TSTP Solution File: SWW175+1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWW175+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 23:21:02 EDT 2022
% Result : Timeout 286.71s 287.12s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SWW175+1 : TPTP v8.1.0. Released v5.2.0.
% 0.00/0.10 % Command : bliksem %s
% 0.10/0.30 % Computer : n032.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % DateTime : Sun Jun 5 06:39:18 EDT 2022
% 0.10/0.30 % CPUTime :
% 0.80/1.37 *** allocated 10000 integers for termspace/termends
% 0.80/1.37 *** allocated 10000 integers for clauses
% 0.80/1.37 *** allocated 10000 integers for justifications
% 0.80/1.37 *** allocated 15000 integers for termspace/termends
% 0.80/1.37 *** allocated 22500 integers for termspace/termends
% 0.80/1.37 *** allocated 33750 integers for termspace/termends
% 0.80/1.37 Bliksem 1.12
% 0.80/1.37
% 0.80/1.37
% 0.80/1.37 Automatic Strategy Selection
% 0.80/1.37
% 0.80/1.37 *** allocated 50625 integers for termspace/termends
% 0.80/1.37 *** allocated 75937 integers for termspace/termends
% 0.80/1.37 *** allocated 113905 integers for termspace/termends
% 0.80/1.37
% 0.80/1.37 Clauses:
% 0.80/1.37
% 0.80/1.37 { c_Int_OBit0( c_Int_OPls ) = c_Int_OPls }.
% 0.80/1.37 { ! c_Int_OPls = c_Int_OBit0( X ), c_Int_OPls = X }.
% 0.80/1.37 { ! c_Int_OPls = X, c_Int_OPls = c_Int_OBit0( X ) }.
% 0.80/1.37 { ! c_Int_OBit0( X ) = c_Int_OPls, X = c_Int_OPls }.
% 0.80/1.37 { ! X = c_Int_OPls, c_Int_OBit0( X ) = c_Int_OPls }.
% 0.80/1.37 { ! c_Int_OBit0( Y ) = c_Int_OBit1( X ) }.
% 0.80/1.37 { ! c_Int_OBit1( Y ) = c_Int_OBit0( X ) }.
% 0.80/1.37 { ! c_Int_OPls = c_Int_OBit1( X ) }.
% 0.80/1.37 { ! c_Int_OBit1( X ) = c_Int_OPls }.
% 0.80/1.37 { ! v_y____ = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.80/1.37 c_Power_Opower__class_Opower( tc_Complex_Ocomplex,
% 0.80/1.37 c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt( v_z ),
% 0.80/1.37 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.37 c_Int_OPls ) ) ) ) = v_z }.
% 0.80/1.37 { ! class_Groups_Omonoid__mult( X ), ! class_Int_Onumber( X ),
% 0.80/1.37 c_Power_Opower__class_Opower( X, c_Int_Onumber__class_Onumber__of( X, Y )
% 0.80/1.37 , c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1
% 0.80/1.37 ( c_Int_OPls ) ) ) ) = c_Groups_Otimes__class_Otimes( X,
% 0.80/1.37 c_Int_Onumber__class_Onumber__of( X, Y ),
% 0.80/1.37 c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.80/1.37 { ! class_Rings_Osemiring__1( X ), c_Power_Opower__class_Opower( X,
% 0.80/1.37 c_Groups_Ozero__class_Ozero( X ), c_Int_Onumber__class_Onumber__of(
% 0.80/1.37 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) =
% 0.80/1.37 c_Groups_Ozero__class_Ozero( X ) }.
% 0.80/1.37 { ! class_Rings_Oring__1__no__zero__divisors( X ), !
% 0.80/1.37 c_Power_Opower__class_Opower( X, Y, c_Int_Onumber__class_Onumber__of(
% 0.80/1.37 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) =
% 0.80/1.37 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 0.80/1.37 .
% 0.80/1.37 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.80/1.37 c_Groups_Ozero__class_Ozero( X ), c_Power_Opower__class_Opower( X, Y,
% 0.80/1.37 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.37 c_Int_OPls ) ) ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.80/1.37 { ! class_Groups_Omonoid__mult( X ), c_Power_Opower__class_Opower( X, Z,
% 0.80/1.37 c_Groups_Otimes__class_Otimes( tc_Nat_Onat,
% 0.80/1.37 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.37 c_Int_OPls ) ) ), Y ) ) = c_Power_Opower__class_Opower( X,
% 0.80/1.37 c_Power_Opower__class_Opower( X, Z, Y ), c_Int_Onumber__class_Onumber__of
% 0.80/1.37 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) }.
% 0.80/1.37 { ! v_y____ = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.80/1.37 { c_Groups_Ozero__class_Ozero( tc_Int_Oint ) =
% 0.80/1.37 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OPls ) }.
% 0.80/1.37 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.80/1.37 c_Groups_Otimes__class_Otimes( tc_Int_Oint, Z, Y ) ) =
% 0.80/1.37 c_Groups_Otimes__class_Otimes( X, c_Int_Onumber__class_Onumber__of( X, Z
% 0.80/1.37 ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.80/1.37 { ! class_Int_Onumber__ring( X ), c_Groups_Otimes__class_Otimes( X,
% 0.80/1.37 c_Int_Onumber__class_Onumber__of( X, Z ),
% 0.80/1.37 c_Int_Onumber__class_Onumber__of( X, Y ) ) =
% 0.80/1.37 c_Int_Onumber__class_Onumber__of( X, c_Groups_Otimes__class_Otimes(
% 0.80/1.37 tc_Int_Oint, Z, Y ) ) }.
% 0.80/1.37 { ! class_Int_Onumber__ring( X ), c_Groups_Otimes__class_Otimes( X,
% 0.80/1.37 c_Int_Onumber__class_Onumber__of( X, T ), c_Groups_Otimes__class_Otimes(
% 0.80/1.37 X, c_Int_Onumber__class_Onumber__of( X, Z ), Y ) ) =
% 0.80/1.37 c_Groups_Otimes__class_Otimes( X, c_Int_Onumber__class_Onumber__of( X,
% 0.80/1.37 c_Groups_Otimes__class_Otimes( tc_Int_Oint, T, Z ) ), Y ) }.
% 0.80/1.37 { c_Power_Opower__class_Opower( tc_Int_Oint, c_Power_Opower__class_Opower(
% 0.80/1.37 tc_Int_Oint, Z, Y ), X ) = c_Power_Opower__class_Opower( tc_Int_Oint, Z,
% 0.80/1.37 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) ) }.
% 0.80/1.37 { c_Groups_Otimes__class_Otimes( tc_Int_Oint, c_Int_OPls, X ) = c_Int_OPls
% 0.80/1.37 }.
% 0.80/1.37 { c_Groups_Otimes__class_Otimes( tc_Int_Oint, c_Int_OBit0( Y ), X ) =
% 0.80/1.37 c_Int_OBit0( c_Groups_Otimes__class_Otimes( tc_Int_Oint, Y, X ) ) }.
% 0.80/1.37 { c_Int_OPls = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.80/1.37 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.80/1.37 c_Int_OPls ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.80/1.37 { ! class_Int_Onumber__ring( X ), c_Groups_Ozero__class_Ozero( X ) =
% 0.80/1.37 c_Int_Onumber__class_Onumber__of( X, c_Int_OPls ) }.
% 0.80/1.37 { c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OPls ) =
% 0.80/1.37 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.80/1.37 { c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) =
% 0.80/1.37 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OPls ) }.
% 0.80/1.37 { ! class_Int_Onumber__ring( X ), c_Groups_Otimes__class_Otimes( X,
% 0.80/1.37 c_Int_Onumber__class_Onumber__of( X, c_Int_OBit1( c_Int_OPls ) ), Y ) = Y
% 0.80/1.37 }.
% 0.80/1.37 { ! class_Int_Onumber__ring( X ), c_Groups_Otimes__class_Otimes( X, Y,
% 0.80/1.37 c_Int_Onumber__class_Onumber__of( X, c_Int_OBit1( c_Int_OPls ) ) ) = Y }
% 0.80/1.37 .
% 0.80/1.37 { ! class_Groups_Omonoid__mult( X ), c_Power_Opower__class_Opower( X, Y,
% 0.80/1.37 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit1( c_Int_OBit1(
% 0.80/1.37 c_Int_OPls ) ) ) ) = c_Groups_Otimes__class_Otimes( X,
% 0.80/1.37 c_Groups_Otimes__class_Otimes( X, Y, Y ), Y ) }.
% 0.80/1.37 { ! class_Int_Onumber__ring( X ), ! class_Int_Oring__char__0( X ), !
% 0.80/1.37 c_Int_Onumber__class_Onumber__of( X, Z ) =
% 0.80/1.37 c_Int_Onumber__class_Onumber__of( X, Y ), Z = Y }.
% 0.80/1.37 { ! class_Int_Onumber__ring( X ), ! class_Int_Oring__char__0( X ), ! Z = Y
% 0.80/1.37 , c_Int_Onumber__class_Onumber__of( X, Z ) =
% 0.80/1.37 c_Int_Onumber__class_Onumber__of( X, Y ) }.
% 0.80/1.37 { ! class_Int_Onumber( X ), ! c_Int_Onumber__class_Onumber__of( X, Z ) = Y
% 0.80/1.37 , Y = c_Int_Onumber__class_Onumber__of( X, Z ) }.
% 0.80/1.37 { ! class_Int_Onumber( X ), ! Y = c_Int_Onumber__class_Onumber__of( X, Z )
% 0.80/1.37 , c_Int_Onumber__class_Onumber__of( X, Z ) = Y }.
% 0.80/1.37 { ! c_Int_OBit1( Y ) = c_Int_OBit1( X ), Y = X }.
% 0.80/1.37 { ! Y = X, c_Int_OBit1( Y ) = c_Int_OBit1( X ) }.
% 0.80/1.37 { ! c_Int_OBit0( Y ) = c_Int_OBit0( X ), Y = X }.
% 0.80/1.37 { ! Y = X, c_Int_OBit0( Y ) = c_Int_OBit0( X ) }.
% 0.80/1.37 { ! class_Groups_Omonoid__mult( X ), c_Power_Opower__class_Opower( X, Y,
% 0.80/1.37 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.37 c_Int_OPls ) ) ) ) = c_Groups_Otimes__class_Otimes( X, Y, Y ) }.
% 0.80/1.37 { ! class_Rings_Ocomm__semiring__1( X ), c_Power_Opower__class_Opower( X, Z
% 0.80/1.37 , c_Groups_Otimes__class_Otimes( tc_Nat_Onat,
% 0.80/1.37 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.37 c_Int_OPls ) ) ), Y ) ) = c_Groups_Otimes__class_Otimes( X,
% 0.80/1.37 c_Power_Opower__class_Opower( X, Z, Y ), c_Power_Opower__class_Opower( X
% 0.80/1.37 , Z, Y ) ) }.
% 0.80/1.37 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.80/1.37 Y, Y ) = c_Power_Opower__class_Opower( X, Y,
% 0.80/1.37 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.37 c_Int_OPls ) ) ) ) }.
% 0.80/1.37 { c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal,
% 0.80/1.37 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.80/1.37 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ),
% 0.80/1.37 c_Power_Opower__class_Opower( tc_RealDef_Oreal, X,
% 0.80/1.37 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.37 c_Int_OPls ) ) ) ) ) = c_Power_Opower__class_Opower( tc_RealDef_Oreal,
% 0.80/1.37 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal,
% 0.80/1.37 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.80/1.37 c_Int_OBit1( c_Int_OPls ) ) ), X ), c_Int_Onumber__class_Onumber__of(
% 0.80/1.37 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) }.
% 0.80/1.37 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.80/1.37 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.80/1.37 , ! c_Power_Opower__class_Opower( X, Z, c_Int_Onumber__class_Onumber__of
% 0.80/1.37 ( tc_Nat_Onat, Y ) ) = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.80/1.37 c_Groups_Ozero__class_Ozero( X ) }.
% 0.80/1.37 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.80/1.37 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.80/1.37 , ! c_Power_Opower__class_Opower( X, Z, c_Int_Onumber__class_Onumber__of
% 0.80/1.37 ( tc_Nat_Onat, Y ) ) = c_Groups_Ozero__class_Ozero( X ), !
% 0.80/1.37 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) =
% 0.80/1.37 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.80/1.37 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.80/1.37 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.80/1.37 , ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.80/1.37 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) =
% 0.80/1.37 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Power_Opower__class_Opower
% 0.80/1.37 ( X, Z, c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) ) =
% 0.80/1.37 c_Groups_Ozero__class_Ozero( X ) }.
% 0.80/1.37 { c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.80/1.37 c_Power_Opower__class_Opower( tc_RealDef_Oreal, X,
% 0.80/1.37 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.37 c_Int_OPls ) ) ) ), c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal,
% 0.80/1.37 c_Int_OBit0( c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) =
% 0.80/1.37 c_Power_Opower__class_Opower( tc_RealDef_Oreal,
% 0.80/1.37 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, X,
% 0.80/1.37 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.80/1.37 c_Int_OBit1( c_Int_OPls ) ) ) ), c_Int_Onumber__class_Onumber__of(
% 0.80/1.37 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) }.
% 0.80/1.37 { c_NthRoot_Osqrt( c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal,
% 0.80/1.37 c_Int_OBit0( c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) =
% 0.80/1.37 c_NthRoot_Osqrt( c_Power_Opower__class_Opower( tc_RealDef_Oreal,
% 0.80/1.37 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.80/1.37 c_Int_OBit1( c_Int_OPls ) ) ), c_Int_Onumber__class_Onumber__of(
% 0.80/1.37 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) }.
% 0.80/1.37 { v_z = c_Complex_Ocomplex_OComplex( v_x____, v_y____ ) }.
% 0.80/1.37 { ! class_Rings_Olinordered__idom( X ), c_Orderings_Oord__class_Oless__eq(
% 0.80/1.37 X, c_Groups_Ozero__class_Ozero( X ), c_Power_Opower__class_Opower( X, Z,
% 0.80/1.37 c_Groups_Otimes__class_Otimes( tc_Nat_Onat,
% 0.80/1.37 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.37 c_Int_OPls ) ) ), Y ) ) ) }.
% 0.80/1.37 { ! class_Rings_Ocomm__semiring__1( X ), c_Power_Opower__class_Opower( X,
% 0.80/1.37 c_Power_Opower__class_Opower( X, T, Z ), Y ) =
% 0.80/1.37 c_Power_Opower__class_Opower( X, T, c_Groups_Otimes__class_Otimes(
% 0.80/1.37 tc_Nat_Onat, Z, Y ) ) }.
% 0.80/1.37 { ! class_Groups_Omonoid__mult( X ), c_Power_Opower__class_Opower( X, T,
% 0.80/1.37 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ) ) =
% 0.80/1.37 c_Power_Opower__class_Opower( X, c_Power_Opower__class_Opower( X, T, Z )
% 0.80/1.37 , Y ) }.
% 0.80/1.37 { ! class_Groups_Omonoid__mult( X ), c_Power_Opower__class_Opower( X, Z,
% 0.80/1.37 c_Nat_OSuc( c_Groups_Otimes__class_Otimes( tc_Nat_Onat,
% 0.80/1.37 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.37 c_Int_OPls ) ) ), Y ) ) ) = c_Groups_Otimes__class_Otimes( X, Z,
% 0.80/1.37 c_Power_Opower__class_Opower( X, c_Power_Opower__class_Opower( X, Z, Y )
% 0.80/1.37 , c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1
% 0.80/1.37 ( c_Int_OPls ) ) ) ) ) }.
% 0.80/1.37 { ! class_Int_Onumber__ring( X ), c_Power_Opower__class_Opower( X,
% 0.80/1.37 c_Groups_Oplus__class_Oplus( X, Z, Y ), c_Int_Onumber__class_Onumber__of
% 0.80/1.37 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) =
% 0.80/1.37 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X,
% 0.80/1.37 c_Power_Opower__class_Opower( X, Z, c_Int_Onumber__class_Onumber__of(
% 0.80/1.37 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ),
% 0.80/1.37 c_Power_Opower__class_Opower( X, Y, c_Int_Onumber__class_Onumber__of(
% 0.80/1.37 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ),
% 0.80/1.37 c_Groups_Otimes__class_Otimes( X, c_Groups_Otimes__class_Otimes( X,
% 0.80/1.37 c_Int_Onumber__class_Onumber__of( X, c_Int_OBit0( c_Int_OBit1( c_Int_OPls
% 0.80/1.37 ) ) ), Z ), Y ) ) }.
% 0.80/1.37 { c_NthRoot_Osqrt( c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal,
% 0.80/1.37 c_Int_OBit0( c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) =
% 0.80/1.37 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.80/1.37 c_Int_OBit1( c_Int_OPls ) ) ) }.
% 0.80/1.37 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.80/1.37 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.80/1.37 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.80/1.37 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_NthRoot_Osqrt(
% 0.80/1.37 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.80/1.37 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Y, Y ),
% 0.80/1.37 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, X ) ) ), Y ),
% 0.80/1.37 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.80/1.37 c_Int_OBit1( c_Int_OPls ) ) ) ) ) }.
% 0.80/1.37 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.80/1.37 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.80/1.37 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.80/1.37 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_NthRoot_Osqrt(
% 0.80/1.37 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.80/1.37 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, v_x____, v_x____ ),
% 0.80/1.37 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, v_y____, v_y____ ) ) ),
% 0.80/1.37 v_x____ ), c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal,
% 0.80/1.37 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) }.
% 0.80/1.37 { c_NthRoot_Osqrt( c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.80/1.37 c_Power_Opower__class_Opower( tc_RealDef_Oreal,
% 0.80/1.37 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_NthRoot_Osqrt(
% 0.80/1.37 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.80/1.37 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, v_x____, v_x____ ),
% 0.80/1.37 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, v_y____, v_y____ ) ) ),
% 0.80/1.37 v_x____ ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0(
% 0.80/1.37 c_Int_OBit1( c_Int_OPls ) ) ) ), c_Int_Onumber__class_Onumber__of(
% 0.80/1.37 tc_RealDef_Oreal, c_Int_OBit0( c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) )
% 0.80/1.37 ) ) ) = c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.80/1.37 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_NthRoot_Osqrt(
% 0.80/1.37 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.80/1.37 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, v_x____, v_x____ ),
% 0.80/1.37 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, v_y____, v_y____ ) ) ),
% 0.80/1.37 v_x____ ), c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal,
% 0.80/1.37 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) }.
% 0.80/1.37 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.80/1.37 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt(
% 0.80/1.37 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.80/1.37 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Y, Y ),
% 0.80/1.37 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, X ) ) ) ) }.
% 0.80/1.37 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, c_NthRoot_Osqrt(
% 0.80/1.37 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.80/1.37 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Y, Y ),
% 0.80/1.37 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, X ) ) ) ) }.
% 0.80/1.37 { c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) = X }.
% 0.80/1.37 { c_NthRoot_Osqrt( c_Power_Opower__class_Opower( tc_RealDef_Oreal, Y, X ) )
% 0.80/1.37 = c_Power_Opower__class_Opower( tc_RealDef_Oreal, c_NthRoot_Osqrt( Y ),
% 0.80/1.37 X ) }.
% 0.80/1.37 { c_NthRoot_Osqrt( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Y, X )
% 0.80/1.37 ) = c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, c_NthRoot_Osqrt( Y
% 0.80/1.37 ), c_NthRoot_Osqrt( X ) ) }.
% 0.80/1.37 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.80/1.37 tc_Int_Oint ), X ) = X }.
% 0.80/1.37 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.80/1.37 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ),
% 0.80/1.37 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.80/1.37 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ) }.
% 0.80/1.37 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.80/1.37 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.80/1.37 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.80/1.37 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ) }
% 0.80/1.37 .
% 0.80/1.37 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero
% 0.80/1.37 ( tc_Int_Oint ) ) = X }.
% 0.80/1.37 { c_Groups_Otimes__class_Otimes( tc_Int_Oint, Y, X ) =
% 0.80/1.37 c_Groups_Otimes__class_Otimes( tc_Int_Oint, X, Y ) }.
% 0.80/1.37 { c_Power_Opower__class_Opower( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus
% 0.80/1.37 ( tc_Nat_Onat, Y, X ) ) = c_Groups_Otimes__class_Otimes( tc_Int_Oint,
% 0.80/1.37 c_Power_Opower__class_Opower( tc_Int_Oint, Z, Y ),
% 0.80/1.37 c_Power_Opower__class_Opower( tc_Int_Oint, Z, X ) ) }.
% 0.80/1.37 { c_Groups_Otimes__class_Otimes( tc_Int_Oint, Z,
% 0.80/1.37 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) =
% 0.80/1.37 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Otimes__class_Otimes(
% 0.80/1.37 tc_Int_Oint, Z, Y ), c_Groups_Otimes__class_Otimes( tc_Int_Oint, Z, X ) )
% 0.80/1.37 }.
% 0.80/1.37 { c_Power_Opower__class_Opower( tc_Nat_Onat, c_Nat_OSuc(
% 0.80/1.37 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) = c_Nat_OSuc(
% 0.80/1.37 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.80/1.37 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Osqrt( X
% 0.80/1.37 ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.80/1.37 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.80/1.37 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.80/1.37 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.80/1.37 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.80/1.37 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Osqrt( X )
% 0.80/1.37 , c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.80/1.37 { c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.80/1.37 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 0.80/1.37 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) =
% 0.80/1.37 c_Int_Onumber__class_Onumber__of( tc_Int_Oint,
% 0.80/1.37 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 0.80/1.37 { c_Groups_Otimes__class_Otimes( tc_Int_Oint,
% 0.80/1.37 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 0.80/1.37 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) =
% 0.80/1.37 c_Int_Onumber__class_Onumber__of( tc_Int_Oint,
% 0.80/1.37 c_Groups_Otimes__class_Otimes( tc_Int_Oint, Y, X ) ) }.
% 0.80/1.37 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.80/1.37 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 0.80/1.37 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ),
% 0.80/1.37 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 0.80/1.37 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.80/1.37 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.80/1.37 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 0.80/1.37 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) }.
% 0.80/1.37 { c_Groups_Otimes__class_Otimes( tc_Int_Oint, c_Groups_Otimes__class_Otimes
% 0.80/1.37 ( tc_Int_Oint, Z, Y ), X ) = c_Groups_Otimes__class_Otimes( tc_Int_Oint,
% 0.80/1.37 Z, c_Groups_Otimes__class_Otimes( tc_Int_Oint, Y, X ) ) }.
% 0.80/1.37 { c_Groups_Otimes__class_Otimes( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.80/1.37 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.80/1.37 c_Groups_Otimes__class_Otimes( tc_Int_Oint, Z, X ),
% 0.80/1.37 c_Groups_Otimes__class_Otimes( tc_Int_Oint, Y, X ) ) }.
% 0.80/1.38 { ! c_Power_Opower__class_Opower( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = c_Nat_OSuc(
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.80/1.38 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.80/1.38 c_Power_Opower__class_Opower( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.80/1.38 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 0.80/1.38 c_Power_Opower__class_Opower( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.80/1.38 { c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Y, X ),
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Y, Y ) ) =
% 0.80/1.38 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, X, Y ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ) }
% 0.80/1.38 .
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), ! c_NthRoot_Osqrt(
% 0.80/1.38 X ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 0.80/1.38 c_Power_Opower__class_Opower( tc_Nat_Onat, X, Y ) ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Osqrt( Y )
% 0.80/1.38 , c_NthRoot_Osqrt( X ) ) }.
% 0.80/1.38 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.80/1.38 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.80/1.38 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X
% 0.80/1.38 , U, Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.80/1.38 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.80/1.38 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.80/1.38 ( X, c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 0.80/1.38 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.80/1.38 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.80/1.38 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Osqrt( Y
% 0.80/1.38 ), c_NthRoot_Osqrt( X ) ), c_Orderings_Oord__class_Oless__eq(
% 0.80/1.38 tc_RealDef_Oreal, Y, X ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Osqrt( Y )
% 0.80/1.38 , c_NthRoot_Osqrt( X ) ) }.
% 0.80/1.38 { ! c_NthRoot_Osqrt( Y ) = c_NthRoot_Osqrt( X ), Y = X }.
% 0.80/1.38 { ! Y = X, c_NthRoot_Osqrt( Y ) = c_NthRoot_Osqrt( X ) }.
% 0.80/1.38 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.80/1.38 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.80/1.38 ( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) }.
% 0.80/1.38 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.80/1.38 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.80/1.38 ( X, Z, c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.80/1.38 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.80/1.38 , Y ) = c_Groups_Oplus__class_Oplus( X, Y, Z ) }.
% 0.80/1.38 { c_NthRoot_Osqrt( c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, Y, X
% 0.80/1.38 ) ) = c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, c_NthRoot_Osqrt
% 0.80/1.38 ( Y ), c_NthRoot_Osqrt( X ) ) }.
% 0.80/1.38 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( X, T ), c_Groups_Oplus__class_Oplus( X
% 0.80/1.38 , c_Int_Onumber__class_Onumber__of( X, Z ), Y ) ) =
% 0.80/1.38 c_Groups_Oplus__class_Oplus( X, c_Int_Onumber__class_Onumber__of( X,
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_Int_Oint, T, Z ) ), Y ) }.
% 0.80/1.38 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( X, Z ),
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( X, Y ) ) =
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( X, c_Groups_Oplus__class_Oplus(
% 0.80/1.38 tc_Int_Oint, Z, Y ) ) }.
% 0.80/1.38 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ) =
% 0.80/1.38 c_Groups_Oplus__class_Oplus( X, c_Int_Onumber__class_Onumber__of( X, Z )
% 0.80/1.38 , c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.80/1.38 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 0.80/1.38 , Z ), c_Int_Onumber__class_Onumber__of( X, Y ) ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z, Y ) }.
% 0.80/1.38 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z, Y ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 0.80/1.38 , Z ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.80/1.38 { ! c_NthRoot_Osqrt( X ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal )
% 0.80/1.38 , X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.80/1.38 { ! X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X
% 0.80/1.38 ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.80/1.38 { c_NthRoot_Osqrt( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.80/1.38 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.80/1.38 ( X ), ! Z = c_Groups_Oplus__class_Oplus( X, Z, Y ), Y =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ) }.
% 0.80/1.38 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.80/1.38 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.80/1.38 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 0.80/1.38 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.80/1.38 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.80/1.38 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.80/1.38 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.80/1.38 ( X ), ! c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X
% 0.80/1.38 , U, T ), c_Groups_Otimes__class_Otimes( X, Z, Y ) ) =
% 0.80/1.38 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, U, Y )
% 0.80/1.38 , c_Groups_Otimes__class_Otimes( X, Z, T ) ), U = Z, T = Y }.
% 0.80/1.38 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.80/1.38 ( X ), ! U = Z, c_Groups_Oplus__class_Oplus( X,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, U, T ), c_Groups_Otimes__class_Otimes(
% 0.80/1.38 X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, U, Y ), c_Groups_Otimes__class_Otimes(
% 0.80/1.38 X, Z, T ) ) }.
% 0.80/1.38 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.80/1.38 ( X ), ! T = Y, c_Groups_Oplus__class_Oplus( X,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, U, T ), c_Groups_Otimes__class_Otimes(
% 0.80/1.38 X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, U, Y ), c_Groups_Otimes__class_Otimes(
% 0.80/1.38 X, Z, T ) ) }.
% 0.80/1.38 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, T, Z ), c_Groups_Otimes__class_Otimes(
% 0.80/1.38 X, Y, Z ) ) = c_Groups_Otimes__class_Otimes( X,
% 0.80/1.38 c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 0.80/1.38 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.80/1.38 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.80/1.38 ( X, c_Groups_Otimes__class_Otimes( X, T, Y ),
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, Z, Y ) ) }.
% 0.80/1.38 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.80/1.38 ( X ), U = T, Z = Y, ! c_Groups_Oplus__class_Oplus( X,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, U, Z ), c_Groups_Otimes__class_Otimes(
% 0.80/1.38 X, T, Y ) ) = c_Groups_Oplus__class_Oplus( X,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, U, Y ), c_Groups_Otimes__class_Otimes(
% 0.80/1.38 X, T, Z ) ) }.
% 0.80/1.38 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.80/1.38 ( X ), c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.80/1.38 U, Z ), c_Groups_Otimes__class_Otimes( X, T, Y ) ) =
% 0.80/1.38 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, U, Y )
% 0.80/1.38 , c_Groups_Otimes__class_Otimes( X, T, Z ) ), ! U = T }.
% 0.80/1.38 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.80/1.38 ( X ), c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.80/1.38 U, Z ), c_Groups_Otimes__class_Otimes( X, T, Y ) ) =
% 0.80/1.38 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, U, Y )
% 0.80/1.38 , c_Groups_Otimes__class_Otimes( X, T, Z ) ), ! Z = Y }.
% 0.80/1.38 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.80/1.38 T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.80/1.38 ( X, c_Groups_Otimes__class_Otimes( X, T, Z ),
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, T, Y ) ) }.
% 0.80/1.38 { ! class_Fields_Ofield__inverse__zero( X ), c_Power_Opower__class_Opower(
% 0.80/1.38 X, c_Rings_Oinverse__class_Odivide( X, T, Z ), Y ) =
% 0.80/1.38 c_Rings_Oinverse__class_Odivide( X, c_Power_Opower__class_Opower( X, T, Y
% 0.80/1.38 ), c_Power_Opower__class_Opower( X, Z, Y ) ) }.
% 0.80/1.38 { ! class_Rings_Olinordered__semidom( X ), ! c_Power_Opower__class_Opower(
% 0.80/1.38 X, Z, c_Nat_OSuc( T ) ) = c_Power_Opower__class_Opower( X, Y, c_Nat_OSuc
% 0.80/1.38 ( T ) ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.80/1.38 ), Z = Y }.
% 0.80/1.38 { ! class_Rings_Olinordered__semidom( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Power_Opower__class_Opower( X, Z
% 0.80/1.38 , c_Nat_OSuc( T ) ), c_Power_Opower__class_Opower( X, Y, c_Nat_OSuc( T )
% 0.80/1.38 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.80/1.38 ( X ), Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.80/1.38 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, Z, Z ), c_Groups_Otimes__class_Otimes(
% 0.80/1.38 X, Y, Y ) ), c_Groups_Ozero__class_Ozero( X ) ), Z =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ) }.
% 0.80/1.38 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, Z, Z ), c_Groups_Otimes__class_Otimes(
% 0.80/1.38 X, Y, Y ) ), c_Groups_Ozero__class_Ozero( X ) ), Y =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ) }.
% 0.80/1.38 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.80/1.38 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, Z, Z ), c_Groups_Otimes__class_Otimes(
% 0.80/1.38 X, Y, Y ) ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.80/1.38 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.80/1.38 X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, Z, Z ), c_Groups_Otimes__class_Otimes(
% 0.80/1.38 X, Y, Y ) ) ) }.
% 0.80/1.38 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, c_NthRoot_Osqrt(
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.80/1.38 c_Power_Opower__class_Opower( tc_RealDef_Oreal, Y,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.38 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal, X,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.38 c_Int_OPls ) ) ) ) ) ) ) }.
% 0.80/1.38 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, c_NthRoot_Osqrt(
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.80/1.38 c_Power_Opower__class_Opower( tc_RealDef_Oreal, X,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.38 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal, Y,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.38 c_Int_OPls ) ) ) ) ) ) ) }.
% 0.80/1.38 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Osqrt(
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.80/1.38 c_Power_Opower__class_Opower( tc_RealDef_Oreal,
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, T, Z ),
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.38 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal,
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.38 c_Int_OPls ) ) ) ) ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.80/1.38 c_NthRoot_Osqrt( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.80/1.38 c_Power_Opower__class_Opower( tc_RealDef_Oreal, T,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.38 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal, Y,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.38 c_Int_OPls ) ) ) ) ) ), c_NthRoot_Osqrt( c_Groups_Oplus__class_Oplus(
% 0.80/1.38 tc_RealDef_Oreal, c_Power_Opower__class_Opower( tc_RealDef_Oreal, Z,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.38 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal, X,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.38 c_Int_OPls ) ) ) ) ) ) ) ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, c_Int_OPls ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, c_Int_OPls ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) }.
% 0.80/1.38 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.80/1.38 c_Groups_Oplus__class_Oplus( X, Y, Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.80/1.38 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.80/1.38 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.80/1.38 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.80/1.38 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Int_OPls, X ) = X }.
% 0.80/1.38 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Int_OPls ) = X }.
% 0.80/1.38 { c_Int_OBit0( X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, X ) }.
% 0.80/1.38 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Int_OBit0( Y ), c_Int_OBit0(
% 0.80/1.38 X ) ) = c_Int_OBit0( c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }
% 0.80/1.38 .
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( Y ),
% 0.80/1.38 c_Int_OBit1( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 0.80/1.38 ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( Y ),
% 0.80/1.38 c_Int_OBit1( X ) ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( Y ),
% 0.80/1.38 c_Int_OBit1( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 0.80/1.38 ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( Y ),
% 0.80/1.38 c_Int_OBit1( X ) ) }.
% 0.80/1.38 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, c_Int_OPls )
% 0.80/1.38 }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.80/1.38 c_Int_OBit0( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 0.80/1.38 ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.80/1.38 c_Int_OBit0( X ) ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.80/1.38 c_Int_OBit0( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 0.80/1.38 ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.80/1.38 c_Int_OBit0( X ) ) }.
% 0.80/1.38 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.80/1.38 c_Power_Opower__class_Opower( X, c_Rings_Oinverse__class_Odivide( X, T, Y
% 0.80/1.38 ), Z ) = c_Rings_Oinverse__class_Odivide( X,
% 0.80/1.38 c_Power_Opower__class_Opower( X, T, Z ), c_Power_Opower__class_Opower( X
% 0.80/1.38 , Y, Z ) ) }.
% 0.80/1.38 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.80/1.38 ( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! W = U, T = Z, !
% 0.80/1.38 c_Groups_Oplus__class_Oplus( X, W, c_Groups_Otimes__class_Otimes( X, Y, T
% 0.80/1.38 ) ) = c_Groups_Oplus__class_Oplus( X, U, c_Groups_Otimes__class_Otimes(
% 0.80/1.38 X, Y, Z ) ) }.
% 0.80/1.38 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt(
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.80/1.38 c_Power_Opower__class_Opower( tc_RealDef_Oreal, Y,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.38 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal, X,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.38 c_Int_OPls ) ) ) ) ) ) ) }.
% 0.80/1.38 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt(
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal,
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.80/1.38 c_Power_Opower__class_Opower( tc_RealDef_Oreal, T,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.38 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal, Z,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.38 c_Int_OPls ) ) ) ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.80/1.38 c_Power_Opower__class_Opower( tc_RealDef_Oreal, Y,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.38 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal, X,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.38 c_Int_OPls ) ) ) ) ) ) ) ) }.
% 0.80/1.38 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ),
% 0.80/1.38 c_Power_Opower__class_Opower( X, c_Groups_Ozero__class_Ozero( X ),
% 0.80/1.38 c_Nat_OSuc( Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.80/1.38 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.80/1.38 c_Power_Opower__class_Opower( X, Z, Y ), Z ) =
% 0.80/1.38 c_Power_Opower__class_Opower( X, Z, c_Nat_OSuc( Y ) ) }.
% 0.80/1.38 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.80/1.38 Z, c_Power_Opower__class_Opower( X, Z, Y ) ) =
% 0.80/1.38 c_Power_Opower__class_Opower( X, Z, c_Nat_OSuc( Y ) ) }.
% 0.80/1.38 { ! class_Groups_Omonoid__mult( X ), c_Power_Opower__class_Opower( X, Z,
% 0.80/1.38 c_Nat_OSuc( Y ) ) = c_Groups_Otimes__class_Otimes( X,
% 0.80/1.38 c_Power_Opower__class_Opower( X, Z, Y ), Z ) }.
% 0.80/1.38 { ! class_Rings_Ocomm__semiring__1( X ), c_Power_Opower__class_Opower( X, Z
% 0.80/1.38 , c_Nat_OSuc( Y ) ) = c_Groups_Otimes__class_Otimes( X, Z,
% 0.80/1.38 c_Power_Opower__class_Opower( X, Z, Y ) ) }.
% 0.80/1.38 { ! class_Power_Opower( X ), c_Power_Opower__class_Opower( X, Z, c_Nat_OSuc
% 0.80/1.38 ( Y ) ) = c_Groups_Otimes__class_Otimes( X, Z,
% 0.80/1.38 c_Power_Opower__class_Opower( X, Z, Y ) ) }.
% 0.80/1.38 { ! class_Rings_Olinordered__semidom( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.80/1.38 ), c_Orderings_Oord__class_Oless__eq( X, c_Power_Opower__class_Opower( X
% 0.80/1.38 , Z, T ), c_Power_Opower__class_Opower( X, Y, T ) ) }.
% 0.80/1.38 { ! class_Rings_Olinordered__semidom( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.80/1.38 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.80/1.38 ), c_Power_Opower__class_Opower( X, Y, Z ) ) }.
% 0.80/1.38 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.80/1.38 c_Power_Opower__class_Opower( X, T, Z ), c_Power_Opower__class_Opower( X
% 0.80/1.38 , T, Y ) ) = c_Power_Opower__class_Opower( X, T,
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ) }.
% 0.80/1.38 { ! class_Groups_Omonoid__mult( X ), c_Power_Opower__class_Opower( X, T,
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ) =
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, c_Power_Opower__class_Opower( X, T, Z )
% 0.80/1.38 , c_Power_Opower__class_Opower( X, T, Y ) ) }.
% 0.80/1.38 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( X, Y ) ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, Y ) }.
% 0.80/1.38 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, Y ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.80/1.38 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 0.80/1.38 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, c_Int_OPls ) }.
% 0.80/1.38 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, c_Int_OPls ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 0.80/1.38 , Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.80/1.38 { c_Power_Opower__class_Opower( tc_RealDef_Oreal, c_NthRoot_Osqrt(
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal,
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.80/1.38 c_Power_Opower__class_Opower( tc_RealDef_Oreal, T,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.38 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal, Z,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.38 c_Int_OPls ) ) ) ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.80/1.38 c_Power_Opower__class_Opower( tc_RealDef_Oreal, Y,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.38 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal, X,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.38 c_Int_OPls ) ) ) ) ) ) ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 0.80/1.38 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) =
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal,
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.80/1.38 c_Power_Opower__class_Opower( tc_RealDef_Oreal, T,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.38 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal, Z,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.38 c_Int_OPls ) ) ) ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.80/1.38 c_Power_Opower__class_Opower( tc_RealDef_Oreal, Y,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.38 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal, X,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.38 c_Int_OPls ) ) ) ) ) ) }.
% 0.80/1.38 { c_Nat_OSuc( c_Nat_OSuc( c_Nat_OSuc( X ) ) ) = c_Groups_Oplus__class_Oplus
% 0.80/1.38 ( tc_Nat_Onat, c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit1
% 0.80/1.38 ( c_Int_OBit1( c_Int_OPls ) ) ), X ) }.
% 0.80/1.38 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt(
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.80/1.38 c_Int_OBit1( c_Int_OPls ) ) ) ) ) }.
% 0.80/1.38 { ! c_NthRoot_Osqrt( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.80/1.38 c_Power_Opower__class_Opower( tc_RealDef_Oreal, Y,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.38 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal, X,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.38 c_Int_OPls ) ) ) ) ) ) = Y, X = c_Groups_Ozero__class_Ozero(
% 0.80/1.38 tc_RealDef_Oreal ) }.
% 0.80/1.38 { ! c_NthRoot_Osqrt( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.80/1.38 c_Power_Opower__class_Opower( tc_RealDef_Oreal, X,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.38 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal, Y,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.38 c_Int_OPls ) ) ) ) ) ) = Y, X = c_Groups_Ozero__class_Ozero(
% 0.80/1.38 tc_RealDef_Oreal ) }.
% 0.80/1.38 { ! c_Power_Opower__class_Opower( tc_RealDef_Oreal, c_NthRoot_Osqrt( X ),
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.38 c_Int_OPls ) ) ) ) = X, c_Orderings_Oord__class_Oless__eq(
% 0.80/1.38 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ) }
% 0.80/1.38 .
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.80/1.38 c_Power_Opower__class_Opower( tc_RealDef_Oreal, c_NthRoot_Osqrt( X ),
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.38 c_Int_OPls ) ) ) ) = X }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.80/1.38 c_Power_Opower__class_Opower( tc_RealDef_Oreal, c_NthRoot_Osqrt( X ),
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.38 c_Int_OPls ) ) ) ) = X }.
% 0.80/1.38 { ! c_Power_Opower__class_Opower( tc_RealDef_Oreal, Y,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.38 c_Int_OPls ) ) ) ) = X, ! c_Orderings_Oord__class_Oless__eq(
% 0.80/1.38 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.80/1.38 c_NthRoot_Osqrt( X ) = Y }.
% 0.80/1.38 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.38 c_Int_OPls ) ) ) ) = c_Nat_OSuc( c_Nat_OSuc( X ) ) }.
% 0.80/1.38 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.38 c_Int_OPls ) ) ), X ) = c_Nat_OSuc( c_Nat_OSuc( X ) ) }.
% 0.80/1.38 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.80/1.38 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, Z, Z )
% 0.80/1.38 , c_Groups_Otimes__class_Otimes( X, Y, Y ) ) =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.80/1.38 .
% 0.80/1.38 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.80/1.38 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, Z, Z )
% 0.80/1.38 , c_Groups_Otimes__class_Otimes( X, Y, Y ) ) =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 0.80/1.38 .
% 0.80/1.38 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.80/1.38 , c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, Z, Z
% 0.80/1.38 ), c_Groups_Otimes__class_Otimes( X, Y, Y ) ) =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ) }.
% 0.80/1.38 { ! class_Int_Onumber( X ), ! class_Rings_Osemiring( X ),
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.80/1.38 , c_Int_Onumber__class_Onumber__of( X, Y ) ) =
% 0.80/1.38 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, T,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( X, Y ) ), c_Groups_Otimes__class_Otimes
% 0.80/1.38 ( X, Z, c_Int_Onumber__class_Onumber__of( X, Y ) ) ) }.
% 0.80/1.38 { ! class_Int_Onumber( X ), ! class_Rings_Osemiring( X ),
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, c_Int_Onumber__class_Onumber__of( X, T
% 0.80/1.38 ), c_Groups_Oplus__class_Oplus( X, Z, Y ) ) =
% 0.80/1.38 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( X, T ), Z ),
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, c_Int_Onumber__class_Onumber__of( X, T
% 0.80/1.38 ), Y ) ) }.
% 0.80/1.38 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( X, c_Int_OPls ) ) = Y }.
% 0.80/1.38 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( X, c_Int_OPls ), Y ) = Y }.
% 0.80/1.38 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Int_OBit0( Y ), c_Int_OBit1(
% 0.80/1.38 X ) ) = c_Int_OBit1( c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }
% 0.80/1.38 .
% 0.80/1.38 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Int_OBit1( Y ), c_Int_OBit0(
% 0.80/1.38 X ) ) = c_Int_OBit1( c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }
% 0.80/1.38 .
% 0.80/1.38 { c_Groups_Otimes__class_Otimes( tc_Int_Oint, c_Int_OBit1( Y ), X ) =
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Int_OBit0(
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_Int_Oint, Y, X ) ), X ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, c_Int_OBit1
% 0.80/1.38 ( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, X )
% 0.80/1.38 }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, X ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, c_Int_OBit1(
% 0.80/1.38 X ) ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.80/1.38 c_Int_OBit1( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 0.80/1.38 ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.80/1.38 c_Int_OBit1( X ) ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.80/1.38 c_Int_OBit1( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 0.80/1.38 ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.80/1.38 c_Int_OBit1( X ) ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, c_Int_OBit0
% 0.80/1.38 ( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, X )
% 0.80/1.38 }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, X ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, c_Int_OBit0(
% 0.80/1.38 X ) ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( X ),
% 0.80/1.38 c_Int_OPls ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.80/1.38 c_Int_OPls ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, c_Int_OPls ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( X ),
% 0.80/1.38 c_Int_OPls ) }.
% 0.80/1.38 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) =
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, c_Int_OPls ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, c_Int_OPls ),
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) =
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) }.
% 0.80/1.38 { ! c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, c_Int_OPls ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, c_Int_OPls ),
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.80/1.38 { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), !
% 0.80/1.38 c_Rings_Oinverse__class_Odivide( X, T, c_Int_Onumber__class_Onumber__of(
% 0.80/1.38 X, Z ) ) = Y, alpha34( X, Y, Z, T ) }.
% 0.80/1.38 { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), !
% 0.80/1.38 c_Rings_Oinverse__class_Odivide( X, T, c_Int_Onumber__class_Onumber__of(
% 0.80/1.38 X, Z ) ) = Y, alpha1( X, Y, Z ) }.
% 0.80/1.38 { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), !
% 0.80/1.38 alpha34( X, Y, Z, T ), ! alpha1( X, Y, Z ),
% 0.80/1.38 c_Rings_Oinverse__class_Odivide( X, T, c_Int_Onumber__class_Onumber__of(
% 0.80/1.38 X, Z ) ) = Y }.
% 0.80/1.38 { ! alpha34( X, Y, Z, T ), c_Int_Onumber__class_Onumber__of( X, Z ) =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ), T = c_Groups_Otimes__class_Otimes( X, Y
% 0.80/1.38 , c_Int_Onumber__class_Onumber__of( X, Z ) ) }.
% 0.80/1.38 { ! c_Int_Onumber__class_Onumber__of( X, Z ) = c_Groups_Ozero__class_Ozero
% 0.80/1.38 ( X ), alpha34( X, Y, Z, T ) }.
% 0.80/1.38 { ! T = c_Groups_Otimes__class_Otimes( X, Y,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( X, Z ) ), alpha34( X, Y, Z, T ) }.
% 0.80/1.38 { ! alpha1( X, Y, Z ), ! c_Int_Onumber__class_Onumber__of( X, Z ) =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 0.80/1.38 .
% 0.80/1.38 { c_Int_Onumber__class_Onumber__of( X, Z ) = c_Groups_Ozero__class_Ozero( X
% 0.80/1.38 ), alpha1( X, Y, Z ) }.
% 0.80/1.38 { ! Y = c_Groups_Ozero__class_Ozero( X ), alpha1( X, Y, Z ) }.
% 0.80/1.38 { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), !
% 0.80/1.38 c_Rings_Oinverse__class_Odivide( X, T, Z ) =
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( X, Y ), alpha35( X, Y, Z, T ) }.
% 0.80/1.38 { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), !
% 0.80/1.38 c_Rings_Oinverse__class_Odivide( X, T, Z ) =
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( X, Y ), alpha2( X, Y, Z ) }.
% 0.80/1.38 { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), !
% 0.80/1.38 alpha35( X, Y, Z, T ), ! alpha2( X, Y, Z ),
% 0.80/1.38 c_Rings_Oinverse__class_Odivide( X, T, Z ) =
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( X, Y ) }.
% 0.80/1.38 { ! alpha35( X, Y, Z, T ), Z = c_Groups_Ozero__class_Ozero( X ), T =
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, c_Int_Onumber__class_Onumber__of( X, Y
% 0.80/1.38 ), Z ) }.
% 0.80/1.38 { ! Z = c_Groups_Ozero__class_Ozero( X ), alpha35( X, Y, Z, T ) }.
% 0.80/1.38 { ! T = c_Groups_Otimes__class_Otimes( X, c_Int_Onumber__class_Onumber__of
% 0.80/1.38 ( X, Y ), Z ), alpha35( X, Y, Z, T ) }.
% 0.80/1.38 { ! alpha2( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.80/1.38 ) }.
% 0.80/1.38 { Z = c_Groups_Ozero__class_Ozero( X ), alpha2( X, Y, Z ) }.
% 0.80/1.38 { ! c_Int_Onumber__class_Onumber__of( X, Y ) = c_Groups_Ozero__class_Ozero
% 0.80/1.38 ( X ), alpha2( X, Y, Z ) }.
% 0.80/1.38 { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), !
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( X, T ) =
% 0.80/1.38 c_Rings_Oinverse__class_Odivide( X, Z, Y ), alpha36( X, Y, Z, T ) }.
% 0.80/1.38 { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), !
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( X, T ) =
% 0.80/1.38 c_Rings_Oinverse__class_Odivide( X, Z, Y ), alpha3( X, Y, T ) }.
% 0.80/1.38 { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), !
% 0.80/1.38 alpha36( X, Y, Z, T ), ! alpha3( X, Y, T ),
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( X, T ) =
% 0.80/1.38 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.80/1.38 { ! alpha36( X, Y, Z, T ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, c_Int_Onumber__class_Onumber__of( X, T
% 0.80/1.38 ), Y ) = Z }.
% 0.80/1.38 { ! Y = c_Groups_Ozero__class_Ozero( X ), alpha36( X, Y, Z, T ) }.
% 0.80/1.38 { ! c_Groups_Otimes__class_Otimes( X, c_Int_Onumber__class_Onumber__of( X,
% 0.80/1.38 T ), Y ) = Z, alpha36( X, Y, Z, T ) }.
% 0.80/1.38 { ! alpha3( X, Y, Z ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( X, Z ) = c_Groups_Ozero__class_Ozero( X
% 0.80/1.38 ) }.
% 0.80/1.38 { Y = c_Groups_Ozero__class_Ozero( X ), alpha3( X, Y, Z ) }.
% 0.80/1.38 { ! c_Int_Onumber__class_Onumber__of( X, Z ) = c_Groups_Ozero__class_Ozero
% 0.80/1.38 ( X ), alpha3( X, Y, Z ) }.
% 0.80/1.38 { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), ! T
% 0.80/1.38 = c_Rings_Oinverse__class_Odivide( X, Z, c_Int_Onumber__class_Onumber__of
% 0.80/1.38 ( X, Y ) ), alpha37( X, Y, Z, T ) }.
% 0.80/1.38 { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), ! T
% 0.80/1.38 = c_Rings_Oinverse__class_Odivide( X, Z, c_Int_Onumber__class_Onumber__of
% 0.80/1.38 ( X, Y ) ), alpha4( X, Y, T ) }.
% 0.80/1.38 { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), !
% 0.80/1.38 alpha37( X, Y, Z, T ), ! alpha4( X, Y, T ), T =
% 0.80/1.38 c_Rings_Oinverse__class_Odivide( X, Z, c_Int_Onumber__class_Onumber__of(
% 0.80/1.38 X, Y ) ) }.
% 0.80/1.38 { ! alpha37( X, Y, Z, T ), c_Int_Onumber__class_Onumber__of( X, Y ) =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ), c_Groups_Otimes__class_Otimes( X, T,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( X, Y ) ) = Z }.
% 0.80/1.38 { ! c_Int_Onumber__class_Onumber__of( X, Y ) = c_Groups_Ozero__class_Ozero
% 0.80/1.38 ( X ), alpha37( X, Y, Z, T ) }.
% 0.80/1.38 { ! c_Groups_Otimes__class_Otimes( X, T, c_Int_Onumber__class_Onumber__of(
% 0.80/1.38 X, Y ) ) = Z, alpha37( X, Y, Z, T ) }.
% 0.80/1.38 { ! alpha4( X, Y, Z ), ! c_Int_Onumber__class_Onumber__of( X, Y ) =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.80/1.38 .
% 0.80/1.38 { c_Int_Onumber__class_Onumber__of( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.80/1.38 ), alpha4( X, Y, Z ) }.
% 0.80/1.38 { ! Z = c_Groups_Ozero__class_Ozero( X ), alpha4( X, Y, Z ) }.
% 0.80/1.38 { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber__ring( X )
% 0.80/1.38 , c_Rings_Oinverse__class_Odivide( X, Y, c_Int_Onumber__class_Onumber__of
% 0.80/1.38 ( X, c_Int_OPls ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.80/1.38 { ! class_Rings_Olinordered__idom( X ), c_Orderings_Oord__class_Oless__eq(
% 0.80/1.38 X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.80/1.38 c_Power_Opower__class_Opower( X, Z, c_Int_Onumber__class_Onumber__of(
% 0.80/1.38 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ),
% 0.80/1.38 c_Power_Opower__class_Opower( X, Y, c_Int_Onumber__class_Onumber__of(
% 0.80/1.38 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) ) }.
% 0.80/1.38 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.80/1.38 ( X, c_Groups_Oplus__class_Oplus( X, c_Power_Opower__class_Opower( X, Z,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.38 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( X, Y,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.38 c_Int_OPls ) ) ) ) ), c_Groups_Ozero__class_Ozero( X ) ), Z =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ) }.
% 0.80/1.38 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.80/1.38 ( X, c_Groups_Oplus__class_Oplus( X, c_Power_Opower__class_Opower( X, Z,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.38 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( X, Y,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.38 c_Int_OPls ) ) ) ) ), c_Groups_Ozero__class_Ozero( X ) ), Y =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ) }.
% 0.80/1.38 { ! class_Rings_Olinordered__idom( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.80/1.38 X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.80/1.38 c_Power_Opower__class_Opower( X, Z, c_Int_Onumber__class_Onumber__of(
% 0.80/1.38 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ),
% 0.80/1.38 c_Power_Opower__class_Opower( X, Y, c_Int_Onumber__class_Onumber__of(
% 0.80/1.38 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ),
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.80/1.38 { ! class_Fields_Ofield( X ), ! class_Int_Onumber__ring( X ),
% 0.80/1.38 c_Rings_Oinverse__class_Odivide( X, Y, c_Int_Onumber__class_Onumber__of(
% 0.80/1.38 X, c_Int_OBit1( c_Int_OPls ) ) ) = Y }.
% 0.80/1.38 { ! class_Fields_Ofield( X ), ! class_Int_Onumber__ring( X ),
% 0.80/1.38 c_Rings_Oinverse__class_Odivide( X, Y, c_Int_Onumber__class_Onumber__of(
% 0.80/1.38 X, c_Int_OBit1( c_Int_OPls ) ) ) = Y }.
% 0.80/1.38 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.80/1.38 c_Int_OBit0( Y ) ) = c_Groups_Oplus__class_Oplus( X,
% 0.80/1.38 c_Groups_Oplus__class_Oplus( X, c_Groups_Ozero__class_Ozero( X ),
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( X, Y ) ),
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.80/1.38 { c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit1( c_Int_OPls )
% 0.80/1.38 ) = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.80/1.38 { c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit1( c_Int_OBit1(
% 0.80/1.38 c_Int_OPls ) ) ) = c_Nat_OSuc( c_Nat_OSuc( c_Nat_OSuc(
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.80/1.38 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, U, T ), c_Groups_Otimes__class_Otimes(
% 0.80/1.38 X, Z, Y ) ) = c_Groups_Otimes__class_Otimes( X,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, U, Z ), c_Groups_Otimes__class_Otimes(
% 0.80/1.38 X, T, Y ) ) }.
% 0.80/1.38 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, U, T ), c_Groups_Otimes__class_Otimes(
% 0.80/1.38 X, Z, Y ) ) = c_Groups_Otimes__class_Otimes( X, Z,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, c_Groups_Otimes__class_Otimes( X, U, T
% 0.80/1.38 ), Y ) ) }.
% 0.80/1.38 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, U, T ), c_Groups_Otimes__class_Otimes(
% 0.80/1.38 X, Z, Y ) ) = c_Groups_Otimes__class_Otimes( X, U,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, T, c_Groups_Otimes__class_Otimes( X, Z
% 0.80/1.38 , Y ) ) ) }.
% 0.80/1.38 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, T, Z ), Y ) =
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, c_Groups_Otimes__class_Otimes( X, T, Y
% 0.80/1.38 ), Z ) }.
% 0.80/1.38 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, T, Z ), Y ) =
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, T, c_Groups_Otimes__class_Otimes( X, Z
% 0.80/1.38 , Y ) ) }.
% 0.80/1.38 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.80/1.38 T, c_Groups_Otimes__class_Otimes( X, Z, Y ) ) =
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, c_Groups_Otimes__class_Otimes( X, T, Z
% 0.80/1.38 ), Y ) }.
% 0.80/1.38 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.80/1.38 T, c_Groups_Otimes__class_Otimes( X, Z, Y ) ) =
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, Z, c_Groups_Otimes__class_Otimes( X, T
% 0.80/1.38 , Y ) ) }.
% 0.80/1.38 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.80/1.38 Z, Y ) = c_Groups_Otimes__class_Otimes( X, Y, Z ) }.
% 0.80/1.38 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.80/1.38 ( X, c_Groups_Ozero__class_Ozero( X ), c_Power_Opower__class_Opower( X, Y
% 0.80/1.38 , c_Nat_OSuc( c_Groups_Otimes__class_Otimes( tc_Nat_Onat,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.38 c_Int_OPls ) ) ), Z ) ) ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.80/1.38 { c_Nat_OSuc( c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) =
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.38 c_Int_OPls ) ) ) }.
% 0.80/1.38 { c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.38 c_Int_OPls ) ) ) = c_Nat_OSuc( c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.80/1.38 tc_Nat_Onat ) ) ) }.
% 0.80/1.38 { ! class_Int_Onumber__ring( X ), c_Groups_Otimes__class_Otimes( X, Y,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( X, c_Int_OBit0( c_Int_OBit1( c_Int_OPls
% 0.80/1.38 ) ) ) ) = c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 0.80/1.38 { ! class_Int_Onumber__ring( X ), c_Groups_Otimes__class_Otimes( X,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( X, c_Int_OBit0( c_Int_OBit1( c_Int_OPls
% 0.80/1.38 ) ) ), Y ) = c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 0.80/1.38 { c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.38 c_Int_OPls ) ) ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, X ) }.
% 0.80/1.38 { c_Groups_Otimes__class_Otimes( tc_Nat_Onat,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.38 c_Int_OPls ) ) ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, X )
% 0.80/1.38 }.
% 0.80/1.38 { ! class_Rings_Ocomm__semiring__1( X ), c_Power_Opower__class_Opower( X, Z
% 0.80/1.38 , c_Nat_OSuc( c_Groups_Otimes__class_Otimes( tc_Nat_Onat,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.38 c_Int_OPls ) ) ), Y ) ) ) = c_Groups_Otimes__class_Otimes( X, Z,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, c_Power_Opower__class_Opower( X, Z, Y )
% 0.80/1.38 , c_Power_Opower__class_Opower( X, Z, Y ) ) ) }.
% 0.80/1.38 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.80/1.38 ( X, c_Power_Opower__class_Opower( X, Y, c_Groups_Otimes__class_Otimes(
% 0.80/1.38 tc_Nat_Onat, c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0(
% 0.80/1.38 c_Int_OBit1( c_Int_OPls ) ) ), Z ) ), c_Groups_Ozero__class_Ozero( X ) )
% 0.80/1.38 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.80/1.38 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Oplus__class_Oplus( X,
% 0.80/1.38 c_Power_Opower__class_Opower( X, Z, c_Int_Onumber__class_Onumber__of(
% 0.80/1.38 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ),
% 0.80/1.38 c_Power_Opower__class_Opower( X, Y, c_Int_Onumber__class_Onumber__of(
% 0.80/1.38 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.80/1.38 .
% 0.80/1.38 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Oplus__class_Oplus( X,
% 0.80/1.38 c_Power_Opower__class_Opower( X, Z, c_Int_Onumber__class_Onumber__of(
% 0.80/1.38 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ),
% 0.80/1.38 c_Power_Opower__class_Opower( X, Y, c_Int_Onumber__class_Onumber__of(
% 0.80/1.38 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 0.80/1.38 .
% 0.80/1.38 { ! class_Rings_Olinordered__idom( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.80/1.38 X ), ! Y = c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus
% 0.80/1.38 ( X, c_Power_Opower__class_Opower( X, Z, c_Int_Onumber__class_Onumber__of
% 0.80/1.38 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ),
% 0.80/1.38 c_Power_Opower__class_Opower( X, Y, c_Int_Onumber__class_Onumber__of(
% 0.80/1.38 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ) }.
% 0.80/1.38 { ! class_Rings_Olinordered__idom( X ), c_Orderings_Oord__class_Oless__eq(
% 0.80/1.38 X, c_Groups_Ozero__class_Ozero( X ), c_Power_Opower__class_Opower( X, Y,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.38 c_Int_OPls ) ) ) ) ) }.
% 0.80/1.38 { ! class_Rings_Olinordered__semidom( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Power_Opower__class_Opower( X, Z
% 0.80/1.38 , c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1
% 0.80/1.38 ( c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( X, Y,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.38 c_Int_OPls ) ) ) ) ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless__eq
% 0.80/1.38 ( X, Z, Y ) }.
% 0.80/1.38 { ! class_Rings_Olinordered__semidom( X ), ! c_Power_Opower__class_Opower(
% 0.80/1.38 X, Z, c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0(
% 0.80/1.38 c_Int_OBit1( c_Int_OPls ) ) ) ) = c_Power_Opower__class_Opower( X, Y,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.38 c_Int_OPls ) ) ) ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.80/1.38 ), Z = Y }.
% 0.80/1.38 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.80/1.38 Y, c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X )
% 0.80/1.38 }.
% 0.80/1.38 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.80/1.38 }.
% 0.80/1.38 { ! class_Rings_Oring__1__no__zero__divisors( X ), Y =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ), ! c_Power_Opower__class_Opower( X, Y, Z
% 0.80/1.38 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.80/1.38 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.80/1.38 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.80/1.38 , ! c_Power_Opower__class_Opower( X, Z, Y ) = c_Groups_Ozero__class_Ozero
% 0.80/1.38 ( X ), Z = c_Groups_Ozero__class_Ozero( X ) }.
% 0.80/1.38 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.80/1.38 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.80/1.38 , ! c_Power_Opower__class_Opower( X, Z, Y ) = c_Groups_Ozero__class_Ozero
% 0.80/1.38 ( X ), ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.80/1.38 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.80/1.38 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.80/1.38 , ! Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 0.80/1.38 ( tc_Nat_Onat ), c_Power_Opower__class_Opower( X, Z, Y ) =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ) }.
% 0.80/1.38 { ! class_Groups_Omonoid__mult( X ), c_Groups_Otimes__class_Otimes( X,
% 0.80/1.38 c_Power_Opower__class_Opower( X, Z, Y ), Z ) =
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, Z, c_Power_Opower__class_Opower( X, Z,
% 0.80/1.38 Y ) ) }.
% 0.80/1.38 { ! class_Groups_Ocomm__monoid__mult( X ), c_Power_Opower__class_Opower( X
% 0.80/1.38 , c_Groups_Otimes__class_Otimes( X, T, Z ), Y ) =
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, c_Power_Opower__class_Opower( X, T, Y )
% 0.80/1.38 , c_Power_Opower__class_Opower( X, Z, Y ) ) }.
% 0.80/1.38 { ! class_Rings_Ocomm__semiring__1( X ), c_Power_Opower__class_Opower( X,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, T, Z ), Y ) =
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, c_Power_Opower__class_Opower( X, T, Y )
% 0.80/1.38 , c_Power_Opower__class_Opower( X, Z, Y ) ) }.
% 0.80/1.38 { c_NthRoot_Osqrt( c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.80/1.38 c_Power_Opower__class_Opower( tc_RealDef_Oreal,
% 0.80/1.38 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, c_NthRoot_Osqrt(
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, v_x____, v_x____ ),
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, v_y____, v_y____ ) ) ),
% 0.80/1.38 v_x____ ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0(
% 0.80/1.38 c_Int_OBit1( c_Int_OPls ) ) ) ), c_Int_Onumber__class_Onumber__of(
% 0.80/1.38 tc_RealDef_Oreal, c_Int_OBit0( c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) )
% 0.80/1.38 ) ) ) = c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.80/1.38 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, c_NthRoot_Osqrt(
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, v_x____, v_x____ ),
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, v_y____, v_y____ ) ) ),
% 0.80/1.38 v_x____ ), c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal,
% 0.80/1.38 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) }.
% 0.80/1.38 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.80/1.38 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.80/1.38 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, c_NthRoot_Osqrt(
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, v_x____, v_x____ ),
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, v_y____, v_y____ ) ) ),
% 0.80/1.38 v_x____ ), c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal,
% 0.80/1.38 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) }.
% 0.80/1.38 { c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, c_NthRoot_Osqrt(
% 0.80/1.38 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal,
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_NthRoot_Osqrt(
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, v_x____, v_x____ ),
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, v_y____, v_y____ ) ) ),
% 0.80/1.38 v_x____ ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_NthRoot_Osqrt
% 0.80/1.38 ( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, v_x____, v_x____ ),
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, v_y____, v_y____ ) ) ),
% 0.80/1.38 v_x____ ) ), c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal,
% 0.80/1.38 c_Int_OBit0( c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) ),
% 0.80/1.38 c_NthRoot_Osqrt( c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal,
% 0.80/1.38 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, c_NthRoot_Osqrt(
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, v_x____, v_x____ ),
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, v_y____, v_y____ ) ) ),
% 0.80/1.38 v_x____ ), c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.80/1.38 c_NthRoot_Osqrt( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, v_x____, v_x____ ),
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, v_y____, v_y____ ) ) ),
% 0.80/1.38 v_x____ ) ), c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal,
% 0.80/1.38 c_Int_OBit0( c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) ) ) = v_x____
% 0.80/1.38 }.
% 0.80/1.38 { c_Power_Opower__class_Opower( tc_RealDef_Oreal,
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.38 c_Int_OPls ) ) ) ) = c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.80/1.38 c_Power_Opower__class_Opower( tc_RealDef_Oreal, Y,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.38 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal, X,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.38 c_Int_OPls ) ) ) ) ), c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.80/1.38 c_Int_OBit1( c_Int_OPls ) ) ), Y ), X ) ) }.
% 0.80/1.38 { ! Z = c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, Y,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.80/1.38 c_Int_OBit1( c_Int_OPls ) ) ), X ) ), c_Groups_Otimes__class_Otimes(
% 0.80/1.38 tc_RealDef_Oreal, c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal,
% 0.80/1.38 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ), Z ) =
% 0.80/1.38 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, Y, X ) }.
% 0.80/1.38 { ! c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.80/1.38 c_Int_OBit1( c_Int_OPls ) ) ), Z ) = c_Rings_Oinverse__class_Odivide(
% 0.80/1.38 tc_RealDef_Oreal, Y, X ), Z = c_Rings_Oinverse__class_Odivide(
% 0.80/1.38 tc_RealDef_Oreal, Y, c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.80/1.38 c_Int_OBit1( c_Int_OPls ) ) ), X ) ) }.
% 0.80/1.38 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.80/1.38 c_Power_Opower__class_Opower( tc_RealDef_Oreal, Y,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.38 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal, X,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.38 c_Int_OPls ) ) ) ) ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y
% 0.80/1.38 = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.80/1.38 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.80/1.38 c_Power_Opower__class_Opower( tc_RealDef_Oreal, Y,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.38 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal, X,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.38 c_Int_OPls ) ) ) ) ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X
% 0.80/1.38 = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.80/1.38 { ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! X =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.80/1.38 c_Power_Opower__class_Opower( tc_RealDef_Oreal, Y,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.38 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal, X,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.38 c_Int_OPls ) ) ) ) ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }
% 0.80/1.38 .
% 0.80/1.38 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.80/1.38 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.80/1.38 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, c_NthRoot_Osqrt(
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Y, Y ),
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, X ) ) ), Y ),
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.80/1.38 c_Int_OBit1( c_Int_OPls ) ) ) ) ) }.
% 0.80/1.38 { v_z = c_Complex_Ocomplex_OComplex( skol1, skol10 ) }.
% 0.80/1.38 { c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.80/1.38 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, X,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.80/1.38 c_Int_OBit1( c_Int_OPls ) ) ) ), c_Rings_Oinverse__class_Odivide(
% 0.80/1.38 tc_RealDef_Oreal, X, c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal,
% 0.80/1.38 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) = X }.
% 0.80/1.38 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.38 c_Int_OPls ) ) ) ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0( X ) ) ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit1( X ) ) ) }.
% 0.80/1.38 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, X ) }.
% 0.80/1.38 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) =
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) }.
% 0.80/1.38 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ) }.
% 0.80/1.38 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus
% 0.80/1.38 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.80/1.38 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.80/1.38 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ),
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Z ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, Z ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ), Y = X }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ), Y = X }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Z ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, Z ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ),
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, X ) ) }.
% 0.80/1.38 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ) }.
% 0.80/1.38 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, X ) }.
% 0.80/1.38 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.80/1.38 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ) =
% 0.80/1.38 c_Groups_Ominus__class_Ominus( X, c_Int_Onumber__class_Onumber__of( X, Z
% 0.80/1.38 ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.80/1.38 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.80/1.38 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.80/1.38 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus(
% 0.80/1.38 X, U, Z ), c_Groups_Ominus__class_Ominus( X, T, Y ) ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.80/1.38 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ),
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.80/1.38 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ),
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.80/1.38 { ! class_Rings_Oring( X ), c_Groups_Ominus__class_Ominus( X,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, U, T ), c_Groups_Otimes__class_Otimes(
% 0.80/1.38 X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, U, c_Groups_Ominus__class_Ominus( X, T
% 0.80/1.38 , Y ) ), c_Groups_Otimes__class_Otimes( X, c_Groups_Ominus__class_Ominus
% 0.80/1.38 ( X, U, Z ), Y ) ) }.
% 0.80/1.38 { c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, hAPP( Z, Y ),
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal,
% 0.80/1.38 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.80/1.38 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, hAPP( Z, X ), hAPP( Z, Y
% 0.80/1.38 ) ), c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, Y ) ), Y ) ) =
% 0.80/1.38 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, hAPP( Z, X ),
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal,
% 0.80/1.38 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.80/1.38 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, hAPP( Z, X ), hAPP( Z, Y
% 0.80/1.38 ) ), c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, Y ) ), X ) ) }
% 0.80/1.38 .
% 0.80/1.38 { c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex,
% 0.80/1.38 c_Complex_Ocomplex_OComplex( T, Z ), c_Complex_Ocomplex_OComplex( Y, X )
% 0.80/1.38 ) = c_Complex_Ocomplex_OComplex( c_Groups_Ominus__class_Ominus(
% 0.80/1.38 tc_RealDef_Oreal, c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, T, Y )
% 0.80/1.38 , c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Z, X ) ),
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, T, X ),
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Z, Y ) ) ) }.
% 0.80/1.38 { ! class_Int_Onumber( X ), ! class_Rings_Oring( X ),
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, c_Int_Onumber__class_Onumber__of( X, T
% 0.80/1.38 ), c_Groups_Ominus__class_Ominus( X, Z, Y ) ) =
% 0.80/1.38 c_Groups_Ominus__class_Ominus( X, c_Groups_Otimes__class_Otimes( X,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( X, T ), Z ),
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, c_Int_Onumber__class_Onumber__of( X, T
% 0.80/1.38 ), Y ) ) }.
% 0.80/1.38 { ! class_Int_Onumber( X ), ! class_Rings_Oring( X ),
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, c_Groups_Ominus__class_Ominus( X, T, Z
% 0.80/1.38 ), c_Int_Onumber__class_Onumber__of( X, Y ) ) =
% 0.80/1.38 c_Groups_Ominus__class_Ominus( X, c_Groups_Otimes__class_Otimes( X, T,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( X, Y ) ), c_Groups_Otimes__class_Otimes
% 0.80/1.38 ( X, Z, c_Int_Onumber__class_Onumber__of( X, Y ) ) ) }.
% 0.80/1.38 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( X, T ), c_Groups_Ominus__class_Ominus(
% 0.80/1.38 X, c_Int_Onumber__class_Onumber__of( X, Z ), Y ) ) =
% 0.80/1.38 c_Groups_Ominus__class_Ominus( X, c_Int_Onumber__class_Onumber__of( X,
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_Int_Oint, T, Z ) ), Y ) }.
% 0.80/1.38 { ! class_RealVector_Oreal__field( X ), c_Rings_Oinverse__class_Odivide( X
% 0.80/1.38 , c_Groups_Ominus__class_Ominus( X, c_Groups_Otimes__class_Otimes( X, W,
% 0.80/1.38 U ), c_Groups_Otimes__class_Otimes( X, T, Z ) ), Y ) =
% 0.80/1.38 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, W,
% 0.80/1.38 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus( X, U,
% 0.80/1.38 Z ), Y ) ), c_Groups_Otimes__class_Otimes( X,
% 0.80/1.38 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus( X, W,
% 0.80/1.38 T ), Y ), Z ) ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.80/1.38 tc_Int_Oint, X, Y ) ) }.
% 0.80/1.38 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Ozero__class_Ozero(
% 0.80/1.38 tc_Int_Oint ) ) }.
% 0.80/1.38 { c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal,
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ), X ) =
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Z, X ),
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Y, X ) ) }.
% 0.80/1.38 { c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Z, Y ), X ) =
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Z,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Y, X ) ) }.
% 0.80/1.38 { c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Y, X ) =
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, Y ) }.
% 0.80/1.38 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X,
% 0.80/1.38 c_Power_Opower__class_Opower( X, Z, c_Nat_OSuc( c_Nat_OSuc(
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ),
% 0.80/1.38 c_Power_Opower__class_Opower( X, Y, c_Nat_OSuc( c_Nat_OSuc(
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) ) =
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.80/1.38 ), c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.80/1.38 { c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.80/1.38 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.80/1.38 c_Int_OBit1( c_Int_OPls ) ) ) ), X ) = c_Rings_Oinverse__class_Odivide(
% 0.80/1.38 tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X )
% 0.80/1.38 , c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.80/1.38 c_Int_OBit1( c_Int_OPls ) ) ) ) }.
% 0.80/1.38 { c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.80/1.38 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.80/1.38 c_Int_OBit1( c_Int_OPls ) ) ) ), Y ) = c_Rings_Oinverse__class_Odivide(
% 0.80/1.38 tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, Y )
% 0.80/1.38 , c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.80/1.38 c_Int_OBit1( c_Int_OPls ) ) ) ) }.
% 0.80/1.38 { ! c_Complex_Ocomplex_OComplex( T, Z ) = c_Complex_Ocomplex_OComplex( Y, X
% 0.80/1.38 ), T = Y }.
% 0.80/1.38 { ! c_Complex_Ocomplex_OComplex( T, Z ) = c_Complex_Ocomplex_OComplex( Y, X
% 0.80/1.38 ), Z = X }.
% 0.80/1.38 { ! T = Y, ! Z = X, c_Complex_Ocomplex_OComplex( T, Z ) =
% 0.80/1.38 c_Complex_Ocomplex_OComplex( Y, X ) }.
% 0.80/1.38 { c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex,
% 0.80/1.38 c_Complex_Ocomplex_OComplex( T, Z ), c_Complex_Ocomplex_OComplex( Y, X )
% 0.80/1.38 ) = c_Complex_Ocomplex_OComplex( c_Groups_Oplus__class_Oplus(
% 0.80/1.38 tc_RealDef_Oreal, T, Y ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.80/1.38 Z, X ) ) }.
% 0.80/1.38 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), !
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Z, X ) =
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Y, X ), Z = Y }.
% 0.80/1.38 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Z, X ) =
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Y, X ) }.
% 0.80/1.38 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), !
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, Z ) =
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, Y ), Z = Y }.
% 0.80/1.38 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, Z ) =
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, Y ) }.
% 0.80/1.38 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Y, Y ),
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, X ) ) =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.80/1.38 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Y, Y ),
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, X ) ) =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.80/1.38 { ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! X =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Y, Y ),
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, X ) ) =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Otimes__class_Otimes
% 0.80/1.38 ( tc_Int_Oint, X, Y ) ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.80/1.38 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, Y, X ) ), alpha5( X, Y
% 0.80/1.38 ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.80/1.38 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, Y, X ) ), alpha38( X,
% 0.80/1.38 Y ) }.
% 0.80/1.38 { ! alpha5( X, Y ), ! alpha38( X, Y ), c_Orderings_Oord__class_Oless__eq(
% 0.80/1.38 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.80/1.38 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, Y, X ) ) }.
% 0.80/1.38 { ! alpha38( X, Y ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), alpha38( X, Y ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), alpha38( X, Y ) }.
% 0.80/1.38 { ! alpha5( X, Y ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y
% 0.80/1.38 , c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), alpha5( X, Y ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), alpha5( X, Y ) }.
% 0.80/1.38 { c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) =
% 0.80/1.38 c_Complex_Ocomplex_OComplex( c_Groups_Ozero__class_Ozero(
% 0.80/1.38 tc_RealDef_Oreal ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.80/1.38 { ! c_Complex_Ocomplex_OComplex( Y, X ) = c_Groups_Ozero__class_Ozero(
% 0.80/1.38 tc_Complex_Ocomplex ), Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal
% 0.80/1.38 ) }.
% 0.80/1.38 { ! c_Complex_Ocomplex_OComplex( Y, X ) = c_Groups_Ozero__class_Ozero(
% 0.80/1.38 tc_Complex_Ocomplex ), X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal
% 0.80/1.38 ) }.
% 0.80/1.38 { ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! X =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.80/1.38 c_Complex_Ocomplex_OComplex( Y, X ) = c_Groups_Ozero__class_Ozero(
% 0.80/1.38 tc_Complex_Ocomplex ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Power_Opower__class_Opower
% 0.80/1.38 ( tc_Int_Oint, X, Y ) ) }.
% 0.80/1.38 { ! class_Int_Onumber__ring( X ), c_Power_Opower__class_Opower( X,
% 0.80/1.38 c_Groups_Ominus__class_Ominus( X, Z, Y ),
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.38 c_Int_OPls ) ) ) ) = c_Groups_Ominus__class_Ominus( X,
% 0.80/1.38 c_Groups_Oplus__class_Oplus( X, c_Power_Opower__class_Opower( X, Z,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.38 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( X, Y,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.38 c_Int_OPls ) ) ) ) ), c_Groups_Otimes__class_Otimes( X,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, c_Int_Onumber__class_Onumber__of( X,
% 0.80/1.38 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ), Z ), Y ) ) }.
% 0.80/1.38 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OPls ) ) }.
% 0.80/1.38 { ! c_Complex_Ocomplex_OComplex( Z, Y ) = c_Int_Onumber__class_Onumber__of
% 0.80/1.38 ( tc_Complex_Ocomplex, X ), Z = c_Int_Onumber__class_Onumber__of(
% 0.80/1.38 tc_RealDef_Oreal, X ) }.
% 0.80/1.38 { ! c_Complex_Ocomplex_OComplex( Z, Y ) = c_Int_Onumber__class_Onumber__of
% 0.80/1.38 ( tc_Complex_Ocomplex, X ), Y = c_Groups_Ozero__class_Ozero(
% 0.80/1.38 tc_RealDef_Oreal ) }.
% 0.80/1.38 { ! Z = c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, X ), ! Y =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.80/1.38 c_Complex_Ocomplex_OComplex( Z, Y ) = c_Int_Onumber__class_Onumber__of(
% 0.80/1.38 tc_Complex_Ocomplex, X ) }.
% 0.80/1.38 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit1( c_Int_OBit1(
% 0.80/1.38 c_Int_OPls ) ) ) ) }.
% 0.80/1.38 { c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.80/1.38 c_Int_OBit1( c_Int_OPls ) ) ), c_Groups_Otimes__class_Otimes(
% 0.80/1.38 tc_RealDef_Oreal, v_y____, c_NthRoot_Osqrt(
% 0.80/1.38 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal,
% 0.80/1.38 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, c_NthRoot_Osqrt(
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, v_x____, v_x____ ),
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, v_y____, v_y____ ) ) ),
% 0.80/1.38 v_x____ ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_NthRoot_Osqrt
% 0.80/1.38 ( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, v_x____, v_x____ ),
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, v_y____, v_y____ ) ) ),
% 0.80/1.38 v_x____ ) ), c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal,
% 0.80/1.38 c_Int_OBit0( c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) ) ) ),
% 0.80/1.38 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, v_y____ ) ) = v_y____ }.
% 0.80/1.38 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.80/1.38 { c_Complex_Ocomplex_Ocomplex__size( c_Complex_Ocomplex_OComplex( Y, X ) )
% 0.80/1.38 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) ) }.
% 0.80/1.38 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.80/1.38 c_Groups_Ominus__class_Ominus( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.80/1.38 Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X,
% 0.80/1.38 c_Groups_Ominus__class_Ominus( X, c_Groups_Otimes__class_Otimes( X, Y, T
% 0.80/1.38 ), Z ), Y ) }.
% 0.80/1.38 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.80/1.38 c_Groups_Ominus__class_Ominus( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.80/1.38 Y ), Z ) = c_Rings_Oinverse__class_Odivide( X,
% 0.80/1.38 c_Groups_Ominus__class_Ominus( X, T, c_Groups_Otimes__class_Otimes( X, Y
% 0.80/1.38 , Z ) ), Y ) }.
% 0.80/1.38 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ominus__class_Ominus( X,
% 0.80/1.38 c_Rings_Oinverse__class_Odivide( X, U, Y ),
% 0.80/1.38 c_Rings_Oinverse__class_Odivide( X, T, Z ) ) =
% 0.80/1.38 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus( X,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, U, Z ), c_Groups_Otimes__class_Otimes(
% 0.80/1.38 X, T, Y ) ), c_Groups_Otimes__class_Otimes( X, Y, Z ) ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.80/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 0.80/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.80/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 0.80/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ),
% 0.80/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.80/1.38 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.80/1.38 ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.80/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.80/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X = Z }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), ! X = Z,
% 0.80/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.80/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.80/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.80/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = Y }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.80/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, Z ),
% 0.80/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.80/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ),
% 0.80/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 0.80/1.38 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.80/1.38 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) =
% 0.80/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ) }.
% 0.80/1.38 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.80/1.38 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) =
% 0.80/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 0.80/1.38 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.80/1.38 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.80/1.38 Z, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.80/1.38 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.80/1.38 tc_Nat_Onat, Y, X ), Y ) = X }.
% 0.80/1.38 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.80/1.38 tc_Nat_Onat, Y, X ), X ) = Y }.
% 0.80/1.38 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.80/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ), Y ) }.
% 0.80/1.38 { ! class_Fields_Olinordered__field__inverse__zero( X ),
% 0.80/1.38 c_Groups_Oabs__class_Oabs( X, c_Rings_Oinverse__class_Odivide( X, Z, Y )
% 0.80/1.38 ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oabs__class_Oabs( X, Z
% 0.80/1.38 ), c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.80/1.38 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.80/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.80/1.38 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, X ) =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.80/1.38 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 0.80/1.38 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.80/1.38 tc_Nat_Onat ), X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.80/1.38 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.80/1.38 X ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 0.80/1.38 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.80/1.38 ( tc_Nat_Onat, c_Nat_OSuc( Z ), Y ), c_Nat_OSuc( X ) ) =
% 0.80/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.80/1.38 ( tc_Nat_Onat, Z, Y ), X ) }.
% 0.80/1.38 { c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z,
% 0.80/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) =
% 0.80/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes
% 0.80/1.38 ( tc_Nat_Onat, Z, Y ), c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X )
% 0.80/1.38 ) }.
% 0.80/1.38 { c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.80/1.38 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ),
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) ) }.
% 0.80/1.38 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X,
% 0.80/1.38 c_Power_Opower__class_Opower( X, Z, Y ) ) = c_Power_Opower__class_Opower
% 0.80/1.38 ( X, c_Groups_Oabs__class_Oabs( X, Z ), Y ) }.
% 0.80/1.38 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Int_OPls ) = X }.
% 0.80/1.38 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, c_Int_OBit0( Y ), c_Int_OBit0
% 0.80/1.38 ( X ) ) = c_Int_OBit0( c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X )
% 0.80/1.38 ) }.
% 0.80/1.38 { c_Groups_Otimes__class_Otimes( tc_Int_Oint, Z,
% 0.80/1.38 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ) =
% 0.80/1.38 c_Groups_Ominus__class_Ominus( tc_Int_Oint, c_Groups_Otimes__class_Otimes
% 0.80/1.38 ( tc_Int_Oint, Z, Y ), c_Groups_Otimes__class_Otimes( tc_Int_Oint, Z, X )
% 0.80/1.38 ) }.
% 0.80/1.38 { c_Groups_Otimes__class_Otimes( tc_Int_Oint, c_Groups_Ominus__class_Ominus
% 0.80/1.38 ( tc_Int_Oint, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Int_Oint,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_Int_Oint, Z, X ),
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_Int_Oint, Y, X ) ) }.
% 0.80/1.38 { ! class_Fields_Olinordered__field( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.80/1.38 X ), c_Groups_Oabs__class_Oabs( X, c_Rings_Oinverse__class_Odivide( X, Z
% 0.80/1.38 , Y ) ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oabs__class_Oabs(
% 0.80/1.38 X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.80/1.38 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y,
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.80/1.38 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.80/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.80/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.80/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) =
% 0.80/1.38 c_Nat_OSuc( c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.80/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z,
% 0.80/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 0.80/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.80/1.38 tc_Nat_Onat, Z, Y ), X ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.80/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.80/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.80/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.80/1.38 tc_Nat_Onat, X, Z ), Y ) ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.80/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = X }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.80/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 0.80/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.80/1.38 tc_Nat_Onat, Z, X ), Y ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.80/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.80/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.80/1.38 tc_Nat_Onat, X, Y ), Y ) = X }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.80/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z, X =
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X =
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.80/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.80/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.80/1.38 tc_Nat_Onat, Z, X ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.80/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.80/1.38 tc_Nat_Onat, X, Y ), Z ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ), Y ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.80/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.80/1.38 tc_Nat_Onat, X, Z ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.80/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), Z ) }.
% 0.80/1.38 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, c_Int_OBit1( Y ), c_Int_OBit0
% 0.80/1.38 ( X ) ) = c_Int_OBit1( c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X )
% 0.80/1.38 ) }.
% 0.80/1.38 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, c_Int_OBit1( Y ), c_Int_OBit1
% 0.80/1.38 ( X ) ) = c_Int_OBit0( c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X )
% 0.80/1.38 ) }.
% 0.80/1.38 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, c_Int_OPls, c_Int_OBit0( X )
% 0.80/1.38 ) = c_Int_OBit0( c_Groups_Ominus__class_Ominus( tc_Int_Oint, c_Int_OPls
% 0.80/1.38 , X ) ) }.
% 0.80/1.38 { c_NthRoot_Osqrt( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, X )
% 0.80/1.38 ) = c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.80/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc(
% 0.80/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), Z ) =
% 0.80/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.80/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, c_Nat_OSuc(
% 0.80/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) ) =
% 0.80/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.80/1.38 tc_Nat_Onat, Z, Y ), c_Nat_OSuc( X ) ) }.
% 0.80/1.38 { c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex,
% 0.80/1.38 c_Complex_Ocomplex_OComplex( T, Z ), c_Complex_Ocomplex_OComplex( Y, X )
% 0.80/1.38 ) = c_Complex_Ocomplex_OComplex( c_Groups_Ominus__class_Ominus(
% 0.80/1.38 tc_RealDef_Oreal, T, Y ), c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal
% 0.80/1.38 , Z, X ) ) }.
% 0.80/1.38 { ! class_Rings_Olinordered__idom( X ), c_Orderings_Oord__class_Oless__eq(
% 0.80/1.38 X, c_Groups_Ozero__class_Ozero( X ), c_Power_Opower__class_Opower( X,
% 0.80/1.38 c_Groups_Oabs__class_Oabs( X, Z ), Y ) ) }.
% 0.80/1.38 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.80/1.38 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.80/1.38 { ! Y = X, c_Nat_OSuc( Y ) = c_Nat_OSuc( X ) }.
% 0.80/1.38 { ! c_Nat_OSuc( X ) = X }.
% 0.80/1.38 { ! X = c_Nat_OSuc( X ) }.
% 0.80/1.38 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.80/1.38 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, c_Groups_Oplus__class_Oplus
% 0.80/1.38 ( tc_Nat_Onat, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.80/1.38 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.80/1.38 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.80/1.38 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ), Y = X }.
% 0.80/1.38 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) }.
% 0.80/1.38 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ), Z = X }.
% 0.80/1.38 { ! Z = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.80/1.38 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, X ) }.
% 0.80/1.38 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ) }.
% 0.80/1.38 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ), Y = X }.
% 0.80/1.38 { c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Groups_Otimes__class_Otimes
% 0.80/1.38 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Otimes__class_Otimes( tc_Nat_Onat,
% 0.80/1.38 Z, c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) ) }.
% 0.80/1.38 { c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) =
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Y ) }.
% 0.80/1.38 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.80/1.38 c_Power_Opower__class_Opower( X, Y, c_Groups_Ominus__class_Ominus(
% 0.80/1.38 tc_Nat_Onat, Z, T ) ) = c_Rings_Oinverse__class_Odivide( X,
% 0.80/1.38 c_Power_Opower__class_Opower( X, Y, Z ), c_Power_Opower__class_Opower( X
% 0.80/1.38 , Y, T ) ) }.
% 0.80/1.38 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X,
% 0.80/1.38 c_Power_Opower__class_Opower( X, Y, c_Int_Onumber__class_Onumber__of(
% 0.80/1.38 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) =
% 0.80/1.38 c_Power_Opower__class_Opower( X, Y, c_Int_Onumber__class_Onumber__of(
% 0.80/1.38 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) }.
% 0.80/1.38 { ! class_Rings_Olinordered__idom( X ), c_Power_Opower__class_Opower( X,
% 0.80/1.38 c_Groups_Oabs__class_Oabs( X, Y ), c_Int_Onumber__class_Onumber__of(
% 0.80/1.38 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) =
% 0.80/1.38 c_Power_Opower__class_Opower( X, Y, c_Int_Onumber__class_Onumber__of(
% 0.80/1.38 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) }.
% 0.80/1.38 { c_NthRoot_Osqrt( c_Power_Opower__class_Opower( tc_RealDef_Oreal, X,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.38 c_Int_OPls ) ) ) ) ) = c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) }
% 0.80/1.38 .
% 0.80/1.38 { ! class_Fields_Ofield__inverse__zero( X ), c_Groups_Otimes__class_Otimes
% 0.80/1.38 ( X, c_Rings_Oinverse__class_Odivide( X, U, T ),
% 0.80/1.38 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 0.80/1.38 c_Rings_Oinverse__class_Odivide( X, c_Groups_Otimes__class_Otimes( X, U,
% 0.80/1.38 Z ), c_Groups_Otimes__class_Otimes( X, T, Y ) ) }.
% 0.80/1.38 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.80/1.38 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.80/1.38 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.80/1.38 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.80/1.38 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.80/1.38 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.80/1.38 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.80/1.38 tc_Nat_Onat ), X ) = X }.
% 0.80/1.38 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero
% 0.80/1.38 ( tc_Nat_Onat ) ) = X }.
% 0.80/1.38 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.80/1.38 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.80/1.38 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.80/1.38 tc_Nat_Onat, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.80/1.38 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = Y, X =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.80/1.38 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.80/1.38 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.80/1.38 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.80/1.38 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.80/1.38 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.80/1.38 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 0.80/1.38 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 0.80/1.38 ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 0.80/1.38 c_Nat_OSuc( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X )
% 0.80/1.38 }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 0.80/1.38 c_Nat_OSuc( X ) ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 0.80/1.38 ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.80/1.38 { ! Y = c_Nat_OSuc( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.80/1.38 , c_Nat_OSuc( X ) ) }.
% 0.80/1.38 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), X ) }
% 0.80/1.38 .
% 0.80/1.38 { ! c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ) =
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Y ), Z = X, Y =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.80/1.38 { ! Z = X, c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ) =
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Y ) }.
% 0.80/1.38 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ) =
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Y ) }.
% 0.80/1.38 { ! c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ) =
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ), Y = X, Z =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.80/1.38 { ! Y = X, c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ) =
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ) }.
% 0.80/1.38 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ) =
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ) }.
% 0.80/1.38 { ! c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.80/1.38 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.80/1.38 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.80/1.38 { c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.80/1.38 { c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.80/1.38 tc_Nat_Onat ), X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.80/1.38 { ! c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Nat_OSuc( Z ), Y ) =
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Nat_OSuc( Z ), X ), Y = X }
% 0.80/1.38 .
% 0.80/1.38 { ! Y = X, c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Nat_OSuc( Z ), Y )
% 0.80/1.38 = c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Nat_OSuc( Z ), X ) }.
% 0.80/1.38 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.80/1.38 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol2( X, Y ) ) }.
% 0.80/1.38 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, T ),
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ), X ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.80/1.38 { c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.80/1.38 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ),
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) ) }.
% 0.80/1.38 { c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z,
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.80/1.38 tc_Nat_Onat, Z, Y ), c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ) )
% 0.80/1.38 }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, T ),
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Z ) ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ),
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ) ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, Z ),
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Z ) ) }.
% 0.80/1.38 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, X ) ) ) }.
% 0.80/1.38 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, X ) ) }.
% 0.80/1.38 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.80/1.38 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ), c_NthRoot_Osqrt(
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.80/1.38 c_Power_Opower__class_Opower( tc_RealDef_Oreal, Y,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.38 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal, X,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.38 c_Int_OPls ) ) ) ) ) ) ) }.
% 0.80/1.38 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.80/1.38 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ), c_NthRoot_Osqrt(
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.80/1.38 c_Power_Opower__class_Opower( tc_RealDef_Oreal, X,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.38 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal, Y,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.38 c_Int_OPls ) ) ) ) ) ) ) }.
% 0.80/1.38 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.80/1.38 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ), alpha6( X, Y, Z ), alpha39
% 0.80/1.38 ( X, Y, Z ) }.
% 0.80/1.38 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha6( X, Y, Z
% 0.80/1.38 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.80/1.38 ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.80/1.38 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha39( X, Y, Z
% 0.80/1.38 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.80/1.38 ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.80/1.38 { ! alpha39( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.80/1.38 { ! alpha39( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.80/1.38 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ) ), alpha39( X, Y, Z ) }.
% 0.80/1.38 { ! alpha6( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.80/1.38 { ! alpha6( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.80/1.38 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ), Y ), alpha6( X, Y, Z ) }.
% 0.80/1.38 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.80/1.38 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ), alpha7( X, Y, Z ), alpha40
% 0.80/1.38 ( X, Y, Z ) }.
% 0.80/1.38 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha7( X, Y, Z
% 0.80/1.38 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 0.80/1.38 ( X, Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.80/1.38 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha40( X, Y, Z
% 0.80/1.38 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 0.80/1.38 ( X, Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.80/1.38 { ! alpha40( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.80/1.38 { ! alpha40( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.80/1.38 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.80/1.38 ( X ), Y ), alpha40( X, Y, Z ) }.
% 0.80/1.38 { ! alpha7( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.80/1.38 { ! alpha7( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.80/1.38 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ) ), alpha7( X, Y, Z ) }.
% 0.80/1.38 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.80/1.38 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 0.80/1.38 ( X, Z, T ), c_Rings_Oinverse__class_Odivide( X, Y, T ) ) }.
% 0.80/1.38 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Ozero__class_Ozero( X )
% 0.80/1.38 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 0.80/1.38 ( X, Y, T ), c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 0.80/1.38 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ), ! c_Rings_Oinverse__class_Odivide( X, U
% 0.80/1.38 , Y ) = c_Rings_Oinverse__class_Odivide( X, T, Z ),
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, U, Z ) = c_Groups_Otimes__class_Otimes
% 0.80/1.38 ( X, T, Y ) }.
% 0.80/1.38 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ), ! c_Groups_Otimes__class_Otimes( X, U,
% 0.80/1.38 Z ) = c_Groups_Otimes__class_Otimes( X, T, Y ),
% 0.80/1.38 c_Rings_Oinverse__class_Odivide( X, U, Y ) =
% 0.80/1.38 c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 0.80/1.38 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, Y, T ), c_Groups_Otimes__class_Otimes(
% 0.80/1.38 X, Y, Z ) ) = c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 0.80/1.38 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, T, Y ), c_Groups_Otimes__class_Otimes(
% 0.80/1.38 X, Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 0.80/1.38 { ! class_Fields_Ofield__inverse__zero( X ), !
% 0.80/1.38 c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y, alpha41( X, Y, Z, T ) }.
% 0.80/1.38 { ! class_Fields_Ofield__inverse__zero( X ), !
% 0.80/1.38 c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y, alpha8( X, Y, Z ) }.
% 0.80/1.38 { ! class_Fields_Ofield__inverse__zero( X ), ! alpha41( X, Y, Z, T ), !
% 0.80/1.38 alpha8( X, Y, Z ), c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y }.
% 0.80/1.38 { ! alpha41( X, Y, Z, T ), Z = c_Groups_Ozero__class_Ozero( X ), T =
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, Y, Z ) }.
% 0.80/1.38 { ! Z = c_Groups_Ozero__class_Ozero( X ), alpha41( X, Y, Z, T ) }.
% 0.80/1.38 { ! T = c_Groups_Otimes__class_Otimes( X, Y, Z ), alpha41( X, Y, Z, T ) }.
% 0.80/1.38 { ! alpha8( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ) }.
% 0.80/1.38 { Z = c_Groups_Ozero__class_Ozero( X ), alpha8( X, Y, Z ) }.
% 0.80/1.38 { ! Y = c_Groups_Ozero__class_Ozero( X ), alpha8( X, Y, Z ) }.
% 0.80/1.38 { ! class_Fields_Ofield__inverse__zero( X ), ! T =
% 0.80/1.38 c_Rings_Oinverse__class_Odivide( X, Z, Y ), alpha42( X, Y, Z, T ) }.
% 0.80/1.38 { ! class_Fields_Ofield__inverse__zero( X ), ! T =
% 0.80/1.38 c_Rings_Oinverse__class_Odivide( X, Z, Y ), alpha9( X, Y, T ) }.
% 0.80/1.38 { ! class_Fields_Ofield__inverse__zero( X ), ! alpha42( X, Y, Z, T ), !
% 0.80/1.38 alpha9( X, Y, T ), T = c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.80/1.38 { ! alpha42( X, Y, Z, T ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, T, Y ) = Z }.
% 0.80/1.38 { ! Y = c_Groups_Ozero__class_Ozero( X ), alpha42( X, Y, Z, T ) }.
% 0.80/1.38 { ! c_Groups_Otimes__class_Otimes( X, T, Y ) = Z, alpha42( X, Y, Z, T ) }.
% 0.80/1.38 { ! alpha9( X, Y, Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ) }.
% 0.80/1.38 { Y = c_Groups_Ozero__class_Ozero( X ), alpha9( X, Y, Z ) }.
% 0.80/1.38 { ! Z = c_Groups_Ozero__class_Ozero( X ), alpha9( X, Y, Z ) }.
% 0.80/1.38 { ! c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ), alpha10( X, Y ),
% 0.80/1.38 alpha43( X, Y ) }.
% 0.80/1.38 { ! alpha10( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.80/1.38 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.80/1.38 { ! alpha43( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.80/1.38 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.80/1.38 { ! alpha43( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.80/1.38 { ! alpha43( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.80/1.38 tc_Nat_Onat ) ) }.
% 0.80/1.38 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha43( X, Y ) }.
% 0.80/1.38 { ! alpha10( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.80/1.38 tc_Nat_Onat ) ) }.
% 0.80/1.38 { ! alpha10( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.80/1.38 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha10( X, Y ) }.
% 0.80/1.38 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha11( X, Y ), alpha44( X
% 0.80/1.38 , Y ) }.
% 0.80/1.38 { ! alpha11( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.80/1.38 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.80/1.38 { ! alpha44( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.80/1.38 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.80/1.38 { ! alpha44( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.80/1.38 { ! alpha44( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.80/1.38 tc_Nat_Onat ) ) }.
% 0.80/1.38 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha44( X, Y ) }.
% 0.80/1.38 { ! alpha11( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.80/1.38 tc_Nat_Onat ) ) }.
% 0.80/1.38 { ! alpha11( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.80/1.38 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha11( X, Y ) }.
% 0.80/1.38 { ! c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y = c_Nat_OSuc(
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.80/1.38 { ! c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X = c_Nat_OSuc(
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.80/1.38 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.80/1.38 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.80/1.38 { c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) ) }.
% 0.80/1.38 { c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Nat_OSuc( Z ), Y ),
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Nat_OSuc( Z ), X ) ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Nat_OSuc( Z ), Y ),
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Nat_OSuc( Z ), X ) ) }.
% 0.80/1.38 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.80/1.38 c_Rings_Oinverse__class_Odivide( X, U, Y ),
% 0.80/1.38 c_Rings_Oinverse__class_Odivide( X, T, Z ) ) =
% 0.80/1.38 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, U, Z ), c_Groups_Otimes__class_Otimes(
% 0.80/1.38 X, T, Y ) ), c_Groups_Otimes__class_Otimes( X, Y, Z ) ) }.
% 0.80/1.38 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.80/1.38 c_Groups_Oplus__class_Oplus( X, c_Rings_Oinverse__class_Odivide( X, T, Y
% 0.80/1.38 ), Z ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus
% 0.80/1.38 ( X, T, c_Groups_Otimes__class_Otimes( X, Y, Z ) ), Y ) }.
% 0.80/1.38 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.80/1.38 c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ) =
% 0.80/1.38 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, Z, Y ) ), Y ) }.
% 0.80/1.38 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.80/1.38 c_Groups_Oplus__class_Oplus( X, T, c_Rings_Oinverse__class_Odivide( X, Z
% 0.80/1.38 , Y ) ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus
% 0.80/1.38 ( X, c_Groups_Otimes__class_Otimes( X, Y, T ), Z ), Y ) }.
% 0.80/1.38 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, T,
% 0.80/1.38 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 0.80/1.38 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, T, Y ) ), Y ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.80/1.38 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ),
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X,
% 0.80/1.38 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Z ) ) ), Y =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.80/1.38 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.80/1.38 tc_Nat_Onat, Z, Y ), c_Power_Opower__class_Opower( X, T,
% 0.80/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) ) =
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, c_Power_Opower__class_Opower( X, T,
% 0.80/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, Z ) ), T ) }.
% 0.80/1.38 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 0.80/1.38 c_Groups_Ominus__class_Ominus( X, c_Groups_Oplus__class_Oplus( X, U, T )
% 0.80/1.38 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) ), c_Groups_Oplus__class_Oplus
% 0.80/1.38 ( X, c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, U, Z
% 0.80/1.38 ) ), c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, T,
% 0.80/1.38 Y ) ) ) ) }.
% 0.80/1.38 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 0.80/1.38 c_Groups_Ominus__class_Ominus( X, Z, Y ) ), c_Groups_Oplus__class_Oplus(
% 0.80/1.38 X, c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) )
% 0.80/1.38 ) }.
% 0.80/1.38 { ! class_Rings_Oordered__ring__abs( X ), alpha101( X, Z ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.80/1.38 ), c_Groups_Oabs__class_Oabs( X, c_Groups_Otimes__class_Otimes( X, Z, Y
% 0.80/1.38 ) ) = c_Groups_Otimes__class_Otimes( X, c_Groups_Oabs__class_Oabs( X, Z
% 0.80/1.38 ), c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.80/1.38 { ! class_Rings_Oordered__ring__abs( X ), alpha101( X, Z ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.80/1.38 ), c_Groups_Oabs__class_Oabs( X, c_Groups_Otimes__class_Otimes( X, Z, Y
% 0.80/1.38 ) ) = c_Groups_Otimes__class_Otimes( X, c_Groups_Oabs__class_Oabs( X, Z
% 0.80/1.38 ), c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.80/1.38 { ! alpha101( X, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.80/1.38 { ! alpha101( X, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.80/1.38 { c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.80/1.38 ), c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero
% 0.80/1.38 ( X ) ), alpha101( X, Y ) }.
% 0.80/1.38 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.80/1.38 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Groups_Otimes__class_Otimes
% 0.80/1.38 ( X, c_Groups_Oabs__class_Oabs( X, Z ), Y ) = c_Groups_Oabs__class_Oabs(
% 0.80/1.38 X, c_Groups_Otimes__class_Otimes( X, Z, Y ) ) }.
% 0.80/1.38 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.80/1.38 , c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, W, U
% 0.80/1.38 ), T ), c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X
% 0.80/1.38 , Z, U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X, T,
% 0.80/1.38 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.80/1.38 c_Groups_Ominus__class_Ominus( X, Z, W ), U ), Y ) ) }.
% 0.80/1.38 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.80/1.38 , T, c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.80/1.38 c_Groups_Ominus__class_Ominus( X, Z, W ), U ), Y ) ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, W, U ), T ),
% 0.80/1.38 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, Z, U )
% 0.80/1.38 , Y ) ) }.
% 0.80/1.38 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.80/1.38 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.80/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ), Y ) }.
% 0.80/1.38 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Power_Opower__class_Opower
% 0.80/1.38 ( tc_Int_Oint, c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ), X ) ) }.
% 0.80/1.38 { ! class_Groups_Ozero( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y, Y =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ) }.
% 0.80/1.38 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 0.80/1.38 { ! class_Groups_Oab__semigroup__mult( X ), c_Groups_Otimes__class_Otimes(
% 0.80/1.38 X, c_Groups_Otimes__class_Otimes( X, T, Z ), Y ) =
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, T, c_Groups_Otimes__class_Otimes( X, Z
% 0.80/1.38 , Y ) ) }.
% 0.80/1.38 { ! class_Groups_Oab__semigroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.80/1.38 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.80/1.38 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.80/1.38 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.80/1.38 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.80/1.38 T, Y ), Z = Y }.
% 0.80/1.38 { ! class_Groups_Ocancel__semigroup__add( X ), ! Z = Y,
% 0.80/1.38 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.80/1.38 T, Y ) }.
% 0.80/1.38 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.80/1.38 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.80/1.38 Y, Z ), T = Y }.
% 0.80/1.38 { ! class_Groups_Ocancel__semigroup__add( X ), ! T = Y,
% 0.80/1.38 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.80/1.38 Y, Z ) }.
% 0.80/1.38 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.80/1.38 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.80/1.38 T, Y ), Z = Y }.
% 0.80/1.38 { ! class_Groups_Ocancel__ab__semigroup__add( X ), !
% 0.80/1.38 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.80/1.38 T, Y ), Z = Y }.
% 0.80/1.38 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.80/1.38 c_Groups_Oplus__class_Oplus( X, Z, T ) = c_Groups_Oplus__class_Oplus( X,
% 0.80/1.38 Y, T ), Z = Y }.
% 0.80/1.38 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.80/1.38 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! U = T, Z = Y }.
% 0.80/1.38 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.80/1.38 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! Z = Y, U = T }.
% 0.80/1.38 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.80/1.38 c_Groups_Oabs__class_Oabs( X, c_Groups_Oabs__class_Oabs( X, Y ) ) =
% 0.80/1.38 c_Groups_Oabs__class_Oabs( X, Y ) }.
% 0.80/1.38 { ! class_Rings_Omult__zero( X ), c_Groups_Otimes__class_Otimes( X,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.80/1.38 }.
% 0.80/1.38 { ! class_Rings_Omult__zero( X ), c_Groups_Otimes__class_Otimes( X, Y,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.80/1.38 { ! class_Rings_Oring__no__zero__divisors( X ), !
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.80/1.38 ), Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 0.80/1.38 ( X ) }.
% 0.80/1.38 { ! class_Rings_Oring__no__zero__divisors( X ), ! Z =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ), c_Groups_Otimes__class_Otimes( X, Z, Y
% 0.80/1.38 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.80/1.38 { ! class_Rings_Oring__no__zero__divisors( X ), ! Y =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ), c_Groups_Otimes__class_Otimes( X, Z, Y
% 0.80/1.38 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.80/1.38 { ! class_Rings_Ono__zero__divisors( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.80/1.38 X ), Z = c_Groups_Ozero__class_Ozero( X ), !
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, Y, Z ) = c_Groups_Ozero__class_Ozero( X
% 0.80/1.38 ) }.
% 0.80/1.38 { ! class_Rings_Ono__zero__divisors( X ), ! c_Groups_Otimes__class_Otimes(
% 0.80/1.38 X, Z, Y ) = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 0.80/1.38 .
% 0.80/1.38 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.80/1.38 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.80/1.38 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.80/1.38 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.80/1.38 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero( X ) =
% 0.80/1.38 c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 0.80/1.38 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.80/1.38 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.80/1.38 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.80/1.38 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.80/1.38 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.80/1.38 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.80/1.38 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.80/1.38 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.80/1.38 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.80/1.38 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.80/1.38 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.80/1.38 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.80/1.38 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.80/1.38 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.80/1.38 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.80/1.38 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.80/1.38 U ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.80/1.38 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.80/1.38 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.80/1.38 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.80/1.38 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.80/1.38 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.80/1.38 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y, Y )
% 0.80/1.38 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.80/1.38 { ! class_Groups_Oab__group__add( X ), ! Z = Y,
% 0.80/1.38 c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.80/1.38 ) }.
% 0.80/1.38 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.80/1.38 Z, Y ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.80/1.38 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.80/1.38 ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.80/1.38 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ominus__class_Ominus(
% 0.80/1.38 X, Z, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.80/1.38 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.80/1.38 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.80/1.38 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.80/1.38 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.80/1.38 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.80/1.38 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, U, T ) }.
% 0.80/1.38 { ! class_Rings_Ocomm__semiring( X ), c_Groups_Otimes__class_Otimes( X,
% 0.80/1.38 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.80/1.38 ( X, c_Groups_Otimes__class_Otimes( X, T, Y ),
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, Z, Y ) ) }.
% 0.80/1.38 { ! class_Rings_Osemiring( X ), c_Groups_Oplus__class_Oplus( X,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, U, T ), c_Groups_Oplus__class_Oplus( X
% 0.80/1.38 , c_Groups_Otimes__class_Otimes( X, Z, T ), Y ) ) =
% 0.80/1.38 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.80/1.38 c_Groups_Oplus__class_Oplus( X, U, Z ), T ), Y ) }.
% 0.80/1.38 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.80/1.38 c_Groups_Ominus__class_Ominus( X, Z, Y ), Y ) = Z }.
% 0.80/1.38 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.80/1.38 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = Z }.
% 0.80/1.38 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.80/1.38 }.
% 0.80/1.38 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.80/1.38 c_Rings_Oinverse__class_Odivide( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 0.80/1.38 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.80/1.38 { ! class_Rings_Odivision__ring( X ), c_Groups_Otimes__class_Otimes( X, T,
% 0.80/1.38 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 0.80/1.38 c_Rings_Oinverse__class_Odivide( X, c_Groups_Otimes__class_Otimes( X, T,
% 0.80/1.38 Z ), Y ) }.
% 0.80/1.38 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.80/1.38 c_Groups_Oabs__class_Oabs( X, Y ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ) }.
% 0.80/1.38 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! Y =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oabs__class_Oabs( X, Y ) =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ) }.
% 0.80/1.38 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.80/1.38 c_Groups_Oabs__class_Oabs( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ) }.
% 0.80/1.38 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.80/1.38 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.80/1.38 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ),
% 0.80/1.38 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.80/1.38 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.80/1.38 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.80/1.38 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oabs__class_Oabs( X, Y
% 0.80/1.38 ) ) }.
% 0.80/1.38 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.80/1.38 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.80/1.38 c_Groups_Ominus__class_Ominus( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.80/1.38 Y ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.80/1.38 { ! class_Rings_Olinordered__idom( X ), c_Groups_Otimes__class_Otimes( X,
% 0.80/1.38 c_Groups_Oabs__class_Oabs( X, Y ), c_Groups_Oabs__class_Oabs( X, Y ) ) =
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, Y, Y ) }.
% 0.80/1.38 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, Z, Y ) ) =
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.80/1.38 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.80/1.38 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.80/1.38 c_Groups_Oabs__class_Oabs( X, c_Groups_Oplus__class_Oplus( X,
% 0.80/1.38 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ) )
% 0.80/1.38 = c_Groups_Oplus__class_Oplus( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.80/1.38 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.80/1.38 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.80/1.38 c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Z, Y ) )
% 0.80/1.38 = c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Y, Z )
% 0.80/1.38 ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol3( X, Y ) ) }.
% 0.80/1.38 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.80/1.38 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.80/1.38 X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Otimes__class_Otimes( X, Y
% 0.80/1.38 , Y ) ) }.
% 0.80/1.38 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, Z, Y ) ), alpha12( X, Y, Z ), alpha45(
% 0.80/1.38 X, Y, Z ) }.
% 0.80/1.38 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha12( X, Y, Z ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, Z, Y ) ) }.
% 0.80/1.38 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha45( X, Y, Z ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, Z, Y ) ) }.
% 0.80/1.38 { ! alpha45( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.80/1.38 { ! alpha45( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.80/1.38 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ) ), alpha45( X, Y, Z ) }.
% 0.80/1.38 { ! alpha12( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.80/1.38 { ! alpha12( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.80/1.38 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ), Y ), alpha12( X, Y, Z ) }.
% 0.80/1.38 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes( X, Z
% 0.80/1.38 , Y ), c_Groups_Ozero__class_Ozero( X ) ), alpha13( X, Y, Z ), alpha46( X
% 0.80/1.38 , Y, Z ) }.
% 0.80/1.38 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha13( X, Y, Z ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes( X, Z
% 0.80/1.38 , Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.80/1.38 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha46( X, Y, Z ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes( X, Z
% 0.80/1.38 , Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.80/1.38 { ! alpha46( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.80/1.38 { ! alpha46( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.80/1.38 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.80/1.38 ( X ), Y ), alpha46( X, Y, Z ) }.
% 0.80/1.38 { ! alpha13( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.80/1.38 { ! alpha13( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.80/1.38 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ) ), alpha13( X, Y, Z ) }.
% 0.80/1.38 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.80/1.38 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.80/1.38 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ), c_Groups_Otimes__class_Otimes( X, Y, Z
% 0.80/1.38 ) ) }.
% 0.80/1.38 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.80/1.38 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.80/1.38 , c_Groups_Otimes__class_Otimes( X, Y, Z ), c_Groups_Ozero__class_Ozero(
% 0.80/1.38 X ) ) }.
% 0.80/1.38 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.80/1.38 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.80/1.38 , c_Groups_Otimes__class_Otimes( X, Z, Y ), c_Groups_Ozero__class_Ozero(
% 0.80/1.38 X ) ) }.
% 0.80/1.38 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.80/1.38 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.80/1.38 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, Y, Z ), c_Groups_Ozero__class_Ozero( X
% 0.80/1.38 ) ) }.
% 0.80/1.38 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.80/1.38 , Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.80/1.38 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.80/1.38 ), c_Groups_Otimes__class_Otimes( X, Y, Z ) ) }.
% 0.80/1.38 { ! class_Rings_Oordered__semiring( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.80/1.38 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes(
% 0.80/1.38 X, Z, T ), c_Groups_Otimes__class_Otimes( X, Y, T ) ) }.
% 0.80/1.38 { ! class_Rings_Oordered__semiring( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.80/1.38 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes(
% 0.80/1.38 X, T, Z ), c_Groups_Otimes__class_Otimes( X, T, Y ) ) }.
% 0.80/1.38 { ! class_Rings_Oordered__comm__semiring( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.80/1.38 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes(
% 0.80/1.38 X, T, Z ), c_Groups_Otimes__class_Otimes( X, T, Y ) ) }.
% 0.80/1.38 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.80/1.38 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.80/1.38 , c_Groups_Otimes__class_Otimes( X, Y, T ), c_Groups_Otimes__class_Otimes
% 0.80/1.38 ( X, Z, T ) ) }.
% 0.80/1.38 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.80/1.38 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.80/1.38 , c_Groups_Otimes__class_Otimes( X, T, Y ), c_Groups_Otimes__class_Otimes
% 0.80/1.38 ( X, T, Z ) ) }.
% 0.80/1.38 { ! class_Rings_Oordered__semiring( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.80/1.38 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.80/1.38 X ), U ), c_Orderings_Oord__class_Oless__eq( X,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, Z, U ), c_Groups_Otimes__class_Otimes(
% 0.80/1.38 X, Y, T ) ) }.
% 0.80/1.38 { ! class_Rings_Oordered__semiring( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.80/1.38 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.80/1.38 X ), U ), c_Orderings_Oord__class_Oless__eq( X,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, Z, U ), c_Groups_Otimes__class_Otimes(
% 0.80/1.38 X, Y, T ) ) }.
% 0.80/1.38 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.80/1.38 , c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.80/1.38 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.80/1.38 ), c_Groups_Otimes__class_Otimes( X, Z, Y ) ) }.
% 0.80/1.38 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.80/1.38 , Z, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.80/1.38 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.80/1.38 ), c_Groups_Otimes__class_Otimes( X, Z, Y ) ) }.
% 0.80/1.38 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.80/1.38 ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.80/1.38 , c_Groups_Otimes__class_Otimes( X, Z, Y ), c_Groups_Ozero__class_Ozero(
% 0.80/1.38 X ) ) }.
% 0.80/1.38 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.80/1.38 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.80/1.38 X ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, Z, Y ), c_Groups_Ozero__class_Ozero( X
% 0.80/1.38 ) ) }.
% 0.80/1.38 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.80/1.38 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.80/1.38 , c_Groups_Oplus__class_Oplus( X, Y, Z ), c_Groups_Ozero__class_Ozero( X
% 0.80/1.38 ) ) }.
% 0.80/1.38 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.80/1.38 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.80/1.38 Z, Y ) ) }.
% 0.80/1.38 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.80/1.38 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.80/1.38 Y, Z ) ) }.
% 0.80/1.38 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.80/1.38 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.80/1.38 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 0.80/1.38 .
% 0.80/1.38 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.80/1.38 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.80/1.38 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.80/1.38 .
% 0.80/1.38 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.80/1.38 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.80/1.38 X ), Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), ! Z =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.80/1.38 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.80/1.38 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.80/1.38 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.80/1.38 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.80/1.38 ) }.
% 0.80/1.38 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Y,
% 0.80/1.38 Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.80/1.38 ) }.
% 0.80/1.38 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.80/1.38 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X
% 0.80/1.38 , Y, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.80/1.38 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.80/1.38 c_Groups_Oplus__class_Oplus( X, Y, Y ) ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.80/1.38 ) }.
% 0.80/1.38 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.80/1.38 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.80/1.38 ), c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.80/1.38 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 0.80/1.38 , Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.80/1.38 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 0.80/1.38 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.80/1.38 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, W, U ), T ) =
% 0.80/1.38 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, Z, U )
% 0.80/1.38 , Y ), c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.80/1.38 c_Groups_Ominus__class_Ominus( X, W, Z ), U ), T ) = Y }.
% 0.80/1.38 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, c_Groups_Ominus__class_Ominus( X, W, Z
% 0.80/1.38 ), U ), T ) = Y, c_Groups_Oplus__class_Oplus( X,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, W, U ), T ) =
% 0.80/1.38 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, Z, U )
% 0.80/1.38 , Y ) }.
% 0.80/1.38 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, W, U ), T ) =
% 0.80/1.38 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, Z, U )
% 0.80/1.38 , Y ), T = c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes
% 0.80/1.38 ( X, c_Groups_Ominus__class_Ominus( X, Z, W ), U ), Y ) }.
% 0.80/1.38 { ! class_Rings_Oring( X ), ! T = c_Groups_Oplus__class_Oplus( X,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, c_Groups_Ominus__class_Ominus( X, Z, W
% 0.80/1.38 ), U ), Y ), c_Groups_Oplus__class_Oplus( X,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, W, U ), T ) =
% 0.80/1.38 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, Z, U )
% 0.80/1.38 , Y ) }.
% 0.80/1.38 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.80/1.38 , ! T = c_Rings_Oinverse__class_Odivide( X, Z, Y ),
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, T, Y ) = Z }.
% 0.80/1.38 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.80/1.38 , ! c_Groups_Otimes__class_Otimes( X, T, Y ) = Z, T =
% 0.80/1.38 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.80/1.38 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.80/1.38 , ! c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z, T =
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, Z, Y ) }.
% 0.80/1.38 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.80/1.38 , ! T = c_Groups_Otimes__class_Otimes( X, Z, Y ),
% 0.80/1.38 c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z }.
% 0.80/1.38 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.80/1.38 , ! T = c_Groups_Otimes__class_Otimes( X, Z, Y ),
% 0.80/1.38 c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z }.
% 0.80/1.38 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.80/1.38 , ! c_Groups_Otimes__class_Otimes( X, T, Y ) = Z, T =
% 0.80/1.38 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.80/1.38 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.80/1.38 ), c_Groups_Oabs__class_Oabs( X, Y ) = Y }.
% 0.80/1.38 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Y ),
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.80/1.38 }.
% 0.80/1.38 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! Y =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq( X,
% 0.80/1.38 c_Groups_Oabs__class_Oabs( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.80/1.38 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.80/1.38 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.80/1.38 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 0.80/1.38 c_Groups_Oplus__class_Oplus( X, Z, Y ) ), c_Groups_Oplus__class_Oplus( X
% 0.80/1.38 , c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) )
% 0.80/1.38 ) }.
% 0.80/1.38 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X,
% 0.80/1.38 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ),
% 0.80/1.38 c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Y, Z ) )
% 0.80/1.38 ) }.
% 0.80/1.38 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X,
% 0.80/1.38 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ),
% 0.80/1.38 c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Z, Y ) )
% 0.80/1.38 ) }.
% 0.80/1.38 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 0.80/1.38 c_Groups_Ominus__class_Ominus( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.80/1.38 c_Groups_Oabs__class_Oabs( X, Y ) ) ), c_Groups_Oabs__class_Oabs( X,
% 0.80/1.38 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) }.
% 0.80/1.38 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.80/1.38 , c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, W, U
% 0.80/1.38 ), T ), c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X
% 0.80/1.38 , Z, U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.80/1.38 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.80/1.38 c_Groups_Ominus__class_Ominus( X, W, Z ), U ), T ), Y ) }.
% 0.80/1.38 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.80/1.38 , c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.80/1.38 c_Groups_Ominus__class_Ominus( X, W, Z ), U ), T ), Y ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, W, U ), T ),
% 0.80/1.38 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, Z, U )
% 0.80/1.38 , Y ) ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.80/1.38 tc_Nat_Onat, X, U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, U ), Z ) ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.80/1.38 tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), U ), T )
% 0.80/1.38 , Z ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.80/1.38 tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), U ), T )
% 0.80/1.38 , Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.80/1.38 tc_Nat_Onat, X, U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, U ), Z ) ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.80/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.80/1.38 tc_Nat_Onat, c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, U ), T ),
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.80/1.38 tc_Nat_Onat, Y, U ), Z ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.80/1.38 tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), U ), T )
% 0.80/1.38 , Z ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.80/1.38 tc_Nat_Onat, X, U ), T ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, U ), Z ),
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.80/1.38 tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), U ), T )
% 0.80/1.38 = Z }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.80/1.38 tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), U ), T )
% 0.80/1.38 = Z, c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, U ), T ) =
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.80/1.38 tc_Nat_Onat, Y, U ), Z ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.80/1.38 tc_Nat_Onat, Y, U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, U ), Z ) ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T,
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.80/1.38 tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), U ), Z )
% 0.80/1.38 ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T,
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.80/1.38 tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), U ), Z )
% 0.80/1.38 ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.80/1.38 tc_Nat_Onat, Y, U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, U ), Z ) ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.80/1.38 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.80/1.38 tc_Nat_Onat, c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, U ), T ),
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.80/1.38 tc_Nat_Onat, X, U ), Z ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.80/1.38 T, c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.80/1.38 ( tc_Nat_Onat, X, Y ), U ), Z ) ) }.
% 0.80/1.38 { ! c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ) =
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ), Z =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.80/1.38 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ) =
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ) }.
% 0.80/1.38 { ! Y = X, c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ) =
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ) }.
% 0.80/1.38 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.80/1.38 tc_Nat_Onat, T, Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, Z ), X ) ) =
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.80/1.38 tc_Nat_Onat, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, Y ), Z ), X ) }
% 0.80/1.38 .
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.80/1.38 tc_Nat_Onat, Y, U ), T ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, U ), Z ), T =
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.80/1.38 tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), U ), Z )
% 0.80/1.38 }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! T =
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.80/1.38 tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), U ), Z )
% 0.80/1.38 , c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes
% 0.80/1.38 ( tc_Nat_Onat, Y, U ), T ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, U ), Z ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y,
% 0.80/1.38 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, X,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.80/1.38 c_Int_OBit1( c_Int_OPls ) ) ) ) ), ! c_Orderings_Oord__class_Oless(
% 0.80/1.38 tc_RealDef_Oreal, Z, c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, X
% 0.80/1.38 , c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.80/1.38 c_Int_OBit1( c_Int_OPls ) ) ) ) ), ! c_Orderings_Oord__class_Oless__eq(
% 0.80/1.38 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ),
% 0.80/1.38 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Osqrt(
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.80/1.38 c_Power_Opower__class_Opower( tc_RealDef_Oreal, Y,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.38 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal, Z,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.38 c_Int_OPls ) ) ) ) ) ), X ) }.
% 0.80/1.38 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.80/1.38 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 0.80/1.38 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, Y, c_NthRoot_Osqrt(
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.80/1.38 c_Power_Opower__class_Opower( tc_RealDef_Oreal, Y,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.38 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal, X,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.38 c_Int_OPls ) ) ) ) ) ) ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal )
% 0.80/1.38 ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.80/1.38 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ),
% 0.80/1.38 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, X, c_NthRoot_Osqrt(
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.80/1.38 c_Int_OBit1( c_Int_OPls ) ) ) ) ) ), ! c_Orderings_Oord__class_Oless(
% 0.80/1.38 tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Z ),
% 0.80/1.38 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, X, c_NthRoot_Osqrt(
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.80/1.38 c_Int_OBit1( c_Int_OPls ) ) ) ) ) ), c_Orderings_Oord__class_Oless(
% 0.80/1.38 tc_RealDef_Oreal, c_NthRoot_Osqrt( c_Groups_Oplus__class_Oplus(
% 0.80/1.38 tc_RealDef_Oreal, c_Power_Opower__class_Opower( tc_RealDef_Oreal, Y,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.38 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal, Z,
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.38 c_Int_OPls ) ) ) ) ) ), X ) }.
% 0.80/1.38 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.80/1.38 c_Groups_Ominus__class_Ominus( X, c_Groups_Otimes__class_Otimes( X, U, T
% 0.80/1.38 ), c_Groups_Otimes__class_Otimes( X, Z, Y ) ) =
% 0.80/1.38 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, c_Groups_Ominus__class_Ominus( X, U, Z
% 0.80/1.38 ), c_Groups_Ominus__class_Ominus( X, T, Y ) ),
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, c_Groups_Ominus__class_Ominus( X, U, Z
% 0.80/1.38 ), Y ) ), c_Groups_Otimes__class_Otimes( X, Z,
% 0.80/1.38 c_Groups_Ominus__class_Ominus( X, T, Y ) ) ) }.
% 0.80/1.38 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X,
% 0.80/1.38 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs
% 0.80/1.38 ( tc_RealDef_Oreal, X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 0.80/1.38 , X ) }.
% 0.80/1.38 { c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal,
% 0.80/1.38 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) = X }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.80/1.38 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Osqrt( Y ),
% 0.80/1.38 c_NthRoot_Osqrt( X ) ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Osqrt( Y ),
% 0.80/1.38 c_NthRoot_Osqrt( X ) ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.80/1.38 Y, X ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.80/1.38 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Osqrt( Y ),
% 0.80/1.38 c_NthRoot_Osqrt( X ) ) }.
% 0.80/1.38 { ! c_NthRoot_Osqrt( X ) = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X
% 0.80/1.38 = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.80/1.38 { ! X = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X )
% 0.80/1.38 = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.80/1.38 { c_NthRoot_Osqrt( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) =
% 0.80/1.38 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.80/1.38 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.80/1.38 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.80/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, Y,
% 0.80/1.38 c_Power_Opower__class_Opower( X, Y, Z ) ), c_Power_Opower__class_Opower(
% 0.80/1.38 X, Y, Z ) ) }.
% 0.80/1.38 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.80/1.38 ( tc_Int_Oint, c_Int_OPls, Y ) }.
% 0.80/1.38 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, Y ),
% 0.80/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.80/1.38 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Y
% 0.80/1.38 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless(
% 0.80/1.38 tc_Int_Oint, Y, c_Int_OPls ) }.
% 0.80/1.38 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, c_Int_OPls ),
% 0.80/1.38 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Y
% 0.80/1.38 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.80/1.38 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.80/1.38 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.80/1.38 c_Orderings_Oord__class_Oless( X, c_Power_Opower__class_Opower( X, Y,
% 0.80/1.38 c_Nat_OSuc( Z ) ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.80/1.38 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.80/1.38 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Power_Opower__class_Opower( X, Y
% 0.80/1.38 , T ), c_Power_Opower__class_Opower( X, Y, Z ) ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.80/1.38 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.80/1.38 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Power_Opower__class_Opower( X, Y
% 0.80/1.38 , T ), c_Power_Opower__class_Opower( X, Y, Z ) ) }.
% 0.80/1.38 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.80/1.38 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Power_Opower__class_Opower( X, Y
% 0.80/1.38 , T ), c_Power_Opower__class_Opower( X, Y, Z ) ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.80/1.38 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Z
% 0.80/1.38 ), c_Int_Onumber__class_Onumber__of( X, Y ) ),
% 0.80/1.38 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, Y ) }.
% 0.80/1.38 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, Y ),
% 0.80/1.38 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Z
% 0.80/1.38 ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.80/1.38 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.80/1.38 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 0.80/1.38 , T, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.80/1.38 c_Power_Opower__class_Opower( X, T, Y ), c_Power_Opower__class_Opower( X
% 0.80/1.38 , T, Z ) ) }.
% 0.80/1.38 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.80/1.38 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.80/1.38 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 0.80/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 0.80/1.38 c_Power_Opower__class_Opower( X, Y, Z ) ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Osqrt( X ),
% 0.80/1.38 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.80/1.38 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.80/1.38 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.80/1.38 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.80/1.38 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Osqrt( X ),
% 0.80/1.38 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.80/1.38 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ),
% 0.80/1.38 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.80/1.38 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.80/1.38 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 0.80/1.38 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.80/1.38 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ) }.
% 0.80/1.38 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.80/1.38 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Power_Opower__class_Opower
% 0.80/1.38 ( X, Y, T ) = c_Power_Opower__class_Opower( X, Y, Z ), T = Z }.
% 0.80/1.38 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.80/1.38 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! T = Z,
% 0.80/1.38 c_Power_Opower__class_Opower( X, Y, T ) = c_Power_Opower__class_Opower( X
% 0.80/1.38 , Y, Z ) }.
% 0.80/1.38 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.80/1.38 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.80/1.38 c_Groups_Oone__class_Oone( X ), T ), c_Orderings_Oord__class_Oless( X,
% 0.80/1.38 c_Power_Opower__class_Opower( X, T, Z ), c_Power_Opower__class_Opower( X
% 0.80/1.38 , T, Y ) ) }.
% 0.80/1.38 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.80/1.38 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.80/1.38 ( X, c_Power_Opower__class_Opower( X, Y, T ),
% 0.80/1.38 c_Power_Opower__class_Opower( X, Y, Z ) ), c_Orderings_Oord__class_Oless
% 0.80/1.38 ( tc_Nat_Onat, T, Z ) }.
% 0.80/1.38 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.80/1.38 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.80/1.38 ( X, c_Power_Opower__class_Opower( X, Y, T ),
% 0.80/1.38 c_Power_Opower__class_Opower( X, Y, Z ) ), c_Orderings_Oord__class_Oless
% 0.80/1.38 ( tc_Nat_Onat, T, Z ) }.
% 0.80/1.38 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.80/1.38 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.80/1.38 ( tc_Nat_Onat, T, Z ), c_Orderings_Oord__class_Oless( X,
% 0.80/1.38 c_Power_Opower__class_Opower( X, Y, T ), c_Power_Opower__class_Opower( X
% 0.80/1.38 , Y, Z ) ) }.
% 0.80/1.38 { ! c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) =
% 0.80/1.38 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), ! Y = X }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), Y = X,
% 0.80/1.38 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.80/1.38 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), Y = X }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.80/1.38 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.80/1.38 { ! class_Groups_Omonoid__mult( X ), c_Power_Opower__class_Opower( X,
% 0.80/1.38 c_Groups_Oone__class_Oone( X ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.80/1.38 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.80/1.38 Y, c_Groups_Oone__class_Oone( X ) ) = Y }.
% 0.80/1.38 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.80/1.38 c_Groups_Oone__class_Oone( X ), Y ) = Y }.
% 0.80/1.38 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.80/1.38 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.80/1.38 X, c_Groups_Oone__class_Oone( X ), c_Power_Opower__class_Opower( X, Y,
% 0.80/1.38 c_Nat_OSuc( Z ) ) ) }.
% 0.80/1.38 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.80/1.38 X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z,
% 0.80/1.38 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.80/1.38 ), c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.80/1.38 c_Groups_Oone__class_Oone( X ) ) ) ) }.
% 0.80/1.38 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.80/1.38 X, Z, Y ), c_Orderings_Oord__class_Oless( X,
% 0.80/1.38 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.80/1.38 ), c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.80/1.38 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.80/1.38 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.80/1.38 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.80/1.38 X, c_Power_Opower__class_Opower( X, Y, Z ), c_Groups_Otimes__class_Otimes
% 0.80/1.38 ( X, Y, c_Power_Opower__class_Opower( X, Y, Z ) ) ) }.
% 0.80/1.38 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.80/1.38 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.80/1.38 X, c_Groups_Oone__class_Oone( X ), c_Groups_Otimes__class_Otimes( X, Y,
% 0.80/1.38 c_Power_Opower__class_Opower( X, Y, Z ) ) ) }.
% 0.80/1.38 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.80/1.38 ( tc_Int_Oint, c_Int_OBit1( c_Int_OPls ), Y ) }.
% 0.80/1.38 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( c_Int_OPls ), Y
% 0.80/1.38 ), c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 0.80/1.38 c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.80/1.38 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Y
% 0.80/1.38 ), c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless(
% 0.80/1.38 tc_Int_Oint, Y, c_Int_OBit1( c_Int_OPls ) ) }.
% 0.80/1.38 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, c_Int_OBit1( c_Int_OPls )
% 0.80/1.38 ), c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X
% 0.80/1.38 , Y ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.80/1.38 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X, Y
% 0.80/1.38 , c_Groups_Oone__class_Oone( X ) ) = Y }.
% 0.80/1.38 { ! class_Rings_Olinordered__idom( X ), Z = Y,
% 0.80/1.38 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.80/1.38 X, Y, Z ) }.
% 0.80/1.38 { ! class_Groups_Oone( X ), ! c_Groups_Oone__class_Oone( X ) = Y, Y =
% 0.80/1.38 c_Groups_Oone__class_Oone( X ) }.
% 0.80/1.38 { ! class_Groups_Oone( X ), ! Y = c_Groups_Oone__class_Oone( X ),
% 0.80/1.38 c_Groups_Oone__class_Oone( X ) = Y }.
% 0.80/1.38 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.80/1.38 ( X, c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero( X ) ) }
% 0.80/1.38 .
% 0.80/1.38 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.80/1.38 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.80/1.38 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.80/1.38 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.80/1.38 ( X, c_Groups_Oone__class_Oone( X ), Z ), c_Orderings_Oord__class_Oless(
% 0.80/1.38 X, c_Groups_Oone__class_Oone( X ), c_Groups_Otimes__class_Otimes( X, Y, Z
% 0.80/1.38 ) ) }.
% 0.80/1.38 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.80/1.38 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.80/1.38 c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ) ) }.
% 0.80/1.38 { ! class_Groups_Ocomm__monoid__mult( X ), c_Groups_Otimes__class_Otimes( X
% 0.80/1.38 , Y, c_Groups_Oone__class_Oone( X ) ) = Y }.
% 0.80/1.38 { ! class_Groups_Omonoid__mult( X ), c_Groups_Otimes__class_Otimes( X, Y,
% 0.80/1.38 c_Groups_Oone__class_Oone( X ) ) = Y }.
% 0.80/1.38 { ! class_Groups_Ocomm__monoid__mult( X ), c_Groups_Otimes__class_Otimes( X
% 0.80/1.38 , c_Groups_Oone__class_Oone( X ), Y ) = Y }.
% 0.80/1.38 { ! class_Groups_Omonoid__mult( X ), c_Groups_Otimes__class_Otimes( X,
% 0.80/1.38 c_Groups_Oone__class_Oone( X ), Y ) = Y }.
% 0.80/1.38 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.80/1.38 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.80/1.38 ( X, Z, Y ) }.
% 0.80/1.38 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, T )
% 0.80/1.38 , c_Groups_Oplus__class_Oplus( X, Y, T ) ), c_Orderings_Oord__class_Oless
% 0.80/1.38 ( X, Z, Y ) }.
% 0.80/1.38 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.80/1.38 ( X, U, T ), c_Orderings_Oord__class_Oless( X,
% 0.80/1.38 c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X, Y
% 0.80/1.38 , T ) ) }.
% 0.80/1.38 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.80/1.38 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.80/1.38 , T, Y ) ) }.
% 0.80/1.38 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.80/1.38 X, c_Groups_Oplus__class_Oplus( X, Z, T ), c_Groups_Oplus__class_Oplus( X
% 0.80/1.38 , Y, T ) ) }.
% 0.80/1.38 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.80/1.38 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.80/1.38 ( X, Z, Y ) }.
% 0.80/1.38 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.80/1.38 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.80/1.38 , T, Y ) ) }.
% 0.80/1.38 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.80/1.38 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ), c_Orderings_Oord__class_Oless
% 0.80/1.38 ( X, T, Y ) }.
% 0.80/1.38 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless( X, T, Y ), c_Orderings_Oord__class_Oless(
% 0.80/1.38 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.80/1.38 , Y, Z ) ) }.
% 0.80/1.38 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.80/1.38 c_Groups_Oone__class_Oone( X ) }.
% 0.80/1.38 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Oone__class_Oone( X ) =
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ) }.
% 0.80/1.38 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.80/1.38 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.80/1.38 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, U, T ),
% 0.80/1.38 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.80/1.38 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.80/1.38 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.80/1.38 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.80/1.38 c_Orderings_Oord__class_Oless( X, U, T ) }.
% 0.80/1.38 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.80/1.38 , Y, c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) )
% 0.80/1.38 ) }.
% 0.80/1.38 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.80/1.38 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oone__class_Oone
% 0.80/1.38 ( tc_RealDef_Oreal ), c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) )
% 0.80/1.38 ) }.
% 0.80/1.38 { ! class_Rings_Olinordered__semiring__1__strict( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.80/1.38 ( X, T, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ), U ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), W
% 0.80/1.38 ), ! c_Groups_Oplus__class_Oplus( X, U, W ) = c_Groups_Oone__class_Oone
% 0.80/1.38 ( X ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X,
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, U, Z ), c_Groups_Otimes__class_Otimes(
% 0.80/1.38 X, W, T ) ), Y ) }.
% 0.80/1.38 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.80/1.38 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ), Z ), ! c_Orderings_Oord__class_Oless(
% 0.80/1.38 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), T ),
% 0.80/1.38 c_Orderings_Oord__class_Oless( X, c_Power_Opower__class_Opower( X, Z, T )
% 0.80/1.38 , c_Power_Opower__class_Opower( X, Y, T ) ) }.
% 0.80/1.38 { ! class_Power_Opower( X ), ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 0.80/1.38 ), c_Power_Opower__class_Opower( X, Y, Z ) = c_Groups_Oone__class_Oone(
% 0.80/1.38 X ) }.
% 0.80/1.38 { ! class_Power_Opower( X ), Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.80/1.38 , c_Power_Opower__class_Opower( X, Y, Z ) = c_Groups_Otimes__class_Otimes
% 0.80/1.38 ( X, Y, c_Power_Opower__class_Opower( X, Y, c_Groups_Ominus__class_Ominus
% 0.80/1.38 ( tc_Nat_Onat, Z, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 0.80/1.38 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.80/1.38 , c_Groups_Otimes__class_Otimes( X, Y, Y ), c_Groups_Ozero__class_Ozero(
% 0.80/1.38 X ) ) }.
% 0.80/1.38 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, T, Z
% 0.80/1.38 ), c_Groups_Otimes__class_Otimes( X, Y, Z ) ), alpha14( X, Y, Z, T ),
% 0.80/1.38 alpha47( X, Y, Z, T ) }.
% 0.80/1.38 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha14( X, Y, Z, T ),
% 0.80/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, T, Z
% 0.80/1.38 ), c_Groups_Otimes__class_Otimes( X, Y, Z ) ) }.
% 0.80/1.38 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha47( X, Y, Z, T ),
% 0.80/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, T, Z
% 0.80/1.38 ), c_Groups_Otimes__class_Otimes( X, Y, Z ) ) }.
% 0.80/1.38 { ! alpha47( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.80/1.38 { ! alpha47( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, T ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.80/1.38 , ! c_Orderings_Oord__class_Oless( X, Y, T ), alpha47( X, Y, Z, T ) }.
% 0.80/1.38 { ! alpha14( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.80/1.38 { ! alpha14( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.80/1.38 , ! c_Orderings_Oord__class_Oless( X, T, Y ), alpha14( X, Y, Z, T ) }.
% 0.80/1.38 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, T, Z
% 0.80/1.38 ), c_Groups_Otimes__class_Otimes( X, T, Y ) ), alpha15( X, Y, Z, T ),
% 0.80/1.38 alpha48( X, Y, Z, T ) }.
% 0.80/1.38 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha15( X, Y, Z, T ),
% 0.80/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, T, Z
% 0.80/1.38 ), c_Groups_Otimes__class_Otimes( X, T, Y ) ) }.
% 0.80/1.38 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha48( X, Y, Z, T ),
% 0.80/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, T, Z
% 0.80/1.38 ), c_Groups_Otimes__class_Otimes( X, T, Y ) ) }.
% 0.80/1.38 { ! alpha48( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.80/1.38 { ! alpha48( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless( X, T, c_Groups_Ozero__class_Ozero( X ) )
% 0.80/1.38 , ! c_Orderings_Oord__class_Oless( X, Y, Z ), alpha48( X, Y, Z, T ) }.
% 0.80/1.38 { ! alpha15( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ), T ) }.
% 0.80/1.38 { ! alpha15( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T )
% 0.80/1.38 , ! c_Orderings_Oord__class_Oless( X, Z, Y ), alpha15( X, Y, Z, T ) }.
% 0.80/1.38 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.80/1.38 ! c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, Y,
% 0.80/1.38 T ), c_Groups_Otimes__class_Otimes( X, Y, Z ) ),
% 0.80/1.38 c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.80/1.38 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.80/1.38 ! c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless
% 0.80/1.38 ( X, c_Groups_Otimes__class_Otimes( X, Y, T ),
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, Y, Z ) ) }.
% 0.80/1.38 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.80/1.38 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.80/1.38 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, Y, Z ) ) }.
% 0.80/1.38 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.80/1.38 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.80/1.38 , c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, Y,
% 0.80/1.38 Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.80/1.38 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.80/1.38 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.80/1.38 , c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, Z,
% 0.80/1.38 Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.80/1.38 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, Z, Y ) ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.80/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.80/1.38 .
% 0.80/1.38 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, Z, Y ) ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.80/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ) }
% 0.80/1.38 .
% 0.80/1.38 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.80/1.38 ! c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, Y,
% 0.80/1.38 T ), c_Groups_Otimes__class_Otimes( X, Y, Z ) ),
% 0.80/1.38 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.80/1.38 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.80/1.38 ! c_Orderings_Oord__class_Oless( X, Z, T ), c_Orderings_Oord__class_Oless
% 0.80/1.38 ( X, c_Groups_Otimes__class_Otimes( X, Y, T ),
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, Y, Z ) ) }.
% 0.80/1.38 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.80/1.38 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.80/1.38 , c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, Y,
% 0.80/1.38 Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.80/1.38 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.80/1.38 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.80/1.38 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, Y, Z ) ) }.
% 0.80/1.38 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.80/1.38 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.80/1.38 ( X, c_Groups_Otimes__class_Otimes( X, Z, T ),
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, Y, T ) ) }.
% 0.80/1.38 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.80/1.38 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.80/1.38 ( X, c_Groups_Otimes__class_Otimes( X, T, Z ),
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, T, Y ) ) }.
% 0.80/1.38 { ! class_Rings_Olinordered__comm__semiring__strict( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.80/1.38 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.80/1.38 ( X, c_Groups_Otimes__class_Otimes( X, T, Z ),
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, T, Y ) ) }.
% 0.80/1.38 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.80/1.38 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.80/1.38 ( X, c_Groups_Otimes__class_Otimes( X, Y, T ),
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, Z, T ) ) }.
% 0.80/1.38 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.80/1.38 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.80/1.38 ( X, c_Groups_Otimes__class_Otimes( X, T, Y ),
% 0.80/1.38 c_Groups_Otimes__class_Otimes( X, T, Z ) ) }.
% 0.80/1.38 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.80/1.38 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.80/1.38 , c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.80/1.38 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.80/1.38 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.80/1.38 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless(
% 0.80/1.38 X, T, c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.80/1.38 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.80/1.38 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.80/1.38 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.80/1.38 c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.80/1.38 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.80/1.38 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Y
% 0.80/1.38 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.80/1.38 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.80/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.80/1.38 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.80/1.38 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.80/1.38 c_Groups_Oplus__class_Oplus( X, Y, Y ) ), c_Orderings_Oord__class_Oless(
% 0.80/1.38 X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.80/1.38 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.80/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.80/1.38 c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.80/1.38 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.80/1.38 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.80/1.38 ) ), c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 0.80/1.38 ) ) }.
% 0.80/1.38 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.80/1.38 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.80/1.38 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.80/1.38 ) ) }.
% 0.80/1.38 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.80/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, U )
% 0.80/1.38 , c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.80/1.38 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless( X, U, T ), c_Orderings_Oord__class_Oless(
% 0.80/1.38 X, c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X
% 0.80/1.38 , Y, T ) ) }.
% 0.80/1.38 { ! class_Int_Onumber( X ), ! class_Orderings_Olinorder( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 0.80/1.38 , Z ), c_Int_Onumber__class_Onumber__of( X, Y ) ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Y
% 0.80/1.38 ), c_Int_Onumber__class_Onumber__of( X, Z ) ) }.
% 0.80/1.38 { ! class_Int_Onumber( X ), ! class_Orderings_Olinorder( X ),
% 0.80/1.38 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Y
% 0.80/1.38 ), c_Int_Onumber__class_Onumber__of( X, Z ) ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 0.80/1.38 , Z ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.80/1.38 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.80/1.38 X, c_Groups_Ominus__class_Ominus( X, Z, Y ), c_Groups_Ozero__class_Ozero
% 0.80/1.38 ( X ) ) }.
% 0.80/1.38 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.80/1.38 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.80/1.38 , Z, Y ) }.
% 0.80/1.38 { ! class_Rings_Olinordered__semidom( X ),
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.80/1.38 c_Groups_Oone__class_Oone( X ) ) }.
% 0.80/1.38 { ! class_Rings_Olinordered__semidom( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.80/1.38 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.80/1.38 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless
% 0.80/1.38 ( X, c_Groups_Ozero__class_Ozero( X ), c_Power_Opower__class_Opower( X, Y
% 0.80/1.38 , Z ) ) }.
% 0.80/1.38 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.80/1.38 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, T,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.80/1.38 c_Rings_Oinverse__class_Odivide( X, Y, T ),
% 0.80/1.38 c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 0.80/1.38 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.80/1.38 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless( X,
% 0.80/1.38 c_Rings_Oinverse__class_Odivide( X, Z, T ),
% 0.80/1.38 c_Rings_Oinverse__class_Odivide( X, Y, T ) ) }.
% 0.80/1.38 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.80/1.38 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.80/1.38 ( X, Z, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.80/1.38 ( X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X
% 0.80/1.38 , Y, Z ) ) }.
% 0.80/1.38 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.80/1.38 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.80/1.38 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless
% 0.80/1.38 ( X, c_Rings_Oinverse__class_Odivide( X, Y, Z ),
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.80/1.38 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.80/1.38 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.80/1.38 ( X, Z, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.80/1.38 ( X, c_Rings_Oinverse__class_Odivide( X, Y, Z ),
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.80/1.38 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.80/1.38 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.80/1.38 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless
% 0.80/1.38 ( X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X
% 0.80/1.38 , Y, Z ) ) }.
% 0.80/1.38 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.80/1.38 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, Z,
% 0.80/1.38 Y ), c_Groups_Ozero__class_Ozero( X ) ), alpha16( X, Y, Z ), alpha49( X,
% 0.80/1.38 Y, Z ) }.
% 0.80/1.38 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha16( X, Y, Z
% 0.80/1.38 ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X
% 0.80/1.38 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.80/1.38 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha49( X, Y, Z
% 0.80/1.38 ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X
% 0.80/1.38 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.80/1.38 { ! alpha49( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.80/1.38 { ! alpha49( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.80/1.38 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.80/1.38 , ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.80/1.38 ), alpha49( X, Y, Z ) }.
% 0.80/1.38 { ! alpha16( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.80/1.38 { ! alpha16( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 0.80/1.38 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.80/1.39 , ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.80/1.39 ), alpha16( X, Y, Z ) }.
% 0.80/1.39 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.80/1.39 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ), alpha17( X, Y, Z ), alpha50
% 0.80/1.39 ( X, Y, Z ) }.
% 0.80/1.39 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha17( X, Y, Z
% 0.80/1.39 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.80/1.39 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.80/1.39 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha50( X, Y, Z
% 0.80/1.39 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.80/1.39 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.80/1.39 { ! alpha50( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.80/1.39 { ! alpha50( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.80/1.39 , ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.80/1.39 ), alpha50( X, Y, Z ) }.
% 0.80/1.39 { ! alpha17( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.80/1.39 { ! alpha17( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.80/1.39 , ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.80/1.39 ), alpha17( X, Y, Z ) }.
% 0.80/1.39 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.80/1.39 c_Groups_Otimes__class_Otimes( X, Z, Y ), Y ) =
% 0.80/1.39 c_Groups_Otimes__class_Otimes( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.80/1.39 c_Groups_Oone__class_Oone( X ) ), Y ) }.
% 0.80/1.39 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.80/1.39 , c_Groups_Otimes__class_Otimes( X, Y, Z ) ) =
% 0.80/1.39 c_Groups_Otimes__class_Otimes( X, c_Groups_Oplus__class_Oplus( X, Y,
% 0.80/1.39 c_Groups_Oone__class_Oone( X ) ), Z ) }.
% 0.80/1.39 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.80/1.39 , Y ) = c_Groups_Otimes__class_Otimes( X, c_Groups_Oplus__class_Oplus( X
% 0.80/1.39 , c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ), Y ) }
% 0.80/1.39 .
% 0.80/1.39 { ! class_Rings_Olinordered__semidom( X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 0.80/1.39 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.80/1.39 c_Power_Opower__class_Opower( X, Y, Z ) ) }.
% 0.80/1.39 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X, Y ),
% 0.80/1.39 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.80/1.39 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.80/1.39 c_Groups_Oabs__class_Oabs( X, Y ) ), ! Y = c_Groups_Ozero__class_Ozero( X
% 0.80/1.39 ) }.
% 0.80/1.39 { ! class_Groups_Oordered__ab__group__add__abs( X ), Y =
% 0.80/1.39 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.80/1.39 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.80/1.39 c_Groups_Oabs__class_Oabs( X, Y ) = Y }.
% 0.80/1.39 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.80/1.39 , ! c_Rings_Oinverse__class_Odivide( X, Z, Y ) =
% 0.80/1.39 c_Groups_Oone__class_Oone( X ), Z = Y }.
% 0.80/1.39 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.80/1.39 , ! Z = Y, c_Rings_Oinverse__class_Odivide( X, Z, Y ) =
% 0.80/1.39 c_Groups_Oone__class_Oone( X ) }.
% 0.80/1.39 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.80/1.39 , c_Rings_Oinverse__class_Odivide( X, Y, Y ) = c_Groups_Oone__class_Oone
% 0.80/1.39 ( X ) }.
% 0.80/1.39 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Y =
% 0.80/1.39 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X, Y,
% 0.80/1.39 Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.80/1.39 { ! class_Rings_Odivision__ring__inverse__zero( X ), Y =
% 0.80/1.39 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X, Y,
% 0.80/1.39 Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.80/1.39 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.80/1.39 , c_Groups_Oabs__class_Oabs( X, Z ), Y ), ! c_Orderings_Oord__class_Oless
% 0.80/1.39 ( X, c_Groups_Oabs__class_Oabs( X, U ), T ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X,
% 0.80/1.39 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, U ) ),
% 0.80/1.39 c_Groups_Otimes__class_Otimes( X, Y, T ) ) }.
% 0.80/1.39 { ! class_Power_Opower( X ), c_Power_Opower__class_Opower( X, Y,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone
% 0.80/1.39 ( X ) }.
% 0.80/1.39 { ! class_Rings_Ocomm__semiring__1( X ), c_Power_Opower__class_Opower( X, Y
% 0.80/1.39 , c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.80/1.39 c_Groups_Oone__class_Oone( X ) }.
% 0.80/1.39 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.80/1.39 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oone__class_Oone( X ),
% 0.80/1.39 c_Power_Opower__class_Opower( X, Z, Y ) ) = c_Power_Opower__class_Opower
% 0.80/1.39 ( X, c_Rings_Oinverse__class_Odivide( X, c_Groups_Oone__class_Oone( X ),
% 0.80/1.39 Z ), Y ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Z, X ),
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Y, X ) ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Z, X ),
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Y, X ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, Y ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, Z ),
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, Y ) ) }.
% 0.80/1.39 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, X ) ), X =
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.80/1.39 { ! X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, X ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ) }
% 0.80/1.39 .
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), ! c_NthRoot_Osqrt(
% 0.80/1.39 X ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Osqrt( X ),
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Osqrt( X ),
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ) }
% 0.80/1.39 .
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.80/1.39 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ),
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.80/1.39 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.80/1.39 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.80/1.39 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Osqrt( X
% 0.80/1.39 ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.80/1.39 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.80/1.39 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Osqrt( X )
% 0.80/1.39 , c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.80/1.39 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.80/1.39 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ) }.
% 0.80/1.39 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.80/1.39 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_NthRoot_Osqrt(
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.80/1.39 c_Int_OBit1( c_Int_OPls ) ) ) ) ) }.
% 0.80/1.39 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.80/1.39 class_Int_Onumber__ring( X ), c_Orderings_Oord__class_Oless( X,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.80/1.39 c_Groups_Oone__class_Oone( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.80/1.39 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) }.
% 0.80/1.39 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.80/1.39 ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes( X
% 0.80/1.39 , Y, T ), c_Groups_Otimes__class_Otimes( X, Y, Z ) ),
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.80/1.39 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.80/1.39 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes( X, Y
% 0.80/1.39 , T ), c_Groups_Otimes__class_Otimes( X, Y, Z ) ) }.
% 0.80/1.39 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.80/1.39 ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes( X
% 0.80/1.39 , Y, T ), c_Groups_Otimes__class_Otimes( X, Y, Z ) ),
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.80/1.39 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.80/1.39 ! c_Orderings_Oord__class_Oless__eq( X, Z, T ),
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes( X, Y
% 0.80/1.39 , T ), c_Groups_Otimes__class_Otimes( X, Y, Z ) ) }.
% 0.80/1.39 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.80/1.39 ( X, U, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.80/1.39 ), c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, Z
% 0.80/1.39 , U ), c_Groups_Otimes__class_Otimes( X, Y, T ) ) }.
% 0.80/1.39 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.80/1.39 ( X, U, T ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.80/1.39 ), c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, Z
% 0.80/1.39 , U ), c_Groups_Otimes__class_Otimes( X, Y, T ) ) }.
% 0.80/1.39 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.80/1.39 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.80/1.39 , U ), c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X
% 0.80/1.39 , Z, U ), c_Groups_Otimes__class_Otimes( X, Y, T ) ) }.
% 0.80/1.39 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless( X, U, T ), ! c_Orderings_Oord__class_Oless
% 0.80/1.39 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.80/1.39 ), c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, Z
% 0.80/1.39 , U ), c_Groups_Otimes__class_Otimes( X, Y, T ) ) }.
% 0.80/1.39 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.80/1.39 ( X, c_Groups_Otimes__class_Otimes( X, T, Z ),
% 0.80/1.39 c_Groups_Otimes__class_Otimes( X, Y, Z ) ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.80/1.39 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.80/1.39 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, T, Z
% 0.80/1.39 ), c_Groups_Otimes__class_Otimes( X, Y, Z ) ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.80/1.39 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.80/1.39 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.80/1.39 ( X, c_Groups_Otimes__class_Otimes( X, T, Z ),
% 0.80/1.39 c_Groups_Otimes__class_Otimes( X, T, Y ) ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.80/1.39 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.80/1.39 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, T, Z
% 0.80/1.39 ), c_Groups_Otimes__class_Otimes( X, T, Y ) ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.80/1.39 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.80/1.39 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes( X, T
% 0.80/1.39 , Z ), c_Groups_Otimes__class_Otimes( X, Y, Z ) ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.80/1.39 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes( X, T
% 0.80/1.39 , Z ), c_Groups_Otimes__class_Otimes( X, T, Y ) ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.80/1.39 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.80/1.39 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.80/1.39 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.80/1.39 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.80/1.39 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.80/1.39 ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.80/1.39 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.80/1.39 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.80/1.39 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.80/1.39 ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.80/1.39 ) ) }.
% 0.80/1.39 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.80/1.39 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.80/1.39 ) ) }.
% 0.80/1.39 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.80/1.39 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.80/1.39 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.80/1.39 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.80/1.39 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.80/1.39 ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.80/1.39 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.80/1.39 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.80/1.39 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.80/1.39 , c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, Z, Z
% 0.80/1.39 ), c_Groups_Otimes__class_Otimes( X, Y, Y ) ),
% 0.80/1.39 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.80/1.39 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.80/1.39 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, Z, Z )
% 0.80/1.39 , c_Groups_Otimes__class_Otimes( X, Y, Y ) ) ), ! Z =
% 0.80/1.39 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.80/1.39 }.
% 0.80/1.39 { ! class_Rings_Olinordered__ring__strict( X ), Z =
% 0.80/1.39 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.80/1.39 c_Groups_Otimes__class_Otimes( X, Z, Z ), c_Groups_Otimes__class_Otimes(
% 0.80/1.39 X, Y, Y ) ) ) }.
% 0.80/1.39 { ! class_Rings_Olinordered__ring__strict( X ), Y =
% 0.80/1.39 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.80/1.39 c_Groups_Otimes__class_Otimes( X, Z, Z ), c_Groups_Otimes__class_Otimes(
% 0.80/1.39 X, Y, Y ) ) ) }.
% 0.80/1.39 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.80/1.39 ( X, c_Power_Opower__class_Opower( X, Z, T ),
% 0.80/1.39 c_Power_Opower__class_Opower( X, Y, T ) ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.80/1.39 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.80/1.39 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.80/1.39 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.80/1.39 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.80/1.39 ( X ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.80/1.39 c_Groups_Otimes__class_Otimes( X, Y, Z ), Y ) }.
% 0.80/1.39 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.80/1.39 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.80/1.39 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.80/1.39 ( X ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.80/1.39 c_Groups_Otimes__class_Otimes( X, Z, Y ), Y ) }.
% 0.80/1.39 { ! class_Fields_Olinordered__field( X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.80/1.39 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.80/1.39 ) ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.80/1.39 X ), c_Rings_Oinverse__class_Odivide( X, Y, Z ) ) }.
% 0.80/1.39 { ! class_Fields_Olinordered__field( X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.80/1.39 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.80/1.39 , Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.80/1.39 c_Rings_Oinverse__class_Odivide( X, Y, Z ), c_Groups_Ozero__class_Ozero(
% 0.80/1.39 X ) ) }.
% 0.80/1.39 { ! class_Fields_Olinordered__field( X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.80/1.39 ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.80/1.39 ! c_Orderings_Oord__class_Oless__eq( X, T, U ),
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.80/1.39 , Y, U ), c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 0.80/1.39 { ! class_Fields_Olinordered__field( X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.80/1.39 ), ! c_Orderings_Oord__class_Oless( X, Y, Z ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.80/1.39 ! c_Orderings_Oord__class_Oless__eq( X, T, U ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, Y,
% 0.80/1.39 U ), c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 0.80/1.39 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.80/1.39 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( X, Y, Z ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.80/1.39 ! c_Orderings_Oord__class_Oless( X, T, U ), c_Orderings_Oord__class_Oless
% 0.80/1.39 ( X, c_Rings_Oinverse__class_Odivide( X, Y, U ),
% 0.80/1.39 c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 0.80/1.39 { ! class_Fields_Olinordered__field( X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.80/1.39 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.80/1.39 ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.80/1.39 c_Rings_Oinverse__class_Odivide( X, Y, Z ), c_Groups_Ozero__class_Ozero(
% 0.80/1.39 X ) ) }.
% 0.80/1.39 { ! class_Fields_Olinordered__field( X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.80/1.39 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.80/1.39 , Z ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.80/1.39 ( X ), c_Rings_Oinverse__class_Odivide( X, Y, Z ) ) }.
% 0.80/1.39 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.80/1.39 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, W, U )
% 0.80/1.39 , T ), c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.80/1.39 Z, U ), Y ) ), c_Orderings_Oord__class_Oless( X,
% 0.80/1.39 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.80/1.39 c_Groups_Ominus__class_Ominus( X, W, Z ), U ), T ), Y ) }.
% 0.80/1.39 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.80/1.39 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.80/1.39 c_Groups_Ominus__class_Ominus( X, W, Z ), U ), T ), Y ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X,
% 0.80/1.39 c_Groups_Otimes__class_Otimes( X, W, U ), T ),
% 0.80/1.39 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, Z, U )
% 0.80/1.39 , Y ) ) }.
% 0.80/1.39 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.80/1.39 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, W, U )
% 0.80/1.39 , T ), c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.80/1.39 Z, U ), Y ) ), c_Orderings_Oord__class_Oless( X, T,
% 0.80/1.39 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.80/1.39 c_Groups_Ominus__class_Ominus( X, Z, W ), U ), Y ) ) }.
% 0.80/1.39 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X, T
% 0.80/1.39 , c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.80/1.39 c_Groups_Ominus__class_Ominus( X, Z, W ), U ), Y ) ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X,
% 0.80/1.39 c_Groups_Otimes__class_Otimes( X, W, U ), T ),
% 0.80/1.39 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, Z, U )
% 0.80/1.39 , Y ) ) }.
% 0.80/1.39 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.80/1.39 Z, Y ) ), alpha51( X, Y, Z, T ) }.
% 0.80/1.39 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.80/1.39 Z, Y ) ), alpha65( X, Y, Z, T ) }.
% 0.80/1.39 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha51( X, Y, Z
% 0.80/1.39 , T ), ! alpha65( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 0.80/1.39 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.80/1.39 { ! alpha65( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( X ), Y ), alpha77( X, Y, Z, T ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.80/1.39 , alpha65( X, Y, Z, T ) }.
% 0.80/1.39 { ! alpha77( X, Y, Z, T ), alpha65( X, Y, Z, T ) }.
% 0.80/1.39 { ! alpha77( X, Y, Z, T ), alpha89( X, Y, Z, T ) }.
% 0.80/1.39 { ! alpha77( X, Y, Z, T ), alpha18( X, Y, T ) }.
% 0.80/1.39 { ! alpha89( X, Y, Z, T ), ! alpha18( X, Y, T ), alpha77( X, Y, Z, T ) }.
% 0.80/1.39 { ! alpha89( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Z,
% 0.80/1.39 c_Groups_Otimes__class_Otimes( X, T, Y ) ) }.
% 0.80/1.39 { c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.80/1.39 alpha89( X, Y, Z, T ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Otimes__class_Otimes( X,
% 0.80/1.39 T, Y ) ), alpha89( X, Y, Z, T ) }.
% 0.80/1.39 { ! alpha51( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X,
% 0.80/1.39 c_Groups_Otimes__class_Otimes( X, T, Y ), Z ) }.
% 0.80/1.39 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.80/1.39 alpha51( X, Y, Z, T ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, T,
% 0.80/1.39 Y ), Z ), alpha51( X, Y, Z, T ) }.
% 0.80/1.39 { ! alpha18( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Z,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 0.80/1.39 , alpha18( X, Y, Z ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.80/1.39 , alpha18( X, Y, Z ) }.
% 0.80/1.39 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.80/1.39 Z ), Y ), alpha52( X, Y, Z, T ) }.
% 0.80/1.39 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.80/1.39 Z ), Y ), alpha66( X, Y, Z, T ) }.
% 0.80/1.39 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha52( X, Y, Z
% 0.80/1.39 , T ), ! alpha66( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.80/1.39 c_Rings_Oinverse__class_Odivide( X, T, Z ), Y ) }.
% 0.80/1.39 { ! alpha66( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( X ), Z ), alpha78( X, Y, Z, T ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.80/1.39 , alpha66( X, Y, Z, T ) }.
% 0.80/1.39 { ! alpha78( X, Y, Z, T ), alpha66( X, Y, Z, T ) }.
% 0.80/1.39 { ! alpha78( X, Y, Z, T ), alpha90( X, Y, Z, T ) }.
% 0.80/1.39 { ! alpha78( X, Y, Z, T ), alpha19( X, Y, Z ) }.
% 0.80/1.39 { ! alpha90( X, Y, Z, T ), ! alpha19( X, Y, Z ), alpha78( X, Y, Z, T ) }.
% 0.80/1.39 { ! alpha90( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.80/1.39 c_Groups_Otimes__class_Otimes( X, Y, Z ), T ) }.
% 0.80/1.39 { c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) ),
% 0.80/1.39 alpha90( X, Y, Z, T ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, Y,
% 0.80/1.39 Z ), T ), alpha90( X, Y, Z, T ) }.
% 0.80/1.39 { ! alpha52( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless( X,
% 0.80/1.39 T, c_Groups_Otimes__class_Otimes( X, Y, Z ) ) }.
% 0.80/1.39 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.80/1.39 alpha52( X, Y, Z, T ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( X, T, c_Groups_Otimes__class_Otimes( X,
% 0.80/1.39 Y, Z ) ), alpha52( X, Y, Z, T ) }.
% 0.80/1.39 { ! alpha19( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.80/1.39 , alpha19( X, Y, Z ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.80/1.39 , alpha19( X, Y, Z ) }.
% 0.80/1.39 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.80/1.39 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.80/1.39 ( X, T, c_Rings_Oinverse__class_Odivide( X, Z, Y ) ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, T, Y
% 0.80/1.39 ), Z ) }.
% 0.80/1.39 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.80/1.39 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.80/1.39 ( X, c_Groups_Otimes__class_Otimes( X, T, Y ), Z ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.80/1.39 Z, Y ) ) }.
% 0.80/1.39 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.80/1.39 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.80/1.39 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( X, T, c_Groups_Otimes__class_Otimes( X, Z
% 0.80/1.39 , Y ) ) }.
% 0.80/1.39 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.80/1.39 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.80/1.39 ( X, T, c_Groups_Otimes__class_Otimes( X, Z, Y ) ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.80/1.39 Y ), Z ) }.
% 0.80/1.39 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.80/1.39 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.80/1.39 ( X, T, c_Groups_Otimes__class_Otimes( X, Z, Y ) ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.80/1.39 Y ), Z ) }.
% 0.80/1.39 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.80/1.39 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.80/1.39 ( X, c_Groups_Otimes__class_Otimes( X, T, Y ), Z ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.80/1.39 Z, Y ) ) }.
% 0.80/1.39 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.80/1.39 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.80/1.39 ( X, T, c_Rings_Oinverse__class_Odivide( X, Z, Y ) ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( X, Z, c_Groups_Otimes__class_Otimes( X, T
% 0.80/1.39 , Y ) ) }.
% 0.80/1.39 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.80/1.39 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.80/1.39 ( X, Z, c_Groups_Otimes__class_Otimes( X, T, Y ) ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.80/1.39 Z, Y ) ) }.
% 0.80/1.39 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.80/1.39 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.80/1.39 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, Z, Y
% 0.80/1.39 ), T ) }.
% 0.80/1.39 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.80/1.39 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.80/1.39 ( X, c_Groups_Otimes__class_Otimes( X, Z, Y ), T ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.80/1.39 Y ), Z ) }.
% 0.80/1.39 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.80/1.39 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 0.80/1.39 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Otimes__class_Otimes( X, Y,
% 0.80/1.39 Z ) ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide
% 0.80/1.39 ( X, T, Y ), c_Rings_Oinverse__class_Odivide( X, T, Z ) ) }.
% 0.80/1.39 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.80/1.39 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, T,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless( X,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( X ), c_Groups_Otimes__class_Otimes( X, Z, Y
% 0.80/1.39 ) ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide(
% 0.80/1.39 X, T, Z ), c_Rings_Oinverse__class_Odivide( X, T, Y ) ) }.
% 0.80/1.39 { ! class_Rings_Oring__1( X ), c_Groups_Ominus__class_Ominus( X,
% 0.80/1.39 c_Groups_Otimes__class_Otimes( X, Y, Y ), c_Groups_Oone__class_Oone( X )
% 0.80/1.39 ) = c_Groups_Otimes__class_Otimes( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.80/1.39 , c_Groups_Oone__class_Oone( X ) ), c_Groups_Ominus__class_Ominus( X, Y,
% 0.80/1.39 c_Groups_Oone__class_Oone( X ) ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.80/1.39 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ),
% 0.80/1.39 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.80/1.39 c_Power_Opower__class_Opower( tc_RealDef_Oreal, X,
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.39 c_Int_OPls ) ) ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.80/1.39 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), ! Y =
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Power_Opower__class_Opower
% 0.80/1.39 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Oone__class_Oone( X
% 0.80/1.39 ) }.
% 0.80/1.39 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), Y =
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Power_Opower__class_Opower
% 0.80/1.39 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero
% 0.80/1.39 ( X ) }.
% 0.80/1.39 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.80/1.39 , c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, T, Z )
% 0.80/1.39 ), Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus
% 0.80/1.39 ( X, Z, Y ), T ) }.
% 0.80/1.39 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.80/1.39 , c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, T, Z )
% 0.80/1.39 ), Y ), c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus
% 0.80/1.39 ( X, Z, Y ) ) }.
% 0.80/1.39 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.80/1.39 , c_Groups_Ominus__class_Ominus( X, Z, Y ), T ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.80/1.39 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X,
% 0.80/1.39 c_Groups_Ominus__class_Ominus( X, T, Z ) ), Y ) }.
% 0.80/1.39 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.80/1.39 c_Int_OBit1( Y ) ) = c_Groups_Oplus__class_Oplus( X,
% 0.80/1.39 c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( X, Y ) ),
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.80/1.39 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.80/1.39 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oabs__class_Oabs( X, Z ), Y
% 0.80/1.39 ) = c_Groups_Oabs__class_Oabs( X, c_Rings_Oinverse__class_Odivide( X, Z
% 0.80/1.39 , Y ) ) }.
% 0.80/1.39 { ! class_Rings_Olinordered__semidom( X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), T )
% 0.80/1.39 , c_Orderings_Oord__class_Oless__eq( X, c_Power_Opower__class_Opower( X,
% 0.80/1.39 T, Z ), c_Power_Opower__class_Opower( X, T, Y ) ) }.
% 0.80/1.39 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.80/1.39 c_Int_OBit1( c_Int_OPls ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.80/1.39 { ! class_Int_Onumber__ring( X ), c_Groups_Oone__class_Oone( X ) =
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( X, c_Int_OBit1( c_Int_OPls ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, Z ),
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, Y ) ),
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ),
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, Z ),
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, Y ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Z, X ),
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Y, X ) ),
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ),
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Z, X ),
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Y, X ) ) }.
% 0.80/1.39 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Ozero__class_Ozero( X )
% 0.80/1.39 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.80/1.39 , c_Groups_Otimes__class_Otimes( X, Z, Y ) ),
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.80/1.39 , T, Z ), c_Rings_Oinverse__class_Odivide( X, T, Y ) ) }.
% 0.80/1.39 { ! class_Fields_Olinordered__field( X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.80/1.39 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.80/1.39 , c_Groups_Otimes__class_Otimes( X, Y, Z ) ),
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.80/1.39 , T, Y ), c_Rings_Oinverse__class_Odivide( X, T, Z ) ) }.
% 0.80/1.39 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.80/1.39 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.80/1.39 , T, Y ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.80/1.39 c_Groups_Otimes__class_Otimes( X, Z, Y ), T ) }.
% 0.80/1.39 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.80/1.39 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes( X, Z
% 0.80/1.39 , Y ), T ), c_Orderings_Oord__class_Oless__eq( X,
% 0.80/1.39 c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ) }.
% 0.80/1.39 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.80/1.39 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.80/1.39 ( X, Z, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.80/1.39 c_Groups_Otimes__class_Otimes( X, T, Y ) ) }.
% 0.80/1.39 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.80/1.39 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Otimes__class_Otimes( X
% 0.80/1.39 , T, Y ) ), c_Orderings_Oord__class_Oless__eq( X, T,
% 0.80/1.39 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.80/1.39 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.80/1.39 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes( X, T
% 0.80/1.39 , Y ), Z ), c_Orderings_Oord__class_Oless__eq( X, T,
% 0.80/1.39 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.80/1.39 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.80/1.39 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Otimes__class_Otimes( X
% 0.80/1.39 , Z, Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.80/1.39 c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ) }.
% 0.80/1.39 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.80/1.39 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.80/1.39 , T, Y ), Z ), c_Orderings_Oord__class_Oless__eq( X, T,
% 0.80/1.39 c_Groups_Otimes__class_Otimes( X, Z, Y ) ) }.
% 0.80/1.39 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.80/1.39 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Otimes__class_Otimes( X
% 0.80/1.39 , Z, Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.80/1.39 c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ) }.
% 0.80/1.39 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.80/1.39 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.80/1.39 ( X, Z, Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.80/1.39 c_Groups_Otimes__class_Otimes( X, T, Y ), Z ) }.
% 0.80/1.39 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.80/1.39 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes( X, T
% 0.80/1.39 , Y ), Z ), c_Orderings_Oord__class_Oless__eq( X, T,
% 0.80/1.39 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.80/1.39 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.80/1.39 , T, Z ), Y ), alpha53( X, Y, Z, T ) }.
% 0.80/1.39 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.80/1.39 , T, Z ), Y ), alpha67( X, Y, Z, T ) }.
% 0.80/1.39 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha53( X, Y, Z
% 0.80/1.39 , T ), ! alpha67( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( X,
% 0.80/1.39 c_Rings_Oinverse__class_Odivide( X, T, Z ), Y ) }.
% 0.80/1.39 { ! alpha67( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( X ), Z ), alpha79( X, Y, Z, T ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.80/1.39 , alpha67( X, Y, Z, T ) }.
% 0.80/1.39 { ! alpha79( X, Y, Z, T ), alpha67( X, Y, Z, T ) }.
% 0.80/1.39 { ! alpha79( X, Y, Z, T ), alpha91( X, Y, Z, T ) }.
% 0.80/1.39 { ! alpha79( X, Y, Z, T ), alpha20( X, Y, Z ) }.
% 0.80/1.39 { ! alpha91( X, Y, Z, T ), ! alpha20( X, Y, Z ), alpha79( X, Y, Z, T ) }.
% 0.80/1.39 { ! alpha91( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.80/1.39 , c_Groups_Otimes__class_Otimes( X, Y, Z ), T ) }.
% 0.80/1.39 { c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) ),
% 0.80/1.39 alpha91( X, Y, Z, T ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes( X
% 0.80/1.39 , Y, Z ), T ), alpha91( X, Y, Z, T ) }.
% 0.80/1.39 { ! alpha53( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless__eq
% 0.80/1.39 ( X, T, c_Groups_Otimes__class_Otimes( X, Y, Z ) ) }.
% 0.80/1.39 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.80/1.39 alpha53( X, Y, Z, T ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Otimes__class_Otimes
% 0.80/1.39 ( X, Y, Z ) ), alpha53( X, Y, Z, T ) }.
% 0.80/1.39 { ! alpha20( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.80/1.39 , c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.80/1.39 , alpha20( X, Y, Z ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.80/1.39 , Y ), alpha20( X, Y, Z ) }.
% 0.80/1.39 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.80/1.39 ( X, Z, Y ) ), alpha54( X, Y, Z, T ) }.
% 0.80/1.39 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.80/1.39 ( X, Z, Y ) ), alpha68( X, Y, Z, T ) }.
% 0.80/1.39 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha54( X, Y, Z
% 0.80/1.39 , T ), ! alpha68( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( X, T,
% 0.80/1.39 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.80/1.39 { ! alpha68( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( X ), Y ), alpha80( X, Y, Z, T ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.80/1.39 , alpha68( X, Y, Z, T ) }.
% 0.80/1.39 { ! alpha80( X, Y, Z, T ), alpha68( X, Y, Z, T ) }.
% 0.80/1.39 { ! alpha80( X, Y, Z, T ), alpha92( X, Y, Z, T ) }.
% 0.80/1.39 { ! alpha80( X, Y, Z, T ), alpha21( X, Y, T ) }.
% 0.80/1.39 { ! alpha92( X, Y, Z, T ), ! alpha21( X, Y, T ), alpha80( X, Y, Z, T ) }.
% 0.80/1.39 { ! alpha92( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.80/1.39 , Z, c_Groups_Otimes__class_Otimes( X, T, Y ) ) }.
% 0.80/1.39 { c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.80/1.39 alpha92( X, Y, Z, T ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Otimes__class_Otimes
% 0.80/1.39 ( X, T, Y ) ), alpha92( X, Y, Z, T ) }.
% 0.80/1.39 { ! alpha54( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless__eq
% 0.80/1.39 ( X, c_Groups_Otimes__class_Otimes( X, T, Y ), Z ) }.
% 0.80/1.39 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.80/1.39 alpha54( X, Y, Z, T ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes( X
% 0.80/1.39 , T, Y ), Z ), alpha54( X, Y, Z, T ) }.
% 0.80/1.39 { ! alpha21( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.80/1.39 , Z, c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 0.80/1.39 , alpha21( X, Y, Z ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.80/1.39 ) ), alpha21( X, Y, Z ) }.
% 0.80/1.39 { ! class_Rings_Olinordered__semiring__1( X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( X, T, Y ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.80/1.39 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.80/1.39 X ), W ), ! c_Groups_Oplus__class_Oplus( X, U, W ) =
% 0.80/1.39 c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless__eq( X,
% 0.80/1.39 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, U, Z )
% 0.80/1.39 , c_Groups_Otimes__class_Otimes( X, W, T ) ), Y ) }.
% 0.80/1.39 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.80/1.39 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless( X, T,
% 0.80/1.39 c_Rings_Oinverse__class_Odivide( X, Z, c_Int_Onumber__class_Onumber__of(
% 0.80/1.39 X, Y ) ) ), alpha55( X, Y, Z, T ) }.
% 0.80/1.39 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.80/1.39 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless( X, T,
% 0.80/1.39 c_Rings_Oinverse__class_Odivide( X, Z, c_Int_Onumber__class_Onumber__of(
% 0.80/1.39 X, Y ) ) ), alpha69( X, Y, Z, T ) }.
% 0.80/1.39 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.80/1.39 class_Int_Onumber( X ), ! alpha55( X, Y, Z, T ), ! alpha69( X, Y, Z, T )
% 0.80/1.39 , c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X
% 0.80/1.39 , Z, c_Int_Onumber__class_Onumber__of( X, Y ) ) ) }.
% 0.80/1.39 { ! alpha69( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( X ), c_Int_Onumber__class_Onumber__of( X, Y
% 0.80/1.39 ) ), alpha81( X, Y, Z, T ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( X, Y ) ), alpha69( X, Y, Z, T ) }.
% 0.80/1.39 { ! alpha81( X, Y, Z, T ), alpha69( X, Y, Z, T ) }.
% 0.80/1.39 { ! alpha81( X, Y, Z, T ), alpha93( X, Y, Z, T ) }.
% 0.80/1.39 { ! alpha81( X, Y, Z, T ), alpha22( X, Y, T ) }.
% 0.80/1.39 { ! alpha93( X, Y, Z, T ), ! alpha22( X, Y, T ), alpha81( X, Y, Z, T ) }.
% 0.80/1.39 { ! alpha93( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.80/1.39 ) ), c_Orderings_Oord__class_Oless( X, Z, c_Groups_Otimes__class_Otimes
% 0.80/1.39 ( X, T, c_Int_Onumber__class_Onumber__of( X, Y ) ) ) }.
% 0.80/1.39 { c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Y
% 0.80/1.39 ), c_Groups_Ozero__class_Ozero( X ) ), alpha93( X, Y, Z, T ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Otimes__class_Otimes( X,
% 0.80/1.39 T, c_Int_Onumber__class_Onumber__of( X, Y ) ) ), alpha93( X, Y, Z, T ) }
% 0.80/1.39 .
% 0.80/1.39 { ! alpha55( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( X ), c_Int_Onumber__class_Onumber__of( X, Y
% 0.80/1.39 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X
% 0.80/1.39 , T, c_Int_Onumber__class_Onumber__of( X, Y ) ), Z ) }.
% 0.80/1.39 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( X, Y ) ), alpha55( X, Y, Z, T ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, T,
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( X, Y ) ), Z ), alpha55( X, Y, Z, T ) }
% 0.80/1.39 .
% 0.80/1.39 { ! alpha22( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.80/1.39 ) ), c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.80/1.39 ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X,
% 0.80/1.39 Y ), c_Groups_Ozero__class_Ozero( X ) ), alpha22( X, Y, Z ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.80/1.39 , alpha22( X, Y, Z ) }.
% 0.80/1.39 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.80/1.39 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( X, T ), c_Rings_Oinverse__class_Odivide
% 0.80/1.39 ( X, Z, Y ) ), alpha56( X, Y, Z, T ) }.
% 0.80/1.39 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.80/1.39 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( X, T ), c_Rings_Oinverse__class_Odivide
% 0.80/1.39 ( X, Z, Y ) ), alpha70( X, Y, Z, T ) }.
% 0.80/1.39 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.80/1.39 class_Int_Onumber( X ), ! alpha56( X, Y, Z, T ), ! alpha70( X, Y, Z, T )
% 0.80/1.39 , c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X,
% 0.80/1.39 T ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.80/1.39 { ! alpha70( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( X ), Y ), alpha82( X, Y, Z, T ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.80/1.39 , alpha70( X, Y, Z, T ) }.
% 0.80/1.39 { ! alpha82( X, Y, Z, T ), alpha70( X, Y, Z, T ) }.
% 0.80/1.39 { ! alpha82( X, Y, Z, T ), alpha94( X, Y, Z, T ) }.
% 0.80/1.39 { ! alpha82( X, Y, Z, T ), alpha23( X, Y, T ) }.
% 0.80/1.39 { ! alpha94( X, Y, Z, T ), ! alpha23( X, Y, T ), alpha82( X, Y, Z, T ) }.
% 0.80/1.39 { ! alpha94( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Z,
% 0.80/1.39 c_Groups_Otimes__class_Otimes( X, c_Int_Onumber__class_Onumber__of( X, T
% 0.80/1.39 ), Y ) ) }.
% 0.80/1.39 { c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.80/1.39 alpha94( X, Y, Z, T ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Otimes__class_Otimes( X,
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( X, T ), Y ) ), alpha94( X, Y, Z, T ) }
% 0.80/1.39 .
% 0.80/1.39 { ! alpha56( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X,
% 0.80/1.39 c_Groups_Otimes__class_Otimes( X, c_Int_Onumber__class_Onumber__of( X, T
% 0.80/1.39 ), Y ), Z ) }.
% 0.80/1.39 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.80/1.39 alpha56( X, Y, Z, T ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X,
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( X, T ), Y ), Z ), alpha56( X, Y, Z, T )
% 0.80/1.39 }.
% 0.80/1.39 { ! alpha23( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( X, Z ), c_Groups_Ozero__class_Ozero( X
% 0.80/1.39 ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 0.80/1.39 , alpha23( X, Y, Z ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X,
% 0.80/1.39 Z ), c_Groups_Ozero__class_Ozero( X ) ), alpha23( X, Y, Z ) }.
% 0.80/1.39 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.80/1.39 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.80/1.39 c_Rings_Oinverse__class_Odivide( X, T, Z ),
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( X, Y ) ), alpha57( X, Y, Z, T ) }.
% 0.80/1.39 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.80/1.39 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.80/1.39 c_Rings_Oinverse__class_Odivide( X, T, Z ),
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( X, Y ) ), alpha71( X, Y, Z, T ) }.
% 0.80/1.39 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.80/1.39 class_Int_Onumber( X ), ! alpha57( X, Y, Z, T ), ! alpha71( X, Y, Z, T )
% 0.80/1.39 , c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T
% 0.80/1.39 , Z ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.80/1.39 { ! alpha71( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( X ), Z ), alpha83( X, Y, Z, T ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.80/1.39 , alpha71( X, Y, Z, T ) }.
% 0.80/1.39 { ! alpha83( X, Y, Z, T ), alpha71( X, Y, Z, T ) }.
% 0.80/1.39 { ! alpha83( X, Y, Z, T ), alpha95( X, Y, Z, T ) }.
% 0.80/1.39 { ! alpha83( X, Y, Z, T ), alpha24( X, Y, Z ) }.
% 0.80/1.39 { ! alpha95( X, Y, Z, T ), ! alpha24( X, Y, Z ), alpha83( X, Y, Z, T ) }.
% 0.80/1.39 { ! alpha95( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.80/1.39 c_Groups_Otimes__class_Otimes( X, c_Int_Onumber__class_Onumber__of( X, Y
% 0.80/1.39 ), Z ), T ) }.
% 0.80/1.39 { c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) ),
% 0.80/1.39 alpha95( X, Y, Z, T ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X,
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( X, Y ), Z ), T ), alpha95( X, Y, Z, T )
% 0.80/1.39 }.
% 0.80/1.39 { ! alpha57( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless( X,
% 0.80/1.39 T, c_Groups_Otimes__class_Otimes( X, c_Int_Onumber__class_Onumber__of( X
% 0.80/1.39 , Y ), Z ) ) }.
% 0.80/1.39 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.80/1.39 alpha57( X, Y, Z, T ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( X, T, c_Groups_Otimes__class_Otimes( X,
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( X, Y ), Z ) ), alpha57( X, Y, Z, T ) }
% 0.80/1.39 .
% 0.80/1.39 { ! alpha24( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( X ), c_Int_Onumber__class_Onumber__of( X, Y
% 0.80/1.39 ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.80/1.39 , alpha24( X, Y, Z ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( X, Y ) ), alpha24( X, Y, Z ) }.
% 0.80/1.39 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.80/1.39 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.80/1.39 c_Rings_Oinverse__class_Odivide( X, T, c_Int_Onumber__class_Onumber__of(
% 0.80/1.39 X, Z ) ), Y ), alpha58( X, Y, Z, T ) }.
% 0.80/1.39 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.80/1.39 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.80/1.39 c_Rings_Oinverse__class_Odivide( X, T, c_Int_Onumber__class_Onumber__of(
% 0.80/1.39 X, Z ) ), Y ), alpha72( X, Y, Z, T ) }.
% 0.80/1.39 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.80/1.39 class_Int_Onumber( X ), ! alpha58( X, Y, Z, T ), ! alpha72( X, Y, Z, T )
% 0.80/1.39 , c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T
% 0.80/1.39 , c_Int_Onumber__class_Onumber__of( X, Z ) ), Y ) }.
% 0.80/1.39 { ! alpha72( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( X ), c_Int_Onumber__class_Onumber__of( X, Z
% 0.80/1.39 ) ), alpha84( X, Y, Z, T ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( X, Z ) ), alpha72( X, Y, Z, T ) }.
% 0.80/1.39 { ! alpha84( X, Y, Z, T ), alpha72( X, Y, Z, T ) }.
% 0.80/1.39 { ! alpha84( X, Y, Z, T ), alpha96( X, Y, Z, T ) }.
% 0.80/1.39 { ! alpha84( X, Y, Z, T ), alpha25( X, Y, Z ) }.
% 0.80/1.39 { ! alpha96( X, Y, Z, T ), ! alpha25( X, Y, Z ), alpha84( X, Y, Z, T ) }.
% 0.80/1.39 { ! alpha96( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( X, Z ), c_Groups_Ozero__class_Ozero( X
% 0.80/1.39 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X
% 0.80/1.39 , Y, c_Int_Onumber__class_Onumber__of( X, Z ) ), T ) }.
% 0.80/1.39 { c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Z
% 0.80/1.39 ), c_Groups_Ozero__class_Ozero( X ) ), alpha96( X, Y, Z, T ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, Y,
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( X, Z ) ), T ), alpha96( X, Y, Z, T ) }
% 0.80/1.39 .
% 0.80/1.39 { ! alpha58( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( X ), c_Int_Onumber__class_Onumber__of( X, Z
% 0.80/1.39 ) ), c_Orderings_Oord__class_Oless( X, T, c_Groups_Otimes__class_Otimes
% 0.80/1.39 ( X, Y, c_Int_Onumber__class_Onumber__of( X, Z ) ) ) }.
% 0.80/1.39 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( X, Z ) ), alpha58( X, Y, Z, T ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( X, T, c_Groups_Otimes__class_Otimes( X,
% 0.80/1.39 Y, c_Int_Onumber__class_Onumber__of( X, Z ) ) ), alpha58( X, Y, Z, T ) }
% 0.80/1.39 .
% 0.80/1.39 { ! alpha25( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( X, Z ), c_Groups_Ozero__class_Ozero( X
% 0.80/1.39 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.80/1.39 , Y ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X,
% 0.80/1.39 Z ), c_Groups_Ozero__class_Ozero( X ) ), alpha25( X, Y, Z ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.80/1.39 , alpha25( X, Y, Z ) }.
% 0.80/1.39 { ! class_Rings_Olinordered__semidom( X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.80/1.39 ), ! c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone
% 0.80/1.39 ( X ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.80/1.39 c_Power_Opower__class_Opower( X, Y, c_Nat_OSuc( Z ) ), Y ) }.
% 0.80/1.39 { ! class_Int_Onumber__ring( X ), c_Groups_Otimes__class_Otimes( X,
% 0.80/1.39 c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.80/1.39 c_Groups_Oone__class_Oone( X ) ), c_Int_Onumber__class_Onumber__of( X, Y
% 0.80/1.39 ) ) = c_Int_Onumber__class_Onumber__of( X, c_Int_OBit0( Y ) ) }.
% 0.80/1.39 { ! class_Rings_Olinordered__semidom( X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.80/1.39 ), ! c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oone__class_Oone
% 0.80/1.39 ( X ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.80/1.39 c_Power_Opower__class_Opower( X, T, Y ), c_Power_Opower__class_Opower( X
% 0.80/1.39 , T, Z ) ) }.
% 0.80/1.39 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), !
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) =
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Power_Opower__class_Opower
% 0.80/1.39 ( X, c_Groups_Ozero__class_Ozero( X ), c_Int_Onumber__class_Onumber__of(
% 0.80/1.39 tc_Nat_Onat, Y ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.80/1.39 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ),
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) =
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Power_Opower__class_Opower
% 0.80/1.39 ( X, c_Groups_Ozero__class_Ozero( X ), c_Int_Onumber__class_Onumber__of(
% 0.80/1.39 tc_Nat_Onat, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.80/1.39 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.80/1.39 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.80/1.39 c_Rings_Oinverse__class_Odivide( X, Z, c_Int_Onumber__class_Onumber__of(
% 0.80/1.39 X, Y ) ) ), alpha59( X, Y, Z, T ) }.
% 0.80/1.39 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.80/1.39 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.80/1.39 c_Rings_Oinverse__class_Odivide( X, Z, c_Int_Onumber__class_Onumber__of(
% 0.80/1.39 X, Y ) ) ), alpha73( X, Y, Z, T ) }.
% 0.80/1.39 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.80/1.39 class_Int_Onumber( X ), ! alpha59( X, Y, Z, T ), ! alpha73( X, Y, Z, T )
% 0.80/1.39 , c_Orderings_Oord__class_Oless__eq( X, T,
% 0.80/1.39 c_Rings_Oinverse__class_Odivide( X, Z, c_Int_Onumber__class_Onumber__of(
% 0.80/1.39 X, Y ) ) ) }.
% 0.80/1.39 { ! alpha73( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( X ), c_Int_Onumber__class_Onumber__of( X, Y
% 0.80/1.39 ) ), alpha85( X, Y, Z, T ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( X, Y ) ), alpha73( X, Y, Z, T ) }.
% 0.80/1.39 { ! alpha85( X, Y, Z, T ), alpha73( X, Y, Z, T ) }.
% 0.80/1.39 { ! alpha85( X, Y, Z, T ), alpha97( X, Y, Z, T ) }.
% 0.80/1.39 { ! alpha85( X, Y, Z, T ), alpha26( X, Y, T ) }.
% 0.80/1.39 { ! alpha97( X, Y, Z, T ), ! alpha26( X, Y, T ), alpha85( X, Y, Z, T ) }.
% 0.80/1.39 { ! alpha97( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.80/1.39 ) ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.80/1.39 c_Groups_Otimes__class_Otimes( X, T, c_Int_Onumber__class_Onumber__of( X
% 0.80/1.39 , Y ) ) ) }.
% 0.80/1.39 { c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Y
% 0.80/1.39 ), c_Groups_Ozero__class_Ozero( X ) ), alpha97( X, Y, Z, T ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Otimes__class_Otimes
% 0.80/1.39 ( X, T, c_Int_Onumber__class_Onumber__of( X, Y ) ) ), alpha97( X, Y, Z, T
% 0.80/1.39 ) }.
% 0.80/1.39 { ! alpha59( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( X ), c_Int_Onumber__class_Onumber__of( X, Y
% 0.80/1.39 ) ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes
% 0.80/1.39 ( X, T, c_Int_Onumber__class_Onumber__of( X, Y ) ), Z ) }.
% 0.80/1.39 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( X, Y ) ), alpha59( X, Y, Z, T ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes( X
% 0.80/1.39 , T, c_Int_Onumber__class_Onumber__of( X, Y ) ), Z ), alpha59( X, Y, Z, T
% 0.80/1.39 ) }.
% 0.80/1.39 { ! alpha26( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.80/1.39 ) ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X,
% 0.80/1.39 Y ), c_Groups_Ozero__class_Ozero( X ) ), alpha26( X, Y, Z ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.80/1.39 ) ), alpha26( X, Y, Z ) }.
% 0.80/1.39 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.80/1.39 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( X, T ), c_Rings_Oinverse__class_Odivide
% 0.80/1.39 ( X, Z, Y ) ), alpha60( X, Y, Z, T ) }.
% 0.80/1.39 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.80/1.39 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( X, T ), c_Rings_Oinverse__class_Odivide
% 0.80/1.39 ( X, Z, Y ) ), alpha74( X, Y, Z, T ) }.
% 0.80/1.39 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.80/1.39 class_Int_Onumber( X ), ! alpha60( X, Y, Z, T ), ! alpha74( X, Y, Z, T )
% 0.80/1.39 , c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of
% 0.80/1.39 ( X, T ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.80/1.39 { ! alpha74( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( X ), Y ), alpha86( X, Y, Z, T ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.80/1.39 , alpha74( X, Y, Z, T ) }.
% 0.80/1.39 { ! alpha86( X, Y, Z, T ), alpha74( X, Y, Z, T ) }.
% 0.80/1.39 { ! alpha86( X, Y, Z, T ), alpha98( X, Y, Z, T ) }.
% 0.80/1.39 { ! alpha86( X, Y, Z, T ), alpha27( X, Y, T ) }.
% 0.80/1.39 { ! alpha98( X, Y, Z, T ), ! alpha27( X, Y, T ), alpha86( X, Y, Z, T ) }.
% 0.80/1.39 { ! alpha98( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.80/1.39 , Z, c_Groups_Otimes__class_Otimes( X, c_Int_Onumber__class_Onumber__of(
% 0.80/1.39 X, T ), Y ) ) }.
% 0.80/1.39 { c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.80/1.39 alpha98( X, Y, Z, T ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Otimes__class_Otimes
% 0.80/1.39 ( X, c_Int_Onumber__class_Onumber__of( X, T ), Y ) ), alpha98( X, Y, Z, T
% 0.80/1.39 ) }.
% 0.80/1.39 { ! alpha60( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless__eq
% 0.80/1.39 ( X, c_Groups_Otimes__class_Otimes( X, c_Int_Onumber__class_Onumber__of(
% 0.80/1.39 X, T ), Y ), Z ) }.
% 0.80/1.39 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.80/1.39 alpha60( X, Y, Z, T ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes( X
% 0.80/1.39 , c_Int_Onumber__class_Onumber__of( X, T ), Y ), Z ), alpha60( X, Y, Z, T
% 0.80/1.39 ) }.
% 0.80/1.39 { ! alpha27( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.80/1.39 , c_Int_Onumber__class_Onumber__of( X, Z ), c_Groups_Ozero__class_Ozero(
% 0.80/1.39 X ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 0.80/1.39 , alpha27( X, Y, Z ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of
% 0.80/1.39 ( X, Z ), c_Groups_Ozero__class_Ozero( X ) ), alpha27( X, Y, Z ) }.
% 0.80/1.39 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.80/1.39 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.80/1.39 c_Rings_Oinverse__class_Odivide( X, T, Z ),
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( X, Y ) ), alpha61( X, Y, Z, T ) }.
% 0.80/1.39 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.80/1.39 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.80/1.39 c_Rings_Oinverse__class_Odivide( X, T, Z ),
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( X, Y ) ), alpha75( X, Y, Z, T ) }.
% 0.80/1.39 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.80/1.39 class_Int_Onumber( X ), ! alpha61( X, Y, Z, T ), ! alpha75( X, Y, Z, T )
% 0.80/1.39 , c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide(
% 0.80/1.39 X, T, Z ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.80/1.39 { ! alpha75( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( X ), Z ), alpha87( X, Y, Z, T ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.80/1.39 , alpha75( X, Y, Z, T ) }.
% 0.80/1.39 { ! alpha87( X, Y, Z, T ), alpha75( X, Y, Z, T ) }.
% 0.80/1.39 { ! alpha87( X, Y, Z, T ), alpha99( X, Y, Z, T ) }.
% 0.80/1.39 { ! alpha87( X, Y, Z, T ), alpha28( X, Y, Z ) }.
% 0.80/1.39 { ! alpha99( X, Y, Z, T ), ! alpha28( X, Y, Z ), alpha87( X, Y, Z, T ) }.
% 0.80/1.39 { ! alpha99( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.80/1.39 , c_Groups_Otimes__class_Otimes( X, c_Int_Onumber__class_Onumber__of( X,
% 0.80/1.39 Y ), Z ), T ) }.
% 0.80/1.39 { c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) ),
% 0.80/1.39 alpha99( X, Y, Z, T ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes( X
% 0.80/1.39 , c_Int_Onumber__class_Onumber__of( X, Y ), Z ), T ), alpha99( X, Y, Z, T
% 0.80/1.39 ) }.
% 0.80/1.39 { ! alpha61( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless__eq
% 0.80/1.39 ( X, T, c_Groups_Otimes__class_Otimes( X,
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( X, Y ), Z ) ) }.
% 0.80/1.39 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.80/1.39 alpha61( X, Y, Z, T ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Otimes__class_Otimes
% 0.80/1.39 ( X, c_Int_Onumber__class_Onumber__of( X, Y ), Z ) ), alpha61( X, Y, Z, T
% 0.80/1.39 ) }.
% 0.80/1.39 { ! alpha28( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.80/1.39 , c_Groups_Ozero__class_Ozero( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.80/1.39 Y ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.80/1.39 , alpha28( X, Y, Z ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.80/1.39 , c_Int_Onumber__class_Onumber__of( X, Y ) ), alpha28( X, Y, Z ) }.
% 0.80/1.39 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.80/1.39 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.80/1.39 c_Rings_Oinverse__class_Odivide( X, T, c_Int_Onumber__class_Onumber__of(
% 0.80/1.39 X, Z ) ), Y ), alpha62( X, Y, Z, T ) }.
% 0.80/1.39 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.80/1.39 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.80/1.39 c_Rings_Oinverse__class_Odivide( X, T, c_Int_Onumber__class_Onumber__of(
% 0.80/1.39 X, Z ) ), Y ), alpha76( X, Y, Z, T ) }.
% 0.80/1.39 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.80/1.39 class_Int_Onumber( X ), ! alpha62( X, Y, Z, T ), ! alpha76( X, Y, Z, T )
% 0.80/1.39 , c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide(
% 0.80/1.39 X, T, c_Int_Onumber__class_Onumber__of( X, Z ) ), Y ) }.
% 0.80/1.39 { ! alpha76( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( X ), c_Int_Onumber__class_Onumber__of( X, Z
% 0.80/1.39 ) ), alpha88( X, Y, Z, T ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( X, Z ) ), alpha76( X, Y, Z, T ) }.
% 0.80/1.39 { ! alpha88( X, Y, Z, T ), alpha76( X, Y, Z, T ) }.
% 0.80/1.39 { ! alpha88( X, Y, Z, T ), alpha100( X, Y, Z, T ) }.
% 0.80/1.39 { ! alpha88( X, Y, Z, T ), alpha29( X, Y, Z ) }.
% 0.80/1.39 { ! alpha100( X, Y, Z, T ), ! alpha29( X, Y, Z ), alpha88( X, Y, Z, T ) }.
% 0.80/1.39 { ! alpha100( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( X, Z ), c_Groups_Ozero__class_Ozero( X
% 0.80/1.39 ) ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes
% 0.80/1.39 ( X, Y, c_Int_Onumber__class_Onumber__of( X, Z ) ), T ) }.
% 0.80/1.39 { c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Z
% 0.80/1.39 ), c_Groups_Ozero__class_Ozero( X ) ), alpha100( X, Y, Z, T ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes( X
% 0.80/1.39 , Y, c_Int_Onumber__class_Onumber__of( X, Z ) ), T ), alpha100( X, Y, Z,
% 0.80/1.39 T ) }.
% 0.80/1.39 { ! alpha62( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( X ), c_Int_Onumber__class_Onumber__of( X, Z
% 0.80/1.39 ) ), c_Orderings_Oord__class_Oless__eq( X, T,
% 0.80/1.39 c_Groups_Otimes__class_Otimes( X, Y, c_Int_Onumber__class_Onumber__of( X
% 0.80/1.39 , Z ) ) ) }.
% 0.80/1.39 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( X, Z ) ), alpha62( X, Y, Z, T ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Otimes__class_Otimes
% 0.80/1.39 ( X, Y, c_Int_Onumber__class_Onumber__of( X, Z ) ) ), alpha62( X, Y, Z, T
% 0.80/1.39 ) }.
% 0.80/1.39 { ! alpha29( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( X, Z ), c_Groups_Ozero__class_Ozero( X
% 0.80/1.39 ) ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.80/1.39 X ), Y ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X,
% 0.80/1.39 Z ), c_Groups_Ozero__class_Ozero( X ) ), alpha29( X, Y, Z ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.80/1.39 , Y ), alpha29( X, Y, Z ) }.
% 0.80/1.39 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 0.80/1.39 , Y ), c_Groups_Oone__class_Oone( X ) ),
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, c_Int_OBit1(
% 0.80/1.39 c_Int_OPls ) ) }.
% 0.80/1.39 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, c_Int_OBit1(
% 0.80/1.39 c_Int_OPls ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( X, Y ), c_Groups_Oone__class_Oone( X )
% 0.80/1.39 ) }.
% 0.80/1.39 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( X, Y ) ),
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( c_Int_OPls )
% 0.80/1.39 , Y ) }.
% 0.80/1.39 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( c_Int_OPls )
% 0.80/1.39 , Y ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X
% 0.80/1.39 ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.80/1.39 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X,
% 0.80/1.39 c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ) =
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( X, c_Int_OBit0( c_Int_OBit1( c_Int_OPls
% 0.80/1.39 ) ) ) }.
% 0.80/1.39 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X,
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( X, Y ), c_Groups_Oone__class_Oone( X )
% 0.80/1.39 ) = c_Int_Onumber__class_Onumber__of( X, c_Groups_Oplus__class_Oplus(
% 0.80/1.39 tc_Int_Oint, Y, c_Int_OBit1( c_Int_OPls ) ) ) }.
% 0.80/1.39 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X,
% 0.80/1.39 c_Groups_Oone__class_Oone( X ), c_Int_Onumber__class_Onumber__of( X, Y )
% 0.80/1.39 ) = c_Int_Onumber__class_Onumber__of( X, c_Groups_Oplus__class_Oplus(
% 0.80/1.39 tc_Int_Oint, c_Int_OBit1( c_Int_OPls ), Y ) ) }.
% 0.80/1.39 { ! class_Rings_Osemiring__1( X ), c_Power_Opower__class_Opower( X,
% 0.80/1.39 c_Groups_Oone__class_Oone( X ), c_Int_Onumber__class_Onumber__of(
% 0.80/1.39 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) =
% 0.80/1.39 c_Groups_Oone__class_Oone( X ) }.
% 0.80/1.39 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.80/1.39 class_Int_Onumber__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X, Y,
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( X, c_Int_OBit0( c_Int_OBit1( c_Int_OPls
% 0.80/1.39 ) ) ) ) ) }.
% 0.80/1.39 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.80/1.39 class_Int_Onumber__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X, Y,
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( X, c_Int_OBit0( c_Int_OBit1( c_Int_OPls
% 0.80/1.39 ) ) ) ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero
% 0.80/1.39 ( X ), Y ) }.
% 0.80/1.39 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.80/1.39 class_Int_Onumber__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X, Y,
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( X, c_Int_OBit0( c_Int_OBit1( c_Int_OPls
% 0.80/1.39 ) ) ) ) ) }.
% 0.80/1.39 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.80/1.39 , c_Groups_Ozero__class_Ozero( X ), c_Power_Opower__class_Opower( X, Y,
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.39 c_Int_OPls ) ) ) ) ), ! Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.80/1.39 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.80/1.39 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.80/1.39 c_Power_Opower__class_Opower( X, Y, c_Int_Onumber__class_Onumber__of(
% 0.80/1.39 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) }.
% 0.80/1.39 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.80/1.39 , c_Power_Opower__class_Opower( X, Y, c_Int_Onumber__class_Onumber__of(
% 0.80/1.39 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ),
% 0.80/1.39 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.80/1.39 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt(
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.80/1.39 c_Int_OBit1( c_Int_OPls ) ) ) ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.80/1.39 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.80/1.39 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.80/1.39 c_Int_OBit1( c_Int_OPls ) ) ) ), X ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y,
% 0.80/1.39 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.80/1.39 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.80/1.39 c_Int_OBit1( c_Int_OPls ) ) ) ) ) }.
% 0.80/1.39 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.80/1.39 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ),
% 0.80/1.39 c_Power_Opower__class_Opower( tc_RealDef_Oreal,
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.80/1.39 c_Int_OBit1( c_Int_OPls ) ) ), X ) ) }.
% 0.80/1.39 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.80/1.39 c_Groups_Otimes__class_Otimes( X, c_Groups_Ozero__class_Ozero( X ), Y ) =
% 0.80/1.39 c_Groups_Ozero__class_Ozero( X ) }.
% 0.80/1.39 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.80/1.39 c_Groups_Otimes__class_Otimes( X, c_Groups_Ozero__class_Ozero( X ), Y ) =
% 0.80/1.39 c_Groups_Ozero__class_Ozero( X ) }.
% 0.80/1.39 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.80/1.39 c_Groups_Otimes__class_Otimes( X, Y, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.80/1.39 c_Groups_Ozero__class_Ozero( X ) }.
% 0.80/1.39 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.80/1.39 c_Groups_Otimes__class_Otimes( X, Y, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.80/1.39 c_Groups_Ozero__class_Ozero( X ) }.
% 0.80/1.39 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.80/1.39 c_Groups_Otimes__class_Otimes( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.80/1.39 ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.80/1.39 T, Z ), c_Groups_Otimes__class_Otimes( X, T, Y ) ) }.
% 0.80/1.39 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.80/1.39 c_Groups_Otimes__class_Otimes( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.80/1.39 ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.80/1.39 T, Z ), c_Groups_Otimes__class_Otimes( X, T, Y ) ) }.
% 0.80/1.39 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.80/1.39 c_Groups_Otimes__class_Otimes( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.80/1.39 , Y ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X
% 0.80/1.39 , T, Y ), c_Groups_Otimes__class_Otimes( X, Z, Y ) ) }.
% 0.80/1.39 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.80/1.39 c_Groups_Otimes__class_Otimes( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.80/1.39 , Y ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X
% 0.80/1.39 , T, Y ), c_Groups_Otimes__class_Otimes( X, Z, Y ) ) }.
% 0.80/1.39 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.80/1.39 c_Groups_Otimes__class_Otimes( X, T, c_Groups_Ominus__class_Ominus( X, Z
% 0.80/1.39 , Y ) ) = c_Groups_Ominus__class_Ominus( X, c_Groups_Otimes__class_Otimes
% 0.80/1.39 ( X, T, Z ), c_Groups_Otimes__class_Otimes( X, T, Y ) ) }.
% 0.80/1.39 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.80/1.39 c_Groups_Otimes__class_Otimes( X, T, c_Groups_Ominus__class_Ominus( X, Z
% 0.80/1.39 , Y ) ) = c_Groups_Ominus__class_Ominus( X, c_Groups_Otimes__class_Otimes
% 0.80/1.39 ( X, T, Z ), c_Groups_Otimes__class_Otimes( X, T, Y ) ) }.
% 0.80/1.39 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.80/1.39 c_Groups_Otimes__class_Otimes( X, c_Groups_Ominus__class_Ominus( X, T, Z
% 0.80/1.39 ), Y ) = c_Groups_Ominus__class_Ominus( X, c_Groups_Otimes__class_Otimes
% 0.80/1.39 ( X, T, Y ), c_Groups_Otimes__class_Otimes( X, Z, Y ) ) }.
% 0.80/1.39 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.80/1.39 c_Groups_Otimes__class_Otimes( X, c_Groups_Ominus__class_Ominus( X, T, Z
% 0.80/1.39 ), Y ) = c_Groups_Ominus__class_Ominus( X, c_Groups_Otimes__class_Otimes
% 0.80/1.39 ( X, T, Y ), c_Groups_Otimes__class_Otimes( X, Z, Y ) ) }.
% 0.80/1.39 { ! class_RealVector_Oreal__normed__field( X ),
% 0.80/1.39 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.80/1.39 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.80/1.39 { ! class_RealVector_Oreal__normed__field( X ),
% 0.80/1.39 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, T, Z
% 0.80/1.39 ), Y ) = c_Groups_Oplus__class_Oplus( X, c_Rings_Oinverse__class_Odivide
% 0.80/1.39 ( X, T, Y ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.80/1.39 { ! class_RealVector_Oreal__normed__field( X ),
% 0.80/1.39 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus( X, T,
% 0.80/1.39 Z ), Y ) = c_Groups_Ominus__class_Ominus( X,
% 0.80/1.39 c_Rings_Oinverse__class_Odivide( X, T, Y ),
% 0.80/1.39 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.80/1.39 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.80/1.39 ( X, c_Power_Opower__class_Opower( X, Z, c_Int_Onumber__class_Onumber__of
% 0.80/1.39 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ),
% 0.80/1.39 c_Power_Opower__class_Opower( X, Y, c_Int_Onumber__class_Onumber__of(
% 0.80/1.39 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.80/1.39 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.80/1.39 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.80/1.39 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.80/1.39 c_Power_Opower__class_Opower( X, Z, c_Int_Onumber__class_Onumber__of(
% 0.80/1.39 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ),
% 0.80/1.39 c_Power_Opower__class_Opower( X, Y, c_Int_Onumber__class_Onumber__of(
% 0.80/1.39 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) ), ! Z =
% 0.80/1.39 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.80/1.39 }.
% 0.80/1.39 { ! class_Rings_Olinordered__idom( X ), Z = c_Groups_Ozero__class_Ozero( X
% 0.80/1.39 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.80/1.39 c_Groups_Oplus__class_Oplus( X, c_Power_Opower__class_Opower( X, Z,
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.39 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( X, Y,
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.39 c_Int_OPls ) ) ) ) ) ) }.
% 0.80/1.39 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.80/1.39 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.80/1.39 c_Groups_Oplus__class_Oplus( X, c_Power_Opower__class_Opower( X, Z,
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.39 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( X, Y,
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.39 c_Int_OPls ) ) ) ) ) ) }.
% 0.80/1.39 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.80/1.39 , c_Groups_Oplus__class_Oplus( X, c_Power_Opower__class_Opower( X, Z,
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.39 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( X, Y,
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.39 c_Int_OPls ) ) ) ) ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.80/1.39 c_Power_Opower__class_Opower( tc_RealDef_Oreal, c_NthRoot_Osqrt( X ),
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.39 c_Int_OPls ) ) ) ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.80/1.39 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, X, c_NthRoot_Osqrt(
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.80/1.39 c_Int_OBit1( c_Int_OPls ) ) ) ) ), X ) }.
% 0.80/1.39 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.80/1.39 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.80/1.39 , c_Power_Opower__class_Opower( X, Y, c_Nat_OSuc(
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat,
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.39 c_Int_OPls ) ) ), Z ) ) ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.80/1.39 { c_Transcendental_Oarctan( X ) = c_Groups_Otimes__class_Otimes(
% 0.80/1.39 tc_RealDef_Oreal, c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal,
% 0.80/1.39 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ), c_Transcendental_Oarctan(
% 0.80/1.39 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, X,
% 0.80/1.39 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oone__class_Oone
% 0.80/1.39 ( tc_RealDef_Oreal ), c_NthRoot_Osqrt( c_Groups_Oplus__class_Oplus(
% 0.80/1.39 tc_RealDef_Oreal, c_Groups_Oone__class_Oone( tc_RealDef_Oreal ),
% 0.80/1.39 c_Power_Opower__class_Opower( tc_RealDef_Oreal, X,
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.39 c_Int_OPls ) ) ) ) ) ) ) ) ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.80/1.39 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ),
% 0.80/1.39 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.80/1.39 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ),
% 0.80/1.39 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.80/1.39 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Transcendental_Oarctan(
% 0.80/1.39 X ), c_Transcendental_Oarctan( Y ) ) = c_Transcendental_Oarctan(
% 0.80/1.39 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.80/1.39 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X, Y ),
% 0.80/1.39 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.80/1.39 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ),
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, Y ) ) ) ) }.
% 0.80/1.39 { c_Nat_Osize__class_Osize( tc_Complex_Ocomplex,
% 0.80/1.39 c_Complex_Ocomplex_OComplex( Y, X ) ) = c_Groups_Ozero__class_Ozero(
% 0.80/1.39 tc_Nat_Onat ) }.
% 0.80/1.39 { ! class_Orderings_Opreorder( X ), c_Orderings_Oord__class_Oless__eq( X, Y
% 0.80/1.39 , Y ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.80/1.39 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( X ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.80/1.39 X ) ) }.
% 0.80/1.39 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.80/1.39 tc_Nat_Onat ), c_Nat_OSuc( X ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oabs__class_Oabs(
% 0.80/1.39 tc_Int_Oint, X ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X =
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.80/1.39 { ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oabs__class_Oabs(
% 0.80/1.39 tc_Int_Oint, X ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.80/1.39 { c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.80/1.39 tc_Nat_Onat ), X ) = X }.
% 0.80/1.39 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) =
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ), Y =
% 0.80/1.39 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.80/1.39 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) =
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ), X =
% 0.80/1.39 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.80/1.39 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.80/1.39 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Groups_Oone__class_Oone(
% 0.80/1.39 tc_Nat_Onat ) = c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) }.
% 0.80/1.39 { c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, c_Groups_Oone__class_Oone
% 0.80/1.39 ( tc_Nat_Onat ) ) = X }.
% 0.80/1.39 { ! c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) =
% 0.80/1.39 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Oone__class_Oone(
% 0.80/1.39 tc_Nat_Onat ) }.
% 0.80/1.39 { ! c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) =
% 0.80/1.39 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X = c_Groups_Oone__class_Oone(
% 0.80/1.39 tc_Nat_Onat ) }.
% 0.80/1.39 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.80/1.39 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Groups_Otimes__class_Otimes(
% 0.80/1.39 tc_Nat_Onat, Y, X ) = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.80/1.39 { c_Groups_Otimes__class_Otimes( tc_Int_Oint, c_Groups_Oone__class_Oone(
% 0.80/1.39 tc_Int_Oint ), X ) = X }.
% 0.80/1.39 { c_Groups_Otimes__class_Otimes( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 0.80/1.39 ( tc_Int_Oint ) ) = X }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.80/1.39 ( tc_Nat_Onat ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, X ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, X ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.80/1.39 tc_Nat_Onat ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.80/1.39 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.80/1.39 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y
% 0.80/1.39 = X }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.80/1.39 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.80/1.39 tc_Int_Oint ) ) ) }.
% 0.80/1.39 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.80/1.39 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.80/1.39 tc_Int_Oint ) ) ) }.
% 0.80/1.39 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.80/1.39 tc_Int_Oint ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.80/1.39 { alpha102( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.80/1.39 hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.80/1.39 { alpha102( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP(
% 0.80/1.39 hAPP( X, Y ), Z ) ) }.
% 0.80/1.39 { ! alpha102( X, Y, Z ), alpha103( X, Y, Z ), Z = Y }.
% 0.80/1.39 { ! alpha102( X, Y, Z ), alpha103( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ),
% 0.80/1.39 Z ) ) }.
% 0.80/1.39 { ! alpha103( X, Y, Z ), alpha102( X, Y, Z ) }.
% 0.80/1.39 { ! Z = Y, hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha102( X, Y, Z ) }.
% 0.80/1.39 { ! alpha103( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y )
% 0.80/1.39 }.
% 0.80/1.39 { ! alpha103( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP(
% 0.80/1.39 X, Y ), Z ) ), alpha103( X, Y, Z ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X = Y }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.80/1.39 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.80/1.39 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.80/1.39 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y = X,
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.80/1.39 { ! c_Groups_Ozero__class_Ozero( tc_Int_Oint ) = c_Groups_Oone__class_Oone
% 0.80/1.39 ( tc_Int_Oint ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.80/1.39 tc_Int_Oint, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.80/1.39 .
% 0.80/1.39 { ! class_Groups_Omonoid__mult( X ), c_Power_Opower__class_Opower( X, Y,
% 0.80/1.39 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = Y }.
% 0.80/1.39 { ! class_Rings_Ocomm__semiring__1( X ), c_Power_Opower__class_Opower( X, Y
% 0.80/1.39 , c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = Y }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.80/1.39 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.80/1.39 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.80/1.39 ( tc_Nat_Onat, Y, Z ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y
% 0.80/1.39 , X ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.80/1.39 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, X ) =
% 0.80/1.39 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.80/1.39 tc_Nat_Onat, Y, T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.80/1.39 .
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.80/1.39 tc_Nat_Onat, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.80/1.39 .
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.80/1.39 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.80/1.39 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.80/1.39 ( tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) )
% 0.80/1.39 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.80/1.39 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }
% 0.80/1.39 .
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.80/1.39 ( tc_Nat_Onat, Y, X ), X ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.80/1.39 ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), ! Y = X }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), Y = X,
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.80/1.39 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.80/1.39 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) )
% 0.80/1.39 }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.80/1.39 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.80/1.39 X ) ) }.
% 0.80/1.39 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y = X }
% 0.80/1.39 .
% 0.80/1.39 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X,
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.80/1.39 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), X = Y }
% 0.80/1.39 .
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) = X
% 0.80/1.39 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.80/1.39 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.80/1.39 c_Int_OBit0( X ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.80/1.39 .
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( Y ), c_Int_OBit0
% 0.80/1.39 ( X ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.80/1.39 c_Int_OBit0( X ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.80/1.39 .
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( Y ), c_Int_OBit0
% 0.80/1.39 ( X ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, c_Int_OPls ) }
% 0.80/1.39 .
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( Y ),
% 0.80/1.39 c_Int_OBit1( X ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.80/1.39 .
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( Y ), c_Int_OBit1
% 0.80/1.39 ( X ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( Y ),
% 0.80/1.39 c_Int_OBit1( X ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.80/1.39 .
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( Y ), c_Int_OBit1
% 0.80/1.39 ( X ) ) }.
% 0.80/1.39 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.80/1.39 tc_Nat_Onat ), X ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X =
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.80/1.39 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.80/1.39 tc_Nat_Onat ), X ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.80/1.39 ( tc_Nat_Onat ), X ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 0.80/1.39 .
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.80/1.39 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 0.80/1.39 ( tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.80/1.39 .
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.80/1.39 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 0.80/1.39 ( tc_Int_Oint ) ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.80/1.39 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.80/1.39 tc_Int_Oint ) ), X ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.80/1.39 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.80/1.39 tc_Int_Oint ) ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X )
% 0.80/1.39 }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.80/1.39 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.80/1.39 tc_Int_Oint ) ), X ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.80/1.39 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.80/1.39 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X )
% 0.80/1.39 }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.80/1.39 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.80/1.39 tc_Int_Oint ) ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.80/1.39 ( tc_Int_Oint ), X ), ! c_Groups_Otimes__class_Otimes( tc_Int_Oint, X, Y
% 0.80/1.39 ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), X =
% 0.80/1.39 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.80/1.39 ( tc_Int_Oint ), X ), ! c_Groups_Otimes__class_Otimes( tc_Int_Oint, X, Y
% 0.80/1.39 ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), Y =
% 0.80/1.39 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.80/1.39 ( tc_Int_Oint ), X ), ! X = c_Groups_Oone__class_Oone( tc_Int_Oint ), ! Y
% 0.80/1.39 = c_Groups_Oone__class_Oone( tc_Int_Oint ),
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_Int_Oint, X, Y ) =
% 0.80/1.39 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.80/1.39 ( tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.80/1.39 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.80/1.39 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.80/1.39 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.80/1.39 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.80/1.39 tc_Int_Oint ), X ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.80/1.39 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.80/1.39 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ), alpha30( X, Y ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.80/1.39 { ! alpha30( X, Y ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) }.
% 0.80/1.39 { ! alpha30( X, Y ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, X ) }.
% 0.80/1.39 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), alpha30( X, Y ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, X ), alpha30( X
% 0.80/1.39 , Y ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oarctan
% 0.80/1.39 ( Y ), c_Transcendental_Oarctan( X ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.80/1.39 ( tc_Nat_Onat, Z, X ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.80/1.39 ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.80/1.39 ( tc_Nat_Onat, Y, Z ), X ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.80/1.39 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.80/1.39 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.80/1.39 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.80/1.39 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) = X }.
% 0.80/1.39 { c_Transcendental_Oarctan( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal )
% 0.80/1.39 ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.80/1.39 c_Transcendental_Oarctan( Y ), c_Transcendental_Oarctan( X ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.80/1.39 tc_Int_Oint ), c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.80/1.39 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) ) }.
% 0.80/1.39 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless(
% 0.80/1.39 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 0.80/1.39 c_Groups_Otimes__class_Otimes( X, c_Power_Opower__class_Opower( X, Z,
% 0.80/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 0.80/1.39 ( tc_Nat_Onat ) ) ), Z ) = c_Power_Opower__class_Opower( X, Z, Y ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.80/1.39 ( tc_Nat_Onat ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ),
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) = c_Nat_OSuc(
% 0.80/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ),
% 0.80/1.39 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( X ),
% 0.80/1.39 c_Int_OPls ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Int_OPls )
% 0.80/1.39 }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Int_OPls ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( X ), c_Int_OPls
% 0.80/1.39 ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( X ),
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( X ),
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( Y ),
% 0.80/1.39 c_Int_OBit0( X ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.80/1.39 .
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( Y ), c_Int_OBit0
% 0.80/1.39 ( X ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( Y ),
% 0.80/1.39 c_Int_OBit0( X ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.80/1.39 .
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( Y ), c_Int_OBit0
% 0.80/1.39 ( X ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, c_Int_OBit0( X
% 0.80/1.39 ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, X ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, X ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, c_Int_OBit0( X )
% 0.80/1.39 ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( X ),
% 0.80/1.39 c_Int_OPls ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Int_OPls )
% 0.80/1.39 }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Int_OPls ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( X ), c_Int_OPls
% 0.80/1.39 ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( X ),
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( X ),
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.80/1.39 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( skol4( X ) ) }.
% 0.80/1.39 { ! X = c_Nat_OSuc( Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X =
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.80/1.39 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y =
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha31( X, Y ) }.
% 0.80/1.39 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.80/1.39 { ! alpha31( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.80/1.39 c_Nat_OSuc( X ) ) }.
% 0.80/1.39 { ! alpha31( X, Y ), Y = c_Nat_OSuc( skol5( Z, Y ) ) }.
% 0.80/1.39 { ! alpha31( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol5( X,
% 0.80/1.39 Y ), X ) }.
% 0.80/1.39 { ! Y = c_Nat_OSuc( Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.80/1.39 ), alpha31( X, Y ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( c_Nat_OSuc(
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X =
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X = c_Nat_OSuc(
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.80/1.39 ( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.80/1.39 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.80/1.39 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.80/1.39 tc_Nat_Onat, Y, X ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.80/1.39 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.80/1.39 tc_Nat_Onat, Y, X ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), X = c_Nat_OSuc(
% 0.80/1.39 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol6( X, Y ) ) ) }.
% 0.80/1.39 { ! X = c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.80/1.39 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 0.80/1.39 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ) }.
% 0.80/1.39 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 0.80/1.39 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X = Y }
% 0.80/1.39 .
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X = Y,
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.80/1.39 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Z ),
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Y ) ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.80/1.39 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 0.80/1.39 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Z ),
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Y ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.80/1.39 ( tc_Nat_Onat ), X ), ! c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Z
% 0.80/1.39 ) = c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Y ), Z = Y }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.80/1.39 ( tc_Nat_Onat ), X ), ! Z = Y, c_Groups_Otimes__class_Otimes( tc_Nat_Onat
% 0.80/1.39 , X, Z ) = c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Y ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.80/1.39 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ),
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.80/1.39 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, Z ),
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Z ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ),
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Y ) ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.80/1.39 tc_Nat_Onat ), Y ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ),
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Y ) ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.80/1.39 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.80/1.39 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ),
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Y ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ),
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ) ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.80/1.39 tc_Nat_Onat ), Z ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ),
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ) ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.80/1.39 ( tc_Nat_Onat ), Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 0.80/1.39 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ),
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.80/1.39 ( tc_Nat_Onat ), c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.80/1.39 tc_Nat_Onat ), Y ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.80/1.39 ( tc_Nat_Onat ), c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.80/1.39 tc_Nat_Onat ), X ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.80/1.39 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.80/1.39 tc_Nat_Onat ), c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.80/1.39 ( tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.80/1.39 tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.80/1.39 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.80/1.39 ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.80/1.39 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_Int_Oint, Z, Y ),
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_Int_Oint, Z, X ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Nat_OSuc( Z ), Y ),
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Nat_OSuc( Z ), X ) ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Otimes__class_Otimes
% 0.80/1.39 ( tc_Nat_Onat, c_Nat_OSuc( Z ), Y ), c_Groups_Otimes__class_Otimes(
% 0.80/1.39 tc_Nat_Onat, c_Nat_OSuc( Z ), X ) ) }.
% 0.80/1.39 { c_Groups_Oone__class_Oone( tc_Nat_Onat ) = c_Nat_OSuc(
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.80/1.39 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.80/1.39 ( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Z ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.80/1.39 tc_Int_Oint, Y, T ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.80/1.39 .
% 0.80/1.39 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.80/1.39 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.80/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) = Y }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z,
% 0.80/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.80/1.39 tc_Nat_Onat, Z, X ), Y ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.80/1.39 ( tc_Nat_Onat, Z, X ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z
% 0.80/1.39 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.80/1.39 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.80/1.39 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.80/1.39 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.80/1.39 ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.80/1.39 ( tc_Nat_Onat, Y, Z ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z )
% 0.80/1.39 ) }.
% 0.80/1.39 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.80/1.39 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X ) }.
% 0.80/1.39 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.80/1.39 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ominus__class_Ominus
% 0.80/1.39 ( tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.80/1.39 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ),
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.80/1.39 { ! Y = c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ), X =
% 0.80/1.39 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Ozero__class_Ozero
% 0.80/1.39 ( tc_Nat_Onat ) }.
% 0.80/1.39 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 0.80/1.39 tc_Int_Oint ) ) }.
% 0.80/1.39 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 0.80/1.39 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.80/1.39 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 0.80/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.80/1.39 ( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) }.
% 0.80/1.39 { c_Int_OBit1( X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.80/1.39 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oone__class_Oone(
% 0.80/1.39 tc_Int_Oint ), X ), X ) }.
% 0.80/1.39 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.80/1.39 tc_Int_Oint, c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ) =
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.80/1.39 ( tc_Nat_Onat ), c_Power_Opower__class_Opower( tc_Nat_Onat, Y, X ) ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.80/1.39 tc_Nat_Onat ), Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.80/1.39 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Power_Opower__class_Opower
% 0.80/1.39 ( tc_Nat_Onat, Y, X ) ) }.
% 0.80/1.39 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.80/1.39 tc_Nat_Onat ), c_Power_Opower__class_Opower( tc_Nat_Onat, Y, X ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.80/1.39 ( tc_Nat_Onat ), c_Power_Opower__class_Opower( tc_Nat_Onat, Y, X ) ), X =
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.80/1.39 tc_Nat_Onat ), Y ) }.
% 0.80/1.39 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.80/1.39 tc_Nat_Onat ), c_Power_Opower__class_Opower( tc_Nat_Onat, Y, X ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.80/1.39 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Power_Opower__class_Opower
% 0.80/1.39 ( tc_Nat_Onat, Y, X ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.80/1.39 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.80/1.39 c_Power_Opower__class_Opower( tc_Nat_Onat, X, Z ),
% 0.80/1.39 c_Power_Opower__class_Opower( tc_Nat_Onat, X, Y ) ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.80/1.39 { ! c_Groups_Oabs__class_Oabs( tc_Int_Oint, c_Groups_Otimes__class_Otimes(
% 0.80/1.39 tc_Int_Oint, X, Y ) ) = c_Groups_Oone__class_Oone( tc_Int_Oint ),
% 0.80/1.39 c_Groups_Oabs__class_Oabs( tc_Int_Oint, X ) = c_Groups_Oone__class_Oone(
% 0.80/1.39 tc_Int_Oint ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.80/1.39 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Z,
% 0.80/1.39 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.80/1.39 tc_Int_Oint, c_Groups_Oabs__class_Oabs( tc_Int_Oint,
% 0.80/1.39 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, Z ) ),
% 0.80/1.39 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.80/1.39 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.80/1.39 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z,
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.80/1.39 tc_Int_Oint, c_Groups_Oabs__class_Oabs( tc_Int_Oint,
% 0.80/1.39 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ),
% 0.80/1.39 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) ), Y ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.39 c_Int_OPls ) ) ) ), X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X =
% 0.80/1.39 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, c_Int_OBit1( X
% 0.80/1.39 ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, X ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, X ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, c_Int_OBit1( X )
% 0.80/1.39 ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( X ),
% 0.80/1.39 c_Int_OPls ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Int_OPls )
% 0.80/1.39 }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Int_OPls ),
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( X ),
% 0.80/1.39 c_Int_OPls ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.80/1.39 c_Int_OBit1( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 0.80/1.39 ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( Y ), c_Int_OBit1
% 0.80/1.39 ( X ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.80/1.39 c_Int_OBit1( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 0.80/1.39 ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( Y ), c_Int_OBit1
% 0.80/1.39 ( X ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( Y ),
% 0.80/1.39 c_Int_OBit0( X ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.80/1.39 .
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( Y ),
% 0.80/1.39 c_Int_OBit0( X ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( Y ),
% 0.80/1.39 c_Int_OBit0( X ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.80/1.39 .
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( Y ),
% 0.80/1.39 c_Int_OBit0( X ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Y ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.80/1.39 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.80/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.80/1.39 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.80/1.39 tc_Nat_Onat, X, c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) )
% 0.80/1.39 ) ) = X }.
% 0.80/1.39 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.80/1.39 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.80/1.39 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.80/1.39 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.80/1.39 hAPP( Y, U ) ) }.
% 0.80/1.39 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.80/1.39 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.80/1.39 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.80/1.39 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.80/1.39 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.80/1.39 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.80/1.39 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.80/1.39 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.80/1.39 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.80/1.39 , Y ), ! Z = T, c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.80/1.39 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y
% 0.80/1.39 ), ! Y = T, c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.80/1.39 { ! class_Orderings_Oorder( X ), ! Z = Y, !
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.80/1.39 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.80/1.39 ( X, Y, T ), c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.80/1.39 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.80/1.39 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.80/1.39 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.80/1.39 , Y ), ! Y = Z, c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.80/1.39 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.80/1.39 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.80/1.39 hAPP( Y, U ) ) }.
% 0.80/1.39 { ! class_Orderings_Opreorder( X ), ! Z = Y,
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.80/1.39 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.80/1.39 ( X, Z, Y ) }.
% 0.80/1.39 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.80/1.39 ( X, Y, Z ) }.
% 0.80/1.39 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.80/1.39 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.80/1.39 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.80/1.39 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.80/1.39 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.80/1.39 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.80/1.39 hAPP( Y, U ) ) }.
% 0.80/1.39 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, hAPP
% 0.80/1.39 ( Z, skol7( X, Y, Z ) ), hAPP( Y, skol7( X, Y, Z ) ) ),
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.80/1.39 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Z ),
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Y ) ),
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.80/1.39 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z
% 0.80/1.39 , Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Z ),
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Y ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ),
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ) ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.80/1.39 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 0.80/1.39 ) }.
% 0.80/1.39 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.80/1.39 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ),
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ),
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ),
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Y ) ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.80/1.39 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X
% 0.80/1.39 ) }.
% 0.80/1.39 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.80/1.39 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ),
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Y ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ),
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ),
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Y ) ) }.
% 0.80/1.39 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.80/1.39 , ! alpha32( X, Y, Z ) }.
% 0.80/1.39 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.80/1.39 , ! alpha63( X, Y, Z ) }.
% 0.80/1.39 { alpha32( X, Y, Z ), alpha63( X, Y, Z ), hBOOL( hAPP( Z,
% 0.80/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.80/1.39 { ! alpha63( X, Y, Z ), ! hBOOL( hAPP( Z, skol8( T, U, Z ) ) ) }.
% 0.80/1.39 { ! alpha63( X, Y, Z ), Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.80/1.39 skol8( X, Y, Z ) ) }.
% 0.80/1.39 { ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, T ), hBOOL( hAPP( Z, T
% 0.80/1.39 ) ), alpha63( X, Y, Z ) }.
% 0.80/1.39 { ! alpha32( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 0.80/1.39 }.
% 0.80/1.39 { ! alpha32( X, Y, Z ), ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero(
% 0.80/1.39 tc_Nat_Onat ) ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), hBOOL( hAPP( Z,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha32( X, Y, Z ) }.
% 0.80/1.39 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.80/1.39 , alpha33( X, Y, Z ) }.
% 0.80/1.39 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.80/1.39 , alpha64( X, Y, Z ) }.
% 0.80/1.39 { ! alpha33( X, Y, Z ), ! alpha64( X, Y, Z ), hBOOL( hAPP( Z,
% 0.80/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.80/1.39 { ! alpha64( X, Y, Z ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.80/1.39 T ), hBOOL( hAPP( Z, T ) ) }.
% 0.80/1.39 { ! hBOOL( hAPP( Z, skol9( T, U, Z ) ) ), alpha64( X, Y, Z ) }.
% 0.80/1.39 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, skol9( X, Y, Z ) ),
% 0.80/1.39 alpha64( X, Y, Z ) }.
% 0.80/1.39 { ! alpha33( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 0.80/1.39 ), hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.80/1.39 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), alpha33( X, Y, Z ) }
% 0.80/1.39 .
% 0.80/1.39 { ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha33
% 0.80/1.39 ( X, Y, Z ) }.
% 0.80/1.39 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.80/1.39 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.80/1.39 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.80/1.39 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.80/1.39 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.80/1.39 , ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.80/1.39 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.80/1.39 Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.80/1.39 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.80/1.39 , ! Z = T, c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.80/1.39 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.80/1.39 ! Y = T, c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.80/1.39 { ! class_Orderings_Oorder( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless(
% 0.80/1.39 X, T, Y ), c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.80/1.39 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X
% 0.80/1.39 , Y, T ), c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.80/1.39 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.80/1.39 , ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.80/1.39 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.80/1.39 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.80/1.39 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.80/1.39 , ! Y = Z }.
% 0.80/1.39 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.80/1.39 , ! Z = Y }.
% 0.80/1.39 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.80/1.39 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.80/1.39 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.80/1.39 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.80/1.39 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.80/1.39 , ! Z = Y }.
% 0.80/1.39 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.80/1.39 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.80/1.39 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.80/1.39 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Y = Z }.
% 0.80/1.39 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.80/1.39 ), ! Y = Z, ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.80/1.39 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.80/1.39 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.80/1.39 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.80/1.39 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Z = Y }.
% 0.80/1.39 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.80/1.39 Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.80/1.39 { ! class_Orderings_Olinorder( X ), ! Z = Y, !
% 0.80/1.39 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.80/1.39 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.80/1.39 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.80/1.39 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.80/1.39 Y ), ! Z = Y }.
% 0.80/1.39 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.80/1.39 Z ), ! Z = Y }.
% 0.80/1.39 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.80/1.39 Y ) }.
% 0.80/1.39 { c_Groups_Oone__class_Oone( tc_Nat_Onat ) =
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit1( c_Int_OPls )
% 0.80/1.39 ) }.
% 0.80/1.39 { c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit1( c_Int_OPls )
% 0.80/1.39 ) = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.80/1.39 { c_Groups_Oone__class_Oone( tc_Int_Oint ) =
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit1( c_Int_OPls )
% 0.80/1.39 ) }.
% 0.80/1.39 { ! c_Complex_Ocomplex_OComplex( Y, X ) = c_Groups_Oone__class_Oone(
% 0.80/1.39 tc_Complex_Ocomplex ), Y = c_Groups_Oone__class_Oone( tc_RealDef_Oreal )
% 0.80/1.39 }.
% 0.80/1.39 { ! c_Complex_Ocomplex_OComplex( Y, X ) = c_Groups_Oone__class_Oone(
% 0.80/1.39 tc_Complex_Ocomplex ), X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal
% 0.80/1.39 ) }.
% 0.80/1.39 { ! Y = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), ! X =
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.80/1.39 c_Complex_Ocomplex_OComplex( Y, X ) = c_Groups_Oone__class_Oone(
% 0.80/1.39 tc_Complex_Ocomplex ) }.
% 0.80/1.39 { c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) =
% 0.80/1.39 c_Complex_Ocomplex_OComplex( c_Groups_Oone__class_Oone( tc_RealDef_Oreal
% 0.80/1.39 ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.80/1.39 ( tc_Nat_Onat ), c_Power_Opower__class_Opower( tc_Nat_Onat, Y,
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) ),
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) =
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Orderings_Oord__class_Oless
% 0.80/1.39 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 0.80/1.39 { ! c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) =
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Orderings_Oord__class_Oless
% 0.80/1.39 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.80/1.39 c_Power_Opower__class_Opower( tc_Nat_Onat, Y,
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.80/1.39 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Power_Opower__class_Opower
% 0.80/1.39 ( tc_Nat_Onat, Y, c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) )
% 0.80/1.39 }.
% 0.80/1.39 { ! class_Rings_Olinordered__semidom( X ), ! c_Power_Opower__class_Opower(
% 0.80/1.39 X, T, Z ) = c_Power_Opower__class_Opower( X, Y, Z ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.80/1.39 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.80/1.39 X ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ), T = Y }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, c_Int_OPls ),
% 0.80/1.39 c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) =
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) }.
% 0.80/1.39 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, c_Int_OPls ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Int_OPls ),
% 0.80/1.39 c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) =
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) }.
% 0.80/1.39 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, c_Int_OPls ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Int_OPls ),
% 0.80/1.39 c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) =
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 0.80/1.39 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.80/1.39 tc_Nat_Onat, c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, U ), T ),
% 0.80/1.39 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.80/1.39 tc_Nat_Onat, Y, U ), Z ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.80/1.39 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.80/1.39 tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), U ), T )
% 0.80/1.39 , Z ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.80/1.39 tc_Nat_Onat, c_Groups_Otimes__class_Otimes( tc_Nat_Onat,
% 0.80/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), U ), T ), Z ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.80/1.39 tc_Nat_Onat, c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, U ), T ),
% 0.80/1.39 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.80/1.39 tc_Nat_Onat, Y, U ), Z ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.80/1.39 tc_Nat_Onat, c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, U ), T ),
% 0.80/1.39 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.80/1.39 tc_Nat_Onat, X, U ), Z ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, T
% 0.80/1.39 , c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes
% 0.80/1.39 ( tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), U ), Z
% 0.80/1.39 ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T,
% 0.80/1.39 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.80/1.39 tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), U ), Z )
% 0.80/1.39 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.80/1.39 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.80/1.39 tc_Nat_Onat, Y, U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, U ), Z ) ) }.
% 0.80/1.39 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.80/1.39 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = X }.
% 0.80/1.39 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.80/1.39 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.80/1.39 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.80/1.39 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) ) }.
% 0.80/1.39 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) =
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.80/1.39 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) =
% 0.80/1.39 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.80/1.39 ( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.80/1.39 ( tc_Int_Oint ), c_Power_Opower__class_Opower( tc_Int_Oint,
% 0.80/1.39 c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ), X ) ), ! Y =
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X =
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.80/1.39 { Y = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.80/1.39 tc_Int_Oint ), c_Power_Opower__class_Opower( tc_Int_Oint,
% 0.80/1.39 c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ), X ) ) }.
% 0.80/1.39 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.80/1.39 tc_Int_Oint ), c_Power_Opower__class_Opower( tc_Int_Oint,
% 0.80/1.39 c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ), X ) ) }.
% 0.80/1.39 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.80/1.39 c_Power_Opower__class_Opower( tc_Nat_Onat, X, Y ) =
% 0.80/1.39 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.80/1.39 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.80/1.39 c_Power_Opower__class_Opower( tc_Nat_Onat, X, Y ) =
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X,
% 0.80/1.39 c_Power_Opower__class_Opower( tc_Nat_Onat, X,
% 0.80/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 0.80/1.39 ( tc_Nat_Onat ) ) ) ) }.
% 0.80/1.39 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.80/1.39 tc_Nat_Onat ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0
% 0.80/1.39 ( c_Int_OBit1( c_Int_OPls ) ) ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, c_Int_OPls ),
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat,
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Z ),
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat,
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ), X ) ) =
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.80/1.39 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, c_Int_OPls ),
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat,
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Z ),
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat,
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ), X ) ) =
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat,
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_Int_Oint, Z, Y ) ), X ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, c_Int_OPls ),
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat,
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) =
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.80/1.39 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, c_Int_OPls ),
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat,
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) =
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_Int_Oint, Y, X ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OPls ), X ),
% 0.80/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.80/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y,
% 0.80/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit1( c_Int_OPls )
% 0.80/1.39 ) ) ) }.
% 0.80/1.39 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.80/1.39 tc_Nat_Onat ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) =
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.39 c_Int_OPls ) ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.39 c_Int_OPls ) ) ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.80/1.39 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.80/1.39 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.80/1.39 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.80/1.39 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.80/1.39 , Y, Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.80/1.39 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.80/1.39 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.80/1.39 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.80/1.39 Z ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.80/1.39 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.80/1.39 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.80/1.39 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.80/1.39 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.80/1.39 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.80/1.39 , ! Z = Y }.
% 0.80/1.39 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.80/1.39 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.80/1.39 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.80/1.39 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.80/1.39 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.80/1.39 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.80/1.39 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.80/1.39 , Z, Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.80/1.39 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.80/1.39 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.80/1.39 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.80/1.39 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.80/1.39 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.80/1.39 ( X, Z, Y ) }.
% 0.80/1.39 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.80/1.39 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.80/1.39 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.80/1.39 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.80/1.39 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.80/1.39 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ), Z = Y }.
% 0.80/1.39 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.80/1.39 ), ! Z = Y, c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.80/1.39 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.80/1.39 ( X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.80/1.39 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.80/1.39 ( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.80/1.39 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.80/1.39 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.80/1.39 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.80/1.39 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.80/1.39 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.80/1.39 , Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.80/1.39 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.80/1.39 , Z, Y ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.80/1.39 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.80/1.39 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.80/1.39 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.80/1.39 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.80/1.39 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.80/1.39 , Y ), Y = Z, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.80/1.39 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.80/1.39 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.80/1.39 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.80/1.39 , ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.80/1.39 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.80/1.39 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.80/1.39 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.80/1.39 , Y ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.80/1.39 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.80/1.39 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_Int_Oint, X, Y ) ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ),
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.80/1.39 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.80/1.39 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_Int_Oint, X, Y ) ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ),
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oone__class_Oone
% 0.80/1.39 ( tc_Int_Oint ), Y ) }.
% 0.80/1.39 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.80/1.39 X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }
% 0.80/1.39 .
% 0.80/1.39 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.80/1.39 X ), Z, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z )
% 0.80/1.39 }.
% 0.80/1.39 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.80/1.39 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z
% 0.80/1.39 ), c_Orderings_Oord__class_Oless( tc_fun( T, X ), Z, Y ) }.
% 0.80/1.39 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Otimes__class_Otimes
% 0.80/1.39 ( tc_Int_Oint, W, U ), T ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_Int_Oint, Z, Y ), X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.80/1.39 tc_Int_Oint, c_Groups_Otimes__class_Otimes( tc_Int_Oint, Z, Y ), X ),
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, T, W ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.80/1.39 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.80/1.39 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, U ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.80/1.39 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Otimes__class_Otimes(
% 0.80/1.39 tc_Int_Oint, U, T ), Z ), c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_Int_Oint, U, Y ), X ) ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, Z ),
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, T ) }.
% 0.80/1.39 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Otimes__class_Otimes
% 0.80/1.39 ( tc_Int_Oint, W, U ), T ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_Int_Oint, Z, Y ), X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.80/1.39 tc_Int_Oint, c_Groups_Otimes__class_Otimes( tc_Int_Oint, Z, Y ), X ) ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.80/1.39 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.80/1.39 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, U, Y ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.80/1.39 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Otimes__class_Otimes(
% 0.80/1.39 tc_Int_Oint, U, T ), Z ), c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.80/1.39 c_Groups_Otimes__class_Otimes( tc_Int_Oint, U, Y ), X ) ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, U ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, U ),
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Y ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.80/1.39 ( tc_Int_Oint, c_Groups_Otimes__class_Otimes( tc_Int_Oint, Z, Y ), X ),
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.80/1.39 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.80/1.39 tc_Int_Oint, c_Groups_Otimes__class_Otimes( tc_Int_Oint, Z, Y ), X ) ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.80/1.39 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Divides_Odiv__class_Omod
% 0.80/1.39 ( tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.80/1.39 c_Groups_Oone__class_Oone( tc_Int_Oint ), c_Groups_Otimes__class_Otimes(
% 0.80/1.39 tc_Int_Oint, c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0(
% 0.80/1.39 c_Int_OBit1( c_Int_OPls ) ) ), Y ) ), c_Groups_Otimes__class_Otimes(
% 0.80/1.39 tc_Int_Oint, c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0(
% 0.80/1.39 c_Int_OBit1( c_Int_OPls ) ) ), X ) ) = c_Groups_Ominus__class_Ominus(
% 0.80/1.39 tc_Int_Oint, c_Groups_Otimes__class_Otimes( tc_Int_Oint,
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.39 c_Int_OPls ) ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint,
% 0.80/1.39 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.80/1.39 tc_Int_Oint ) ), X ) ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ) ),
% 0.80/1.39 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Int_Onumber__class_Onumber__of
% 0.80/1.39 ( tc_Int_Oint, c_Int_OBit1( X ) ), c_Int_Onumber__class_Onumber__of(
% 0.80/1.39 tc_Int_Oint, c_Int_OBit0( Y ) ) ) = c_Groups_Oplus__class_Oplus(
% 0.80/1.39 tc_Int_Oint, c_Groups_Otimes__class_Otimes( tc_Int_Oint,
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.39 c_Int_OPls ) ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint,
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ),
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ) ) ),
% 0.80/1.39 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.80/1.39 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ) ),
% 0.80/1.39 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Int_Onumber__class_Onumber__of
% 0.80/1.39 ( tc_Int_Oint, c_Int_OBit1( X ) ), c_Int_Onumber__class_Onumber__of(
% 0.80/1.39 tc_Int_Oint, c_Int_OBit0( Y ) ) ) = c_Groups_Ominus__class_Ominus(
% 0.80/1.39 tc_Int_Oint, c_Groups_Otimes__class_Otimes( tc_Int_Oint,
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.39 c_Int_OPls ) ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint,
% 0.80/1.39 c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ),
% 0.80/1.39 c_Groups_Oone__class_Oone( tc_Int_Oint ) ),
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ) ) ),
% 0.80/1.39 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.80/1.39 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.80/1.39 tc_Int_Oint, Y, X ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.80/1.39 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.80/1.39 tc_Int_Oint, Y, X ) ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.80/1.39 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.80/1.39 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ), X ) }.
% 0.80/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.80/1.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.80/1.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ),
% 0.80/1.39 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ) = X }.
% 0.80/1.39 { ! class_Orderings_Opreorder( X ), class_Orderings_Opreorder( tc_fun( Y, X
% 0.80/1.39 ) ) }.
% 0.80/1.39 { ! class_Orderings_Oorder( X ), class_Orderings_Oorder( tc_fun( Y, X ) ) }
% 0.80/1.39 .
% 0.80/1.39 { ! class_Orderings_Oord( X ), class_Orderings_Oord( tc_fun( Y, X ) ) }.
% 0.80/1.39 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.80/1.39 tc_Int_Oint ) }.
% 0.80/1.39 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.80/1.39 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Int_Oint ) }.
% 0.80/1.39 { class_Rings_Olinordered__comm__semiring__strict( tc_Int_Oint ) }.
% 0.80/1.39 { class_Rings_Olinordered__semiring__1__strict( tc_Int_Oint ) }.
% 0.80/1.39 { class_Rings_Olinordered__semiring__strict( tc_Int_Oint ) }.
% 0.80/1.39 { class_Groups_Oordered__ab__semigroup__add( tc_Int_Oint ) }.
% 0.80/1.39 { class_Groups_Oordered__ab__group__add__abs( tc_Int_Oint ) }.
% 0.80/1.39 { class_Groups_Oordered__comm__monoid__add( tc_Int_Oint ) }.
% 0.80/1.39 { class_Groups_Olinordered__ab__group__add( tc_Int_Oint ) }.
% 0.80/1.39 { class_Groups_Ocancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.80/1.39 { class_Rings_Oring__1__no__zero__divisors( tc_Int_Oint ) }.
% 0.80/1.39 { class_Rings_Oordered__cancel__semiring( tc_Int_Oint ) }.
% 0.80/1.39 { class_Rings_Olinordered__ring__strict( tc_Int_Oint ) }.
% 0.80/1.39 { class_Rings_Oring__no__zero__divisors( tc_Int_Oint ) }.
% 0.80/1.39 { class_Rings_Oordered__comm__semiring( tc_Int_Oint ) }.
% 0.80/1.39 { class_Rings_Olinordered__semiring__1( tc_Int_Oint ) }.
% 0.80/1.39 { class_Groups_Oordered__ab__group__add( tc_Int_Oint ) }.
% 0.80/1.39 { class_Groups_Ocancel__semigroup__add( tc_Int_Oint ) }.
% 0.80/1.39 { class_Rings_Olinordered__semiring( tc_Int_Oint ) }.
% 0.80/1.39 { class_Rings_Olinordered__semidom( tc_Int_Oint ) }.
% 0.80/1.39 { class_Groups_Oab__semigroup__mult( tc_Int_Oint ) }.
% 0.80/1.39 { class_Groups_Ocomm__monoid__mult( tc_Int_Oint ) }.
% 0.80/1.39 { class_Groups_Oab__semigroup__add( tc_Int_Oint ) }.
% 0.80/1.39 { class_Rings_Oordered__semiring( tc_Int_Oint ) }.
% 0.80/1.39 { class_Rings_Oordered__ring__abs( tc_Int_Oint ) }.
% 0.80/1.39 { class_Rings_Ono__zero__divisors( tc_Int_Oint ) }.
% 0.80/1.39 { class_Groups_Ocomm__monoid__add( tc_Int_Oint ) }.
% 0.80/1.39 { class_Rings_Olinordered__ring( tc_Int_Oint ) }.
% 0.80/1.39 { class_Rings_Olinordered__idom( tc_Int_Oint ) }.
% 0.80/1.39 { class_Rings_Ocomm__semiring__1( tc_Int_Oint ) }.
% 0.80/1.39 { class_Rings_Ocomm__semiring( tc_Int_Oint ) }.
% 0.80/1.39 { class_Groups_Oab__group__add( tc_Int_Oint ) }.
% 0.80/1.39 { class_Rings_Ozero__neq__one( tc_Int_Oint ) }.
% 0.80/1.39 { class_Rings_Oordered__ring( tc_Int_Oint ) }.
% 0.80/1.39 { class_Orderings_Opreorder( tc_Int_Oint ) }.
% 0.80/1.39 { class_Orderings_Olinorder( tc_Int_Oint ) }.
% 0.80/1.39 { class_Groups_Omonoid__mult( tc_Int_Oint ) }.
% 0.80/1.39 { class_Rings_Ocomm__ring__1( tc_Int_Oint ) }.
% 0.80/1.39 { class_Groups_Omonoid__add( tc_Int_Oint ) }.
% 0.80/1.39 { class_Rings_Osemiring__1( tc_Int_Oint ) }.
% 0.80/1.39 { class_Rings_Osemiring__0( tc_Int_Oint ) }.
% 0.80/1.39 { class_Groups_Ogroup__add( tc_Int_Oint ) }.
% 0.80/1.39 { class_Rings_Omult__zero( tc_Int_Oint ) }.
% 0.80/1.39 { class_Orderings_Oorder( tc_Int_Oint ) }.
% 0.80/1.39 { class_Int_Oring__char__0( tc_Int_Oint ) }.
% 0.80/1.39 { class_Int_Onumber__ring( tc_Int_Oint ) }.
% 0.80/1.39 { class_Rings_Osemiring( tc_Int_Oint ) }.
% 0.80/1.39 { class_Orderings_Oord( tc_Int_Oint ) }.
% 0.80/1.39 { class_Rings_Oring__1( tc_Int_Oint ) }.
% 0.80/1.39 { class_Power_Opower( tc_Int_Oint ) }.
% 0.80/1.39 { class_Groups_Ozero( tc_Int_Oint ) }.
% 0.80/1.39 { class_Rings_Oring( tc_Int_Oint ) }.
% 0.80/1.39 { class_Int_Onumber( tc_Int_Oint ) }.
% 0.80/1.39 { class_Groups_Oone( tc_Int_Oint ) }.
% 0.80/1.39 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.80/1.39 tc_Nat_Onat ) }.
% 0.80/1.39 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.80/1.39 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Nat_Onat ) }.
% 0.80/1.39 { class_Rings_Olinordered__comm__semiring__strict( tc_Nat_Onat ) }.
% 0.80/1.39 { class_Rings_Olinordered__semiring__strict( tc_Nat_Onat ) }.
% 0.80/1.39 { class_Groups_Oordered__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.80/1.39 { class_Groups_Oordered__comm__monoid__add( tc_Nat_Onat ) }.
% 0.80/1.39 { class_Groups_Ocancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.80/1.39 { class_Rings_Oordered__cancel__semiring( tc_Nat_Onat ) }.
% 0.80/1.39 { class_Rings_Oordered__comm__semiring( tc_Nat_Onat ) }.
% 0.80/1.39 { class_Groups_Ocancel__semigroup__add( tc_Nat_Onat ) }.
% 0.80/1.39 { class_Rings_Olinordered__semiring( tc_Nat_Onat ) }.
% 0.80/1.39 { class_Rings_Olinordered__semidom( tc_Nat_Onat ) }.
% 0.80/1.39 { class_Groups_Oab__semigroup__mult( tc_Nat_Onat ) }.
% 0.80/1.39 { class_Groups_Ocomm__monoid__mult( tc_Nat_Onat ) }.
% 0.80/1.39 { class_Groups_Oab__semigroup__add( tc_Nat_Onat ) }.
% 0.80/1.39 { class_Rings_Oordered__semiring( tc_Nat_Onat ) }.
% 0.80/1.39 { class_Rings_Ono__zero__divisors( tc_Nat_Onat ) }.
% 0.80/1.39 { class_Groups_Ocomm__monoid__add( tc_Nat_Onat ) }.
% 0.80/1.39 { class_Rings_Ocomm__semiring__1( tc_Nat_Onat ) }.
% 0.80/1.39 { class_Rings_Ocomm__semiring( tc_Nat_Onat ) }.
% 0.80/1.39 { class_Rings_Ozero__neq__one( tc_Nat_Onat ) }.
% 0.80/1.39 { class_Orderings_Opreorder( tc_Nat_Onat ) }.
% 0.80/1.39 { class_Orderings_Olinorder( tc_Nat_Onat ) }.
% 0.80/1.39 { class_Groups_Omonoid__mult( tc_Nat_Onat ) }.
% 0.80/1.39 { class_Groups_Omonoid__add( tc_Nat_Onat ) }.
% 0.80/1.39 { class_Rings_Osemiring__1( tc_Nat_Onat ) }.
% 0.80/1.39 { class_Rings_Osemiring__0( tc_Nat_Onat ) }.
% 0.80/1.39 { class_Rings_Omult__zero( tc_Nat_Onat ) }.
% 0.80/1.39 { class_Orderings_Oorder( tc_Nat_Onat ) }.
% 0.80/1.39 { class_Rings_Osemiring( tc_Nat_Onat ) }.
% 0.80/1.39 { class_Orderings_Oord( tc_Nat_Onat ) }.
% 0.80/1.39 { class_Power_Opower( tc_Nat_Onat ) }.
% 0.80/1.39 { class_Groups_Ozero( tc_Nat_Onat ) }.
% 0.80/1.39 { class_Int_Onumber( tc_Nat_Onat ) }.
% 0.80/1.39 { class_Groups_Oone( tc_Nat_Onat ) }.
% 0.80/1.39 { class_Orderings_Opreorder( tc_HOL_Obool ) }.
% 0.80/1.39 { class_Orderings_Oorder( tc_HOL_Obool ) }.
% 0.80/1.39 { class_Orderings_Oord( tc_HOL_Obool ) }.
% 0.80/1.39 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.80/1.39 tc_RealDef_Oreal ) }.
% 0.80/1.39 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.80/1.39 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_RealDef_Oreal ) }
% 0.80/1.39 .
% 0.80/1.39 { class_Rings_Olinordered__comm__semiring__strict( tc_RealDef_Oreal ) }.
% 0.80/1.39 { class_Fields_Olinordered__field__inverse__zero( tc_RealDef_Oreal ) }.
% 0.80/1.39 { class_Rings_Olinordered__semiring__1__strict( tc_RealDef_Oreal ) }.
% 0.80/1.39 { class_Rings_Olinordered__semiring__strict( tc_RealDef_Oreal ) }.
% 0.80/1.39 { class_Rings_Odivision__ring__inverse__zero( tc_RealDef_Oreal ) }.
% 0.80/1.39 { class_Groups_Oordered__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.80/1.39 { class_Groups_Oordered__ab__group__add__abs( tc_RealDef_Oreal ) }.
% 0.80/1.39 { class_RealVector_Oreal__normed__algebra( tc_RealDef_Oreal ) }.
% 0.80/1.39 { class_Groups_Oordered__comm__monoid__add( tc_RealDef_Oreal ) }.
% 0.80/1.39 { class_Groups_Olinordered__ab__group__add( tc_RealDef_Oreal ) }.
% 0.80/1.39 { class_Groups_Ocancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.80/1.39 { class_Rings_Oring__1__no__zero__divisors( tc_RealDef_Oreal ) }.
% 0.80/1.39 { class_Rings_Oordered__cancel__semiring( tc_RealDef_Oreal ) }.
% 0.80/1.39 { class_Rings_Olinordered__ring__strict( tc_RealDef_Oreal ) }.
% 0.80/1.39 { class_RealVector_Oreal__normed__field( tc_RealDef_Oreal ) }.
% 0.80/1.39 { class_Rings_Oring__no__zero__divisors( tc_RealDef_Oreal ) }.
% 0.80/1.39 { class_Rings_Oordered__comm__semiring( tc_RealDef_Oreal ) }.
% 0.80/1.39 { class_Rings_Olinordered__semiring__1( tc_RealDef_Oreal ) }.
% 0.80/1.39 { class_Groups_Oordered__ab__group__add( tc_RealDef_Oreal ) }.
% 0.80/1.39 { class_Groups_Ocancel__semigroup__add( tc_RealDef_Oreal ) }.
% 0.80/1.39 { class_Rings_Olinordered__semiring( tc_RealDef_Oreal ) }.
% 0.80/1.39 { class_Fields_Ofield__inverse__zero( tc_RealDef_Oreal ) }.
% 0.80/1.39 { class_Rings_Olinordered__semidom( tc_RealDef_Oreal ) }.
% 0.80/1.39 { class_Groups_Oab__semigroup__mult( tc_RealDef_Oreal ) }.
% 0.80/1.39 { class_Groups_Ocomm__monoid__mult( tc_RealDef_Oreal ) }.
% 0.80/1.39 { class_Groups_Oab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.80/1.39 { class_Fields_Olinordered__field( tc_RealDef_Oreal ) }.
% 0.80/1.39 { class_Rings_Oordered__semiring( tc_RealDef_Oreal ) }.
% 0.80/1.39 { class_Rings_Oordered__ring__abs( tc_RealDef_Oreal ) }.
% 0.80/1.39 { class_Rings_Ono__zero__divisors( tc_RealDef_Oreal ) }.
% 0.80/1.39 { class_Groups_Ocomm__monoid__add( tc_RealDef_Oreal ) }.
% 0.80/1.39 { class_Rings_Olinordered__ring( tc_RealDef_Oreal ) }.
% 0.80/1.39 { class_Rings_Olinordered__idom( tc_RealDef_Oreal ) }.
% 0.80/1.39 { class_Rings_Ocomm__semiring__1( tc_RealDef_Oreal ) }.
% 0.80/1.39 { class_RealVector_Oreal__field( tc_RealDef_Oreal ) }.
% 0.80/1.39 { class_Rings_Odivision__ring( tc_RealDef_Oreal ) }.
% 0.80/1.39 { class_Rings_Ocomm__semiring( tc_RealDef_Oreal ) }.
% 0.80/1.39 { class_Groups_Oab__group__add( tc_RealDef_Oreal ) }.
% 0.80/1.39 { class_Rings_Ozero__neq__one( tc_RealDef_Oreal ) }.
% 0.80/1.39 { class_Rings_Oordered__ring( tc_RealDef_Oreal ) }.
% 0.80/1.39 { class_Orderings_Opreorder( tc_RealDef_Oreal ) }.
% 0.80/1.39 { class_Orderings_Olinorder( tc_RealDef_Oreal ) }.
% 0.80/1.39 { class_Groups_Omonoid__mult( tc_RealDef_Oreal ) }.
% 0.80/1.39 { class_Rings_Ocomm__ring__1( tc_RealDef_Oreal ) }.
% 0.80/1.39 { class_Groups_Omonoid__add( tc_RealDef_Oreal ) }.
% 0.80/1.39 { class_Rings_Osemiring__1( tc_RealDef_Oreal ) }.
% 0.80/1.39 { class_Rings_Osemiring__0( tc_RealDef_Oreal ) }.
% 0.80/1.39 { class_Groups_Ogroup__add( tc_RealDef_Oreal ) }.
% 0.80/1.39 { class_Rings_Omult__zero( tc_RealDef_Oreal ) }.
% 0.80/1.39 { class_Orderings_Oorder( tc_RealDef_Oreal ) }.
% 0.80/1.39 { class_Int_Oring__char__0( tc_RealDef_Oreal ) }.
% 0.80/1.39 { class_Int_Onumber__ring( tc_RealDef_Oreal ) }.
% 0.80/1.39 { class_Rings_Osemiring( tc_RealDef_Oreal ) }.
% 0.80/1.39 { class_Orderings_Oord( tc_RealDef_Oreal ) }.
% 0.80/1.39 { class_Rings_Oring__1( tc_RealDef_Oreal ) }.
% 0.80/1.39 { class_Fields_Ofield( tc_RealDef_Oreal ) }.
% 0.80/1.39 { class_Power_Opower( tc_RealDef_Oreal ) }.
% 0.80/1.39 { class_Groups_Ozero( tc_RealDef_Oreal ) }.
% 0.80/1.39 { class_Rings_Oring( tc_RealDef_Oreal ) }.
% 0.80/1.39 { class_Int_Onumber( tc_RealDef_Oreal ) }.
% 0.80/1.39 { class_Groups_Oone( tc_RealDef_Oreal ) }.
% 0.80/1.39 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.80/1.39 tc_Complex_Ocomplex ) }.
% 0.80/1.39 { class_Rings_Odivision__ring__inverse__zero( tc_Complex_Ocomplex ) }.
% 0.80/1.39 { class_RealVector_Oreal__normed__algebra( tc_Complex_Ocomplex ) }.
% 0.80/1.39 { class_Groups_Ocancel__ab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.80/1.39 { class_Rings_Oring__1__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.80/1.39 { class_RealVector_Oreal__normed__field( tc_Complex_Ocomplex ) }.
% 0.80/1.39 { class_Rings_Oring__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.80/1.39 { class_Groups_Ocancel__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.80/1.39 { class_Fields_Ofield__inverse__zero( tc_Complex_Ocomplex ) }.
% 0.80/1.39 { class_Groups_Oab__semigroup__mult( tc_Complex_Ocomplex ) }.
% 0.80/1.39 { class_Groups_Ocomm__monoid__mult( tc_Complex_Ocomplex ) }.
% 0.80/1.39 { class_Groups_Oab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.80/1.39 { class_Rings_Ono__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.80/1.39 { class_Groups_Ocomm__monoid__add( tc_Complex_Ocomplex ) }.
% 0.80/1.39 { class_Rings_Ocomm__semiring__1( tc_Complex_Ocomplex ) }.
% 0.80/1.39 { class_RealVector_Oreal__field( tc_Complex_Ocomplex ) }.
% 0.80/1.39 { class_Rings_Odivision__ring( tc_Complex_Ocomplex ) }.
% 0.80/1.39 { class_Rings_Ocomm__semiring( tc_Complex_Ocomplex ) }.
% 0.80/1.39 { class_Groups_Oab__group__add( tc_Complex_Ocomplex ) }.
% 0.80/1.39 { class_Rings_Ozero__neq__one( tc_Complex_Ocomplex ) }.
% 0.80/1.39 { class_Groups_Omonoid__mult( tc_Complex_Ocomplex ) }.
% 0.80/1.39 { class_Rings_Ocomm__ring__1( tc_Complex_Ocomplex ) }.
% 0.80/1.39 { class_Groups_Omonoid__add( tc_Complex_Ocomplex ) }.
% 0.80/1.39 { class_Rings_Osemiring__1( tc_Complex_Ocomplex ) }.
% 0.80/1.39 { class_Rings_Osemiring__0( tc_Complex_Ocomplex ) }.
% 0.80/1.39 { class_Groups_Ogroup__add( tc_Complex_Ocomplex ) }.
% 0.80/1.39 { class_Rings_Omult__zero( tc_Complex_Ocomplex ) }.
% 0.80/1.39 { class_Int_Oring__char__0( tc_Complex_Ocomplex ) }.
% 0.80/1.39 { class_Int_Onumber__ring( tc_Complex_Ocomplex ) }.
% 0.80/1.39 { class_Rings_Osemiring( tc_Complex_Ocomplex ) }.
% 0.80/1.39 { class_Rings_Oring__1( tc_Complex_Ocomplex ) }.
% 0.80/1.39 { class_Fields_Ofield( tc_Complex_Ocomplex ) }.
% 0.80/1.39 { class_Power_Opower( tc_Complex_Ocomplex ) }.
% 0.80/1.39 { class_Groups_Ozero( tc_Complex_Ocomplex ) }.
% 0.80/1.39 { class_Rings_Oring( tc_Complex_Ocomplex ) }.
% 0.80/1.39 { class_Int_Onumber( tc_Complex_Ocomplex ) }.
% 0.80/1.39 { class_Groups_Oone( tc_Complex_Ocomplex ) }.
% 0.80/1.39 { ! c_Power_Opower__class_Opower( tc_Complex_Ocomplex,
% 0.80/1.39 c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt( v_z ),
% 0.80/1.39 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.80/1.39 c_Int_OPls ) ) ) ) = v_z }.
% 0.80/1.39
% 0.80/1.39 *** allocated 15000 integers for clauses
% 0.80/1.39 *** allocated 22500 integers for clauses
% 0.80/1.39 *** allocated 33750 integers for clauses
% 0.80/1.39 *** allocated 50625 integers for clauses
% 0.80/1.39 *** allocated 75937 integers for clauses
% 0.80/1.39 *** allocated 113905 integers for clauses
% 0.80/1.39 percentage equality = 0.232809, percentage horn = 0.896210
% 0.80/1.39 This is a problem with some equality
% 0.80/1.39
% 0.80/1.39
% 0.80/1.39
% 0.80/1.39 Options Used:
% 0.80/1.39
% 0.80/1.39 useres = 1
% 0.80/1.39 useparamod = 1
% 0.80/1.39 useeqrefl = 1
% 0.80/1.39 useeqfact = 1
% 0.80/1.39 usefactor = 1
% 0.80/1.39 usesimpsplitting = 0
% 0.80/1.39 usesimpdemod = 5
% 0.80/1.39 usesimpres = 3
% 0.80/1.39
% 0.80/1.39 resimpinuse = 1000
% 0.80/1.39 resimpclauses = 20000
% 0.80/1.39 substype = eqrewr
% 0.80/1.39 backwardsubs = 1
% 0.80/1.39 selectoldest = 5
% 0.80/1.39
% 0.80/1.39 litorderings [0] = split
% 0.80/1.39 litorderings [1] = extend the termordering, first sorting on arguments
% 0.80/1.39
% 0.80/1.39 termordering = kbo
% 0.80/1.39
% 0.80/1.39 litapriori = 0
% 0.80/1.39 termapriori = 1
% 0.80/1.39 litaposteriori = 0
% 0.80/1.39 termaposteriori = 0
% 0.80/1.39 demodaposteriori = 0
% 0.80/1.39 ordereqreflfact = 0
% 0.80/1.39
% 0.80/1.39 litselect = negord
% 0.80/1.39
% 0.80/1.39 maxweight = 15
% 0.80/1.39 maxdepth = 30000
% 0.80/1.39 maxlength = 115
% 0.80/1.39 maxnrvars = 195
% 0.80/1.39 excuselevel = 1
% 0.80/1.39 increasemaxweight = 1
% 0.80/1.39
% 0.80/1.39 maxselected = 10000000
% 0.80/1.39 maxnrclauses = 10000000
% 0.80/1.39
% 0.80/1.39 showgenerated = 0
% 0.80/1.39 showkept = 0
% 0.80/1.39 showselected = 0
% 0.80/1.39 showdeleted = 0
% 0.80/1.39 showresimp = 1
% 0.80/1.39 showstatus = 2000
% 0.80/1.39
% 0.80/1.39 prologoutput = 0
% 0.80/1.39 nrgoals = 5000000
% 0.80/1.39 totalproof = 1
% 0.80/1.39
% 0.80/1.39 Symbols occurring in the translation:
% 0.80/1.39
% 0.80/1.39 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.80/1.40 . [1, 2] (w:1, o:182, a:1, s:1, b:0),
% 0.80/1.40 ! [4, 1] (w:0, o:102, a:1, s:1, b:0),
% 0.80/1.40 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.80/1.40 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.80/1.40 c_Int_OPls [35, 0] (w:1, o:6, a:1, s:1, b:0),
% 0.80/1.40 c_Int_OBit0 [36, 1] (w:1, o:107, a:1, s:1, b:0),
% 0.80/1.40 c_Int_OBit1 [41, 1] (w:1, o:108, a:1, s:1, b:0),
% 0.80/1.40 v_y____ [42, 0] (w:1, o:17, a:1, s:1, b:0),
% 0.80/1.40 tc_RealDef_Oreal [43, 0] (w:1, o:20, a:1, s:1, b:0),
% 0.80/1.40 c_Groups_Ozero__class_Ozero [44, 1] (w:1, o:110, a:1, s:1, b:0),
% 0.80/1.40 tc_Complex_Ocomplex [45, 0] (w:1, o:21, a:1, s:1, b:0),
% 0.80/1.40 v_z [46, 0] (w:1, o:22, a:1, s:1, b:0),
% 0.80/1.40 c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt [47, 1] (w:1, o:109
% 0.80/1.40 , a:1, s:1, b:0),
% 0.80/1.40 tc_Nat_Onat [48, 0] (w:1, o:23, a:1, s:1, b:0),
% 0.80/1.40 c_Int_Onumber__class_Onumber__of [49, 2] (w:1, o:206, a:1, s:1, b:0)
% 0.80/1.40 ,
% 0.80/1.40 c_Power_Opower__class_Opower [50, 3] (w:1, o:227, a:1, s:1, b:0),
% 0.80/1.40 class_Groups_Omonoid__mult [53, 1] (w:1, o:116, a:1, s:1, b:0),
% 0.80/1.40 class_Int_Onumber [54, 1] (w:1, o:117, a:1, s:1, b:0),
% 0.80/1.40 c_Groups_Otimes__class_Otimes [55, 3] (w:1, o:228, a:1, s:1, b:0),
% 0.80/1.40 class_Rings_Osemiring__1 [57, 1] (w:1, o:123, a:1, s:1, b:0),
% 0.80/1.40 class_Rings_Oring__1__no__zero__divisors [59, 1] (w:1, o:118, a:1, s:
% 0.80/1.40 1, b:0),
% 0.80/1.40 tc_Int_Oint [62, 0] (w:1, o:42, a:1, s:1, b:0),
% 0.80/1.40 class_Int_Onumber__ring [64, 1] (w:1, o:124, a:1, s:1, b:0),
% 0.80/1.40 class_Int_Oring__char__0 [70, 1] (w:1, o:125, a:1, s:1, b:0),
% 0.80/1.40 class_Rings_Ocomm__semiring__1 [72, 1] (w:1, o:127, a:1, s:1, b:0),
% 0.80/1.40 class_Power_Opower [73, 1] (w:1, o:132, a:1, s:1, b:0),
% 0.80/1.40 class_Rings_Omult__zero [74, 1] (w:1, o:142, a:1, s:1, b:0),
% 0.80/1.40 class_Rings_Ono__zero__divisors [75, 1] (w:1, o:143, a:1, s:1, b:0),
% 0.80/1.40
% 0.80/1.40 class_Rings_Ozero__neq__one [76, 1] (w:1, o:144, a:1, s:1, b:0),
% 0.80/1.40 c_Rings_Oinverse__class_Odivide [77, 3] (w:1, o:229, a:1, s:1, b:0),
% 0.80/1.40
% 0.80/1.40 c_NthRoot_Osqrt [78, 1] (w:1, o:145, a:1, s:1, b:0),
% 0.80/1.40 v_x____ [79, 0] (w:1, o:16, a:1, s:1, b:0),
% 0.80/1.40 c_Complex_Ocomplex_OComplex [80, 2] (w:1, o:207, a:1, s:1, b:0),
% 0.80/1.40 class_Rings_Olinordered__idom [81, 1] (w:1, o:133, a:1, s:1, b:0),
% 0.80/1.40 c_Orderings_Oord__class_Oless__eq [82, 3] (w:1, o:225, a:1, s:1, b:0)
% 0.80/1.40 ,
% 0.80/1.40 c_Nat_OSuc [86, 1] (w:1, o:146, a:1, s:1, b:0),
% 0.80/1.40 c_Groups_Oplus__class_Oplus [87, 3] (w:1, o:230, a:1, s:1, b:0),
% 0.80/1.40 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct [98
% 0.80/1.40 , 1] (w:1, o:159, a:1, s:1, b:0),
% 0.80/1.40 class_Fields_Ofield__inverse__zero [102, 1] (w:1, o:111, a:1, s:1, b:
% 0.80/1.40 0),
% 0.80/1.40 class_Rings_Olinordered__semidom [103, 1] (w:1, o:136, a:1, s:1, b:0)
% 0.80/1.40 ,
% 0.80/1.40 class_Rings_Olinordered__ring__strict [104, 1] (w:1, o:134, a:1, s:1
% 0.80/1.40 , b:0),
% 0.80/1.40 class_Rings_Olinordered__ring [105, 1] (w:1, o:135, a:1, s:1, b:0),
% 0.80/1.40 class_Groups_Olinordered__ab__group__add [108, 1] (w:1, o:115, a:1
% 0.80/1.40 , s:1, b:0),
% 0.80/1.40 class_Fields_Ofield [111, 1] (w:1, o:112, a:1, s:1, b:0),
% 0.80/1.40 class_Rings_Osemiring__0 [114, 1] (w:1, o:122, a:1, s:1, b:0),
% 0.80/1.40 class_Rings_Osemiring [115, 1] (w:1, o:147, a:1, s:1, b:0),
% 0.80/1.40 class_Groups_Ocomm__monoid__mult [121, 1] (w:1, o:160, a:1, s:1, b:0)
% 0.80/1.40 ,
% 0.80/1.40 c_Groups_Ominus__class_Ominus [122, 3] (w:1, o:231, a:1, s:1, b:0),
% 0.80/1.40 class_Groups_Oab__group__add [126, 1] (w:1, o:161, a:1, s:1, b:0),
% 0.80/1.40 class_Rings_Oring [127, 1] (w:1, o:119, a:1, s:1, b:0),
% 0.80/1.40 hAPP [129, 2] (w:1, o:208, a:1, s:1, b:0),
% 0.80/1.40 class_RealVector_Oreal__field [131, 1] (w:1, o:148, a:1, s:1, b:0),
% 0.80/1.40 class_Rings_Ocomm__ring__1 [132, 1] (w:1, o:126, a:1, s:1, b:0),
% 0.80/1.40 c_Groups_Oabs__class_Oabs [137, 2] (w:1, o:209, a:1, s:1, b:0),
% 0.80/1.40 c_Complex_Ocomplex_Ocomplex__size [140, 1] (w:1, o:162, a:1, s:1, b:0
% 0.80/1.40 ),
% 0.80/1.40 class_Fields_Olinordered__field__inverse__zero [141, 1] (w:1, o:113
% 0.80/1.40 , a:1, s:1, b:0),
% 0.80/1.40 class_Fields_Olinordered__field [142, 1] (w:1, o:114, a:1, s:1, b:0)
% 0.80/1.40 ,
% 0.80/1.40 class_Groups_Oordered__ab__group__add__abs [150, 1] (w:1, o:163, a:1
% 0.80/1.40 , s:1, b:0),
% 0.80/1.40 class_Rings_Oordered__ring__abs [151, 1] (w:1, o:149, a:1, s:1, b:0)
% 0.80/1.40 ,
% 0.80/1.40 class_Rings_Oordered__ring [153, 1] (w:1, o:150, a:1, s:1, b:0),
% 0.80/1.40 class_Groups_Ozero [154, 1] (w:1, o:164, a:1, s:1, b:0),
% 0.80/1.40 class_Groups_Oab__semigroup__mult [155, 1] (w:1, o:165, a:1, s:1, b:0
% 0.80/1.40 ),
% 0.80/1.40 class_Groups_Oab__semigroup__add [156, 1] (w:1, o:166, a:1, s:1, b:0)
% 0.80/1.40 ,
% 0.80/1.40 class_Groups_Ocancel__semigroup__add [157, 1] (w:1, o:167, a:1, s:1
% 0.80/1.40 , b:0),
% 0.80/1.40 class_Groups_Ocancel__ab__semigroup__add [158, 1] (w:1, o:168, a:1
% 0.80/1.40 , s:1, b:0),
% 0.80/1.40 class_Rings_Oring__no__zero__divisors [159, 1] (w:1, o:120, a:1, s:1
% 0.80/1.40 , b:0),
% 0.80/1.40 class_Groups_Omonoid__add [160, 1] (w:1, o:169, a:1, s:1, b:0),
% 0.80/1.40 class_Groups_Ocomm__monoid__add [161, 1] (w:1, o:170, a:1, s:1, b:0)
% 0.80/1.40 ,
% 0.80/1.40 class_Groups_Oordered__ab__semigroup__add__imp__le [162, 1] (w:1, o:
% 0.80/1.40 171, a:1, s:1, b:0),
% 0.80/1.40 class_Groups_Oordered__ab__semigroup__add [163, 1] (w:1, o:172, a:1
% 0.80/1.40 , s:1, b:0),
% 0.80/1.40 class_Groups_Ogroup__add [164, 1] (w:1, o:173, a:1, s:1, b:0),
% 0.80/1.40 class_Groups_Oordered__ab__group__add [165, 1] (w:1, o:174, a:1, s:1
% 0.80/1.40 , b:0),
% 0.80/1.40 class_Rings_Ocomm__semiring [166, 1] (w:1, o:151, a:1, s:1, b:0),
% 0.80/1.40 class_Rings_Odivision__ring [168, 1] (w:1, o:152, a:1, s:1, b:0),
% 0.80/1.40 class_Rings_Odivision__ring__inverse__zero [169, 1] (w:1, o:153, a:1
% 0.80/1.40 , s:1, b:0),
% 0.80/1.40 class_Rings_Oordered__cancel__semiring [171, 1] (w:1, o:154, a:1, s:1
% 0.80/1.40 , b:0),
% 0.80/1.40 class_Rings_Oordered__semiring [172, 1] (w:1, o:155, a:1, s:1, b:0),
% 0.80/1.40
% 0.80/1.40 class_Rings_Oordered__comm__semiring [173, 1] (w:1, o:156, a:1, s:1
% 0.80/1.40 , b:0),
% 0.80/1.40 class_Groups_Oordered__comm__monoid__add [174, 1] (w:1, o:175, a:1
% 0.80/1.40 , s:1, b:0),
% 0.80/1.40 c_Orderings_Oord__class_Oless [177, 3] (w:1, o:226, a:1, s:1, b:0),
% 0.80/1.40 c_Groups_Oone__class_Oone [178, 1] (w:1, o:176, a:1, s:1, b:0),
% 0.80/1.40 class_RealVector_Oreal__normed__algebra [179, 1] (w:1, o:157, a:1, s:
% 0.80/1.40 1, b:0),
% 0.80/1.40 class_Groups_Oone [181, 1] (w:1, o:177, a:1, s:1, b:0),
% 0.80/1.40 class_Groups_Oordered__cancel__ab__semigroup__add [182, 1] (w:1, o:
% 0.80/1.40 178, a:1, s:1, b:0),
% 0.80/1.40 class_Rings_Olinordered__semiring__1__strict [183, 1] (w:1, o:137, a:
% 0.80/1.40 1, s:1, b:0),
% 0.80/1.40 class_Rings_Olinordered__semiring__strict [184, 1] (w:1, o:138, a:1
% 0.80/1.40 , s:1, b:0),
% 0.80/1.40 class_Rings_Olinordered__comm__semiring__strict [185, 1] (w:1, o:139
% 0.80/1.40 , a:1, s:1, b:0),
% 0.80/1.40 class_Orderings_Olinorder [186, 1] (w:1, o:128, a:1, s:1, b:0),
% 0.80/1.40 class_Rings_Olinordered__semiring [187, 1] (w:1, o:140, a:1, s:1, b:0
% 0.80/1.40 ),
% 0.80/1.40 class_Rings_Oring__1 [188, 1] (w:1, o:121, a:1, s:1, b:0),
% 0.80/1.40 class_Rings_Olinordered__semiring__1 [190, 1] (w:1, o:141, a:1, s:1
% 0.80/1.40 , b:0),
% 0.80/1.40 class_RealVector_Oreal__normed__field [193, 1] (w:1, o:158, a:1, s:1
% 0.80/1.40 , b:0),
% 0.80/1.40 c_Transcendental_Oarctan [194, 1] (w:1, o:179, a:1, s:1, b:0),
% 0.80/1.40 c_Nat_Osize__class_Osize [195, 2] (w:1, o:210, a:1, s:1, b:0),
% 0.80/1.40 class_Orderings_Opreorder [196, 1] (w:1, o:131, a:1, s:1, b:0),
% 0.80/1.40 hBOOL [198, 1] (w:1, o:180, a:1, s:1, b:0),
% 0.80/1.40 class_Orderings_Oord [206, 1] (w:1, o:129, a:1, s:1, b:0),
% 0.80/1.40 tc_fun [207, 2] (w:1, o:215, a:1, s:1, b:0),
% 0.80/1.40 class_Orderings_Oorder [208, 1] (w:1, o:130, a:1, s:1, b:0),
% 0.80/1.40 c_Divides_Odiv__class_Omod [213, 3] (w:1, o:232, a:1, s:1, b:0),
% 0.80/1.40 tc_HOL_Obool [216, 0] (w:1, o:41, a:1, s:1, b:0),
% 0.80/1.40 alpha1 [217, 3] (w:1, o:233, a:1, s:1, b:1),
% 0.80/1.40 alpha2 [218, 3] (w:1, o:242, a:1, s:1, b:1),
% 0.80/1.40 alpha3 [219, 3] (w:1, o:253, a:1, s:1, b:1),
% 0.80/1.40 alpha4 [220, 3] (w:1, o:257, a:1, s:1, b:1),
% 0.80/1.40 alpha5 [221, 2] (w:1, o:218, a:1, s:1, b:1),
% 0.80/1.40 alpha6 [222, 3] (w:1, o:259, a:1, s:1, b:1),
% 0.80/1.40 alpha7 [223, 3] (w:1, o:262, a:1, s:1, b:1),
% 0.80/1.40 alpha8 [224, 3] (w:1, o:263, a:1, s:1, b:1),
% 0.80/1.40 alpha9 [225, 3] (w:1, o:264, a:1, s:1, b:1),
% 0.80/1.40 alpha10 [226, 2] (w:1, o:219, a:1, s:1, b:1),
% 0.80/1.40 alpha11 [227, 2] (w:1, o:221, a:1, s:1, b:1),
% 0.80/1.40 alpha12 [228, 3] (w:1, o:234, a:1, s:1, b:1),
% 0.80/1.40 alpha13 [229, 3] (w:1, o:235, a:1, s:1, b:1),
% 0.80/1.40 alpha14 [230, 4] (w:1, o:272, a:1, s:1, b:1),
% 0.80/1.40 alpha15 [231, 4] (w:1, o:273, a:1, s:1, b:1),
% 0.80/1.40 alpha16 [232, 3] (w:1, o:236, a:1, s:1, b:1),
% 7.14/7.58 alpha17 [233, 3] (w:1, o:237, a:1, s:1, b:1),
% 7.14/7.58 alpha18 [234, 3] (w:1, o:238, a:1, s:1, b:1),
% 7.14/7.58 alpha19 [235, 3] (w:1, o:239, a:1, s:1, b:1),
% 7.14/7.58 alpha20 [236, 3] (w:1, o:243, a:1, s:1, b:1),
% 7.14/7.58 alpha21 [237, 3] (w:1, o:244, a:1, s:1, b:1),
% 7.14/7.58 alpha22 [238, 3] (w:1, o:245, a:1, s:1, b:1),
% 7.14/7.58 alpha23 [239, 3] (w:1, o:246, a:1, s:1, b:1),
% 7.14/7.58 alpha24 [240, 3] (w:1, o:247, a:1, s:1, b:1),
% 7.14/7.58 alpha25 [241, 3] (w:1, o:248, a:1, s:1, b:1),
% 7.14/7.58 alpha26 [242, 3] (w:1, o:249, a:1, s:1, b:1),
% 7.14/7.58 alpha27 [243, 3] (w:1, o:250, a:1, s:1, b:1),
% 7.14/7.58 alpha28 [244, 3] (w:1, o:251, a:1, s:1, b:1),
% 7.14/7.58 alpha29 [245, 3] (w:1, o:252, a:1, s:1, b:1),
% 7.14/7.58 alpha30 [246, 2] (w:1, o:222, a:1, s:1, b:1),
% 7.14/7.58 alpha31 [247, 2] (w:1, o:223, a:1, s:1, b:1),
% 7.14/7.58 alpha32 [248, 3] (w:1, o:254, a:1, s:1, b:1),
% 7.14/7.58 alpha33 [249, 3] (w:1, o:255, a:1, s:1, b:1),
% 7.14/7.58 alpha34 [250, 4] (w:1, o:274, a:1, s:1, b:1),
% 7.14/7.58 alpha35 [251, 4] (w:1, o:275, a:1, s:1, b:1),
% 7.14/7.58 alpha36 [252, 4] (w:1, o:276, a:1, s:1, b:1),
% 7.14/7.58 alpha37 [253, 4] (w:1, o:277, a:1, s:1, b:1),
% 7.14/7.58 alpha38 [254, 2] (w:1, o:224, a:1, s:1, b:1),
% 7.14/7.58 alpha39 [255, 3] (w:1, o:256, a:1, s:1, b:1),
% 7.14/7.58 alpha40 [256, 3] (w:1, o:265, a:1, s:1, b:1),
% 7.14/7.58 alpha41 [257, 4] (w:1, o:278, a:1, s:1, b:1),
% 7.14/7.58 alpha42 [258, 4] (w:1, o:279, a:1, s:1, b:1),
% 7.14/7.58 alpha43 [259, 2] (w:1, o:216, a:1, s:1, b:1),
% 7.14/7.58 alpha44 [260, 2] (w:1, o:217, a:1, s:1, b:1),
% 7.14/7.58 alpha45 [261, 3] (w:1, o:266, a:1, s:1, b:1),
% 7.14/7.58 alpha46 [262, 3] (w:1, o:267, a:1, s:1, b:1),
% 7.14/7.58 alpha47 [263, 4] (w:1, o:280, a:1, s:1, b:1),
% 7.14/7.58 alpha48 [264, 4] (w:1, o:281, a:1, s:1, b:1),
% 7.14/7.58 alpha49 [265, 3] (w:1, o:268, a:1, s:1, b:1),
% 7.14/7.58 alpha50 [266, 3] (w:1, o:258, a:1, s:1, b:1),
% 7.14/7.58 alpha51 [267, 4] (w:1, o:282, a:1, s:1, b:1),
% 7.14/7.58 alpha52 [268, 4] (w:1, o:283, a:1, s:1, b:1),
% 7.14/7.58 alpha53 [269, 4] (w:1, o:284, a:1, s:1, b:1),
% 7.14/7.58 alpha54 [270, 4] (w:1, o:285, a:1, s:1, b:1),
% 7.14/7.58 alpha55 [271, 4] (w:1, o:286, a:1, s:1, b:1),
% 7.14/7.58 alpha56 [272, 4] (w:1, o:287, a:1, s:1, b:1),
% 7.14/7.58 alpha57 [273, 4] (w:1, o:288, a:1, s:1, b:1),
% 7.14/7.58 alpha58 [274, 4] (w:1, o:289, a:1, s:1, b:1),
% 7.14/7.58 alpha59 [275, 4] (w:1, o:290, a:1, s:1, b:1),
% 7.14/7.58 alpha60 [276, 4] (w:1, o:291, a:1, s:1, b:1),
% 7.14/7.58 alpha61 [277, 4] (w:1, o:292, a:1, s:1, b:1),
% 7.14/7.58 alpha62 [278, 4] (w:1, o:293, a:1, s:1, b:1),
% 7.14/7.58 alpha63 [279, 3] (w:1, o:260, a:1, s:1, b:1),
% 7.14/7.58 alpha64 [280, 3] (w:1, o:261, a:1, s:1, b:1),
% 7.14/7.58 alpha65 [281, 4] (w:1, o:294, a:1, s:1, b:1),
% 7.14/7.58 alpha66 [282, 4] (w:1, o:295, a:1, s:1, b:1),
% 7.14/7.58 alpha67 [283, 4] (w:1, o:296, a:1, s:1, b:1),
% 7.14/7.58 alpha68 [284, 4] (w:1, o:297, a:1, s:1, b:1),
% 7.14/7.58 alpha69 [285, 4] (w:1, o:298, a:1, s:1, b:1),
% 7.14/7.58 alpha70 [286, 4] (w:1, o:299, a:1, s:1, b:1),
% 7.14/7.58 alpha71 [287, 4] (w:1, o:300, a:1, s:1, b:1),
% 7.14/7.58 alpha72 [288, 4] (w:1, o:301, a:1, s:1, b:1),
% 7.14/7.58 alpha73 [289, 4] (w:1, o:302, a:1, s:1, b:1),
% 7.14/7.58 alpha74 [290, 4] (w:1, o:303, a:1, s:1, b:1),
% 7.14/7.58 alpha75 [291, 4] (w:1, o:304, a:1, s:1, b:1),
% 7.14/7.58 alpha76 [292, 4] (w:1, o:305, a:1, s:1, b:1),
% 7.14/7.58 alpha77 [293, 4] (w:1, o:306, a:1, s:1, b:1),
% 7.14/7.58 alpha78 [294, 4] (w:1, o:307, a:1, s:1, b:1),
% 7.14/7.58 alpha79 [295, 4] (w:1, o:308, a:1, s:1, b:1),
% 7.14/7.58 alpha80 [296, 4] (w:1, o:309, a:1, s:1, b:1),
% 7.14/7.58 alpha81 [297, 4] (w:1, o:310, a:1, s:1, b:1),
% 7.14/7.58 alpha82 [298, 4] (w:1, o:311, a:1, s:1, b:1),
% 7.14/7.58 alpha83 [299, 4] (w:1, o:312, a:1, s:1, b:1),
% 7.14/7.58 alpha84 [300, 4] (w:1, o:313, a:1, s:1, b:1),
% 7.14/7.58 alpha85 [301, 4] (w:1, o:314, a:1, s:1, b:1),
% 7.14/7.58 alpha86 [302, 4] (w:1, o:315, a:1, s:1, b:1),
% 7.14/7.58 alpha87 [303, 4] (w:1, o:316, a:1, s:1, b:1),
% 7.14/7.58 alpha88 [304, 4] (w:1, o:317, a:1, s:1, b:1),
% 7.14/7.58 alpha89 [305, 4] (w:1, o:318, a:1, s:1, b:1),
% 7.14/7.58 alpha90 [306, 4] (w:1, o:319, a:1, s:1, b:1),
% 7.14/7.58 alpha91 [307, 4] (w:1, o:320, a:1, s:1, b:1),
% 7.14/7.58 alpha92 [308, 4] (w:1, o:321, a:1, s:1, b:1),
% 7.14/7.58 alpha93 [309, 4] (w:1, o:322, a:1, s:1, b:1),
% 40.87/41.27 alpha94 [310, 4] (w:1, o:323, a:1, s:1, b:1),
% 40.87/41.27 alpha95 [311, 4] (w:1, o:324, a:1, s:1, b:1),
% 40.87/41.27 alpha96 [312, 4] (w:1, o:325, a:1, s:1, b:1),
% 40.87/41.27 alpha97 [313, 4] (w:1, o:326, a:1, s:1, b:1),
% 40.87/41.27 alpha98 [314, 4] (w:1, o:327, a:1, s:1, b:1),
% 40.87/41.27 alpha99 [315, 4] (w:1, o:328, a:1, s:1, b:1),
% 40.87/41.27 alpha100 [316, 4] (w:1, o:329, a:1, s:1, b:1),
% 40.87/41.27 alpha101 [317, 2] (w:1, o:220, a:1, s:1, b:1),
% 40.87/41.27 alpha102 [318, 3] (w:1, o:240, a:1, s:1, b:1),
% 40.87/41.27 alpha103 [319, 3] (w:1, o:241, a:1, s:1, b:1),
% 40.87/41.27 skol1 [320, 0] (w:1, o:18, a:1, s:1, b:1),
% 40.87/41.27 skol2 [321, 2] (w:1, o:211, a:1, s:1, b:1),
% 40.87/41.27 skol3 [322, 2] (w:1, o:212, a:1, s:1, b:1),
% 40.87/41.27 skol4 [323, 1] (w:1, o:181, a:1, s:1, b:1),
% 40.87/41.27 skol5 [324, 2] (w:1, o:213, a:1, s:1, b:1),
% 40.87/41.27 skol6 [325, 2] (w:1, o:214, a:1, s:1, b:1),
% 40.87/41.27 skol7 [326, 3] (w:1, o:269, a:1, s:1, b:1),
% 40.87/41.27 skol8 [327, 3] (w:1, o:270, a:1, s:1, b:1),
% 40.87/41.27 skol9 [328, 3] (w:1, o:271, a:1, s:1, b:1),
% 40.87/41.27 skol10 [329, 0] (w:1, o:19, a:1, s:1, b:1).
% 40.87/41.27
% 40.87/41.27
% 40.87/41.27 Starting Search:
% 40.87/41.27
% 40.87/41.27 *** allocated 170857 integers for clauses
% 40.87/41.27 Resimplifying inuse:
% 40.87/41.27 Done
% 40.87/41.27
% 40.87/41.27
% 40.87/41.27 Intermediate Status:
% 40.87/41.27 Generated: 2743
% 40.87/41.27 Kept: 2000
% 40.87/41.27 Inuse: 34
% 40.87/41.27 Deleted: 1
% 40.87/41.27 Deletedinuse: 0
% 40.87/41.27
% 40.87/41.27 *** allocated 256285 integers for clauses
% 40.87/41.27 Resimplifying inuse:
% 40.87/41.27 Done
% 40.87/41.27
% 40.87/41.27 *** allocated 170857 integers for termspace/termends
% 40.87/41.27 Resimplifying inuse:
% 40.87/41.27 Done
% 40.87/41.27
% 40.87/41.27
% 40.87/41.27 Intermediate Status:
% 40.87/41.27 Generated: 9091
% 40.87/41.27 Kept: 4016
% 40.87/41.27 Inuse: 292
% 40.87/41.27 Deleted: 30
% 40.87/41.27 Deletedinuse: 1
% 40.87/41.27
% 40.87/41.27 *** allocated 384427 integers for clauses
% 40.87/41.27 Resimplifying inuse:
% 40.87/41.27 Done
% 40.87/41.27
% 40.87/41.27
% 40.87/41.27 Intermediate Status:
% 40.87/41.27 Generated: 16506
% 40.87/41.27 Kept: 6368
% 40.87/41.27 Inuse: 416
% 40.87/41.27 Deleted: 36
% 40.87/41.27 Deletedinuse: 1
% 40.87/41.27
% 40.87/41.27 Resimplifying inuse:
% 40.87/41.27 Done
% 40.87/41.27
% 40.87/41.27 *** allocated 576640 integers for clauses
% 40.87/41.27 *** allocated 256285 integers for termspace/termends
% 40.87/41.27 Resimplifying inuse:
% 40.87/41.27 Done
% 40.87/41.27
% 40.87/41.27
% 40.87/41.27 Intermediate Status:
% 40.87/41.27 Generated: 29509
% 40.87/41.27 Kept: 8582
% 40.87/41.27 Inuse: 466
% 40.87/41.27 Deleted: 37
% 40.87/41.27 Deletedinuse: 2
% 40.87/41.27
% 40.87/41.27 Resimplifying inuse:
% 40.87/41.27 Done
% 40.87/41.27
% 40.87/41.27 Resimplifying inuse:
% 40.87/41.27 Done
% 40.87/41.27
% 40.87/41.27 *** allocated 384427 integers for termspace/termends
% 40.87/41.27 *** allocated 864960 integers for clauses
% 40.87/41.27
% 40.87/41.27 Intermediate Status:
% 40.87/41.27 Generated: 36031
% 40.87/41.27 Kept: 11004
% 40.87/41.27 Inuse: 521
% 40.87/41.27 Deleted: 42
% 40.87/41.27 Deletedinuse: 2
% 40.87/41.27
% 40.87/41.27 Resimplifying inuse:
% 40.87/41.27 Done
% 40.87/41.27
% 40.87/41.27 Resimplifying inuse:
% 40.87/41.27 Done
% 40.87/41.27
% 40.87/41.27
% 40.87/41.27 Intermediate Status:
% 40.87/41.27 Generated: 50208
% 40.87/41.27 Kept: 13558
% 40.87/41.27 Inuse: 566
% 40.87/41.27 Deleted: 42
% 40.87/41.27 Deletedinuse: 2
% 40.87/41.27
% 40.87/41.27 Resimplifying inuse:
% 40.87/41.27 Done
% 40.87/41.27
% 40.87/41.27 Resimplifying inuse:
% 40.87/41.27 Done
% 40.87/41.27
% 40.87/41.27 *** allocated 576640 integers for termspace/termends
% 40.87/41.27
% 40.87/41.27 Intermediate Status:
% 40.87/41.27 Generated: 59164
% 40.87/41.27 Kept: 15617
% 40.87/41.27 Inuse: 639
% 40.87/41.27 Deleted: 44
% 40.87/41.27 Deletedinuse: 2
% 40.87/41.27
% 40.87/41.27 Resimplifying inuse:
% 40.87/41.27 Done
% 40.87/41.27
% 40.87/41.27 *** allocated 1297440 integers for clauses
% 40.87/41.27 Resimplifying inuse:
% 40.87/41.27 Done
% 40.87/41.27
% 40.87/41.27
% 40.87/41.27 Intermediate Status:
% 40.87/41.27 Generated: 68278
% 40.87/41.27 Kept: 17957
% 40.87/41.27 Inuse: 690
% 40.87/41.27 Deleted: 53
% 40.87/41.27 Deletedinuse: 2
% 40.87/41.27
% 40.87/41.27 Resimplifying inuse:
% 40.87/41.27 Done
% 40.87/41.27
% 40.87/41.27 Resimplifying inuse:
% 40.87/41.27 Done
% 40.87/41.27
% 40.87/41.27
% 40.87/41.27 Intermediate Status:
% 40.87/41.27 Generated: 78212
% 40.87/41.27 Kept: 20003
% 40.87/41.27 Inuse: 760
% 40.87/41.27 Deleted: 53
% 40.87/41.27 Deletedinuse: 2
% 40.87/41.27
% 40.87/41.27 Resimplifying inuse:
% 40.87/41.27 Done
% 40.87/41.27
% 40.87/41.27 Resimplifying clauses:
% 40.87/41.27 Done
% 40.87/41.27
% 40.87/41.27 Resimplifying inuse:
% 40.87/41.27 Done
% 40.87/41.27
% 40.87/41.27
% 40.87/41.27 Intermediate Status:
% 40.87/41.27 Generated: 87744
% 40.87/41.27 Kept: 22452
% 40.87/41.27 Inuse: 800
% 40.87/41.27 Deleted: 729
% 40.87/41.27 Deletedinuse: 2
% 40.87/41.27
% 40.87/41.27 Resimplifying inuse:
% 40.87/41.27 Done
% 40.87/41.27
% 40.87/41.27 *** allocated 864960 integers for termspace/termends
% 40.87/41.27 Resimplifying inuse:
% 40.87/41.27 Done
% 40.87/41.27
% 40.87/41.27
% 40.87/41.27 Intermediate Status:
% 40.87/41.27 Generated: 94593
% 40.87/41.27 Kept: 24924
% 40.87/41.27 Inuse: 822
% 40.87/41.27 Deleted: 729
% 40.87/41.27 Deletedinuse: 2
% 40.87/41.27
% 40.87/41.27 Resimplifying inuse:
% 40.87/41.27 Done
% 40.87/41.27
% 40.87/41.27 *** allocated 1946160 integers for clauses
% 40.87/41.27 Resimplifying inuse:
% 40.87/41.27 Done
% 40.87/41.27
% 40.87/41.27
% 40.87/41.27 Intermediate Status:
% 40.87/41.27 Generated: 103885
% 40.87/41.27 Kept: 27030
% 40.87/41.27 Inuse: 860
% 40.87/41.27 Deleted: 729
% 40.87/41.27 Deletedinuse: 2
% 40.87/41.27
% 40.87/41.27 Resimplifying inuse:
% 40.87/41.27 Done
% 40.87/41.27
% 40.87/41.27
% 40.87/41.27 Intermediate Status:
% 40.87/41.27 Generated: 107489
% 40.87/41.27 Kept: 29116
% 40.87/41.27 Inuse: 885
% 40.87/41.27 Deleted: 729
% 40.87/41.27 Deletedinuse: 2
% 40.87/41.27
% 40.87/41.27 Resimplifying inuse:
% 40.87/41.27 Done
% 40.87/41.27
% 40.87/41.27
% 40.87/41.27 Intermediate Status:
% 40.87/41.27 Generated: 118950
% 40.87/41.27 Kept: 32697
% 40.87/41.27 Inuse: 910
% 40.87/41.27 Deleted: 729
% 40.87/41.27 Deletedinuse: 2
% 40.87/41.27
% 40.87/41.27 Resimplifying inuse:
% 40.87/41.27 Done
% 40.87/41.27
% 40.87/41.27 Resimplifying inuse:
% 40.87/41.27 Done
% 40.87/41.27
% 40.87/41.27
% 40.87/41.27 Intermediate Status:
% 40.87/41.27 Generated: 126336
% 40.87/41.27 Kept: 34702
% 40.87/41.27 Inuse: 945
% 40.87/41.27 Deleted: 729
% 40.87/41.27 Deletedinuse: 2
% 118.74/119.15
% 118.74/119.15 Resimplifying inuse:
% 118.74/119.15 Done
% 118.74/119.15
% 118.74/119.15 Resimplifying inuse:
% 118.74/119.15 Done
% 118.74/119.15
% 118.74/119.15 *** allocated 1297440 integers for termspace/termends
% 118.74/119.15
% 118.74/119.15 Intermediate Status:
% 118.74/119.15 Generated: 134901
% 118.74/119.15 Kept: 36849
% 118.74/119.15 Inuse: 995
% 118.74/119.15 Deleted: 729
% 118.74/119.15 Deletedinuse: 2
% 118.74/119.15
% 118.74/119.15 Resimplifying inuse:
% 118.74/119.15 Done
% 118.74/119.15
% 118.74/119.15 Resimplifying inuse:
% 118.74/119.15 Done
% 118.74/119.15
% 118.74/119.15
% 118.74/119.15 Intermediate Status:
% 118.74/119.15 Generated: 141675
% 118.74/119.15 Kept: 38959
% 118.74/119.15 Inuse: 1015
% 118.74/119.15 Deleted: 729
% 118.74/119.15 Deletedinuse: 2
% 118.74/119.15
% 118.74/119.15 Resimplifying inuse:
% 118.74/119.15 Done
% 118.74/119.15
% 118.74/119.15 Resimplifying clauses:
% 118.74/119.15 Done
% 118.74/119.15
% 118.74/119.15 *** allocated 2919240 integers for clauses
% 118.74/119.15
% 118.74/119.15 Intermediate Status:
% 118.74/119.15 Generated: 155086
% 118.74/119.15 Kept: 41741
% 118.74/119.15 Inuse: 1045
% 118.74/119.15 Deleted: 1013
% 118.74/119.15 Deletedinuse: 2
% 118.74/119.15
% 118.74/119.15 Resimplifying inuse:
% 118.74/119.15 Done
% 118.74/119.15
% 118.74/119.15 Resimplifying inuse:
% 118.74/119.15 Done
% 118.74/119.15
% 118.74/119.15
% 118.74/119.15 Intermediate Status:
% 118.74/119.15 Generated: 168257
% 118.74/119.15 Kept: 45280
% 118.74/119.15 Inuse: 1085
% 118.74/119.15 Deleted: 1013
% 118.74/119.15 Deletedinuse: 2
% 118.74/119.15
% 118.74/119.15 Resimplifying inuse:
% 118.74/119.15 Done
% 118.74/119.15
% 118.74/119.15
% 118.74/119.15 Intermediate Status:
% 118.74/119.15 Generated: 175832
% 118.74/119.15 Kept: 47373
% 118.74/119.15 Inuse: 1090
% 118.74/119.15 Deleted: 1013
% 118.74/119.15 Deletedinuse: 2
% 118.74/119.15
% 118.74/119.15 Resimplifying inuse:
% 118.74/119.15 Done
% 118.74/119.15
% 118.74/119.15 Resimplifying inuse:
% 118.74/119.15 Done
% 118.74/119.15
% 118.74/119.15
% 118.74/119.15 Intermediate Status:
% 118.74/119.15 Generated: 183942
% 118.74/119.15 Kept: 50262
% 118.74/119.15 Inuse: 1131
% 118.74/119.15 Deleted: 1013
% 118.74/119.15 Deletedinuse: 2
% 118.74/119.15
% 118.74/119.15 Resimplifying inuse:
% 118.74/119.15 Done
% 118.74/119.15
% 118.74/119.15 Resimplifying inuse:
% 118.74/119.15 Done
% 118.74/119.15
% 118.74/119.15
% 118.74/119.15 Intermediate Status:
% 118.74/119.15 Generated: 192511
% 118.74/119.15 Kept: 52267
% 118.74/119.15 Inuse: 1172
% 118.74/119.15 Deleted: 1014
% 118.74/119.15 Deletedinuse: 2
% 118.74/119.15
% 118.74/119.15 Resimplifying inuse:
% 118.74/119.15 Done
% 118.74/119.15
% 118.74/119.15 *** allocated 1946160 integers for termspace/termends
% 118.74/119.15
% 118.74/119.15 Intermediate Status:
% 118.74/119.15 Generated: 204539
% 118.74/119.15 Kept: 55724
% 118.74/119.15 Inuse: 1194
% 118.74/119.15 Deleted: 1014
% 118.74/119.15 Deletedinuse: 2
% 118.74/119.15
% 118.74/119.15 Resimplifying inuse:
% 118.74/119.15 Done
% 118.74/119.15
% 118.74/119.15 *** allocated 4378860 integers for clauses
% 118.74/119.15
% 118.74/119.15 Intermediate Status:
% 118.74/119.15 Generated: 212749
% 118.74/119.15 Kept: 58238
% 118.74/119.15 Inuse: 1199
% 118.74/119.15 Deleted: 1014
% 118.74/119.15 Deletedinuse: 2
% 118.74/119.15
% 118.74/119.15 Resimplifying inuse:
% 118.74/119.15 Done
% 118.74/119.15
% 118.74/119.15
% 118.74/119.15 Intermediate Status:
% 118.74/119.15 Generated: 231677
% 118.74/119.15 Kept: 60579
% 118.74/119.15 Inuse: 1214
% 118.74/119.15 Deleted: 1014
% 118.74/119.15 Deletedinuse: 2
% 118.74/119.15
% 118.74/119.15 Resimplifying inuse:
% 118.74/119.15 Done
% 118.74/119.15
% 118.74/119.15 Resimplifying clauses:
% 118.74/119.15 Done
% 118.74/119.15
% 118.74/119.15 Resimplifying inuse:
% 118.74/119.15 Done
% 118.74/119.15
% 118.74/119.15
% 118.74/119.15 Intermediate Status:
% 118.74/119.15 Generated: 255906
% 118.74/119.15 Kept: 63501
% 118.74/119.15 Inuse: 1224
% 118.74/119.15 Deleted: 1257
% 118.74/119.15 Deletedinuse: 2
% 118.74/119.15
% 118.74/119.15 Resimplifying inuse:
% 118.74/119.15 Done
% 118.74/119.15
% 118.74/119.15 Resimplifying inuse:
% 118.74/119.15 Done
% 118.74/119.15
% 118.74/119.15
% 118.74/119.15 Intermediate Status:
% 118.74/119.15 Generated: 267084
% 118.74/119.15 Kept: 65666
% 118.74/119.15 Inuse: 1234
% 118.74/119.15 Deleted: 1257
% 118.74/119.15 Deletedinuse: 2
% 118.74/119.15
% 118.74/119.15 Resimplifying inuse:
% 118.74/119.15 Done
% 118.74/119.15
% 118.74/119.15 Resimplifying inuse:
% 118.74/119.15 Done
% 118.74/119.15
% 118.74/119.15
% 118.74/119.15 Intermediate Status:
% 118.74/119.15 Generated: 275705
% 118.74/119.15 Kept: 67672
% 118.74/119.15 Inuse: 1266
% 118.74/119.15 Deleted: 1257
% 118.74/119.15 Deletedinuse: 2
% 118.74/119.15
% 118.74/119.15 Resimplifying inuse:
% 118.74/119.15 Done
% 118.74/119.15
% 118.74/119.15
% 118.74/119.15 Intermediate Status:
% 118.74/119.15 Generated: 283342
% 118.74/119.15 Kept: 70959
% 118.74/119.15 Inuse: 1299
% 118.74/119.15 Deleted: 1257
% 118.74/119.15 Deletedinuse: 2
% 118.74/119.15
% 118.74/119.15 Resimplifying inuse:
% 118.74/119.15 Done
% 118.74/119.15
% 118.74/119.15
% 118.74/119.15 Intermediate Status:
% 118.74/119.15 Generated: 287408
% 118.74/119.15 Kept: 73290
% 118.74/119.15 Inuse: 1304
% 118.74/119.15 Deleted: 1257
% 118.74/119.15 Deletedinuse: 2
% 118.74/119.15
% 118.74/119.15 Resimplifying inuse:
% 118.74/119.15 Done
% 118.74/119.15
% 118.74/119.15
% 118.74/119.15 Intermediate Status:
% 118.74/119.15 Generated: 294346
% 118.74/119.15 Kept: 76023
% 118.74/119.15 Inuse: 1319
% 118.74/119.15 Deleted: 1257
% 118.74/119.15 Deletedinuse: 2
% 118.74/119.15
% 118.74/119.15 Resimplifying inuse:
% 118.74/119.15 Done
% 118.74/119.15
% 118.74/119.15
% 118.74/119.15 Intermediate Status:
% 118.74/119.15 Generated: 299053
% 118.74/119.15 Kept: 78504
% 118.74/119.15 Inuse: 1324
% 118.74/119.15 Deleted: 1257
% 118.74/119.15 Deletedinuse: 2
% 118.74/119.15
% 118.74/119.15 Resimplifying inuse:
% 118.74/119.15 Done
% 118.74/119.15
% 118.74/119.15 Resimplifying inuse:
% 118.74/119.15 Done
% 118.74/119.15
% 118.74/119.15 *** allocated 2919240 integers for termspace/termends
% 118.74/119.15
% 118.74/119.15 Intermediate Status:
% 118.74/119.15 Generated: 312308
% 118.74/119.15 Kept: 81661
% 118.74/119.15 Inuse: 1344
% 118.74/119.15 Deleted: 1257
% 118.74/119.15 Deletedinuse: 2
% 118.74/119.15
% 118.74/119.15 Resimplifying inuse:
% 118.74/119.15 Done
% 118.74/119.15
% 118.74/119.15 Resimplifying clauses:
% 118.74/119.15 Done
% 118.74/119.15
% 118.74/119.15
% 118.74/119.15 Intermediate Status:
% 118.74/119.15 Generated: 331711
% 118.74/119.15 Kept: 84092
% 118.74/119.15 Inuse: 1349
% 118.74/119.15 Deleted: 1483
% 118.74/119.15 Deletedinuse: 2
% 118.74/119.15
% 118.74/119.15 Resimplifying inuse:
% 118.74/119.15 Done
% 118.74/119.15
% 118.74/119.15 Resimplifying inuse:
% 118.74/119.15 Done
% 118.74/119.15
% 118.74/119.15
% 118.74/119.15 Intermediate Status:
% 118.74/119.15 Generated: 345392
% 118.74/119.15 Kept: 86097
% 118.74/119.15 Inuse: 1373
% 118.74/119.15 Deleted: 1483
% 118.74/119.15 Deletedinuse: 2
% 118.74/119.15
% 118.74/119.15 Resimplifying inuse:
% 118.74/119.15 Done
% 118.74/119.15
% 118.74/119.15
% 118.74/119.15 Intermediate Status:
% 118.74/119.15 Generated: 358283
% 118.74/119.15 Kept: 88460
% 118.74/119.15 Inuse: 1404
% 118.74/119.15 Deleted: 1483
% 118.74/119.15 Deletedinuse: 2
% 118.74/119.15
% 118.74/119.15 Resimplifying inuse:
% 118.74/119.15 Done
% 118.74/119.15
% 118.74/119.15 *** allocated 6568290 integers for clauses
% 118.74/119.15
% 118.74/119.15 Intermediate Status:
% 118.74/119.15 Generated: 365885
% 118.74/119.15 Kept: 91137
% 118.74/119.15 Inuse: 1421
% 118.74/119.15 Deleted: 1483
% 118.74/119.15 Deletedinuse: 2
% 118.74/119.15
% 118.74/119.15 Resimplifying inuse:
% 118.74/119.15 Done
% 118.74/119.15
% 118.74/119.15 Resimplifying inuse:
% 118.74/119.15 Done
% 118.74/119.15
% 118.74/119.15
% 118.74/119.15 Intermediate Status:
% 118.74/119.15 Generated: 374330
% 118.74/119.15 Kept: 93149
% 118.74/119.15 Inuse: 1461
% 118.74/119.15 Deleted: 1485
% 118.74/119.15 Deletedinuse: 3
% 118.74/119.15
% 118.74/119.15 Resimplifying inuse:
% 118.74/119.15 Done
% 118.74/119.15
% 118.74/119.15 Resimplifying inuse:
% 118.74/119.15 Done
% 118.74/119.15
% 118.74/119.15
% 118.74/119.15 Intermediate Status:
% 118.74/119.15 Generated: 382882
% 286.71/287.12 Kept: 95153
% 286.71/287.12 Inuse: 1483
% 286.71/287.12 Deleted: 1485
% 286.71/287.12 Deletedinuse: 3
% 286.71/287.12
% 286.71/287.12 Resimplifying inuse:
% 286.71/287.12 Done
% 286.71/287.12
% 286.71/287.12 Resimplifying inuse:
% 286.71/287.12 Done
% 286.71/287.12
% 286.71/287.12
% 286.71/287.12 Intermediate Status:
% 286.71/287.12 Generated: 395552
% 286.71/287.12 Kept: 97991
% 286.71/287.12 Inuse: 1522
% 286.71/287.12 Deleted: 1486
% 286.71/287.12 Deletedinuse: 3
% 286.71/287.12
% 286.71/287.12 Resimplifying inuse:
% 286.71/287.12 Done
% 286.71/287.12
% 286.71/287.12 Resimplifying inuse:
% 286.71/287.12 Done
% 286.71/287.12
% 286.71/287.12
% 286.71/287.12 Intermediate Status:
% 286.71/287.12 Generated: 403792
% 286.71/287.12 Kept: 99997
% 286.71/287.12 Inuse: 1566
% 286.71/287.12 Deleted: 1488
% 286.71/287.12 Deletedinuse: 4
% 286.71/287.12
% 286.71/287.12
% 286.71/287.12 Intermediate Status:
% 286.71/287.12 Generated: 414340
% 286.71/287.12 Kept: 102898
% 286.71/287.12 Inuse: 1571
% 286.71/287.12 Deleted: 1488
% 286.71/287.12 Deletedinuse: 4
% 286.71/287.12
% 286.71/287.12 Resimplifying inuse:
% 286.71/287.12 Done
% 286.71/287.12
% 286.71/287.12 Resimplifying clauses:
% 286.71/287.12 Done
% 286.71/287.12
% 286.71/287.12
% 286.71/287.12 Intermediate Status:
% 286.71/287.12 Generated: 428851
% 286.71/287.12 Kept: 106778
% 286.71/287.12 Inuse: 1591
% 286.71/287.12 Deleted: 1728
% 286.71/287.12 Deletedinuse: 4
% 286.71/287.12
% 286.71/287.12 Resimplifying inuse:
% 286.71/287.12 Done
% 286.71/287.12
% 286.71/287.12
% 286.71/287.12 Intermediate Status:
% 286.71/287.12 Generated: 441676
% 286.71/287.12 Kept: 110290
% 286.71/287.12 Inuse: 1601
% 286.71/287.12 Deleted: 1729
% 286.71/287.12 Deletedinuse: 5
% 286.71/287.12
% 286.71/287.12 Resimplifying inuse:
% 286.71/287.12 Done
% 286.71/287.12
% 286.71/287.12 Resimplifying inuse:
% 286.71/287.12 Done
% 286.71/287.12
% 286.71/287.12
% 286.71/287.12 Intermediate Status:
% 286.71/287.12 Generated: 456828
% 286.71/287.12 Kept: 114180
% 286.71/287.12 Inuse: 1626
% 286.71/287.12 Deleted: 1729
% 286.72/287.12 Deletedinuse: 5
% 286.72/287.12
% 286.72/287.12 Resimplifying inuse:
% 286.72/287.12 Done
% 286.72/287.12
% 286.72/287.12 Resimplifying inuse:
% 286.72/287.12 Done
% 286.72/287.12
% 286.72/287.12
% 286.72/287.12 Intermediate Status:
% 286.72/287.12 Generated: 465702
% 286.72/287.12 Kept: 116201
% 286.72/287.12 Inuse: 1642
% 286.72/287.12 Deleted: 1729
% 286.72/287.12 Deletedinuse: 5
% 286.72/287.12
% 286.72/287.12 *** allocated 4378860 integers for termspace/termends
% 286.72/287.12
% 286.72/287.12 Intermediate Status:
% 286.72/287.12 Generated: 473949
% 286.72/287.12 Kept: 119864
% 286.72/287.12 Inuse: 1661
% 286.72/287.12 Deleted: 1729
% 286.72/287.12 Deletedinuse: 5
% 286.72/287.12
% 286.72/287.12 Resimplifying inuse:
% 286.72/287.12 Done
% 286.72/287.12
% 286.72/287.12
% 286.72/287.12 Intermediate Status:
% 286.72/287.12 Generated: 479244
% 286.72/287.12 Kept: 122784
% 286.72/287.12 Inuse: 1666
% 286.72/287.12 Deleted: 1730
% 286.72/287.12 Deletedinuse: 6
% 286.72/287.12
% 286.72/287.12 Resimplifying inuse:
% 286.72/287.12 Done
% 286.72/287.12
% 286.72/287.12
% 286.72/287.12 Intermediate Status:
% 286.72/287.12 Generated: 484491
% 286.72/287.12 Kept: 125675
% 286.72/287.12 Inuse: 1671
% 286.72/287.12 Deleted: 1730
% 286.72/287.12 Deletedinuse: 6
% 286.72/287.12
% 286.72/287.12 Resimplifying inuse:
% 286.72/287.12 Done
% 286.72/287.12
% 286.72/287.12 Resimplifying clauses:
% 286.72/287.12 Done
% 286.72/287.12
% 286.72/287.12
% 286.72/287.12 Intermediate Status:
% 286.72/287.12 Generated: 493546
% 286.72/287.12 Kept: 128585
% 286.72/287.12 Inuse: 1676
% 286.72/287.12 Deleted: 1974
% 286.72/287.12 Deletedinuse: 6
% 286.72/287.12
% 286.72/287.12 Resimplifying inuse:
% 286.72/287.12 Done
% 286.72/287.12
% 286.72/287.12
% 286.72/287.12 Intermediate Status:
% 286.72/287.12 Generated: 501092
% 286.72/287.12 Kept: 130892
% 286.72/287.12 Inuse: 1690
% 286.72/287.12 Deleted: 1976
% 286.72/287.12 Deletedinuse: 7
% 286.72/287.12
% 286.72/287.12 Resimplifying inuse:
% 286.72/287.12 Done
% 286.72/287.12
% 286.72/287.12 Resimplifying inuse:
% 286.72/287.12 Done
% 286.72/287.12
% 286.72/287.12
% 286.72/287.12 Intermediate Status:
% 286.72/287.12 Generated: 508108
% 286.72/287.12 Kept: 132957
% 286.72/287.12 Inuse: 1712
% 286.72/287.12 Deleted: 1983
% 286.72/287.12 Deletedinuse: 11
% 286.72/287.12
% 286.72/287.12 Resimplifying inuse:
% 286.72/287.12 Done
% 286.72/287.12
% 286.72/287.12
% 286.72/287.12 Intermediate Status:
% 286.72/287.12 Generated: 533240
% 286.72/287.12 Kept: 135374
% 286.72/287.12 Inuse: 1717
% 286.72/287.12 Deleted: 1983
% 286.72/287.12 Deletedinuse: 11
% 286.72/287.12
% 286.72/287.12 Resimplifying inuse:
% 286.72/287.12 Done
% 286.72/287.12
% 286.72/287.12
% 286.72/287.12 Intermediate Status:
% 286.72/287.12 Generated: 561818
% 286.72/287.12 Kept: 138395
% 286.72/287.12 Inuse: 1725
% 286.72/287.12 Deleted: 1985
% 286.72/287.12 Deletedinuse: 11
% 286.72/287.12
% 286.72/287.12 Resimplifying inuse:
% 286.72/287.12 Done
% 286.72/287.12
% 286.72/287.12
% 286.72/287.12 Intermediate Status:
% 286.72/287.12 Generated: 569089
% 286.72/287.12 Kept: 141112
% 286.72/287.12 Inuse: 1733
% 286.72/287.12 Deleted: 1985
% 286.72/287.12 Deletedinuse: 11
% 286.72/287.12
% 286.72/287.12 Resimplifying inuse:
% 286.72/287.12 Done
% 286.72/287.12
% 286.72/287.12 *** allocated 9852435 integers for clauses
% 286.72/287.12
% 286.72/287.12 Intermediate Status:
% 286.72/287.12 Generated: 586647
% 286.72/287.12 Kept: 143378
% 286.72/287.12 Inuse: 1735
% 286.72/287.12 Deleted: 1985
% 286.72/287.12 Deletedinuse: 11
% 286.72/287.12
% 286.72/287.12 Resimplifying inuse:
% 286.72/287.12 Done
% 286.72/287.12
% 286.72/287.12 Resimplifying inuse:
% 286.72/287.12 Done
% 286.72/287.12
% 286.72/287.12
% 286.72/287.12 Intermediate Status:
% 286.72/287.12 Generated: 602958
% 286.72/287.12 Kept: 146075
% 286.72/287.12 Inuse: 1760
% 286.72/287.12 Deleted: 1985
% 286.72/287.12 Deletedinuse: 11
% 286.72/287.12
% 286.72/287.12 Resimplifying inuse:
% 286.72/287.12 Done
% 286.72/287.12
% 286.72/287.12 Resimplifying clauses:
% 286.72/287.12 Done
% 286.72/287.12
% 286.72/287.12 Resimplifying inuse:
% 286.72/287.12 Done
% 286.72/287.12
% 286.72/287.12
% 286.72/287.12 Intermediate Status:
% 286.72/287.12 Generated: 610400
% 286.72/287.12 Kept: 148077
% 286.72/287.12 Inuse: 1792
% 286.72/287.12 Deleted: 2367
% 286.72/287.12 Deletedinuse: 22
% 286.72/287.12
% 286.72/287.12 Resimplifying inuse:
% 286.72/287.12 Done
% 286.72/287.12
% 286.72/287.12 Resimplifying inuse:
% 286.72/287.12 Done
% 286.72/287.12
% 286.72/287.12
% 286.72/287.12 Intermediate Status:
% 286.72/287.12 Generated: 617942
% 286.72/287.12 Kept: 150101
% 286.72/287.12 Inuse: 1823
% 286.72/287.12 Deleted: 2367
% 286.72/287.12 Deletedinuse: 22
% 286.72/287.12
% 286.72/287.12 Resimplifying inuse:
% 286.72/287.12 Done
% 286.72/287.12
% 286.72/287.12 Resimplifying inuse:
% 286.72/287.12 Done
% 286.72/287.12
% 286.72/287.12
% 286.72/287.12 Intermediate Status:
% 286.72/287.12 Generated: 626393
% 286.72/287.12 Kept: 152107
% 286.72/287.12 Inuse: 1850
% 286.72/287.12 Deleted: 2367
% 286.72/287.12 Deletedinuse: 22
% 286.72/287.12
% 286.72/287.12 Resimplifying inuse:
% 286.72/287.12 Done
% 286.72/287.12
% 286.72/287.12 Resimplifying inuse:
% 286.72/287.12 Done
% 286.72/287.12
% 286.72/287.12
% 286.72/287.12 Intermediate Status:
% 286.72/287.12 Generated: 632048
% 286.72/287.12 Kept: 154159
% 286.72/287.12 Inuse: 1885
% 286.72/287.12 Deleted: 2367
% 286.72/287.12 Deletedinuse: 22
% 286.72/287.12
% 286.72/287.12 Resimplifying inuse:
% 286.72/287.12 Done
% 286.72/287.12
% 286.72/287.12 Resimplifying inuse:
% 286.72/287.12 Done
% 286.72/287.12
% 286.72/287.12
% 286.72/287.12 Intermediate Status:
% 286.72/287.12 Generated: 637496
% 286.72/287.12 Kept: 156167
% 286.72/287.12 Inuse: 1921
% 286.72/287.12 Deleted: 2369
% 286.72/287.12 Deletedinuse: 22
% 286.72/287.12
% 286.72/287.12 Resimplifying inuse:
% 286.72/287.12 Done
% 286.72/287.12
% 286.72/287.12 Resimplifying inuse:
% 286.72/287.12 Done
% 286.72/287.12
% 286.72/287.12
% 286.72/287.12 Intermediate Status:
% 286.72/287.12 Generated: 644181
% 286.72/287.12 Kept: 158495
% 286.72/287.12 Inuse: 1953
% 286.72/287.12 Deleted: 2369
% 286.72/287.12 Deletedinuse: 22
% 286.72/287.12
% 286.72/287.12 Resimplifying inuse:
% 286.72/287.12 Done
% 286.72/287.12
% 286.72/287.12 ResimplifyingCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------