otimes( X,
% 0.77/1.33 c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 0.77/1.33 { ! class_Rings_Osemiring( X ), c_Groups_Oplus__class_Oplus( X,
% 0.77/1.33 c_Groups_Otimes__class_Otimes( X, U, T ), c_Groups_Oplus__class_Oplus( X
% 0.77/1.33 , c_Groups_Otimes__class_Otimes( X, Z, T ), Y ) ) =
% 0.77/1.33 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.77/1.33 c_Groups_Oplus__class_Oplus( X, U, Z ), T ), Y ) }.
% 0.77/1.33 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.77/1.33 ( X ), ! c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X
% 0.77/1.33 , U, T ), c_Groups_Otimes__class_Otimes( X, Z, Y ) ) =
% 0.77/1.33 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, U, Y )
% 0.77/1.33 , c_Groups_Otimes__class_Otimes( X, Z, T ) ), U = Z, T = Y }.
% 0.77/1.33 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.77/1.33 ( X ), ! U = Z, c_Groups_Oplus__class_Oplus( X,
% 0.77/1.33 c_Groups_Otimes__class_Otimes( X, U, T ), c_Groups_Otimes__class_Otimes(
% 0.77/1.33 X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X,
% 0.77/1.33 c_Groups_Otimes__class_Otimes( X, U, Y ), c_Groups_Otimes__class_Otimes(
% 0.77/1.33 X, Z, T ) ) }.
% 0.77/1.33 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.77/1.33 ( X ), ! T = Y, c_Groups_Oplus__class_Oplus( X,
% 0.77/1.33 c_Groups_Otimes__class_Otimes( X, U, T ), c_Groups_Otimes__class_Otimes(
% 0.77/1.33 X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X,
% 0.77/1.33 c_Groups_Otimes__class_Otimes( X, U, Y ), c_Groups_Otimes__class_Otimes(
% 0.77/1.33 X, Z, T ) ) }.
% 0.77/1.33 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.77/1.33 c_Groups_Oone__class_Oone( X ), Y ) = Y }.
% 0.77/1.33 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.77/1.33 Y, c_Groups_Oone__class_Oone( X ) ) = Y }.
% 0.77/1.33 { ! class_Rings_Ocomm__semiring__1( X ), c_Power_Opower__class_Opower( X,
% 0.77/1.33 c_Groups_Otimes__class_Otimes( X, T, Z ), Y ) =
% 0.77/1.33 c_Groups_Otimes__class_Otimes( X, c_Power_Opower__class_Opower( X, T, Y )
% 0.77/1.33 , c_Power_Opower__class_Opower( X, Z, Y ) ) }.
% 0.77/1.33 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.77/1.33 c_Power_Opower__class_Opower( X, T, Z ), c_Power_Opower__class_Opower( X
% 0.77/1.33 , T, Y ) ) = c_Power_Opower__class_Opower( X, T,
% 0.77/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ) }.
% 0.77/1.33 { ! c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ) =
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ), Z =
% 0.77/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.77/1.33 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ) =
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ) }.
% 0.77/1.33 { ! Y = X, c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ) =
% 0.77/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ) }.
% 0.77/1.33 { ! class_Rings_Ocomm__semiring__1( X ), c_Power_Opower__class_Opower( X,
% 0.77/1.33 c_Power_Opower__class_Opower( X, T, Z ), Y ) =
% 0.77/1.33 c_Power_Opower__class_Opower( X, T, c_Groups_Otimes__class_Otimes(
% 0.77/1.33 tc_Nat_Onat, Z, Y ) ) }.
% 0.77/1.33 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.77/1.33 ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.77/1.33 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.77/1.33 , c_Groups_Otimes__class_Otimes( X, Z, Y ), c_Groups_Ozero__class_Ozero(
% 0.77/1.33 X ) ) }.
% 0.77/1.33 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.77/1.33 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.77/1.33 X ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.77/1.33 c_Groups_Otimes__class_Otimes( X, Z, Y ), c_Groups_Ozero__class_Ozero( X
% 0.77/1.33 ) ) }.
% 0.77/1.33 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.77/1.33 , c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.77/1.33 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.77/1.33 ), c_Groups_Otimes__class_Otimes( X, Z, Y ) ) }.
% 0.77/1.33 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.77/1.33 , Z, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.77/1.33 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.77/1.33 ), c_Groups_Otimes__class_Otimes( X, Z, Y ) ) }.
% 0.77/1.33 { ! class_Rings_Oordered__semiring( X ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.77/1.33 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.77/1.33 X ), U ), c_Orderings_Oord__class_Oless__eq( X,
% 0.77/1.33 c_Groups_Otimes__class_Otimes( X, Z, U ), c_Groups_Otimes__class_Otimes(
% 0.77/1.33 X, Y, T ) ) }.
% 0.77/1.33 { ! class_Rings_Oordered__semiring( X ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.77/1.33 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.77/1.33 X ), U ), c_Orderings_Oord__class_Oless__eq( X,
% 0.77/1.33 c_Groups_Otimes__class_Otimes( X, Z, U ), c_Groups_Otimes__class_Otimes(
% 0.77/1.33 X, Y, T ) ) }.
% 0.77/1.33 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.77/1.33 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.77/1.33 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.77/1.33 , c_Groups_Otimes__class_Otimes( X, T, Y ), c_Groups_Otimes__class_Otimes
% 0.77/1.33 ( X, T, Z ) ) }.
% 0.77/1.33 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.77/1.33 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.77/1.33 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.77/1.33 , c_Groups_Otimes__class_Otimes( X, Y, T ), c_Groups_Otimes__class_Otimes
% 0.77/1.33 ( X, Z, T ) ) }.
% 0.77/1.33 { ! class_Rings_Oordered__comm__semiring( X ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.77/1.33 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes(
% 0.77/1.33 X, T, Z ), c_Groups_Otimes__class_Otimes( X, T, Y ) ) }.
% 0.77/1.33 { ! class_Rings_Oordered__semiring( X ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.77/1.33 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes(
% 0.77/1.33 X, T, Z ), c_Groups_Otimes__class_Otimes( X, T, Y ) ) }.
% 0.77/1.33 { ! class_Rings_Oordered__semiring( X ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.77/1.33 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes(
% 0.77/1.33 X, Z, T ), c_Groups_Otimes__class_Otimes( X, Y, T ) ) }.
% 0.77/1.33 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.77/1.33 , Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.77/1.33 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.77/1.33 ), c_Groups_Otimes__class_Otimes( X, Y, Z ) ) }.
% 0.77/1.33 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.77/1.33 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.77/1.33 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.77/1.33 c_Groups_Otimes__class_Otimes( X, Y, Z ), c_Groups_Ozero__class_Ozero( X
% 0.77/1.33 ) ) }.
% 0.77/1.33 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.77/1.33 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.77/1.33 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.77/1.33 , c_Groups_Otimes__class_Otimes( X, Z, Y ), c_Groups_Ozero__class_Ozero(
% 0.77/1.33 X ) ) }.
% 0.77/1.33 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.77/1.33 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.77/1.33 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.77/1.33 , c_Groups_Otimes__class_Otimes( X, Y, Z ), c_Groups_Ozero__class_Ozero(
% 0.77/1.33 X ) ) }.
% 0.77/1.33 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.77/1.33 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.77/1.33 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.77/1.33 c_Groups_Ozero__class_Ozero( X ), c_Groups_Otimes__class_Otimes( X, Y, Z
% 0.77/1.33 ) ) }.
% 0.77/1.33 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes( X, Z
% 0.77/1.33 , Y ), c_Groups_Ozero__class_Ozero( X ) ), alpha5( X, Y, Z ), alpha23( X
% 0.77/1.33 , Y, Z ) }.
% 0.77/1.33 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha5( X, Y, Z ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes( X, Z
% 0.77/1.33 , Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.77/1.33 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha23( X, Y, Z ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes( X, Z
% 0.77/1.33 , Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.77/1.33 { ! alpha23( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.77/1.33 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.77/1.33 { ! alpha23( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.77/1.33 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.77/1.33 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.77/1.33 ( X ), Y ), alpha23( X, Y, Z ) }.
% 0.77/1.33 { ! alpha5( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.77/1.33 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.77/1.33 { ! alpha5( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.77/1.33 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.77/1.33 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.77/1.33 c_Groups_Ozero__class_Ozero( X ) ), alpha5( X, Y, Z ) }.
% 0.77/1.33 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.77/1.33 c_Groups_Otimes__class_Otimes( X, Z, Y ) ), alpha6( X, Y, Z ), alpha24( X
% 0.77/1.33 , Y, Z ) }.
% 0.77/1.33 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha6( X, Y, Z ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.77/1.33 c_Groups_Otimes__class_Otimes( X, Z, Y ) ) }.
% 0.77/1.33 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha24( X, Y, Z ),
% 0.77/1.33 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.77/1.33 c_Groups_Otimes__class_Otimes( X, Z, Y ) ) }.
% 0.77/1.33 { ! alpha24( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.77/1.33 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.77/1.33 { ! alpha24( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.77/1.33 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.77/1.33 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.77/1.33 c_Groups_Ozero__class_Ozero( X ) ), alpha24( X, Y, Z ) }.
% 0.77/1.33 { ! alpha6( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.77/1.33 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.77/1.33 { ! alpha6( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.77/1.33 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.77/1.33 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.77/1.33 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.77/1.33 c_Groups_Ozero__class_Ozero( X ), Y ), alpha6( X, Y, Z ) }.
% 0.77/1.33 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.77/1.33 X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Otimes__class_Otimes( X, Y
% 0.77/1.33 , Y ) ) }.
% 0.77/1.33 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.77/1.33 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.77/1.33 ( X, c_Groups_Otimes__class_Otimes( X, T, Y ),
% 0.77/1.33 c_Groups_Otimes__class_Otimes( X, T, Z ) ) }.
% 0.77/1.33 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.77/1.33 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.77/1.33 ( X, c_Groups_Otimes__class_Otimes( X, Y, T ),
% 0.77/1.33 c_Groups_Otimes__class_Otimes( X, Z, T ) ) }.
% 0.77/1.33 { ! class_Rings_Olinordered__comm__semiring__strict( X ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.77/1.33 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.77/1.33 ( X, c_Groups_Otimes__class_Otimes( X, T, Z ),
% 0.77/1.33 c_Groups_Otimes__class_Otimes( X, T, Y ) ) }.
% 0.77/1.33 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.77/1.33 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.77/1.33 ( X, c_Groups_Otimes__class_Otimes( X, T, Z ),
% 0.77/1.33 c_Groups_Otimes__class_Otimes( X, T, Y ) ) }.
% 0.77/1.33 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.77/1.33 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.77/1.33 ( X, c_Groups_Otimes__class_Otimes( X, Z, T ),
% 0.77/1.33 c_Groups_Otimes__class_Otimes( X, Y, T ) ) }.
% 0.77/1.33 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.77/1.33 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.77/1.33 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.77/1.33 c_Groups_Otimes__class_Otimes( X, Y, Z ) ) }.
% 0.77/1.33 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.77/1.33 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.77/1.33 , c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, Y,
% 0.77/1.33 Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.77/1.33 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.77/1.33 ! c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, Y,
% 0.77/1.33 T ), c_Groups_Otimes__class_Otimes( X, Y, Z ) ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.77/1.33 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.77/1.33 ! c_Orderings_Oord__class_Oless( X, Z, T ), c_Orderings_Oord__class_Oless
% 0.77/1.33 ( X, c_Groups_Otimes__class_Otimes( X, Y, T ),
% 0.77/1.33 c_Groups_Otimes__class_Otimes( X, Y, Z ) ) }.
% 0.77/1.33 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.77/1.33 c_Groups_Otimes__class_Otimes( X, Z, Y ) ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ) }
% 0.77/1.33 .
% 0.77/1.33 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.77/1.33 c_Groups_Otimes__class_Otimes( X, Z, Y ) ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.77/1.33 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.77/1.33 .
% 0.77/1.33 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.77/1.33 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.77/1.33 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.77/1.33 , c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, Z,
% 0.77/1.33 Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.77/1.33 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.77/1.34 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.77/1.34 , c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, Y,
% 0.77/1.34 Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.77/1.34 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.77/1.34 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.77/1.34 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.77/1.34 c_Groups_Otimes__class_Otimes( X, Y, Z ) ) }.
% 0.77/1.34 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.77/1.34 ! c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, Y,
% 0.77/1.34 T ), c_Groups_Otimes__class_Otimes( X, Y, Z ) ),
% 0.77/1.34 c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.77/1.34 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.77/1.34 ! c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless
% 0.77/1.34 ( X, c_Groups_Otimes__class_Otimes( X, Y, T ),
% 0.77/1.34 c_Groups_Otimes__class_Otimes( X, Y, Z ) ) }.
% 0.77/1.34 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, T, Z
% 0.77/1.34 ), c_Groups_Otimes__class_Otimes( X, T, Y ) ), alpha7( X, Y, Z, T ),
% 0.77/1.34 alpha25( X, Y, Z, T ) }.
% 0.77/1.34 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha7( X, Y, Z, T ),
% 0.77/1.34 c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, T, Z
% 0.77/1.34 ), c_Groups_Otimes__class_Otimes( X, T, Y ) ) }.
% 0.77/1.34 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha25( X, Y, Z, T ),
% 0.77/1.34 c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, T, Z
% 0.77/1.34 ), c_Groups_Otimes__class_Otimes( X, T, Y ) ) }.
% 0.77/1.34 { ! alpha25( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.77/1.34 { ! alpha25( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( X, T, c_Groups_Ozero__class_Ozero( X ) )
% 0.77/1.34 , ! c_Orderings_Oord__class_Oless( X, Y, Z ), alpha25( X, Y, Z, T ) }.
% 0.77/1.34 { ! alpha7( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( X ), T ) }.
% 0.77/1.34 { ! alpha7( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T )
% 0.77/1.34 , ! c_Orderings_Oord__class_Oless( X, Z, Y ), alpha7( X, Y, Z, T ) }.
% 0.77/1.34 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, T, Z
% 0.77/1.34 ), c_Groups_Otimes__class_Otimes( X, Y, Z ) ), alpha8( X, Y, Z, T ),
% 0.77/1.34 alpha26( X, Y, Z, T ) }.
% 0.77/1.34 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha8( X, Y, Z, T ),
% 0.77/1.34 c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, T, Z
% 0.77/1.34 ), c_Groups_Otimes__class_Otimes( X, Y, Z ) ) }.
% 0.77/1.34 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha26( X, Y, Z, T ),
% 0.77/1.34 c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, T, Z
% 0.77/1.34 ), c_Groups_Otimes__class_Otimes( X, Y, Z ) ) }.
% 0.77/1.34 { ! alpha26( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.77/1.34 { ! alpha26( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, T ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.77/1.34 , ! c_Orderings_Oord__class_Oless( X, Y, T ), alpha26( X, Y, Z, T ) }.
% 0.77/1.34 { ! alpha8( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.77/1.34 { ! alpha8( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.77/1.34 , ! c_Orderings_Oord__class_Oless( X, T, Y ), alpha8( X, Y, Z, T ) }.
% 0.77/1.34 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.77/1.34 , c_Groups_Otimes__class_Otimes( X, Y, Y ), c_Groups_Ozero__class_Ozero(
% 0.77/1.34 X ) ) }.
% 0.77/1.34 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.77/1.34 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless(
% 0.77/1.34 X, T, c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.77/1.34 { ! class_Rings_Olinordered__semidom( X ),
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.77/1.34 c_Groups_Oone__class_Oone( X ) ) }.
% 0.77/1.34 { ! class_Rings_Olinordered__semidom( X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.77/1.34 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.77/1.34 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.77/1.34 ( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! W = U, T = Z, !
% 0.77/1.34 c_Groups_Oplus__class_Oplus( X, W, c_Groups_Otimes__class_Otimes( X, Y, T
% 0.77/1.34 ) ) = c_Groups_Oplus__class_Oplus( X, U, c_Groups_Otimes__class_Otimes(
% 0.77/1.34 X, Y, Z ) ) }.
% 0.77/1.34 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.77/1.34 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.77/1.34 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.77/1.34 ( X, c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero( X ) ) }
% 0.77/1.34 .
% 0.77/1.34 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.77/1.34 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.77/1.34 ( X, c_Groups_Oone__class_Oone( X ), Z ), c_Orderings_Oord__class_Oless(
% 0.77/1.34 X, c_Groups_Oone__class_Oone( X ), c_Groups_Otimes__class_Otimes( X, Y, Z
% 0.77/1.34 ) ) }.
% 0.77/1.34 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.77/1.34 , Y, c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) )
% 0.77/1.34 ) }.
% 0.77/1.34 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.77/1.34 , Y ) = c_Groups_Otimes__class_Otimes( X, c_Groups_Oplus__class_Oplus( X
% 0.77/1.34 , c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ), Y ) }
% 0.77/1.34 .
% 0.77/1.34 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.77/1.34 , c_Groups_Otimes__class_Otimes( X, Y, Z ) ) =
% 0.77/1.34 c_Groups_Otimes__class_Otimes( X, c_Groups_Oplus__class_Oplus( X, Y,
% 0.77/1.34 c_Groups_Oone__class_Oone( X ) ), Z ) }.
% 0.77/1.34 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( X, Z, Y ), Y ) =
% 0.77/1.34 c_Groups_Otimes__class_Otimes( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.77/1.34 c_Groups_Oone__class_Oone( X ) ), Y ) }.
% 0.77/1.34 { ! class_Rings_Ocomm__semiring__1( X ), c_Power_Opower__class_Opower( X, Z
% 0.77/1.34 , c_Nat_OSuc( Y ) ) = c_Groups_Otimes__class_Otimes( X, Z,
% 0.77/1.34 c_Power_Opower__class_Opower( X, Z, Y ) ) }.
% 0.77/1.34 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.77/1.34 Z, c_Power_Opower__class_Opower( X, Z, Y ) ) =
% 0.77/1.34 c_Power_Opower__class_Opower( X, Z, c_Nat_OSuc( Y ) ) }.
% 0.77/1.34 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.77/1.34 c_Power_Opower__class_Opower( X, Z, Y ), Z ) =
% 0.77/1.34 c_Power_Opower__class_Opower( X, Z, c_Nat_OSuc( Y ) ) }.
% 0.77/1.34 { ! class_Rings_Ocomm__semiring__1( X ), c_Power_Opower__class_Opower( X, Y
% 0.77/1.34 , c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.77/1.34 c_Groups_Oone__class_Oone( X ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.77/1.34 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Z ),
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Y ) ),
% 0.77/1.34 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.77/1.34 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 0.77/1.34 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Z ),
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Y ) ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.77/1.34 ( tc_Nat_Onat ), X ), ! c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Z
% 0.77/1.34 ) = c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Y ), Z = Y }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.77/1.34 ( tc_Nat_Onat ), X ), ! Z = Y, c_Groups_Otimes__class_Otimes( tc_Nat_Onat
% 0.77/1.34 , X, Z ) = c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Y ) }.
% 0.77/1.34 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes( X, T
% 0.77/1.34 , Z ), c_Groups_Otimes__class_Otimes( X, T, Y ) ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.77/1.34 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes( X, T
% 0.77/1.34 , Z ), c_Groups_Otimes__class_Otimes( X, Y, Z ) ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.77/1.34 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, T, Z
% 0.77/1.34 ), c_Groups_Otimes__class_Otimes( X, T, Y ) ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.77/1.34 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.77/1.34 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.77/1.34 ( X, c_Groups_Otimes__class_Otimes( X, T, Z ),
% 0.77/1.34 c_Groups_Otimes__class_Otimes( X, T, Y ) ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.77/1.34 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.77/1.34 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, T, Z
% 0.77/1.34 ), c_Groups_Otimes__class_Otimes( X, Y, Z ) ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.77/1.34 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.77/1.34 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.77/1.34 ( X, c_Groups_Otimes__class_Otimes( X, T, Z ),
% 0.77/1.34 c_Groups_Otimes__class_Otimes( X, Y, Z ) ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.77/1.34 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.77/1.34 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( X, U, T ), ! c_Orderings_Oord__class_Oless
% 0.77/1.34 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.77/1.34 ), c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, Z
% 0.77/1.34 , U ), c_Groups_Otimes__class_Otimes( X, Y, T ) ) }.
% 0.77/1.34 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.77/1.34 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.77/1.34 , U ), c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X
% 0.77/1.34 , Z, U ), c_Groups_Otimes__class_Otimes( X, Y, T ) ) }.
% 0.77/1.34 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.77/1.34 ( X, U, T ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.77/1.34 ), c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, Z
% 0.77/1.34 , U ), c_Groups_Otimes__class_Otimes( X, Y, T ) ) }.
% 0.77/1.34 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.77/1.34 ( X, U, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.77/1.34 ), c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, Z
% 0.77/1.34 , U ), c_Groups_Otimes__class_Otimes( X, Y, T ) ) }.
% 0.77/1.34 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.77/1.34 ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes( X
% 0.77/1.34 , Y, T ), c_Groups_Otimes__class_Otimes( X, Y, Z ) ),
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.77/1.34 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.77/1.34 ! c_Orderings_Oord__class_Oless__eq( X, Z, T ),
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes( X, Y
% 0.77/1.34 , T ), c_Groups_Otimes__class_Otimes( X, Y, Z ) ) }.
% 0.77/1.34 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.77/1.34 ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes( X
% 0.77/1.34 , Y, T ), c_Groups_Otimes__class_Otimes( X, Y, Z ) ),
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.77/1.34 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.77/1.34 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes( X, Y
% 0.77/1.34 , T ), c_Groups_Otimes__class_Otimes( X, Y, Z ) ) }.
% 0.77/1.34 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.77/1.34 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.77/1.34 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.77/1.34 ( X ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( X, Y, Z ), Y ) }.
% 0.77/1.34 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.77/1.34 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.77/1.34 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.77/1.34 ( X ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( X, Z, Y ), Y ) }.
% 0.77/1.34 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.77/1.34 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.77/1.34 c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ) ) }.
% 0.77/1.34 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.77/1.34 c_Power_Opower__class_Opower( tc_RealDef_Oreal, Y,
% 0.77/1.34 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.77/1.34 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal, X,
% 0.77/1.34 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.77/1.34 c_Int_OPls ) ) ) ) ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y
% 0.77/1.34 = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.77/1.34 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.77/1.34 c_Power_Opower__class_Opower( tc_RealDef_Oreal, Y,
% 0.77/1.34 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.77/1.34 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal, X,
% 0.77/1.34 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.77/1.34 c_Int_OPls ) ) ) ) ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X
% 0.77/1.34 = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.77/1.34 { ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! X =
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.77/1.34 c_Power_Opower__class_Opower( tc_RealDef_Oreal, Y,
% 0.77/1.34 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.77/1.34 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal, X,
% 0.77/1.34 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.77/1.34 c_Int_OPls ) ) ) ) ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }
% 0.77/1.34 .
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.77/1.34 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Int_Oint, X, Y ) ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ),
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oone__class_Oone
% 0.77/1.34 ( tc_Int_Oint ), Y ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.77/1.34 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Int_Oint, X, Y ) ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ),
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.77/1.34 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.77/1.34 tc_Int_Oint, c_Groups_Otimes__class_Otimes( tc_Int_Oint, Z, Y ), X ) ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.77/1.34 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.77/1.34 ( tc_Int_Oint, c_Groups_Otimes__class_Otimes( tc_Int_Oint, Z, Y ), X ),
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.77/1.34 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.77/1.34 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, X ) ), X =
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.77/1.34 { ! X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, X ) ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), ! Y = X }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), Y = X,
% 0.77/1.34 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.77/1.34 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), Y = X }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.77/1.34 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Z, X ),
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Y, X ) ),
% 0.77/1.34 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 0.77/1.34 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Z, X ),
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Y, X ) ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Z, X ),
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Y, X ) ),
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ),
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Z, X ),
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Y, X ) ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, Z ),
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, Y ) ),
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ),
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, Z ),
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, Y ) ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.77/1.34 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, Y ) ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 0.77/1.34 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, Z ),
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, Y ) ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ),
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, X ) ) }.
% 0.77/1.34 { c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal,
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ), X ) =
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Z, X ),
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Y, X ) ) }.
% 0.77/1.34 { c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Z, Y ), X ) =
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Z,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Y, X ) ) }.
% 0.77/1.34 { c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Y, X ) =
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, Y ) }.
% 0.77/1.34 { c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal,
% 0.77/1.34 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) = X }.
% 0.77/1.34 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), !
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, Z ) =
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, Y ), Z = Y }.
% 0.77/1.34 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, Z ) =
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, Y ) }.
% 0.77/1.34 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), !
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Z, X ) =
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Y, X ), Z = Y }.
% 0.77/1.34 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Z, X ) =
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Y, X ) }.
% 0.77/1.34 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Y, Y ),
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, X ) ) =
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y =
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.77/1.34 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Y, Y ),
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, X ) ) =
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X =
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.77/1.34 { ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! X =
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Y, Y ),
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, X ) ) =
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.77/1.34 { ! c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) =
% 0.77/1.34 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.77/1.34 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, X ) }.
% 0.77/1.34 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Z ),
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, Z ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ), Y = X }.
% 0.77/1.34 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Otimes__class_Otimes
% 0.77/1.34 ( tc_Int_Oint, W, U ), T ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Int_Oint, Z, Y ), X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.77/1.34 tc_Int_Oint, c_Groups_Otimes__class_Otimes( tc_Int_Oint, Z, Y ), X ),
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, T, W ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.77/1.34 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.77/1.34 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, U ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Otimes__class_Otimes(
% 0.77/1.34 tc_Int_Oint, U, T ), Z ), c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Int_Oint, U, Y ), X ) ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, Z ),
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, T ) }.
% 0.77/1.34 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Otimes__class_Otimes
% 0.77/1.34 ( tc_Int_Oint, W, U ), T ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Int_Oint, Z, Y ), X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.77/1.34 tc_Int_Oint, c_Groups_Otimes__class_Otimes( tc_Int_Oint, Z, Y ), X ) ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.77/1.34 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.77/1.34 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, U, Y ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Otimes__class_Otimes(
% 0.77/1.34 tc_Int_Oint, U, T ), Z ), c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Int_Oint, U, Y ), X ) ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, U ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, U ),
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Y ) }.
% 0.77/1.34 { c_Power_Opower__class_Opower( tc_RealDef_Oreal,
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.77/1.34 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.77/1.34 c_Int_OPls ) ) ) ) = c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.77/1.34 c_Power_Opower__class_Opower( tc_RealDef_Oreal, Y,
% 0.77/1.34 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.77/1.34 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal, X,
% 0.77/1.34 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.77/1.34 c_Int_OPls ) ) ) ) ), c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal,
% 0.77/1.34 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.77/1.34 c_Int_OBit1( c_Int_OPls ) ) ), Y ), X ) ) }.
% 0.77/1.34 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.77/1.34 ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.77/1.34 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.77/1.34 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.77/1.34 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.77/1.34 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.77/1.34 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.77/1.34 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.77/1.34 { ! class_Groups_Ozero( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y, Y =
% 0.77/1.34 c_Groups_Ozero__class_Ozero( X ) }.
% 0.77/1.34 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.77/1.34 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 0.77/1.34 { ! class_Groups_Oab__semigroup__mult( X ), c_Groups_Otimes__class_Otimes(
% 0.77/1.34 X, c_Groups_Otimes__class_Otimes( X, T, Z ), Y ) =
% 0.77/1.34 c_Groups_Otimes__class_Otimes( X, T, c_Groups_Otimes__class_Otimes( X, Z
% 0.77/1.34 , Y ) ) }.
% 0.77/1.34 { ! class_Groups_Oab__semigroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.77/1.34 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.77/1.34 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.77/1.34 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.77/1.34 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.77/1.34 T, Y ), Z = Y }.
% 0.77/1.34 { ! class_Groups_Ocancel__semigroup__add( X ), ! Z = Y,
% 0.77/1.34 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.77/1.34 T, Y ) }.
% 0.77/1.34 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.77/1.34 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.77/1.34 Y, Z ), T = Y }.
% 0.77/1.34 { ! class_Groups_Ocancel__semigroup__add( X ), ! T = Y,
% 0.77/1.34 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.77/1.34 Y, Z ) }.
% 0.77/1.34 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.77/1.34 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.77/1.34 T, Y ), Z = Y }.
% 0.77/1.34 { ! class_Groups_Ocancel__ab__semigroup__add( X ), !
% 0.77/1.34 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.77/1.34 T, Y ), Z = Y }.
% 0.77/1.34 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.77/1.34 c_Groups_Oplus__class_Oplus( X, Z, T ) = c_Groups_Oplus__class_Oplus( X,
% 0.77/1.34 Y, T ), Z = Y }.
% 0.77/1.34 { ! class_Groups_Oone( X ), ! c_Groups_Oone__class_Oone( X ) = Y, Y =
% 0.77/1.34 c_Groups_Oone__class_Oone( X ) }.
% 0.77/1.34 { ! class_Groups_Oone( X ), ! Y = c_Groups_Oone__class_Oone( X ),
% 0.77/1.34 c_Groups_Oone__class_Oone( X ) = Y }.
% 0.77/1.34 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.77/1.34 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.77/1.34 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.77/1.34 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.77/1.34 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.77/1.34 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.77/1.34 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero( X ) =
% 0.77/1.34 c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 0.77/1.34 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.77/1.34 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.77/1.34 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.77/1.34 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.77/1.34 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ),
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.77/1.34 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.77/1.34 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.77/1.34 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.77/1.34 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.77/1.34 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.77/1.34 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.77/1.34 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.77/1.34 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.77/1.34 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.77/1.34 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.77/1.34 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.77/1.34 U ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.77/1.34 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.77/1.34 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ),
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.77/1.34 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.77/1.34 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.77/1.34 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.77/1.34 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.77/1.34 ( X, Z, Y ) }.
% 0.77/1.34 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, T )
% 0.77/1.34 , c_Groups_Oplus__class_Oplus( X, Y, T ) ), c_Orderings_Oord__class_Oless
% 0.77/1.34 ( X, Z, Y ) }.
% 0.77/1.34 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.77/1.34 ( X, U, T ), c_Orderings_Oord__class_Oless( X,
% 0.77/1.34 c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X, Y
% 0.77/1.34 , T ) ) }.
% 0.77/1.34 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.77/1.34 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.77/1.34 , T, Y ) ) }.
% 0.77/1.34 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.77/1.34 X, c_Groups_Oplus__class_Oplus( X, Z, T ), c_Groups_Oplus__class_Oplus( X
% 0.77/1.34 , Y, T ) ) }.
% 0.77/1.34 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.77/1.34 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.77/1.34 ( X, Z, Y ) }.
% 0.77/1.34 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.77/1.34 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.77/1.34 , T, Y ) ) }.
% 0.77/1.34 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.77/1.34 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ), c_Orderings_Oord__class_Oless
% 0.77/1.34 ( X, T, Y ) }.
% 0.77/1.34 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( X, T, Y ), c_Orderings_Oord__class_Oless(
% 0.77/1.34 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.77/1.34 , Y, Z ) ) }.
% 0.77/1.34 { ! class_Groups_Omonoid__mult( X ), c_Groups_Otimes__class_Otimes( X,
% 0.77/1.34 c_Groups_Oone__class_Oone( X ), Y ) = Y }.
% 0.77/1.34 { ! class_Groups_Ocomm__monoid__mult( X ), c_Groups_Otimes__class_Otimes( X
% 0.77/1.34 , c_Groups_Oone__class_Oone( X ), Y ) = Y }.
% 0.77/1.34 { ! class_Groups_Omonoid__mult( X ), c_Groups_Otimes__class_Otimes( X, Y,
% 0.77/1.34 c_Groups_Oone__class_Oone( X ) ) = Y }.
% 0.77/1.34 { ! class_Groups_Ocomm__monoid__mult( X ), c_Groups_Otimes__class_Otimes( X
% 0.77/1.34 , Y, c_Groups_Oone__class_Oone( X ) ) = Y }.
% 0.77/1.34 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.77/1.34 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.77/1.34 , c_Groups_Oplus__class_Oplus( X, Y, Z ), c_Groups_Ozero__class_Ozero( X
% 0.77/1.34 ) ) }.
% 0.77/1.34 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.77/1.34 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.77/1.34 Z, Y ) ) }.
% 0.77/1.34 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.77/1.34 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.77/1.34 Y, Z ) ) }.
% 0.77/1.34 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.77/1.34 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.77/1.34 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.77/1.34 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 0.77/1.34 .
% 0.77/1.34 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.77/1.34 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.77/1.34 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.77/1.34 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.77/1.34 .
% 0.77/1.34 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.77/1.34 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.77/1.34 X ), Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), ! Z =
% 0.77/1.34 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.77/1.34 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.77/1.34 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.77/1.34 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.77/1.34 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.77/1.34 ) }.
% 0.77/1.34 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Y,
% 0.77/1.34 Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.77/1.34 ) }.
% 0.77/1.34 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.77/1.34 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X
% 0.77/1.34 , Y, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.77/1.34 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.77/1.34 c_Groups_Oplus__class_Oplus( X, Y, Y ) ),
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.77/1.34 ) }.
% 0.77/1.34 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.77/1.34 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.77/1.34 ), c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.77/1.34 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.77/1.34 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.77/1.34 , c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.77/1.34 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.77/1.34 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.77/1.34 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.77/1.34 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.77/1.34 c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.77/1.34 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.77/1.34 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Y
% 0.77/1.34 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.77/1.34 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.77/1.34 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.77/1.34 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.77/1.34 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.77/1.34 c_Groups_Oplus__class_Oplus( X, Y, Y ) ), c_Orderings_Oord__class_Oless(
% 0.77/1.34 X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.77/1.34 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.77/1.34 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.77/1.34 c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.77/1.34 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( X, U, T ), c_Orderings_Oord__class_Oless(
% 0.77/1.34 X, c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X
% 0.77/1.34 , Y, T ) ) }.
% 0.77/1.34 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.77/1.34 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, U )
% 0.77/1.34 , c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.77/1.34 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.77/1.34 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.77/1.34 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.77/1.34 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.77/1.34 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.77/1.34 ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.77/1.34 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.77/1.34 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.77/1.34 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.77/1.34 ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.77/1.34 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.77/1.34 ) ) }.
% 0.77/1.34 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.77/1.34 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.77/1.34 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.77/1.34 ) ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.77/1.34 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.77/1.34 tc_Int_Oint, c_Groups_Oone__class_Oone( tc_Int_Oint ),
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Int_Oint,
% 0.77/1.34 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0( c_Int_OBit1(
% 0.77/1.34 c_Int_OPls ) ) ), Y ) ), c_Groups_Otimes__class_Otimes( tc_Int_Oint,
% 0.77/1.34 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0( c_Int_OBit1(
% 0.77/1.34 c_Int_OPls ) ) ), X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.77/1.34 c_Groups_Oone__class_Oone( tc_Int_Oint ), c_Groups_Otimes__class_Otimes(
% 0.77/1.34 tc_Int_Oint, c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0(
% 0.77/1.34 c_Int_OBit1( c_Int_OPls ) ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Y
% 0.77/1.34 , X ) ) ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.77/1.34 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.77/1.34 tc_Int_Oint, c_Groups_Oone__class_Oone( tc_Int_Oint ),
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Int_Oint,
% 0.77/1.34 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0( c_Int_OBit1(
% 0.77/1.34 c_Int_OPls ) ) ), Y ) ), c_Groups_Otimes__class_Otimes( tc_Int_Oint,
% 0.77/1.34 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0( c_Int_OBit1(
% 0.77/1.34 c_Int_OPls ) ) ), X ) ) = c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X )
% 0.77/1.34 }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Divides_Odiv__class_Odiv
% 0.77/1.34 ( tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.77/1.34 c_Groups_Oone__class_Oone( tc_Int_Oint ), c_Groups_Otimes__class_Otimes(
% 0.77/1.34 tc_Int_Oint, c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0(
% 0.77/1.34 c_Int_OBit1( c_Int_OPls ) ) ), Y ) ), c_Groups_Otimes__class_Otimes(
% 0.77/1.34 tc_Int_Oint, c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0(
% 0.77/1.34 c_Int_OBit1( c_Int_OPls ) ) ), X ) ) = c_Divides_Odiv__class_Odiv(
% 0.77/1.34 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.77/1.34 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) }.
% 0.77/1.34 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( X, Z, Y ), Z ) =
% 0.77/1.34 c_Groups_Ozero__class_Ozero( X ) }.
% 0.77/1.34 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( X, Z, Y ), Y ) =
% 0.77/1.34 c_Groups_Ozero__class_Ozero( X ) }.
% 0.77/1.34 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y,
% 0.77/1.34 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.77/1.34 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.77/1.34 c_Groups_Oplus__class_Oplus( X, T, c_Groups_Otimes__class_Otimes( X, Z, Y
% 0.77/1.34 ) ), Y ) = c_Divides_Odiv__class_Omod( X, T, Y ) }.
% 0.77/1.34 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.77/1.34 c_Groups_Oplus__class_Oplus( X, T, c_Groups_Otimes__class_Otimes( X, Z, Y
% 0.77/1.34 ) ), Z ) = c_Divides_Odiv__class_Omod( X, T, Z ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.77/1.34 ( tc_Int_Oint ), X ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Z,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Int_Oint, Y, X ) ) =
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Otimes__class_Otimes(
% 0.77/1.34 tc_Int_Oint, Y, c_Divides_Odiv__class_Omod( tc_Int_Oint,
% 0.77/1.34 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Z, Y ), X ) ),
% 0.77/1.34 c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y ) ) }.
% 0.77/1.34 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero(
% 0.77/1.34 tc_Int_Oint ) ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.77/1.34 { c_Divides_Odiv__class_Omod( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero(
% 0.77/1.34 tc_Int_Oint ) ) = X }.
% 0.77/1.34 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X,
% 0.77/1.34 c_Divides_Odiv__class_Omod( X, Z, Y ), Y ) = c_Groups_Ozero__class_Ozero
% 0.77/1.34 ( X ) }.
% 0.77/1.34 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Divides_Odiv__class_Omod(
% 0.77/1.34 tc_Int_Oint, Y, X ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.77/1.34 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.77/1.34 }.
% 0.77/1.34 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.77/1.34 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y, Y
% 0.77/1.34 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.77/1.34 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.77/1.34 c_Divides_Odiv__class_Omod( X, Z, Y ), Y ) = c_Divides_Odiv__class_Omod(
% 0.77/1.34 X, Z, Y ) }.
% 0.77/1.34 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.77/1.34 }.
% 0.77/1.34 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X, Y,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.77/1.34 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.77/1.34 tc_Int_Oint ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.77/1.34 { c_Divides_Odiv__class_Omod( tc_Int_Oint, X, X ) =
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.77/1.34 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.77/1.34 tc_Int_Oint ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.77/1.34 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Power_Opower__class_Opower(
% 0.77/1.34 tc_Int_Oint, c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y ), X ), Y ) =
% 0.77/1.34 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Power_Opower__class_Opower(
% 0.77/1.34 tc_Int_Oint, Z, X ), Y ) }.
% 0.77/1.34 { Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Int_Oint, X, c_Divides_Odiv__class_Odiv
% 0.77/1.34 ( tc_Int_Oint, Y, X ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X )
% 0.77/1.34 ) }.
% 0.77/1.34 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X, Y,
% 0.77/1.34 c_Groups_Oone__class_Oone( X ) ) = Y }.
% 0.77/1.34 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.77/1.34 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = c_Divides_Odiv__class_Omod
% 0.77/1.34 ( X, Z, Y ) }.
% 0.77/1.34 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.77/1.34 c_Groups_Oplus__class_Oplus( X, Z, Y ), Z ) = c_Divides_Odiv__class_Omod
% 0.77/1.34 ( X, Y, Z ) }.
% 0.77/1.34 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.77/1.34 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 0.77/1.34 ( X, c_Groups_Oplus__class_Oplus( X, T, c_Divides_Odiv__class_Omod( X, Z
% 0.77/1.34 , Y ) ), Y ) }.
% 0.77/1.34 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( X, T, Z ), Y ) =
% 0.77/1.34 c_Divides_Odiv__class_Omod( X, c_Groups_Otimes__class_Otimes( X, T,
% 0.77/1.34 c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 0.77/1.34 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Otimes__class_Otimes(
% 0.77/1.34 tc_Int_Oint, Z, Y ), X ) = c_Divides_Odiv__class_Omod( tc_Int_Oint,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Int_Oint, Z, c_Divides_Odiv__class_Omod
% 0.77/1.34 ( tc_Int_Oint, Y, X ) ), X ) }.
% 0.77/1.34 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Otimes__class_Otimes(
% 0.77/1.34 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Int_Oint, Z, c_Divides_Odiv__class_Odiv
% 0.77/1.34 ( tc_Int_Oint, Y, X ) ), c_Divides_Odiv__class_Odiv( tc_Int_Oint,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Int_Oint, Z, c_Divides_Odiv__class_Omod
% 0.77/1.34 ( tc_Int_Oint, Y, X ) ), X ) ) }.
% 0.77/1.34 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.77/1.34 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 0.77/1.34 ( X, c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Y
% 0.77/1.34 ), Z ), Y ) }.
% 0.77/1.34 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( X, T, Z ), Y ) =
% 0.77/1.34 c_Divides_Odiv__class_Omod( X, c_Groups_Otimes__class_Otimes( X,
% 0.77/1.34 c_Divides_Odiv__class_Omod( X, T, Y ), Z ), Y ) }.
% 0.77/1.34 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.77/1.34 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 0.77/1.34 ( X, c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Y
% 0.77/1.34 ), c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 0.77/1.34 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( X, T, Z ), Y ) =
% 0.77/1.34 c_Divides_Odiv__class_Omod( X, c_Groups_Otimes__class_Otimes( X,
% 0.77/1.34 c_Divides_Odiv__class_Omod( X, T, Y ), c_Divides_Odiv__class_Omod( X, Z,
% 0.77/1.34 Y ) ), Y ) }.
% 0.77/1.34 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.77/1.34 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.77/1.34 tc_Int_Oint, Z, X ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 0.77/1.34 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.77/1.34 tc_Int_Oint, c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, X ),
% 0.77/1.34 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) ) }.
% 0.77/1.34 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( X, T, Z ), c_Groups_Otimes__class_Otimes(
% 0.77/1.34 X, T, Y ) ) = c_Groups_Otimes__class_Otimes( X, T,
% 0.77/1.34 c_Divides_Odiv__class_Omod( X, Z, Y ) ) }.
% 0.77/1.34 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( X, T, Z ), c_Groups_Otimes__class_Otimes(
% 0.77/1.34 X, Y, Z ) ) = c_Groups_Otimes__class_Otimes( X,
% 0.77/1.34 c_Divides_Odiv__class_Omod( X, T, Y ), Z ) }.
% 0.77/1.34 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X,
% 0.77/1.34 c_Divides_Odiv__class_Omod( X, Z, Y ), c_Groups_Otimes__class_Otimes( X,
% 0.77/1.34 c_Divides_Odiv__class_Odiv( X, Z, Y ), Y ) ) = Z }.
% 0.77/1.34 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.77/1.34 c_Groups_Oplus__class_Oplus( X, T, c_Divides_Odiv__class_Omod( X, Z, Y )
% 0.77/1.34 ), Y ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X,
% 0.77/1.34 T, Z ), Y ) }.
% 0.77/1.34 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Otimes__class_Otimes(
% 0.77/1.34 tc_Int_Oint, Z, c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) =
% 0.77/1.34 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Otimes__class_Otimes(
% 0.77/1.34 tc_Int_Oint, Z, Y ), X ) }.
% 0.77/1.34 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( X, Z, c_Divides_Odiv__class_Odiv( X, Y, Z
% 0.77/1.34 ) ), c_Divides_Odiv__class_Omod( X, Y, Z ) ) = Y }.
% 0.77/1.34 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.77/1.34 c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Z ), Y
% 0.77/1.34 ), Z ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X,
% 0.77/1.34 T, Y ), Z ) }.
% 0.77/1.34 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( X, c_Divides_Odiv__class_Omod( X, T, Z ),
% 0.77/1.34 Y ), Z ) = c_Divides_Odiv__class_Omod( X, c_Groups_Otimes__class_Otimes(
% 0.77/1.34 X, T, Y ), Z ) }.
% 0.77/1.34 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( X, c_Divides_Odiv__class_Odiv( X, Z, Y ),
% 0.77/1.34 Y ), c_Divides_Odiv__class_Omod( X, Z, Y ) ) = Z }.
% 0.77/1.34 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X,
% 0.77/1.34 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, T,
% 0.77/1.34 c_Divides_Odiv__class_Odiv( X, Z, T ) ), c_Divides_Odiv__class_Omod( X, Z
% 0.77/1.34 , T ) ), Y ) = c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 0.77/1.34 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.77/1.34 tc_Int_Oint, c_Groups_Otimes__class_Otimes( tc_Int_Oint, Z,
% 0.77/1.34 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ) ),
% 0.77/1.34 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, Z ) ), X ) =
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) }.
% 0.77/1.34 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X,
% 0.77/1.34 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.77/1.34 c_Divides_Odiv__class_Odiv( X, T, Z ), Z ), c_Divides_Odiv__class_Omod( X
% 0.77/1.34 , T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus( X, T, Y ) }.
% 0.77/1.34 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.77/1.34 tc_Int_Oint, c_Groups_Otimes__class_Otimes( tc_Int_Oint,
% 0.77/1.34 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Z, Y ), Y ),
% 0.77/1.34 c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y ) ), X ) =
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) }.
% 0.77/1.34 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, T,
% 0.77/1.34 Z ) = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod
% 0.77/1.34 ( X, W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 0.77/1.34 c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X, T, W ), Z
% 0.77/1.34 ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X, Y, U
% 0.77/1.34 ), Z ) }.
% 0.77/1.34 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, T,
% 0.77/1.34 Z ) = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod
% 0.77/1.34 ( X, W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 0.77/1.34 c_Divides_Odiv__class_Omod( X, c_Groups_Otimes__class_Otimes( X, T, W ),
% 0.77/1.34 Z ) = c_Divides_Odiv__class_Omod( X, c_Groups_Otimes__class_Otimes( X, Y
% 0.77/1.34 , U ), Z ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.77/1.34 tc_Int_Oint, X, Y ) ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.77/1.34 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.77/1.34 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ),
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.77/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.77/1.34 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.77/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.77/1.34 tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.77/1.34 tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.77/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.77/1.34 tc_Int_Oint ), Y ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.77/1.34 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.77/1.34 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ),
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.77/1.34 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.77/1.34 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.77/1.34 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.77/1.34 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, X ) =
% 0.77/1.34 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.77/1.34 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Int_Onumber__class_Onumber__of
% 0.77/1.34 ( tc_Int_Oint, c_Int_OBit0( Y ) ), c_Int_Onumber__class_Onumber__of(
% 0.77/1.34 tc_Int_Oint, c_Int_OBit0( X ) ) ) = c_Divides_Odiv__class_Odiv(
% 0.77/1.34 tc_Int_Oint, c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 0.77/1.34 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.34 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ), X ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.77/1.34 tc_Int_Oint, X, Y ) ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.77/1.34 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.77/1.34 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ), X ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.77/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Divides_Odiv__class_Omod
% 0.77/1.34 ( tc_Int_Oint, Y, X ) ) }.
% 0.77/1.34 { ! c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y =
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Int_Oint, X, skol7( X, Y ) ) }.
% 0.77/1.34 { ! Y = c_Groups_Otimes__class_Otimes( tc_Int_Oint, X, Z ),
% 0.77/1.34 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.77/1.34 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.77/1.34 , c_Divides_Odiv__class_Odiv( X, c_Groups_Otimes__class_Otimes( X, Y, T )
% 0.77/1.34 , c_Groups_Otimes__class_Otimes( X, Y, Z ) ) = c_Divides_Odiv__class_Odiv
% 0.77/1.34 ( X, T, Z ) }.
% 0.77/1.34 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.77/1.34 , c_Divides_Odiv__class_Odiv( X, c_Groups_Otimes__class_Otimes( X, T, Y )
% 0.77/1.34 , c_Groups_Otimes__class_Otimes( X, Z, Y ) ) = c_Divides_Odiv__class_Odiv
% 0.77/1.34 ( X, T, Z ) }.
% 0.77/1.34 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.77/1.34 , c_Divides_Odiv__class_Odiv( X, c_Groups_Otimes__class_Otimes( X, Y, Z )
% 0.77/1.34 , Y ) = Z }.
% 0.77/1.34 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.77/1.34 , c_Divides_Odiv__class_Odiv( X, c_Groups_Otimes__class_Otimes( X, Z, Y )
% 0.77/1.34 , Y ) = Z }.
% 0.77/1.34 { ! class_Divides_Osemiring__div( X ), ! T = c_Groups_Ozero__class_Ozero( X
% 0.77/1.34 ), c_Divides_Odiv__class_Odiv( X, c_Groups_Otimes__class_Otimes( X, T, Z
% 0.77/1.34 ), c_Groups_Otimes__class_Otimes( X, T, Y ) ) =
% 0.77/1.34 c_Groups_Ozero__class_Ozero( X ) }.
% 0.77/1.34 { ! class_Divides_Osemiring__div( X ), T = c_Groups_Ozero__class_Ozero( X )
% 0.77/1.34 , c_Divides_Odiv__class_Odiv( X, c_Groups_Otimes__class_Otimes( X, T, Z )
% 0.77/1.34 , c_Groups_Otimes__class_Otimes( X, T, Y ) ) = c_Divides_Odiv__class_Odiv
% 0.77/1.34 ( X, Z, Y ) }.
% 0.77/1.34 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.77/1.34 , c_Divides_Odiv__class_Odiv( X, Y, Y ) = c_Groups_Oone__class_Oone( X )
% 0.77/1.34 }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! hBOOL( hAPP( hAPP( Z,
% 0.77/1.34 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 0.77/1.34 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ), ! alpha9( X, Y, T, U
% 0.77/1.34 ), hBOOL( hAPP( hAPP( Z, T ), U ) ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha9( X, Y, skol8( X, Y,
% 0.77/1.34 Z ), skol29( X, Y, Z ) ), hBOOL( hAPP( hAPP( Z,
% 0.77/1.34 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 0.77/1.34 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! hBOOL( hAPP( hAPP( Z,
% 0.77/1.34 skol8( X, Y, Z ) ), skol29( X, Y, Z ) ) ), hBOOL( hAPP( hAPP( Z,
% 0.77/1.34 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 0.77/1.34 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 0.77/1.34 { ! alpha9( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, T
% 0.77/1.34 ) }.
% 0.77/1.34 { ! alpha9( X, Y, Z, T ), alpha27( X, Y, Z, T ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, T ), ! alpha27( X, Y, Z
% 0.77/1.34 , T ), alpha9( X, Y, Z, T ) }.
% 0.77/1.34 { ! alpha27( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.34 T, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.77/1.34 { ! alpha27( X, Y, Z, T ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Int_Oint, X, Z ), T ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! Y =
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Otimes__class_Otimes(
% 0.77/1.34 tc_Int_Oint, X, Z ), T ), alpha27( X, Y, Z, T ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.77/1.34 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( hAPP( Z, c_Divides_Odiv__class_Odiv
% 0.77/1.34 ( tc_Int_Oint, Y, X ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X )
% 0.77/1.34 ) ), ! alpha10( X, Y, T, U ), hBOOL( hAPP( hAPP( Z, T ), U ) ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.77/1.34 ( tc_Int_Oint ), X ), alpha10( X, Y, skol9( X, Y, Z ), skol30( X, Y, Z )
% 0.77/1.34 ), hBOOL( hAPP( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X )
% 0.77/1.34 ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.77/1.34 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( hAPP( Z, skol9( X, Y, Z ) ), skol30
% 0.77/1.34 ( X, Y, Z ) ) ), hBOOL( hAPP( hAPP( Z, c_Divides_Odiv__class_Odiv(
% 0.77/1.34 tc_Int_Oint, Y, X ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) )
% 0.77/1.34 ) }.
% 0.77/1.34 { ! alpha10( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ) }.
% 0.77/1.34 { ! alpha10( X, Y, Z, T ), alpha28( X, Y, Z, T ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! alpha28( X, Y, Z, T )
% 0.77/1.34 , alpha10( X, Y, Z, T ) }.
% 0.77/1.34 { ! alpha28( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X
% 0.77/1.34 ) }.
% 0.77/1.34 { ! alpha28( X, Y, Z, T ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Int_Oint, X, Z ), T ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X ), ! Y =
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Otimes__class_Otimes(
% 0.77/1.34 tc_Int_Oint, X, Z ), T ), alpha28( X, Y, Z, T ) }.
% 0.77/1.34 { ! c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X =
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), alpha11( X, Y ) }.
% 0.77/1.34 { ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.77/1.34 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.77/1.34 { ! alpha11( X, Y ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.77/1.34 { ! alpha11( X, Y ), alpha29( X, Y ), alpha39( X, Y ) }.
% 0.77/1.34 { ! alpha29( X, Y ), alpha11( X, Y ) }.
% 0.77/1.34 { ! alpha39( X, Y ), alpha11( X, Y ) }.
% 0.77/1.34 { ! alpha39( X, Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.77/1.34 { ! alpha39( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ), alpha39( X, Y ) }.
% 0.77/1.34 { ! alpha29( X, Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.77/1.34 { ! alpha29( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), alpha29( X, Y ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.77/1.34 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.77/1.34 tc_Int_Oint, Y, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.77/1.34 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.77/1.34 tc_Int_Oint, Y, X ) ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.77/1.34 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.77/1.34 tc_Int_Oint, Y, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X
% 0.77/1.34 , Y ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.77/1.34 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X
% 0.77/1.34 , Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.77/1.34 tc_Int_Oint, Y, X ) ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.77/1.34 tc_Int_Oint ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ),
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.77/1.34 tc_Int_Oint ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ),
% 0.77/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.77/1.34 tc_Int_Oint ), Y ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.77/1.34 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.77/1.34 tc_Int_Oint, X, Y ) ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.77/1.34 tc_Int_Oint ), Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.77/1.34 Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.34 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ),
% 0.77/1.34 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.34 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ),
% 0.77/1.34 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) =
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.77/1.34 tc_Int_Oint, Y, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y
% 0.77/1.34 , c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.77/1.34 tc_Int_Oint, Y, X ) ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.77/1.34 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.34 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.77/1.34 tc_Int_Oint ), Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.77/1.34 Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.34 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 0.77/1.34 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ) ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.77/1.34 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) =
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.77/1.34 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.34 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ),
% 0.77/1.34 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ) ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.34 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ),
% 0.77/1.34 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ) ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.77/1.34 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.77/1.34 c_Groups_Oone__class_Oone( tc_Int_Oint ), Y ),
% 0.77/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.77/1.34 tc_Int_Oint, X, Y ), X ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.77/1.34 ( tc_Int_Oint ), X ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Z,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Int_Oint, Y, X ) ) =
% 0.77/1.34 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.77/1.34 tc_Int_Oint, Z, Y ), X ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.77/1.34 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.77/1.34 tc_Int_Oint, Y, X ) ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.77/1.34 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.77/1.34 tc_Int_Oint, Y, X ) ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.77/1.34 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.77/1.34 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ), X ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ),
% 0.77/1.34 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ) = X }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.34 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ),
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.34 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ),
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.77/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Divides_Odiv__class_Omod
% 0.77/1.34 ( tc_Int_Oint, Y, X ) ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.77/1.34 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ) = X }.
% 0.77/1.34 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.77/1.34 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( X, Z, Y ) ), Y ) =
% 0.77/1.34 c_Groups_Oplus__class_Oplus( X, Z, c_Divides_Odiv__class_Odiv( X, T, Y )
% 0.77/1.34 ) }.
% 0.77/1.34 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.77/1.34 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( X, Y, Z ) ), Y ) =
% 0.77/1.34 c_Groups_Oplus__class_Oplus( X, Z, c_Divides_Odiv__class_Odiv( X, T, Y )
% 0.77/1.34 ) }.
% 0.77/1.34 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.77/1.34 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, Y, Z ),
% 0.77/1.34 Y ) = c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Z, Y
% 0.77/1.34 ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.77/1.34 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.77/1.34 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, Z, Y ),
% 0.77/1.34 Y ) = c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Z, Y
% 0.77/1.34 ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.77/1.34 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ),
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Divides_Odiv__class_Omod
% 0.77/1.34 ( tc_Int_Oint, X, Y ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y )
% 0.77/1.34 }.
% 0.77/1.34 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ),
% 0.77/1.34 alpha12( X, Z ) }.
% 0.77/1.34 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ),
% 0.77/1.34 alpha30( X, Y, Z ) }.
% 0.77/1.34 { ! alpha12( X, Z ), ! alpha30( X, Y, Z ), hBOOL( hAPP( Z,
% 0.77/1.34 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ) }.
% 0.77/1.34 { ! alpha30( X, Y, Z ), alpha40( X, Y, Z ) }.
% 0.77/1.34 { ! alpha30( X, Y, Z ), alpha45( X, Y, Z ) }.
% 0.77/1.34 { ! alpha40( X, Y, Z ), ! alpha45( X, Y, Z ), alpha30( X, Y, Z ) }.
% 0.77/1.34 { ! alpha45( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha51( X, Y, Z ) }.
% 0.77/1.34 { c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha45( X, Y, Z ) }.
% 0.77/1.34 { ! alpha51( X, Y, Z ), alpha45( X, Y, Z ) }.
% 0.77/1.34 { ! alpha51( X, Y, Z ), ! alpha55( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 0.77/1.34 { ! hBOOL( hAPP( Z, skol10( T, U, Z ) ) ), alpha51( X, Y, Z ) }.
% 0.77/1.34 { alpha55( X, Y, skol10( X, Y, Z ) ), alpha51( X, Y, Z ) }.
% 0.77/1.34 { ! alpha55( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.77/1.34 skol11( X, T, U ) ) }.
% 0.77/1.34 { ! alpha55( X, Y, Z ), alpha59( X, Y, Z, skol11( X, Y, Z ) ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, T ), ! alpha59( X, Y, Z
% 0.77/1.34 , T ), alpha55( X, Y, Z ) }.
% 0.77/1.34 { ! alpha59( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.34 T, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.77/1.34 { ! alpha59( X, Y, Z, T ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Int_Oint, X, Z ), T ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! Y =
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Otimes__class_Otimes(
% 0.77/1.34 tc_Int_Oint, X, Z ), T ), alpha59( X, Y, Z, T ) }.
% 0.77/1.34 { ! alpha40( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), alpha46( X, Y, Z ) }.
% 0.77/1.34 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.77/1.34 tc_Int_Oint ), X ), alpha40( X, Y, Z ) }.
% 0.77/1.34 { ! alpha46( X, Y, Z ), alpha40( X, Y, Z ) }.
% 0.77/1.34 { ! alpha46( X, Y, Z ), ! alpha52( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 0.77/1.34 { ! hBOOL( hAPP( Z, skol12( T, U, Z ) ) ), alpha46( X, Y, Z ) }.
% 0.77/1.34 { alpha52( X, Y, skol12( X, Y, Z ) ), alpha46( X, Y, Z ) }.
% 0.77/1.34 { ! alpha52( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), skol13( T, U, W ) ) }.
% 0.77/1.34 { ! alpha52( X, Y, Z ), alpha56( X, Y, Z, skol13( X, Y, Z ) ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! alpha56( X, Y, Z, T )
% 0.77/1.34 , alpha52( X, Y, Z ) }.
% 0.77/1.34 { ! alpha56( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X
% 0.77/1.34 ) }.
% 0.77/1.34 { ! alpha56( X, Y, Z, T ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Int_Oint, X, Z ), T ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X ), ! Y =
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Otimes__class_Otimes(
% 0.77/1.34 tc_Int_Oint, X, Z ), T ), alpha56( X, Y, Z, T ) }.
% 0.77/1.34 { ! alpha12( X, Y ), ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.77/1.34 hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 0.77/1.34 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), alpha12( X, Y ) }.
% 0.77/1.34 { ! hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), alpha12
% 0.77/1.34 ( X, Y ) }.
% 0.77/1.34 { ! T = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Int_Oint, Z, Y ), X ), alpha62( X, Z )
% 0.77/1.34 , ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), Z =
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.77/1.34 tc_Int_Oint, T, Z ) = Y }.
% 0.77/1.34 { ! T = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Int_Oint, Z, Y ), X ), alpha62( X, Z )
% 0.77/1.34 , ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Z =
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.77/1.34 tc_Int_Oint, T, Z ) = Y }.
% 0.77/1.34 { ! alpha62( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.77/1.34 { ! alpha62( X, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.77/1.34 ( tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), alpha62( X, Y ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.77/1.34 ( tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y )
% 0.77/1.34 , alpha62( X, Y ) }.
% 0.77/1.34 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Int_Onumber__class_Onumber__of
% 0.77/1.34 ( tc_Int_Oint, c_Int_OBit0( Y ) ), c_Int_Onumber__class_Onumber__of(
% 0.77/1.34 tc_Int_Oint, c_Int_OBit0( X ) ) ) = c_Groups_Otimes__class_Otimes(
% 0.77/1.34 tc_Int_Oint, c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0(
% 0.77/1.34 c_Int_OBit1( c_Int_OPls ) ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint,
% 0.77/1.34 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 0.77/1.34 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) ) }.
% 0.77/1.34 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ),
% 0.77/1.34 alpha13( X, Y, Z ) }.
% 0.77/1.34 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ),
% 0.77/1.34 alpha31( X, Y, Z ) }.
% 0.77/1.34 { ! alpha13( X, Y, Z ), ! alpha31( X, Y, Z ), hBOOL( hAPP( Z,
% 0.77/1.34 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 0.77/1.34 { ! alpha31( X, Y, Z ), alpha41( X, Y, Z ) }.
% 0.77/1.34 { ! alpha31( X, Y, Z ), alpha47( X, Y, Z ) }.
% 0.77/1.34 { ! alpha41( X, Y, Z ), ! alpha47( X, Y, Z ), alpha31( X, Y, Z ) }.
% 0.77/1.34 { ! alpha47( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha53( X, Y, Z ) }.
% 0.77/1.34 { c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha47( X, Y, Z ) }.
% 0.77/1.34 { ! alpha53( X, Y, Z ), alpha47( X, Y, Z ) }.
% 0.77/1.34 { ! alpha53( X, Y, Z ), ! alpha57( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 0.77/1.34 { ! hBOOL( hAPP( Z, skol14( T, U, Z ) ) ), alpha53( X, Y, Z ) }.
% 0.77/1.34 { alpha57( X, Y, skol14( X, Y, Z ) ), alpha53( X, Y, Z ) }.
% 0.77/1.34 { ! alpha57( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z )
% 0.77/1.34 }.
% 0.77/1.34 { ! alpha57( X, Y, Z ), alpha60( X, Y, Z ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), ! alpha60( X, Y, Z
% 0.77/1.34 ), alpha57( X, Y, Z ) }.
% 0.77/1.34 { ! alpha60( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.77/1.34 { ! alpha60( X, Y, Z ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Int_Oint, X, skol15( X, Y, Z ) ), Z ) }
% 0.77/1.34 .
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! Y =
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Otimes__class_Otimes(
% 0.77/1.34 tc_Int_Oint, X, T ), Z ), alpha60( X, Y, Z ) }.
% 0.77/1.34 { ! alpha41( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), alpha48( X, Y, Z ) }.
% 0.77/1.34 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.77/1.34 tc_Int_Oint ), X ), alpha41( X, Y, Z ) }.
% 0.77/1.34 { ! alpha48( X, Y, Z ), alpha41( X, Y, Z ) }.
% 0.77/1.34 { ! alpha48( X, Y, Z ), ! alpha54( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 0.77/1.34 { ! hBOOL( hAPP( Z, skol16( T, U, Z ) ) ), alpha48( X, Y, Z ) }.
% 0.77/1.34 { alpha54( X, Y, skol16( X, Y, Z ) ), alpha48( X, Y, Z ) }.
% 0.77/1.34 { ! alpha54( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ) }.
% 0.77/1.34 { ! alpha54( X, Y, Z ), alpha58( X, Y, Z ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), ! alpha58( X, Y, Z ),
% 0.77/1.34 alpha54( X, Y, Z ) }.
% 0.77/1.34 { ! alpha58( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X )
% 0.77/1.34 }.
% 0.77/1.34 { ! alpha58( X, Y, Z ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Int_Oint, X, skol17( X, Y, Z ) ), Z ) }
% 0.77/1.34 .
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ), ! Y =
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Otimes__class_Otimes(
% 0.77/1.34 tc_Int_Oint, X, T ), Z ), alpha58( X, Y, Z ) }.
% 0.77/1.34 { ! alpha13( X, Y, Z ), ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.77/1.34 hBOOL( hAPP( Z, Y ) ) }.
% 0.77/1.34 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), alpha13( X, Y, Z ) }.
% 0.77/1.34 { ! hBOOL( hAPP( Z, Y ) ), alpha13( X, Y, Z ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.77/1.34 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, Z ),
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.77/1.34 tc_Int_Oint, c_Groups_Otimes__class_Otimes( tc_Int_Oint, Z,
% 0.77/1.34 c_Divides_Odiv__class_Omod( tc_Int_Oint, T, X ) ), Y ) ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.77/1.34 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, Z ),
% 0.77/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.77/1.34 tc_Int_Oint, c_Groups_Otimes__class_Otimes( tc_Int_Oint, Z,
% 0.77/1.34 c_Divides_Odiv__class_Omod( tc_Int_Oint, T, X ) ), Y ),
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Int_Oint, Z, X ) ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.77/1.34 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, Y
% 0.77/1.34 ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.77/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Otimes__class_Otimes
% 0.77/1.34 ( tc_Int_Oint, Z, X ), c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Int_Oint, Z, c_Divides_Odiv__class_Omod
% 0.77/1.34 ( tc_Int_Oint, T, X ) ), Y ) ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.77/1.34 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, Y
% 0.77/1.34 ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Otimes__class_Otimes(
% 0.77/1.34 tc_Int_Oint, Z, c_Divides_Odiv__class_Omod( tc_Int_Oint, T, X ) ), Y ),
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.77/1.34 { ! Z = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Int_Oint, Y, T ), X ), alpha63( X, Y )
% 0.77/1.34 , ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), Y =
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.77/1.34 tc_Int_Oint, Z, Y ) = X }.
% 0.77/1.34 { ! Z = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Int_Oint, Y, T ), X ), alpha63( X, Y )
% 0.77/1.34 , ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y =
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.77/1.34 tc_Int_Oint, Z, Y ) = X }.
% 0.77/1.34 { ! alpha63( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.77/1.34 { ! alpha63( X, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.77/1.34 ( tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), alpha63( X, Y ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.77/1.34 ( tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y )
% 0.77/1.34 , alpha63( X, Y ) }.
% 0.77/1.34 { c_Divides_Odiv__class_Omod( tc_Int_Oint, X,
% 0.77/1.34 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0( c_Int_OBit1(
% 0.77/1.34 c_Int_OPls ) ) ) ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.77/1.34 c_Divides_Odiv__class_Omod( tc_Int_Oint, X,
% 0.77/1.34 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0( c_Int_OBit1(
% 0.77/1.34 c_Int_OPls ) ) ) ) = c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.77/1.34 { ! c_Divides_Odiv__class_Omod( tc_Int_Oint, X,
% 0.77/1.34 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0( c_Int_OBit1(
% 0.77/1.34 c_Int_OPls ) ) ) ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), !
% 0.77/1.34 c_Divides_Odiv__class_Omod( tc_Int_Oint, X,
% 0.77/1.34 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0( c_Int_OBit1(
% 0.77/1.34 c_Int_OPls ) ) ) ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.77/1.34 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ) ),
% 0.77/1.34 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Int_Onumber__class_Onumber__of
% 0.77/1.34 ( tc_Int_Oint, c_Int_OBit1( X ) ), c_Int_Onumber__class_Onumber__of(
% 0.77/1.34 tc_Int_Oint, c_Int_OBit0( Y ) ) ) = c_Divides_Odiv__class_Odiv(
% 0.77/1.34 tc_Int_Oint, c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ),
% 0.77/1.34 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ) ) }.
% 0.77/1.34 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.77/1.34 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ) ),
% 0.77/1.34 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Int_Onumber__class_Onumber__of
% 0.77/1.34 ( tc_Int_Oint, c_Int_OBit1( X ) ), c_Int_Onumber__class_Onumber__of(
% 0.77/1.34 tc_Int_Oint, c_Int_OBit0( Y ) ) ) = c_Divides_Odiv__class_Odiv(
% 0.77/1.34 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.77/1.34 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ),
% 0.77/1.34 c_Groups_Oone__class_Oone( tc_Int_Oint ) ),
% 0.77/1.34 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ) ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Divides_Odiv__class_Omod
% 0.77/1.34 ( tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.77/1.34 c_Groups_Oone__class_Oone( tc_Int_Oint ), c_Groups_Otimes__class_Otimes(
% 0.77/1.34 tc_Int_Oint, c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0(
% 0.77/1.34 c_Int_OBit1( c_Int_OPls ) ) ), Y ) ), c_Groups_Otimes__class_Otimes(
% 0.77/1.34 tc_Int_Oint, c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0(
% 0.77/1.34 c_Int_OBit1( c_Int_OPls ) ) ), X ) ) = c_Groups_Ominus__class_Ominus(
% 0.77/1.34 tc_Int_Oint, c_Groups_Otimes__class_Otimes( tc_Int_Oint,
% 0.77/1.34 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0( c_Int_OBit1(
% 0.77/1.34 c_Int_OPls ) ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint,
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.77/1.34 tc_Int_Oint ) ), X ) ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.77/1.34 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ) ),
% 0.77/1.34 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Int_Onumber__class_Onumber__of
% 0.77/1.34 ( tc_Int_Oint, c_Int_OBit1( X ) ), c_Int_Onumber__class_Onumber__of(
% 0.77/1.34 tc_Int_Oint, c_Int_OBit0( Y ) ) ) = c_Groups_Oplus__class_Oplus(
% 0.77/1.34 tc_Int_Oint, c_Groups_Otimes__class_Otimes( tc_Int_Oint,
% 0.77/1.34 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0( c_Int_OBit1(
% 0.77/1.34 c_Int_OPls ) ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint,
% 0.77/1.34 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ),
% 0.77/1.34 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ) ) ),
% 0.77/1.34 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.77/1.34 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.77/1.34 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ) ),
% 0.77/1.34 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Int_Onumber__class_Onumber__of
% 0.77/1.34 ( tc_Int_Oint, c_Int_OBit1( X ) ), c_Int_Onumber__class_Onumber__of(
% 0.77/1.34 tc_Int_Oint, c_Int_OBit0( Y ) ) ) = c_Groups_Ominus__class_Ominus(
% 0.77/1.34 tc_Int_Oint, c_Groups_Otimes__class_Otimes( tc_Int_Oint,
% 0.77/1.34 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0( c_Int_OBit1(
% 0.77/1.34 c_Int_OPls ) ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint,
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.77/1.34 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ),
% 0.77/1.34 c_Groups_Oone__class_Oone( tc_Int_Oint ) ),
% 0.77/1.34 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ) ) ),
% 0.77/1.34 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.77/1.34 { c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, X ),
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Otimes__class_Otimes(
% 0.77/1.34 tc_Int_Oint, c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0(
% 0.77/1.34 c_Int_OBit1( c_Int_OPls ) ) ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, X
% 0.77/1.34 , c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0( c_Int_OBit1
% 0.77/1.34 ( c_Int_OPls ) ) ) ) ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = X }
% 0.77/1.34 .
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.77/1.34 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) = Y }.
% 0.77/1.34 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.77/1.34 tc_Nat_Onat, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ),
% 0.77/1.34 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Nat_OSuc(
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ),
% 0.77/1.34 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.77/1.34 tc_Nat_Onat, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ),
% 0.77/1.34 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc(
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), X ) ) }.
% 0.77/1.34 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Odiv(
% 0.77/1.34 tc_Polynomial_Opoly( X ), T, c_Groups_Otimes__class_Otimes(
% 0.77/1.34 tc_Polynomial_Opoly( X ), Z, Y ) ) = c_Divides_Odiv__class_Odiv(
% 0.77/1.34 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly
% 0.77/1.34 ( X ), T, Z ), Y ) }.
% 0.77/1.34 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.77/1.34 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.77/1.34 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, T,
% 0.77/1.34 c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 0.77/1.34 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.77/1.34 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.77/1.34 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X,
% 0.77/1.34 c_Divides_Odiv__class_Omod( X, T, Y ), Z ), Y ) }.
% 0.77/1.34 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.77/1.34 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.77/1.34 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X,
% 0.77/1.34 c_Divides_Odiv__class_Omod( X, T, Y ), c_Divides_Odiv__class_Omod( X, Z,
% 0.77/1.34 Y ) ), Y ) }.
% 0.77/1.34 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 0.77/1.34 tc_Int_Oint, Z, c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) =
% 0.77/1.34 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 0.77/1.34 tc_Int_Oint, Z, Y ), X ) }.
% 0.77/1.34 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 0.77/1.34 tc_Int_Oint, c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y ), X ), Y ) =
% 0.77/1.34 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 0.77/1.34 tc_Int_Oint, Z, X ), Y ) }.
% 0.77/1.34 { ! class_Divides_Oring__div( X ), ! c_Divides_Odiv__class_Omod( X, T, Z )
% 0.77/1.34 = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod( X
% 0.77/1.34 , W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 0.77/1.34 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, T, W ),
% 0.77/1.34 Z ) = c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, Y
% 0.77/1.34 , U ), Z ) }.
% 0.77/1.34 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.77/1.34 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ), Y ) }.
% 0.77/1.34 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.77/1.34 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ), Y ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.77/1.34 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, Z ),
% 0.77/1.34 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, X, Z ) ) }.
% 0.77/1.34 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.77/1.34 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc(
% 0.77/1.34 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ), X ) }.
% 0.77/1.34 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, c_Groups_Otimes__class_Otimes
% 0.77/1.34 ( tc_Nat_Onat, Y, X ) ) = c_Divides_Odiv__class_Odiv( tc_Nat_Onat,
% 0.77/1.34 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, Y ), X ) }.
% 0.77/1.34 { c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, c_Divides_Odiv__class_Omod
% 0.77/1.34 ( tc_Nat_Onat, Y, X ) ) = c_Divides_Odiv__class_Omod( tc_Nat_Onat,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ),
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ) ) }.
% 0.77/1.34 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, c_Groups_Otimes__class_Otimes
% 0.77/1.34 ( tc_Nat_Onat, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, c_Divides_Odiv__class_Omod
% 0.77/1.34 ( tc_Nat_Onat, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, Y ), X ) ),
% 0.77/1.34 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, Y ) ) }.
% 0.77/1.34 { c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Divides_Odiv__class_Omod(
% 0.77/1.34 tc_Nat_Onat, Z, Y ), X ) = c_Divides_Odiv__class_Omod( tc_Nat_Onat,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ),
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) ) }.
% 0.77/1.34 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.77/1.34 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, c_Divides_Odiv__class_Odiv
% 0.77/1.34 ( tc_Nat_Onat, Y, X ) ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, c_Divides_Odiv__class_Omod
% 0.77/1.34 ( tc_Nat_Onat, Y, X ) ), X ) ) }.
% 0.77/1.34 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.77/1.34 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 0.77/1.34 tc_Nat_Onat, Z, X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ),
% 0.77/1.34 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.77/1.34 tc_Nat_Onat, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, X ),
% 0.77/1.34 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ), X ) ) }.
% 0.77/1.34 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Omod(
% 0.77/1.34 tc_Polynomial_Opoly( X ), T, c_Groups_Otimes__class_Otimes(
% 0.77/1.34 tc_Polynomial_Opoly( X ), Z, Y ) ) = c_Groups_Oplus__class_Oplus(
% 0.77/1.34 tc_Polynomial_Opoly( X ), c_Groups_Otimes__class_Otimes(
% 0.77/1.34 tc_Polynomial_Opoly( X ), Z, c_Divides_Odiv__class_Omod(
% 0.77/1.34 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly
% 0.77/1.34 ( X ), T, Z ), Y ) ), c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X
% 0.77/1.34 ), T, Z ) ) }.
% 0.77/1.34 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 0.77/1.34 , Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.77/1.34 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 0.77/1.34 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.77/1.34 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.77/1.34 X, c_Groups_Ominus__class_Ominus( X, Z, Y ), c_Groups_Ozero__class_Ozero
% 0.77/1.34 ( X ) ) }.
% 0.77/1.34 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.77/1.34 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.77/1.34 , Z, Y ) }.
% 0.77/1.34 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) = X }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.77/1.34 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) =
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.77/1.34 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( X, W, U ), T ) =
% 0.77/1.34 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, Z, U )
% 0.77/1.34 , Y ), c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.77/1.34 c_Groups_Ominus__class_Ominus( X, W, Z ), U ), T ) = Y }.
% 0.77/1.34 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( X, c_Groups_Ominus__class_Ominus( X, W, Z
% 0.77/1.34 ), U ), T ) = Y, c_Groups_Oplus__class_Oplus( X,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( X, W, U ), T ) =
% 0.77/1.34 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, Z, U )
% 0.77/1.34 , Y ) }.
% 0.77/1.34 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( X, W, U ), T ) =
% 0.77/1.34 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, Z, U )
% 0.77/1.34 , Y ), T = c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes
% 0.77/1.34 ( X, c_Groups_Ominus__class_Ominus( X, Z, W ), U ), Y ) }.
% 0.77/1.34 { ! class_Rings_Oring( X ), ! T = c_Groups_Oplus__class_Oplus( X,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( X, c_Groups_Ominus__class_Ominus( X, Z, W
% 0.77/1.34 ), U ), Y ), c_Groups_Oplus__class_Oplus( X,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( X, W, U ), T ) =
% 0.77/1.34 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, Z, U )
% 0.77/1.34 , Y ) }.
% 0.77/1.34 { ! class_Rings_Oring( X ), c_Groups_Ominus__class_Ominus( X,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( X, U, T ), c_Groups_Otimes__class_Otimes(
% 0.77/1.34 X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( X, U, c_Groups_Ominus__class_Ominus( X, T
% 0.77/1.34 , Y ) ), c_Groups_Otimes__class_Otimes( X, c_Groups_Ominus__class_Ominus
% 0.77/1.34 ( X, U, Z ), Y ) ) }.
% 0.77/1.34 { ! class_Int_Onumber( X ), ! class_Rings_Oring( X ),
% 0.77/1.34 c_Groups_Otimes__class_Otimes( X, c_Int_Onumber__class_Onumber__of( X, T
% 0.77/1.34 ), c_Groups_Ominus__class_Ominus( X, Z, Y ) ) =
% 0.77/1.34 c_Groups_Ominus__class_Ominus( X, c_Groups_Otimes__class_Otimes( X,
% 0.77/1.34 c_Int_Onumber__class_Onumber__of( X, T ), Z ),
% 0.77/1.34 c_Groups_Otimes__class_Otimes( X, c_Int_Onumber__class_Onumber__of( X, T
% 0.77/1.34 ), Y ) ) }.
% 0.77/1.34 { ! class_Int_Onumber( X ), ! class_Rings_Oring( X ),
% 0.77/1.34 c_Groups_Otimes__class_Otimes( X, c_Groups_Ominus__class_Ominus( X, T, Z
% 0.77/1.34 ), c_Int_Onumber__class_Onumber__of( X, Y ) ) =
% 0.77/1.34 c_Groups_Ominus__class_Ominus( X, c_Groups_Otimes__class_Otimes( X, T,
% 0.77/1.34 c_Int_Onumber__class_Onumber__of( X, Y ) ), c_Groups_Otimes__class_Otimes
% 0.77/1.34 ( X, Z, c_Int_Onumber__class_Onumber__of( X, Y ) ) ) }.
% 0.77/1.34 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.77/1.34 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.77/1.34 tc_Nat_Onat, Z, Y ), c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ) )
% 0.77/1.34 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.77/1.34 { Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.77/1.34 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.77/1.34 tc_Nat_Onat, Z, Y ), c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ) )
% 0.77/1.34 = c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) }.
% 0.77/1.34 { ! c_Nat_OSuc( c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) = X,
% 0.77/1.34 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.77/1.34 { c_Nat_OSuc( c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) = X,
% 0.77/1.34 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.77/1.34 c_Nat_OSuc( c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) }.
% 0.77/1.34 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) =
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.77/1.34 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.77/1.34 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ), X ) }.
% 0.77/1.34 { ! c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, skol18( X, Y ) ) }.
% 0.77/1.34 { ! Y = c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Z ),
% 0.77/1.34 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.77/1.34 { ! class_Fields_Ofield( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 0.77/1.34 , c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) ),
% 0.77/1.34 c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), Z, Y ) = Z }.
% 0.77/1.34 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.77/1.34 tc_Nat_Onat, c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ), X ), Y )
% 0.77/1.34 = c_Divides_Odiv__class_Omod( tc_Nat_Onat, X, Y ) }.
% 0.77/1.34 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, c_Int_OBit1( Y ), c_Int_OBit0
% 0.77/1.34 ( X ) ) = c_Int_OBit1( c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X )
% 0.77/1.34 ) }.
% 0.77/1.34 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, c_Int_OBit1( Y ), c_Int_OBit1
% 0.77/1.34 ( X ) ) = c_Int_OBit0( c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X )
% 0.77/1.34 ) }.
% 0.77/1.34 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, c_Int_OPls, c_Int_OBit0( X )
% 0.77/1.34 ) = c_Int_OBit0( c_Groups_Ominus__class_Ominus( tc_Int_Oint, c_Int_OPls
% 0.77/1.34 , X ) ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.77/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ominus__class_Ominus
% 0.77/1.34 ( tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.77/1.34 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ),
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.77/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.77/1.34 { c_Groups_Otimes__class_Otimes( tc_Int_Oint, Z,
% 0.77/1.34 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ) =
% 0.77/1.34 c_Groups_Ominus__class_Ominus( tc_Int_Oint, c_Groups_Otimes__class_Otimes
% 0.77/1.34 ( tc_Int_Oint, Z, Y ), c_Groups_Otimes__class_Otimes( tc_Int_Oint, Z, X )
% 0.77/1.34 ) }.
% 0.77/1.34 { c_Groups_Otimes__class_Otimes( tc_Int_Oint, c_Groups_Ominus__class_Ominus
% 0.77/1.34 ( tc_Int_Oint, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Int_Oint,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Int_Oint, Z, X ),
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Int_Oint, Y, X ) ) }.
% 0.77/1.34 { c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.77/1.34 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.77/1.34 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ) =
% 0.77/1.34 c_Groups_Ominus__class_Ominus( X, c_Int_Onumber__class_Onumber__of( X, Z
% 0.77/1.34 ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.77/1.34 { ! c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint,
% 0.77/1.34 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.77/1.34 { c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, X ),
% 0.77/1.34 c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, Y ),
% 0.77/1.34 c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint,
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) ) }.
% 0.77/1.34 { c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, X ), !
% 0.77/1.34 c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, Y ), !
% 0.77/1.34 c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint,
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) ) }.
% 0.77/1.34 { ! c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, X ),
% 0.77/1.34 c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, Y ), !
% 0.77/1.34 c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint,
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) ) }.
% 0.77/1.34 { ! c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, X ), !
% 0.77/1.34 c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, Y ),
% 0.77/1.34 c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint,
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) ) }.
% 0.77/1.34 { ! c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint,
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ), alpha14( X, Y ),
% 0.77/1.34 alpha32( X, Y ) }.
% 0.77/1.34 { ! alpha14( X, Y ), c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint,
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 0.77/1.34 { ! alpha32( X, Y ), c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint,
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 0.77/1.34 { ! alpha32( X, Y ), ! c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, Y ) }
% 0.77/1.34 .
% 0.77/1.34 { ! alpha32( X, Y ), ! c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, X ) }
% 0.77/1.34 .
% 0.77/1.34 { c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, Y ),
% 0.77/1.34 c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, X ), alpha32( X, Y ) }.
% 0.77/1.34 { ! alpha14( X, Y ), c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, Y ) }.
% 0.77/1.34 { ! alpha14( X, Y ), c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, X ) }.
% 0.77/1.34 { ! c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, Y ), !
% 0.77/1.34 c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, X ), alpha14( X, Y ) }.
% 0.77/1.34 { c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, X ),
% 0.77/1.34 c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, Y ), !
% 0.77/1.34 c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Int_Oint, X, Y ) ) }.
% 0.77/1.34 { ! c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, X ),
% 0.77/1.34 c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Int_Oint, Y, X ) ) }.
% 0.77/1.34 { ! c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, X ),
% 0.77/1.34 c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Int_Oint, X, Y ) ) }.
% 0.77/1.34 { ! c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Int_Oint, Y, X ) ),
% 0.77/1.34 c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, Y ),
% 0.77/1.34 c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, X ) }.
% 0.77/1.34 { ! c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, Y ),
% 0.77/1.34 c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Int_Oint, Y, X ) ) }.
% 0.77/1.34 { ! c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, X ),
% 0.77/1.34 c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Int_Oint, Y, X ) ) }.
% 0.77/1.34 { c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, X ), !
% 0.77/1.34 c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint,
% 0.77/1.34 c_Power_Opower__class_Opower( tc_Int_Oint, X, Y ) ) }.
% 0.77/1.34 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 0.77/1.34 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.77/1.34 c_Groups_Ominus__class_Ominus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 0.77/1.34 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.77/1.34 { ! c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint,
% 0.77/1.34 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ), alpha15( X, Y ),
% 0.77/1.34 alpha33( X, Y ) }.
% 0.77/1.34 { ! alpha15( X, Y ), c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint,
% 0.77/1.34 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ) }.
% 0.77/1.34 { ! alpha33( X, Y ), c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint,
% 0.77/1.34 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ) }.
% 0.77/1.34 { ! alpha33( X, Y ), ! c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, Y ) }
% 0.77/1.34 .
% 0.77/1.34 { ! alpha33( X, Y ), ! c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, X ) }
% 0.77/1.34 .
% 0.77/1.34 { c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, Y ),
% 0.77/1.34 c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, X ), alpha33( X, Y ) }.
% 0.77/1.34 { ! alpha15( X, Y ), c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, Y ) }.
% 0.77/1.34 { ! alpha15( X, Y ), c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, X ) }.
% 0.77/1.34 { ! c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, Y ), !
% 0.77/1.34 c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, X ), alpha15( X, Y ) }.
% 0.77/1.34 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, c_Int_OBit0( Y ), c_Int_OBit0
% 0.77/1.34 ( X ) ) = c_Int_OBit0( c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X )
% 0.77/1.34 ) }.
% 0.77/1.34 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Int_OPls ) = X }.
% 0.77/1.34 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.77/1.34 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! U = T, Z = Y }.
% 0.77/1.34 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.77/1.34 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! Z = Y, U = T }.
% 0.77/1.34 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.77/1.34 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.77/1.34 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, U, T ),
% 0.77/1.34 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.77/1.34 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.77/1.34 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.77/1.34 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.77/1.34 c_Orderings_Oord__class_Oless( X, U, T ) }.
% 0.77/1.34 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.77/1.34 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.77/1.34 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.77/1.34 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.77/1.34 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.77/1.34 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( X, U, T ) }.
% 0.77/1.34 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.77/1.34 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y, Y )
% 0.77/1.34 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.77/1.34 { ! class_Groups_Oab__group__add( X ), ! Z = Y,
% 0.77/1.34 c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.77/1.34 ) }.
% 0.77/1.34 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.77/1.34 Z, Y ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.77/1.34 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.77/1.34 ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.77/1.34 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ominus__class_Ominus(
% 0.77/1.34 X, Z, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.77/1.34 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.77/1.34 c_Groups_Ominus__class_Ominus( X, Z, Y ), Y ) = Z }.
% 0.77/1.34 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.77/1.34 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = Z }.
% 0.77/1.34 { ! c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint,
% 0.77/1.34 c_Power_Opower__class_Opower( tc_Int_Oint, Y, X ) ),
% 0.77/1.34 c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, Y ) }.
% 0.77/1.34 { ! c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint,
% 0.77/1.34 c_Power_Opower__class_Opower( tc_Int_Oint, Y, X ) ), ! X =
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.77/1.34 { ! c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, Y ), X =
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.77/1.34 c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint,
% 0.77/1.34 c_Power_Opower__class_Opower( tc_Int_Oint, Y, X ) ) }.
% 0.77/1.34 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.77/1.34 , c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, W, U
% 0.77/1.34 ), T ), c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X
% 0.77/1.34 , Z, U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X, T,
% 0.77/1.34 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.77/1.34 c_Groups_Ominus__class_Ominus( X, Z, W ), U ), Y ) ) }.
% 0.77/1.34 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.77/1.34 , T, c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.77/1.34 c_Groups_Ominus__class_Ominus( X, Z, W ), U ), Y ) ),
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( X, W, U ), T ),
% 0.77/1.34 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, Z, U )
% 0.77/1.34 , Y ) ) }.
% 0.77/1.34 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.77/1.34 , c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, W, U
% 0.77/1.34 ), T ), c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X
% 0.77/1.34 , Z, U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.77/1.34 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.77/1.34 c_Groups_Ominus__class_Ominus( X, W, Z ), U ), T ), Y ) }.
% 0.77/1.34 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.77/1.34 , c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.77/1.34 c_Groups_Ominus__class_Ominus( X, W, Z ), U ), T ), Y ),
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( X, W, U ), T ),
% 0.77/1.34 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, Z, U )
% 0.77/1.34 , Y ) ) }.
% 0.77/1.34 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.77/1.34 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, W, U )
% 0.77/1.34 , T ), c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.77/1.34 Z, U ), Y ) ), c_Orderings_Oord__class_Oless( X, T,
% 0.77/1.34 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.77/1.34 c_Groups_Ominus__class_Ominus( X, Z, W ), U ), Y ) ) }.
% 0.77/1.34 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X, T
% 0.77/1.34 , c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.77/1.34 c_Groups_Ominus__class_Ominus( X, Z, W ), U ), Y ) ),
% 0.77/1.34 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( X, W, U ), T ),
% 0.77/1.34 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, Z, U )
% 0.77/1.34 , Y ) ) }.
% 0.77/1.34 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.77/1.34 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, W, U )
% 0.77/1.34 , T ), c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.77/1.34 Z, U ), Y ) ), c_Orderings_Oord__class_Oless( X,
% 0.77/1.34 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.77/1.34 c_Groups_Ominus__class_Ominus( X, W, Z ), U ), T ), Y ) }.
% 0.77/1.34 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.77/1.34 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.77/1.34 c_Groups_Ominus__class_Ominus( X, W, Z ), U ), T ), Y ),
% 0.77/1.34 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( X, W, U ), T ),
% 0.77/1.34 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, Z, U )
% 0.77/1.34 , Y ) ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.77/1.34 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X
% 0.77/1.34 , Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.77/1.34 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, Y ),
% 0.77/1.34 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, X ) ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.77/1.34 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Z ),
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Y ) ) =
% 0.77/1.34 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, Y ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.77/1.34 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ), X ) = Y }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.77/1.34 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Y ), X ) = Y }.
% 0.77/1.34 { ! class_Rings_Oring__1( X ), c_Groups_Ominus__class_Ominus( X,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( X, Y, Y ), c_Groups_Oone__class_Oone( X )
% 0.77/1.34 ) = c_Groups_Otimes__class_Otimes( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.77/1.34 , c_Groups_Oone__class_Oone( X ) ), c_Groups_Ominus__class_Ominus( X, Y,
% 0.77/1.34 c_Groups_Oone__class_Oone( X ) ) ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.77/1.34 tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 0.77/1.34 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 0.77/1.34 tc_Nat_Onat, Y, X ), Y ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.77/1.34 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.77/1.34 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ), X ) }.
% 0.77/1.34 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X,
% 0.77/1.34 c_Int_Onumber__class_Onumber__of( X, T ), c_Groups_Ominus__class_Ominus(
% 0.77/1.34 X, c_Int_Onumber__class_Onumber__of( X, Z ), Y ) ) =
% 0.77/1.34 c_Groups_Ominus__class_Ominus( X, c_Int_Onumber__class_Onumber__of( X,
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_Int_Oint, T, Z ) ), Y ) }.
% 0.77/1.34 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc(
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.77/1.34 tc_Nat_Onat, Z, Y ), X ) ), Y ) = c_Divides_Odiv__class_Omod( tc_Nat_Onat
% 0.77/1.34 , c_Nat_OSuc( X ), Y ) }.
% 0.77/1.34 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.77/1.34 tc_Polynomial_Opoly( X ) ), c_Divides_Odiv__class_Omod(
% 0.77/1.34 tc_Polynomial_Opoly( X ), Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.77/1.34 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.77/1.34 c_Polynomial_Odegree( X, c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly
% 0.77/1.34 ( X ), Z, Y ) ), c_Polynomial_Odegree( X, Y ) ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.77/1.34 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 0.77/1.34 ( tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.77/1.34 .
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.77/1.34 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 0.77/1.34 ( tc_Int_Oint ) ) ) }.
% 0.77/1.34 { c_Groups_Otimes__class_Otimes( tc_Int_Oint, Y, c_Divides_Odiv__class_Odiv
% 0.77/1.34 ( tc_Int_Oint, X, Y ) ) = c_Groups_Ominus__class_Ominus( tc_Int_Oint, X,
% 0.77/1.34 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ) ) }.
% 0.77/1.34 { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.77/1.34 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.77/1.34 tc_Int_Oint, Y, X ), X ) ) }.
% 0.77/1.34 { ! class_Fields_Ofield( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 0.77/1.34 , c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) ),
% 0.77/1.34 c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly( X ), Z, Y ) =
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.77/1.34 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 0.77/1.34 alpha16( X, Z ) }.
% 0.77/1.34 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 0.77/1.34 alpha34( X, Y, Z ) }.
% 0.77/1.34 { ! alpha16( X, Z ), ! alpha34( X, Y, Z ), hBOOL( hAPP( Z,
% 0.77/1.34 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ) }.
% 0.77/1.34 { ! alpha34( X, Y, Z ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.77/1.34 alpha42( X, Y, Z ) }.
% 0.77/1.34 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha34( X, Y, Z ) }.
% 0.77/1.34 { ! alpha42( X, Y, Z ), alpha34( X, Y, Z ) }.
% 0.77/1.34 { ! alpha42( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, X
% 0.77/1.34 ), alpha49( X, Y, Z, T ) }.
% 0.77/1.34 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol19( X, T, U ), X ),
% 0.77/1.34 alpha42( X, Y, Z ) }.
% 0.77/1.34 { ! alpha49( X, Y, Z, skol19( X, Y, Z ) ), alpha42( X, Y, Z ) }.
% 0.77/1.34 { ! alpha49( X, Y, Z, T ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, U ), T ), hBOOL( hAPP( Z,
% 0.77/1.34 U ) ) }.
% 0.77/1.34 { ! hBOOL( hAPP( Z, skol20( U, W, Z, V0 ) ) ), alpha49( X, Y, Z, T ) }.
% 0.77/1.34 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, skol20( X, Y, Z, T ) ), T
% 0.77/1.34 ), alpha49( X, Y, Z, T ) }.
% 0.77/1.34 { ! alpha16( X, Y ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.77/1.34 hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.77/1.34 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha16( X, Y ) }.
% 0.77/1.34 { ! hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha16
% 0.77/1.34 ( X, Y ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.77/1.34 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 0.77/1.34 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.77/1.34 tc_Nat_Onat, Y, c_Divides_Odiv__class_Omod( tc_Nat_Onat, T, X ) ), Z ),
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) ) }.
% 0.77/1.34 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) ),
% 0.77/1.34 alpha17( X, Y, Z ) }.
% 0.77/1.34 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) ),
% 0.77/1.34 alpha35( X, Y, Z ) }.
% 0.77/1.34 { ! alpha17( X, Y, Z ), ! alpha35( X, Y, Z ), hBOOL( hAPP( Z,
% 0.77/1.34 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) ) }.
% 0.77/1.34 { ! alpha35( X, Y, Z ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.77/1.34 alpha43( X, Y, Z ) }.
% 0.77/1.34 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha35( X, Y, Z ) }.
% 0.77/1.34 { ! alpha43( X, Y, Z ), alpha35( X, Y, Z ) }.
% 0.77/1.34 { ! alpha43( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, X
% 0.77/1.34 ), alpha50( X, Y, Z, T ) }.
% 0.77/1.34 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol21( X, T, U ), X ),
% 0.77/1.34 alpha43( X, Y, Z ) }.
% 0.77/1.34 { ! alpha50( X, Y, Z, skol21( X, Y, Z ) ), alpha43( X, Y, Z ) }.
% 0.77/1.34 { ! alpha50( X, Y, Z, T ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, U ), T ), hBOOL( hAPP( Z,
% 0.77/1.34 T ) ) }.
% 0.77/1.34 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, skol22( X, Y, T ) ), T ),
% 0.77/1.34 alpha50( X, Y, Z, T ) }.
% 0.77/1.34 { ! hBOOL( hAPP( Z, T ) ), alpha50( X, Y, Z, T ) }.
% 0.77/1.34 { ! alpha17( X, Y, Z ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.77/1.34 hBOOL( hAPP( Z, Y ) ) }.
% 0.77/1.34 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha17( X, Y, Z ) }.
% 0.77/1.34 { ! hBOOL( hAPP( Z, Y ) ), alpha17( X, Y, Z ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.77/1.34 tc_Nat_Onat ), X ), c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc(
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Y ) ), X ) =
% 0.77/1.34 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.77/1.34 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Nat_OSuc( c_Nat_OSuc( X ) ),
% 0.77/1.34 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.77/1.34 c_Int_OPls ) ) ) ) = c_Nat_OSuc( c_Divides_Odiv__class_Odiv( tc_Nat_Onat
% 0.77/1.34 , X, c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0(
% 0.77/1.34 c_Int_OBit1( c_Int_OPls ) ) ) ) ) }.
% 0.77/1.34 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Nat_OSuc( c_Nat_OSuc(
% 0.77/1.34 c_Nat_OSuc( Y ) ) ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) )
% 0.77/1.34 = c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.77/1.34 tc_Nat_Onat, c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit1(
% 0.77/1.34 c_Int_OBit1( c_Int_OPls ) ) ), Y ), c_Int_Onumber__class_Onumber__of(
% 0.77/1.34 tc_Nat_Onat, X ) ) }.
% 0.77/1.34 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Nat_OSuc( c_Nat_OSuc(
% 0.77/1.34 c_Nat_OSuc( Y ) ) ), X ) = c_Divides_Odiv__class_Odiv( tc_Nat_Onat,
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.77/1.34 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit1( c_Int_OBit1(
% 0.77/1.34 c_Int_OPls ) ) ), Y ), X ) }.
% 0.77/1.34 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, c_Nat_OSuc( c_Nat_OSuc(
% 0.77/1.34 c_Nat_OSuc( X ) ) ) ) = c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y,
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.77/1.34 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit1( c_Int_OBit1(
% 0.77/1.34 c_Int_OPls ) ) ), X ) ) }.
% 0.77/1.34 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.77/1.34 tc_Nat_Onat, X, X ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 0.77/1.34 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) = X }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.77/1.34 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Z ), Y ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, c_Nat_OSuc( Z ) ) ), Z =
% 0.77/1.34 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.77/1.34 ( tc_Nat_Onat ), X ), ! Z = c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X
% 0.77/1.34 ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Z ), Y ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.77/1.34 ( tc_Nat_Onat ), X ), ! Z = c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X
% 0.77/1.34 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, c_Nat_OSuc( Z ) ) ) }.
% 0.77/1.34 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 0.77/1.34 alpha18( X, Z ), alpha36( X, Y, Z ) }.
% 0.77/1.34 { ! alpha18( X, Z ), hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv(
% 0.77/1.34 tc_Nat_Onat, Y, X ) ) ) }.
% 0.77/1.34 { ! alpha36( X, Y, Z ), hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv(
% 0.77/1.34 tc_Nat_Onat, Y, X ) ) ) }.
% 0.77/1.34 { ! alpha36( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, skol23( X, Y, T ) ), Y ) }
% 0.77/1.34 .
% 0.77/1.34 { ! alpha36( X, Y, Z ), alpha44( X, Y, Z, skol23( X, Y, Z ) ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, T ), Y ), ! alpha44( X, Y
% 0.77/1.34 , Z, T ), alpha36( X, Y, Z ) }.
% 0.77/1.34 { ! alpha44( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, c_Nat_OSuc( T ) ) ) }.
% 0.77/1.34 { ! alpha44( X, Y, Z, T ), hBOOL( hAPP( Z, T ) ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, c_Nat_OSuc( T ) ) ), !
% 0.77/1.34 hBOOL( hAPP( Z, T ) ), alpha44( X, Y, Z, T ) }.
% 0.77/1.34 { ! alpha18( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.77/1.34 { ! alpha18( X, Y ), hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero(
% 0.77/1.34 tc_Nat_Onat ) ) ) }.
% 0.77/1.34 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hBOOL( hAPP( Y,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha18( X, Y ) }.
% 0.77/1.34 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X,
% 0.77/1.34 c_Power_Opower__class_Opower( X, Z, c_Nat_OSuc( c_Nat_OSuc(
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ),
% 0.77/1.34 c_Power_Opower__class_Opower( X, Y, c_Nat_OSuc( c_Nat_OSuc(
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) ) =
% 0.77/1.34 c_Groups_Otimes__class_Otimes( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.77/1.34 ), c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.77/1.34 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc( c_Nat_OSuc( X ) ),
% 0.77/1.34 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.77/1.34 c_Int_OPls ) ) ) ) = c_Divides_Odiv__class_Omod( tc_Nat_Onat, X,
% 0.77/1.34 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.77/1.34 c_Int_OPls ) ) ) ) }.
% 0.77/1.34 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc( c_Nat_OSuc(
% 0.77/1.34 c_Nat_OSuc( Y ) ) ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) )
% 0.77/1.34 = c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.77/1.34 tc_Nat_Onat, c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit1(
% 0.77/1.34 c_Int_OBit1( c_Int_OPls ) ) ), Y ), c_Int_Onumber__class_Onumber__of(
% 0.77/1.34 tc_Nat_Onat, X ) ) }.
% 0.77/1.34 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc( c_Nat_OSuc(
% 0.77/1.34 c_Nat_OSuc( Y ) ) ), X ) = c_Divides_Odiv__class_Omod( tc_Nat_Onat,
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.77/1.34 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit1( c_Int_OBit1(
% 0.77/1.34 c_Int_OPls ) ) ), Y ), X ) }.
% 0.77/1.34 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, c_Nat_OSuc( c_Nat_OSuc(
% 0.77/1.34 c_Nat_OSuc( X ) ) ) ) = c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y,
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.77/1.34 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit1( c_Int_OBit1(
% 0.77/1.34 c_Int_OPls ) ) ), X ) ) }.
% 0.77/1.34 { ! c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, X ), X =
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Int_Oint,
% 0.77/1.34 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0( c_Int_OBit1(
% 0.77/1.34 c_Int_OPls ) ) ), skol24( X ) ) }.
% 0.77/1.34 { ! X = c_Groups_Otimes__class_Otimes( tc_Int_Oint,
% 0.77/1.34 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0( c_Int_OBit1(
% 0.77/1.34 c_Int_OPls ) ) ), Y ), c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, X )
% 0.77/1.34 }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.77/1.34 tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Divides_Odiv__class_Odiv(
% 0.77/1.34 tc_Nat_Onat, X, c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 0.77/1.34 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.77/1.34 ( tc_Nat_Onat ), c_Divides_Odiv__class_Omod( tc_Nat_Onat, X,
% 0.77/1.34 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.77/1.34 c_Int_OPls ) ) ) ) ), c_Divides_Odiv__class_Omod( tc_Nat_Onat, X,
% 0.77/1.34 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.77/1.34 c_Int_OPls ) ) ) ) = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.77/1.34 { ! c_Divides_Odiv__class_Omod( tc_Nat_Onat, X,
% 0.77/1.34 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.77/1.34 c_Int_OPls ) ) ) ) = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 0.77/1.34 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.77/1.34 tc_Nat_Onat ), c_Divides_Odiv__class_Omod( tc_Nat_Onat, X,
% 0.77/1.34 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.77/1.34 c_Int_OPls ) ) ) ) ) }.
% 0.77/1.34 { ! c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, X ),
% 0.77/1.34 c_Divides_Odiv__class_Omod( tc_Int_Oint, X,
% 0.77/1.34 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0( c_Int_OBit1(
% 0.77/1.34 c_Int_OPls ) ) ) ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.77/1.34 { ! c_Divides_Odiv__class_Omod( tc_Int_Oint, X,
% 0.77/1.34 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0( c_Int_OBit1(
% 0.77/1.34 c_Int_OPls ) ) ) ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.77/1.34 c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, X ) }.
% 0.77/1.34 { ! c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, X ),
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Int_Oint,
% 0.77/1.34 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0( c_Int_OBit1(
% 0.77/1.34 c_Int_OPls ) ) ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, X,
% 0.77/1.34 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0( c_Int_OBit1(
% 0.77/1.34 c_Int_OPls ) ) ) ) ) = X }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.77/1.34 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Divides_Odiv__class_Odiv(
% 0.77/1.34 tc_Nat_Onat, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.77/1.34 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ),
% 0.77/1.34 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.77/1.34 c_Int_OPls ) ) ) ) ) }.
% 0.77/1.34 { ! class_Int_Onumber__ring( X ), c_Power_Opower__class_Opower( X,
% 0.77/1.34 c_Groups_Ominus__class_Ominus( X, Z, Y ),
% 0.77/1.34 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.77/1.34 c_Int_OPls ) ) ) ) = c_Groups_Ominus__class_Ominus( X,
% 0.77/1.34 c_Groups_Oplus__class_Oplus( X, c_Power_Opower__class_Opower( X, Z,
% 0.77/1.34 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.77/1.34 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( X, Y,
% 0.77/1.34 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.77/1.34 c_Int_OPls ) ) ) ) ), c_Groups_Otimes__class_Otimes( X,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( X, c_Int_Onumber__class_Onumber__of( X,
% 0.77/1.34 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ), Z ), Y ) ) }.
% 0.77/1.34 { c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, X ), X =
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Otimes__class_Otimes(
% 0.77/1.34 tc_Int_Oint, c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0(
% 0.77/1.34 c_Int_OBit1( c_Int_OPls ) ) ), skol25( X ) ), c_Groups_Oone__class_Oone(
% 0.77/1.34 tc_Int_Oint ) ) }.
% 0.77/1.34 { ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Int_Oint,
% 0.77/1.34 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0( c_Int_OBit1(
% 0.77/1.34 c_Int_OPls ) ) ), Y ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ), !
% 0.77/1.34 c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, X ) }.
% 0.77/1.34 { c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, X ),
% 0.77/1.34 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.77/1.34 tc_Int_Oint, X, c_Groups_Oone__class_Oone( tc_Int_Oint ) ),
% 0.77/1.34 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0( c_Int_OBit1(
% 0.77/1.34 c_Int_OPls ) ) ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.77/1.34 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X,
% 0.77/1.34 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0( c_Int_OBit1(
% 0.77/1.34 c_Int_OPls ) ) ) ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.77/1.34 { ! c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, X ),
% 0.77/1.34 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.77/1.34 tc_Int_Oint, X, c_Groups_Oone__class_Oone( tc_Int_Oint ) ),
% 0.77/1.34 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0( c_Int_OBit1(
% 0.77/1.34 c_Int_OPls ) ) ) ) = c_Divides_Odiv__class_Odiv( tc_Int_Oint, X,
% 0.77/1.34 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0( c_Int_OBit1(
% 0.77/1.34 c_Int_OPls ) ) ) ) }.
% 0.77/1.34 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.77/1.34 c_Groups_Ominus__class_Ominus( X, c_Groups_Otimes__class_Otimes( X, U, T
% 0.77/1.34 ), c_Groups_Otimes__class_Otimes( X, Z, Y ) ) =
% 0.77/1.34 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( X, c_Groups_Ominus__class_Ominus( X, U, Z
% 0.77/1.34 ), c_Groups_Ominus__class_Ominus( X, T, Y ) ),
% 0.77/1.34 c_Groups_Otimes__class_Otimes( X, c_Groups_Ominus__class_Ominus( X, U, Z
% 0.77/1.34 ), Y ) ), c_Groups_Otimes__class_Otimes( X, Z,
% 0.77/1.34 c_Groups_Ominus__class_Ominus( X, T, Y ) ) ) }.
% 0.77/1.34 { ! X = c_Groups_Ozero__class_Ozero( tc_Code__Numeral_Ocode__numeral ),
% 0.77/1.34 c_Code__Numeral_Oint__of( X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint
% 0.77/1.34 ) }.
% 0.77/1.34 { X = c_Groups_Ozero__class_Ozero( tc_Code__Numeral_Ocode__numeral ), !
% 0.77/1.34 c_Divides_Odiv__class_Omod( tc_Code__Numeral_Ocode__numeral, X,
% 0.77/1.34 c_Int_Onumber__class_Onumber__of( tc_Code__Numeral_Ocode__numeral,
% 0.77/1.34 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) =
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Code__Numeral_Ocode__numeral ),
% 0.77/1.34 c_Code__Numeral_Oint__of( X ) = c_Groups_Otimes__class_Otimes(
% 0.77/1.34 tc_Int_Oint, c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0(
% 0.77/1.34 c_Int_OBit1( c_Int_OPls ) ) ), c_Code__Numeral_Oint__of(
% 0.77/1.34 c_Divides_Odiv__class_Odiv( tc_Code__Numeral_Ocode__numeral, X,
% 0.77/1.34 c_Int_Onumber__class_Onumber__of( tc_Code__Numeral_Ocode__numeral,
% 0.77/1.34 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) ) }.
% 0.77/1.34 { X = c_Groups_Ozero__class_Ozero( tc_Code__Numeral_Ocode__numeral ),
% 0.77/1.34 c_Divides_Odiv__class_Omod( tc_Code__Numeral_Ocode__numeral, X,
% 0.77/1.34 c_Int_Onumber__class_Onumber__of( tc_Code__Numeral_Ocode__numeral,
% 0.77/1.34 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) =
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Code__Numeral_Ocode__numeral ),
% 0.77/1.34 c_Code__Numeral_Oint__of( X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint
% 0.77/1.34 , c_Groups_Otimes__class_Otimes( tc_Int_Oint,
% 0.77/1.34 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0( c_Int_OBit1(
% 0.77/1.34 c_Int_OPls ) ) ), c_Code__Numeral_Oint__of( c_Divides_Odiv__class_Odiv(
% 0.77/1.34 tc_Code__Numeral_Ocode__numeral, X, c_Int_Onumber__class_Onumber__of(
% 0.77/1.34 tc_Code__Numeral_Ocode__numeral, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) )
% 0.77/1.34 ) ) ) ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.77/1.34 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) = Y }.
% 0.77/1.34 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.77/1.34 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 0.77/1.34 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.77/1.34 tc_Nat_Onat, Y, X ), X ) }.
% 0.77/1.34 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.77/1.34 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 0.77/1.34 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.77/1.34 tc_Nat_Onat, Y, X ), X ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.77/1.34 c_Divides_Odiv__class_Omod( tc_Nat_Onat, X, Y ) =
% 0.77/1.34 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.77/1.34 tc_Nat_Onat, X, Y ), Y ) }.
% 0.77/1.34 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 0.77/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 0.77/1.34 tc_Nat_Onat, Y, X ), X ) ) }.
% 0.77/1.34 { c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, c_Divides_Odiv__class_Odiv
% 0.77/1.34 ( tc_Nat_Onat, X, Y ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.77/1.34 c_Divides_Odiv__class_Omod( tc_Nat_Onat, X, Y ) ) }.
% 0.77/1.34 { c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 0.77/1.34 tc_Nat_Onat, Y, X ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y
% 0.77/1.34 , c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.77/1.34 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ),
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.77/1.34 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ),
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.77/1.34 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 0.77/1.34 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.77/1.34 ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.77/1.34 ( tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 0.77/1.34 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ),
% 0.77/1.34 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.77/1.34 tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 0.77/1.34 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.77/1.34 ( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) ) }.
% 0.77/1.34 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y,
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.77/1.34 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.77/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.77/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.77/1.34 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.77/1.34 tc_Nat_Onat, Y, X ), X ) = Y }.
% 0.77/1.34 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.77/1.34 tc_Nat_Onat, Y, X ), Y ) = X }.
% 0.77/1.34 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.77/1.34 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.77/1.34 Z, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.77/1.34 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.77/1.34 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) =
% 0.77/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 0.77/1.34 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.77/1.34 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) =
% 0.77/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ) }.
% 0.77/1.34 { c_Groups_Ominus__class_Ominus( tc_Code__Numeral_Ocode__numeral,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Code__Numeral_Ocode__numeral ),
% 0.77/1.34 c_Groups_Oone__class_Oone( tc_Code__Numeral_Ocode__numeral ) ) =
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Code__Numeral_Ocode__numeral ) }.
% 0.77/1.34 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.77/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.77/1.34 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, X ) =
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.77/1.34 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 0.77/1.34 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.77/1.34 tc_Nat_Onat ), X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.77/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 0.77/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ),
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.77/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 0.77/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ),
% 0.77/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.77/1.34 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.77/1.34 ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.77/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.77/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X = Z }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), ! X = Z,
% 0.77/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.77/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.77/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.77/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = Y }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.77/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, Z ),
% 0.77/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.77/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ),
% 0.77/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 0.77/1.34 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.77/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ), Y ) }.
% 0.77/1.34 { c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.77/1.34 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ),
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) ) }.
% 0.77/1.34 { c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z,
% 0.77/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) =
% 0.77/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes
% 0.77/1.34 ( tc_Nat_Onat, Z, Y ), c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X )
% 0.77/1.34 ) }.
% 0.77/1.34 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.77/1.34 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 0.77/1.34 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.77/1.34 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.77/1.34 X ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 0.77/1.34 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.77/1.34 ( tc_Nat_Onat, c_Nat_OSuc( Z ), Y ), c_Nat_OSuc( X ) ) =
% 0.77/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.77/1.34 ( tc_Nat_Onat, Z, Y ), X ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.77/1.34 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.77/1.34 ( tc_Nat_Onat, Z, X ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.77/1.34 ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.77/1.34 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.77/1.34 ( tc_Nat_Onat, Y, Z ), X ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.77/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) =
% 0.77/1.34 c_Nat_OSuc( c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.77/1.34 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.77/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) = Y }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z,
% 0.77/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 0.77/1.34 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.77/1.34 tc_Nat_Onat, Z, X ), Y ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.77/1.34 ( tc_Nat_Onat, Z, X ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z
% 0.77/1.34 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 0.77/1.34 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.77/1.34 ( tc_Nat_Onat, Y, Z ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z )
% 0.77/1.34 ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.77/1.34 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.77/1.34 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 0.77/1.34 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.77/1.34 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.77/1.34 ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.77/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z,
% 0.77/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 0.77/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.77/1.34 tc_Nat_Onat, Z, Y ), X ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.77/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ),
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ),
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.77/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.77/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.77/1.34 tc_Nat_Onat, X, Z ), Y ) ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.77/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = X }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.77/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 0.77/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.77/1.34 tc_Nat_Onat, Z, X ), Y ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.77/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ),
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.77/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.77/1.34 tc_Nat_Onat, X, Y ), Y ) = X }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.77/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z, X =
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X =
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.77/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.77/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.77/1.34 tc_Nat_Onat, Z, X ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.77/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.77/1.34 tc_Nat_Onat, X, Y ), Z ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ), Y ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.77/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.77/1.34 tc_Nat_Onat, X, Z ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.77/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), Z ) }.
% 0.77/1.34 { ! class_Groups_Oab__group__add( X ), ! c_Orderings_Oord__class_Oless(
% 0.77/1.34 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, T )
% 0.77/1.34 , Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree(
% 0.77/1.34 X, c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Z, T ) ), Y )
% 0.77/1.34 }.
% 0.77/1.34 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 0.77/1.34 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.77/1.34 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 0.77/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.77/1.34 ( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) }.
% 0.77/1.34 { ! class_Groups_Oab__group__add( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.77/1.34 ( tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 0.77/1.34 T ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.77/1.34 c_Polynomial_Odegree( X, c_Groups_Ominus__class_Ominus(
% 0.77/1.34 tc_Polynomial_Opoly( X ), Z, T ) ), Y ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.77/1.34 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.77/1.34 tc_Nat_Onat, X, c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) )
% 0.77/1.34 ) ) = X }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.77/1.34 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.77/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.77/1.34 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 0.77/1.34 ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) =
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.77/1.34 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 0.77/1.34 , c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.77/1.34 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.77/1.34 tc_Nat_Onat, Y, X ), X ) ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.77/1.34 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 0.77/1.34 , c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.77/1.34 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.77/1.34 tc_Nat_Onat, Y, X ), X ) ) }.
% 0.77/1.34 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.77/1.34 , ! alpha19( X, Y, Z ) }.
% 0.77/1.34 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.77/1.34 , ! alpha37( X, Y, Z ) }.
% 0.77/1.34 { alpha19( X, Y, Z ), alpha37( X, Y, Z ), hBOOL( hAPP( Z,
% 0.77/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.77/1.34 { ! alpha37( X, Y, Z ), ! hBOOL( hAPP( Z, skol26( T, U, Z ) ) ) }.
% 0.77/1.34 { ! alpha37( X, Y, Z ), Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.77/1.34 skol26( X, Y, Z ) ) }.
% 0.77/1.34 { ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, T ), hBOOL( hAPP( Z, T
% 0.77/1.34 ) ), alpha37( X, Y, Z ) }.
% 0.77/1.34 { ! alpha19( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 0.77/1.34 }.
% 0.77/1.34 { ! alpha19( X, Y, Z ), ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero(
% 0.77/1.34 tc_Nat_Onat ) ) ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), hBOOL( hAPP( Z,
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha19( X, Y, Z ) }.
% 0.77/1.34 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.77/1.34 , alpha20( X, Y, Z ) }.
% 0.77/1.34 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.77/1.34 , alpha38( X, Y, Z ) }.
% 0.77/1.34 { ! alpha20( X, Y, Z ), ! alpha38( X, Y, Z ), hBOOL( hAPP( Z,
% 0.77/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.77/1.34 { ! alpha38( X, Y, Z ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.77/1.34 T ), hBOOL( hAPP( Z, T ) ) }.
% 0.77/1.34 { ! hBOOL( hAPP( Z, skol27( T, U, Z ) ) ), alpha38( X, Y, Z ) }.
% 0.77/1.34 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, skol27( X, Y, Z ) ),
% 0.77/1.34 alpha38( X, Y, Z ) }.
% 0.77/1.34 { ! alpha20( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 0.77/1.34 ), hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.77/1.34 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), alpha20( X, Y, Z ) }
% 0.77/1.34 .
% 0.77/1.34 { ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha20
% 0.77/1.34 ( X, Y, Z ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.77/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, c_Nat_OSuc(
% 0.77/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) ) =
% 0.77/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.77/1.34 tc_Nat_Onat, Z, Y ), c_Nat_OSuc( X ) ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.77/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc(
% 0.77/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), Z ) =
% 0.77/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.77/1.34 tc_Nat_Onat, X, U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, U ), Z ) ),
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.77/1.34 tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), U ), T )
% 0.77/1.34 , Z ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.77/1.34 tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), U ), T )
% 0.77/1.34 , Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.77/1.34 tc_Nat_Onat, X, U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, U ), Z ) ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.77/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.77/1.34 tc_Nat_Onat, c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, U ), T ),
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.77/1.34 tc_Nat_Onat, Y, U ), Z ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.77/1.34 tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), U ), T )
% 0.77/1.34 , Z ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.77/1.34 tc_Nat_Onat, X, U ), T ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, U ), Z ),
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.77/1.34 tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), U ), T )
% 0.77/1.34 = Z }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.77/1.34 tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), U ), T )
% 0.77/1.34 = Z, c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, U ), T ) =
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.77/1.34 tc_Nat_Onat, Y, U ), Z ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.77/1.34 tc_Nat_Onat, Y, U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, U ), Z ) ),
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T,
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.77/1.34 tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), U ), Z )
% 0.77/1.34 ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T,
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.77/1.34 tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), U ), Z )
% 0.77/1.34 ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.77/1.34 tc_Nat_Onat, Y, U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, U ), Z ) ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.77/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.77/1.34 tc_Nat_Onat, c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, U ), T ),
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.77/1.34 tc_Nat_Onat, X, U ), Z ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.77/1.34 T, c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.77/1.34 ( tc_Nat_Onat, X, Y ), U ), Z ) ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.77/1.34 tc_Nat_Onat, Y, U ), T ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, U ), Z ), T =
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.77/1.34 tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), U ), Z )
% 0.77/1.34 }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! T =
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.77/1.34 tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), U ), Z )
% 0.77/1.34 , c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes
% 0.77/1.34 ( tc_Nat_Onat, Y, U ), T ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, U ), Z ) }.
% 0.77/1.34 { c_Groups_Ozero__class_Ozero( tc_Code__Numeral_Ocode__numeral ) =
% 0.77/1.34 c_Int_Onumber__class_Onumber__of( tc_Code__Numeral_Ocode__numeral,
% 0.77/1.34 c_Int_OPls ) }.
% 0.77/1.34 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Odegree( X,
% 0.77/1.34 c_Polynomial_Osynthetic__div( X, Z, Y ) ) = c_Groups_Ominus__class_Ominus
% 0.77/1.34 ( tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Groups_Oone__class_Oone(
% 0.77/1.34 tc_Nat_Onat ) ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.77/1.34 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X
% 0.77/1.34 , Y ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.77/1.34 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.77/1.34 tc_Nat_Onat, Y, X ), X ) ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.77/1.34 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.77/1.34 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.77/1.34 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.77/1.34 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) = X }.
% 0.77/1.34 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = X }.
% 0.77/1.34 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.77/1.34 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.77/1.34 tc_Nat_Onat, c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, U ), T ),
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.77/1.34 tc_Nat_Onat, X, U ), Z ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, T
% 0.77/1.34 , c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes
% 0.77/1.34 ( tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), U ), Z
% 0.77/1.34 ) ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T,
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.77/1.34 tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), U ), Z )
% 0.77/1.34 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.77/1.34 tc_Nat_Onat, Y, U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, U ), Z ) ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.77/1.34 tc_Nat_Onat, c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, U ), T ),
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.77/1.34 tc_Nat_Onat, Y, U ), Z ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.77/1.34 tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), U ), T )
% 0.77/1.34 , Z ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.77/1.34 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.77/1.34 tc_Nat_Onat, c_Groups_Otimes__class_Otimes( tc_Nat_Onat,
% 0.77/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), U ), T ), Z ),
% 0.77/1.34 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.77/1.34 tc_Nat_Onat, c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, U ), T ),
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.77/1.34 tc_Nat_Onat, Y, U ), Z ) ) }.
% 0.77/1.34 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) =
% 0.77/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.77/1.34 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) =
% 0.77/1.34 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.77/1.34 ( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) ) }.
% 0.77/1.34 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.77/1.34 c_Power_Opower__class_Opower( tc_Nat_Onat, X, Y ) =
% 0.77/1.34 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.77/1.34 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.77/1.34 c_Power_Opower__class_Opower( tc_Nat_Onat, X, Y ) =
% 0.77/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X,
% 0.77/1.34 c_Power_Opower__class_Opower( tc_Nat_Onat, X,
% 0.77/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 0.77/1.34 ( tc_Nat_Onat ) ) ) ) }.
% 0.77/1.34 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless(
% 0.77/1.34 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 0.77/1.34 c_Groups_Otimes__class_Otimes( X, c_Power_Opower__class_Opower( X, Z,
% 0.77/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 0.77/1.34 ( tc_Nat_Onat ) ) ), Z ) = c_Power_Opower__class_Opower( X, Z, Y ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.77/1.34 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OPls ), X ),
% 0.77/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.77/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y,
% 0.77/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.77/1.34 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit1( c_Int_OPls )
% 0.77/1.34 ) ) ) }.
% 0.77/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.77/1.34 ( tc_Nat_Onat ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ),
% 0.77/1.34 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) = c_Nat_OSuc(
% 0.77/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.77/1.34 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ),
% 0.77/1.34 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) }.
% 0.77/1.34 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.77/1.34 c_Groups_Otimes__class_Otimes( X, Y, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.77/1.34 c_Groups_Ozero__class_Ozero( X ) }.
% 0.77/1.34 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.77/1.34 c_Groups_Otimes__class_Otimes( X, Y, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.77/1.34 c_Groups_Ozero__class_Ozero( X ) }.
% 0.77/1.34 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.77/1.34 c_Groups_Otimes__class_Otimes( X, c_Groups_Ozero__class_Ozero( X ), Y ) =
% 0.77/1.34 c_Groups_Ozero__class_Ozero( X ) }.
% 0.77/1.34 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.77/1.34 c_Groups_Otimes__class_Otimes( X, c_Groups_Ozero__class_Ozero( X ), Y ) =
% 0.77/1.34 c_Groups_Ozero__class_Ozero( X ) }.
% 0.77/1.34 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.77/1.34 c_Groups_Otimes__class_Otimes( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.77/1.34 , Y ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X
% 0.77/1.34 , T, Y ), c_Groups_Otimes__class_Otimes( X, Z, Y ) ) }.
% 0.77/1.34 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.77/1.34 c_Groups_Otimes__class_Otimes( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.77/1.34 , Y ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X
% 0.77/1.34 , T, Y ), c_Groups_Otimes__class_Otimes( X, Z, Y ) ) }.
% 0.77/1.34 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.77/1.34 c_Groups_Otimes__class_Otimes( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.77/1.34 ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.77/1.34 T, Z ), c_Groups_Otimes__class_Otimes( X, T, Y ) ) }.
% 0.77/1.34 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.77/1.34 c_Groups_Otimes__class_Otimes( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.77/1.34 ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.77/1.34 T, Z ), c_Groups_Otimes__class_Otimes( X, T, Y ) ) }.
% 0.77/1.34 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.77/1.34 c_Groups_Otimes__class_Otimes( X, T, c_Groups_Ominus__class_Ominus( X, Z
% 0.77/1.34 , Y ) ) = c_Groups_Ominus__class_Ominus( X, c_Groups_Otimes__class_Otimes
% 0.77/1.34 ( X, T, Z ), c_Groups_Otimes__class_Otimes( X, T, Y ) ) }.
% 0.77/1.34 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.77/1.34 c_Groups_Otimes__class_Otimes( X, T, c_Groups_Ominus__class_Ominus( X, Z
% 0.77/1.34 , Y ) ) = c_Groups_Ominus__class_Ominus( X, c_Groups_Otimes__class_Otimes
% 0.77/1.34 ( X, T, Z ), c_Groups_Otimes__class_Otimes( X, T, Y ) ) }.
% 0.77/1.34 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.77/1.34 c_Groups_Otimes__class_Otimes( X, c_Groups_Ominus__class_Ominus( X, T, Z
% 0.77/1.34 ), Y ) = c_Groups_Ominus__class_Ominus( X, c_Groups_Otimes__class_Otimes
% 0.77/1.34 ( X, T, Y ), c_Groups_Otimes__class_Otimes( X, Z, Y ) ) }.
% 0.77/1.34 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Oab__semigroup__mult
% 0.77/1.34 ( X ) }.
% 0.77/1.34 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Oab__semigroup__add(
% 0.77/1.34 X ) }.
% 0.77/1.34 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Ocomm__monoid__add( X
% 0.77/1.34 ) }.
% 0.77/1.34 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring( X ) }
% 0.77/1.34 .
% 0.77/1.34 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Omonoid__add( X ) }.
% 0.77/1.34 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring__0( X ) }.
% 0.77/1.34 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Omult__zero( X ) }.
% 0.77/1.34 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring( X ) }.
% 0.77/1.34 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Ozero( X ) }.
% 0.77/1.34 { class_Groups_Ocancel__comm__monoid__add( tc_Code__Numeral_Ocode__numeral
% 0.77/1.34 ) }.
% 0.77/1.34 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.77/1.34 class_Groups_Ocancel__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 0.77/1.34 { class_Groups_Ocancel__comm__monoid__add( tc_Complex_Ocomplex ) }.
% 0.77/1.34 { class_Groups_Ocancel__comm__monoid__add( tc_RealDef_Oreal ) }.
% 0.77/1.34 { class_Groups_Ocancel__comm__monoid__add( tc_Nat_Onat ) }.
% 0.77/1.34 { class_Groups_Ocancel__comm__monoid__add( tc_Int_Oint ) }.
% 0.77/1.34 { ! class_Orderings_Opreorder( X ), class_Orderings_Opreorder( tc_fun( Y, X
% 0.77/1.34 ) ) }.
% 0.77/1.34 { ! class_Orderings_Oorder( X ), class_Orderings_Oorder( tc_fun( Y, X ) ) }
% 0.77/1.34 .
% 0.77/1.34 { ! class_Orderings_Oord( X ), class_Orderings_Oord( tc_fun( Y, X ) ) }.
% 0.77/1.34 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.77/1.34 tc_Int_Oint ) }.
% 0.77/1.34 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.77/1.34 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Int_Oint ) }.
% 0.77/1.34 { class_Rings_Olinordered__comm__semiring__strict( tc_Int_Oint ) }.
% 0.77/1.34 { class_Rings_Olinordered__semiring__1__strict( tc_Int_Oint ) }.
% 0.77/1.34 { class_Rings_Olinordered__semiring__strict( tc_Int_Oint ) }.
% 0.77/1.34 { class_Groups_Oordered__ab__semigroup__add( tc_Int_Oint ) }.
% 0.77/1.34 { class_Groups_Oordered__comm__monoid__add( tc_Int_Oint ) }.
% 0.77/1.34 { class_Groups_Olinordered__ab__group__add( tc_Int_Oint ) }.
% 0.77/1.34 { class_Groups_Ocancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.77/1.34 { class_Rings_Oring__1__no__zero__divisors( tc_Int_Oint ) }.
% 0.77/1.34 { class_Rings_Oordered__cancel__semiring( tc_Int_Oint ) }.
% 0.77/1.34 { class_Rings_Olinordered__ring__strict( tc_Int_Oint ) }.
% 0.77/1.34 { class_Rings_Oring__no__zero__divisors( tc_Int_Oint ) }.
% 0.77/1.34 { class_Rings_Oordered__comm__semiring( tc_Int_Oint ) }.
% 0.77/1.34 { class_Rings_Olinordered__semiring__1( tc_Int_Oint ) }.
% 0.77/1.34 { class_Groups_Oordered__ab__group__add( tc_Int_Oint ) }.
% 0.77/1.34 { class_Groups_Ocancel__semigroup__add( tc_Int_Oint ) }.
% 0.77/1.34 { class_Rings_Olinordered__semiring( tc_Int_Oint ) }.
% 0.77/1.34 { class_Rings_Olinordered__semidom( tc_Int_Oint ) }.
% 0.77/1.34 { class_Groups_Oab__semigroup__mult( tc_Int_Oint ) }.
% 0.77/1.34 { class_Groups_Ocomm__monoid__mult( tc_Int_Oint ) }.
% 0.77/1.34 { class_Groups_Oab__semigroup__add( tc_Int_Oint ) }.
% 0.77/1.34 { class_Rings_Oordered__semiring( tc_Int_Oint ) }.
% 0.77/1.34 { class_Rings_Ono__zero__divisors( tc_Int_Oint ) }.
% 0.77/1.34 { class_Groups_Ocomm__monoid__add( tc_Int_Oint ) }.
% 0.77/1.34 { class_Rings_Olinordered__ring( tc_Int_Oint ) }.
% 0.77/1.34 { class_Rings_Olinordered__idom( tc_Int_Oint ) }.
% 0.77/1.34 { class_Rings_Ocomm__semiring__1( tc_Int_Oint ) }.
% 0.77/1.34 { class_Rings_Ocomm__semiring__0( tc_Int_Oint ) }.
% 0.77/1.34 { class_Divides_Osemiring__div( tc_Int_Oint ) }.
% 0.77/1.34 { class_Rings_Ocomm__semiring( tc_Int_Oint ) }.
% 0.77/1.34 { class_Groups_Oab__group__add( tc_Int_Oint ) }.
% 0.77/1.34 { class_Rings_Ozero__neq__one( tc_Int_Oint ) }.
% 0.77/1.34 { class_Rings_Oordered__ring( tc_Int_Oint ) }.
% 0.77/1.34 { class_Orderings_Opreorder( tc_Int_Oint ) }.
% 0.77/1.34 { class_Orderings_Olinorder( tc_Int_Oint ) }.
% 0.77/1.34 { class_Groups_Omonoid__mult( tc_Int_Oint ) }.
% 0.77/1.34 { class_Rings_Ocomm__ring__1( tc_Int_Oint ) }.
% 0.77/1.34 { class_Groups_Omonoid__add( tc_Int_Oint ) }.
% 0.77/1.34 { class_Rings_Osemiring__1( tc_Int_Oint ) }.
% 0.77/1.34 { class_Rings_Osemiring__0( tc_Int_Oint ) }.
% 0.77/1.34 { class_Groups_Ogroup__add( tc_Int_Oint ) }.
% 0.77/1.34 { class_Divides_Oring__div( tc_Int_Oint ) }.
% 0.77/1.34 { class_Rings_Omult__zero( tc_Int_Oint ) }.
% 0.77/1.34 { class_Rings_Ocomm__ring( tc_Int_Oint ) }.
% 0.77/1.34 { class_Orderings_Oorder( tc_Int_Oint ) }.
% 0.77/1.34 { class_Int_Oring__char__0( tc_Int_Oint ) }.
% 0.77/1.34 { class_Int_Onumber__ring( tc_Int_Oint ) }.
% 0.77/1.34 { class_Rings_Osemiring( tc_Int_Oint ) }.
% 0.77/1.34 { class_Orderings_Oord( tc_Int_Oint ) }.
% 0.77/1.34 { class_Rings_Oring__1( tc_Int_Oint ) }.
% 0.77/1.34 { class_Power_Opower( tc_Int_Oint ) }.
% 0.77/1.34 { class_Groups_Ozero( tc_Int_Oint ) }.
% 0.77/1.34 { class_Rings_Oring( tc_Int_Oint ) }.
% 0.77/1.34 { class_Rings_Oidom( tc_Int_Oint ) }.
% 0.77/1.34 { class_Int_Onumber( tc_Int_Oint ) }.
% 0.77/1.34 { class_Groups_Oone( tc_Int_Oint ) }.
% 0.77/1.34 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.77/1.34 tc_Nat_Onat ) }.
% 0.77/1.34 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.77/1.34 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Nat_Onat ) }.
% 0.77/1.34 { class_Rings_Olinordered__comm__semiring__strict( tc_Nat_Onat ) }.
% 0.77/1.34 { class_Rings_Olinordered__semiring__strict( tc_Nat_Onat ) }.
% 0.77/1.34 { class_Groups_Oordered__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.77/1.34 { class_Groups_Oordered__comm__monoid__add( tc_Nat_Onat ) }.
% 0.77/1.34 { class_Groups_Ocancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.77/1.34 { class_Rings_Oordered__cancel__semiring( tc_Nat_Onat ) }.
% 0.77/1.34 { class_Rings_Oordered__comm__semiring( tc_Nat_Onat ) }.
% 0.77/1.34 { class_Groups_Ocancel__semigroup__add( tc_Nat_Onat ) }.
% 0.77/1.34 { class_Rings_Olinordered__semiring( tc_Nat_Onat ) }.
% 0.77/1.34 { class_Rings_Olinordered__semidom( tc_Nat_Onat ) }.
% 0.77/1.34 { class_Groups_Oab__semigroup__mult( tc_Nat_Onat ) }.
% 0.77/1.34 { class_Groups_Ocomm__monoid__mult( tc_Nat_Onat ) }.
% 0.77/1.34 { class_Groups_Oab__semigroup__add( tc_Nat_Onat ) }.
% 0.77/1.34 { class_Rings_Oordered__semiring( tc_Nat_Onat ) }.
% 0.77/1.34 { class_Rings_Ono__zero__divisors( tc_Nat_Onat ) }.
% 0.77/1.34 { class_Groups_Ocomm__monoid__add( tc_Nat_Onat ) }.
% 0.77/1.34 { class_Rings_Ocomm__semiring__1( tc_Nat_Onat ) }.
% 0.77/1.34 { class_Rings_Ocomm__semiring__0( tc_Nat_Onat ) }.
% 0.77/1.34 { class_Divides_Osemiring__div( tc_Nat_Onat ) }.
% 0.77/1.34 { class_Rings_Ocomm__semiring( tc_Nat_Onat ) }.
% 0.77/1.34 { class_Rings_Ozero__neq__one( tc_Nat_Onat ) }.
% 0.77/1.34 { class_Orderings_Opreorder( tc_Nat_Onat ) }.
% 0.77/1.34 { class_Orderings_Olinorder( tc_Nat_Onat ) }.
% 0.77/1.34 { class_Groups_Omonoid__mult( tc_Nat_Onat ) }.
% 0.77/1.34 { class_Groups_Omonoid__add( tc_Nat_Onat ) }.
% 0.77/1.34 { class_Rings_Osemiring__1( tc_Nat_Onat ) }.
% 0.77/1.34 { class_Rings_Osemiring__0( tc_Nat_Onat ) }.
% 0.77/1.34 { class_Rings_Omult__zero( tc_Nat_Onat ) }.
% 0.77/1.34 { class_Orderings_Oorder( tc_Nat_Onat ) }.
% 0.77/1.34 { class_Rings_Osemiring( tc_Nat_Onat ) }.
% 0.77/1.34 { class_Orderings_Oord( tc_Nat_Onat ) }.
% 0.77/1.34 { class_Power_Opower( tc_Nat_Onat ) }.
% 0.77/1.34 { class_Groups_Ozero( tc_Nat_Onat ) }.
% 0.77/1.34 { class_Int_Onumber( tc_Nat_Onat ) }.
% 0.77/1.34 { class_Groups_Oone( tc_Nat_Onat ) }.
% 0.77/1.34 { class_Orderings_Opreorder( tc_HOL_Obool ) }.
% 0.77/1.34 { class_Orderings_Oorder( tc_HOL_Obool ) }.
% 0.77/1.34 { class_Orderings_Oord( tc_HOL_Obool ) }.
% 0.77/1.34 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.77/1.34 tc_RealDef_Oreal ) }.
% 0.77/1.34 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.77/1.34 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_RealDef_Oreal ) }
% 0.77/1.34 .
% 0.77/1.34 { class_Rings_Olinordered__comm__semiring__strict( tc_RealDef_Oreal ) }.
% 0.77/1.34 { class_Rings_Olinordered__semiring__1__strict( tc_RealDef_Oreal ) }.
% 0.77/1.34 { class_Rings_Olinordered__semiring__strict( tc_RealDef_Oreal ) }.
% 0.77/1.34 { class_Groups_Oordered__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.77/1.34 { class_RealVector_Oreal__normed__algebra( tc_RealDef_Oreal ) }.
% 0.77/1.34 { class_Groups_Oordered__comm__monoid__add( tc_RealDef_Oreal ) }.
% 0.77/1.34 { class_Groups_Olinordered__ab__group__add( tc_RealDef_Oreal ) }.
% 0.77/1.34 { class_Groups_Ocancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.77/1.34 { class_Rings_Oring__1__no__zero__divisors( tc_RealDef_Oreal ) }.
% 0.77/1.34 { class_Rings_Oordered__cancel__semiring( tc_RealDef_Oreal ) }.
% 0.77/1.34 { class_Rings_Olinordered__ring__strict( tc_RealDef_Oreal ) }.
% 0.77/1.34 { class_Rings_Oring__no__zero__divisors( tc_RealDef_Oreal ) }.
% 0.77/1.34 { class_Rings_Oordered__comm__semiring( tc_RealDef_Oreal ) }.
% 0.77/1.34 { class_Rings_Olinordered__semiring__1( tc_RealDef_Oreal ) }.
% 0.77/1.34 { class_Groups_Oordered__ab__group__add( tc_RealDef_Oreal ) }.
% 0.77/1.34 { class_Groups_Ocancel__semigroup__add( tc_RealDef_Oreal ) }.
% 0.77/1.34 { class_Rings_Olinordered__semiring( tc_RealDef_Oreal ) }.
% 0.77/1.34 { class_Rings_Olinordered__semidom( tc_RealDef_Oreal ) }.
% 0.77/1.34 { class_Groups_Oab__semigroup__mult( tc_RealDef_Oreal ) }.
% 0.77/1.34 { class_Groups_Ocomm__monoid__mult( tc_RealDef_Oreal ) }.
% 0.77/1.34 { class_Groups_Oab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.77/1.34 { class_Rings_Oordered__semiring( tc_RealDef_Oreal ) }.
% 0.77/1.34 { class_Rings_Ono__zero__divisors( tc_RealDef_Oreal ) }.
% 0.77/1.34 { class_Groups_Ocomm__monoid__add( tc_RealDef_Oreal ) }.
% 0.77/1.34 { class_Rings_Olinordered__ring( tc_RealDef_Oreal ) }.
% 0.77/1.34 { class_Rings_Olinordered__idom( tc_RealDef_Oreal ) }.
% 0.77/1.34 { class_Rings_Ocomm__semiring__1( tc_RealDef_Oreal ) }.
% 0.77/1.34 { class_Rings_Ocomm__semiring__0( tc_RealDef_Oreal ) }.
% 0.77/1.34 { class_Rings_Ocomm__semiring( tc_RealDef_Oreal ) }.
% 0.77/1.34 { class_Groups_Oab__group__add( tc_RealDef_Oreal ) }.
% 0.77/1.34 { class_Rings_Ozero__neq__one( tc_RealDef_Oreal ) }.
% 0.77/1.34 { class_Rings_Oordered__ring( tc_RealDef_Oreal ) }.
% 0.77/1.34 { class_Orderings_Opreorder( tc_RealDef_Oreal ) }.
% 0.77/1.34 { class_Orderings_Olinorder( tc_RealDef_Oreal ) }.
% 0.77/1.34 { class_Groups_Omonoid__mult( tc_RealDef_Oreal ) }.
% 0.77/1.34 { class_Rings_Ocomm__ring__1( tc_RealDef_Oreal ) }.
% 0.77/1.34 { class_Groups_Omonoid__add( tc_RealDef_Oreal ) }.
% 0.77/1.34 { class_Rings_Osemiring__1( tc_RealDef_Oreal ) }.
% 0.77/1.34 { class_Rings_Osemiring__0( tc_RealDef_Oreal ) }.
% 0.77/1.34 { class_Groups_Ogroup__add( tc_RealDef_Oreal ) }.
% 0.77/1.34 { class_Rings_Omult__zero( tc_RealDef_Oreal ) }.
% 0.77/1.34 { class_Rings_Ocomm__ring( tc_RealDef_Oreal ) }.
% 0.77/1.34 { class_Orderings_Oorder( tc_RealDef_Oreal ) }.
% 0.77/1.34 { class_Int_Oring__char__0( tc_RealDef_Oreal ) }.
% 0.77/1.34 { class_Int_Onumber__ring( tc_RealDef_Oreal ) }.
% 0.77/1.34 { class_Rings_Osemiring( tc_RealDef_Oreal ) }.
% 0.77/1.34 { class_Orderings_Oord( tc_RealDef_Oreal ) }.
% 0.77/1.34 { class_Rings_Oring__1( tc_RealDef_Oreal ) }.
% 0.77/1.34 { class_Fields_Ofield( tc_RealDef_Oreal ) }.
% 0.77/1.34 { class_Power_Opower( tc_RealDef_Oreal ) }.
% 0.77/1.34 { class_Groups_Ozero( tc_RealDef_Oreal ) }.
% 0.77/1.34 { class_Rings_Oring( tc_RealDef_Oreal ) }.
% 0.77/1.34 { class_Rings_Oidom( tc_RealDef_Oreal ) }.
% 0.77/1.34 { class_Int_Onumber( tc_RealDef_Oreal ) }.
% 0.77/1.34 { class_Groups_Oone( tc_RealDef_Oreal ) }.
% 0.77/1.34 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.77/1.34 tc_Complex_Ocomplex ) }.
% 0.77/1.34 { class_RealVector_Oreal__normed__algebra( tc_Complex_Ocomplex ) }.
% 0.77/1.34 { class_Groups_Ocancel__ab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.77/1.34 { class_Rings_Oring__1__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.77/1.34 { class_Rings_Oring__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.77/1.34 { class_Groups_Ocancel__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.77/1.34 { class_Groups_Oab__semigroup__mult( tc_Complex_Ocomplex ) }.
% 0.77/1.34 { class_Groups_Ocomm__monoid__mult( tc_Complex_Ocomplex ) }.
% 0.77/1.34 { class_Groups_Oab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.77/1.34 { class_Rings_Ono__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.77/1.34 { class_Groups_Ocomm__monoid__add( tc_Complex_Ocomplex ) }.
% 0.77/1.34 { class_Rings_Ocomm__semiring__1( tc_Complex_Ocomplex ) }.
% 0.77/1.34 { class_Rings_Ocomm__semiring__0( tc_Complex_Ocomplex ) }.
% 0.77/1.34 { class_Rings_Ocomm__semiring( tc_Complex_Ocomplex ) }.
% 0.77/1.34 { class_Groups_Oab__group__add( tc_Complex_Ocomplex ) }.
% 0.77/1.34 { class_Rings_Ozero__neq__one( tc_Complex_Ocomplex ) }.
% 0.77/1.34 { class_Groups_Omonoid__mult( tc_Complex_Ocomplex ) }.
% 0.77/1.34 { class_Rings_Ocomm__ring__1( tc_Complex_Ocomplex ) }.
% 0.77/1.34 { class_Groups_Omonoid__add( tc_Complex_Ocomplex ) }.
% 0.77/1.34 { class_Rings_Osemiring__1( tc_Complex_Ocomplex ) }.
% 0.77/1.34 { class_Rings_Osemiring__0( tc_Complex_Ocomplex ) }.
% 0.77/1.34 { class_Groups_Ogroup__add( tc_Complex_Ocomplex ) }.
% 0.77/1.34 { class_Rings_Omult__zero( tc_Complex_Ocomplex ) }.
% 0.77/1.34 { class_Rings_Ocomm__ring( tc_Complex_Ocomplex ) }.
% 0.77/1.34 { class_Int_Oring__char__0( tc_Complex_Ocomplex ) }.
% 0.77/1.34 { class_Int_Onumber__ring( tc_Complex_Ocomplex ) }.
% 0.77/1.34 { class_Rings_Osemiring( tc_Complex_Ocomplex ) }.
% 0.77/1.34 { class_Rings_Oring__1( tc_Complex_Ocomplex ) }.
% 0.77/1.34 { class_Fields_Ofield( tc_Complex_Ocomplex ) }.
% 0.77/1.34 { class_Power_Opower( tc_Complex_Ocomplex ) }.
% 0.77/1.34 { class_Groups_Ozero( tc_Complex_Ocomplex ) }.
% 0.77/1.34 { class_Rings_Oring( tc_Complex_Ocomplex ) }.
% 0.77/1.34 { class_Rings_Oidom( tc_Complex_Ocomplex ) }.
% 0.77/1.34 { class_Int_Onumber( tc_Complex_Ocomplex ) }.
% 0.77/1.34 { class_Groups_Oone( tc_Complex_Ocomplex ) }.
% 0.77/1.34 { ! class_Rings_Oidom( X ),
% 0.77/1.34 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.77/1.34 tc_Polynomial_Opoly( X ) ) }.
% 0.77/1.34 { ! class_Rings_Olinordered__idom( X ),
% 0.77/1.34 class_Groups_Oordered__cancel__ab__semigroup__add( tc_Polynomial_Opoly( X
% 0.77/1.34 ) ) }.
% 0.77/1.34 { ! class_Rings_Olinordered__idom( X ),
% 0.77/1.34 class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Polynomial_Opoly(
% 0.77/1.34 X ) ) }.
% 0.77/1.34 { ! class_Rings_Olinordered__idom( X ),
% 0.77/1.34 class_Rings_Olinordered__comm__semiring__strict( tc_Polynomial_Opoly( X )
% 0.77/1.34 ) }.
% 0.77/1.34 { ! class_Rings_Olinordered__idom( X ),
% 0.77/1.34 class_Rings_Olinordered__semiring__1__strict( tc_Polynomial_Opoly( X ) )
% 0.77/1.34 }.
% 0.77/1.34 { ! class_Rings_Olinordered__idom( X ),
% 0.77/1.34 class_Rings_Olinordered__semiring__strict( tc_Polynomial_Opoly( X ) ) }.
% 0.77/1.34 { ! class_Rings_Olinordered__idom( X ),
% 0.77/1.34 class_Groups_Oordered__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.77/1.34 { ! class_Rings_Olinordered__idom( X ),
% 0.77/1.34 class_Groups_Oordered__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 0.77/1.34 { ! class_Rings_Olinordered__idom( X ),
% 0.77/1.34 class_Groups_Olinordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 0.77/1.34 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.77/1.34 class_Groups_Ocancel__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.77/1.34 { ! class_Rings_Oidom( X ), class_Rings_Oring__1__no__zero__divisors(
% 0.77/1.34 tc_Polynomial_Opoly( X ) ) }.
% 0.77/1.34 { ! class_Rings_Olinordered__idom( X ),
% 0.77/1.34 class_Rings_Oordered__cancel__semiring( tc_Polynomial_Opoly( X ) ) }.
% 0.77/1.34 { ! class_Rings_Olinordered__idom( X ),
% 0.77/1.34 class_Rings_Olinordered__ring__strict( tc_Polynomial_Opoly( X ) ) }.
% 0.77/1.34 { ! class_Rings_Oidom( X ), class_Rings_Oring__no__zero__divisors(
% 0.77/1.34 tc_Polynomial_Opoly( X ) ) }.
% 0.77/1.34 { ! class_Rings_Olinordered__idom( X ),
% 0.77/1.34 class_Rings_Oordered__comm__semiring( tc_Polynomial_Opoly( X ) ) }.
% 0.77/1.34 { ! class_Rings_Olinordered__idom( X ),
% 0.77/1.34 class_Rings_Olinordered__semiring__1( tc_Polynomial_Opoly( X ) ) }.
% 0.77/1.34 { ! class_Rings_Olinordered__idom( X ),
% 0.77/1.34 class_Groups_Oordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 0.77/1.34 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.77/1.34 class_Groups_Ocancel__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.77/1.34 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semiring(
% 0.77/1.34 tc_Polynomial_Opoly( X ) ) }.
% 0.77/1.34 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semidom(
% 0.77/1.34 tc_Polynomial_Opoly( X ) ) }.
% 0.77/1.34 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Oab__semigroup__mult
% 0.77/1.34 ( tc_Polynomial_Opoly( X ) ) }.
% 0.77/1.34 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Ocomm__monoid__mult(
% 0.77/1.34 tc_Polynomial_Opoly( X ) ) }.
% 0.77/1.34 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Oab__semigroup__add
% 0.77/1.34 ( tc_Polynomial_Opoly( X ) ) }.
% 0.77/1.34 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__semiring(
% 0.77/1.34 tc_Polynomial_Opoly( X ) ) }.
% 0.77/1.34 { ! class_Rings_Oidom( X ), class_Rings_Ono__zero__divisors(
% 0.77/1.34 tc_Polynomial_Opoly( X ) ) }.
% 0.77/1.34 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Ocomm__monoid__add(
% 0.77/1.34 tc_Polynomial_Opoly( X ) ) }.
% 0.77/1.34 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__ring(
% 0.77/1.34 tc_Polynomial_Opoly( X ) ) }.
% 0.77/1.34 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__idom(
% 0.77/1.34 tc_Polynomial_Opoly( X ) ) }.
% 0.77/1.34 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ocomm__semiring__1(
% 0.77/1.34 tc_Polynomial_Opoly( X ) ) }.
% 0.77/1.34 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring__0(
% 0.77/1.34 tc_Polynomial_Opoly( X ) ) }.
% 0.77/1.34 { ! class_Fields_Ofield( X ), class_Divides_Osemiring__div(
% 0.77/1.34 tc_Polynomial_Opoly( X ) ) }.
% 0.77/1.34 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring(
% 0.77/1.34 tc_Polynomial_Opoly( X ) ) }.
% 0.77/1.34 { ! class_Groups_Oab__group__add( X ), class_Groups_Oab__group__add(
% 0.77/1.34 tc_Polynomial_Opoly( X ) ) }.
% 0.77/1.34 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ozero__neq__one(
% 0.77/1.34 tc_Polynomial_Opoly( X ) ) }.
% 0.77/1.34 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__ring(
% 0.77/1.34 tc_Polynomial_Opoly( X ) ) }.
% 0.77/1.34 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Opreorder(
% 0.77/1.34 tc_Polynomial_Opoly( X ) ) }.
% 0.77/1.34 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Olinorder(
% 0.77/1.34 tc_Polynomial_Opoly( X ) ) }.
% 0.77/1.34 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Omonoid__mult(
% 0.77/1.34 tc_Polynomial_Opoly( X ) ) }.
% 0.77/1.34 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Ocomm__ring__1(
% 0.77/1.34 tc_Polynomial_Opoly( X ) ) }.
% 0.77/1.34 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Omonoid__add(
% 0.77/1.34 tc_Polynomial_Opoly( X ) ) }.
% 0.77/1.34 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Osemiring__1(
% 0.77/1.34 tc_Polynomial_Opoly( X ) ) }.
% 0.77/1.34 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring__0(
% 0.77/1.34 tc_Polynomial_Opoly( X ) ) }.
% 0.77/1.34 { ! class_Groups_Oab__group__add( X ), class_Groups_Ogroup__add(
% 0.77/1.34 tc_Polynomial_Opoly( X ) ) }.
% 0.77/1.34 { ! class_Fields_Ofield( X ), class_Divides_Oring__div( tc_Polynomial_Opoly
% 0.77/1.34 ( X ) ) }.
% 0.77/1.34 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Omult__zero(
% 0.77/1.34 tc_Polynomial_Opoly( X ) ) }.
% 0.77/1.34 { ! class_Rings_Ocomm__ring( X ), class_Rings_Ocomm__ring(
% 0.77/1.34 tc_Polynomial_Opoly( X ) ) }.
% 0.77/1.34 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oorder(
% 0.77/1.34 tc_Polynomial_Opoly( X ) ) }.
% 0.77/1.34 { ! class_Rings_Olinordered__idom( X ), class_Int_Oring__char__0(
% 0.77/1.34 tc_Polynomial_Opoly( X ) ) }.
% 0.77/1.34 { ! class_Rings_Ocomm__ring__1( X ), class_Int_Onumber__ring(
% 0.77/1.34 tc_Polynomial_Opoly( X ) ) }.
% 0.77/1.34 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring(
% 0.77/1.34 tc_Polynomial_Opoly( X ) ) }.
% 0.77/1.34 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oord(
% 0.77/1.34 tc_Polynomial_Opoly( X ) ) }.
% 0.77/1.34 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Oring__1(
% 0.77/1.34 tc_Polynomial_Opoly( X ) ) }.
% 0.77/1.34 { ! class_Rings_Ocomm__semiring__1( X ), class_Power_Opower(
% 0.77/1.34 tc_Polynomial_Opoly( X ) ) }.
% 0.77/1.34 { ! class_Groups_Ozero( X ), class_Groups_Ozero( tc_Polynomial_Opoly( X ) )
% 0.77/1.34 }.
% 0.77/1.34 { ! class_Rings_Ocomm__ring( X ), class_Rings_Oring( tc_Polynomial_Opoly( X
% 0.77/1.34 ) ) }.
% 0.77/1.34 { ! class_Rings_Oidom( X ), class_Rings_Oidom( tc_Polynomial_Opoly( X ) ) }
% 0.77/1.34 .
% 0.77/1.34 { ! class_Rings_Ocomm__ring__1( X ), class_Int_Onumber( tc_Polynomial_Opoly
% 0.77/1.34 ( X ) ) }.
% 0.77/1.34 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Oone(
% 0.77/1.34 tc_Polynomial_Opoly( X ) ) }.
% 0.77/1.34 { class_Groups_Oordered__cancel__ab__semigroup__add(
% 0.77/1.34 tc_Code__Numeral_Ocode__numeral ) }.
% 0.77/1.34 { class_Groups_Oordered__ab__semigroup__add__imp__le(
% 0.77/1.34 tc_Code__Numeral_Ocode__numeral ) }.
% 0.77/1.34 { class_Rings_Olinordered__comm__semiring__strict(
% 0.77/1.34 tc_Code__Numeral_Ocode__numeral ) }.
% 0.77/1.34 { class_Rings_Olinordered__semiring__strict(
% 0.77/1.34 tc_Code__Numeral_Ocode__numeral ) }.
% 0.77/1.34 { class_Groups_Oordered__ab__semigroup__add(
% 0.77/1.34 tc_Code__Numeral_Ocode__numeral ) }.
% 0.77/1.34 { class_Groups_Oordered__comm__monoid__add( tc_Code__Numeral_Ocode__numeral
% 0.77/1.34 ) }.
% 0.77/1.34 { class_Groups_Ocancel__ab__semigroup__add( tc_Code__Numeral_Ocode__numeral
% 0.77/1.34 ) }.
% 0.77/1.34 { class_Rings_Oordered__cancel__semiring( tc_Code__Numeral_Ocode__numeral )
% 0.77/1.34 }.
% 0.77/1.34 { class_Rings_Oordered__comm__semiring( tc_Code__Numeral_Ocode__numeral ) }
% 0.77/1.34 .
% 0.77/1.34 { class_Groups_Ocancel__semigroup__add( tc_Code__Numeral_Ocode__numeral ) }
% 0.77/1.34 .
% 0.77/1.34 { class_Rings_Olinordered__semiring( tc_Code__Numeral_Ocode__numeral ) }.
% 0.77/1.34 { class_Rings_Olinordered__semidom( tc_Code__Numeral_Ocode__numeral ) }.
% 0.77/1.34 { class_Groups_Oab__semigroup__mult( tc_Code__Numeral_Ocode__numeral ) }.
% 0.77/1.34 { class_Groups_Ocomm__monoid__mult( tc_Code__Numeral_Ocode__numeral ) }.
% 0.77/1.34 { class_Groups_Oab__semigroup__add( tc_Code__Numeral_Ocode__numeral ) }.
% 0.77/1.34 { class_Rings_Oordered__semiring( tc_Code__Numeral_Ocode__numeral ) }.
% 0.77/1.34 { class_Rings_Ono__zero__divisors( tc_Code__Numeral_Ocode__numeral ) }.
% 0.77/1.34 { class_Groups_Ocomm__monoid__add( tc_Code__Numeral_Ocode__numeral ) }.
% 0.77/1.34 { class_Rings_Ocomm__semiring__1( tc_Code__Numeral_Ocode__numeral ) }.
% 0.77/1.34 { class_Rings_Ocomm__semiring__0( tc_Code__Numeral_Ocode__numeral ) }.
% 0.77/1.35 { class_Divides_Osemiring__div( tc_Code__Numeral_Ocode__numeral ) }.
% 0.77/1.35 { class_Rings_Ocomm__semiring( tc_Code__Numeral_Ocode__numeral ) }.
% 0.77/1.35 { class_Rings_Ozero__neq__one( tc_Code__Numeral_Ocode__numeral ) }.
% 0.77/1.35 { class_Orderings_Opreorder( tc_Code__Numeral_Ocode__numeral ) }.
% 0.77/1.35 { class_Orderings_Olinorder( tc_Code__Numeral_Ocode__numeral ) }.
% 0.77/1.35 { class_Groups_Omonoid__mult( tc_Code__Numeral_Ocode__numeral ) }.
% 0.77/1.35 { class_Groups_Omonoid__add( tc_Code__Numeral_Ocode__numeral ) }.
% 0.77/1.35 { class_Rings_Osemiring__1( tc_Code__Numeral_Ocode__numeral ) }.
% 0.77/1.35 { class_Rings_Osemiring__0( tc_Code__Numeral_Ocode__numeral ) }.
% 0.77/1.35 { class_Rings_Omult__zero( tc_Code__Numeral_Ocode__numeral ) }.
% 0.77/1.35 { class_Orderings_Oorder( tc_Code__Numeral_Ocode__numeral ) }.
% 0.77/1.35 { class_Rings_Osemiring( tc_Code__Numeral_Ocode__numeral ) }.
% 0.77/1.35 { class_Orderings_Oord( tc_Code__Numeral_Ocode__numeral ) }.
% 0.77/1.35 { class_Power_Opower( tc_Code__Numeral_Ocode__numeral ) }.
% 0.77/1.35 { class_Groups_Ozero( tc_Code__Numeral_Ocode__numeral ) }.
% 0.77/1.35 { class_Int_Onumber( tc_Code__Numeral_Ocode__numeral ) }.
% 0.77/1.35 { class_Groups_Oone( tc_Code__Numeral_Ocode__numeral ) }.
% 0.77/1.35 { ! hBOOL( c_fequal( Y, X ) ), Y = X }.
% 0.77/1.35 { ! Y = X, hBOOL( c_fequal( Y, X ) ) }.
% 0.77/1.35 { ! hAPP( c_Polynomial_Opoly( t_a, v_p ), skol28 ) = hAPP(
% 0.77/1.35 c_Polynomial_Opoly( t_a, v_p ), skol31 ) }.
% 0.77/1.35 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.77/1.35 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.77/1.35 c_Int_OPls ) ) ), c_If( tc_Nat_Onat, c_fequal( v_p,
% 0.77/1.35 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( t_a ) ) ),
% 0.77/1.35 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Nat_OSuc(
% 0.77/1.35 c_Polynomial_Odegree( t_a, v_p ) ) ) ) }.
% 0.77/1.35 { class_Rings_Ocomm__semiring__0( t_a ) }.
% 0.77/1.35
% 0.77/1.35 *** allocated 15000 integers for clauses
% 0.77/1.35 *** allocated 22500 integers for clauses
% 0.77/1.35 *** allocated 33750 integers for clauses
% 0.77/1.35 *** allocated 50625 integers for clauses
% 0.77/1.35 *** allocated 75937 integers for clauses
% 0.77/1.35 *** allocated 113905 integers for clauses
% 0.77/1.35 percentage equality = 0.254541, percentage horn = 0.911923
% 0.77/1.35 This is a problem with some equality
% 0.77/1.35
% 0.77/1.35
% 0.77/1.35
% 0.77/1.35 Options Used:
% 0.77/1.35
% 0.77/1.35 useres = 1
% 0.77/1.35 useparamod = 1
% 0.77/1.35 useeqrefl = 1
% 0.77/1.35 useeqfact = 1
% 0.77/1.35 usefactor = 1
% 0.77/1.35 usesimpsplitting = 0
% 0.77/1.35 usesimpdemod = 5
% 0.77/1.35 usesimpres = 3
% 0.77/1.35
% 0.77/1.35 resimpinuse = 1000
% 0.77/1.35 resimpclauses = 20000
% 0.77/1.35 substype = eqrewr
% 0.77/1.35 backwardsubs = 1
% 0.77/1.35 selectoldest = 5
% 0.77/1.35
% 0.77/1.35 litorderings [0] = split
% 0.77/1.35 litorderings [1] = extend the termordering, first sorting on arguments
% 0.77/1.35
% 0.77/1.35 termordering = kbo
% 0.77/1.35
% 0.77/1.35 litapriori = 0
% 0.77/1.35 termapriori = 1
% 0.77/1.35 litaposteriori = 0
% 0.77/1.35 termaposteriori = 0
% 0.77/1.35 demodaposteriori = 0
% 0.77/1.35 ordereqreflfact = 0
% 0.77/1.35
% 0.77/1.35 litselect = negord
% 0.77/1.35
% 0.77/1.35 maxweight = 15
% 0.77/1.35 maxdepth = 30000
% 0.77/1.35 maxlength = 115
% 0.77/1.35 maxnrvars = 195
% 0.77/1.35 excuselevel = 1
% 0.77/1.35 increasemaxweight = 1
% 0.77/1.35
% 0.77/1.35 maxselected = 10000000
% 0.77/1.35 maxnrclauses = 10000000
% 0.77/1.35
% 0.77/1.35 showgenerated = 0
% 0.77/1.35 showkept = 0
% 0.77/1.35 showselected = 0
% 0.77/1.35 showdeleted = 0
% 0.77/1.35 showresimp = 1
% 0.77/1.35 showstatus = 2000
% 0.77/1.35
% 0.77/1.35 prologoutput = 0
% 0.77/1.35 nrgoals = 5000000
% 0.77/1.35 totalproof = 1
% 0.77/1.35
% 0.77/1.35 Symbols occurring in the translation:
% 0.77/1.35
% 0.77/1.35 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.77/1.35 . [1, 2] (w:1, o:181, a:1, s:1, b:0),
% 0.77/1.35 ! [4, 1] (w:0, o:103, a:1, s:1, b:0),
% 0.77/1.35 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.77/1.35 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.77/1.35 hAPP [38, 2] (w:1, o:205, a:1, s:1, b:0),
% 0.77/1.35 tc_Nat_Onat [39, 0] (w:1, o:13, a:1, s:1, b:0),
% 0.77/1.35 c_Groups_Ozero__class_Ozero [40, 1] (w:1, o:109, a:1, s:1, b:0),
% 0.77/1.35 c_Nat_OSuc [41, 1] (w:1, o:110, a:1, s:1, b:0),
% 0.77/1.35 c_Int_OPls [42, 0] (w:1, o:14, a:1, s:1, b:0),
% 0.77/1.35 c_Int_OBit1 [43, 1] (w:1, o:112, a:1, s:1, b:0),
% 0.77/1.35 c_Int_OBit0 [44, 1] (w:1, o:111, a:1, s:1, b:0),
% 0.77/1.35 c_Int_Onumber__class_Onumber__of [45, 2] (w:1, o:206, a:1, s:1, b:0)
% 0.77/1.35 ,
% 0.77/1.35 c_Orderings_Oord__class_Oless__eq [47, 3] (w:1, o:237, a:1, s:1, b:0)
% 0.77/1.35 ,
% 0.77/1.35 class_Groups_Ozero [50, 1] (w:1, o:114, a:1, s:1, b:0),
% 0.77/1.35 tc_Polynomial_Opoly [51, 1] (w:1, o:118, a:1, s:1, b:0),
% 0.77/1.35 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize [52, 2] (w:1, o:207
% 0.77/1.35 , a:1, s:1, b:0),
% 0.77/1.35 c_Polynomial_Odegree [53, 2] (w:1, o:208, a:1, s:1, b:0),
% 0.77/1.35 class_Int_Onumber__ring [56, 1] (w:1, o:119, a:1, s:1, b:0),
% 0.77/1.35 class_Rings_Olinordered__idom [57, 1] (w:1, o:120, a:1, s:1, b:0),
% 0.77/1.35 tc_Int_Oint [58, 0] (w:1, o:38, a:1, s:1, b:0),
% 0.77/1.35 class_Rings_Ocomm__semiring__0 [61, 1] (w:1, o:123, a:1, s:1, b:0),
% 0.77/1.35 c_Polynomial_Opoly [62, 2] (w:1, o:209, a:1, s:1, b:0),
% 0.77/1.35 class_Int_Oring__char__0 [74, 1] (w:1, o:124, a:1, s:1, b:0),
% 0.77/1.35 class_Int_Onumber [76, 1] (w:1, o:125, a:1, s:1, b:0),
% 0.77/1.35 class_Rings_Oidom [83, 1] (w:1, o:126, a:1, s:1, b:0),
% 0.77/1.35 c_Polynomial_Oorder [90, 3] (w:1, o:239, a:1, s:1, b:0),
% 0.77/1.35 class_Orderings_Opreorder [91, 1] (w:1, o:129, a:1, s:1, b:0),
% 0.77/1.35 c_Orderings_Oord__class_Oless [93, 3] (w:1, o:238, a:1, s:1, b:0),
% 0.77/1.35 c_Polynomial_Osynthetic__div [95, 3] (w:1, o:240, a:1, s:1, b:0),
% 0.77/1.35 class_Rings_Olinordered__semidom [96, 1] (w:1, o:132, a:1, s:1, b:0)
% 0.77/1.35 ,
% 0.77/1.35 c_Power_Opower__class_Opower [97, 3] (w:1, o:241, a:1, s:1, b:0),
% 0.77/1.35 hBOOL [101, 1] (w:1, o:133, a:1, s:1, b:0),
% 0.77/1.35 class_Orderings_Olinorder [102, 1] (w:1, o:134, a:1, s:1, b:0),
% 0.77/1.35 class_Orderings_Oorder [103, 1] (w:1, o:127, a:1, s:1, b:0),
% 0.77/1.35 class_Orderings_Oord [106, 1] (w:1, o:128, a:1, s:1, b:0),
% 0.77/1.35 class_Rings_Ocomm__semiring__1 [107, 1] (w:1, o:135, a:1, s:1, b:0),
% 0.77/1.35
% 0.77/1.35 tc_fun [111, 2] (w:1, o:216, a:1, s:1, b:0),
% 0.77/1.35 class_Rings_Osemiring__1 [112, 1] (w:1, o:141, a:1, s:1, b:0),
% 0.77/1.35 class_Rings_Oring__1__no__zero__divisors [113, 1] (w:1, o:136, a:1
% 0.77/1.35 , s:1, b:0),
% 0.77/1.35 tc_Complex_Ocomplex [114, 0] (w:1, o:82, a:1, s:1, b:0),
% 0.77/1.35 c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt [115, 1] (w:1, o:
% 0.77/1.35 108, a:1, s:1, b:0),
% 0.77/1.35 class_Power_Opower [116, 1] (w:1, o:142, a:1, s:1, b:0),
% 0.77/1.35 class_Rings_Omult__zero [117, 1] (w:1, o:148, a:1, s:1, b:0),
% 0.77/1.35 class_Rings_Ono__zero__divisors [118, 1] (w:1, o:149, a:1, s:1, b:0)
% 0.77/1.35 ,
% 0.77/1.35 class_Rings_Ozero__neq__one [119, 1] (w:1, o:150, a:1, s:1, b:0),
% 0.77/1.35 class_Rings_Osemiring__0 [121, 1] (w:1, o:140, a:1, s:1, b:0),
% 0.77/1.35 c_Groups_Otimes__class_Otimes [122, 3] (w:1, o:242, a:1, s:1, b:0),
% 0.77/1.35 c_Groups_Oone__class_Oone [123, 1] (w:1, o:151, a:1, s:1, b:0),
% 0.77/1.35 c_Groups_Oplus__class_Oplus [124, 3] (w:1, o:243, a:1, s:1, b:0),
% 0.77/1.35 class_Groups_Omonoid__mult [125, 1] (w:1, o:153, a:1, s:1, b:0),
% 0.77/1.35 class_Rings_Osemiring [128, 1] (w:1, o:154, a:1, s:1, b:0),
% 0.77/1.35 class_Rings_Olinordered__ring__strict [129, 1] (w:1, o:130, a:1, s:1
% 0.77/1.35 , b:0),
% 0.77/1.35 class_Rings_Olinordered__ring [130, 1] (w:1, o:131, a:1, s:1, b:0),
% 0.77/1.35 class_Groups_Olinordered__ab__group__add [131, 1] (w:1, o:152, a:1
% 0.77/1.35 , s:1, b:0),
% 0.77/1.35 class_Groups_Ocomm__monoid__mult [132, 1] (w:1, o:155, a:1, s:1, b:0)
% 0.77/1.35 ,
% 0.77/1.35 class_Groups_Ocomm__monoid__add [134, 1] (w:1, o:156, a:1, s:1, b:0)
% 0.77/1.35 ,
% 0.77/1.35 class_Rings_Olinordered__semiring__1__strict [141, 1] (w:1, o:143, a:
% 0.77/1.35 1, s:1, b:0),
% 0.77/1.35 class_Rings_Olinordered__semiring__1 [143, 1] (w:1, o:144, a:1, s:1
% 0.77/1.35 , b:0),
% 0.77/1.35 tc_RealDef_Oreal [147, 0] (w:1, o:91, a:1, s:1, b:0),
% 0.77/1.35 class_Rings_Oring__no__zero__divisors [153, 1] (w:1, o:137, a:1, s:1
% 0.77/1.35 , b:0),
% 0.77/1.35 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct [
% 0.77/1.35 154, 1] (w:1, o:163, a:1, s:1, b:0),
% 0.77/1.35 class_Rings_Ocomm__semiring [156, 1] (w:1, o:157, a:1, s:1, b:0),
% 0.77/1.35 class_Rings_Oordered__cancel__semiring [158, 1] (w:1, o:158, a:1, s:1
% 0.77/1.35 , b:0),
% 0.77/1.35 class_Rings_Oordered__ring [159, 1] (w:1, o:159, a:1, s:1, b:0),
% 0.77/1.35 class_Rings_Oordered__semiring [160, 1] (w:1, o:160, a:1, s:1, b:0),
% 0.77/1.35
% 0.77/1.35 class_Rings_Oordered__comm__semiring [161, 1] (w:1, o:161, a:1, s:1
% 0.77/1.35 , b:0),
% 0.77/1.35 class_Rings_Olinordered__comm__semiring__strict [162, 1] (w:1, o:145
% 0.77/1.35 , a:1, s:1, b:0),
% 0.77/1.35 class_Rings_Olinordered__semiring__strict [163, 1] (w:1, o:146, a:1
% 0.77/1.35 , s:1, b:0),
% 0.77/1.35 class_Rings_Olinordered__semiring [164, 1] (w:1, o:147, a:1, s:1, b:0
% 0.77/1.35 ),
% 0.77/1.35 class_Groups_Oordered__comm__monoid__add [168, 1] (w:1, o:164, a:1
% 0.77/1.35 , s:1, b:0),
% 0.77/1.35 class_Groups_Oab__semigroup__mult [169, 1] (w:1, o:165, a:1, s:1, b:0
% 0.77/1.64 ),
% 0.77/1.64 class_Groups_Oab__semigroup__add [170, 1] (w:1, o:166, a:1, s:1, b:0)
% 0.77/1.64 ,
% 0.77/1.64 class_Groups_Ocancel__semigroup__add [171, 1] (w:1, o:167, a:1, s:1
% 0.77/1.64 , b:0),
% 0.77/1.64 class_Groups_Ocancel__ab__semigroup__add [172, 1] (w:1, o:168, a:1
% 0.77/1.64 , s:1, b:0),
% 0.77/1.64 class_Groups_Oone [173, 1] (w:1, o:169, a:1, s:1, b:0),
% 0.77/1.64 class_Groups_Omonoid__add [174, 1] (w:1, o:170, a:1, s:1, b:0),
% 0.77/1.64 class_Groups_Oordered__ab__semigroup__add__imp__le [175, 1] (w:1, o:
% 0.77/1.64 171, a:1, s:1, b:0),
% 0.77/1.64 class_Groups_Oordered__ab__semigroup__add [176, 1] (w:1, o:172, a:1
% 0.77/1.64 , s:1, b:0),
% 0.77/1.64 class_Groups_Oordered__cancel__ab__semigroup__add [177, 1] (w:1, o:
% 0.77/1.64 173, a:1, s:1, b:0),
% 0.77/1.64 c_Divides_Odiv__class_Omod [178, 3] (w:1, o:244, a:1, s:1, b:0),
% 0.77/1.64 c_Divides_Odiv__class_Odiv [179, 3] (w:1, o:245, a:1, s:1, b:0),
% 0.77/1.64 class_Divides_Osemiring__div [180, 1] (w:1, o:175, a:1, s:1, b:0),
% 0.77/1.64 c_Groups_Ominus__class_Ominus [189, 3] (w:1, o:246, a:1, s:1, b:0),
% 0.77/1.64 c_Parity_Oeven__odd__class_Oeven [190, 2] (w:1, o:217, a:1, s:1, b:0)
% 0.77/1.64 ,
% 0.77/1.64 class_Fields_Ofield [191, 1] (w:1, o:113, a:1, s:1, b:0),
% 0.77/1.64 class_Divides_Oring__div [192, 1] (w:1, o:174, a:1, s:1, b:0),
% 0.77/1.64 class_Groups_Oordered__ab__group__add [193, 1] (w:1, o:176, a:1, s:1
% 0.77/1.64 , b:0),
% 0.77/1.64 class_Rings_Oring [195, 1] (w:1, o:138, a:1, s:1, b:0),
% 0.77/1.64 class_Rings_Ocomm__ring [196, 1] (w:1, o:121, a:1, s:1, b:0),
% 0.77/1.64 class_Groups_Oab__group__add [197, 1] (w:1, o:177, a:1, s:1, b:0),
% 0.77/1.64 class_Groups_Ogroup__add [198, 1] (w:1, o:178, a:1, s:1, b:0),
% 0.77/1.64 class_Rings_Oring__1 [199, 1] (w:1, o:139, a:1, s:1, b:0),
% 0.77/1.64 class_Rings_Ocomm__ring__1 [200, 1] (w:1, o:122, a:1, s:1, b:0),
% 0.77/1.64 class_RealVector_Oreal__normed__algebra [202, 1] (w:1, o:162, a:1, s:
% 0.77/1.64 1, b:0),
% 0.77/1.64 tc_Code__Numeral_Ocode__numeral [203, 0] (w:1, o:96, a:1, s:1, b:0),
% 0.77/1.64
% 0.77/1.64 c_Code__Numeral_Oint__of [204, 1] (w:1, o:179, a:1, s:1, b:0),
% 0.77/1.64 class_Groups_Ocancel__comm__monoid__add [211, 1] (w:1, o:180, a:1, s:
% 0.77/1.64 1, b:0),
% 0.77/1.64 tc_HOL_Obool [214, 0] (w:1, o:37, a:1, s:1, b:0),
% 0.77/1.64 c_fequal [215, 2] (w:1, o:218, a:1, s:1, b:0),
% 0.77/1.64 t_a [216, 0] (w:1, o:101, a:1, s:1, b:0),
% 0.77/1.64 v_p [217, 0] (w:1, o:102, a:1, s:1, b:0),
% 0.77/1.64 c_If [218, 4] (w:1, o:299, a:1, s:1, b:0),
% 0.77/1.64 alpha1 [219, 2] (w:1, o:219, a:1, s:1, b:1),
% 0.77/1.64 alpha2 [220, 2] (w:1, o:226, a:1, s:1, b:1),
% 0.77/1.64 alpha3 [221, 2] (w:1, o:230, a:1, s:1, b:1),
% 0.77/1.64 alpha4 [222, 2] (w:1, o:234, a:1, s:1, b:1),
% 0.77/1.64 alpha5 [223, 3] (w:1, o:255, a:1, s:1, b:1),
% 0.77/1.64 alpha6 [224, 3] (w:1, o:263, a:1, s:1, b:1),
% 0.77/1.64 alpha7 [225, 4] (w:1, o:300, a:1, s:1, b:1),
% 0.77/1.64 alpha8 [226, 4] (w:1, o:301, a:1, s:1, b:1),
% 0.77/1.64 alpha9 [227, 4] (w:1, o:302, a:1, s:1, b:1),
% 0.77/1.64 alpha10 [228, 4] (w:1, o:303, a:1, s:1, b:1),
% 0.77/1.64 alpha11 [229, 2] (w:1, o:220, a:1, s:1, b:1),
% 0.77/1.64 alpha12 [230, 2] (w:1, o:221, a:1, s:1, b:1),
% 0.77/1.64 alpha13 [231, 3] (w:1, o:264, a:1, s:1, b:1),
% 0.77/1.64 alpha14 [232, 2] (w:1, o:222, a:1, s:1, b:1),
% 0.77/1.64 alpha15 [233, 2] (w:1, o:223, a:1, s:1, b:1),
% 0.77/1.64 alpha16 [234, 2] (w:1, o:224, a:1, s:1, b:1),
% 0.77/1.64 alpha17 [235, 3] (w:1, o:265, a:1, s:1, b:1),
% 0.77/1.64 alpha18 [236, 2] (w:1, o:225, a:1, s:1, b:1),
% 0.77/1.64 alpha19 [237, 3] (w:1, o:266, a:1, s:1, b:1),
% 0.77/1.64 alpha20 [238, 3] (w:1, o:267, a:1, s:1, b:1),
% 0.77/1.64 alpha21 [239, 2] (w:1, o:227, a:1, s:1, b:1),
% 0.77/1.64 alpha22 [240, 2] (w:1, o:228, a:1, s:1, b:1),
% 0.77/1.64 alpha23 [241, 3] (w:1, o:268, a:1, s:1, b:1),
% 0.77/1.64 alpha24 [242, 3] (w:1, o:269, a:1, s:1, b:1),
% 0.77/1.64 alpha25 [243, 4] (w:1, o:304, a:1, s:1, b:1),
% 0.77/1.64 alpha26 [244, 4] (w:1, o:305, a:1, s:1, b:1),
% 0.77/1.64 alpha27 [245, 4] (w:1, o:306, a:1, s:1, b:1),
% 0.77/1.64 alpha28 [246, 4] (w:1, o:307, a:1, s:1, b:1),
% 0.77/1.64 alpha29 [247, 2] (w:1, o:229, a:1, s:1, b:1),
% 0.77/1.64 alpha30 [248, 3] (w:1, o:270, a:1, s:1, b:1),
% 0.77/1.64 alpha31 [249, 3] (w:1, o:271, a:1, s:1, b:1),
% 0.77/1.64 alpha32 [250, 2] (w:1, o:231, a:1, s:1, b:1),
% 0.77/1.64 alpha33 [251, 2] (w:1, o:232, a:1, s:1, b:1),
% 0.77/1.64 alpha34 [252, 3] (w:1, o:272, a:1, s:1, b:1),
% 10.58/10.97 alpha35 [253, 3] (w:1, o:273, a:1, s:1, b:1),
% 10.58/10.97 alpha36 [254, 3] (w:1, o:274, a:1, s:1, b:1),
% 10.58/10.97 alpha37 [255, 3] (w:1, o:275, a:1, s:1, b:1),
% 10.58/10.97 alpha38 [256, 3] (w:1, o:276, a:1, s:1, b:1),
% 10.58/10.97 alpha39 [257, 2] (w:1, o:233, a:1, s:1, b:1),
% 10.58/10.97 alpha40 [258, 3] (w:1, o:247, a:1, s:1, b:1),
% 10.58/10.97 alpha41 [259, 3] (w:1, o:248, a:1, s:1, b:1),
% 10.58/10.97 alpha42 [260, 3] (w:1, o:249, a:1, s:1, b:1),
% 10.58/10.97 alpha43 [261, 3] (w:1, o:250, a:1, s:1, b:1),
% 10.58/10.97 alpha44 [262, 4] (w:1, o:308, a:1, s:1, b:1),
% 10.58/10.97 alpha45 [263, 3] (w:1, o:251, a:1, s:1, b:1),
% 10.58/10.97 alpha46 [264, 3] (w:1, o:252, a:1, s:1, b:1),
% 10.58/10.97 alpha47 [265, 3] (w:1, o:253, a:1, s:1, b:1),
% 10.58/10.97 alpha48 [266, 3] (w:1, o:254, a:1, s:1, b:1),
% 10.58/10.97 alpha49 [267, 4] (w:1, o:309, a:1, s:1, b:1),
% 10.58/10.97 alpha50 [268, 4] (w:1, o:310, a:1, s:1, b:1),
% 10.58/10.97 alpha51 [269, 3] (w:1, o:256, a:1, s:1, b:1),
% 10.58/10.97 alpha52 [270, 3] (w:1, o:257, a:1, s:1, b:1),
% 10.58/10.97 alpha53 [271, 3] (w:1, o:258, a:1, s:1, b:1),
% 10.58/10.97 alpha54 [272, 3] (w:1, o:259, a:1, s:1, b:1),
% 10.58/10.97 alpha55 [273, 3] (w:1, o:260, a:1, s:1, b:1),
% 10.58/10.97 alpha56 [274, 4] (w:1, o:311, a:1, s:1, b:1),
% 10.58/10.97 alpha57 [275, 3] (w:1, o:261, a:1, s:1, b:1),
% 10.58/10.97 alpha58 [276, 3] (w:1, o:262, a:1, s:1, b:1),
% 10.58/10.97 alpha59 [277, 4] (w:1, o:312, a:1, s:1, b:1),
% 10.58/10.97 alpha60 [278, 3] (w:1, o:277, a:1, s:1, b:1),
% 10.58/10.97 alpha61 [279, 3] (w:1, o:278, a:1, s:1, b:1),
% 10.58/10.97 alpha62 [280, 2] (w:1, o:235, a:1, s:1, b:1),
% 10.58/10.97 alpha63 [281, 2] (w:1, o:236, a:1, s:1, b:1),
% 10.58/10.97 alpha64 [282, 3] (w:1, o:279, a:1, s:1, b:1),
% 10.58/10.97 skol1 [283, 2] (w:1, o:210, a:1, s:1, b:1),
% 10.58/10.97 skol2 [284, 1] (w:1, o:115, a:1, s:1, b:1),
% 10.58/10.97 skol3 [285, 2] (w:1, o:211, a:1, s:1, b:1),
% 10.58/10.97 skol4 [286, 3] (w:1, o:281, a:1, s:1, b:1),
% 10.58/10.97 skol5 [287, 2] (w:1, o:212, a:1, s:1, b:1),
% 10.58/10.97 skol6 [288, 2] (w:1, o:213, a:1, s:1, b:1),
% 10.58/10.97 skol7 [289, 2] (w:1, o:214, a:1, s:1, b:1),
% 10.58/10.97 skol8 [290, 3] (w:1, o:282, a:1, s:1, b:1),
% 10.58/10.97 skol9 [291, 3] (w:1, o:283, a:1, s:1, b:1),
% 10.58/10.97 skol10 [292, 3] (w:1, o:284, a:1, s:1, b:1),
% 10.58/10.97 skol11 [293, 3] (w:1, o:285, a:1, s:1, b:1),
% 10.58/10.97 skol12 [294, 3] (w:1, o:286, a:1, s:1, b:1),
% 10.58/10.97 skol13 [295, 3] (w:1, o:287, a:1, s:1, b:1),
% 10.58/10.97 skol14 [296, 3] (w:1, o:288, a:1, s:1, b:1),
% 10.58/10.97 skol15 [297, 3] (w:1, o:289, a:1, s:1, b:1),
% 10.58/10.97 skol16 [298, 3] (w:1, o:290, a:1, s:1, b:1),
% 10.58/10.97 skol17 [299, 3] (w:1, o:291, a:1, s:1, b:1),
% 10.58/10.97 skol18 [300, 2] (w:1, o:215, a:1, s:1, b:1),
% 10.58/10.97 skol19 [301, 3] (w:1, o:292, a:1, s:1, b:1),
% 10.58/10.97 skol20 [302, 4] (w:1, o:313, a:1, s:1, b:1),
% 10.58/10.97 skol21 [303, 3] (w:1, o:293, a:1, s:1, b:1),
% 10.58/10.97 skol22 [304, 3] (w:1, o:294, a:1, s:1, b:1),
% 10.58/10.97 skol23 [305, 3] (w:1, o:295, a:1, s:1, b:1),
% 10.58/10.97 skol24 [306, 1] (w:1, o:116, a:1, s:1, b:1),
% 10.58/10.97 skol25 [307, 1] (w:1, o:117, a:1, s:1, b:1),
% 10.58/10.97 skol26 [308, 3] (w:1, o:296, a:1, s:1, b:1),
% 10.58/10.97 skol27 [309, 3] (w:1, o:297, a:1, s:1, b:1),
% 10.58/10.97 skol28 [310, 0] (w:1, o:11, a:1, s:1, b:1),
% 10.58/10.97 skol29 [311, 3] (w:1, o:298, a:1, s:1, b:1),
% 10.58/10.97 skol30 [312, 3] (w:1, o:280, a:1, s:1, b:1),
% 10.58/10.97 skol31 [313, 0] (w:1, o:12, a:1, s:1, b:1).
% 10.58/10.97
% 10.58/10.97
% 10.58/10.97 Starting Search:
% 10.58/10.97
% 10.58/10.97 *** allocated 170857 integers for clauses
% 10.58/10.97 Resimplifying inuse:
% 10.58/10.97 Done
% 10.58/10.97
% 10.58/10.97
% 10.58/10.97 Intermediate Status:
% 10.58/10.97 Generated: 2908
% 10.58/10.97 Kept: 2007
% 10.58/10.97 Inuse: 48
% 10.58/10.97 Deleted: 3
% 10.58/10.97 Deletedinuse: 0
% 10.58/10.97
% 10.58/10.97 *** allocated 256285 integers for clauses
% 10.58/10.97 Resimplifying inuse:
% 10.58/10.97 Done
% 10.58/10.97
% 10.58/10.97 *** allocated 170857 integers for termspace/termends
% 10.58/10.97 Resimplifying inuse:
% 10.58/10.97 Done
% 10.58/10.97
% 10.58/10.97
% 10.58/10.97 Intermediate Status:
% 10.58/10.97 Generated: 7996
% 10.58/10.97 Kept: 4012
% 10.58/10.97 Inuse: 214
% 10.58/10.97 Deleted: 6
% 10.58/10.97 Deletedinuse: 0
% 10.58/10.97
% 10.58/10.97 *** allocated 384427 integers for clauses
% 10.58/10.97 Resimplifying inuse:
% 10.58/10.97 Done
% 10.58/10.97
% 10.58/10.97
% 10.58/10.97 Intermediate Status:
% 10.58/10.97 Generated: 14442
% 10.58/10.97 Kept: 6023
% 10.58/10.97 Inuse: 280
% 10.58/10.97 Deleted: 7
% 10.58/10.97 Deletedinuse: 1
% 10.58/10.97
% 10.58/10.97 Resimplifying inuse:
% 10.58/10.97 Done
% 10.58/10.97
% 10.58/10.97 Resimplifying inuse:
% 10.58/10.97 Done
% 10.58/10.97
% 10.58/10.97 *** allocated 576640 integers for clauses
% 10.58/10.97 *** allocated 256285 integers for termspace/termends
% 10.58/10.97
% 10.58/10.97 Intermediate Status:
% 10.58/10.97 Generated: 18682
% 10.58/10.97 Kept: 8028
% 10.58/10.97 Inuse: 341
% 10.58/10.97 Deleted: 12
% 39.30/39.71 Deletedinuse: 1
% 39.30/39.71
% 39.30/39.71 Resimplifying inuse:
% 39.30/39.71 Done
% 39.30/39.71
% 39.30/39.71 Resimplifying inuse:
% 39.30/39.71 Done
% 39.30/39.71
% 39.30/39.71
% 39.30/39.71 Intermediate Status:
% 39.30/39.71 Generated: 22648
% 39.30/39.71 Kept: 10043
% 39.30/39.71 Inuse: 380
% 39.30/39.71 Deleted: 16
% 39.30/39.71 Deletedinuse: 1
% 39.30/39.71
% 39.30/39.71 Resimplifying inuse:
% 39.30/39.71 Done
% 39.30/39.71
% 39.30/39.71 Resimplifying inuse:
% 39.30/39.71 Done
% 39.30/39.71
% 39.30/39.71 *** allocated 864960 integers for clauses
% 39.30/39.71
% 39.30/39.71 Intermediate Status:
% 39.30/39.71 Generated: 27255
% 39.30/39.71 Kept: 12044
% 39.30/39.71 Inuse: 436
% 39.30/39.71 Deleted: 20
% 39.30/39.71 Deletedinuse: 1
% 39.30/39.71
% 39.30/39.71 *** allocated 384427 integers for termspace/termends
% 39.30/39.71 Resimplifying inuse:
% 39.30/39.71 Done
% 39.30/39.71
% 39.30/39.71
% 39.30/39.71 Intermediate Status:
% 39.30/39.71 Generated: 31874
% 39.30/39.71 Kept: 14378
% 39.30/39.71 Inuse: 452
% 39.30/39.71 Deleted: 20
% 39.30/39.71 Deletedinuse: 1
% 39.30/39.71
% 39.30/39.71 Resimplifying inuse:
% 39.30/39.71 Done
% 39.30/39.71
% 39.30/39.71 Resimplifying inuse:
% 39.30/39.71 Done
% 39.30/39.71
% 39.30/39.71
% 39.30/39.71 Intermediate Status:
% 39.30/39.71 Generated: 37343
% 39.30/39.71 Kept: 16417
% 39.30/39.71 Inuse: 494
% 39.30/39.71 Deleted: 21
% 39.30/39.71 Deletedinuse: 1
% 39.30/39.71
% 39.30/39.71 Resimplifying inuse:
% 39.30/39.71 Done
% 39.30/39.71
% 39.30/39.71 Resimplifying inuse:
% 39.30/39.71 Done
% 39.30/39.71
% 39.30/39.71
% 39.30/39.71 Intermediate Status:
% 39.30/39.71 Generated: 42400
% 39.30/39.71 Kept: 18431
% 39.30/39.71 Inuse: 558
% 39.30/39.71 Deleted: 22
% 39.30/39.71 Deletedinuse: 1
% 39.30/39.71
% 39.30/39.71 Resimplifying inuse:
% 39.30/39.71 Done
% 39.30/39.71
% 39.30/39.71 *** allocated 1297440 integers for clauses
% 39.30/39.71 Resimplifying inuse:
% 39.30/39.71 Done
% 39.30/39.71
% 39.30/39.71 *** allocated 576640 integers for termspace/termends
% 39.30/39.71
% 39.30/39.71 Intermediate Status:
% 39.30/39.71 Generated: 47007
% 39.30/39.71 Kept: 21189
% 39.30/39.71 Inuse: 585
% 39.30/39.71 Deleted: 22
% 39.30/39.71 Deletedinuse: 1
% 39.30/39.71
% 39.30/39.71 Resimplifying inuse:
% 39.30/39.71 Done
% 39.30/39.71
% 39.30/39.71 Resimplifying clauses:
% 39.30/39.71 Done
% 39.30/39.71
% 39.30/39.71 Resimplifying inuse:
% 39.30/39.71 Done
% 39.30/39.71
% 39.30/39.71
% 39.30/39.71 Intermediate Status:
% 39.30/39.71 Generated: 52353
% 39.30/39.71 Kept: 24087
% 39.30/39.71 Inuse: 610
% 39.30/39.71 Deleted: 235
% 39.30/39.71 Deletedinuse: 1
% 39.30/39.71
% 39.30/39.71 Resimplifying inuse:
% 39.30/39.71 Done
% 39.30/39.71
% 39.30/39.71 Resimplifying inuse:
% 39.30/39.71 Done
% 39.30/39.71
% 39.30/39.71
% 39.30/39.71 Intermediate Status:
% 39.30/39.71 Generated: 58264
% 39.30/39.71 Kept: 26861
% 39.30/39.71 Inuse: 645
% 39.30/39.71 Deleted: 235
% 39.30/39.71 Deletedinuse: 1
% 39.30/39.71
% 39.30/39.71 Resimplifying inuse:
% 39.30/39.71 Done
% 39.30/39.71
% 39.30/39.71 *** allocated 1946160 integers for clauses
% 39.30/39.71
% 39.30/39.71 Intermediate Status:
% 39.30/39.71 Generated: 63309
% 39.30/39.71 Kept: 29926
% 39.30/39.71 Inuse: 665
% 39.30/39.71 Deleted: 235
% 39.30/39.71 Deletedinuse: 1
% 39.30/39.71
% 39.30/39.71 Resimplifying inuse:
% 39.30/39.71 Done
% 39.30/39.71
% 39.30/39.71 Resimplifying inuse:
% 39.30/39.71 Done
% 39.30/39.71
% 39.30/39.71
% 39.30/39.71 Intermediate Status:
% 39.30/39.71 Generated: 67825
% 39.30/39.71 Kept: 32234
% 39.30/39.71 Inuse: 685
% 39.30/39.71 Deleted: 235
% 39.30/39.71 Deletedinuse: 1
% 39.30/39.71
% 39.30/39.71 Resimplifying inuse:
% 39.30/39.71 Done
% 39.30/39.71
% 39.30/39.71 Resimplifying inuse:
% 39.30/39.71 Done
% 39.30/39.71
% 39.30/39.71 *** allocated 864960 integers for termspace/termends
% 39.30/39.71
% 39.30/39.71 Intermediate Status:
% 39.30/39.71 Generated: 73771
% 39.30/39.71 Kept: 35791
% 39.30/39.71 Inuse: 705
% 39.30/39.71 Deleted: 235
% 39.30/39.71 Deletedinuse: 1
% 39.30/39.71
% 39.30/39.71 Resimplifying inuse:
% 39.30/39.71 Done
% 39.30/39.71
% 39.30/39.71 Resimplifying inuse:
% 39.30/39.71 Done
% 39.30/39.71
% 39.30/39.71
% 39.30/39.71 Intermediate Status:
% 39.30/39.71 Generated: 77984
% 39.30/39.71 Kept: 37889
% 39.30/39.71 Inuse: 730
% 39.30/39.71 Deleted: 235
% 39.30/39.71 Deletedinuse: 1
% 39.30/39.71
% 39.30/39.71 Resimplifying inuse:
% 39.30/39.71 Done
% 39.30/39.71
% 39.30/39.71 Resimplifying inuse:
% 39.30/39.71 Done
% 39.30/39.71
% 39.30/39.71
% 39.30/39.71 Intermediate Status:
% 39.30/39.71 Generated: 81225
% 39.30/39.71 Kept: 39907
% 39.30/39.71 Inuse: 742
% 39.30/39.71 Deleted: 235
% 39.30/39.71 Deletedinuse: 1
% 39.30/39.71
% 39.30/39.71 Resimplifying inuse:
% 39.30/39.71 Done
% 39.30/39.71
% 39.30/39.71 Resimplifying clauses:
% 39.30/39.71 Done
% 39.30/39.71
% 39.30/39.71 Resimplifying inuse:
% 39.30/39.71 Done
% 39.30/39.71
% 39.30/39.71
% 39.30/39.71 Intermediate Status:
% 39.30/39.71 Generated: 85433
% 39.30/39.71 Kept: 41924
% 39.30/39.71 Inuse: 778
% 39.30/39.71 Deleted: 386
% 39.30/39.71 Deletedinuse: 2
% 39.30/39.71
% 39.30/39.71 *** allocated 2919240 integers for clauses
% 39.30/39.71
% 39.30/39.71 Intermediate Status:
% 39.30/39.71 Generated: 90242
% 39.30/39.71 Kept: 45282
% 39.30/39.71 Inuse: 790
% 39.30/39.71 Deleted: 386
% 39.30/39.71 Deletedinuse: 2
% 39.30/39.71
% 39.30/39.71 Resimplifying inuse:
% 39.30/39.71 Done
% 39.30/39.71
% 39.30/39.71 Resimplifying inuse:
% 39.30/39.71 Done
% 39.30/39.71
% 39.30/39.71
% 39.30/39.71 Intermediate Status:
% 39.30/39.71 Generated: 97988
% 39.30/39.71 Kept: 48223
% 39.30/39.71 Inuse: 815
% 39.30/39.71 Deleted: 386
% 39.30/39.71 Deletedinuse: 2
% 39.30/39.71
% 39.30/39.71 Resimplifying inuse:
% 39.30/39.71 Done
% 39.30/39.71
% 39.30/39.71 Resimplifying inuse:
% 39.30/39.71 Done
% 39.30/39.71
% 39.30/39.71
% 39.30/39.71 Intermediate Status:
% 39.30/39.71 Generated: 102462
% 39.30/39.71 Kept: 50253
% 39.30/39.71 Inuse: 846
% 39.30/39.71 Deleted: 386
% 39.30/39.71 Deletedinuse: 2
% 39.30/39.71
% 39.30/39.71 Resimplifying inuse:
% 39.30/39.71 Done
% 39.30/39.71
% 39.30/39.71 *** allocated 1297440 integers for termspace/termends
% 39.30/39.71 Resimplifying inuse:
% 39.30/39.71 Done
% 39.30/39.71
% 39.30/39.71
% 39.30/39.71 Intermediate Status:
% 39.30/39.71 Generated: 111081
% 39.30/39.71 Kept: 52270
% 39.30/39.71 Inuse: 863
% 39.30/39.71 Deleted: 386
% 39.30/39.71 Deletedinuse: 2
% 39.30/39.71
% 39.30/39.71 Resimplifying inuse:
% 39.30/39.71 Done
% 39.30/39.71
% 39.30/39.71
% 39.30/39.71 Intermediate Status:
% 39.30/39.71 Generated: 119280
% 39.30/39.71 Kept: 54270
% 39.30/39.71 Inuse: 877
% 39.30/39.71 Deleted: 386
% 39.30/39.71 Deletedinuse: 2
% 39.30/39.71
% 39.30/39.71 Resimplifying inuse:
% 39.30/39.71 Done
% 39.30/39.71
% 39.30/39.71
% 39.30/39.71 Intermediate Status:
% 39.30/39.71 Generated: 127219
% 39.30/39.71 Kept: 57021
% 39.30/39.71 Inuse: 895
% 39.30/39.71 Deleted: 386
% 39.30/39.71 Deletedinuse: 2
% 39.30/39.71
% 39.30/39.71 Resimplifying inuse:
% 39.30/39.71 Done
% 39.30/39.71
% 39.30/39.71 Resimplifying inuse:
% 39.30/39.71 Done
% 39.30/39.71
% 39.30/39.71
% 39.30/39.71 Intermediate Status:
% 39.30/39.71 Generated: 131753
% 39.30/39.71 Kept: 59062
% 39.30/39.71 Inuse: 920
% 39.30/39.71 Deleted: 386
% 39.30/39.71 Deletedinuse: 2
% 39.30/39.71
% 39.30/39.71 Resimplifying inuse:
% 39.30/39.71 Done
% 39.30/39.71
% 39.30/39.71
% 39.30/39.71 Intermediate Status:
% 39.30/39.71 Generated: 137642
% 39.30/39.71 Kept: 63174
% 39.30/39.71 Inuse: 930
% 39.30/39.71 Deleted: 386
% 39.30/39.71 Deletedinuse: 2
% 39.30/39.71
% 39.30/39.71 Resimplifying inuse:
% 39.30/39.71 Done
% 39.30/39.71
% 39.30/39.71 Resimplifying clauses:
% 39.30/39.71 Done
% 39.30/39.71
% 39.30/39.71 Resimplifying inuse:
% 39.30/39.71 Done
% 39.30/39.71
% 39.30/39.71
% 39.30/39.71 Intermediate Status:
% 112.70/113.22 Generated: 144297
% 112.70/113.22 Kept: 65226
% 112.70/113.22 Inuse: 959
% 112.70/113.22 Deleted: 643
% 112.70/113.22 Deletedinuse: 2
% 112.70/113.22
% 112.70/113.22 Resimplifying inuse:
% 112.70/113.22 Done
% 112.70/113.22
% 112.70/113.22 Resimplifying inuse:
% 112.70/113.22 Done
% 112.70/113.22
% 112.70/113.22 *** allocated 4378860 integers for clauses
% 112.70/113.22
% 112.70/113.22 Intermediate Status:
% 112.70/113.22 Generated: 150647
% 112.70/113.22 Kept: 67247
% 112.70/113.22 Inuse: 983
% 112.70/113.22 Deleted: 643
% 112.70/113.22 Deletedinuse: 2
% 112.70/113.22
% 112.70/113.22 Resimplifying inuse:
% 112.70/113.22 Done
% 112.70/113.22
% 112.70/113.22 Resimplifying inuse:
% 112.70/113.22 Done
% 112.70/113.22
% 112.70/113.22
% 112.70/113.22 Intermediate Status:
% 112.70/113.22 Generated: 156487
% 112.70/113.22 Kept: 69254
% 112.70/113.22 Inuse: 1005
% 112.70/113.22 Deleted: 643
% 112.70/113.22 Deletedinuse: 2
% 112.70/113.22
% 112.70/113.22 Resimplifying inuse:
% 112.70/113.22 Done
% 112.70/113.22
% 112.70/113.22 Resimplifying inuse:
% 112.70/113.22 Done
% 112.70/113.22
% 112.70/113.22
% 112.70/113.22 Intermediate Status:
% 112.70/113.22 Generated: 162474
% 112.70/113.22 Kept: 71291
% 112.70/113.22 Inuse: 1027
% 112.70/113.22 Deleted: 643
% 112.70/113.22 Deletedinuse: 2
% 112.70/113.22
% 112.70/113.22 Resimplifying inuse:
% 112.70/113.22 Done
% 112.70/113.22
% 112.70/113.22 Resimplifying inuse:
% 112.70/113.22 Done
% 112.70/113.22
% 112.70/113.22 *** allocated 1946160 integers for termspace/termends
% 112.70/113.22
% 112.70/113.22 Intermediate Status:
% 112.70/113.22 Generated: 169713
% 112.70/113.22 Kept: 75129
% 112.70/113.22 Inuse: 1050
% 112.70/113.22 Deleted: 643
% 112.70/113.22 Deletedinuse: 2
% 112.70/113.22
% 112.70/113.22 Resimplifying inuse:
% 112.70/113.22 Done
% 112.70/113.22
% 112.70/113.22 Resimplifying inuse:
% 112.70/113.22 Done
% 112.70/113.22
% 112.70/113.22
% 112.70/113.22 Intermediate Status:
% 112.70/113.22 Generated: 177091
% 112.70/113.22 Kept: 77190
% 112.70/113.22 Inuse: 1065
% 112.70/113.22 Deleted: 644
% 112.70/113.22 Deletedinuse: 3
% 112.70/113.22
% 112.70/113.22 Resimplifying inuse:
% 112.70/113.22 Done
% 112.70/113.22
% 112.70/113.22 Resimplifying inuse:
% 112.70/113.22 Done
% 112.70/113.22
% 112.70/113.22
% 112.70/113.22 Intermediate Status:
% 112.70/113.22 Generated: 185258
% 112.70/113.22 Kept: 79897
% 112.70/113.22 Inuse: 1085
% 112.70/113.22 Deleted: 644
% 112.70/113.22 Deletedinuse: 3
% 112.70/113.22
% 112.70/113.22 Resimplifying inuse:
% 112.70/113.22 Done
% 112.70/113.22
% 112.70/113.22 Resimplifying inuse:
% 112.70/113.22 Done
% 112.70/113.22
% 112.70/113.22
% 112.70/113.22 Intermediate Status:
% 112.70/113.22 Generated: 193499
% 112.70/113.22 Kept: 81941
% 112.70/113.22 Inuse: 1099
% 112.70/113.22 Deleted: 644
% 112.70/113.22 Deletedinuse: 3
% 112.70/113.22
% 112.70/113.22 Resimplifying inuse:
% 112.70/113.22 Done
% 112.70/113.22
% 112.70/113.22 Resimplifying clauses:
% 112.70/113.22 Done
% 112.70/113.22
% 112.70/113.22 Resimplifying inuse:
% 112.70/113.22 Done
% 112.70/113.22
% 112.70/113.22
% 112.70/113.22 Intermediate Status:
% 112.70/113.22 Generated: 199243
% 112.70/113.22 Kept: 84033
% 112.70/113.22 Inuse: 1120
% 112.70/113.22 Deleted: 910
% 112.70/113.22 Deletedinuse: 4
% 112.70/113.22
% 112.70/113.22 Resimplifying inuse:
% 112.70/113.22 Done
% 112.70/113.22
% 112.70/113.22 Resimplifying inuse:
% 112.70/113.22 Done
% 112.70/113.22
% 112.70/113.22
% 112.70/113.22 Intermediate Status:
% 112.70/113.22 Generated: 205537
% 112.70/113.22 Kept: 86087
% 112.70/113.22 Inuse: 1143
% 112.70/113.22 Deleted: 910
% 112.70/113.22 Deletedinuse: 4
% 112.70/113.22
% 112.70/113.22 Resimplifying inuse:
% 112.70/113.22 Done
% 112.70/113.22
% 112.70/113.22 Resimplifying inuse:
% 112.70/113.22 Done
% 112.70/113.22
% 112.70/113.22
% 112.70/113.22 Intermediate Status:
% 112.70/113.22 Generated: 211672
% 112.70/113.22 Kept: 88111
% 112.70/113.22 Inuse: 1166
% 112.70/113.22 Deleted: 910
% 112.70/113.22 Deletedinuse: 4
% 112.70/113.22
% 112.70/113.22 Resimplifying inuse:
% 112.70/113.22 Done
% 112.70/113.22
% 112.70/113.22 Resimplifying inuse:
% 112.70/113.22 Done
% 112.70/113.22
% 112.70/113.22
% 112.70/113.22 Intermediate Status:
% 112.70/113.22 Generated: 217655
% 112.70/113.22 Kept: 90118
% 112.70/113.22 Inuse: 1189
% 112.70/113.22 Deleted: 910
% 112.70/113.22 Deletedinuse: 4
% 112.70/113.22
% 112.70/113.22
% 112.70/113.22 Intermediate Status:
% 112.70/113.22 Generated: 226645
% 112.70/113.22 Kept: 92747
% 112.70/113.22 Inuse: 1194
% 112.70/113.22 Deleted: 910
% 112.70/113.22 Deletedinuse: 4
% 112.70/113.22
% 112.70/113.22 Resimplifying inuse:
% 112.70/113.22 Done
% 112.70/113.22
% 112.70/113.22 Resimplifying inuse:
% 112.70/113.22 Done
% 112.70/113.22
% 112.70/113.22
% 112.70/113.22 Intermediate Status:
% 112.70/113.22 Generated: 235697
% 112.70/113.22 Kept: 95398
% 112.70/113.22 Inuse: 1210
% 112.70/113.22 Deleted: 910
% 112.70/113.22 Deletedinuse: 4
% 112.70/113.22
% 112.70/113.22 Resimplifying inuse:
% 112.70/113.22 Done
% 112.70/113.22
% 112.70/113.22 Resimplifying inuse:
% 112.70/113.22 Done
% 112.70/113.22
% 112.70/113.22
% 112.70/113.22 Intermediate Status:
% 112.70/113.22 Generated: 244793
% 112.70/113.22 Kept: 98414
% 112.70/113.22 Inuse: 1235
% 112.70/113.22 Deleted: 910
% 112.70/113.22 Deletedinuse: 4
% 112.70/113.22
% 112.70/113.22 Resimplifying inuse:
% 112.70/113.22 Done
% 112.70/113.22
% 112.70/113.22 Resimplifying inuse:
% 112.70/113.22 Done
% 112.70/113.22
% 112.70/113.22 *** allocated 6568290 integers for clauses
% 112.70/113.22
% 112.70/113.22 Intermediate Status:
% 112.70/113.22 Generated: 254245
% 112.70/113.22 Kept: 101243
% 112.70/113.22 Inuse: 1250
% 112.70/113.22 Deleted: 910
% 112.70/113.22 Deletedinuse: 4
% 112.70/113.22
% 112.70/113.22 Resimplifying inuse:
% 112.70/113.22 Done
% 112.70/113.22
% 112.70/113.22 Resimplifying inuse:
% 112.70/113.22 Done
% 112.70/113.22
% 112.70/113.22
% 112.70/113.22 Intermediate Status:
% 112.70/113.22 Generated: 261037
% 112.70/113.22 Kept: 103339
% 112.70/113.22 Inuse: 1269
% 112.70/113.22 Deleted: 911
% 112.70/113.22 Deletedinuse: 4
% 112.70/113.22
% 112.70/113.22 Resimplifying clauses:
% 112.70/113.22 Done
% 112.70/113.22
% 112.70/113.22 *** allocated 2919240 integers for termspace/termends
% 112.70/113.22
% 112.70/113.22 Intermediate Status:
% 112.70/113.22 Generated: 265205
% 112.70/113.22 Kept: 105589
% 112.70/113.22 Inuse: 1274
% 112.70/113.22 Deleted: 1211
% 112.70/113.22 Deletedinuse: 4
% 112.70/113.22
% 112.70/113.22 Resimplifying inuse:
% 112.70/113.22 Done
% 112.70/113.22
% 112.70/113.22
% 112.70/113.22 Intermediate Status:
% 112.70/113.22 Generated: 271999
% 112.70/113.22 Kept: 109329
% 112.70/113.22 Inuse: 1294
% 112.70/113.22 Deleted: 1211
% 112.70/113.22 Deletedinuse: 4
% 112.70/113.22
% 112.70/113.22 Resimplifying inuse:
% 112.70/113.22 Done
% 112.70/113.22
% 112.70/113.22
% 112.70/113.22 Intermediate Status:
% 112.70/113.22 Generated: 276229
% 112.70/113.22 Kept: 112355
% 112.70/113.22 Inuse: 1299
% 112.70/113.22 Deleted: 1211
% 112.70/113.22 Deletedinuse: 4
% 112.70/113.22
% 112.70/113.22 Resimplifying inuse:
% 112.70/113.22 Done
% 112.70/113.22
% 112.70/113.22
% 112.70/113.22 Intermediate Status:
% 112.70/113.22 Generated: 280462
% 112.70/113.22 Kept: 115394
% 112.70/113.22 Inuse: 1304
% 112.70/113.22 Deleted: 1211
% 112.70/113.22 Deletedinuse: 4
% 112.70/113.22
% 112.70/113.22 Resimplifying inuse:
% 112.70/113.22 Done
% 112.70/113.22
% 112.70/113.22 Resimplifying inuse:
% 112.70/113.22 Done
% 112.70/113.22
% 112.70/113.22
% 112.70/113.22 Intermediate Status:
% 112.70/113.22 Generated: 298151
% 112.70/113.22 Kept: 119934
% 112.70/113.22 Inuse: 1344
% 112.70/113.22 Deleted: 1211
% 112.70/113.22 Deletedinuse: 4
% 112.70/113.22
% 112.70/113.22 Resimplifying inuse:
% 112.70/113.22 Done
% 112.70/113.22
% 112.70/113.22
% 112.70/113.22 Intermediate Status:
% 112.70/113.22 Generated: 318186
% 112.70/113.22 Kept: 122550
% 112.70/113.22 Inuse: 1359
% 112.70/113.22 Deleted: 1211
% 112.70/113.22 Deletedinuse: 4
% 112.70/113.22
% 112.70/113.22 Resimplifying inuse:
% 112.70/113.22 Done
% 112.70/113.22
% 112.70/113.22
% 112.70/113.22 Intermediate Status:
% 112.70/113.22 Generated: 337770
% 112.70/113.22 Kept: 124949
% 112.70/113.22 Inuse: 1369
% 112.70/113.22 Deleted: 1211
% 112.70/113.22 Deletedinuse: 4
% 112.70/113.22
% 112.70/113.22 Resimplifying inuse:
% 112.70/113.22 Done
% 112.70/113.22
% 112.70/113.22 Resimplifying clauses:
% 260.38/260.90 Done
% 260.38/260.90
% 260.38/260.90 Resimplifying inuse:
% 260.38/260.90 Done
% 260.38/260.90
% 260.38/260.90
% 260.38/260.90 Intermediate Status:
% 260.38/260.90 Generated: 345305
% 260.38/260.90 Kept: 127038
% 260.38/260.90 Inuse: 1404
% 260.38/260.90 Deleted: 1387
% 260.38/260.90 Deletedinuse: 4
% 260.38/260.90
% 260.38/260.90 Resimplifying inuse:
% 260.38/260.90 Done
% 260.38/260.90
% 260.38/260.90 Resimplifying inuse:
% 260.38/260.90 Done
% 260.38/260.90
% 260.38/260.90
% 260.38/260.90 Intermediate Status:
% 260.38/260.90 Generated: 352744
% 260.38/260.90 Kept: 129068
% 260.38/260.90 Inuse: 1432
% 260.38/260.90 Deleted: 1387
% 260.38/260.90 Deletedinuse: 4
% 260.38/260.90
% 260.38/260.90 Resimplifying inuse:
% 260.38/260.90 Done
% 260.38/260.90
% 260.38/260.90
% 260.38/260.90 Intermediate Status:
% 260.38/260.90 Generated: 365155
% 260.38/260.90 Kept: 132120
% 260.38/260.90 Inuse: 1444
% 260.38/260.90 Deleted: 1390
% 260.38/260.90 Deletedinuse: 7
% 260.38/260.90
% 260.38/260.90 Resimplifying inuse:
% 260.38/260.90 Done
% 260.38/260.90
% 260.38/260.90 Resimplifying inuse:
% 260.38/260.90 Done
% 260.38/260.90
% 260.38/260.90
% 260.38/260.90 Intermediate Status:
% 260.38/260.90 Generated: 372204
% 260.38/260.90 Kept: 134127
% 260.38/260.90 Inuse: 1477
% 260.38/260.90 Deleted: 1390
% 260.38/260.90 Deletedinuse: 7
% 260.38/260.90
% 260.38/260.90 Resimplifying inuse:
% 260.38/260.90 Done
% 260.38/260.90
% 260.38/260.90 Resimplifying inuse:
% 260.38/260.90 Done
% 260.38/260.90
% 260.38/260.90
% 260.38/260.90 Intermediate Status:
% 260.38/260.90 Generated: 379302
% 260.38/260.90 Kept: 136141
% 260.38/260.90 Inuse: 1509
% 260.38/260.90 Deleted: 1390
% 260.38/260.90 Deletedinuse: 7
% 260.38/260.90
% 260.38/260.90 Resimplifying inuse:
% 260.38/260.90 Done
% 260.38/260.90
% 260.38/260.90 Resimplifying inuse:
% 260.38/260.90 Done
% 260.38/260.90
% 260.38/260.90
% 260.38/260.90 Intermediate Status:
% 260.38/260.90 Generated: 388256
% 260.38/260.90 Kept: 140781
% 260.38/260.90 Inuse: 1545
% 260.38/260.90 Deleted: 1390
% 260.38/260.90 Deletedinuse: 7
% 260.38/260.90
% 260.38/260.90 Resimplifying inuse:
% 260.38/260.90 Done
% 260.38/260.90
% 260.38/260.90 Resimplifying inuse:
% 260.38/260.90 Done
% 260.38/260.90
% 260.38/260.90
% 260.38/260.90 Intermediate Status:
% 260.38/260.90 Generated: 394112
% 260.38/260.90 Kept: 142818
% 260.38/260.90 Inuse: 1569
% 260.38/260.90 Deleted: 1390
% 260.38/260.90 Deletedinuse: 7
% 260.38/260.90
% 260.38/260.90 Resimplifying inuse:
% 260.38/260.90 Done
% 260.38/260.90
% 260.38/260.90 Resimplifying inuse:
% 260.38/260.90 Done
% 260.38/260.90
% 260.38/260.90
% 260.38/260.90 Intermediate Status:
% 260.38/260.90 Generated: 406701
% 260.38/260.90 Kept: 145141
% 260.38/260.90 Inuse: 1594
% 260.38/260.90 Deleted: 1390
% 260.38/260.90 Deletedinuse: 7
% 260.38/260.90
% 260.38/260.90 Resimplifying inuse:
% 260.38/260.90 Done
% 260.38/260.90
% 260.38/260.90 Resimplifying clauses:
% 260.38/260.90 Done
% 260.38/260.90
% 260.38/260.90 Resimplifying inuse:
% 260.38/260.90 Done
% 260.38/260.90
% 260.38/260.90
% 260.38/260.90 Intermediate Status:
% 260.38/260.90 Generated: 414535
% 260.38/260.90 Kept: 149607
% 260.38/260.90 Inuse: 1614
% 260.38/260.90 Deleted: 1825
% 260.38/260.90 Deletedinuse: 7
% 260.38/260.90
% 260.38/260.90 Resimplifying inuse:
% 260.38/260.90 Done
% 260.38/260.90
% 260.38/260.90
% 260.38/260.90 Intermediate Status:
% 260.38/260.90 Generated: 419042
% 260.38/260.90 Kept: 152913
% 260.38/260.90 Inuse: 1619
% 260.38/260.90 Deleted: 1825
% 260.38/260.90 Deletedinuse: 7
% 260.38/260.90
% 260.38/260.90 Resimplifying inuse:
% 260.38/260.90 Done
% 260.38/260.90
% 260.38/260.90
% 260.38/260.90 Intermediate Status:
% 260.38/260.90 Generated: 423560
% 260.38/260.90 Kept: 156227
% 260.38/260.90 Inuse: 1624
% 260.38/260.90 Deleted: 1825
% 260.38/260.90 Deletedinuse: 7
% 260.38/260.90
% 260.38/260.90 Resimplifying inuse:
% 260.38/260.90 Done
% 260.38/260.90
% 260.38/260.90 *** allocated 4378860 integers for termspace/termends
% 260.38/260.90 *** allocated 9852435 integers for clauses
% 260.38/260.90
% 260.38/260.90 Intermediate Status:
% 260.38/260.90 Generated: 428090
% 260.38/260.90 Kept: 159547
% 260.38/260.90 Inuse: 1629
% 260.38/260.90 Deleted: 1825
% 260.38/260.90 Deletedinuse: 7
% 260.38/260.90
% 260.38/260.90 Resimplifying inuse:
% 260.38/260.90 Done
% 260.38/260.90
% 260.38/260.90 Resimplifying inuse:
% 260.38/260.90 Done
% 260.38/260.90
% 260.38/260.90
% 260.38/260.90 Intermediate Status:
% 260.38/260.90 Generated: 434030
% 260.38/260.90 Kept: 161558
% 260.38/260.90 Inuse: 1663
% 260.38/260.90 Deleted: 1826
% 260.38/260.90 Deletedinuse: 8
% 260.38/260.90
% 260.38/260.90 Resimplifying inuse:
% 260.38/260.90 Done
% 260.38/260.90
% 260.38/260.90 Resimplifying inuse:
% 260.38/260.90 Done
% 260.38/260.90
% 260.38/260.90
% 260.38/260.90 Intermediate Status:
% 260.38/260.90 Generated: 441097
% 260.38/260.90 Kept: 163792
% 260.38/260.90 Inuse: 1689
% 260.38/260.90 Deleted: 1828
% 260.38/260.90 Deletedinuse: 10
% 260.38/260.90
% 260.38/260.90 Resimplifying inuse:
% 260.38/260.90 Done
% 260.38/260.90
% 260.38/260.90 Resimplifying inuse:
% 260.38/260.90 Done
% 260.38/260.90
% 260.38/260.90 Resimplifying clauses:
% 260.38/260.90 Done
% 260.38/260.90
% 260.38/260.90
% 260.38/260.90 Intermediate Status:
% 260.38/260.90 Generated: 446892
% 260.38/260.90 Kept: 165903
% 260.38/260.90 Inuse: 1713
% 260.38/260.90 Deleted: 2216
% 260.38/260.90 Deletedinuse: 10
% 260.38/260.90
% 260.38/260.90 Resimplifying inuse:
% 260.38/260.90 Done
% 260.38/260.90
% 260.38/260.90 Resimplifying inuse:
% 260.38/260.90 Done
% 260.38/260.90
% 260.38/260.90
% 260.38/260.90 Intermediate Status:
% 260.38/260.90 Generated: 457238
% 260.38/260.90 Kept: 169034
% 260.38/260.90 Inuse: 1733
% 260.38/260.90 Deleted: 2216
% 260.38/260.90 Deletedinuse: 10
% 260.38/260.90
% 260.38/260.90 Resimplifying inuse:
% 260.38/260.90 Done
% 260.38/260.90
% 260.38/260.90 Resimplifying inuse:
% 260.38/260.90 Done
% 260.38/260.90
% 260.38/260.90
% 260.38/260.90 Intermediate Status:
% 260.38/260.90 Generated: 462461
% 260.38/260.90 Kept: 171120
% 260.38/260.90 Inuse: 1753
% 260.38/260.90 Deleted: 2216
% 260.38/260.90 Deletedinuse: 10
% 260.38/260.90
% 260.38/260.90 Resimplifying inuse:
% 260.38/260.90 Done
% 260.38/260.90
% 260.38/260.90 Resimplifying inuse:
% 260.38/260.90 Done
% 260.38/260.90
% 260.38/260.90
% 260.38/260.90 Intermediate Status:
% 260.38/260.90 Generated: 469088
% 260.38/260.90 Kept: 173415
% 260.38/260.90 Inuse: 1783
% 260.38/260.90 Deleted: 2217
% 260.38/260.90 Deletedinuse: 11
% 260.38/260.90
% 260.38/260.90 Resimplifying inuse:
% 260.38/260.90 Done
% 260.38/260.90
% 260.38/260.90 Resimplifying inuse:
% 260.38/260.90 Done
% 260.38/260.90
% 260.38/260.90
% 260.38/260.90 Intermediate Status:
% 260.38/260.90 Generated: 475391
% 260.38/260.90 Kept: 175420
% 260.38/260.90 Inuse: 1801
% 260.38/260.90 Deleted: 2217
% 260.38/260.90 Deletedinuse: 11
% 260.38/260.90
% 260.38/260.90 Resimplifying inuse:
% 260.38/260.90 Done
% 260.38/260.90
% 260.38/260.90 Resimplifying inuse:
% 260.38/260.90 Done
% 260.38/260.90
% 260.38/260.90
% 260.38/260.90 Intermediate Status:
% 260.38/260.90 Generated: 479877
% 260.38/260.90 Kept: 177627
% 260.38/260.90 Inuse: 1822
% 260.38/260.90 Deleted: 2218
% 260.38/260.90 Deletedinuse: 11
% 260.38/260.90
% 260.38/260.90 Resimplifying inuse:
% 260.38/260.90 Done
% 260.38/260.90
% 260.38/260.90 Resimplifying inuse:
% 260.38/260.90 Done
% 260.38/260.90
% 260.38/260.90
% 260.38/260.90 Intermediate Status:
% 260.38/260.90 Generated: 484263
% 260.38/260.90 Kept: 179786
% 260.38/260.90 Inuse: 1842
% 260.38/260.90 Deleted: 2218
% 260.38/260.90 Deletedinuse: 11
% 260.38/260.90
% 260.38/260.90 Resimplifying inuse:
% 260.38/260.90 Done
% 260.38/260.90
% 260.38/260.90 Resimplifying inuse:
% 260.38/260.90 Done
% 260.38/260.90
% 260.38/260.90
% 260.38/260.90 Intermediate Status:
% 260.38/260.90 Generated: 490049
% 260.38/260.90 Kept: 181826
% 260.38/260.90 Inuse: 1860
% 260.38/260.90 Deleted: 2218
% 260.38/260.90 Deletedinuse: 11
% 260.38/260.90
% 260.38/260.90 Resimplifying inuse:
% 260.38/260.90 Done
% 260.38/260.90
% 260.38/260.90
% 260.38/260.90 Intermediate Status:
% 260.38/260.90 Generated: 499860
% 260.38/260.90 Kept: 183848
% 260.38/260.90 Inuse: 1888
% 260.38/260.90 Deleted: 2218
% 260.38/260.90 Deletedinuse: 11
% 260.38/260.90
% 260.38/260.90 Resimplifying inuse:
% 260.38/260.90 Done
% 260.38/260.90
% 260.38/260.90 Resimplifying inuse:
% 260.38/260.90 Done
% 260.38/260.90
% 260.38/260.90
% 260.38/260.90 Intermediate Status:
% 260.38/260.90 Generated: 516Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------